LMFDB - Embedded newform 690.2.x.a.77.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (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:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.17
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(0.959317 + 1.44212i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.937919 + 2.02985i) q^{5} +(0.579579 - 1.63220i) q^{6} +(0.495106 + 2.27597i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.15942 + 2.76690i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(0.959317 + 1.44212i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.937919 + 2.02985i) q^{5} +(0.579579 - 1.63220i) q^{6} +(0.495106 + 2.27597i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.15942 + 2.76690i) q^{9} +(2.18706 - 0.465603i) q^{10} +(-0.949300 + 0.136489i) q^{11} +(-1.65397 + 0.514166i) q^{12} +(0.368799 - 1.69534i) q^{13} +(1.52530 - 1.76029i) q^{14} +(-3.82706 + 0.594683i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-1.16542 + 2.13431i) q^{17} +(2.90983 - 0.729979i) q^{18} +(-0.288979 + 0.984173i) q^{19} +(-1.68339 - 1.47180i) q^{20} +(-2.80725 + 2.89738i) q^{21} +(0.678159 + 0.678159i) q^{22} +(-0.625958 - 4.75481i) q^{23} +(1.40280 + 1.01595i) q^{24} +(-3.24062 - 3.80768i) q^{25} +(-1.57821 + 0.720742i) q^{26} +(-5.10246 + 0.982315i) q^{27} +(-2.32326 - 0.166163i) q^{28} +(3.08194 - 0.904938i) q^{29} +(2.76954 + 2.70734i) q^{30} +(-2.06179 + 4.51468i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-1.10751 - 1.23807i) q^{33} +(2.40702 - 0.346077i) q^{34} +(-5.08425 - 1.12968i) q^{35} +(-2.32818 - 1.89198i) q^{36} +(-5.35891 + 0.383277i) q^{37} +(0.961050 - 0.358453i) q^{38} +(2.79868 - 1.09452i) q^{39} +(-0.169422 + 2.22964i) q^{40} +(-2.47717 + 2.14648i) q^{41} +(4.00179 + 0.510988i) q^{42} +(5.02097 + 1.87273i) q^{43} +(0.136489 - 0.949300i) q^{44} +(-4.52897 - 4.94858i) q^{45} +(-3.43130 + 3.35055i) q^{46} +(-3.13810 + 3.13810i) q^{47} +(-0.0273603 - 1.73183i) q^{48} +(1.43253 - 0.654216i) q^{49} +(-1.10617 + 4.87610i) q^{50} +(-4.19595 + 0.366804i) q^{51} +(1.52277 + 0.831494i) q^{52} +(0.607474 + 2.79251i) q^{53} +(3.84417 + 3.49605i) q^{54} +(0.613315 - 2.05496i) q^{55} +(1.25926 + 1.95944i) q^{56} +(-1.69652 + 0.527392i) q^{57} +(-2.57138 - 1.92491i) q^{58} +(4.97177 - 3.19516i) q^{59} +(0.507612 - 3.83957i) q^{60} +(-0.466203 + 1.02084i) q^{61} +(4.84977 - 1.05500i) q^{62} +(-6.87141 - 1.26889i) q^{63} +(0.755750 - 0.654861i) q^{64} +(3.09540 + 2.33870i) q^{65} +(-0.327417 + 1.62856i) q^{66} +(-9.58947 + 7.17859i) q^{67} +(-1.71952 - 1.71952i) q^{68} +(6.25651 - 5.46407i) q^{69} +(2.14252 + 4.74714i) q^{70} +(13.2180 + 1.90046i) q^{71} +(-0.119385 + 2.99762i) q^{72} +(-2.87938 + 1.57226i) q^{73} +(3.51831 + 4.06034i) q^{74} +(2.38235 - 8.32613i) q^{75} +(-0.862893 - 0.554547i) q^{76} +(-0.780648 - 2.09300i) q^{77} +(-2.55340 - 1.58454i) q^{78} +(0.753226 + 1.17204i) q^{79} +(1.88645 - 1.20054i) q^{80} +(-6.31149 - 6.41600i) q^{81} +(3.20286 + 0.696740i) q^{82} +(2.20250 - 0.157526i) q^{83} +(-1.98912 - 3.50982i) q^{84} +(-3.23927 - 4.36745i) q^{85} +(-1.50976 - 5.14178i) q^{86} +(4.26158 + 3.57640i) q^{87} +(-0.841749 + 0.459630i) q^{88} +(-0.161243 - 0.353074i) q^{89} +(-1.24744 + 6.59120i) q^{90} +4.04114 q^{91} +(4.73856 + 0.738982i) q^{92} +(-8.48862 + 1.35767i) q^{93} +(4.39278 + 0.631586i) q^{94} +(-1.72669 - 1.50966i) q^{95} +(-1.37001 + 1.05975i) q^{96} +(-0.180905 + 2.52938i) q^{97} +(-1.38221 - 0.754745i) q^{98} +(0.722987 - 2.78487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	0.959317	+	1.44212i	0.553862	+	0.832608i
$3$	0.959317	+	1.44212i	0.553862	+	0.832608i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	−0.937919	+	2.02985i	−0.419450	+	0.907778i
$5$	−0.937919	+	2.02985i	−0.419450	+	0.907778i
$6$	0.579579	−	1.63220i	0.236612	−	0.666344i
$7$	0.495106	+	2.27597i	0.187133	+	0.860234i	0.970957	+	0.239252i	$0.0769023\pi$
$7$	0.495106	+	2.27597i	0.187133	+	0.860234i	−0.783825	+	0.620982i	$0.786734\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−1.15942	+	2.76690i	−0.386473	+	0.922301i
$10$	2.18706	−	0.465603i	0.691608	−	0.147237i
$11$	−0.949300	+	0.136489i	−0.286225	+	0.0411529i	−0.283932	−	0.958844i	$-0.591639\pi$
$11$	−0.949300	+	0.136489i	−0.286225	+	0.0411529i	−0.00229297	+	0.999997i	$0.500730\pi$
$12$	−1.65397	+	0.514166i	−0.477461	+	0.148427i
$13$	0.368799	−	1.69534i	0.102287	−	0.470204i	−0.897299	−	0.441423i	$-0.854474\pi$
$13$	0.368799	−	1.69534i	0.102287	−	0.470204i	0.999586	−	0.0287808i	$-0.00916246\pi$
$14$	1.52530	−	1.76029i	0.407653	−	0.470457i
$15$	−3.82706	+	0.594683i	−0.988141	+	0.153546i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−1.16542	+	2.13431i	−0.282657	+	0.517647i	−0.979977	−	0.199113i	$-0.936194\pi$
$17$	−1.16542	+	2.13431i	−0.282657	+	0.517647i	0.697320	+	0.716760i	$0.254376\pi$
$18$	2.90983	−	0.729979i	0.685854	−	0.172058i
$19$	−0.288979	+	0.984173i	−0.0662964	+	0.225785i	−0.985977	−	0.166883i	$-0.946630\pi$
$19$	−0.288979	+	0.984173i	−0.0662964	+	0.225785i	0.919680	+	0.392668i	$0.128448\pi$
$20$	−1.68339	−	1.47180i	−0.376417	−	0.329105i
$21$	−2.80725	+	2.89738i	−0.612593	+	0.632259i
$22$	0.678159	+	0.678159i	0.144584	+	0.144584i
$23$	−0.625958	−	4.75481i	−0.130521	−	0.991446i
$23$	−0.625958	−	4.75481i	−0.130521	−	0.991446i
$24$	1.40280	+	1.01595i	0.286346	+	0.207379i
$25$	−3.24062	−	3.80768i	−0.648123	−	0.761535i
$26$	−1.57821	+	0.720742i	−0.309512	+	0.141349i
$27$	−5.10246	+	0.982315i	−0.981968	+	0.189047i
$28$	−2.32326	−	0.166163i	−0.439055	−	0.0314018i
$29$	3.08194	−	0.904938i	0.572301	−	0.168043i	0.0172386	−	0.999851i	$-0.494513\pi$
$29$	3.08194	−	0.904938i	0.572301	−	0.168043i	0.555063	+	0.831809i	$0.312694\pi$
$30$	2.76954	+	2.70734i	0.505646	+	0.494290i
$31$	−2.06179	+	4.51468i	−0.370308	+	0.810861i	0.629129	+	0.777301i	$0.283412\pi$
$31$	−2.06179	+	4.51468i	−0.370308	+	0.810861i	−0.999437	+	0.0335599i	$0.989316\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	−1.10751	−	1.23807i	−0.192793	−	0.215520i
$34$	2.40702	−	0.346077i	0.412800	−	0.0593517i
$35$	−5.08425	−	1.12968i	−0.859395	−	0.190951i
$36$	−2.32818	−	1.89198i	−0.388029	−	0.315330i
$37$	−5.35891	+	0.383277i	−0.881000	+	0.0630103i	−0.504505	−	0.863409i	$-0.668325\pi$
$37$	−5.35891	+	0.383277i	−0.881000	+	0.0630103i	−0.376494	+	0.926419i	$0.622871\pi$
$38$	0.961050	−	0.358453i	0.155903	−	0.0581488i
$39$	2.79868	−	1.09452i	0.448148	−	0.175263i
$40$	−0.169422	+	2.22964i	−0.0267879	+	0.352537i
$41$	−2.47717	+	2.14648i	−0.386870	+	0.335224i	−0.826482	−	0.562963i	$-0.809661\pi$
$41$	−2.47717	+	2.14648i	−0.386870	+	0.335224i	0.439612	+	0.898188i	$0.355116\pi$
$42$	4.00179	+	0.510988i	0.617490	+	0.0788472i
$43$	5.02097	+	1.87273i	0.765691	+	0.285588i	0.701805	−	0.712369i	$-0.252378\pi$
$43$	5.02097	+	1.87273i	0.765691	+	0.285588i	0.0638861	+	0.997957i	$0.479651\pi$
$44$	0.136489	−	0.949300i	0.0205765	−	0.143112i
$45$	−4.52897	−	4.94858i	−0.675138	−	0.737691i
$46$	−3.43130	+	3.35055i	−0.505917	+	0.494012i
$47$	−3.13810	+	3.13810i	−0.457739	+	0.457739i	−0.897913	−	0.440173i	$-0.854917\pi$
$47$	−3.13810	+	3.13810i	−0.457739	+	0.457739i	0.440173	+	0.897913i	$0.354917\pi$
$48$	−0.0273603	−	1.73183i	−0.00394912	−	0.249969i
$49$	1.43253	−	0.654216i	0.204648	−	0.0934594i
$50$	−1.10617	+	4.87610i	−0.156437	+	0.689585i
$51$	−4.19595	+	0.366804i	−0.587550	+	0.0513629i
$52$	1.52277	+	0.831494i	0.211170	+	0.115307i
$53$	0.607474	+	2.79251i	0.0834430	+	0.383581i	0.999862	−	0.0166399i	$-0.00529689\pi$
$53$	0.607474	+	2.79251i	0.0834430	+	0.383581i	−0.916419	+	0.400221i	$0.868933\pi$
$54$	3.84417	+	3.49605i	0.523125	+	0.475752i
$55$	0.613315	−	2.05496i	0.0826993	−	0.277090i
$56$	1.25926	+	1.95944i	0.168275	+	0.261842i
$57$	−1.69652	+	0.527392i	−0.224709	+	0.0698548i
$58$	−2.57138	−	1.92491i	−0.337638	−	0.252753i
$59$	4.97177	−	3.19516i	0.647269	−	0.415975i	−0.175398	−	0.984498i	$-0.556121\pi$
$59$	4.97177	−	3.19516i	0.647269	−	0.415975i	0.822667	+	0.568523i	$0.192485\pi$
$60$	0.507612	−	3.83957i	0.0655324	−	0.495687i
$61$	−0.466203	+	1.02084i	−0.0596912	+	0.130706i	−0.937127	−	0.348989i	$-0.886525\pi$
$61$	−0.466203	+	1.02084i	−0.0596912	+	0.130706i	0.877436	+	0.479694i	$0.159252\pi$
$62$	4.84977	−	1.05500i	0.615922	−	0.133986i
$63$	−6.87141	−	1.26889i	−0.865716	−	0.159865i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	3.09540	+	2.33870i	0.383937	+	0.290080i
$66$	−0.327417	+	1.62856i	−0.0403023	+	0.200462i
$67$	−9.58947	+	7.17859i	−1.17154	+	0.877004i	−0.994243	−	0.107153i	$-0.965827\pi$
$67$	−9.58947	+	7.17859i	−1.17154	+	0.877004i	−0.177298	+	0.984157i	$0.556736\pi$
$68$	−1.71952	−	1.71952i	−0.208523	−	0.208523i
$69$	6.25651	−	5.46407i	0.753195	−	0.657797i
$70$	2.14252	+	4.74714i	0.256080	+	0.567392i
$71$	13.2180	+	1.90046i	1.56869	+	0.225544i	0.871156	−	0.491007i	$-0.163371\pi$
$71$	13.2180	+	1.90046i	1.56869	+	0.225544i	0.697535	+	0.716551i	$0.254280\pi$
$72$	−0.119385	+	2.99762i	−0.0140697	+	0.353273i
$73$	−2.87938	+	1.57226i	−0.337006	+	0.184019i	−0.638837	−	0.769342i	$-0.720584\pi$
$73$	−2.87938	+	1.57226i	−0.337006	+	0.184019i	0.301831	+	0.953361i	$0.402402\pi$
$74$	3.51831	+	4.06034i	0.408995	+	0.472005i
$75$	2.38235	−	8.32613i	0.275090	−	0.961419i
$76$	−0.862893	−	0.554547i	−0.0989806	−	0.0636109i
$77$	−0.780648	−	2.09300i	−0.0889631	−	0.238519i
$78$	−2.55340	−	1.58454i	−0.289115	−	0.179414i
$79$	0.753226	+	1.17204i	0.0847445	+	0.131865i	0.881038	−	0.473045i	$-0.156845\pi$
$79$	0.753226	+	1.17204i	0.0847445	+	0.131865i	−0.796294	+	0.604910i	$0.793209\pi$
$80$	1.88645	−	1.20054i	0.210911	−	0.134225i
$81$	−6.31149	−	6.41600i	−0.701277	−	0.712889i
$82$	3.20286	+	0.696740i	0.353697	+	0.0769421i
$83$	2.20250	−	0.157526i	0.241755	−	0.0172907i	0.0500643	−	0.998746i	$-0.484057\pi$
$83$	2.20250	−	0.157526i	0.241755	−	0.0172907i	0.191691	+	0.981455i	$0.438603\pi$
$84$	−1.98912	−	3.50982i	−0.217031	−	0.382953i
$85$	−3.23927	−	4.36745i	−0.351349	−	0.473717i
$86$	−1.50976	−	5.14178i	−0.162802	−	0.554452i
$87$	4.26158	+	3.57640i	0.456890	+	0.383430i
$88$	−0.841749	+	0.459630i	−0.0897307	+	0.0489967i
$89$	−0.161243	−	0.353074i	−0.0170918	−	0.0374258i	0.900894	−	0.434040i	$-0.142912\pi$
$89$	−0.161243	−	0.353074i	−0.0170918	−	0.0374258i	−0.917985	+	0.396614i	$0.870185\pi$
$90$	−1.24744	+	6.59120i	−0.131491	+	0.694773i
$91$	4.04114			0.423626
$92$	4.73856	+	0.738982i	0.494029	+	0.0770442i
$93$	−8.48862	+	1.35767i	−0.880229	+	0.140784i
$94$	4.39278	+	0.631586i	0.453080	+	0.0651431i
$95$	−1.72669	−	1.50966i	−0.177155	−	0.154888i
$96$	−1.37001	+	1.05975i	−0.139826	+	0.108161i
$97$	−0.180905	+	2.52938i	−0.0183681	+	0.256820i	0.979968	+	0.199155i	$0.0638199\pi$
$97$	−0.180905	+	2.52938i	−0.0183681	+	0.256820i	−0.998336	+	0.0576644i	$0.981635\pi$
$98$	−1.38221	−	0.754745i	−0.139624	−	0.0762407i
$99$	0.722987	−	2.78487i	0.0726629	−	0.279890i
$100$	4.56643	−	2.03660i	0.456643	−	0.203660i
$101$	14.0732	+	12.1945i	1.40033	+	1.21340i	0.946663	+	0.322225i	$0.104431\pi$
$101$	14.0732	+	12.1945i	1.40033	+	1.21340i	0.453670	+	0.891170i	$0.350115\pi$
$102$	2.80818	+	3.13921i	0.278051	+	0.310828i
$103$	6.25247	+	4.68054i	0.616075	+	0.461188i	0.861174	−	0.508310i	$-0.169730\pi$
$103$	6.25247	+	4.68054i	0.616075	+	0.461188i	−0.245099	+	0.969498i	$0.578821\pi$
$104$	−0.246915	−	1.71733i	−0.0242120	−	0.168398i
$105$	−3.24828	−	8.41582i	−0.316999	−	0.821300i
$106$	1.87148	−	2.15980i	0.181774	−	0.209778i
$107$	4.99659	+	13.3964i	0.483039	+	1.29508i	0.918696	+	0.394964i	$0.129243\pi$
$107$	4.99659	+	13.3964i	0.483039	+	1.29508i	−0.435658	+	0.900112i	$0.643484\pi$
$108$	0.495004	−	5.17252i	0.0476318	−	0.497726i
$109$	4.31345	+	14.6903i	0.413154	+	1.40707i	0.859006	+	0.511965i	$0.171082\pi$
$109$	4.31345	+	14.6903i	0.413154	+	1.40707i	−0.445852	+	0.895106i	$0.647099\pi$
$110$	−2.01262	+	0.740506i	−0.191896	+	0.0706045i
$111$	−5.69363	−	7.36051i	−0.540415	−	0.698629i
$112$	0.813970	−	2.18234i	0.0769130	−	0.206212i
$113$	6.57771	−	4.92402i	0.618779	−	0.463212i	−0.243324	−	0.969945i	$-0.578238\pi$
$113$	6.57771	−	4.92402i	0.618779	−	0.463212i	0.862103	+	0.506733i	$0.169147\pi$
$114$	1.43888	+	1.04208i	0.134764	+	0.0975997i
$115$	10.2387	+	3.18902i	0.954760	+	0.297378i
$116$			3.21205i			0.298231i
$117$	4.26325	+	2.98605i	0.394138	+	0.276060i
$118$	−5.53733	−	2.06532i	−0.509752	−	0.190128i
$119$	−5.43464	−	1.59575i	−0.498192	−	0.146282i
$120$	−3.37794	+	1.89461i	−0.308362	+	0.172953i
$121$	−9.67188	+	2.83992i	−0.879262	+	0.258175i
$122$	1.09661	−	0.238553i	0.0992826	−	0.0215976i
$123$	−5.47188	−	1.51322i	−0.493383	−	0.136443i
$124$	−3.75093	−	3.25020i	−0.336844	−	0.291877i
$125$	10.7685	−	3.00669i	0.963161	−	0.268926i
$126$	3.10208	+	6.26126i	0.276356	+	0.557798i
$127$	−2.48139	+	3.31475i	−0.220188	+	0.294136i	−0.897010	−	0.442010i	$-0.854266\pi$
$127$	−2.48139	+	3.31475i	−0.220188	+	0.294136i	0.676823	+	0.736146i	$0.263356\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	2.11601	+	9.03738i	0.186304	+	0.795697i
$130$	0.0172271	−	3.87952i	0.00151091	−	0.340257i
$131$	7.38090	−	11.4849i	0.644873	−	1.00344i	−0.352829	−	0.935688i	$-0.614780\pi$
$131$	7.38090	−	11.4849i	0.644873	−	1.00344i	0.997702	−	0.0677537i	$-0.0215832\pi$
$132$	1.49994	−	0.713847i	0.130553	−	0.0621324i
$133$	−2.38302	−	0.170437i	−0.206634	−	0.0147788i
$134$	11.4935	+	3.37480i	0.992888	+	0.291538i
$135$	2.79173	−	11.2786i	0.240274	−	0.970705i
$136$	−0.346077	+	2.40702i	−0.0296759	+	0.206400i
$137$	−6.27307	+	6.27307i	−0.535945	+	0.535945i	−0.922335	−	0.386391i	$-0.873722\pi$
$137$	−6.27307	+	6.27307i	−0.535945	+	0.535945i	0.386391	+	0.922335i	$0.373722\pi$
$138$	−8.12360	−	1.73410i	−0.691527	−	0.147616i
$139$		−	14.4154i		−	1.22270i	−0.791360	−	0.611351i	$-0.790626\pi$
$139$		−	14.4154i		−	1.22270i	0.791360	−	0.611351i	$-0.209374\pi$
$140$	2.51632	−	4.56003i	0.212668	−	0.385393i
$141$	−7.53596	−	1.51508i	−0.634642	−	0.127593i
$142$	−6.39986	−	11.7205i	−0.537065	−	0.983561i
$143$	−0.118706	+	1.65973i	−0.00992670	+	0.138793i
$144$	2.47127	−	1.70084i	0.205939	−	0.141736i
$145$	−1.05371	+	7.10464i	−0.0875062	+	0.590008i
$146$	2.98421	+	1.36284i	0.246975	+	0.112790i
$147$	2.31771	+	1.43828i	0.191162	+	0.118628i
$148$	1.14203	−	5.24982i	0.0938742	−	0.431533i
$149$	−1.78256	−	12.3980i	−0.146033	−	1.01568i	−0.922631	−	0.385684i	$-0.873965\pi$
$149$	−1.78256	−	12.3980i	−0.146033	−	1.01568i	0.776598	−	0.629996i	$-0.216944\pi$
$150$	−8.09310	+	3.08250i	−0.660799	+	0.251685i
$151$	18.0098	−	11.5742i	1.46561	−	0.941893i	0.467285	−	0.884107i	$-0.345232\pi$
$151$	18.0098	−	11.5742i	1.46561	−	0.941893i	0.998329	−	0.0577859i	$-0.0184041\pi$
$152$	0.0731742	+	1.02311i	0.00593521	+	0.0829851i
$153$	−4.55422	−	5.69918i	−0.368187	−	0.460751i
$154$	−1.20771	+	1.87923i	−0.0973198	+	0.151433i
$155$	−7.23036	−	8.41953i	−0.580756	−	0.676273i
$156$	0.261703	+	2.99368i	0.0209530	+	0.239686i
$157$	−5.81322	−	10.6461i	−0.463946	−	0.849653i	−0.999985	−	0.00546026i	$-0.998262\pi$
$157$	−5.81322	−	10.6461i	−0.463946	−	0.849653i	0.536039	−	0.844193i	$-0.319920\pi$
$158$	0.486877	−	1.30537i	0.0387338	−	0.103849i
$159$	−3.44438	+	3.55496i	−0.273157	+	0.281927i
$160$	−2.09159	−	0.790721i	−0.165355	−	0.0625120i
$161$	10.5119	−	3.77879i	0.828451	−	0.297810i
$162$	−1.35394	+	8.89758i	−0.106375	+	0.699060i
$163$	−12.9028	−	17.2361i	−1.01062	−	1.35003i	−0.935681	−	0.352847i	$-0.885214\pi$
$163$	−12.9028	−	17.2361i	−1.01062	−	1.35003i	−0.0749422	−	0.997188i	$-0.523877\pi$
$164$	−1.36164	−	2.98157i	−0.106326	−	0.232821i
$165$	3.55186	−	1.08688i	0.276512	−	0.0846137i
$166$	−1.44601	−	1.66879i	−0.112232	−	0.129523i
$167$	−5.31657	+	9.73658i	−0.411409	+	0.753439i	−0.998423	−	0.0561377i	$-0.982121\pi$
$167$	−5.31657	+	9.73658i	−0.411409	+	0.753439i	0.587014	+	0.809577i	$0.300303\pi$
$168$	−1.61772	+	3.69573i	−0.124810	+	0.285132i
$169$	9.08704	+	4.14991i	0.699003	+	0.319224i
$170$	−1.55510	+	5.21049i	−0.119271	+	0.399626i
$171$	−2.38806	−	1.94065i	−0.182620	−	0.148405i
$172$	−3.21144	+	4.28998i	−0.244870	+	0.327108i
$173$	−12.0678	+	16.1207i	−0.917497	+	1.22563i	0.0563467	+	0.998411i	$0.482055\pi$
$173$	−12.0678	+	16.1207i	−0.917497	+	1.22563i	−0.973843	+	0.227221i	$0.927036\pi$
$174$	0.309182	−	5.55483i	0.0234390	−	0.421111i
$175$	7.06170	−	9.26074i	0.533814	−	0.700046i
$176$	0.872394	+	0.398409i	0.0657592	+	0.0300312i
$177$	9.37731	+	4.10471i	0.704842	+	0.308529i
$178$	−0.186021	+	0.340671i	−0.0139428	+	0.0255344i
$179$	0.153466	+	0.177110i	0.0114706	+	0.0132378i	0.761456	−	0.648217i	$-0.224485\pi$
$179$	0.153466	+	0.177110i	0.0114706	+	0.0132378i	−0.749985	+	0.661455i	$0.769939\pi$
$180$	6.02409	−	2.95133i	0.449009	−	0.219979i
$181$	2.95150	+	6.46288i	0.219383	+	0.480382i	0.987039	−	0.160480i	$-0.0513043\pi$
$181$	2.95150	+	6.46288i	0.219383	+	0.480382i	−0.767656	+	0.640862i	$0.778577\pi$
$182$	−2.42176	−	3.23510i	−0.179513	−	0.239801i
$183$	−1.91942	+	0.306991i	−0.141887	+	0.0226935i
$184$	−2.24813	−	4.23626i	−0.165734	−	0.312302i
$185$	4.24823	−	11.2373i	0.312336	−	0.826182i
$186$	6.17391	+	5.98187i	0.452693	+	0.438612i
$187$	0.815027	−	2.18517i	0.0596007	−	0.159796i
$188$	−2.12688	−	3.89509i	−0.155119	−	0.284079i
$189$	−4.76197	−	11.1267i	−0.346382	−	0.809346i
$190$	−0.173780	+	2.28699i	−0.0126073	+	0.165916i
$191$	13.1460	−	20.4556i	0.951213	−	1.48012i	0.0755806	−	0.997140i	$-0.475919\pi$
$191$	13.1460	−	20.4556i	0.951213	−	1.48012i	0.875633	−	0.482977i	$-0.160445\pi$
$192$	1.66939	+	0.461662i	0.120478	+	0.0333176i
$193$	−1.01776	−	14.2301i	−0.0732596	−	1.02430i	−0.892557	−	0.450935i	$-0.851091\pi$
$193$	−1.01776	−	14.2301i	−0.0732596	−	1.02430i	0.819297	−	0.573369i	$-0.194364\pi$
$194$	2.13329	−	1.37098i	0.153161	−	0.0984307i
$195$	−0.403224	+	6.70749i	−0.0288755	+	0.480333i
$196$	0.224124	+	1.55882i	0.0160089	+	0.111344i
$197$	3.60167	−	16.5566i	0.256608	−	1.17961i	−0.650764	−	0.759280i	$-0.725551\pi$
$197$	3.60167	−	16.5566i	0.256608	−	1.17961i	0.907372	−	0.420328i	$-0.138085\pi$
$198$	−2.66267	+	1.09013i	−0.189228	+	0.0774721i
$199$	8.75553	+	3.99852i	0.620663	+	0.283447i	0.700824	−	0.713335i	$-0.252816\pi$
$199$	8.75553	+	3.99852i	0.620663	+	0.283447i	−0.0801606	+	0.996782i	$0.525543\pi$
$200$	−4.36694	−	2.43512i	−0.308789	−	0.172189i
$201$	−19.5517	−	6.94262i	−1.37907	−	0.489695i
$202$	1.32844	−	18.5740i	0.0934687	−	1.30686i
$203$	3.58549	+	6.56634i	0.251652	+	0.460867i
$204$	0.830189	−	4.12932i	0.0581249	−	0.289111i
$205$	−2.03366	−	7.04153i	−0.142037	−	0.491802i
$206$		−	7.81031i		−	0.544170i
$207$	13.8818	+	3.78085i	0.964854	+	0.262787i
$208$	−1.22683	+	1.22683i	−0.0850650	+	0.0850650i
$209$	0.140000	−	0.973719i	0.00968398	−	0.0673535i
$210$	−4.79059	+	7.64379i	−0.330582	+	0.527472i
$211$	−5.53241	−	1.62446i	−0.380867	−	0.111833i	0.0856945	−	0.996321i	$-0.472689\pi$
$211$	−5.53241	−	1.62446i	−0.380867	−	0.111833i	−0.466561	+	0.884489i	$0.654507\pi$
$212$	−2.85054	−	0.203875i	−0.195776	−	0.0140022i
$213$	9.93958	+	20.8851i	0.681049	+	1.43102i
$214$	7.73001	−	12.0281i	0.528413	−	0.822226i
$215$	−8.51062	+	8.43538i	−0.580420	+	0.575288i
$216$	−4.43746	+	2.70351i	−0.301931	+	0.183950i
$217$	−11.2961	−	2.45731i	−0.766827	−	0.166813i
$218$	9.17521	−	12.2566i	0.621423	−	0.830124i
$219$	−5.02963	−	2.64411i	−0.339871	−	0.178673i
$220$	1.79893	+	1.16742i	0.121284	+	0.0787074i
$221$	3.18859	+	2.76293i	0.214488	+	0.185855i
$222$	−2.48033	+	8.96897i	−0.166469	+	0.601958i
$223$	20.7508	−	4.51406i	1.38958	−	0.302284i	0.545322	−	0.838227i	$-0.316407\pi$
$223$	20.7508	−	4.51406i	1.38958	−	0.302284i	0.844254	+	0.535943i	$0.180044\pi$
$224$	−2.23485	+	0.656210i	−0.149322	+	0.0438449i
$225$	14.2927	−	4.55177i	0.952847	−	0.303451i
$226$	−7.88375	−	2.31488i	−0.524420	−	0.153983i
$227$	−6.51062	−	2.42833i	−0.432125	−	0.161174i	0.123983	−	0.992284i	$-0.460433\pi$
$227$	−6.51062	−	2.42833i	−0.432125	−	0.161174i	−0.556108	+	0.831110i	$0.687706\pi$
$228$	−0.0280641	−	1.77638i	−0.00185859	−	0.117644i
$229$			25.9342i			1.71378i	0.515497	+	0.856892i	$0.327607\pi$
$229$			25.9342i			1.71378i	−0.515497	+	0.856892i	$0.672393\pi$
$230$	−3.58286	−	10.1076i	−0.236247	−	0.666474i
$231$	2.26947	−	3.13364i	0.149320	−	0.206178i
$232$	2.57138	−	1.92491i	0.168819	−	0.126376i
$233$	−10.3401	+	27.7228i	−0.677401	+	1.81618i	−0.107949	+	0.994156i	$0.534428\pi$
$233$	−10.3401	+	27.7228i	−0.677401	+	1.81618i	−0.569452	+	0.822025i	$0.692844\pi$
$234$	−0.164420	−	5.20238i	−0.0107485	−	0.340090i
$235$	−3.42661	−	9.31318i	−0.223527	−	0.607525i
$236$	1.66503	+	5.67056i	0.108384	+	0.369122i
$237$	−0.967643	+	2.21060i	−0.0628551	+	0.143594i
$238$	1.97939	+	5.30695i	0.128305	+	0.343998i
$239$	6.52060	−	7.52518i	0.421783	−	0.486763i	−0.504596	−	0.863355i	$-0.668359\pi$
$239$	6.52060	−	7.52518i	0.421783	−	0.486763i	0.926379	+	0.376592i	$0.122904\pi$
$240$	3.54103	+	1.56878i	0.228573	+	0.101265i
$241$	1.66630	+	11.5893i	0.107336	+	0.746535i	0.970411	+	0.241460i	$0.0776262\pi$
$241$	1.66630	+	11.5893i	0.107336	+	0.746535i	−0.863075	+	0.505075i	$0.831465\pi$
$242$	8.06962	+	6.04084i	0.518735	+	0.388320i
$243$	3.19792	−	15.2569i	0.205147	−	0.978731i
$244$	−0.848147	−	0.734924i	−0.0542971	−	0.0470487i
$245$	−0.0156370	+	3.52143i	−0.000999010	+	0.224976i
$246$	2.06778	+	5.28731i	0.131837	+	0.337107i
$247$	1.56194	+	0.852882i	0.0993836	+	0.0542676i
$248$	−0.354070	+	4.95055i	−0.0224835	+	0.314360i
$249$	2.34006	+	3.02515i	0.148295	+	0.191711i
$250$	−8.86028	−	6.81876i	−0.560373	−	0.431256i
$251$	9.28273	+	1.33465i	0.585921	+	0.0842427i	0.428899	−	0.903352i	$-0.358902\pi$
$251$	9.28273	+	1.33465i	0.585921	+	0.0842427i	0.157022	+	0.987595i	$0.449811\pi$
$252$	3.15339	−	6.23558i	0.198645	−	0.392805i
$253$	1.24320	+	4.42830i	0.0781593	+	0.278405i
$254$	4.14063			0.259806
$255$	3.19090	−	8.86120i	0.199822	−	0.554910i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−7.35320	+	4.01515i	−0.458680	+	0.250458i	−0.691938	−	0.721957i	$-0.743243\pi$
$257$	−7.35320	+	4.01515i	−0.458680	+	0.250458i	0.233259	+	0.972415i	$0.425061\pi$
$258$	5.96672	−	7.10986i	0.371472	−	0.442640i
$259$	−3.52555	−	12.0069i	−0.219067	−	0.746075i
$260$	−3.11604	+	2.31112i	−0.193249	+	0.143330i
$261$	−1.06938	+	9.57662i	−0.0661932	+	0.592778i
$262$	−13.6174	+	0.973933i	−0.841283	+	0.0601698i
$263$	0.0836973	+	0.0182072i	0.00516100	+	0.00112271i	0.215145	−	0.976582i	$-0.430978\pi$
$263$	0.0836973	+	0.0182072i	0.00516100	+	0.00112271i	−0.209984	+	0.977705i	$0.567341\pi$
$264$	−1.47035	−	0.772972i	−0.0904935	−	0.0475731i
$265$	−6.23816	−	1.38607i	−0.383207	−	0.0851455i
$266$	1.29165	+	2.00985i	0.0791961	+	0.123232i
$267$	0.354491	−	0.571242i	0.0216945	−	0.0349595i
$268$	−4.18614	−	11.2235i	−0.255709	−	0.685583i
$269$	−1.04080	−	0.668881i	−0.0634586	−	0.0407824i	0.508527	−	0.861046i	$-0.330190\pi$
$269$	−1.04080	−	0.668881i	−0.0634586	−	0.0407824i	−0.571985	+	0.820264i	$0.693827\pi$
$270$	−10.7020	+	4.52410i	−0.651302	+	0.275328i
$271$	12.9371	+	14.9302i	0.785875	+	0.906948i	0.997519	−	0.0703989i	$-0.0224272\pi$
$271$	12.9371	+	14.9302i	0.785875	+	0.906948i	−0.211644	+	0.977347i	$0.567882\pi$
$272$	2.13431	−	1.16542i	0.129412	−	0.0706642i
$273$	3.87673	+	5.82781i	0.234631	+	0.352715i
$274$	8.78116	+	1.26254i	0.530490	+	0.0762729i
$275$	3.59602	+	3.17232i	0.216848	+	0.191298i
$276$	3.48008	+	7.54248i	0.209476	+	0.454004i
$277$	−12.6245	−	12.6245i	−0.758535	−	0.758535i	0.217521	−	0.976056i	$-0.430203\pi$
$277$	−12.6245	−	12.6245i	−0.758535	−	0.758535i	−0.976056	+	0.217521i	$0.930203\pi$
$278$	−11.5402	+	8.63885i	−0.692132	+	0.518124i
$279$	−10.1012	−	10.9392i	−0.604743	−	0.654911i
$280$	−5.15847	+	0.718311i	−0.308277	+	0.0429273i
$281$	−14.0385	+	12.1644i	−0.837464	+	0.725667i	−0.963888	−	0.266310i	$-0.914196\pi$
$281$	−14.0385	+	12.1644i	−0.837464	+	0.725667i	0.126424	+	0.991976i	$0.459650\pi$
$282$	3.30324	+	6.94080i	0.196705	+	0.413319i
$283$	21.4768	−	4.67199i	1.27666	−	0.277721i	0.477392	−	0.878691i	$-0.341582\pi$
$283$	21.4768	−	4.67199i	1.27666	−	0.277721i	0.799272	+	0.600969i	$0.205219\pi$
$284$	−5.54743	+	12.1472i	−0.329179	+	0.720802i
$285$	0.520669	−	3.93834i	0.0308418	−	0.233287i
$286$	1.39982	−	0.899608i	0.0827730	−	0.0531950i
$287$	−6.11179	−	4.57523i	−0.360767	−	0.270067i
$288$	−2.84256	−	0.959077i	−0.167500	−	0.0565142i
$289$	5.99381	+	9.32655i	0.352577	+	0.548620i
$290$	6.31902	−	3.41411i	0.371066	−	0.200483i
$291$	−3.82122	+	2.16559i	−0.224004	+	0.126949i
$292$	−0.697357	−	3.20570i	−0.0408098	−	0.187599i
$293$	15.0971	+	8.24366i	0.881984	+	0.481599i	0.855353	−	0.518046i	$-0.173340\pi$
$293$	15.0971	+	8.24366i	0.881984	+	0.481599i	0.0266307	+	0.999645i	$0.491522\pi$
$294$	−0.237548	−	2.71736i	−0.0138541	−	0.158479i
$295$	1.82260	+	13.0888i	0.106116	+	0.762058i
$296$	−4.88709	+	2.23186i	−0.284056	+	0.129724i
$297$	4.70969	−	1.62894i	0.273284	−	0.0945207i
$298$	−8.85683	+	8.85683i	−0.513063	+	0.513063i
$299$	−8.29188	−	0.692356i	−0.479532	−	0.0400400i
$300$	7.31768	+	4.63159i	0.422486	+	0.267405i
$301$	−1.77635	+	12.3548i	−0.102387	+	0.712116i
$302$	−20.0585	−	7.48142i	−1.15423	−	0.430507i
$303$	−4.08525	+	31.9936i	−0.234692	+	1.83798i
$304$	0.775189	−	0.671705i	0.0444602	−	0.0385249i
$305$	−1.63490	−	1.90379i	−0.0936142	−	0.109011i
$306$	−1.83318	+	7.06123i	−0.104796	+	0.403664i
$307$	−9.34055	+	3.48384i	−0.533093	+	0.198833i	−0.601571	−	0.798819i	$-0.705458\pi$
$307$	−9.34055	+	3.48384i	−0.533093	+	0.198833i	0.0684780	+	0.997653i	$0.478186\pi$
$308$	2.22815	−	0.159361i	0.126961	−	0.00908041i
$309$	−0.751797	+	13.5069i	−0.0427683	+	0.768383i
$310$	−2.40719	+	10.8338i	−0.136719	+	0.615321i
$311$	−18.6257	+	2.67797i	−1.05617	+	0.151854i	−0.648452	−	0.761256i	$-0.724583\pi$
$311$	−18.6257	+	2.67797i	−1.05617	+	0.151854i	−0.407714	+	0.913109i	$0.633674\pi$
$312$	2.23973	−	2.00355i	0.126800	−	0.113429i
$313$	0.285150	+	3.98692i	0.0161176	+	0.225354i	0.999126	+	0.0417943i	$0.0133074\pi$
$313$	0.285150	+	3.98692i	0.0161176	+	0.225354i	−0.983009	+	0.183559i	$0.941238\pi$
$314$	−5.03893	+	11.0337i	−0.284363	+	0.622668i
$315$	9.02049	−	12.7578i	0.508247	−	0.718823i
$316$	−1.33677	+	0.392512i	−0.0751994	+	0.0220805i
$317$	21.4555	+	1.53453i	1.20506	+	0.0861876i	0.659382	−	0.751808i	$-0.270818\pi$
$317$	21.4555	+	1.53453i	1.20506	+	0.0861876i	0.545677	+	0.837995i	$0.316272\pi$
$318$	4.91003	+	0.626961i	0.275341	+	0.0351582i
$319$	−2.80217	+	1.27971i	−0.156891	+	0.0716499i
$320$	0.620440	+	2.14827i	0.0346836	+	0.120092i
$321$	−14.5259	+	20.0571i	−0.810755	+	1.11948i
$322$	−9.32460	−	6.15063i	−0.519640	−	0.342761i
$323$	−1.76375	−	1.76375i	−0.0981378	−	0.0981378i
$324$	7.93426	−	4.24823i	0.440792	−	0.236013i
$325$	−7.65046	+	4.08969i	−0.424371	+	0.226855i
$326$	−6.06586	+	20.6584i	−0.335957	+	1.14416i
$327$	−17.0472	+	20.3131i	−0.942710	+	1.12332i
$328$	−1.57087	+	2.87683i	−0.0867367	+	0.158846i
$329$	−8.69591	−	5.58852i	−0.479421	−	0.308105i
$330$	−2.99864	−	2.19206i	−0.165070	−	0.120669i
$331$	18.4538	−	21.2969i	1.01431	−	1.17058i	0.0290438	−	0.999578i	$-0.490754\pi$
$331$	18.4538	−	21.2969i	1.01431	−	1.17058i	0.985271	−	0.171003i	$-0.0547008\pi$
$332$	−0.469370	+	2.15766i	−0.0257600	+	0.118417i
$333$	5.15274	−	15.2720i	0.282368	−	0.836898i
$334$	10.9806	−	1.57878i	0.600834	−	0.0863868i
$335$	−5.57734	−	26.1982i	−0.304723	−	1.43136i
$336$	3.92805	−	0.919713i	0.214293	−	0.0501745i
$337$	5.54138	−	2.06683i	0.301858	−	0.112587i	−0.193971	−	0.981007i	$-0.562137\pi$
$337$	5.54138	−	2.06683i	0.301858	−	0.112587i	0.495829	+	0.868420i	$0.334864\pi$
$338$	−2.12348	−	9.76150i	−0.115502	−	0.530956i
$339$	13.4111	+	4.76216i	0.728393	+	0.258645i
$340$	5.10315	−	1.87761i	0.276757	−	0.101828i
$341$	1.34105	−	4.56720i	0.0726220	−	0.247328i
$342$	−0.122456	+	3.07473i	−0.00662166	+	0.166262i
$343$	11.9691	+	15.9888i	0.646269	+	0.863315i
$344$	5.35885			0.288930
$345$	5.22318	+	17.8247i	0.281206	+	0.959647i
$346$	20.1372			1.08258
$347$	−19.6413	−	26.2376i	−1.05440	−	1.40851i	−0.907844	−	0.419308i	$-0.862273\pi$
$347$	−19.6413	−	26.2376i	−1.05440	−	1.40851i	−0.146554	−	0.989203i	$-0.546818\pi$
$348$	−4.63216	+	3.08137i	−0.248310	+	0.165179i
$349$	−7.94357	+	27.0533i	−0.425210	+	1.44813i	0.416963	+	0.908923i	$0.363094\pi$
$349$	−7.94357	+	27.0533i	−0.425210	+	1.44813i	−0.842173	+	0.539208i	$0.818724\pi$
$350$	−11.6455	−	0.103426i	−0.622479	−	0.00552836i
$351$	−0.216422	+	9.01269i	−0.0115518	+	0.481062i
$352$	−0.203863	−	0.937145i	−0.0108660	−	0.0499500i
$353$	−15.3241	+	5.71560i	−0.815621	+	0.304211i	−0.722436	−	0.691438i	$-0.756978\pi$
$353$	−15.3241	+	5.71560i	−0.815621	+	0.304211i	−0.0931851	+	0.995649i	$0.529705\pi$
$354$	−2.33362	−	9.96679i	−0.124031	−	0.529729i
$355$	−16.2551	+	25.0482i	−0.862731	+	1.32942i
$356$	0.384200	−	0.0552396i	0.0203625	−	0.00292769i
$357$	−2.91227	−	9.36823i	−0.154134	−	0.495819i
$358$	0.0498146	−	0.228994i	0.00263278	−	0.0121027i
$359$	−10.8684	+	12.5428i	−0.573614	+	0.661986i	−0.966219	−	0.257721i	$-0.917028\pi$
$359$	−10.8684	+	12.5428i	−0.573614	+	0.661986i	0.392605	+	0.919707i	$0.371574\pi$
$360$	−5.97277	−	3.05386i	−0.314792	−	0.160953i
$361$	15.0987	+	9.70336i	0.794670	+	0.510703i
$362$	3.40503	−	6.23585i	0.178965	−	0.327749i
$363$	−13.3739	−	11.2236i	−0.701948	−	0.589088i
$364$	−1.13852	+	3.87744i	−0.0596747	+	0.203233i
$365$	−0.490834	−	7.31937i	−0.0256914	−	0.383113i
$366$	1.39602	+	1.35260i	0.0729712	+	0.0707014i
$367$	22.0792	+	22.0792i	1.15252	+	1.15252i	0.986045	+	0.166479i	$0.0532397\pi$
$367$	22.0792	+	22.0792i	1.15252	+	1.15252i	0.166479	+	0.986045i	$0.446760\pi$
$368$	−2.04405	+	4.33842i	−0.106554	+	0.226156i
$369$	−3.06702	−	9.34277i	−0.159663	−	0.486365i
$370$	−11.5418	+	3.33338i	−0.600029	+	0.173294i
$371$	−6.05490	+	2.76518i	−0.314355	+	0.143561i
$372$	1.08885	−	8.52727i	0.0564540	−	0.442118i
$373$	−4.44526	−	0.317931i	−0.230167	−	0.0164618i	−0.0442205	−	0.999022i	$-0.514080\pi$
$373$	−4.44526	−	0.317931i	−0.230167	−	0.0164618i	−0.185946	+	0.982560i	$0.559535\pi$
$374$	−2.23775	+	0.657062i	−0.115711	+	0.0339759i
$375$	14.6664	+	12.6451i	0.757368	+	0.652988i
$376$	−1.84359	+	4.03690i	−0.0950759	+	0.208187i
$377$	−0.397565	−	5.55868i	−0.0204756	−	0.286287i
$378$	−6.05361	+	10.4801i	−0.311364	+	0.539039i
$379$	26.9879	−	3.88028i	1.38628	−	0.199316i	0.591542	−	0.806274i	$-0.298519\pi$
$379$	26.9879	−	3.88028i	1.38628	−	0.199316i	0.794734	+	0.606958i	$0.207610\pi$
$380$	1.93497	−	1.23143i	0.0992621	−	0.0631708i
$381$	−7.16070	−	0.398565i	−0.366854	−	0.0204191i
$382$	−24.2537	+	1.73466i	−1.24093	+	0.0887528i
$383$	−20.0002	+	7.45971i	−1.02196	+	0.381173i	−0.803902	−	0.594762i	$-0.797246\pi$
$383$	−20.0002	+	7.45971i	−1.02196	+	0.381173i	−0.218063	+	0.975935i	$0.569974\pi$
$384$	−0.630849	−	1.61308i	−0.0321929	−	0.0823172i
$385$	4.98067	+	0.378461i	0.253838	+	0.0192882i
$386$	−10.7818	+	9.34253i	−0.548782	+	0.475522i
$387$	−11.0031	+	11.7213i	−0.559317	+	0.595825i
$388$	−2.37596	−	0.886186i	−0.120621	−	0.0449893i
$389$	2.28095	−	15.8643i	0.115649	−	0.804353i	−0.846609	−	0.532215i	$-0.821360\pi$
$389$	2.28095	−	15.8643i	0.115649	−	0.804353i	0.962258	−	0.272139i	$-0.0877310\pi$
$390$	5.61127	−	3.69685i	0.284137	−	0.187197i
$391$	10.8778	+	4.20537i	0.550112	+	0.212675i
$392$	1.11359	−	1.11359i	0.0562446	−	0.0562446i
$393$	23.6433	−	0.373527i	1.19264	−	0.0188419i
$394$	−15.4126	+	7.03872i	−0.776477	+	0.354605i
$395$	−3.08554	+	0.429658i	−0.155250	+	0.0216184i
$396$	2.46837	+	1.47829i	0.124040	+	0.0742868i
$397$	−4.08465	−	2.23039i	−0.205003	−	0.111940i	0.373468	−	0.927643i	$-0.378169\pi$
$397$	−4.08465	−	2.23039i	−0.205003	−	0.111940i	−0.578471	+	0.815703i	$0.696350\pi$
$398$	−2.04602	−	9.40538i	−0.102558	−	0.471449i
$399$	−2.04028	−	3.60010i	−0.102142	−	0.180231i
$400$	0.667594	+	4.95523i	0.0333797	+	0.247762i
$401$	8.47409	+	13.1859i	0.423176	+	0.658475i	0.985739	−	0.168280i	$-0.0538212\pi$
$401$	8.47409	+	13.1859i	0.423176	+	0.658475i	−0.562563	+	0.826754i	$0.690185\pi$
$402$	6.15906	+	19.8125i	0.307186	+	0.988159i
$403$	6.89355	+	5.16045i	0.343392	+	0.257060i
$404$	−15.6654	+	10.0675i	−0.779382	+	0.500878i
$405$	18.9432	−	6.79372i	0.941296	−	0.337582i
$406$	3.10792	−	6.80540i	0.154243	−	0.337746i
$407$	5.03490	−	1.09528i	0.249571	−	0.0542908i
$408$	−3.80321	+	1.81001i	−0.188287	+	0.0896089i
$409$	−18.1129	+	15.6949i	−0.895626	+	0.776064i	−0.975329	−	0.220754i	$-0.929148\pi$
$409$	−18.1129	+	15.6949i	−0.895626	+	0.776064i	0.0797036	+	0.996819i	$0.474603\pi$
$410$	−4.41831	+	5.84786i	−0.218205	+	0.288805i
$411$	−15.0644	−	3.02865i	−0.743071	−	0.149393i
$412$	−6.25247	+	4.68054i	−0.308037	+	0.230594i
$413$	9.73363	+	9.73363i	0.478961	+	0.478961i
$414$	−5.29234	−	13.3788i	−0.260104	−	0.657530i
$415$	−1.74601	+	4.61849i	−0.0857082	+	0.226713i
$416$	1.71733	+	0.246915i	0.0841992	+	0.0121060i
$417$	20.7888	−	13.8290i	1.01803	−	0.677208i
$418$	−0.863401	+	0.471452i	−0.0422303	+	0.0230595i
$419$	−17.0242	−	19.6470i	−0.831689	−	0.959820i	0.167974	−	0.985791i	$-0.446278\pi$
$419$	−17.0242	−	19.6470i	−0.831689	−	0.959820i	−0.999663	+	0.0259715i	$0.991732\pi$
$420$	8.99006	−	0.745689i	0.438670	−	0.0363859i
$421$	6.54319	+	4.20505i	0.318896	+	0.204942i	0.690289	−	0.723534i	$-0.257483\pi$
$421$	6.54319	+	4.20505i	0.318896	+	0.204942i	−0.371393	+	0.928476i	$0.621120\pi$
$422$	2.01500	+	5.40243i	0.0980887	+	0.262986i
$423$	−5.04444	−	12.3212i	−0.245269	−	0.599077i
$424$	1.54506	+	2.40416i	0.0750346	+	0.116756i
$425$	11.9035	−	2.47894i	0.577403	−	0.120246i
$426$	10.7628	−	20.4730i	0.521461	−	0.991922i
$427$	−2.55422	−	0.555638i	−0.123608	−	0.0268892i
$428$	−14.2614	+	1.02000i	−0.689352	+	0.0493035i
$429$	−2.50740	+	1.42102i	−0.121059	+	0.0686073i
$430$	11.8531	+	1.75797i	0.571607	+	0.0847770i
$431$	−1.97759	−	6.73507i	−0.0952574	−	0.324417i	0.898054	−	0.439886i	$-0.144981\pi$
$431$	−1.97759	−	6.73507i	−0.0952574	−	0.324417i	−0.993311	+	0.115469i	$0.963163\pi$
$432$	4.82354	+	1.93222i	0.232073	+	0.0929640i
$433$	24.5209	−	13.3894i	1.17840	−	0.643454i	0.233993	−	0.972238i	$-0.424821\pi$
$433$	24.5209	−	13.3894i	1.17840	−	0.643454i	0.944405	+	0.328784i	$0.106639\pi$
$434$	4.80230	+	10.5156i	0.230518	+	0.504764i
$435$	−11.2566	+	5.29602i	−0.539712	+	0.253925i
$436$	−15.3104			−0.733237
$437$	4.86044	+	0.757990i	0.232506	+	0.0362596i
$438$	0.897421	+	5.61098i	0.0428804	+	0.268103i
$439$	−0.489855	−	0.0704306i	−0.0233795	−	0.00336147i	0.130615	−	0.991433i	$-0.458305\pi$
$439$	−0.489855	−	0.0704306i	−0.0233795	−	0.00336147i	−0.153995	+	0.988072i	$0.549214\pi$
$440$	−0.143489	−	2.13972i	−0.00684057	−	0.102007i
$441$	0.149244	+	4.72219i	0.00710685	+	0.224866i
$442$	0.300988	−	4.20836i	0.0143165	−	0.200171i
$443$	−12.2091	−	6.66667i	−0.580072	−	0.316743i	0.162289	−	0.986743i	$-0.448112\pi$
$443$	−12.2091	−	6.66667i	−0.580072	−	0.316743i	−0.742361	+	0.670000i	$0.766294\pi$
$444$	8.66644	−	3.38930i	0.411291	−	0.160849i
$445$	0.867922	+	0.00385402i	0.0411434	+	0.000182698i
$446$	−16.0492	−	13.9067i	−0.759951	−	0.658501i
$447$	16.1693	−	14.4642i	0.764782	−	0.684135i
$448$	1.86462	+	1.39583i	0.0880949	+	0.0659470i
$449$	3.22325	+	22.4182i	0.152114	+	1.05798i	0.912667	+	0.408703i	$0.134019\pi$
$449$	3.22325	+	22.4182i	0.152114	+	1.05798i	−0.760553	+	0.649276i	$0.775072\pi$
$450$	−12.2092	−	8.71413i	−0.575546	−	0.410788i
$451$	2.05861	−	2.37576i	0.0969362	−	0.111870i
$452$	2.87140	+	7.69853i	0.135059	+	0.362108i
$453$	33.9684	+	14.8689i	1.59598	+	0.698603i
$454$	1.95768	+	6.66726i	0.0918787	+	0.312910i
$455$	−3.79026	+	8.20292i	−0.177690	+	0.384559i
$456$	−1.40525	+	1.08701i	−0.0658068	+	0.0509040i
$457$	−3.74103	+	10.0301i	−0.174998	+	0.469188i	−0.994605	−	0.103739i	$-0.966919\pi$
$457$	−3.74103	+	10.0301i	−0.174998	+	0.469188i	0.819607	+	0.572927i	$0.194192\pi$
$458$	20.7614	−	15.5418i	0.970118	−	0.726221i
$459$	3.84996	−	12.0351i	0.179701	−	0.561748i
$460$	−5.94441	+	8.92547i	−0.277159	+	0.416152i
$461$		−	23.3811i		−	1.08897i	−0.838771	−	0.544484i	$-0.816726\pi$
$461$		−	23.3811i		−	1.08897i	0.838771	−	0.544484i	$-0.183274\pi$
$462$	−3.86865	+	0.0611186i	−0.179986	+	0.00284350i
$463$	−11.1211	−	4.14797i	−0.516843	−	0.192772i	0.0774877	−	0.996993i	$-0.475310\pi$
$463$	−11.1211	−	4.14797i	−0.516843	−	0.192772i	−0.594330	+	0.804221i	$0.702583\pi$
$464$	−3.08194	−	0.904938i	−0.143075	−	0.0420107i
$465$	5.20577	−	18.5040i	0.241412	−	0.858105i
$466$	28.3898	−	8.33600i	1.31513	−	0.386158i
$467$	11.7307	−	2.55186i	0.542832	−	0.118086i	0.0672154	−	0.997738i	$-0.478589\pi$
$467$	11.7307	−	2.55186i	0.542832	−	0.118086i	0.475617	+	0.879653i	$0.342225\pi$
$468$	−4.06619	+	3.24930i	−0.187960	+	0.150199i
$469$	−21.0860	−	18.2712i	−0.973663	−	0.843683i
$470$	−5.40210	+	8.32432i	−0.249180	+	0.383972i
$471$	9.77626	−	18.5964i	0.450466	−	0.856876i
$472$	3.54170	−	4.73116i	0.163020	−	0.217769i
$473$	−5.02202	−	1.09247i	−0.230913	−	0.0502320i
$474$	2.34957	−	0.550127i	0.107919	−	0.0252682i
$475$	4.68389	−	2.08899i	0.214911	−	0.0958493i
$476$	3.06223	−	4.76492i	0.140357	−	0.218400i
$477$	−8.43093	−	1.55688i	−0.386026	−	0.0712844i
$478$	−9.93187	−	0.710341i	−0.454273	−	0.0324903i
$479$	31.8686	+	9.35747i	1.45611	+	0.427554i	0.911558	−	0.411171i	$-0.134880\pi$
$479$	31.8686	+	9.35747i	1.45611	+	0.427554i	0.544555	+	0.838725i	$0.316698\pi$
$480$	−0.866187	−	3.77488i	−0.0395358	−	0.172299i
$481$	−1.32658	+	9.22655i	−0.0604867	+	0.420694i
$482$	8.27917	−	8.27917i	0.377106	−	0.377106i
$483$	15.5337	+	11.5343i	0.706807	+	0.524829i
$484$		−	10.0802i		−	0.458191i
$485$	−4.96460	−	2.73957i	−0.225431	−	0.124397i
$486$	−14.1302	+	6.58306i	−0.640960	+	0.298614i
$487$	−6.57940	−	12.0493i	−0.298141	−	0.546004i	0.685070	−	0.728477i	$-0.259772\pi$
$487$	−6.57940	−	12.0493i	−0.298141	−	0.546004i	−0.983211	+	0.182473i	$0.941590\pi$
$488$	−0.0800611	+	1.11940i	−0.00362419	+	0.0506729i
$489$	12.4787	−	35.1422i	0.564304	−	1.58919i
$490$	2.82842	−	2.09780i	0.127775	−	0.0947689i
$491$	−25.3822	−	11.5917i	−1.14548	−	0.523124i	−0.250011	−	0.968243i	$-0.580434\pi$
$491$	−25.3822	−	11.5917i	−1.14548	−	0.523124i	−0.895472	+	0.445118i	$0.853162\pi$
$492$	2.99353	−	4.82391i	0.134959	−	0.217479i
$493$	−1.66034	+	7.63246i	−0.0747779	+	0.343749i
$494$	−0.253267	−	1.76151i	−0.0113950	−	0.0792540i
$495$	4.97478	+	4.07954i	0.223600	+	0.183362i
$496$	4.17531	−	2.68331i	0.187477	−	0.120484i
$497$	2.21893	+	31.0247i	0.0995326	+	1.39165i
$498$	1.01941	−	3.68622i	0.0456807	−	0.165183i
$499$	6.89383	−	10.7270i	0.308610	−	0.480207i	−0.651957	−	0.758256i	$-0.726052\pi$
$499$	6.89383	−	10.7270i	0.308610	−	0.480207i	0.960567	+	0.278050i	$0.0896879\pi$
$500$	−0.148934	+	11.1793i	−0.00666053	+	0.499956i
$501$	−19.1416	+	1.67333i	−0.855183	+	0.0747590i
$502$	−4.49449	−	8.23103i	−0.200599	−	0.367369i
$503$	−0.0685967	+	0.183915i	−0.00305858	+	0.00820036i	−0.938470	−	0.345361i	$-0.887757\pi$
$503$	−0.0685967	+	0.183915i	−0.00305858	+	0.00820036i	0.935411	+	0.353561i	$0.115029\pi$
$504$	−6.88160	+	1.21243i	−0.306531	+	0.0540057i
$505$	−37.9525	+	17.1291i	−1.68886	+	0.762233i
$506$	2.80002	−	3.64902i	0.124476	−	0.162219i
$507$	2.73269	+	17.0857i	0.121363	+	0.758802i
$508$	−2.48139	−	3.31475i	−0.110094	−	0.147068i
$509$	−4.71285	−	10.3197i	−0.208893	−	0.457413i	0.775964	−	0.630777i	$-0.217264\pi$
$509$	−4.71285	−	10.3197i	−0.208893	−	0.457413i	−0.984858	+	0.173364i	$0.944536\pi$
$510$	−9.00599	+	2.75587i	−0.398792	+	0.122032i
$511$	−5.00401	−	5.77493i	−0.221364	−	0.255468i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	0.507737	−	5.30557i	0.0224171	−	0.234247i
$514$	7.62090	+	3.48035i	0.336143	+	0.153512i
$515$	−15.3651	+	8.30164i	−0.677069	+	0.365814i
$516$	−9.26745	−	0.515827i	−0.407977	−	0.0227080i
$517$	2.55069	−	3.40732i	0.112179	−	0.149854i
$518$	−7.49926	+	10.0178i	−0.329499	+	0.440159i
$519$	−34.8248	−	1.93835i	−1.52864	−	0.0850841i
$520$	3.71752	+	1.10952i	0.163024	+	0.0486556i
$521$	−18.0695	−	8.25206i	−0.791639	−	0.361529i	−0.0217958	−	0.999762i	$-0.506938\pi$
$521$	−18.0695	−	8.25206i	−0.791639	−	0.361529i	−0.769843	+	0.638233i	$0.779666\pi$
$522$	8.30733	−	4.88297i	0.363602	−	0.213722i
$523$	19.2933	−	35.3330i	0.843636	−	1.54500i	0.00521046	−	0.999986i	$-0.498341\pi$
$523$	19.2933	−	35.3330i	0.843636	−	1.54500i	0.838425	−	0.545017i	$-0.183477\pi$
$524$	8.94025	+	10.3176i	0.390557	+	0.450726i
$525$	20.1295	+	1.29983i	0.878523	+	0.0567291i
$526$	−0.0355823	−	0.0779143i	−0.00155146	−	0.00339723i
$527$	−7.23290	−	9.66202i	−0.315070	−	0.420884i
$528$	0.262349	+	1.64030i	0.0114173	+	0.0713848i
$529$	−22.2164	+	5.95261i	−0.965928	+	0.258809i
$530$	2.62879	+	5.82454i	0.114187	+	0.253002i
$531$	3.07633	+	17.4609i	0.133501	+	0.757740i
$532$	0.834908	−	2.23847i	0.0361978	−	0.0970502i
$533$	2.72545	+	4.99128i	0.118052	+	0.216196i
$534$	−0.669742	+	0.0585479i	−0.0289826	+	0.00253362i
$535$	−31.8791	−	2.42237i	−1.37825	−	0.104728i
$536$	−6.47619	+	10.0772i	−0.279729	+	0.435267i
$537$	−0.108190	+	0.391221i	−0.00466876	+	0.0168824i
$538$	0.0882608	+	1.23405i	0.00380519	+	0.0532036i
$539$	−1.27061	+	0.816572i	−0.0547291	+	0.0351723i
$540$	10.0352	+	5.85619i	0.431846	+	0.252010i
$541$	−6.13081	−	42.6407i	−0.263584	−	1.83327i	−0.505328	−	0.862927i	$-0.668628\pi$
$541$	−6.13081	−	42.6407i	−0.263584	−	1.83327i	0.241744	−	0.970340i	$-0.422281\pi$
$542$	4.19934	−	19.3041i	0.180377	−	0.829181i
$543$	−6.48882	+	10.4564i	−0.278462	+	0.448725i
$544$	−2.21202	−	1.01019i	−0.0948394	−	0.0433117i
$545$	−33.8648	−	5.02260i	−1.45061	−	0.215145i
$546$	2.34216	−	6.59596i	0.100235	−	0.282281i
$547$	2.00796	−	28.0750i	0.0858544	−	1.20040i	−0.753735	−	0.657179i	$-0.771750\pi$
$547$	2.00796	−	28.0750i	0.0858544	−	1.20040i	0.839589	−	0.543222i	$-0.182796\pi$
$548$	−4.25164	−	7.78630i	−0.181621	−	0.332614i
$549$	−2.28405	−	2.47353i	−0.0974808	−	0.105567i
$550$	0.384558	−	4.77987i	0.0163976	−	0.203814i
$551$			3.29467i			0.140358i
$552$	3.95254	−	7.30599i	0.168231	−	0.310964i
$553$	−2.29460	+	2.29460i	−0.0975764	+	0.0975764i
$554$	−2.54086	+	17.6721i	−0.107951	+	0.750814i
$555$	20.2809	−	4.65368i	0.860877	−	0.197538i
$556$	13.8315	+	4.06130i	0.586587	+	0.172237i
$557$	30.0711	+	2.15073i	1.27415	+	0.0911293i	0.691969	−	0.721927i	$-0.256744\pi$
$557$	30.0711	+	2.15073i	1.27415	+	0.0911293i	0.582185	+	0.813057i	$0.302198\pi$
$558$	−2.70383	+	14.6420i	−0.114462	+	0.619847i
$559$	5.02664	−	7.82161i	0.212604	−	0.330819i
$560$	3.66639	+	3.69910i	0.154933	+	0.156315i
$561$	3.93315	−	0.920907i	0.166058	−	0.0388807i
$562$	18.1510	+	3.94851i	0.765655	+	0.166558i
$563$	16.5662	−	22.1299i	0.698184	−	0.932665i	−0.301600	−	0.953434i	$-0.597521\pi$
$563$	16.5662	−	22.1299i	0.698184	−	0.932665i	0.999784	+	0.0207697i	$0.00661169\pi$
$564$	3.57684	−	6.80385i	0.150612	−	0.286494i
$565$	3.82567	+	17.9701i	0.160947	+	0.756009i
$566$	−16.6107	−	14.3932i	−0.698200	−	0.604993i
$567$	11.4777	−	17.5413i	0.482020	−	0.736667i
$568$	13.0488	−	2.83859i	0.547514	−	0.119104i
$569$	−27.4456	+	8.05876i	−1.15058	+	0.337841i	−0.800765	−	0.598978i	$-0.795574\pi$
$569$	−27.4456	+	8.05876i	−1.15058	+	0.337841i	−0.349815	+	0.936819i	$0.613756\pi$
$570$	−3.46483	+	1.94334i	−0.145126	+	0.0813976i
$571$	−40.1509	−	11.7894i	−1.68026	−	0.493370i	−0.704044	−	0.710156i	$-0.748624\pi$
$571$	−40.1509	−	11.7894i	−1.68026	−	0.493370i	−0.976219	+	0.216786i	$0.930443\pi$
$572$	−1.55905	−	0.581497i	−0.0651873	−	0.0243136i
$573$	42.1107	−	0.665284i	1.75920	−	0.0277926i
$574$			7.63457i			0.318661i
$575$	−16.0763	+	17.7919i	−0.670427	+	0.741975i
$576$	0.935704	+	2.85034i	0.0389877	+	0.118764i
$577$	−15.8971	+	11.9004i	−0.661807	+	0.495422i	−0.876589	−	0.481240i	$-0.840187\pi$
$577$	−15.8971	+	11.9004i	−0.661807	+	0.495422i	0.214782	+	0.976662i	$0.431096\pi$
$578$	3.87433	−	10.3875i	0.161151	−	0.432062i
$579$	19.5451	−	15.1189i	0.812268	−	0.628320i
$580$	−6.51999	−	3.01264i	−0.270728	−	0.125093i
$581$	1.44899	+	4.93481i	0.0601143	+	0.204731i
$582$	4.02362	+	1.76125i	0.166784	+	0.0730062i
$583$	−0.957823	−	2.56802i	−0.0396690	−	0.106357i
$584$	−2.14838	+	2.47937i	−0.0889008	+	0.102597i
$585$	−10.0598	+	5.85312i	−0.415923	+	0.241997i
$586$	−2.44799	−	17.0261i	−0.101125	−	0.703342i
$587$	5.10355	+	3.82047i	0.210646	+	0.157688i	0.699392	−	0.714739i	$-0.253454\pi$
$587$	5.10355	+	3.82047i	0.210646	+	0.157688i	−0.488745	+	0.872426i	$0.662545\pi$
$588$	−2.03300	+	1.81862i	−0.0838394	+	0.0749985i
$589$	−3.84742	−	3.33381i	−0.158530	−	0.137367i
$590$	9.38586	−	9.30287i	0.386410	−	0.382993i
$591$	27.3317	−	10.6890i	1.12428	−	0.439687i
$592$	4.71542	+	2.57481i	0.193803	+	0.105824i
$593$	−0.0794357	+	1.11066i	−0.00326203	+	0.0456092i	−0.998822	−	0.0485159i	$-0.984551\pi$
$593$	−0.0794357	+	1.11066i	−0.00326203	+	0.0456092i	0.995560	+	0.0941251i	$0.0300054\pi$
$594$	−4.12645	−	2.79411i	−0.169310	−	0.114644i
$595$	8.33639	−	9.53483i	0.341759	−	0.390890i
$596$	12.3980	+	1.78256i	0.507840	+	0.0730164i
$597$	2.63299	+	16.4624i	0.107761	+	0.673760i
$598$	4.41488	+	7.05291i	0.180538	+	0.288415i
$599$	31.8098			1.29971			0.649857	−	0.760057i	$-0.274829\pi$
$599$	31.8098			1.29971			0.649857	+	0.760057i	$0.274829\pi$
$600$	−0.677543	−	8.63371i	−0.0276606	−	0.352470i
$601$	−18.8181	−	41.2059i	−0.767607	−	1.68082i	−0.731852	−	0.681464i	$-0.761344\pi$
$601$	−18.8181	−	41.2059i	−0.767607	−	1.68082i	−0.0357546	−	0.999361i	$-0.511383\pi$
$602$	10.9550	−	5.98189i	0.446493	−	0.243804i
$603$	−8.74423	−	34.8561i	−0.356092	−	1.41945i
$604$	6.03140	+	20.5411i	0.245414	+	0.835804i
$605$	3.30682	−	22.2961i	0.134441	−	0.906466i
$606$	28.0604	−	15.9026i	1.13987	−	0.646000i
$607$	26.5918	−	1.90188i	1.07933	−	0.0771951i	0.479668	−	0.877450i	$-0.340757\pi$
$607$	26.5918	−	1.90188i	1.07933	−	0.0771951i	0.599660	+	0.800255i	$0.295303\pi$
$608$	−1.00228	−	0.218033i	−0.0406479	−	0.00884240i
$609$	−6.02982	+	11.4699i	−0.244341	+	0.464784i
$610$	−0.544305	+	2.44971i	−0.0220383	+	0.0991857i
$611$	4.16283	+	6.47749i	0.168410	+	0.262051i
$612$	6.75140	−	2.76410i	0.272909	−	0.111732i
$613$	−16.2130	−	43.4686i	−0.654835	−	1.75568i	−0.654941	−	0.755680i	$-0.727306\pi$
$613$	−16.2130	−	43.4686i	−0.654835	−	1.75568i	0.000105806	−	1.00000i	$-0.499966\pi$
$614$	8.38654	+	5.38970i	0.338453	+	0.217511i
$615$	8.20381	−	9.68784i	0.330809	−	0.390652i
$616$	−1.46286	−	1.68823i	−0.0589402	−	0.0680206i
$617$	−7.73403	+	4.22310i	−0.311360	+	0.170016i	−0.627330	−	0.778754i	$-0.715852\pi$
$617$	−7.73403	+	4.22310i	−0.311360	+	0.170016i	0.315969	+	0.948769i	$0.397670\pi$
$618$	11.2634	−	7.49257i	0.453080	−	0.301395i
$619$	−31.8844	−	4.58428i	−1.28154	−	0.184258i	−0.532301	−	0.846555i	$-0.678672\pi$
$619$	−31.8844	−	4.58428i	−1.28154	−	0.184258i	−0.749241	+	0.662298i	$0.769581\pi$
$620$	10.1155	−	4.56542i	0.406249	−	0.183352i
$621$	7.86464	+	23.6463i	0.315597	+	0.948893i
$622$	13.3058	+	13.3058i	0.533514	+	0.533514i
$623$	0.723752	−	0.541794i	0.0289965	−	0.0217065i
$624$	−2.94614	−	0.592314i	−0.117940	−	0.0237116i
$625$	−3.99682	+	24.6784i	−0.159873	+	0.987138i
$626$	3.02081	−	2.61754i	0.120736	−	0.104618i
$627$	1.53852	−	0.732209i	0.0614427	−	0.0292416i
$628$	11.8527	−	2.57839i	0.472973	−	0.102889i
$629$	5.42737	−	11.8843i	0.216403	−	0.473857i
$630$	−15.6190	+	0.424218i	−0.622274	+	0.0169013i
$631$	−16.3715	+	10.5213i	−0.651739	+	0.418847i	−0.824301	−	0.566151i	$-0.808432\pi$
$631$	−16.3715	+	10.5213i	−0.651739	+	0.418847i	0.172562	+	0.984999i	$0.444795\pi$
$632$	1.11532	+	0.834919i	0.0443651	+	0.0332113i
$633$	−2.96467	−	9.53677i	−0.117835	−	0.379053i
$634$	−11.6293	−	18.0956i	−0.461860	−	0.718668i
$635$	−4.40111	−	8.14582i	−0.174653	−	0.323257i
$636$	−2.44056	−	4.30641i	−0.0967747	−	0.170760i
$637$	−0.580803	−	2.66991i	−0.0230123	−	0.105786i
$638$	2.70374	+	1.47635i	0.107042	+	0.0584493i
$639$	−20.5836	+	34.3695i	−0.814276	+	1.35964i
$640$	1.34796	−	1.78410i	0.0532828	−	0.0705226i
$641$	11.5916	−	5.29370i	0.457841	−	0.209089i	−0.173125	−	0.984900i	$-0.555386\pi$
$641$	11.5916	−	5.29370i	0.457841	−	0.209089i	0.630965	+	0.775811i	$0.282659\pi$
$642$	24.7615	−	0.391194i	0.977260	−	0.0154392i
$643$	−19.5531	+	19.5531i	−0.771098	+	0.771098i	−0.978299	−	0.207200i	$-0.933565\pi$
$643$	−19.5531	+	19.5531i	−0.771098	+	0.771098i	0.207200	+	0.978299i	$0.433565\pi$
$644$	0.664191	+	11.1507i	0.0261728	+	0.439398i
$645$	−20.3292	−	4.18114i	−0.800462	−	0.164632i
$646$	−0.354979	+	2.46893i	−0.0139665	+	0.0971389i
$647$	35.7737	+	13.3429i	1.40641	+	0.524564i	0.934145	−	0.356893i	$-0.116164\pi$
$647$	35.7737	+	13.3429i	1.40641	+	0.524564i	0.472264	+	0.881457i	$0.343437\pi$
$648$	−8.15571	−	3.80583i	−0.320387	−	0.149507i
$649$	−4.28360	+	3.71176i	−0.168146	+	0.145699i
$650$	7.85871	+	3.67365i	0.308244	+	0.144092i
$651$	−7.29278	−	18.6476i	−0.285827	−	0.730858i
$652$	20.1730	−	7.52415i	0.790037	−	0.294669i
$653$	−17.0735	+	1.22112i	−0.668138	+	0.0477862i	−0.401288	−	0.915952i	$-0.631437\pi$
$653$	−17.0735	+	1.22112i	−0.668138	+	0.0477862i	−0.266850	+	0.963738i	$0.585983\pi$
$654$	26.4775	+	1.47374i	1.03535	+	0.0576277i
$655$	16.3900	+	25.7541i	0.640411	+	1.00630i
$656$	3.24441	−	0.466475i	0.126673	−	0.0182128i
$657$	−1.01188	−	9.78987i	−0.0394772	−	0.381939i
$658$	0.737422	+	10.3105i	0.0287477	+	0.401946i
$659$	−13.1144	+	28.7166i	−0.510866	+	1.11864i	0.461917	+	0.886923i	$0.347162\pi$
$659$	−13.1144	+	28.7166i	−0.510866	+	1.11864i	−0.972783	+	0.231717i	$0.925566\pi$
$660$	0.0421826	+	3.71419i	0.00164196	+	0.144575i
$661$	27.5807	−	8.09843i	1.07277	−	0.314992i	0.302784	−	0.953059i	$-0.402084\pi$
$661$	27.5807	−	8.09843i	1.07277	−	0.314992i	0.769981	+	0.638067i	$0.220266\pi$
$662$	−28.1080	−	2.01032i	−1.09245	−	0.0781334i
$663$	−0.925604	+	7.24885i	−0.0359475	+	0.281522i
$664$	2.00858	−	0.917287i	0.0779480	−	0.0355976i
$665$	2.58104	−	4.67733i	0.100089	−	0.181379i
$666$	−15.3138	+	5.02716i	−0.593396	+	0.194799i
$667$	−6.23197	−	14.0876i	−0.241303	−	0.545472i
$668$	−7.84433	−	7.84433i	−0.303506	−	0.303506i
$669$	26.4164	+	25.5947i	1.02132	+	0.989549i
$670$	−17.6303	+	20.1649i	−0.681119	+	0.779037i
$671$	0.303233	−	1.03272i	0.0117062	−	0.0398677i
$672$	−3.09026	−	2.59340i	−0.119209	−	0.100043i
$673$	−2.93669	+	5.37815i	−0.113201	+	0.207313i	−0.928137	−	0.372239i	$-0.878590\pi$
$673$	−2.93669	+	5.37815i	−0.113201	+	0.207313i	0.814936	+	0.579551i	$0.196772\pi$
$674$	−4.97541	−	3.19750i	−0.191645	−	0.123163i
$675$	20.2754	+	16.2452i	0.780402	+	0.625278i
$676$	−6.54193	+	7.54979i	−0.251613	+	0.290376i
$677$	−2.96685	+	13.6384i	−0.114025	+	0.524165i	0.884331	+	0.466860i	$0.154615\pi$
$677$	−2.96685	+	13.6384i	−0.114025	+	0.524165i	−0.998357	+	0.0573058i	$0.981749\pi$
$678$	−4.22469	−	13.5900i	−0.162248	−	0.521922i
$679$	−5.84636	+	0.840579i	−0.224363	+	0.0322585i
$680$	−4.56131	−	2.96008i	−0.174918	−	0.113514i
$681$	−2.74380	−	11.7186i	−0.105143	−	0.449059i
$682$	−4.45989	+	1.66345i	−0.170778	+	0.0636970i
$683$	−3.04893	−	14.0157i	−0.116664	−	0.536296i	−0.997966	−	0.0637429i	$-0.979696\pi$
$683$	−3.04893	−	14.0157i	−0.116664	−	0.536296i	0.881302	−	0.472553i	$-0.156667\pi$
$684$	2.53483	−	1.74459i	0.0969218	−	0.0667059i
$685$	−6.84979	−	18.6171i	−0.261717	−	0.711321i
$686$	5.62690	−	19.1635i	0.214836	−	0.731665i
$687$	−37.4003	+	24.8792i	−1.42691	+	0.949200i
$688$	−3.21144	−	4.28998i	−0.122435	−	0.163554i
$689$	4.95831			0.188896
$690$	11.1392	−	14.8633i	0.424064	−	0.565836i
$691$	22.7480			0.865376			0.432688	−	0.901544i	$-0.357565\pi$
$691$	22.7480			0.865376			0.432688	+	0.901544i	$0.357565\pi$
$692$	−12.0678	−	16.1207i	−0.458748	−	0.612816i
$693$	6.69622	+	0.266688i	0.254368	+	0.0101306i
$694$	−9.23375	+	31.4473i	−0.350508	+	1.19372i
$695$	29.2612	+	13.5205i	1.10994	+	0.512862i
$696$	5.24271	+	1.86163i	0.198725	+	0.0705651i
$697$	−1.69431	−	7.78863i	−0.0641767	−	0.295015i
$698$	26.4177	−	9.85330i	0.999925	−	0.372953i
$699$	−49.8990	+	11.6833i	−1.88735	+	0.441905i
$700$	6.89610	+	9.38470i	0.260648	+	0.354708i
$701$	36.3394	−	5.22482i	1.37252	−	0.197339i	0.583704	−	0.811967i	$-0.301603\pi$
$701$	36.3394	−	5.22482i	1.37252	−	0.197339i	0.788817	+	0.614628i	$0.210694\pi$
$702$	7.34473	−	5.22785i	0.277209	−	0.197312i
$703$	1.17140	−	5.38486i	0.0441803	−	0.203094i
$704$	−0.628052	+	0.724811i	−0.0236706	+	0.0273173i
$705$	10.1435	−	13.8759i	0.382027	−	0.522596i
$706$	13.7590	+	8.84236i	0.517826	+	0.332787i
$707$	−20.7865	+	38.0676i	−0.781756	+	1.43168i
$708$	−6.58034	+	7.84103i	−0.247304	+	0.294684i
$709$	−11.4955	+	39.1500i	−0.431722	+	1.47031i	0.400721	+	0.916200i	$0.368760\pi$
$709$	−11.4955	+	39.1500i	−0.431722	+	1.47031i	−0.832443	+	0.554110i	$0.813059\pi$
$710$	29.7934	−	1.99793i	1.11813	−	0.0749811i
$711$	−4.11623	+	0.725213i	−0.154371	+	0.0271976i
$712$	−0.274464	−	0.274464i	−0.0102860	−	0.0102860i
$713$	22.7570	+	6.97739i	0.852257	+	0.261305i
$714$	−5.75439	+	7.94557i	−0.215353	+	0.297355i
$715$	−3.25767	−	1.79765i	−0.121830	−	0.0672281i
$716$	−0.213172	+	0.0973523i	−0.00796661	+	0.00363823i
$717$	17.1075	+	2.18446i	0.638893	+	0.0815801i
$718$	16.5543	+	1.18398i	0.617800	+	0.0441859i
$719$	12.8258	−	3.76600i	0.478322	−	0.140448i	−0.0336792	−	0.999433i	$-0.510722\pi$
$719$	12.8258	−	3.76600i	0.478322	−	0.140448i	0.512001	+	0.858985i	$0.328904\pi$
$720$	1.13460	+	6.61156i	0.0422841	+	0.246398i
$721$	−7.55712	+	16.5478i	−0.281442	+	0.616272i
$722$	−1.28039	−	17.9022i	−0.0476511	−	0.666250i
$723$	−15.1147	+	13.5209i	−0.562122	+	0.502846i
$724$	−7.03262	+	1.01114i	−0.261365	+	0.0375786i
$725$	−13.4331	−	8.80246i	−0.498892	−	0.326915i
$726$	−0.970291	+	17.4324i	−0.0360109	+	0.646978i
$727$	12.9255	−	0.924452i	0.479382	−	0.0342860i	0.170442	−	0.985368i	$-0.445480\pi$
$727$	12.9255	−	0.924452i	0.479382	−	0.0342860i	0.308940	+	0.951082i	$0.400026\pi$
$728$	3.78634	−	1.41223i	0.140331	−	0.0523408i
$729$	25.0701	−	10.0244i	0.928523	−	0.371275i
$730$	−5.56531	+	4.77927i	−0.205981	+	0.176889i
$731$	−9.84855	+	8.53381i	−0.364262	+	0.315634i
$732$	0.246206	−	1.92816i	0.00910003	−	0.0712667i
$733$	41.0564	+	15.3133i	1.51645	+	0.565608i	0.963525	−	0.267620i	$-0.0862371\pi$
$733$	41.0564	+	15.3133i	1.51645	+	0.565608i	0.552930	+	0.833228i	$0.313510\pi$
$734$	4.44373	−	30.9068i	0.164021	−	1.14079i
$735$	−5.09333	+	3.35562i	−0.187870	+	0.123774i
$736$	4.69804	−	0.963567i	0.173172	−	0.0355175i
$737$	8.12349	−	8.12349i	0.299233	−	0.299233i
$738$	−5.64128	+	8.05419i	−0.207658	+	0.296479i
$739$	5.40588	−	2.46878i	0.198858	−	0.0908156i	−0.313497	−	0.949589i	$-0.601500\pi$
$739$	5.40588	−	2.46878i	0.198858	−	0.0908156i	0.512355	+	0.858774i	$0.328773\pi$
$740$	9.58524	+	7.24206i	0.352360	+	0.266223i
$741$	0.268435	+	3.07068i	0.00986121	+	0.112804i
$742$	5.84221	+	3.19009i	0.214474	+	0.117112i
$743$	−2.09160	−	9.61491i	−0.0767332	−	0.352737i	0.922732	−	0.385443i	$-0.125951\pi$
$743$	−2.09160	−	9.61491i	−0.0767332	−	0.352737i	−0.999465	+	0.0327058i	$0.989588\pi$
$744$	−7.47895	+	4.23854i	−0.274192	+	0.155392i
$745$	26.8380	+	8.00995i	0.983266	+	0.293462i
$746$	2.40943	+	3.74914i	0.0882153	+	0.137266i
$747$	−2.11776	+	6.27673i	−0.0774848	+	0.229653i
$748$	1.86704	+	1.39765i	0.0682657	+	0.0511031i
$749$	−28.0159	+	18.0047i	−1.02368	+	0.657877i
$750$	1.33365	−	19.3189i	0.0486982	−	0.705428i
$751$	−0.183503	+	0.401815i	−0.00669611	+	0.0146624i	−0.912951	−	0.408070i	$-0.866202\pi$
$751$	−0.183503	+	0.401815i	−0.00669611	+	0.0146624i	0.906254	+	0.422733i	$0.138929\pi$
$752$	4.33653	−	0.943354i	0.158137	−	0.0344006i
$753$	6.98035	+	14.6672i	0.254378	+	0.534501i
$754$	−4.21170	+	3.64946i	−0.153381	+	0.132905i
$755$	6.60218	+	47.4128i	0.240278	+	1.72553i
$756$	12.0176	−	1.43433i	0.437074	−	0.0521662i
$757$	26.8914	−	20.1306i	0.977384	−	0.731661i	0.0140323	−	0.999902i	$-0.495533\pi$
$757$	26.8914	−	20.1306i	0.977384	−	0.731661i	0.963352	+	0.268241i	$0.0864423\pi$
$758$	−19.2796	−	19.2796i	−0.700266	−	0.700266i
$759$	−5.19352	+	6.04099i	−0.188513	+	0.219274i
$760$	−2.14539	−	0.811060i	−0.0778216	−	0.0294203i
$761$	−15.5640	−	2.23777i	−0.564195	−	0.0811190i	−0.145685	−	0.989331i	$-0.546539\pi$
$761$	−15.5640	−	2.23777i	−0.564195	−	0.0811190i	−0.418510	+	0.908212i	$0.637448\pi$
$762$	3.97218	+	5.97129i	0.143897	+	0.216317i
$763$	−31.2989	+	17.0905i	−1.13310	+	0.618718i
$764$	15.9234	+	18.3765i	0.576087	+	0.664840i
$765$	15.8400	−	3.89904i	0.572696	−	0.140970i
$766$	17.9575	+	11.5406i	0.648831	+	0.416978i
$767$	−3.58331	−	9.60723i	−0.129386	−	0.346897i
$768$	−0.913284	+	1.47170i	−0.0329553	+	0.0531055i
$769$	−25.8657	−	40.2478i	−0.932741	−	1.45137i	−0.891913	−	0.452207i	$-0.850637\pi$
$769$	−25.8657	−	40.2478i	−0.932741	−	1.45137i	−0.0408284	−	0.999166i	$-0.513000\pi$
$770$	−2.68183	−	4.21403i	−0.0966464	−	0.151863i
$771$	−12.8444	−	6.75239i	−0.462579	−	0.243181i
$772$	13.9404	+	3.03255i	0.501726	+	0.109144i
$773$	−6.75948	+	0.483448i	−0.243122	+	0.0173884i	−0.192368	−	0.981323i	$-0.561617\pi$
$773$	−6.75948	+	0.483448i	−0.243122	+	0.0173884i	−0.0507535	+	0.998711i	$0.516162\pi$
$774$	15.9772	+	1.78412i	0.574290	+	0.0641287i
$775$	23.8719	−	6.77973i	0.857504	−	0.243535i
$776$	0.714430	+	2.43312i	0.0256465	+	0.0873441i
$777$	13.9333	−	16.6027i	0.499855	−	0.595620i
$778$	−14.0670	+	7.68115i	−0.504325	+	0.275382i
$779$	−1.39666	−	3.05826i	−0.0500405	−	0.109573i
$780$	−6.32219	−	2.27661i	−0.226371	−	0.0815157i
$781$	−12.8073			−0.458280
$782$	−3.15222	−	11.2283i	−0.112723	−	0.401522i
$783$	−14.8365	+	7.64484i	−0.530214	+	0.273204i
$784$	−1.55882	−	0.224124i	−0.0556721	−	0.00800444i
$785$	27.0624	−	1.81479i	0.965899	−	0.0647728i
$786$	−14.4679	−	18.7036i	−0.516053	−	0.667134i
$787$	0.988688	−	13.8237i	0.0352429	−	0.492760i	−0.948923	−	0.315509i	$-0.897825\pi$
$787$	0.988688	−	13.8237i	0.0352429	−	0.492760i	0.984166	−	0.177252i	$-0.0567206\pi$
$788$	14.8712	+	8.12031i	0.529766	+	0.289274i
$789$	0.0540353	+	0.138168i	0.00192371	+	0.00491891i
$790$	2.19305	+	2.21262i	0.0780253	+	0.0787214i
$791$	14.4636	+	12.5327i	0.514265	+	0.445613i
$792$	−0.295810	−	2.86194i	−0.0105111	−	0.101695i
$793$	1.55874	+	1.16686i	0.0553526	+	0.0414365i
$794$	0.662323	+	4.60656i	0.0235050	+	0.163481i
$795$	−3.98550	−	10.3259i	−0.141351	−	0.366220i
$796$	−6.30327	+	7.27436i	−0.223413	+	0.257833i
$797$	−13.8647	−	37.1726i	−0.491112	−	1.31672i	−0.912216	−	0.409710i	$-0.865630\pi$
$797$	−13.8647	−	37.1726i	−0.491112	−	1.31672i	0.421104	−	0.907013i	$-0.361643\pi$
$798$	−1.65934	+	3.79079i	−0.0587399	+	0.134193i
$799$	−3.04048	−	10.3549i	−0.107564	−	0.366331i
$800$	3.56679	−	3.50400i	0.126105	−	0.123885i
$801$	1.16387	−	0.0367839i	0.0411233	−	0.00129969i
$802$	5.47756	−	14.6859i	0.193419	−	0.518577i
$803$	2.51880	−	1.88555i	0.0888865	−	0.0665396i
$804$	12.1698	−	16.8038i	0.429194	−	0.592624i
$805$	−2.18888	+	24.8817i	−0.0771478	+	0.876966i
$806$		−	8.61111i		−	0.303313i
$807$	−0.0338502	−	2.14263i	−0.00119158	−	0.0754240i
$808$	17.4474	+	6.50754i	0.613797	+	0.228934i
$809$	−30.9761	−	9.09541i	−1.08906	−	0.319777i	−0.312564	−	0.949897i	$-0.601188\pi$
$809$	−30.9761	−	9.09541i	−1.08906	−	0.319777i	−0.776498	+	0.630119i	$0.783006\pi$
$810$	−16.7909	−	11.0935i	−0.589972	−	0.389786i
$811$	−18.3508	+	5.38828i	−0.644383	+	0.189208i	−0.587565	−	0.809177i	$-0.699914\pi$
$811$	−18.3508	+	5.38828i	−0.644383	+	0.189208i	−0.0568176	+	0.998385i	$0.518095\pi$
$812$	−7.31051	+	1.59030i	−0.256549	+	0.0558087i
$813$	−9.12039	+	32.9797i	−0.319866	+	1.15665i
$814$	−3.89412	−	3.37427i	−0.136489	−	0.118268i
$815$	47.0885	−	10.0247i	1.64944	−	0.351150i
$816$	3.72817	+	1.95993i	0.130512	+	0.0686111i
$817$	−3.29404	+	4.40033i	−0.115244	+	0.153948i
$818$	23.4191	+	5.09451i	0.818830	+	0.178125i
$819$	−4.68538	+	11.1814i	−0.163720	+	0.390711i
$820$	7.32925	+	0.0325456i	0.255948	+	0.00113654i
$821$	−3.21765	+	5.00677i	−0.112297	+	0.174737i	−0.892853	−	0.450349i	$-0.851300\pi$
$821$	−3.21765	+	5.00677i	−0.112297	+	0.174737i	0.780556	+	0.625086i	$0.214936\pi$
$822$	6.60319	+	13.8747i	0.230313	+	0.483935i
$823$	7.60070	+	0.543613i	0.264944	+	0.0189492i	0.203179	−	0.979142i	$-0.434873\pi$
$823$	7.60070	+	0.543613i	0.264944	+	0.0189492i	0.0617647	+	0.998091i	$0.480327\pi$
$824$	7.49394	+	2.20042i	0.261064	+	0.0766552i
$825$	−1.12514	+	8.22916i	−0.0391724	+	0.286503i
$826$	1.95903	−	13.6253i	0.0681632	−	0.474086i
$827$	−33.7981	+	33.7981i	−1.17528	+	1.17528i	−0.194341	+	0.980934i	$0.562257\pi$
$827$	−33.7981	+	33.7981i	−1.17528	+	1.17528i	−0.980934	+	0.194341i	$0.937743\pi$
$828$	−7.53866	+	12.2543i	−0.261987	+	0.425867i
$829$		−	32.9518i		−	1.14446i	−0.820092	−	0.572231i	$-0.806078\pi$
$829$		−	32.9518i		−	1.14446i	0.820092	−	0.572231i	$-0.193922\pi$
$830$	4.74364	−	1.37001i	0.164654	−	0.0475536i
$831$	6.09516	−	30.3170i	0.211439	−	1.05169i
$832$	−0.831494	−	1.52277i	−0.0288269	−	0.0527924i
$833$	−0.273206	+	3.81991i	−0.00946602	+	0.132352i
$834$	−23.5289	−	8.35488i	−0.814740	−	0.289306i
$835$	−14.7773	−	19.9240i	−0.511390	−	0.689498i
$836$	0.894834	+	0.408657i	0.0309485	+	0.0141337i
$837$	6.08534	−	25.0613i	0.210340	−	0.866245i
$838$	−5.52600	+	25.4026i	−0.190893	+	0.877519i
$839$	−3.99717	−	27.8009i	−0.137998	−	0.959794i	−0.934704	−	0.355427i	$-0.884335\pi$
$839$	−3.99717	−	27.8009i	−0.137998	−	0.959794i	0.796706	−	0.604367i	$-0.206574\pi$
$840$	−5.98450	−	6.75004i	−0.206485	−	0.232899i
$841$	−15.7169	+	10.1007i	−0.541963	+	0.348299i
$842$	−0.554869	−	7.75809i	−0.0191221	−	0.267361i
$843$	−31.0098	−	8.57562i	−1.06804	−	0.295360i
$844$	3.11732	−	4.85064i	0.107303	−	0.166966i
$845$	−16.9466	+	14.5531i	−0.582982	+	0.500641i
$846$	−6.84061	+	11.4221i	−0.235185	+	0.392700i
$847$	−11.2522	−	20.6068i	−0.386629	−	0.708058i
$848$	0.998707	−	2.67764i	0.0342958	−	0.0919505i
$849$	27.3407	+	26.4902i	0.938329	+	0.909142i
$850$	−9.11798	−	8.04365i	−0.312744	−	0.275895i
$851$	5.17686	+	25.2407i	0.177460	+	0.865239i
$852$	−22.8394	+	3.65294i	−0.782466	+	0.125148i
$853$	−17.9962	−	24.0401i	−0.616177	−	0.823116i	0.378560	−	0.925577i	$-0.376419\pi$
$853$	−17.9962	−	24.0401i	−0.616177	−	0.823116i	−0.994737	+	0.102460i	$0.967328\pi$
$854$	1.08588	+	2.37774i	0.0371580	+	0.0813647i
$855$	6.17904	−	3.02725i	0.211319	−	0.103530i
$856$	9.36311	+	10.8056i	0.320024	+	0.369328i
$857$	3.30567	−	6.05388i	0.112919	−	0.206796i	−0.815107	−	0.579310i	$-0.803322\pi$
$857$	3.30567	−	6.05388i	0.112919	−	0.206796i	0.928027	+	0.372513i	$0.121504\pi$
$858$	2.64021	+	1.15570i	0.0901354	+	0.0394548i
$859$	31.3976	+	14.3388i	1.07127	+	0.489234i	0.871392	−	0.490587i	$-0.163217\pi$
$859$	31.3976	+	14.3388i	1.07127	+	0.489234i	0.199880	+	0.979820i	$0.435945\pi$
$860$	−5.69596	−	10.5424i	−0.194231	−	0.359493i
$861$	0.734881	−	13.2030i	0.0250447	−	0.449958i
$862$	−4.20657	+	5.61932i	−0.143276	+	0.191395i
$863$	9.52141	−	12.7191i	0.324112	−	0.432964i	−0.608659	−	0.793432i	$-0.708292\pi$
$863$	9.52141	−	12.7191i	0.324112	−	0.432964i	0.932771	+	0.360468i	$0.117383\pi$
$864$	−1.34382	−	5.01938i	−0.0457176	−	0.170763i
$865$	−21.4040	−	39.6157i	−0.727758	−	1.34698i
$866$	−25.4136	−	11.6060i	−0.863589	−	0.394388i
$867$	−7.70004	+	17.5909i	−0.261507	+	0.597419i
$868$	5.54024	−	10.1462i	0.188048	−	0.344384i
$869$	−0.875008	−	1.00981i	−0.0296826	−	0.0342556i
$870$	10.9855	+	5.83757i	0.372444	+	0.197912i
$871$	8.63358	+	18.9049i	0.292538	+	0.640568i
$872$	9.17521	+	12.2566i	0.310712	+	0.415062i
$873$	−6.78881	−	3.43316i	−0.229766	−	0.116195i
$874$	−2.30595	−	4.34523i	−0.0780000	−	0.146980i
$875$	12.1746	+	23.0200i	0.411578	+	0.778219i
$876$	3.95402	−	4.08096i	0.133594	−	0.137883i
$877$	5.86932	−	15.7362i	0.198193	−	0.531375i	−0.799394	−	0.600807i	$-0.794846\pi$
$877$	5.86932	−	15.7362i	0.198193	−	0.531375i	0.997587	+	0.0694319i	$0.0221187\pi$
$878$	0.237177	+	0.434357i	0.00800433	+	0.0146588i
$879$	2.59460	+	29.6802i	0.0875136	+	1.00109i
$880$	−1.62695	+	1.39716i	−0.0548444	+	0.0470982i
$881$	3.60329	−	5.60682i	0.121398	−	0.188899i	−0.775236	−	0.631672i	$-0.782369\pi$
$881$	3.60329	−	5.60682i	0.121398	−	0.188899i	0.896634	+	0.442773i	$0.146005\pi$
$882$	3.69087	−	2.94938i	0.124278	−	0.0993107i
$883$	−0.600168	−	8.39144i	−0.0201972	−	0.282394i	−0.997506	−	0.0705764i	$-0.977516\pi$
$883$	−0.600168	−	8.39144i	−0.0201972	−	0.282394i	0.977309	−	0.211818i	$-0.0679384\pi$
$884$	−3.54934	+	2.28102i	−0.119377	+	0.0767190i
$885$	−17.1271	+	15.1847i	−0.575722	+	0.510428i
$886$	1.97969	+	13.7691i	0.0665091	+	0.462581i
$887$	1.56236	−	7.18205i	0.0524589	−	0.241150i	−0.943450	−	0.331516i	$-0.892440\pi$
$887$	1.56236	−	7.18205i	0.0524589	−	0.241150i	0.995909	+	0.0903659i	$0.0288037\pi$
$888$	−7.90688	−	4.90671i	−0.265337	−	0.164658i
$889$	−8.77280	−	4.00640i	−0.294230	−	0.134370i
$890$	−0.517041	−	0.697117i	−0.0173313	−	0.0233674i
$891$	6.86721	+	5.22927i	0.230060	+	0.175187i
$892$	−1.51497	+	21.1820i	−0.0507248	+	0.709226i
$893$	−2.18159	−	3.99529i	−0.0730042	−	0.133697i
$894$	−21.2691	−	4.27610i	−0.711346	−	0.143014i
$895$	−0.503446	+	0.145400i	−0.0168283	+	0.00486018i
$896$		−	2.32920i		−	0.0778130i
$897$	−6.95608	−	12.6221i	−0.232257	−	0.421439i
$898$	16.0150	−	16.0150i	0.534429	−	0.534429i
$899$	−2.26879	+	15.7797i	−0.0756682	+	0.526284i
$900$	0.340670	+	14.9961i	0.0113557	+	0.499871i
$901$	−6.66807	−	1.95792i	−0.222146	−	0.0652278i
$902$	−3.13558	−	0.224261i	−0.104403	−	0.00746707i
$903$	−19.5211	+	9.29043i	−0.649622	+	0.309166i
$904$	4.44222	−	6.91223i	0.147746	−	0.229897i
$905$	−15.8870	−	0.0705463i	−0.528100	−	0.00234504i
$906$	−8.45332	−	36.1037i	−0.280843	−	1.19947i
$907$	−32.7255	−	7.11900i	−1.08663	−	0.236383i	−0.366639	−	0.930363i	$-0.619492\pi$
$907$	−32.7255	−	7.11900i	−1.08663	−	0.236383i	−0.719994	+	0.693981i	$0.755855\pi$
$908$	4.16422	−	5.56275i	0.138195	−	0.184606i
$909$	−50.0576	+	24.8006i	−1.66031	+	0.822583i
$910$	8.83819	−	1.88157i	0.292983	−	0.0623734i
$911$	−10.8979	−	9.44312i	−0.361065	−	0.312864i	0.455370	−	0.890302i	$-0.349507\pi$
$911$	−10.8979	−	9.44312i	−0.361065	−	0.312864i	−0.816435	+	0.577438i	$0.804053\pi$
$912$	1.71233	+	0.473537i	0.0567010	+	0.0156804i
$913$	−2.06933	+	0.450155i	−0.0684848	+	0.0148980i
$914$	10.2714	−	3.01596i	0.339748	−	0.0997590i
$915$	1.17711	−	4.18407i	0.0389140	−	0.138321i
$916$	−24.8837	−	7.30652i	−0.822181	−	0.241414i
$917$	29.7936	+	11.1124i	0.983871	+	0.366965i
$918$	−11.9418	+	4.13029i	−0.394137	+	0.136320i
$919$		−	30.2530i		−	0.997955i	−0.866615	−	0.498978i	$-0.833709\pi$
$919$		−	30.2530i		−	0.997955i	0.866615	−	0.498978i	$-0.166291\pi$
$920$	10.7076	−	0.590094i	0.353018	−	0.0194548i
$921$	−13.9847	−	10.1281i	−0.460811	−	0.333732i
$922$	−18.7176	+	14.0118i	−0.616430	+	0.461454i
$923$	8.09674	−	21.7082i	0.266507	−	0.714534i
$924$	2.36732	+	3.06039i	0.0778792	+	0.100679i
$925$	18.8256	+	19.1630i	0.618981	+	0.630074i
$926$	3.34403	+	11.3887i	0.109892	+	0.374256i
$927$	−20.1998	+	11.8733i	−0.663450	+	0.389969i
$928$	1.12250	+	3.00953i	0.0368477	+	0.0987925i
$929$	4.10385	−	4.73610i	0.134643	−	0.155386i	−0.684424	−	0.729084i	$-0.739946\pi$
$929$	4.10385	−	4.73610i	0.134643	−	0.155386i	0.819067	+	0.573698i	$0.194492\pi$
$930$	−17.9330	+	6.92163i	−0.588045	+	0.226969i
$931$	0.229889	+	1.59892i	0.00753432	+	0.0524024i
$932$	−23.6867	−	17.7316i	−0.775884	−	0.580819i
$933$	−21.7299	−	24.2915i	−0.711405	−	0.795267i
$934$	−9.07282	−	7.86164i	−0.296872	−	0.257241i
$935$	3.67115	+	3.70390i	0.120060	+	0.121131i
$936$	5.03797	+	1.30792i	0.164671	+	0.0427507i
$937$	−38.8628	−	21.2207i	−1.26959	−	0.693250i	−0.303842	−	0.952722i	$-0.598270\pi$
$937$	−38.8628	−	21.2207i	−1.26959	−	0.693250i	−0.965751	+	0.259472i	$0.916451\pi$
$938$	−1.99042	+	27.8297i	−0.0649896	+	0.908673i
$939$	−5.47606	+	4.23594i	−0.178704	+	0.138235i
$940$	9.90132	−	0.663978i	0.322945	−	0.0216566i
$941$	−47.1115	−	6.77361i	−1.53579	−	0.220813i	−0.678096	−	0.734974i	$-0.737195\pi$
$941$	−47.1115	−	6.77361i	−1.53579	−	0.220813i	−0.857694	+	0.514160i	$0.828104\pi$
$942$	−20.7459	+	3.31809i	−0.675937	+	0.108109i
$943$	11.7567	+	10.4349i	0.382851	+	0.339806i
$944$	−5.90995			−0.192353
$945$	27.0519	+	0.769803i	0.879997	+	0.0250417i
$946$	2.13501	+	4.67503i	0.0694153	+	0.151998i
$947$	−1.51310	+	0.826218i	−0.0491693	+	0.0268485i	−0.503646	−	0.863910i	$-0.668008\pi$
$947$	−1.51310	+	0.826218i	−0.0491693	+	0.0268485i	0.454476	+	0.890759i	$0.349826\pi$
$948$	−1.84844	−	1.55125i	−0.0600346	−	0.0503821i
$949$	1.60361	+	5.46138i	0.0520553	+	0.177284i
$950$	−4.47927	−	2.49776i	−0.145327	−	0.0810380i
$951$	18.3696	+	32.4135i	0.595677	+	1.05108i
$952$	−5.64964	+	0.404070i	−0.183106	+	0.0130960i
$953$	−2.60005	−	0.565606i	−0.0842239	−	0.0183218i	0.170256	−	0.985400i	$-0.445541\pi$
$953$	−2.60005	−	0.565606i	−0.0842239	−	0.0183218i	−0.254480	+	0.967078i	$0.581904\pi$
$954$	3.80613	+	7.68231i	0.123228	+	0.248724i
$955$	29.1920	+	45.8702i	0.944632	+	1.48433i
$956$	5.38329	+	8.37656i	0.174108	+	0.270917i
$957$	−4.53366	−	2.81342i	−0.146552	−	0.0909449i
$958$	−11.6071	−	31.1199i	−0.375009	−	1.00544i
$959$	−17.3831	−	11.1715i	−0.561331	−	0.360745i
$960$	−2.50286	+	2.95562i	−0.0807795	+	0.0953922i
$961$	4.16929	+	4.81162i	0.134493	+	0.155214i
$962$	8.18122	−	4.46728i	0.263773	−	0.144031i
$963$	−42.8596	−	1.70695i	−1.38113	−	0.0550058i
$964$	−11.5893	−	1.66630i	−0.373268	−	0.0536678i
$965$	29.8396	+	11.2808i	0.960570	+	0.363141i
$966$	−0.0753037	−	19.3476i	−0.00242286	−	0.622499i
$967$	14.6578	+	14.6578i	0.471362	+	0.471362i	0.902355	−	0.430993i	$-0.141837\pi$
$967$	14.6578	+	14.6578i	0.471362	+	0.471362i	−0.430993	+	0.902355i	$0.641837\pi$
$968$	−8.06962	+	6.04084i	−0.259367	+	0.194160i
$969$	0.851544	−	4.23554i	0.0273555	−	0.136065i
$970$	0.782040	+	5.61613i	0.0251098	+	0.180323i
$971$	27.6144	−	23.9280i	0.886189	−	0.767887i	−0.0874054	−	0.996173i	$-0.527858\pi$
$971$	27.6144	−	23.9280i	0.886189	−	0.767887i	0.973594	+	0.228286i	$0.0733121\pi$
$972$	13.7379	+	7.36675i	0.440645	+	0.236289i
$973$	32.8090	−	7.13717i	1.05181	−	0.228807i
$974$	−5.70305	+	12.4879i	−0.182737	+	0.400139i
$975$	−13.2370	−	7.10957i	−0.423924	−	0.227688i
$976$	0.944105	−	0.606739i	0.0302201	−	0.0194213i
$977$	−45.4153	−	33.9975i	−1.45297	−	1.08768i	−0.978224	−	0.207551i	$-0.933451\pi$
$977$	−45.4153	−	33.9975i	−1.45297	−	1.08768i	−0.474741	−	0.880125i	$-0.657458\pi$
$978$	−35.6110	+	11.0703i	−1.13871	+	0.353988i
$979$	0.201259	+	0.313165i	0.00643227	+	0.0100088i
$980$	−3.37439	−	1.00711i	−0.107791	−	0.0321708i
$981$	−45.6476	−	5.09729i	−1.45742	−	0.162744i
$982$	5.93138	+	27.2661i	0.189278	+	0.870097i
$983$	49.2580	+	26.8969i	1.57109	+	0.857878i	0.999298	+	0.0374767i	$0.0119320\pi$
$983$	49.2580	+	26.8969i	1.57109	+	0.857878i	0.571788	+	0.820401i	$0.306250\pi$
$984$	−5.65570	+	0.494413i	−0.180297	+	0.0157613i
$985$	30.2294	+	22.8396i	0.963189	+	0.727730i
$986$	7.10510	−	3.24479i	0.226272	−	0.103335i
$987$	−0.282819	−	17.9017i	−0.00900224	−	0.569818i
$988$	−1.25838	+	1.25838i	−0.0400345	+	0.0400345i
$989$	5.76153	−	25.0460i	0.183206	−	0.796416i
$990$	0.284568	−	6.42729i	0.00904416	−	0.204273i
$991$	2.70152	−	18.7895i	0.0858165	−	0.596867i	−0.900852	−	0.434126i	$-0.857057\pi$
$991$	2.70152	−	18.7895i	0.0858165	−	0.596867i	0.986669	−	0.162741i	$-0.0520335\pi$
$992$	−4.65027	−	1.73446i	−0.147646	−	0.0550691i
$993$	48.4157	+	6.18219i	1.53643	+	0.196186i
$994$	23.5068	−	20.3688i	0.745590	−	0.646058i
$995$	−16.3284	+	14.0222i	−0.517644	+	0.444532i
$996$	−3.56188	+	1.39299i	−0.112862	+	0.0441387i
$997$	−11.1767	+	4.16870i	−0.353970	+	0.132024i	−0.520158	−	0.854070i	$-0.674127\pi$
$997$	−11.1767	+	4.16870i	−0.353970	+	0.132024i	0.166188	+	0.986094i	$0.446854\pi$
$998$	−12.7187	+	0.909661i	−0.402604	+	0.0287948i
$999$	26.9671	−	7.21979i	0.853202	−	0.228424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.17	✓	960
3.2	odd	2	inner	690.2.x.a.77.47	yes	960
5.3	odd	4	inner	690.2.x.a.353.4	yes	960
15.8	even	4	inner	690.2.x.a.353.39	yes	960
23.3	even	11	inner	690.2.x.a.647.39	yes	960
69.26	odd	22	inner	690.2.x.a.647.4	yes	960
115.3	odd	44	inner	690.2.x.a.233.47	yes	960
345.233	even	44	inner	690.2.x.a.233.17	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.17	✓	960	1.1	even	1	trivial
690.2.x.a.77.47	yes	960	3.2	odd	2	inner
690.2.x.a.233.17	yes	960	345.233	even	44	inner
690.2.x.a.233.47	yes	960	115.3	odd	44	inner
690.2.x.a.353.4	yes	960	5.3	odd	4	inner
690.2.x.a.353.39	yes	960	15.8	even	4	inner
690.2.x.a.647.4	yes	960	69.26	odd	22	inner
690.2.x.a.647.39	yes	960	23.3	even	11	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.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(0.959317 + 1.44212i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.937919 + 2.02985i) q^{5} +(0.579579 - 1.63220i) q^{6} +(0.495106 + 2.27597i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.15942 + 2.76690i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(0.959317 + 1.44212i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.937919 + 2.02985i) q^{5} +(0.579579 - 1.63220i) q^{6} +(0.495106 + 2.27597i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.15942 + 2.76690i) q^{9} +(2.18706 - 0.465603i) q^{10} +(-0.949300 + 0.136489i) q^{11} +(-1.65397 + 0.514166i) q^{12} +(0.368799 - 1.69534i) q^{13} +(1.52530 - 1.76029i) q^{14} +(-3.82706 + 0.594683i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-1.16542 + 2.13431i) q^{17} +(2.90983 - 0.729979i) q^{18} +(-0.288979 + 0.984173i) q^{19} +(-1.68339 - 1.47180i) q^{20} +(-2.80725 + 2.89738i) q^{21} +(0.678159 + 0.678159i) q^{22} +(-0.625958 - 4.75481i) q^{23} +(1.40280 + 1.01595i) q^{24} +(-3.24062 - 3.80768i) q^{25} +(-1.57821 + 0.720742i) q^{26} +(-5.10246 + 0.982315i) q^{27} +(-2.32326 - 0.166163i) q^{28} +(3.08194 - 0.904938i) q^{29} +(2.76954 + 2.70734i) q^{30} +(-2.06179 + 4.51468i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-1.10751 - 1.23807i) q^{33} +(2.40702 - 0.346077i) q^{34} +(-5.08425 - 1.12968i) q^{35} +(-2.32818 - 1.89198i) q^{36} +(-5.35891 + 0.383277i) q^{37} +(0.961050 - 0.358453i) q^{38} +(2.79868 - 1.09452i) q^{39} +(-0.169422 + 2.22964i) q^{40} +(-2.47717 + 2.14648i) q^{41} +(4.00179 + 0.510988i) q^{42} +(5.02097 + 1.87273i) q^{43} +(0.136489 - 0.949300i) q^{44} +(-4.52897 - 4.94858i) q^{45} +(-3.43130 + 3.35055i) q^{46} +(-3.13810 + 3.13810i) q^{47} +(-0.0273603 - 1.73183i) q^{48} +(1.43253 - 0.654216i) q^{49} +(-1.10617 + 4.87610i) q^{50} +(-4.19595 + 0.366804i) q^{51} +(1.52277 + 0.831494i) q^{52} +(0.607474 + 2.79251i) q^{53} +(3.84417 + 3.49605i) q^{54} +(0.613315 - 2.05496i) q^{55} +(1.25926 + 1.95944i) q^{56} +(-1.69652 + 0.527392i) q^{57} +(-2.57138 - 1.92491i) q^{58} +(4.97177 - 3.19516i) q^{59} +(0.507612 - 3.83957i) q^{60} +(-0.466203 + 1.02084i) q^{61} +(4.84977 - 1.05500i) q^{62} +(-6.87141 - 1.26889i) q^{63} +(0.755750 - 0.654861i) q^{64} +(3.09540 + 2.33870i) q^{65} +(-0.327417 + 1.62856i) q^{66} +(-9.58947 + 7.17859i) q^{67} +(-1.71952 - 1.71952i) q^{68} +(6.25651 - 5.46407i) q^{69} +(2.14252 + 4.74714i) q^{70} +(13.2180 + 1.90046i) q^{71} +(-0.119385 + 2.99762i) q^{72} +(-2.87938 + 1.57226i) q^{73} +(3.51831 + 4.06034i) q^{74} +(2.38235 - 8.32613i) q^{75} +(-0.862893 - 0.554547i) q^{76} +(-0.780648 - 2.09300i) q^{77} +(-2.55340 - 1.58454i) q^{78} +(0.753226 + 1.17204i) q^{79} +(1.88645 - 1.20054i) q^{80} +(-6.31149 - 6.41600i) q^{81} +(3.20286 + 0.696740i) q^{82} +(2.20250 - 0.157526i) q^{83} +(-1.98912 - 3.50982i) q^{84} +(-3.23927 - 4.36745i) q^{85} +(-1.50976 - 5.14178i) q^{86} +(4.26158 + 3.57640i) q^{87} +(-0.841749 + 0.459630i) q^{88} +(-0.161243 - 0.353074i) q^{89} +(-1.24744 + 6.59120i) q^{90} +4.04114 q^{91} +(4.73856 + 0.738982i) q^{92} +(-8.48862 + 1.35767i) q^{93} +(4.39278 + 0.631586i) q^{94} +(-1.72669 - 1.50966i) q^{95} +(-1.37001 + 1.05975i) q^{96} +(-0.180905 + 2.52938i) q^{97} +(-1.38221 - 0.754745i) q^{98} +(0.722987 - 2.78487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

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