LMFDB - Embedded newform 690.2.w.a.217.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.4
Character	$\chi$	$=$	690.217
Dual form			690.2.w.a.283.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0118400 + 2.23604i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(1.21462 - 0.663233i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0118400 + 2.23604i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(1.21462 - 0.663233i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-2.22949 - 0.171327i) q^{10} +(3.43475 + 2.97623i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(-0.0572451 + 0.104837i) q^{13} +(0.574893 + 1.25884i) q^{14} +(-0.463734 - 2.18745i) q^{15} +(0.959493 + 0.281733i) q^{16} +(2.58366 + 1.93410i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-0.165605 + 1.15181i) q^{19} +(0.329941 - 2.21159i) q^{20} +(-1.04588 + 0.906262i) q^{21} +(-3.21368 + 3.21368i) q^{22} +(-4.43205 + 1.83219i) q^{23} +1.00000i q^{24} +(-4.99972 - 0.0529496i) q^{25} +(-0.100486 - 0.0645782i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(-1.29664 + 0.483624i) q^{28} +(2.45088 - 0.352383i) q^{29} +(2.21496 - 0.306502i) q^{30} +(-5.49019 + 3.52833i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-3.98890 - 2.17810i) q^{33} +(-2.11349 + 2.43910i) q^{34} +(1.46863 + 2.72379i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.721730 + 0.269191i) q^{37} +(-1.13706 - 0.247352i) q^{38} +(0.0336523 - 0.114609i) q^{39} +(2.18242 + 0.486873i) q^{40} +(-1.09634 + 2.40066i) q^{41} +(-0.829340 - 1.10787i) q^{42} +(-1.03140 - 4.74127i) q^{43} +(-2.97623 - 3.43475i) q^{44} +(0.918113 + 2.03889i) q^{45} +(-1.51134 - 4.55147i) q^{46} +(-3.35604 - 3.35604i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(-2.74906 + 4.27762i) q^{49} +(0.409491 - 4.98320i) q^{50} +(-2.93574 - 1.34071i) q^{51} +(0.0715823 - 0.0956227i) q^{52} +(2.37831 + 4.35555i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-6.69562 + 7.64499i) q^{55} +(-0.389890 - 1.32784i) q^{56} +(-0.0830141 - 1.16069i) q^{57} +(0.176641 + 2.46977i) q^{58} +(-0.267799 - 0.912041i) q^{59} +(0.147707 + 2.23118i) q^{60} +(6.89732 + 10.7324i) q^{61} +(-3.12768 - 5.72791i) q^{62} +(0.829340 - 1.10787i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-0.233741 - 0.129243i) q^{65} +(2.45712 - 3.82335i) q^{66} +(-14.4218 - 1.03147i) q^{67} +(-2.28211 - 2.28211i) q^{68} +(3.94130 - 2.73242i) q^{69} +(-2.82162 + 1.27058i) q^{70} +(5.17109 + 5.96775i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(-6.67685 - 8.91923i) q^{73} +(-0.319993 + 0.700687i) q^{74} +(4.89672 - 1.01103i) q^{75} +(0.327839 - 1.11652i) q^{76} +(6.14585 + 1.33695i) q^{77} +(0.111916 + 0.0417427i) q^{78} +(11.2840 - 3.31328i) q^{79} +(-0.641325 + 2.14213i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.31633 - 1.26481i) q^{82} +(0.511355 - 1.37100i) q^{83} +(1.16421 - 0.748193i) q^{84} +(-4.35532 + 5.75426i) q^{85} +(4.80277 - 0.690534i) q^{86} +(-2.31996 + 0.865301i) q^{87} +(3.63832 - 2.72361i) q^{88} +(7.15307 + 4.59700i) q^{89} +(-2.09919 + 0.770321i) q^{90} +0.165304i q^{91} +(4.64769 - 1.18280i) q^{92} +(4.61472 - 4.61472i) q^{93} +(3.58691 - 3.10807i) q^{94} +(-2.57353 - 0.383937i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.90938 + 13.1626i) q^{97} +(-4.07061 - 3.04722i) q^{98} +(4.36073 + 1.28042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−0.0118400	+	2.23604i	−0.00529503	+	0.999986i
$5$	−0.0118400	+	2.23604i	−0.00529503	+	0.999986i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	1.21462	−	0.663233i	0.459083	−	0.250678i	−0.233027	−	0.972470i	$-0.574863\pi$
$7$	1.21462	−	0.663233i	0.459083	−	0.250678i	0.692110	+	0.721792i	$0.256681\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−2.22949	−	0.171327i	−0.705028	−	0.0541783i
$11$	3.43475	+	2.97623i	1.03562	+	0.897366i	0.994805	−	0.101801i	$-0.0324604\pi$
$11$	3.43475	+	2.97623i	1.03562	+	0.897366i	0.0408110	+	0.999167i	$0.487006\pi$
$12$	0.997452	−	0.0713392i	0.287940	−	0.0205938i
$13$	−0.0572451	+	0.104837i	−0.0158769	+	0.0290765i	−0.885497	−	0.464645i	$-0.846182\pi$
$13$	−0.0572451	+	0.104837i	−0.0158769	+	0.0290765i	0.869620	+	0.493721i	$0.164364\pi$
$14$	0.574893	+	1.25884i	0.153647	+	0.336439i
$15$	−0.463734	−	2.18745i	−0.119736	−	0.564798i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	2.58366	+	1.93410i	0.626630	+	0.469089i	0.864788	−	0.502137i	$-0.167453\pi$
$17$	2.58366	+	1.93410i	0.626630	+	0.469089i	−0.238158	+	0.971226i	$0.576544\pi$
$18$	0.349464	+	0.936950i	0.0823695	+	0.220841i
$19$	−0.165605	+	1.15181i	−0.0379924	+	0.264243i	−0.999960	−	0.00891976i	$-0.997161\pi$
$19$	−0.165605	+	1.15181i	−0.0379924	+	0.264243i	0.961968	+	0.273163i	$0.0880698\pi$
$20$	0.329941	−	2.21159i	0.0737770	−	0.494527i
$21$	−1.04588	+	0.906262i	−0.228230	+	0.197763i
$22$	−3.21368	+	3.21368i	−0.685158	+	0.685158i
$23$	−4.43205	+	1.83219i	−0.924146	+	0.382038i
$23$	−4.43205	+	1.83219i	−0.924146	+	0.382038i
$24$			1.00000i			0.204124i
$25$	−4.99972	−	0.0529496i	−0.999944	−	0.0105899i
$26$	−0.100486	−	0.0645782i	−0.0197069	−	0.0126648i
$27$	−0.800541	+	0.599278i	−0.154064	+	0.115331i
$28$	−1.29664	+	0.483624i	−0.245043	+	0.0913963i
$29$	2.45088	−	0.352383i	0.455116	−	0.0654358i	0.0890552	−	0.996027i	$-0.471615\pi$
$29$	2.45088	−	0.352383i	0.455116	−	0.0654358i	0.366061	+	0.930591i	$0.380706\pi$
$30$	2.21496	−	0.306502i	0.404395	−	0.0559593i
$31$	−5.49019	+	3.52833i	−0.986067	+	0.633707i	−0.931093	−	0.364781i	$-0.881144\pi$
$31$	−5.49019	+	3.52833i	−0.986067	+	0.633707i	−0.0549739	+	0.998488i	$0.517508\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	−3.98890	−	2.17810i	−0.694378	−	0.379159i
$34$	−2.11349	+	2.43910i	−0.362461	+	0.418302i
$35$	1.46863	+	2.72379i	0.248244	+	0.460404i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	0.721730	+	0.269191i	0.118652	+	0.0442548i	0.408089	−	0.912942i	$-0.366195\pi$
$37$	0.721730	+	0.269191i	0.118652	+	0.0442548i	−0.289437	+	0.957197i	$0.593468\pi$
$38$	−1.13706	−	0.247352i	−0.184456	−	0.0401258i
$39$	0.0336523	−	0.114609i	0.00538868	−	0.0183521i
$40$	2.18242	+	0.486873i	0.345071	+	0.0769814i
$41$	−1.09634	+	2.40066i	−0.171220	+	0.374920i	−0.975716	−	0.219038i	$-0.929708\pi$
$41$	−1.09634	+	2.40066i	−0.171220	+	0.374920i	0.804496	+	0.593958i	$0.202435\pi$
$42$	−0.829340	−	1.10787i	−0.127970	−	0.170948i
$43$	−1.03140	−	4.74127i	−0.157287	−	0.723037i	−0.986454	−	0.164036i	$-0.947549\pi$
$43$	−1.03140	−	4.74127i	−0.157287	−	0.723037i	0.829167	−	0.559000i	$-0.188815\pi$
$44$	−2.97623	−	3.43475i	−0.448683	−	0.517808i
$45$	0.918113	+	2.03889i	0.136864	+	0.303940i
$46$	−1.51134	−	4.55147i	−0.222836	−	0.671077i
$47$	−3.35604	−	3.35604i	−0.489529	−	0.489529i	0.418629	−	0.908157i	$-0.362511\pi$
$47$	−3.35604	−	3.35604i	−0.489529	−	0.489529i	−0.908157	+	0.418629i	$0.862511\pi$
$48$	−0.997452	−	0.0713392i	−0.143970	−	0.0102969i
$49$	−2.74906	+	4.27762i	−0.392723	+	0.611089i
$50$	0.409491	−	4.98320i	0.0579107	−	0.704731i
$51$	−2.93574	−	1.34071i	−0.411086	−	0.187737i
$52$	0.0715823	−	0.0956227i	0.00992667	−	0.0132605i
$53$	2.37831	+	4.35555i	0.326686	+	0.598281i	0.988471	−	0.151413i	$-0.0483823\pi$
$53$	2.37831	+	4.35555i	0.326686	+	0.598281i	−0.661784	+	0.749694i	$0.730201\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−6.69562	+	7.64499i	−0.902837	+	1.03085i
$56$	−0.389890	−	1.32784i	−0.0521012	−	0.177440i
$57$	−0.0830141	−	1.16069i	−0.0109955	−	0.153737i
$58$	0.176641	+	2.46977i	0.0231942	+	0.324297i
$59$	−0.267799	−	0.912041i	−0.0348645	−	0.118738i	0.940222	−	0.340562i	$-0.110617\pi$
$59$	−0.267799	−	0.912041i	−0.0348645	−	0.118738i	−0.975087	+	0.221824i	$0.928799\pi$
$60$	0.147707	+	2.23118i	0.0190689	+	0.288045i
$61$	6.89732	+	10.7324i	0.883111	+	1.37415i	0.926980	+	0.375110i	$0.122395\pi$
$61$	6.89732	+	10.7324i	0.883111	+	1.37415i	−0.0438696	+	0.999037i	$0.513969\pi$
$62$	−3.12768	−	5.72791i	−0.397215	−	0.727445i
$63$	0.829340	−	1.10787i	0.104487	−	0.139578i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−0.233741	−	0.129243i	−0.0289920	−	0.0160307i
$66$	2.45712	−	3.82335i	0.302450	−	0.470622i
$67$	−14.4218	−	1.03147i	−1.76191	−	0.126014i	−0.847497	−	0.530800i	$-0.821892\pi$
$67$	−14.4218	−	1.03147i	−1.76191	−	0.126014i	−0.914412	+	0.404786i	$0.867346\pi$
$68$	−2.28211	−	2.28211i	−0.276747	−	0.276747i
$69$	3.94130	−	2.73242i	0.474477	−	0.328945i
$70$	−2.82162	+	1.27058i	−0.337248	+	0.151863i
$71$	5.17109	+	5.96775i	0.613695	+	0.708242i	0.974497	−	0.224401i	$-0.0720424\pi$
$71$	5.17109	+	5.96775i	0.613695	+	0.708242i	−0.360802	+	0.932642i	$0.617497\pi$
$72$	−0.212565	−	0.977147i	−0.0250511	−	0.115158i
$73$	−6.67685	−	8.91923i	−0.781467	−	1.04392i	−0.997714	−	0.0675786i	$-0.978473\pi$
$73$	−6.67685	−	8.91923i	−0.781467	−	1.04392i	0.216247	−	0.976339i	$-0.430618\pi$
$74$	−0.319993	+	0.700687i	−0.0371984	+	0.0814532i
$75$	4.89672	−	1.01103i	0.565424	−	0.116743i
$76$	0.327839	−	1.11652i	0.0376057	−	0.128073i
$77$	6.14585	+	1.33695i	0.700384	+	0.152359i
$78$	0.111916	+	0.0417427i	0.0126720	+	0.00472642i
$79$	11.2840	−	3.31328i	1.26955	−	0.372773i	0.423507	−	0.905893i	$-0.360799\pi$
$79$	11.2840	−	3.31328i	1.26955	−	0.372773i	0.846040	+	0.533120i	$0.178981\pi$
$80$	−0.641325	+	2.14213i	−0.0717023	+	0.239497i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−2.31633	−	1.26481i	−0.255796	−	0.139675i
$83$	0.511355	−	1.37100i	0.0561285	−	0.150486i	−0.905859	−	0.423579i	$-0.860774\pi$
$83$	0.511355	−	1.37100i	0.0561285	−	0.150486i	0.961988	+	0.273092i	$0.0880465\pi$
$84$	1.16421	−	0.748193i	0.127026	−	0.0816345i
$85$	−4.35532	+	5.75426i	−0.472401	+	0.624137i
$86$	4.80277	−	0.690534i	0.517896	−	0.0744621i
$87$	−2.31996	+	0.865301i	−0.248726	+	0.0927700i
$88$	3.63832	−	2.72361i	0.387846	−	0.290338i
$89$	7.15307	+	4.59700i	0.758224	+	0.487281i	0.861742	−	0.507347i	$-0.169374\pi$
$89$	7.15307	+	4.59700i	0.758224	+	0.487281i	−0.103518	+	0.994628i	$0.533010\pi$
$90$	−2.09919	+	0.770321i	−0.221274	+	0.0811990i
$91$			0.165304i			0.0173285i
$92$	4.64769	−	1.18280i	0.484555	−	0.123315i
$93$	4.61472	−	4.61472i	0.478524	−	0.478524i
$94$	3.58691	−	3.10807i	0.369961	−	0.320573i
$95$	−2.57353	−	0.383937i	−0.264038	−	0.0393911i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	4.90938	+	13.1626i	0.498472	+	1.33645i	0.906006	+	0.423265i	$0.139116\pi$
$97$	4.90938	+	13.1626i	0.498472	+	1.33645i	−0.407534	+	0.913190i	$0.633611\pi$
$98$	−4.07061	−	3.04722i	−0.411194	−	0.307816i
$99$	4.36073	+	1.28042i	0.438270	+	0.128688i
$100$	4.94129	+	0.763945i	0.494129	+	0.0763945i
$101$	1.34406	+	2.94307i	0.133738	+	0.292846i	0.964639	−	0.263574i	$-0.0849015\pi$
$101$	1.34406	+	2.94307i	0.133738	+	0.292846i	−0.830901	+	0.556421i	$0.812174\pi$
$102$	1.54672	−	2.83261i	0.153149	−	0.280471i
$103$	12.5287	−	0.896073i	1.23449	−	0.0882927i	0.561208	−	0.827675i	$-0.310337\pi$
$103$	12.5287	−	0.896073i	1.23449	−	0.0882927i	0.673286	+	0.739382i	$0.264882\pi$
$104$	0.0902725	+	0.0782215i	0.00885194	+	0.00767025i
$105$	−2.01405	−	2.34936i	−0.196551	−	0.229274i
$106$	−4.51412	+	2.06153i	−0.438450	+	0.200234i
$107$	4.29679	−	19.7520i	0.415386	−	1.90950i	−0.000316212	−	1.00000i	$-0.500101\pi$
$107$	4.29679	−	19.7520i	0.415386	−	1.90950i	0.415703	−	0.909501i	$-0.363536\pi$
$108$	0.877679	−	0.479249i	0.0844547	−	0.0461158i
$109$	−0.692730	−	4.81805i	−0.0663515	−	0.461485i	−0.995727	−	0.0923486i	$-0.970563\pi$
$109$	−0.692730	−	4.81805i	−0.0663515	−	0.461485i	0.929375	−	0.369137i	$-0.120347\pi$
$110$	−7.14785	−	7.22395i	−0.681521	−	0.688776i
$111$	−0.762457	−	0.109625i	−0.0723692	−	0.0104051i
$112$	1.35227	−	0.294169i	0.127778	−	0.0277964i
$113$	−0.504610	+	7.05537i	−0.0474697	+	0.663714i	0.916894	+	0.399132i	$0.130688\pi$
$113$	−0.504610	+	7.05537i	−0.0474697	+	0.663714i	−0.964363	+	0.264582i	$0.914766\pi$
$114$	1.16365			0.108986
$115$	−4.04437	−	9.93192i	−0.377140	−	0.926156i
$116$	−2.47608			−0.229898
$117$	−0.00852129	+	0.119143i	−0.000787794	+	0.0110148i
$118$	0.928822	−	0.202053i	0.0855050	−	0.0186005i
$119$	4.42093	+	0.635633i	0.405266	+	0.0582684i
$120$	−2.23604	−	0.0118400i	−0.204121	−	0.00108084i
$121$	1.37411	+	9.55715i	0.124919	+	0.868832i
$122$	−11.1971	+	6.11410i	−1.01374	+	0.553545i
$123$	0.560993	−	2.57884i	0.0505830	−	0.232526i
$124$	5.93644	−	2.71108i	0.533108	−	0.243462i
$125$	0.177594	−	11.1789i	0.0158845	−	0.999874i
$126$	1.04588	+	0.906262i	0.0931746	+	0.0807362i
$127$	−16.1841	+	1.15751i	−1.43610	+	0.102712i	−0.767568	−	0.640967i	$-0.778534\pi$
$127$	−16.1841	+	1.15751i	−1.43610	+	0.102712i	−0.668537	+	0.743679i	$0.733079\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	2.01566	+	4.41367i	0.177469	+	0.388602i
$130$	0.145589	−	0.223925i	0.0127690	−	0.0196395i
$131$	11.2349	+	3.29887i	0.981599	+	0.288223i	0.732884	−	0.680353i	$-0.238174\pi$
$131$	11.2349	+	3.29887i	0.981599	+	0.288223i	0.248715	+	0.968577i	$0.419992\pi$
$132$	3.63832	+	2.72361i	0.316675	+	0.237060i
$133$	0.562770	+	1.50885i	0.0487984	+	0.130833i
$134$	2.05769	−	14.3115i	0.177757	−	1.23633i
$135$	−1.33053	−	1.79714i	−0.114514	−	0.154673i
$136$	2.43910	−	2.11349i	0.209151	−	0.181230i
$137$	3.02677	−	3.02677i	0.258595	−	0.258595i	−0.565888	−	0.824482i	$-0.691466\pi$
$137$	3.02677	−	3.02677i	0.258595	−	0.258595i	0.824482	+	0.565888i	$0.191466\pi$
$138$	2.44429	+	4.12619i	0.208072	+	0.351245i
$139$		−	20.0843i		−	1.70353i	−0.523926	−	0.851764i	$-0.675533\pi$
$139$		−	20.0843i		−	1.70353i	0.523926	−	0.851764i	$-0.324467\pi$
$140$	−1.06605	−	2.90507i	−0.0900975	−	0.245523i
$141$	3.99272	+	2.56597i	0.336248	+	0.216093i
$142$	−6.32145	+	4.73218i	−0.530484	+	0.397115i
$143$	−0.508640	+	0.189713i	−0.0425346	+	0.0158646i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	0.758922	+	5.48442i	0.0630251	+	0.455456i
$146$	9.37283	−	6.02355i	0.775701	−	0.498513i
$147$	1.77696	−	4.76422i	0.146561	−	0.392946i
$148$	−0.676074	−	0.369164i	−0.0555729	−	0.0303451i
$149$	11.4473	−	13.2109i	0.937799	−	1.08228i	−0.0586669	−	0.998278i	$-0.518685\pi$
$149$	11.4473	−	13.2109i	0.937799	−	1.08228i	0.996466	−	0.0840000i	$-0.0267696\pi$
$150$	0.659124	+	4.95637i	0.0538172	+	0.404686i
$151$	−0.312870	+	0.0918669i	−0.0254610	+	0.00747602i	−0.294438	−	0.955671i	$-0.595133\pi$
$151$	−0.312870	+	0.0918669i	−0.0254610	+	0.00747602i	0.268977	+	0.963147i	$0.413314\pi$
$152$	1.09028	+	0.406655i	0.0884338	+	0.0329841i
$153$	3.15364	+	0.686031i	0.254956	+	0.0554624i
$154$	−1.77198	+	6.03481i	−0.142790	+	0.486299i
$155$	−7.82447	−	12.3180i	−0.628477	−	0.989409i
$156$	−0.0496203	+	0.108653i	−0.00397281	+	0.00869923i
$157$	9.67521	+	12.9246i	0.772166	+	1.03149i	0.998351	+	0.0574081i	$0.0182836\pi$
$157$	9.67521	+	12.9246i	0.772166	+	1.03149i	−0.226185	+	0.974084i	$0.572625\pi$
$158$	2.49984	+	11.4916i	0.198877	+	0.914222i
$159$	−3.24980	−	3.75047i	−0.257726	−	0.297432i
$160$	−2.09092	−	0.792508i	−0.165301	−	0.0626533i
$161$	−4.16809	+	5.16490i	−0.328491	+	0.407051i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−1.65165	−	0.118128i	−0.129367	−	0.00925252i	0.00650542	−	0.999979i	$-0.497929\pi$
$163$	−1.65165	−	0.118128i	−0.129367	−	0.00925252i	−0.135873	+	0.990726i	$0.543384\pi$
$164$	1.42683	−	2.22020i	0.111417	−	0.173368i
$165$	4.91755	−	8.89353i	0.382830	−	0.692360i
$166$	1.33102	+	0.607858i	0.103307	+	0.0471789i
$167$	−1.40520	+	1.87712i	−0.108737	+	0.145256i	−0.851609	−	0.524178i	$-0.824373\pi$
$167$	−1.40520	+	1.87712i	−0.108737	+	0.145256i	0.742871	+	0.669434i	$0.233463\pi$
$168$	0.663233	+	1.21462i	0.0511695	+	0.0937100i
$169$	7.02062	+	10.9243i	0.540047	+	0.840330i
$170$	−5.42889	−	4.75472i	−0.416377	−	0.364671i
$171$	0.327839	+	1.11652i	0.0250705	+	0.0853822i
$172$	0.346149	+	4.83979i	0.0263936	+	0.369031i
$173$	−0.188699	−	2.63836i	−0.0143465	−	0.200591i	−0.999570	−	0.0293178i	$-0.990667\pi$
$173$	−0.188699	−	2.63836i	−0.0143465	−	0.200591i	0.985224	−	0.171273i	$-0.0547880\pi$
$174$	−0.697592	−	2.37578i	−0.0528843	−	0.180107i
$175$	−6.10788	+	3.25166i	−0.461712	+	0.245803i
$176$	2.45712	+	3.82335i	0.185212	+	0.288196i
$177$	0.455548	+	0.834273i	0.0342411	+	0.0627078i
$178$	−5.09558	+	6.80690i	−0.381930	+	0.510199i
$179$	14.9223	+	6.81479i	1.11535	+	0.509361i	0.885861	−	0.463951i	$-0.153569\pi$
$179$	14.9223	+	6.81479i	1.11535	+	0.509361i	0.229484	+	0.973312i	$0.426296\pi$
$180$	−0.618604	−	2.14880i	−0.0461080	−	0.160162i
$181$	0.126469	−	0.196790i	0.00940040	−	0.0146273i	−0.836522	−	0.547934i	$-0.815414\pi$
$181$	0.126469	−	0.196790i	0.00940040	−	0.0146273i	0.845922	+	0.533307i	$0.179051\pi$
$182$	−0.164882	−	0.0117926i	−0.0122219	−	0.000874127i
$183$	−9.02103	−	9.02103i	−0.666854	−	0.666854i
$184$	0.848220	+	4.72022i	0.0625316	+	0.347980i
$185$	−0.610467	+	1.61063i	−0.0448824	+	0.118416i
$186$	4.27375	+	4.93217i	0.313367	+	0.361645i
$187$	3.11789	+	14.3327i	0.228003	+	1.04811i
$188$	2.84427	+	3.79949i	0.207439	+	0.277107i
$189$	−0.574893	+	1.25884i	−0.0418173	+	0.0915671i
$190$	0.566552	−	2.53958i	0.0411020	−	0.184240i
$191$	−1.64227	+	5.59305i	−0.118830	+	0.404699i	−0.997329	−	0.0730469i	$-0.976728\pi$
$191$	−1.64227	+	5.59305i	−0.118830	+	0.404699i	0.878498	+	0.477746i	$0.158546\pi$
$192$	0.977147	+	0.212565i	0.0705195	+	0.0153406i
$193$	2.21221	+	0.825112i	0.159238	+	0.0593928i	0.427819	−	0.903864i	$-0.359282\pi$
$193$	2.21221	+	0.825112i	0.159238	+	0.0593928i	−0.268581	+	0.963257i	$0.586555\pi$
$194$	−13.4792	+	3.95786i	−0.967754	+	0.284158i
$195$	0.255872	+	0.0766047i	0.0183234	+	0.00548578i
$196$	3.32985	−	3.84285i	0.237846	−	0.274489i
$197$	2.49472	+	1.36222i	0.177742	+	0.0970543i	0.565657	−	0.824641i	$-0.308623\pi$
$197$	2.49472	+	1.36222i	0.177742	+	0.0970543i	−0.387915	+	0.921695i	$0.626805\pi$
$198$	−1.58825	+	4.25827i	−0.112872	+	0.302622i
$199$	1.40425	−	0.902454i	0.0995444	−	0.0639733i	−0.489922	−	0.871767i	$-0.662975\pi$
$199$	1.40425	−	0.902454i	0.0995444	−	0.0639733i	0.589466	+	0.807793i	$0.299338\pi$
$200$	−1.11451	+	4.87421i	−0.0788075	+	0.344658i
$201$	14.3115	−	2.05769i	1.00946	−	0.145138i
$202$	−3.03146	+	1.13067i	−0.213292	+	0.0795540i
$203$	2.74317	−	2.05351i	0.192533	−	0.144128i
$204$	2.71505	+	1.74486i	0.190092	+	0.122165i
$205$	−5.35498	−	2.47989i	−0.374008	−	0.173203i
$206$			12.5607i			0.875149i
$207$	−3.27042	+	3.50776i	−0.227310	+	0.243806i
$208$	−0.0844622	+	0.0844622i	−0.00585640	+	0.00585640i
$209$	−3.99686	+	3.46330i	−0.276468	+	0.239561i
$210$	2.48706	−	1.84132i	0.171623	−	0.127063i
$211$	3.71676	−	25.8506i	0.255872	−	1.77963i	−0.305625	−	0.952152i	$-0.598865\pi$
$211$	3.71676	−	25.8506i	0.255872	−	1.77963i	0.561497	−	0.827479i	$-0.310226\pi$
$212$	−1.73424	−	4.64969i	−0.119108	−	0.319342i
$213$	−6.32145	−	4.73218i	−0.433138	−	0.324243i
$214$	19.3952	+	5.69494i	1.32583	+	0.389298i
$215$	10.6139	−	2.25011i	0.723859	−	0.153456i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−4.32839	+	7.92686i	−0.293830	+	0.538110i
$218$	4.85519	−	0.347250i	0.328835	−	0.0235187i
$219$	8.42019	+	7.29613i	0.568983	+	0.493027i
$220$	7.71546	−	6.61428i	0.520176	−	0.445935i
$221$	−0.350667	+	0.160144i	−0.0235884	+	0.0107725i
$222$	0.163738	−	0.752694i	0.0109894	−	0.0505175i
$223$	4.82585	−	2.63511i	0.323163	−	0.176460i	−0.309476	−	0.950907i	$-0.600154\pi$
$223$	4.82585	−	2.63511i	0.323163	−	0.176460i	0.632639	+	0.774447i	$0.281972\pi$
$224$	0.196950	+	1.36981i	0.0131592	+	0.0915246i
$225$	−4.56990	+	2.02879i	−0.304660	+	0.135253i
$226$	−7.00140	−	1.00665i	−0.465726	−	0.0669613i
$227$	21.4203	−	4.65969i	1.42171	−	0.309275i	0.565010	−	0.825084i	$-0.308872\pi$
$227$	21.4203	−	4.65969i	1.42171	−	0.309275i	0.856703	+	0.515809i	$0.172509\pi$
$228$	−0.0830141	+	1.16069i	−0.00549774	+	0.0768685i
$229$	−3.90909			−0.258320			−0.129160	−	0.991624i	$-0.541228\pi$
$229$	−3.90909			−0.258320			−0.129160	+	0.991624i	$0.541228\pi$
$230$	10.1951	−	3.32553i	0.672247	−	0.219279i
$231$	−6.28958			−0.413824
$232$	0.176641	−	2.46977i	0.0115971	−	0.162148i
$233$	−2.55654	+	0.556142i	−0.167485	+	0.0364341i	−0.295526	−	0.955335i	$-0.595495\pi$
$233$	−2.55654	+	0.556142i	−0.167485	+	0.0364341i	0.128041	+	0.991769i	$0.459131\pi$
$234$	−0.118232	−	0.0169992i	−0.00772905	−	0.00111127i
$235$	7.54396	−	7.46449i	0.492114	−	0.486930i
$236$	0.135277	+	0.940870i	0.00880576	+	0.0612454i
$237$	−10.3218	+	5.63614i	−0.670474	+	0.366107i
$238$	−0.949399	+	4.36432i	−0.0615404	+	0.282897i
$239$	−2.86996	+	1.31067i	−0.185642	+	0.0847800i	−0.506068	−	0.862494i	$-0.668901\pi$
$239$	−2.86996	+	1.31067i	−0.185642	+	0.0847800i	0.320425	+	0.947274i	$0.396174\pi$
$240$	0.171327	−	2.22949i	0.0110591	−	0.143913i
$241$	−3.90791	−	3.38623i	−0.251731	−	0.218126i	0.519850	−	0.854258i	$-0.325988\pi$
$241$	−3.90791	−	3.38623i	−0.251731	−	0.218126i	−0.771580	+	0.636132i	$0.780533\pi$
$242$	−9.63083	+	0.688810i	−0.619093	+	0.0442784i
$243$	−0.479249	+	0.877679i	−0.0307438	+	0.0563031i
$244$	−5.29973	−	11.6048i	−0.339280	−	0.742920i
$245$	−9.53237	−	6.19765i	−0.609001	−	0.395953i
$246$	2.53225	+	0.743536i	0.161450	+	0.0474061i
$247$	−0.111272	−	0.0832970i	−0.00708005	−	0.00530006i
$248$	2.28067	+	6.11472i	0.144823	+	0.388285i
$249$	−0.208243	+	1.44836i	−0.0131969	+	0.0917861i
$250$	11.1378	+	0.974637i	0.704415	+	0.0616415i
$251$	−22.3965	+	19.4067i	−1.41366	+	1.22494i	−0.475048	+	0.879960i	$0.657569\pi$
$251$	−22.3965	+	19.4067i	−1.41366	+	1.22494i	−0.938610	+	0.344981i	$0.887885\pi$
$252$	−0.978565	+	0.978565i	−0.0616438	+	0.0616438i
$253$	−20.6760	−	6.89767i	−1.29989	−	0.433653i
$254$		−	16.2254i		−	1.01807i
$255$	3.03263	−	6.54855i	0.189911	−	0.410086i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	7.19817	−	5.38848i	0.449009	−	0.336124i	−0.350725	−	0.936479i	$-0.614065\pi$
$257$	7.19817	−	5.38848i	0.449009	−	0.336124i	0.799734	+	0.600354i	$0.204974\pi$
$258$	−4.54622	+	1.69565i	−0.283036	+	0.105567i
$259$	1.05516	−	0.151710i	0.0655647	−	0.00942678i
$260$	0.212968	+	0.161193i	0.0132077	+	0.00999675i
$261$	2.08301	−	1.33867i	0.128935	−	0.0828615i
$262$	−4.09195	+	10.9709i	−0.252802	+	0.677787i
$263$	−6.68668	−	3.65121i	−0.412319	−	0.225143i	0.259681	−	0.965694i	$-0.416383\pi$
$263$	−6.68668	−	3.65121i	−0.412319	−	0.225143i	−0.672000	+	0.740551i	$0.734564\pi$
$264$	−2.97623	+	3.43475i	−0.183174	+	0.211394i
$265$	−9.76734	+	5.26642i	−0.600003	+	0.323514i
$266$	−1.54515	+	0.453697i	−0.0947391	+	0.0278179i
$267$	−7.96676	−	2.97145i	−0.487558	−	0.181850i
$268$	14.1283	+	3.07341i	0.863021	+	0.187739i
$269$	−5.69461	+	19.3941i	−0.347206	+	1.18248i	0.582085	+	0.813128i	$0.302237\pi$
$269$	−5.69461	+	19.3941i	−0.347206	+	1.18248i	−0.929291	+	0.369348i	$0.879581\pi$
$270$	1.88747	−	1.19893i	0.114868	−	0.0729647i
$271$	7.17312	−	15.7069i	0.435736	−	0.954129i	−0.556625	−	0.830764i	$-0.687904\pi$
$271$	7.17312	−	15.7069i	0.435736	−	0.954129i	0.992361	−	0.123365i	$-0.0393687\pi$
$272$	1.93410	+	2.58366i	0.117272	+	0.156657i
$273$	−0.0351378	−	0.161526i	−0.00212664	−	0.00977599i
$274$	2.80313	+	3.23499i	0.169343	+	0.195433i
$275$	−17.0152	−	15.0622i	−1.02605	−	0.908283i
$276$	−4.29005	+	2.14370i	−0.258231	+	0.129036i
$277$	−7.00123	−	7.00123i	−0.420663	−	0.420663i	0.464769	−	0.885432i	$-0.346137\pi$
$277$	−7.00123	−	7.00123i	−0.420663	−	0.420663i	−0.885432	+	0.464769i	$0.846137\pi$
$278$	20.0331	+	1.43280i	1.20151	+	0.0859335i
$279$	−3.52833	+	5.49019i	−0.211236	+	0.328689i
$280$	2.97372	−	0.856086i	0.177714	−	0.0511609i
$281$	−5.34860	−	2.44263i	−0.319071	−	0.145715i	0.249441	−	0.968390i	$-0.419753\pi$
$281$	−5.34860	−	2.44263i	−0.319071	−	0.145715i	−0.568512	+	0.822675i	$0.692481\pi$
$282$	−2.84427	+	3.79949i	−0.169374	+	0.226257i
$283$	−10.7560	−	19.6982i	−0.639379	−	1.17094i	−0.973561	−	0.228427i	$-0.926642\pi$
$283$	−10.7560	−	19.6982i	−0.639379	−	1.17094i	0.334182	−	0.942509i	$-0.391540\pi$
$284$	−4.26915	−	6.64293i	−0.253328	−	0.394185i
$285$	2.59633	−	0.171880i	0.153793	−	0.0101813i
$286$	−0.152944	−	0.520878i	−0.00904375	−	0.0308002i
$287$	0.260554	+	3.64302i	0.0153800	+	0.215041i
$288$	0.0713392	+	0.997452i	0.00420370	+	0.0587754i
$289$	−1.85491	−	6.31725i	−0.109112	−	0.371603i
$290$	−5.52459	+	0.365735i	−0.324415	+	0.0214767i
$291$	−7.59509	−	11.8182i	−0.445232	−	0.692794i
$292$	5.33955	+	9.77866i	0.312474	+	0.572253i
$293$	−11.1310	+	14.8693i	−0.650280	+	0.868672i	−0.997612	−	0.0690704i	$-0.977997\pi$
$293$	−11.1310	+	14.8693i	−0.650280	+	0.868672i	0.347332	+	0.937742i	$0.387088\pi$
$294$	4.62532	+	2.11231i	0.269754	+	0.123192i
$295$	2.04253	−	0.588011i	0.118921	−	0.0342353i
$296$	0.416454	−	0.648015i	0.0242059	−	0.0376651i
$297$	−4.53324	−	0.324224i	−0.263046	−	0.0188134i
$298$	12.3606	+	12.3606i	0.716029	+	0.716029i
$299$	0.0616325	−	0.569525i	0.00356430	−	0.0329365i
$300$	−4.99076	+	0.303861i	−0.288142	+	0.0175434i
$301$	−4.39732	−	5.07478i	−0.253457	−	0.292506i
$302$	−0.0693130	−	0.318627i	−0.00398851	−	0.0183349i
$303$	−1.93893	−	2.59011i	−0.111389	−	0.148798i
$304$	−0.483399	+	1.05850i	−0.0277248	+	0.0607089i
$305$	−24.0798	+	15.2956i	−1.37880	+	0.875822i
$306$	−0.909261	+	3.09666i	−0.0519790	+	0.177024i
$307$	15.8990	+	3.45861i	0.907401	+	0.197393i	0.641964	−	0.766735i	$-0.278120\pi$
$307$	15.8990	+	3.45861i	0.907401	+	0.197393i	0.265437	+	0.964128i	$0.414484\pi$
$308$	−5.89302	−	2.19798i	−0.335786	−	0.125242i
$309$	−12.0519	+	3.53877i	−0.685611	+	0.201314i
$310$	12.8448	−	6.92578i	0.729538	−	0.393358i
$311$	−12.5096	+	14.4368i	−0.709352	+	0.818636i	−0.989984	−	0.141179i	$-0.954911\pi$
$311$	−12.5096	+	14.4368i	−0.709352	+	0.818636i	0.280632	+	0.959815i	$0.409456\pi$
$312$	−0.104837	−	0.0572451i	−0.00593521	−	0.00324087i
$313$	7.36372	−	19.7429i	0.416222	−	1.11593i	−0.544582	−	0.838707i	$-0.683312\pi$
$313$	7.36372	−	19.7429i	0.416222	−	1.11593i	0.960804	−	0.277227i	$-0.0894155\pi$
$314$	−13.5819	+	8.72853i	−0.766468	+	0.492579i
$315$	2.46742	+	1.86755i	0.139023	+	0.105225i
$316$	−11.6407	+	1.67367i	−0.654838	+	0.0941515i
$317$	15.3731	−	5.73389i	0.863442	−	0.322047i	0.121565	−	0.992583i	$-0.461209\pi$
$317$	15.3731	−	5.73389i	0.863442	−	0.322047i	0.741877	+	0.670536i	$0.233936\pi$
$318$	3.97275	−	2.97396i	0.222781	−	0.166772i
$319$	9.46691	+	6.08402i	0.530045	+	0.340640i
$320$	0.939653	−	2.02905i	0.0525282	−	0.113427i
$321$			20.2140i			1.12823i
$322$	−4.85439	−	4.52593i	−0.270525	−	0.252220i
$323$	−2.65559	+	2.65559i	−0.147761	+	0.147761i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	0.291761	−	0.521123i	0.0161840	−	0.0289067i
$326$	0.235655	−	1.63901i	0.0130517	−	0.0907766i
$327$	1.70105	+	4.56069i	0.0940682	+	0.252207i
$328$	2.11275	+	1.58159i	0.116657	+	0.0873285i
$329$	−6.30215	−	1.85048i	−0.347449	−	0.102020i
$330$	8.52006	+	5.53947i	0.469014	+	0.304938i
$331$	−8.76458	−	19.1918i	−0.481745	−	1.05487i	−0.981980	−	0.188985i	$-0.939480\pi$
$331$	−8.76458	−	19.1918i	−0.481745	−	1.05487i	0.500235	−	0.865890i	$-0.333247\pi$
$332$	−0.701263	+	1.28427i	−0.0384868	+	0.0704833i
$333$	0.768335	−	0.0549524i	0.0421045	−	0.00301137i
$334$	−1.77210	−	1.53553i	−0.0969647	−	0.0840204i
$335$	2.47716	−	32.2356i	0.135342	−	1.76122i
$336$	−1.25884	+	0.574893i	−0.0686753	+	0.0313630i
$337$	4.77610	−	21.9554i	0.260171	−	1.19599i	−0.642715	−	0.766105i	$-0.722192\pi$
$337$	4.77610	−	21.9554i	0.260171	−	1.19599i	0.902886	−	0.429880i	$-0.141444\pi$
$338$	−11.3973	+	6.22340i	−0.619932	+	0.338508i
$339$	−1.00665	−	7.00140i	−0.0546737	−	0.380264i
$340$	5.12990	−	5.07586i	0.278208	−	0.275277i
$341$	−29.3585	−	4.22112i	−1.58985	−	0.228587i
$342$	−1.13706	+	0.247352i	−0.0614852	+	0.0133753i
$343$	−1.19309	+	16.6816i	−0.0644208	+	0.900720i
$344$	−4.85215			−0.261611
$345$	6.06313	+	8.84525i	0.326428	+	0.476212i
$346$	2.64510			0.142202
$347$	−1.67618	+	23.4361i	−0.0899822	+	1.25811i	0.729087	+	0.684421i	$0.239945\pi$
$347$	−1.67618	+	23.4361i	−0.0899822	+	1.25811i	−0.819070	+	0.573694i	$0.805510\pi$
$348$	2.41949	−	0.526328i	0.129698	−	0.0282142i
$349$	−5.35172	−	0.769461i	−0.286471	−	0.0411883i	−0.00241856	−	0.999997i	$-0.500770\pi$
$349$	−5.35172	−	0.769461i	−0.286471	−	0.0411883i	−0.284052	+	0.958809i	$0.591679\pi$
$350$	−2.80765	−	6.32429i	−0.150075	−	0.338047i
$351$	−0.0169992	−	0.118232i	−0.000907348	−	0.00631075i
$352$	−3.98890	+	2.17810i	−0.212609	+	0.116093i
$353$	5.30199	−	24.3728i	0.282196	−	1.29724i	−0.589731	−	0.807600i	$-0.700766\pi$
$353$	5.30199	−	24.3728i	0.282196	−	1.29724i	0.871927	−	0.489636i	$-0.162870\pi$
$354$	−0.864646	+	0.394871i	−0.0459554	+	0.0209871i
$355$	−13.4053	+	11.4921i	−0.711481	+	0.609936i
$356$	−6.42604	−	5.56820i	−0.340580	−	0.295114i
$357$	−4.45501	+	0.318628i	−0.235784	+	0.0168636i
$358$	−7.86197	+	14.3981i	−0.415518	+	0.760964i
$359$	0.168571	+	0.369119i	0.00889685	+	0.0194814i	0.914028	−	0.405651i	$-0.132955\pi$
$359$	0.168571	+	0.369119i	0.00889685	+	0.0194814i	−0.905131	+	0.425132i	$0.860228\pi$
$360$	2.18745	−	0.463734i	0.115289	−	0.0244409i
$361$	16.9311	+	4.97143i	0.891112	+	0.261654i
$362$	0.187267	+	0.140186i	0.00984252	+	0.00736802i
$363$	−3.37423	−	9.04665i	−0.177101	−	0.474826i
$364$	0.0235251	−	0.163621i	0.00123305	−	0.00857607i
$365$	20.0228	−	14.8241i	1.04804	−	0.775928i
$366$	9.64160	−	8.35450i	0.503975	−	0.436696i
$367$	−7.95998	+	7.95998i	−0.415508	+	0.415508i	−0.883652	−	0.468144i	$-0.844923\pi$
$367$	−7.95998	+	7.95998i	−0.415508	+	0.415508i	0.468144	+	0.883652i	$0.344923\pi$
$368$	−4.76871	+	0.509322i	−0.248586	+	0.0265503i
$369$			2.63915i			0.137389i
$370$	−1.56297	−	0.723812i	−0.0812551	−	0.0376292i
$371$	5.77749	+	3.71297i	0.299952	+	0.192768i
$372$	−5.22449	+	3.91101i	−0.270877	+	0.202776i
$373$	11.5554	−	4.30996i	0.598318	−	0.223161i	−0.0320129	−	0.999487i	$-0.510192\pi$
$373$	11.5554	−	4.30996i	0.598318	−	0.223161i	0.630331	+	0.776326i	$0.282919\pi$
$374$	−14.5186	+	2.08746i	−0.750740	+	0.107940i
$375$	2.20272	+	10.9612i	0.113748	+	0.566034i
$376$	−3.99272	+	2.56597i	−0.205909	+	0.132330i
$377$	−0.103358	+	0.277114i	−0.00532321	+	0.0142721i
$378$	−1.21462	−	0.663233i	−0.0624733	−	0.0341130i
$379$	17.4589	−	20.1486i	0.896803	−	1.03497i	−0.102387	−	0.994745i	$-0.532648\pi$
$379$	17.4589	−	20.1486i	0.896803	−	1.03497i	0.999191	−	0.0402217i	$-0.0128064\pi$
$380$	2.49269	+	0.746280i	0.127872	+	0.0382833i
$381$	15.5682	−	4.57123i	0.797582	−	0.234191i
$382$	−5.46164	−	2.03709i	−0.279442	−	0.104226i
$383$	3.15201	+	0.685677i	0.161060	+	0.0350365i	0.292372	−	0.956305i	$-0.405555\pi$
$383$	3.15201	+	0.685677i	0.161060	+	0.0350365i	−0.131312	+	0.991341i	$0.541919\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	−3.06223	+	13.7265i	−0.156066	+	0.699568i
$386$	−0.980827	+	2.14771i	−0.0499228	+	0.109316i
$387$	−2.90779	−	3.88435i	−0.147811	−	0.197453i
$388$	−2.98618	−	13.7273i	−0.151600	−	0.696896i
$389$	−3.20245	−	3.69583i	−0.162371	−	0.187386i	0.668734	−	0.743502i	$-0.266837\pi$
$389$	−3.20245	−	3.69583i	−0.162371	−	0.187386i	−0.831105	+	0.556116i	$0.812291\pi$
$390$	−0.0946632	+	0.249755i	−0.00479346	+	0.0126468i
$391$	−14.9946	−	3.83828i	−0.758308	−	0.194110i
$392$	3.59551	+	3.59551i	0.181601	+	0.181601i
$393$	−11.6794	−	0.835326i	−0.589147	−	0.0421366i
$394$	−1.53672	+	2.39119i	−0.0774190	+	0.120466i
$395$	7.27500	+	25.2706i	0.366045	+	1.27150i
$396$	−4.13412	−	1.88799i	−0.207747	−	0.0948750i
$397$	−6.73595	+	8.99817i	−0.338067	+	0.451605i	−0.937070	−	0.349142i	$-0.886473\pi$
$397$	−6.73595	+	8.99817i	−0.338067	+	0.451605i	0.599002	+	0.800747i	$0.295564\pi$
$398$	0.799977	+	1.46505i	0.0400992	+	0.0734363i
$399$	−0.870637	−	1.35474i	−0.0435864	−	0.0678217i
$400$	−4.78228	−	1.45939i	−0.239114	−	0.0729694i
$401$	4.67283	+	15.9142i	0.233350	+	0.794718i	0.990021	+	0.140922i	$0.0450065\pi$
$401$	4.67283	+	15.9142i	0.233350	+	0.794718i	−0.756671	+	0.653796i	$0.773175\pi$
$402$	1.03147	+	14.4218i	0.0514451	+	0.719296i
$403$	−0.0556117	−	0.777553i	−0.00277021	−	0.0387327i
$404$	−0.911532	−	3.10439i	−0.0453504	−	0.154449i
$405$	1.68213	+	1.47324i	0.0835857	+	0.0732059i
$406$	1.85258	+	2.88268i	0.0919422	+	0.143065i
$407$	1.67779	+	3.07264i	0.0831648	+	0.152305i
$408$	−1.93410	+	2.58366i	−0.0957524	+	0.127910i
$409$	20.8341	+	9.51462i	1.03018	+	0.470468i	0.857486	−	0.514508i	$-0.172025\pi$
$409$	20.8341	+	9.51462i	1.03018	+	0.470468i	0.172695	+	0.984975i	$0.444753\pi$
$410$	2.85559	−	5.16442i	0.141028	−	0.255053i
$411$	−2.31421	+	3.60099i	−0.114152	+	0.177624i
$412$	−12.5287	−	0.896073i	−0.617247	−	0.0441464i
$413$	−0.930170	−	0.930170i	−0.0457707	−	0.0457707i
$414$	−3.26551	−	3.51232i	−0.160491	−	0.172621i
$415$	3.05954	+	1.15964i	0.150187	+	0.0569245i
$416$	−0.0782215	−	0.0902725i	−0.00383513	−	0.00442597i
$417$	4.26923	+	19.6253i	0.209065	+	0.961056i
$418$	−3.16934	−	4.23374i	−0.155017	−	0.207079i
$419$	−8.60647	+	18.8455i	−0.420454	+	0.920665i	0.574327	+	0.818626i	$0.305264\pi$
$419$	−8.60647	+	18.8455i	−0.420454	+	0.920665i	−0.994780	+	0.102039i	$0.967463\pi$
$420$	1.65920	+	2.61208i	0.0809608	+	0.127456i
$421$	3.64401	−	12.4104i	0.177598	−	0.604845i	−0.821787	−	0.569795i	$-0.807023\pi$
$421$	3.64401	−	12.4104i	0.177598	−	0.604845i	0.999386	−	0.0350500i	$-0.0111591\pi$
$422$	25.5196	+	5.55145i	1.24228	+	0.270241i
$423$	−4.44691	−	1.65861i	−0.216216	−	0.0806445i
$424$	4.76156	−	1.39812i	0.231242	−	0.0678988i
$425$	−12.8152	−	9.80678i	−0.621627	−	0.475699i
$426$	5.17109	−	5.96775i	0.250540	−	0.289139i
$427$	15.4957	+	8.46130i	0.749890	+	0.409471i
$428$	−7.06406	+	18.9395i	−0.341454	+	0.915474i
$429$	0.456690	−	0.293497i	0.0220492	−	0.0141702i
$430$	1.48719	+	10.7473i	0.0717188	+	0.518283i
$431$	−14.0564	+	2.02101i	−0.677075	+	0.0973486i	−0.472270	−	0.881454i	$-0.656565\pi$
$431$	−14.0564	+	2.02101i	−0.677075	+	0.0973486i	−0.204805	+	0.978803i	$0.565656\pi$
$432$	−0.936950	+	0.349464i	−0.0450790	+	0.0168136i
$433$	−19.9152	+	14.9083i	−0.957062	+	0.716448i	−0.958957	−	0.283550i	$-0.908488\pi$
$433$	−19.9152	+	14.9083i	−0.957062	+	0.716448i	0.00189501	+	0.999998i	$0.499397\pi$
$434$	−7.59788	−	4.88286i	−0.364710	−	0.234385i
$435$	−1.90738	−	5.19776i	−0.0914517	−	0.249214i
$436$			4.86759i			0.233115i
$437$	−1.37636	−	5.40830i	−0.0658405	−	0.258714i
$438$	−7.87823	+	7.87823i	−0.376436	+	0.376436i
$439$	5.16502	−	4.47551i	0.246513	−	0.213605i	−0.522836	−	0.852433i	$-0.675126\pi$
$439$	5.16502	−	4.47551i	0.246513	−	0.213605i	0.769349	+	0.638828i	$0.220581\pi$
$440$	6.04702	+	8.16766i	0.288280	+	0.389378i
$441$	−0.723645	+	5.03306i	−0.0344593	+	0.239670i
$442$	−0.134720	−	0.361198i	−0.00640797	−	0.0171804i
$443$	−21.7290	−	16.2661i	−1.03238	−	0.772827i	−0.0581287	−	0.998309i	$-0.518513\pi$
$443$	−21.7290	−	16.2661i	−1.03238	−	0.772827i	−0.974247	+	0.225482i	$0.927604\pi$
$444$	0.739095	+	0.217018i	0.0350759	+	0.0102992i
$445$	−10.3638	+	15.9401i	−0.491289	+	0.755633i
$446$	2.28413	+	5.00154i	0.108157	+	0.236830i
$447$	−8.37751	+	15.3423i	−0.396243	+	0.725664i
$448$	−1.38037	+	0.0987263i	−0.0652165	+	0.00466438i
$449$	1.12903	+	0.978314i	0.0532824	+	0.0461695i	0.681095	−	0.732195i	$-0.261504\pi$
$449$	1.12903	+	0.978314i	0.0532824	+	0.0461695i	−0.627813	+	0.778365i	$0.716050\pi$
$450$	−1.69761	−	4.70299i	−0.0800262	−	0.221701i
$451$	−10.9106	+	4.98269i	−0.513759	+	0.234626i
$452$	1.50356	−	6.91175i	0.0707214	−	0.325101i
$453$	0.286192	−	0.156273i	0.0134465	−	0.00734234i
$454$	3.11972	+	21.6981i	0.146416	+	1.01834i
$455$	−0.369625	−	0.00195720i	−0.0173283	−	9.17550e-5i
$456$	−1.15181	−	0.165605i	−0.0539384	−	0.00775517i
$457$	39.7898	−	8.65573i	1.86129	−	0.404898i	0.865848	−	0.500306i	$-0.166779\pi$
$457$	39.7898	−	8.65573i	1.86129	−	0.404898i	0.995438	+	0.0954083i	$0.0304157\pi$
$458$	0.278871	−	3.89913i	0.0130308	−	0.182194i
$459$	−3.22739			−0.150642
$460$	2.58975	+	10.4064i	0.120748	+	0.485201i
$461$	26.9244			1.25399			0.626997	−	0.779021i	$-0.284284\pi$
$461$	26.9244			1.25399			0.626997	+	0.779021i	$0.284284\pi$
$462$	0.448694	−	6.27356i	0.0208751	−	0.291872i
$463$	−19.6748	+	4.27999i	−0.914365	+	0.198908i	−0.645047	−	0.764143i	$-0.723162\pi$
$463$	−19.6748	+	4.27999i	−0.914365	+	0.198908i	−0.269318	+	0.963051i	$0.586798\pi$
$464$	2.45088	+	0.352383i	0.113779	+	0.0163590i
$465$	10.2640	+	10.3733i	0.475984	+	0.481051i
$466$	−0.372343	−	2.58970i	−0.0172485	−	0.119966i
$467$	−1.28417	+	0.701211i	−0.0594244	+	0.0324482i	−0.508686	−	0.860952i	$-0.669869\pi$
$467$	−1.28417	+	0.701211i	−0.0594244	+	0.0324482i	0.449262	+	0.893400i	$0.351687\pi$
$468$	0.0253904	−	0.116718i	0.00117367	−	0.00539528i
$469$	−18.2012	+	8.31220i	−0.840452	+	0.383822i
$470$	6.90729	+	8.05725i	0.318610	+	0.371653i
$471$	−12.2014	−	10.5726i	−0.562211	−	0.487159i
$472$	−0.948123	+	0.0678111i	−0.0436409	+	0.00312126i
$473$	10.5685	−	19.3547i	0.485940	−	0.889932i
$474$	−4.88543	−	10.6976i	−0.224395	−	0.491357i
$475$	0.888967	−	5.74995i	0.0407886	−	0.263826i
$476$	−4.28547	−	1.25833i	−0.196424	−	0.0576753i
$477$	3.97275	+	2.97396i	0.181900	+	0.136168i
$478$	−1.10259	−	2.95615i	−0.0504312	−	0.135211i
$479$	2.03278	−	14.1383i	0.0928801	−	0.645995i	−0.889198	−	0.457522i	$-0.848737\pi$
$479$	2.03278	−	14.1383i	0.0928801	−	0.645995i	0.982078	−	0.188473i	$-0.0603538\pi$
$480$	2.21159	+	0.329941i	0.100945	+	0.0150597i
$481$	−0.0695366	+	0.0602538i	−0.00317060	+	0.00274734i
$482$	3.65639	−	3.65639i	0.166544	−	0.166544i
$483$	2.97496	−	5.93286i	0.135365	−	0.269954i
$484$		−	9.65543i		−	0.438883i
$485$	−29.4901	+	10.8217i	−1.33908	+	0.491388i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	6.96958	−	5.21736i	0.315822	−	0.236421i	−0.429592	−	0.903023i	$-0.641343\pi$
$487$	6.96958	−	5.21736i	0.315822	−	0.236421i	0.745414	+	0.666602i	$0.232252\pi$
$488$	11.9533	−	4.45835i	0.541100	−	0.201820i
$489$	1.63901	−	0.235655i	0.0741188	−	0.0106567i
$490$	6.86189	−	9.06595i	0.309989	−	0.409558i
$491$	19.6322	−	12.6168i	0.885988	−	0.569390i	−0.0166160	−	0.999862i	$-0.505289\pi$
$491$	19.6322	−	12.6168i	0.885988	−	0.569390i	0.902604	+	0.430472i	$0.141653\pi$
$492$	−0.922290	+	2.47276i	−0.0415800	+	0.111480i
$493$	7.01378	+	3.82981i	0.315885	+	0.172486i
$494$	0.0910228	−	0.105046i	0.00409531	−	0.00472624i
$495$	−2.91471	+	9.73558i	−0.131006	+	0.437582i
$496$	−6.26184	+	1.83864i	−0.281165	+	0.0825575i
$497$	10.2389	+	3.81892i	0.459278	+	0.171302i
$498$	−1.42981	−	0.311037i	−0.0640715	−	0.0139379i
$499$	2.94846	−	10.0415i	0.131991	−	0.449520i	−0.866801	−	0.498654i	$-0.833828\pi$
$499$	2.94846	−	10.0415i	0.131991	−	0.449520i	0.998792	+	0.0491337i	$0.0156460\pi$
$500$	−1.76671	+	11.0399i	−0.0790098	+	0.493718i
$501$	0.974073	−	2.13292i	0.0435184	−	0.0952919i
$502$	−17.7595	−	23.7239i	−0.792646	−	1.05885i
$503$	8.27515	+	38.0402i	0.368971	+	1.69613i	0.669873	+	0.742475i	$0.266348\pi$
$503$	8.27515	+	38.0402i	0.368971	+	1.69613i	−0.300903	+	0.953655i	$0.597288\pi$
$504$	−0.906262	−	1.04588i	−0.0403681	−	0.0465873i
$505$	−6.59673	+	2.97051i	−0.293551	+	0.132186i
$506$	8.35510	−	20.1312i	0.371430	−	0.894943i
$507$	−9.18230	−	9.18230i	−0.407800	−	0.407800i
$508$	16.1841	+	1.15751i	0.718052	+	0.0513561i
$509$	−3.02734	+	4.71063i	−0.134184	+	0.208795i	−0.901843	−	0.432064i	$-0.857785\pi$
$509$	−3.02734	+	4.71063i	−0.134184	+	0.208795i	0.767658	+	0.640859i	$0.221422\pi$
$510$	6.31552	+	3.49207i	0.279656	+	0.154631i
$511$	−14.0254	−	6.40517i	−0.620446	−	0.283348i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	−0.557680	−	1.02131i	−0.0246222	−	0.0450921i
$514$	4.86124	+	7.56424i	0.214420	+	0.333644i
$515$	1.85531	+	28.0253i	0.0817548	+	1.23494i
$516$	−1.36701	−	4.65561i	−0.0601793	−	0.204952i
$517$	−1.53882	−	21.5155i	−0.0676772	−	0.946250i
$518$	0.0760486	+	1.06330i	0.00334138	+	0.0467187i
$519$	0.745211	+	2.53796i	0.0327111	+	0.111404i
$520$	−0.175975	+	0.200926i	−0.00771702	+	0.00881120i
$521$	11.7241	+	18.2430i	0.513640	+	0.799240i	0.997098	−	0.0761276i	$-0.0242556\pi$
$521$	11.7241	+	18.2430i	0.513640	+	0.799240i	−0.483458	+	0.875368i	$0.660619\pi$
$522$	1.18666	+	2.17320i	0.0519386	+	0.0951185i
$523$	−0.776294	+	1.03701i	−0.0339450	+	0.0453451i	−0.817193	−	0.576365i	$-0.804471\pi$
$523$	−0.776294	+	1.03701i	−0.0339450	+	0.0453451i	0.783248	+	0.621710i	$0.213562\pi$
$524$	−10.6511	−	4.86418i	−0.465295	−	0.212493i
$525$	5.27710	−	4.47568i	0.230312	−	0.195335i
$526$	4.11893	−	6.40917i	0.179594	−	0.279453i
$527$	−21.0089	−	1.50259i	−0.915164	−	0.0654538i
$528$	−3.21368	−	3.21368i	−0.139857	−	0.139857i
$529$	16.2861	−	16.2407i	0.708093	−	0.706119i
$530$	−4.55621	−	10.1182i	−0.197909	−	0.439505i
$531$	−0.622475	−	0.718374i	−0.0270131	−	0.0311748i
$532$	−0.342311	−	1.57358i	−0.0148411	−	0.0682233i
$533$	−0.188917	−	0.252363i	−0.00818289	−	0.0109311i
$534$	3.53222	−	7.73448i	0.152854	−	0.334704i
$535$	44.1154	+	9.84165i	1.90727	+	0.425491i
$536$	−4.07348	+	13.8730i	−0.175948	+	0.599223i
$537$	−16.0299	−	3.48708i	−0.691740	−	0.150479i
$538$	−18.9384	−	7.06366i	−0.816492	−	0.304536i
$539$	−22.1735	+	6.51073i	−0.955081	+	0.280437i
$540$	1.06123	+	1.96820i	0.0456679	+	0.0846977i
$541$	19.4598	−	22.4578i	0.836642	−	0.965537i	−0.163136	−	0.986604i	$-0.552161\pi$
$541$	19.4598	−	22.4578i	0.836642	−	0.965537i	0.999778	+	0.0210669i	$0.00670629\pi$
$542$	15.1552	+	8.27537i	0.650972	+	0.355457i
$543$	−0.0817484	+	0.219176i	−0.00350816	+	0.00940574i
$544$	−2.71505	+	1.74486i	−0.116407	+	0.0748102i
$545$	10.7815	−	1.49192i	0.461830	−	0.0639070i
$546$	0.163621	−	0.0235251i	0.00700233	−	0.00100678i
$547$	15.2948	−	5.70466i	0.653958	−	0.243914i	−0.000514350	−	1.00000i	$-0.500164\pi$
$547$	15.2948	−	5.70466i	0.653958	−	0.243914i	0.654472	+	0.756086i	$0.272891\pi$
$548$	−3.42672	+	2.56521i	−0.146382	+	0.109580i
$549$	10.7324	+	6.89732i	0.458049	+	0.294370i
$550$	16.2376	−	15.8973i	0.692375	−	0.677864i
$551$			2.88130i			0.122747i
$552$	−1.83219	−	4.43205i	−0.0779833	−	0.188641i
$553$	11.5083	−	11.5083i	0.489382	−	0.489382i
$554$	7.48285	−	6.48393i	0.317916	−	0.275476i
$555$	0.254152	−	1.70358i	0.0107882	−	0.0723131i
$556$	−2.85829	+	19.8799i	−0.121219	+	0.843094i
$557$	8.03613	+	21.5457i	0.340502	+	0.912921i	0.988492	+	0.151272i	$0.0483370\pi$
$557$	8.03613	+	21.5457i	0.340502	+	0.912921i	−0.647990	+	0.761649i	$0.724390\pi$
$558$	−5.22449	−	3.91101i	−0.221170	−	0.165566i
$559$	0.556101	+	0.163286i	0.0235206	+	0.00690626i
$560$	0.641762	+	3.02722i	0.0271194	+	0.127923i
$561$	−6.09328	−	13.3424i	−0.257258	−	0.563317i
$562$	2.81797	−	5.16072i	0.118869	−	0.217692i
$563$	21.4758	−	1.53598i	0.905096	−	0.0647337i	0.388974	−	0.921249i	$-0.372830\pi$
$563$	21.4758	−	1.53598i	0.905096	−	0.0647337i	0.516122	+	0.856515i	$0.327375\pi$
$564$	−3.58691	−	3.10807i	−0.151036	−	0.130873i
$565$	−15.7701	−	1.21186i	−0.663453	−	0.0509835i
$566$	20.4153	−	9.32337i	0.858120	−	0.391890i
$567$	0.294169	−	1.35227i	0.0123539	−	0.0567902i
$568$	6.93056	−	3.78437i	0.290800	−	0.158789i
$569$	−2.05603	−	14.3000i	−0.0861931	−	0.599486i	−0.986442	−	0.164110i	$-0.947525\pi$
$569$	−2.05603	−	14.3000i	−0.0861931	−	0.599486i	0.900249	−	0.435376i	$-0.143384\pi$
$570$	−0.0137777	+	2.60197i	−0.000577085	+	0.108985i
$571$	−45.3962	−	6.52699i	−1.89977	−	0.273146i	−0.909870	−	0.414894i	$-0.863819\pi$
$571$	−45.3962	−	6.52699i	−1.89977	−	0.273146i	−0.989903	+	0.141748i	$0.954728\pi$
$572$	0.530462	−	0.115395i	0.0221797	−	0.00482491i
$573$	0.415848	−	5.81432i	0.0173723	−	0.242897i
$574$	−3.65233			−0.152445
$575$	22.2560	−	8.92577i	0.928140	−	0.372230i
$576$	−1.00000			−0.0416667
$577$	0.156360	−	2.18620i	0.00650935	−	0.0910127i	−0.993159	−	0.116771i	$-0.962746\pi$
$577$	0.156360	−	2.18620i	0.00650935	−	0.0910127i	0.999668	+	0.0257586i	$0.00820011\pi$
$578$	6.43348	−	1.39952i	0.267597	−	0.0582123i
$579$	−2.33704	−	0.336016i	−0.0971242	−	0.0139644i
$580$	0.0293169	−	5.53660i	0.00121732	−	0.229895i
$581$	−0.288187	−	2.00439i	−0.0119560	−	0.0831560i
$582$	12.3299	−	6.73264i	0.511091	−	0.279077i
$583$	−4.79421	+	22.0386i	−0.198556	+	0.912747i
$584$	−10.1347	+	4.62835i	−0.419376	+	0.191522i
$585$	−0.266308	−	0.0204646i	−0.0110105	−	0.000846106i
$586$	−14.0373	−	12.1634i	−0.579876	−	0.502465i
$587$	24.9754	−	1.78627i	1.03084	−	0.0737274i	0.454345	−	0.890826i	$-0.349873\pi$
$587$	24.9754	−	1.78627i	1.03084	−	0.0737274i	0.576498	+	0.817098i	$0.304419\pi$
$588$	−2.43689	+	4.46284i	−0.100496	+	0.184044i
$589$	−3.15476	−	6.90796i	−0.129990	−	0.284638i
$590$	0.440800	+	2.07927i	0.0181475	+	0.0856023i
$591$	−2.72727	−	0.800799i	−0.112185	−	0.0329405i
$592$	0.616655	+	0.461622i	0.0253444	+	0.0189725i
$593$	6.65986	+	17.8558i	0.273488	+	0.733249i	0.998986	+	0.0450249i	$0.0143367\pi$
$593$	6.65986	+	17.8558i	0.273488	+	0.733249i	−0.725498	+	0.688224i	$0.758391\pi$
$594$	0.646796	−	4.49856i	0.0265384	−	0.184578i
$595$	−1.47364	+	9.87783i	−0.0604135	+	0.404951i
$596$	−13.2109	+	11.4473i	−0.541139	+	0.468899i
$597$	−1.18032	+	1.18032i	−0.0483075	+	0.0483075i
$598$	0.563677	+	0.102105i	0.0230505	+	0.00417538i
$599$			13.2826i			0.542713i	0.962479	+	0.271357i	$0.0874723\pi$
$599$			13.2826i			0.542713i	−0.962479	+	0.271357i	$0.912528\pi$
$600$	0.0529496	−	4.99972i	0.00216166	−	0.204113i
$601$	34.9040	+	22.4315i	1.42376	+	0.914998i	0.999957	+	0.00924582i	$0.00294308\pi$
$601$	34.9040	+	22.4315i	1.42376	+	0.914998i	0.423808	+	0.905752i	$0.360693\pi$
$602$	5.37555	−	4.02409i	0.219091	−	0.164010i
$603$	−13.5471	+	5.05279i	−0.551679	+	0.205766i
$604$	0.322759	−	0.0464058i	0.0131329	−	0.00188823i
$605$	−21.3864	+	2.95940i	−0.869481	+	0.120317i
$606$	2.72184	−	1.74922i	0.110567	−	0.0710571i
$607$	12.6624	−	33.9492i	0.513950	−	1.37795i	−0.377993	−	0.925808i	$-0.623386\pi$
$607$	12.6624	−	33.9492i	0.513950	−	1.37795i	0.891944	−	0.452146i	$-0.149342\pi$
$608$	−1.02131	−	0.557680i	−0.0414198	−	0.0226169i
$609$	−2.24398	+	2.58969i	−0.0909305	+	0.104939i
$610$	−13.5388	−	25.1096i	−0.548169	−	1.01666i
$611$	0.543953	−	0.159719i	0.0220060	−	0.00646154i
$612$	−3.02390	−	1.12786i	−0.122234	−	0.0455909i
$613$	30.1011	+	6.54810i	1.21577	+	0.264475i	0.774311	−	0.632805i	$-0.218097\pi$
$613$	30.1011	+	6.54810i	1.21577	+	0.264475i	0.441462	+	0.897280i	$0.354460\pi$
$614$	−4.58401	+	15.6117i	−0.184996	+	0.630037i
$615$	5.75974	+	1.28493i	0.232255	+	0.0518135i
$616$	2.61279	−	5.72121i	0.105272	−	0.230514i
$617$	−23.8921	−	31.9161i	−0.961860	−	1.28489i	−0.958557	−	0.284900i	$-0.908039\pi$
$617$	−23.8921	−	31.9161i	−0.961860	−	1.28489i	−0.00330313	−	0.999995i	$-0.501051\pi$
$618$	−2.66998	−	12.2737i	−0.107402	−	0.493720i
$619$	−29.5497	−	34.1021i	−1.18770	−	1.37068i	−0.912388	−	0.409326i	$-0.865764\pi$
$619$	−29.5497	−	34.1021i	−1.18770	−	1.37068i	−0.275313	−	0.961355i	$-0.588781\pi$
$620$	5.99179	+	13.3062i	0.240636	+	0.534390i
$621$	2.45005	−	4.12277i	0.0983170	−	0.165441i
$622$	−13.5076	−	13.5076i	−0.541605	−	0.541605i
$623$	11.7371	+	0.839457i	0.470239	+	0.0336321i
$624$	0.0645782	−	0.100486i	0.00258520	−	0.00402265i
$625$	24.9944	+	0.529466i	0.999776	+	0.0211786i
$626$	19.1673	+	8.75340i	0.766078	+	0.349856i
$627$	3.16934	−	4.23374i	0.126571	−	0.169079i
$628$	−7.73737	−	14.1699i	−0.308755	−	0.565442i
$629$	1.34406	+	2.09140i	0.0535912	+	0.0833895i
$630$	−2.03882	+	2.32790i	−0.0812285	+	0.0927458i
$631$	−1.19686	−	4.07614i	−0.0476464	−	0.162269i	0.932233	−	0.361858i	$-0.117857\pi$
$631$	−1.19686	−	4.07614i	−0.0476464	−	0.162269i	−0.979880	+	0.199589i	$0.936039\pi$
$632$	−0.838974	−	11.7304i	−0.0333726	−	0.466610i
$633$	1.86313	+	26.0499i	0.0740527	+	1.03539i
$634$	4.62257	+	15.7430i	0.183586	+	0.625235i
$635$	−2.39661	−	36.2019i	−0.0951066	−	1.43663i
$636$	2.68297	+	4.17479i	0.106387	+	0.165541i
$637$	−0.291081	−	0.533075i	−0.0115331	−	0.0211212i
$638$	−6.74388	+	9.00877i	−0.266993	+	0.356660i
$639$	7.18288	+	3.28031i	0.284150	+	0.129767i
$640$	1.95685	+	1.08201i	0.0773512	+	0.0427702i
$641$	3.21254	−	4.99880i	0.126888	−	0.197441i	−0.771997	−	0.635626i	$-0.780742\pi$
$641$	3.21254	−	4.99880i	0.126888	−	0.197441i	0.898885	+	0.438185i	$0.144378\pi$
$642$	−20.1625	−	1.44205i	−0.795749	−	0.0569131i
$643$	5.99603	+	5.99603i	0.236460	+	0.236460i	0.815383	−	0.578922i	$-0.196527\pi$
$643$	5.99603	+	5.99603i	0.236460	+	0.236460i	−0.578922	+	0.815383i	$0.696527\pi$
$644$	4.86070	−	4.51915i	0.191539	−	0.178079i
$645$	−9.89300	+	4.45483i	−0.389537	+	0.175409i
$646$	−2.45937	−	2.83827i	−0.0967627	−	0.111670i
$647$	7.46560	+	34.3188i	0.293503	+	1.34921i	0.853662	+	0.520827i	$0.174376\pi$
$647$	7.46560	+	34.3188i	0.293503	+	1.34921i	−0.560159	+	0.828385i	$0.689260\pi$
$648$	−0.599278	−	0.800541i	−0.0235419	−	0.0314482i
$649$	1.79462	−	3.92966i	0.0704449	−	0.154253i
$650$	0.498981	+	0.328194i	0.0195716	+	0.0128728i
$651$	2.54450	−	8.66577i	0.0997268	−	0.339638i
$652$	1.61803	+	0.351980i	0.0633668	+	0.0137846i
$653$	42.1941	+	15.7376i	1.65118	+	0.615860i	0.990832	−	0.135096i	$-0.0431343\pi$
$653$	42.1941	+	15.7376i	1.65118	+	0.615860i	0.660352	+	0.750956i	$0.270407\pi$
$654$	−4.67042	+	1.37136i	−0.182628	+	0.0536244i
$655$	−7.50941	+	25.0826i	−0.293417	+	0.980059i
$656$	−1.72828	+	1.99454i	−0.0674779	+	0.0778737i
$657$	−9.77866	−	5.33955i	−0.381502	−	0.208316i
$658$	2.29535	−	6.15408i	0.0894822	−	0.239911i
$659$	−19.6946	+	12.6570i	−0.767193	+	0.493045i	−0.864761	−	0.502184i	$-0.832530\pi$
$659$	−19.6946	+	12.6570i	−0.767193	+	0.493045i	0.0975679	+	0.995229i	$0.468894\pi$
$660$	−6.13317	+	8.10317i	−0.238733	+	0.315415i
$661$	35.8609	−	5.15603i	1.39483	−	0.200546i	0.596425	−	0.802669i	$-0.296587\pi$
$661$	35.8609	−	5.15603i	1.39483	−	0.200546i	0.798404	+	0.602122i	$0.205678\pi$
$662$	19.7681	−	7.37313i	0.768310	−	0.286565i
$663$	0.308612	−	0.231024i	0.0119855	−	0.00897223i
$664$	−1.23097	−	0.791095i	−0.0477708	−	0.0307004i
$665$	−3.38050	+	1.24051i	−0.131090	+	0.0481049i
$666$			0.770297i			0.0298484i
$667$	−10.2168	+	6.05225i	−0.395595	+	0.234344i
$668$	1.65804	−	1.65804i	0.0641514	−	0.0641514i
$669$	−4.15543	+	3.60070i	−0.160658	+	0.139211i
$670$	31.9767	+	4.77051i	1.23537	+	0.184301i
$671$	−8.25161	+	57.3912i	−0.318550	+	2.21556i
$672$	−0.483624	−	1.29664i	−0.0186562	−	0.0500192i
$673$	−0.450892	−	0.337533i	−0.0173806	−	0.0130110i	0.590552	−	0.807000i	$-0.298910\pi$
$673$	−0.450892	−	0.337533i	−0.0173806	−	0.0130110i	−0.607933	+	0.793989i	$0.708001\pi$
$674$	21.5587	+	6.33021i	0.830410	+	0.243830i
$675$	4.03421	−	2.95383i	0.155277	−	0.113693i
$676$	−5.39447	−	11.8122i	−0.207480	−	0.454317i
$677$	17.9558	−	32.8835i	0.690096	−	1.26382i	−0.264060	−	0.964506i	$-0.585062\pi$
$677$	17.9558	−	32.8835i	0.690096	−	1.26382i	0.954156	−	0.299310i	$-0.0967566\pi$
$678$	7.05537	−	0.504610i	0.270960	−	0.0193794i
$679$	14.6929	+	12.7314i	0.563861	+	0.488588i
$680$	4.69697	+	5.47894i	0.180120	+	0.210108i
$681$	−19.9403	+	9.10641i	−0.764112	+	0.348958i
$682$	6.30478	−	28.9826i	0.241423	−	1.10980i
$683$	9.85128	−	5.37920i	0.376949	−	0.205830i	−0.279594	−	0.960118i	$-0.590200\pi$
$683$	9.85128	−	5.37920i	0.376949	−	0.205830i	0.656543	+	0.754289i	$0.272018\pi$
$684$	−0.165605	−	1.15181i	−0.00633207	−	0.0440405i
$685$	6.73213	+	6.80381i	0.257222	+	0.259960i
$686$	−16.5540	−	2.38010i	−0.632033	−	0.0908726i
$687$	3.81975	−	0.830936i	0.145733	−	0.0317022i
$688$	0.346149	−	4.83979i	0.0131968	−	0.184515i
$689$	−0.592768			−0.0225827
$690$	−9.25525	+	5.41667i	−0.352341	+	0.206209i
$691$	7.33264			0.278947			0.139473	−	0.990226i	$-0.455459\pi$
$691$	7.33264			0.278947			0.139473	+	0.990226i	$0.455459\pi$
$692$	−0.188699	+	2.63836i	−0.00717327	+	0.100295i
$693$	6.14585	−	1.33695i	0.233461	−	0.0507864i
$694$	−23.2568	−	3.34382i	−0.882816	−	0.126930i
$695$	44.9092	+	0.237799i	1.70350	+	0.00902023i
$696$	0.352383	+	2.45088i	0.0133570	+	0.0929002i
$697$	−7.47571	+	4.08204i	−0.283163	+	0.154618i
$698$	1.14929	−	5.28319i	0.0435012	−	0.199972i
$699$	2.37990	−	1.08686i	0.0900161	−	0.0411090i
$700$	6.50847	−	2.34933i	0.245997	−	0.0887962i
$701$	−30.4455	−	26.3812i	−1.14991	−	0.996402i	−0.999970	−	0.00770716i	$-0.997547\pi$
$701$	−30.4455	−	26.3812i	−1.14991	−	0.996402i	−0.149939	−	0.988695i	$-0.547908\pi$
$702$	0.119143	−	0.00852129i	0.00449677	−	0.000321615i
$703$	−0.429579	+	0.786716i	−0.0162019	+	0.0296715i
$704$	−1.88799	−	4.13412i	−0.0711562	−	0.155810i
$705$	−5.78487	+	8.89749i	−0.217871	+	0.335099i
$706$	23.9325	+	7.02722i	0.900712	+	0.264473i
$707$	3.58446	+	2.68329i	0.134807	+	0.100916i
$708$	−0.332181	−	0.890613i	−0.0124841	−	0.0334713i
$709$	−1.11198	+	7.73396i	−0.0417611	+	0.290455i	0.958229	+	0.286002i	$0.0923265\pi$
$709$	−1.11198	+	7.73396i	−0.0417611	+	0.290455i	−0.999990	+	0.00445288i	$0.998583\pi$
$710$	−10.5065	−	14.1910i	−0.394301	−	0.532579i
$711$	8.88789	−	7.70140i	0.333322	−	0.288825i
$712$	6.01244	−	6.01244i	0.225326	−	0.225326i
$713$	17.8682	−	25.6968i	0.669170	−	0.962354i
$714$		−	4.46639i		−	0.167150i
$715$	−0.418183	−	1.13958i	−0.0156392	−	0.0426180i
$716$	−13.8006	−	8.86909i	−0.515751	−	0.331453i
$717$	2.52577	−	1.89077i	0.0943266	−	0.0706120i
$718$	−0.380205	+	0.141809i	−0.0141891	+	0.00529227i
$719$	40.9483	−	5.88748i	1.52711	−	0.219566i	0.672996	−	0.739646i	$-0.265007\pi$
$719$	40.9483	−	5.88748i	1.52711	−	0.219566i	0.854118	+	0.520080i	$0.174098\pi$
$720$	0.306502	+	2.21496i	0.0114226	+	0.0825468i
$721$	14.6234	−	9.39786i	0.544602	−	0.349995i
$722$	−6.16661	+	16.5333i	−0.229498	+	0.615307i
$723$	4.53840	+	2.47815i	0.168785	+	0.0921636i
$724$	−0.153188	+	0.176789i	−0.00569320	+	0.00657030i
$725$	−12.2724	+	1.63204i	−0.455784	+	0.0606125i
$726$	9.26432	−	2.72025i	0.343831	−	0.100958i
$727$	−7.73645	−	2.88554i	−0.286929	−	0.107019i	0.201879	−	0.979411i	$-0.435295\pi$
$727$	−7.73645	−	2.88554i	−0.286929	−	0.107019i	−0.488808	+	0.872392i	$0.662568\pi$
$728$	0.161526	+	0.0351378i	0.00598655	+	0.00130229i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	13.3579	+	21.0293i	0.494398	+	0.778330i
$731$	6.50532	−	14.2447i	0.240608	−	0.526858i
$732$	7.64538	+	10.2130i	0.282582	+	0.377485i
$733$	3.83554	+	17.6317i	0.141669	+	0.651241i	0.992131	+	0.125205i	$0.0399587\pi$
$733$	3.83554	+	17.6317i	0.141669	+	0.651241i	−0.850462	+	0.526036i	$0.823678\pi$
$734$	−7.37184	−	8.50756i	−0.272100	−	0.314020i
$735$	10.6319	+	4.02976i	0.392165	+	0.148640i
$736$	−0.167829	−	4.79289i	−0.00618625	−	0.176668i
$737$	−46.4655	−	46.4655i	−1.71158	−	1.71158i
$738$	−2.63243	−	0.188275i	−0.0969011	−	0.00693050i
$739$	−18.2046	+	28.3269i	−0.669668	+	1.04202i	0.325662	+	0.945486i	$0.394413\pi$
$739$	−18.2046	+	28.3269i	−0.669668	+	1.04202i	−0.995329	+	0.0965368i	$0.969223\pi$
$740$	0.833469	−	1.50735i	0.0306389	−	0.0554115i
$741$	0.126435	+	0.0577409i	0.00464470	+	0.00212116i
$742$	−4.11567	+	5.49789i	−0.151091	+	0.201834i
$743$	5.45829	+	9.99610i	0.200245	+	0.366722i	0.958434	−	0.285313i	$-0.0920975\pi$
$743$	5.45829	+	9.99610i	0.200245	+	0.366722i	−0.758189	+	0.652034i	$0.773916\pi$
$744$	−3.52833	−	5.49019i	−0.129355	−	0.201280i
$745$	29.4045	+	25.7530i	1.07730	+	0.943516i
$746$	3.47462	+	11.8335i	0.127215	+	0.433254i
$747$	−0.104387	−	1.45953i	−0.00381933	−	0.0534013i
$748$	−1.04640	−	14.6306i	−0.0382601	−	0.534946i
$749$	−7.88122	−	26.8410i	−0.287974	−	0.980748i
$750$	−11.0904	+	1.41514i	−0.404965	+	0.0516736i
$751$	−10.7969	−	16.8003i	−0.393984	−	0.613050i	0.586430	−	0.810000i	$-0.300533\pi$
$751$	−10.7969	−	16.8003i	−0.393984	−	0.613050i	−0.980414	+	0.196949i	$0.936897\pi$
$752$	−2.27459	−	4.16560i	−0.0829458	−	0.151904i
$753$	17.7595	−	23.7239i	0.647193	−	0.864548i
$754$	−0.269034	−	0.122864i	−0.00979765	−	0.00447444i
$755$	−0.201713	−	0.700677i	−0.00734110	−	0.0255002i
$756$	0.748193	−	1.16421i	0.0272115	−	0.0423419i
$757$	−44.9605	−	3.21564i	−1.63412	−	0.116874i	−0.776139	−	0.630561i	$-0.782825\pi$
$757$	−44.9605	−	3.21564i	−1.63412	−	0.116874i	−0.857978	+	0.513687i	$0.828279\pi$
$758$	18.8518	+	18.8518i	0.684728	+	0.684728i
$759$	21.6697	+	2.34504i	0.786560	+	0.0851194i
$760$	−0.922205	+	2.43310i	−0.0334519	+	0.0882579i
$761$	−34.5379	−	39.8588i	−1.25200	−	1.44488i	−0.847892	−	0.530170i	$-0.822128\pi$
$761$	−34.5379	−	39.8588i	−1.25200	−	1.44488i	−0.404106	−	0.914712i	$-0.632417\pi$
$762$	3.44896	+	15.8546i	0.124943	+	0.574352i
$763$	−4.03689	−	5.39265i	−0.146145	−	0.195227i
$764$	2.42152	−	5.30240i	0.0876077	−	0.191834i
$765$	−1.57133	+	7.04352i	−0.0568116	+	0.254659i
$766$	−0.908792	+	3.09506i	−0.0328360	+	0.111829i
$767$	0.110946	+	0.0241347i	0.00400601	+	0.000871454i
$768$	−0.936950	−	0.349464i	−0.0338093	−	0.0126102i
$769$	−13.5328	+	3.97358i	−0.488004	+	0.143291i	−0.516472	−	0.856304i	$-0.672755\pi$
$769$	−13.5328	+	3.97358i	−0.488004	+	0.143291i	0.0284687	+	0.999595i	$0.490937\pi$
$770$	−13.4731	−	4.03367i	−0.485536	−	0.145363i
$771$	−5.88826	+	6.79542i	−0.212061	+	0.244731i
$772$	−2.07227	−	1.13154i	−0.0745825	−	0.0407251i
$773$	−8.54320	+	22.9052i	−0.307278	+	0.823843i	0.687905	+	0.725801i	$0.258531\pi$
$773$	−8.54320	+	22.9052i	−0.307278	+	0.823843i	−0.995182	+	0.0980420i	$0.968742\pi$
$774$	4.08189	−	2.62327i	0.146721	−	0.0942916i
$775$	27.6362	−	17.3500i	0.992723	−	0.623229i
$776$	13.9053	−	1.99928i	0.499172	−	0.0717700i
$777$	−0.998802	+	0.372534i	−0.0358318	+	0.0133646i
$778$	3.91487	−	2.93064i	0.140355	−	0.105068i
$779$	−2.58354	−	1.66034i	−0.0925650	−	0.0594879i
$780$	−0.242365	−	0.112239i	−0.00867807	−	0.00401881i
$781$			35.8881i			1.28418i
$782$	4.89821	−	14.6825i	0.175159	−	0.525046i
$783$	−1.75085	+	1.75085i	−0.0625704	+	0.0625704i
$784$	−3.84285	+	3.32985i	−0.137245	+	0.118923i
$785$	−29.0144	+	21.4811i	−1.03557	+	0.766693i
$786$	1.66640	−	11.5900i	0.0594384	−	0.413403i
$787$	−7.40676	−	19.8583i	−0.264022	−	0.707871i	−0.999539	−	0.0303647i	$-0.990333\pi$
$787$	−7.40676	−	19.8583i	−0.264022	−	0.707871i	0.735516	−	0.677507i	$-0.236940\pi$
$788$	−2.27547	−	1.70339i	−0.0810601	−	0.0606808i
$789$	7.30999	+	2.14641i	0.260243	+	0.0764141i
$790$	−25.7252	+	5.45368i	−0.915263	+	0.194033i
$791$	4.06644	+	8.90427i	0.144586	+	0.316599i
$792$	2.17810	−	3.98890i	0.0773955	−	0.141739i
$793$	−1.51999	+	0.108712i	−0.0539764	+	0.00386047i
$794$	−8.49471	−	7.36070i	−0.301466	−	0.261222i
$795$	8.42466	−	7.22227i	0.298792	−	0.256147i
$796$	−1.51839	+	0.693423i	−0.0538177	+	0.0245777i
$797$	9.37542	−	43.0981i	0.332094	−	1.52661i	−0.444017	−	0.896018i	$-0.646447\pi$
$797$	9.37542	−	43.0981i	0.332094	−	1.52661i	0.776112	−	0.630595i	$-0.217189\pi$
$798$	1.41340	−	0.771773i	0.0500337	−	0.0273205i
$799$	−2.17994	−	15.1618i	−0.0771206	−	0.536386i
$800$	1.79683	−	4.66598i	0.0635277	−	0.164967i
$801$	8.41633	+	1.21008i	0.297376	+	0.0427562i
$802$	−16.2070	+	3.52562i	−0.572290	+	0.124494i
$803$	3.61234	−	50.5072i	0.127477	−	1.78236i
$804$	−14.4587			−0.509919
$805$	−11.4996	−	9.38115i	−0.405306	−	0.330642i
$806$	0.779539			0.0274581
$807$	1.44197	−	20.1613i	0.0507596	−	0.709712i
$808$	3.16151	−	0.687745i	0.111222	−	0.0241948i
$809$	−53.2570	−	7.65720i	−1.87242	−	0.269213i	−0.890007	−	0.455948i	$-0.849300\pi$
$809$	−53.2570	−	7.65720i	−1.87242	−	0.269213i	−0.982410	+	0.186735i	$0.940210\pi$
$810$	−1.58949	+	1.57274i	−0.0558489	+	0.0552606i
$811$	−3.54828	−	24.6788i	−0.124597	−	0.866592i	−0.952243	−	0.305341i	$-0.901230\pi$
$811$	−3.54828	−	24.6788i	−0.124597	−	0.866592i	0.827646	−	0.561250i	$-0.189680\pi$
$812$	−3.00750	+	1.64222i	−0.105542	+	0.0576305i
$813$	−3.67044	+	16.8728i	−0.128728	+	0.591753i
$814$	−3.18450	+	1.45431i	−0.111617	+	0.0509736i
$815$	0.283695	−	3.69175i	0.00993740	−	0.129316i
$816$	−2.43910	−	2.11349i	−0.0853856	−	0.0739870i
$817$	5.63184	−	0.402797i	0.197033	−	0.0140921i
$818$	−10.9767	+	20.1023i	−0.383790	+	0.702859i
$819$	0.0686696	+	0.150365i	0.00239951	+	0.00525419i
$820$	4.94755	+	3.21674i	0.172776	+	0.112333i
$821$	10.5374	+	3.09407i	0.367759	+	0.107984i	0.460390	−	0.887717i	$-0.347709\pi$
$821$	10.5374	+	3.09407i	0.367759	+	0.107984i	−0.0926309	+	0.995701i	$0.529528\pi$
$822$	−3.42672	−	2.56521i	−0.119521	−	0.0894719i
$823$	13.8241	+	37.0640i	0.481879	+	1.29197i	0.919599	+	0.392857i	$0.128513\pi$
$823$	13.8241	+	37.0640i	0.481879	+	1.29197i	−0.437720	+	0.899111i	$0.644214\pi$
$824$	1.78758	−	12.4329i	0.0622733	−	0.433120i
$825$	19.8280	+	11.1011i	0.690324	+	0.386491i
$826$	0.994158	−	0.861443i	0.0345912	−	0.0299734i
$827$	33.0073	−	33.0073i	1.14778	−	1.14778i	0.160787	−	0.986989i	$-0.448597\pi$
$827$	33.0073	−	33.0073i	1.14778	−	1.14778i	0.986989	−	0.160787i	$-0.0514032\pi$
$828$	3.73633	−	3.00663i	0.129847	−	0.104488i
$829$		−	32.4035i		−	1.12542i	−0.826655	−	0.562710i	$-0.809759\pi$
$829$		−	32.4035i		−	1.12542i	0.826655	−	0.562710i	$-0.190241\pi$
$830$	−1.37495	+	2.96902i	−0.0477253	+	0.103056i
$831$	8.32945	+	5.35301i	0.288945	+	0.185694i
$832$	0.0956227	−	0.0715823i	0.00331512	−	0.00248167i
$833$	−15.3760	+	5.73495i	−0.532747	+	0.198704i
$834$	−19.8799	+	2.85829i	−0.688384	+	0.0989746i
$835$	−4.18068	−	3.16430i	−0.144678	−	0.109505i
$836$	4.44905	−	2.85923i	0.153874	−	0.0988887i
$837$	2.28067	−	6.11472i	0.0788316	−	0.211356i
$838$	−18.1835	−	9.92897i	−0.628140	−	0.342990i
$839$	−20.8449	+	24.0563i	−0.719646	+	0.830516i	−0.991265	−	0.131889i	$-0.957896\pi$
$839$	−20.8449	+	24.0563i	−0.719646	+	0.830516i	0.271618	+	0.962405i	$0.412441\pi$
$840$	−2.72379	+	1.46863i	−0.0939796	+	0.0506726i
$841$	−21.9427	+	6.44295i	−0.756644	+	0.222171i
$842$	12.1188	+	4.52008i	0.417641	+	0.155772i
$843$	5.74559	+	1.24988i	0.197889	+	0.0430480i
$844$	−7.35786	+	25.0586i	−0.253268	+	0.862551i
$845$	−24.5102	+	15.5690i	−0.843178	+	0.535590i
$846$	1.97162	−	4.31726i	0.0677859	−	0.148430i
$847$	8.00764	+	10.6970i	0.275146	+	0.367552i
$848$	1.05487	+	4.84917i	0.0362245	+	0.166521i
$849$	14.6974	+	16.9617i	0.504412	+	0.582123i
$850$	10.6960	−	12.0829i	0.366870	−	0.414440i
$851$	−3.69195	+	0.129278i	−0.126559	+	0.00443159i
$852$	5.58365	+	5.58365i	0.191293	+	0.191293i
$853$	13.1626	+	0.941411i	0.450680	+	0.0322333i	0.294835	−	0.955548i	$-0.404735\pi$
$853$	13.1626	+	0.941411i	0.450680	+	0.0322333i	0.155845	+	0.987781i	$0.450190\pi$
$854$	−9.54520	+	14.8526i	−0.326630	+	0.508246i
$855$	−2.50046	+	0.719841i	−0.0855138	+	0.0246180i
$856$	−18.3873	−	8.39719i	−0.628464	−	0.287010i
$857$	12.2821	−	16.4070i	0.419550	−	0.560453i	−0.540118	−	0.841589i	$-0.681620\pi$
$857$	12.2821	−	16.4070i	0.419550	−	0.560453i	0.959668	+	0.281136i	$0.0907113\pi$
$858$	0.260169	+	0.476464i	0.00888203	+	0.0162662i
$859$	16.9434	+	26.3645i	0.578102	+	0.899544i	0.999975	−	0.00711093i	$-0.00226350\pi$
$859$	16.9434	+	26.3645i	0.578102	+	0.899544i	−0.421873	+	0.906655i	$0.638627\pi$
$860$	−10.8260	+	0.716698i	−0.369165	+	0.0244392i
$861$	−1.02898	−	3.50438i	−0.0350675	−	0.119429i
$862$	−1.01309	−	14.1648i	−0.0345059	−	0.482455i
$863$	1.49848	+	20.9516i	0.0510090	+	0.713199i	0.957034	+	0.289975i	$0.0936471\pi$
$863$	1.49848	+	20.9516i	0.0510090	+	0.713199i	−0.906025	+	0.423224i	$0.860898\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	5.90171	−	0.390700i	0.200664	−	0.0132842i
$866$	−13.4496	−	20.9280i	−0.457036	−	0.711162i
$867$	3.15535	+	5.77859i	0.107161	+	0.196251i
$868$	5.41244	−	7.23018i	0.183710	−	0.245408i
$869$	48.6187	+	22.2034i	1.64928	+	0.753199i
$870$	5.32059	−	1.53171i	0.180385	−	0.0519299i
$871$	0.933716	−	1.45289i	0.0316378	−	0.0492293i
$872$	−4.85519	−	0.347250i	−0.164417	−	0.0117594i
$873$	9.93365	+	9.93365i	0.336203	+	0.336203i
$874$	5.49271	−	0.987035i	0.185794	−	0.0333869i
$875$	−7.19852	−	13.6959i	−0.243354	−	0.463007i
$876$	−7.29613	−	8.42019i	−0.246513	−	0.284492i
$877$	6.74075	+	30.9867i	0.227619	+	1.04635i	0.939100	+	0.343643i	$0.111661\pi$
$877$	6.74075	+	30.9867i	0.227619	+	1.04635i	−0.711482	+	0.702705i	$0.751975\pi$
$878$	4.09564	+	5.47114i	0.138221	+	0.184642i
$879$	7.71593	−	16.8955i	0.260252	−	0.569872i
$880$	−8.57824	+	5.44894i	−0.289172	+	0.183684i
$881$	−7.46357	+	25.4186i	−0.251454	+	0.856374i	0.732924	+	0.680310i	$0.238155\pi$
$881$	−7.46357	+	25.4186i	−0.251454	+	0.856374i	−0.984379	+	0.176064i	$0.943663\pi$
$882$	−4.96862	−	1.08086i	−0.167302	−	0.0363943i
$883$	−54.5170	−	20.3338i	−1.83464	−	0.684287i	−0.988478	−	0.151367i	$-0.951633\pi$
$883$	−54.5170	−	20.3338i	−1.83464	−	0.684287i	−0.846166	−	0.532920i	$-0.821095\pi$
$884$	0.369889	−	0.108609i	0.0124407	−	0.00365292i
$885$	−1.87086	+	1.00874i	−0.0628882	+	0.0339085i
$886$	17.7748	−	20.5132i	0.597156	−	0.689155i
$887$	−0.986052	−	0.538425i	−0.0331084	−	0.0180785i	0.462610	−	0.886562i	$-0.346913\pi$
$887$	−0.986052	−	0.538425i	−0.0331084	−	0.0180785i	−0.495718	+	0.868484i	$0.665095\pi$
$888$	−0.269191	+	0.721730i	−0.00903347	+	0.0242197i
$889$	−18.8898	+	12.1397i	−0.633544	+	0.407154i
$890$	−15.1601	−	11.4745i	−0.508169	−	0.384626i
$891$	4.49856	−	0.646796i	0.150708	−	0.0216685i
$892$	−5.15174	+	1.92150i	−0.172493	+	0.0643366i
$893$	4.42129	−	3.30974i	0.147953	−	0.110756i
$894$	−14.7055	−	9.45067i	−0.491827	−	0.316078i
$895$	−15.4148	+	33.2861i	−0.515260	+	1.11263i
$896$		−	1.38390i		−	0.0462329i
$897$	0.0608373	+	0.569611i	0.00203130	+	0.0190188i
$898$	−1.05637	+	1.05637i	−0.0352514	+	0.0352514i
$899$	−12.2125	+	10.5821i	−0.407308	+	0.352934i
$900$	4.81211	−	1.35778i	0.160404	−	0.0452593i
$901$	−2.27934	+	15.8532i	−0.0759359	+	0.528146i
$902$	−4.19165	−	11.2382i	−0.139567	−	0.374192i
$903$	5.37555	+	4.02409i	0.178887	+	0.133913i
$904$	6.78687	+	1.99281i	0.225728	+	0.0662797i
$905$	0.438533	+	0.285120i	0.0145773	+	0.00947772i
$906$	0.135458	+	0.296611i	0.00450029	+	0.00985425i
$907$	−24.5227	+	44.9100i	−0.814263	+	1.49121i	0.0558943	+	0.998437i	$0.482199\pi$
$907$	−24.5227	+	44.9100i	−0.814263	+	1.49121i	−0.870157	+	0.492774i	$0.835983\pi$
$908$	−21.8654	+	1.56384i	−0.725628	+	0.0518980i
$909$	2.44519	+	2.11877i	0.0811019	+	0.0702752i
$910$	0.0283209	−	0.368543i	0.000938830	−	0.0122171i
$911$	34.5795	−	15.7919i	1.14567	−	0.523209i	0.250138	−	0.968210i	$-0.419524\pi$
$911$	34.5795	−	15.7919i	1.14567	−	0.523209i	0.895530	+	0.445001i	$0.146797\pi$
$912$	0.247352	−	1.13706i	0.00819065	−	0.0376518i
$913$	5.83677	−	3.18712i	0.193169	−	0.105478i
$914$	5.79511	+	40.3059i	0.191685	+	1.33320i
$915$	20.2782	−	20.0646i	0.670376	−	0.663314i
$916$	3.86930	+	0.556321i	0.127845	+	0.0183814i
$917$	15.8341	−	3.44449i	0.522887	−	0.113747i
$918$	0.230239	−	3.21917i	0.00759904	−	0.106248i
$919$	−35.8078			−1.18119			−0.590596	−	0.806968i	$-0.701107\pi$
$919$	−35.8078			−1.18119			−0.590596	+	0.806968i	$0.701107\pi$
$920$	−10.5646	+	1.84076i	−0.348306	+	0.0606882i
$921$	−16.2708			−0.536141
$922$	−1.92077	+	26.8558i	−0.0632570	+	0.884449i
$923$	−0.921659	+	0.200495i	−0.0303368	+	0.00659936i
$924$	6.22556	+	0.895101i	0.204806	+	0.0294467i
$925$	−3.59419	−	1.38410i	−0.118176	−	0.0455088i
$926$	−2.86550	−	19.9300i	−0.0941662	−	0.654940i
$927$	11.0243	−	6.01972i	0.362086	−	0.197714i
$928$	−0.526328	+	2.41949i	−0.0172776	+	0.0794237i
$929$	−43.7604	+	19.9847i	−1.43573	+	0.655677i	−0.972997	−	0.230820i	$-0.925859\pi$
$929$	−43.7604	+	19.9847i	−1.43573	+	0.655677i	−0.462735	+	0.886496i	$0.653132\pi$
$930$	−11.0791	+	9.49787i	−0.363299	+	0.311447i
$931$	−4.47175	−	3.87479i	−0.146556	−	0.126991i
$932$	2.60967	−	0.186647i	0.0854825	−	0.00611383i
$933$	9.15492	−	16.7660i	0.299718	−	0.548893i
$934$	−0.607813	−	1.33092i	−0.0198882	−	0.0435492i
$935$	−32.0854	+	6.80202i	−1.04930	+	0.222450i
$936$	0.114609	+	0.0336523i	0.00374612	+	0.00109996i
$937$	14.8167	+	11.0916i	0.484039	+	0.362347i	0.813255	−	0.581908i	$-0.197693\pi$
$937$	14.8167	+	11.0916i	0.484039	+	0.362347i	−0.329216	+	0.944255i	$0.606784\pi$
$938$	−6.99256	−	18.7478i	−0.228315	−	0.612137i
$939$	−2.99878	+	20.8570i	−0.0978615	+	0.680642i
$940$	−8.52948	+	6.31490i	−0.278201	+	0.205969i
$941$	19.6085	−	16.9908i	0.639218	−	0.553886i	−0.273809	−	0.961784i	$-0.588284\pi$
$941$	19.6085	−	16.9908i	0.639218	−	0.553886i	0.913027	+	0.407898i	$0.133738\pi$
$942$	11.4161	−	11.4161i	0.371956	−	0.371956i
$943$	0.460585	−	12.6486i	0.0149987	−	0.411894i
$944$		−	0.950545i		−	0.0309376i
$945$	−2.80801	−	1.30039i	−0.0913444	−	0.0423016i
$946$	18.5515	+	11.9223i	0.603161	+	0.387628i
$947$	−15.4544	+	11.5690i	−0.502200	+	0.375942i	−0.820135	−	0.572170i	$-0.806102\pi$
$947$	−15.4544	+	11.5690i	−0.502200	+	0.375942i	0.317935	+	0.948113i	$0.397011\pi$
$948$	11.0189	−	4.10982i	0.357876	−	0.133481i
$949$	1.31728	−	0.189396i	0.0427607	−	0.00614806i
$950$	5.67189	+	1.29690i	0.184020	+	0.0420770i
$951$	−13.8030	+	8.87064i	−0.447593	+	0.287650i
$952$	1.56084	−	4.18478i	0.0505872	−	0.135630i
$953$	−5.34494	−	2.91856i	−0.173140	−	0.0945414i	0.390342	−	0.920670i	$-0.372357\pi$
$953$	−5.34494	−	2.91856i	−0.173140	−	0.0945414i	−0.563482	+	0.826128i	$0.690539\pi$
$954$	−3.24980	+	3.75047i	−0.105216	+	0.121426i
$955$	−12.4868	−	3.73839i	−0.404064	−	0.120971i
$956$	3.02728	−	0.888889i	0.0979091	−	0.0287487i
$957$	−10.5438	−	3.93264i	−0.340833	−	0.127124i
$958$	13.9573	+	3.03621i	0.450938	+	0.0980956i
$959$	1.66892	−	5.68383i	0.0538924	−	0.183540i
$960$	−0.486873	+	2.18242i	−0.0157138	+	0.0704373i
$961$	4.81520	−	10.5438i	0.155329	−	0.340123i
$962$	−0.0551396	−	0.0736579i	−0.00177777	−	0.00237483i
$963$	−4.29679	−	19.7520i	−0.138462	−	0.636500i
$964$	3.38623	+	3.90791i	0.109063	+	0.125865i
$965$	−1.87117	+	4.93681i	−0.0602352	+	0.158922i
$966$	5.70551	+	3.39062i	0.183572	+	0.109091i
$967$	27.8010	+	27.8010i	0.894021	+	0.894021i	0.994899	−	0.100877i	$-0.0321650\pi$
$967$	27.8010	+	27.8010i	0.894021	+	0.894021i	−0.100877	+	0.994899i	$0.532165\pi$
$968$	9.63083	+	0.688810i	0.309547	+	0.0221392i
$969$	2.03041	−	3.15938i	0.0652262	−	0.101494i
$970$	−8.69034	−	30.1870i	−0.279030	−	0.969245i
$971$	17.1325	+	7.82413i	0.549807	+	0.251088i	0.670894	−	0.741554i	$-0.265911\pi$
$971$	17.1325	+	7.82413i	0.549807	+	0.251088i	−0.121087	+	0.992642i	$0.538638\pi$
$972$	0.599278	−	0.800541i	0.0192218	−	0.0256774i
$973$	−13.3206	−	24.3948i	−0.427038	−	0.782061i
$974$	4.70687	+	7.32403i	0.150818	+	0.234677i
$975$	−0.174320	+	0.571232i	−0.00558272	+	0.0182941i
$976$	3.59425	+	12.2409i	0.115049	+	0.391821i
$977$	−3.33534	−	46.6341i	−0.106707	−	1.49196i	−0.715491	−	0.698622i	$-0.753797\pi$
$977$	−3.33534	−	46.6341i	−0.106707	−	1.49196i	0.608784	−	0.793336i	$-0.291658\pi$
$978$	0.118128	+	1.65165i	0.00377733	+	0.0528139i
$979$	10.8873	+	37.0787i	0.347959	+	1.18504i
$980$	8.55333	+	7.49116i	0.273226	+	0.239296i
$981$	−2.63162	−	4.09488i	−0.0840211	−	0.130739i
$982$	11.1841	+	20.4822i	0.356900	+	0.653614i
$983$	3.09567	−	4.13533i	0.0987365	−	0.131897i	−0.748452	−	0.663189i	$-0.769203\pi$
$983$	3.09567	−	4.13533i	0.0987365	−	0.131897i	0.847188	+	0.531292i	$0.178293\pi$
$984$	−2.40066	−	1.09634i	−0.0765302	−	0.0349502i
$985$	−3.07552	+	5.56216i	−0.0979941	+	0.177225i
$986$	−4.32041	+	6.72269i	−0.137590	+	0.214094i
$987$	6.55147	+	0.468571i	0.208536	+	0.0149148i
$988$	0.0982847	+	0.0982847i	0.00312685	+	0.00312685i
$989$	13.2581	+	19.1238i	0.421584	+	0.608102i
$990$	−9.50285	−	3.60181i	−0.302020	−	0.114473i
$991$	16.2153	+	18.7135i	0.515097	+	0.594454i	0.952396	−	0.304862i	$-0.0986104\pi$
$991$	16.2153	+	18.7135i	0.515097	+	0.594454i	−0.437299	+	0.899316i	$0.644065\pi$
$992$	−1.38724	−	6.37706i	−0.0440450	−	0.202472i
$993$	12.6438	+	16.8901i	0.401239	+	0.535992i
$994$	−4.53962	+	9.94039i	−0.143988	+	0.315290i
$995$	2.00129	+	3.15063i	0.0634453	+	0.0998817i
$996$	0.412246	−	1.40398i	0.0130625	−	0.0444869i
$997$	−15.3740	−	3.34442i	−0.486901	−	0.105919i	−0.0375881	−	0.999293i	$-0.511967\pi$
$997$	−15.3740	−	3.34442i	−0.486901	−	0.105919i	−0.449313	+	0.893375i	$0.648331\pi$
$998$	9.80560	+	3.65730i	0.310391	+	0.115770i
$999$	−0.739095	+	0.217018i	−0.0233839	+	0.00686614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.217.4	yes	240
5.3	odd	4	inner	690.2.w.a.493.12	yes	240
23.7	odd	22	inner	690.2.w.a.7.12	✓	240
115.53	even	44	inner	690.2.w.a.283.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.12	✓	240	23.7	odd	22	inner
690.2.w.a.217.4	yes	240	1.1	even	1	trivial
690.2.w.a.283.4	yes	240	115.53	even	44	inner
690.2.w.a.493.12	yes	240	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0118400 + 2.23604i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(1.21462 - 0.663233i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0118400 + 2.23604i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(1.21462 - 0.663233i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-2.22949 - 0.171327i) q^{10} +(3.43475 + 2.97623i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(-0.0572451 + 0.104837i) q^{13} +(0.574893 + 1.25884i) q^{14} +(-0.463734 - 2.18745i) q^{15} +(0.959493 + 0.281733i) q^{16} +(2.58366 + 1.93410i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-0.165605 + 1.15181i) q^{19} +(0.329941 - 2.21159i) q^{20} +(-1.04588 + 0.906262i) q^{21} +(-3.21368 + 3.21368i) q^{22} +(-4.43205 + 1.83219i) q^{23} +1.00000i q^{24} +(-4.99972 - 0.0529496i) q^{25} +(-0.100486 - 0.0645782i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(-1.29664 + 0.483624i) q^{28} +(2.45088 - 0.352383i) q^{29} +(2.21496 - 0.306502i) q^{30} +(-5.49019 + 3.52833i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-3.98890 - 2.17810i) q^{33} +(-2.11349 + 2.43910i) q^{34} +(1.46863 + 2.72379i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.721730 + 0.269191i) q^{37} +(-1.13706 - 0.247352i) q^{38} +(0.0336523 - 0.114609i) q^{39} +(2.18242 + 0.486873i) q^{40} +(-1.09634 + 2.40066i) q^{41} +(-0.829340 - 1.10787i) q^{42} +(-1.03140 - 4.74127i) q^{43} +(-2.97623 - 3.43475i) q^{44} +(0.918113 + 2.03889i) q^{45} +(-1.51134 - 4.55147i) q^{46} +(-3.35604 - 3.35604i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(-2.74906 + 4.27762i) q^{49} +(0.409491 - 4.98320i) q^{50} +(-2.93574 - 1.34071i) q^{51} +(0.0715823 - 0.0956227i) q^{52} +(2.37831 + 4.35555i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-6.69562 + 7.64499i) q^{55} +(-0.389890 - 1.32784i) q^{56} +(-0.0830141 - 1.16069i) q^{57} +(0.176641 + 2.46977i) q^{58} +(-0.267799 - 0.912041i) q^{59} +(0.147707 + 2.23118i) q^{60} +(6.89732 + 10.7324i) q^{61} +(-3.12768 - 5.72791i) q^{62} +(0.829340 - 1.10787i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-0.233741 - 0.129243i) q^{65} +(2.45712 - 3.82335i) q^{66} +(-14.4218 - 1.03147i) q^{67} +(-2.28211 - 2.28211i) q^{68} +(3.94130 - 2.73242i) q^{69} +(-2.82162 + 1.27058i) q^{70} +(5.17109 + 5.96775i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(-6.67685 - 8.91923i) q^{73} +(-0.319993 + 0.700687i) q^{74} +(4.89672 - 1.01103i) q^{75} +(0.327839 - 1.11652i) q^{76} +(6.14585 + 1.33695i) q^{77} +(0.111916 + 0.0417427i) q^{78} +(11.2840 - 3.31328i) q^{79} +(-0.641325 + 2.14213i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.31633 - 1.26481i) q^{82} +(0.511355 - 1.37100i) q^{83} +(1.16421 - 0.748193i) q^{84} +(-4.35532 + 5.75426i) q^{85} +(4.80277 - 0.690534i) q^{86} +(-2.31996 + 0.865301i) q^{87} +(3.63832 - 2.72361i) q^{88} +(7.15307 + 4.59700i) q^{89} +(-2.09919 + 0.770321i) q^{90} +0.165304i q^{91} +(4.64769 - 1.18280i) q^{92} +(4.61472 - 4.61472i) q^{93} +(3.58691 - 3.10807i) q^{94} +(-2.57353 - 0.383937i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.90938 + 13.1626i) q^{97} +(-4.07061 - 3.04722i) q^{98} +(4.36073 + 1.28042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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