LMFDB - Embedded newform 11.7.d.a.2.1

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			2.1
Root			$14.6250i$ of defining polynomial
Character	$\chi$	$=$	11.2
Dual form			11.7.d.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.7912 - 4.15611i) q^{2} +(0.366417 - 0.266218i) q^{3} +(94.5639 + 68.7047i) q^{4} +(50.5827 + 155.677i) q^{5} +(-5.79334 + 1.88237i) q^{6} +(50.6754 - 69.7488i) q^{7} +(-418.095 - 575.459i) q^{8} +(-225.210 + 693.125i) q^{9} +O(q^{10})$	\(q+(-12.7912 - 4.15611i) q^{2} +(0.366417 - 0.266218i) q^{3} +(94.5639 + 68.7047i) q^{4} +(50.5827 + 155.677i) q^{5} +(-5.79334 + 1.88237i) q^{6} +(50.6754 - 69.7488i) q^{7} +(-418.095 - 575.459i) q^{8} +(-225.210 + 693.125i) q^{9} -2201.52i q^{10} +(-990.819 + 888.729i) q^{11} +52.9403 q^{12} +(3651.66 + 1186.50i) q^{13} +(-938.082 + 681.556i) q^{14} +(59.9785 + 43.5769i) q^{15} +(644.571 + 1983.78i) q^{16} +(-5292.88 + 1719.76i) q^{17} +(5761.40 - 7929.89i) q^{18} +(-3017.45 - 4153.17i) q^{19} +(-5912.48 + 18196.7i) q^{20} -39.0479i q^{21} +(16367.4 - 7249.94i) q^{22} +10819.1 q^{23} +(-306.395 - 99.5537i) q^{24} +(-9035.96 + 6565.01i) q^{25} +(-41777.8 - 30353.4i) q^{26} +(204.031 + 627.944i) q^{27} +(9584.14 - 3114.07i) q^{28} +(7982.55 - 10987.0i) q^{29} +(-586.085 - 806.677i) q^{30} +(-6689.73 + 20588.9i) q^{31} +17469.8i q^{32} +(-126.458 + 589.419i) q^{33} +74849.7 q^{34} +(13421.6 + 4360.94i) q^{35} +(-68917.7 + 50071.6i) q^{36} +(9088.66 + 6603.30i) q^{37} +(21335.8 + 65664.8i) q^{38} +(1653.90 - 537.384i) q^{39} +(68437.6 - 94196.2i) q^{40} +(-13734.7 - 18904.2i) q^{41} +(-162.287 + 499.468i) q^{42} -94150.7i q^{43} +(-154756. + 15967.7i) q^{44} -119296. q^{45} +(-138389. - 44965.3i) q^{46} +(151191. - 109847. i) q^{47} +(764.301 + 555.297i) q^{48} +(34058.7 + 104822. i) q^{49} +(142865. - 46419.8i) q^{50} +(-1481.57 + 2039.21i) q^{51} +(263798. + 363086. i) q^{52} +(15463.5 - 47591.8i) q^{53} -8880.12i q^{54} +(-188473. - 109294. i) q^{55} -61324.7 q^{56} +(-2211.29 - 718.493i) q^{57} +(-147770. + 107361. i) q^{58} +(8389.87 + 6095.60i) q^{59} +(2677.86 + 8241.60i) q^{60} +(-62625.2 + 20348.2i) q^{61} +(171139. - 235553. i) q^{62} +(36932.0 + 50832.5i) q^{63} +(113859. - 350421. i) q^{64} +628497. i q^{65} +(4067.23 - 7013.79i) q^{66} +366915. q^{67} +(-618672. - 201019. i) q^{68} +(3964.30 - 2880.23i) q^{69} +(-153554. - 111563. i) q^{70} +(-17496.3 - 53848.1i) q^{71} +(493024. - 160193. i) q^{72} +(-238637. + 328456. i) q^{73} +(-88810.6 - 122237. i) q^{74} +(-1563.21 + 4811.07i) q^{75} -600053. i q^{76} +(11777.5 + 114145. i) q^{77} -23388.7 q^{78} +(368663. + 119786. i) q^{79} +(-276226. + 200690. i) q^{80} +(-429582. - 312110. i) q^{81} +(97115.2 + 298890. i) q^{82} +(29182.3 - 9481.89i) q^{83} +(2682.77 - 3692.52i) q^{84} +(-535456. - 736992. i) q^{85} +(-391300. + 1.20430e6i) q^{86} -6150.94i q^{87} +(925684. + 198602. i) q^{88} +279184. q^{89} +(1.52593e6 + 495805. i) q^{90} +(267806. - 194573. i) q^{91} +(1.02310e6 + 743323. i) q^{92} +(3029.89 + 9325.05i) q^{93} +(-2.39045e6 + 776703. i) q^{94} +(493924. - 679828. i) q^{95} +(4650.76 + 6401.22i) q^{96} +(-112496. + 346226. i) q^{97} -1.48234e6i q^{98} +(-392858. - 886912. 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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−12.7912	−	4.15611i	−1.59890	−	0.519513i	−0.632063	−	0.774917i	$-0.717792\pi$
$2$	−12.7912	−	4.15611i	−1.59890	−	0.519513i	−0.966834	+	0.255404i	$0.917792\pi$
$3$	0.366417	−	0.266218i	0.0135710	−	0.00985992i	−0.580979	−	0.813918i	$-0.697330\pi$
$3$	0.366417	−	0.266218i	0.0135710	−	0.00985992i	0.594550	+	0.804059i	$0.297330\pi$
$4$	94.5639	+	68.7047i	1.47756	+	1.07351i
$5$	50.5827	+	155.677i	0.404661	+	1.24542i	0.921178	+	0.389142i	$0.127228\pi$
$5$	50.5827	+	155.677i	0.404661	+	1.24542i	−0.516516	+	0.856277i	$0.672772\pi$
$6$	−5.79334	+	1.88237i	−0.0268210	+	0.00871467i
$7$	50.6754	−	69.7488i	0.147742	−	0.203349i	−0.728732	−	0.684799i	$-0.759890\pi$
$7$	50.6754	−	69.7488i	0.147742	−	0.203349i	0.876473	+	0.481450i	$0.159890\pi$
$8$	−418.095	−	575.459i	−0.816592	−	1.12394i
$9$	−225.210	+	693.125i	−0.308930	+	0.950789i
$10$		−	2201.52i		−	2.20152i
$11$	−990.819	+	888.729i	−0.744417	+	0.667715i
$11$	−990.819	+	888.729i	−0.744417	+	0.667715i
$12$	52.9403			0.0306367
$13$	3651.66	+	1186.50i	1.66211	+	0.540053i	0.981313	−	0.192417i	$-0.0616325\pi$
$13$	3651.66	+	1186.50i	1.66211	+	0.540053i	0.680800	+	0.732470i	$0.261632\pi$
$14$	−938.082	+	681.556i	−0.341867	+	0.248381i
$15$	59.9785	+	43.5769i	0.0177714	+	0.0129117i
$16$	644.571	+	1983.78i	0.157366	+	0.484322i
$17$	−5292.88	+	1719.76i	−1.07732	+	0.350043i	−0.793335	−	0.608785i	$-0.791657\pi$
$17$	−5292.88	+	1719.76i	−1.07732	+	0.350043i	−0.283987	+	0.958828i	$0.591657\pi$
$18$	5761.40	−	7929.89i	0.987895	−	1.35972i
$19$	−3017.45	−	4153.17i	−0.439926	−	0.605506i	0.530270	−	0.847829i	$-0.322091\pi$
$19$	−3017.45	−	4153.17i	−0.439926	−	0.605506i	−0.970196	+	0.242323i	$0.922091\pi$
$20$	−5912.48	+	18196.7i	−0.739060	+	2.27459i
$21$		−	39.0479i		−	0.00421638i
$22$	16367.4	−	7249.94i	1.53713	−	0.680873i
$23$	10819.1			0.889216			0.444608	−	0.895725i	$-0.353343\pi$
$23$	10819.1			0.889216			0.444608	+	0.895725i	$0.353343\pi$
$24$	−306.395	−	99.5537i	−0.0221640	−	0.00720151i
$25$	−9035.96	+	6565.01i	−0.578302	+	0.420161i
$26$	−41777.8	−	30353.4i	−2.37698	−	1.72698i
$27$	204.031	+	627.944i	0.0103659	+	0.0319029i
$28$	9584.14	−	3114.07i	0.436595	−	0.141858i
$29$	7982.55	−	10987.0i	0.327301	−	0.450492i	−0.613378	−	0.789790i	$-0.710190\pi$
$29$	7982.55	−	10987.0i	0.327301	−	0.450492i	0.940679	+	0.339298i	$0.110190\pi$
$30$	−586.085	−	806.677i	−0.0217068	−	0.0298769i
$31$	−6689.73	+	20588.9i	−0.224555	+	0.691111i	0.773781	+	0.633453i	$0.218363\pi$
$31$	−6689.73	+	20588.9i	−0.224555	+	0.691111i	−0.998336	+	0.0576574i	$0.981637\pi$
$32$			17469.8i			0.533134i
$33$	−126.458	+	589.419i	−0.00351888	+	0.0164015i
$34$	74849.7			1.90438
$35$	13421.6	+	4360.94i	0.313040	+	0.101713i
$36$	−68917.7	+	50071.6i	−1.47715	+	1.07321i
$37$	9088.66	+	6603.30i	0.179430	+	0.130363i	0.673875	−	0.738845i	$-0.264629\pi$
$37$	9088.66	+	6603.30i	0.179430	+	0.130363i	−0.494445	+	0.869209i	$0.664629\pi$
$38$	21335.8	+	65664.8i	0.388828	+	1.19669i
$39$	1653.90	−	537.384i	0.0278814	−	0.00905923i
$40$	68437.6	−	94196.2i	1.06934	−	1.47182i
$41$	−13734.7	−	18904.2i	−0.199282	−	0.274288i	0.697667	−	0.716422i	$-0.254221\pi$
$41$	−13734.7	−	18904.2i	−0.199282	−	0.274288i	−0.896949	+	0.442134i	$0.854221\pi$
$42$	−162.287	+	499.468i	−0.00219046	+	0.00674155i
$43$		−	94150.7i		−	1.18418i	−0.805872	−	0.592090i	$-0.798303\pi$
$43$		−	94150.7i		−	1.18418i	0.805872	−	0.592090i	$-0.201697\pi$
$44$	−154756.	+	15967.7i	−1.81672	+	0.187450i
$45$	−119296.			−1.30914
$46$	−138389.	−	44965.3i	−1.42177	−	0.461960i
$47$	151191.	−	109847.i	1.45624	−	1.05802i	0.471917	−	0.881643i	$-0.343562\pi$
$47$	151191.	−	109847.i	1.45624	−	1.05802i	0.984323	−	0.176377i	$-0.0564377\pi$
$48$	764.301	+	555.297i	0.00691099	+	0.00502113i
$49$	34058.7	+	104822.i	0.289494	+	0.890970i
$50$	142865.	−	46419.8i	1.14292	−	0.371358i
$51$	−1481.57	+	2039.21i	−0.0111690	+	0.0153727i
$52$	263798.	+	363086.i	1.87612	+	2.58226i
$53$	15463.5	−	47591.8i	0.103868	−	0.319672i	−0.885595	−	0.464458i	$-0.846249\pi$
$53$	15463.5	−	47591.8i	0.103868	−	0.319672i	0.989463	+	0.144786i	$0.0462493\pi$
$54$		−	8880.12i		−	0.0563946i
$55$	−188473.	−	109294.i	−1.13282	−	0.656913i
$56$	−61324.7			−0.349198
$57$	−2211.29	−	718.493i	−0.0119405	−	0.00387970i
$58$	−147770.	+	107361.i	−0.757358	+	0.550252i
$59$	8389.87	+	6095.60i	0.0408507	+	0.0296798i	0.608023	−	0.793919i	$-0.291963\pi$
$59$	8389.87	+	6095.60i	0.0408507	+	0.0296798i	−0.567173	+	0.823599i	$0.691963\pi$
$60$	2677.86	+	8241.60i	0.0123975	+	0.0381556i
$61$	−62625.2	+	20348.2i	−0.275905	+	0.0896469i	−0.443701	−	0.896175i	$-0.646335\pi$
$61$	−62625.2	+	20348.2i	−0.275905	+	0.0896469i	0.167796	+	0.985822i	$0.446335\pi$
$62$	171139.	−	235553.i	0.718082	−	0.988355i
$63$	36932.0	+	50832.5i	0.147700	+	0.203292i
$64$	113859.	−	350421.i	0.434336	−	1.33675i
$65$			628497.i			2.28857i
$66$	4067.23	−	7013.79i	0.0141471	−	0.0243961i
$67$	366915.			1.21995			0.609974	−	0.792422i	$-0.291180\pi$
$67$	366915.			1.21995			0.609974	+	0.792422i	$0.291180\pi$
$68$	−618672.	−	201019.i	−1.96758	−	0.639307i
$69$	3964.30	−	2880.23i	0.0120676	−	0.00876760i
$70$	−153554.	−	111563.i	−0.447678	−	0.325257i
$71$	−17496.3	−	53848.1i	−0.0488845	−	0.150451i	0.923635	−	0.383274i	$-0.125204\pi$
$71$	−17496.3	−	53848.1i	−0.0488845	−	0.150451i	−0.972519	+	0.232823i	$0.925204\pi$
$72$	493024.	−	160193.i	1.32090	−	0.429187i
$73$	−238637.	+	328456.i	−0.613437	+	0.844323i	−0.996855	−	0.0792516i	$-0.974747\pi$
$73$	−238637.	+	328456.i	−0.613437	+	0.844323i	0.383418	+	0.923575i	$0.374747\pi$
$74$	−88810.6	−	122237.i	−0.219164	−	0.301654i
$75$	−1563.21	+	4811.07i	−0.00370539	+	0.0114040i
$76$		−	600053.i		−	1.36694i
$77$	11777.5	+	114145.i	0.0257978	+	0.250026i
$78$	−23388.7			−0.0492859
$79$	368663.	+	119786.i	0.747736	+	0.242954i	0.658007	−	0.753012i	$-0.271400\pi$
$79$	368663.	+	119786.i	0.747736	+	0.242954i	0.0897291	+	0.995966i	$0.471400\pi$
$80$	−276226.	+	200690.i	−0.539505	+	0.391973i
$81$	−429582.	−	312110.i	−0.808334	−	0.587289i
$82$	97115.2	+	298890.i	0.176135	+	0.542088i
$83$	29182.3	−	9481.89i	0.0510369	−	0.0165829i	−0.283387	−	0.959006i	$-0.591458\pi$
$83$	29182.3	−	9481.89i	0.0510369	−	0.0165829i	0.334424	+	0.942423i	$0.391458\pi$
$84$	2682.77	−	3692.52i	0.00452633	−	0.00622995i
$85$	−535456.	−	736992.i	−0.871901	−	1.20007i
$86$	−391300.	+	1.20430e6i	−0.615197	+	1.89338i
$87$		−	6150.94i		−	0.00934079i
$88$	925684.	+	198602.i	1.35836	+	0.291431i
$89$	279184.			0.396023			0.198012	−	0.980200i	$-0.436552\pi$
$89$	279184.			0.396023			0.198012	+	0.980200i	$0.436552\pi$
$90$	1.52593e6	+	495805.i	2.09318	+	0.680117i
$91$	267806.	−	194573.i	0.355383	−	0.258201i
$92$	1.02310e6	+	743323.i	1.31387	+	0.954584i
$93$	3029.89	+	9325.05i	0.00376685	+	0.0115932i
$94$	−2.39045e6	+	776703.i	−2.87803	+	0.935129i
$95$	493924.	−	679828.i	0.576088	−	0.792918i
$96$	4650.76	+	6401.22i	0.00525666	+	0.00723517i
$97$	−112496.	+	346226.i	−0.123259	+	0.379354i	−0.993580	−	0.113132i	$-0.963912\pi$
$97$	−112496.	+	346226.i	−0.123259	+	0.379354i	0.870321	+	0.492486i	$0.163912\pi$
$98$		−	1.48234e6i		−	1.57497i
$99$	−392858.	−	886912.i	−0.404883	−	0.914061i
$100$	−1.30552e6			−1.30552
$101$	334998.	+	108848.i	0.325146	+	0.105646i	0.467042	−	0.884235i	$-0.345320\pi$
$101$	334998.	+	108848.i	0.325146	+	0.105646i	−0.141896	+	0.989882i	$0.545320\pi$
$102$	27426.2	−	19926.3i	0.0258444	−	0.0187770i
$103$	−331798.	−	241066.i	−0.303642	−	0.220609i	0.425521	−	0.904948i	$-0.360091\pi$
$103$	−331798.	−	241066.i	−0.303642	−	0.220609i	−0.729164	+	0.684339i	$0.760091\pi$
$104$	−843963.	−	2.59745e6i	−0.750280	−	2.30912i
$105$	6078.87	−	1975.14i	0.00525116	−	0.00170620i
$106$	−395593.	+	544487.i	−0.332148	+	0.457162i
$107$	−721664.	−	993285.i	−0.589093	−	0.810817i	0.405563	−	0.914067i	$-0.367076\pi$
$107$	−721664.	−	993285.i	−0.589093	−	0.810817i	−0.994655	+	0.103251i	$0.967076\pi$
$108$	−23848.7	+	73398.8i	−0.0189319	+	0.0582663i
$109$			1.43359e6i			1.10700i	0.832850	+	0.553499i	$0.186708\pi$
$109$			1.43359e6i			1.10700i	−0.832850	+	0.553499i	$0.813292\pi$
$110$	1.95656e6	+	2.18131e6i	1.46999	+	1.63885i
$111$	5088.16			0.00372042
$112$	171030.	+	55571.2i	0.121736	+	0.0395545i
$113$	1.70837e6	−	1.24120e6i	1.18399	−	0.860216i	0.191370	−	0.981518i	$-0.438707\pi$
$113$	1.70837e6	−	1.24120e6i	1.18399	−	0.860216i	0.992616	+	0.121302i	$0.0387070\pi$
$114$	25298.9	+	18380.7i	0.0170761	+	0.0124065i
$115$	547259.	+	1.68429e6i	0.359831	+	1.10745i
$116$	1.50972e6	−	490539.i	0.967216	−	0.314267i
$117$	−1.64478e6	+	2.26385e6i	−1.02695	+	1.41348i
$118$	−81982.4	−	112839.i	−0.0498970	−	0.0686773i
$119$	−148268.	+	456322.i	−0.0879846	+	0.270789i
$120$		−	52734.4i		−	0.0305176i
$121$	191884.	−	1.76114e6i	0.108313	−	0.994117i
$122$	885619.			0.487716
$123$	−10065.3	−	3270.40i	−0.00540891	−	0.00175746i
$124$	−2.04716e6	+	1.48735e6i	−1.07371	+	0.780096i
$125$	590087.	+	428723.i	0.302124	+	0.219506i
$126$	−261138.	−	803701.i	−0.130545	−	0.401775i
$127$	583581.	−	189617.i	0.284898	−	0.0925691i	−0.163082	−	0.986613i	$-0.552143\pi$
$127$	583581.	−	189617.i	0.284898	−	0.0925691i	0.447980	+	0.894043i	$0.352143\pi$
$128$	−2.25559e6	+	3.10455e6i	−1.07555	+	1.48037i
$129$	−25064.6	−	34498.4i	−0.0116759	−	0.0160705i
$130$	2.61210e6	−	8.03922e6i	1.18894	−	3.65918i
$131$			2.95873e6i			1.31611i	0.752972	+	0.658053i	$0.228620\pi$
$131$			2.95873e6i			1.31611i	−0.752972	+	0.658053i	$0.771380\pi$
$132$	−52454.2	+	47049.5i	−0.0228065	+	0.0204566i
$133$	−442589.			−0.188125
$134$	−4.69328e6	−	1.52494e6i	−1.95057	−	0.633779i
$135$	−87436.3	+	63526.2i	−0.0355378	+	0.0258197i
$136$	3.20258e6	+	2.32681e6i	1.27316	+	0.925006i
$137$	−936801.	−	2.88318e6i	−0.364322	−	1.12127i	−0.950404	−	0.311017i	$-0.899330\pi$
$137$	−936801.	−	2.88318e6i	−0.364322	−	1.12127i	0.586082	−	0.810252i	$-0.300670\pi$
$138$	−62678.7	+	20365.5i	−0.0238497	+	0.00774923i
$139$	1.33124e6	−	1.83229e6i	0.495690	−	0.682259i	−0.485734	−	0.874106i	$-0.661448\pi$
$139$	1.33124e6	−	1.83229e6i	0.495690	−	0.682259i	0.981425	+	0.191847i	$0.0614478\pi$
$140$	969582.	+	1.33452e6i	0.353346	+	0.486339i
$141$	26155.9	−	80499.5i	0.00933065	−	0.0287168i
$142$			761497.i			0.265952i
$143$	−4.67261e6	+	2.06973e6i	−1.59791	+	0.707793i
$144$	−1.52017e6			−0.509103
$145$	2.11421e6	+	686949.i	0.693497	+	0.225331i
$146$	4.41755e6	−	3.20954e6i	1.41946	−	1.03130i
$147$	40385.1	+	29341.5i	0.0127136	+	0.00923698i
$148$	405782.	+	1.24887e6i	0.125172	+	0.385240i
$149$	772142.	−	250884.i	0.233420	−	0.0758428i	−0.189971	−	0.981790i	$-0.560840\pi$
$149$	772142.	−	250884.i	0.233420	−	0.0758428i	0.423391	+	0.905947i	$0.360840\pi$
$150$	39990.6	−	55042.3i	0.0118491	−	0.0163088i
$151$	1.29299e6	+	1.77965e6i	0.375548	+	0.516898i	0.954398	−	0.298536i	$-0.0964984\pi$
$151$	1.29299e6	+	1.77965e6i	0.375548	+	0.516898i	−0.578850	+	0.815434i	$0.696498\pi$
$152$	−1.12839e6	+	3.47284e6i	−0.321314	+	0.988904i
$153$		−	4.05594e6i		−	1.13244i
$154$	323751.	−	1.50900e6i	0.0886438	−	0.413168i
$155$	−3.54361e6			−0.951592
$156$	193320.	+	62813.5i	0.0509217	+	0.0165455i
$157$	−5414.86	+	3934.12i	−0.00139923	+	0.00101660i	−0.588485	−	0.808508i	$-0.700275\pi$
$157$	−5414.86	+	3934.12i	−0.00139923	+	0.00101660i	0.587085	+	0.809525i	$0.300275\pi$
$158$	−4.21779e6	−	3.06440e6i	−1.06933	−	0.776917i
$159$	−7003.69	−	21555.1i	−0.00174235	−	0.00536240i
$160$	−2.71965e6	+	883666.i	−0.663976	+	0.215739i
$161$	548262.	−	754619.i	0.131374	−	0.180821i
$162$	4.19770e6	+	5.77764e6i	0.987339	+	1.35896i
$163$	−1.11062e6	+	3.41814e6i	−0.256450	+	0.789273i	0.737090	+	0.675795i	$0.236199\pi$
$163$	−1.11062e6	+	3.41814e6i	−0.256450	+	0.789273i	−0.993540	+	0.113479i	$0.963801\pi$
$164$		−	2.73129e6i		−	0.619208i
$165$	−98155.8	+	10127.7i	−0.0218506	+	0.00225456i
$166$	−412683.			−0.0902179
$167$	2.12070e6	+	689057.i	0.455334	+	0.147947i	0.527699	−	0.849431i	$-0.323055\pi$
$167$	2.12070e6	+	689057.i	0.455334	+	0.147947i	−0.0723656	+	0.997378i	$0.523055\pi$
$168$	−22470.4	+	16325.7i	−0.00473897	+	0.00344306i
$169$	8.02189e6	+	5.82824e6i	1.66194	+	1.20747i
$170$	3.78610e6	+	1.16524e7i	0.770629	+	2.37175i
$171$	3.55823e6	−	1.15614e6i	0.711615	−	0.231218i
$172$	6.46859e6	−	8.90325e6i	1.27123	−	1.74970i
$173$	−3.85311e6	−	5.30335e6i	−0.744172	−	1.02426i	−0.998368	−	0.0571120i	$-0.981811\pi$
$173$	−3.85311e6	−	5.30335e6i	−0.744172	−	1.02426i	0.254196	−	0.967153i	$-0.418189\pi$
$174$	−25564.0	+	78677.7i	−0.00485266	+	0.0149350i
$175$			962932.i			0.179672i
$176$	−2.40170e6	−	1.39272e6i	−0.440535	−	0.255462i
$177$	4696.95			0.000847025
$178$	−3.57110e6	−	1.16032e6i	−0.633201	−	0.205739i
$179$	−6.57033e6	+	4.77362e6i	−1.14559	+	0.832317i	−0.987888	−	0.155170i	$-0.950408\pi$
$179$	−6.57033e6	+	4.77362e6i	−1.14559	+	0.832317i	−0.157699	+	0.987487i	$0.550408\pi$
$180$	−1.12811e7	−	8.19617e6i	−1.93434	−	1.40538i
$181$	−1.51804e6	−	4.67205e6i	−0.256005	−	0.787901i	−0.993630	−	0.112691i	$-0.964053\pi$
$181$	−1.51804e6	−	4.67205e6i	−0.256005	−	0.787901i	0.737625	−	0.675210i	$-0.235947\pi$
$182$	−4.23422e6	+	1.37578e6i	−0.702360	+	0.228210i
$183$	−17529.9	+	24127.8i	−0.00286040	+	0.00393700i
$184$	−4.52341e6	−	6.22594e6i	−0.726127	−	0.999428i
$185$	−568256.	+	1.74891e6i	−0.0897488	+	0.276218i
$186$		−	131871.i		−	0.0204932i
$187$	3.71589e6	−	6.40791e6i	0.568248	−	0.979922i
$188$	2.18442e7			3.28748
$189$	54137.7	+	17590.4i	0.00801889	+	0.00260550i
$190$	−9.14330e6	+	6.64300e6i	−1.33304	+	0.968508i
$191$	−9.98046e6	−	7.25123e6i	−1.43235	−	1.04067i	−0.989572	−	0.144036i	$-0.953992\pi$
$191$	−9.98046e6	−	7.25123e6i	−1.43235	−	1.04067i	−0.442781	−	0.896630i	$-0.646008\pi$
$192$	−51568.5	−	158711.i	−0.00728586	−	0.0224236i
$193$	5.44688e6	−	1.76980e6i	0.757663	−	0.246180i	0.0953877	−	0.995440i	$-0.469591\pi$
$193$	5.44688e6	−	1.76980e6i	0.757663	−	0.246180i	0.662275	+	0.749261i	$0.269591\pi$
$194$	2.87790e6	−	3.96109e6i	0.394158	−	0.542512i
$195$	167317.	+	230292.i	0.0225651	+	0.0310582i
$196$	−3.98103e6	+	1.22523e7i	−0.528722	+	1.62724i
$197$			833295.i			0.108993i	0.998514	+	0.0544967i	$0.0173554\pi$
$197$			833295.i			0.108993i	−0.998514	+	0.0544967i	$0.982645\pi$
$198$	1.33901e6	+	1.29774e7i	0.172500	+	1.67183i
$199$	6.03794e6			0.766177			0.383089	−	0.923712i	$-0.374860\pi$
$199$	6.03794e6			0.766177			0.383089	+	0.923712i	$0.374860\pi$
$200$	7.55579e6	+	2.45502e6i	0.944473	+	0.306878i
$201$	134444.	−	97679.3i	0.0165559	−	0.0120286i
$202$	−3.83264e6	−	2.78458e6i	−0.464990	−	0.337835i
$203$	−361813.	−	1.11355e6i	−0.0432510	−	0.133113i
$204$	−280207.	+	91044.7i	−0.0330056	+	0.0107242i
$205$	2.24822e6	−	3.09441e6i	0.260962	−	0.359183i
$206$	3.24220e6	+	4.46250e6i	0.370884	+	0.510478i
$207$	−2.43657e6	+	7.49899e6i	−0.274706	+	0.845457i
$208$			8.00889e6i			0.889985i
$209$	6.68079e6	+	1.43334e6i	0.731794	+	0.157004i
$210$	−85964.8			−0.00928245
$211$	−1.13175e7	−	3.67727e6i	−1.20477	−	0.391452i	−0.363253	−	0.931690i	$-0.618334\pi$
$211$	−1.13175e7	−	3.67727e6i	−1.20477	−	0.391452i	−0.841512	+	0.540238i	$0.818334\pi$
$212$	4.73207e6	−	3.43805e6i	0.496643	−	0.360832i
$213$	−20746.3	−	15073.0i	−0.00214685	−	0.00155977i
$214$	5.10273e6	+	1.57046e7i	0.520669	+	1.60245i
$215$	1.46571e7	−	4.76239e6i	1.47480	−	0.479192i
$216$	276051.	−	379952.i	0.0273923	−	0.0377023i
$217$	1.09704e6	+	1.50995e6i	0.107361	+	0.147769i
$218$	5.95817e6	−	1.83373e7i	0.575100	−	1.76997i
$219$			183882.i			0.0175068i
$220$	−1.03138e7	−	2.32843e7i	−0.968610	−	2.18673i
$221$	−2.13683e7			−1.97967
$222$	−65083.5	−	21146.9i	−0.00594856	−	0.00193281i
$223$	−1.01898e7	+	7.40333e6i	−0.918864	+	0.667594i	−0.943241	−	0.332109i	$-0.892240\pi$
$223$	−1.01898e7	+	7.40333e6i	−0.918864	+	0.667594i	0.0243770	+	0.999703i	$0.492240\pi$
$224$	1.21849e6	+	885287.i	0.108412	+	0.0787663i
$225$	−2.51539e6	−	7.74156e6i	−0.220829	−	0.679643i
$226$	−2.70106e7	+	8.77628e6i	−2.33996	+	0.760301i
$227$	−1.14871e6	+	1.58106e6i	−0.0982048	+	0.135167i	−0.855292	−	0.518147i	$-0.826622\pi$
$227$	−1.14871e6	+	1.58106e6i	−0.0982048	+	0.135167i	0.757087	+	0.653314i	$0.226622\pi$
$228$	−159745.	−	219870.i	−0.0134779	−	0.0185507i
$229$	−1.37388e6	+	4.22838e6i	−0.114405	+	0.352101i	−0.991822	−	0.127626i	$-0.959264\pi$
$229$	−1.37388e6	+	4.22838e6i	−0.114405	+	0.352101i	0.877418	+	0.479727i	$0.159264\pi$
$230$		−	2.38185e7i		−	1.95763i
$231$	34702.9	+	38689.4i	0.00281534	+	0.00313874i
$232$	−9.66006e6			−0.773599
$233$	8.84239e6	+	2.87307e6i	0.699040	+	0.227132i	0.636912	−	0.770936i	$-0.280211\pi$
$233$	8.84239e6	+	2.87307e6i	0.699040	+	0.227132i	0.0621277	+	0.998068i	$0.480211\pi$
$234$	3.04475e7	−	2.21214e7i	2.37631	−	1.72649i
$235$	2.47483e7	+	1.79807e7i	1.90696	+	1.38549i
$236$	374583.	+	1.15285e6i	0.0284978	+	0.0877073i
$237$	166974.	−	54253.0i	0.0125430	−	0.00407548i
$238$	3.79304e6	−	5.22068e6i	0.281357	−	0.387254i
$239$	1.09002e7	+	1.50028e7i	0.798436	+	1.09895i	0.993006	+	0.118064i	$0.0376689\pi$
$239$	1.09002e7	+	1.50028e7i	0.798436	+	1.09895i	−0.194570	+	0.980889i	$0.562331\pi$
$240$	−47786.8	+	147073.i	−0.00345680	+	0.0106389i
$241$			1.16182e7i			0.830017i	0.909817	+	0.415009i	$0.136221\pi$
$241$			1.16182e7i			0.830017i	−0.909817	+	0.415009i	$0.863779\pi$
$242$	−9.77390e6	+	2.17295e7i	−0.689639	+	1.53322i
$243$	−721825.			−0.0503052
$244$	−7.32010e6	−	2.37844e6i	−0.503903	−	0.163728i
$245$	−1.45956e7	+	1.06043e7i	−0.992485	+	0.721082i
$246$	115154.	+	83664.6i	0.00773527	+	0.00562000i
$247$	−6.09100e6	−	1.87462e7i	−0.404201	−	1.24400i
$248$	1.46450e7	−	4.75845e6i	0.960139	−	0.311968i
$249$	8168.64	−	11243.2i	0.000529117	−	0.000728267i
$250$	−5.76608e6	−	7.93634e6i	−0.369029	−	0.507925i
$251$	3.87868e6	−	1.19373e7i	0.245280	−	0.754895i	−0.750310	−	0.661086i	$-0.770096\pi$
$251$	3.87868e6	−	1.19373e7i	0.245280	−	0.754895i	0.995590	−	0.0938088i	$-0.0299042\pi$
$252$			7.34433e6i			0.458934i
$253$	−1.07198e7	+	9.61524e6i	−0.661948	+	0.593743i
$254$	−8.25276e6			−0.503614
$255$	−392401.	−	127499.i	−0.0236652	−	0.00768928i
$256$	2.26770e7	−	1.64758e7i	1.35166	−	0.982036i
$257$	−222110.	−	161373.i	−0.0130849	−	0.00950672i	0.581224	−	0.813744i	$-0.302574\pi$
$257$	−222110.	−	161373.i	−0.0130849	−	0.00950672i	−0.594308	+	0.804237i	$0.702574\pi$
$258$	177226.	+	545446.i	0.0103197	+	0.0317609i
$259$	921144.	−	299298.i	0.0530186	−	0.0172268i
$260$	−4.31807e7	+	5.94332e7i	−2.45680	+	3.38150i
$261$	5.81764e6	+	8.00730e6i	0.327209	+	0.450365i
$262$	1.22968e7	−	3.78456e7i	0.683734	−	2.10432i
$263$		−	1.63388e7i		−	0.898159i	−0.893492	−	0.449080i	$-0.851752\pi$
$263$		−	1.63388e7i		−	0.898159i	0.893492	−	0.449080i	$-0.148248\pi$
$264$	392058.	−	173662.i	0.0213078	−	0.00943829i
$265$	8.19116e6			0.440157
$266$	5.66124e6	+	1.83945e6i	0.300792	+	0.0977333i
$267$	102298.	−	74323.8i	0.00537444	−	0.00390476i
$268$	3.46969e7	+	2.52088e7i	1.80255	+	1.30963i
$269$	−794948.	−	2.44660e6i	−0.0408397	−	0.125692i	0.928558	−	0.371187i	$-0.121049\pi$
$269$	−794948.	−	2.44660e6i	−0.0408397	−	0.125692i	−0.969398	+	0.245496i	$0.921049\pi$
$270$	1.38243e6	−	449180.i	0.0702349	−	0.0228207i
$271$	6.58493e6	−	9.06338e6i	0.330859	−	0.455389i	−0.610885	−	0.791720i	$-0.709186\pi$
$271$	6.58493e6	−	9.06338e6i	0.330859	−	0.455389i	0.941744	+	0.336331i	$0.109186\pi$
$272$	−6.82328e6	−	9.39144e6i	−0.339068	−	0.466687i
$273$	46330.2	−	142590.i	0.00227707	−	0.00700809i
$274$			4.07727e7i			1.98206i
$275$	3.11849e6	−	1.45353e7i	0.149950	−	0.698915i
$276$	572766.			0.0272427
$277$	−1.99133e7	−	6.47021e6i	−0.936921	−	0.304424i	−0.199531	−	0.979891i	$-0.563942\pi$
$277$	−1.99133e7	−	6.47021e6i	−0.936921	−	0.304424i	−0.737390	+	0.675467i	$0.763942\pi$
$278$	−2.46433e7	+	1.79044e7i	−1.14700	+	0.833345i
$279$	−1.27641e7	−	9.27364e6i	−0.587728	−	0.427010i
$280$	−3.10197e6	−	9.54687e6i	−0.141307	−	0.434898i
$281$	2.01299e7	−	6.54060e6i	0.907241	−	0.294780i	0.182019	−	0.983295i	$-0.441737\pi$
$281$	2.01299e7	−	6.54060e6i	0.907241	−	0.294780i	0.725222	+	0.688515i	$0.241737\pi$
$282$	−669129.	+	920977.i	−0.0298375	+	0.0410678i
$283$	−2.23842e7	−	3.08091e7i	−0.987601	−	1.35932i	−0.932632	−	0.360828i	$-0.882494\pi$
$283$	−2.23842e7	−	3.08091e7i	−0.987601	−	1.35932i	−0.0549682	−	0.998488i	$-0.517506\pi$
$284$	2.04510e6	−	6.29416e6i	0.0892810	−	0.274779i
$285$		−	380592.i		−	0.0164409i
$286$	6.83702e7	−	7.05446e6i	2.92260	−	0.301554i
$287$	−2.01456e6			−0.0852185
$288$	−1.21087e7	−	3.93436e6i	−0.506898	−	0.164701i
$289$	5.52934e6	−	4.01730e6i	0.229076	−	0.166434i
$290$	−2.41882e7	−	1.75738e7i	−0.991768	−	0.720562i
$291$	50951.1	+	156811.i	0.00206764	+	0.00636354i
$292$	−4.51330e7	+	1.46646e7i	−1.81278	+	0.589008i
$293$	−8.92470e6	+	1.22838e7i	−0.354806	+	0.488348i	−0.948692	−	0.316201i	$-0.897593\pi$
$293$	−8.92470e6	+	1.22838e7i	−0.354806	+	0.488348i	0.593887	+	0.804549i	$0.297593\pi$
$294$	−394626.	−	543157.i	−0.0155290	−	0.0213739i
$295$	−524565.	+	1.61445e6i	−0.0204331	+	0.0628865i
$296$		−	7.99096e6i		−	0.308123i
$297$	−760230.	−	440850.i	−0.0290186	−	0.0168276i
$298$	−1.09193e7			−0.412616
$299$	3.95077e7	+	1.28368e7i	1.47798	+	0.480224i
$300$	−478366.	+	347553.i	−0.0177173	+	0.0128723i
$301$	−6.56689e6	−	4.77113e6i	−0.240802	−	0.174953i
$302$	−9.14249e6	−	2.81377e7i	−0.331928	−	1.02157i
$303$	151726.	−	49298.9i	0.00545422	−	0.00177218i
$304$	6.29403e6	−	8.66299e6i	0.224031	−	0.308352i
$305$	−6.33550e6	−	8.72006e6i	−0.223296	−	0.307341i
$306$	−1.68569e7	+	5.18802e7i	−0.588320	+	1.81066i
$307$		−	1.35496e6i		−	0.0468288i	−0.999726	−	0.0234144i	$-0.992546\pi$
$307$		−	1.35496e6i		−	0.0468288i	0.999726	−	0.0234144i	$-0.00745371\pi$
$308$	−6.72858e6	+	1.16032e7i	−0.230288	+	0.397123i
$309$	−185753.			−0.00629592
$310$	4.53269e7	+	1.47276e7i	1.52150	+	0.494364i
$311$	3.12056e7	−	2.26722e7i	1.03741	−	0.753723i	0.0676323	−	0.997710i	$-0.478456\pi$
$311$	3.12056e7	−	2.26722e7i	1.03741	−	0.753723i	0.969778	+	0.243987i	$0.0784555\pi$
$312$	−1.00073e6	−	727073.i	−0.0329498	−	0.0239394i
$313$	5.84611e6	+	1.79925e7i	0.190649	+	0.586757i	1.00000		0.000568542i	$-0.000180972\pi$
$313$	5.84611e6	+	1.79925e7i	0.190649	+	0.586757i	−0.809351	+	0.587325i	$0.800181\pi$
$314$	85613.0	−	27817.4i	0.00276536	−	0.000898519i
$315$	−6.04536e6	+	8.32072e6i	−0.193415	+	0.266213i
$316$	2.66324e7	+	3.66563e7i	0.844011	+	1.16168i
$317$	−1.42811e7	+	4.39528e7i	−0.448316	+	1.37978i	0.430489	+	0.902596i	$0.358341\pi$
$317$	−1.42811e7	+	4.39528e7i	−0.448316	+	1.37978i	−0.878805	+	0.477180i	$0.841659\pi$
$318$			304824.i			0.00947910i
$319$	1.85523e6	+	1.79805e7i	0.0571513	+	0.553898i
$320$	6.03119e7			1.84057
$321$	−528860.	−	171837.i	−0.0159892	−	0.00519520i
$322$	−1.01492e7	+	7.37382e6i	−0.303993	+	0.220864i
$323$	2.31135e7	+	1.67929e7i	0.685896	+	0.498332i
$324$	−1.91796e7	−	5.90286e7i	−0.563902	−	1.73551i
$325$	−4.07856e7	+	1.32521e7i	−1.18811	+	0.386041i
$326$	2.84123e7	−	3.91062e7i	0.820076	−	1.12874i
$327$	381648.	+	525293.i	0.0109149	+	0.0150231i
$328$	−5.13617e6	+	1.58075e7i	−0.145552	+	0.447963i
$329$		−	1.61119e7i		−	0.452439i
$330$	1.29762e6	+	278400.i	0.0361082	+	0.00774689i
$331$	−4.99555e7			−1.37752			−0.688762	−	0.724988i	$-0.741846\pi$
$331$	−4.99555e7			−1.37752			−0.688762	+	0.724988i	$0.741846\pi$
$332$	3.41104e6	+	1.10831e6i	0.0932121	+	0.0302865i
$333$	−6.62377e6	+	4.81245e6i	−0.179379	+	0.130327i
$334$	−2.42624e7	−	1.76277e7i	−0.651171	−	0.473104i
$335$	1.85595e7	+	5.71204e7i	0.493666	+	1.51935i
$336$	77462.5	−	25169.1i	0.00204209	−	0.000663514i
$337$	3.16892e7	−	4.36164e7i	0.827982	−	1.13962i	−0.160313	−	0.987066i	$-0.551250\pi$
$337$	3.16892e7	−	4.36164e7i	0.827982	−	1.13962i	0.988295	−	0.152553i	$-0.0487496\pi$
$338$	−7.83866e7	−	1.07890e8i	−2.02998	−	2.79403i
$339$	295546.	−	909596.i	0.00758622	−	0.0233480i
$340$		−	1.06481e8i		−	2.70917i
$341$	−1.16696e7	−	2.63452e7i	−0.294302	−	0.664414i
$342$	−5.03189e7			−1.25792
$343$	1.86837e7	+	6.07070e6i	0.463000	+	0.150438i
$344$	−5.41798e7	+	3.93639e7i	−1.33095	+	0.966993i
$345$	648913.	+	471463.i	0.0158026	+	0.0114813i
$346$	2.72445e7	+	8.38501e7i	0.657735	+	2.02430i
$347$	−3.25460e7	+	1.05748e7i	−0.778950	+	0.253096i	−0.671392	−	0.741103i	$-0.734303\pi$
$347$	−3.25460e7	+	1.05748e7i	−0.778950	+	0.253096i	−0.107558	+	0.994199i	$0.534303\pi$
$348$	422598.	−	581657.i	0.0100274	−	0.0138016i
$349$	8.55071e6	+	1.17690e7i	0.201153	+	0.276863i	0.897662	−	0.440685i	$-0.145264\pi$
$349$	8.55071e6	+	1.17690e7i	0.201153	+	0.276863i	−0.696509	+	0.717548i	$0.745264\pi$
$350$	4.00205e6	−	1.23170e7i	0.0933422	−	0.287278i
$351$			2.53512e6i			0.0586243i
$352$	−1.55259e7	−	1.73094e7i	−0.355982	−	0.396874i
$353$	8.36830e7			1.90245			0.951225	−	0.308497i	$-0.0998261\pi$
$353$	8.36830e7			1.90245			0.951225	+	0.308497i	$0.0998261\pi$
$354$	−60079.5	−	19521.0i	−0.00135431	−	0.000440041i
$355$	7.49792e6	−	5.44756e6i	0.167593	−	0.121763i
$356$	2.64008e7	+	1.91813e7i	0.585149	+	0.425136i
$357$	67153.0	+	206676.i	0.00147591	+	0.00454240i
$358$	1.03882e8	−	3.37533e7i	2.26408	−	0.735643i
$359$	−2.99715e7	+	4.12523e7i	−0.647777	+	0.891588i	−0.999000	−	0.0447033i	$-0.985766\pi$
$359$	−2.99715e7	+	4.12523e7i	−0.647777	+	0.891588i	0.351223	+	0.936292i	$0.385766\pi$
$360$	4.98770e7	+	6.86497e7i	1.06904	+	1.47140i
$361$	6.39419e6	−	1.96793e7i	0.135914	−	0.418300i
$362$			6.60702e7i			1.39277i
$363$	−398537.	−	696394.i	−0.00833199	−	0.0145591i
$364$	3.86929e7			0.802281
$365$	−6.32041e7	−	2.05363e7i	−1.29977	−	0.422321i
$366$	324506.	−	235767.i	0.00661880	−	0.00480884i
$367$	−5.22046e7	−	3.79289e7i	−1.05611	−	0.767311i	−0.0827480	−	0.996571i	$-0.526370\pi$
$367$	−5.22046e7	−	3.79289e7i	−1.05611	−	0.767311i	−0.973365	+	0.229259i	$0.926370\pi$
$368$	6.97367e6	+	2.14628e7i	0.139932	+	0.430667i
$369$	1.61962e7	−	5.26245e6i	0.322354	−	0.104739i
$370$	1.45373e7	−	2.00089e7i	0.286998	−	0.395019i
$371$	−2.53585e6	−	3.49030e6i	−0.0496594	−	0.0683504i
$372$	−354156.	+	1.08998e6i	−0.00687964	+	0.0211734i
$373$			7.66985e7i			1.47795i	0.673732	+	0.738976i	$0.264690\pi$
$373$			7.66985e7i			1.47795i	−0.673732	+	0.738976i	$0.735310\pi$
$374$	−7.41625e7	+	6.65211e7i	−1.41765	+	1.27158i
$375$	330352.			0.00626445
$376$	−1.26425e8	−	4.10778e7i	−2.37831	−	0.772759i
$377$	4.21857e7	−	3.06497e7i	0.787301	−	0.572008i
$378$	−619377.	−	450004.i	−0.0114678	−	0.00833184i
$379$	−2.36977e7	−	7.29339e7i	−0.435299	−	1.33971i	−0.892780	−	0.450493i	$-0.851248\pi$
$379$	−2.36977e7	−	7.29339e7i	−0.435299	−	1.33971i	0.457481	−	0.889220i	$-0.348752\pi$
$380$	9.34147e7	−	3.03523e7i	1.70241	−	0.553147i
$381$	163355.	−	224839.i	0.00295364	−	0.00406533i
$382$	9.75249e7	+	1.34232e8i	1.74955	+	2.40804i
$383$	2.42758e7	−	7.47131e7i	0.432092	−	1.32984i	−0.463945	−	0.885864i	$-0.653566\pi$
$383$	2.42758e7	−	7.47131e7i	0.432092	−	1.32984i	0.896037	−	0.443979i	$-0.146434\pi$
$384$			1.73804e6i			0.0306949i
$385$	−1.71741e7	+	7.60726e6i	−0.300948	+	0.133305i
$386$	−7.70275e7			−1.33932
$387$	6.52582e7	+	2.12037e7i	1.12591	+	0.365829i
$388$	−3.44254e7	+	2.50115e7i	−0.589364	+	0.428198i
$389$	−3.39829e7	−	2.46900e7i	−0.577313	−	0.419442i	0.260441	−	0.965490i	$-0.416132\pi$
$389$	−3.39829e7	−	2.46900e7i	−0.577313	−	0.419442i	−0.837754	+	0.546047i	$0.816132\pi$
$390$	−1.18306e6	−	3.64110e6i	−0.0199441	−	0.0613816i
$391$	−5.72642e7	+	1.86063e7i	−0.957973	+	0.311264i
$392$	4.60808e7	−	6.34248e7i	0.765001	−	1.05293i
$393$	787665.	+	1.08413e6i	0.0129767	+	0.0178609i
$394$	3.46326e6	−	1.06588e7i	0.0566235	−	0.174269i
$395$			6.34516e7i			1.02956i
$396$	2.37849e7	−	1.10861e8i	0.383015	−	1.78523i
$397$	6.89244e7			1.10154			0.550772	−	0.834656i	$-0.314333\pi$
$397$	6.89244e7			1.10154			0.550772	+	0.834656i	$0.314333\pi$
$398$	−7.72323e7	−	2.50943e7i	−1.22504	−	0.398039i
$399$	−162172.	+	117825.i	−0.00255304	+	0.00185489i
$400$	−1.88479e7	−	1.36938e7i	−0.294498	−	0.213966i
$401$	1.43299e7	+	4.41028e7i	0.222233	+	0.683963i	0.998561	+	0.0536336i	$0.0170803\pi$
$401$	1.43299e7	+	4.41028e7i	0.222233	+	0.683963i	−0.776328	+	0.630330i	$0.782920\pi$
$402$	−2.12566e6	+	690670.i	−0.0327202	+	0.0106314i
$403$	−4.88573e7	+	6.72463e7i	−0.746473	+	1.02743i
$404$	2.42004e7	+	3.33090e7i	0.367011	+	0.505147i
$405$	2.68590e7	−	8.26635e7i	0.404320	−	1.24437i
$406$			1.57473e7i			0.235303i
$407$	−1.48738e7	+	1.53468e6i	−0.220616	+	0.0227632i
$408$	1.79292e6			0.0263986
$409$	−1.82814e7	−	5.94000e6i	−0.267202	−	0.0868193i	0.172352	−	0.985035i	$-0.444863\pi$
$409$	−1.82814e7	−	5.94000e6i	−0.267202	−	0.0868193i	−0.439554	+	0.898216i	$0.644863\pi$
$410$	−4.16180e7	+	3.02373e7i	−0.603851	+	0.438724i
$411$	−1.11081e6	−	807053.i	−0.0159998	−	0.0116246i
$412$	−1.48138e7	−	4.55922e7i	−0.211824	−	0.651927i
$413$	850321.	−	276286.i	0.0120707	−	0.00392201i
$414$	6.23332e7	−	8.57942e7i	0.878452	−	1.20909i
$415$	2.95223e6	+	4.06340e6i	0.0413054	+	0.0568519i
$416$	−2.07278e7	+	6.37936e7i	−0.287921	+	0.886130i
$417$		−	1.02578e6i		−	0.0141464i
$418$	−7.94981e7	−	4.61002e7i	−1.08850	−	0.631210i
$419$	2.97719e7			0.404729			0.202365	−	0.979310i	$-0.435137\pi$
$419$	2.97719e7			0.404729			0.202365	+	0.979310i	$0.435137\pi$
$420$	710543.	+	230870.i	0.00959053	+	0.00311615i
$421$	9.31515e7	−	6.76785e7i	1.24837	−	0.906995i	0.250245	−	0.968183i	$-0.419489\pi$
$421$	9.31515e7	−	6.76785e7i	1.24837	−	0.906995i	0.998126	+	0.0611881i	$0.0194890\pi$
$422$	1.29481e8	+	9.40733e7i	1.72293	+	1.25178i
$423$	4.20878e7	+	1.29533e8i	0.556077	+	1.71143i
$424$	−3.38524e7	+	1.09993e7i	−0.444111	+	0.144300i
$425$	3.65361e7	−	5.02876e7i	0.475943	−	0.655079i
$426$	202724.	+	279026.i	0.00262226	+	0.00360923i
$427$	−1.75430e6	+	5.39918e6i	−0.0225331	+	0.0693496i
$428$		−	1.43511e8i		−	1.83043i
$429$	−1.16113e6	+	2.00232e6i	−0.0147064	+	0.0253607i
$430$	−2.07275e8			−2.60700
$431$	−8.72915e7	−	2.83627e7i	−1.09029	−	0.354255i	−0.291929	−	0.956440i	$-0.594297\pi$
$431$	−8.72915e7	−	2.83627e7i	−1.09029	−	0.354255i	−0.798357	+	0.602185i	$0.794297\pi$
$432$	−1.11419e6	+	809509.i	−0.0138200	+	0.0100408i
$433$	−3.97301e7	−	2.88656e7i	−0.489391	−	0.355564i	0.315559	−	0.948906i	$-0.397808\pi$
$433$	−3.97301e7	−	2.88656e7i	−0.489391	−	0.355564i	−0.804950	+	0.593342i	$0.797808\pi$
$434$	−7.75696e6	−	2.38735e7i	−0.0948905	−	0.292043i
$435$	957562.	−	311131.i	0.0116332	−	0.00377986i
$436$	−9.84946e7	+	1.35566e8i	−1.18837	+	1.63566i
$437$	−3.26461e7	−	4.49335e7i	−0.391190	−	0.538426i
$438$	764231.	−	2.35206e6i	0.00909499	−	0.0279915i
$439$		−	9.76531e7i		−	1.15423i	−0.816663	−	0.577115i	$-0.804178\pi$
$439$		−	9.76531e7i		−	1.15423i	0.816663	−	0.577115i	$-0.195822\pi$
$440$	1.59056e7	+	1.54154e8i	0.186721	+	1.80966i
$441$	−8.03249e7			−0.936558
$442$	2.73326e8	+	8.88090e7i	3.16529	+	1.02847i
$443$	−3.71397e7	+	2.69836e7i	−0.427196	+	0.310376i	−0.780527	−	0.625122i	$-0.785049\pi$
$443$	−3.71397e7	+	2.69836e7i	−0.427196	+	0.310376i	0.353331	+	0.935498i	$0.385049\pi$
$444$	481156.	+	349580.i	0.00549714	+	0.00399391i
$445$	1.41219e7	+	4.34627e7i	0.160255	+	0.493215i
$446$	1.61109e8	−	5.23474e7i	1.81599	−	0.590052i
$447$	216136.	−	297486.i	0.00241994	−	0.00333077i
$448$	−1.86716e7	−	2.56992e7i	−0.207657	−	0.285816i
$449$	−2.05856e7	+	6.33559e7i	−0.227418	+	0.699919i	0.770620	+	0.637295i	$0.219947\pi$
$449$	−2.05856e7	+	6.33559e7i	−0.227418	+	0.699919i	−0.998037	+	0.0626239i	$0.980053\pi$
$450$			1.09478e8i			1.20140i
$451$	3.04093e7	+	6.52421e6i	0.331495	+	0.0711211i
$452$	2.46827e8			2.67286
$453$	947551.	+	307878.i	0.0101931	+	0.00331195i
$454$	2.12644e7	−	1.54495e7i	0.227241	−	0.165100i
$455$	4.38369e7	+	3.18494e7i	0.465378	+	0.338117i
$456$	511069.	+	1.57291e6i	0.00538995	+	0.0165886i
$457$	−3.51252e7	+	1.14129e7i	−0.368019	+	0.119577i	−0.487187	−	0.873297i	$-0.661977\pi$
$457$	−3.51252e7	+	1.14129e7i	−0.368019	+	0.119577i	0.119168	+	0.992874i	$0.461977\pi$
$458$	3.51472e7	−	4.83760e7i	0.365843	−	0.503539i
$459$	−2.15983e6	−	2.97275e6i	−0.0223348	−	0.0307412i
$460$	−6.39676e7	+	1.96872e8i	−0.657184	+	2.02260i
$461$		−	1.41520e8i		−	1.44449i	−0.691638	−	0.722244i	$-0.743111\pi$
$461$		−	1.41520e8i		−	1.44449i	0.691638	−	0.722244i	$-0.256889\pi$
$462$	−283094.	−	639112.i	−0.00287082	−	0.00648113i
$463$	8.37673e7			0.843979			0.421989	−	0.906601i	$-0.361332\pi$
$463$	8.37673e7			0.843979			0.421989	+	0.906601i	$0.361332\pi$
$464$	2.69412e7	+	8.75374e6i	0.269689	+	0.0876274i
$465$	−1.29844e6	+	943371.i	−0.0129141	+	0.00938261i
$466$	−1.01164e8	−	7.34998e7i	−0.999695	−	0.726321i
$467$	−2.36788e7	−	7.28757e7i	−0.232492	−	0.715537i	−0.997444	−	0.0714501i	$-0.977237\pi$
$467$	−2.36788e7	−	7.28757e7i	−0.232492	−	0.715537i	0.764952	−	0.644087i	$-0.222763\pi$
$468$	−3.11074e8	+	1.01074e8i	−3.03477	+	0.986057i
$469$	1.85936e7	−	2.55919e7i	0.180237	−	0.248075i
$470$	−2.41830e8	−	3.32851e8i	−2.32926	−	3.20595i
$471$	−936.764	+	2883.06i	−8.96535e−6	+	2.75925e-5i
$472$		−	7.37657e6i		−	0.0701501i
$473$	8.36744e7	+	9.32863e7i	0.790695	+	0.881524i
$474$	−2.36127e6			−0.0221723
$475$	5.45312e7	+	1.77183e7i	0.508820	+	0.165326i
$476$	−4.53723e7	+	3.29649e7i	−0.420697	+	0.305654i
$477$	2.95045e7	+	2.14363e7i	0.271853	+	0.197513i
$478$	−7.70729e7	−	2.37206e8i	−0.705697	−	2.17191i
$479$	−1.43142e8	+	4.65095e7i	−1.30244	+	0.423190i	−0.876431	−	0.481527i	$-0.840082\pi$
$479$	−1.43142e8	+	4.65095e7i	−1.30244	+	0.423190i	−0.426013	+	0.904717i	$0.640082\pi$
$480$	−761277.	+	1.04781e6i	−0.00688366	+	0.00947454i
$481$	2.53539e7	+	3.48967e7i	0.227829	+	0.313580i
$482$	4.82864e7	−	1.48610e8i	0.431205	−	1.32711i
$483$		−	422462.i		−	0.00374927i
$484$	1.39144e8	−	1.53357e8i	1.22724	−	1.35259i
$485$	−5.95899e7			−0.522333
$486$	9.23299e6	+	2.99998e6i	0.0804328	+	0.0261342i
$487$	−7.96071e7	+	5.78379e7i	−0.689231	+	0.500756i	−0.876407	−	0.481571i	$-0.840066\pi$
$487$	−7.96071e7	+	5.78379e7i	−0.689231	+	0.500756i	0.187176	+	0.982326i	$0.440066\pi$
$488$	3.78928e7	+	2.75307e7i	0.326060	+	0.236896i
$489$	503019.	+	1.54813e6i	0.00430188	+	0.0132398i
$490$	2.30768e8	−	7.49809e7i	1.96149	−	0.637328i
$491$	−4.66191e7	+	6.41657e7i	−0.393840	+	0.542074i	−0.959185	−	0.282781i	$-0.908743\pi$
$491$	−4.66191e7	+	6.41657e7i	−0.393840	+	0.542074i	0.565345	+	0.824855i	$0.308743\pi$
$492$	−727119.	−	1.00079e6i	−0.00610534	−	0.00840328i
$493$	−2.33556e7	+	7.18812e7i	−0.194917	+	0.599894i
$494$			2.65100e8i			2.19902i
$495$	1.18200e8	−	1.06021e8i	0.974548	−	0.874134i
$496$	−4.51559e7			−0.370058
$497$	−4.64247e6	−	1.50843e6i	−0.0378164	−	0.0122873i
$498$	−151214.	+	109864.i	−0.00122435	+	0.000889541i
$499$	−1.10338e8	−	8.01651e7i	−0.888020	−	0.645184i	0.0473409	−	0.998879i	$-0.484925\pi$
$499$	−1.10338e8	−	8.01651e7i	−0.888020	−	0.645184i	−0.935361	+	0.353694i	$0.884925\pi$
$500$	2.63456e7	+	8.10835e7i	0.210765	+	0.648668i
$501$	960500.	−	312085.i	0.00763808	−	0.00248176i
$502$	−9.92257e7	+	1.36572e8i	−0.784356	+	1.07957i
$503$	1.19910e8	+	1.65042e8i	0.942217	+	1.29685i	0.954899	+	0.296931i	$0.0959633\pi$
$503$	1.19910e8	+	1.65042e8i	0.942217	+	1.29685i	−0.0126813	+	0.999920i	$0.504037\pi$
$504$	1.38109e7	−	4.25057e7i	0.107878	−	0.332013i
$505$			5.76575e7i			0.447694i
$506$	1.77080e8	−	7.84378e7i	1.36684	−	0.605443i
$507$	4.49094e6			0.0344599
$508$	6.82133e7	+	2.21638e7i	0.520329	+	0.169065i
$509$	−3.37419e7	+	2.45149e7i	−0.255868	+	0.185899i	−0.708323	−	0.705888i	$-0.750548\pi$
$509$	−3.37419e7	+	2.45149e7i	−0.255868	+	0.185899i	0.452455	+	0.891787i	$0.350548\pi$
$510$	4.48937e6	+	3.26172e6i	0.0338435	+	0.0245887i
$511$	1.08164e7	+	3.32893e7i	0.0810622	+	0.249484i
$512$	−1.24965e8	+	4.06037e7i	−0.931064	+	0.302521i
$513$	1.99230e6	−	2.74217e6i	0.0147572	−	0.0203115i
$514$	2.17037e6	+	2.98726e6i	0.0159825	+	0.0219980i
$515$	2.07452e7	−	6.38473e7i	0.151879	−	0.467434i
$516$		−	4.98436e6i		−	0.0362794i
$517$	−5.21791e7	+	2.43206e8i	−0.377594	+	1.75996i
$518$	−1.30264e7			−0.0937208
$519$	−2.82369e6	−	917474.i	−0.0201983	−	0.00656284i
$520$	3.61674e8	−	2.62772e8i	2.57222	−	1.86883i
$521$	8.13390e7	+	5.90962e7i	0.575156	+	0.417875i	0.836974	−	0.547242i	$-0.184322\pi$
$521$	8.13390e7	+	5.90962e7i	0.575156	+	0.417875i	−0.261819	+	0.965117i	$0.584322\pi$
$522$	−4.11353e7	−	1.26602e8i	−0.289203	−	0.890077i
$523$	1.64163e8	−	5.33398e7i	1.14755	−	0.372860i	0.327328	−	0.944911i	$-0.393852\pi$
$523$	1.64163e8	−	5.33398e7i	1.14755	−	0.372860i	0.820218	+	0.572051i	$0.193852\pi$
$524$	−2.03278e8	+	2.79789e8i	−1.41285	+	1.94463i
$525$	256350.	+	352835.i	0.00177156	+	0.00243834i
$526$	−6.79059e7	+	2.08993e8i	−0.466606	+	1.43606i
$527$		−	1.20479e8i		−	0.823153i
$528$	−1.25079e6	+	129057.i	−0.00849735	+	0.000876759i
$529$	−3.09831e7			−0.209294
$530$	−1.04775e8	−	3.40433e7i	−0.703766	−	0.228667i
$531$	−6.11450e6	+	4.44244e6i	−0.0408392	+	0.0296714i
$532$	−4.18530e7	−	3.04080e7i	−0.277966	−	0.201954i
$533$	−2.77247e7	−	8.53279e7i	−0.183099	−	0.563520i
$534$	−1.61741e6	+	525528.i	−0.0106217	+	0.00345121i
$535$	1.18128e8	−	1.62590e8i	0.771424	−	1.06177i
$536$	−1.53405e8	−	2.11145e8i	−0.996200	−	1.37115i
$537$	−1.13666e6	+	3.49828e6i	−0.00734019	+	0.0225908i
$538$			3.45988e7i			0.222185i
$539$	−1.26904e8	−	7.35905e7i	−0.810418	−	0.469954i
$540$	−1.26329e7			−0.0802270
$541$	−7.01487e7	−	2.27927e7i	−0.443024	−	0.143947i	0.0790062	−	0.996874i	$-0.474825\pi$
$541$	−7.01487e7	−	2.27927e7i	−0.443024	−	0.143947i	−0.522031	+	0.852927i	$0.674825\pi$
$542$	−1.21897e8	+	8.85636e7i	−0.765590	+	0.556234i
$543$	−1.80002e6	−	1.30779e6i	−0.0112429	−	0.00816843i
$544$	−3.00438e7	−	9.24654e7i	−0.186620	−	0.574358i
$545$	−2.23178e8	+	7.25150e7i	−1.37868	+	0.447959i
$546$	−1.18523e6	+	1.63134e6i	−0.00728159	+	0.0100223i
$547$	4.88150e7	+	6.71880e7i	0.298257	+	0.410516i	0.931674	−	0.363295i	$-0.118348\pi$
$547$	4.88150e7	+	6.71880e7i	0.298257	+	0.410516i	−0.633417	+	0.773811i	$0.718348\pi$
$548$	1.09500e8	−	3.37007e8i	0.665386	−	2.04785i
$549$		−	4.79897e7i		−	0.290022i
$550$	−1.00299e8	+	1.72962e8i	−0.602850	+	1.03959i
$551$	−6.97180e7			−0.416764
$552$	−3.31491e6	−	1.07708e6i	−0.0197086	−	0.00640370i
$553$	2.70371e7	−	1.96436e7i	0.159876	−	0.116157i
$554$	2.27823e8	+	1.65523e8i	1.33989	+	0.973486i
$555$	257372.	+	792111.i	0.00150551	+	0.00463348i
$556$	2.51774e8	−	8.18062e7i	1.46483	−	0.475951i
$557$	4.55331e7	−	6.26709e7i	0.263488	−	0.362660i	−0.656690	−	0.754161i	$-0.728044\pi$
$557$	4.55331e7	−	6.26709e7i	0.263488	−	0.362660i	0.920178	+	0.391500i	$0.128044\pi$
$558$	1.24725e8	+	1.71670e8i	0.717880	+	0.988077i
$559$	1.11709e8	−	3.43806e8i	0.639521	−	1.96824i
$560$			2.94365e7i			0.167619i
$561$	−344334.	−	3.33720e6i	−0.00195025	−	0.0189014i
$562$	−2.84669e8			−1.60373
$563$	1.49577e8	+	4.86005e7i	0.838184	+	0.272343i	0.696489	−	0.717568i	$-0.254745\pi$
$563$	1.49577e8	+	4.86005e7i	0.838184	+	0.272343i	0.141696	+	0.989910i	$0.454745\pi$
$564$	8.00410e6	−	5.81532e6i	0.0446144	−	0.0324143i
$565$	2.79641e8	+	2.03171e8i	1.55044	+	1.12646i
$566$	1.58274e8	+	4.87116e8i	0.872890	+	2.68648i
$567$	−4.35385e7	+	1.41465e7i	−0.238850	+	0.0776069i
$568$	−2.36722e7	+	3.25820e7i	−0.129180	+	0.177801i
$569$	−7.22023e7	−	9.93779e7i	−0.391935	−	0.539452i	0.566762	−	0.823882i	$-0.308196\pi$
$569$	−7.22023e7	−	9.93779e7i	−0.391935	−	0.539452i	−0.958697	+	0.284429i	$0.908196\pi$
$570$	−1.58178e6	+	4.86822e6i	−0.00854125	+	0.0262873i
$571$		−	2.13698e8i		−	1.14787i	−0.818901	−	0.573935i	$-0.805416\pi$
$571$		−	2.13698e8i		−	1.14787i	0.818901	−	0.573935i	$-0.194584\pi$
$572$	−5.84061e8	−	1.25308e8i	−3.12083	−	0.669563i
$573$	−5.58742e6			−0.0296994
$574$	2.57685e7	+	8.37271e6i	0.136256	+	0.0442721i
$575$	−9.77609e7	+	7.10275e7i	−0.514235	+	0.373614i
$576$	2.17243e8	+	1.57837e8i	1.13679	+	0.825924i
$577$	−1.03563e8	−	3.18733e8i	−0.539108	−	1.65920i	−0.734602	−	0.678498i	$-0.762631\pi$
$577$	−1.03563e8	−	3.18733e8i	−0.539108	−	1.65920i	0.195494	−	0.980705i	$-0.437369\pi$
$578$	−8.74231e7	+	2.84055e7i	−0.452734	+	0.147102i
$579$	1.52468e6	−	2.09854e6i	0.00785494	−	0.0108114i
$580$	1.52732e8	+	2.10217e8i	0.782789	+	1.07742i
$581$	817474.	−	2.51593e6i	0.00416817	−	0.0128283i
$582$		−	2.21756e6i		−	0.0112488i
$583$	2.69747e7	+	6.08978e7i	0.136129	+	0.307323i
$584$	2.88786e8			1.44990
$585$	−4.35627e8	−	1.41544e8i	−2.17594	−	0.707007i
$586$	1.65210e8	−	1.20032e8i	0.821001	−	0.596492i
$587$	−7.36494e7	−	5.35094e7i	−0.364129	−	0.264555i	0.390643	−	0.920542i	$-0.372253\pi$
$587$	−7.36494e7	−	5.35094e7i	−0.364129	−	0.264555i	−0.754772	+	0.655987i	$0.772253\pi$
$588$	1.80307e6	+	5.54929e6i	0.00886914	+	0.0272964i
$589$	1.05695e8	−	3.43424e7i	0.517260	−	0.168068i
$590$	1.34196e7	−	1.84705e7i	0.0653407	−	0.0899338i
$591$	221838.	+	305334.i	0.00107467	+	0.00147915i
$592$	−7.24124e6	+	2.22862e7i	−0.0349018	+	0.107417i
$593$		−	7.60702e6i		−	0.0364797i	−0.999834	−	0.0182398i	$-0.994194\pi$
$593$		−	7.60702e6i		−	0.0364797i	0.999834	−	0.0182398i	$-0.00580624\pi$
$594$	7.89202e6	+	8.79859e6i	0.0376555	+	0.0419811i
$595$	−7.85388e7			−0.372849
$596$	9.02536e7	+	2.93252e7i	0.426310	+	0.138517i
$597$	2.21240e6	−	1.60741e6i	0.0103978	−	0.00755445i
$598$	−4.51999e8	−	3.28396e8i	−2.11365	−	1.53566i
$599$	9.83039e7	+	3.02548e8i	0.457394	+	1.40771i	0.868302	+	0.496036i	$0.165212\pi$
$599$	9.83039e7	+	3.02548e8i	0.457394	+	1.40771i	−0.410908	+	0.911677i	$0.634788\pi$
$600$	3.42214e6	−	1.11192e6i	0.0158433	−	0.00514778i
$601$	−1.92949e8	+	2.65572e8i	−0.888831	+	1.22337i	0.0850646	+	0.996375i	$0.472890\pi$
$601$	−1.92949e8	+	2.65572e8i	−0.888831	+	1.22337i	−0.973896	+	0.226996i	$0.927110\pi$
$602$	6.41690e7	+	8.83210e7i	0.294127	+	0.404832i
$603$	−8.26330e7	+	2.54318e8i	−0.376878	+	1.15991i
$604$			2.57126e8i			1.16690i
$605$	2.83876e8	−	5.92111e7i	1.28192	−	0.267385i
$606$	−2.14565e6			−0.00964142
$607$	6.83908e7	+	2.22215e7i	0.305796	+	0.0993590i	0.457895	−	0.889006i	$-0.348603\pi$
$607$	6.83908e7	+	2.22215e7i	0.305796	+	0.0993590i	−0.152100	+	0.988365i	$0.548603\pi$
$608$	7.25548e7	−	5.27142e7i	0.322816	−	0.234540i
$609$	−429020.	−	311702.i	−0.00189944	−	0.00138003i
$610$	4.47970e7	+	1.37871e8i	0.197360	+	0.607411i
$611$	6.82432e8	−	2.21736e8i	2.99182	−	0.972102i
$612$	2.78662e8	−	3.83545e8i	1.21569	−	1.67326i
$613$	1.35145e8	+	1.86012e8i	0.586704	+	0.807529i	0.994410	−	0.105584i	$-0.0336711\pi$
$613$	1.35145e8	+	1.86012e8i	0.586704	+	0.807529i	−0.407706	+	0.913113i	$0.633671\pi$
$614$	−5.63138e6	+	1.73316e7i	−0.0243282	+	0.0748744i
$615$		−	1.73236e6i		−	0.00744754i
$616$	6.07617e7	−	5.45010e7i	0.259949	−	0.233165i
$617$	3.37400e7			0.143645			0.0718223	−	0.997417i	$-0.477119\pi$
$617$	3.37400e7			0.143645			0.0718223	+	0.997417i	$0.477119\pi$
$618$	2.37599e6	+	772007.i	0.0100665	+	0.00327082i
$619$	−2.82610e8	+	2.05328e8i	−1.19156	+	0.865718i	−0.993428	−	0.114458i	$-0.963487\pi$
$619$	−2.82610e8	+	2.05328e8i	−1.19156	+	0.865718i	−0.198130	+	0.980176i	$0.563487\pi$
$620$	−3.35097e8	−	2.43463e8i	−1.40603	−	1.02154i
$621$	2.20744e6	+	6.79379e6i	0.00921750	+	0.0283686i
$622$	−4.93384e8	+	1.60310e8i	−2.05028	+	0.666177i
$623$	1.41478e7	−	1.94728e7i	0.0585092	−	0.0805310i
$624$	2.13211e6	+	2.93460e6i	0.00877517	+	0.0120780i
$625$	−9.08230e7	+	2.79524e8i	−0.372011	+	1.14493i
$626$		−	2.54442e8i		−	1.03721i
$627$	2.82954e6	−	1.25334e6i	0.0114792	−	0.00508473i
$628$	−782343.			−0.00315877
$629$	−5.94613e7	−	1.93202e7i	−0.238937	−	0.0776352i
$630$	1.11909e8	−	8.13067e7i	0.447552	−	0.325166i
$631$	−2.19349e8	−	1.59366e8i	−0.873066	−	0.634319i	0.0583421	−	0.998297i	$-0.481419\pi$
$631$	−2.19349e8	−	1.59366e8i	−0.873066	−	0.634319i	−0.931408	+	0.363977i	$0.881419\pi$
$632$	−8.52044e7	−	2.62232e8i	−0.337529	−	1.03881i
$633$	−5.12588e6	+	1.66550e6i	−0.0202096	+	0.00656649i
$634$	3.65345e8	−	5.02854e8i	1.43362	−	1.97321i
$635$	5.90382e7	+	8.12591e7i	0.230575	+	0.317359i
$636$	818643.	−	2.51952e6i	0.00318217	−	0.00979371i
$637$			4.23184e8i			1.63723i
$638$	5.09982e7	−	2.37702e8i	0.196378	−	0.915316i
$639$	4.12638e7			0.158149
$640$	−5.97403e8	−	1.94108e8i	−2.27891	−	0.740463i
$641$	−7.60598e7	+	5.52606e7i	−0.288789	+	0.209818i	−0.722742	−	0.691118i	$-0.757118\pi$
$641$	−7.60598e7	+	5.52606e7i	−0.288789	+	0.209818i	0.433953	+	0.900936i	$0.357118\pi$
$642$	6.05057e6	+	4.39600e6i	0.0228661	+	0.0166132i
$643$	−2.37645e7	−	7.31396e7i	−0.0893914	−	0.275119i	0.896360	−	0.443327i	$-0.146202\pi$
$643$	−2.37645e7	−	7.31396e7i	−0.0893914	−	0.275119i	−0.985751	+	0.168208i	$0.946202\pi$
$644$	1.03692e8	−	3.36915e7i	0.388228	−	0.126143i
$645$	4.10279e6	−	5.64701e6i	0.0152898	−	0.0210445i
$646$	−2.25856e8	−	3.10864e8i	−0.837786	−	1.15311i
$647$	5.28928e7	−	1.62787e8i	0.195292	−	0.601046i	−0.804681	−	0.593707i	$-0.797664\pi$
$647$	5.28928e7	−	1.62787e8i	0.195292	−	0.601046i	0.999973	−	0.00733918i	$-0.00233616\pi$
$648$			3.77698e8i			1.38810i
$649$	−1.37302e7	+	1.41668e6i	−0.0502276	+	0.00518249i
$650$	5.76773e8			2.10022
$651$	803952.	+	261220.i	0.00291398	+	0.000946810i
$652$	−3.39867e8	+	2.46928e8i	−1.22621	+	0.890897i
$653$	−6.74330e7	−	4.89929e7i	−0.242177	−	0.175952i	0.460076	−	0.887880i	$-0.347822\pi$
$653$	−6.74330e7	−	4.89929e7i	−0.242177	−	0.175952i	−0.702253	+	0.711928i	$0.747822\pi$
$654$	−2.69855e6	−	8.30529e6i	−0.00964712	−	0.0296908i
$655$	−4.60607e8	+	1.49660e8i	−1.63910	+	0.532577i
$656$	2.86489e7	−	3.94318e7i	0.101484	−	0.139680i
$657$	−1.73918e8	−	2.39377e8i	−0.613264	−	0.844086i
$658$	−6.69629e7	+	2.06091e8i	−0.235048	+	0.723403i
$659$			1.52408e8i			0.532540i	0.963898	+	0.266270i	$0.0857913\pi$
$659$			1.52408e8i			0.532540i	−0.963898	+	0.266270i	$0.914209\pi$
$660$	−9.97782e6	−	5.78605e6i	−0.0347060	−	0.0201257i
$661$	4.14657e8			1.43577			0.717884	−	0.696162i	$-0.245111\pi$
$661$	4.14657e8			1.43577			0.717884	+	0.696162i	$0.245111\pi$
$662$	6.38989e8	+	2.07620e8i	2.20252	+	0.715642i
$663$	−7.82972e6	+	5.68863e6i	−0.0268662	+	0.0195194i
$664$	−1.76574e7	−	1.28289e7i	−0.0603146	−	0.0438211i
$665$	−2.23873e7	−	6.89011e7i	−0.0761268	−	0.234294i
$666$	1.04727e8	−	3.40278e7i	0.354516	−	0.115189i
$667$	8.63640e7	−	1.18870e8i	0.291042	−	0.400585i
$668$	1.53200e8	+	2.10862e8i	0.513961	+	0.707406i
$669$	−1.76282e6	+	5.42541e6i	−0.00588749	+	0.0181198i
$670$		−	8.07773e8i		−	2.68574i
$671$	4.39662e7	−	7.58181e7i	0.145530	−	0.250961i
$672$	682156.			0.00224790
$673$	2.77910e8	+	9.02984e7i	0.911714	+	0.296234i	0.727063	−	0.686570i	$-0.240885\pi$
$673$	2.77910e8	+	9.02984e7i	0.911714	+	0.296234i	0.184651	+	0.982804i	$0.440885\pi$
$674$	−5.86616e8	+	4.26201e8i	−1.91591	+	1.39199i
$675$	−5.96608e6	−	4.33461e6i	−0.0193989	−	0.0140942i
$676$	3.58153e8	+	1.10228e9i	1.15939	+	3.56823i
$677$	9.29765e7	−	3.02099e7i	0.299645	−	0.0973606i	−0.155336	−	0.987862i	$-0.549646\pi$
$677$	9.29765e7	−	3.02099e7i	0.299645	−	0.0973606i	0.454981	+	0.890501i	$0.349646\pi$
$678$	−7.56076e6	+	1.04065e7i	−0.0242592	+	0.0333899i
$679$	1.84481e7	+	2.53916e7i	0.0589307	+	0.0811111i
$680$	−2.00237e8	+	6.16266e8i	−0.636821	+	1.95993i
$681$			885136.i			0.00280265i
$682$	3.97746e7	+	3.85486e8i	0.125387	+	1.21522i
$683$	−5.93532e8			−1.86287			−0.931434	−	0.363910i	$-0.881442\pi$
$683$	−5.93532e8			−1.86287			−0.931434	+	0.363910i	$0.881442\pi$
$684$	4.15912e8	+	1.35138e8i	1.29967	+	0.422288i
$685$	4.01460e8	−	2.91678e8i	1.24902	−	0.907468i
$686$	−2.13756e8	−	1.55303e8i	−0.662134	−	0.481069i
$687$	622255.	+	1.91510e6i	0.00191910	+	0.00590639i
$688$	1.86775e8	−	6.06868e7i	0.573525	−	0.186350i
$689$	1.12935e8	−	1.55442e8i	0.345280	−	0.475237i
$690$	−6.34091e6	−	8.72751e6i	−0.0193021	−	0.0265670i
$691$	−6.75081e7	+	2.07768e8i	−0.204607	+	0.629717i	0.795122	+	0.606450i	$0.207407\pi$
$691$	−6.75081e7	+	2.07768e8i	−0.204607	+	0.629717i	−0.999729	+	0.0232673i	$0.992593\pi$
$692$		−	7.66233e8i		−	2.31229i
$693$	−8.17693e7	−	1.75433e7i	−0.245692	−	0.0527123i
$694$	4.60252e8			1.37695
$695$	3.52583e8	+	1.14561e8i	1.05029	+	0.341258i
$696$	−3.53961e6	+	2.57168e6i	−0.0104985	+	0.00762762i
$697$	1.05207e8	+	7.64373e7i	0.310703	+	0.225739i
$698$	−6.04602e7	−	1.86077e8i	−0.177788	−	0.547177i
$699$	4.00487e6	−	1.30126e6i	0.0117262	−	0.00381007i
$700$	−6.61580e7	+	9.10586e7i	−0.192880	+	0.265477i
$701$	−3.78916e8	−	5.21532e8i	−1.09999	−	1.51400i	−0.835399	−	0.549644i	$-0.814763\pi$
$701$	−3.78916e8	−	5.21532e8i	−1.09999	−	1.51400i	−0.264590	−	0.964361i	$-0.585237\pi$
$702$	1.05362e7	−	3.24272e7i	0.0304561	−	0.0937342i
$703$		−	5.76719e7i		−	0.165996i
$704$	1.98616e8	+	4.48393e8i	0.569240	+	1.28511i
$705$	1.38550e7			0.0395402
$706$	−1.07040e9	−	3.47796e8i	−3.04182	−	0.988348i
$707$	2.45682e7	−	1.78498e7i	0.0695208	−	0.0505098i
$708$	444162.	+	322703.i	0.00125153	+	0.000909291i
$709$	−1.66520e8	−	5.12495e8i	−0.467226	−	1.43797i	−0.856161	−	0.516709i	$-0.827157\pi$
$709$	−1.66520e8	−	5.12495e8i	−0.467226	−	1.43797i	0.388935	−	0.921265i	$-0.372843\pi$
$710$	−1.18548e8	+	3.85185e7i	−0.331222	+	0.107620i
$711$	−1.66053e8	+	2.28553e8i	−0.461996	+	0.635883i
$712$	−1.16726e8	−	1.60659e8i	−0.323390	−	0.445108i
$713$	−7.23769e7	+	2.22753e8i	−0.199678	+	0.614547i
$714$		−	2.92272e6i		−	0.00802958i
$715$	−5.58564e8	−	6.22727e8i	−1.52811	−	1.70365i
$716$	−9.49286e8			−2.58618
$717$	7.98803e6	+	2.59547e6i	0.0216712	+	0.00704139i
$718$	5.54820e8	−	4.03100e8i	1.49892	−	1.08903i
$719$	1.30320e8	+	9.46829e7i	0.350610	+	0.254733i	0.749125	−	0.662429i	$-0.230474\pi$
$719$	1.30320e8	+	9.46829e7i	0.350610	+	0.254733i	−0.398515	+	0.917162i	$0.630474\pi$
$720$	−7.68945e7	−	2.36657e8i	−0.206014	−	0.634047i
$721$	−3.36281e7	+	1.09264e7i	−0.0897214	+	0.0291522i
$722$	−1.63579e8	+	2.25147e8i	−0.434625	+	0.598210i
$723$	3.09297e6	+	4.25710e6i	0.00818390	+	0.0112642i
$724$	1.77440e8	−	5.46104e8i	0.467558	−	1.43900i
$725$			1.51684e8i			0.398039i
$726$	2.20347e6	+	1.05641e7i	0.00575833	+	0.0276071i
$727$	3.33557e8			0.868094			0.434047	−	0.900890i	$-0.357085\pi$
$727$	3.33557e8			0.868094			0.434047	+	0.900890i	$0.357085\pi$
$728$	−2.23937e8	−	7.27616e7i	−0.580406	−	0.188585i
$729$	3.12901e8	−	2.27336e8i	0.807651	−	0.586793i
$730$	7.23104e8	+	5.25366e8i	1.85880	+	1.35050i
$731$	1.61917e8	+	4.98329e8i	0.414514	+	1.27574i
$732$	−3.31539e6	+	1.07724e6i	−0.00845282	+	0.00274649i
$733$	2.70262e8	−	3.71984e8i	0.686236	−	0.944523i	−0.313752	−	0.949505i	$-0.601586\pi$
$733$	2.70262e8	−	3.71984e8i	0.686236	−	0.944523i	0.999988	+	0.00498247i	$0.00158598\pi$
$734$	5.10122e8	+	7.02123e8i	1.28999	+	1.77552i
$735$	−2.52502e6	+	7.77122e6i	−0.00635921	+	0.0195716i
$736$			1.89007e8i			0.474072i
$737$	−3.63546e8	+	3.26088e8i	−0.908150	+	0.814577i
$738$	−2.29039e8			−0.569824
$739$	6.09539e8	+	1.98051e8i	1.51032	+	0.490731i	0.943007	−	0.332773i	$-0.107984\pi$
$739$	6.09539e8	+	1.98051e8i	1.51032	+	0.490731i	0.567309	+	0.823505i	$0.307984\pi$
$740$	−1.73895e8	+	1.26342e8i	−0.429133	+	0.311783i
$741$	−7.22241e6	−	5.24739e6i	−0.0177512	−	0.0128970i
$742$	1.79305e7	+	5.51843e7i	0.0438914	+	0.135084i
$743$	−1.58396e8	+	5.14661e7i	−0.386170	+	0.125474i	−0.495667	−	0.868513i	$-0.665076\pi$
$743$	−1.58396e8	+	5.14661e7i	−0.386170	+	0.125474i	0.109496	+	0.993987i	$0.465076\pi$
$744$	4.09940e6	−	5.64234e6i	0.00995408	−	0.0137006i
$745$	7.81140e7	+	1.07515e8i	0.188912	+	0.260015i
$746$	3.18767e8	−	9.81064e8i	0.767815	−	2.36309i
$747$			2.23624e7i			0.0536483i
$748$	7.91643e8	−	3.50658e8i	1.89158	−	0.837875i
$749$	−1.05851e8			−0.251913
$750$	−4.22559e6	−	1.37298e6i	−0.0100162	−	0.00325446i
$751$	−3.18460e8	+	2.31375e8i	−0.751857	+	0.546256i	−0.896402	−	0.443242i	$-0.853828\pi$
$751$	−3.18460e8	+	2.31375e8i	−0.751857	+	0.546256i	0.144545	+	0.989498i	$0.453828\pi$
$752$	3.15366e8	+	2.29127e8i	0.741585	+	0.538793i
$753$	−1.75672e6	−	5.40662e6i	−0.00411450	−	0.0126631i
$754$	−6.66988e8	+	2.16717e8i	−1.55598	+	0.505568i
$755$	−2.11649e8	+	2.91310e8i	−0.491785	+	0.676884i
$756$	3.91093e6	+	5.38293e6i	0.00905138	+	0.0124582i
$757$	1.06424e8	−	3.27538e8i	0.245330	−	0.755047i	−0.750252	−	0.661152i	$-0.770068\pi$
$757$	1.06424e8	−	3.27538e8i	0.245330	−	0.755047i	0.995582	−	0.0938956i	$-0.0299320\pi$
$758$			1.03140e9i			2.36821i
$759$	−1.36816e6	+	6.37698e6i	−0.00312904	+	0.0145844i
$760$	−5.97720e8			−1.36162
$761$	−7.38799e8	−	2.40050e8i	−1.67638	−	0.544688i	−0.692175	−	0.721730i	$-0.743347\pi$
$761$	−7.38799e8	−	2.40050e8i	−1.67638	−	0.544688i	−0.984203	+	0.177041i	$0.943347\pi$
$762$	−3.02395e6	+	2.19703e6i	−0.00683455	+	0.00496559i
$763$	9.99914e7	+	7.26480e7i	0.225107	+	0.163550i
$764$	−4.45598e8	−	1.37141e9i	−0.999224	−	3.07529i
$765$	6.31418e8	−	2.05160e8i	1.41037	−	0.458257i
$766$	−6.21031e8	+	8.54776e8i	−1.38174	+	1.90181i
$767$	2.34046e7	+	3.22136e7i	0.0518698	+	0.0713927i
$768$	3.92310e6	−	1.20741e7i	0.00866055	−	0.0266544i
$769$			5.98902e8i			1.31697i	0.752592	+	0.658487i	$0.228803\pi$
$769$			5.98902e8i			1.31697i	−0.752592	+	0.658487i	$0.771197\pi$
$770$	2.51293e8	−	2.59285e7i	0.550438	−	0.0567944i
$771$	−124345.			−0.000271310
$772$	6.36672e8	+	2.06867e8i	1.38377	+	0.449614i
$773$	5.85276e8	−	4.25228e8i	1.26713	−	0.920626i	0.268048	−	0.963405i	$-0.413621\pi$
$773$	5.85276e8	−	4.25228e8i	1.26713	−	0.920626i	0.999085	+	0.0427795i	$0.0136213\pi$
$774$	−7.46604e8	−	5.42440e8i	−1.61015	−	1.16985i
$775$	−7.47181e7	−	2.29959e8i	−0.160517	−	0.494020i
$776$	2.46273e8	−	8.00188e7i	0.527025	−	0.171241i
$777$	257845.	−	354893.i	0.000549661	−	0.000756544i
$778$	3.32067e8	+	4.57051e8i	0.705158	+	0.970567i
$779$	−3.70685e7	+	1.14085e8i	−0.0784138	+	0.241333i
$780$			3.32728e7i			0.0701142i
$781$	6.51920e7	+	3.78042e7i	0.136849	+	0.0793574i
$782$	8.09806e8			1.69341
$783$	8.52794e6	+	2.77090e6i	0.0177647	+	0.00577211i
$784$	−1.85991e8	+	1.35130e8i	−0.385960	+	0.280417i
$785$	−886352.	−	643973.i	−0.00183230	−	0.00133125i
$786$	−5.56942e6	−	1.71409e7i	−0.0114694	−	0.0352993i
$787$	7.16186e7	−	2.32703e7i	0.146927	−	0.0477395i	−0.234630	−	0.972085i	$-0.575388\pi$
$787$	7.16186e7	−	2.32703e7i	0.146927	−	0.0477395i	0.381557	+	0.924345i	$0.375388\pi$
$788$	−5.72513e7	+	7.87996e7i	−0.117006	+	0.161044i
$789$	−4.34968e6	−	5.98683e6i	−0.00885578	−	0.0121889i
$790$	2.63711e8	−	8.11620e8i	0.534869	−	1.64616i
$791$		−	1.82055e8i		−	0.367852i
$792$	−3.46129e8	+	5.96887e8i	−0.696728	+	1.20148i
$793$	−2.52829e8			−0.506999
$794$	−8.81625e8	−	2.86457e8i	−1.76126	−	0.572267i
$795$	3.00138e6	−	2.18063e6i	0.00597338	−	0.00433991i
$796$	5.70971e8	+	4.14835e8i	1.13207	+	0.822500i
$797$	1.12862e8	+	3.47354e8i	0.222933	+	0.686116i	0.998495	+	0.0548452i	$0.0174665\pi$
$797$	1.12862e8	+	3.47354e8i	0.222933	+	0.686116i	−0.775562	+	0.631271i	$0.782533\pi$
$798$	2.56407e6	−	833116.i	0.00504569	−	0.00163945i
$799$	−6.11327e8	+	8.41419e8i	−1.19849	+	1.64958i
$800$	−1.14689e8	−	1.57856e8i	−0.224002	−	0.308313i
$801$	−6.28751e7	+	1.93510e8i	−0.122344	+	0.376535i
$802$		−	6.23683e8i		−	1.20904i
$803$	−5.54619e7	−	5.37525e8i	−0.107115	−	1.03813i
$804$	1.94246e7			0.0373752
$805$	1.45210e8	+	4.71815e7i	0.278361	+	0.0904448i
$806$	9.04425e8	−	6.57103e8i	1.72730	−	1.25496i
$807$	−942611.	−	684847.i	−0.00179354	−	0.00130309i
$808$	−7.74239e7	−	2.38286e8i	−0.146771	−	0.451716i
$809$	4.50954e8	−	1.46524e8i	0.851701	−	0.276734i	0.149543	−	0.988755i	$-0.452220\pi$
$809$	4.50954e8	−	1.46524e8i	0.851701	−	0.276734i	0.702158	+	0.712021i	$0.252220\pi$
$810$	−6.87117e8	+	9.45735e8i	−1.29293	+	1.77957i
$811$	−4.77124e8	−	6.56705e8i	−0.894476	−	1.23114i	−0.972197	−	0.234166i	$-0.924764\pi$
$811$	−4.77124e8	−	6.56705e8i	−0.894476	−	1.23114i	0.0777207	−	0.996975i	$-0.475236\pi$
$812$	4.22914e7	−	1.30160e8i	0.0789922	−	0.243113i
$813$		−	5.07400e6i		−	0.00944233i
$814$	1.96631e8	+	4.21866e7i	0.364568	+	0.0782169i
$815$	−5.88306e8			−1.08675
$816$	−5.00033e6	−	1.62471e6i	−0.00920298	−	0.00299023i
$817$	−3.91024e8	+	2.84095e8i	−0.717029	+	0.520952i
$818$	2.09154e8	+	1.51959e8i	0.382125	+	0.277630i
$819$	7.45505e7	+	2.29443e8i	0.135706	+	0.417660i
$820$	4.25201e8	−	1.38156e8i	0.771174	−	0.250570i
$821$	2.41800e8	−	3.32810e8i	0.436946	−	0.601404i	−0.532584	−	0.846377i	$-0.678779\pi$
$821$	2.41800e8	−	3.32810e8i	0.436946	−	0.601404i	0.969530	+	0.244973i	$0.0787790\pi$
$822$	1.08544e7	+	1.49398e7i	0.0195430	+	0.0268986i
$823$	2.37746e8	−	7.31706e8i	0.426494	−	1.31261i	−0.475062	−	0.879952i	$-0.657575\pi$
$823$	2.37746e8	−	7.31706e8i	0.426494	−	1.31261i	0.901556	−	0.432662i	$-0.142425\pi$
$824$			2.91725e8i			0.521425i
$825$	−2.72687e6	−	6.15617e6i	−0.00485628	−	0.0109635i
$826$	−1.20249e7			−0.0213374
$827$	1.74252e8	+	5.66178e7i	0.308078	+	0.100101i	0.458976	−	0.888449i	$-0.348217\pi$
$827$	1.74252e8	+	5.66178e7i	0.308078	+	0.100101i	−0.150898	+	0.988549i	$0.548217\pi$
$828$	−7.45627e8	+	5.41730e8i	−1.31350	+	0.954315i
$829$	2.45096e8	+	1.78073e8i	0.430203	+	0.312561i	0.781730	−	0.623617i	$-0.214337\pi$
$829$	2.45096e8	+	1.78073e8i	0.430203	+	0.312561i	−0.351527	+	0.936178i	$0.614337\pi$
$830$	−2.08746e7	−	6.42455e7i	−0.0365077	−	0.112359i
$831$	−9.01904e6	+	2.93047e6i	−0.0157166	+	0.00510662i
$832$	8.31547e8	−	1.14453e9i	1.44383	−	1.98726i
$833$	−3.60537e8	−	4.96237e8i	−0.623756	−	0.858527i
$834$	−4.26325e6	+	1.31209e7i	−0.00734925	+	0.0226187i
$835$			3.64999e8i			0.626950i
$836$	5.33284e8	+	5.94544e8i	0.912725	+	1.01757i
$837$	−1.42936e7			−0.0243761
$838$	−3.80818e8	−	1.23735e8i	−0.647120	−	0.210262i
$839$	6.55647e8	−	4.76355e8i	1.11016	−	0.806576i	0.127468	−	0.991843i	$-0.459315\pi$
$839$	6.55647e8	−	4.76355e8i	1.11016	−	0.806576i	0.982688	+	0.185267i	$0.0593150\pi$
$840$	−3.67816e6	−	2.67234e6i	−0.00620573	−	0.00450873i
$841$	1.26817e8	+	3.90301e8i	0.213200	+	0.656163i
$842$	−1.47280e9	+	4.78541e8i	−2.46721	+	0.801646i
$843$	5.63472e6	−	7.75553e6i	0.00940567	−	0.0129458i
$844$	−8.17579e8	−	1.12530e9i	−1.35989	−	1.87172i
$845$	−5.01557e8	+	1.54364e9i	−0.831286	+	2.55844i
$846$		−	1.83180e9i		−	3.02529i
$847$	−1.13113e8	−	1.02630e8i	−0.186150	−	0.168898i
$848$	1.04379e8			0.171170
$849$	−1.64039e7	−	5.32994e6i	−0.0268055	−	0.00870963i
$850$	−6.76339e8	+	4.91389e8i	−1.10131	+	0.800146i
$851$	9.83311e7	+	7.14417e7i	0.159552	+	0.115921i
$852$	−926259.	−	2.85073e6i	−0.00149766	−	0.00460933i
$853$	−9.56645e8	+	3.10833e8i	−1.54136	+	0.500818i	−0.951751	−	0.306872i	$-0.900718\pi$
$853$	−9.56645e8	+	3.10833e8i	−1.54136	+	0.500818i	−0.589608	+	0.807689i	$0.700718\pi$
$854$	4.48791e7	−	6.17708e7i	0.0720561	−	0.0991767i
$855$	3.59969e8	+	4.95455e8i	0.575926	+	0.792694i
$856$	−2.69870e8	+	8.30576e8i	−0.430263	+	1.32421i
$857$			3.80361e7i			0.0604300i	0.999543	+	0.0302150i	$0.00961921\pi$
$857$			3.80361e7i			0.0604300i	−0.999543	+	0.0302150i	$0.990381\pi$
$858$	2.31740e7	−	2.07862e7i	0.0366893	−	0.0329090i
$859$	6.94187e8			1.09521			0.547604	−	0.836737i	$-0.315540\pi$
$859$	6.94187e8			1.09521			0.547604	+	0.836737i	$0.315540\pi$
$860$	1.71323e9	+	5.56664e8i	2.69353	+	0.875180i
$861$	−738168.	+	536311.i	−0.00115650	+	0.000840247i
$862$	9.98683e8	+	7.25585e8i	1.55921	+	1.13284i
$863$	−1.53195e8	−	4.71485e8i	−0.238348	−	0.733560i	−0.996660	−	0.0816675i	$-0.973975\pi$
$863$	−1.53195e8	−	4.71485e8i	−0.238348	−	0.733560i	0.758312	−	0.651892i	$-0.226025\pi$
$864$	−1.09700e7	+	3.56438e6i	−0.0170085	+	0.00552640i
$865$	6.30712e8	−	8.68100e8i	0.974502	−	1.34129i
$866$	3.88226e8	+	5.34348e8i	0.597766	+	0.822755i
$867$	956569.	−	2.94402e6i	0.00146777	−	0.00451734i
$868$			2.18159e8i			0.333591i
$869$	−4.71735e8	+	2.08955e8i	−0.718851	+	0.318415i
$870$	−1.35414e7			−0.0205640
$871$	1.33985e9	+	4.35344e8i	2.02769	+	0.658837i
$872$	8.24974e8	−	5.99379e8i	1.24420	−	0.903965i
$873$	−2.14643e8	−	1.55947e8i	−0.322607	−	0.234387i
$874$	2.30834e8	+	7.10433e8i	0.345752	+	1.06412i
$875$	5.98058e7	−	1.94321e7i	0.0892728	−	0.0290065i
$876$	−1.26335e7	+	1.73886e7i	−0.0187937	+	0.0258673i
$877$	1.43021e8	+	1.96851e8i	0.212031	+	0.291836i	0.901765	−	0.432227i	$-0.142272\pi$
$877$	1.43021e8	+	1.96851e8i	0.212031	+	0.291836i	−0.689733	+	0.724064i	$0.742272\pi$
$878$	−4.05856e8	+	1.24910e9i	−0.599638	+	1.84549i
$879$			6.87691e6i			0.0101257i
$880$	9.53312e7	−	4.44338e8i	0.139890	−	0.652027i
$881$	6.01333e8			0.879402			0.439701	−	0.898144i	$-0.355084\pi$
$881$	6.01333e8			0.879402			0.439701	+	0.898144i	$0.355084\pi$
$882$	1.02745e9	+	3.33839e8i	1.49746	+	0.486554i
$883$	−1.09540e9	+	7.95856e8i	−1.59108	+	1.15599i	−0.688696	+	0.725051i	$0.741816\pi$
$883$	−1.09540e9	+	7.95856e8i	−1.59108	+	1.15599i	−0.902383	+	0.430935i	$0.858184\pi$
$884$	−2.02067e9	−	1.46810e9i	−2.92509	−	2.12520i
$885$	237584.	+	731209.i	0.000342758	+	0.00105490i
$886$	5.87207e8	−	1.90795e8i	0.844287	−	0.274325i
$887$	−3.41909e8	+	4.70598e8i	−0.489937	+	0.674340i	−0.980376	−	0.197135i	$-0.936836\pi$
$887$	−3.41909e8	+	4.70598e8i	−0.489937	+	0.674340i	0.490440	+	0.871475i	$0.336836\pi$
$888$	−2.12733e6	−	2.92802e6i	−0.00303806	−	0.00418154i
$889$	1.63477e7	−	5.03130e7i	0.0232676	−	0.0716102i
$890$		−	6.14631e8i		−	0.871855i
$891$	7.03019e8	−	7.25377e7i	0.993879	−	0.102549i
$892$	−1.47223e9			−2.07435
$893$	−9.12424e8	−	2.96465e8i	−1.28128	−	0.416312i
$894$	−4.00102e6	+	2.90691e6i	−0.00559962	+	0.00406836i
$895$	−1.07549e9	−	7.81389e8i	−1.50016	−	1.08993i
$896$	1.02236e8	+	3.14649e8i	0.142128	+	0.437424i
$897$	1.78937e7	−	5.81401e6i	0.0247926	−	0.00805561i
$898$	5.26627e8	−	7.24841e8i	0.727235	−	1.00095i
$899$	1.72810e8	+	2.37852e8i	0.237842	+	0.327362i
$900$	2.94017e8	−	9.04891e8i	0.403315	−	1.24128i
$901$			2.78492e8i			0.380748i
$902$	−3.61855e8	−	2.09837e8i	−0.493078	−	0.285931i
$903$	−3.67638e6			−0.00499295
$904$	−1.42852e9	−	4.64155e8i	−1.93367	−	0.628287i
$905$	6.50546e8	−	4.72650e8i	0.877672	−	0.637666i
$906$	−1.08407e7	−	7.87624e6i	−0.0145772	−	0.0105909i
$907$	−3.34382e8	−	1.02912e9i	−0.448148	−	1.37926i	−0.878994	−	0.476833i	$-0.841785\pi$
$907$	−3.34382e8	−	1.02912e9i	−0.448148	−	1.37926i	0.430846	−	0.902425i	$-0.358215\pi$
$908$	−2.17253e8	+	7.05898e7i	−0.290207	+	0.0942941i
$909$	−1.50890e8	+	2.07682e8i	−0.200895	+	0.276508i
$910$	−4.28356e8	−	5.89582e8i	−0.568435	−	0.782384i
$911$	1.35166e7	−	4.16000e7i	0.0178778	−	0.0550222i	−0.941720	−	0.336399i	$-0.890791\pi$
$911$	1.35166e7	−	4.16000e7i	0.0178778	−	0.0550222i	0.959597	+	0.281377i	$0.0907910\pi$
$912$		−	4.84985e6i		−	0.00639358i
$913$	−2.04875e7	+	3.53300e7i	−0.0269201	+	0.0464227i
$914$	4.96726e8			0.650546
$915$	−4.64287e6	−	1.50856e6i	−0.00606071	−	0.00196924i
$916$	−4.20430e8	+	3.05460e8i	−0.547025	+	0.397437i
$917$	2.06367e8	+	1.49935e8i	0.267629	+	0.194444i
$918$	1.52717e7	+	4.70015e7i	0.0197406	+	0.0607552i
$919$	4.68129e8	−	1.52104e8i	0.603142	−	0.195973i	0.00850066	−	0.999964i	$-0.497294\pi$
$919$	4.68129e8	−	1.52104e8i	0.603142	−	0.195973i	0.594641	+	0.803991i	$0.297294\pi$
$920$	7.40433e8	−	1.01912e9i	0.950872	−	1.30876i
$921$	−360716.	−	496482.i	−0.000461728	−	0.000635514i
$922$	−5.88170e8	+	1.81020e9i	−0.750430	+	2.30959i
$923$		−	2.17394e8i		−	0.276467i
$924$	623505.	+	6.04287e6i	0.000790359	+	0.00765998i
$925$	−1.25476e8			−0.158538
$926$	−1.07148e9	−	3.48146e8i	−1.34944	−	0.438458i
$927$	2.41813e8	−	1.75687e8i	0.303557	−	0.220547i
$928$	1.91941e8	+	1.39453e8i	0.240173	+	0.174496i
$929$	−2.21417e8	−	6.81451e8i	−0.276162	−	0.849939i	−0.988910	−	0.148518i	$-0.952550\pi$
$929$	−2.21417e8	−	6.81451e8i	−0.276162	−	0.849939i	0.712748	−	0.701420i	$-0.247450\pi$
$930$	2.05293e7	−	6.67038e6i	0.0255226	−	0.00829281i
$931$	3.32572e8	−	4.57746e8i	0.412132	−	0.567251i
$932$	6.38778e8	+	8.79202e8i	0.789046	+	1.08603i
$933$	5.39852e6	−	1.66149e7i	0.00664707	−	0.0204576i
$934$			1.03058e9i			1.26485i
$935$	1.18553e9	+	2.54351e8i	1.45036	+	0.311170i
$936$	1.99043e9			2.42727
$937$	−6.91609e8	−	2.24717e8i	−0.840702	−	0.273161i	−0.143155	−	0.989700i	$-0.545725\pi$
$937$	−6.91609e8	−	2.24717e8i	−0.840702	−	0.273161i	−0.697546	+	0.716540i	$0.745725\pi$
$938$	−3.44196e8	+	2.50073e8i	−0.417059	+	0.303011i
$939$	6.93203e6	+	5.03642e6i	0.00837267	+	0.00608310i
$940$	1.10494e9	+	3.40065e9i	1.33032	+	4.09429i
$941$	3.60855e7	−	1.17249e7i	0.0433076	−	0.0140715i	−0.287283	−	0.957846i	$-0.592752\pi$
$941$	3.60855e7	−	1.17249e7i	0.0433076	−	0.0140715i	0.330591	+	0.943774i	$0.392752\pi$
$942$	23964.6	−	32984.5i	2.86694e−5	−	3.94600e-5i
$943$	−1.48597e8	−	2.04526e8i	−0.177205	−	0.243901i
$944$	−6.68449e6	+	2.05727e7i	−0.00794607	+	0.0244555i
$945$			9.31779e6i			0.0110412i
$946$	−6.82586e8	−	1.54100e9i	−0.806277	−	1.82024i
$947$	−1.18813e8			−0.139899			−0.0699494	−	0.997551i	$-0.522284\pi$
$947$	−1.18813e8			−0.139899			−0.0699494	+	0.997551i	$0.522284\pi$
$948$	1.95171e7	+	6.34149e6i	0.0229082	+	0.00744332i
$949$	−1.26114e9	+	9.16268e8i	−1.47558	+	1.07207i
$950$	−6.23879e8	−	4.53275e8i	−0.727662	−	0.528677i
$951$	6.46816e6	+	1.99069e7i	0.00752037	+	0.0231453i
$952$	3.24585e8	−	1.05464e8i	0.376199	−	0.122234i
$953$	−1.75903e7	+	2.42110e7i	−0.0203233	+	0.0279726i	−0.819058	−	0.573711i	$-0.805503\pi$
$953$	−1.75903e7	+	2.42110e7i	−0.0203233	+	0.0279726i	0.798734	+	0.601684i	$0.205503\pi$
$954$	−2.88306e8	−	3.96820e8i	−0.332054	−	0.457034i
$955$	6.24014e8	−	1.92052e9i	0.716447	−	2.20500i
$956$			2.16762e9i			2.48090i
$957$	5.46652e6	+	6.09447e6i	0.00623699	+	0.00695344i
$958$	2.02425e9			2.30233
$959$	−2.48571e8	−	8.07656e7i	−0.281835	−	0.0915736i
$960$	2.20993e7	−	1.60561e7i	0.0249784	−	0.0181479i
$961$	3.38856e8	+	2.46193e8i	0.381808	+	0.277400i
$962$	−1.79272e8	−	5.51743e8i	−0.201367	−	0.619743i
$963$	8.50997e8	−	2.76506e8i	0.952904	−	0.309617i
$964$	−7.98224e8	+	1.09866e9i	−0.891033	+	1.22640i
$965$	5.51036e8	+	7.58436e8i	0.613194	+	0.843989i
$966$	−1.75580e6	+	5.40379e6i	−0.00194780	+	0.00599470i
$967$		−	6.28531e8i		−	0.695100i	−0.937661	−	0.347550i	$-0.887014\pi$
$967$		−	6.28531e8i		−	0.695100i	0.937661	−	0.347550i	$-0.112986\pi$
$968$	−1.09369e9	+	6.25902e8i	−1.20578	+	0.690050i
$969$	1.29398e7			0.0142218
$970$	7.62224e8	+	2.47662e8i	0.835156	+	0.271359i
$971$	−8.43657e8	+	6.12953e8i	−0.921528	+	0.669529i	−0.943904	−	0.330220i	$-0.892877\pi$
$971$	−8.43657e8	+	6.12953e8i	−0.921528	+	0.669529i	0.0223760	+	0.999750i	$0.492877\pi$
$972$	−6.82586e7	−	4.95927e7i	−0.0743290	−	0.0540032i
$973$	−6.03389e7	−	1.85704e8i	−0.0655027	−	0.201596i
$974$	1.25865e9	−	4.08960e8i	1.36216	−	0.442592i
$975$	−1.14166e7	+	1.57136e7i	−0.0123175	+	0.0169536i
$976$	−8.07327e7	−	1.11119e8i	−0.0868361	−	0.119520i
$977$	−2.52232e6	+	7.76291e6i	−0.00270469	+	0.00832417i	−0.952400	−	0.304852i	$-0.901393\pi$
$977$	−2.52232e6	+	7.76291e6i	−0.00270469	+	0.00832417i	0.949695	+	0.313176i	$0.101393\pi$
$978$		−	2.18931e7i		−	0.0234040i
$979$	−2.76621e8	+	2.48119e8i	−0.294807	+	0.264431i
$980$	−2.10878e9			−2.24055
$981$	−9.93660e8	−	3.22860e8i	−1.05252	−	0.341985i
$982$	8.62993e8	−	6.27001e8i	0.911324	−	0.662116i
$983$	3.26083e8	+	2.36913e8i	0.343295	+	0.249418i	0.746051	−	0.665889i	$-0.231948\pi$
$983$	3.26083e8	+	2.36913e8i	0.343295	+	0.249418i	−0.402756	+	0.915307i	$0.631948\pi$
$984$	2.32626e6	+	7.15948e6i	0.00244159	+	0.00751444i
$985$	−1.29725e8	+	4.21503e7i	−0.135742	+	0.0441054i
$986$	5.97492e8	−	8.22377e8i	0.623306	−	0.857907i
$987$	−4.28928e6	−	5.90369e6i	−0.00446101	−	0.00614005i
$988$	7.11961e8	−	2.19119e9i	0.738219	−	2.27201i
$989$		−	1.01862e9i		−	1.05299i
$990$	−1.95256e9	+	8.64886e8i	−2.01233	+	0.891360i
$991$	−1.27319e9			−1.30820			−0.654098	−	0.756410i	$-0.726952\pi$
$991$	−1.27319e9			−1.30820			−0.654098	+	0.756410i	$0.726952\pi$
$992$	−3.59683e8	−	1.16868e8i	−0.368455	−	0.119718i
$993$	−1.83046e7	+	1.32990e7i	−0.0186944	+	0.0135823i
$994$	5.31134e7	+	3.85892e7i	0.0540811	+	0.0392922i
$995$	3.05415e8	+	9.39971e8i	0.310042	+	0.954212i
$996$	1.54492e6	−	501974.i	0.00156360	−	0.000508046i
$997$	7.24871e7	−	9.97699e7i	0.0731434	−	0.100673i	−0.770878	−	0.636983i	$-0.780182\pi$
$997$	7.24871e7	−	9.97699e7i	0.0731434	−	0.100673i	0.844021	+	0.536310i	$0.180182\pi$
$998$	1.07818e9	+	1.48398e9i	1.08467	+	1.49292i
$999$	−2.29213e6	+	7.05445e6i	−0.00229902	+	0.00707566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.2.1	✓	20
3.2	odd	2		99.7.k.a.46.5		20
11.4	even	5		121.7.b.c.120.3		20
11.6	odd	10	inner	11.7.d.a.6.1	yes	20
11.7	odd	10		121.7.b.c.120.18		20
33.17	even	10		99.7.k.a.28.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.2.1	✓	20	1.1	even	1	trivial
11.7.d.a.6.1	yes	20	11.6	odd	10	inner
99.7.k.a.28.5		20	33.17	even	10
99.7.k.a.46.5		20	3.2	odd	2
121.7.b.c.120.3		20	11.4	even	5
121.7.b.c.120.18		20	11.7	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)

\(f(q)\)	\(=\)	\(q+(-12.7912 - 4.15611i) q^{2} +(0.366417 - 0.266218i) q^{3} +(94.5639 + 68.7047i) q^{4} +(50.5827 + 155.677i) q^{5} +(-5.79334 + 1.88237i) q^{6} +(50.6754 - 69.7488i) q^{7} +(-418.095 - 575.459i) q^{8} +(-225.210 + 693.125i) q^{9} +O(q^{10})\)	\(q+(-12.7912 - 4.15611i) q^{2} +(0.366417 - 0.266218i) q^{3} +(94.5639 + 68.7047i) q^{4} +(50.5827 + 155.677i) q^{5} +(-5.79334 + 1.88237i) q^{6} +(50.6754 - 69.7488i) q^{7} +(-418.095 - 575.459i) q^{8} +(-225.210 + 693.125i) q^{9} -2201.52i q^{10} +(-990.819 + 888.729i) q^{11} +52.9403 q^{12} +(3651.66 + 1186.50i) q^{13} +(-938.082 + 681.556i) q^{14} +(59.9785 + 43.5769i) q^{15} +(644.571 + 1983.78i) q^{16} +(-5292.88 + 1719.76i) q^{17} +(5761.40 - 7929.89i) q^{18} +(-3017.45 - 4153.17i) q^{19} +(-5912.48 + 18196.7i) q^{20} -39.0479i q^{21} +(16367.4 - 7249.94i) q^{22} +10819.1 q^{23} +(-306.395 - 99.5537i) q^{24} +(-9035.96 + 6565.01i) q^{25} +(-41777.8 - 30353.4i) q^{26} +(204.031 + 627.944i) q^{27} +(9584.14 - 3114.07i) q^{28} +(7982.55 - 10987.0i) q^{29} +(-586.085 - 806.677i) q^{30} +(-6689.73 + 20588.9i) q^{31} +17469.8i q^{32} +(-126.458 + 589.419i) q^{33} +74849.7 q^{34} +(13421.6 + 4360.94i) q^{35} +(-68917.7 + 50071.6i) q^{36} +(9088.66 + 6603.30i) q^{37} +(21335.8 + 65664.8i) q^{38} +(1653.90 - 537.384i) q^{39} +(68437.6 - 94196.2i) q^{40} +(-13734.7 - 18904.2i) q^{41} +(-162.287 + 499.468i) q^{42} -94150.7i q^{43} +(-154756. + 15967.7i) q^{44} -119296. q^{45} +(-138389. - 44965.3i) q^{46} +(151191. - 109847. i) q^{47} +(764.301 + 555.297i) q^{48} +(34058.7 + 104822. i) q^{49} +(142865. - 46419.8i) q^{50} +(-1481.57 + 2039.21i) q^{51} +(263798. + 363086. i) q^{52} +(15463.5 - 47591.8i) q^{53} -8880.12i q^{54} +(-188473. - 109294. i) q^{55} -61324.7 q^{56} +(-2211.29 - 718.493i) q^{57} +(-147770. + 107361. i) q^{58} +(8389.87 + 6095.60i) q^{59} +(2677.86 + 8241.60i) q^{60} +(-62625.2 + 20348.2i) q^{61} +(171139. - 235553. i) q^{62} +(36932.0 + 50832.5i) q^{63} +(113859. - 350421. i) q^{64} +628497. i q^{65} +(4067.23 - 7013.79i) q^{66} +366915. q^{67} +(-618672. - 201019. i) q^{68} +(3964.30 - 2880.23i) q^{69} +(-153554. - 111563. i) q^{70} +(-17496.3 - 53848.1i) q^{71} +(493024. - 160193. i) q^{72} +(-238637. + 328456. i) q^{73} +(-88810.6 - 122237. i) q^{74} +(-1563.21 + 4811.07i) q^{75} -600053. i q^{76} +(11777.5 + 114145. i) q^{77} -23388.7 q^{78} +(368663. + 119786. i) q^{79} +(-276226. + 200690. i) q^{80} +(-429582. - 312110. i) q^{81} +(97115.2 + 298890. i) q^{82} +(29182.3 - 9481.89i) q^{83} +(2682.77 - 3692.52i) q^{84} +(-535456. - 736992. i) q^{85} +(-391300. + 1.20430e6i) q^{86} -6150.94i q^{87} +(925684. + 198602. i) q^{88} +279184. q^{89} +(1.52593e6 + 495805. i) q^{90} +(267806. - 194573. i) q^{91} +(1.02310e6 + 743323. i) q^{92} +(3029.89 + 9325.05i) q^{93} +(-2.39045e6 + 776703. i) q^{94} +(493924. - 679828. i) q^{95} +(4650.76 + 6401.22i) q^{96} +(-112496. + 346226. i) q^{97} -1.48234e6i q^{98} +(-392858. - 886912. 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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