LMFDB - Embedded newform 11.7.d.a.6.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,7,Mod(2,11)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.53059491982$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			6.4
Root			$6.47390i$ of defining polynomial
Character	$\chi$	$=$	11.6
Dual form			11.7.d.a.2.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27508 - 2.36382i) q^{2} +(23.2263 + 16.8749i) q^{3} +(-4.43797 + 3.22437i) q^{4} +(31.2971 - 96.3226i) q^{5} +(208.862 + 67.8633i) q^{6} +(-91.3973 - 125.798i) q^{7} +(-312.424 + 430.015i) q^{8} +(29.4247 + 90.5599i) q^{9} +O(q^{10})$	\(q+(7.27508 - 2.36382i) q^{2} +(23.2263 + 16.8749i) q^{3} +(-4.43797 + 3.22437i) q^{4} +(31.2971 - 96.3226i) q^{5} +(208.862 + 67.8633i) q^{6} +(-91.3973 - 125.798i) q^{7} +(-312.424 + 430.015i) q^{8} +(29.4247 + 90.5599i) q^{9} -774.735i q^{10} +(-1276.79 + 376.005i) q^{11} -157.488 q^{12} +(-119.738 + 38.9052i) q^{13} +(-962.284 - 699.140i) q^{14} +(2352.35 - 1709.08i) q^{15} +(-1147.94 + 3533.01i) q^{16} +(7821.98 + 2541.52i) q^{17} +(428.134 + 589.275i) q^{18} +(4947.75 - 6809.99i) q^{19} +(171.684 + 528.390i) q^{20} -4464.12i q^{21} +(-8399.91 + 5753.55i) q^{22} -14737.0 q^{23} +(-14512.9 + 4715.53i) q^{24} +(4342.36 + 3154.91i) q^{25} +(-779.138 + 566.077i) q^{26} +(5622.67 - 17304.8i) q^{27} +(811.236 + 263.587i) q^{28} +(8628.78 + 11876.5i) q^{29} +(13073.5 - 17994.2i) q^{30} +(10515.0 + 32361.9i) q^{31} -5601.34i q^{32} +(-36000.0 - 12812.4i) q^{33} +62913.2 q^{34} +(-14977.6 + 4866.52i) q^{35} +(-422.584 - 307.026i) q^{36} +(-38171.1 + 27732.9i) q^{37} +(19897.7 - 61238.8i) q^{38} +(-3437.59 - 1116.94i) q^{39} +(31642.2 + 43551.8i) q^{40} +(31217.4 - 42967.0i) q^{41} +(-10552.4 - 32476.8i) q^{42} +101242. i q^{43} +(4453.95 - 5785.53i) q^{44} +9643.87 q^{45} +(-107213. + 34835.6i) q^{46} +(-134958. - 98052.5i) q^{47} +(-86281.6 + 62687.2i) q^{48} +(28884.0 - 88895.8i) q^{49} +(39048.6 + 12687.7i) q^{50} +(138788. + 191025. i) q^{51} +(405.948 - 558.740i) q^{52} +(-67093.4 - 206492. i) q^{53} -139185. i q^{54} +(-3741.90 + 134751. i) q^{55} +82649.6 q^{56} +(229835. - 74678.1i) q^{57} +(90848.9 + 66005.6i) q^{58} +(-126742. + 92083.2i) q^{59} +(-4928.93 + 15169.7i) q^{60} +(138582. + 45028.2i) q^{61} +(152995. + 210580. i) q^{62} +(8702.87 - 11978.5i) q^{63} +(-86709.0 - 266863. i) q^{64} +12751.1i q^{65} +(-292189. - 8113.78i) q^{66} +103619. q^{67} +(-42908.5 + 13941.8i) q^{68} +(-342286. - 248685. i) q^{69} +(-97459.7 + 70808.6i) q^{70} +(5415.59 - 16667.5i) q^{71} +(-48135.1 - 15640.0i) q^{72} +(-160622. - 221077. i) q^{73} +(-212142. + 291989. i) q^{74} +(47618.1 + 146553. i) q^{75} +46175.9i q^{76} +(163995. + 126251. i) q^{77} -27649.0 q^{78} +(-399408. + 129775. i) q^{79} +(304381. + 221146. i) q^{80} +(478768. - 347845. i) q^{81} +(125543. - 386380. i) q^{82} +(422305. + 137215. i) q^{83} +(14394.0 + 19811.6i) q^{84} +(489611. - 673891. i) q^{85} +(239318. + 736544. i) q^{86} +421456. i q^{87} +(237211. - 666510. i) q^{88} -432440. q^{89} +(70159.9 - 22796.3i) q^{90} +(15837.9 + 11506.9i) q^{91} +(65402.5 - 47517.7i) q^{92} +(-301878. + 929086. i) q^{93} +(-1.21361e6 - 394324. i) q^{94} +(-501106. - 689713. i) q^{95} +(94521.9 - 130098. i) q^{96} +(338984. + 1.04328e6i) q^{97} -715000. i q^{98} +(-71620.0 - 104562. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	7.27508	−	2.36382i	0.909385	−	0.295477i	0.183280	−	0.983061i	$-0.441329\pi$
$2$	7.27508	−	2.36382i	0.909385	−	0.295477i	0.726105	+	0.687584i	$0.241329\pi$
$3$	23.2263	+	16.8749i	0.860232	+	0.624995i	0.927948	−	0.372710i	$-0.121571\pi$
$3$	23.2263	+	16.8749i	0.860232	+	0.624995i	−0.0677162	+	0.997705i	$0.521571\pi$
$4$	−4.43797	+	3.22437i	−0.0693432	+	0.0503808i
$5$	31.2971	−	96.3226i	0.250377	−	0.770581i	−0.744329	−	0.667814i	$-0.767230\pi$
$5$	31.2971	−	96.3226i	0.250377	−	0.770581i	0.994705	−	0.102767i	$-0.0327697\pi$
$6$	208.862	+	67.8633i	0.966953	+	0.314182i
$7$	−91.3973	−	125.798i	−0.266464	−	0.366757i	0.654728	−	0.755865i	$-0.272783\pi$
$7$	−91.3973	−	125.798i	−0.266464	−	0.366757i	−0.921192	+	0.389108i	$0.872783\pi$
$8$	−312.424	+	430.015i	−0.610204	+	0.839874i
$9$	29.4247	+	90.5599i	0.0403631	+	0.124225i
$10$		−	774.735i		−	0.774735i
$11$	−1276.79	+	376.005i	−0.959268	+	0.282498i
$11$	−1276.79	+	376.005i	−0.959268	+	0.282498i
$12$	−157.488			−0.0911390
$13$	−119.738	+	38.9052i	−0.0545007	+	0.0177083i	−0.336140	−	0.941812i	$-0.609122\pi$
$13$	−119.738	+	38.9052i	−0.0545007	+	0.0177083i	0.281640	+	0.959520i	$0.409122\pi$
$14$	−962.284	−	699.140i	−0.350687	−	0.254789i
$15$	2352.35	−	1709.08i	0.696991	−	0.506394i
$16$	−1147.94	+	3533.01i	−0.280260	+	0.862552i
$17$	7821.98	+	2541.52i	1.59210	+	0.517304i	0.965137	−	0.261746i	$-0.0842982\pi$
$17$	7821.98	+	2541.52i	1.59210	+	0.517304i	0.626962	+	0.779050i	$0.284298\pi$
$18$	428.134	+	589.275i	0.0734111	+	0.101042i
$19$	4947.75	−	6809.99i	0.721351	−	0.992855i	−0.278126	−	0.960544i	$-0.589713\pi$
$19$	4947.75	−	6809.99i	0.721351	−	0.992855i	0.999478	−	0.0323106i	$-0.0102866\pi$
$20$	171.684	+	528.390i	0.0214605	+	0.0660488i
$21$		−	4464.12i		−	0.482035i
$22$	−8399.91	+	5753.55i	−0.788872	+	0.540341i
$23$	−14737.0			−1.21123			−0.605615	−	0.795758i	$-0.707073\pi$
$23$	−14737.0			−1.21123			−0.605615	+	0.795758i	$0.707073\pi$
$24$	−14512.9	+	4715.53i	−1.04983	+	0.341112i
$25$	4342.36	+	3154.91i	0.277911	+	0.201914i
$26$	−779.138	+	566.077i	−0.0443297	+	0.0322074i
$27$	5622.67	−	17304.8i	0.285661	−	0.879174i
$28$	811.236	+	263.587i	0.0369550	+	0.0120074i
$29$	8628.78	+	11876.5i	0.353798	+	0.486961i	0.948408	−	0.317053i	$-0.102693\pi$
$29$	8628.78	+	11876.5i	0.353798	+	0.486961i	−0.594610	+	0.804015i	$0.702693\pi$
$30$	13073.5	−	17994.2i	0.484206	−	0.666452i
$31$	10515.0	+	32361.9i	0.352960	+	1.08630i	0.957183	+	0.289483i	$0.0934834\pi$
$31$	10515.0	+	32361.9i	0.352960	+	1.08630i	−0.604224	+	0.796815i	$0.706517\pi$
$32$		−	5601.34i		−	0.170939i
$33$	−36000.0	−	12812.4i	−1.00175	−	0.356524i
$34$	62913.2			1.60068
$35$	−14977.6	+	4866.52i	−0.349332	+	0.113505i
$36$	−422.584	−	307.026i	−0.00905745	−	0.00658062i
$37$	−38171.1	+	27732.9i	−0.753580	+	0.547508i	−0.896935	−	0.442163i	$-0.854211\pi$
$37$	−38171.1	+	27732.9i	−0.753580	+	0.547508i	0.143354	+	0.989671i	$0.454211\pi$
$38$	19897.7	−	61238.8i	0.362620	−	1.11603i
$39$	−3437.59	−	1116.94i	−0.0579509	−	0.0188294i
$40$	31642.2	+	43551.8i	0.494410	+	0.680496i
$41$	31217.4	−	42967.0i	0.452944	−	0.623424i	−0.520083	−	0.854116i	$-0.674099\pi$
$41$	31217.4	−	42967.0i	0.452944	−	0.623424i	0.973027	+	0.230692i	$0.0740989\pi$
$42$	−10552.4	−	32476.8i	−0.142430	−	0.438355i
$43$			101242.i			1.27337i	0.771123	+	0.636686i	$0.219695\pi$
$43$			101242.i			1.27337i	−0.771123	+	0.636686i	$0.780305\pi$
$44$	4453.95	−	5785.53i	0.0522862	−	0.0679180i
$45$	9643.87			0.105831
$46$	−107213.	+	34835.6i	−1.10147	+	0.357890i
$47$	−134958.	−	98052.5i	−1.29988	−	0.944420i	−0.299928	−	0.953962i	$-0.596963\pi$
$47$	−134958.	−	98052.5i	−1.29988	−	0.944420i	−0.999954	+	0.00954179i	$0.996963\pi$
$48$	−86281.6	+	62687.2i	−0.780179	+	0.566833i
$49$	28884.0	−	88895.8i	0.245510	−	0.755601i
$50$	39048.6	+	12687.7i	0.312389	+	0.101501i
$51$	138788.	+	191025.i	1.04626	+	1.44006i
$52$	405.948	−	558.740i	0.00288709	−	0.00397374i
$53$	−67093.4	−	206492.i	−0.450664	−	1.38700i	−0.876151	−	0.482036i	$-0.839897\pi$
$53$	−67093.4	−	206492.i	−0.450664	−	1.38700i	0.425488	−	0.904964i	$-0.360103\pi$
$54$		−	139185.i		−	0.883914i
$55$	−3741.90	+	134751.i	−0.0224908	+	0.809924i
$56$	82649.6			0.470627
$57$	229835.	−	74678.1i	1.24106	−	0.403244i
$58$	90848.9	+	66005.6i	0.465624	+	0.338296i
$59$	−126742.	+	92083.2i	−0.617111	+	0.448357i	−0.851911	−	0.523686i	$-0.824556\pi$
$59$	−126742.	+	92083.2i	−0.617111	+	0.448357i	0.234800	+	0.972044i	$0.424556\pi$
$60$	−4928.93	+	15169.7i	−0.0228191	+	0.0702300i
$61$	138582.	+	45028.2i	0.610546	+	0.198379i	0.597938	−	0.801542i	$-0.295987\pi$
$61$	138582.	+	45028.2i	0.610546	+	0.198379i	0.0126078	+	0.999921i	$0.495987\pi$
$62$	152995.	+	210580.i	0.641952	+	0.883571i
$63$	8702.87	−	11978.5i	0.0348049	−	0.0479049i
$64$	−86709.0	−	266863.i	−0.330769	−	1.01800i
$65$			12751.1i			0.0464309i
$66$	−292189.	−	8113.78i	−1.01632	−	0.0282222i
$67$	103619.			0.344520			0.172260	−	0.985052i	$-0.444893\pi$
$67$	103619.			0.344520			0.172260	+	0.985052i	$0.444893\pi$
$68$	−42908.5	+	13941.8i	−0.136463	+	0.0443397i
$69$	−342286.	−	248685.i	−1.04194	−	0.757012i
$70$	−97459.7	+	70808.6i	−0.284139	+	0.206439i
$71$	5415.59	−	16667.5i	0.0151311	−	0.0465688i	−0.943206	−	0.332209i	$-0.892206\pi$
$71$	5415.59	−	16667.5i	0.0151311	−	0.0465688i	0.958337	+	0.285640i	$0.0922062\pi$
$72$	−48135.1	−	15640.0i	−0.128963	−	0.0419026i
$73$	−160622.	−	221077.i	−0.412892	−	0.568297i	0.551029	−	0.834486i	$-0.314235\pi$
$73$	−160622.	−	221077.i	−0.412892	−	0.568297i	−0.963921	+	0.266189i	$0.914235\pi$
$74$	−212142.	+	291989.i	−0.523518	+	0.720561i
$75$	47618.1	+	146553.i	0.112872	+	0.347386i
$76$			46175.9i			0.105190i
$77$	163995.	+	126251.i	0.359219	+	0.276542i
$78$	−27649.0			−0.0582633
$79$	−399408.	+	129775.i	−0.810094	+	0.263215i	−0.684637	−	0.728884i	$-0.740039\pi$
$79$	−399408.	+	129775.i	−0.810094	+	0.263215i	−0.125456	+	0.992099i	$0.540039\pi$
$80$	304381.	+	221146.i	0.594495	+	0.431926i
$81$	478768.	−	347845.i	0.900886	−	0.654532i
$82$	125543.	−	386380.i	0.227693	−	0.700767i
$83$	422305.	+	137215.i	0.738570	+	0.239976i	0.654056	−	0.756446i	$-0.273066\pi$
$83$	422305.	+	137215.i	0.738570	+	0.239976i	0.0845142	+	0.996422i	$0.473066\pi$
$84$	14394.0	+	19811.6i	0.0242853	+	0.0334258i
$85$	489611.	−	673891.i	0.797249	−	1.09732i
$86$	239318.	+	736544.i	0.376252	+	1.15799i
$87$			421456.i			0.640022i
$88$	237211.	−	666510.i	0.348086	−	0.978045i
$89$	−432440.			−0.613418			−0.306709	−	0.951803i	$-0.599228\pi$
$89$	−432440.			−0.613418			−0.306709	+	0.951803i	$0.599228\pi$
$90$	70159.9	−	22796.3i	0.0962413	−	0.0312707i
$91$	15837.9	+	11506.9i	0.0210171	+	0.0152698i
$92$	65402.5	−	47517.7i	0.0839906	−	0.0610227i
$93$	−301878.	+	929086.i	−0.375304	+	1.15507i
$94$	−1.21361e6	−	394324.i	−1.46115	−	0.474756i
$95$	−501106.	−	689713.i	−0.584465	−	0.804448i
$96$	94521.9	−	130098.i	0.106836	−	0.147048i
$97$	338984.	+	1.04328e6i	0.371418	+	1.14311i	0.945863	+	0.324565i	$0.105218\pi$
$97$	338984.	+	1.04328e6i	0.371418	+	1.14311i	−0.574445	+	0.818543i	$0.694782\pi$
$98$		−	715000.i		−	0.759675i
$99$	−71620.0	−	104562.i	−0.0738123	−	0.107762i
$100$	−29443.8			−0.0294438
$101$	−74147.8	+	24092.1i	−0.0719671	+	0.0233835i	−0.344779	−	0.938684i	$-0.612046\pi$
$101$	−74147.8	+	24092.1i	−0.0719671	+	0.0233835i	0.272812	+	0.962067i	$0.412046\pi$
$102$	1.46124e6	+	1.06165e6i	1.37696	+	1.00042i
$103$	−93171.5	+	67693.0i	−0.0852651	+	0.0619487i	−0.629601	−	0.776919i	$-0.716782\pi$
$103$	−93171.5	+	67693.0i	−0.0852651	+	0.0619487i	0.544336	+	0.838867i	$0.316782\pi$
$104$	20679.2	−	63644.1i	0.0183838	−	0.0565794i
$105$	−429996.	−	139714.i	−0.371447	−	0.120690i
$106$	−976220.	−	1.34365e6i	−0.819653	−	1.12816i
$107$	−387437.	+	533261.i	−0.316264	+	0.435300i	−0.937322	−	0.348465i	$-0.886703\pi$
$107$	−387437.	+	533261.i	−0.316264	+	0.435300i	0.621058	+	0.783765i	$0.286703\pi$
$108$	30843.9	+	94927.7i	0.0244849	+	0.0753566i
$109$		−	704672.i		−	0.544136i	−0.962278	−	0.272068i	$-0.912292\pi$
$109$		−	704672.i		−	0.544136i	0.962278	−	0.272068i	$-0.0877075\pi$
$110$	291304.	+	989170.i	0.218861	+	0.743178i
$111$	−1.35456e6			−0.990443
$112$	549363.	−	178499.i	0.391026	−	0.127052i
$113$	−321992.	−	233941.i	−0.223157	−	0.162133i	0.470590	−	0.882352i	$-0.344041\pi$
$113$	−321992.	−	233941.i	−0.223157	−	0.162133i	−0.693747	+	0.720219i	$0.744041\pi$
$114$	1.49555e6	−	1.08658e6i	1.00945	−	0.733409i
$115$	−461226.	+	1.41951e6i	−0.303264	+	0.933350i
$116$	−76588.5	−	24885.1i	−0.0490670	−	0.0159428i
$117$	−7046.51	−	9698.68i	−0.00439963	−	0.00605557i
$118$	−704387.	+	969506.i	−0.428712	+	0.590071i
$119$	−395191.	−	1.21627e6i	−0.234513	−	0.721756i
$120$			1.54550e6i			0.894388i
$121$	1.48880e6	−	960156.i	0.840389	−	0.541983i
$122$	1.11464e6			0.613838
$123$	1.45012e6	−	471174.i	0.779274	−	0.253201i
$124$	−151012.	−	109717.i	−0.0792039	−	0.0575450i
$125$	1.72006e6	−	1.24969e6i	0.880669	−	0.639843i
$126$	34999.1	−	107716.i	0.0174963	−	0.0538480i
$127$	3.28523e6	+	1.06744e6i	1.60382	+	0.521112i	0.968047	−	0.250768i	$-0.0806830\pi$
$127$	3.28523e6	+	1.06744e6i	1.60382	+	0.521112i	0.635769	+	0.771879i	$0.280683\pi$
$128$	−1.05092e6	−	1.44646e6i	−0.501116	−	0.689727i
$129$	−1.70845e6	+	2.35147e6i	−0.795852	+	1.09540i
$130$	30141.3	+	92765.2i	0.0137193	+	0.0422236i
$131$		−	836748.i		−	0.372204i	−0.982530	−	0.186102i	$-0.940415\pi$
$131$		−	836748.i		−	0.372204i	0.982530	−	0.186102i	$-0.0595854\pi$
$132$	201079.	−	59216.4i	0.0874267	−	0.0257466i
$133$	−1.30889e6			−0.556351
$134$	753835.	−	244936.i	0.313301	−	0.101798i
$135$	−1.49087e6	−	1.08318e6i	−0.605952	−	0.440250i
$136$	−3.53667e6	+	2.56954e6i	−1.40597	+	1.02150i
$137$	−939277.	+	2.89080e6i	−0.365285	+	1.12423i	0.584517	+	0.811381i	$0.301284\pi$
$137$	−939277.	+	2.89080e6i	−0.365285	+	1.12423i	−0.949802	+	0.312851i	$0.898716\pi$
$138$	−3.07800e6	−	1.00010e6i	−1.17120	−	0.380547i
$139$	1.06260e6	+	1.46255e6i	0.395665	+	0.544586i	0.959649	−	0.281199i	$-0.0907322\pi$
$139$	1.06260e6	+	1.46255e6i	0.395665	+	0.544586i	−0.563985	+	0.825785i	$0.690732\pi$
$140$	50778.7	−	69890.9i	0.0185054	−	0.0254704i
$141$	−1.47994e6	−	4.55479e6i	−0.527943	−	1.62484i
$142$		−	134059.i		−	0.0468198i
$143$	138251.	−	94695.8i	0.0472782	−	0.0323834i
$144$	−353727.			−0.118462
$145$	1.41403e6	−	459447.i	0.463826	−	0.150706i
$146$	−1.69112e6	−	1.22867e6i	−0.543396	−	0.394801i
$147$	2.17097e6	−	1.57730e6i	0.683442	−	0.496550i
$148$	79980.8	−	246156.i	0.0246718	−	0.0759320i
$149$	−1.58690e6	−	515614.i	−0.479722	−	0.155871i	0.0591667	−	0.998248i	$-0.481156\pi$
$149$	−1.58690e6	−	515614.i	−0.479722	−	0.155871i	−0.538889	+	0.842377i	$0.681156\pi$
$150$	692850.	+	953626.i	0.205289	+	0.282556i
$151$	−44937.9	+	61851.7i	−0.0130521	+	0.0179647i	−0.815493	−	0.578767i	$-0.803534\pi$
$151$	−44937.9	+	61851.7i	−0.0130521	+	0.0179647i	0.802441	+	0.596731i	$0.203534\pi$
$152$	1.38260e6	+	4.25522e6i	0.393701	+	1.21169i
$153$			783141.i			0.218658i
$154$	1.49151e6	+	530828.i	0.408380	+	0.145342i
$155$	3.44627e6			0.925453
$156$	18857.3	−	6127.12i	0.00496714	−	0.00161392i
$157$	4.47374e6	+	3.25036e6i	1.15604	+	0.839910i	0.989272	−	0.146087i	$-0.0466679\pi$
$157$	4.47374e6	+	3.25036e6i	1.15604	+	0.839910i	0.166765	+	0.985997i	$0.446668\pi$
$158$	−2.59896e6	+	1.88825e6i	−0.658913	+	0.478728i
$159$	1.92620e6	−	5.92824e6i	0.479193	−	1.47480i
$160$	−539536.	−	175306.i	−0.131723	−	0.0427993i
$161$	1.34692e6	+	1.85388e6i	0.322749	+	0.444226i
$162$	2.66083e6	−	3.66232e6i	0.625853	−	0.861413i
$163$	−1.01099e6	−	3.11151e6i	−0.233445	−	0.718469i	−0.997324	−	0.0731099i	$-0.976708\pi$
$163$	−1.01099e6	−	3.11151e6i	−0.233445	−	0.718469i	0.763879	−	0.645359i	$-0.223292\pi$
$164$			291343.i			0.0660499i
$165$	−2.36082e6	+	3.06662e6i	−0.525546	+	0.682666i
$166$	3.39665e6			0.742551
$167$	−5.69919e6	+	1.85178e6i	−1.22367	+	0.397594i	−0.848416	−	0.529330i	$-0.822444\pi$
$167$	−5.69919e6	+	1.85178e6i	−1.22367	+	0.397594i	−0.375251	+	0.926923i	$0.622444\pi$
$168$	1.91964e6	+	1.39470e6i	0.404848	+	0.294139i
$169$	−3.89215e6	+	2.82781e6i	−0.806360	+	0.585855i
$170$	1.96900e6	−	6.05996e6i	0.400774	−	1.23345i
$171$	762298.	+	247686.i	0.152453	+	0.0495350i
$172$	−326442.	−	449309.i	−0.0641535	−	0.0882998i
$173$	880803.	−	1.21232e6i	0.170114	−	0.234142i	−0.715445	−	0.698669i	$-0.753776\pi$
$173$	880803.	−	1.21232e6i	0.170114	−	0.234142i	0.885559	+	0.464527i	$0.153776\pi$
$174$	996245.	+	3.06613e6i	0.189112	+	0.582026i
$175$		−	834607.i		−	0.155728i
$176$	137249.	−	4.94253e6i	0.0251751	−	0.906591i
$177$	−4.49762e6			−0.811079
$178$	−3.14604e6	+	1.02221e6i	−0.557833	+	0.181251i
$179$	−5.93052e6	−	4.30878e6i	−1.03403	−	0.751268i	−0.0649200	−	0.997890i	$-0.520679\pi$
$179$	−5.93052e6	−	4.30878e6i	−1.03403	−	0.751268i	−0.969112	+	0.246623i	$0.920679\pi$
$180$	−42799.2	+	31095.4i	−0.00733868	+	0.00533186i
$181$	−2.29047e6	+	7.04935e6i	−0.386269	+	1.18881i	0.549287	+	0.835634i	$0.314899\pi$
$181$	−2.29047e6	+	7.04935e6i	−0.386269	+	1.18881i	−0.935556	+	0.353179i	$0.885101\pi$
$182$	142422.	+	46275.8i	0.0236246	+	0.00767608i
$183$	2.45891e6	+	3.38440e6i	0.401226	+	0.552240i
$184$	4.60421e6	−	6.33715e6i	0.739097	−	1.01728i
$185$	1.47666e6	+	4.54470e6i	0.233220	+	0.717778i
$186$			7.47275e6i			1.16129i
$187$	−1.09426e7	−	303865.i	−1.67339	−	0.0464682i
$188$	915096.			0.137719
$189$	−2.69080e6	+	874293.i	−0.398562	+	0.129500i
$190$	−5.27594e6	−	3.83319e6i	−0.769200	−	0.558856i
$191$	3.40987e6	−	2.47742e6i	0.489371	−	0.355549i	−0.315571	−	0.948902i	$-0.602196\pi$
$191$	3.40987e6	−	2.47742e6i	0.489371	−	0.355549i	0.804942	+	0.593353i	$0.202196\pi$
$192$	2.48935e6	−	7.66143e6i	0.351708	−	1.08245i
$193$	1.15532e7	+	3.75386e6i	1.60705	+	0.522163i	0.968838	−	0.247697i	$-0.0796736\pi$
$193$	1.15532e7	+	3.75386e6i	1.60705	+	0.522163i	0.638214	+	0.769859i	$0.279674\pi$
$194$	4.93226e6	+	6.78868e6i	0.675524	+	0.929779i
$195$	−215173.	+	296160.i	−0.0290191	+	0.0399414i
$196$	158447.	+	487649.i	0.0210434	+	0.0647648i
$197$		−	9.57600e6i		−	1.25252i	−0.779614	−	0.626261i	$-0.784584\pi$
$197$		−	9.57600e6i		−	1.25252i	0.779614	−	0.626261i	$-0.215416\pi$
$198$	−768205.	−	591398.i	−0.0989650	−	0.0761876i
$199$	4.87908e6			0.619125			0.309563	−	0.950879i	$-0.399817\pi$
$199$	4.87908e6			0.619125			0.309563	+	0.950879i	$0.399817\pi$
$200$	−2.71332e6	+	881610.i	−0.339164	+	0.110201i
$201$	2.40668e6	+	1.74855e6i	0.296367	+	0.215323i
$202$	−482481.	+	350543.i	−0.0585365	+	0.0425292i
$203$	705387.	−	2.17096e6i	0.0843217	−	0.259516i
$204$	−1.23187e6	−	400259.i	−0.145102	−	0.0471466i
$205$	−3.16168e6	−	4.35168e6i	−0.366992	−	0.505121i
$206$	−517816.	+	712712.i	−0.0592343	+	0.0815291i
$207$	−433632.	−	1.33458e6i	−0.0488889	−	0.150465i
$208$		−	467697.i		−	0.0519726i
$209$	−3.75662e6	+	1.05553e7i	−0.411489	+	1.15619i
$210$	−3.45851e6			−0.373449
$211$	7.27408e6	−	2.36349e6i	0.774338	−	0.251598i	0.104917	−	0.994481i	$-0.466542\pi$
$211$	7.27408e6	−	2.36349e6i	0.774338	−	0.251598i	0.669421	+	0.742883i	$0.266542\pi$
$212$	963567.	+	700072.i	0.101129	+	0.0734743i
$213$	407045.	−	295736.i	0.0421215	−	0.0306031i
$214$	−1.55810e6	+	4.79534e6i	−0.158984	+	0.489303i
$215$	9.75190e6	+	3.16858e6i	0.981237	+	0.318823i
$216$	5.68467e6	+	7.82427e6i	0.564084	+	0.776395i
$217$	3.11000e6	−	4.28055e6i	0.304356	−	0.418910i
$218$	−1.66571e6	−	5.12654e6i	−0.160780	−	0.494829i
$219$		−	7.84527e6i		−	0.746923i
$220$	−417881.	−	610087.i	−0.0392451	−	0.0572959i
$221$	−1.03547e6			−0.0959311
$222$	−9.85454e6	+	3.20193e6i	−0.900694	+	0.292653i
$223$	4.71361e6	+	3.42464e6i	0.425049	+	0.308816i	0.779666	−	0.626195i	$-0.215389\pi$
$223$	4.71361e6	+	3.42464e6i	0.425049	+	0.308816i	−0.354617	+	0.935012i	$0.615389\pi$
$224$	−704635.	+	511947.i	−0.0626932	+	0.0455493i
$225$	−157935.	+	486075.i	−0.0138654	+	0.0426733i
$226$	−2.89551e6	−	940809.i	−0.250842	−	0.0815035i
$227$	−4.04752e6	−	5.57093e6i	−0.346028	−	0.476266i	0.600162	−	0.799878i	$-0.295103\pi$
$227$	−4.04752e6	−	5.57093e6i	−0.346028	−	0.476266i	−0.946190	+	0.323612i	$0.895103\pi$
$228$	−779212.	+	1.07249e6i	−0.0657433	+	0.0904878i
$229$	−6.53489e6	−	2.01123e7i	−0.544166	−	1.67477i	−0.722964	−	0.690886i	$-0.757221\pi$
$229$	−6.53489e6	−	2.01123e7i	−0.544166	−	1.67477i	0.178798	−	0.983886i	$-0.442779\pi$
$230$			1.14173e7i			0.938382i
$231$	1.67853e6	+	5.69973e6i	0.136174	+	0.462400i
$232$	−7.80292e6			−0.624875
$233$	1.16590e7	−	3.78824e6i	0.921708	−	0.299481i	0.190541	−	0.981679i	$-0.438976\pi$
$233$	1.16590e7	−	3.78824e6i	0.921708	−	0.299481i	0.731167	+	0.682198i	$0.238976\pi$
$234$	−74189.8	−	53902.0i	−0.00579024	−	0.00420685i
$235$	−1.36685e7	+	9.93072e6i	−1.05321	+	0.765204i
$236$	265565.	−	817324.i	0.0202039	−	0.0621811i
$237$	−1.14667e7	−	3.72575e6i	−0.861377	−	0.279878i
$238$	−5.75009e6	−	7.91432e6i	−0.426524	−	0.587061i
$239$	−1.51061e7	+	2.07918e7i	−1.10652	+	1.52299i	−0.280072	+	0.959979i	$0.590358\pi$
$239$	−1.51061e7	+	2.07918e7i	−1.10652	+	1.52299i	−0.826447	+	0.563014i	$0.809642\pi$
$240$	3.33783e6	+	1.02728e7i	0.241452	+	0.743113i
$241$		−	5.37848e6i		−	0.384245i	−0.981371	−	0.192123i	$-0.938463\pi$
$241$		−	5.37848e6i		−	0.384245i	0.981371	−	0.192123i	$-0.0615371\pi$
$242$	8.56151e6	−	1.05045e7i	0.604094	−	0.741187i
$243$	3.72543e6			0.259632
$244$	−760212.	+	247008.i	−0.0523317	+	0.0170036i
$245$	−7.65869e6	−	5.56436e6i	−0.520782	−	0.378370i
$246$	9.43600e6	−	6.85566e6i	0.633844	−	0.460515i
$247$	−327489.	+	1.00791e6i	−0.0217323	+	0.0668852i
$248$	−1.72013e7	−	5.58903e6i	−1.12773	−	0.366422i
$249$	7.49307e6	+	1.03133e7i	0.485358	+	0.668037i
$250$	9.55949e6	−	1.31575e7i	0.611808	−	0.842081i
$251$	4.88902e6	+	1.50469e7i	0.309172	+	0.951535i	0.978087	+	0.208196i	$0.0667591\pi$
$251$	4.88902e6	+	1.50469e7i	0.309172	+	0.951535i	−0.668915	+	0.743339i	$0.733241\pi$
$252$			81221.4i			0.00507538i
$253$	1.88160e7	−	5.54120e6i	1.16189	−	0.342170i
$254$	2.64235e7			1.61246
$255$	2.27437e7	−	7.38986e6i	1.37164	−	0.445672i
$256$	3.46379e6	+	2.51659e6i	0.206458	+	0.150000i
$257$	9.01021e6	−	6.54630e6i	0.530806	−	0.385653i	−0.289853	−	0.957071i	$-0.593607\pi$
$257$	9.01021e6	−	6.54630e6i	0.530806	−	0.385653i	0.820659	+	0.571418i	$0.193607\pi$
$258$	−6.87062e6	+	2.11456e7i	−0.400071	+	1.23129i
$259$	6.97747e6	+	2.26712e6i	0.401604	+	0.130489i
$260$	−41114.3	−	56589.0i	−0.00233923	−	0.00321967i
$261$	−821635.	+	1.13088e6i	−0.0462123	+	0.0636058i
$262$	−1.97792e6	−	6.08740e6i	−0.109978	−	0.338476i
$263$			1.81868e7i			0.999744i	0.866099	+	0.499872i	$0.166620\pi$
$263$			1.81868e7i			0.999744i	−0.866099	+	0.499872i	$0.833380\pi$
$264$	1.67568e7	−	1.14776e7i	0.910708	−	0.623794i
$265$	−2.19897e7			−1.18163
$266$	−9.52228e6	+	3.09398e6i	−0.505937	+	0.164389i
$267$	−1.00440e7	−	7.29738e6i	−0.527681	−	0.383383i
$268$	−459857.	+	334106.i	−0.0238901	+	0.0173572i
$269$	4.78920e6	−	1.47396e7i	0.246040	−	0.757234i	−0.749423	−	0.662091i	$-0.769669\pi$
$269$	4.78920e6	−	1.47396e7i	0.246040	−	0.757234i	0.995464	−	0.0951429i	$-0.0303308\pi$
$270$	−1.34066e7	−	4.35608e6i	−0.681127	−	0.221312i
$271$	−1.50392e7	−	2.06996e7i	−0.755641	−	1.04005i	−0.997564	−	0.0697555i	$-0.977778\pi$
$271$	−1.50392e7	−	2.06996e7i	−0.755641	−	1.04005i	0.241923	−	0.970295i	$-0.422222\pi$
$272$	−1.79584e7	+	2.47176e7i	−0.892403	+	1.22829i
$273$	173678.	+	534525.i	0.00853604	+	0.0262712i
$274$			2.32510e7i			1.13029i
$275$	−6.73052e6	−	2.39539e6i	−0.323631	−	0.115180i
$276$	2.32091e6			0.110390
$277$	−1.15324e6	+	374711.i	−0.0542601	+	0.0176302i	−0.336021	−	0.941854i	$-0.609081\pi$
$277$	−1.15324e6	+	374711.i	−0.0542601	+	0.0176302i	0.281761	+	0.959485i	$0.409081\pi$
$278$	1.11877e7	+	8.12836e6i	0.520724	+	0.378328i
$279$	−2.62129e6	+	1.90448e6i	−0.120699	+	0.0876927i
$280$	2.58669e6	−	7.96102e6i	0.117834	−	0.362656i
$281$	−1.06514e7	−	3.46086e6i	−0.480053	−	0.155979i	0.0589870	−	0.998259i	$-0.481213\pi$
$281$	−1.06514e7	−	3.46086e6i	−0.480053	−	0.155979i	−0.539040	+	0.842280i	$0.681213\pi$
$282$	−2.15334e7	−	2.96381e7i	−0.960206	−	1.32161i
$283$	−1.11109e7	+	1.52928e7i	−0.490217	+	0.674725i	−0.980428	−	0.196878i	$-0.936920\pi$
$283$	−1.11109e7	+	1.52928e7i	−0.490217	+	0.674725i	0.490211	+	0.871604i	$0.336920\pi$
$284$	29707.9	+	91431.6i	0.00129693	+	0.00399155i
$285$		−	2.44756e7i		−	1.05730i
$286$	781945.	−	1.01572e6i	0.0334255	−	0.0434186i
$287$	−8.25832e6			−0.349338
$288$	507257.	−	164818.i	0.0212349	−	0.00689964i
$289$	3.51964e7	+	2.55717e7i	1.45816	+	1.05941i
$290$	9.20114e6	−	6.68502e6i	0.377266	−	0.274100i
$291$	−9.73196e6	+	2.99519e7i	−0.394931	+	1.21547i
$292$	1.42567e6	+	463228.i	0.0572625	+	0.0186057i
$293$	−1.01651e7	−	1.39911e7i	−0.404120	−	0.556223i	0.557652	−	0.830075i	$-0.311702\pi$
$293$	−1.01651e7	−	1.39911e7i	−0.404120	−	0.556223i	−0.961772	+	0.273851i	$0.911702\pi$
$294$	1.20655e7	−	1.66068e7i	0.474793	−	0.653496i
$295$	4.90304e6	+	1.50900e7i	0.190985	+	0.587792i
$296$		−	2.50786e7i		−	0.967004i
$297$	−672249.	+	2.42087e7i	−0.0256602	+	0.924062i
$298$	−1.27636e7			−0.482308
$299$	1.76458e6	−	573348.i	0.0660128	−	0.0214489i
$300$	−683870.	−	496861.i	−0.0253285	−	0.0184022i
$301$	1.27360e7	−	9.25324e6i	0.467018	−	0.339308i
$302$	−180721.	+	556201.i	−0.00656126	+	0.0201935i
$303$	−2.12873e6	−	691665.i	−0.0765230	−	0.0248638i
$304$	1.83800e7	+	2.52979e7i	0.654223	+	0.900460i
$305$	8.67446e6	−	1.19394e7i	0.305733	−	0.420806i
$306$	1.85120e6	+	5.69741e6i	0.0646084	+	0.198844i
$307$			9.10859e6i			0.314801i	0.987535	+	0.157400i	$0.0503113\pi$
$307$			9.10859e6i			0.314801i	−0.987535	+	0.157400i	$0.949689\pi$
$308$	−1.13488e6	−	31514.5i	−0.0388418	−	0.00107860i
$309$	−3.30634e6			−0.112065
$310$	2.50719e7	−	8.14635e6i	0.841593	−	0.273450i
$311$	−1.89729e7	−	1.37846e7i	−0.630742	−	0.458261i	0.225915	−	0.974147i	$-0.427463\pi$
$311$	−1.89729e7	−	1.37846e7i	−0.630742	−	0.458261i	−0.856657	+	0.515886i	$0.827463\pi$
$312$	1.55429e6	−	1.12926e6i	0.0511761	−	0.0371816i
$313$	−1.00620e7	+	3.09676e7i	−0.328133	+	1.00989i	0.641873	+	0.766811i	$0.278158\pi$
$313$	−1.00620e7	+	3.09676e7i	−0.328133	+	1.00989i	−0.970006	+	0.243079i	$0.921842\pi$
$314$	4.02300e7	+	1.30715e7i	1.29946	+	0.422219i
$315$	−881423.	−	1.21317e6i	−0.0282002	−	0.0388143i
$316$	1.35411e6	−	1.86378e6i	0.0429135	−	0.0590654i
$317$	−2.00914e6	−	6.18349e6i	−0.0630713	−	0.194114i	0.914555	−	0.404460i	$-0.132541\pi$
$317$	−2.00914e6	−	6.18349e6i	−0.0630713	−	0.194114i	−0.977627	+	0.210347i	$0.932541\pi$
$318$		−	4.76816e7i		−	1.48275i
$319$	−1.54827e7	−	1.19193e7i	−0.476953	−	0.367179i
$320$	−2.84187e7			−0.867269
$321$	−1.79974e7	+	5.84771e6i	−0.544120	+	0.176795i
$322$	1.41812e7	+	1.03033e7i	0.424762	+	0.308608i
$323$	5.60089e7	−	4.06928e7i	1.66207	−	1.20756i
$324$	−1.00317e6	+	3.08745e6i	−0.0294945	+	0.0907748i
$325$	−642687.	−	208822.i	−0.0187219	−	0.00608311i
$326$	−1.47101e7	−	2.02467e7i	−0.424582	−	0.584387i
$327$	1.18912e7	−	1.63669e7i	0.340082	−	0.468083i
$328$	8.72341e6	+	2.68479e7i	0.247209	+	0.760832i
$329$			2.59391e7i			0.728395i
$330$	−9.92621e6	+	2.78904e7i	−0.276211	+	0.776093i
$331$	−8.11879e6			−0.223876			−0.111938	−	0.993715i	$-0.535706\pi$
$331$	−8.11879e6			−0.223876			−0.111938	+	0.993715i	$0.535706\pi$
$332$	−2.31661e6	+	752711.i	−0.0633050	+	0.0205690i
$333$	−3.63466e6	−	2.64074e6i	−0.0984309	−	0.0715142i
$334$	−3.70848e7	+	2.69437e7i	−0.995305	+	0.723131i
$335$	3.24297e6	−	9.98084e6i	0.0862599	−	0.265481i
$336$	1.57718e7	+	5.12457e6i	0.415780	+	0.135095i
$337$	1.94214e7	+	2.67312e7i	0.507447	+	0.698440i	0.983486	−	0.180984i	$-0.0579281\pi$
$337$	1.94214e7	+	2.67312e7i	0.507447	+	0.698440i	−0.476040	+	0.879424i	$0.657928\pi$
$338$	−2.16312e7	+	2.97729e7i	−0.560185	+	0.771028i
$339$	−3.53095e6	−	1.08672e7i	−0.0906343	−	0.278944i
$340$			4.56940e6i			0.116258i
$341$	−2.55937e7	−	3.73655e7i	−0.645460	−	0.942340i
$342$	6.13126e6			0.153275
$343$	−3.12212e7	+	1.01444e7i	−0.773690	+	0.251387i
$344$	−4.35356e7	−	3.16305e7i	−1.06947	−	0.777017i
$345$	−3.46666e7	+	2.51868e7i	−0.844217	+	0.613359i
$346$	3.54220e6	−	1.09018e7i	0.0855156	−	0.263190i
$347$	4.25545e7	+	1.38268e7i	1.01849	+	0.330927i	0.770230	−	0.637766i	$-0.220141\pi$
$347$	4.25545e7	+	1.38268e7i	1.01849	+	0.330927i	0.248260	+	0.968693i	$0.420141\pi$
$348$	−1.35893e6	−	1.87041e6i	−0.0322448	−	0.0443812i
$349$	3.38003e7	−	4.65222e7i	0.795142	−	1.09442i	−0.198307	−	0.980140i	$-0.563544\pi$
$349$	3.38003e7	−	4.65222e7i	0.795142	−	1.09442i	0.993449	−	0.114279i	$-0.0364558\pi$
$350$	−1.97286e6	−	6.07183e6i	−0.0460142	−	0.141617i
$351$			2.29079e6i			0.0529742i
$352$	2.10613e6	+	7.15171e6i	0.0482901	+	0.163977i
$353$	4.22645e7			0.960841			0.480421	−	0.877038i	$-0.340484\pi$
$353$	4.22645e7			0.960841			0.480421	+	0.877038i	$0.340484\pi$
$354$	−3.27206e7	+	1.06316e7i	−0.737583	+	0.239655i
$355$	−1.43596e6	−	1.04329e6i	−0.0320965	−	0.0233195i
$356$	1.91916e6	−	1.39435e6i	0.0425364	−	0.0309045i
$357$	1.13456e7	−	3.49183e7i	0.249359	−	0.767447i
$358$	−5.33302e7	−	1.73280e7i	−1.16231	−	0.377659i
$359$	−1.43885e6	−	1.98041e6i	−0.0310981	−	0.0428028i	0.793185	−	0.608981i	$-0.208421\pi$
$359$	−1.43885e6	−	1.98041e6i	−0.0310981	−	0.0428028i	−0.824283	+	0.566178i	$0.808421\pi$
$360$	−3.01298e6	+	4.14701e6i	−0.0645786	+	0.0888848i
$361$	−7.35780e6	−	2.26450e7i	−0.156396	−	0.481338i
$362$			5.66988e7i			1.19522i
$363$	5.07818e7	+	2.82249e6i	1.06167	+	0.0590082i
$364$	−107391.			−0.00222670
$365$	−2.63217e7	+	8.55245e6i	−0.541297	+	0.175878i
$366$	2.58888e7	+	1.88093e7i	0.528043	+	0.383645i
$367$	−7.00232e6	+	5.08748e6i	−0.141659	+	0.102921i	−0.656358	−	0.754450i	$-0.727904\pi$
$367$	−7.00232e6	+	5.08748e6i	−0.141659	+	0.102921i	0.514699	+	0.857371i	$0.327904\pi$
$368$	1.69173e7	−	5.20661e7i	0.339459	−	1.04475i
$369$	4.80965e6	+	1.56275e6i	0.0957269	+	0.0311036i
$370$	2.14857e7	+	2.95725e7i	0.424174	+	0.583825i
$371$	−1.98441e7	+	2.73130e7i	−0.388606	+	0.534870i
$372$	−1.65599e6	−	5.09662e6i	−0.0321684	−	0.0990041i
$373$		−	1.18069e6i		−	0.0227514i	−0.999935	−	0.0113757i	$-0.996379\pi$
$373$		−	1.18069e6i		−	0.0227514i	0.999935	−	0.0113757i	$-0.00362108\pi$
$374$	−8.03266e7	+	2.36557e7i	−1.53548	+	0.452190i
$375$	6.10389e7			1.15748
$376$	8.43282e7	−	2.73999e7i	1.58639	−	0.515448i
$377$	−1.49525e6	−	1.08636e6i	−0.0279055	−	0.0202746i
$378$	−1.75091e7	+	1.27211e7i	−0.324181	+	0.235531i
$379$	2.16852e7	−	6.67403e7i	0.398333	−	1.22594i	−0.528002	−	0.849243i	$-0.677058\pi$
$379$	2.16852e7	−	6.67403e7i	0.398333	−	1.22594i	0.926335	−	0.376701i	$-0.122942\pi$
$380$	4.44778e6	+	1.44517e6i	0.0810574	+	0.0263372i
$381$	5.82908e7	+	8.02304e7i	1.05396	+	1.45065i
$382$	1.89509e7	−	2.60837e7i	0.339970	−	0.467928i
$383$	1.19384e7	+	3.67426e7i	0.212496	+	0.653994i	0.999322	+	0.0368196i	$0.0117227\pi$
$383$	1.19384e7	+	3.67426e7i	0.212496	+	0.653994i	−0.786826	+	0.617174i	$0.788277\pi$
$384$		−	5.13300e7i		−	0.906520i
$385$	1.72934e7	−	1.18452e7i	0.303038	−	0.207567i
$386$	9.29237e7			1.61571
$387$	−9.16846e6	+	2.97901e6i	−0.158184	+	0.0513972i
$388$	−4.86833e6	−	3.53705e6i	−0.0833461	−	0.0605545i
$389$	−7.56047e7	+	5.49300e7i	−1.28440	+	0.933170i	−0.999676	−	0.0254401i	$-0.991901\pi$
$389$	−7.56047e7	+	5.49300e7i	−1.28440	+	0.933170i	−0.284722	+	0.958610i	$0.591901\pi$
$390$	−865332.	+	2.66322e6i	−0.0145878	+	0.0448966i
$391$	−1.15273e8	−	3.74544e7i	−1.92840	−	0.626574i
$392$	2.92025e7	+	4.01938e7i	0.484799	+	0.667268i
$393$	1.41200e7	−	1.94345e7i	0.232625	−	0.320181i
$394$	−2.26359e7	−	6.96661e7i	−0.370091	−	1.13902i
$395$			4.25336e7i			0.690146i
$396$	654993.	+	233112.i	0.0105475	+	0.00375387i
$397$	−2.13761e7			−0.341632			−0.170816	−	0.985303i	$-0.554640\pi$
$397$	−2.13761e7			−0.341632			−0.170816	+	0.985303i	$0.554640\pi$
$398$	3.54957e7	−	1.15332e7i	0.563023	−	0.182937i
$399$	−3.04006e7	−	2.20874e7i	−0.478590	−	0.347716i
$400$	−1.61311e7	+	1.17199e7i	−0.252048	+	0.183124i
$401$	−1.70271e7	+	5.24041e7i	−0.264064	+	0.812704i	0.727844	+	0.685743i	$0.240522\pi$
$401$	−1.70271e7	+	5.24041e7i	−0.264064	+	0.812704i	−0.991908	+	0.126961i	$0.959478\pi$
$402$	2.16420e7	+	7.03192e6i	0.333135	+	0.108242i
$403$	−2.51810e6	−	3.46586e6i	−0.0384731	−	0.0529537i
$404$	251384.	−	346000.i	0.00381235	−	0.00524725i
$405$	−1.85213e7	−	5.70027e7i	−0.278809	−	0.858085i
$406$		−	1.74613e7i		−	0.260915i
$407$	3.83086e7	−	4.97615e7i	0.568215	−	0.738092i
$408$	−1.25504e8			−1.84790
$409$	−1.16434e8	+	3.78317e7i	−1.70181	+	0.552950i	−0.988936	−	0.148346i	$-0.952605\pi$
$409$	−1.16434e8	+	3.78317e7i	−1.70181	+	0.552950i	−0.712870	+	0.701296i	$0.752605\pi$
$410$	−3.32880e7	−	2.41852e7i	−0.482988	−	0.350912i
$411$	−7.05977e7	+	5.12922e7i	−1.01687	+	0.738799i
$412$	195224.	−	600839.i	0.00279153	−	0.00859145i
$413$	2.31677e7	+	7.52763e6i	0.328876	+	0.106858i
$414$	−6.30942e6	−	8.68417e6i	−0.0889177	−	0.122385i
$415$	2.64338e7	−	3.63830e7i	0.369842	−	0.509043i
$416$	217922.	+	670694.i	0.00302706	+	0.00931632i
$417$			5.19009e7i			0.715759i
$418$	−2.37898e6	+	8.56704e7i	−0.0325733	+	1.17301i
$419$	−5.94779e6			−0.0808562			−0.0404281	−	0.999182i	$-0.512872\pi$
$419$	−5.94779e6			−0.0808562			−0.0404281	+	0.999182i	$0.512872\pi$
$420$	2.35880e6	−	766420.i	0.0318378	−	0.0103447i
$421$	−3.39892e7	−	2.46946e7i	−0.455506	−	0.330945i	0.336260	−	0.941769i	$-0.390838\pi$
$421$	−3.39892e7	−	2.46946e7i	−0.455506	−	0.330945i	−0.791766	+	0.610825i	$0.790838\pi$
$422$	4.73326e7	−	3.43891e7i	0.629830	−	0.457598i
$423$	4.90853e6	−	1.51069e7i	0.0648531	−	0.199597i
$424$	1.09757e8	+	3.56621e7i	1.43990	+	0.467852i
$425$	2.59476e7	+	3.57138e7i	0.338010	+	0.465231i
$426$	2.26222e6	−	3.11368e6i	0.0292621	−	0.0402759i
$427$	−7.00162e6	−	2.15488e7i	−0.0899321	−	0.276783i
$428$		−	3.61583e6i		−	0.0461187i
$429$	4.80904e6	+	133542.i	0.0609097	+	0.00169140i
$430$	7.84357e7			0.986526
$431$	8.95660e7	−	2.91018e7i	1.11869	−	0.363486i	0.309425	−	0.950924i	$-0.399863\pi$
$431$	8.95660e7	−	2.91018e7i	1.11869	−	0.363486i	0.809269	+	0.587438i	$0.199863\pi$
$432$	5.46835e7	+	3.97299e7i	0.678274	+	0.492795i
$433$	1.10719e8	−	8.04419e7i	1.36382	−	0.990874i	0.365630	−	0.930760i	$-0.380854\pi$
$433$	1.10719e8	−	8.04419e7i	1.36382	−	0.990874i	0.998192	−	0.0601142i	$-0.0191465\pi$
$434$	1.25071e7	−	3.84928e7i	0.152998	−	0.470880i
$435$	4.05958e7	+	1.31904e7i	0.493189	+	0.160247i
$436$	2.27212e6	+	3.12731e6i	0.0274140	+	0.0377321i
$437$	−7.29151e7	+	1.00359e8i	−0.873722	+	1.20258i
$438$	−1.85448e7	−	5.70750e7i	−0.220698	−	0.679240i
$439$		−	4.84442e7i		−	0.572596i	−0.958141	−	0.286298i	$-0.907575\pi$
$439$		−	4.84442e7i		−	0.572596i	0.958141	−	0.286298i	$-0.0924247\pi$
$440$	−5.67760e7	−	4.37086e7i	−0.666510	−	0.513108i
$441$	8.90029e6			0.103774
$442$	−7.53310e6	+	2.44765e6i	−0.0872382	+	0.0283454i
$443$	−1.04099e7	−	7.56326e6i	−0.119739	−	0.0869958i	0.526304	−	0.850297i	$-0.323577\pi$
$443$	−1.04099e7	−	7.56326e6i	−0.119739	−	0.0869958i	−0.646043	+	0.763301i	$0.723577\pi$
$444$	6.01150e6	−	4.36761e6i	0.0686806	−	0.0498993i
$445$	−1.35341e7	+	4.16538e7i	−0.153586	+	0.472688i
$446$	4.23871e7	+	1.37724e7i	0.477781	+	0.155240i
$447$	−2.81567e7	−	3.87544e7i	−0.315253	−	0.433909i
$448$	−2.56457e7	+	3.52983e7i	−0.285221	+	0.392573i
$449$	4.07823e7	+	1.25515e8i	0.450540	+	1.38662i	0.876293	+	0.481779i	$0.160009\pi$
$449$	4.07823e7	+	1.25515e8i	0.450540	+	1.38662i	−0.425753	+	0.904840i	$0.639991\pi$
$450$			3.90956e6i			0.0429033i
$451$	−2.37021e7	+	6.65975e7i	−0.258378	+	0.725986i
$452$	2.18330e6			0.0236428
$453$	−2.08748e6	+	678263.i	−0.0224558	+	0.00729632i
$454$	−4.26146e7	−	3.09613e7i	−0.455398	−	0.330866i
$455$	1.60406e6	−	1.16542e6i	0.0170289	−	0.0123722i
$456$	−3.96935e7	+	1.22164e8i	−0.418625	+	1.28839i
$457$	−5.70166e7	−	1.85258e7i	−0.597382	−	0.194101i	−0.00530974	−	0.999986i	$-0.501690\pi$
$457$	−5.70166e7	−	1.85258e7i	−0.597382	−	0.194101i	−0.592073	+	0.805885i	$0.701690\pi$
$458$	−9.50836e7	−	1.30871e8i	−0.989713	−	1.36222i
$459$	8.79608e7	−	1.21068e8i	0.909601	−	1.25196i
$460$	−2.53012e6	−	7.78690e6i	−0.0259936	−	0.0800002i
$461$		−	6.69341e7i		−	0.683195i	−0.939846	−	0.341598i	$-0.889032\pi$
$461$		−	6.69341e7i		−	0.683195i	0.939846	−	0.341598i	$-0.110968\pi$
$462$	2.56846e7	+	3.74982e7i	0.260463	+	0.380263i
$463$	−8.46676e7			−0.853050			−0.426525	−	0.904476i	$-0.640262\pi$
$463$	−8.46676e7			−0.853050			−0.426525	+	0.904476i	$0.640262\pi$
$464$	−5.18652e7	+	1.68520e7i	−0.519185	+	0.168693i
$465$	8.00440e7	+	5.81554e7i	0.796104	+	0.578404i
$466$	7.58654e7	−	5.51195e7i	0.749698	−	0.544687i
$467$	2.74935e7	−	8.46164e7i	0.269948	−	0.830814i	−0.720564	−	0.693388i	$-0.756117\pi$
$467$	2.74935e7	−	8.46164e7i	0.269948	−	0.830814i	0.990512	−	0.137426i	$-0.0438829\pi$
$468$	62544.3	+	20321.9i	0.000610169	+	0.000198256i
$469$	−9.47048e6	−	1.30350e7i	−0.0918023	−	0.126355i
$470$	−7.59647e7	+	1.04556e8i	−0.731675	+	1.00706i
$471$	4.90588e7	+	1.50987e8i	0.469520	+	1.44503i
$472$		−	8.32699e7i		−	0.791884i
$473$	−3.80675e7	−	1.29264e8i	−0.359726	−	1.22151i
$474$	−9.22281e7			−0.866020
$475$	4.29698e7	−	1.39617e7i	0.400943	−	0.130274i
$476$	5.67556e6	+	4.12354e6i	0.0526245	+	0.0382339i
$477$	1.67257e7	−	1.21519e7i	0.154110	−	0.111967i
$478$	−6.07502e7	+	1.86970e8i	−0.556242	+	1.71194i
$479$	−1.64124e7	−	5.33270e6i	−0.149336	−	0.0485222i	0.233395	−	0.972382i	$-0.425016\pi$
$479$	−1.64124e7	−	5.33270e6i	−0.149336	−	0.0485222i	−0.382731	+	0.923860i	$0.625016\pi$
$480$	−9.57314e6	−	1.31763e7i	−0.0865627	−	0.119143i
$481$	3.49158e6	−	4.80574e6i	0.0313752	−	0.0431842i
$482$	−1.27137e7	−	3.91289e7i	−0.113536	−	0.349427i
$483$			6.57879e7i			0.583855i
$484$	−3.51135e6	+	9.06159e6i	−0.0309698	+	0.0799224i
$485$	1.11101e8			0.973852
$486$	2.71028e7	−	8.80624e6i	0.236105	−	0.0767152i
$487$	8.75936e7	+	6.36405e7i	0.758377	+	0.550993i	0.898412	−	0.439153i	$-0.144721\pi$
$487$	8.75936e7	+	6.36405e7i	0.758377	+	0.550993i	−0.140035	+	0.990147i	$0.544721\pi$
$488$	−6.26593e7	+	4.55247e7i	−0.539171	+	0.391730i
$489$	2.90248e7	−	8.93291e7i	0.248223	−	0.763952i
$490$	−6.88706e7	−	2.23774e7i	−0.585391	−	0.190205i
$491$	−1.18755e8	−	1.63453e8i	−1.00325	−	1.38086i	−0.923310	−	0.384056i	$-0.874527\pi$
$491$	−1.18755e8	−	1.63453e8i	−1.00325	−	1.38086i	−0.0799401	−	0.996800i	$-0.525473\pi$
$492$	−4.91637e6	+	6.76680e6i	−0.0412809	+	0.0568183i
$493$	3.73099e7	+	1.14828e8i	0.311374	+	0.958312i
$494$			8.10674e6i			0.0672458i
$495$	−1.23132e7	+	3.62614e6i	−0.101520	+	0.0298971i
$496$	−1.26406e8			−1.03591
$497$	−2.59170e6	+	842093.i	−0.0211113	+	0.00685948i
$498$	7.88915e7	+	5.73180e7i	0.638766	+	0.464091i
$499$	1.83773e7	−	1.33519e7i	0.147904	−	0.107458i	−0.511372	−	0.859359i	$-0.670863\pi$
$499$	1.83773e7	−	1.33519e7i	0.147904	−	0.107458i	0.659276	+	0.751901i	$0.270863\pi$
$500$	−3.60407e6	+	1.10922e7i	−0.0288326	+	0.0887376i
$501$	−1.63619e8	−	5.31631e7i	−1.30113	−	0.422763i
$502$	7.11360e7	+	9.79103e7i	0.562313	+	0.773958i
$503$	3.49886e7	−	4.81577e7i	0.274931	−	0.378410i	−0.649116	−	0.760689i	$-0.724861\pi$
$503$	3.49886e7	−	4.81577e7i	0.274931	−	0.378410i	0.924047	+	0.382280i	$0.124861\pi$
$504$	2.43194e6	+	7.48474e6i	0.0189959	+	0.0584635i
$505$			7.89612e6i			0.0613112i
$506$	1.23790e8	−	8.47903e7i	0.955505	−	0.654477i
$507$	−1.38119e8			−1.05981
$508$	−1.80216e7	+	5.85556e6i	−0.137468	+	0.0446660i
$509$	2.62176e7	+	1.90482e7i	0.198810	+	0.144444i	0.682737	−	0.730665i	$-0.260790\pi$
$509$	2.62176e7	+	1.90482e7i	0.198810	+	0.144444i	−0.483926	+	0.875109i	$0.660790\pi$
$510$	1.47994e8	−	1.07524e8i	1.11566	−	0.810575i
$511$	−1.31306e7	+	4.04117e7i	−0.0984058	+	0.302862i
$512$	1.39975e8	+	4.54806e7i	1.04289	+	0.338857i
$513$	−9.00259e7	−	1.23910e8i	−0.666831	−	0.917814i
$514$	5.00757e7	−	6.89233e7i	0.368755	−	0.507548i
$515$	3.60437e6	+	1.10931e7i	0.0263881	+	0.0812142i
$516$		−	1.59444e7i		−	0.116054i
$517$	2.09180e8	+	7.44472e7i	1.51373	+	0.538737i
$518$	5.61207e7			0.403769
$519$	4.09155e7	−	1.32943e7i	0.292675	−	0.0950959i
$520$	−5.48317e6	−	3.98375e6i	−0.0389961	−	0.0283323i
$521$	5.41617e7	−	3.93508e7i	0.382983	−	0.278253i	−0.379591	−	0.925154i	$-0.623935\pi$
$521$	5.41617e7	−	3.93508e7i	0.382983	−	0.278253i	0.762574	+	0.646901i	$0.223935\pi$
$522$	−3.30426e6	+	1.01695e7i	−0.0232307	+	0.0714968i
$523$	−8.01026e7	−	2.60269e7i	−0.559940	−	0.181936i	0.0153541	−	0.999882i	$-0.495112\pi$
$523$	−8.01026e7	−	2.60269e7i	−0.559940	−	0.181936i	−0.575294	+	0.817947i	$0.695112\pi$
$524$	2.69799e6	+	3.71346e6i	0.0187519	+	0.0258098i
$525$	1.40839e7	−	1.93848e7i	0.0973295	−	0.133963i
$526$	4.29902e7	+	1.32310e8i	0.295401	+	0.909152i
$527$			2.79858e8i			1.91208i
$528$	8.65923e7	−	1.12480e8i	0.588271	−	0.764144i
$529$	6.91442e7			0.467077
$530$	−1.59977e8	+	5.19796e7i	−1.07456	+	0.349145i
$531$	−1.20684e7	−	8.76818e6i	−0.0806056	−	0.0585634i
$532$	5.80882e6	−	4.22035e6i	0.0385791	−	0.0280294i
$533$	−2.06626e6	+	6.35930e6i	−0.0136460	+	0.0419979i
$534$	−9.03203e7	−	2.93469e7i	−0.593146	−	0.192725i
$535$	3.92394e7	+	5.40084e7i	0.256248	+	0.352696i
$536$	−3.23731e7	+	4.45577e7i	−0.210227	+	0.289353i
$537$	−6.50338e7	−	2.00154e8i	−0.419968	−	1.29253i
$538$		−	1.18553e8i		−	0.761316i
$539$	−3.45338e6	+	1.24361e8i	−0.0220536	+	0.794180i
$540$	1.01090e7			0.0641988
$541$	5.17858e7	−	1.68262e7i	0.327053	−	0.106266i	−0.140888	−	0.990026i	$-0.544996\pi$
$541$	5.17858e7	−	1.68262e7i	0.327053	−	0.106266i	0.467942	+	0.883759i	$0.344996\pi$
$542$	−1.58341e8	−	1.15042e8i	−0.994480	−	0.722532i
$543$	−1.72156e8	+	1.25079e8i	−1.07528	+	0.781239i
$544$	1.42359e7	−	4.38136e7i	0.0884277	−	0.272152i
$545$	−6.78758e7	−	2.20542e7i	−0.419301	−	0.136239i
$546$	2.52704e6	+	3.47817e6i	0.0155251	+	0.0213684i
$547$	−1.30085e8	+	1.79046e8i	−0.794811	+	1.09396i	0.198682	+	0.980064i	$0.436334\pi$
$547$	−1.30085e8	+	1.79046e8i	−0.794811	+	1.09396i	−0.993492	+	0.113899i	$0.963666\pi$
$548$	−5.15252e6	−	1.58578e7i	−0.0313097	−	0.0963612i
$549$			1.38749e7i			0.0838521i
$550$	−5.46273e7	−	1.51694e6i	−0.328338	−	0.00911761i
$551$	1.23572e8			0.738695
$552$	2.13877e8	−	6.94929e7i	1.27159	−	0.413165i
$553$	5.28302e7	+	3.83834e7i	0.312397	+	0.226970i
$554$	−7.50417e6	+	5.45210e6i	−0.0441340	+	0.0320652i
$555$	−4.23939e7	+	1.30475e8i	−0.247984	+	0.763217i
$556$	−9.43161e6	−	3.06452e6i	−0.0548734	−	0.0178294i
$557$	−1.34821e8	−	1.85566e8i	−0.780178	−	1.07382i	−0.995262	−	0.0972270i	$-0.969003\pi$
$557$	−1.34821e8	−	1.85566e8i	−0.780178	−	1.07382i	0.215085	−	0.976595i	$-0.430997\pi$
$558$	−1.45682e7	+	2.00515e7i	−0.0838503	+	0.115410i
$559$	−3.93885e6	−	1.21225e7i	−0.0225493	−	0.0693997i
$560$		−	5.85026e7i		−	0.333128i
$561$	−2.49028e8	−	1.91713e8i	−1.41046	−	1.08583i
$562$	−8.56709e7			−0.482641
$563$	1.73360e8	−	5.63280e7i	0.971456	−	0.315645i	0.220053	−	0.975488i	$-0.429377\pi$
$563$	1.73360e8	−	5.63280e7i	0.971456	−	0.315645i	0.751404	+	0.659843i	$0.229377\pi$
$564$	2.12543e7	+	1.54421e7i	0.118470	+	0.0860735i
$565$	−3.26112e7	+	2.36935e7i	−0.180810	+	0.131366i
$566$	−4.46830e7	+	1.37520e8i	−0.246430	+	0.758433i
$567$	−8.75161e7	−	2.84357e7i	−0.480108	−	0.155997i
$568$	5.47530e6	+	7.53611e6i	0.0298788	+	0.0411247i
$569$	−1.95563e8	+	2.69170e8i	−1.06157	+	1.46113i	−0.183251	+	0.983066i	$0.558662\pi$
$569$	−1.95563e8	+	2.69170e8i	−1.06157	+	1.46113i	−0.878324	+	0.478067i	$0.841338\pi$
$570$	−5.78557e7	−	1.78062e8i	−0.312408	−	0.961492i
$571$		−	1.97011e8i		−	1.05824i	−0.848548	−	0.529118i	$-0.822523\pi$
$571$		−	1.97011e8i		−	1.05824i	0.848548	−	0.529118i	$-0.177477\pi$
$572$	−308220.	+	866030.i	−0.00164692	+	0.00462748i
$573$	1.21005e8			0.643189
$574$	−6.00799e7	+	1.95212e7i	−0.317683	+	0.103221i
$575$	−6.39934e7	−	4.64939e7i	−0.336614	−	0.244564i
$576$	2.16157e7	−	1.57047e7i	0.113110	−	0.0821793i
$577$	8.32813e7	−	2.56313e8i	0.433531	−	1.33427i	−0.461054	−	0.887372i	$-0.652529\pi$
$577$	8.32813e7	−	2.56313e8i	0.433531	−	1.33427i	0.894585	−	0.446898i	$-0.147471\pi$
$578$	3.16503e8	+	1.02838e8i	1.63906	+	0.532562i
$579$	2.04991e8	+	2.82147e8i	1.05609	+	1.45358i
$580$	−4.79400e6	+	6.59837e6i	−0.0245705	+	0.0338184i
$581$	−2.13362e7	−	6.56660e7i	−0.108790	−	0.334820i
$582$			2.40907e8i			1.22203i
$583$	1.63306e8	+	2.38419e8i	0.824132	+	1.20319i
$584$	1.45249e8			0.729246
$585$	−1.15474e6	+	375197.i	−0.00576787	+	0.00187410i
$586$	−1.07025e8	−	7.77579e7i	−0.531852	−	0.386413i
$587$	−1.07386e8	+	7.80206e7i	−0.530926	+	0.385740i	−0.820704	−	0.571353i	$-0.806419\pi$
$587$	−1.07386e8	+	7.80206e7i	−0.530926	+	0.385740i	0.289778	+	0.957094i	$0.406419\pi$
$588$	−4.54889e6	+	1.40000e7i	−0.0223755	+	0.0688648i
$589$	2.72410e8	+	8.85114e7i	1.33314	+	0.433165i
$590$	7.13400e7	+	9.81912e7i	0.347358	+	0.478097i
$591$	1.61594e8	−	2.22415e8i	0.782820	−	1.07746i
$592$	−5.41624e7	−	1.66695e8i	−0.261056	−	0.803446i
$593$		−	1.68072e8i		−	0.805993i	−0.915201	−	0.402997i	$-0.867969\pi$
$593$		−	1.68072e8i		−	0.805993i	0.915201	−	0.402997i	$-0.132031\pi$
$594$	5.23341e7	+	1.77709e8i	0.249704	+	0.847910i
$595$	−1.29523e8			−0.614888
$596$	8.70512e6	−	2.82847e6i	0.0411184	−	0.0133602i
$597$	1.13323e8	+	8.23338e7i	0.532591	+	0.386950i
$598$	1.14822e7	−	8.34230e6i	0.0536934	−	0.0390106i
$599$	4.60500e7	−	1.41727e8i	0.214264	−	0.659436i	−0.784941	−	0.619570i	$-0.787307\pi$
$599$	4.60500e7	−	1.41727e8i	0.214264	−	0.659436i	0.999205	−	0.0398660i	$-0.0126931\pi$
$600$	−7.78972e7	−	2.53103e7i	−0.360635	−	0.117178i
$601$	9.52759e7	+	1.31136e8i	0.438894	+	0.604085i	0.969966	−	0.243241i	$-0.0782106\pi$
$601$	9.52759e7	+	1.31136e8i	0.438894	+	0.604085i	−0.531072	+	0.847327i	$0.678211\pi$
$602$	7.07824e7	−	9.74236e7i	0.324441	−	0.446555i
$603$	3.04895e6	+	9.38371e6i	0.0139059	+	0.0427979i
$604$		−	419393.i		−	0.00190331i
$605$	−4.58895e7	−	1.73455e8i	−0.207228	−	0.783288i
$606$	−1.71216e7			−0.0769355
$607$	−6.15401e7	+	1.99956e7i	−0.275164	+	0.0894063i	−0.443349	−	0.896349i	$-0.646210\pi$
$607$	−6.15401e7	+	1.99956e7i	−0.275164	+	0.0894063i	0.168184	+	0.985756i	$0.446210\pi$
$608$	−3.81451e7	−	2.77140e7i	−0.169718	−	0.123307i
$609$	5.30182e7	−	3.85199e7i	0.234732	−	0.170543i
$610$	3.48849e7	−	1.07365e8i	0.153691	−	0.473012i
$611$	1.99743e7	+	6.49005e6i	0.0875686	+	0.0284528i
$612$	−2.52514e6	−	3.47555e6i	−0.0110162	−	0.0151625i
$613$	−5.16229e7	+	7.10528e7i	−0.224110	+	0.308461i	−0.906235	−	0.422775i	$-0.861056\pi$
$613$	−5.16229e7	+	7.10528e7i	−0.224110	+	0.308461i	0.682125	+	0.731236i	$0.261056\pi$
$614$	2.15310e7	+	6.62657e7i	0.0930164	+	0.286275i
$615$		−	1.54426e8i		−	0.663889i
$616$	−1.05526e8	+	3.10767e7i	−0.451457	+	0.132951i
$617$	−1.01076e8			−0.430321			−0.215161	−	0.976579i	$-0.569028\pi$
$617$	−1.01076e8			−0.430321			−0.215161	+	0.976579i	$0.569028\pi$
$618$	−2.40538e7	+	7.81557e6i	−0.101911	+	0.0331127i
$619$	−1.60552e8	−	1.16648e8i	−0.676930	−	0.491819i	0.195408	−	0.980722i	$-0.437397\pi$
$619$	−1.60552e8	−	1.16648e8i	−0.676930	−	0.491819i	−0.872338	+	0.488904i	$0.837397\pi$
$620$	−1.52944e7	+	1.11121e7i	−0.0641739	+	0.0466251i
$621$	−8.28614e7	+	2.55021e8i	−0.346001	+	1.06488i
$622$	−1.70613e8	−	5.54356e7i	−0.708992	−	0.230366i
$623$	3.95239e7	+	5.43999e7i	0.163454	+	0.224975i
$624$	7.89232e6	−	1.08628e7i	0.0324826	−	0.0447085i
$625$	−4.06249e7	−	1.25030e8i	−0.166399	−	0.512125i
$626$			2.49076e8i			1.01533i
$627$	−2.65371e8	+	1.81767e8i	−1.07659	+	0.737416i
$628$	−3.03347e7			−0.122479
$629$	−3.69057e8	+	1.19914e8i	−1.48300	+	0.481857i
$630$	−9.28014e6	−	6.74242e6i	−0.0371136	−	0.0269646i
$631$	−1.49613e8	+	1.08700e8i	−0.595500	+	0.432656i	−0.844279	−	0.535904i	$-0.819971\pi$
$631$	−1.49613e8	+	1.08700e8i	−0.595500	+	0.432656i	0.248779	+	0.968560i	$0.419971\pi$
$632$	6.89793e7	−	2.12296e8i	0.273255	−	0.840991i
$633$	2.08833e8	+	6.78540e7i	0.823357	+	0.267525i
$634$	−2.92333e7	−	4.02361e7i	−0.114712	−	0.157888i
$635$	2.05636e8	−	2.83034e8i	0.803117	−	1.10540i
$636$	1.05664e7	+	3.25201e7i	0.0410730	+	0.126410i
$637$			1.17679e7i			0.0455284i
$638$	−1.40813e8	−	5.01153e7i	−0.542227	−	0.192978i
$639$	1.66876e6			0.00639573
$640$	−1.72218e8	+	5.59569e7i	−0.656958	+	0.213459i
$641$	−3.44873e7	−	2.50565e7i	−0.130944	−	0.0951363i	0.520385	−	0.853932i	$-0.325788\pi$
$641$	−3.44873e7	−	2.50565e7i	−0.130944	−	0.0951363i	−0.651329	+	0.758795i	$0.725788\pi$
$642$	−1.17110e8	+	8.50851e7i	−0.442576	+	0.321550i
$643$	2.07719e7	−	6.39293e7i	0.0781345	−	0.240473i	−0.904358	−	0.426774i	$-0.859650\pi$
$643$	2.07719e7	−	6.39293e7i	0.0781345	−	0.240473i	0.982493	+	0.186301i	$0.0596499\pi$
$644$	−1.19552e7	−	3.88448e6i	−0.0447610	−	0.0145437i
$645$	1.73031e8	+	2.38156e8i	0.644828	+	0.887530i
$646$	3.11279e8	−	4.28438e8i	1.15465	−	1.58924i
$647$	4.02553e7	+	1.23893e8i	0.148631	+	0.457440i	0.997460	−	0.0712277i	$-0.0226917\pi$
$647$	4.02553e7	+	1.23893e8i	0.148631	+	0.457440i	−0.848829	+	0.528668i	$0.822692\pi$
$648$			3.14553e8i			1.15603i
$649$	1.27198e8	−	1.65226e8i	0.465314	−	0.604427i
$650$	−5.16922e6			−0.0188228
$651$	1.44467e8	−	4.69403e7i	0.523633	−	0.170139i
$652$	1.45194e7	+	1.05490e7i	0.0523849	+	0.0380599i
$653$	1.44373e8	−	1.04893e8i	0.518496	−	0.376710i	−0.297541	−	0.954709i	$-0.596166\pi$
$653$	1.44373e8	−	1.04893e8i	0.518496	−	0.376710i	0.816037	+	0.577999i	$0.196166\pi$
$654$	4.78214e7	−	1.47179e8i	0.170958	−	0.526154i
$655$	−8.05977e7	−	2.61878e7i	−0.286813	−	0.0931912i
$656$	1.15967e8	+	1.59615e8i	0.410793	+	0.565408i
$657$	1.52945e7	−	2.10510e7i	0.0539310	−	0.0742296i
$658$	6.13152e7	+	1.88709e8i	0.215224	+	0.662391i
$659$		−	2.39351e8i		−	0.836333i	−0.908370	−	0.418167i	$-0.862673\pi$
$659$		−	2.39351e8i		−	0.836333i	0.908370	−	0.418167i	$-0.137327\pi$
$660$	589305.	−	2.12217e7i	0.00204979	−	0.0738157i
$661$	4.19434e8			1.45231			0.726154	−	0.687532i	$-0.241306\pi$
$661$	4.19434e8			1.45231			0.726154	+	0.687532i	$0.241306\pi$
$662$	−5.90648e7	+	1.91913e7i	−0.203589	+	0.0661502i
$663$	−2.40500e7	−	1.74734e7i	−0.0825230	−	0.0599564i
$664$	−1.90943e8	+	1.38728e8i	−0.652228	+	0.473871i
$665$	−4.09645e7	+	1.26076e8i	−0.139297	+	0.428713i
$666$	−3.26847e7	−	1.06199e7i	−0.110642	−	0.0359499i
$667$	−1.27163e8	−	1.75024e8i	−0.428531	−	0.589822i
$668$	1.93220e7	−	2.65944e7i	0.0648220	−	0.0892198i
$669$	5.16892e7	+	1.59083e8i	0.172632	+	0.531307i
$670$		−	8.02772e7i		−	0.266912i
$671$	−1.93871e8	−	5.38359e6i	−0.641719	−	0.0178199i
$672$	−2.50051e7			−0.0823987
$673$	−3.04181e8	+	9.88343e7i	−0.997899	+	0.324237i	−0.762026	−	0.647547i	$-0.775795\pi$
$673$	−3.04181e8	+	9.88343e7i	−0.997899	+	0.324237i	−0.235873	+	0.971784i	$0.575795\pi$
$674$	2.04480e8	+	1.48563e8i	0.667837	+	0.485212i
$675$	7.90106e7	−	5.74046e7i	0.256906	−	0.186653i
$676$	8.15531e6	−	2.50995e7i	0.0263998	−	0.0812502i
$677$	1.58212e8	+	5.14062e7i	0.509886	+	0.165672i	0.552651	−	0.833413i	$-0.313616\pi$
$677$	1.58212e8	+	5.14062e7i	0.509886	+	0.165672i	−0.0427641	+	0.999085i	$0.513616\pi$
$678$	−5.13759e7	−	7.07128e7i	−0.164843	−	0.226887i
$679$	1.00260e8	−	1.37997e8i	0.320273	−	0.440818i
$680$	1.36817e8	+	4.21080e8i	0.435125	+	1.33918i
$681$		−	1.97693e8i		−	0.625965i
$682$	−2.74521e8	−	2.11338e8i	−0.865411	−	0.666231i
$683$	6.80406e7			0.213553			0.106777	−	0.994283i	$-0.465947\pi$
$683$	6.80406e7			0.213553			0.106777	+	0.994283i	$0.465947\pi$
$684$	−4.18168e6	+	1.35871e6i	−0.0130672	+	0.00424579i
$685$	2.49052e8	+	1.80947e8i	0.774853	+	0.562963i
$686$	−2.03157e8	+	1.47602e8i	−0.629302	+	0.457215i
$687$	1.87612e8	−	5.77409e8i	0.578615	−	1.78079i
$688$	−3.57689e8	−	1.16220e8i	−1.09835	−	0.356875i
$689$	1.60673e7	+	2.21147e7i	0.0491230	+	0.0676120i
$690$	−1.92665e8	+	2.65181e8i	−0.586484	+	0.807226i
$691$	2.29289e7	+	7.05679e7i	0.0694942	+	0.213881i	0.979772	−	0.200117i	$-0.0641321\pi$
$691$	2.29289e7	+	7.05679e7i	0.0694942	+	0.213881i	−0.910278	+	0.413998i	$0.864132\pi$
$692$			8.22028e6i			0.0248067i
$693$	−6.60773e6	+	1.85663e7i	−0.0198542	+	0.0557860i
$694$	3.42271e8			1.02398
$695$	1.74133e8	−	5.65793e7i	0.518713	−	0.168540i
$696$	−1.81233e8	−	1.31673e8i	−0.537537	−	0.390544i
$697$	3.53383e8	−	2.56748e8i	1.04363	−	0.758243i
$698$	1.35930e8	−	4.18350e8i	0.399714	−	1.23019i
$699$	3.34721e8	+	1.08757e8i	0.980057	+	0.318440i
$700$	2.69108e6	+	3.70396e6i	0.00784573	+	0.0107987i
$701$	−3.47346e8	+	4.78081e8i	−1.00834	+	1.38787i	−0.0882815	+	0.996096i	$0.528137\pi$
$701$	−3.47346e8	+	4.78081e8i	−1.00834	+	1.38787i	−0.920063	+	0.391771i	$0.871863\pi$
$702$	5.41501e6	+	1.66657e7i	0.0156527	+	0.0481739i
$703$			3.97160e8i			1.14314i
$704$	2.11051e8	+	3.08124e8i	0.604879	+	0.883094i
$705$	−4.85047e8			−1.38426
$706$	3.07478e8	−	9.99055e7i	0.873774	−	0.283907i
$707$	9.80762e6	+	7.12566e6i	0.0277527	+	0.0201635i
$708$	1.99603e7	−	1.45020e7i	0.0562429	−	0.0408628i
$709$	−1.12467e8	+	3.46139e8i	−0.315564	+	0.971207i	0.659957	+	0.751303i	$0.270574\pi$
$709$	−1.12467e8	+	3.46139e8i	−0.315564	+	0.971207i	−0.975522	+	0.219904i	$0.929426\pi$
$710$	−1.29129e7	−	4.19565e6i	−0.0360784	−	0.0117226i
$711$	−2.35049e7	−	3.23517e7i	−0.0653957	−	0.0900095i
$712$	1.35105e8	−	1.85956e8i	0.374310	−	0.515193i
$713$	−1.54960e8	−	4.76918e8i	−0.427515	−	1.31576i
$714$		−	2.80852e8i		−	0.771584i
$715$	−4.79448e6	−	1.62804e7i	−0.0131167	−	0.0445397i
$716$	4.02126e7			0.109553
$717$	−7.01717e8	+	2.28002e8i	−1.90373	+	0.618558i
$718$	−1.51491e7	−	1.10065e7i	−0.0409274	−	0.0297355i
$719$	−4.37577e7	+	3.17918e7i	−0.117725	+	0.0855320i	−0.645090	−	0.764107i	$-0.723180\pi$
$719$	−4.37577e7	+	3.17918e7i	−0.117725	+	0.0855320i	0.527365	+	0.849639i	$0.323180\pi$
$720$	−1.10706e7	+	3.40719e7i	−0.0296603	+	0.0912849i
$721$	1.70312e7	+	5.53378e6i	0.0454402	+	0.0147644i
$722$	−1.07057e8	−	1.47351e8i	−0.284449	−	0.391510i
$723$	9.07611e7	−	1.24922e8i	0.240151	−	0.330540i
$724$	−1.25647e7	−	3.86701e7i	−0.0331082	−	0.101897i
$725$			7.87950e7i			0.206769i
$726$	3.76113e8	−	9.95050e7i	0.982899	−	0.260037i
$727$	−6.61240e8			−1.72090			−0.860450	−	0.509535i	$-0.829818\pi$
$727$	−6.61240e8			−1.72090			−0.860450	+	0.509535i	$0.829818\pi$
$728$	−9.89630e6	+	3.21550e6i	−0.0256495	+	0.00833402i
$729$	−2.62494e8	−	1.90713e8i	−0.677543	−	0.492264i
$730$	−1.71276e8	+	1.24439e8i	−0.440280	+	0.319882i
$731$	−2.57308e8	+	7.91913e8i	−0.658721	+	2.02733i
$732$	−2.18251e7	−	7.09140e6i	−0.0556446	−	0.0180800i
$733$	6.59801e7	+	9.08138e7i	0.167533	+	0.230590i	0.884526	−	0.466491i	$-0.154482\pi$
$733$	6.59801e7	+	9.08138e7i	0.167533	+	0.230590i	−0.716993	+	0.697081i	$0.754482\pi$
$734$	−3.89165e7	+	5.35640e7i	−0.0984115	+	0.135452i
$735$	−8.39848e7	−	2.58479e8i	−0.211514	−	0.650972i
$736$			8.25472e7i			0.207047i
$737$	−1.32299e8	+	3.89612e7i	−0.330487	+	0.0973263i
$738$	3.86846e7			0.0962430
$739$	5.03126e8	−	1.63476e8i	1.24665	−	0.405060i	0.389929	−	0.920845i	$-0.372500\pi$
$739$	5.03126e8	−	1.63476e8i	1.24665	−	0.405060i	0.856718	+	0.515785i	$0.172500\pi$
$740$	−2.12072e7	−	1.54079e7i	−0.0523345	−	0.0380232i
$741$	−2.46147e7	+	1.78836e7i	−0.0604978	+	0.0439542i
$742$	−7.98042e7	+	2.45612e8i	−0.195350	+	0.601226i
$743$	−2.92693e7	−	9.51019e6i	−0.0713586	−	0.0231858i	0.273120	−	0.961980i	$-0.411944\pi$
$743$	−2.92693e7	−	9.51019e6i	−0.0713586	−	0.0231858i	−0.344479	+	0.938794i	$0.611944\pi$
$744$	−3.05207e8	−	4.20081e8i	−0.741098	−	1.02003i
$745$	−9.93305e7	+	1.36717e8i	−0.240223	+	0.330638i
$746$	−2.79093e6	−	8.58959e6i	−0.00672252	−	0.0206898i
$747$			4.22814e7i			0.101435i
$748$	4.95427e7	−	3.39345e7i	0.118379	−	0.0810843i
$749$	1.02494e8			0.243922
$750$	4.44063e8	−	1.44285e8i	1.05259	−	0.342008i
$751$	−2.16663e8	−	1.57415e8i	−0.511523	−	0.371643i	0.301878	−	0.953347i	$-0.402386\pi$
$751$	−2.16663e8	−	1.57415e8i	−0.511523	−	0.371643i	−0.813401	+	0.581703i	$0.802386\pi$
$752$	5.01345e8	−	3.64248e8i	1.17892	−	0.856533i
$753$	−1.40360e8	+	4.31984e8i	−0.328745	+	1.01177i
$754$	−1.34460e7	−	4.36888e6i	−0.0313675	−	0.0101919i
$755$	4.55129e6	+	6.26432e6i	0.0105753	+	0.0145557i
$756$	9.12262e6	−	1.25562e7i	0.0211132	−	0.0290598i
$757$	−1.29235e8	−	3.97744e8i	−0.297914	−	0.916886i	−0.982227	−	0.187697i	$-0.939898\pi$
$757$	−1.29235e8	−	3.97744e8i	−0.297914	−	0.916886i	0.684312	−	0.729189i	$-0.260102\pi$
$758$		−	5.36801e8i		−	1.23255i
$759$	5.30533e8	+	1.88817e8i	1.21335	+	0.431832i
$760$	4.53145e8			1.03228
$761$	6.24492e8	−	2.02910e8i	1.41701	−	0.460414i	0.502359	−	0.864659i	$-0.332466\pi$
$761$	6.24492e8	−	2.02910e8i	1.41701	−	0.460414i	0.914651	+	0.404245i	$0.132466\pi$
$762$	6.13720e8	+	4.45893e8i	1.38709	+	1.00778i
$763$	−8.86459e7	+	6.44050e7i	−0.199565	+	0.144993i
$764$	−7.14479e6	+	2.19894e7i	−0.0160217	+	0.0493098i
$765$	7.54341e7	+	2.45100e7i	0.168494	+	0.0547469i
$766$	1.73706e8	+	2.39085e8i	0.386480	+	0.531945i
$767$	1.15933e7	−	1.59568e7i	0.0256933	−	0.0353638i
$768$	3.79837e7	+	1.16902e8i	0.0838521	+	0.258070i
$769$			2.67290e8i			0.587765i	0.955842	+	0.293882i	$0.0949474\pi$
$769$			2.67290e8i			0.587765i	−0.955842	+	0.293882i	$0.905053\pi$
$770$	9.78108e7	−	1.27053e8i	0.214247	−	0.278299i
$771$	3.19741e8			0.697647
$772$	−6.33765e7	+	2.05923e7i	−0.137745	+	0.0447561i
$773$	−1.38285e8	−	1.00470e8i	−0.299389	−	0.217519i	0.427941	−	0.903807i	$-0.359239\pi$
$773$	−1.38285e8	−	1.00470e8i	−0.299389	−	0.217519i	−0.727330	+	0.686288i	$0.759239\pi$
$774$	−5.96594e7	+	4.33451e7i	−0.128664	+	0.0934797i
$775$	−5.64388e7	+	1.73701e8i	−0.121247	+	0.373161i
$776$	−5.54535e8	−	1.80179e8i	−1.18671	−	0.385585i
$777$	1.23803e8	+	1.70400e8i	0.263918	+	0.363252i
$778$	−4.20185e8	+	5.78335e8i	−0.892282	+	1.22812i
$779$	−1.38149e8	−	4.25180e8i	−0.292238	−	0.899416i
$780$		−	2.00815e6i		−	0.00423167i
$781$	−647491.	+	2.33171e7i	−0.00135919	+	0.0489464i
$782$	−9.27153e8			−1.93879
$783$	2.54037e8	−	8.25417e7i	0.529190	−	0.171944i
$784$	2.80912e8	+	2.04095e8i	0.582939	+	0.423530i
$785$	4.53098e8	−	3.29195e8i	0.936663	−	0.680526i
$786$	5.67845e7	−	1.74765e8i	0.116940	−	0.359904i
$787$	4.98250e8	+	1.61891e8i	1.02217	+	0.332123i	0.771690	−	0.635998i	$-0.219412\pi$
$787$	4.98250e8	+	1.61891e8i	1.02217	+	0.332123i	0.250480	+	0.968122i	$0.419412\pi$
$788$	3.08766e7	+	4.24980e7i	0.0631031	+	0.0868539i
$789$	−3.06900e8	+	4.22411e8i	−0.624835	+	0.860012i
$790$	1.00542e8	+	3.09435e8i	0.203922	+	0.627608i
$791$			6.18874e7i			0.125047i
$792$	6.73389e7	+	1.86993e6i	0.135547	+	0.00376401i
$793$	−1.83454e7			−0.0367881
$794$	−1.55513e8	+	5.05293e7i	−0.310674	+	0.100944i
$795$	−5.10739e8	−	3.71074e8i	−1.01648	−	0.738514i
$796$	−2.16532e7	+	1.57320e7i	−0.0429322	+	0.0311920i
$797$	−1.85130e7	+	5.69773e7i	−0.0365682	+	0.112545i	−0.967674	−	0.252203i	$-0.918845\pi$
$797$	−1.85130e7	+	5.69773e7i	−0.0365682	+	0.112545i	0.931106	+	0.364748i	$0.118845\pi$
$798$	−2.73377e8	−	8.88257e7i	−0.537965	−	0.174795i
$799$	−8.06435e8	−	1.10996e9i	−1.58099	−	2.17604i
$800$	1.76717e7	−	2.43230e7i	0.0345151	−	0.0475059i
$801$	−1.27244e7	−	3.91617e7i	−0.0247594	−	0.0762017i
$802$			4.21493e8i			0.817085i
$803$	2.88206e8	+	2.21873e8i	0.556617	+	0.428508i
$804$	−1.63188e7			−0.0313992
$805$	2.20726e8	−	7.17181e7i	0.423121	−	0.137480i
$806$	−2.65120e7	−	1.92621e7i	−0.0506334	−	0.0367873i
$807$	3.59965e8	−	2.61530e8i	0.684919	−	0.497623i
$808$	1.28056e7	−	3.94116e7i	0.0242754	−	0.0747120i
$809$	−6.83450e8	−	2.22066e8i	−1.29081	−	0.419408i	−0.418432	−	0.908248i	$-0.637420\pi$
$809$	−6.83450e8	−	2.22066e8i	−1.29081	−	0.419408i	−0.872374	+	0.488840i	$0.837420\pi$
$810$	−2.69488e8	−	3.70918e8i	−0.507089	−	0.697948i
$811$	−1.32752e8	+	1.82717e8i	−0.248873	+	0.342544i	−0.915116	−	0.403190i	$-0.867901\pi$
$811$	−1.32752e8	+	1.82717e8i	−0.248873	+	0.342544i	0.666243	+	0.745735i	$0.267901\pi$
$812$	3.86949e6	+	1.19091e7i	0.00722747	+	0.0222439i
$813$		−	7.34559e8i		−	1.36696i
$814$	1.61071e8	−	4.52573e8i	0.298637	−	0.839104i
$815$	−3.31350e8			−0.612088
$816$	−8.34213e8	+	2.71052e8i	−1.53535	+	0.498864i
$817$	6.89458e8	+	5.00920e8i	1.26427	+	0.918549i
$818$	−7.57639e8	+	5.50457e8i	−1.38421	+	1.00569i
$819$	−576039.	+	1.77287e6i	−0.00104858	+	0.00322719i
$820$	2.80629e7	+	9.11818e6i	0.0508968	+	0.0165374i
$821$	2.51917e8	+	3.46734e8i	0.455227	+	0.626566i	0.973510	−	0.228643i	$-0.0734287\pi$
$821$	2.51917e8	+	3.46734e8i	0.455227	+	0.626566i	−0.518283	+	0.855209i	$0.673429\pi$
$822$	−3.92358e8	+	5.40035e8i	−0.706427	+	0.972314i
$823$	1.51694e8	+	4.66866e8i	0.272125	+	0.837516i	0.989966	+	0.141308i	$0.0451308\pi$
$823$	1.51694e8	+	4.66866e8i	0.272125	+	0.837516i	−0.717840	+	0.696208i	$0.754869\pi$
$824$		−	6.12141e7i		−	0.109413i
$825$	−1.15903e8	−	1.69213e8i	−0.206411	−	0.301350i
$826$	1.86341e8			0.330649
$827$	6.84776e8	−	2.22497e8i	1.21069	−	0.393376i	0.367005	−	0.930219i	$-0.380383\pi$
$827$	6.84776e8	−	2.22497e8i	1.21069	−	0.393376i	0.843682	+	0.536843i	$0.180383\pi$
$828$	6.22764e6	+	4.52465e6i	0.0109707	+	0.00797065i
$829$	−4.06360e8	+	2.95238e8i	−0.713259	+	0.518213i	−0.884224	−	0.467064i	$-0.845312\pi$
$829$	−4.06360e8	+	2.95238e8i	−0.713259	+	0.518213i	0.170964	+	0.985277i	$0.445312\pi$
$830$	1.06305e8	−	3.27174e8i	0.185918	−	0.572196i
$831$	−3.31087e7	−	1.07577e7i	−0.0576951	−	0.0187463i
$832$	2.07647e7	+	2.85802e7i	0.0360542	+	0.0496244i
$833$	4.51860e8	−	6.21932e8i	0.781752	−	1.07599i
$834$	1.22684e8	+	3.77583e8i	0.211490	+	0.650900i
$835$			6.06916e8i			1.04248i
$836$	−1.73624e7	−	5.89567e7i	−0.0297160	−	0.100905i
$837$	6.19138e8			1.05587
$838$	−4.32706e7	+	1.40595e7i	−0.0735294	+	0.0238912i
$839$	1.04838e7	+	7.61695e6i	0.0177515	+	0.0128972i	0.596626	−	0.802520i	$-0.296508\pi$
$839$	1.04838e7	+	7.61695e6i	0.0177515	+	0.0128972i	−0.578874	+	0.815417i	$0.696508\pi$
$840$	1.94420e8	−	1.41255e8i	0.328023	−	0.238323i
$841$	1.17215e8	−	3.60751e8i	0.197059	−	0.606484i
$842$	−3.05647e8	−	9.93108e7i	−0.512017	−	0.166364i
$843$	−1.88992e8	−	2.60125e8i	−0.315471	−	0.434209i
$844$	−2.46613e7	+	3.39434e7i	−0.0410194	+	0.0564584i
$845$	1.50569e8	+	4.63404e8i	0.249555	+	0.768050i
$846$		−	1.21507e8i		−	0.200673i
$847$	−2.56858e8	−	9.95319e7i	−0.422710	−	0.163799i
$848$	8.06560e8			1.32266
$849$	−5.16127e8	+	1.67700e8i	−0.843400	+	0.274037i
$850$	2.73191e8	+	1.98485e8i	0.444847	+	0.323200i
$851$	5.62529e8	−	4.08701e8i	0.912759	−	0.663158i
$852$	−852892.	+	2.62493e6i	−0.00137903	+	0.00424423i
$853$	8.25717e8	+	2.68292e8i	1.33041	+	0.432275i	0.886056	−	0.463578i	$-0.153435\pi$
$853$	8.25717e8	+	2.68292e8i	1.33041	+	0.432275i	0.444350	+	0.895853i	$0.353435\pi$
$854$	−1.01875e8	−	1.40218e8i	−0.163566	−	0.225129i
$855$	4.77154e7	−	6.56747e7i	0.0763415	−	0.105075i
$856$	−1.08266e8	−	3.33207e8i	−0.172611	−	0.531243i
$857$			6.99490e8i			1.11132i	0.831410	+	0.555660i	$0.187534\pi$
$857$			6.99490e8i			1.11132i	−0.831410	+	0.555660i	$0.812466\pi$
$858$	3.53018e7	−	1.03961e7i	0.0558901	−	0.0164593i
$859$	−1.01183e9			−1.59635			−0.798177	−	0.602423i	$-0.794202\pi$
$859$	−1.01183e9			−1.59635			−0.798177	+	0.602423i	$0.794202\pi$
$860$	−5.34953e7	+	1.73817e7i	−0.0841047	+	0.0273273i
$861$	−1.91810e8	−	1.39358e8i	−0.300512	−	0.218335i
$862$	5.82808e8	−	4.23435e8i	0.909922	−	0.661097i
$863$	2.14532e7	−	6.60263e7i	0.0333780	−	0.102727i	−0.932980	−	0.359929i	$-0.882801\pi$
$863$	2.14532e7	−	6.60263e7i	0.0333780	−	0.102727i	0.966358	+	0.257203i	$0.0828008\pi$
$864$	−9.69301e7	−	3.14945e7i	−0.150286	−	0.0488307i
$865$	−8.92073e7	−	1.22783e8i	−0.137833	−	0.189710i
$866$	6.15338e8	−	8.46940e8i	0.947458	−	1.30406i
$867$	3.85962e8	+	1.18787e9i	0.592225	+	1.82268i
$868$			2.90248e7i			0.0443823i
$869$	4.61162e8	−	3.15875e8i	0.702739	−	0.481344i
$870$	3.26517e8			0.495847
$871$	−1.24071e7	+	4.03132e6i	−0.0187766	+	0.00610088i
$872$	3.03020e8	+	2.20157e8i	0.457005	+	0.332034i
$873$	−8.45052e7	+	6.13966e7i	−0.127011	+	0.0922787i
$874$	−2.93233e8	+	9.02478e8i	−0.439216	+	1.35177i
$875$	−3.14417e8	−	1.02160e8i	−0.469334	−	0.152496i
$876$	2.52961e7	+	3.48171e7i	0.0376306	+	0.0517940i
$877$	5.08939e8	−	7.00494e8i	0.754513	−	1.03850i	−0.243138	−	0.969992i	$-0.578177\pi$
$877$	5.08939e8	−	7.00494e8i	0.754513	−	1.03850i	0.997651	−	0.0685059i	$-0.0218232\pi$
$878$	−1.14513e8	−	3.52435e8i	−0.169189	−	0.520710i
$879$		−	4.96496e8i		−	0.731054i
$880$	−4.71782e8	−	1.67907e8i	−0.692298	−	0.246389i
$881$	−7.52005e8			−1.09975			−0.549874	−	0.835248i	$-0.685324\pi$
$881$	−7.52005e8			−1.09975			−0.549874	+	0.835248i	$0.685324\pi$
$882$	6.47503e7	−	2.10386e7i	0.0943704	−	0.0306628i
$883$	−8.60106e8	−	6.24904e8i	−1.24931	−	0.907676i	−0.251128	−	0.967954i	$-0.580801\pi$
$883$	−8.60106e8	−	6.24904e8i	−1.24931	−	0.907676i	−0.998182	+	0.0602776i	$0.980801\pi$
$884$	4.59537e6	−	3.33873e6i	0.00665217	−	0.00483309i
$885$	−1.40763e8	+	4.33223e8i	−0.203076	+	0.625002i
$886$	−9.36113e7	−	3.04161e7i	−0.134594	−	0.0437324i
$887$	5.92252e8	+	8.15164e8i	0.848663	+	1.16808i	0.984156	+	0.177306i	$0.0567384\pi$
$887$	5.92252e8	+	8.15164e8i	0.848663	+	1.16808i	−0.135492	+	0.990778i	$0.543262\pi$
$888$	4.23198e8	−	5.82482e8i	0.604372	−	0.831847i
$889$	−1.65980e8	−	5.10835e8i	−0.236239	−	0.727068i
$890$			3.35027e8i			0.475236i
$891$	−4.80492e8	+	6.24143e8i	−0.679287	+	0.882370i
$892$	−3.19612e7			−0.0450327
$893$	−1.33547e9	+	4.33922e8i	−1.87534	+	0.609336i
$894$	−2.96451e8	−	2.15384e8i	−0.414897	−	0.301440i
$895$	−6.00641e8	+	4.36391e8i	−0.837810	+	0.608705i
$896$	−8.59105e7	+	2.64405e8i	−0.119432	+	0.367575i
$897$	5.06598e7	+	1.64604e7i	0.0701918	+	0.0228067i
$898$	5.93389e8	+	8.16730e8i	0.819428	+	1.12785i
$899$	−2.93614e8	+	4.04126e8i	−0.404109	+	0.556208i
$900$	−866375.	−	2.66643e6i	−0.00118844	−	0.00365765i
$901$		−	1.78570e9i		−	2.44137i
$902$	−1.50099e7	+	5.40529e8i	−0.0204531	+	0.736546i
$903$	4.51957e8			0.613810
$904$	2.01196e8	−	6.53727e7i	0.272342	−	0.0884894i
$905$	6.07327e8	+	4.41249e8i	0.819364	+	0.595303i
$906$	−1.35833e7	+	9.86883e6i	−0.0182650	+	0.0132703i
$907$	3.52660e8	−	1.08538e9i	0.472644	−	1.45465i	−0.376465	−	0.926431i	$-0.622860\pi$
$907$	3.52660e8	−	1.08538e9i	0.472644	−	1.45465i	0.849109	−	0.528218i	$-0.177140\pi$
$908$	3.59255e7	+	1.16729e7i	0.0479894	+	0.0155927i
$909$	−4.36355e6	−	6.00591e6i	−0.00580963	−	0.00799626i
$910$	8.91481e6	−	1.22702e7i	0.0118301	−	0.0162827i
$911$	1.99525e8	+	6.14076e8i	0.263902	+	0.812207i	0.991944	+	0.126675i	$0.0404304\pi$
$911$	1.99525e8	+	6.14076e8i	0.263902	+	0.812207i	−0.728042	+	0.685532i	$0.759570\pi$
$912$			8.97737e8i			1.18349i
$913$	−5.90786e8	−	1.64055e7i	−0.776279	−	0.0215565i
$914$	−4.58591e8			−0.600603
$915$	4.02950e8	−	1.30927e8i	0.526003	−	0.170909i
$916$	9.38512e7	+	6.81869e7i	0.122111	+	0.0887186i
$917$	−1.05261e8	+	7.64764e7i	−0.136508	+	0.0991790i
$918$	3.53740e8	−	1.08870e9i	0.457252	−	1.40728i
$919$	9.25814e8	+	3.00815e8i	1.19283	+	0.387573i	0.837117	−	0.547024i	$-0.184239\pi$
$919$	9.25814e8	+	3.00815e8i	1.19283	+	0.387573i	0.355710	+	0.934597i	$0.384239\pi$
$920$	−4.66312e8	−	6.41824e8i	−0.598843	−	0.824237i
$921$	−1.53706e8	+	2.11558e8i	−0.196749	+	0.270802i
$922$	−1.58220e8	−	4.86951e8i	−0.201868	−	0.621287i
$923$			2.20642e6i			0.00280598i
$924$	−2.58273e7	−	1.98830e7i	−0.0327388	−	0.0252038i
$925$	−2.53247e8			−0.319978
$926$	−6.15963e8	+	2.00139e8i	−0.775750	+	0.252057i
$927$	−8.87181e6	−	6.44575e6i	−0.0111371	−	0.00809160i
$928$	6.65244e7	−	4.83328e7i	0.0832409	−	0.0604781i
$929$	−1.11568e7	+	3.43370e7i	−0.0139152	+	0.0428267i	−0.957773	−	0.287525i	$-0.907167\pi$
$929$	−1.11568e7	+	3.43370e7i	−0.0139152	+	0.0428267i	0.943858	+	0.330352i	$0.107167\pi$
$930$	7.19795e8	+	2.33876e8i	0.894870	+	0.290761i
$931$	−4.62469e8	−	6.36534e8i	−0.573104	−	0.788810i
$932$	−3.95276e7	+	5.44050e7i	−0.0488261	+	0.0672034i
$933$	−2.08055e8	−	6.40329e8i	−0.256173	−	0.788421i
$934$		−	6.80581e8i		−	0.835293i
$935$	−3.71741e8	+	1.04451e9i	−0.454785	+	1.27784i
$936$	6.37208e6			0.00777059
$937$	1.49990e8	−	4.87346e7i	0.182323	−	0.0592405i	−0.216432	−	0.976298i	$-0.569442\pi$
$937$	1.49990e8	−	4.87346e7i	0.182323	−	0.0592405i	0.398756	+	0.917057i	$0.369442\pi$
$938$	−9.97108e7	−	7.24441e7i	−0.120819	−	0.0877798i
$939$	−7.56276e8	+	5.49466e8i	−0.913447	+	0.663658i
$940$	2.86399e7	−	8.81444e7i	0.0344816	−	0.106123i
$941$	1.41100e8	+	4.58461e7i	0.169339	+	0.0550217i	0.392460	−	0.919769i	$-0.371624\pi$
$941$	1.41100e8	+	4.58461e7i	0.169339	+	0.0550217i	−0.223120	+	0.974791i	$0.571624\pi$
$942$	7.13813e8	+	9.82479e8i	0.853949	+	1.17536i
$943$	−4.60051e8	+	6.33206e8i	−0.548619	+	0.755110i
$944$	−1.79838e8	−	5.53486e8i	−0.213780	−	0.657946i
$945$			2.86547e8i			0.339548i
$946$	−5.82501e8	−	8.50424e8i	−0.688056	−	1.00453i
$947$	1.54208e8			0.181575			0.0907877	−	0.995870i	$-0.471062\pi$
$947$	1.54208e8			0.181575			0.0907877	+	0.995870i	$0.471062\pi$
$948$	6.29020e7	−	2.04381e7i	0.0738311	−	0.0239892i
$949$	2.78336e7	+	2.02223e7i	0.0325665	+	0.0236609i
$950$	2.79605e8	−	2.03145e8i	0.326118	−	0.236939i
$951$	5.76808e7	−	1.77523e8i	0.0670641	−	0.206402i
$952$	6.46483e8	+	2.10055e8i	0.749284	+	0.243457i
$953$	9.49725e8	+	1.30718e9i	1.09728	+	1.51028i	0.838935	+	0.544231i	$0.183179\pi$
$953$	9.49725e8	+	1.30718e9i	1.09728	+	1.51028i	0.258349	+	0.966052i	$0.416821\pi$
$954$	9.29559e7	−	1.27943e8i	0.107061	−	0.147357i
$955$	−1.31912e8	−	4.05984e8i	−0.151452	−	0.466121i
$956$		−	1.40981e8i		−	0.161357i
$957$	−1.58470e8	−	5.38109e8i	−0.180805	−	0.613952i
$958$	−1.32007e8			−0.150141
$959$	4.49502e8	−	1.46052e8i	0.509655	−	0.165597i
$960$	−6.60059e8	−	4.79561e8i	−0.746052	−	0.542039i
$961$	−2.18722e8	+	1.58911e8i	−0.246446	+	0.179053i
$962$	1.40416e7	−	4.32156e7i	0.0157722	−	0.0485417i
$963$	−5.96922e7	−	1.93952e7i	−0.0668404	−	0.0217178i
$964$	1.73422e7	+	2.38695e7i	0.0193586	+	0.0266448i
$965$	7.23163e8	−	9.95348e8i	0.804737	−	1.10763i
$966$	1.55510e8	+	4.78612e8i	0.172516	+	0.530948i
$967$			1.48707e9i			1.64457i	0.569077	+	0.822284i	$0.307300\pi$
$967$			1.48707e9i			1.64457i	−0.569077	+	0.822284i	$0.692700\pi$
$968$	−5.22561e7	+	9.40183e8i	−0.0576117	+	1.03654i
$969$	1.98756e9			2.18449
$970$	8.08269e8	−	2.62622e8i	0.885606	−	0.287751i
$971$	3.89036e8	+	2.82651e8i	0.424944	+	0.308740i	0.779624	−	0.626248i	$-0.215410\pi$
$971$	3.89036e8	+	2.82651e8i	0.424944	+	0.308740i	−0.354680	+	0.934988i	$0.615410\pi$
$972$	−1.65333e7	+	1.20122e7i	−0.0180037	+	0.0130805i
$973$	8.68660e7	−	2.67346e8i	0.0942999	−	0.290225i
$974$	7.87684e8	+	2.55934e8i	0.852463	+	0.276982i
$975$	−1.14034e7	−	1.56954e7i	−0.0123033	−	0.0169340i
$976$	−3.18170e8	+	4.37923e8i	−0.342223	+	0.471030i
$977$	−4.55342e8	−	1.40140e9i	−0.488263	−	1.50272i	−0.827199	−	0.561909i	$-0.810067\pi$
$977$	−4.55342e8	−	1.40140e9i	−0.488263	−	1.50272i	0.338936	−	0.940809i	$-0.389933\pi$
$978$		−	7.18485e8i		−	0.768071i
$979$	5.52134e8	−	1.62600e8i	0.588432	−	0.173289i
$980$	5.19306e7			0.0551753
$981$	6.38150e7	−	2.07347e7i	0.0675951	−	0.0219630i
$982$	−1.25033e9	−	9.08416e8i	−1.32035	−	0.959291i
$983$	−3.88205e8	+	2.82048e8i	−0.408697	+	0.296935i	−0.773074	−	0.634316i	$-0.781282\pi$
$983$	−3.88205e8	+	2.82048e8i	−0.408697	+	0.296935i	0.364377	+	0.931251i	$0.381282\pi$
$984$	−2.50442e8	+	7.70782e8i	−0.262859	+	0.808996i
$985$	−9.22385e8	−	2.99701e8i	−0.965169	−	0.313603i
$986$	5.42864e8	+	7.47189e8i	0.566318	+	0.779470i
$987$	−4.37718e8	+	6.02468e8i	−0.455243	+	0.626588i
$988$	−1.79648e6	−	5.52901e6i	−0.00186274	−	0.00573293i
$989$		−	1.49201e9i		−	1.54235i
$990$	−8.10076e7	+	5.54865e7i	−0.0834872	+	0.0571850i
$991$	1.75681e9			1.80511			0.902556	−	0.430572i	$-0.141688\pi$
$991$	1.75681e9			1.80511			0.902556	+	0.430572i	$0.141688\pi$
$992$	1.81270e8	−	5.88982e7i	0.185691	−	0.0603347i
$993$	−1.88569e8	−	1.37003e8i	−0.192585	−	0.139921i
$994$	−1.68642e7	+	1.22526e7i	−0.0171715	+	0.0124758i
$995$	1.52701e8	−	4.69966e8i	0.155015	−	0.477086i
$996$	−6.65080e7	−	2.16098e7i	−0.0673125	−	0.0218712i
$997$	6.51547e7	+	8.96777e7i	0.0657446	+	0.0904897i	0.840623	−	0.541620i	$-0.182189\pi$
$997$	6.51547e7	+	8.96777e7i	0.0657446	+	0.0904897i	−0.774879	+	0.632110i	$0.782189\pi$
$998$	1.02135e8	−	1.40576e8i	0.102750	−	0.141423i
$999$	2.65289e8	+	8.16476e8i	0.266087	+	0.818930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.6.4	yes	20
3.2	odd	2		99.7.k.a.28.2		20
11.2	odd	10	inner	11.7.d.a.2.4	✓	20
11.3	even	5		121.7.b.c.120.5		20
11.8	odd	10		121.7.b.c.120.16		20
33.2	even	10		99.7.k.a.46.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.2.4	✓	20	11.2	odd	10	inner
11.7.d.a.6.4	yes	20	1.1	even	1	trivial
99.7.k.a.28.2		20	3.2	odd	2
99.7.k.a.46.2		20	33.2	even	10
121.7.b.c.120.5		20	11.3	even	5
121.7.b.c.120.16		20	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27508 - 2.36382i) q^{2} +(23.2263 + 16.8749i) q^{3} +(-4.43797 + 3.22437i) q^{4} +(31.2971 - 96.3226i) q^{5} +(208.862 + 67.8633i) q^{6} +(-91.3973 - 125.798i) q^{7} +(-312.424 + 430.015i) q^{8} +(29.4247 + 90.5599i) q^{9} +O(q^{10})\)	\(q+(7.27508 - 2.36382i) q^{2} +(23.2263 + 16.8749i) q^{3} +(-4.43797 + 3.22437i) q^{4} +(31.2971 - 96.3226i) q^{5} +(208.862 + 67.8633i) q^{6} +(-91.3973 - 125.798i) q^{7} +(-312.424 + 430.015i) q^{8} +(29.4247 + 90.5599i) q^{9} -774.735i q^{10} +(-1276.79 + 376.005i) q^{11} -157.488 q^{12} +(-119.738 + 38.9052i) q^{13} +(-962.284 - 699.140i) q^{14} +(2352.35 - 1709.08i) q^{15} +(-1147.94 + 3533.01i) q^{16} +(7821.98 + 2541.52i) q^{17} +(428.134 + 589.275i) q^{18} +(4947.75 - 6809.99i) q^{19} +(171.684 + 528.390i) q^{20} -4464.12i q^{21} +(-8399.91 + 5753.55i) q^{22} -14737.0 q^{23} +(-14512.9 + 4715.53i) q^{24} +(4342.36 + 3154.91i) q^{25} +(-779.138 + 566.077i) q^{26} +(5622.67 - 17304.8i) q^{27} +(811.236 + 263.587i) q^{28} +(8628.78 + 11876.5i) q^{29} +(13073.5 - 17994.2i) q^{30} +(10515.0 + 32361.9i) q^{31} -5601.34i q^{32} +(-36000.0 - 12812.4i) q^{33} +62913.2 q^{34} +(-14977.6 + 4866.52i) q^{35} +(-422.584 - 307.026i) q^{36} +(-38171.1 + 27732.9i) q^{37} +(19897.7 - 61238.8i) q^{38} +(-3437.59 - 1116.94i) q^{39} +(31642.2 + 43551.8i) q^{40} +(31217.4 - 42967.0i) q^{41} +(-10552.4 - 32476.8i) q^{42} +101242. i q^{43} +(4453.95 - 5785.53i) q^{44} +9643.87 q^{45} +(-107213. + 34835.6i) q^{46} +(-134958. - 98052.5i) q^{47} +(-86281.6 + 62687.2i) q^{48} +(28884.0 - 88895.8i) q^{49} +(39048.6 + 12687.7i) q^{50} +(138788. + 191025. i) q^{51} +(405.948 - 558.740i) q^{52} +(-67093.4 - 206492. i) q^{53} -139185. i q^{54} +(-3741.90 + 134751. i) q^{55} +82649.6 q^{56} +(229835. - 74678.1i) q^{57} +(90848.9 + 66005.6i) q^{58} +(-126742. + 92083.2i) q^{59} +(-4928.93 + 15169.7i) q^{60} +(138582. + 45028.2i) q^{61} +(152995. + 210580. i) q^{62} +(8702.87 - 11978.5i) q^{63} +(-86709.0 - 266863. i) q^{64} +12751.1i q^{65} +(-292189. - 8113.78i) q^{66} +103619. q^{67} +(-42908.5 + 13941.8i) q^{68} +(-342286. - 248685. i) q^{69} +(-97459.7 + 70808.6i) q^{70} +(5415.59 - 16667.5i) q^{71} +(-48135.1 - 15640.0i) q^{72} +(-160622. - 221077. i) q^{73} +(-212142. + 291989. i) q^{74} +(47618.1 + 146553. i) q^{75} +46175.9i q^{76} +(163995. + 126251. i) q^{77} -27649.0 q^{78} +(-399408. + 129775. i) q^{79} +(304381. + 221146. i) q^{80} +(478768. - 347845. i) q^{81} +(125543. - 386380. i) q^{82} +(422305. + 137215. i) q^{83} +(14394.0 + 19811.6i) q^{84} +(489611. - 673891. i) q^{85} +(239318. + 736544. i) q^{86} +421456. i q^{87} +(237211. - 666510. i) q^{88} -432440. q^{89} +(70159.9 - 22796.3i) q^{90} +(15837.9 + 11506.9i) q^{91} +(65402.5 - 47517.7i) q^{92} +(-301878. + 929086. i) q^{93} +(-1.21361e6 - 394324. i) q^{94} +(-501106. - 689713. i) q^{95} +(94521.9 - 130098. i) q^{96} +(338984. + 1.04328e6i) q^{97} -715000. i q^{98} +(-71620.0 - 104562. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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