LMFDB - Embedded newform 495.2.bc.c.353.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(23,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("495.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bc (of order $12$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.17
Character	$\chi$	$=$	495.353
Dual form			495.2.bc.c.122.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0274785 + 0.00736284i) q^{2} +(-1.57310 + 0.724814i) q^{3} +(-1.73135 + 0.999595i) q^{4} +(2.18362 + 0.481456i) q^{5} +(0.0378897 - 0.0314993i) q^{6} +(-0.830150 - 3.09816i) q^{7} +(0.0804463 - 0.0804463i) q^{8} +(1.94929 - 2.28041i) q^{9} +O(q^{10})$	\(q+(-0.0274785 + 0.00736284i) q^{2} +(-1.57310 + 0.724814i) q^{3} +(-1.73135 + 0.999595i) q^{4} +(2.18362 + 0.481456i) q^{5} +(0.0378897 - 0.0314993i) q^{6} +(-0.830150 - 3.09816i) q^{7} +(0.0804463 - 0.0804463i) q^{8} +(1.94929 - 2.28041i) q^{9} +(-0.0635475 + 0.00284797i) q^{10} +(0.866025 + 0.500000i) q^{11} +(1.99907 - 2.82737i) q^{12} +(0.776816 - 2.89912i) q^{13} +(0.0456225 + 0.0790205i) q^{14} +(-3.78402 + 0.825341i) q^{15} +(1.99757 - 3.45990i) q^{16} +(3.59908 + 3.59908i) q^{17} +(-0.0367732 + 0.0770146i) q^{18} +7.26476i q^{19} +(-4.26187 + 1.34917i) q^{20} +(3.55150 + 4.27201i) q^{21} +(-0.0274785 - 0.00736284i) q^{22} +(-0.219998 - 0.0589483i) q^{23} +(-0.0682415 + 0.184859i) q^{24} +(4.53640 + 2.10263i) q^{25} +0.0853829i q^{26} +(-1.41355 + 5.00019i) q^{27} +(4.53419 + 4.53419i) q^{28} +(2.30368 - 3.99009i) q^{29} +(0.0979023 - 0.0505403i) q^{30} +(3.22955 + 5.59375i) q^{31} +(-0.0883064 + 0.329564i) q^{32} +(-1.72475 - 0.158842i) q^{33} +(-0.125397 - 0.0723979i) q^{34} +(-0.321104 - 7.16489i) q^{35} +(-1.09541 + 5.89669i) q^{36} +(6.56691 - 6.56691i) q^{37} +(-0.0534892 - 0.199625i) q^{38} +(0.879312 + 5.12365i) q^{39} +(0.214396 - 0.136933i) q^{40} +(-1.51514 + 0.874766i) q^{41} +(-0.129044 - 0.0912393i) q^{42} +(-6.25522 + 1.67608i) q^{43} -1.99919 q^{44} +(5.35442 - 4.04106i) q^{45} +0.00647924 q^{46} +(11.2236 - 3.00735i) q^{47} +(-0.634599 + 6.89063i) q^{48} +(-2.84727 + 1.64387i) q^{49} +(-0.140135 - 0.0243764i) q^{50} +(-8.27039 - 3.05305i) q^{51} +(1.55300 + 5.79589i) q^{52} +(4.30627 - 4.30627i) q^{53} +(0.00202667 - 0.147805i) q^{54} +(1.65034 + 1.50876i) q^{55} +(-0.316018 - 0.182453i) q^{56} +(-5.26560 - 11.4282i) q^{57} +(-0.0339232 + 0.126603i) q^{58} +(1.55836 + 2.69917i) q^{59} +(5.72646 - 5.21144i) q^{60} +(-3.46648 + 6.00411i) q^{61} +(-0.129929 - 0.129929i) q^{62} +(-8.68328 - 4.14613i) q^{63} +7.98058i q^{64} +(3.09207 - 5.95657i) q^{65} +(0.0485631 - 0.00833432i) q^{66} +(3.23891 + 0.867862i) q^{67} +(-9.82890 - 2.63365i) q^{68} +(0.388806 - 0.0667262i) q^{69} +(0.0615774 + 0.194516i) q^{70} -9.40355i q^{71} +(-0.0266376 - 0.340264i) q^{72} +(1.17731 + 1.17731i) q^{73} +(-0.132098 + 0.228800i) q^{74} +(-8.66023 - 0.0196065i) q^{75} +(-7.26182 - 12.5778i) q^{76} +(0.830150 - 3.09816i) q^{77} +(-0.0618868 - 0.134316i) q^{78} +(6.40956 + 3.70056i) q^{79} +(6.02773 - 6.59336i) q^{80} +(-1.40055 - 8.89036i) q^{81} +(0.0351930 - 0.0351930i) q^{82} +(-2.08279 - 7.77308i) q^{83} +(-10.4192 - 3.84629i) q^{84} +(6.12623 + 9.59183i) q^{85} +(0.159543 - 0.0921124i) q^{86} +(-0.731843 + 7.94654i) q^{87} +(0.109892 - 0.0294454i) q^{88} -7.03497 q^{89} +(-0.117378 + 0.150466i) q^{90} -9.62680 q^{91} +(0.439818 - 0.117849i) q^{92} +(-9.13484 - 6.45870i) q^{93} +(-0.286264 + 0.165275i) q^{94} +(-3.49766 + 15.8635i) q^{95} +(-0.0999579 - 0.582443i) q^{96} +(-2.33501 - 8.71439i) q^{97} +(0.0661352 - 0.0661352i) q^{98} +(2.82834 - 1.00025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9}+O(q^{10}) $ 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9	\( 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9} + 6 q^{10} + 6 q^{12} - 12 q^{13} + 10 q^{14} - 18 q^{15} + 62 q^{16} + 8 q^{17} - 12 q^{18} - 18 q^{20} - 10 q^{21} - 4 q^{22} - 40 q^{23} + 62 q^{24} - 6 q^{25} - 58 q^{27} + 18 q^{28} + 2 q^{29} - 70 q^{30} - 2 q^{31} - 66 q^{32} + 24 q^{34} - 2 q^{35} + 24 q^{36} - 14 q^{37} - 6 q^{38} - 4 q^{39} - 100 q^{40} + 6 q^{41} - 30 q^{42} - 22 q^{43} + 120 q^{44} + 94 q^{45} - 44 q^{46} + 32 q^{47} + 108 q^{48} + 18 q^{49} - 22 q^{50} - 8 q^{51} - 126 q^{52} + 44 q^{53} - 28 q^{54} + 2 q^{55} + 42 q^{56} + 20 q^{57} + 2 q^{58} - 22 q^{59} - 68 q^{60} - 10 q^{61} + 16 q^{62} - 8 q^{63} - 60 q^{65} + 6 q^{66} + 36 q^{67} - 48 q^{68} + 76 q^{69} + 154 q^{70} - 228 q^{72} + 12 q^{73} + 8 q^{74} - 72 q^{75} - 6 q^{76} - 8 q^{77} - 110 q^{78} + 6 q^{79} - 4 q^{80} + 44 q^{81} - 50 q^{82} + 30 q^{83} - 222 q^{84} - 126 q^{85} + 90 q^{86} + 112 q^{87} + 2 q^{88} - 8 q^{89} + 72 q^{90} + 72 q^{91} - 132 q^{92} + 112 q^{93} - 42 q^{94} + 78 q^{95} + 68 q^{96} - 72 q^{97} - 16 q^{98} + 4 q^{99}+O(q^{100}) \) 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9 + 6 * q^10 + 6 * q^12 - 12 * q^13 + 10 * q^14 - 18 * q^15 + 62 * q^16 + 8 * q^17 - 12 * q^18 - 18 * q^20 - 10 * q^21 - 4 * q^22 - 40 * q^23 + 62 * q^24 - 6 * q^25 - 58 * q^27 + 18 * q^28 + 2 * q^29 - 70 * q^30 - 2 * q^31 - 66 * q^32 + 24 * q^34 - 2 * q^35 + 24 * q^36 - 14 * q^37 - 6 * q^38 - 4 * q^39 - 100 * q^40 + 6 * q^41 - 30 * q^42 - 22 * q^43 + 120 * q^44 + 94 * q^45 - 44 * q^46 + 32 * q^47 + 108 * q^48 + 18 * q^49 - 22 * q^50 - 8 * q^51 - 126 * q^52 + 44 * q^53 - 28 * q^54 + 2 * q^55 + 42 * q^56 + 20 * q^57 + 2 * q^58 - 22 * q^59 - 68 * q^60 - 10 * q^61 + 16 * q^62 - 8 * q^63 - 60 * q^65 + 6 * q^66 + 36 * q^67 - 48 * q^68 + 76 * q^69 + 154 * q^70 - 228 * q^72 + 12 * q^73 + 8 * q^74 - 72 * q^75 - 6 * q^76 - 8 * q^77 - 110 * q^78 + 6 * q^79 - 4 * q^80 + 44 * q^81 - 50 * q^82 + 30 * q^83 - 222 * q^84 - 126 * q^85 + 90 * q^86 + 112 * q^87 + 2 * q^88 - 8 * q^89 + 72 * q^90 + 72 * q^91 - 132 * q^92 + 112 * q^93 - 42 * q^94 + 78 * q^95 + 68 * q^96 - 72 * q^97 - 16 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0274785	+	0.00736284i	−0.0194302	+	0.00520631i	−0.268521	−	0.963274i	$-0.586535\pi$
$2$	−0.0274785	+	0.00736284i	−0.0194302	+	0.00520631i	0.249091	+	0.968480i	$0.419868\pi$
$3$	−1.57310	+	0.724814i	−0.908230	+	0.418472i
$3$	−1.57310	+	0.724814i	−0.908230	+	0.418472i
$4$	−1.73135	+	0.999595i	−0.865675	+	0.499798i
$5$	2.18362	+	0.481456i	0.976545	+	0.215314i
$5$	2.18362	+	0.481456i	0.976545	+	0.215314i
$6$	0.0378897	−	0.0314993i	0.0154684	−	0.0128595i
$7$	−0.830150	−	3.09816i	−0.313767	−	1.17099i	−0.925132	−	0.379646i	$-0.876046\pi$
$7$	−0.830150	−	3.09816i	−0.313767	−	1.17099i	0.611365	−	0.791349i	$-0.290621\pi$
$8$	0.0804463	−	0.0804463i	0.0284421	−	0.0284421i
$9$	1.94929	−	2.28041i	0.649763	−	0.760137i
$10$	−0.0635475	+	0.00284797i	−0.0200955	+	0.000900606i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$12$	1.99907	−	2.82737i	0.577081	−	0.816192i
$13$	0.776816	−	2.89912i	0.215450	−	0.804070i	−0.770558	−	0.637370i	$-0.780022\pi$
$13$	0.776816	−	2.89912i	0.215450	−	0.804070i	0.986008	−	0.166700i	$-0.0533111\pi$
$14$	0.0456225	+	0.0790205i	0.0121931	+	0.0211191i
$15$	−3.78402	+	0.825341i	−0.977030	+	0.213102i
$16$	1.99757	−	3.45990i	0.499393	−	0.864974i
$17$	3.59908	+	3.59908i	0.872906	+	0.872906i	0.992788	−	0.119882i	$-0.0382517\pi$
$17$	3.59908	+	3.59908i	0.872906	+	0.872906i	−0.119882	+	0.992788i	$0.538252\pi$
$18$	−0.0367732	+	0.0770146i	−0.00866753	+	0.0181525i
$19$			7.26476i			1.66665i	0.552784	+	0.833325i	$0.313566\pi$
$19$			7.26476i			1.66665i	−0.552784	+	0.833325i	$0.686434\pi$
$20$	−4.26187	+	1.34917i	−0.952984	+	0.301683i
$21$	3.55150	+	4.27201i	0.775001	+	0.932230i
$22$	−0.0274785	−	0.00736284i	−0.00585843	−	0.00156976i
$23$	−0.219998	−	0.0589483i	−0.0458728	−	0.0122916i	0.235810	−	0.971799i	$-0.424226\pi$
$23$	−0.219998	−	0.0589483i	−0.0458728	−	0.0122916i	−0.281682	+	0.959508i	$0.590892\pi$
$24$	−0.0682415	+	0.184859i	−0.0139297	+	0.0377341i
$25$	4.53640	+	2.10263i	0.907280	+	0.420527i
$26$			0.0853829i			0.0167450i
$27$	−1.41355	+	5.00019i	−0.272038	+	0.962287i
$28$	4.53419	+	4.53419i	0.856881	+	0.856881i
$29$	2.30368	−	3.99009i	0.427782	−	0.740940i	−0.568894	−	0.822411i	$-0.692628\pi$
$29$	2.30368	−	3.99009i	0.427782	−	0.740940i	0.996676	+	0.0814709i	$0.0259618\pi$
$30$	0.0979023	−	0.0505403i	0.0178744	−	0.00922735i
$31$	3.22955	+	5.59375i	0.580045	+	1.00467i	0.995473	+	0.0950412i	$0.0302983\pi$
$31$	3.22955	+	5.59375i	0.580045	+	1.00467i	−0.415429	+	0.909626i	$0.636368\pi$
$32$	−0.0883064	+	0.329564i	−0.0156105	+	0.0582592i
$33$	−1.72475	−	0.158842i	−0.300241	−	0.0276509i
$34$	−0.125397	−	0.0723979i	−0.0215054	−	0.0124161i
$35$	−0.321104	−	7.16489i	−0.0542765	−	1.21109i
$36$	−1.09541	+	5.89669i	−0.182569	+	0.982782i
$37$	6.56691	−	6.56691i	1.07959	−	1.07959i	0.0830473	−	0.996546i	$-0.473535\pi$
$37$	6.56691	−	6.56691i	1.07959	−	1.07959i	0.996546	−	0.0830473i	$-0.0264653\pi$
$38$	−0.0534892	−	0.199625i	−0.00867710	−	0.0323834i
$39$	0.879312	+	5.12365i	0.140803	+	0.820440i
$40$	0.214396	−	0.136933i	0.0338989	−	0.0216510i
$41$	−1.51514	+	0.874766i	−0.236625	+	0.136616i	−0.613625	−	0.789598i	$-0.710289\pi$
$41$	−1.51514	+	0.874766i	−0.236625	+	0.136616i	0.377000	+	0.926213i	$0.376956\pi$
$42$	−0.129044	−	0.0912393i	−0.0199119	−	0.0140785i
$43$	−6.25522	+	1.67608i	−0.953913	+	0.255600i	−0.702022	−	0.712156i	$-0.747719\pi$
$43$	−6.25522	+	1.67608i	−0.953913	+	0.255600i	−0.251891	+	0.967756i	$0.581052\pi$
$44$	−1.99919			−0.301389
$45$	5.35442	−	4.04106i	0.798190	−	0.602405i
$46$	0.00647924			0.000955312
$47$	11.2236	−	3.00735i	1.63713	−	0.438667i	0.681158	−	0.732137i	$-0.261477\pi$
$47$	11.2236	−	3.00735i	1.63713	−	0.438667i	0.955968	+	0.293470i	$0.0948100\pi$
$48$	−0.634599	+	6.89063i	−0.0915964	+	0.994577i
$49$	−2.84727	+	1.64387i	−0.406753	+	0.234839i
$50$	−0.140135	−	0.0243764i	−0.0198181	−	0.00344735i
$51$	−8.27039	−	3.05305i	−1.15809	−	0.427513i
$52$	1.55300	+	5.79589i	0.215363	+	0.803745i
$53$	4.30627	−	4.30627i	0.591512	−	0.591512i	−0.346528	−	0.938040i	$-0.612639\pi$
$53$	4.30627	−	4.30627i	0.591512	−	0.591512i	0.938040	+	0.346528i	$0.112639\pi$
$54$	0.00202667	−	0.147805i	0.000275795	−	0.0201138i
$55$	1.65034	+	1.50876i	0.222532	+	0.203442i
$56$	−0.316018	−	0.182453i	−0.0422297	−	0.0243813i
$57$	−5.26560	−	11.4282i	−0.697446	−	1.51370i
$58$	−0.0339232	+	0.126603i	−0.00445434	+	0.0166238i
$59$	1.55836	+	2.69917i	0.202882	+	0.351402i	0.949456	−	0.313901i	$-0.101636\pi$
$59$	1.55836	+	2.69917i	0.202882	+	0.351402i	−0.746574	+	0.665302i	$0.768303\pi$
$60$	5.72646	−	5.21144i	0.739282	−	0.672795i
$61$	−3.46648	+	6.00411i	−0.443837	+	0.768748i	−0.997970	−	0.0636800i	$-0.979716\pi$
$61$	−3.46648	+	6.00411i	−0.443837	+	0.768748i	0.554134	+	0.832428i	$0.313050\pi$
$62$	−0.129929	−	0.129929i	−0.0165010	−	0.0165010i
$63$	−8.68328	−	4.14613i	−1.09399	−	0.522363i
$64$			7.98058i			0.997573i
$65$	3.09207	−	5.95657i	0.383524	−	0.738821i
$66$	0.0485631	−	0.00833432i	0.00597771	−	0.00102588i
$67$	3.23891	+	0.867862i	0.395695	+	0.106026i	0.451179	−	0.892433i	$-0.351003\pi$
$67$	3.23891	+	0.867862i	0.395695	+	0.106026i	−0.0554839	+	0.998460i	$0.517670\pi$
$68$	−9.82890	−	2.63365i	−1.19193	−	0.319376i
$69$	0.388806	−	0.0667262i	0.0468067	−	0.00803289i
$70$	0.0615774	+	0.194516i	0.00735991	+	0.0232491i
$71$		−	9.40355i		−	1.11600i	−0.829842	−	0.557998i	$-0.811570\pi$
$71$		−	9.40355i		−	1.11600i	0.829842	−	0.557998i	$-0.188430\pi$
$72$	−0.0266376	−	0.340264i	−0.00313927	−	0.0401005i
$73$	1.17731	+	1.17731i	0.137794	+	0.137794i	0.772639	−	0.634845i	$-0.218936\pi$
$73$	1.17731	+	1.17731i	0.137794	+	0.137794i	−0.634845	+	0.772639i	$0.718936\pi$
$74$	−0.132098	+	0.228800i	−0.0153560	+	0.0265974i
$75$	−8.66023	−	0.0196065i	−0.999997	−	0.00226397i
$76$	−7.26182	−	12.5778i	−0.832987	−	1.44278i
$77$	0.830150	−	3.09816i	0.0946043	−	0.353068i
$78$	−0.0618868	−	0.134316i	−0.00700730	−	0.0152083i
$79$	6.40956	+	3.70056i	0.721132	+	0.416346i	0.815169	−	0.579223i	$-0.196644\pi$
$79$	6.40956	+	3.70056i	0.721132	+	0.416346i	−0.0940370	+	0.995569i	$0.529977\pi$
$80$	6.02773	−	6.59336i	0.673921	−	0.737160i
$81$	−1.40055	−	8.89036i	−0.155617	−	0.987818i
$82$	0.0351930	−	0.0351930i	0.00388642	−	0.00388642i
$83$	−2.08279	−	7.77308i	−0.228616	−	0.853207i	−0.980923	−	0.194394i	$-0.937726\pi$
$83$	−2.08279	−	7.77308i	−0.228616	−	0.853207i	0.752307	−	0.658812i	$-0.228941\pi$
$84$	−10.4192	−	3.84629i	−1.13683	−	0.419664i
$85$	6.12623	+	9.59183i	0.664483	+	1.04038i
$86$	0.159543	−	0.0921124i	0.0172040	−	0.00993274i
$87$	−0.731843	+	7.94654i	−0.0784618	+	0.851959i
$88$	0.109892	−	0.0294454i	0.0117145	−	0.00313889i
$89$	−7.03497			−0.745706			−0.372853	−	0.927890i	$-0.621620\pi$
$89$	−7.03497			−0.745706			−0.372853	+	0.927890i	$0.621620\pi$
$90$	−0.117378	+	0.150466i	−0.0123727	+	0.0158605i
$91$	−9.62680			−1.00916
$92$	0.439818	−	0.117849i	0.0458542	−	0.0122866i
$93$	−9.13484	−	6.45870i	−0.947239	−	0.669736i
$94$	−0.286264	+	0.165275i	−0.0295259	+	0.0170468i
$95$	−3.49766	+	15.8635i	−0.358852	+	1.62756i
$96$	−0.0999579	−	0.582443i	−0.0102019	−	0.0594453i
$97$	−2.33501	−	8.71439i	−0.237085	−	0.884813i	−0.977198	−	0.212330i	$-0.931895\pi$
$97$	−2.33501	−	8.71439i	−0.237085	−	0.884813i	0.740113	−	0.672482i	$-0.234772\pi$
$98$	0.0661352	−	0.0661352i	0.00668066	−	0.00668066i
$99$	2.82834	−	1.00025i	0.284259	−	0.100529i
$100$	−9.95588	+	0.894169i	−0.995588	+	0.0894169i
$101$	−5.55308	−	3.20608i	−0.552553	−	0.319016i	0.197598	−	0.980283i	$-0.436686\pi$
$101$	−5.55308	−	3.20608i	−0.552553	−	0.319016i	−0.750151	+	0.661267i	$0.770019\pi$
$102$	0.249737	+	0.0229997i	0.0247276	+	0.00227731i
$103$	−1.37279	+	5.12333i	−0.135265	+	0.504817i	0.864731	+	0.502235i	$0.167489\pi$
$103$	−1.37279	+	5.12333i	−0.135265	+	0.504817i	−0.999997	+	0.00258222i	$0.999178\pi$
$104$	−0.170731	−	0.295715i	−0.0167416	−	0.0289973i
$105$	5.69834	+	11.0383i	0.556101	+	1.07723i
$106$	−0.0866235	+	0.150036i	−0.00841361	+	0.0145728i
$107$	−7.39693	−	7.39693i	−0.715089	−	0.715089i	0.252507	−	0.967595i	$-0.418745\pi$
$107$	−7.39693	−	7.39693i	−0.715089	−	0.715089i	−0.967595	+	0.252507i	$0.918745\pi$
$108$	−2.55081	−	10.0701i	−0.245452	−	0.968991i
$109$			16.0982i			1.54193i	0.636880	+	0.770963i	$0.280225\pi$
$109$			16.0982i			1.54193i	−0.636880	+	0.770963i	$0.719775\pi$
$110$	−0.0564577	−	0.0293073i	−0.00538303	−	0.00279434i
$111$	−5.57061	+	15.0902i	−0.528739	+	1.43230i
$112$	−12.3776	−	3.31657i	−1.16957	−	0.313386i
$113$	5.60771	+	1.50258i	0.527529	+	0.141351i	0.512747	−	0.858540i	$-0.328628\pi$
$113$	5.60771	+	1.50258i	0.527529	+	0.141351i	0.0147820	+	0.999891i	$0.495295\pi$
$114$	0.228835	+	0.275260i	0.0214323	+	0.0257804i
$115$	−0.452011	−	0.234640i	−0.0421503	−	0.0218803i
$116$			9.21098i			0.855218i
$117$	−5.09694	−	7.42267i	−0.471212	−	0.686226i
$118$	−0.0626950	−	0.0626950i	−0.00577155	−	0.00577155i
$119$	8.16276	−	14.1383i	0.748279	−	1.29606i
$120$	−0.238015	+	0.370806i	−0.0217277	+	0.0338498i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	0.0510462	−	0.190507i	0.00462151	−	0.0172477i
$123$	1.74942	−	2.47429i	0.157740	−	0.223099i
$124$	−11.1830	−	6.45649i	−1.00426	−	0.579810i
$125$	8.89345	+	6.77543i	0.795455	+	0.606013i
$126$	0.269131	+	0.0499957i	0.0239761	+	0.00445397i
$127$	1.48023	−	1.48023i	0.131349	−	0.131349i	−0.638376	−	0.769725i	$-0.720393\pi$
$127$	1.48023	−	1.48023i	0.131349	−	0.131349i	0.769725	+	0.638376i	$0.220393\pi$
$128$	−0.235373	−	0.878423i	−0.0208042	−	0.0776423i
$129$	8.62524	−	7.17052i	0.759410	−	0.631329i
$130$	−0.0411081	+	0.186444i	−0.00360542	+	0.0163522i
$131$	−4.82135	+	2.78361i	−0.421243	+	0.243205i	−0.695609	−	0.718421i	$-0.744865\pi$
$131$	−4.82135	+	2.78361i	−0.421243	+	0.243205i	0.274366	+	0.961625i	$0.411532\pi$
$132$	3.14493	−	1.44904i	0.273731	−	0.126123i
$133$	22.5074	−	6.03083i	1.95164	−	0.522940i
$134$	−0.0953902			−0.00824046
$135$	−5.49403	+	10.2380i	−0.472851	+	0.881143i
$136$	0.579066			0.0496545
$137$	6.39609	−	1.71383i	0.546455	−	0.146422i	0.0249787	−	0.999688i	$-0.492048\pi$
$137$	6.39609	−	1.71383i	0.546455	−	0.146422i	0.521476	+	0.853266i	$0.325382\pi$
$138$	−0.0101925	+	0.00469625i	−0.000867643	+	0.000399771i
$139$	18.1389	−	10.4725i	1.53852	−	0.888266i	0.539597	−	0.841924i	$-0.318577\pi$
$139$	18.1389	−	10.4725i	1.53852	−	0.888266i	0.998926	−	0.0463425i	$-0.0147566\pi$
$140$	7.71793	+	12.0840i	0.652284	+	1.02128i
$141$	−15.4760	+	12.8659i	−1.30332	+	1.08350i
$142$	0.0692368	+	0.258395i	0.00581023	+	0.0216841i
$143$	2.12230	−	2.12230i	0.177476	−	0.177476i
$144$	−3.99614	−	11.2996i	−0.333012	−	0.941635i
$145$	6.95141	−	7.60371i	0.577283	−	0.631454i
$146$	−0.0410191	−	0.0236824i	−0.00339476	−	0.00195997i
$147$	3.28754	−	4.64972i	0.271152	−	0.383503i
$148$	−4.80536	+	17.9339i	−0.394999	+	1.47415i
$149$	1.15178	+	1.99494i	0.0943577	+	0.163432i	0.909340	−	0.416053i	$-0.136587\pi$
$149$	1.15178	+	1.99494i	0.0943577	+	0.163432i	−0.814983	+	0.579485i	$0.803254\pi$
$150$	0.238114	−	0.0632251i	0.0194420	−	0.00516231i
$151$	−1.39474	+	2.41577i	−0.113503	+	0.196592i	−0.917180	−	0.398473i	$-0.869540\pi$
$151$	−1.39474	+	2.41577i	−0.113503	+	0.196592i	0.803678	+	0.595065i	$0.202874\pi$
$152$	0.584423	+	0.584423i	0.0474030	+	0.0474030i
$153$	15.2230	−	1.19174i	1.23071	−	0.0963464i
$154$			0.0912450i			0.00735274i
$155$	4.35897	+	13.7695i	0.350121	+	1.10599i
$156$	−6.64397	−	7.99187i	−0.531943	−	0.639862i
$157$	−2.45722	−	0.658410i	−0.196107	−	0.0525468i	0.159428	−	0.987209i	$-0.449035\pi$
$157$	−2.45722	−	0.658410i	−0.196107	−	0.0525468i	−0.355536	+	0.934663i	$0.615702\pi$
$158$	−0.203372	−	0.0544933i	−0.0161794	−	0.00433526i
$159$	−3.65295	+	9.89544i	−0.289698	+	0.784760i
$160$	−0.351498	+	0.677127i	−0.0277884	+	0.0535316i
$161$			0.730525i			0.0575735i
$162$	0.103943	+	0.233982i	0.00816656	+	0.0183833i
$163$	−15.3525	−	15.3525i	−1.20250	−	1.20250i	−0.973404	−	0.229097i	$-0.926423\pi$
$163$	−15.3525	−	15.3525i	−1.20250	−	1.20250i	−0.229097	−	0.973404i	$-0.573577\pi$
$164$	1.74882	−	3.02905i	0.136560	−	0.236529i
$165$	−3.68973	−	1.17724i	−0.287245	−	0.0916483i
$166$	0.114464	+	0.198257i	0.00888412	+	0.0153878i
$167$	−3.78396	+	14.1219i	−0.292812	+	1.09279i	0.650128	+	0.759824i	$0.274715\pi$
$167$	−3.78396	+	14.1219i	−0.292812	+	1.09279i	−0.942940	+	0.332963i	$0.891952\pi$
$168$	0.629373	+	0.0579626i	0.0485572	+	0.00447191i
$169$	3.45690	+	1.99584i	0.265915	+	0.153526i
$170$	−0.238963	−	0.218463i	−0.0183276	−	0.0167553i
$171$	16.5666	+	14.1611i	1.26688	+	1.08293i
$172$	9.15458	−	9.15458i	0.698030	−	0.698030i
$173$	−4.20905	−	15.7084i	−0.320008	−	1.19429i	−0.919236	−	0.393707i	$-0.871192\pi$
$173$	−4.20905	−	15.7084i	−0.320008	−	1.19429i	0.599228	−	0.800578i	$-0.295474\pi$
$174$	−0.0383992	−	0.223747i	−0.00291103	−	0.0169622i
$175$	2.74841	−	15.8000i	0.207760	−	1.19437i
$176$	3.45990	−	1.99757i	0.260800	−	0.150573i
$177$	−4.40786	−	3.11653i	−0.331315	−	0.234253i
$178$	0.193310	−	0.0517974i	0.0144892	−	0.00388238i
$179$	−23.5544			−1.76054			−0.880270	−	0.474473i	$-0.842639\pi$
$179$	−23.5544			−1.76054			−0.880270	+	0.474473i	$0.842639\pi$
$180$	−5.23096	+	12.3487i	−0.389893	+	0.920421i
$181$	−3.83503			−0.285056			−0.142528	−	0.989791i	$-0.545523\pi$
$181$	−3.83503			−0.285056			−0.142528	+	0.989791i	$0.545523\pi$
$182$	0.264530	−	0.0708806i	0.0196083	−	0.00525402i
$183$	1.10125	−	11.9576i	0.0814065	−	0.883933i
$184$	−0.0224402	+	0.0129559i	−0.00165431	+	0.000955119i
$185$	17.5013	−	11.1780i	1.28672	−	0.821820i
$186$	0.298566	+	0.110217i	0.0218919	+	0.00808151i
$187$	1.31736	+	4.91644i	0.0963346	+	0.359526i
$188$	−16.4258	+	16.4258i	−1.19797	+	1.19797i
$189$	16.6648	+	0.228504i	1.21219	+	0.0166212i
$190$	−0.0206898	−	0.461657i	−0.00150100	−	0.0334921i
$191$	18.4798	+	10.6693i	1.33715	+	0.772005i	0.986384	−	0.164458i	$-0.0525874\pi$
$191$	18.4798	+	10.6693i	1.33715	+	0.772005i	0.350767	+	0.936463i	$0.385921\pi$
$192$	−5.78444	−	12.5543i	−0.417456	−	0.906026i
$193$	−3.98620	+	14.8767i	−0.286933	+	1.07085i	0.660482	+	0.750842i	$0.270352\pi$
$193$	−3.98620	+	14.8767i	−0.286933	+	1.07085i	−0.947415	+	0.320007i	$0.896315\pi$
$194$	0.128325	+	0.222266i	0.00921322	+	0.0159578i
$195$	−0.546727	+	11.6115i	−0.0391519	+	0.831513i
$196$	3.28642	−	5.69224i	0.234744	−	0.406589i
$197$	−12.2773	−	12.2773i	−0.874724	−	0.874724i	0.118259	−	0.992983i	$-0.462269\pi$
$197$	−12.2773	−	12.2773i	−0.874724	−	0.874724i	−0.992983	+	0.118259i	$0.962269\pi$
$198$	−0.0703538	+	0.0483100i	−0.00499983	+	0.00343324i
$199$			10.9617i			0.777056i	0.921437	+	0.388528i	$0.127016\pi$
$199$			10.9617i			0.777056i	−0.921437	+	0.388528i	$0.872984\pi$
$200$	0.534086	−	0.195788i	0.0377656	−	0.0138443i
$201$	−5.72416	+	0.982371i	−0.403751	+	0.0692911i
$202$	0.176196	+	0.0472116i	0.0123971	+	0.00332180i
$203$	−14.2743	−	3.82479i	−1.00186	−	0.268448i
$204$	17.3707	−	2.98114i	1.21620	−	0.208721i
$205$	−3.72965	+	1.18068i	−0.260490	+	0.0824626i
$206$		−	0.150889i		−	0.0105129i
$207$	−0.563266	+	0.386779i	−0.0391497	+	0.0268830i
$208$	−8.47890	−	8.47890i	−0.587906	−	0.587906i
$209$	−3.63238	+	6.29146i	−0.251257	+	0.435190i
$210$	−0.237855	−	0.261361i	−0.0164136	−	0.0180356i
$211$	−9.95356	−	17.2401i	−0.685231	−	1.18686i	−0.973364	−	0.229265i	$-0.926368\pi$
$211$	−9.95356	−	17.2401i	−0.685231	−	1.18686i	0.288133	−	0.957591i	$-0.406966\pi$
$212$	−3.15113	+	11.7602i	−0.216421	+	0.807693i
$213$	6.81583	+	14.7927i	0.467013	+	1.01358i
$214$	0.257719	+	0.148794i	0.0176173	+	0.0101714i
$215$	−14.4660	+	0.648313i	−0.986573	+	0.0442146i
$216$	0.288532	+	0.515962i	0.0196321	+	0.0351067i
$217$	14.6493	−	14.6493i	0.994461	−	0.994461i
$218$	−0.118528	−	0.442354i	−0.00802775	−	0.0299600i
$219$	−2.70536	−	0.998696i	−0.182811	−	0.0674856i
$220$	−4.36547	−	0.962522i	−0.294320	−	0.0648932i
$221$	13.2300	−	7.63834i	0.889945	−	0.513810i
$222$	0.0419654	−	0.455671i	0.00281653	−	0.0305827i
$223$	10.7078	−	2.86914i	0.717046	−	0.192132i	0.118193	−	0.992991i	$-0.462290\pi$
$223$	10.7078	−	2.86914i	0.717046	−	0.192132i	0.598853	+	0.800859i	$0.295623\pi$
$224$	1.09435			0.0731193
$225$	13.6376	−	6.24622i	0.909175	−	0.416414i
$226$	−0.165155			−0.0109859
$227$	−22.6559	+	6.07062i	−1.50372	+	0.402921i	−0.914345	−	0.404936i	$-0.867294\pi$
$227$	−22.6559	+	6.07062i	−1.50372	+	0.402921i	−0.589378	+	0.807858i	$0.700627\pi$
$228$	20.5402	+	14.5227i	1.36031	+	0.961791i
$229$	−11.0779	+	6.39583i	−0.732048	+	0.422648i	−0.819171	−	0.573549i	$-0.805566\pi$
$229$	−11.0779	+	6.39583i	−0.732048	+	0.422648i	0.0871230	+	0.996198i	$0.472233\pi$
$230$	0.0141482	+	0.00311947i	0.000932906	+	0.000205692i
$231$	0.939683	+	5.47542i	0.0618266	+	0.360256i
$232$	−0.135665	−	0.506310i	−0.00890687	−	0.0332409i
$233$	−4.58631	+	4.58631i	−0.300459	+	0.300459i	−0.841193	−	0.540734i	$-0.818146\pi$
$233$	−4.58631	+	4.58631i	−0.300459	+	0.300459i	0.540734	+	0.841193i	$0.318146\pi$
$234$	0.194708	+	0.166436i	0.0127285	+	0.0108803i
$235$	25.9559	−	1.16325i	1.69318	−	0.0758821i
$236$	−5.39615	−	3.11547i	−0.351259	−	0.202800i
$237$	−12.7651	−	1.17561i	−0.829183	−	0.0763643i
$238$	−0.120202	+	0.448601i	−0.00779155	+	0.0290785i
$239$	−1.43753	−	2.48987i	−0.0929859	−	0.161056i	0.815780	−	0.578362i	$-0.196308\pi$
$239$	−1.43753	−	2.48987i	−0.0929859	−	0.161056i	−0.908766	+	0.417306i	$0.862974\pi$
$240$	−4.70326	+	14.7410i	−0.303594	+	0.951528i
$241$	1.09124	−	1.89009i	0.0702932	−	0.121751i	−0.828737	−	0.559639i	$-0.810940\pi$
$241$	1.09124	−	1.89009i	0.0702932	−	0.121751i	0.899030	+	0.437887i	$0.144273\pi$
$242$	−0.0201157	−	0.0201157i	−0.00129308	−	0.00129308i
$243$	8.64706	+	12.9703i	0.554709	+	0.832044i
$244$		−	13.8603i		−	0.887314i
$245$	−7.00882	+	2.21876i	−0.447777	+	0.141751i
$246$	−0.0298537	+	0.0808705i	−0.00190340	+	0.00515611i
$247$	21.0614	+	5.64338i	1.34010	+	0.359080i
$248$	0.709802	+	0.190191i	0.0450725	+	0.0120771i
$249$	8.91048	+	10.7182i	0.564679	+	0.679238i
$250$	−0.294265	−	0.120698i	−0.0186110	−	0.00763359i
$251$		−	20.5741i		−	1.29863i	−0.760521	−	0.649314i	$-0.775056\pi$
$251$		−	20.5741i		−	1.29863i	0.760521	−	0.649314i	$-0.224944\pi$
$252$	19.1782	−	1.50137i	1.20812	−	0.0945776i
$253$	−0.161050	−	0.161050i	−0.0101251	−	0.0101251i
$254$	−0.0297757	+	0.0515730i	−0.00186829	+	0.00323598i
$255$	−16.5895	−	10.6485i	−1.03887	−	0.666837i
$256$	−7.96765	−	13.8004i	−0.497978	−	0.862523i
$257$	−4.14081	+	15.4537i	−0.258297	+	0.963976i	0.707930	+	0.706283i	$0.249629\pi$
$257$	−4.14081	+	15.4537i	−0.258297	+	0.963976i	−0.966227	+	0.257694i	$0.917037\pi$
$258$	−0.184213	+	0.260541i	−0.0114686	+	0.0162206i
$259$	−25.7968	−	14.8938i	−1.60294	−	0.925457i
$260$	0.600706	+	13.4037i	0.0372542	+	0.831264i
$261$	−4.60850	−	13.0312i	−0.285259	−	0.806608i
$262$	0.111988	−	0.111988i	0.00691865	−	0.00691865i
$263$	−4.09840	−	15.2955i	−0.252718	−	0.943158i	−0.969346	−	0.245701i	$-0.920982\pi$
$263$	−4.09840	−	15.2955i	−0.252718	−	0.943158i	0.716627	−	0.697456i	$-0.245685\pi$
$264$	−0.151528	+	0.125972i	−0.00932592	+	0.00775302i
$265$	11.4765	−	7.32998i	0.704998	−	0.450277i
$266$	−0.574065	+	0.331437i	−0.0351982	+	0.0203217i
$267$	11.0667	−	5.09905i	0.677272	−	0.312057i
$268$	−6.47519	+	1.73502i	−0.395535	+	0.105983i
$269$	15.4729			0.943401			0.471701	−	0.881759i	$-0.343640\pi$
$269$	15.4729			0.943401			0.471701	+	0.881759i	$0.343640\pi$
$270$	0.0755873	−	0.321775i	0.00460009	−	0.0195826i
$271$	−11.0221			−0.669544			−0.334772	−	0.942299i	$-0.608659\pi$
$271$	−11.0221			−0.669544			−0.334772	+	0.942299i	$0.608659\pi$
$272$	19.6419	−	5.26303i	1.19096	−	0.319118i
$273$	15.1439	−	6.97764i	0.916552	−	0.422306i
$274$	−0.163136	+	0.0941868i	−0.00985542	+	0.00569003i
$275$	2.87732	+	4.08914i	0.173509	+	0.246584i
$276$	−0.606460	+	0.504175i	−0.0365046	+	0.0303478i
$277$	4.35081	+	16.2374i	0.261415	+	0.975613i	0.964408	+	0.264417i	$0.0851795\pi$
$277$	4.35081	+	16.2374i	0.261415	+	0.975613i	−0.702994	+	0.711196i	$0.748154\pi$
$278$	−0.421323	+	0.421323i	−0.0252692	+	0.0252692i
$279$	19.0514	+	3.53912i	1.14058	+	0.211882i
$280$	−0.602221	−	0.550557i	−0.0359896	−	0.0329021i
$281$	21.3923	+	12.3509i	1.27616	+	0.736792i	0.976140	−	0.217141i	$-0.0696732\pi$
$281$	21.3923	+	12.3509i	1.27616	+	0.736792i	0.300020	+	0.953933i	$0.403007\pi$
$282$	0.330529	−	0.467482i	0.0196827	−	0.0278382i
$283$	−7.73008	+	28.8490i	−0.459505	+	1.71490i	0.214988	+	0.976617i	$0.431029\pi$
$283$	−7.73008	+	28.8490i	−0.459505	+	1.71490i	−0.674494	+	0.738281i	$0.735638\pi$
$284$	9.39974	+	16.2808i	0.557772	+	0.966090i
$285$	−5.99590	−	27.4900i	−0.355167	−	1.62837i
$286$	−0.0426915	+	0.0739438i	−0.00252440	+	0.00437239i
$287$	3.96796	+	3.96796i	0.234221	+	0.234221i
$288$	0.579407	+	0.843790i	0.0341419	+	0.0497208i
$289$			8.90680i			0.523929i
$290$	−0.135029	+	0.260121i	−0.00792919	+	0.0152748i
$291$	9.98953	+	12.0162i	0.585597	+	0.704400i
$292$	−3.21517	−	0.861502i	−0.188154	−	0.0504156i
$293$	19.6705	+	5.27070i	1.14916	+	0.307917i	0.782630	−	0.622487i	$-0.213878\pi$
$293$	19.6705	+	5.27070i	1.14916	+	0.307917i	0.366534	+	0.930405i	$0.380544\pi$
$294$	−0.0561016	+	0.151973i	−0.00327191	+	0.00886325i
$295$	2.10335	+	6.64424i	0.122462	+	0.386843i
$296$		−	1.05657i		−	0.0614117i
$297$	−3.72426	+	3.62351i	−0.216104	+	0.210258i
$298$	−0.0463377	−	0.0463377i	−0.00268427	−	0.00268427i
$299$	−0.341796	+	0.592008i	−0.0197666	+	0.0342367i
$300$	15.0135	−	8.62278i	0.866804	−	0.497837i
$301$	10.3855	+	17.9883i	0.598613	+	1.03683i
$302$	0.0205386	−	0.0766510i	0.00118186	−	0.00441077i
$303$	11.0594	+	1.01852i	0.635344	+	0.0585125i
$304$	25.1353	+	14.5119i	1.44161	+	0.832313i
$305$	−10.4602	+	11.4417i	−0.598948	+	0.655153i
$306$	−0.409532	+	0.144832i	−0.0234114	+	0.00827949i
$307$	−9.57123	+	9.57123i	−0.546259	+	0.546259i	−0.925357	−	0.379098i	$-0.876234\pi$
$307$	−9.57123	+	9.57123i	−0.546259	+	0.546259i	0.379098	+	0.925357i	$0.376234\pi$
$308$	1.65963	+	6.19381i	0.0945661	+	0.352925i
$309$	−1.55392	−	9.05453i	−0.0883996	−	0.515094i
$310$	−0.221161	−	0.346271i	−0.0125611	−	0.0196669i
$311$	25.5791	−	14.7681i	1.45046	−	0.837421i	0.451948	−	0.892044i	$-0.350729\pi$
$311$	25.5791	−	14.7681i	1.45046	−	0.837421i	0.998507	+	0.0546232i	$0.0173958\pi$
$312$	0.482916	+	0.341441i	0.0273397	+	0.0193303i
$313$	−21.3975	+	5.73344i	−1.20946	+	0.324073i	−0.806549	−	0.591167i	$-0.798668\pi$
$313$	−21.3975	+	5.73344i	−1.20946	+	0.324073i	−0.402909	+	0.915240i	$0.632001\pi$
$314$	0.0723684			0.00408399
$315$	−16.9648	−	13.2342i	−0.955859	−	0.745662i
$316$	−14.7963			−0.832355
$317$	−8.53857	+	2.28790i	−0.479574	+	0.128501i	−0.490504	−	0.871439i	$-0.663187\pi$
$317$	−8.53857	+	2.28790i	−0.479574	+	0.128501i	0.0109304	+	0.999940i	$0.496521\pi$
$318$	0.0275190	−	0.298808i	0.00154319	−	0.0167563i
$319$	3.99009	−	2.30368i	0.223402	−	0.128981i
$320$	−3.84230	+	17.4266i	−0.214791	+	0.974175i
$321$	16.9975	+	6.27471i	0.948709	+	0.350220i
$322$	−0.00537874	−	0.0200737i	−0.000299746	−	0.00111867i
$323$	−26.1465	+	26.1465i	−1.45483	+	1.45483i
$324$	11.3116	+	13.9923i	0.628422	+	0.777352i
$325$	9.61973	−	11.5182i	0.533607	−	0.638914i
$326$	0.534902	+	0.308826i	0.0296255	+	0.0171043i
$327$	−11.6682	−	25.3240i	−0.645252	−	1.40042i
$328$	−0.0515157	+	0.192259i	−0.00284448	+	0.0106157i
$329$	−18.6345	−	32.2759i	−1.02735	−	1.77943i
$330$	0.110056	+	0.00518200i	0.00605839	+	0.000285260i
$331$	−0.539604	+	0.934621i	−0.0296593	+	0.0513714i	−0.880474	−	0.474094i	$-0.842776\pi$
$331$	−0.539604	+	0.934621i	−0.0296593	+	0.0513714i	0.850815	+	0.525466i	$0.176109\pi$
$332$	11.3760	+	11.3760i	0.624338	+	0.624338i
$333$	−2.17445	−	27.7760i	−0.119159	−	1.52212i
$334$		−	0.415910i		−	0.0227576i
$335$	6.65471	+	3.45447i	0.363585	+	0.188738i
$336$	21.8751	−	3.75417i	1.19338	−	0.204807i
$337$	−3.14146	−	0.841753i	−0.171126	−	0.0458532i	0.172238	−	0.985055i	$-0.444900\pi$
$337$	−3.14146	−	0.841753i	−0.171126	−	0.0458532i	−0.343365	+	0.939202i	$0.611567\pi$
$338$	−0.109685	−	0.0293901i	−0.00596610	−	0.00159861i
$339$	−9.91058	+	1.70084i	−0.538269	+	0.0923768i
$340$	−20.1946	−	10.4831i	−1.09521	−	0.568524i
$341$			6.45911i			0.349780i
$342$	−0.559492	−	0.267148i	−0.0302539	−	0.0144457i
$343$	−8.41943	−	8.41943i	−0.454606	−	0.454606i
$344$	−0.368375	+	0.638044i	−0.0198615	+	0.0344010i
$345$	0.881130	+	0.0414881i	0.0474384	+	0.00223364i
$346$	0.231316	+	0.400652i	0.0124357	+	0.0215392i
$347$	6.04227	−	22.5501i	0.324366	−	1.21055i	−0.590581	−	0.806978i	$-0.701101\pi$
$347$	6.04227	−	22.5501i	0.324366	−	1.21055i	0.914947	−	0.403573i	$-0.132232\pi$
$348$	−6.67625	−	14.4898i	−0.357885	−	0.776734i
$349$	−23.2810	−	13.4413i	−1.24620	−	0.719497i	−0.275854	−	0.961199i	$-0.588961\pi$
$349$	−23.2810	−	13.4413i	−1.24620	−	0.719497i	−0.970350	+	0.241703i	$0.922294\pi$
$350$	0.0408107	+	0.454396i	0.00218143	+	0.0242885i
$351$	13.3981	+	7.98227i	0.715135	+	0.426062i
$352$	−0.241258	+	0.241258i	−0.0128591	+	0.0128591i
$353$	6.82549	+	25.4731i	0.363284	+	1.35580i	0.869732	+	0.493525i	$0.164292\pi$
$353$	6.82549	+	25.4731i	0.363284	+	1.35580i	−0.506447	+	0.862271i	$0.669042\pi$
$354$	0.144068	+	0.0531833i	0.00765712	+	0.00282666i
$355$	4.52739	−	20.5338i	0.240289	−	1.08982i
$356$	12.1800	−	7.03213i	0.645539	−	0.372702i
$357$	−2.59319	+	28.1575i	−0.137246	+	1.49025i
$358$	0.647240	−	0.173427i	0.0342077	−	0.00916593i
$359$	−21.4338			−1.13124			−0.565618	−	0.824668i	$-0.691362\pi$
$359$	−21.4338			−1.13124			−0.565618	+	0.824668i	$0.691362\pi$
$360$	0.105656	−	0.755832i	0.00556854	−	0.0398358i
$361$	−33.7767			−1.77772
$362$	0.105381	−	0.0282367i	0.00553870	−	0.00148409i
$363$	−1.41426	−	0.999938i	−0.0742293	−	0.0524831i
$364$	16.6674	−	9.62291i	0.873607	−	0.504377i
$365$	2.00398	+	3.13762i	0.104893	+	0.164231i
$366$	0.0577814	+	0.336686i	0.00302028	+	0.0175988i
$367$	3.19542	+	11.9255i	0.166799	+	0.622504i	0.997804	+	0.0662381i	$0.0210997\pi$
$367$	3.19542	+	11.9255i	0.166799	+	0.622504i	−0.831004	+	0.556266i	$0.812234\pi$
$368$	−0.643417	+	0.643417i	−0.0335404	+	0.0335404i
$369$	−0.958617	+	5.16031i	−0.0499036	+	0.268635i
$370$	−0.398608	+	0.436013i	−0.0207227	+	0.0226672i
$371$	−16.9164	−	9.76667i	−0.878254	−	0.507060i
$372$	22.2717	+	2.05113i	1.15473	+	0.106346i
$373$	−3.91584	+	14.6141i	−0.202755	+	0.756691i	0.787367	+	0.616484i	$0.211443\pi$
$373$	−3.91584	+	14.6141i	−0.202755	+	0.756691i	−0.990122	+	0.140207i	$0.955223\pi$
$374$	−0.0723979	−	0.125397i	−0.00374361	−	0.00648412i
$375$	−18.9012	−	4.21233i	−0.976055	−	0.217524i
$376$	0.660965	−	1.14483i	0.0340867	−	0.0590399i
$377$	−9.77819	−	9.77819i	−0.503602	−	0.503602i
$378$	−0.459607	+	0.116422i	−0.0236396	+	0.00598808i
$379$		−	4.29816i		−	0.220782i	−0.993888	−	0.110391i	$-0.964790\pi$
$379$		−	4.29816i		−	0.220782i	0.993888	−	0.110391i	$-0.0352103\pi$
$380$	−9.80138	−	30.9615i	−0.502800	−	1.58829i
$381$	−1.25565	+	3.40143i	−0.0643291	+	0.174261i
$382$	−0.586354	−	0.157113i	−0.0300005	−	0.00803860i
$383$	−36.1970	−	9.69896i	−1.84958	−	0.495594i	−0.850064	−	0.526679i	$-0.823437\pi$
$383$	−36.1970	−	9.69896i	−1.84958	−	0.495594i	−0.999517	+	0.0310854i	$0.990104\pi$
$384$	1.00696	+	1.21125i	0.0513861	+	0.0618111i
$385$	3.30436	−	6.36553i	0.168406	−	0.324417i
$386$		−	0.438139i		−	0.0223007i
$387$	−8.37108	+	17.5316i	−0.425526	+	0.891184i
$388$	12.7536	+	12.7536i	0.647466	+	0.647466i
$389$	−12.9332	+	22.4010i	−0.655740	+	1.13578i	0.325967	+	0.945381i	$0.394310\pi$
$389$	−12.9332	+	22.4010i	−0.655740	+	1.13578i	−0.981708	+	0.190395i	$0.939023\pi$
$390$	−0.0704701	−	0.323091i	−0.00356839	−	0.0163603i
$391$	−0.579632	−	1.00395i	−0.0293132	−	0.0507720i
$392$	−0.0968091	+	0.361296i	−0.00488960	+	0.0182482i
$393$	5.56686	−	7.87347i	0.280811	−	0.397164i
$394$	0.427759	+	0.246967i	0.0215502	+	0.0124420i
$395$	12.2144	+	11.1665i	0.614573	+	0.561850i
$396$	−3.89700	+	4.55898i	−0.195832	+	0.229097i
$397$	−6.36702	+	6.36702i	−0.319552	+	0.319552i	−0.848595	−	0.529043i	$-0.822551\pi$
$397$	−6.36702	+	6.36702i	−0.319552	+	0.319552i	0.529043	+	0.848595i	$0.322551\pi$
$398$	−0.0807094	−	0.301212i	−0.00404560	−	0.0150984i
$399$	−31.0351	+	25.8008i	−1.55370	+	1.29165i
$400$	16.3367	−	11.4953i	0.816834	−	0.574766i
$401$	−2.42720	+	1.40135i	−0.121209	+	0.0699799i	−0.559379	−	0.828912i	$-0.688960\pi$
$401$	−2.42720	+	1.40135i	−0.121209	+	0.0699799i	0.438170	+	0.898892i	$0.355627\pi$
$402$	0.150058	−	0.0691402i	0.00748423	−	0.00344840i
$403$	18.7257	−	5.01754i	0.932793	−	0.249941i
$404$	12.8191			0.637775
$405$	1.22204	−	20.0875i	0.0607239	−	0.998155i
$406$	0.420398			0.0208640
$407$	8.97056	−	2.40365i	0.444654	−	0.119145i
$408$	−0.910929	+	0.419715i	−0.0450977	+	0.0207790i
$409$	11.8194	−	6.82391i	0.584430	−	0.337421i	−0.178462	−	0.983947i	$-0.557112\pi$
$409$	11.8194	−	6.82391i	0.584430	−	0.337421i	0.762892	+	0.646526i	$0.223779\pi$
$410$	0.0937920	−	0.0599043i	0.00463206	−	0.00295846i
$411$	−8.81949	+	7.33200i	−0.435033	+	0.361661i
$412$	−2.74447	−	10.2425i	−0.135211	−	0.504613i
$413$	7.06878	−	7.06878i	0.347832	−	0.347832i
$414$	0.0126299	−	0.0147753i	0.000620726	−	0.000726168i
$415$	−0.805630	−	17.9762i	−0.0395468	−	0.882419i
$416$	0.886847	+	0.512021i	0.0434812	+	0.0251039i
$417$	−20.9437	+	29.6216i	−1.02562	+	1.45058i
$418$	0.0534892	−	0.199625i	0.00261624	−	0.00976396i
$419$	14.4028	+	24.9464i	0.703624	+	1.21871i	0.967186	+	0.254070i	$0.0817694\pi$
$419$	14.4028	+	24.9464i	0.703624	+	1.21871i	−0.263562	+	0.964643i	$0.584897\pi$
$420$	−20.8997	−	13.4152i	−1.01980	−	0.654595i
$421$	−9.81986	+	17.0085i	−0.478591	+	0.828943i	−0.999699	−	0.0245475i	$-0.992186\pi$
$421$	−9.81986	+	17.0085i	−0.478591	+	0.828943i	0.521108	+	0.853491i	$0.325519\pi$
$422$	0.400445	+	0.400445i	0.0194933	+	0.0194933i
$423$	15.0200	−	31.4565i	0.730297	−	1.52947i
$424$		−	0.692847i		−	0.0336476i
$425$	8.75933	+	23.8944i	0.424890	+	1.15905i
$426$	−0.296205	−	0.356298i	−0.0143512	−	0.0172627i
$427$	21.4794	+	5.75539i	1.03946	+	0.278523i
$428$	20.2006	+	5.41274i	0.976434	+	0.261635i
$429$	−1.80032	+	4.87687i	−0.0869201	+	0.235457i
$430$	0.392730	−	0.124325i	0.0189391	−	0.00599551i
$431$		−	23.0868i		−	1.11205i	−0.831165	−	0.556025i	$-0.812326\pi$
$431$		−	23.0868i		−	1.11205i	0.831165	−	0.556025i	$-0.187674\pi$
$432$	14.4765	+	14.8790i	0.696499	+	0.715865i
$433$	−4.93579	−	4.93579i	−0.237199	−	0.237199i	0.578490	−	0.815689i	$-0.303642\pi$
$433$	−4.93579	−	4.93579i	−0.237199	−	0.237199i	−0.815689	+	0.578490i	$0.803642\pi$
$434$	−0.294681	+	0.510402i	−0.0141451	+	0.0245001i
$435$	−5.42398	+	16.9999i	−0.260060	+	0.815082i
$436$	−16.0917	−	27.8716i	−0.770651	−	1.33481i
$437$	0.428245	−	1.59823i	0.0204857	−	0.0764538i
$438$	0.0816924	+	0.00752353i	0.00390342	+	0.000359488i
$439$	−29.3931	−	16.9701i	−1.40286	−	0.809939i	−0.408171	−	0.912905i	$-0.633833\pi$
$439$	−29.3931	−	16.9701i	−1.40286	−	0.809939i	−0.994685	+	0.102966i	$0.967167\pi$
$440$	0.254139	−	0.0113896i	0.0121156	−	0.000542976i
$441$	−1.80145	+	9.69734i	−0.0857832	+	0.461778i
$442$	−0.307300	+	0.307300i	−0.0146168	+	0.0146168i
$443$	0.430042	+	1.60494i	0.0204319	+	0.0762530i	0.975389	−	0.220491i	$-0.0707659\pi$
$443$	0.430042	+	1.60494i	0.0204319	+	0.0762530i	−0.954957	+	0.296744i	$0.904099\pi$
$444$	−5.43940	−	31.6948i	−0.258143	−	1.50417i
$445$	−15.3617	−	3.38703i	−0.728215	−	0.160561i
$446$	−0.273109	+	0.157679i	−0.0129321	+	0.00746633i
$447$	−3.25783	−	2.30342i	−0.154090	−	0.108948i
$448$	24.7251	−	6.62508i	1.16815	−	0.313006i
$449$	−21.4074			−1.01028			−0.505138	−	0.863039i	$-0.668558\pi$
$449$	−21.4074			−1.01028			−0.505138	+	0.863039i	$0.668558\pi$
$450$	−0.328751	+	0.272048i	−0.0154975	+	0.0128245i
$451$	−1.74953			−0.0823823
$452$	−11.2109	+	3.00395i	−0.527316	+	0.141294i
$453$	0.443089	−	4.81118i	0.0208182	−	0.226049i
$454$	0.577852	−	0.333623i	0.0271199	−	0.0156577i
$455$	−21.0213	−	4.63488i	−0.985493	−	0.217287i
$456$	−1.34295	−	0.495758i	−0.0628896	−	0.0232160i
$457$	1.60626	+	5.99463i	0.0751375	+	0.280417i	0.993264	−	0.115869i	$-0.0369654\pi$
$457$	1.60626	+	5.99463i	0.0751375	+	0.280417i	−0.918127	+	0.396286i	$0.870299\pi$
$458$	0.257312	−	0.257312i	0.0120234	−	0.0120234i
$459$	−23.0836	+	12.9086i	−1.07745	+	0.602522i
$460$	1.01714	−	0.0455843i	0.0474242	−	0.00212538i
$461$	10.3969	+	6.00263i	0.484230	+	0.279571i	0.722178	−	0.691708i	$-0.243141\pi$
$461$	10.3969	+	6.00263i	0.484230	+	0.279571i	−0.237947	+	0.971278i	$0.576475\pi$
$462$	−0.0661357	−	0.143538i	−0.00307691	−	0.00667797i
$463$	8.21481	−	30.6581i	0.381775	−	1.42480i	−0.461414	−	0.887185i	$-0.652658\pi$
$463$	8.21481	−	30.6581i	0.381775	−	1.42480i	0.843189	−	0.537618i	$-0.180676\pi$
$464$	−9.20352	−	15.9410i	−0.427263	−	0.740041i
$465$	−16.8374	−	18.5014i	−0.780818	−	0.857981i
$466$	0.0922566	−	0.159793i	0.00427371	−	0.00740228i
$467$	7.68283	+	7.68283i	0.355519	+	0.355519i	0.862158	−	0.506639i	$-0.169112\pi$
$467$	7.68283	+	7.68283i	0.355519	+	0.355519i	−0.506639	+	0.862158i	$0.669112\pi$
$468$	16.2443	+	7.75637i	0.750891	+	0.358538i
$469$		−	10.7551i		−	0.496625i
$470$	−0.704665	+	0.223074i	−0.0325038	+	0.0102896i
$471$	4.34268	−	0.745283i	0.200100	−	0.0343408i
$472$	0.342503	+	0.0917733i	0.0157650	+	0.00422421i
$473$	−6.25522	−	1.67608i	−0.287615	−	0.0770663i
$474$	0.359422	−	0.0616834i	0.0165088	−	0.00283321i
$475$	−15.2751	+	32.9558i	−0.700871	+	1.51212i
$476$			32.6378i			1.49595i
$477$	−1.42590	−	18.2142i	−0.0652877	−	0.833972i
$478$	0.0578336	+	0.0578336i	0.00264525	+	0.00264525i
$479$	18.7658	−	32.5033i	0.857432	−	1.48512i	−0.0169383	−	0.999857i	$-0.505392\pi$
$479$	18.7658	−	32.5033i	0.857432	−	1.48512i	0.874370	−	0.485259i	$-0.161275\pi$
$480$	0.0621505	−	1.31996i	0.00283677	−	0.0602477i
$481$	−13.9370	−	24.1395i	−0.635470	−	1.10067i
$482$	−0.0160693	+	0.0599715i	−0.000731937	+	0.00273163i
$483$	−0.529495	−	1.14919i	−0.0240929	−	0.0522899i
$484$	−1.73135	−	0.999595i	−0.0786977	−	0.0454362i
$485$	−0.903190	−	20.1531i	−0.0410118	−	0.915107i
$486$	−0.333106	−	0.292737i	−0.0151100	−	0.0132788i
$487$	−1.70686	+	1.70686i	−0.0773451	+	0.0773451i	−0.744721	−	0.667376i	$-0.767417\pi$
$487$	−1.70686	+	1.70686i	−0.0773451	+	0.0773451i	0.667376	+	0.744721i	$0.267417\pi$
$488$	0.204144	+	0.761874i	0.00924114	+	0.0344884i
$489$	35.2787	+	13.0233i	1.59536	+	0.588934i
$490$	0.176255	−	0.112573i	0.00796241	−	0.00508553i
$491$	2.08785	−	1.20542i	0.0942235	−	0.0544000i	−0.452148	−	0.891943i	$-0.649342\pi$
$491$	2.08785	−	1.20542i	0.0942235	−	0.0544000i	0.546371	+	0.837543i	$0.316009\pi$
$492$	−0.555575	+	6.03258i	−0.0250473	+	0.271970i
$493$	22.6518	−	6.06952i	1.02018	−	0.273358i
$494$	−0.620286			−0.0279080
$495$	6.65760	−	0.822446i	0.299237	−	0.0369662i
$496$	25.8051			1.15868
$497$	−29.1337	+	7.80635i	−1.30683	+	0.350163i
$498$	−0.323763	−	0.228914i	−0.0145082	−	0.0102579i
$499$	−17.3958	+	10.0435i	−0.778744	+	0.449608i	−0.835985	−	0.548753i	$-0.815103\pi$
$499$	−17.3958	+	10.0435i	−0.778744	+	0.449608i	0.0572413	+	0.998360i	$0.481770\pi$
$500$	−22.1704	−	2.84079i	−0.991489	−	0.127044i
$501$	−4.28323	−	24.9579i	−0.191361	−	1.11504i
$502$	0.151484	+	0.565346i	0.00676106	+	0.0252326i
$503$	6.67948	−	6.67948i	0.297823	−	0.297823i	−0.542338	−	0.840161i	$-0.682461\pi$
$503$	6.67948	−	6.67948i	0.297823	−	0.297823i	0.840161	+	0.542338i	$0.182461\pi$
$504$	−1.03208	+	0.364998i	−0.0459724	+	0.0162583i
$505$	−10.5822	−	9.67442i	−0.470904	−	0.430506i
$506$	0.00561119	+	0.00323962i	0.000249448	+	0.000144019i
$507$	−6.88466	−	0.634048i	−0.305759	−	0.0281591i
$508$	−1.08316	+	4.04242i	−0.0480575	+	0.179353i
$509$	−3.24681	−	5.62364i	−0.143912	−	0.249264i	0.785054	−	0.619427i	$-0.212635\pi$
$509$	−3.24681	−	5.62364i	−0.143912	−	0.249264i	−0.928967	+	0.370163i	$0.879302\pi$
$510$	0.534257	+	0.170460i	0.0236573	+	0.00754809i
$511$	2.67015	−	4.62484i	0.118121	−	0.204591i
$512$	1.60665	+	1.60665i	0.0710045	+	0.0710045i
$513$	−36.3251	−	10.2691i	−1.60379	−	0.453392i
$514$		−	0.455133i		−	0.0200751i
$515$	−5.46432	+	10.5265i	−0.240787	+	0.463852i
$516$	−7.76570	+	21.0364i	−0.341866	+	0.926077i
$517$	11.2236	+	3.00735i	0.493612	+	0.132263i
$518$	0.818519	+	0.219322i	0.0359637	+	0.00963644i
$519$	18.0069	+	21.6601i	0.790415	+	0.950771i
$520$	−0.230439	−	0.727930i	−0.0101054	−	0.0319218i
$521$		−	35.3245i		−	1.54759i	−0.633434	−	0.773797i	$-0.718355\pi$
$521$		−	35.3245i		−	1.54759i	0.633434	−	0.773797i	$-0.281645\pi$
$522$	0.222581	+	0.324145i	0.00974211	+	0.0141874i
$523$	16.0303	+	16.0303i	0.700955	+	0.700955i	0.964615	−	0.263661i	$-0.0849300\pi$
$523$	16.0303	+	16.0303i	0.700955	+	0.700955i	−0.263661	+	0.964615i	$0.584930\pi$
$524$	5.56496	−	9.63879i	0.243106	−	0.421072i
$525$	7.12854	+	26.8471i	0.311115	+	1.17170i
$526$	0.225236	+	0.390120i	0.00982075	+	0.0170100i
$527$	−8.50894	+	31.7558i	−0.370655	+	1.38330i
$528$	−3.99490	+	5.65016i	−0.173856	+	0.245892i
$529$	−19.8737	−	11.4741i	−0.864072	−	0.498872i
$530$	−0.261389	+	0.285917i	−0.0113540	+	0.0124194i
$531$	9.19291	+	1.70774i	0.398938	+	0.0741097i
$532$	−32.9398	+	32.9398i	−1.42812	+	1.42812i
$533$	1.35906	+	5.07210i	0.0588676	+	0.219697i
$534$	−0.266553	+	0.221597i	−0.0115349	+	0.00958943i
$535$	−12.5908	−	19.7134i	−0.544348	−	0.852284i
$536$	0.330374	−	0.190742i	0.0142700	−	0.00823879i
$537$	37.0535	−	17.0726i	1.59898	−	0.736736i
$538$	−0.425173	+	0.113925i	−0.0183305	+	0.00491164i
$539$	−3.28775			−0.141613
$540$	−0.721721	−	23.2173i	−0.0310579	−	0.999113i
$541$	39.5238			1.69926			0.849630	−	0.527378i	$-0.176825\pi$
$541$	39.5238			1.69926			0.849630	+	0.527378i	$0.176825\pi$
$542$	0.302870	−	0.0811539i	0.0130094	−	0.00348586i
$543$	6.03289	−	2.77969i	0.258896	−	0.119288i
$544$	−1.50395	+	0.868306i	−0.0644813	+	0.0372283i
$545$	−7.75056	+	35.1523i	−0.331998	+	1.50576i
$546$	−0.364757	+	0.303237i	−0.0156102	+	0.0129774i
$547$	−4.53350	−	16.9192i	−0.193838	−	0.723414i	−0.992565	−	0.121720i	$-0.961159\pi$
$547$	−4.53350	−	16.9192i	−0.193838	−	0.723414i	0.798726	−	0.601695i	$-0.205508\pi$
$548$	−9.36074	+	9.36074i	−0.399871	+	0.399871i
$549$	6.93468	+	19.6087i	0.295965	+	0.836880i
$550$	−0.109172	−	0.0911780i	−0.00465511	−	0.00388784i
$551$	28.9870	+	16.7356i	1.23489	+	0.712963i
$552$	0.0259101	−	0.0366459i	0.00110281	−	0.00155975i
$553$	6.14404	−	22.9299i	0.261271	−	0.975078i
$554$	−0.239107	−	0.414146i	−0.0101587	−	0.0175954i
$555$	−19.4294	+	30.2693i	−0.824731	+	1.28486i
$556$	−20.9365	+	36.2631i	−0.887907	+	1.53790i
$557$	−25.8166	−	25.8166i	−1.09388	−	1.09388i	−0.995110	−	0.0987730i	$-0.968508\pi$
$557$	−25.8166	−	25.8166i	−1.09388	−	1.09388i	−0.0987730	−	0.995110i	$-0.531492\pi$
$558$	−0.549561	+	0.0430225i	−0.0232648	+	0.00182129i
$559$			19.4366i			0.822082i
$560$	−25.4312	−	13.2014i	−1.07466	−	0.557861i
$561$	−5.63584	−	6.77921i	−0.237945	−	0.286219i
$562$	−0.678767	−	0.181875i	−0.0286321	−	0.00767194i
$563$	−6.89036	−	1.84627i	−0.290394	−	0.0778108i	0.110681	−	0.993856i	$-0.464697\pi$
$563$	−6.89036	−	1.84627i	−0.290394	−	0.0778108i	−0.401075	+	0.916045i	$0.631363\pi$
$564$	13.9338	−	37.7451i	0.586718	−	1.58935i
$565$	11.5217	+	5.98093i	0.484721	+	0.251620i
$566$		−	0.849643i		−	0.0357132i
$567$	−26.3811	+	11.7195i	−1.10790	+	0.492171i
$568$	−0.756481	−	0.756481i	−0.0317412	−	0.0317412i
$569$	9.19967	−	15.9343i	0.385670	−	0.668000i	−0.606192	−	0.795319i	$-0.707304\pi$
$569$	9.19967	−	15.9343i	0.385670	−	0.668000i	0.991862	+	0.127318i	$0.0406369\pi$
$570$	0.367163	+	0.711237i	0.0153788	+	0.0297904i
$571$	22.3140	+	38.6489i	0.933810	+	1.61741i	0.776741	+	0.629820i	$0.216871\pi$
$571$	22.3140	+	38.6489i	0.933810	+	1.61741i	0.157069	+	0.987588i	$0.449795\pi$
$572$	−1.55300	+	5.79589i	−0.0649343	+	0.242338i
$573$	−36.8039	−	3.38948i	−1.53750	−	0.141598i
$574$	−0.138249	−	0.0798181i	−0.00577040	−	0.00333154i
$575$	−0.874053	−	0.729989i	−0.0364505	−	0.0304426i
$576$	18.1990	+	15.5565i	0.758292	+	0.648186i
$577$	−8.48653	+	8.48653i	−0.353299	+	0.353299i	−0.861335	−	0.508037i	$-0.830371\pi$
$577$	−8.48653	+	8.48653i	−0.353299	+	0.353299i	0.508037	+	0.861335i	$0.330371\pi$
$578$	−0.0655793	−	0.244745i	−0.00272774	−	0.0101801i
$579$	−4.51216	−	26.2918i	−0.187519	−	1.09265i
$580$	−4.43468	+	20.1133i	−0.184140	+	0.835159i
$581$	−22.3532	+	12.9056i	−0.927368	+	0.535416i
$582$	−0.362970	−	0.256635i	−0.0150456	−	0.0106379i
$583$	5.88248	−	1.57620i	0.243627	−	0.0652797i
$584$	0.189421			0.00783828
$585$	−7.55609	−	18.6623i	−0.312406	−	0.771589i
$586$	−0.579323			−0.0239316
$587$	11.4861	−	3.07768i	0.474080	−	0.127029i	−0.0138645	−	0.999904i	$-0.504413\pi$
$587$	11.4861	−	3.07768i	0.474080	−	0.127029i	0.487945	+	0.872874i	$0.337747\pi$
$588$	−1.04405	+	11.3365i	−0.0430557	+	0.467510i
$589$	−40.6372	+	23.4619i	−1.67443	+	0.966731i
$590$	−0.106717	−	0.167087i	−0.00439348	−	0.00687887i
$591$	28.2123	+	10.4147i	1.16050	+	0.428403i
$592$	−9.60295	−	35.8387i	−0.394679	−	1.47296i
$593$	27.6174	−	27.6174i	1.13411	−	1.13411i	0.144622	−	0.989487i	$-0.453803\pi$
$593$	27.6174	−	27.6174i	1.13411	−	1.13411i	0.989487	−	0.144622i	$-0.0461965\pi$
$594$	0.0756578	−	0.126990i	0.00310428	−	0.00521046i
$595$	24.6313	−	26.9427i	1.00979	−	1.10454i
$596$	−3.98828	−	2.30263i	−0.163366	−	0.0943195i
$597$	−7.94522	−	17.2439i	−0.325176	−	0.705746i
$598$	0.00503318	−	0.0187841i	0.000205822	−	0.000768138i
$599$	−8.55530	−	14.8182i	−0.349560	−	0.605456i	0.636611	−	0.771185i	$-0.280336\pi$
$599$	−8.55530	−	14.8182i	−0.349560	−	0.605456i	−0.986171	+	0.165729i	$0.947002\pi$
$600$	−0.698261	+	0.695107i	−0.0285064	+	0.0283776i
$601$	15.0104	−	25.9988i	0.612288	−	1.06051i	−0.378566	−	0.925574i	$-0.623583\pi$
$601$	15.0104	−	25.9988i	0.612288	−	1.06051i	0.990854	−	0.134939i	$-0.0430840\pi$
$602$	−0.417824	−	0.417824i	−0.0170292	−	0.0170292i
$603$	8.29264	−	5.69432i	0.337703	−	0.231891i
$604$		−	5.57672i		−	0.226914i
$605$	0.674857	+	2.13180i	0.0274369	+	0.0866700i
$606$	−0.311394	+	0.0534409i	−0.0126495	+	0.00217089i
$607$	−27.5361	−	7.37827i	−1.11765	−	0.299475i	−0.347721	−	0.937598i	$-0.613044\pi$
$607$	−27.5361	−	7.37827i	−1.11765	−	0.299475i	−0.769934	+	0.638123i	$0.779711\pi$
$608$	−2.39420	−	0.641525i	−0.0970977	−	0.0260173i
$609$	25.2272	−	4.32945i	1.02226	−	0.175438i
$610$	0.203186	−	0.391419i	0.00822677	−	0.0158481i
$611$		−	34.8746i		−	1.41088i
$612$	−25.1652	+	17.2802i	−1.01724	+	0.698511i
$613$	−15.6053	−	15.6053i	−0.630291	−	0.630291i	0.317850	−	0.948141i	$-0.397039\pi$
$613$	−15.6053	−	15.6053i	−0.630291	−	0.630291i	−0.948141	+	0.317850i	$0.897039\pi$
$614$	0.192531	−	0.333474i	0.00776994	−	0.0134579i
$615$	5.01134	−	4.56064i	0.202077	−	0.183903i
$616$	−0.182453	−	0.316018i	−0.00735125	−	0.0127327i
$617$	−4.79160	+	17.8825i	−0.192903	+	0.719922i	0.799897	+	0.600137i	$0.204887\pi$
$617$	−4.79160	+	17.8825i	−0.192903	+	0.719922i	−0.992800	+	0.119785i	$0.961779\pi$
$618$	0.109367	+	0.237364i	0.00439937	+	0.00954817i
$619$	25.4965	+	14.7204i	1.02479	+	0.591663i	0.915488	−	0.402345i	$-0.131805\pi$
$619$	25.4965	+	14.7204i	1.02479	+	0.591663i	0.109303	+	0.994009i	$0.465138\pi$
$620$	−21.3109	−	19.4826i	−0.855865	−	0.782442i
$621$	0.605731	−	1.01671i	0.0243072	−	0.0407990i
$622$	−0.594139	+	0.594139i	−0.0238228	+	0.0238228i
$623$	5.84008	+	21.7955i	0.233978	+	0.873218i
$624$	19.4838	+	7.19253i	0.779976	+	0.287932i
$625$	16.1579	+	19.0768i	0.646314	+	0.763071i
$626$	0.545757	−	0.315093i	0.0218128	−	0.0125936i
$627$	1.15395	−	12.5299i	0.0460844	−	0.500396i
$628$	4.91245	−	1.31629i	0.196028	−	0.0525255i
$629$	47.2697			1.88477
$630$	0.563609	+	0.238746i	0.0224547	+	0.00951188i
$631$	0.564520			0.0224732			0.0112366	−	0.999937i	$-0.496423\pi$
$631$	0.564520			0.0224732			0.0112366	+	0.999937i	$0.496423\pi$
$632$	0.813323	−	0.217929i	0.0323522	−	0.00866876i
$633$	28.1538	+	19.9059i	1.11901	+	0.791188i
$634$	0.217782	−	0.125736i	0.00864921	−	0.00499362i
$635$	3.94492	−	2.51959i	0.156549	−	0.0999868i
$636$	−3.56691	−	20.7839i	−0.141437	−	0.824137i
$637$	2.55398	+	9.53156i	0.101192	+	0.377654i
$638$	−0.0926799	+	0.0926799i	−0.00366923	+	0.00366923i
$639$	−21.4440	−	18.3302i	−0.848310	−	0.725133i
$640$	−0.0910428	−	2.03146i	−0.00359878	−	0.0803006i
$641$	−1.08228	−	0.624855i	−0.0427475	−	0.0246803i	0.478474	−	0.878102i	$-0.341190\pi$
$641$	−1.08228	−	0.624855i	−0.0427475	−	0.0246803i	−0.521221	+	0.853421i	$0.674523\pi$
$642$	−0.513266	−	0.0472697i	−0.0202570	−	0.00186558i
$643$	−2.57798	+	9.62115i	−0.101666	+	0.379421i	−0.997946	−	0.0640676i	$-0.979593\pi$
$643$	−2.57798	+	9.62115i	−0.101666	+	0.379421i	0.896280	+	0.443489i	$0.146259\pi$
$644$	−0.730230	−	1.26480i	−0.0287751	−	0.0498399i
$645$	22.2866	−	11.5050i	0.877532	−	0.453010i
$646$	0.525953	−	0.910978i	0.0206933	−	0.0358419i
$647$	28.0800	+	28.0800i	1.10394	+	1.10394i	0.993931	+	0.110008i	$0.0350877\pi$
$647$	28.0800	+	28.0800i	1.10394	+	1.10394i	0.110008	+	0.993931i	$0.464912\pi$
$648$	−0.827866	−	0.602528i	−0.0325216	−	0.0236695i
$649$			3.11673i			0.122342i
$650$	−0.179529	+	0.387331i	−0.00704171	+	0.0151924i
$651$	−12.4268	+	33.6629i	−0.487045	+	1.31935i
$652$	41.9268	+	11.2343i	1.64198	+	0.439968i
$653$	11.5069	+	3.08328i	0.450301	+	0.120658i	0.476840	−	0.878990i	$-0.341782\pi$
$653$	11.5069	+	3.08328i	0.450301	+	0.120658i	−0.0265390	+	0.999648i	$0.508449\pi$
$654$	0.507081	+	0.609956i	0.0198284	+	0.0238512i
$655$	−11.8682	+	3.75707i	−0.463728	+	0.146801i
$656$			6.98964i			0.272899i
$657$	4.97967	−	0.389834i	0.194275	−	0.0152089i
$658$	0.749690	+	0.749690i	0.0292260	+	0.0292260i
$659$	10.5233	−	18.2269i	0.409930	−	0.710019i	−0.584952	−	0.811068i	$-0.698887\pi$
$659$	10.5233	−	18.2269i	0.409930	−	0.710019i	0.994881	+	0.101049i	$0.0322198\pi$
$660$	7.56498	−	1.65001i	0.294466	−	0.0642267i
$661$	−9.04860	−	15.6726i	−0.351950	−	0.609595i	0.634641	−	0.772807i	$-0.281148\pi$
$661$	−9.04860	−	15.6726i	−0.351950	−	0.609595i	−0.986591	+	0.163212i	$0.947815\pi$
$662$	0.00794603	−	0.0296550i	0.000308831	−	0.00115257i
$663$	−15.2757	+	21.6052i	−0.593260	+	0.839075i
$664$	−0.792869	−	0.457763i	−0.0307693	−	0.0177647i
$665$	52.0512	−	2.33274i	2.01846	−	0.0904599i
$666$	0.264261	+	0.747234i	0.0102399	+	0.0289547i
$667$	−0.742013	+	0.742013i	−0.0287309	+	0.0287309i
$668$	−7.56486	−	28.2324i	−0.292693	−	1.09235i
$669$	−14.7648	+	12.2746i	−0.570841	+	0.474563i
$670$	−0.208296	−	0.0459262i	−0.00804718	−	0.00177428i
$671$	−6.00411	+	3.46648i	−0.231786	+	0.133822i
$672$	−1.72152	+	0.793201i	−0.0664092	+	0.0305984i
$673$	−11.8791	+	3.18300i	−0.457906	+	0.122696i	−0.480396	−	0.877052i	$-0.659507\pi$
$673$	−11.8791	+	3.18300i	−0.457906	+	0.122696i	0.0224904	+	0.999747i	$0.492840\pi$
$674$	0.0925204			0.00356375
$675$	−16.9260	+	19.7107i	−0.651482	+	0.758664i
$676$	−7.98013			−0.306928
$677$	−23.1107	+	6.19250i	−0.888218	+	0.237997i	−0.673949	−	0.738778i	$-0.735403\pi$
$677$	−23.1107	+	6.19250i	−0.888218	+	0.237997i	−0.214268	+	0.976775i	$0.568737\pi$
$678$	0.259805	−	0.119706i	0.00997775	−	0.00459730i
$679$	−25.0602	+	14.4685i	−0.961721	+	0.555250i
$680$	1.26446	+	0.278795i	0.0484899	+	0.0106913i
$681$	31.2399	−	25.9710i	1.19711	−	0.995210i
$682$	−0.0475574	−	0.177486i	−0.00182107	−	0.00679631i
$683$	−2.35896	+	2.35896i	−0.0902632	+	0.0902632i	−0.750797	−	0.660533i	$-0.770330\pi$
$683$	−2.35896	+	2.35896i	−0.0902632	+	0.0902632i	0.660533	+	0.750797i	$0.270330\pi$
$684$	−42.8380	−	7.95790i	−1.63795	−	0.304278i
$685$	14.7918	−	0.662913i	0.565164	−	0.0253286i
$686$	0.293344	+	0.169362i	0.0111999	+	0.00646628i
$687$	12.7909	−	18.0907i	0.488001	−	0.690203i
$688$	−6.69619	+	24.9905i	−0.255290	+	0.952755i
$689$	−9.13920	−	15.8296i	−0.348176	−	0.603058i
$690$	−0.0245176	+	0.00534759i	−0.000933369	+	0.000203579i
$691$	6.41886	−	11.1178i	0.244185	−	0.422941i	−0.717717	−	0.696335i	$-0.754813\pi$
$691$	6.41886	−	11.1178i	0.244185	−	0.422941i	0.961902	+	0.273394i	$0.0881462\pi$
$692$	22.9893	+	22.9893i	0.873924	+	0.873924i
$693$	−5.44688	−	7.93229i	−0.206910	−	0.301323i
$694$			0.664130i			0.0252100i
$695$	44.6505	−	14.1349i	1.69369	−	0.536167i
$696$	0.580396	+	0.698144i	0.0219999	+	0.0264631i
$697$	−8.60147	−	2.30476i	−0.325804	−	0.0872989i
$698$	0.738694	+	0.197932i	0.0279600	+	0.00749185i
$699$	3.89050	−	10.5389i	0.147152	−	0.398620i
$700$	11.0351	+	30.1026i	0.417089	+	1.13777i
$701$			25.8725i			0.977189i	0.872511	+	0.488595i	$0.162490\pi$
$701$			25.8725i			0.977189i	−0.872511	+	0.488595i	$0.837510\pi$
$702$	−0.426931	−	0.120693i	−0.0161135	−	0.00455527i
$703$	47.7070	+	47.7070i	1.79930	+	1.79930i
$704$	−3.99029	+	6.91139i	−0.150390	+	0.260483i
$705$	−39.9881	+	20.6431i	−1.50604	+	0.777466i
$706$	−0.375109	−	0.649707i	−0.0141174	−	0.0244521i
$707$	−5.32304	+	19.8659i	−0.200194	+	0.747133i
$708$	10.7468	+	0.989737i	0.403890	+	0.0371966i
$709$	−9.51442	−	5.49315i	−0.357321	−	0.206300i	0.310584	−	0.950546i	$-0.399475\pi$
$709$	−9.51442	−	5.49315i	−0.357321	−	0.206300i	−0.667905	+	0.744246i	$0.732809\pi$
$710$	0.0267810	+	0.597572i	0.00100507	+	0.0224265i
$711$	20.9329	−	7.40298i	0.785045	−	0.277633i
$712$	−0.565938	+	0.565938i	−0.0212094	+	0.0212094i
$713$	−0.380753	−	1.42099i	−0.0142593	−	0.0532165i
$714$	−0.136062	−	0.792818i	−0.00509200	−	0.0296705i
$715$	5.65609	−	3.61251i	0.211526	−	0.135100i
$716$	40.7810	−	23.5449i	1.52406	−	0.879914i
$717$	4.06607	+	2.87488i	0.151850	+	0.107364i
$718$	0.588970	−	0.157814i	0.0219802	−	0.00588957i
$719$	45.6020			1.70067			0.850334	−	0.526244i	$-0.176400\pi$
$719$	45.6020			1.70067			0.850334	+	0.526244i	$0.176400\pi$
$720$	−3.28579	−	26.5981i	−0.122454	−	0.991251i
$721$	17.0125			0.633580
$722$	0.928132	−	0.248692i	0.0345415	−	0.00925537i
$723$	−0.346672	+	3.76425i	−0.0128929	+	0.139994i
$724$	6.63978	−	3.83348i	0.246766	−	0.142470i
$725$	18.8401	−	13.2568i	0.699703	−	0.492346i
$726$	0.0462241	+	0.0170638i	0.00171554	+	0.000633298i
$727$	8.24857	+	30.7841i	0.305923	+	1.14172i	0.932148	+	0.362077i	$0.117932\pi$
$727$	8.24857	+	30.7841i	0.305923	+	1.14172i	−0.626226	+	0.779642i	$0.715401\pi$
$728$	−0.774441	+	0.774441i	−0.0287027	+	0.0287027i
$729$	−23.0037	−	14.1360i	−0.851991	−	0.523557i
$730$	−0.0781681	−	0.0714622i	−0.00289313	−	0.00264493i
$731$	−28.5454	−	16.4807i	−1.05579	−	0.609561i
$732$	10.0461	+	21.8036i	0.371316	+	0.805885i
$733$	−12.0153	+	44.8415i	−0.443794	+	1.65626i	0.275308	+	0.961356i	$0.411220\pi$
$733$	−12.0153	+	44.8415i	−0.443794	+	1.65626i	−0.719102	+	0.694904i	$0.755447\pi$
$734$	−0.175610	−	0.304166i	−0.00648190	−	0.0112270i
$735$	9.41738	−	8.57043i	0.347365	−	0.316125i
$736$	0.0388545	−	0.0672980i	0.00143220	−	0.00248064i
$737$	2.37104	+	2.37104i	0.0873385	+	0.0873385i
$738$	−0.0116532	−	0.148856i	−0.000428960	−	0.00547946i
$739$			38.1714i			1.40416i	0.712099	+	0.702079i	$0.247745\pi$
$739$			38.1714i			1.40416i	−0.712099	+	0.702079i	$0.752255\pi$
$740$	−19.1275	+	36.8472i	−0.703139	+	1.35453i
$741$	−37.2221	+	6.38799i	−1.36739	+	0.234669i
$742$	0.536747	+	0.143821i	0.0197046	+	0.00527983i
$743$	−29.3573	−	7.86627i	−1.07702	−	0.288585i	−0.323643	−	0.946179i	$-0.604908\pi$
$743$	−29.3573	−	7.86627i	−1.07702	−	0.288585i	−0.753373	+	0.657594i	$0.771574\pi$
$744$	−1.25444	+	0.215285i	−0.0459901	+	0.00789275i
$745$	1.55458	+	4.91074i	0.0569553	+	0.179915i
$746$		−	0.430406i		−	0.0157583i
$747$	−21.7858	−	10.4024i	−0.797100	−	0.380602i
$748$	−7.19525	−	7.19525i	−0.263085	−	0.263085i
$749$	−16.7763	+	29.0575i	−0.612994	+	1.06174i
$750$	0.550392	−	0.0234181i	0.0200975	−	0.000855109i
$751$	13.3968	+	23.2039i	0.488855	+	0.846721i	0.999918	−	0.0128219i	$-0.00408146\pi$
$751$	13.3968	+	23.2039i	0.488855	+	0.846721i	−0.511063	+	0.859543i	$0.670748\pi$
$752$	12.0148	−	44.8398i	0.438134	−	1.63514i
$753$	14.9124	+	32.3652i	0.543439	+	1.17945i
$754$	0.340685	+	0.196695i	0.0124070	+	0.00716320i
$755$	−4.20868	+	4.60362i	−0.153170	+	0.167543i
$756$	−29.0811	+	16.2625i	−1.05767	+	0.591461i
$757$	−11.4087	+	11.4087i	−0.414657	+	0.414657i	−0.883357	−	0.468700i	$-0.844722\pi$
$757$	−11.4087	+	11.4087i	−0.414657	+	0.414657i	0.468700	+	0.883357i	$0.344722\pi$
$758$	0.0316467	+	0.118107i	0.00114946	+	0.00428984i
$759$	0.370079	+	0.136616i	0.0134330	+	0.00495886i
$760$	0.994784	+	1.55753i	0.0360846	+	0.0564976i
$761$	25.7323	−	14.8565i	0.932795	−	0.538549i	0.0451005	−	0.998982i	$-0.485639\pi$
$761$	25.7323	−	14.8565i	0.932795	−	0.538549i	0.887694	+	0.460433i	$0.152306\pi$
$762$	0.00945929	−	0.102711i	0.000342674	−	0.00372084i
$763$	49.8747	−	13.3639i	1.80559	−	0.483806i
$764$	−42.6600			−1.54338
$765$	33.8151	+	4.72692i	1.22259	+	0.170902i
$766$	1.06605			0.0385180
$767$	9.03576	−	2.42112i	0.326262	−	0.0874217i
$768$	22.5366	+	15.9343i	0.813220	+	0.574980i
$769$	24.3067	−	14.0335i	0.876523	−	0.506061i	0.00701246	−	0.999975i	$-0.497768\pi$
$769$	24.3067	−	14.0335i	0.876523	−	0.506061i	0.869510	+	0.493915i	$0.164435\pi$
$770$	−0.0439305	+	0.199245i	−0.00158314	+	0.00718028i
$771$	−4.68717	−	27.3116i	−0.168804	−	0.983602i
$772$	−7.96918	−	29.7414i	−0.286817	−	1.07042i
$773$	7.97067	−	7.97067i	0.286685	−	0.286685i	−0.549083	−	0.835768i	$-0.685023\pi$
$773$	7.97067	−	7.97067i	0.286685	−	0.286685i	0.835768	+	0.549083i	$0.185023\pi$
$774$	0.100942	−	0.543378i	0.00362828	−	0.0195313i
$775$	2.88893	+	32.1661i	0.103774	+	1.15544i
$776$	−0.888884	−	0.513198i	−0.0319091	−	0.0184227i
$777$	51.3763	+	4.73154i	1.84311	+	0.169743i
$778$	0.190451	−	0.710771i	0.00682798	−	0.0254824i
$779$	−6.35496	−	11.0071i	−0.227690	−	0.394371i
$780$	−10.6602	−	20.6500i	−0.381696	−	0.739388i
$781$	4.70177	−	8.14371i	0.168243	−	0.291405i
$782$	0.0233193	+	0.0233193i	0.000833898	+	0.000833898i
$783$	16.6948	+	17.1590i	0.596624	+	0.613213i
$784$			13.1350i			0.469108i
$785$	−5.04864	−	2.62076i	−0.180194	−	0.0935389i
$786$	−0.0949979	+	0.257339i	−0.00338846	+	0.00917898i
$787$	12.0235	+	3.22168i	0.428590	+	0.114840i	0.466664	−	0.884435i	$-0.345456\pi$
$787$	12.0235	+	3.22168i	0.428590	+	0.114840i	−0.0380742	+	0.999275i	$0.512122\pi$
$788$	33.5287	+	8.98400i	1.19441	+	0.320042i
$789$	17.5336	+	21.0907i	0.624211	+	0.750849i
$790$	−0.417851	−	0.216907i	−0.0148665	−	0.00771722i
$791$		−	18.6210i		−	0.662085i
$792$	0.147063	−	0.307996i	0.00522566	−	0.0109442i
$793$	14.7138	+	14.7138i	0.522503	+	0.522503i
$794$	0.128077	−	0.221835i	0.00454527	−	0.00787265i
$795$	−12.7409	+	19.8492i	−0.451872	+	0.703977i
$796$	−10.9573	−	18.9786i	−0.388371	−	0.672678i
$797$	8.35922	−	31.1970i	0.296099	−	1.10506i	−0.644242	−	0.764821i	$-0.722827\pi$
$797$	8.35922	−	31.1970i	0.296099	−	1.10506i	0.940341	−	0.340234i	$-0.110506\pi$
$798$	0.662832	−	0.937473i	0.0234640	−	0.0331862i
$799$	51.2183	+	29.5709i	1.81197	+	1.04614i
$800$	−1.09355	+	1.30936i	−0.0386627	+	0.0462928i
$801$	−13.7132	+	16.0426i	−0.484532	+	0.566839i
$802$	0.0563780	−	0.0563780i	0.00199078	−	0.00199078i
$803$	0.430926	+	1.60824i	0.0152070	+	0.0567534i
$804$	8.92855	−	7.42267i	0.314886	−	0.261778i
$805$	−0.351716	+	1.59519i	−0.0123964	+	0.0562231i
$806$	−0.477611	+	0.275749i	−0.0168231	+	0.00971283i
$807$	−24.3405	+	11.2150i	−0.856825	+	0.394787i
$808$	−0.704642	+	0.188808i	−0.0247892	+	0.00664225i
$809$	−1.79619			−0.0631505			−0.0315753	−	0.999501i	$-0.510052\pi$
$809$	−1.79619			−0.0631505			−0.0315753	+	0.999501i	$0.510052\pi$
$810$	0.114321	+	0.560971i	0.00401683	+	0.0197105i
$811$	−31.1802			−1.09488			−0.547442	−	0.836844i	$-0.684398\pi$
$811$	−31.1802			−1.09488			−0.547442	+	0.836844i	$0.684398\pi$
$812$	28.5371	−	7.64649i	1.00146	−	0.268339i
$813$	17.3389	−	7.98897i	0.608100	−	0.280185i
$814$	−0.228800	+	0.132098i	−0.00801943	+	0.00463002i
$815$	−26.1325	−	40.9156i	−0.915381	−	1.43321i
$816$	−27.0839	+	22.5160i	−0.948127	+	0.788217i
$817$	−12.1763	−	45.4427i	−0.425996	−	1.58984i
$818$	−0.274535	+	0.274535i	−0.00959888	+	0.00959888i
$819$	−18.7654	+	21.9531i	−0.655717	+	0.767102i
$820$	5.27713	−	5.77232i	0.184285	−	0.201578i
$821$	5.30733	+	3.06419i	0.185227	+	0.106941i	0.589746	−	0.807589i	$-0.299228\pi$
$821$	5.30733	+	3.06419i	0.185227	+	0.106941i	−0.404519	+	0.914530i	$0.632561\pi$
$822$	0.188362	−	0.266409i	0.00656987	−	0.00929207i
$823$	4.44794	−	16.5999i	0.155045	−	0.578637i	−0.844056	−	0.536255i	$-0.819839\pi$
$823$	4.44794	−	16.5999i	0.155045	−	0.578637i	0.999101	−	0.0423825i	$-0.0134948\pi$
$824$	0.301717	+	0.522589i	0.0105108	+	0.0182053i
$825$	−7.49018	−	4.34710i	−0.260775	−	0.151346i
$826$	−0.142193	+	0.246286i	−0.00494753	+	0.00856937i
$827$	−13.3792	−	13.3792i	−0.465240	−	0.465240i	0.435128	−	0.900369i	$-0.356703\pi$
$827$	−13.3792	−	13.3792i	−0.465240	−	0.465240i	−0.900369	+	0.435128i	$0.856703\pi$
$828$	0.588588	−	1.23269i	0.0204549	−	0.0428389i
$829$		−	46.0040i		−	1.59778i	−0.601474	−	0.798892i	$-0.705420\pi$
$829$		−	46.0040i		−	1.59778i	0.601474	−	0.798892i	$-0.294580\pi$
$830$	0.154494	+	0.488028i	0.00536255	+	0.0169397i
$831$	−18.6134	−	22.3896i	−0.645691	−	0.776686i
$832$	23.1366	+	6.19944i	0.802119	+	0.214927i
$833$	−16.1640	−	4.33113i	−0.560050	−	0.150065i
$834$	0.357402	−	0.968163i	0.0123758	−	0.0335247i
$835$	−15.0618	+	29.0151i	−0.521236	+	1.00411i
$836$		−	14.5236i		−	0.502310i
$837$	−32.5349	+	8.24132i	−1.12457	+	0.284862i
$838$	−0.579444	−	0.579444i	−0.0200166	−	0.0200166i
$839$	4.56651	−	7.90943i	0.157653	−	0.273064i	−0.776369	−	0.630279i	$-0.782940\pi$
$839$	4.56651	−	7.90943i	0.157653	−	0.273064i	0.934022	+	0.357215i	$0.116274\pi$
$840$	1.34641	+	0.429584i	0.0464554	+	0.0148220i
$841$	3.88615	+	6.73100i	0.134005	+	0.232104i
$842$	0.144604	−	0.539670i	0.00498339	−	0.0185982i
$843$	−42.6044	−	3.92369i	−1.46737	−	0.135139i
$844$	34.4662	+	19.8991i	1.18638	+	0.684954i
$845$	6.58764	+	6.02250i	0.226622	+	0.207180i
$846$	−0.181117	+	0.974968i	−0.00622694	+	0.0335201i
$847$	2.26801	−	2.26801i	0.0779298	−	0.0779298i
$848$	−6.29717	−	23.5013i	−0.216246	−	0.807039i
$849$	−8.75001	−	50.9853i	−0.300300	−	1.74981i
$850$	−0.416624	−	0.592090i	−0.0142901	−	0.0203085i
$851$	−1.83182	+	1.05760i	−0.0627938	+	0.0362540i
$852$	−26.5873	−	18.7983i	−0.910867	−	0.644020i
$853$	−27.8546	+	7.46361i	−0.953722	+	0.255549i	−0.701941	−	0.712235i	$-0.747683\pi$
$853$	−27.8546	+	7.46361i	−0.953722	+	0.255549i	−0.251781	+	0.967784i	$0.581016\pi$
$854$	−0.632597			−0.0216470
$855$	29.3573	+	38.8986i	1.00400	+	1.33030i
$856$	−1.19011			−0.0406772
$857$	−16.1520	+	4.32792i	−0.551743	+	0.147839i	−0.523910	−	0.851774i	$-0.675527\pi$
$857$	−16.1520	+	4.32792i	−0.551743	+	0.147839i	−0.0278327	+	0.999613i	$0.508861\pi$
$858$	0.0135624	−	0.147264i	0.000463014	−	0.00502752i
$859$	27.0868	−	15.6386i	0.924191	−	0.533582i	0.0392215	−	0.999231i	$-0.487512\pi$
$859$	27.0868	−	15.6386i	0.924191	−	0.533582i	0.884970	+	0.465648i	$0.154179\pi$
$860$	24.3976	−	15.5826i	0.831953	−	0.531362i
$861$	−9.11803	−	3.36596i	−0.310742	−	0.114712i
$862$	0.169984	+	0.634390i	0.00578969	+	0.0216074i
$863$	27.1480	−	27.1480i	0.924130	−	0.924130i	−0.0731879	−	0.997318i	$-0.523317\pi$
$863$	27.1480	−	27.1480i	0.924130	−	0.924130i	0.997318	+	0.0731879i	$0.0233173\pi$
$864$	−1.52306	−	0.907404i	−0.0518154	−	0.0308705i
$865$	−1.62807	−	36.3276i	−0.0553561	−	1.23518i
$866$	0.171969	+	0.0992866i	0.00584376	+	0.00337389i
$867$	−6.45577	−	14.0113i	−0.219250	−	0.475848i
$868$	−10.7197	+	40.0065i	−0.363851	+	1.35791i
$869$	3.70056	+	6.40956i	0.125533	+	0.217430i
$870$	0.0238753	−	0.507067i	0.000809449	−	0.0171912i
$871$	5.03207	−	8.71580i	0.170505	−	0.295323i
$872$	1.29504	+	1.29504i	0.0438556	+	0.0438556i
$873$	−24.4240	−	11.6621i	−0.826628	−	0.394701i
$874$			0.0470701i			0.00159217i
$875$	13.6085	−	33.1780i	0.460051	−	1.12162i
$876$	5.68222	−	0.975172i	0.191984	−	0.0329480i
$877$	−14.3370	−	3.84160i	−0.484128	−	0.129722i	0.00849635	−	0.999964i	$-0.497295\pi$
$877$	−14.3370	−	3.84160i	−0.484128	−	0.129722i	−0.492624	+	0.870242i	$0.663962\pi$
$878$	0.932626	+	0.249897i	0.0314746	+	0.00843360i
$879$	−34.7640	+	5.96613i	−1.17256	+	0.201233i
$880$	8.51685	−	2.69615i	0.287103	−	0.0908873i
$881$			43.3440i			1.46030i	0.683289	+	0.730148i	$0.260549\pi$
$881$			43.3440i			1.46030i	−0.683289	+	0.730148i	$0.739451\pi$
$882$	−0.0218989	−	0.279732i	−0.000737374	−	0.00941907i
$883$	−11.7828	−	11.7828i	−0.396524	−	0.396524i	0.480481	−	0.877005i	$-0.340462\pi$
$883$	−11.7828	−	11.7828i	−0.396524	−	0.396524i	−0.877005	+	0.480481i	$0.840462\pi$
$884$	−15.2705	+	26.4493i	−0.513602	+	0.889585i
$885$	−8.12462	−	8.92752i	−0.273106	−	0.300095i
$886$	−0.0236338	−	0.0409350i	−0.000793994	−	0.00137524i
$887$	0.428358	−	1.59865i	0.0143828	−	0.0536775i	−0.958361	−	0.285558i	$-0.907821\pi$
$887$	0.428358	−	1.59865i	0.0143828	−	0.0536775i	0.972744	+	0.231880i	$0.0744878\pi$
$888$	0.765815	+	1.66209i	0.0256991	+	0.0557760i
$889$	−5.81479	−	3.35717i	−0.195022	−	0.112596i
$890$	0.447055	−	0.0200354i	0.0149853	−	0.000671587i
$891$	3.23227	−	8.39955i	0.108285	−	0.281396i
$892$	−15.6709	+	15.6709i	−0.524702	+	0.524702i
$893$	21.8476	+	81.5365i	0.731103	+	2.72852i
$894$	0.106480	+	0.0393076i	0.00356123	+	0.00131464i
$895$	−51.4339	−	11.3404i	−1.71925	−	0.379068i
$896$	−2.52610	+	1.45844i	−0.0843911	+	0.0487232i
$897$	0.108583	−	1.17903i	0.00362550	−	0.0393666i
$898$	0.588242	−	0.157619i	0.0196299	−	0.00525981i
$899$	29.7594			0.992531
$900$	−17.3678	+	24.4465i	−0.578927	+	0.814883i
$901$	30.9973			1.03267
$902$	0.0480745	−	0.0128815i	0.00160071	−	0.000428908i
$903$	−29.3757	−	20.7698i	−0.977561	−	0.691175i
$904$	0.571997	−	0.330243i	0.0190243	−	0.0109837i
$905$	−8.37425	−	1.84640i	−0.278370	−	0.0613764i
$906$	0.0232485	+	0.135466i	0.000772380	+	0.00450057i
$907$	3.00340	+	11.2088i	0.0997261	+	0.372183i	0.997694	−	0.0678789i	$-0.0216232\pi$
$907$	3.00340	+	11.2088i	0.0997261	+	0.372183i	−0.897967	+	0.440062i	$0.854956\pi$
$908$	33.1571	−	33.1571i	1.10036	−	1.10036i
$909$	−18.1357	+	6.41375i	−0.601524	+	0.212731i
$910$	0.611759	−	0.0274168i	0.0202796	−	0.000908859i
$911$	−22.0149	−	12.7103i	−0.729388	−	0.421112i	0.0888105	−	0.996049i	$-0.471693\pi$
$911$	−22.0149	−	12.7103i	−0.729388	−	0.421112i	−0.818198	+	0.574936i	$0.805027\pi$
$912$	−50.0588	−	4.61020i	−1.65761	−	0.152659i
$913$	2.08279	−	7.77308i	0.0689303	−	0.257252i
$914$	−0.0882750	−	0.152897i	−0.00291988	−	0.00505738i
$915$	8.16177	−	25.5807i	0.269820	−	0.845672i
$916$	12.7865	−	22.1468i	0.422477	−	0.731752i
$917$	12.6265	+	12.6265i	0.416964	+	0.416964i
$918$	0.539258	−	0.524670i	0.0177982	−	0.0173167i
$919$		−	0.140888i		−	0.00464747i	−0.999997	−	0.00232373i	$-0.999260\pi$
$919$		−	0.140888i		−	0.00464747i	0.999997	−	0.00232373i	$-0.000739668\pi$
$920$	−0.0552386	+	0.0174867i	−0.00182116	+	0.000576520i
$921$	8.11914	−	21.9939i	0.267535	−	0.724722i
$922$	−0.329887	−	0.0883929i	−0.0108642	−	0.00291106i
$923$	−27.2620	−	7.30483i	−0.897339	−	0.240441i
$924$	−7.10013	−	8.54057i	−0.233577	−	0.280964i
$925$	43.5979	−	15.9823i	1.43349	−	0.525495i
$926$			0.902923i			0.0296719i
$927$	9.00733	+	13.1174i	0.295840	+	0.430831i
$928$	1.11156	+	1.11156i	0.0364887	+	0.0364887i
$929$	7.76864	−	13.4557i	0.254881	−	0.441467i	−0.709982	−	0.704220i	$-0.751297\pi$
$929$	7.76864	−	13.4557i	0.254881	−	0.441467i	0.964863	+	0.262753i	$0.0846304\pi$
$930$	0.598890	+	0.384419i	0.0196384	+	0.0126056i
$931$	−11.9423	−	20.6847i	−0.391395	−	0.677915i
$932$	3.35605	−	12.5250i	0.109931	−	0.410269i
$933$	−29.5343	+	41.7717i	−0.966910	+	1.36755i
$934$	−0.267680	−	0.154545i	−0.00875876	−	0.00505687i
$935$	0.509557	+	11.3699i	0.0166643	+	0.371835i
$936$	−1.00716	−	0.187097i	−0.0329200	−	0.00611545i
$937$	−3.96712	+	3.96712i	−0.129600	+	0.129600i	−0.768931	−	0.639331i	$-0.779211\pi$
$937$	−3.96712	+	3.96712i	−0.129600	+	0.129600i	0.639331	+	0.768931i	$0.279211\pi$
$938$	0.0791881	+	0.295534i	0.00258558	+	0.00964953i
$939$	29.5047	−	24.5285i	0.962851	−	0.800457i
$940$	−43.7760	+	27.9594i	−1.42782	+	0.911936i
$941$	−7.10353	+	4.10123i	−0.231569	+	0.133696i	−0.611295	−	0.791402i	$-0.709351\pi$
$941$	−7.10353	+	4.10123i	−0.231569	+	0.133696i	0.379727	+	0.925099i	$0.376018\pi$
$942$	−0.113843	+	0.0524537i	−0.00370920	+	0.00170903i
$943$	0.384894	−	0.103132i	0.0125339	−	0.00335844i
$944$	12.4518			0.405271
$945$	36.2797	+	8.52235i	1.18018	+	0.277232i
$946$	0.184225			0.00598967
$947$	−12.9682	+	3.47481i	−0.421409	+	0.112916i	−0.463290	−	0.886206i	$-0.653331\pi$
$947$	−12.9682	+	3.47481i	−0.421409	+	0.112916i	0.0418819	+	0.999123i	$0.486665\pi$
$948$	23.2760	−	10.7245i	0.755969	−	0.348317i
$949$	4.32771	−	2.49861i	0.140484	−	0.0811082i
$950$	0.177089	−	1.01805i	0.00574552	−	0.0330297i
$951$	11.7737	−	9.78798i	0.381789	−	0.317397i
$952$	−0.480712	−	1.79404i	−0.0155799	−	0.0581452i
$953$	−12.1659	+	12.1659i	−0.394091	+	0.394091i	−0.876143	−	0.482052i	$-0.839892\pi$
$953$	−12.1659	+	12.1659i	−0.394091	+	0.394091i	0.482052	+	0.876143i	$0.339892\pi$
$954$	0.173290	+	0.490001i	0.00561048	+	0.0158644i
$955$	35.2161	+	32.1950i	1.13957	+	1.04180i
$956$	4.97773	+	2.87389i	0.160991	+	0.0929483i
$957$	−4.60707	+	6.51599i	−0.148925	+	0.210632i
$958$	−0.276339	+	1.03131i	−0.00892812	+	0.0333202i
$959$	−10.6194	−	18.3934i	−0.342919	−	0.593953i
$960$	−6.58671	−	30.1987i	−0.212585	−	0.974659i
$961$	−5.36002	+	9.28383i	−0.172904	+	0.299478i
$962$	0.560702	+	0.560702i	0.0180777	+	0.0180777i
$963$	−31.2868	+	2.44929i	−1.00820	+	0.0789274i
$964$			4.36321i			0.140530i
$965$	−15.8668	+	30.5659i	−0.510772	+	0.983952i
$966$	0.0230110	+	0.0276794i	0.000740368	+	0.000890571i
$967$	3.09214	+	0.828536i	0.0994365	+	0.0266439i	0.308194	−	0.951323i	$-0.400275\pi$
$967$	3.09214	+	0.828536i	0.0994365	+	0.0266439i	−0.208758	+	0.977967i	$0.566942\pi$
$968$	0.109892	+	0.0294454i	0.00353205	+	0.000946411i
$969$	22.1797	−	60.0823i	0.712514	−	1.93012i
$970$	0.173203	+	0.547128i	0.00556120	+	0.0175672i
$971$			54.7305i			1.75639i	0.478307	+	0.878193i	$0.341251\pi$
$971$			54.7305i			1.75639i	−0.478307	+	0.878193i	$0.658749\pi$
$972$	−27.9361	−	13.8125i	−0.896052	−	0.443037i
$973$	−47.5035	−	47.5035i	−1.52289	−	1.52289i
$974$	0.0343346	−	0.0594692i	0.00110015	−	0.00190552i
$975$	−6.78425	+	25.0918i	−0.217270	+	0.803580i
$976$	13.8491	+	23.9873i	0.443298	+	0.767815i
$977$	3.77921	−	14.1042i	0.120908	−	0.451233i	−0.878753	−	0.477276i	$-0.841624\pi$
$977$	3.77921	−	14.1042i	0.120908	−	0.451233i	0.999661	+	0.0260431i	$0.00829071\pi$
$978$	−1.06530	−	0.0981092i	−0.0340644	−	0.00313719i
$979$	−6.09247	−	3.51749i	−0.194716	−	0.112419i
$980$	9.91685	−	10.8474i	0.316782	−	0.346509i
$981$	36.7105	+	31.3800i	1.17207	+	1.00189i
$982$	−0.0484957	+	0.0484957i	−0.00154756	+	0.00154756i
$983$	−14.3325	−	53.4896i	−0.457135	−	1.70605i	−0.681733	−	0.731601i	$-0.738774\pi$
$983$	−14.3325	−	53.4896i	−0.457135	−	1.70605i	0.224598	−	0.974452i	$-0.427893\pi$
$984$	−0.0583129	−	0.339782i	−0.00185895	−	0.0108319i
$985$	−20.8981	−	32.7201i	−0.665867	−	1.04255i
$986$	−0.577748	+	0.333563i	−0.0183992	+	0.0106228i
$987$	52.7079	+	37.2666i	1.67771	+	1.18621i
$988$	−42.1057	+	11.2822i	−1.33956	+	0.358934i
$989$	1.47494			0.0469003
$990$	−0.176885	+	0.0716184i	−0.00562178	+	0.00227618i
$991$	−30.3795			−0.965038			−0.482519	−	0.875885i	$-0.660278\pi$
$991$	−30.3795			−0.965038			−0.482519	+	0.875885i	$0.660278\pi$
$992$	−2.12869	+	0.570380i	−0.0675859	+	0.0181096i
$993$	0.171424	−	1.86137i	0.00543998	−	0.0590686i
$994$	0.743073	−	0.429014i	0.0235689	−	0.0136075i
$995$	−5.27759	+	23.9363i	−0.167311	+	0.758830i
$996$	−26.1410	−	9.65008i	−0.828310	−	0.305775i
$997$	4.80890	+	17.9471i	0.152299	+	0.568389i	0.999321	+	0.0368314i	$0.0117265\pi$
$997$	4.80890	+	17.9471i	0.152299	+	0.568389i	−0.847022	+	0.531558i	$0.821607\pi$
$998$	0.404062	−	0.404062i	0.0127904	−	0.0127904i
$999$	23.5531	+	42.1184i	0.745187	+	1.33257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bc.c.353.17	yes	116
5.2	odd	4		495.2.bc.d.452.17	yes	116
9.5	odd	6		495.2.bc.d.23.17	yes	116
45.32	even	12	inner	495.2.bc.c.122.17	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.bc.c.122.17	✓	116	45.32	even	12	inner
495.2.bc.c.353.17	yes	116	1.1	even	1	trivial
495.2.bc.d.23.17	yes	116	9.5	odd	6
495.2.bc.d.452.17	yes	116	5.2	odd	4

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0274785 + 0.00736284i) q^{2} +(-1.57310 + 0.724814i) q^{3} +(-1.73135 + 0.999595i) q^{4} +(2.18362 + 0.481456i) q^{5} +(0.0378897 - 0.0314993i) q^{6} +(-0.830150 - 3.09816i) q^{7} +(0.0804463 - 0.0804463i) q^{8} +(1.94929 - 2.28041i) q^{9} +O(q^{10})\)	\(q+(-0.0274785 + 0.00736284i) q^{2} +(-1.57310 + 0.724814i) q^{3} +(-1.73135 + 0.999595i) q^{4} +(2.18362 + 0.481456i) q^{5} +(0.0378897 - 0.0314993i) q^{6} +(-0.830150 - 3.09816i) q^{7} +(0.0804463 - 0.0804463i) q^{8} +(1.94929 - 2.28041i) q^{9} +(-0.0635475 + 0.00284797i) q^{10} +(0.866025 + 0.500000i) q^{11} +(1.99907 - 2.82737i) q^{12} +(0.776816 - 2.89912i) q^{13} +(0.0456225 + 0.0790205i) q^{14} +(-3.78402 + 0.825341i) q^{15} +(1.99757 - 3.45990i) q^{16} +(3.59908 + 3.59908i) q^{17} +(-0.0367732 + 0.0770146i) q^{18} +7.26476i q^{19} +(-4.26187 + 1.34917i) q^{20} +(3.55150 + 4.27201i) q^{21} +(-0.0274785 - 0.00736284i) q^{22} +(-0.219998 - 0.0589483i) q^{23} +(-0.0682415 + 0.184859i) q^{24} +(4.53640 + 2.10263i) q^{25} +0.0853829i q^{26} +(-1.41355 + 5.00019i) q^{27} +(4.53419 + 4.53419i) q^{28} +(2.30368 - 3.99009i) q^{29} +(0.0979023 - 0.0505403i) q^{30} +(3.22955 + 5.59375i) q^{31} +(-0.0883064 + 0.329564i) q^{32} +(-1.72475 - 0.158842i) q^{33} +(-0.125397 - 0.0723979i) q^{34} +(-0.321104 - 7.16489i) q^{35} +(-1.09541 + 5.89669i) q^{36} +(6.56691 - 6.56691i) q^{37} +(-0.0534892 - 0.199625i) q^{38} +(0.879312 + 5.12365i) q^{39} +(0.214396 - 0.136933i) q^{40} +(-1.51514 + 0.874766i) q^{41} +(-0.129044 - 0.0912393i) q^{42} +(-6.25522 + 1.67608i) q^{43} -1.99919 q^{44} +(5.35442 - 4.04106i) q^{45} +0.00647924 q^{46} +(11.2236 - 3.00735i) q^{47} +(-0.634599 + 6.89063i) q^{48} +(-2.84727 + 1.64387i) q^{49} +(-0.140135 - 0.0243764i) q^{50} +(-8.27039 - 3.05305i) q^{51} +(1.55300 + 5.79589i) q^{52} +(4.30627 - 4.30627i) q^{53} +(0.00202667 - 0.147805i) q^{54} +(1.65034 + 1.50876i) q^{55} +(-0.316018 - 0.182453i) q^{56} +(-5.26560 - 11.4282i) q^{57} +(-0.0339232 + 0.126603i) q^{58} +(1.55836 + 2.69917i) q^{59} +(5.72646 - 5.21144i) q^{60} +(-3.46648 + 6.00411i) q^{61} +(-0.129929 - 0.129929i) q^{62} +(-8.68328 - 4.14613i) q^{63} +7.98058i q^{64} +(3.09207 - 5.95657i) q^{65} +(0.0485631 - 0.00833432i) q^{66} +(3.23891 + 0.867862i) q^{67} +(-9.82890 - 2.63365i) q^{68} +(0.388806 - 0.0667262i) q^{69} +(0.0615774 + 0.194516i) q^{70} -9.40355i q^{71} +(-0.0266376 - 0.340264i) q^{72} +(1.17731 + 1.17731i) q^{73} +(-0.132098 + 0.228800i) q^{74} +(-8.66023 - 0.0196065i) q^{75} +(-7.26182 - 12.5778i) q^{76} +(0.830150 - 3.09816i) q^{77} +(-0.0618868 - 0.134316i) q^{78} +(6.40956 + 3.70056i) q^{79} +(6.02773 - 6.59336i) q^{80} +(-1.40055 - 8.89036i) q^{81} +(0.0351930 - 0.0351930i) q^{82} +(-2.08279 - 7.77308i) q^{83} +(-10.4192 - 3.84629i) q^{84} +(6.12623 + 9.59183i) q^{85} +(0.159543 - 0.0921124i) q^{86} +(-0.731843 + 7.94654i) q^{87} +(0.109892 - 0.0294454i) q^{88} -7.03497 q^{89} +(-0.117378 + 0.150466i) q^{90} -9.62680 q^{91} +(0.439818 - 0.117849i) q^{92} +(-9.13484 - 6.45870i) q^{93} +(-0.286264 + 0.165275i) q^{94} +(-3.49766 + 15.8635i) q^{95} +(-0.0999579 - 0.582443i) q^{96} +(-2.33501 - 8.71439i) q^{97} +(0.0661352 - 0.0661352i) q^{98} +(2.82834 - 1.00025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9}+O(q^{10}) \) 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9	\( 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9} + 6 q^{10} + 6 q^{12} - 12 q^{13} + 10 q^{14} - 18 q^{15} + 62 q^{16} + 8 q^{17} - 12 q^{18} - 18 q^{20} - 10 q^{21} - 4 q^{22} - 40 q^{23} + 62 q^{24} - 6 q^{25} - 58 q^{27} + 18 q^{28} + 2 q^{29} - 70 q^{30} - 2 q^{31} - 66 q^{32} + 24 q^{34} - 2 q^{35} + 24 q^{36} - 14 q^{37} - 6 q^{38} - 4 q^{39} - 100 q^{40} + 6 q^{41} - 30 q^{42} - 22 q^{43} + 120 q^{44} + 94 q^{45} - 44 q^{46} + 32 q^{47} + 108 q^{48} + 18 q^{49} - 22 q^{50} - 8 q^{51} - 126 q^{52} + 44 q^{53} - 28 q^{54} + 2 q^{55} + 42 q^{56} + 20 q^{57} + 2 q^{58} - 22 q^{59} - 68 q^{60} - 10 q^{61} + 16 q^{62} - 8 q^{63} - 60 q^{65} + 6 q^{66} + 36 q^{67} - 48 q^{68} + 76 q^{69} + 154 q^{70} - 228 q^{72} + 12 q^{73} + 8 q^{74} - 72 q^{75} - 6 q^{76} - 8 q^{77} - 110 q^{78} + 6 q^{79} - 4 q^{80} + 44 q^{81} - 50 q^{82} + 30 q^{83} - 222 q^{84} - 126 q^{85} + 90 q^{86} + 112 q^{87} + 2 q^{88} - 8 q^{89} + 72 q^{90} + 72 q^{91} - 132 q^{92} + 112 q^{93} - 42 q^{94} + 78 q^{95} + 68 q^{96} - 72 q^{97} - 16 q^{98} + 4 q^{99}+O(q^{100}) \) 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9 + 6 * q^10 + 6 * q^12 - 12 * q^13 + 10 * q^14 - 18 * q^15 + 62 * q^16 + 8 * q^17 - 12 * q^18 - 18 * q^20 - 10 * q^21 - 4 * q^22 - 40 * q^23 + 62 * q^24 - 6 * q^25 - 58 * q^27 + 18 * q^28 + 2 * q^29 - 70 * q^30 - 2 * q^31 - 66 * q^32 + 24 * q^34 - 2 * q^35 + 24 * q^36 - 14 * q^37 - 6 * q^38 - 4 * q^39 - 100 * q^40 + 6 * q^41 - 30 * q^42 - 22 * q^43 + 120 * q^44 + 94 * q^45 - 44 * q^46 + 32 * q^47 + 108 * q^48 + 18 * q^49 - 22 * q^50 - 8 * q^51 - 126 * q^52 + 44 * q^53 - 28 * q^54 + 2 * q^55 + 42 * q^56 + 20 * q^57 + 2 * q^58 - 22 * q^59 - 68 * q^60 - 10 * q^61 + 16 * q^62 - 8 * q^63 - 60 * q^65 + 6 * q^66 + 36 * q^67 - 48 * q^68 + 76 * q^69 + 154 * q^70 - 228 * q^72 + 12 * q^73 + 8 * q^74 - 72 * q^75 - 6 * q^76 - 8 * q^77 - 110 * q^78 + 6 * q^79 - 4 * q^80 + 44 * q^81 - 50 * q^82 + 30 * q^83 - 222 * q^84 - 126 * q^85 + 90 * q^86 + 112 * q^87 + 2 * q^88 - 8 * q^89 + 72 * q^90 + 72 * q^91 - 132 * q^92 + 112 * q^93 - 42 * q^94 + 78 * q^95 + 68 * q^96 - 72 * q^97 - 16 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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