LMFDB - Embedded newform 11.7.d.a.8.1

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			8.1
Root			$-12.4579i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.7.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.44062 - 11.6175i) q^{2} +(-3.65047 - 11.2350i) q^{3} +(-43.9455 + 135.250i) q^{4} +(22.0305 + 16.0061i) q^{5} +(-99.7104 + 137.240i) q^{6} +(-547.554 - 177.911i) q^{7} +(1068.14 - 347.060i) q^{8} +(476.874 - 346.469i) q^{9} +O(q^{10})$	\(q+(-8.44062 - 11.6175i) q^{2} +(-3.65047 - 11.2350i) q^{3} +(-43.9455 + 135.250i) q^{4} +(22.0305 + 16.0061i) q^{5} +(-99.7104 + 137.240i) q^{6} +(-547.554 - 177.911i) q^{7} +(1068.14 - 347.060i) q^{8} +(476.874 - 346.469i) q^{9} -391.041i q^{10} +(-1293.90 + 312.071i) q^{11} +1679.96 q^{12} +(-1314.65 - 1809.46i) q^{13} +(2554.81 + 7862.90i) q^{14} +(99.4068 - 305.943i) q^{15} +(-5684.48 - 4130.01i) q^{16} +(2281.44 - 3140.13i) q^{17} +(-8050.23 - 2615.68i) q^{18} +(2754.33 - 894.935i) q^{19} +(-3132.98 + 2276.24i) q^{20} +6801.23i q^{21} +(14546.8 + 12397.8i) q^{22} +12010.2 q^{23} +(-7798.42 - 10733.6i) q^{24} +(-4599.24 - 14155.0i) q^{25} +(-9924.95 + 30545.9i) q^{26} +(-12600.5 - 9154.79i) q^{27} +(48125.1 - 66238.5i) q^{28} +(8235.73 + 2675.95i) q^{29} +(-4393.35 + 1427.49i) q^{30} +(-31865.5 + 23151.6i) q^{31} +29020.4i q^{32} +(8229.45 + 13397.7i) q^{33} -55737.2 q^{34} +(-9215.24 - 12683.7i) q^{35} +(25903.6 + 79723.2i) q^{36} +(1215.85 - 3742.02i) q^{37} +(-33645.1 - 24444.6i) q^{38} +(-15530.1 + 21375.4i) q^{39} +(29086.8 + 9450.86i) q^{40} +(18816.1 - 6113.71i) q^{41} +(79013.3 - 57406.6i) q^{42} +4699.27i q^{43} +(14653.3 - 188714. i) q^{44} +16051.4 q^{45} +(-101373. - 139528. i) q^{46} +(20375.7 + 62710.0i) q^{47} +(-25649.7 + 78941.5i) q^{48} +(172983. + 125680. i) q^{49} +(-125626. + 172909. i) q^{50} +(-43607.6 - 14169.0i) q^{51} +(302503. - 98289.0i) q^{52} +(31777.8 - 23087.9i) q^{53} +223658. i q^{54} +(-33500.3 - 13835.2i) q^{55} -646610. q^{56} +(-20109.2 - 27677.9i) q^{57} +(-38426.8 - 118265. i) q^{58} +(93734.6 - 288486. i) q^{59} +(37010.4 + 26889.6i) q^{60} +(-6237.01 + 8584.50i) q^{61} +(537929. + 174784. i) q^{62} +(-322755. + 104870. i) q^{63} +(-26661.5 + 19370.7i) q^{64} -60905.7i q^{65} +(86186.6 - 208691. i) q^{66} -151620. q^{67} +(324445. + 446560. i) q^{68} +(-43842.8 - 134934. i) q^{69} +(-69570.6 + 214116. i) q^{70} +(-106471. - 77355.5i) q^{71} +(389123. - 535582. i) q^{72} +(-151315. - 49165.2i) q^{73} +(-53735.5 + 17459.7i) q^{74} +(-142242. + 103345. i) q^{75} +411852. i q^{76} +(764000. + 59322.9i) q^{77} +379413. q^{78} +(-389580. - 536210. i) q^{79} +(-59126.5 - 181973. i) q^{80} +(75930.9 - 233691. i) q^{81} +(-229845. - 166992. i) q^{82} +(-333113. + 458490. i) q^{83} +(-919869. - 298883. i) q^{84} +(100522. - 32661.7i) q^{85} +(54593.8 - 39664.7i) q^{86} -102297. i q^{87} +(-1.27376e6 + 782396. i) q^{88} +1.10426e6 q^{89} +(-135484. - 186478. i) q^{90} +(397918. + 1.22467e6i) q^{91} +(-527794. + 1.62438e6i) q^{92} +(376432. + 273494. i) q^{93} +(556551. - 766026. i) q^{94} +(75003.7 + 24370.2i) q^{95} +(326044. - 105938. i) q^{96} +(-596314. + 433247. i) q^{97} -3.07045e6i q^{98} +(-508904. + 597115. 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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−8.44062	−	11.6175i	−1.05508	−	1.45219i	−0.884323	−	0.466876i	$-0.845380\pi$
$2$	−8.44062	−	11.6175i	−1.05508	−	1.45219i	−0.170754	−	0.985314i	$-0.554620\pi$
$3$	−3.65047	−	11.2350i	−0.135203	−	0.416111i	0.860419	−	0.509587i	$-0.170202\pi$
$3$	−3.65047	−	11.2350i	−0.135203	−	0.416111i	−0.995621	+	0.0934767i	$0.970202\pi$
$4$	−43.9455	+	135.250i	−0.686649	+	2.11329i
$5$	22.0305	+	16.0061i	0.176244	+	0.128049i	0.672410	−	0.740179i	$-0.265259\pi$
$5$	22.0305	+	16.0061i	0.176244	+	0.128049i	−0.496166	+	0.868228i	$0.665259\pi$
$6$	−99.7104	+	137.240i	−0.461622	+	0.635369i
$7$	−547.554	−	177.911i	−1.59637	−	0.518691i	−0.630162	−	0.776463i	$-0.717012\pi$
$7$	−547.554	−	177.911i	−1.59637	−	0.518691i	−0.966206	+	0.257772i	$0.917012\pi$
$8$	1068.14	−	347.060i	2.08621	−	0.677851i
$9$	476.874	−	346.469i	0.654149	−	0.475267i
$10$		−	391.041i		−	0.391041i
$11$	−1293.90	+	312.071i	−0.972125	+	0.234464i
$11$	−1293.90	+	312.071i	−0.972125	+	0.234464i
$12$	1679.96			0.972198
$13$	−1314.65	−	1809.46i	−0.598383	−	0.823603i	0.397176	−	0.917742i	$-0.369990\pi$
$13$	−1314.65	−	1809.46i	−0.598383	−	0.823603i	−0.995559	+	0.0941391i	$0.969990\pi$
$14$	2554.81	+	7862.90i	0.931054	+	2.86549i
$15$	99.4068	−	305.943i	0.0294539	−	0.0906497i
$16$	−5684.48	−	4130.01i	−1.38781	−	1.00830i
$17$	2281.44	−	3140.13i	0.464367	−	0.639147i	−0.511040	−	0.859557i	$-0.670740\pi$
$17$	2281.44	−	3140.13i	0.464367	−	0.639147i	0.975407	+	0.220410i	$0.0707396\pi$
$18$	−8050.23	−	2615.68i	−1.38035	−	0.448504i
$19$	2754.33	−	894.935i	0.401564	−	0.130476i	−0.101270	−	0.994859i	$-0.532291\pi$
$19$	2754.33	−	894.935i	0.401564	−	0.130476i	0.502834	+	0.864383i	$0.332291\pi$
$20$	−3132.98	+	2276.24i	−0.391622	+	0.284530i
$21$			6801.23i			0.734394i
$22$	14546.8	+	12397.8i	1.36615	+	1.16433i
$23$	12010.2			0.987111			0.493556	−	0.869714i	$-0.335697\pi$
$23$	12010.2			0.987111			0.493556	+	0.869714i	$0.335697\pi$
$24$	−7798.42	−	10733.6i	−0.564122	−	0.776448i
$25$	−4599.24	−	14155.0i	−0.294351	−	0.905921i
$26$	−9924.95	+	30545.9i	−0.564688	+	1.73793i
$27$	−12600.5	−	9154.79i	−0.640171	−	0.465112i
$28$	48125.1	−	66238.5i	2.19229	−	3.01743i
$29$	8235.73	+	2675.95i	0.337682	+	0.109720i	0.472949	−	0.881090i	$-0.343189\pi$
$29$	8235.73	+	2675.95i	0.337682	+	0.109720i	−0.135267	+	0.990809i	$0.543189\pi$
$30$	−4393.35	+	1427.49i	−0.162717	+	0.0528698i
$31$	−31865.5	+	23151.6i	−1.06963	+	0.777135i	−0.975847	−	0.218457i	$-0.929898\pi$
$31$	−31865.5	+	23151.6i	−1.06963	+	0.777135i	−0.0937882	+	0.995592i	$0.529898\pi$
$32$			29020.4i			0.885633i
$33$	8229.45	+	13397.7i	0.228997	+	0.372811i
$34$	−55737.2			−1.41811
$35$	−9215.24	−	12683.7i	−0.214933	−	0.295830i
$36$	25903.6	+	79723.2i	0.555205	+	1.70875i
$37$	1215.85	−	3742.02i	0.0240036	−	0.0738755i	−0.938337	−	0.345722i	$-0.887634\pi$
$37$	1215.85	−	3742.02i	0.0240036	−	0.0738755i	0.962341	+	0.271846i	$0.0876342\pi$
$38$	−33645.1	−	24444.6i	−0.613157	−	0.445484i
$39$	−15530.1	+	21375.4i	−0.261807	+	0.360347i
$40$	29086.8	+	9450.86i	0.454481	+	0.147670i
$41$	18816.1	−	6113.71i	0.273009	−	0.0887061i	−0.169313	−	0.985562i	$-0.554155\pi$
$41$	18816.1	−	6113.71i	0.273009	−	0.0887061i	0.442322	+	0.896856i	$0.354155\pi$
$42$	79013.3	−	57406.6i	1.06648	−	0.774843i
$43$			4699.27i			0.0591051i	0.999563	+	0.0295525i	$0.00940823\pi$
$43$			4699.27i			0.0591051i	−0.999563	+	0.0295525i	$0.990592\pi$
$44$	14653.3	−	188714.i	0.172019	−	2.21537i
$45$	16051.4			0.176147
$46$	−101373.	−	139528.i	−1.04148	−	1.43347i
$47$	20375.7	+	62710.0i	0.196254	+	0.604009i	0.999960	+	0.00898124i	$0.00285885\pi$
$47$	20375.7	+	62710.0i	0.196254	+	0.604009i	−0.803705	+	0.595028i	$0.797141\pi$
$48$	−25649.7	+	78941.5i	−0.231931	+	0.713809i
$49$	172983.	+	125680.i	1.47033	+	1.06826i
$50$	−125626.	+	172909.i	−1.00500	+	1.38327i
$51$	−43607.6	−	14169.0i	−0.328739	−	0.106814i
$52$	302503.	−	98289.0i	2.15139	−	0.699029i
$53$	31777.8	−	23087.9i	0.213450	−	0.155080i	−0.475923	−	0.879487i	$-0.657886\pi$
$53$	31777.8	−	23087.9i	0.213450	−	0.155080i	0.689373	+	0.724406i	$0.257886\pi$
$54$			223658.i			1.42038i
$55$	−33500.3	−	13835.2i	−0.201354	−	0.0831566i
$56$	−646610.			−3.68196
$57$	−20109.2	−	27677.9i	−0.108585	−	0.149454i
$58$	−38426.8	−	118265.i	−0.196947	−	0.606141i
$59$	93734.6	−	288486.i	0.456398	−	1.40465i	−0.413087	−	0.910691i	$-0.635550\pi$
$59$	93734.6	−	288486.i	0.456398	−	1.40465i	0.869486	−	0.493958i	$-0.164450\pi$
$60$	37010.4	+	26889.6i	0.171344	+	0.124489i
$61$	−6237.01	+	8584.50i	−0.0274781	+	0.0378204i	−0.822535	−	0.568714i	$-0.807441\pi$
$61$	−6237.01	+	8584.50i	−0.0274781	+	0.0378204i	0.795057	+	0.606535i	$0.207441\pi$
$62$	537929.	+	174784.i	2.25709	+	0.733375i
$63$	−322755.	+	104870.i	−1.29078	+	0.419399i
$64$	−26661.5	+	19370.7i	−0.101705	+	0.0738933i
$65$		−	60905.7i		−	0.221778i
$66$	86186.6	−	208691.i	0.299784	−	0.725892i
$67$	−151620.			−0.504117			−0.252058	−	0.967712i	$-0.581108\pi$
$67$	−151620.			−0.504117			−0.252058	+	0.967712i	$0.581108\pi$
$68$	324445.	+	446560.i	1.03184	+	1.42021i
$69$	−43842.8	−	134934.i	−0.133460	−	0.410748i
$70$	−69570.6	+	214116.i	−0.202830	+	0.624246i
$71$	−106471.	−	77355.5i	−0.297478	−	0.216131i	0.429027	−	0.903292i	$-0.358857\pi$
$71$	−106471.	−	77355.5i	−0.297478	−	0.216131i	−0.726505	+	0.687161i	$0.758857\pi$
$72$	389123.	−	535582.i	1.04253	−	1.43492i
$73$	−151315.	−	49165.2i	−0.388967	−	0.126383i	0.108003	−	0.994151i	$-0.465554\pi$
$73$	−151315.	−	49165.2i	−0.388967	−	0.126383i	−0.496971	+	0.867767i	$0.665554\pi$
$74$	−53735.5	+	17459.7i	−0.132607	+	0.0430866i
$75$	−142242.	+	103345.i	−0.337166	+	0.244966i
$76$			411852.i			0.938211i
$77$	764000.	+	59322.9i	1.67348	+	0.129942i
$78$	379413.			0.799519
$79$	−389580.	−	536210.i	−0.790160	−	1.08756i	−0.994088	−	0.108576i	$-0.965371\pi$
$79$	−389580.	−	536210.i	−0.790160	−	1.08756i	0.203928	−	0.978986i	$-0.434629\pi$
$80$	−59126.5	−	181973.i	−0.115482	−	0.355416i
$81$	75930.9	−	233691.i	0.142877	−	0.439731i
$82$	−229845.	−	166992.i	−0.416864	−	0.302869i
$83$	−333113.	+	458490.i	−0.582581	+	0.801855i	−0.993975	−	0.109603i	$-0.965042\pi$
$83$	−333113.	+	458490.i	−0.582581	+	0.801855i	0.411394	+	0.911458i	$0.365042\pi$
$84$	−919869.	−	298883.i	−1.55199	−	0.504271i
$85$	100522.	−	32661.7i	0.163684	−	0.0531842i
$86$	54593.8	−	39664.7i	0.0858317	−	0.0623604i
$87$		−	102297.i		−	0.155348i
$88$	−1.27376e6	+	782396.i	−1.86913	+	1.14810i
$89$	1.10426e6			1.56639			0.783197	−	0.621774i	$-0.213588\pi$
$89$	1.10426e6			1.56639			0.783197	+	0.621774i	$0.213588\pi$
$90$	−135484.	−	186478.i	−0.185849	−	0.255799i
$91$	397918.	+	1.22467e6i	0.528043	+	1.62515i
$92$	−527794.	+	1.62438e6i	−0.677799	+	2.08605i
$93$	376432.	+	273494.i	0.467992	+	0.340016i
$94$	556551.	−	766026.i	0.670072	−	0.922274i
$95$	75003.7	+	24370.2i	0.0874806	+	0.0284242i
$96$	326044.	−	105938.i	0.368521	−	0.119740i
$97$	−596314.	+	433247.i	−0.653371	+	0.474702i	−0.864418	−	0.502774i	$-0.832313\pi$
$97$	−596314.	+	433247.i	−0.653371	+	0.474702i	0.211047	+	0.977476i	$0.432313\pi$
$98$		−	3.07045e6i		−	3.26230i
$99$	−508904.	+	597115.i	−0.524481	+	0.615393i
$100$	2.11659e6			2.11659
$101$	−480836.	−	661815.i	−0.466695	−	0.642351i	0.509185	−	0.860657i	$-0.329947\pi$
$101$	−480836.	−	661815.i	−0.466695	−	0.642351i	−0.975880	+	0.218306i	$0.929947\pi$
$102$	203467.	+	626207.i	0.191731	+	0.590089i
$103$	525555.	−	1.61749e6i	0.480957	−	1.48023i	−0.356794	−	0.934183i	$-0.616130\pi$
$103$	525555.	−	1.61749e6i	0.480957	−	1.48023i	0.837752	−	0.546051i	$-0.183870\pi$
$104$	−2.03222e6	−	1.47649e6i	−1.80663	−	1.31260i
$105$	−108861.	+	149835.i	−0.0940384	+	0.129433i
$106$	−536448.	−	174303.i	−0.450412	−	0.146348i
$107$	495494.	−	160996.i	0.404470	−	0.131420i	−0.0997146	−	0.995016i	$-0.531793\pi$
$107$	495494.	−	160996.i	0.404470	−	0.131420i	0.504185	+	0.863596i	$0.331793\pi$
$108$	1.79192e6	−	1.30191e6i	1.42249	−	1.03350i
$109$			2.40616e6i			1.85800i	0.370079	+	0.929000i	$0.379330\pi$
$109$			2.40616e6i			1.85800i	−0.370079	+	0.929000i	$0.620670\pi$
$110$	122033.	+	505968.i	0.0916851	+	0.380141i
$111$	−46480.0			−0.0339857
$112$	2.37778e6	+	3.27274e6i	1.69246	+	2.32947i
$113$	−362917.	−	1.11694e6i	−0.251520	−	0.774098i	−0.994495	−	0.104780i	$-0.966586\pi$
$113$	−362917.	−	1.11694e6i	−0.251520	−	0.774098i	0.742976	−	0.669318i	$-0.233414\pi$
$114$	−151815.	+	467237.i	−0.102470	+	0.315372i
$115$	264591.	+	192236.i	0.173973	+	0.126398i
$116$	−723847.	+	996290.i	−0.463738	+	0.638281i
$117$	−1.25384e6	−	407398.i	−0.782862	−	0.254367i
$118$	−4.14266e6	+	1.34603e6i	−2.52135	+	0.819237i
$119$	−1.80787e6	+	1.31350e6i	−1.07282	+	0.779450i
$120$		−	361290.i		−	0.209080i
$121$	1.57678e6	−	807577.i	0.890053	−	0.455856i
$122$	152375.			0.0839138
$123$	−137375.	−	189080.i	−0.0738231	−	0.101609i
$124$	−1.73092e6	−	5.32723e6i	−0.907847	−	2.79407i
$125$	256726.	−	790121.i	0.131444	−	0.404542i
$126$	3.94258e6	+	2.86445e6i	1.97092	+	1.43196i
$127$	−197266.	+	271513.i	−0.0963031	+	0.132550i	−0.854449	−	0.519535i	$-0.826105\pi$
$127$	−197266.	+	271513.i	−0.0963031	+	0.132550i	0.758146	+	0.652085i	$0.226105\pi$
$128$	2.21648e6	+	720179.i	1.05690	+	0.343408i
$129$	52796.2	−	17154.5i	0.0245942	−	0.00799116i
$130$	−707572.	+	514081.i	−0.322063	+	0.233992i
$131$		−	2.83210e6i		−	1.25978i	−0.776684	−	0.629890i	$-0.783100\pi$
$131$		−	2.83210e6i		−	1.25978i	0.776684	−	0.629890i	$-0.216900\pi$
$132$	−2.17370e6	+	524267.i	−0.945098	+	0.227945i
$133$	−1.66736e6			−0.708720
$134$	1.27976e6	+	1.76144e6i	0.531882	+	0.732073i
$135$	−131063.	−	403370.i	−0.0532694	−	0.163946i
$136$	1.34708e6	−	4.14589e6i	0.535522	−	1.64817i
$137$	−165563.	−	120288.i	−0.0643873	−	0.0467801i	0.555126	−	0.831766i	$-0.312670\pi$
$137$	−165563.	−	120288.i	−0.0643873	−	0.0467801i	−0.619513	+	0.784986i	$0.712670\pi$
$138$	−1.19754e6	+	1.64827e6i	−0.455673	+	0.627180i
$139$	2.28698e6	+	743083.i	0.851564	+	0.276690i	0.702101	−	0.712078i	$-0.252246\pi$
$139$	2.28698e6	+	743083.i	0.851564	+	0.276690i	0.149463	+	0.988767i	$0.452246\pi$
$140$	2.12044e6	−	688974.i	0.772756	−	0.251084i
$141$	630165.	−	457842.i	0.224800	−	0.163327i
$142$			1.88985e6i			0.660029i
$143$	2.26570e6	+	1.93099e6i	0.774808	+	0.660346i
$144$	−4.14170e6			−1.38705
$145$	138606.	+	190775.i	0.0454650	+	0.0625773i
$146$	706014.	+	2.17289e6i	0.226858	+	0.698198i
$147$	780540.	−	2.40225e6i	0.245721	−	0.756253i
$148$	452678.	+	328890.i	0.139638	+	0.101453i
$149$	−2.85428e6	+	3.92858e6i	−0.862855	+	1.18762i	0.118026	+	0.993010i	$0.462343\pi$
$149$	−2.85428e6	+	3.92858e6i	−0.862855	+	1.18762i	−0.980881	+	0.194608i	$0.937657\pi$
$150$	2.40122e6	+	780204.i	0.711473	+	0.231172i
$151$	3.14467e6	−	1.02177e6i	0.913365	−	0.296770i	0.185623	−	0.982621i	$-0.440570\pi$
$151$	3.14467e6	−	1.02177e6i	0.913365	−	0.296770i	0.727742	+	0.685851i	$0.240570\pi$
$152$	2.63141e6	−	1.91183e6i	0.749303	−	0.544401i
$153$		−	2.28789e6i		−	0.638795i
$154$	−5.75945e6	−	9.37651e6i	−1.57695	−	2.56731i
$155$	−1.07258e6			−0.288028
$156$	−2.20855e6	−	3.03981e6i	−0.581747	−	0.800706i
$157$	516502.	+	1.58963e6i	0.133467	+	0.410768i	0.995348	−	0.0963412i	$-0.0307140\pi$
$157$	516502.	+	1.58963e6i	0.133467	+	0.410768i	−0.861882	+	0.507109i	$0.830714\pi$
$158$	−2.94114e6	+	9.05190e6i	−0.745666	+	2.29492i
$159$	−375396.	−	272741.i	−0.0933896	−	0.0678515i
$160$	−464504.	+	639335.i	−0.113404	+	0.156088i
$161$	−6.57622e6	−	2.13675e6i	−1.57579	−	0.512006i
$162$	−3.35582e6	+	1.09037e6i	−0.789320	+	0.256466i
$163$	3.02440e6	−	2.19735e6i	0.698355	−	0.507384i	−0.181041	−	0.983476i	$-0.557947\pi$
$163$	3.02440e6	−	2.19735e6i	0.698355	−	0.507384i	0.879396	+	0.476091i	$0.157947\pi$
$164$			2.81355e6i			0.637857i
$165$	−33146.3	+	426881.i	−0.00737876	+	0.0950286i
$166$	8.13819e6			1.77911
$167$	874791.	+	1.20405e6i	0.187826	+	0.258520i	0.892537	−	0.450974i	$-0.148923\pi$
$167$	874791.	+	1.20405e6i	0.187826	+	0.258520i	−0.704711	+	0.709494i	$0.748923\pi$
$168$	2.36043e6	+	7.26466e6i	0.497810	+	1.53210i
$169$	−54269.4	+	167024.i	−0.0112433	+	0.0346034i
$170$	−1.22792e6	−	892136.i	−0.249933	−	0.181587i
$171$	1.00340e6	−	1.38106e6i	0.200671	−	0.276201i
$172$	−635578.	−	206512.i	−0.124906	−	0.0405844i
$173$	−946003.	+	307375.i	−0.182707	+	0.0593650i	−0.398941	−	0.916976i	$-0.630622\pi$
$173$	−946003.	+	307375.i	−0.182707	+	0.0593650i	0.216235	+	0.976341i	$0.430622\pi$
$174$	−1.18843e6	+	863448.i	−0.225594	+	0.163904i
$175$			8.56889e6i			1.59886i
$176$	8.64399e6	+	3.56986e6i	1.58554	+	0.654806i
$177$	−3.58331e6			−0.646196
$178$	−9.32063e6	−	1.28287e7i	−1.65267	−	2.27470i
$179$	−8956.74	−	27566.0i	−0.00156168	−	0.00480634i	0.950273	−	0.311419i	$-0.100804\pi$
$179$	−8956.74	−	27566.0i	−0.00156168	−	0.00480634i	−0.951834	+	0.306613i	$0.900804\pi$
$180$	−705388.	+	2.17096e6i	−0.120951	+	0.372250i
$181$	−4.04799e6	−	2.94104e6i	−0.682660	−	0.495981i	0.191579	−	0.981477i	$-0.438639\pi$
$181$	−4.04799e6	−	2.94104e6i	−0.682660	−	0.495981i	−0.874239	+	0.485496i	$0.838639\pi$
$182$	1.08689e7	−	1.49598e7i	1.80290	−	2.48148i
$183$	119215.	+	38735.2i	0.0194526	+	0.00632052i
$184$	1.28286e7	−	4.16825e6i	2.05932	−	0.669114i
$185$	86681.0	−	62977.5i	0.0136902	−	0.00994649i
$186$		−	6.68167e6i		−	1.03836i
$187$	−1.97200e6	+	4.77498e6i	−0.301566	+	0.730208i
$188$	−9.37698e6			−1.41120
$189$	5.27071e6	+	7.25451e6i	0.780699	+	1.07454i
$190$	−349957.	−	1.07706e6i	−0.0510215	−	0.157028i
$191$	627418.	−	1.93099e6i	0.0900444	−	0.277128i	−0.895886	−	0.444284i	$-0.853458\pi$
$191$	627418.	−	1.93099e6i	0.0900444	−	0.277128i	0.985931	+	0.167156i	$0.0534582\pi$
$192$	314956.	+	228829.i	0.0444986	+	0.0323301i
$193$	5.12652e6	−	7.05604e6i	0.713100	−	0.981498i	−0.286625	−	0.958043i	$-0.592533\pi$
$193$	5.12652e6	−	7.05604e6i	0.713100	−	0.981498i	0.999725	−	0.0234549i	$-0.00746661\pi$
$194$	1.00665e7	+	3.27081e6i	1.37871	+	0.447971i
$195$	−684275.	+	222334.i	−0.0922840	+	0.0299849i
$196$	−2.46001e7	+	1.78730e7i	−3.26714	+	2.37372i
$197$			1.64963e6i			0.215769i	0.994163	+	0.107884i	$0.0344076\pi$
$197$			1.64963e6i			0.215769i	−0.994163	+	0.107884i	$0.965592\pi$
$198$	1.12325e7	+	872175.i	1.44704	+	0.112359i
$199$	2.61784e6			0.332188			0.166094	−	0.986110i	$-0.446884\pi$
$199$	2.61784e6			0.332188			0.166094	+	0.986110i	$0.446884\pi$
$200$	−9.82527e6	−	1.35233e7i	−1.22816	−	1.69042i
$201$	553483.	+	1.70345e6i	0.0681579	+	0.209768i
$202$	−3.63008e6	+	1.11722e7i	−0.440415	+	1.35546i
$203$	−4.03343e6	−	2.93046e6i	−0.482154	−	0.350306i
$204$	3.83272e6	−	5.27529e6i	0.451457	−	0.621377i
$205$	512385.	+	166484.i	0.0594750	+	0.0193246i
$206$	−2.32272e7	+	7.54699e6i	−2.65703	+	0.863321i
$207$	5.72735e6	−	4.16116e6i	0.645717	−	0.469141i
$208$			1.57153e7i			1.74636i
$209$	−3.28453e6	+	2.01750e6i	−0.359778	+	0.220991i
$210$	2.65956e6			0.287179
$211$	8.74501e6	+	1.20365e7i	0.930921	+	1.28130i	0.959499	+	0.281712i	$0.0909022\pi$
$211$	8.74501e6	+	1.20365e7i	0.930921	+	1.28130i	−0.0285777	+	0.999592i	$0.509098\pi$
$212$	1.72616e6	+	5.31257e6i	0.181165	+	0.557567i
$213$	−480420.	+	1.47858e6i	−0.0497144	+	0.153005i
$214$	−6.05264e6	−	4.39750e6i	−0.617595	−	0.448709i
$215$	−75217.0	+	103527.i	−0.00756834	+	0.0104169i
$216$	−1.66363e7	−	5.40548e6i	−1.65081	−	0.536380i
$217$	2.15670e7	−	7.00755e6i	2.11062	−	0.685783i
$218$	2.79536e7	−	2.03095e7i	2.69817	−	1.96033i
$219$			1.87950e6i			0.178941i
$220$	3.34340e6	−	3.92294e6i	0.313994	−	0.368420i
$221$	−8.68121e6			−0.804273
$222$	392320.	+	539982.i	0.0358576	+	0.0493537i
$223$	−4.03984e6	−	1.24334e7i	−0.364292	−	1.12118i	−0.950423	−	0.310960i	$-0.899349\pi$
$223$	−4.03984e6	−	1.24334e7i	−0.364292	−	1.12118i	0.586131	−	0.810217i	$-0.300651\pi$
$224$	5.16305e6	−	1.58902e7i	0.459370	−	1.41380i
$225$	−7.09754e6	−	5.15666e6i	−0.623104	−	0.452711i
$226$	−9.91287e6	+	1.36439e7i	−0.858764	+	1.18199i
$227$	−1.38136e7	−	4.48830e6i	−1.18094	−	0.383711i	−0.348224	−	0.937411i	$-0.613215\pi$
$227$	−1.38136e7	−	4.48830e6i	−1.18094	−	0.383711i	−0.832716	+	0.553701i	$0.813215\pi$
$228$	4.62715e6	−	1.50345e6i	0.390400	−	0.126849i
$229$	−5.45793e6	+	3.96542e6i	−0.454487	+	0.330204i	−0.791365	−	0.611344i	$-0.790629\pi$
$229$	−5.45793e6	+	3.96542e6i	−0.454487	+	0.330204i	0.336878	+	0.941548i	$0.390629\pi$
$230$		−	4.69648e6i		−	0.386001i
$231$	−2.12247e6	−	8.80009e6i	−0.172189	−	0.713923i
$232$	9.72563e6			0.778850
$233$	−1.84721e6	−	2.54247e6i	−0.146032	−	0.200996i	0.729734	−	0.683731i	$-0.239644\pi$
$233$	−1.84721e6	−	2.54247e6i	−0.146032	−	0.200996i	−0.875767	+	0.482734i	$0.839644\pi$
$234$	5.85025e6	+	1.80052e7i	0.456591	+	1.40524i
$235$	−554856.	+	1.70767e6i	−0.0427540	+	0.131583i
$236$	3.48986e7	+	2.53553e7i	2.65504	+	1.92900i
$237$	−4.60217e6	+	6.33434e6i	−0.345715	+	0.475835i
$238$	3.05191e7	+	9.91627e6i	2.26382	+	0.735559i
$239$	4.07499e6	−	1.32404e6i	0.298492	−	0.0969859i	−0.155942	−	0.987766i	$-0.549841\pi$
$239$	4.07499e6	−	1.32404e6i	0.298492	−	0.0969859i	0.454434	+	0.890780i	$0.349841\pi$
$240$	−1.82862e6	+	1.32857e6i	−0.132279	+	0.0961062i
$241$		−	4.56310e6i		−	0.325994i	−0.986627	−	0.162997i	$-0.947884\pi$
$241$		−	4.56310e6i		−	0.325994i	0.986627	−	0.162997i	$-0.0521160\pi$
$242$	−2.26911e7	−	1.15019e7i	−1.60106	−	0.811563i
$243$	−1.42569e7			−0.993589
$244$	−886969.	−	1.22081e6i	−0.0610575	−	0.0840384i
$245$	1.79927e6	+	5.53758e6i	0.122348	+	0.376549i
$246$	−1.03711e6	+	3.19191e6i	−0.0696661	+	0.214410i
$247$	−5.24031e6	−	3.80731e6i	−0.347749	−	0.252655i
$248$	−2.60018e7	+	3.57884e7i	−1.70470	+	2.34632i
$249$	6.36715e6	+	2.06881e6i	0.412427	+	0.134006i
$250$	−1.13462e7	+	3.68660e6i	−0.726155	+	0.235942i
$251$	1.17864e7	−	8.56334e6i	0.745351	−	0.541529i	−0.149031	−	0.988833i	$-0.547615\pi$
$251$	1.17864e7	−	8.56334e6i	0.745351	−	0.541529i	0.894382	+	0.447303i	$0.147615\pi$
$252$		−	4.82613e7i		−	3.01577i
$253$	−1.55399e7	+	3.74803e6i	−0.959595	+	0.231442i
$254$	4.81935e6			0.294095
$255$	−733908.	−	1.01014e6i	−0.0442610	−	0.0609201i
$256$	−9.69003e6	−	2.98228e7i	−0.577571	−	1.77758i
$257$	5.72577e6	−	1.76221e7i	0.337314	−	1.03815i	−0.628257	−	0.778006i	$-0.716231\pi$
$257$	5.72577e6	−	1.76221e7i	0.337314	−	1.03815i	0.965571	−	0.260140i	$-0.0837686\pi$
$258$	−644926.	−	468566.i	−0.0375535	−	0.0272842i
$259$	−1.33149e6	+	1.83264e6i	−0.0766372	+	0.105482i
$260$	8.23752e6	+	2.67653e6i	0.468680	+	0.152283i
$261$	4.85454e6	−	1.57734e6i	0.273040	−	0.0887162i
$262$	−3.29020e7	+	2.39047e7i	−1.82944	+	1.32917i
$263$			2.32724e7i			1.27930i	0.768664	+	0.639652i	$0.220922\pi$
$263$			2.32724e7i			1.27930i	−0.768664	+	0.639652i	$0.779078\pi$
$264$	1.34400e7	+	1.14545e7i	0.730446	+	0.622538i
$265$	1.06963e6			0.0574772
$266$	1.40736e7	+	1.93706e7i	0.747755	+	1.02920i
$267$	−4.03106e6	−	1.24063e7i	−0.211780	−	0.651793i
$268$	6.66301e6	−	2.05066e7i	0.346151	−	1.06534i
$269$	2.52138e7	+	1.83189e7i	1.29533	+	0.941115i	0.999898	−	0.0142475i	$-0.00453527\pi$
$269$	2.52138e7	+	1.83189e7i	1.29533	+	0.941115i	0.295435	+	0.955363i	$0.404535\pi$
$270$	−3.57990e6	+	4.92731e6i	−0.181878	+	0.250333i
$271$	−1.60484e7	−	5.21445e6i	−0.806352	−	0.262000i	−0.123300	−	0.992369i	$-0.539348\pi$
$271$	−1.60484e7	−	5.21445e6i	−0.806352	−	0.262000i	−0.683052	+	0.730370i	$0.739348\pi$
$272$	−2.59375e7	+	8.42762e6i	−1.28891	+	0.418792i
$273$	1.23065e7	−	8.94121e6i	0.604850	−	0.439449i
$274$			2.93873e6i			0.142859i
$275$	1.03683e7	+	1.68799e7i	0.498552	+	0.811653i
$276$	2.01766e7			0.959668
$277$	2.03922e7	+	2.80674e7i	0.959454	+	1.32058i	0.947198	+	0.320650i	$0.103901\pi$
$277$	2.03922e7	+	2.80674e7i	0.959454	+	1.32058i	0.0122563	+	0.999925i	$0.496099\pi$
$278$	−1.06707e7	−	3.28411e7i	−0.496660	−	1.52856i
$279$	−7.17450e6	+	2.20808e7i	−0.330354	+	1.01672i
$280$	−1.42452e7	−	1.03497e7i	−0.648923	−	0.471470i
$281$	1.98441e7	−	2.73131e7i	0.894360	−	1.23098i	−0.0778719	−	0.996963i	$-0.524813\pi$
$281$	1.98441e7	−	2.73131e7i	0.894360	−	1.23098i	0.972232	−	0.234018i	$-0.0751875\pi$
$282$	−1.06380e7	−	3.45649e6i	−0.474364	−	0.154130i
$283$	−2.11723e7	+	6.87929e6i	−0.934132	+	0.303518i	−0.736251	−	0.676708i	$-0.763406\pi$
$283$	−2.11723e7	+	6.87929e6i	−0.934132	+	0.303518i	−0.197881	+	0.980226i	$0.563406\pi$
$284$	1.51413e7	−	1.10008e7i	0.661009	−	0.480251i
$285$		−	931628.i		−	0.0402446i
$286$	3.30939e6	−	4.26205e7i	0.141465	−	1.82188i
$287$	−1.13905e7			−0.481834
$288$	1.00547e7	+	1.38391e7i	0.420912	+	0.579335i
$289$	2.80347e6	+	8.62819e6i	0.116145	+	0.357459i
$290$	1.04641e6	−	3.22051e6i	0.0429049	−	0.132048i
$291$	7.04435e6	+	5.11802e6i	0.285866	+	0.207694i
$292$	1.32992e7	−	1.83048e7i	0.534168	−	0.735219i
$293$	1.99717e7	+	6.48919e6i	0.793983	+	0.257981i	0.677799	−	0.735247i	$-0.262934\pi$
$293$	1.99717e7	+	6.48919e6i	0.793983	+	0.257981i	0.116184	+	0.993228i	$0.462934\pi$
$294$	−3.44965e7	+	1.12086e7i	−1.35748	+	0.441071i
$295$	6.68256e6	−	4.85516e6i	0.260301	−	0.189120i
$296$		−	4.41897e6i		−	0.170391i
$297$	1.91607e7	+	7.91312e6i	0.731378	+	0.302050i
$298$	6.97322e7			2.63503
$299$	−1.57891e7	−	2.17319e7i	−0.590670	−	0.812988i
$300$	−7.72654e6	−	2.37798e7i	−0.286168	−	0.880735i
$301$	836052.	−	2.57310e6i	0.0306573	−	0.0943534i
$302$	−3.84133e7	−	2.79089e7i	−1.39464	−	1.01326i
$303$	−5.68020e6	+	7.81813e6i	−0.204191	+	0.281044i
$304$	−1.93530e7	−	6.28817e6i	−0.688854	−	0.223822i
$305$	−274809.	+	89290.9i	−0.00968571	+	0.00314708i
$306$	−2.65796e7	+	1.93112e7i	−0.927652	+	0.673978i
$307$		−	1.51140e7i		−	0.522352i	−0.965291	−	0.261176i	$-0.915890\pi$
$307$		−	1.51140e7i		−	0.522352i	0.965291	−	0.261176i	$-0.0841103\pi$
$308$	−4.15978e7	+	1.00724e8i	−1.42370	+	3.44733i
$309$	−2.00910e7			−0.680968
$310$	9.05325e6	+	1.24607e7i	0.303892	+	0.418272i
$311$	8.12197e6	+	2.49969e7i	0.270010	+	0.831006i	0.990497	+	0.137537i	$0.0439186\pi$
$311$	8.12197e6	+	2.49969e7i	0.270010	+	0.831006i	−0.720486	+	0.693469i	$0.756081\pi$
$312$	−9.16982e6	+	2.82218e7i	−0.301924	+	0.929226i
$313$	−4.25540e7	−	3.09173e7i	−1.38774	−	1.00825i	−0.996109	−	0.0881252i	$-0.971912\pi$
$313$	−4.25540e7	−	3.09173e7i	−1.38774	−	1.00825i	−0.391627	−	0.920124i	$-0.628088\pi$
$314$	1.41079e7	−	1.94179e7i	0.455696	−	0.627211i
$315$	−8.78902e6	−	2.85573e6i	−0.281196	−	0.0913661i
$316$	8.96430e7	−	2.91268e7i	2.84089	−	0.923062i
$317$	−3.12355e7	+	2.26939e7i	−0.980551	+	0.712412i	−0.957832	−	0.287330i	$-0.907232\pi$
$317$	−3.12355e7	+	2.26939e7i	−0.980551	+	0.712412i	−0.0227192	+	0.999742i	$0.507232\pi$
$318$			6.66328e6i			0.207208i
$319$	−1.14913e7	−	892272.i	−0.353994	−	0.0274869i
$320$	−897415.			−0.0273869
$321$	−3.61757e6	−	4.97916e6i	−0.109371	−	0.150536i
$322$	3.06837e7	+	9.44348e7i	0.919053	+	2.82856i
$323$	3.47361e6	−	1.06907e7i	0.103080	−	0.317247i
$324$	2.82700e7	+	2.05394e7i	0.831172	+	0.603882i
$325$	−1.95665e7	+	2.69310e7i	−0.569984	+	0.784516i
$326$	−5.10556e7	−	1.65890e7i	−1.47364	−	0.478814i
$327$	2.70332e7	−	8.78363e6i	0.773134	−	0.251206i
$328$	1.79764e7	−	1.30606e7i	0.509425	−	0.370119i
$329$		−	3.79622e7i		−	1.06602i
$330$	5.23907e6	−	3.21806e6i	0.145785	−	0.0895472i
$331$	4.98018e7			1.37328			0.686642	−	0.726995i	$-0.259084\pi$
$331$	4.98018e7			1.37328			0.686642	+	0.726995i	$0.259084\pi$
$332$	−4.73722e7	−	6.52022e7i	−1.29452	−	1.78175i
$333$	−716684.	−	2.20573e6i	−0.0194086	−	0.0597337i
$334$	6.60425e6	−	2.03258e7i	0.177249	−	0.545517i
$335$	−3.34026e6	−	2.42684e6i	−0.0888477	−	0.0645516i
$336$	2.80892e7	−	3.86614e7i	0.740493	−	1.01920i
$337$	−1.59845e7	−	5.19368e6i	−0.417647	−	0.135702i	0.0926524	−	0.995699i	$-0.470465\pi$
$337$	−1.59845e7	−	5.19368e6i	−0.417647	−	0.135702i	−0.510300	+	0.859997i	$0.670465\pi$
$338$	2.39847e6	−	779311.i	0.0621133	−	0.0201818i
$339$	−1.12240e7	+	8.15474e6i	−0.288104	+	0.209320i
$340$			1.50310e7i			0.382430i
$341$	3.40057e7	−	3.99002e7i	0.857608	−	1.00626i
$342$	−2.45138e7			−0.612820
$343$	−3.25446e7	−	4.47938e7i	−0.806486	−	1.11003i
$344$	1.63093e6	+	5.01947e6i	0.0400644	+	0.123306i
$345$	1.19389e6	−	3.67443e6i	0.0290742	−	0.0894813i
$346$	1.15558e7	+	8.39577e6i	0.278979	+	0.202690i
$347$	−9.80529e6	+	1.34958e7i	−0.234678	+	0.323006i	−0.910072	−	0.414451i	$-0.863974\pi$
$347$	−9.80529e6	+	1.34958e7i	−0.234678	+	0.323006i	0.675394	+	0.737457i	$0.263974\pi$
$348$	1.38357e7	+	4.49549e6i	0.328294	+	0.106669i
$349$	−4.21122e7	+	1.36831e7i	−0.990676	+	0.321890i	−0.759134	−	0.650935i	$-0.774377\pi$
$349$	−4.21122e7	+	1.36831e7i	−0.990676	+	0.321890i	−0.231542	+	0.972825i	$0.574377\pi$
$350$	9.95492e7	−	7.23268e7i	2.32185	−	1.68692i
$351$			3.48354e7i			0.805562i
$352$	−9.05644e6	−	3.75495e7i	−0.207649	−	0.860946i
$353$	8.24774e7			1.87504			0.937521	−	0.347929i	$-0.113115\pi$
$353$	8.24774e7			1.87504			0.937521	+	0.347929i	$0.113115\pi$
$354$	3.02453e7	+	4.16291e7i	0.681787	+	0.938399i
$355$	−1.10745e6	−	3.40837e6i	−0.0247535	−	0.0761835i
$356$	−4.85272e7	+	1.49351e8i	−1.07556	+	3.31024i
$357$	2.13567e7	+	1.55166e7i	0.469386	+	0.341029i
$358$	−244648.	+	336729.i	−0.00533203	+	0.00733891i
$359$	3.33150e7	+	1.08247e7i	0.720040	+	0.233955i	0.646040	−	0.763303i	$-0.276424\pi$
$359$	3.33150e7	+	1.08247e7i	0.720040	+	0.233955i	0.0739992	+	0.997258i	$0.476424\pi$
$360$	1.71452e7	−	5.57080e6i	0.367480	−	0.119402i
$361$	−3.12755e7	+	2.27230e7i	−0.664787	+	0.482996i
$362$			7.18518e7i			1.51465i
$363$	−1.48291e7	−	1.47671e7i	−0.310024	−	0.308728i
$364$	−1.83123e8			−3.79699
$365$	−2.54660e6	−	3.50510e6i	−0.0523700	−	0.0720811i
$366$	−556240.	−	1.71193e6i	−0.0113454	−	0.0349175i
$367$	2.28010e7	−	7.01743e7i	0.461271	−	1.41964i	−0.402342	−	0.915489i	$-0.631804\pi$
$367$	2.28010e7	−	7.01743e7i	0.461271	−	1.41964i	0.863613	−	0.504155i	$-0.168196\pi$
$368$	−6.82716e7	−	4.96022e7i	−1.36992	−	0.995308i
$369$	6.85468e6	−	9.43466e6i	0.136430	−	0.187779i
$370$	−1.46328e6	−	475450.i	−0.0288884	−	0.00938641i
$371$	−2.15077e7	+	6.98826e6i	−0.421184	+	0.136851i
$372$	−5.35327e7	+	3.88938e7i	−1.03990	+	0.755530i
$373$			1.36795e7i			0.263599i	0.991276	+	0.131799i	$0.0420754\pi$
$373$			1.36795e7i			0.263599i	−0.991276	+	0.131799i	$0.957925\pi$
$374$	7.21183e7	−	1.73940e7i	1.37858	−	0.332494i
$375$	−9.81418e6			−0.186106
$376$	4.35282e7	+	5.99115e7i	0.818856	+	1.12706i
$377$	−5.98506e6	−	1.84201e7i	−0.111698	−	0.343770i
$378$	3.97913e7	−	1.22465e8i	0.736738	−	2.26745i
$379$	6.80907e7	+	4.94708e7i	1.25075	+	0.908722i	0.998265	−	0.0588793i	$-0.0187527\pi$
$379$	6.80907e7	+	4.94708e7i	1.25075	+	0.908722i	0.252483	+	0.967601i	$0.418753\pi$
$380$	−6.59215e6	+	9.07332e6i	−0.120137	+	0.165354i
$381$	3.77056e6	+	1.22513e6i	0.0681759	+	0.0221517i
$382$	−2.77291e7	+	9.00975e6i	−0.497447	+	0.161630i
$383$	−2.49330e7	+	1.81149e7i	−0.443790	+	0.322433i	−0.787139	−	0.616775i	$-0.788439\pi$
$383$	−2.49330e7	+	1.81149e7i	−0.443790	+	0.322433i	0.343349	+	0.939208i	$0.388439\pi$
$384$		−	2.75311e7i		−	0.486217i
$385$	1.58818e7	+	1.35356e7i	0.278303	+	0.237189i
$386$	−1.25245e8			−2.17770
$387$	1.62815e6	+	2.24096e6i	0.0280907	+	0.0386635i
$388$	−3.23916e7	−	9.96910e7i	−0.554545	−	1.70671i
$389$	−1.31512e7	+	4.04752e7i	−0.223417	+	0.687607i	0.775031	+	0.631923i	$0.217734\pi$
$389$	−1.31512e7	+	4.04752e7i	−0.223417	+	0.687607i	−0.998448	+	0.0556843i	$0.982266\pi$
$390$	8.35867e6	+	6.07293e6i	0.140911	+	0.102377i
$391$	2.74005e7	−	3.77135e7i	0.458382	−	0.630909i
$392$	2.28389e8	+	7.42080e7i	3.79155	+	1.23195i
$393$	−3.18186e7	+	1.03385e7i	−0.524208	+	0.170326i
$394$	1.91646e7	−	1.39239e7i	0.313337	−	0.227653i
$395$		−	1.80487e7i		−	0.292856i
$396$	−5.83960e7	−	9.50700e7i	−0.940368	−	1.53094i
$397$	−6.57578e7			−1.05093			−0.525467	−	0.850814i	$-0.676109\pi$
$397$	−6.57578e7			−1.05093			−0.525467	+	0.850814i	$0.676109\pi$
$398$	−2.20962e7	−	3.04128e7i	−0.350484	−	0.482400i
$399$	6.08665e6	+	1.87328e7i	0.0958208	+	0.294906i
$400$	−3.23161e7	+	9.94588e7i	−0.504939	+	1.55404i
$401$	−1.88314e7	−	1.36818e7i	−0.292045	−	0.212183i	0.432109	−	0.901821i	$-0.357770\pi$
$401$	−1.88314e7	−	1.36818e7i	−0.292045	−	0.212183i	−0.724154	+	0.689638i	$0.757770\pi$
$402$	1.51181e7	−	2.08082e7i	0.232712	−	0.320300i
$403$	8.37837e7	+	2.72230e7i	1.28010	+	0.415930i
$404$	1.10641e8	−	3.59495e7i	1.67793	−	0.545192i
$405$	5.41329e6	−	3.93298e6i	0.0814884	−	0.0592048i
$406$			7.15933e7i			1.06978i
$407$	−405416.	+	5.22122e6i	−0.00601337	+	0.0774442i
$408$	−5.14965e7			−0.758224
$409$	−5.87769e7	−	8.08994e7i	−0.859086	−	1.18243i	−0.981787	−	0.189987i	$-0.939156\pi$
$409$	−5.87769e7	−	8.08994e7i	−0.859086	−	1.18243i	0.122701	−	0.992444i	$-0.460844\pi$
$410$	−2.39071e6	−	7.35786e6i	−0.0346877	−	0.106758i
$411$	−747056.	+	2.29920e6i	−0.0107604	+	0.0331171i
$412$	1.95671e8	+	1.42163e8i	2.79791	+	2.03280i
$413$	−1.02650e8	+	1.41285e8i	−1.45716	+	2.00561i
$414$	−9.66847e7	−	3.14148e7i	−1.36256	−	0.442724i
$415$	−1.46773e7	+	4.76894e6i	−0.205353	+	0.0667233i
$416$	5.25112e7	−	3.81516e7i	0.729410	−	0.529947i
$417$		−	2.84068e7i		−	0.391754i
$418$	5.11618e7	+	2.11292e7i	0.700515	+	0.289303i
$419$	5.78620e7			0.786595			0.393298	−	0.919411i	$-0.371334\pi$
$419$	5.78620e7			0.786595			0.393298	+	0.919411i	$0.371334\pi$
$420$	−1.54812e7	−	2.13081e7i	−0.208957	−	0.287605i
$421$	−1.00331e7	−	3.08786e7i	−0.134458	−	0.413820i	0.861047	−	0.508525i	$-0.169809\pi$
$421$	−1.00331e7	−	3.08786e7i	−0.134458	−	0.413820i	−0.995505	+	0.0947051i	$0.969809\pi$
$422$	6.60206e7	−	2.03191e8i	0.878501	−	2.70375i
$423$	3.14438e7	+	2.28452e7i	0.415445	+	0.301838i
$424$	2.59302e7	−	3.56899e7i	0.340180	−	0.468218i
$425$	−5.49414e7	−	1.78515e7i	−0.715703	−	0.232546i
$426$	2.12325e7	−	6.89885e6i	0.274645	−	0.0892377i
$427$	4.94238e6	−	3.59085e6i	0.0634823	−	0.0461226i
$428$			7.40907e7i			0.945002i
$429$	1.34238e7	−	3.25041e7i	0.170021	−	0.411686i
$430$	1.83761e6			0.0231125
$431$	6.25507e6	+	8.60936e6i	0.0781268	+	0.107532i	0.846292	−	0.532720i	$-0.178830\pi$
$431$	6.25507e6	+	8.60936e6i	0.0781268	+	0.107532i	−0.768165	+	0.640252i	$0.778830\pi$
$432$	3.38178e7	+	1.04080e8i	0.419463	+	1.29097i
$433$	−3.80265e7	+	1.17034e8i	−0.468406	+	1.44161i	0.386242	+	0.922398i	$0.373773\pi$
$433$	−3.80265e7	+	1.17034e8i	−0.468406	+	1.44161i	−0.854648	+	0.519208i	$0.826227\pi$
$434$	−2.63449e8	−	1.91407e8i	−3.22276	−	2.34147i
$435$	1.63737e6	−	2.25365e6i	0.0198921	−	0.0273791i
$436$	−3.25435e8	−	1.05740e8i	−3.92649	−	1.27579i
$437$	3.30800e7	−	1.07483e7i	0.396388	−	0.128794i
$438$	2.18351e7	−	1.58641e7i	0.259856	−	0.188796i
$439$		−	1.00256e8i		−	1.18500i	−0.805571	−	0.592500i	$-0.798141\pi$
$439$		−	1.00256e8i		−	1.18500i	0.805571	−	0.592500i	$-0.201859\pi$
$440$	−4.05846e7	−	3.15131e6i	−0.476435	−	0.0369941i
$441$	1.26035e8			1.46952
$442$	7.32748e7	+	1.00854e8i	0.848570	+	1.16796i
$443$	2.03309e7	+	6.25721e7i	0.233855	+	0.719730i	0.997271	+	0.0738241i	$0.0235203\pi$
$443$	2.03309e7	+	6.25721e7i	0.233855	+	0.719730i	−0.763417	+	0.645906i	$0.776480\pi$
$444$	2.04259e6	−	6.28643e6i	0.0233363	−	0.0718217i
$445$	2.43274e7	+	1.76749e7i	0.276068	+	0.200575i
$446$	−1.10346e8	+	1.51878e8i	−1.24380	+	1.71195i
$447$	5.45570e7	+	1.77267e7i	0.610841	+	0.198474i
$448$	1.80449e7	−	5.86313e6i	0.200687	−	0.0652072i
$449$	−560350.	+	407118.i	−0.00619042	+	0.00449760i	−0.590876	−	0.806762i	$-0.701218\pi$
$449$	−560350.	+	407118.i	−0.00619042	+	0.00449760i	0.584686	+	0.811260i	$0.301218\pi$
$450$			1.25981e8i			1.38251i
$451$	−2.24382e7	+	1.37825e7i	−0.244601	+	0.150244i
$452$	1.67016e8			1.80860
$453$	−2.29591e7	−	3.16004e7i	−0.246979	−	0.339937i
$454$	6.44521e7	+	1.98363e8i	0.688763	+	2.11979i
$455$	−1.08358e7	+	3.33492e7i	−0.115034	+	0.354039i
$456$	−3.10853e7	−	2.25848e7i	−0.327839	−	0.238189i
$457$	4.53132e7	−	6.23682e7i	0.474762	−	0.653454i	−0.502726	−	0.864446i	$-0.667669\pi$
$457$	4.53132e7	−	6.23682e7i	0.474762	−	0.653454i	0.977488	+	0.210992i	$0.0676695\pi$
$458$	9.21366e7	+	2.99370e7i	0.959037	+	0.311610i
$459$	−5.74944e7	+	1.86811e7i	−0.594549	+	0.193181i
$460$	−3.76276e7	+	2.73381e7i	−0.386574	+	0.280863i
$461$		−	5.69425e7i		−	0.581211i	−0.956843	−	0.290606i	$-0.906143\pi$
$461$		−	5.69425e7i		−	0.581211i	0.956843	−	0.290606i	$-0.0938568\pi$
$462$	−8.43203e7	+	9.89360e7i	−0.855079	+	1.00329i
$463$	−9.72255e7			−0.979574			−0.489787	−	0.871842i	$-0.662925\pi$
$463$	−9.72255e7			−0.979574			−0.489787	+	0.871842i	$0.662925\pi$
$464$	−3.57641e7	−	4.92251e7i	−0.358008	−	0.492756i
$465$	3.91543e6	+	1.20504e7i	0.0389422	+	0.119852i
$466$	−1.39456e7	+	4.29201e7i	−0.137809	+	0.424134i
$467$	−3.00278e7	−	2.18165e7i	−0.294831	−	0.214207i	0.430529	−	0.902577i	$-0.358327\pi$
$467$	−3.00278e7	−	2.18165e7i	−0.294831	−	0.214207i	−0.725360	+	0.688369i	$0.758327\pi$
$468$	1.10202e8	−	1.51679e8i	1.07510	−	1.47975i
$469$	8.30200e7	+	2.69748e7i	0.804756	+	0.261481i
$470$	2.45222e7	−	7.96775e6i	0.236192	−	0.0767436i
$471$	1.59740e7	−	1.16058e7i	0.152880	−	0.111074i
$472$		−	3.40674e8i		−	3.23977i
$473$	−1.46651e6	−	6.08037e6i	−0.0138580	−	0.0574575i
$474$	1.12435e8			1.05576
$475$	−2.53356e7	−	3.48715e7i	−0.236402	−	0.325379i
$476$	−9.82031e7	−	3.02238e8i	−0.910551	−	2.80239i
$477$	7.15475e6	−	2.20201e7i	0.0659234	−	0.202891i
$478$	−4.97775e7	−	3.61655e7i	−0.455774	−	0.331139i
$479$	1.20009e8	−	1.65178e8i	1.09196	−	1.50295i	0.246328	−	0.969187i	$-0.420776\pi$
$479$	1.20009e8	−	1.65178e8i	1.09196	−	1.50295i	0.845632	−	0.533767i	$-0.179224\pi$
$480$	8.87858e6	+	2.88483e6i	0.0802823	+	0.0260853i
$481$	−8.36943e6	+	2.71939e6i	−0.0752074	+	0.0244364i
$482$	−5.30119e7	+	3.85154e7i	−0.473405	+	0.343949i
$483$			8.16839e7i			0.724929i
$484$	3.99325e7	+	2.48750e8i	0.352201	+	2.19395i
$485$	−2.00717e7			−0.175938
$486$	1.20337e8	+	1.65630e8i	1.04831	+	1.44288i
$487$	3.14855e7	+	9.69023e7i	0.272598	+	0.838971i	0.989845	+	0.142152i	$0.0454022\pi$
$487$	3.14855e7	+	9.69023e7i	0.272598	+	0.838971i	−0.717246	+	0.696820i	$0.754598\pi$
$488$	−3.68266e6	+	1.13341e7i	−0.0316885	+	0.0975273i
$489$	−3.57277e7	−	2.59577e7i	−0.305547	−	0.221993i
$490$	4.91460e7	−	6.76436e7i	0.417734	−	0.574961i
$491$	−1.25607e8	−	4.08121e7i	−1.06113	−	0.344782i	−0.274103	−	0.961700i	$-0.588381\pi$
$491$	−1.25607e8	−	4.08121e7i	−1.06113	−	0.344782i	−0.787027	+	0.616918i	$0.788381\pi$
$492$	3.16102e7	−	1.02708e7i	0.265419	−	0.0862399i
$493$	2.71921e7	−	1.97562e7i	0.226935	−	0.164878i
$494$			9.30155e7i			0.771568i
$495$	−2.07689e7	+	5.00919e6i	−0.171237	+	0.0413002i
$496$	2.76755e8			2.26804
$497$	4.45361e7	+	6.12987e7i	0.362780	+	0.499323i
$498$	−2.97082e7	−	9.14325e7i	−0.240541	−	0.740308i
$499$	1.70149e7	−	5.23666e7i	0.136940	−	0.421457i	−0.858947	−	0.512064i	$-0.828881\pi$
$499$	1.70149e7	−	5.23666e7i	0.136940	−	0.421457i	0.995887	+	0.0906078i	$0.0288810\pi$
$500$	9.55823e7	+	6.94446e7i	0.764658	+	0.555557i
$501$	1.03341e7	−	1.42236e7i	0.0821784	−	0.113109i
$502$	−1.98969e8	−	6.46491e7i	−1.57281	−	0.511036i
$503$	−2.01206e8	+	6.53759e7i	−1.58102	+	0.513705i	−0.962319	−	0.271922i	$-0.912341\pi$
$503$	−2.01206e8	+	6.53759e7i	−1.58102	+	0.513705i	−0.618701	+	0.785627i	$0.712341\pi$
$504$	−3.08352e8	+	2.24031e8i	−2.40855	+	1.74991i
$505$		−	2.22764e7i		−	0.172970i
$506$	1.74710e8	+	1.48900e8i	1.34854	+	1.14932i
$507$	2.07462e6			0.0159190
$508$	−2.80533e7	−	3.86120e7i	−0.213990	−	0.294531i
$509$	−7.22816e7	−	2.22460e8i	−0.548118	−	1.68694i	−0.713458	−	0.700698i	$-0.752872\pi$
$509$	−7.22816e7	−	2.22460e8i	−0.548118	−	1.68694i	0.165339	−	0.986237i	$-0.447128\pi$
$510$	−5.54066e6	+	1.70524e7i	−0.0417687	+	0.128551i
$511$	7.41061e7	+	5.38412e7i	0.555381	+	0.403508i
$512$	−1.77006e8	+	2.43628e8i	−1.31880	+	1.81517i
$513$	−4.28988e7	−	1.39387e7i	−0.317755	−	0.103245i
$514$	−2.53054e8	+	8.22222e7i	−1.86348	+	0.605480i
$515$	3.74680e7	−	2.72221e7i	0.274308	−	0.199297i
$516$			7.89457e6i			0.0574618i
$517$	−4.59341e7	−	7.47817e7i	−0.332402	−	0.541157i
$518$	3.25294e7			0.234038
$519$	6.90671e6	+	9.50627e6i	0.0494048	+	0.0679999i
$520$	−2.11379e7	−	6.50558e7i	−0.150332	−	0.462675i
$521$	−7.81042e7	+	2.40380e8i	−0.552282	+	1.69975i	0.150732	+	0.988575i	$0.451837\pi$
$521$	−7.81042e7	+	2.40380e8i	−0.552282	+	1.69975i	−0.703014	+	0.711176i	$0.748163\pi$
$522$	−5.93001e7	−	4.30840e7i	−0.416911	−	0.302904i
$523$	7.77463e7	−	1.07009e8i	0.543469	−	0.748020i	−0.445639	−	0.895213i	$-0.647024\pi$
$523$	7.77463e7	−	1.07009e8i	0.543469	−	0.748020i	0.989108	+	0.147192i	$0.0470236\pi$
$524$	3.83043e8	+	1.24458e8i	2.66228	+	0.865027i
$525$	9.62714e7	−	3.12805e7i	0.665303	−	0.216170i
$526$	2.70367e8	−	1.96433e8i	1.85779	−	1.34977i
$527$			1.52881e8i			1.04453i
$528$	8.55265e6	−	1.10147e8i	0.0581031	−	0.748290i
$529$	−3.79147e6			−0.0256118
$530$	−9.02833e6	−	1.24264e7i	−0.0606429	−	0.0834678i
$531$	−5.52518e7	−	1.70048e8i	−0.369031	−	1.13576i
$532$	7.32731e7	−	2.25511e8i	0.486642	−	1.49773i
$533$	−3.57990e7	−	2.60095e7i	−0.236423	−	0.171771i
$534$	−1.10106e8	+	1.51548e8i	−0.723082	+	0.995237i
$535$	1.34929e7	+	4.38411e6i	0.0881138	+	0.0286299i
$536$	−1.61951e8	+	5.26211e7i	−1.05169	+	0.341716i
$537$	−277008.	+	201258.i	−0.00178883	+	0.00129966i
$538$		−	4.47545e8i		−	2.87402i
$539$	−2.63044e8	−	1.08634e8i	−1.67982	−	0.693742i
$540$	6.03155e7			0.383043
$541$	1.19188e8	+	1.64048e8i	0.752732	+	1.03605i	0.997784	+	0.0665372i	$0.0211951\pi$
$541$	1.19188e8	+	1.64048e8i	0.752732	+	1.03605i	−0.245052	+	0.969510i	$0.578805\pi$
$542$	7.48797e7	+	2.30456e8i	0.470291	+	1.44741i
$543$	−1.82655e7	+	5.62154e7i	−0.114086	+	0.351120i
$544$	9.11278e7	+	6.62082e7i	0.566049	+	0.411259i
$545$	−3.85133e7	+	5.30091e7i	−0.237915	+	0.327462i
$546$	−2.07749e8	−	6.75018e7i	−1.27633	−	0.414703i
$547$	2.75037e7	−	8.93651e6i	0.168047	−	0.0546017i	−0.223785	−	0.974638i	$-0.571841\pi$
$547$	2.75037e7	−	8.93651e6i	0.168047	−	0.0546017i	0.391832	+	0.920037i	$0.371841\pi$
$548$	2.35448e7	−	1.71063e7i	0.143071	−	0.103947i
$549$			6.25466e6i			0.0377996i
$550$	1.08587e8	−	2.62931e8i	0.652663	−	1.58035i
$551$	2.50787e7			0.149917
$552$	−9.36605e7	−	1.28913e8i	−0.556851	−	0.766440i
$553$	1.17918e8	+	3.62915e8i	0.697277	+	2.14600i
$554$	1.53951e8	−	4.73813e8i	0.905427	−	2.78662i
$555$	−1.02398e6	−	743963.i	−0.00598979	−	0.00435184i
$556$	−2.01005e8	+	2.76659e8i	−1.16945	+	1.60961i
$557$	3.19063e8	+	1.03670e8i	1.84634	+	0.599911i	0.997453	+	0.0713308i	$0.0227246\pi$
$557$	3.19063e8	+	1.03670e8i	1.84634	+	0.599911i	0.848883	+	0.528580i	$0.177275\pi$
$558$	3.17082e8	−	1.03026e8i	1.82502	−	0.592986i
$559$	8.50312e6	−	6.17788e6i	0.0486791	−	0.0353674i
$560$			1.10159e8i			0.627273i
$561$	6.08455e7	+	4.72452e6i	0.344620	+	0.0267590i
$562$	−4.84806e8			−2.73124
$563$	1.01207e8	+	1.39300e8i	0.567135	+	0.780594i	0.992212	−	0.124563i	$-0.0397530\pi$
$563$	1.01207e8	+	1.39300e8i	0.567135	+	0.780594i	−0.425077	+	0.905157i	$0.639753\pi$
$564$	3.42304e7	+	1.05350e8i	0.190798	+	0.587216i
$565$	9.88268e6	−	3.04157e7i	0.0547935	−	0.168637i
$566$	2.58627e8	+	1.87904e8i	1.42635	+	1.03630i
$567$	−8.31526e7	+	1.14450e8i	−0.456170	+	0.627864i
$568$	−1.40573e8	−	4.56748e7i	−0.767107	−	0.249248i
$569$	3.05387e8	−	9.92261e7i	1.65773	−	0.538628i	0.677334	−	0.735676i	$-0.263135\pi$
$569$	3.05387e8	−	9.92261e7i	1.65773	−	0.538628i	0.980394	+	0.197048i	$0.0631353\pi$
$570$	−1.08232e7	+	7.86352e6i	−0.0584428	+	0.0424612i
$571$			6.64211e7i			0.356778i	0.983960	+	0.178389i	$0.0570885\pi$
$571$			6.64211e7i			0.356778i	−0.983960	+	0.178389i	$0.942911\pi$
$572$	−3.60734e8	+	2.21578e8i	−1.92752	+	1.18397i
$573$	−2.39851e7			−0.127490
$574$	9.61430e7	+	1.32329e8i	0.508372	+	0.699714i
$575$	−5.52377e7	−	1.70004e8i	−0.290558	−	0.894244i
$576$	−6.00281e6	+	1.84748e7i	−0.0314114	+	0.0966744i
$577$	−2.85543e8	−	2.07459e8i	−1.48643	−	1.07995i	−0.975413	−	0.220383i	$-0.929269\pi$
$577$	−2.85543e8	−	2.07459e8i	−1.48643	−	1.07995i	−0.511016	−	0.859571i	$-0.670731\pi$
$578$	7.65751e7	−	1.05397e8i	0.396556	−	0.545812i
$579$	−9.79888e7	−	3.18385e7i	−0.504825	−	0.164027i
$580$	−3.18935e7	+	1.03628e7i	−0.163462	+	0.0531121i
$581$	2.63968e8	−	1.91784e8i	1.34593	−	0.977875i
$582$		−	1.25037e8i		−	0.634264i
$583$	−3.39121e7	+	3.97904e7i	−0.171139	+	0.200804i
$584$	−1.78689e8			−0.897136
$585$	−2.11020e7	−	2.90443e7i	−0.105404	−	0.145075i
$586$	−9.31850e7	−	2.86794e8i	−0.463077	−	1.42520i
$587$	−4.17005e7	+	1.28341e8i	−0.206171	+	0.634529i	0.793492	+	0.608580i	$0.208261\pi$
$587$	−4.17005e7	+	1.28341e8i	−0.206171	+	0.634529i	−0.999663	+	0.0259485i	$0.991739\pi$
$588$	2.90605e8	+	2.11137e8i	1.42946	+	1.03856i
$589$	−6.70487e7	+	9.22847e7i	−0.328129	+	0.451631i
$590$	−1.12810e8	−	3.66541e7i	−0.549276	−	0.178471i
$591$	1.85336e7	−	6.02193e6i	0.0897836	−	0.0291725i
$592$	−2.23661e7	+	1.62499e7i	−0.107801	+	0.0783224i
$593$		−	6.76612e7i		−	0.324471i	−0.986752	−	0.162236i	$-0.948130\pi$
$593$		−	6.76612e7i		−	0.324471i	0.986752	−	0.162236i	$-0.0518704\pi$
$594$	−6.97974e7	−	2.89391e8i	−0.333027	−	1.38079i
$595$	−6.08524e7			−0.288886
$596$	−4.05909e8	−	5.58686e8i	−1.91730	−	2.63894i
$597$	−9.55635e6	−	2.94114e7i	−0.0449127	−	0.138227i
$598$	−1.19200e8	+	3.66861e8i	−0.557410	+	1.71553i
$599$	1.88196e8	+	1.36733e8i	0.875651	+	0.636198i	0.932097	−	0.362208i	$-0.117977\pi$
$599$	1.88196e8	+	1.36733e8i	0.875651	+	0.636198i	−0.0564463	+	0.998406i	$0.517977\pi$
$600$	−1.16068e8	+	1.59753e8i	−0.537350	+	0.739598i
$601$	2.33411e8	+	7.58399e7i	1.07522	+	0.349361i	0.792519	−	0.609847i	$-0.208769\pi$
$601$	2.33411e8	+	7.58399e7i	1.07522	+	0.349361i	0.282703	+	0.959208i	$0.408769\pi$
$602$	−3.69499e7	+	1.20057e7i	−0.169365	+	0.0550300i
$603$	−7.23036e7	+	5.25316e7i	−0.329767	+	0.239590i
$604$			4.70220e8i			2.13398i
$605$	4.76636e7	+	7.44683e6i	0.215239	+	0.0336283i
$606$	1.38772e8			0.623567
$607$	2.39888e7	+	3.30177e7i	0.107261	+	0.147632i	0.859273	−	0.511517i	$-0.170916\pi$
$607$	2.39888e7	+	3.30177e7i	0.107261	+	0.147632i	−0.752012	+	0.659150i	$0.770916\pi$
$608$	2.59714e7	+	7.99317e7i	0.115554	+	0.355638i
$609$	−1.81997e7	+	5.60131e7i	−0.0805774	+	0.247992i
$610$	3.35690e6	+	2.43893e6i	0.0147893	+	0.0107451i
$611$	8.66841e7	−	1.19310e8i	0.380028	−	0.523064i
$612$	3.09439e8	+	1.00543e8i	1.34996	+	0.438628i
$613$	−2.46893e8	+	8.02203e7i	−1.07183	+	0.348259i	−0.791201	−	0.611556i	$-0.790544\pi$
$613$	−2.46893e8	+	8.02203e7i	−1.07183	+	0.348259i	−0.280631	+	0.959816i	$0.590544\pi$
$614$	−1.75587e8	+	1.27571e8i	−0.758554	+	0.551122i
$615$		−	6.36438e6i		−	0.0273609i
$616$	8.36648e8	−	2.01789e8i	3.57932	−	0.863285i
$617$	−1.66277e8			−0.707907			−0.353953	−	0.935263i	$-0.615163\pi$
$617$	−1.66277e8			−0.707907			−0.353953	+	0.935263i	$0.615163\pi$
$618$	1.69581e8	+	2.33408e8i	0.718474	+	0.988895i
$619$	−3.37805e7	−	1.03966e8i	−0.142428	−	0.438347i	0.854244	−	0.519873i	$-0.174021\pi$
$619$	−3.37805e7	−	1.03966e8i	−0.142428	−	0.438347i	−0.996671	+	0.0815256i	$0.974021\pi$
$620$	4.71351e7	−	1.45067e8i	0.197774	−	0.608687i
$621$	−1.51334e8	−	1.09951e8i	−0.631920	−	0.459117i
$622$	2.21847e8	−	3.05346e8i	0.921896	−	1.26888i
$623$	−6.04642e8	−	1.96460e8i	−2.50054	−	0.812475i
$624$	1.76561e8	−	5.73683e7i	0.726678	−	0.236112i
$625$	−1.69838e8	+	1.23394e8i	−0.695655	+	0.505423i
$626$			7.55332e8i			3.07904i
$627$	3.46567e7	+	2.95369e7i	0.140600	+	0.119829i
$628$	−2.37696e8			−0.959716
$629$	−8.97651e6	−	1.23551e7i	−0.0360708	−	0.0496472i
$630$	4.10083e7	+	1.26211e8i	0.164003	+	0.504748i
$631$	5.92325e7	−	1.82299e8i	0.235761	−	0.725597i	−0.761259	−	0.648448i	$-0.775418\pi$
$631$	5.92325e7	−	1.82299e8i	0.235761	−	0.725597i	0.997020	−	0.0771491i	$-0.0245818\pi$
$632$	−6.02223e8	−	4.37540e8i	−2.38565	−	1.73327i
$633$	1.03306e8	−	1.42189e8i	0.407301	−	0.560602i
$634$	5.27293e8	+	1.71328e8i	2.06911	+	0.672296i
$635$	−8.69173e6	+	2.82412e6i	−0.0339457	+	0.0110296i
$636$	5.33854e7	−	3.87868e7i	0.207516	−	0.150769i
$637$		−	4.78230e8i		−	1.85020i
$638$	8.66275e7	+	1.41031e8i	0.333575	+	0.543068i
$639$	−7.75745e7			−0.297315
$640$	3.73030e7	+	5.13432e7i	0.142300	+	0.195859i
$641$	−1.12047e7	−	3.44846e7i	−0.0425429	−	0.130934i	0.927529	−	0.373751i	$-0.121928\pi$
$641$	−1.12047e7	−	3.44846e7i	−0.0425429	−	0.130934i	−0.970072	+	0.242817i	$0.921928\pi$
$642$	−2.73109e7	+	8.40543e7i	−0.103212	+	0.317654i
$643$	2.38104e8	+	1.72993e8i	0.895641	+	0.650721i	0.937343	−	0.348409i	$-0.113278\pi$
$643$	2.38104e8	+	1.72993e8i	0.895641	+	0.650721i	−0.0417020	+	0.999130i	$0.513278\pi$
$644$	5.77991e8	−	7.95537e8i	2.16403	−	2.97853i
$645$	1.43771e6	+	467139.i	0.00535785	+	0.00174087i
$646$	−1.53518e8	+	4.98812e7i	−0.569460	+	0.185029i
$647$	2.35637e8	−	1.71200e8i	0.870023	−	0.632109i	−0.0605699	−	0.998164i	$-0.519292\pi$
$647$	2.35637e8	−	1.71200e8i	0.870023	−	0.632109i	0.930593	+	0.366055i	$0.119292\pi$
$648$		−	2.75968e8i		−	1.01422i
$649$	−3.12550e7	+	4.02523e8i	−0.114337	+	1.47250i
$650$	4.78024e8			1.74064
$651$	−1.57459e8	−	2.16724e8i	−0.570724	−	0.785534i
$652$	1.64284e8	+	5.05615e8i	0.592725	+	1.82422i
$653$	8.44943e7	−	2.60047e8i	0.303451	−	0.933925i	−0.676800	−	0.736167i	$-0.736634\pi$
$653$	8.44943e7	−	2.60047e8i	0.303451	−	0.933925i	0.980251	−	0.197758i	$-0.0633661\pi$
$654$	−3.30221e8	−	2.39920e8i	−1.18052	−	0.857695i
$655$	4.53309e7	−	6.23927e7i	0.161314	−	0.222029i
$656$	−1.32209e8	−	4.29574e7i	−0.468328	−	0.152169i
$657$	−8.91924e7	+	2.89804e7i	−0.314508	+	0.102190i
$658$	−4.41026e8	+	3.20424e8i	−1.54806	+	1.12473i
$659$			2.56471e8i			0.896151i	0.893996	+	0.448076i	$0.147891\pi$
$659$			2.56471e8i			0.896151i	−0.893996	+	0.448076i	$0.852109\pi$
$660$	−5.62791e7	−	2.32425e7i	−0.195756	−	0.0808448i
$661$	−8.26931e7			−0.286329			−0.143164	−	0.989699i	$-0.545728\pi$
$661$	−8.26931e7			−0.286329			−0.143164	+	0.989699i	$0.545728\pi$
$662$	−4.20358e8	−	5.78573e8i	−1.44892	−	1.99427i
$663$	3.16905e7	+	9.75333e7i	0.108740	+	0.334666i
$664$	−1.96687e8	+	6.05341e8i	−0.671850	+	2.06774i
$665$	−3.67329e7	−	2.66880e7i	−0.124908	−	0.0907509i
$666$	−1.95758e7	+	2.69438e7i	−0.0662670	+	0.0912087i
$667$	9.89126e7	+	3.21386e7i	0.333330	+	0.108305i
$668$	−2.01291e8	+	6.54034e7i	−0.675297	+	0.219417i
$669$	−1.24941e8	+	9.07752e7i	−0.417280	+	0.303172i
$670$			5.92896e7i			0.197131i
$671$	5.39107e6	−	1.30539e7i	0.0178446	−	0.0432087i
$672$	−1.97374e8			−0.650404
$673$	1.22022e8	+	1.67949e8i	0.400306	+	0.550974i	0.960821	−	0.277170i	$-0.0893966\pi$
$673$	1.22022e8	+	1.67949e8i	0.400306	+	0.550974i	−0.560514	+	0.828145i	$0.689397\pi$
$674$	7.45815e7	+	2.29538e8i	0.243585	+	0.749679i
$675$	−7.16335e7	+	2.20465e8i	−0.232919	+	0.716851i
$676$	−2.02052e7	−	1.46799e7i	−0.0654068	−	0.0475208i
$677$	−7.80037e6	+	1.07363e7i	−0.0251391	+	0.0346010i	−0.821402	−	0.570350i	$-0.806807\pi$
$677$	−7.80037e6	+	1.07363e7i	−0.0251391	+	0.0346010i	0.796262	+	0.604951i	$0.206807\pi$
$678$	1.89476e8	+	6.15643e7i	0.607945	+	0.197533i
$679$	4.03594e8	−	1.31136e8i	1.28924	−	0.418901i
$680$	9.60365e7	−	6.97746e7i	0.305429	−	0.221907i
$681$			1.71580e8i			0.543281i
$682$	−7.50570e8	−	5.82801e7i	−2.36613	−	0.183725i
$683$	2.10622e8			0.661062			0.330531	−	0.943795i	$-0.392772\pi$
$683$	2.10622e8			0.661062			0.330531	+	0.943795i	$0.392772\pi$
$684$	1.42694e8	+	1.96402e8i	0.445901	+	0.613729i
$685$	−1.72208e6	−	5.30003e6i	−0.00535775	−	0.0164895i
$686$	−2.45696e8	+	7.56175e8i	−0.761073	+	2.34234i
$687$	6.44754e7	+	4.68441e7i	0.198849	+	0.144472i
$688$	1.94080e7	−	2.67129e7i	0.0595959	−	0.0820267i
$689$	−8.35532e7	−	2.71481e7i	−0.255450	−	0.0830006i
$690$	−5.27649e7	+	1.71444e7i	−0.160619	+	0.0521884i
$691$	9.09446e7	−	6.60751e7i	0.275640	−	0.200264i	−0.441373	−	0.897324i	$-0.645509\pi$
$691$	9.09446e7	−	6.60751e7i	0.275640	−	0.200264i	0.717014	+	0.697059i	$0.245509\pi$
$692$		−	1.41455e8i		−	0.426874i
$693$	3.84886e8	−	2.36413e8i	1.15646	−	0.710350i
$694$	2.39551e8			0.716669
$695$	3.84894e7	+	5.29761e7i	0.114653	+	0.157807i
$696$	−3.55031e7	−	1.09267e8i	−0.105302	−	0.324088i
$697$	2.37298e7	−	7.30329e7i	0.0700803	−	0.215685i
$698$	5.14416e8	+	3.73745e8i	1.51268	+	1.09903i
$699$	−2.18214e7	+	3.00346e7i	−0.0638928	+	0.0879409i
$700$	−1.15895e9	−	3.76565e8i	−3.37885	−	1.09786i
$701$	3.87657e8	−	1.25957e8i	1.12537	−	0.365653i	0.313553	−	0.949571i	$-0.398481\pi$
$701$	3.87657e8	−	1.25957e8i	1.12537	−	0.365653i	0.811813	+	0.583917i	$0.198481\pi$
$702$	4.04700e8	−	2.94032e8i	1.16983	−	0.849930i
$703$		−	1.13948e7i		−	0.0327976i
$704$	2.84522e7	−	3.33840e7i	0.0815450	−	0.0956797i
$705$	2.12111e7			0.0605336
$706$	−6.96160e8	−	9.58183e8i	−1.97831	−	2.72292i
$707$	1.45540e8	+	4.47926e8i	0.411835	+	1.26750i
$708$	1.57470e8	−	4.84644e8i	0.443710	−	1.36560i
$709$	−3.84046e8	−	2.79026e8i	−1.07757	−	0.782899i	−0.100311	−	0.994956i	$-0.531984\pi$
$709$	−3.84046e8	−	2.79026e8i	−1.07757	−	0.782899i	−0.977257	+	0.212057i	$0.931984\pi$
$710$	−3.02492e7	+	4.16345e7i	−0.0845160	+	0.116326i
$711$	−3.71561e8	−	1.20728e8i	−1.03376	−	0.335890i
$712$	1.17950e9	−	3.83244e8i	3.26783	−	1.06178i
$713$	−3.82710e8	+	2.78055e8i	−1.05585	+	0.767119i
$714$		−	3.79081e8i		−	1.04145i
$715$	1.90069e7	+	7.88057e7i	0.0519988	+	0.215595i
$716$	4.12192e6			0.0112295
$717$	−2.97512e7	−	4.09491e7i	−0.0807137	−	0.111093i
$718$	−1.55443e8	−	4.78405e8i	−0.419950	−	1.29247i
$719$	1.10737e8	−	3.40813e8i	0.297924	−	0.916915i	−0.684300	−	0.729201i	$-0.739892\pi$
$719$	1.10737e8	−	3.40813e8i	0.297924	−	0.916915i	0.982224	−	0.187714i	$-0.0601079\pi$
$720$	−9.12439e7	−	6.62926e7i	−0.244459	−	0.177610i
$721$	−5.75540e8	+	7.92162e8i	−1.53557	+	2.11353i
$722$	5.27969e8	+	1.71548e8i	1.40280	+	0.455799i
$723$	−5.12664e7	+	1.66575e7i	−0.135649	+	0.0440752i
$724$	5.75668e8	−	4.18247e8i	1.51690	−	1.10209i
$725$		−	1.28884e8i		−	0.338209i
$726$	−4.63902e7	+	2.96921e8i	−0.121232	+	0.775946i
$727$	3.95260e8			1.02868			0.514339	−	0.857587i	$-0.328037\pi$
$727$	3.95260e8			1.02868			0.514339	+	0.857587i	$0.328037\pi$
$728$	8.50064e8	+	1.17001e9i	2.20322	+	3.03247i
$729$	−3.30917e6	−	1.01846e7i	−0.00854155	−	0.0262882i
$730$	−1.92256e7	+	5.91704e7i	−0.0494210	+	0.152102i
$731$	1.47563e7	+	1.07211e7i	0.0377768	+	0.0274465i
$732$	−1.04779e7	+	1.44216e7i	−0.0267142	+	0.0367689i
$733$	2.59901e8	+	8.44468e7i	0.659926	+	0.214423i	0.619786	−	0.784771i	$-0.287219\pi$
$733$	2.59901e8	+	8.44468e7i	0.659926	+	0.214423i	0.0401405	+	0.999194i	$0.487219\pi$
$734$	−1.00771e9	+	3.27423e8i	−2.54827	+	0.827983i
$735$	5.56465e7	−	4.04295e7i	0.140144	−	0.101821i
$736$			3.48540e8i			0.874218i
$737$	1.96180e8	−	4.73162e7i	0.490065	−	0.118197i
$738$	−1.67465e8			−0.416635
$739$	9.85608e6	+	1.35657e7i	0.0244214	+	0.0336132i	0.821053	−	0.570852i	$-0.193387\pi$
$739$	9.85608e6	+	1.35657e7i	0.0244214	+	0.0336132i	−0.796632	+	0.604465i	$0.793387\pi$
$740$	4.70848e6	+	1.44912e7i	0.0116195	+	0.0357610i
$741$	−2.36455e7	+	7.27733e7i	−0.0581157	+	0.178862i
$742$	2.62724e8	+	1.90880e8i	0.643115	+	0.467250i
$743$	−1.29122e8	+	1.77721e8i	−0.314799	+	0.433283i	−0.936870	−	0.349677i	$-0.886291\pi$
$743$	−1.29122e8	+	1.77721e8i	−0.314799	+	0.433283i	0.622072	+	0.782960i	$0.286291\pi$
$744$	4.97001e8	+	1.61485e8i	1.20681	+	0.392116i
$745$	−1.25763e8	+	4.08627e7i	−0.304146	+	0.0988232i
$746$	1.58922e8	−	1.15463e8i	0.382795	−	0.278117i
$747$			3.34055e8i			0.801414i
$748$	−5.59157e8	−	4.76553e8i	−1.33607	−	1.13869i
$749$	−2.99953e8			−0.713850
$750$	8.28377e7	+	1.14016e8i	0.196356	+	0.270261i
$751$	−2.72721e7	−	8.39348e7i	−0.0643870	−	0.198163i	0.913688	−	0.406417i	$-0.133222\pi$
$751$	−2.72721e7	−	8.39348e7i	−0.0643870	−	0.198163i	−0.978075	+	0.208254i	$0.933222\pi$
$752$	1.43168e8	−	4.40626e8i	0.336661	−	1.03613i
$753$	−1.39235e8	−	1.01160e8i	−0.326110	−	0.236933i
$754$	−1.63478e8	+	2.25009e8i	−0.381370	+	0.524911i
$755$	8.56333e7	+	2.78239e7i	0.198976	+	0.0646514i
$756$	−1.21280e9	+	3.94063e8i	−2.80688	+	0.912010i
$757$	−5.94353e8	+	4.31823e8i	−1.37011	+	0.995446i	−0.372386	+	0.928078i	$0.621460\pi$
$757$	−5.94353e8	+	4.31823e8i	−1.37011	+	0.995446i	−0.997728	+	0.0673685i	$0.978540\pi$
$758$		−	1.20861e9i		−	2.77510i
$759$	9.88372e7	+	1.60909e8i	0.226045	+	0.368006i
$760$	8.85723e7			0.201770
$761$	−1.45454e8	−	2.00200e8i	−0.330043	−	0.454265i	0.611457	−	0.791277i	$-0.290584\pi$
$761$	−1.45454e8	−	2.00200e8i	−0.330043	−	0.454265i	−0.941500	+	0.337012i	$0.890584\pi$
$762$	−1.75929e7	−	5.41454e7i	−0.0397624	−	0.122376i
$763$	4.28083e8	−	1.31751e9i	0.963729	−	2.96605i
$764$	2.33596e8	+	1.69717e8i	0.523823	+	0.380580i
$765$	3.66203e7	−	5.04035e7i	0.0817970	−	0.112584i
$766$	4.20900e8	+	1.36759e8i	0.936466	+	0.304276i
$767$	−6.45230e8	+	2.09648e8i	−1.42997	+	0.464627i
$768$	−2.99686e8	+	2.17735e8i	−0.661581	+	0.480667i
$769$			7.57156e7i			0.166497i	0.996529	+	0.0832485i	$0.0265295\pi$
$769$			7.57156e7i			0.166497i	−0.996529	+	0.0832485i	$0.973470\pi$
$770$	2.31977e7	−	2.98756e8i	0.0508128	−	0.654401i
$771$	−2.18886e8			−0.477589
$772$	7.29045e8	+	1.00344e9i	1.58454	+	2.18093i
$773$	−1.16918e8	−	3.59837e8i	−0.253130	−	0.779054i	−0.994192	−	0.107618i	$-0.965678\pi$
$773$	−1.16918e8	−	3.59837e8i	−0.253130	−	0.779054i	0.741062	−	0.671436i	$-0.234322\pi$
$774$	1.22918e7	−	3.78302e7i	0.0265089	−	0.0815859i
$775$	4.74269e8	+	3.44576e8i	1.01887	+	0.740253i
$776$	−4.86584e8	+	6.69725e8i	−1.04129	+	1.43322i
$777$	2.54503e7	+	8.26930e6i	0.0542538	+	0.0176281i
$778$	5.81226e8	−	1.88852e8i	1.23426	−	0.401035i
$779$	4.63542e7	−	3.36783e7i	0.0980566	−	0.0712423i
$780$		−	1.02319e8i		−	0.215612i
$781$	1.61903e8	+	6.68637e7i	0.339861	+	0.140358i
$782$	−6.69414e8			−1.39983
$783$	−7.92764e7	−	1.09115e8i	−0.165143	−	0.227299i
$784$	−4.64260e8	−	1.42885e9i	−0.963415	−	2.96509i
$785$	−1.40650e7	+	4.32876e7i	−0.0290757	+	0.0894858i
$786$	3.88677e8	+	2.82390e8i	0.800425	+	0.581543i
$787$	4.57413e8	−	6.29575e8i	0.938391	−	1.29158i	−0.0181035	−	0.999836i	$-0.505763\pi$
$787$	4.57413e8	−	6.29575e8i	0.938391	−	1.29158i	0.956495	−	0.291749i	$-0.0942371\pi$
$788$	−2.23113e8	−	7.24939e7i	−0.455981	−	0.148157i
$789$	2.61465e8	−	8.49552e7i	0.532332	−	0.172965i
$790$	−2.09681e8	+	1.52342e8i	−0.425282	+	0.308985i
$791$			6.76154e8i			1.36621i
$792$	−3.36346e8	+	8.14422e8i	−0.677034	+	1.63936i
$793$	2.37327e7			0.0475914
$794$	5.55036e8	+	7.63942e8i	1.10882	+	1.52616i
$795$	−3.90465e6	−	1.20173e7i	−0.00777107	−	0.0239169i
$796$	−1.15042e8	+	3.54064e8i	−0.228097	+	0.702009i
$797$	3.74864e7	+	2.72355e7i	0.0740456	+	0.0537973i	0.624192	−	0.781271i	$-0.285428\pi$
$797$	3.74864e7	+	2.72355e7i	0.0740456	+	0.0537973i	−0.550147	+	0.835068i	$0.685428\pi$
$798$	1.66253e8	−	2.28828e8i	0.327161	−	0.450299i
$799$	2.43403e8	+	7.90865e7i	0.477184	+	0.155047i
$800$	4.10784e8	−	1.33472e8i	0.802313	−	0.260687i
$801$	5.26593e8	−	3.82592e8i	1.02465	−	0.744455i
$802$			3.34257e8i			0.647974i
$803$	2.11129e8	+	1.63937e7i	0.407757	+	0.0316614i
$804$	−2.54715e8			−0.490102
$805$	−1.10677e8	−	1.52333e8i	−0.212162	−	0.292017i
$806$	−3.90923e8	−	1.20314e9i	−0.746597	−	2.29779i
$807$	1.13771e8	−	3.50150e8i	0.216476	−	0.666244i
$808$	−7.43290e8	−	5.40032e8i	−1.40904	−	1.02373i
$809$	−5.59606e8	+	7.70231e8i	−1.05691	+	1.45471i	−0.174243	+	0.984703i	$0.555748\pi$
$809$	−5.59606e8	+	7.70231e8i	−1.05691	+	1.45471i	−0.882664	+	0.470005i	$0.844252\pi$
$810$	−9.13830e7	−	2.96921e7i	−0.171953	−	0.0558710i
$811$	−1.83592e8	+	5.96528e7i	−0.344185	+	0.111833i	−0.476009	−	0.879441i	$-0.657917\pi$
$811$	−1.83592e8	+	5.96528e7i	−0.344185	+	0.111833i	0.131823	+	0.991273i	$0.457917\pi$
$812$	5.73596e8	−	4.16742e8i	1.07137	−	0.778394i
$813$			1.99339e8i			0.370955i
$814$	6.40796e7	−	3.93604e7i	0.118808	−	0.0729771i
$815$	1.01800e8			0.188051
$816$	1.89368e8	+	2.60643e8i	0.348528	+	0.479707i
$817$	4.20554e6	+	1.29433e7i	0.00771179	+	0.0237345i
$818$	−4.43737e8	+	1.36568e9i	−0.810711	+	2.49511i
$819$	6.14066e8	+	4.46145e8i	1.11780	+	0.812128i
$820$	−4.50340e7	+	6.19840e7i	−0.0816769	+	0.112419i
$821$	−6.46741e8	−	2.10139e8i	−1.16870	−	0.379732i	−0.340539	−	0.940230i	$-0.610610\pi$
$821$	−6.46741e8	−	2.10139e8i	−1.16870	−	0.379732i	−0.828156	+	0.560498i	$0.810610\pi$
$822$	3.30166e7	−	1.07278e7i	0.0594453	−	0.0193149i
$823$	−3.51602e8	+	2.55454e8i	−0.630742	+	0.458261i	−0.856657	−	0.515886i	$-0.827463\pi$
$823$	−3.51602e8	+	2.55454e8i	−0.630742	+	0.458261i	0.225915	+	0.974147i	$0.427463\pi$
$824$		−	1.91011e9i		−	3.41410i
$825$	1.51796e8	−	1.78107e8i	0.270332	−	0.317190i
$826$	2.50781e9			4.44994
$827$	−3.76706e8	−	5.18491e8i	−0.666017	−	0.916694i	0.333644	−	0.942699i	$-0.391722\pi$
$827$	−3.76706e8	−	5.18491e8i	−0.666017	−	0.916694i	−0.999662	+	0.0260046i	$0.991722\pi$
$828$	3.11107e8	+	9.57490e8i	0.548049	+	1.68672i
$829$	5.74825e7	−	1.76913e8i	0.100896	−	0.310525i	−0.887850	−	0.460134i	$-0.847801\pi$
$829$	5.74825e7	−	1.76913e8i	0.100896	−	0.310525i	0.988745	+	0.149609i	$0.0478015\pi$
$830$	1.79289e8	+	1.30261e8i	0.313558	+	0.227814i
$831$	2.40896e8	−	3.31565e8i	0.419785	−	0.577784i
$832$	7.01008e7	+	2.27771e7i	0.121717	+	0.0395484i
$833$	7.89300e8	−	2.56459e8i	1.36555	−	0.443694i
$834$	−3.30016e8	+	2.39771e8i	−0.568901	+	0.413331i
$835$			4.05278e7i			0.0696135i
$836$	−1.28527e8	−	5.32895e8i	−0.219977	−	0.912058i
$837$	6.13469e8			1.04620
$838$	−4.88391e8	−	6.72212e8i	−0.829919	−	1.14229i
$839$	1.12268e8	+	3.45525e8i	0.190094	+	0.585050i	0.999999	−	0.00151153i	$-0.000481136\pi$
$839$	1.12268e8	+	3.45525e8i	0.190094	+	0.585050i	−0.809905	+	0.586562i	$0.800481\pi$
$840$	−6.42774e7	+	1.97826e8i	−0.108448	+	0.333768i
$841$	−4.20556e8	−	3.05552e8i	−0.707026	−	0.513685i
$842$	−2.74048e8	+	3.77194e8i	−0.459081	+	0.631871i
$843$	−3.79302e8	−	1.23243e8i	−0.633144	−	0.205721i
$844$	−2.01224e9	+	6.53817e8i	−3.34698	+	1.08750i
$845$	−3.86899e6	+	2.81099e6i	−0.00641251	+	0.00465896i
$846$		−	5.58126e8i		−	0.921767i
$847$	−1.00705e9	+	1.61665e8i	−1.65730	+	0.266051i
$848$	−2.75994e8			−0.452597
$849$	1.54577e8	+	2.12758e8i	0.252594	+	0.347666i
$850$	2.56349e8	+	7.88961e8i	0.417421	+	1.28469i
$851$	1.46026e7	−	4.49423e7i	0.0236942	−	0.0729233i
$852$	−1.78866e8	−	1.29954e8i	−0.289208	−	0.210122i
$853$	2.42087e8	−	3.33204e8i	0.390054	−	0.536863i	−0.568159	−	0.822919i	$-0.692344\pi$
$853$	2.42087e8	−	3.33204e8i	0.390054	−	0.536863i	0.958213	+	0.286056i	$0.0923443\pi$
$854$	−8.34335e7	−	2.71092e7i	−0.133957	−	0.0435254i
$855$	4.42109e7	−	1.43650e7i	0.0707344	−	0.0229830i
$856$	4.73381e8	−	3.43932e8i	0.754727	−	0.548341i
$857$		−	1.13705e9i		−	1.80650i	−0.429116	−	0.903249i	$-0.641175\pi$
$857$		−	1.13705e9i		−	1.80650i	0.429116	−	0.903249i	$-0.358825\pi$
$858$	−4.90922e8	+	1.18404e8i	−0.777232	+	0.187458i
$859$	−1.16909e9			−1.84446			−0.922231	−	0.386640i	$-0.873636\pi$
$859$	−1.16909e9			−1.84446			−0.922231	+	0.386640i	$0.873636\pi$
$860$	−1.06967e7	−	1.47227e7i	−0.0168172	−	0.0231468i
$861$	4.15807e7	+	1.27972e8i	0.0651452	+	0.200496i
$862$	4.72228e7	−	1.45337e8i	0.0737275	−	0.226910i
$863$	−4.58958e8	−	3.33452e8i	−0.714069	−	0.518802i	0.170415	−	0.985372i	$-0.445489\pi$
$863$	−4.58958e8	−	3.33452e8i	−0.714069	−	0.518802i	−0.884484	+	0.466571i	$0.845489\pi$
$864$	2.65676e8	−	3.65671e8i	0.411918	−	0.566956i
$865$	−2.57608e7	−	8.37020e6i	−0.0398026	−	0.0129326i
$866$	1.68061e9	−	5.46062e8i	2.58769	−	0.840791i
$867$	8.67037e7	−	6.29939e7i	0.133039	−	0.0966588i
$868$			3.22490e9i			4.93125i
$869$	6.71412e8	+	5.72225e8i	1.02313	+	0.871982i
$870$	−4.00023e7			−0.0607473
$871$	1.99326e8	+	2.74349e8i	0.301655	+	0.415192i
$872$	8.35083e8	+	2.57012e9i	1.25945	+	3.87618i
$873$	−1.34260e8	+	4.13209e8i	−0.201792	+	0.621051i
$874$	−4.04084e8	−	2.93584e8i	−0.605254	−	0.439743i
$875$	−2.81143e8	+	3.86960e8i	−0.419665	+	0.577619i
$876$	−2.54203e8	−	8.25955e7i	−0.378153	−	0.122869i
$877$	5.11706e7	−	1.66263e7i	0.0758615	−	0.0246489i	−0.270840	−	0.962624i	$-0.587302\pi$
$877$	5.11706e7	−	1.66263e7i	0.0758615	−	0.0246489i	0.346702	+	0.937975i	$0.387302\pi$
$878$	−1.16473e9	+	8.46225e8i	−1.72084	+	1.25027i
$879$		−	2.48070e8i		−	0.365265i
$880$	1.33292e8	+	2.17003e8i	0.195595	+	0.318432i
$881$	3.03084e8			0.443236			0.221618	−	0.975134i	$-0.428866\pi$
$881$	3.03084e8			0.443236			0.221618	+	0.975134i	$0.428866\pi$
$882$	−1.06382e9	−	1.46422e9i	−1.55046	−	2.13403i
$883$	1.82533e8	+	5.61779e8i	0.265131	+	0.815988i	0.991663	+	0.128856i	$0.0411305\pi$
$883$	1.82533e8	+	5.61779e8i	0.265131	+	0.815988i	−0.726533	+	0.687132i	$0.758869\pi$
$884$	3.81500e8	−	1.17414e9i	0.552253	−	1.69966i
$885$	−7.89422e7	−	5.73548e7i	−0.113888	−	0.0827447i
$886$	5.55327e8	−	7.64342e8i	0.798450	−	1.09897i
$887$	−1.27327e8	−	4.13712e7i	−0.182453	−	0.0592825i	0.216366	−	0.976312i	$-0.430580\pi$
$887$	−1.27327e8	−	4.13712e7i	−0.182453	−	0.0592825i	−0.398819	+	0.917030i	$0.630580\pi$
$888$	−4.96471e7	+	1.61313e7i	−0.0709014	+	0.0230373i
$889$	1.56319e8	−	1.13572e8i	0.222488	−	0.161647i
$890$		−	4.31811e8i		−	0.612525i
$891$	−2.53185e7	+	3.26069e8i	−0.0357936	+	0.460973i
$892$	1.85915e9			2.61951
$893$	1.12243e8	+	1.54489e8i	0.157617	+	0.216942i
$894$	−2.54555e8	−	7.83441e8i	−0.356262	−	1.09646i
$895$	243903.	−	750656.i	0.000340211	−	0.00104706i
$896$	−1.08552e9	−	7.88674e8i	−1.50908	−	1.09641i
$897$	−1.86520e8	+	2.56723e8i	−0.258433	+	0.355702i
$898$	9.45940e6	+	3.07354e6i	0.0130627	+	0.00424434i
$899$	−3.24388e8	+	1.05400e8i	−0.446463	+	0.145065i
$900$	1.00935e9	−	7.33333e8i	1.38456	−	1.00594i
$901$		−	1.52460e8i		−	0.208440i
$902$	3.49510e8	+	1.44343e8i	0.476256	+	0.196687i
$903$	−3.19608e7			−0.0434064
$904$	−7.75292e8	−	1.06710e9i	−1.04945	−	1.44444i
$905$	−4.21048e7	−	1.29585e8i	−0.0568049	−	0.174828i
$906$	−1.73330e8	+	5.33454e8i	−0.233071	+	0.717319i
$907$	−1.36246e8	−	9.89889e7i	−0.182601	−	0.132667i	0.492730	−	0.870182i	$-0.335999\pi$
$907$	−1.36246e8	−	9.89889e7i	−0.182601	−	0.132667i	−0.675331	+	0.737515i	$0.735999\pi$
$908$	1.21409e9	−	1.67105e9i	1.62178	−	2.23219i
$909$	−4.58597e8	−	1.49007e8i	−0.610576	−	0.198388i
$910$	4.78895e8	−	1.55602e8i	0.635501	−	0.206487i
$911$	4.57871e6	−	3.32663e6i	0.00605603	−	0.00439997i	−0.584753	−	0.811211i	$-0.698809\pi$
$911$	4.57871e6	−	3.32663e6i	0.00605603	−	0.00439997i	0.590809	+	0.806811i	$0.298809\pi$
$912$			2.40386e8i			0.316901i
$913$	2.87932e8	−	6.97194e8i	0.378336	−	0.916097i
$914$	−1.10703e9			−1.44985
$915$	2.00636e6	+	2.76152e6i	0.00261907	+	0.00360484i
$916$	−2.96473e8	−	9.12449e8i	−0.385743	−	1.18720i
$917$	−5.03862e8	+	1.55073e9i	−0.653437	+	2.01107i
$918$	7.02316e8	+	5.10262e8i	0.907830	+	0.659577i
$919$	5.60294e8	−	7.71178e8i	0.721887	−	0.993592i	−0.277572	−	0.960705i	$-0.589530\pi$
$919$	5.60294e8	−	7.71178e8i	0.721887	−	0.993592i	0.999459	−	0.0328871i	$-0.0104702\pi$
$920$	3.49337e8	+	1.13507e8i	0.448623	+	0.145766i
$921$	−1.69805e8	+	5.51730e7i	−0.217356	+	0.0706233i
$922$	−6.61531e8	+	4.80630e8i	−0.844029	+	0.613223i
$923$			2.94349e8i			0.374333i
$924$	1.28349e9	+	9.96601e7i	1.62696	+	0.126330i
$925$	−5.85603e7			−0.0739908
$926$	8.20643e8	+	1.12952e9i	1.03353	+	1.42253i
$927$	−3.09788e8	−	9.53429e8i	−0.388889	−	1.19688i
$928$	−7.76572e7	+	2.39004e8i	−0.0971712	+	0.299062i
$929$	9.92668e8	+	7.21216e8i	1.23810	+	0.899535i	0.997471	−	0.0710813i	$-0.0226450\pi$
$929$	9.92668e8	+	7.21216e8i	1.23810	+	0.899535i	0.240633	+	0.970616i	$0.422645\pi$
$930$	1.06948e8	−	1.47201e8i	0.132960	−	0.183004i
$931$	5.88927e8	+	1.91354e8i	0.729815	+	0.237131i
$932$	4.25047e8	−	1.38106e8i	0.525036	−	0.170595i
$933$	2.51190e8	−	1.82500e8i	0.309284	−	0.224708i
$934$			5.32993e8i			0.654156i
$935$	−1.19873e8	+	7.36311e7i	−0.146652	+	0.0900797i
$936$	−1.48067e9			−1.80564
$937$	4.01964e8	+	5.53256e8i	0.488617	+	0.672523i	0.980132	−	0.198346i	$-0.0635568\pi$
$937$	4.01964e8	+	5.53256e8i	0.488617	+	0.672523i	−0.491515	+	0.870869i	$0.663557\pi$
$938$	−3.87360e8	−	1.19217e9i	−0.469360	−	1.44454i
$939$	−1.92013e8	+	5.90956e8i	−0.231918	+	0.713770i
$940$	−2.06580e8	−	1.50089e8i	−0.248716	−	0.180703i
$941$	8.33851e7	−	1.14770e8i	0.100074	−	0.137739i	−0.756044	−	0.654521i	$-0.772870\pi$
$941$	8.33851e7	−	1.14770e8i	0.100074	−	0.137739i	0.856117	+	0.516782i	$0.172870\pi$
$942$	−2.69661e8	−	8.76181e7i	−0.322601	−	0.104819i
$943$	2.25984e8	−	7.34268e7i	0.269490	−	0.0875627i
$944$	−1.72428e9	+	1.25276e9i	−2.04971	+	1.48920i
$945$			2.44184e8i			0.289349i
$946$	−5.82606e7	+	6.83593e7i	−0.0688179	+	0.0807465i
$947$	2.03019e8			0.239049			0.119524	−	0.992831i	$-0.461863\pi$
$947$	2.03019e8			0.239049			0.119524	+	0.992831i	$0.461863\pi$
$948$	−6.54478e8	−	9.00812e8i	−0.768192	−	1.05733i
$949$	1.09963e8	+	3.38432e8i	0.128662	+	0.395980i
$950$	−1.91272e8	+	5.88674e8i	−0.223090	+	0.686600i
$951$	3.68990e8	+	2.68087e8i	0.429015	+	0.311698i
$952$	−1.47520e9	+	2.03044e9i	−1.70978	+	2.35331i
$953$	3.95322e8	+	1.28448e8i	0.456743	+	0.148405i	0.528347	−	0.849028i	$-0.322812\pi$
$953$	3.95322e8	+	1.28448e8i	0.456743	+	0.148405i	−0.0716043	+	0.997433i	$0.522812\pi$
$954$	−3.16209e8	+	1.02743e8i	−0.364191	+	0.118333i
$955$	4.47301e7	−	3.24983e7i	0.0513558	−	0.0373122i
$956$			6.09330e8i			0.697395i
$957$	3.19239e7	+	1.32362e8i	0.0364234	+	0.151017i
$958$	−2.93191e9			−3.33467
$959$	6.92539e7	+	9.53198e7i	0.0785214	+	0.108075i
$960$	3.27599e6	+	1.00824e7i	0.00370278	+	0.0113960i
$961$	2.05158e8	−	6.31410e8i	0.231163	−	0.711445i
$962$	1.02236e8	+	7.42787e7i	0.114836	+	0.0834332i
$963$	1.80508e8	−	2.48448e8i	0.202124	−	0.278200i
$964$	6.17162e8	+	2.00528e8i	0.688918	+	0.223843i
$965$	2.25880e8	−	7.33927e7i	0.251359	−	0.0816716i
$966$	9.48964e8	−	6.89463e8i	1.05273	−	0.764856i
$967$			6.96144e8i			0.769874i	0.922943	+	0.384937i	$0.125777\pi$
$967$			6.96144e8i			0.769874i	−0.922943	+	0.384937i	$0.874223\pi$
$968$	1.40395e9	−	1.40984e9i	1.54784	−	1.55434i
$969$	−1.32790e8			−0.145947
$970$	1.69418e8	+	2.33183e8i	0.185628	+	0.255495i
$971$	−7.58461e7	−	2.33430e8i	−0.0828467	−	0.254976i	0.901050	−	0.433716i	$-0.142798\pi$
$971$	−7.58461e7	−	2.33430e8i	−0.0828467	−	0.254976i	−0.983896	+	0.178740i	$0.942798\pi$
$972$	6.26528e8	−	1.92825e9i	0.682247	−	2.09974i
$973$	−1.12004e9	−	8.13757e8i	−1.21589	−	0.883398i
$974$	8.60007e8	−	1.18370e9i	0.930733	−	1.28104i
$975$	3.73996e8	+	1.21519e8i	0.403509	+	0.131108i
$976$	7.09082e7	−	2.30395e7i	0.0762689	−	0.0247813i
$977$	4.81470e8	−	3.49808e8i	0.516280	−	0.375100i	−0.298920	−	0.954278i	$-0.596627\pi$
$977$	4.81470e8	−	3.49808e8i	0.516280	−	0.375100i	0.815201	+	0.579178i	$0.196627\pi$
$978$			6.34166e8i			0.677933i
$979$	−1.42880e9	+	3.44608e8i	−1.52273	+	0.367263i
$980$	−8.28030e8			−0.879767
$981$	8.33662e8	+	1.14744e9i	0.883046	+	1.21541i
$982$	5.86064e8	+	1.80372e9i	0.618886	+	1.90473i
$983$	2.90900e8	−	8.95299e8i	0.306255	−	0.942557i	−0.672951	−	0.739687i	$-0.734973\pi$
$983$	2.90900e8	−	8.95299e8i	0.306255	−	0.942557i	0.979206	−	0.202869i	$-0.0650266\pi$
$984$	−2.12358e8	−	1.54287e8i	−0.222886	−	0.161936i
$985$	−2.64042e7	+	3.63422e7i	−0.0276289	+	0.0380280i
$986$	−4.59037e8	−	1.49150e8i	−0.478869	−	0.155594i
$987$	−4.26505e8	+	1.38580e8i	−0.443581	+	0.144128i
$988$	7.45228e8	−	5.41440e8i	0.772714	−	0.561409i
$989$			5.64390e7i			0.0583433i
$990$	2.33497e8	+	1.99002e8i	0.240644	+	0.205094i
$991$	−9.35613e8			−0.961336			−0.480668	−	0.876903i	$-0.659606\pi$
$991$	−9.35613e8			−0.961336			−0.480668	+	0.876903i	$0.659606\pi$
$992$	−6.71870e8	−	9.24750e8i	−0.688256	−	0.947303i
$993$	−1.81800e8	−	5.59522e8i	−0.185672	−	0.571439i
$994$	3.36226e8	−	1.03480e9i	0.342351	−	1.05365i
$995$	5.76724e7	+	4.19015e7i	0.0585462	+	0.0425363i
$996$	−5.59615e8	+	7.70244e8i	−0.566385	+	0.779562i
$997$	9.06615e8	+	2.94577e8i	0.914824	+	0.297244i	0.728342	−	0.685214i	$-0.240291\pi$
$997$	9.06615e8	+	2.94577e8i	0.914824	+	0.297244i	0.186482	+	0.982458i	$0.440291\pi$
$998$	−7.51986e8	+	2.44335e8i	−0.756516	+	0.245807i
$999$	−4.95777e7	+	3.60203e7i	−0.0497268	+	0.0361286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.8.1	yes	20
3.2	odd	2		99.7.k.a.19.5		20
11.2	odd	10		121.7.b.c.120.2		20
11.7	odd	10	inner	11.7.d.a.7.1	✓	20
11.9	even	5		121.7.b.c.120.19		20
33.29	even	10		99.7.k.a.73.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.7.1	✓	20	11.7	odd	10	inner
11.7.d.a.8.1	yes	20	1.1	even	1	trivial
99.7.k.a.19.5		20	3.2	odd	2
99.7.k.a.73.5		20	33.29	even	10
121.7.b.c.120.2		20	11.2	odd	10
121.7.b.c.120.19		20	11.9	even	5

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)

\(f(q)\)	\(=\)	\(q+(-8.44062 - 11.6175i) q^{2} +(-3.65047 - 11.2350i) q^{3} +(-43.9455 + 135.250i) q^{4} +(22.0305 + 16.0061i) q^{5} +(-99.7104 + 137.240i) q^{6} +(-547.554 - 177.911i) q^{7} +(1068.14 - 347.060i) q^{8} +(476.874 - 346.469i) q^{9} +O(q^{10})\)	\(q+(-8.44062 - 11.6175i) q^{2} +(-3.65047 - 11.2350i) q^{3} +(-43.9455 + 135.250i) q^{4} +(22.0305 + 16.0061i) q^{5} +(-99.7104 + 137.240i) q^{6} +(-547.554 - 177.911i) q^{7} +(1068.14 - 347.060i) q^{8} +(476.874 - 346.469i) q^{9} -391.041i q^{10} +(-1293.90 + 312.071i) q^{11} +1679.96 q^{12} +(-1314.65 - 1809.46i) q^{13} +(2554.81 + 7862.90i) q^{14} +(99.4068 - 305.943i) q^{15} +(-5684.48 - 4130.01i) q^{16} +(2281.44 - 3140.13i) q^{17} +(-8050.23 - 2615.68i) q^{18} +(2754.33 - 894.935i) q^{19} +(-3132.98 + 2276.24i) q^{20} +6801.23i q^{21} +(14546.8 + 12397.8i) q^{22} +12010.2 q^{23} +(-7798.42 - 10733.6i) q^{24} +(-4599.24 - 14155.0i) q^{25} +(-9924.95 + 30545.9i) q^{26} +(-12600.5 - 9154.79i) q^{27} +(48125.1 - 66238.5i) q^{28} +(8235.73 + 2675.95i) q^{29} +(-4393.35 + 1427.49i) q^{30} +(-31865.5 + 23151.6i) q^{31} +29020.4i q^{32} +(8229.45 + 13397.7i) q^{33} -55737.2 q^{34} +(-9215.24 - 12683.7i) q^{35} +(25903.6 + 79723.2i) q^{36} +(1215.85 - 3742.02i) q^{37} +(-33645.1 - 24444.6i) q^{38} +(-15530.1 + 21375.4i) q^{39} +(29086.8 + 9450.86i) q^{40} +(18816.1 - 6113.71i) q^{41} +(79013.3 - 57406.6i) q^{42} +4699.27i q^{43} +(14653.3 - 188714. i) q^{44} +16051.4 q^{45} +(-101373. - 139528. i) q^{46} +(20375.7 + 62710.0i) q^{47} +(-25649.7 + 78941.5i) q^{48} +(172983. + 125680. i) q^{49} +(-125626. + 172909. i) q^{50} +(-43607.6 - 14169.0i) q^{51} +(302503. - 98289.0i) q^{52} +(31777.8 - 23087.9i) q^{53} +223658. i q^{54} +(-33500.3 - 13835.2i) q^{55} -646610. q^{56} +(-20109.2 - 27677.9i) q^{57} +(-38426.8 - 118265. i) q^{58} +(93734.6 - 288486. i) q^{59} +(37010.4 + 26889.6i) q^{60} +(-6237.01 + 8584.50i) q^{61} +(537929. + 174784. i) q^{62} +(-322755. + 104870. i) q^{63} +(-26661.5 + 19370.7i) q^{64} -60905.7i q^{65} +(86186.6 - 208691. i) q^{66} -151620. q^{67} +(324445. + 446560. i) q^{68} +(-43842.8 - 134934. i) q^{69} +(-69570.6 + 214116. i) q^{70} +(-106471. - 77355.5i) q^{71} +(389123. - 535582. i) q^{72} +(-151315. - 49165.2i) q^{73} +(-53735.5 + 17459.7i) q^{74} +(-142242. + 103345. i) q^{75} +411852. i q^{76} +(764000. + 59322.9i) q^{77} +379413. q^{78} +(-389580. - 536210. i) q^{79} +(-59126.5 - 181973. i) q^{80} +(75930.9 - 233691. i) q^{81} +(-229845. - 166992. i) q^{82} +(-333113. + 458490. i) q^{83} +(-919869. - 298883. i) q^{84} +(100522. - 32661.7i) q^{85} +(54593.8 - 39664.7i) q^{86} -102297. i q^{87} +(-1.27376e6 + 782396. i) q^{88} +1.10426e6 q^{89} +(-135484. - 186478. i) q^{90} +(397918. + 1.22467e6i) q^{91} +(-527794. + 1.62438e6i) q^{92} +(376432. + 273494. i) q^{93} +(556551. - 766026. i) q^{94} +(75003.7 + 24370.2i) q^{95} +(326044. - 105938. i) q^{96} +(-596314. + 433247. i) q^{97} -3.07045e6i q^{98} +(-508904. + 597115. 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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