LMFDB - Embedded newform 690.2.w.a.7.12

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			7.12
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.68213 + 1.47324i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.663233 + 1.21462i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.68213 + 1.47324i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.663233 + 1.21462i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.78294 + 1.34949i) q^{10} +(3.43475 - 2.97623i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-0.104837 + 0.0572451i) q^{13} +(-0.574893 + 1.25884i) q^{14} +(-1.79714 + 1.33053i) q^{15} +(0.959493 - 0.281733i) q^{16} +(1.93410 + 2.58366i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(0.165605 + 1.15181i) q^{19} +(1.87467 + 1.21885i) q^{20} +(-1.04588 - 0.906262i) q^{21} +(3.21368 - 3.21368i) q^{22} +(-1.83219 + 4.43205i) q^{23} +1.00000i q^{24} +(0.659124 + 4.95637i) q^{25} +(-0.100486 + 0.0645782i) q^{26} +(0.599278 - 0.800541i) q^{27} +(-0.483624 + 1.29664i) q^{28} +(-2.45088 - 0.352383i) q^{29} +(-1.69764 + 1.45534i) q^{30} +(-5.49019 - 3.52833i) q^{31} +(0.936950 - 0.349464i) q^{32} +(2.17810 + 3.98890i) q^{33} +(2.11349 + 2.43910i) q^{34} +(-2.90507 + 1.06605i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.269191 + 0.721730i) q^{37} +(0.247352 + 1.13706i) q^{38} +(-0.0336523 - 0.114609i) q^{39} +(1.95685 + 1.08201i) q^{40} +(-1.09634 - 2.40066i) q^{41} +(-1.10787 - 0.829340i) q^{42} +(4.74127 + 1.03140i) 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} +(0.0713392 + 0.997452i) q^{48} +(2.74906 + 4.27762i) q^{49} +(1.01103 + 4.89672i) q^{50} +(-2.93574 + 1.34071i) q^{51} +(-0.0956227 + 0.0715823i) q^{52} +(-4.35555 - 2.37831i) q^{53} +(0.540641 - 0.841254i) q^{54} +(10.1624 + 0.0538109i) q^{55} +(-0.389890 + 1.32784i) q^{56} +(-1.16069 - 0.0830141i) q^{57} +(-2.46977 - 0.176641i) q^{58} +(0.267799 - 0.912041i) q^{59} +(-1.58949 + 1.57274i) q^{60} +(6.89732 - 10.7324i) q^{61} +(-5.72791 - 3.12768i) q^{62} +(1.10787 - 0.829340i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-0.260685 - 0.0581558i) q^{65} +(2.45712 + 3.82335i) q^{66} +(-1.03147 - 14.4218i) 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} +(-0.977147 - 0.212565i) q^{72} +(8.91923 + 6.67685i) q^{73} +(0.319993 + 0.700687i) q^{74} +(-4.98320 - 0.409491i) q^{75} +(0.327839 + 1.11652i) q^{76} +(1.33695 + 6.14585i) q^{77} +(-0.0417427 - 0.111916i) q^{78} +(-11.2840 - 3.31328i) q^{79} +(2.02905 + 0.939653i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-1.26481 - 2.31633i) q^{82} +(1.37100 - 0.511355i) q^{83} +(-1.16421 - 0.748193i) q^{84} +(-0.552939 + 7.19545i) q^{85} +(4.80277 + 0.690534i) q^{86} +(0.865301 - 2.31996i) q^{87} +(2.72361 - 3.63832i) q^{88} +(-7.15307 + 4.59700i) q^{89} +(-1.06123 - 1.96820i) q^{90} -0.165304i q^{91} +(-1.18280 + 4.64769i) q^{92} +(4.61472 - 4.61472i) q^{93} +(-3.58691 - 3.10807i) q^{94} +(-1.41832 + 2.18147i) q^{95} +(0.142315 + 0.989821i) q^{96} +(13.1626 + 4.90938i) q^{97} +(3.04722 + 4.07061i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	1.68213	+	1.47324i	0.752271	+	0.658853i
$5$	1.68213	+	1.47324i	0.752271	+	0.658853i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−0.663233	+	1.21462i	−0.250678	+	0.459083i	−0.972470	−	0.233027i	$-0.925137\pi$
$7$	−0.663233	+	1.21462i	−0.250678	+	0.459083i	0.721792	+	0.692110i	$0.243319\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	1.78294	+	1.34949i	0.563816	+	0.426745i
$11$	3.43475	−	2.97623i	1.03562	−	0.897366i	0.0408110	−	0.999167i	$-0.487006\pi$
$11$	3.43475	−	2.97623i	1.03562	−	0.897366i	0.994805	+	0.101801i	$0.0324604\pi$
$12$	−0.0713392	+	0.997452i	−0.0205938	+	0.287940i
$13$	−0.104837	+	0.0572451i	−0.0290765	+	0.0158769i	−0.493721	−	0.869620i	$-0.664364\pi$
$13$	−0.104837	+	0.0572451i	−0.0290765	+	0.0158769i	0.464645	+	0.885497i	$0.346182\pi$
$14$	−0.574893	+	1.25884i	−0.153647	+	0.336439i
$15$	−1.79714	+	1.33053i	−0.464018	+	0.343541i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	1.93410	+	2.58366i	0.469089	+	0.626630i	0.971226	−	0.238158i	$-0.0765437\pi$
$17$	1.93410	+	2.58366i	0.469089	+	0.626630i	−0.502137	+	0.864788i	$0.667453\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	0.165605	+	1.15181i	0.0379924	+	0.264243i	0.999960	−	0.00891976i	$-0.00283929\pi$
$19$	0.165605	+	1.15181i	0.0379924	+	0.264243i	−0.961968	+	0.273163i	$0.911930\pi$
$20$	1.87467	+	1.21885i	0.419190	+	0.272544i
$21$	−1.04588	−	0.906262i	−0.228230	−	0.197763i
$22$	3.21368	−	3.21368i	0.685158	−	0.685158i
$23$	−1.83219	+	4.43205i	−0.382038	+	0.924146i
$23$	−1.83219	+	4.43205i	−0.382038	+	0.924146i
$24$			1.00000i			0.204124i
$25$	0.659124	+	4.95637i	0.131825	+	0.991273i
$26$	−0.100486	+	0.0645782i	−0.0197069	+	0.0126648i
$27$	0.599278	−	0.800541i	0.115331	−	0.154064i
$28$	−0.483624	+	1.29664i	−0.0913963	+	0.245043i
$29$	−2.45088	−	0.352383i	−0.455116	−	0.0654358i	−0.0890552	−	0.996027i	$-0.528385\pi$
$29$	−2.45088	−	0.352383i	−0.455116	−	0.0654358i	−0.366061	+	0.930591i	$0.619294\pi$
$30$	−1.69764	+	1.45534i	−0.309945	+	0.265708i
$31$	−5.49019	−	3.52833i	−0.986067	−	0.633707i	−0.0549739	−	0.998488i	$-0.517508\pi$
$31$	−5.49019	−	3.52833i	−0.986067	−	0.633707i	−0.931093	+	0.364781i	$0.881144\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	2.17810	+	3.98890i	0.379159	+	0.694378i
$34$	2.11349	+	2.43910i	0.362461	+	0.418302i
$35$	−2.90507	+	1.06605i	−0.491047	+	0.180195i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	0.269191	+	0.721730i	0.0442548	+	0.118652i	0.957197	−	0.289437i	$-0.0934681\pi$
$37$	0.269191	+	0.721730i	0.0442548	+	0.118652i	−0.912942	+	0.408089i	$0.866195\pi$
$38$	0.247352	+	1.13706i	0.0401258	+	0.184456i
$39$	−0.0336523	−	0.114609i	−0.00538868	−	0.0183521i
$40$	1.95685	+	1.08201i	0.309405	+	0.171081i
$41$	−1.09634	−	2.40066i	−0.171220	−	0.374920i	0.804496	−	0.593958i	$-0.202435\pi$
$41$	−1.09634	−	2.40066i	−0.171220	−	0.374920i	−0.975716	+	0.219038i	$0.929708\pi$
$42$	−1.10787	−	0.829340i	−0.170948	−	0.127970i
$43$	4.74127	+	1.03140i	0.723037	+	0.157287i	0.559000	−	0.829167i	$-0.311185\pi$
$43$	4.74127	+	1.03140i	0.723037	+	0.157287i	0.164036	+	0.986454i	$0.447549\pi$
$44$	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	$0.862511\pi$
$48$	0.0713392	+	0.997452i	0.0102969	+	0.143970i
$49$	2.74906	+	4.27762i	0.392723	+	0.611089i
$50$	1.01103	+	4.89672i	0.142981	+	0.692500i
$51$	−2.93574	+	1.34071i	−0.411086	+	0.187737i
$52$	−0.0956227	+	0.0715823i	−0.0132605	+	0.00992667i
$53$	−4.35555	−	2.37831i	−0.598281	−	0.326686i	0.151413	−	0.988471i	$-0.451618\pi$
$53$	−4.35555	−	2.37831i	−0.598281	−	0.326686i	−0.749694	+	0.661784i	$0.769799\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	10.1624	+	0.0538109i	1.37030	+	0.00725586i
$56$	−0.389890	+	1.32784i	−0.0521012	+	0.177440i
$57$	−1.16069	−	0.0830141i	−0.153737	−	0.0109955i
$58$	−2.46977	−	0.176641i	−0.324297	−	0.0231942i
$59$	0.267799	−	0.912041i	0.0348645	−	0.118738i	−0.940222	−	0.340562i	$-0.889383\pi$
$59$	0.267799	−	0.912041i	0.0348645	−	0.118738i	0.975087	+	0.221824i	$0.0712010\pi$
$60$	−1.58949	+	1.57274i	−0.205202	+	0.203040i
$61$	6.89732	−	10.7324i	0.883111	−	1.37415i	−0.0438696	−	0.999037i	$-0.513969\pi$
$61$	6.89732	−	10.7324i	0.883111	−	1.37415i	0.926980	−	0.375110i	$-0.122395\pi$
$62$	−5.72791	−	3.12768i	−0.727445	−	0.397215i
$63$	1.10787	−	0.829340i	0.139578	−	0.104487i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−0.260685	−	0.0581558i	−0.0323340	−	0.00721334i
$66$	2.45712	+	3.82335i	0.302450	+	0.470622i
$67$	−1.03147	−	14.4218i	−0.126014	−	1.76191i	−0.530800	−	0.847497i	$-0.678108\pi$
$67$	−1.03147	−	14.4218i	−0.126014	−	1.76191i	0.404786	−	0.914412i	$-0.367346\pi$
$68$	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	−0.360802	−	0.932642i	$-0.617497\pi$
$71$	5.17109	−	5.96775i	0.613695	−	0.708242i	0.974497	+	0.224401i	$0.0720424\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	8.91923	+	6.67685i	1.04392	+	0.781467i	0.976339	−	0.216247i	$-0.0693818\pi$
$73$	8.91923	+	6.67685i	1.04392	+	0.781467i	0.0675786	+	0.997714i	$0.478473\pi$
$74$	0.319993	+	0.700687i	0.0371984	+	0.0814532i
$75$	−4.98320	−	0.409491i	−0.575411	−	0.0472839i
$76$	0.327839	+	1.11652i	0.0376057	+	0.128073i
$77$	1.33695	+	6.14585i	0.152359	+	0.700384i
$78$	−0.0417427	−	0.111916i	−0.00472642	−	0.0126720i
$79$	−11.2840	−	3.31328i	−1.26955	−	0.372773i	−0.423507	−	0.905893i	$-0.639201\pi$
$79$	−11.2840	−	3.31328i	−1.26955	−	0.372773i	−0.846040	+	0.533120i	$0.821019\pi$
$80$	2.02905	+	0.939653i	0.226855	+	0.105056i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	−1.26481	−	2.31633i	−0.139675	−	0.255796i
$83$	1.37100	−	0.511355i	0.150486	−	0.0561285i	−0.273092	−	0.961988i	$-0.588046\pi$
$83$	1.37100	−	0.511355i	0.150486	−	0.0561285i	0.423579	+	0.905859i	$0.360774\pi$
$84$	−1.16421	−	0.748193i	−0.127026	−	0.0816345i
$85$	−0.552939	+	7.19545i	−0.0599747	+	0.780456i
$86$	4.80277	+	0.690534i	0.517896	+	0.0744621i
$87$	0.865301	−	2.31996i	0.0927700	−	0.248726i
$88$	2.72361	−	3.63832i	0.290338	−	0.387846i
$89$	−7.15307	+	4.59700i	−0.758224	+	0.487281i	−0.861742	−	0.507347i	$-0.830626\pi$
$89$	−7.15307	+	4.59700i	−0.758224	+	0.487281i	0.103518	+	0.994628i	$0.466990\pi$
$90$	−1.06123	−	1.96820i	−0.111863	−	0.207466i
$91$		−	0.165304i		−	0.0173285i
$92$	−1.18280	+	4.64769i	−0.123315	+	0.484555i
$93$	4.61472	−	4.61472i	0.478524	−	0.478524i
$94$	−3.58691	−	3.10807i	−0.369961	−	0.320573i
$95$	−1.41832	+	2.18147i	−0.145517	+	0.223814i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	13.1626	+	4.90938i	1.33645	+	0.498472i	0.913190	−	0.407534i	$-0.133611\pi$
$97$	13.1626	+	4.90938i	1.33645	+	0.498472i	0.423265	+	0.906006i	$0.360884\pi$
$98$	3.04722	+	4.07061i	0.307816	+	0.411194i
$99$	−4.36073	+	1.28042i	−0.438270	+	0.128688i
$100$	1.35778	+	4.81211i	0.135778	+	0.481211i
$101$	1.34406	−	2.94307i	0.133738	−	0.292846i	−0.830901	−	0.556421i	$-0.812174\pi$
$101$	1.34406	−	2.94307i	0.133738	−	0.292846i	0.964639	+	0.263574i	$0.0849015\pi$
$102$	−2.83261	+	1.54672i	−0.280471	+	0.153149i
$103$	0.896073	−	12.5287i	0.0882927	−	1.23449i	−0.739382	−	0.673286i	$-0.764882\pi$
$103$	0.896073	−	12.5287i	0.0882927	−	1.23449i	0.827675	−	0.561208i	$-0.189663\pi$
$104$	−0.0902725	+	0.0782215i	−0.00885194	+	0.00767025i
$105$	−0.424168	−	3.06529i	−0.0413945	−	0.299141i
$106$	−4.51412	−	2.06153i	−0.438450	−	0.200234i
$107$	−19.7520	+	4.29679i	−1.90950	+	0.415386i	−1.00000		0.000316212i	$-0.999899\pi$
$107$	−19.7520	+	4.29679i	−1.90950	+	0.415386i	−0.909501	+	0.415703i	$0.863536\pi$
$108$	0.479249	−	0.877679i	0.0461158	−	0.0844547i
$109$	0.692730	−	4.81805i	0.0663515	−	0.461485i	−0.929375	−	0.369137i	$-0.879653\pi$
$109$	0.692730	−	4.81805i	0.0663515	−	0.461485i	0.995727	−	0.0923486i	$-0.0294374\pi$
$110$	10.1403	−	0.671303i	0.966843	−	0.0640062i
$111$	−0.762457	+	0.109625i	−0.0723692	+	0.0104051i
$112$	−0.294169	+	1.35227i	−0.0277964	+	0.127778i
$113$	−7.05537	+	0.504610i	−0.663714	+	0.0474697i	−0.399132	−	0.916894i	$-0.630688\pi$
$113$	−7.05537	+	0.504610i	−0.663714	+	0.0474697i	−0.264582	+	0.964363i	$0.585234\pi$
$114$	−1.16365			−0.108986
$115$	−9.61146	+	4.75603i	−0.896274	+	0.443502i
$116$	−2.47608			−0.229898
$117$	0.119143	−	0.00852129i	0.0110148	−	0.000787794i
$118$	0.202053	−	0.928822i	0.0186005	−	0.0855050i
$119$	−4.42093	+	0.635633i	−0.405266	+	0.0582684i
$120$	−1.47324	+	1.68213i	−0.134488	+	0.153557i
$121$	1.37411	−	9.55715i	0.124919	−	0.868832i
$122$	6.11410	−	11.1971i	0.553545	−	1.01374i
$123$	2.57884	−	0.560993i	0.232526	−	0.0505830i
$124$	−5.93644	−	2.71108i	−0.533108	−	0.243462i
$125$	−6.19319	+	9.30830i	−0.553935	+	0.832560i
$126$	1.04588	−	0.906262i	0.0931746	−	0.0807362i
$127$	1.15751	−	16.1841i	0.102712	−	1.43610i	−0.640967	−	0.767568i	$-0.721466\pi$
$127$	1.15751	−	16.1841i	0.102712	−	1.43610i	0.743679	−	0.668537i	$-0.233079\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	−2.01566	+	4.41367i	−0.177469	+	0.388602i
$130$	−0.264169	−	0.0394106i	−0.0231692	−	0.00345654i
$131$	11.2349	−	3.29887i	0.981599	−	0.288223i	0.248715	−	0.968577i	$-0.419992\pi$
$131$	11.2349	−	3.29887i	0.981599	−	0.288223i	0.732884	+	0.680353i	$0.238174\pi$
$132$	2.72361	+	3.63832i	0.237060	+	0.316675i
$133$	−1.50885	−	0.562770i	−0.130833	−	0.0487984i
$134$	−2.05769	−	14.3115i	−0.177757	−	1.23633i
$135$	2.18745	−	0.463734i	0.188266	−	0.0399119i
$136$	2.43910	+	2.11349i	0.209151	+	0.181230i
$137$	−3.02677	+	3.02677i	−0.258595	+	0.258595i	−0.824482	−	0.565888i	$-0.808534\pi$
$137$	−3.02677	+	3.02677i	−0.258595	+	0.258595i	0.565888	+	0.824482i	$0.308534\pi$
$138$	−4.12619	−	2.44429i	−0.351245	−	0.208072i
$139$		−	20.0843i		−	1.70353i	−0.523926	−	0.851764i	$-0.675533\pi$
$139$		−	20.0843i		−	1.70353i	0.523926	−	0.851764i	$-0.324467\pi$
$140$	−2.72379	+	1.46863i	−0.230202	+	0.124122i
$141$	3.99272	−	2.56597i	0.336248	−	0.216093i
$142$	4.73218	−	6.32145i	0.397115	−	0.530484i
$143$	−0.189713	+	0.508640i	−0.0158646	+	0.0425346i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	−3.60355	−	4.20348i	−0.299258	−	0.349080i
$146$	9.37283	+	6.02355i	0.775701	+	0.498513i
$147$	−4.76422	+	1.77696i	−0.392946	+	0.146561i
$148$	0.369164	+	0.676074i	0.0303451	+	0.0555729i
$149$	−11.4473	−	13.2109i	−0.937799	−	1.08228i	−0.996466	−	0.0840000i	$-0.973230\pi$
$149$	−11.4473	−	13.2109i	−0.937799	−	1.08228i	0.0586669	−	0.998278i	$-0.481315\pi$
$150$	−4.99972	−	0.0529496i	−0.408225	−	0.00432331i
$151$	−0.312870	−	0.0918669i	−0.0254610	−	0.00747602i	0.268977	−	0.963147i	$-0.413314\pi$
$151$	−0.312870	−	0.0918669i	−0.0254610	−	0.00747602i	−0.294438	+	0.955671i	$0.595133\pi$
$152$	0.406655	+	1.09028i	0.0329841	+	0.0884338i
$153$	−0.686031	−	3.15364i	−0.0554624	−	0.254956i
$154$	1.77198	+	6.03481i	0.142790	+	0.486299i
$155$	−4.03713	−	14.0235i	−0.324270	−	1.12639i
$156$	−0.0496203	−	0.108653i	−0.00397281	−	0.00869923i
$157$	12.9246	+	9.67521i	1.03149	+	0.772166i	0.974084	−	0.226185i	$-0.0726255\pi$
$157$	12.9246	+	9.67521i	1.03149	+	0.772166i	0.0574081	+	0.998351i	$0.481716\pi$
$158$	−11.4916	−	2.49984i	−0.914222	−	0.198877i
$159$	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
$163$	0.118128	+	1.65165i	0.00925252	+	0.129367i	0.999979	−	0.00650542i	$-0.00207075\pi$
$163$	0.118128	+	1.65165i	0.00925252	+	0.129367i	−0.990726	+	0.135873i	$0.956616\pi$
$164$	−1.42683	−	2.22020i	−0.111417	−	0.173368i
$165$	−2.21275	+	9.91871i	−0.172263	+	0.772171i
$166$	1.33102	−	0.607858i	0.103307	−	0.0471789i
$167$	1.87712	−	1.40520i	0.145256	−	0.108737i	−0.524178	−	0.851609i	$-0.675627\pi$
$167$	1.87712	−	1.40520i	0.145256	−	0.108737i	0.669434	+	0.742871i	$0.266537\pi$
$168$	−1.21462	−	0.663233i	−0.0937100	−	0.0511695i
$169$	−7.02062	+	10.9243i	−0.540047	+	0.840330i
$170$	−0.0382125	+	7.21657i	−0.00293076	+	0.553485i
$171$	0.327839	−	1.11652i	0.0250705	−	0.0853822i
$172$	4.83979	+	0.346149i	0.369031	+	0.0263936i
$173$	2.63836	+	0.188699i	0.200591	+	0.0143465i	0.171273	−	0.985224i	$-0.445212\pi$
$173$	2.63836	+	0.188699i	0.200591	+	0.0143465i	0.0293178	+	0.999570i	$0.490667\pi$
$174$	0.697592	−	2.37578i	0.0528843	−	0.180107i
$175$	−6.45725	−	2.48664i	−0.488122	−	0.187972i
$176$	2.45712	−	3.82335i	0.185212	−	0.288196i
$177$	0.834273	+	0.455548i	0.0627078	+	0.0342411i
$178$	−6.80690	+	5.09558i	−0.510199	+	0.381930i
$179$	−14.9223	+	6.81479i	−1.11535	+	0.509361i	−0.885861	−	0.463951i	$-0.846431\pi$
$179$	−14.9223	+	6.81479i	−1.11535	+	0.509361i	−0.229484	+	0.973312i	$0.573704\pi$
$180$	−1.19893	−	1.88747i	−0.0893631	−	0.140684i
$181$	0.126469	+	0.196790i	0.00940040	+	0.0146273i	0.845922	−	0.533307i	$-0.179051\pi$
$181$	0.126469	+	0.196790i	0.00940040	+	0.0146273i	−0.836522	+	0.547934i	$0.815414\pi$
$182$	−0.0117926	−	0.164882i	−0.000874127	−	0.0122219i
$183$	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
$187$	14.3327	+	3.11789i	1.04811	+	0.228003i
$188$	−3.79949	−	2.84427i	−0.277107	−	0.207439i
$189$	0.574893	+	1.25884i	0.0418173	+	0.0915671i
$190$	−1.25908	+	2.27709i	−0.0913436	+	0.165198i
$191$	−1.64227	−	5.59305i	−0.118830	−	0.404699i	0.878498	−	0.477746i	$-0.158546\pi$
$191$	−1.64227	−	5.59305i	−0.118830	−	0.404699i	−0.997329	+	0.0730469i	$0.976728\pi$
$192$	0.212565	+	0.977147i	0.0153406	+	0.0705195i
$193$	−0.825112	−	2.21221i	−0.0593928	−	0.159238i	0.903864	−	0.427819i	$-0.140718\pi$
$193$	−0.825112	−	2.21221i	−0.0593928	−	0.159238i	−0.963257	+	0.268581i	$0.913445\pi$
$194$	13.4792	+	3.95786i	0.967754	+	0.284158i
$195$	0.112239	−	0.242365i	0.00803762	−	0.0173561i
$196$	3.32985	+	3.84285i	0.237846	+	0.274489i
$197$	1.36222	+	2.49472i	0.0970543	+	0.177742i	0.921695	−	0.387915i	$-0.126805\pi$
$197$	1.36222	+	2.49472i	0.0970543	+	0.177742i	−0.824641	+	0.565657i	$0.808623\pi$
$198$	−4.25827	+	1.58825i	−0.302622	+	0.112872i
$199$	−1.40425	−	0.902454i	−0.0995444	−	0.0639733i	0.489922	−	0.871767i	$-0.337025\pi$
$199$	−1.40425	−	0.902454i	−0.0995444	−	0.0639733i	−0.589466	+	0.807793i	$0.700662\pi$
$200$	1.69761	+	4.70299i	0.120039	+	0.332552i
$201$	14.3115	+	2.05769i	1.00946	+	0.145138i
$202$	1.13067	−	3.03146i	0.0795540	−	0.213292i
$203$	2.05351	−	2.74317i	0.144128	−	0.192533i
$204$	−2.71505	+	1.74486i	−0.190092	+	0.122165i
$205$	1.69256	−	5.65340i	0.118213	−	0.394851i
$206$		−	12.5607i		−	0.875149i
$207$	3.50776	−	3.27042i	0.243806	−	0.227310i
$208$	−0.0844622	+	0.0844622i	−0.00585640	+	0.00585640i
$209$	3.99686	+	3.46330i	0.276468	+	0.239561i
$210$	−0.641762	−	3.02722i	−0.0442858	−	0.208898i
$211$	3.71676	+	25.8506i	0.255872	+	1.77963i	0.561497	+	0.827479i	$0.310226\pi$
$211$	3.71676	+	25.8506i	0.255872	+	1.77963i	−0.305625	+	0.952152i	$0.598865\pi$
$212$	−4.64969	−	1.73424i	−0.319342	−	0.119108i
$213$	4.73218	+	6.32145i	0.324243	+	0.433138i
$214$	−19.3952	+	5.69494i	−1.32583	+	0.389298i
$215$	6.45593	+	8.71998i	0.440291	+	0.594697i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	7.92686	−	4.32839i	0.538110	−	0.293830i
$218$	0.347250	−	4.85519i	0.0235187	−	0.328835i
$219$	−8.42019	+	7.29613i	−0.568983	+	0.493027i
$220$	10.0666	−	1.39300i	0.678691	−	0.0939158i
$221$	−0.350667	−	0.160144i	−0.0235884	−	0.0107725i
$222$	−0.752694	+	0.163738i	−0.0505175	+	0.0109894i
$223$	2.63511	−	4.82585i	0.176460	−	0.323163i	−0.774447	−	0.632639i	$-0.781972\pi$
$223$	2.63511	−	4.82585i	0.176460	−	0.323163i	0.950907	+	0.309476i	$0.100154\pi$
$224$	−0.196950	+	1.36981i	−0.0131592	+	0.0915246i
$225$	1.45939	−	4.78228i	0.0972926	−	0.318819i
$226$	−7.00140	+	1.00665i	−0.465726	+	0.0669613i
$227$	−4.65969	+	21.4203i	−0.309275	+	1.42171i	0.515809	+	0.856703i	$0.327491\pi$
$227$	−4.65969	+	21.4203i	−0.309275	+	1.42171i	−0.825084	+	0.565010i	$0.808872\pi$
$228$	−1.16069	+	0.0830141i	−0.0768685	+	0.00549774i
$229$	3.90909			0.258320			0.129160	−	0.991624i	$-0.458772\pi$
$229$	3.90909			0.258320			0.129160	+	0.991624i	$0.458772\pi$
$230$	−9.24768	+	5.42958i	−0.609774	+	0.358016i
$231$	−6.28958			−0.413824
$232$	−2.46977	+	0.176641i	−0.162148	+	0.0115971i
$233$	−0.556142	+	2.55654i	−0.0364341	+	0.167485i	−0.991769	−	0.128041i	$-0.959131\pi$
$233$	−0.556142	+	2.55654i	−0.0364341	+	0.167485i	0.955335	+	0.295526i	$0.0954948\pi$
$234$	0.118232	−	0.0169992i	0.00772905	−	0.00111127i
$235$	−0.701041	−	10.5896i	−0.0457309	−	0.690786i
$236$	0.135277	−	0.940870i	0.00880576	−	0.0612454i
$237$	5.63614	−	10.3218i	0.366107	−	0.670474i
$238$	−4.36432	+	0.949399i	−0.282897	+	0.0615404i
$239$	2.86996	+	1.31067i	0.185642	+	0.0847800i	0.506068	−	0.862494i	$-0.331099\pi$
$239$	2.86996	+	1.31067i	0.185642	+	0.0847800i	−0.320425	+	0.947274i	$0.603826\pi$
$240$	−1.34949	+	1.78294i	−0.0871089	+	0.115089i
$241$	−3.90791	+	3.38623i	−0.251731	+	0.218126i	−0.771580	−	0.636132i	$-0.780533\pi$
$241$	−3.90791	+	3.38623i	−0.251731	+	0.218126i	0.519850	+	0.854258i	$0.325988\pi$
$242$	0.688810	−	9.63083i	0.0442784	−	0.619093i
$243$	−0.877679	+	0.479249i	−0.0563031	+	0.0307438i
$244$	5.29973	−	11.6048i	0.339280	−	0.742920i
$245$	−1.67769	+	11.2455i	−0.107184	+	0.718452i
$246$	2.53225	−	0.743536i	0.161450	−	0.0474061i
$247$	−0.0832970	−	0.111272i	−0.00530006	−	0.00708005i
$248$	−6.11472	−	2.28067i	−0.388285	−	0.144823i
$249$	0.208243	+	1.44836i	0.0131969	+	0.0917861i
$250$	−5.51336	+	9.72640i	−0.348696	+	0.615152i
$251$	−22.3965	−	19.4067i	−1.41366	−	1.22494i	−0.938610	−	0.344981i	$-0.887885\pi$
$251$	−22.3965	−	19.4067i	−1.41366	−	1.22494i	−0.475048	−	0.879960i	$-0.657569\pi$
$252$	0.978565	−	0.978565i	0.0616438	−	0.0616438i
$253$	6.89767	+	20.6760i	0.433653	+	1.29989i
$254$		−	16.2254i		−	1.01807i
$255$	−6.91348	−	2.06981i	−0.432939	−	0.129616i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−5.38848	+	7.19817i	−0.336124	+	0.449009i	−0.936479	−	0.350725i	$-0.885935\pi$
$257$	−5.38848	+	7.19817i	−0.336124	+	0.449009i	0.600354	+	0.799734i	$0.295026\pi$
$258$	−1.69565	+	4.54622i	−0.105567	+	0.283036i
$259$	−1.05516	−	0.151710i	−0.0655647	−	0.00942678i
$260$	−0.266308	−	0.0204646i	−0.0165157	−	0.00126916i
$261$	2.08301	+	1.33867i	0.128935	+	0.0828615i
$262$	10.9709	−	4.09195i	0.677787	−	0.252802i
$263$	3.65121	+	6.68668i	0.225143	+	0.412319i	0.965694	−	0.259681i	$-0.0836174\pi$
$263$	3.65121	+	6.68668i	0.225143	+	0.412319i	−0.740551	+	0.672000i	$0.765436\pi$
$264$	2.97623	+	3.43475i	0.183174	+	0.211394i
$265$	−3.82278	−	10.4174i	−0.234832	−	0.639936i
$266$	−1.54515	−	0.453697i	−0.0947391	−	0.0278179i
$267$	−2.97145	−	7.96676i	−0.181850	−	0.487558i
$268$	−3.07341	−	14.1283i	−0.187739	−	0.863021i
$269$	5.69461	+	19.3941i	0.347206	+	1.18248i	0.929291	+	0.369348i	$0.120419\pi$
$269$	5.69461	+	19.3941i	0.347206	+	1.18248i	−0.582085	+	0.813128i	$0.697763\pi$
$270$	2.14880	−	0.618604i	0.130772	−	0.0376470i
$271$	7.17312	+	15.7069i	0.435736	+	0.954129i	0.992361	+	0.123365i	$0.0393687\pi$
$271$	7.17312	+	15.7069i	0.435736	+	0.954129i	−0.556625	+	0.830764i	$0.687904\pi$
$272$	2.58366	+	1.93410i	0.156657	+	0.117272i
$273$	0.161526	+	0.0351378i	0.00977599	+	0.00212664i
$274$	−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	$0.846137\pi$
$278$	−1.43280	−	20.0331i	−0.0859335	−	1.20151i
$279$	3.52833	+	5.49019i	0.211236	+	0.328689i
$280$	−2.61208	+	1.65920i	−0.156101	+	0.0991563i
$281$	−5.34860	+	2.44263i	−0.319071	+	0.145715i	−0.568512	−	0.822675i	$-0.692481\pi$
$281$	−5.34860	+	2.44263i	−0.319071	+	0.145715i	0.249441	+	0.968390i	$0.419753\pi$
$282$	3.79949	−	2.84427i	0.226257	−	0.169374i
$283$	19.6982	+	10.7560i	1.17094	+	0.639379i	0.942509	−	0.334182i	$-0.108460\pi$
$283$	19.6982	+	10.7560i	1.17094	+	0.639379i	0.228427	+	0.973561i	$0.426642\pi$
$284$	4.26915	−	6.64293i	0.253328	−	0.394185i
$285$	−1.83013	−	1.84961i	−0.108408	−	0.109562i
$286$	−0.152944	+	0.520878i	−0.00904375	+	0.0308002i
$287$	3.64302	+	0.260554i	0.215041	+	0.0153800i
$288$	−0.997452	−	0.0713392i	−0.0587754	−	0.00420370i
$289$	1.85491	−	6.31725i	0.109112	−	0.371603i
$290$	−3.89424	−	3.93570i	−0.228678	−	0.231112i
$291$	−7.59509	+	11.8182i	−0.445232	+	0.692794i
$292$	9.77866	+	5.33955i	0.572253	+	0.312474i
$293$	−14.8693	+	11.1310i	−0.868672	+	0.650280i	−0.937742	−	0.347332i	$-0.887088\pi$
$293$	−14.8693	+	11.1310i	−0.868672	+	0.650280i	0.0690704	+	0.997612i	$0.477997\pi$
$294$	−4.62532	+	2.11231i	−0.269754	+	0.123192i
$295$	1.79413	−	1.13964i	0.104458	−	0.0663523i
$296$	0.416454	+	0.648015i	0.0242059	+	0.0376651i
$297$	−0.324224	−	4.53324i	−0.0188134	−	0.263046i
$298$	−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
$302$	−0.318627	−	0.0693130i	−0.0183349	−	0.00398851i
$303$	2.59011	+	1.93893i	0.148798	+	0.111389i
$304$	0.483399	+	1.05850i	0.0277248	+	0.0607089i
$305$	27.4136	−	7.89194i	1.56970	−	0.451891i
$306$	−0.909261	−	3.09666i	−0.0519790	−	0.177024i
$307$	3.45861	+	15.8990i	0.197393	+	0.907401i	0.964128	+	0.265437i	$0.0855164\pi$
$307$	3.45861	+	15.8990i	0.197393	+	0.907401i	−0.766735	+	0.641964i	$0.778120\pi$
$308$	2.19798	+	5.89302i	0.125242	+	0.335786i
$309$	12.0519	+	3.53877i	0.685611	+	0.201314i
$310$	−5.02727	−	13.6997i	−0.285530	−	0.778093i
$311$	−12.5096	−	14.4368i	−0.709352	−	0.818636i	0.280632	−	0.959815i	$-0.409456\pi$
$311$	−12.5096	−	14.4368i	−0.709352	−	0.818636i	−0.989984	+	0.141179i	$0.954911\pi$
$312$	−0.0572451	−	0.104837i	−0.00324087	−	0.00593521i
$313$	19.7429	−	7.36372i	1.11593	−	0.416222i	0.277227	−	0.960804i	$-0.410585\pi$
$313$	19.7429	−	7.36372i	1.11593	−	0.416222i	0.838707	+	0.544582i	$0.183312\pi$
$314$	13.5819	+	8.72853i	0.766468	+	0.492579i
$315$	3.08540	+	0.237099i	0.173842	+	0.0133590i
$316$	−11.6407	−	1.67367i	−0.654838	−	0.0941515i
$317$	−5.73389	+	15.3731i	−0.322047	+	0.863442i	0.670536	+	0.741877i	$0.266064\pi$
$317$	−5.73389	+	15.3731i	−0.322047	+	0.863442i	−0.992583	+	0.121565i	$0.961209\pi$
$318$	2.97396	−	3.97275i	0.166772	−	0.222781i
$319$	−9.46691	+	6.08402i	−0.530045	+	0.340640i
$320$	2.14213	+	0.641325i	0.119748	+	0.0358511i
$321$		−	20.2140i		−	1.12823i
$322$	−4.52593	−	4.85439i	−0.252220	−	0.270525i
$323$	−2.65559	+	2.65559i	−0.147761	+	0.147761i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−0.352828	−	0.481877i	−0.0195714	−	0.0267297i
$326$	0.235655	+	1.63901i	0.0130517	+	0.0907766i
$327$	4.56069	+	1.70105i	0.252207	+	0.0940682i
$328$	−1.58159	−	2.11275i	−0.0873285	−	0.116657i
$329$	6.30215	−	1.85048i	0.347449	−	0.102020i
$330$	−1.49952	+	10.0513i	−0.0825460	+	0.553306i
$331$	−8.76458	+	19.1918i	−0.481745	+	1.05487i	0.500235	+	0.865890i	$0.333247\pi$
$331$	−8.76458	+	19.1918i	−0.481745	+	1.05487i	−0.981980	+	0.188985i	$0.939480\pi$
$332$	1.28427	−	0.701263i	0.0704833	−	0.0384868i
$333$	0.0549524	−	0.768335i	0.00301137	−	0.0421045i
$334$	1.77210	−	1.53553i	0.0969647	−	0.0840204i
$335$	19.5118	−	25.7790i	1.06604	−	1.40846i
$336$	−1.25884	−	0.574893i	−0.0686753	−	0.0313630i
$337$	−21.9554	+	4.77610i	−1.19599	+	0.260171i	−0.766105	−	0.642715i	$-0.777808\pi$
$337$	−21.9554	+	4.77610i	−1.19599	+	0.260171i	−0.429880	+	0.902886i	$0.641444\pi$
$338$	−6.22340	+	11.3973i	−0.338508	+	0.619932i
$339$	1.00665	−	7.00140i	0.0546737	−	0.380264i
$340$	0.476709	+	7.20091i	0.0258532	+	0.390524i
$341$	−29.3585	+	4.22112i	−1.58985	+	0.228587i
$342$	0.247352	−	1.13706i	0.0133753	−	0.0614852i
$343$	−16.6816	+	1.19309i	−0.900720	+	0.0644208i
$344$	4.85215			0.261611
$345$	−2.60427	−	10.4028i	−0.140209	−	0.560067i
$346$	2.64510			0.142202
$347$	23.4361	−	1.67618i	1.25811	−	0.0899822i	0.573694	−	0.819070i	$-0.305510\pi$
$347$	23.4361	−	1.67618i	1.25811	−	0.0899822i	0.684421	+	0.729087i	$0.260055\pi$
$348$	0.526328	−	2.41949i	0.0282142	−	0.129698i
$349$	5.35172	−	0.769461i	0.286471	−	0.0411883i	0.00241856	−	0.999997i	$-0.499230\pi$
$349$	5.35172	−	0.769461i	0.286471	−	0.0411883i	0.284052	+	0.958809i	$0.408321\pi$
$350$	−6.61820	−	2.01965i	−0.353757	−	0.107955i
$351$	−0.0169992	+	0.118232i	−0.000907348	+	0.00631075i
$352$	2.17810	−	3.98890i	0.116093	−	0.212609i
$353$	24.3728	−	5.30199i	1.29724	−	0.282196i	0.489636	−	0.871927i	$-0.337130\pi$
$353$	24.3728	−	5.30199i	1.29724	−	0.282196i	0.807600	+	0.589731i	$0.200766\pi$
$354$	0.864646	+	0.394871i	0.0459554	+	0.0209871i
$355$	17.4904	−	2.42028i	0.928293	−	0.128455i
$356$	−6.42604	+	5.56820i	−0.340580	+	0.295114i
$357$	0.318628	−	4.45501i	0.0168636	−	0.235784i
$358$	−14.3981	+	7.86197i	−0.760964	+	0.415518i
$359$	−0.168571	+	0.369119i	−0.00889685	+	0.0194814i	−0.914028	−	0.405651i	$-0.867045\pi$
$359$	−0.168571	+	0.369119i	−0.00889685	+	0.0194814i	0.905131	+	0.425132i	$0.139772\pi$
$360$	−1.33053	−	1.79714i	−0.0701250	−	0.0947173i
$361$	16.9311	−	4.97143i	0.891112	−	0.261654i
$362$	0.140186	+	0.187267i	0.00736802	+	0.00984252i
$363$	9.04665	+	3.37423i	0.474826	+	0.177101i
$364$	−0.0235251	−	0.163621i	−0.00123305	−	0.00857607i
$365$	5.16670	+	24.3715i	0.270437	+	1.27566i
$366$	9.64160	+	8.35450i	0.503975	+	0.436696i
$367$	7.95998	−	7.95998i	0.415508	−	0.415508i	−0.468144	−	0.883652i	$-0.655077\pi$
$367$	7.95998	−	7.95998i	0.415508	−	0.415508i	0.883652	+	0.468144i	$0.155077\pi$
$368$	−0.509322	+	4.76871i	−0.0265503	+	0.248586i
$369$			2.63915i			0.137389i
$370$	−0.494011	+	1.65007i	−0.0256824	+	0.0857832i
$371$	5.77749	−	3.71297i	0.299952	−	0.192768i
$372$	3.91101	−	5.22449i	0.202776	−	0.270877i
$373$	4.30996	−	11.5554i	0.223161	−	0.598318i	−0.776326	−	0.630331i	$-0.782919\pi$
$373$	4.30996	−	11.5554i	0.223161	−	0.598318i	0.999487	+	0.0320129i	$0.0101918\pi$
$374$	14.5186	+	2.08746i	0.750740	+	0.107940i
$375$	−7.77912	−	8.03027i	−0.401712	−	0.414682i
$376$	−3.99272	−	2.56597i	−0.205909	−	0.132330i
$377$	0.277114	−	0.103358i	0.0142721	−	0.00532321i
$378$	0.663233	+	1.21462i	0.0341130	+	0.0624733i
$379$	−17.4589	−	20.1486i	−0.896803	−	1.03497i	−0.999191	−	0.0402217i	$-0.987194\pi$
$379$	−17.4589	−	20.1486i	−0.896803	−	1.03497i	0.102387	−	0.994745i	$-0.467352\pi$
$380$	−1.09343	+	2.36111i	−0.0560918	+	0.121123i
$381$	15.5682	+	4.57123i	0.797582	+	0.234191i
$382$	−2.03709	−	5.46164i	−0.104226	−	0.279442i
$383$	−0.685677	−	3.15201i	−0.0350365	−	0.161060i	0.956305	−	0.292372i	$-0.0944446\pi$
$383$	−0.685677	−	3.15201i	−0.0350365	−	0.161060i	−0.991341	+	0.131312i	$0.958081\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	−6.80539	+	12.3078i	−0.346835	+	0.627261i
$386$	−0.980827	−	2.14771i	−0.0499228	−	0.109316i
$387$	−3.88435	−	2.90779i	−0.197453	−	0.147811i
$388$	13.7273	+	2.98618i	0.696896	+	0.151600i
$389$	3.20245	−	3.69583i	0.162371	−	0.187386i	−0.668734	−	0.743502i	$-0.733163\pi$
$389$	3.20245	−	3.69583i	0.162371	−	0.187386i	0.831105	+	0.556116i	$0.187709\pi$
$390$	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
$393$	0.835326	+	11.6794i	0.0421366	+	0.589147i
$394$	1.53672	+	2.39119i	0.0774190	+	0.120466i
$395$	−14.0999	−	22.1974i	−0.709442	−	1.11687i
$396$	−4.13412	+	1.88799i	−0.207747	+	0.0948750i
$397$	8.99817	−	6.73595i	0.451605	−	0.338067i	−0.349142	−	0.937070i	$-0.613527\pi$
$397$	8.99817	−	6.73595i	0.451605	−	0.338067i	0.800747	+	0.599002i	$0.204436\pi$
$398$	−1.46505	−	0.799977i	−0.0734363	−	0.0400992i
$399$	0.870637	−	1.35474i	0.0435864	−	0.0678217i
$400$	2.02879	+	4.56990i	0.101440	+	0.228495i
$401$	4.67283	−	15.9142i	0.233350	−	0.794718i	−0.756671	−	0.653796i	$-0.773175\pi$
$401$	4.67283	−	15.9142i	0.233350	−	0.794718i	0.990021	−	0.140922i	$-0.0450065\pi$
$402$	14.4218	+	1.03147i	0.719296	+	0.0514451i
$403$	0.777553	+	0.0556117i	0.0387327	+	0.00277021i
$404$	0.911532	−	3.10439i	0.0453504	−	0.154449i
$405$	−0.0118400	+	2.23604i	−0.000588337	+	0.111110i
$406$	1.85258	−	2.88268i	0.0919422	−	0.143065i
$407$	3.07264	+	1.67779i	0.152305	+	0.0831648i
$408$	−2.58366	+	1.93410i	−0.127910	+	0.0957524i
$409$	−20.8341	+	9.51462i	−1.03018	+	0.470468i	−0.857486	−	0.514508i	$-0.827975\pi$
$409$	−20.8341	+	9.51462i	−1.03018	+	0.470468i	−0.172695	+	0.984975i	$0.555247\pi$
$410$	1.28493	−	5.75974i	0.0634584	−	0.284453i
$411$	−2.31421	−	3.60099i	−0.114152	−	0.177624i
$412$	−0.896073	−	12.5287i	−0.0441464	−	0.617247i
$413$	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
$417$	19.6253	+	4.26923i	0.961056	+	0.209065i
$418$	4.23374	+	3.16934i	0.207079	+	0.155017i
$419$	8.60647	+	18.8455i	0.420454	+	0.920665i	0.994780	+	0.102039i	$0.0325366\pi$
$419$	8.60647	+	18.8455i	0.420454	+	0.920665i	−0.574327	+	0.818626i	$0.694736\pi$
$420$	−0.856086	−	2.97372i	−0.0417727	−	0.145103i
$421$	3.64401	+	12.4104i	0.177598	+	0.604845i	0.999386	+	0.0350500i	$0.0111591\pi$
$421$	3.64401	+	12.4104i	0.177598	+	0.604845i	−0.821787	+	0.569795i	$0.807023\pi$
$422$	5.55145	+	25.5196i	0.270241	+	1.24228i
$423$	1.65861	+	4.44691i	0.0806445	+	0.216216i
$424$	−4.76156	−	1.39812i	−0.231242	−	0.0678988i
$425$	−11.5307	+	11.2891i	−0.559324	+	0.547601i
$426$	5.17109	+	5.96775i	0.250540	+	0.289139i
$427$	8.46130	+	15.4957i	0.409471	+	0.749890i
$428$	−18.9395	+	7.06406i	−0.915474	+	0.341454i
$429$	−0.456690	−	0.293497i	−0.0220492	−	0.0141702i
$430$	7.06156	+	8.23720i	0.340538	+	0.397233i
$431$	−14.0564	−	2.02101i	−0.677075	−	0.0973486i	−0.204805	−	0.978803i	$-0.565656\pi$
$431$	−14.0564	−	2.02101i	−0.677075	−	0.0973486i	−0.472270	+	0.881454i	$0.656565\pi$
$432$	0.349464	−	0.936950i	0.0168136	−	0.0450790i
$433$	−14.9083	+	19.9152i	−0.716448	+	0.957062i	−0.999998	−	0.00189501i	$-0.999397\pi$
$433$	−14.9083	+	19.9152i	−0.716448	+	0.957062i	0.283550	+	0.958957i	$0.408488\pi$
$434$	7.59788	−	4.88286i	0.364710	−	0.234385i
$435$	4.87341	−	2.62768i	0.233662	−	0.125988i
$436$		−	4.86759i		−	0.233115i
$437$	−5.40830	−	1.37636i	−0.258714	−	0.0658405i
$438$	−7.87823	+	7.87823i	−0.376436	+	0.376436i
$439$	−5.16502	−	4.47551i	−0.246513	−	0.213605i	0.522836	−	0.852433i	$-0.324874\pi$
$439$	−5.16502	−	4.47551i	−0.246513	−	0.213605i	−0.769349	+	0.638828i	$0.779419\pi$
$440$	9.94159	−	2.10759i	0.473947	−	0.100475i
$441$	−0.723645	−	5.03306i	−0.0344593	−	0.239670i
$442$	−0.361198	−	0.134720i	−0.0171804	−	0.00640797i
$443$	16.2661	+	21.7290i	0.772827	+	1.03238i	0.998309	+	0.0581287i	$0.0185134\pi$
$443$	16.2661	+	21.7290i	0.772827	+	1.03238i	−0.225482	+	0.974247i	$0.572396\pi$
$444$	−0.739095	+	0.217018i	−0.0350759	+	0.0102992i
$445$	−18.8049	−	2.80544i	−0.891437	−	0.132991i
$446$	2.28413	−	5.00154i	0.108157	−	0.236830i
$447$	15.3423	−	8.37751i	0.725664	−	0.396243i
$448$	−0.0987263	+	1.38037i	−0.00466438	+	0.0652165i
$449$	−1.12903	+	0.978314i	−0.0532824	+	0.0461695i	−0.681095	−	0.732195i	$-0.738496\pi$
$449$	−1.12903	+	0.978314i	−0.0532824	+	0.0461695i	0.627813	+	0.778365i	$0.283950\pi$
$450$	1.11451	−	4.87421i	0.0525383	−	0.229772i
$451$	−10.9106	−	4.98269i	−0.513759	−	0.234626i
$452$	−6.91175	+	1.50356i	−0.325101	+	0.0707214i
$453$	0.156273	−	0.286192i	0.00734234	−	0.0134465i
$454$	−3.11972	+	21.6981i	−0.146416	+	1.01834i
$455$	0.243532	−	0.278062i	0.0114170	−	0.0130358i
$456$	−1.15181	+	0.165605i	−0.0539384	+	0.00775517i
$457$	−8.65573	+	39.7898i	−0.404898	+	1.86129i	0.0954083	+	0.995438i	$0.469584\pi$
$457$	−8.65573	+	39.7898i	−0.404898	+	1.86129i	−0.500306	+	0.865848i	$0.666779\pi$
$458$	3.89913	−	0.278871i	0.182194	−	0.0130308i
$459$	3.22739			0.150642
$460$	−8.83678	+	6.07547i	−0.412017	+	0.283270i
$461$	26.9244			1.25399			0.626997	−	0.779021i	$-0.284284\pi$
$461$	26.9244			1.25399			0.626997	+	0.779021i	$0.284284\pi$
$462$	−6.27356	+	0.448694i	−0.291872	+	0.0208751i
$463$	−4.27999	+	19.6748i	−0.198908	+	0.914365i	0.764143	+	0.645047i	$0.223162\pi$
$463$	−4.27999	+	19.6748i	−0.198908	+	0.914365i	−0.963051	+	0.269318i	$0.913202\pi$
$464$	−2.45088	+	0.352383i	−0.113779	+	0.0163590i
$465$	14.5612	−	0.963967i	0.675258	−	0.0447029i
$466$	−0.372343	+	2.58970i	−0.0172485	+	0.119966i
$467$	0.701211	−	1.28417i	0.0324482	−	0.0594244i	−0.860952	−	0.508686i	$-0.830131\pi$
$467$	0.701211	−	1.28417i	0.0324482	−	0.0594244i	0.893400	+	0.449262i	$0.148313\pi$
$468$	0.116718	−	0.0253904i	0.00539528	−	0.00117367i
$469$	18.2012	+	8.31220i	0.840452	+	0.383822i
$470$	−1.45470	−	10.5126i	−0.0671005	−	0.484908i
$471$	−12.2014	+	10.5726i	−0.562211	+	0.487159i
$472$	0.0678111	−	0.948123i	0.00312126	−	0.0436409i
$473$	19.3547	−	10.5685i	0.889932	−	0.485940i
$474$	4.88543	−	10.6976i	0.224395	−	0.491357i
$475$	−5.59963	+	1.57998i	−0.256929	+	0.0724947i
$476$	−4.28547	+	1.25833i	−0.196424	+	0.0576753i
$477$	2.97396	+	3.97275i	0.136168	+	0.181900i
$478$	2.95615	+	1.10259i	0.135211	+	0.0504312i
$479$	−2.03278	−	14.1383i	−0.0928801	−	0.645995i	−0.982078	−	0.188473i	$-0.939646\pi$
$479$	−2.03278	−	14.1383i	−0.0928801	−	0.645995i	0.889198	−	0.457522i	$-0.151263\pi$
$480$	−1.21885	+	1.87467i	−0.0556328	+	0.0855667i
$481$	−0.0695366	−	0.0602538i	−0.00317060	−	0.00274734i
$482$	−3.65639	+	3.65639i	−0.166544	+	0.166544i
$483$	5.93286	−	2.97496i	0.269954	−	0.135365i
$484$		−	9.65543i		−	0.438883i
$485$	14.9084	+	27.6498i	0.676957	+	1.25551i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−5.21736	+	6.96958i	−0.236421	+	0.315822i	−0.903023	−	0.429592i	$-0.858657\pi$
$487$	−5.21736	+	6.96958i	−0.236421	+	0.315822i	0.666602	+	0.745414i	$0.267748\pi$
$488$	4.45835	−	11.9533i	0.201820	−	0.541100i
$489$	−1.63901	−	0.235655i	−0.0741188	−	0.0106567i
$490$	−0.871167	+	11.3366i	−0.0393553	+	0.512134i
$491$	19.6322	+	12.6168i	0.885988	+	0.569390i	0.902604	−	0.430472i	$-0.141653\pi$
$491$	19.6322	+	12.6168i	0.885988	+	0.569390i	−0.0166160	+	0.999862i	$0.505289\pi$
$492$	2.47276	−	0.922290i	0.111480	−	0.0415800i
$493$	−3.82981	−	7.01378i	−0.172486	−	0.315885i
$494$	−0.0910228	−	0.105046i	−0.00409531	−	0.00472624i
$495$	−9.22168	−	4.27056i	−0.414484	−	0.191947i
$496$	−6.26184	−	1.83864i	−0.281165	−	0.0825575i
$497$	3.81892	+	10.2389i	0.171302	+	0.459278i
$498$	0.311037	+	1.42981i	0.0139379	+	0.0640715i
$499$	−2.94846	−	10.0415i	−0.131991	−	0.449520i	0.866801	−	0.498654i	$-0.166172\pi$
$499$	−2.94846	−	10.0415i	−0.131991	−	0.449520i	−0.998792	+	0.0491337i	$0.984354\pi$
$500$	−4.80544	+	10.0949i	−0.214906	+	0.451459i
$501$	0.974073	+	2.13292i	0.0435184	+	0.0952919i
$502$	−23.7239	−	17.7595i	−1.05885	−	0.792646i
$503$	−38.0402	−	8.27515i	−1.69613	−	0.368971i	−0.742475	−	0.669873i	$-0.766348\pi$
$503$	−38.0402	−	8.27515i	−1.69613	−	0.368971i	−0.953655	+	0.300903i	$0.902712\pi$
$504$	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
$508$	−1.15751	−	16.1841i	−0.0513561	−	0.718052i
$509$	3.02734	+	4.71063i	0.134184	+	0.208795i	0.901843	−	0.432064i	$-0.142215\pi$
$509$	3.02734	+	4.71063i	0.134184	+	0.208795i	−0.767658	+	0.640859i	$0.778578\pi$
$510$	−7.04352	−	1.57133i	−0.311892	−	0.0695797i
$511$	−14.0254	+	6.40517i	−0.620446	+	0.283348i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	1.02131	+	0.557680i	0.0450921	+	0.0246222i
$514$	−4.86124	+	7.56424i	−0.214420	+	0.333644i
$515$	19.9652	−	19.7548i	0.879770	−	0.870502i
$516$	−1.36701	+	4.65561i	−0.0601793	+	0.204952i
$517$	−21.5155	−	1.53882i	−0.946250	−	0.0676772i
$518$	−1.06330	−	0.0760486i	−0.0467187	−	0.00334138i
$519$	−0.745211	+	2.53796i	−0.0327111	+	0.111404i
$520$	−0.267089	−	0.00141427i	−0.0117126	−	6.20196e-5i
$521$	11.7241	−	18.2430i	0.513640	−	0.799240i	−0.483458	−	0.875368i	$-0.660619\pi$
$521$	11.7241	−	18.2430i	0.513640	−	0.799240i	0.997098	+	0.0761276i	$0.0242556\pi$
$522$	2.17320	+	1.18666i	0.0951185	+	0.0519386i
$523$	−1.03701	+	0.776294i	−0.0453451	+	0.0339450i	−0.621710	−	0.783248i	$-0.713562\pi$
$523$	−1.03701	+	0.776294i	−0.0453451	+	0.0339450i	0.576365	+	0.817193i	$0.304471\pi$
$524$	10.6511	−	4.86418i	0.465295	−	0.212493i
$525$	3.80240	−	5.78111i	0.165950	−	0.252308i
$526$	4.11893	+	6.40917i	0.179594	+	0.279453i
$527$	−1.50259	−	21.0089i	−0.0654538	−	0.915164i
$528$	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
$532$	−1.57358	−	0.342311i	−0.0682233	−	0.0148411i
$533$	0.252363	+	0.188917i	0.0109311	+	0.00818289i
$534$	−3.53222	−	7.73448i	−0.152854	−	0.334704i
$535$	−39.5557	−	21.8717i	−1.71014	−	0.945597i
$536$	−4.07348	−	13.8730i	−0.175948	−	0.599223i
$537$	−3.48708	−	16.0299i	−0.150479	−	0.691740i
$538$	7.06366	+	18.9384i	0.304536	+	0.816492i
$539$	22.1735	+	6.51073i	0.955081	+	0.280437i
$540$	2.09919	−	0.770321i	0.0903348	−	0.0331493i
$541$	19.4598	+	22.4578i	0.836642	+	0.965537i	0.999778	−	0.0210669i	$-0.00670629\pi$
$541$	19.4598	+	22.4578i	0.836642	+	0.965537i	−0.163136	+	0.986604i	$0.552161\pi$
$542$	8.27537	+	15.1552i	0.355457	+	0.650972i
$543$	−0.219176	+	0.0817484i	−0.00940574	+	0.00350816i
$544$	2.71505	+	1.74486i	0.116407	+	0.0748102i
$545$	8.26340	−	7.08402i	0.353965	−	0.303446i
$546$	0.163621	+	0.0235251i	0.00700233	+	0.00100678i
$547$	−5.70466	+	15.2948i	−0.243914	+	0.653958i	−1.00000		0.000514350i	$-0.999836\pi$
$547$	−5.70466	+	15.2948i	−0.243914	+	0.653958i	0.756086	+	0.654472i	$0.227109\pi$
$548$	−2.56521	+	3.42672i	−0.109580	+	0.146382i
$549$	−10.7324	+	6.89732i	−0.458049	+	0.294370i
$550$	18.0464	+	13.8099i	0.769499	+	0.588858i
$551$		−	2.88130i		−	0.122747i
$552$	−4.43205	−	1.83219i	−0.188641	−	0.0779833i
$553$	11.5083	−	11.5083i	0.489382	−	0.489382i
$554$	−7.48285	−	6.48393i	−0.317916	−	0.275476i
$555$	−1.44406	−	0.938879i	−0.0612967	−	0.0398532i
$556$	−2.85829	−	19.8799i	−0.121219	−	0.843094i
$557$	21.5457	+	8.03613i	0.912921	+	0.340502i	0.761649	−	0.647990i	$-0.224390\pi$
$557$	21.5457	+	8.03613i	0.912921	+	0.340502i	0.151272	+	0.988492i	$0.451663\pi$
$558$	3.91101	+	5.22449i	0.165566	+	0.221170i
$559$	−0.556101	+	0.163286i	−0.0235206	+	0.00690626i
$560$	−2.48706	+	1.84132i	−0.105097	+	0.0778099i
$561$	−6.09328	+	13.3424i	−0.257258	+	0.563317i
$562$	−5.16072	+	2.81797i	−0.217692	+	0.118869i
$563$	1.53598	−	21.4758i	0.0647337	−	0.905096i	−0.856515	−	0.516122i	$-0.827375\pi$
$563$	1.53598	−	21.4758i	0.0647337	−	0.905096i	0.921249	−	0.388974i	$-0.127170\pi$
$564$	3.58691	−	3.10807i	0.151036	−	0.130873i
$565$	−12.6115	−	9.54544i	−0.530568	−	0.401580i
$566$	20.4153	+	9.32337i	0.858120	+	0.391890i
$567$	−1.35227	+	0.294169i	−0.0567902	+	0.0123539i
$568$	3.78437	−	6.93056i	0.158789	−	0.290800i
$569$	2.05603	−	14.3000i	0.0861931	−	0.599486i	−0.900249	−	0.435376i	$-0.856616\pi$
$569$	2.05603	−	14.3000i	0.0861931	−	0.599486i	0.986442	−	0.164110i	$-0.0524753\pi$
$570$	−1.95742	−	1.71434i	−0.0819872	−	0.0718059i
$571$	−45.3962	+	6.52699i	−1.89977	+	0.273146i	−0.989903	−	0.141748i	$-0.954728\pi$
$571$	−45.3962	+	6.52699i	−1.89977	+	0.273146i	−0.909870	+	0.414894i	$0.863819\pi$
$572$	−0.115395	+	0.530462i	−0.00482491	+	0.0221797i
$573$	5.81432	−	0.415848i	0.242897	−	0.0173723i
$574$	3.65233			0.152445
$575$	−23.1745	−	6.15974i	−0.966444	−	0.256879i
$576$	−1.00000			−0.0416667
$577$	−2.18620	+	0.156360i	−0.0910127	+	0.00650935i	−0.116771	−	0.993159i	$-0.537254\pi$
$577$	−2.18620	+	0.156360i	−0.0910127	+	0.00650935i	0.0257586	+	0.999668i	$0.491800\pi$
$578$	1.39952	−	6.43348i	0.0582123	−	0.267597i
$579$	2.33704	−	0.336016i	0.0971242	−	0.0139644i
$580$	−4.16509	−	3.64786i	−0.172946	−	0.151469i
$581$	−0.288187	+	2.00439i	−0.0119560	+	0.0831560i
$582$	−6.73264	+	12.3299i	−0.279077	+	0.511091i
$583$	−22.0386	+	4.79421i	−0.912747	+	0.198556i
$584$	10.1347	+	4.62835i	0.419376	+	0.191522i
$585$	0.212968	+	0.161193i	0.00880516	+	0.00666450i
$586$	−14.0373	+	12.1634i	−0.579876	+	0.502465i
$587$	−1.78627	+	24.9754i	−0.0737274	+	1.03084i	0.817098	+	0.576498i	$0.195581\pi$
$587$	−1.78627	+	24.9754i	−0.0737274	+	1.03084i	−0.890826	+	0.454345i	$0.849873\pi$
$588$	−4.46284	+	2.43689i	−0.184044	+	0.100496i
$589$	3.15476	−	6.90796i	0.129990	−	0.284638i
$590$	1.70826	−	1.26473i	0.0703278	−	0.0520680i
$591$	−2.72727	+	0.800799i	−0.112185	+	0.0329405i
$592$	0.461622	+	0.616655i	0.0189725	+	0.0253444i
$593$	−17.8558	−	6.65986i	−0.733249	−	0.273488i	−0.0450249	−	0.998986i	$-0.514337\pi$
$593$	−17.8558	−	6.65986i	−0.733249	−	0.273488i	−0.688224	+	0.725498i	$0.741609\pi$
$594$	−0.646796	−	4.49856i	−0.0265384	−	0.184578i
$595$	−8.37301	−	5.44387i	−0.343260	−	0.223177i
$596$	−13.2109	−	11.4473i	−0.541139	−	0.468899i
$597$	1.18032	−	1.18032i	0.0483075	−	0.0483075i
$598$	−0.102105	−	0.563677i	−0.00417538	−	0.0230505i
$599$			13.2826i			0.542713i	0.962479	+	0.271357i	$0.0874723\pi$
$599$			13.2826i			0.542713i	−0.962479	+	0.271357i	$0.912528\pi$
$600$	−4.95637	+	0.659124i	−0.202343	+	0.0269086i
$601$	34.9040	−	22.4315i	1.42376	−	0.914998i	0.423808	−	0.905752i	$-0.360693\pi$
$601$	34.9040	−	22.4315i	1.42376	−	0.914998i	0.999957	−	0.00924582i	$-0.00294308\pi$
$602$	−4.02409	+	5.37555i	−0.164010	+	0.219091i
$603$	−5.05279	+	13.5471i	−0.205766	+	0.551679i
$604$	−0.322759	−	0.0464058i	−0.0131329	−	0.00188823i
$605$	16.3914	−	14.0520i	0.666406	−	0.571294i
$606$	2.72184	+	1.74922i	0.110567	+	0.0710571i
$607$	−33.9492	+	12.6624i	−1.37795	+	0.513950i	−0.925808	−	0.377993i	$-0.876614\pi$
$607$	−33.9492	+	12.6624i	−1.37795	+	0.513950i	−0.452146	+	0.891944i	$0.649342\pi$
$608$	0.557680	+	1.02131i	0.0226169	+	0.0414198i
$609$	2.24398	+	2.58969i	0.0909305	+	0.104939i
$610$	26.7808	−	9.82750i	1.08432	−	0.397904i
$611$	0.543953	+	0.159719i	0.0220060	+	0.00646154i
$612$	−1.12786	−	3.02390i	−0.0455909	−	0.122234i
$613$	−6.54810	−	30.1011i	−0.264475	−	1.21577i	−0.897280	−	0.441462i	$-0.854460\pi$
$613$	−6.54810	−	30.1011i	−0.264475	−	1.21577i	0.632805	−	0.774311i	$-0.281903\pi$
$614$	4.58401	+	15.6117i	0.184996	+	0.630037i
$615$	5.16442	+	2.85559i	0.208250	+	0.115149i
$616$	2.61279	+	5.72121i	0.105272	+	0.230514i
$617$	−31.9161	−	23.8921i	−1.28489	−	0.961860i	−0.999995	−	0.00330313i	$-0.998949\pi$
$617$	−31.9161	−	23.8921i	−1.28489	−	0.961860i	−0.284900	−	0.958557i	$-0.591961\pi$
$618$	12.2737	+	2.66998i	0.493720	+	0.107402i
$619$	29.5497	−	34.1021i	1.18770	−	1.37068i	0.275313	−	0.961355i	$-0.411219\pi$
$619$	29.5497	−	34.1021i	1.18770	−	1.37068i	0.912388	−	0.409326i	$-0.134236\pi$
$620$	−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
$623$	−0.839457	−	11.7371i	−0.0336321	−	0.470239i
$624$	−0.0645782	−	0.100486i	−0.00258520	−	0.00402265i
$625$	−24.1311	+	6.53372i	−0.965244	+	0.261349i
$626$	19.1673	−	8.75340i	0.766078	−	0.349856i
$627$	−4.23374	+	3.16934i	−0.169079	+	0.126571i
$628$	14.1699	+	7.73737i	0.565442	+	0.308755i
$629$	−1.34406	+	2.09140i	−0.0535912	+	0.0833895i
$630$	3.09445	+	0.0163854i	0.123286	+	0.000652812i
$631$	−1.19686	+	4.07614i	−0.0476464	+	0.162269i	−0.979880	−	0.199589i	$-0.936039\pi$
$631$	−1.19686	+	4.07614i	−0.0476464	+	0.162269i	0.932233	+	0.361858i	$0.117857\pi$
$632$	−11.7304	−	0.838974i	−0.466610	−	0.0333726i
$633$	−26.0499	−	1.86313i	−1.03539	−	0.0740527i
$634$	−4.62257	+	15.7430i	−0.183586	+	0.625235i
$635$	25.7901	−	25.5184i	1.02345	−	1.01267i
$636$	2.68297	−	4.17479i	0.106387	−	0.165541i
$637$	−0.533075	−	0.291081i	−0.0211212	−	0.0115331i
$638$	−9.00877	+	6.74388i	−0.356660	+	0.266993i
$639$	−7.18288	+	3.28031i	−0.284150	+	0.129767i
$640$	2.18242	+	0.486873i	0.0862677	+	0.0192454i
$641$	3.21254	+	4.99880i	0.126888	+	0.197441i	0.898885	−	0.438185i	$-0.144378\pi$
$641$	3.21254	+	4.99880i	0.126888	+	0.197441i	−0.771997	+	0.635626i	$0.780742\pi$
$642$	−1.44205	−	20.1625i	−0.0569131	−	0.795749i
$643$	−5.99603	−	5.99603i	−0.236460	−	0.236460i	0.578922	−	0.815383i	$-0.303473\pi$
$643$	−5.99603	−	5.99603i	−0.236460	−	0.236460i	−0.815383	+	0.578922i	$0.803473\pi$
$644$	−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
$647$	34.3188	+	7.46560i	1.34921	+	0.293503i	0.828385	−	0.560159i	$-0.189260\pi$
$647$	34.3188	+	7.46560i	1.34921	+	0.293503i	0.520827	+	0.853662i	$0.325624\pi$
$648$	0.800541	+	0.599278i	0.0314482	+	0.0235419i
$649$	−1.79462	−	3.92966i	−0.0704449	−	0.154253i
$650$	−0.386306	−	0.455479i	−0.0151522	−	0.0178653i
$651$	2.54450	+	8.66577i	0.0997268	+	0.339638i
$652$	0.351980	+	1.61803i	0.0137846	+	0.0633668i
$653$	−15.7376	−	42.1941i	−0.615860	−	1.65118i	−0.750956	−	0.660352i	$-0.770407\pi$
$653$	−15.7376	−	42.1941i	−0.615860	−	1.65118i	0.135096	−	0.990832i	$-0.456866\pi$
$654$	4.67042	+	1.37136i	0.182628	+	0.0536244i
$655$	23.7586	+	11.0026i	0.928326	+	0.429907i
$656$	−1.72828	−	1.99454i	−0.0674779	−	0.0778737i
$657$	−5.33955	−	9.77866i	−0.208316	−	0.381502i
$658$	6.15408	−	2.29535i	0.239911	−	0.0894822i
$659$	19.6946	+	12.6570i	0.767193	+	0.493045i	0.864761	−	0.502184i	$-0.167470\pi$
$659$	19.6946	+	12.6570i	0.767193	+	0.493045i	−0.0975679	+	0.995229i	$0.531106\pi$
$660$	−0.778651	+	10.1327i	−0.0303089	+	0.394413i
$661$	35.8609	+	5.15603i	1.39483	+	0.200546i	0.798404	−	0.602122i	$-0.205678\pi$
$661$	35.8609	+	5.15603i	1.39483	+	0.200546i	0.596425	+	0.802669i	$0.296587\pi$
$662$	−7.37313	+	19.7681i	−0.286565	+	0.768310i
$663$	0.231024	−	0.308612i	0.00897223	−	0.0119855i
$664$	1.23097	−	0.791095i	0.0477708	−	0.0307004i
$665$	−1.70898	−	3.16955i	−0.0662713	−	0.122910i
$666$		−	0.770297i		−	0.0298484i
$667$	6.05225	−	10.2168i	0.234344	−	0.395595i
$668$	1.65804	−	1.65804i	0.0641514	−	0.0641514i
$669$	4.15543	+	3.60070i	0.160658	+	0.139211i
$670$	17.6230	−	27.1053i	0.680836	−	1.04717i
$671$	−8.25161	−	57.3912i	−0.318550	−	2.21556i
$672$	−1.29664	−	0.483624i	−0.0500192	−	0.0186562i
$673$	0.337533	+	0.450892i	0.0130110	+	0.0173806i	0.807000	−	0.590552i	$-0.201090\pi$
$673$	0.337533	+	0.450892i	0.0130110	+	0.0173806i	−0.793989	+	0.607933i	$0.791999\pi$
$674$	−21.5587	+	6.33021i	−0.830410	+	0.243830i
$675$	4.36277	+	2.44258i	0.167923	+	0.0940151i
$676$	−5.39447	+	11.8122i	−0.207480	+	0.454317i
$677$	−32.8835	+	17.9558i	−1.26382	+	0.690096i	−0.964506	−	0.264060i	$-0.914938\pi$
$677$	−32.8835	+	17.9558i	−1.26382	+	0.690096i	−0.299310	+	0.954156i	$0.596757\pi$
$678$	0.504610	−	7.05537i	0.0193794	−	0.270960i
$679$	−14.6929	+	12.7314i	−0.563861	+	0.488588i
$680$	0.989201	+	7.14855i	0.0379341	+	0.274134i
$681$	−19.9403	−	9.10641i	−0.764112	−	0.348958i
$682$	−28.9826	+	6.30478i	−1.10980	+	0.241423i
$683$	5.37920	−	9.85128i	0.205830	−	0.376949i	−0.754289	−	0.656543i	$-0.772018\pi$
$683$	5.37920	−	9.85128i	0.205830	−	0.376949i	0.960118	+	0.279594i	$0.0901999\pi$
$684$	0.165605	−	1.15181i	0.00633207	−	0.0440405i
$685$	−9.55059	+	0.632261i	−0.364909	+	0.0241574i
$686$	−16.5540	+	2.38010i	−0.632033	+	0.0908726i
$687$	−0.830936	+	3.81975i	−0.0317022	+	0.145733i
$688$	4.83979	−	0.346149i	0.184515	−	0.0131968i
$689$	0.592768			0.0225827
$690$	−3.33976	−	10.1905i	−0.127143	−	0.387945i
$691$	7.33264			0.278947			0.139473	−	0.990226i	$-0.455459\pi$
$691$	7.33264			0.278947			0.139473	+	0.990226i	$0.455459\pi$
$692$	2.63836	−	0.188699i	0.100295	−	0.00717327i
$693$	1.33695	−	6.14585i	0.0507864	−	0.233461i
$694$	23.2568	−	3.34382i	0.882816	−	0.126930i
$695$	29.5890	−	33.7844i	1.12238	−	1.28152i
$696$	0.352383	−	2.45088i	0.0133570	−	0.0929002i
$697$	4.08204	−	7.47571i	0.154618	−	0.283163i
$698$	5.28319	−	1.14929i	0.199972	−	0.0435012i
$699$	−2.37990	−	1.08686i	−0.0900161	−	0.0411090i
$700$	−6.74541	−	1.54237i	−0.254953	−	0.0582959i
$701$	−30.4455	+	26.3812i	−1.14991	+	0.996402i	−0.149939	+	0.988695i	$0.547908\pi$
$701$	−30.4455	+	26.3812i	−1.14991	+	0.996402i	−0.999970	+	0.00770716i	$0.997547\pi$
$702$	−0.00852129	+	0.119143i	−0.000321615	+	0.00449677i
$703$	−0.786716	+	0.429579i	−0.0296715	+	0.0162019i
$704$	1.88799	−	4.13412i	0.0711562	−	0.155810i
$705$	10.4966	+	1.56595i	0.395323	+	0.0589771i
$706$	23.9325	−	7.02722i	0.900712	−	0.264473i
$707$	2.68329	+	3.58446i	0.100916	+	0.134807i
$708$	0.890613	+	0.332181i	0.0334713	+	0.0124841i
$709$	1.11198	+	7.73396i	0.0417611	+	0.290455i	0.999990	+	0.00445288i	$0.00141740\pi$
$709$	1.11198	+	7.73396i	0.0417611	+	0.290455i	−0.958229	+	0.286002i	$0.907674\pi$
$710$	17.2732	−	3.66186i	0.648250	−	0.137427i
$711$	8.88789	+	7.70140i	0.333322	+	0.288825i
$712$	−6.01244	+	6.01244i	−0.225326	+	0.225326i
$713$	25.6968	−	17.8682i	0.962354	−	0.669170i
$714$		−	4.46639i		−	0.167150i
$715$	−1.06847	+	0.576106i	−0.0399586	+	0.0215452i
$716$	−13.8006	+	8.86909i	−0.515751	+	0.331453i
$717$	−1.89077	+	2.52577i	−0.0706120	+	0.0943266i
$718$	−0.141809	+	0.380205i	−0.00529227	+	0.0141891i
$719$	−40.9483	−	5.88748i	−1.52711	−	0.219566i	−0.672996	−	0.739646i	$-0.734993\pi$
$719$	−40.9483	−	5.88748i	−1.52711	−	0.219566i	−0.854118	+	0.520080i	$0.825902\pi$
$720$	−1.45534	−	1.69764i	−0.0542375	−	0.0632672i
$721$	14.6234	+	9.39786i	0.544602	+	0.349995i
$722$	16.5333	−	6.16661i	0.615307	−	0.229498i
$723$	−2.47815	−	4.53840i	−0.0921636	−	0.168785i
$724$	0.153188	+	0.176789i	0.00569320	+	0.00657030i
$725$	0.131107	−	12.3797i	0.00486920	−	0.459771i
$726$	9.26432	+	2.72025i	0.343831	+	0.100958i
$727$	−2.88554	−	7.73645i	−0.107019	−	0.286929i	0.872392	−	0.488808i	$-0.162568\pi$
$727$	−2.88554	−	7.73645i	−0.107019	−	0.286929i	−0.979411	+	0.201879i	$0.935295\pi$
$728$	−0.0351378	−	0.161526i	−0.00130229	−	0.00598655i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	6.89218	+	23.9408i	0.255091	+	0.886090i
$731$	6.50532	+	14.2447i	0.240608	+	0.526858i
$732$	10.2130	+	7.64538i	0.377485	+	0.282582i
$733$	−17.6317	−	3.83554i	−0.651241	−	0.141669i	−0.125205	−	0.992131i	$-0.539959\pi$
$733$	−17.6317	−	3.83554i	−0.651241	−	0.141669i	−0.526036	+	0.850462i	$0.676322\pi$
$734$	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
$738$	0.188275	+	2.63243i	0.00693050	+	0.0969011i
$739$	18.2046	+	28.3269i	0.669668	+	1.04202i	0.995329	+	0.0965368i	$0.0307765\pi$
$739$	18.2046	+	28.3269i	0.669668	+	1.04202i	−0.325662	+	0.945486i	$0.605587\pi$
$740$	−0.375037	+	1.68111i	−0.0137866	+	0.0617989i
$741$	0.126435	−	0.0577409i	0.00464470	−	0.00212116i
$742$	5.49789	−	4.11567i	0.201834	−	0.151091i
$743$	−9.99610	−	5.45829i	−0.366722	−	0.200245i	0.285313	−	0.958434i	$-0.407902\pi$
$743$	−9.99610	−	5.45829i	−0.366722	−	0.200245i	−0.652034	+	0.758189i	$0.726084\pi$
$744$	3.52833	−	5.49019i	0.129355	−	0.201280i
$745$	0.206970	−	39.0870i	0.00758279	−	1.43204i
$746$	3.47462	−	11.8335i	0.127215	−	0.433254i
$747$	−1.45953	−	0.104387i	−0.0534013	−	0.00381933i
$748$	14.6306	+	1.04640i	0.534946	+	0.0382601i
$749$	7.88122	−	26.8410i	0.287974	−	0.980748i
$750$	−8.33217	−	7.45486i	−0.304248	−	0.272213i
$751$	−10.7969	+	16.8003i	−0.393984	+	0.613050i	−0.980414	−	0.196949i	$-0.936897\pi$
$751$	−10.7969	+	16.8003i	−0.393984	+	0.613050i	0.586430	+	0.810000i	$0.300533\pi$
$752$	−4.16560	−	2.27459i	−0.151904	−	0.0829458i
$753$	23.7239	−	17.7595i	0.864548	−	0.647193i
$754$	0.269034	−	0.122864i	0.00979765	−	0.00447444i
$755$	−0.390946	−	0.615465i	−0.0142280	−	0.0223991i
$756$	0.748193	+	1.16421i	0.0272115	+	0.0423419i
$757$	−3.21564	−	44.9605i	−0.116874	−	1.63412i	−0.630561	−	0.776139i	$-0.717175\pi$
$757$	−3.21564	−	44.9605i	−0.116874	−	1.63412i	0.513687	−	0.857978i	$-0.328279\pi$
$758$	−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	−0.404106	+	0.914712i	$0.632417\pi$
$761$	−34.5379	+	39.8588i	−1.25200	+	1.44488i	−0.847892	+	0.530170i	$0.822128\pi$
$762$	15.8546	+	3.44896i	0.574352	+	0.124943i
$763$	5.39265	+	4.03689i	0.195227	+	0.146145i
$764$	−2.42152	−	5.30240i	−0.0876077	−	0.191834i
$765$	3.49207	−	6.31552i	0.126256	−	0.228338i
$766$	−0.908792	−	3.09506i	−0.0328360	−	0.111829i
$767$	0.0241347	+	0.110946i	0.000871454	+	0.00400601i
$768$	0.349464	+	0.936950i	0.0126102	+	0.0338093i
$769$	13.5328	+	3.97358i	0.488004	+	0.143291i	0.516472	−	0.856304i	$-0.327245\pi$
$769$	13.5328	+	3.97358i	0.488004	+	0.143291i	−0.0284687	+	0.999595i	$0.509063\pi$
$770$	−5.91003	+	12.7619i	−0.212983	+	0.459907i
$771$	−5.88826	−	6.79542i	−0.212061	−	0.244731i
$772$	−1.13154	−	2.07227i	−0.0407251	−	0.0745825i
$773$	−22.9052	+	8.54320i	−0.823843	+	0.307278i	−0.725801	−	0.687905i	$-0.758531\pi$
$773$	−22.9052	+	8.54320i	−0.823843	+	0.307278i	−0.0980420	+	0.995182i	$0.531258\pi$
$774$	−4.08189	−	2.62327i	−0.146721	−	0.0942916i
$775$	13.8690	−	29.5370i	0.498189	−	1.06100i
$776$	13.9053	+	1.99928i	0.499172	+	0.0717700i
$777$	0.372534	−	0.998802i	0.0133646	−	0.0358318i
$778$	2.93064	−	3.91487i	0.105068	−	0.140355i
$779$	2.58354	−	1.66034i	0.0925650	−	0.0594879i
$780$	0.0766047	−	0.255872i	0.00274289	−	0.00916168i
$781$		−	35.8881i		−	1.28418i
$782$	−14.6825	+	4.89821i	−0.525046	+	0.175159i
$783$	−1.75085	+	1.75085i	−0.0625704	+	0.0625704i
$784$	3.84285	+	3.32985i	0.137245	+	0.118923i
$785$	7.48689	+	35.3159i	0.267219	+	1.26048i
$786$	1.66640	+	11.5900i	0.0594384	+	0.413403i
$787$	−19.8583	−	7.40676i	−0.707871	−	0.264022i	−0.0303647	−	0.999539i	$-0.509667\pi$
$787$	−19.8583	−	7.40676i	−0.707871	−	0.264022i	−0.677507	+	0.735516i	$0.736940\pi$
$788$	1.70339	+	2.27547i	0.0606808	+	0.0810601i
$789$	−7.30999	+	2.14641i	−0.260243	+	0.0764141i
$790$	−15.6475	−	21.1350i	−0.556713	−	0.751948i
$791$	4.06644	−	8.90427i	0.144586	−	0.316599i
$792$	−3.98890	+	2.17810i	−0.141739	+	0.0773955i
$793$	−0.108712	+	1.51999i	−0.00386047	+	0.0539764i
$794$	8.49471	−	7.36070i	0.301466	−	0.261222i
$795$	10.9919	−	1.52104i	0.389844	−	0.0539457i
$796$	−1.51839	−	0.693423i	−0.0538177	−	0.0245777i
$797$	−43.0981	+	9.37542i	−1.52661	+	0.332094i	−0.896018	−	0.444017i	$-0.853553\pi$
$797$	−43.0981	+	9.37542i	−1.52661	+	0.332094i	−0.630595	+	0.776112i	$0.717189\pi$
$798$	0.771773	−	1.41340i	0.0273205	−	0.0500337i
$799$	2.17994	−	15.1618i	0.0771206	−	0.536386i
$800$	2.34964	+	4.41352i	0.0830722	+	0.156042i
$801$	8.41633	−	1.21008i	0.297376	−	0.0427562i
$802$	3.52562	−	16.2070i	0.124494	−	0.572290i
$803$	50.5072	−	3.61234i	1.78236	−	0.127477i
$804$	14.4587			0.509919
$805$	0.597871	−	14.8286i	0.0210722	−	0.522640i
$806$	0.779539			0.0274581
$807$	−20.1613	+	1.44197i	−0.709712	+	0.0507596i
$808$	0.687745	−	3.16151i	0.0241948	−	0.111222i
$809$	53.2570	−	7.65720i	1.87242	−	0.269213i	0.890007	−	0.455948i	$-0.150700\pi$
$809$	53.2570	−	7.65720i	1.87242	−	0.269213i	0.982410	+	0.186735i	$0.0597905\pi$
$810$	0.147707	+	2.23118i	0.00518990	+	0.0783958i
$811$	−3.54828	+	24.6788i	−0.124597	+	0.866592i	0.827646	+	0.561250i	$0.189680\pi$
$811$	−3.54828	+	24.6788i	−0.124597	+	0.866592i	−0.952243	+	0.305341i	$0.901230\pi$
$812$	1.64222	−	3.00750i	0.0576305	−	0.105542i
$813$	−16.8728	+	3.67044i	−0.591753	+	0.128728i
$814$	3.18450	+	1.45431i	0.111617	+	0.0509736i
$815$	−2.23457	+	2.95232i	−0.0782736	+	0.103415i
$816$	−2.43910	+	2.11349i	−0.0853856	+	0.0739870i
$817$	−0.402797	+	5.63184i	−0.0140921	+	0.197033i
$818$	−20.1023	+	10.9767i	−0.702859	+	0.383790i
$819$	−0.0686696	+	0.150365i	−0.00239951	+	0.00525419i
$820$	0.870765	−	5.83673i	0.0304084	−	0.203828i
$821$	10.5374	−	3.09407i	0.367759	−	0.107984i	−0.0926309	−	0.995701i	$-0.529528\pi$
$821$	10.5374	−	3.09407i	0.367759	−	0.107984i	0.460390	+	0.887717i	$0.347709\pi$
$822$	−2.56521	−	3.42672i	−0.0894719	−	0.119521i
$823$	−37.0640	−	13.8241i	−1.29197	−	0.481879i	−0.392857	−	0.919599i	$-0.628513\pi$
$823$	−37.0640	−	13.8241i	−1.29197	−	0.481879i	−0.899111	+	0.437720i	$0.855786\pi$
$824$	−1.78758	−	12.4329i	−0.0622733	−	0.433120i
$825$	−18.3348	+	13.4246i	−0.638335	+	0.467386i
$826$	0.994158	+	0.861443i	0.0345912	+	0.0299734i
$827$	−33.0073	+	33.0073i	−1.14778	+	1.14778i	−0.160787	+	0.986989i	$0.551403\pi$
$827$	−33.0073	+	33.0073i	−1.14778	+	1.14778i	−0.986989	+	0.160787i	$0.948597\pi$
$828$	3.00663	−	3.73633i	0.104488	−	0.129847i
$829$		−	32.4035i		−	1.12542i	−0.826655	−	0.562710i	$-0.809759\pi$
$829$		−	32.4035i		−	1.12542i	0.826655	−	0.562710i	$-0.190241\pi$
$830$	3.13447	+	0.938421i	0.108799	+	0.0325731i
$831$	8.32945	−	5.35301i	0.288945	−	0.185694i
$832$	−0.0715823	+	0.0956227i	−0.00248167	+	0.00331512i
$833$	−5.73495	+	15.3760i	−0.198704	+	0.532747i
$834$	19.8799	+	2.85829i	0.688384	+	0.0989746i
$835$	5.22776	+	0.401730i	0.180914	+	0.0139025i
$836$	4.44905	+	2.85923i	0.153874	+	0.0988887i
$837$	−6.11472	+	2.28067i	−0.211356	+	0.0788316i
$838$	9.92897	+	18.1835i	0.342990	+	0.628140i
$839$	20.8449	+	24.0563i	0.719646	+	0.830516i	0.991265	−	0.131889i	$-0.0421042\pi$
$839$	20.8449	+	24.0563i	0.719646	+	0.830516i	−0.271618	+	0.962405i	$0.587559\pi$
$840$	−1.06605	−	2.90507i	−0.0367821	−	0.100234i
$841$	−21.9427	−	6.44295i	−0.756644	−	0.222171i
$842$	4.52008	+	12.1188i	0.155772	+	0.417641i
$843$	−1.24988	−	5.74559i	−0.0430480	−	0.197889i
$844$	7.35786	+	25.0586i	0.253268	+	0.862551i
$845$	−27.9037	+	8.03302i	−0.959917	+	0.276344i
$846$	1.97162	+	4.31726i	0.0677859	+	0.148430i
$847$	10.6970	+	8.00764i	0.367552	+	0.275146i
$848$	−4.84917	−	1.05487i	−0.166521	−	0.0362245i
$849$	−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
$853$	−0.941411	−	13.1626i	−0.0322333	−	0.450680i	−0.987781	−	0.155845i	$-0.950190\pi$
$853$	−0.941411	−	13.1626i	−0.0322333	−	0.450680i	0.955548	−	0.294835i	$-0.0952647\pi$
$854$	9.54520	+	14.8526i	0.326630	+	0.508246i
$855$	2.19637	−	1.39514i	0.0751142	−	0.0477128i
$856$	−18.3873	+	8.39719i	−0.628464	+	0.287010i
$857$	−16.4070	+	12.2821i	−0.560453	+	0.419550i	−0.841589	−	0.540118i	$-0.818380\pi$
$857$	−16.4070	+	12.2821i	−0.560453	+	0.419550i	0.281136	+	0.959668i	$0.409289\pi$
$858$	−0.476464	−	0.260169i	−0.0162662	−	0.00888203i
$859$	−16.9434	+	26.3645i	−0.578102	+	0.899544i	−0.999975	−	0.00711093i	$-0.997737\pi$
$859$	−16.9434	+	26.3645i	−0.578102	+	0.899544i	0.421873	+	0.906655i	$0.361373\pi$
$860$	7.63120	+	7.71245i	0.260222	+	0.262992i
$861$	−1.02898	+	3.50438i	−0.0350675	+	0.119429i
$862$	−14.1648	−	1.01309i	−0.482455	−	0.0345059i
$863$	−20.9516	−	1.49848i	−0.713199	−	0.0510090i	−0.289975	−	0.957034i	$-0.593647\pi$
$863$	−20.9516	−	1.49848i	−0.713199	−	0.0510090i	−0.423224	+	0.906025i	$0.639102\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	4.16007	+	4.20436i	0.141447	+	0.142952i
$866$	−13.4496	+	20.9280i	−0.457036	+	0.711162i
$867$	5.77859	+	3.15535i	0.196251	+	0.107161i
$868$	7.23018	−	5.41244i	0.245408	−	0.183710i
$869$	−48.6187	+	22.2034i	−1.64928	+	0.753199i
$870$	4.67354	−	2.96865i	0.158448	−	0.100647i
$871$	0.933716	+	1.45289i	0.0316378	+	0.0492293i
$872$	−0.347250	−	4.85519i	−0.0117594	−	0.164417i
$873$	−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
$877$	30.9867	+	6.74075i	1.04635	+	0.227619i	0.702705	−	0.711482i	$-0.251975\pi$
$877$	30.9867	+	6.74075i	1.04635	+	0.227619i	0.343643	+	0.939100i	$0.388339\pi$
$878$	−5.47114	−	4.09564i	−0.184642	−	0.138221i
$879$	−7.71593	−	16.8955i	−0.260252	−	0.569872i
$880$	9.76591	−	2.81145i	0.329209	−	0.0947738i
$881$	−7.46357	−	25.4186i	−0.251454	−	0.856374i	−0.984379	−	0.176064i	$-0.943663\pi$
$881$	−7.46357	−	25.4186i	−0.251454	−	0.856374i	0.732924	−	0.680310i	$-0.238155\pi$
$882$	−1.08086	−	4.96862i	−0.0363943	−	0.167302i
$883$	20.3338	+	54.5170i	0.684287	+	1.83464i	0.532920	+	0.846166i	$0.321095\pi$
$883$	20.3338	+	54.5170i	0.684287	+	1.83464i	0.151367	+	0.988478i	$0.451633\pi$
$884$	−0.369889	−	0.108609i	−0.0124407	−	0.00365292i
$885$	0.732225	+	1.99538i	0.0246135	+	0.0670738i
$886$	17.7748	+	20.5132i	0.597156	+	0.689155i
$887$	−0.538425	−	0.986052i	−0.0180785	−	0.0331084i	0.868484	−	0.495718i	$-0.165095\pi$
$887$	−0.538425	−	0.986052i	−0.0180785	−	0.0331084i	−0.886562	+	0.462610i	$0.846913\pi$
$888$	−0.721730	+	0.269191i	−0.0242197	+	0.00903347i
$889$	18.8898	+	12.1397i	0.633544	+	0.407154i
$890$	−18.9571	−	1.45677i	−0.635444	−	0.0488311i
$891$	4.49856	+	0.646796i	0.150708	+	0.0216685i
$892$	1.92150	−	5.15174i	0.0643366	−	0.172493i
$893$	3.30974	−	4.42129i	0.110756	−	0.147953i
$894$	14.7055	−	9.45067i	0.491827	−	0.316078i
$895$	−35.1411	−	10.5208i	−1.17464	−	0.351671i
$896$			1.38390i			0.0462329i
$897$	0.569611	+	0.0608373i	0.0190188	+	0.00203130i
$898$	−1.05637	+	1.05637i	−0.0352514	+	0.0352514i
$899$	12.2125	+	10.5821i	0.407308	+	0.352934i
$900$	0.763945	−	4.94129i	0.0254648	−	0.164710i
$901$	−2.27934	−	15.8532i	−0.0759359	−	0.528146i
$902$	−11.2382	−	4.19165i	−0.374192	−	0.139567i
$903$	−4.02409	−	5.37555i	−0.133913	−	0.178887i
$904$	−6.78687	+	1.99281i	−0.225728	+	0.0662797i
$905$	−0.0771814	+	0.517347i	−0.00256560	+	0.0171972i
$906$	0.135458	−	0.296611i	0.00450029	−	0.00985425i
$907$	44.9100	−	24.5227i	1.49121	−	0.814263i	0.492774	−	0.870157i	$-0.335983\pi$
$907$	44.9100	−	24.5227i	1.49121	−	0.814263i	0.998437	+	0.0558943i	$0.0178010\pi$
$908$	−1.56384	+	21.8654i	−0.0518980	+	0.725628i
$909$	−2.44519	+	2.11877i	−0.0811019	+	0.0702752i
$910$	0.223075	−	0.294727i	0.00739485	−	0.00977010i
$911$	34.5795	+	15.7919i	1.14567	+	0.523209i	0.895530	−	0.445001i	$-0.146797\pi$
$911$	34.5795	+	15.7919i	1.14567	+	0.523209i	0.250138	+	0.968210i	$0.419524\pi$
$912$	−1.13706	+	0.247352i	−0.0376518	+	0.00819065i
$913$	3.18712	−	5.83677i	0.105478	−	0.193169i
$914$	−5.79511	+	40.3059i	−0.191685	+	1.33320i
$915$	1.88440	+	28.4647i	0.0622963	+	0.941014i
$916$	3.86930	−	0.556321i	0.127845	−	0.0183814i
$917$	−3.44449	+	15.8341i	−0.113747	+	0.522887i
$918$	3.21917	−	0.230239i	0.106248	−	0.00759904i
$919$	35.8078			1.18119			0.590596	−	0.806968i	$-0.298893\pi$
$919$	35.8078			1.18119			0.590596	+	0.806968i	$0.298893\pi$
$920$	−8.38084	+	6.69040i	−0.276308	+	0.220576i
$921$	−16.2708			−0.536141
$922$	26.8558	−	1.92077i	0.884449	−	0.0632570i
$923$	−0.200495	+	0.921659i	−0.00659936	+	0.0303368i
$924$	−6.22556	+	0.895101i	−0.204806	+	0.0294467i
$925$	−3.39973	+	1.80992i	−0.111782	+	0.0595098i
$926$	−2.86550	+	19.9300i	−0.0941662	+	0.654940i
$927$	−6.01972	+	11.0243i	−0.197714	+	0.362086i
$928$	−2.41949	+	0.526328i	−0.0794237	+	0.0172776i
$929$	43.7604	+	19.9847i	1.43573	+	0.655677i	0.972997	−	0.230820i	$-0.0741408\pi$
$929$	43.7604	+	19.9847i	1.43573	+	0.655677i	0.462735	+	0.886496i	$0.346868\pi$
$930$	14.4553	−	2.00029i	0.474008	−	0.0655921i
$931$	−4.47175	+	3.87479i	−0.146556	+	0.126991i
$932$	−0.186647	+	2.60967i	−0.00611383	+	0.0854825i
$933$	16.7660	−	9.15492i	0.548893	−	0.299718i
$934$	0.607813	−	1.33092i	0.0198882	−	0.0435492i
$935$	19.5161	+	26.3602i	0.638245	+	0.862072i
$936$	0.114609	−	0.0336523i	0.00374612	−	0.00109996i
$937$	11.0916	+	14.8167i	0.362347	+	0.484039i	0.944255	−	0.329216i	$-0.106784\pi$
$937$	11.0916	+	14.8167i	0.362347	+	0.484039i	−0.581908	+	0.813255i	$0.697693\pi$
$938$	18.7478	+	6.99256i	0.612137	+	0.228315i
$939$	2.99878	+	20.8570i	0.0978615	+	0.680642i
$940$	−2.20096	−	10.3820i	−0.0717873	−	0.338623i
$941$	19.6085	+	16.9908i	0.639218	+	0.553886i	0.913027	−	0.407898i	$-0.133738\pi$
$941$	19.6085	+	16.9908i	0.639218	+	0.553886i	−0.273809	+	0.961784i	$0.588284\pi$
$942$	−11.4161	+	11.4161i	−0.371956	+	0.371956i
$943$	12.6486	−	0.460585i	0.411894	−	0.0149987i
$944$		−	0.950545i		−	0.0309376i
$945$	−0.887529	+	2.96449i	−0.0288713	+	0.0964348i
$946$	18.5515	−	11.9223i	0.603161	−	0.387628i
$947$	11.5690	−	15.4544i	0.375942	−	0.502200i	−0.572170	−	0.820135i	$-0.693898\pi$
$947$	11.5690	−	15.4544i	0.375942	−	0.502200i	0.948113	+	0.317935i	$0.102989\pi$
$948$	4.10982	−	11.0189i	0.133481	−	0.357876i
$949$	−1.31728	−	0.189396i	−0.0427607	−	0.00614806i
$950$	−5.47265	+	1.97543i	−0.177556	+	0.0640915i
$951$	−13.8030	−	8.87064i	−0.447593	−	0.287650i
$952$	−4.18478	+	1.56084i	−0.135630	+	0.0505872i
$953$	2.91856	+	5.34494i	0.0945414	+	0.173140i	0.920670	−	0.390342i	$-0.127643\pi$
$953$	2.91856	+	5.34494i	0.0945414	+	0.173140i	−0.826128	+	0.563482i	$0.809461\pi$
$954$	3.24980	+	3.75047i	0.105216	+	0.121426i
$955$	5.47740	−	11.8277i	0.177244	−	0.382735i
$956$	3.02728	+	0.888889i	0.0979091	+	0.0287487i
$957$	−3.93264	−	10.5438i	−0.127124	−	0.340833i
$958$	−3.03621	−	13.9573i	−0.0980956	−	0.450938i
$959$	−1.66892	−	5.68383i	−0.0538924	−	0.183540i
$960$	−1.08201	+	1.95685i	−0.0349217	+	0.0631570i
$961$	4.81520	+	10.5438i	0.155329	+	0.340123i
$962$	−0.0736579	−	0.0551396i	−0.00237483	−	0.00177777i
$963$	19.7520	+	4.29679i	0.636500	+	0.138462i
$964$	−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	$0.532165\pi$
$968$	−0.688810	−	9.63083i	−0.0221392	−	0.309547i
$969$	−2.03041	−	3.15938i	−0.0652262	−	0.101494i
$970$	16.8430	+	26.5158i	0.540795	+	0.851372i
$971$	17.1325	−	7.82413i	0.549807	−	0.251088i	−0.121087	−	0.992642i	$-0.538638\pi$
$971$	17.1325	−	7.82413i	0.549807	−	0.251088i	0.670894	+	0.741554i	$0.265911\pi$
$972$	−0.800541	+	0.599278i	−0.0256774	+	0.0192218i
$973$	24.3948	+	13.3206i	0.782061	+	0.427038i
$974$	−4.70687	+	7.32403i	−0.150818	+	0.234677i
$975$	0.545864	−	0.242335i	0.0174816	−	0.00776092i
$976$	3.59425	−	12.2409i	0.115049	−	0.391821i
$977$	−46.6341	−	3.33534i	−1.49196	−	0.106707i	−0.698622	−	0.715491i	$-0.746203\pi$
$977$	−46.6341	−	3.33534i	−1.49196	−	0.106707i	−0.793336	+	0.608784i	$0.791658\pi$
$978$	−1.65165	−	0.118128i	−0.0528139	−	0.00377733i
$979$	−10.8873	+	37.0787i	−0.347959	+	1.18504i
$980$	−0.0602045	+	11.3698i	−0.00192316	+	0.363196i
$981$	−2.63162	+	4.09488i	−0.0840211	+	0.130739i
$982$	20.4822	+	11.1841i	0.653614	+	0.356900i
$983$	4.13533	−	3.09567i	0.131897	−	0.0987365i	−0.531292	−	0.847188i	$-0.678293\pi$
$983$	4.13533	−	3.09567i	0.131897	−	0.0987365i	0.663189	+	0.748452i	$0.269203\pi$
$984$	2.40066	−	1.09634i	0.0765302	−	0.0349502i
$985$	−1.38389	+	6.20333i	−0.0440945	+	0.197654i
$986$	−4.32041	−	6.72269i	−0.137590	−	0.214094i
$987$	0.468571	+	6.55147i	0.0149148	+	0.208536i
$988$	−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	−0.437299	−	0.899316i	$-0.644065\pi$
$991$	16.2153	−	18.7135i	0.515097	−	0.594454i	0.952396	+	0.304862i	$0.0986104\pi$
$992$	−6.37706	−	1.38724i	−0.202472	−	0.0440450i
$993$	−16.8901	−	12.6438i	−0.535992	−	0.401239i
$994$	4.53962	+	9.94039i	0.143988	+	0.315290i
$995$	−1.03259	−	3.58684i	−0.0327354	−	0.113710i
$996$	0.412246	+	1.40398i	0.0130625	+	0.0444869i
$997$	−3.34442	−	15.3740i	−0.105919	−	0.486901i	−0.999293	−	0.0375881i	$-0.988033\pi$
$997$	−3.34442	−	15.3740i	−0.105919	−	0.486901i	0.893375	−	0.449313i	$-0.148331\pi$
$998$	−3.65730	−	9.80560i	−0.115770	−	0.310391i
$999$	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.7.12	✓	240
5.3	odd	4	inner	690.2.w.a.283.4	yes	240
23.10	odd	22	inner	690.2.w.a.217.4	yes	240
115.33	even	44	inner	690.2.w.a.493.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.12	✓	240	1.1	even	1	trivial
690.2.w.a.217.4	yes	240	23.10	odd	22	inner
690.2.w.a.283.4	yes	240	5.3	odd	4	inner
690.2.w.a.493.12	yes	240	115.33	even	44	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)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.68213 + 1.47324i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.663233 + 1.21462i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.68213 + 1.47324i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.663233 + 1.21462i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.78294 + 1.34949i) q^{10} +(3.43475 - 2.97623i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-0.104837 + 0.0572451i) q^{13} +(-0.574893 + 1.25884i) q^{14} +(-1.79714 + 1.33053i) q^{15} +(0.959493 - 0.281733i) q^{16} +(1.93410 + 2.58366i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(0.165605 + 1.15181i) q^{19} +(1.87467 + 1.21885i) q^{20} +(-1.04588 - 0.906262i) q^{21} +(3.21368 - 3.21368i) q^{22} +(-1.83219 + 4.43205i) q^{23} +1.00000i q^{24} +(0.659124 + 4.95637i) q^{25} +(-0.100486 + 0.0645782i) q^{26} +(0.599278 - 0.800541i) q^{27} +(-0.483624 + 1.29664i) q^{28} +(-2.45088 - 0.352383i) q^{29} +(-1.69764 + 1.45534i) q^{30} +(-5.49019 - 3.52833i) q^{31} +(0.936950 - 0.349464i) q^{32} +(2.17810 + 3.98890i) q^{33} +(2.11349 + 2.43910i) q^{34} +(-2.90507 + 1.06605i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.269191 + 0.721730i) q^{37} +(0.247352 + 1.13706i) q^{38} +(-0.0336523 - 0.114609i) q^{39} +(1.95685 + 1.08201i) q^{40} +(-1.09634 - 2.40066i) q^{41} +(-1.10787 - 0.829340i) q^{42} +(4.74127 + 1.03140i) 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} +(0.0713392 + 0.997452i) q^{48} +(2.74906 + 4.27762i) q^{49} +(1.01103 + 4.89672i) q^{50} +(-2.93574 + 1.34071i) q^{51} +(-0.0956227 + 0.0715823i) q^{52} +(-4.35555 - 2.37831i) q^{53} +(0.540641 - 0.841254i) q^{54} +(10.1624 + 0.0538109i) q^{55} +(-0.389890 + 1.32784i) q^{56} +(-1.16069 - 0.0830141i) q^{57} +(-2.46977 - 0.176641i) q^{58} +(0.267799 - 0.912041i) q^{59} +(-1.58949 + 1.57274i) q^{60} +(6.89732 - 10.7324i) q^{61} +(-5.72791 - 3.12768i) q^{62} +(1.10787 - 0.829340i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-0.260685 - 0.0581558i) q^{65} +(2.45712 + 3.82335i) q^{66} +(-1.03147 - 14.4218i) 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} +(-0.977147 - 0.212565i) q^{72} +(8.91923 + 6.67685i) q^{73} +(0.319993 + 0.700687i) q^{74} +(-4.98320 - 0.409491i) q^{75} +(0.327839 + 1.11652i) q^{76} +(1.33695 + 6.14585i) q^{77} +(-0.0417427 - 0.111916i) q^{78} +(-11.2840 - 3.31328i) q^{79} +(2.02905 + 0.939653i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-1.26481 - 2.31633i) q^{82} +(1.37100 - 0.511355i) q^{83} +(-1.16421 - 0.748193i) q^{84} +(-0.552939 + 7.19545i) q^{85} +(4.80277 + 0.690534i) q^{86} +(0.865301 - 2.31996i) q^{87} +(2.72361 - 3.63832i) q^{88} +(-7.15307 + 4.59700i) q^{89} +(-1.06123 - 1.96820i) q^{90} -0.165304i q^{91} +(-1.18280 + 4.64769i) q^{92} +(4.61472 - 4.61472i) q^{93} +(-3.58691 - 3.10807i) q^{94} +(-1.41832 + 2.18147i) q^{95} +(0.142315 + 0.989821i) q^{96} +(13.1626 + 4.90938i) q^{97} +(3.04722 + 4.07061i) 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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