LMFDB - Embedded newform 961.2.g.v.547.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			547.4
Character	$\chi$	$=$	961.547
Dual form			961.2.g.v.448.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.557046 - 1.71441i) q^{2} +(0.127782 + 0.141916i) q^{3} +(-1.01088 + 0.734444i) q^{4} +(1.23318 + 2.13593i) q^{5} +(0.172123 - 0.298125i) q^{6} +(0.109980 + 1.04639i) q^{7} +(-1.09449 - 0.795192i) q^{8} +(0.309773 - 2.94730i) q^{9} +(2.97493 - 3.30400i) q^{10} +(-4.90535 - 2.18400i) q^{11} +(-0.233401 - 0.0496110i) q^{12} +(1.20649 - 0.256448i) q^{13} +(1.73268 - 0.771437i) q^{14} +(-0.145545 + 0.447943i) q^{15} +(-1.52585 + 4.69607i) q^{16} +(5.18337 - 2.30778i) q^{17} +(-5.22544 + 1.11070i) q^{18} +(4.56093 + 0.969455i) q^{19} +(-2.81532 - 1.25346i) q^{20} +(-0.134446 + 0.149317i) q^{21} +(-1.01177 + 9.62638i) q^{22} +(-4.84106 - 3.51724i) q^{23} +(-0.0270052 - 0.256937i) q^{24} +(-0.541477 + 0.937865i) q^{25} +(-1.11173 - 1.92557i) q^{26} +(0.921341 - 0.669393i) q^{27} +(-0.879689 - 0.976993i) q^{28} +(-1.11492 - 3.43137i) q^{29} +0.849035 q^{30} +6.19525 q^{32} +(-0.316870 - 0.975226i) q^{33} +(-6.84387 - 7.60089i) q^{34} +(-2.09939 + 1.52530i) q^{35} +(1.85148 + 3.20686i) q^{36} +(2.67703 - 4.63676i) q^{37} +(-0.878602 - 8.35934i) q^{38} +(0.190562 + 0.138451i) q^{39} +(0.348775 - 3.31837i) q^{40} +(7.06792 - 7.84972i) q^{41} +(0.330884 + 0.147319i) q^{42} +(-2.95770 - 0.628679i) q^{43} +(6.56272 - 1.39495i) q^{44} +(6.67724 - 2.97290i) q^{45} +(-3.33330 + 10.2588i) q^{46} +(1.74104 - 5.35837i) q^{47} +(-0.861426 + 0.383532i) q^{48} +(5.76420 - 1.22522i) q^{49} +(1.90952 + 0.405880i) q^{50} +(0.989854 + 0.440711i) q^{51} +(-1.03127 + 1.14534i) q^{52} +(0.0949835 - 0.903708i) q^{53} +(-1.66085 - 1.20668i) q^{54} +(-1.38430 - 13.1708i) q^{55} +(0.711707 - 1.23271i) q^{56} +(0.445223 + 0.771149i) q^{57} +(-5.26172 + 3.82286i) q^{58} +(2.05099 + 2.27786i) q^{59} +(-0.181861 - 0.559710i) q^{60} -9.12376 q^{61} +3.11808 q^{63} +(-0.399349 - 1.22907i) q^{64} +(2.03558 + 2.26074i) q^{65} +(-1.49543 + 1.08649i) q^{66} +(-3.98244 - 6.89779i) q^{67} +(-3.54480 + 6.13978i) q^{68} +(-0.119447 - 1.13647i) q^{69} +(3.78444 + 2.74956i) q^{70} +(-0.634341 + 6.03535i) q^{71} +(-2.68271 + 2.97945i) q^{72} +(3.46139 + 1.54111i) q^{73} +(-9.44055 - 2.00665i) q^{74} +(-0.202290 + 0.0429980i) q^{75} +(-5.32254 + 2.36975i) q^{76} +(1.74582 - 5.37309i) q^{77} +(0.131211 - 0.403826i) q^{78} +(7.77440 - 3.46139i) q^{79} +(-11.9122 + 2.53201i) q^{80} +(-8.48358 - 1.80324i) q^{81} +(-17.3948 - 7.74468i) q^{82} +(-8.85485 + 9.83430i) q^{83} +(0.0262429 - 0.249684i) q^{84} +(11.3213 + 8.22541i) q^{85} +(0.569762 + 5.42092i) q^{86} +(0.344501 - 0.596693i) q^{87} +(3.63214 + 6.29106i) q^{88} +(0.713499 - 0.518388i) q^{89} +(-8.81631 - 9.79150i) q^{90} +(0.401033 + 1.23425i) q^{91} +7.47693 q^{92} -10.1563 q^{94} +(3.55376 + 10.9374i) q^{95} +(0.791642 + 0.879208i) q^{96} +(-6.99151 + 5.07963i) q^{97} +(-5.31146 - 9.19972i) q^{98} +(-7.95645 + 13.7810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) $ 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.557046	−	1.71441i	−0.393891	−	1.21227i	−0.929822	−	0.368011i	$-0.880039\pi$
$2$	−0.557046	−	1.71441i	−0.393891	−	1.21227i	0.535930	−	0.844262i	$-0.319961\pi$
$3$	0.127782	+	0.141916i	0.0737750	+	0.0819355i	0.778902	−	0.627145i	$-0.215777\pi$
$3$	0.127782	+	0.141916i	0.0737750	+	0.0819355i	−0.705127	+	0.709081i	$0.749110\pi$
$4$	−1.01088	+	0.734444i	−0.505438	+	0.367222i
$5$	1.23318	+	2.13593i	0.551496	+	0.955219i	0.998167	+	0.0605206i	$0.0192761\pi$
$5$	1.23318	+	2.13593i	0.551496	+	0.955219i	−0.446671	+	0.894698i	$0.647391\pi$
$6$	0.172123	−	0.298125i	0.0702688	−	0.121709i
$7$	0.109980	+	1.04639i	0.0415684	+	0.395497i	0.995448	+	0.0953073i	$0.0303834\pi$
$7$	0.109980	+	1.04639i	0.0415684	+	0.395497i	−0.953879	+	0.300190i	$0.902950\pi$
$8$	−1.09449	−	0.795192i	−0.386960	−	0.281143i
$9$	0.309773	−	2.94730i	0.103258	−	0.982432i
$10$	2.97493	−	3.30400i	0.940756	−	1.04482i
$11$	−4.90535	−	2.18400i	−1.47902	−	0.658501i	−0.500702	−	0.865620i	$-0.666925\pi$
$11$	−4.90535	−	2.18400i	−1.47902	−	0.658501i	−0.978316	+	0.207119i	$0.933591\pi$
$12$	−0.233401	−	0.0496110i	−0.0673772	−	0.0143215i
$13$	1.20649	−	0.256448i	0.334620	−	0.0711258i	−0.0375374	−	0.999295i	$-0.511951\pi$
$13$	1.20649	−	0.256448i	0.334620	−	0.0711258i	0.372158	+	0.928169i	$0.378618\pi$
$14$	1.73268	−	0.771437i	0.463077	−	0.206175i
$15$	−0.145545	+	0.447943i	−0.0375797	+	0.115658i
$16$	−1.52585	+	4.69607i	−0.381462	+	1.17402i
$17$	5.18337	−	2.30778i	1.25715	−	0.559720i	0.333426	−	0.942776i	$-0.391795\pi$
$17$	5.18337	−	2.30778i	1.25715	−	0.559720i	0.923725	+	0.383056i	$0.125129\pi$
$18$	−5.22544	+	1.11070i	−1.23165	+	0.261795i
$19$	4.56093	+	0.969455i	1.04635	+	0.222408i	0.698847	−	0.715271i	$-0.253697\pi$
$19$	4.56093	+	0.969455i	1.04635	+	0.222408i	0.347501	+	0.937679i	$0.387030\pi$
$20$	−2.81532	−	1.25346i	−0.629524	−	0.280282i
$21$	−0.134446	+	0.149317i	−0.0293385	+	0.0325837i
$22$	−1.01177	+	9.62638i	−0.215711	+	2.05235i
$23$	−4.84106	−	3.51724i	−1.00943	−	0.733395i	−0.0453419	−	0.998972i	$-0.514438\pi$
$23$	−4.84106	−	3.51724i	−1.00943	−	0.733395i	−0.964090	+	0.265576i	$0.914438\pi$
$24$	−0.0270052	−	0.256937i	−0.00551241	−	0.0524471i
$25$	−0.541477	+	0.937865i	−0.108295	+	0.187573i
$26$	−1.11173	−	1.92557i	−0.218028	−	0.377635i
$27$	0.921341	−	0.669393i	0.177312	−	0.128825i
$28$	−0.879689	−	0.976993i	−0.166246	−	0.184634i
$29$	−1.11492	−	3.43137i	−0.207035	−	0.637189i	−0.999624	−	0.0274321i	$-0.991267\pi$
$29$	−1.11492	−	3.43137i	−0.207035	−	0.637189i	0.792588	−	0.609757i	$-0.208733\pi$
$30$	0.849035			0.155012
$31$		0			0
$31$		0			0
$32$	6.19525			1.09518
$33$	−0.316870	−	0.975226i	−0.0551600	−	0.169765i
$34$	−6.84387	−	7.60089i	−1.17371	−	1.30354i
$35$	−2.09939	+	1.52530i	−0.354862	+	0.257822i
$36$	1.85148	+	3.20686i	0.308580	+	0.534477i
$37$	2.67703	−	4.63676i	0.440102	−	0.762278i	−0.557595	−	0.830113i	$-0.688276\pi$
$37$	2.67703	−	4.63676i	0.440102	−	0.762278i	0.997697	+	0.0678348i	$0.0216091\pi$
$38$	−0.878602	−	8.35934i	−0.142528	−	1.35606i
$39$	0.190562	+	0.138451i	0.0305144	+	0.0221700i
$40$	0.348775	−	3.31837i	0.0551462	−	0.524681i
$41$	7.06792	−	7.84972i	1.10382	−	1.22592i	0.131741	−	0.991284i	$-0.457943\pi$
$41$	7.06792	−	7.84972i	1.10382	−	1.22592i	0.972083	−	0.234637i	$-0.0753900\pi$
$42$	0.330884	+	0.147319i	0.0510566	+	0.0227319i
$43$	−2.95770	−	0.628679i	−0.451045	−	0.0958726i	−0.0232125	−	0.999731i	$-0.507389\pi$
$43$	−2.95770	−	0.628679i	−0.451045	−	0.0958726i	−0.427833	+	0.903858i	$0.640723\pi$
$44$	6.56272	−	1.39495i	0.989368	−	0.210297i
$45$	6.67724	−	2.97290i	0.995384	−	0.443174i
$46$	−3.33330	+	10.2588i	−0.491468	+	1.51258i
$47$	1.74104	−	5.35837i	0.253957	−	0.781599i	−0.740076	−	0.672523i	$-0.765211\pi$
$47$	1.74104	−	5.35837i	0.253957	−	0.781599i	0.994033	−	0.109076i	$-0.0347893\pi$
$48$	−0.861426	+	0.383532i	−0.124336	+	0.0553580i
$49$	5.76420	−	1.22522i	0.823458	−	0.175031i
$50$	1.90952	+	0.405880i	0.270046	+	0.0574001i
$51$	0.989854	+	0.440711i	0.138607	+	0.0617119i
$52$	−1.03127	+	1.14534i	−0.143011	+	0.158830i
$53$	0.0949835	−	0.903708i	0.0130470	−	0.124134i	−0.986060	−	0.166392i	$-0.946788\pi$
$53$	0.0949835	−	0.903708i	0.0130470	−	0.124134i	0.999107	+	0.0422578i	$0.0134551\pi$
$54$	−1.66085	−	1.20668i	−0.226012	−	0.164208i
$55$	−1.38430	−	13.1708i	−0.186659	−	1.77595i
$56$	0.711707	−	1.23271i	0.0951059	−	0.164728i
$57$	0.445223	+	0.771149i	0.0589713	+	0.102141i
$58$	−5.26172	+	3.82286i	−0.690898	+	0.501967i
$59$	2.05099	+	2.27786i	0.267017	+	0.296552i	0.861711	−	0.507400i	$-0.169393\pi$
$59$	2.05099	+	2.27786i	0.267017	+	0.296552i	−0.594694	+	0.803952i	$0.702727\pi$
$60$	−0.181861	−	0.559710i	−0.0234781	−	0.0722582i
$61$	−9.12376			−1.16818			−0.584089	−	0.811690i	$-0.698548\pi$
$61$	−9.12376			−1.16818			−0.584089	+	0.811690i	$0.698548\pi$
$62$		0			0
$63$	3.11808			0.392841
$64$	−0.399349	−	1.22907i	−0.0499186	−	0.153634i
$65$	2.03558	+	2.26074i	0.252482	+	0.280410i
$66$	−1.49543	+	1.08649i	−0.184074	+	0.133738i
$67$	−3.98244	−	6.89779i	−0.486532	−	0.842699i	0.513348	−	0.858181i	$-0.328405\pi$
$67$	−3.98244	−	6.89779i	−0.486532	−	0.842699i	−0.999880	+	0.0154820i	$0.995072\pi$
$68$	−3.54480	+	6.13978i	−0.429870	+	0.744557i
$69$	−0.119447	−	1.13647i	−0.0143798	−	0.136815i
$70$	3.78444	+	2.74956i	0.452327	+	0.328635i
$71$	−0.634341	+	6.03535i	−0.0752824	+	0.716265i	0.890160	+	0.455648i	$0.150592\pi$
$71$	−0.634341	+	6.03535i	−0.0752824	+	0.716265i	−0.965442	+	0.260616i	$0.916074\pi$
$72$	−2.68271	+	2.97945i	−0.316160	+	0.351132i
$73$	3.46139	+	1.54111i	0.405125	+	0.180373i	0.599175	−	0.800618i	$-0.295496\pi$
$73$	3.46139	+	1.54111i	0.405125	+	0.180373i	−0.194049	+	0.980992i	$0.562162\pi$
$74$	−9.44055	−	2.00665i	−1.09744	−	0.233268i
$75$	−0.202290	+	0.0429980i	−0.0233584	+	0.00496498i
$76$	−5.32254	+	2.36975i	−0.610537	+	0.271829i
$77$	1.74582	−	5.37309i	0.198955	−	0.612320i
$78$	0.131211	−	0.403826i	0.0148567	−	0.0457243i
$79$	7.77440	−	3.46139i	0.874688	−	0.389436i	0.0802454	−	0.996775i	$-0.474430\pi$
$79$	7.77440	−	3.46139i	0.874688	−	0.389436i	0.794443	+	0.607339i	$0.207763\pi$
$80$	−11.9122	+	2.53201i	−1.33182	+	0.283087i
$81$	−8.48358	−	1.80324i	−0.942621	−	0.200360i
$82$	−17.3948	−	7.74468i	−1.92094	−	0.855256i
$83$	−8.85485	+	9.83430i	−0.971946	+	1.07945i	0.0248682	+	0.999691i	$0.492083\pi$
$83$	−8.85485	+	9.83430i	−0.971946	+	1.07945i	−0.996814	+	0.0797642i	$0.974583\pi$
$84$	0.0262429	−	0.249684i	0.00286333	−	0.0272428i
$85$	11.3213	+	8.22541i	1.22797	+	0.892171i
$86$	0.569762	+	5.42092i	0.0614390	+	0.584553i
$87$	0.344501	−	0.596693i	0.0369344	−	0.0639722i
$88$	3.63214	+	6.29106i	0.387188	+	0.670629i
$89$	0.713499	−	0.518388i	0.0756308	−	0.0549490i	−0.549327	−	0.835607i	$-0.685116\pi$
$89$	0.713499	−	0.518388i	0.0756308	−	0.0549490i	0.624958	+	0.780658i	$0.285116\pi$
$90$	−8.81631	−	9.79150i	−0.929320	−	1.03211i
$91$	0.401033	+	1.23425i	0.0420397	+	0.129385i
$92$	7.47693			0.779524
$93$		0			0
$94$	−10.1563			−1.04754
$95$	3.55376	+	10.9374i	0.364608	+	1.12215i
$96$	0.791642	+	0.879208i	0.0807967	+	0.0897338i
$97$	−6.99151	+	5.07963i	−0.709881	+	0.515759i	−0.883135	−	0.469119i	$-0.844572\pi$
$97$	−6.99151	+	5.07963i	−0.709881	+	0.515759i	0.173254	+	0.984877i	$0.444572\pi$
$98$	−5.31146	−	9.19972i	−0.536538	−	0.929312i
$99$	−7.95645	+	13.7810i	−0.799653	+	1.38504i
$100$	−0.141444	−	1.34575i	−0.0141444	−	0.134575i
$101$	−8.04270	−	5.84336i	−0.800278	−	0.581436i	0.110718	−	0.993852i	$-0.464685\pi$
$101$	−8.04270	−	5.84336i	−0.800278	−	0.581436i	−0.910996	+	0.412416i	$0.864685\pi$
$102$	0.204167	−	1.94251i	0.0202155	−	0.192338i
$103$	−6.02757	+	6.69429i	−0.593914	+	0.659608i	−0.962910	−	0.269823i	$-0.913035\pi$
$103$	−6.02757	+	6.69429i	−0.593914	+	0.659608i	0.368996	+	0.929431i	$0.379702\pi$
$104$	−1.52442	−	0.678714i	−0.149481	−	0.0665533i
$105$	−0.484729	−	0.103032i	−0.0473047	−	0.0100549i
$106$	−1.60224	+	0.340566i	−0.155623	+	0.0330787i
$107$	0.269362	−	0.119928i	0.0260402	−	0.0115938i	−0.393675	−	0.919250i	$-0.628797\pi$
$107$	0.269362	−	0.119928i	0.0260402	−	0.0115938i	0.419715	+	0.907656i	$0.362130\pi$
$108$	−0.439729	+	1.35335i	−0.0423129	+	0.130226i
$109$	0.675483	−	2.07892i	0.0646996	−	0.199125i	−0.913481	−	0.406881i	$-0.866616\pi$
$109$	0.675483	−	2.07892i	0.0646996	−	0.199125i	0.978181	+	0.207757i	$0.0666162\pi$
$110$	−21.8090	+	9.71000i	−2.07941	+	0.925812i
$111$	1.00011	−	0.212580i	0.0949261	−	0.0201772i
$112$	−5.08172	−	1.08015i	−0.480178	−	0.102065i
$113$	9.69066	+	4.31456i	0.911621	+	0.405880i	0.808302	−	0.588768i	$-0.200387\pi$
$113$	9.69066	+	4.31456i	0.911621	+	0.405880i	0.103319	+	0.994648i	$0.467054\pi$
$114$	1.07406	−	1.19286i	0.100595	−	0.111722i
$115$	1.54268	−	14.6776i	0.143855	−	1.36869i
$116$	3.64719	+	2.64984i	0.338633	+	0.246032i
$117$	−0.382088	−	3.63533i	−0.0353241	−	0.336086i
$118$	2.76269	−	4.78512i	0.254326	−	0.440506i
$119$	2.98490	+	5.17000i	0.273625	+	0.473933i
$120$	0.515499	−	0.374532i	0.0470584	−	0.0341899i
$121$	11.9321	+	13.2520i	1.08474	+	1.20472i
$122$	5.08236	+	15.6419i	0.460135	+	1.41615i
$123$	2.01716			0.181881
$124$		0			0
$125$	9.66086			0.864094
$126$	−1.73692	−	5.34568i	−0.154737	−	0.476231i
$127$	13.6055	+	15.1104i	1.20729	+	1.34083i	0.924280	+	0.381715i	$0.124667\pi$
$127$	13.6055	+	15.1104i	1.20729	+	1.34083i	0.283011	+	0.959117i	$0.408667\pi$
$128$	8.13945	−	5.91366i	0.719433	−	0.522698i
$129$	−0.288721	−	0.500080i	−0.0254205	−	0.0440296i
$130$	2.74193	−	4.74916i	0.240483	−	0.416529i
$131$	−0.568569	−	5.40958i	−0.0496761	−	0.472637i	−0.990875	−	0.134784i	$-0.956966\pi$
$131$	−0.568569	−	5.40958i	−0.0496761	−	0.472637i	0.941199	−	0.337853i	$-0.109701\pi$
$132$	1.03656	+	0.753108i	0.0902214	+	0.0655497i
$133$	−0.512816	+	4.87912i	−0.0444668	+	0.423073i
$134$	−9.60725	+	10.6699i	−0.829940	+	0.921741i
$135$	2.56596	+	1.14244i	0.220843	+	0.0983255i
$136$	−7.50827	−	1.59593i	−0.643828	−	0.136850i
$137$	−4.29393	+	0.912702i	−0.366855	+	0.0779774i	−0.387651	−	0.921806i	$-0.626713\pi$
$137$	−4.29393	+	0.912702i	−0.366855	+	0.0779774i	0.0207958	+	0.999784i	$0.493380\pi$
$138$	−1.88183	+	0.837847i	−0.160192	+	0.0713223i
$139$	−2.07819	+	6.39602i	−0.176270	+	0.542504i	−0.999689	−	0.0249300i	$-0.992064\pi$
$139$	−2.07819	+	6.39602i	−0.176270	+	0.542504i	0.823419	+	0.567434i	$0.192064\pi$
$140$	1.00198	−	3.08377i	0.0846825	−	0.260626i
$141$	0.982915	−	0.437622i	0.0827764	−	0.0368544i
$142$	10.7004	−	2.27445i	0.897961	−	0.190868i
$143$	−6.47834	−	1.37701i	−0.541746	−	0.115152i
$144$	13.3681	+	5.95184i	1.11400	+	0.495987i
$145$	5.95428	−	6.61290i	0.494476	−	0.549171i
$146$	0.713944	−	6.79272i	0.0590864	−	0.562170i
$147$	0.910441	+	0.661474i	0.0750919	+	0.0545574i
$148$	0.699292	+	6.65332i	0.0574814	+	0.546899i
$149$	−1.10847	+	1.91993i	−0.0908097	+	0.157287i	−0.907852	−	0.419291i	$-0.862279\pi$
$149$	−1.10847	+	1.91993i	−0.0908097	+	0.157287i	0.817042	+	0.576578i	$0.195612\pi$
$150$	0.186401	+	0.322856i	0.0152196	+	0.0263611i
$151$	3.83884	−	2.78908i	0.312400	−	0.226972i	−0.420525	−	0.907281i	$-0.638154\pi$
$151$	3.83884	−	2.78908i	0.312400	−	0.226972i	0.732926	+	0.680309i	$0.238154\pi$
$152$	−4.22098	−	4.68787i	−0.342366	−	0.380236i
$153$	−5.19605	−	15.9918i	−0.420076	−	1.29286i
$154$	−10.1842			−0.820666
$155$		0			0
$156$	−0.294319			−0.0235644
$157$	1.25102	+	3.85024i	0.0998423	+	0.307283i	0.988485	−	0.151317i	$-0.0483513\pi$
$157$	1.25102	+	3.85024i	0.0998423	+	0.307283i	−0.888643	+	0.458599i	$0.848351\pi$
$158$	−10.2649	−	11.4004i	−0.816635	−	0.906965i
$159$	0.140388	−	0.101998i	0.0111335	−	0.00808897i
$160$	7.63987	+	13.2327i	0.603985	+	1.04613i
$161$	3.14797	−	5.45245i	0.248095	−	0.429713i
$162$	1.63425	+	15.5489i	0.128399	+	1.22163i
$163$	0.877212	+	0.637332i	0.0687085	+	0.0499197i	0.621609	−	0.783327i	$-0.286479\pi$
$163$	0.877212	+	0.637332i	0.0687085	+	0.0499197i	−0.552901	+	0.833247i	$0.686479\pi$
$164$	−1.37961	+	13.1261i	−0.107729	+	1.02498i
$165$	1.69226	−	1.87944i	0.131742	−	0.146315i
$166$	21.7926	+	9.70270i	1.69143	+	0.753075i
$167$	10.9064	+	2.31822i	0.843960	+	0.179389i	0.609549	−	0.792748i	$-0.291351\pi$
$167$	10.9064	+	2.31822i	0.843960	+	0.179389i	0.234411	+	0.972138i	$0.424684\pi$
$168$	0.265886	−	0.0565157i	0.0205135	−	0.00436028i
$169$	−10.4862	+	4.66877i	−0.806633	+	0.359136i
$170$	7.79526	−	23.9913i	0.597869	−	1.84005i
$171$	4.27013	−	13.1421i	0.326545	−	1.00500i
$172$	3.45160	−	1.53675i	0.263182	−	0.117176i
$173$	7.47126	−	1.58807i	0.568029	−	0.120738i	0.0850603	−	0.996376i	$-0.472892\pi$
$173$	7.47126	−	1.58807i	0.568029	−	0.120738i	0.482969	+	0.875637i	$0.339558\pi$
$174$	−1.21488	−	0.258231i	−0.0920999	−	0.0195764i
$175$	−1.04092	−	0.463448i	−0.0786863	−	0.0350334i
$176$	17.7410	−	19.7034i	1.33728	−	1.48520i
$177$	−0.0611853	+	0.582140i	−0.00459897	+	0.0437563i
$178$	−1.28618	−	0.934466i	−0.0964035	−	0.0700412i
$179$	1.39353	+	13.2585i	0.104157	+	0.990990i	0.914377	+	0.404864i	$0.132681\pi$
$179$	1.39353	+	13.2585i	0.104157	+	0.990990i	−0.810220	+	0.586126i	$0.800652\pi$
$180$	−4.56643	+	7.90929i	−0.340362	+	0.589524i
$181$	−10.4890	−	18.1674i	−0.779638	−	1.35037i	−0.932151	−	0.362070i	$-0.882070\pi$
$181$	−10.4890	−	18.1674i	−0.779638	−	1.35037i	0.152513	−	0.988301i	$-0.451263\pi$
$182$	1.89262	−	1.37507i	0.140291	−	0.101927i
$183$	−1.16585	−	1.29481i	−0.0861824	−	0.0957152i
$184$	2.50161	+	7.69915i	0.184421	+	0.567589i
$185$	13.2051			0.970857
$186$		0			0
$187$	−30.4664			−2.22793
$188$	2.17545	+	6.69534i	0.158661	+	0.488308i
$189$	0.801773	+	0.890459i	0.0583204	+	0.0647714i
$190$	16.7715	−	12.1852i	1.21673	−	0.884009i
$191$	−3.78330	−	6.55288i	−0.273750	−	0.474149i	0.696069	−	0.717975i	$-0.254931\pi$
$191$	−3.78330	−	6.55288i	−0.273750	−	0.474149i	−0.969819	+	0.243826i	$0.921598\pi$
$192$	0.123395	−	0.213727i	0.00890530	−	0.0154244i
$193$	1.34084	+	12.7572i	0.0965154	+	0.918283i	0.930450	+	0.366419i	$0.119416\pi$
$193$	1.34084	+	12.7572i	0.0965154	+	0.918283i	−0.833934	+	0.551864i	$0.813917\pi$
$194$	12.6032	+	9.15675i	0.904856	+	0.657416i
$195$	−0.0607255	+	0.577764i	−0.00434864	+	0.0413745i
$196$	−4.92704	+	5.47203i	−0.351931	+	0.390859i
$197$	−16.1893	−	7.20796i	−1.15344	−	0.513546i	−0.261281	−	0.965263i	$-0.584145\pi$
$197$	−16.1893	−	7.20796i	−1.15344	−	0.513546i	−0.892161	+	0.451717i	$0.850812\pi$
$198$	28.0584	+	5.96399i	1.99402	+	0.423842i
$199$	−0.229366	+	0.0487533i	−0.0162594	+	0.00345603i	−0.216034	−	0.976386i	$-0.569312\pi$
$199$	−0.229366	+	0.0487533i	−0.0162594	+	0.00345603i	0.199775	+	0.979842i	$0.435979\pi$
$200$	1.33842	−	0.595904i	0.0946408	−	0.0421368i
$201$	0.470025	−	1.44659i	0.0331530	−	0.102034i
$202$	−5.53778	+	17.0435i	−0.389637	+	1.19918i
$203$	3.46792	−	1.54402i	0.243400	−	0.108369i
$204$	−1.32430	+	0.281488i	−0.0927193	+	0.0197081i
$205$	25.4825	+	5.41648i	1.77978	+	0.378303i
$206$	14.8344	+	6.60471i	1.03356	+	0.460172i
$207$	−11.8660	+	13.1785i	−0.824743	+	0.915970i
$208$	−0.636624	+	6.05707i	−0.0441419	+	0.419982i
$209$	−20.2556	−	14.7166i	−1.40111	−	1.01797i
$210$	0.0933766	+	0.888419i	0.00644360	+	0.0613067i
$211$	−8.18778	+	14.1817i	−0.563670	+	0.976305i	0.433502	+	0.901153i	$0.357278\pi$
$211$	−8.18778	+	14.1817i	−0.563670	+	0.976305i	−0.997172	+	0.0751525i	$0.976056\pi$
$212$	0.567706	+	0.983296i	0.0389902	+	0.0675331i
$213$	−0.937573	+	0.681187i	−0.0642414	+	0.0466741i
$214$	−0.355652	−	0.394992i	−0.0243119	−	0.0270011i
$215$	−2.30457	−	7.09273i	−0.157170	−	0.483720i
$216$	−1.54069			−0.104831
$217$		0			0
$218$	−3.94041			−0.266878
$219$	0.223595	+	0.688154i	0.0151091	+	0.0465012i
$220$	11.0726	+	12.2973i	0.746511	+	0.829085i
$221$	5.66186	−	4.11358i	0.380858	−	0.276710i
$222$	−0.921556	−	1.59618i	−0.0618508	−	0.107129i
$223$	4.89874	−	8.48486i	0.328044	−	0.568188i	−0.654080	−	0.756426i	$-0.726944\pi$
$223$	4.89874	−	8.48486i	0.328044	−	0.568188i	0.982124	+	0.188237i	$0.0602773\pi$
$224$	0.681352	+	6.48263i	0.0455247	+	0.433139i
$225$	2.59643	+	1.88642i	0.173095	+	0.125761i
$226$	1.99879	−	19.0172i	0.132957	−	1.26501i
$227$	−0.965334	+	1.07211i	−0.0640715	+	0.0711586i	−0.774328	−	0.632784i	$-0.781912\pi$
$227$	−0.965334	+	1.07211i	−0.0640715	+	0.0711586i	0.710257	+	0.703943i	$0.248579\pi$
$228$	−1.01643	−	0.452544i	−0.0673148	−	0.0299705i
$229$	27.2492	+	5.79199i	1.80068	+	0.382745i	0.981601	−	0.190942i	$-0.0611543\pi$
$229$	27.2492	+	5.79199i	1.80068	+	0.382745i	0.819074	+	0.573688i	$0.194488\pi$
$230$	−26.0228	+	5.53131i	−1.71589	+	0.364724i
$231$	0.985614	−	0.438824i	0.0648486	−	0.0288725i
$232$	−1.50833	+	4.64217i	−0.0990268	+	0.304773i
$233$	−4.72131	+	14.5307i	−0.309303	+	0.951938i	0.668733	+	0.743503i	$0.266837\pi$
$233$	−4.72131	+	14.5307i	−0.309303	+	0.951938i	−0.978036	+	0.208435i	$0.933163\pi$
$234$	−6.01961	+	2.68010i	−0.393514	+	0.175204i
$235$	13.5922	−	2.88910i	0.886654	−	0.188464i
$236$	−3.74626	−	0.796292i	−0.243861	−	0.0518342i
$237$	1.48466	+	0.661012i	0.0964388	+	0.0429373i
$238$	7.20078	−	7.99728i	0.466757	−	0.518387i
$239$	−0.476443	+	4.53306i	−0.0308186	+	0.293219i	0.968247	+	0.249996i	$0.0804293\pi$
$239$	−0.476443	+	4.53306i	−0.0308186	+	0.293219i	−0.999065	+	0.0432231i	$0.986237\pi$
$240$	−1.88149	−	1.36698i	−0.121450	−	0.0882385i
$241$	0.838370	+	7.97656i	0.0540042	+	0.513815i	0.987769	+	0.155927i	$0.0498364\pi$
$241$	0.838370	+	7.97656i	0.0540042	+	0.513815i	−0.933764	+	0.357888i	$0.883497\pi$
$242$	16.0726	−	27.8386i	1.03319	−	1.78953i
$243$	−2.53640	−	4.39317i	−0.162710	−	0.281822i
$244$	9.22299	−	6.70089i	0.590441	−	0.428981i
$245$	9.72530	+	10.8010i	0.621327	+	0.690053i
$246$	−1.12365	−	3.45824i	−0.0716414	−	0.220489i
$247$	5.75133			0.365949
$248$		0			0
$249$	−2.52714			−0.160151
$250$	−5.38155	−	16.5627i	−0.340359	−	1.04752i
$251$	−7.89829	−	8.77194i	−0.498535	−	0.553680i	0.440387	−	0.897808i	$-0.354841\pi$
$251$	−7.89829	−	8.77194i	−0.498535	−	0.553680i	−0.938923	+	0.344128i	$0.888175\pi$
$252$	−3.15199	+	2.29006i	−0.198557	+	0.144260i
$253$	16.0654	+	27.8262i	1.01003	+	1.74942i
$254$	18.3266	−	31.7426i	1.14991	−	1.99171i
$255$	0.279340	+	2.65774i	0.0174929	+	0.166434i
$256$	−16.7635	−	12.1794i	−1.04772	−	0.761213i
$257$	−0.0111021	+	0.105629i	−0.000692529	+	0.00658897i	−0.994863	−	0.101233i	$-0.967721\pi$
$257$	−0.0111021	+	0.105629i	−0.000692529	+	0.00658897i	0.994170	+	0.107822i	$0.0343878\pi$
$258$	−0.696513	+	0.773556i	−0.0433630	+	0.0481595i
$259$	5.14626	+	2.29126i	0.319773	+	0.142372i
$260$	−3.71810	−	0.790307i	−0.230587	−	0.0490128i
$261$	−10.4586	+	2.22305i	−0.647373	+	0.137603i
$262$	−8.95752	+	3.98815i	−0.553398	+	0.246389i
$263$	7.34257	−	22.5981i	0.452763	−	1.39346i	−0.420980	−	0.907070i	$-0.638314\pi$
$263$	7.34257	−	22.5981i	0.452763	−	1.39346i	0.873742	−	0.486390i	$-0.161686\pi$
$264$	−0.428681	+	1.31935i	−0.0263835	+	0.0812001i
$265$	2.04739	−	0.911558i	0.125770	−	0.0559966i
$266$	8.65048	−	1.83872i	0.530395	−	0.112739i
$267$	0.164740	+	0.0350166i	0.0100819	+	0.00214298i
$268$	9.09179	+	4.04792i	0.555369	+	0.247266i
$269$	1.72447	−	1.91522i	0.105143	−	0.116773i	−0.688276	−	0.725449i	$-0.741632\pi$
$269$	1.72447	−	1.91522i	0.105143	−	0.116773i	0.793419	+	0.608676i	$0.208299\pi$
$270$	0.529253	−	5.03551i	0.0322093	−	0.306451i
$271$	23.5264	+	17.0929i	1.42912	+	1.03832i	0.990179	+	0.139806i	$0.0446479\pi$
$271$	23.5264	+	17.0929i	1.42912	+	1.03832i	0.438946	+	0.898514i	$0.355352\pi$
$272$	2.92850	+	27.8628i	0.177566	+	1.68943i
$273$	−0.123916	+	0.214629i	−0.00749973	+	0.0129899i
$274$	3.95666	+	6.85314i	0.239031	+	0.414014i
$275$	4.70443	−	3.41797i	0.283688	−	0.206111i
$276$	0.955418	+	1.06110i	0.0575094	+	0.0638707i
$277$	3.71797	+	11.4427i	0.223391	+	0.687527i	0.998451	+	0.0556392i	$0.0177196\pi$
$277$	3.71797	+	11.4427i	0.223391	+	0.687527i	−0.775060	+	0.631888i	$0.782280\pi$
$278$	12.1231			0.727094
$279$		0			0
$280$	3.51066			0.209802
$281$	−9.62207	−	29.6137i	−0.574005	−	1.76660i	−0.639544	−	0.768755i	$-0.720877\pi$
$281$	−9.62207	−	29.6137i	−0.574005	−	1.76660i	0.0655393	−	0.997850i	$-0.479123\pi$
$282$	−1.29779	−	1.44135i	−0.0772825	−	0.0858309i
$283$	−4.64215	+	3.37272i	−0.275947	+	0.200487i	−0.717148	−	0.696921i	$-0.754553\pi$
$283$	−4.64215	+	3.37272i	−0.275947	+	0.200487i	0.441201	+	0.897409i	$0.354553\pi$
$284$	−3.79139	−	6.56688i	−0.224978	−	0.389673i
$285$	−1.09808	+	1.90194i	−0.0650448	+	0.112661i
$286$	1.24797	+	11.8736i	0.0737938	+	0.702101i
$287$	8.99118	+	6.53247i	0.530732	+	0.385600i
$288$	1.91912	−	18.2592i	0.113085	−	1.07594i
$289$	10.1662	−	11.2907i	0.598012	−	0.664160i
$290$	−14.6540	−	6.52440i	−0.860515	−	0.383126i
$291$	−1.61427	−	0.343124i	−0.0946304	−	0.0201143i
$292$	−4.63089	+	0.984327i	−0.271003	+	0.0576034i
$293$	1.16845	−	0.520227i	0.0682615	−	0.0303920i	−0.372322	−	0.928104i	$-0.621438\pi$
$293$	1.16845	−	0.520227i	0.0682615	−	0.0303920i	0.440583	+	0.897712i	$0.354772\pi$
$294$	0.626881	−	1.92934i	0.0365605	−	0.112522i
$295$	−2.33611	+	7.18981i	−0.136014	+	0.418607i
$296$	−6.61709	+	2.94612i	−0.384611	+	0.171240i
$297$	−5.98145	+	1.27140i	−0.347079	+	0.0737739i
$298$	3.90903	+	0.830889i	0.226444	+	0.0481321i
$299$	−6.74269	−	3.00204i	−0.389940	−	0.173612i
$300$	0.172910	−	0.192036i	0.00998296	−	0.0110872i
$301$	0.332554	−	3.16404i	0.0191681	−	0.182372i
$302$	−6.92005	−	5.02771i	−0.398204	−	0.289312i
$303$	−0.198444	−	1.88807i	−0.0114003	−	0.108467i
$304$	−11.5119	+	19.9392i	−0.660253	+	1.14359i
$305$	−11.2513	−	19.4878i	−0.644245	−	1.11587i
$306$	−24.5221	+	17.8164i	−1.40184	+	1.01849i
$307$	−10.5008	−	11.6623i	−0.599311	−	0.665603i	0.364805	−	0.931084i	$-0.381136\pi$
$307$	−10.5008	−	11.6623i	−0.599311	−	0.665603i	−0.964116	+	0.265481i	$0.914469\pi$
$308$	2.18142	+	6.71373i	0.124298	+	0.382550i
$309$	−1.72025			−0.0978613
$310$		0			0
$311$	27.4565			1.55692			0.778459	−	0.627695i	$-0.216002\pi$
$311$	27.4565			1.55692			0.778459	+	0.627695i	$0.216002\pi$
$312$	−0.0984724	−	0.303067i	−0.00557490	−	0.0171578i
$313$	8.57035	+	9.51833i	0.484425	+	0.538008i	0.934961	−	0.354750i	$-0.115434\pi$
$313$	8.57035	+	9.51833i	0.484425	+	0.538008i	−0.450537	+	0.892758i	$0.648767\pi$
$314$	5.90403	−	4.28953i	0.333184	−	0.242072i
$315$	3.84516	+	6.66002i	0.216650	+	0.375250i
$316$	−5.31676	+	9.20889i	−0.299091	+	0.518041i
$317$	0.995409	+	9.47069i	0.0559078	+	0.531927i	0.986253	+	0.165242i	$0.0528406\pi$
$317$	0.995409	+	9.47069i	0.0559078	+	0.531927i	−0.930345	+	0.366685i	$0.880493\pi$
$318$	−0.253069	−	0.183866i	−0.0141914	−	0.0103107i
$319$	−2.02505	+	19.2670i	−0.113381	+	1.07875i
$320$	2.13274	−	2.36865i	0.119224	−	0.132412i
$321$	0.0514393	+	0.0229023i	0.00287106	+	0.00127828i
$322$	−11.1013	−	2.35966i	−0.618652	−	0.131499i
$323$	25.8783	−	5.50059i	1.43990	−	0.306061i
$324$	9.90023	−	4.40787i	0.550013	−	0.244881i
$325$	−0.412774	+	1.27039i	−0.0228966	+	0.0704684i
$326$	0.604002	−	1.85893i	0.0334526	−	0.102956i
$327$	0.381348	−	0.169787i	0.0210886	−	0.00938925i
$328$	−13.9778	+	2.97107i	−0.771795	+	0.164050i
$329$	5.79841	+	1.23249i	0.319677	+	0.0679494i
$330$	−4.16481	−	1.85429i	−0.229265	−	0.102075i
$331$	14.4420	−	16.0394i	0.793801	−	0.881606i	−0.201394	−	0.979510i	$-0.564547\pi$
$331$	14.4420	−	16.0394i	0.793801	−	0.881606i	0.995196	+	0.0979044i	$0.0312139\pi$
$332$	1.72840	−	16.4446i	0.0948584	−	0.902517i
$333$	−12.8366	−	9.32636i	−0.703443	−	0.511081i
$334$	−2.10097	−	19.9894i	−0.114960	−	1.09377i
$335$	9.82214	−	17.0125i	0.536641	−	0.929490i
$336$	−0.496062	−	0.859204i	−0.0270624	−	0.0468734i
$337$	3.67939	−	2.67324i	0.200429	−	0.145620i	−0.483044	−	0.875596i	$-0.660469\pi$
$337$	3.67939	−	2.67324i	0.200429	−	0.145620i	0.683473	+	0.729976i	$0.260469\pi$
$338$	13.8455	+	15.3770i	0.753097	+	0.836399i
$339$	0.625986	+	1.92659i	0.0339989	+	0.104638i
$340$	−17.4855			−0.948287
$341$		0			0
$342$	−24.9096			−1.34696
$343$	4.19193	+	12.9014i	0.226343	+	0.696611i
$344$	2.73725	+	3.04002i	0.147583	+	0.163907i
$345$	2.28012	−	1.65660i	0.122757	−	0.0891885i
$346$	−6.88444	−	11.9242i	−0.370110	−	0.641049i
$347$	−14.6947	+	25.4520i	−0.788855	+	1.36634i	0.137813	+	0.990458i	$0.455993\pi$
$347$	−14.6947	+	25.4520i	−0.788855	+	1.36634i	−0.926669	+	0.375879i	$0.877341\pi$
$348$	0.0899901	+	0.856199i	0.00482398	+	0.0458971i
$349$	5.46187	+	3.96828i	0.292367	+	0.212417i	0.724294	−	0.689492i	$-0.242166\pi$
$349$	5.46187	+	3.96828i	0.292367	+	0.212417i	−0.431926	+	0.901909i	$0.642166\pi$
$350$	−0.214700	+	2.04273i	−0.0114762	+	0.109189i
$351$	0.939925	−	1.04389i	0.0501695	−	0.0557189i
$352$	−30.3899	−	13.5304i	−1.61979	−	0.721175i
$353$	−7.61066	−	1.61770i	−0.405074	−	0.0861012i	0.000868570	−	1.00000i	$-0.499724\pi$
$353$	−7.61066	−	1.61770i	−0.405074	−	0.0861012i	−0.405943	+	0.913898i	$0.633057\pi$
$354$	1.03211	−	0.219382i	0.0548560	−	0.0116600i
$355$	−13.6734	+	6.08778i	−0.725707	+	0.323106i
$356$	−0.340532	+	1.04805i	−0.0180482	+	0.0555466i
$357$	−0.352291	+	1.08424i	−0.0186452	+	0.0573840i
$358$	21.9544	−	9.77471i	1.16032	−	0.516610i
$359$	−2.53082	+	0.537943i	−0.133572	+	0.0283916i	−0.274212	−	0.961669i	$-0.588417\pi$
$359$	−2.53082	+	0.537943i	−0.133572	+	0.0283916i	0.140641	+	0.990061i	$0.455084\pi$
$360$	−9.67218	−	2.05589i	−0.509769	−	0.108355i
$361$	2.50485	+	1.11523i	0.131834	+	0.0586963i
$362$	−25.3036	+	28.1025i	−1.32993	+	1.47703i
$363$	−0.355960	+	3.38673i	−0.0186830	+	0.177757i
$364$	−1.31188	−	0.953140i	−0.0687614	−	0.0499581i
$365$	0.976815	+	9.29377i	0.0511288	+	0.486458i
$366$	−1.57041	+	2.72002i	−0.0820865	+	0.142178i
$367$	17.6139	+	30.5081i	0.919437	+	1.59251i	0.800271	+	0.599638i	$0.204689\pi$
$367$	17.6139	+	30.5081i	0.919437	+	1.59251i	0.119166	+	0.992874i	$0.461978\pi$
$368$	23.9039	−	17.3672i	1.24608	−	0.905329i
$369$	−20.9460	−	23.2629i	−1.09041	−	1.21102i
$370$	−7.35584	−	22.6390i	−0.382412	−	1.17694i
$371$	0.956075			0.0496369
$372$		0			0
$373$	6.68493			0.346133			0.173066	−	0.984910i	$-0.444632\pi$
$373$	6.68493			0.346133			0.173066	+	0.984910i	$0.444632\pi$
$374$	16.9712	+	52.2320i	0.877560	+	2.70085i
$375$	1.23449	+	1.37104i	0.0637486	+	0.0708000i
$376$	−6.16648	+	4.48021i	−0.318012	+	0.231049i
$377$	−2.22511	−	3.85400i	−0.114599	−	0.198491i
$378$	1.07999	−	1.87060i	0.0555487	−	0.0962131i
$379$	−1.83749	−	17.4826i	−0.0943856	−	0.898019i	−0.934585	−	0.355741i	$-0.884229\pi$
$379$	−1.83749	−	17.4826i	−0.0943856	−	0.898019i	0.840199	−	0.542278i	$-0.182438\pi$
$380$	−11.6253	−	8.44626i	−0.596365	−	0.433284i
$381$	−0.405879	+	3.86168i	−0.0207938	+	0.197840i
$382$	−9.12686	+	10.1364i	−0.466971	+	0.518623i
$383$	29.7612	+	13.2506i	1.52073	+	0.677072i	0.985815	−	0.167835i	$-0.0536777\pi$
$383$	29.7612	+	13.2506i	1.52073	+	0.677072i	0.534913	+	0.844907i	$0.320344\pi$
$384$	1.87932	+	0.399462i	0.0959037	+	0.0203850i
$385$	13.6295	−	2.89704i	0.694623	−	0.147647i
$386$	21.1242	−	9.40509i	1.07519	−	0.478707i
$387$	−2.76912	+	8.52248i	−0.140762	+	0.433222i
$388$	3.33684	−	10.2698i	0.169403	−	0.521368i
$389$	7.66282	−	3.41171i	0.388521	−	0.172980i	−0.203174	−	0.979143i	$-0.565126\pi$
$389$	7.66282	−	3.41171i	0.388521	−	0.172980i	0.591695	+	0.806162i	$0.298459\pi$
$390$	1.02435	−	0.217733i	0.0518701	−	0.0110253i
$391$	−33.2100	−	7.05901i	−1.67950	−	0.356990i
$392$	−7.28314	−	3.24266i	−0.367854	−	0.163779i
$393$	0.695055	−	0.771936i	0.0350609	−	0.0389390i
$394$	−3.33920	+	31.7704i	−0.168226	+	1.60057i
$395$	16.9805	+	12.3371i	0.854384	+	0.620746i
$396$	−2.07837	−	19.7744i	−0.104442	−	0.993701i
$397$	−13.1250	+	22.7332i	−0.658727	+	1.14095i	0.322219	+	0.946665i	$0.395571\pi$
$397$	−13.1250	+	22.7332i	−0.658727	+	1.14095i	−0.980946	+	0.194283i	$0.937762\pi$
$398$	0.211351	+	0.366071i	0.0105941	+	0.0183495i
$399$	−0.757955	+	0.550687i	−0.0379452	+	0.0275688i
$400$	−3.57807	−	3.97385i	−0.178904	−	0.198693i
$401$	0.830713	+	2.55667i	0.0414838	+	0.127674i	0.969654	−	0.244483i	$-0.0786182\pi$
$401$	0.830713	+	2.55667i	0.0414838	+	0.127674i	−0.928170	+	0.372157i	$0.878618\pi$
$402$	−2.74187			−0.136752
$403$		0			0
$404$	12.4218			0.618007
$405$	−6.61020	−	20.3441i	−0.328463	−	1.01091i
$406$	−4.57888	−	5.08536i	−0.227246	−	0.252382i
$407$	−23.2585	+	16.8983i	−1.15288	+	0.837616i
$408$	−0.732933	−	1.26948i	−0.0362856	−	0.0628485i
$409$	−1.54776	+	2.68079i	−0.0765316	+	0.132557i	−0.901751	−	0.432255i	$-0.857718\pi$
$409$	−1.54776	+	2.68079i	−0.0765316	+	0.132557i	0.825220	+	0.564812i	$0.191051\pi$
$410$	−4.90887	−	46.7048i	−0.242432	−	2.30659i
$411$	−0.678214	−	0.492752i	−0.0334538	−	0.0243056i
$412$	1.17654	−	11.1940i	0.0579639	−	0.551489i
$413$	−2.15796	+	2.39665i	−0.106186	+	0.117932i
$414$	29.2033	+	13.0021i	1.43526	+	0.639021i
$415$	−31.9251	−	6.78588i	−1.56714	−	0.333106i
$416$	7.47452	−	1.58876i	0.366468	−	0.0778953i
$417$	−1.17326	+	0.522368i	−0.0574546	+	0.0255805i
$418$	−13.9470	+	42.9243i	−0.682168	+	2.09950i
$419$	10.0985	−	31.0801i	0.493346	−	1.51836i	−0.326173	−	0.945310i	$-0.605759\pi$
$419$	10.0985	−	31.0801i	0.493346	−	1.51836i	0.819519	−	0.573052i	$-0.194241\pi$
$420$	0.565672	−	0.251853i	0.0276020	−	0.0122892i
$421$	−13.3364	+	2.83474i	−0.649976	+	0.138157i	−0.521089	−	0.853503i	$-0.674474\pi$
$421$	−13.3364	+	2.83474i	−0.649976	+	0.138157i	−0.128887	+	0.991659i	$0.541141\pi$
$422$	28.8742	+	6.13739i	1.40557	+	0.298764i
$423$	−15.2534	−	6.79125i	−0.741645	−	0.330202i
$424$	−0.822580	+	0.913567i	−0.0399480	+	0.0443668i
$425$	−0.642283	+	6.11091i	−0.0311553	+	0.296423i
$426$	1.69011	+	1.22793i	0.0818859	+	0.0594936i
$427$	−1.00343	−	9.54699i	−0.0485593	−	0.462011i
$428$	−0.184211	+	0.319063i	−0.00890418	+	0.0154225i
$429$	−0.632395	−	1.09534i	−0.0305323	−	0.0528835i
$430$	−10.8761	+	7.90196i	−0.524493	+	0.381066i
$431$	18.6196	+	20.6792i	0.896877	+	0.996083i	0.999999	+	0.00141390i	$0.000450058\pi$
$431$	18.6196	+	20.6792i	0.896877	+	0.996083i	−0.103122	+	0.994669i	$0.532883\pi$
$432$	1.73770	+	5.34808i	0.0836049	+	0.257309i
$433$	2.12857			0.102292			0.0511462	−	0.998691i	$-0.483713\pi$
$433$	2.12857			0.102292			0.0511462	+	0.998691i	$0.483713\pi$
$434$		0			0
$435$	1.69933			0.0814766
$436$	0.844024	+	2.59764i	0.0404214	+	0.124404i
$437$	−18.6699	−	20.7351i	−0.893104	−	0.991893i
$438$	1.05523	−	0.766668i	0.0504207	−	0.0366328i
$439$	−4.69991	−	8.14048i	−0.224314	−	0.388524i	0.731799	−	0.681520i	$-0.238681\pi$
$439$	−4.69991	−	8.14048i	−0.224314	−	0.388524i	−0.956114	+	0.292997i	$0.905348\pi$
$440$	−8.95819	+	15.5160i	−0.427065	+	0.739698i
$441$	−1.82549	−	17.3684i	−0.0869280	−	0.827065i
$442$	−10.2063	−	7.41531i	−0.485464	−	0.352710i
$443$	−3.28305	+	31.2361i	−0.155982	+	1.48407i	0.584169	+	0.811632i	$0.301420\pi$
$443$	−3.28305	+	31.2361i	−0.155982	+	1.48407i	−0.740152	+	0.672440i	$0.765246\pi$
$444$	−0.854858	+	0.949416i	−0.0405698	+	0.0450573i
$445$	1.98712	+	0.884721i	0.0941984	+	0.0419398i
$446$	−17.2754	−	3.67200i	−0.818013	−	0.173874i
$447$	−0.414113	+	0.0880224i	−0.0195869	+	0.00416332i
$448$	1.24216	−	0.553046i	0.0586866	−	0.0261290i
$449$	−7.45194	+	22.9347i	−0.351679	+	1.08236i	0.606231	+	0.795288i	$0.292680\pi$
$449$	−7.45194	+	22.9347i	−0.351679	+	1.08236i	−0.957910	+	0.287068i	$0.907320\pi$
$450$	1.78777	−	5.50218i	0.0842761	−	0.259375i
$451$	−51.8144	+	23.0693i	−2.43985	+	1.08629i
$452$	−12.9649	+	2.75577i	−0.609816	+	0.129620i
$453$	0.886351	+	0.188400i	0.0416444	+	0.00885180i
$454$	2.37578	+	1.05776i	0.111501	+	0.0496434i
$455$	−2.14174	+	2.37864i	−0.100406	+	0.111512i
$456$	0.125920	−	1.19805i	0.00589676	−	0.0561039i
$457$	−2.99832	−	2.17841i	−0.140255	−	0.101902i	0.515445	−	0.856923i	$-0.327627\pi$
$457$	−2.99832	−	2.17841i	−0.140255	−	0.101902i	−0.655701	+	0.755021i	$0.727627\pi$
$458$	−5.24919	−	49.9427i	−0.245279	−	2.33367i
$459$	3.23083	−	5.59597i	0.150802	−	0.261197i
$460$	9.22042	+	15.9702i	0.429904	+	0.744616i
$461$	−13.8119	+	10.0349i	−0.643285	+	0.467374i	−0.860977	−	0.508644i	$-0.830147\pi$
$461$	−13.8119	+	10.0349i	−0.643285	+	0.467374i	0.217692	+	0.976017i	$0.430147\pi$
$462$	−1.30136	−	1.44530i	−0.0605446	−	0.0672416i
$463$	1.51803	+	4.67202i	0.0705489	+	0.217127i	0.980114	−	0.198434i	$-0.0635854\pi$
$463$	1.51803	+	4.67202i	0.0705489	+	0.217127i	−0.909565	+	0.415561i	$0.863585\pi$
$464$	17.8152			0.827048
$465$		0			0
$466$	27.5416			1.27584
$467$	−0.794318	−	2.44466i	−0.0367567	−	0.113125i	0.930995	−	0.365033i	$-0.118942\pi$
$467$	−0.794318	−	2.44466i	−0.0367567	−	0.113125i	−0.967751	+	0.251907i	$0.918942\pi$
$468$	3.05619	+	3.39424i	0.141272	+	0.156899i
$469$	6.77977	−	4.92579i	0.313060	−	0.227452i
$470$	−12.5246	−	21.6932i	−0.577715	−	1.00063i
$471$	−0.386555	+	0.669533i	−0.0178115	+	0.0308504i
$472$	−0.433453	−	4.12403i	−0.0199513	−	0.189824i
$473$	13.1355	+	9.54351i	0.603972	+	0.438811i
$474$	0.306224	−	2.91353i	0.0140653	−	0.133823i
$475$	−3.37885	+	3.75260i	−0.155032	+	0.172181i
$476$	−6.81444	−	3.03398i	−0.312339	−	0.139062i
$477$	−2.63407	−	0.559889i	−0.120606	−	0.0256356i
$478$	8.03693	−	1.70830i	0.367601	−	0.0781359i
$479$	1.87571	−	0.835122i	0.0857036	−	0.0381577i	−0.363437	−	0.931619i	$-0.618397\pi$
$479$	1.87571	−	0.835122i	0.0857036	−	0.0381577i	0.449141	+	0.893461i	$0.351730\pi$
$480$	−0.901691	+	2.77512i	−0.0411564	+	0.126666i
$481$	2.04073	−	6.28073i	0.0930494	−	0.286377i
$482$	13.2081	−	5.88062i	0.601612	−	0.267855i
$483$	1.17605	−	0.249977i	0.0535120	−	0.0113743i
$484$	−21.7947	−	4.63261i	−0.990670	−	0.210573i
$485$	−19.4716	−	8.66930i	−0.884159	−	0.393653i
$486$	−6.11882	+	6.79564i	−0.277555	+	0.308256i
$487$	1.85134	−	17.6143i	0.0838922	−	0.798181i	−0.868988	−	0.494834i	$-0.835229\pi$
$487$	1.85134	−	17.6143i	0.0838922	−	0.798181i	0.952880	−	0.303348i	$-0.0981044\pi$
$488$	9.98585	+	7.25514i	0.452038	+	0.328425i
$489$	0.0216441	+	0.205930i	0.000978782	+	0.00931249i
$490$	13.1000	−	22.6899i	0.591797	−	1.02502i
$491$	−11.2360	−	19.4613i	−0.507072	−	0.878275i	−0.999966	−	0.00818549i	$-0.997394\pi$
$491$	−11.2360	−	19.4613i	−0.507072	−	0.878275i	0.492894	−	0.870089i	$-0.335939\pi$
$492$	−2.03910	+	1.48149i	−0.0919296	+	0.0667907i
$493$	−13.6979	−	15.2131i	−0.616922	−	0.685161i
$494$	−3.20376	−	9.86016i	−0.144144	−	0.443629i
$495$	−39.2470			−1.76402
$496$		0			0
$497$	−6.38508			−0.286410
$498$	1.40773	+	4.33256i	0.0630821	+	0.194147i
$499$	−13.3828	−	14.8631i	−0.599097	−	0.665365i	0.364971	−	0.931019i	$-0.381079\pi$
$499$	−13.3828	−	14.8631i	−0.599097	−	0.665365i	−0.964068	+	0.265654i	$0.914412\pi$
$500$	−9.76593	+	7.09536i	−0.436746	+	0.317314i
$501$	1.06464	+	1.84402i	0.0475648	+	0.0823847i
$502$	−10.6390	+	18.4273i	−0.474842	+	0.822451i
$503$	−1.30982	−	12.4621i	−0.0584019	−	0.555657i	−0.984128	−	0.177462i	$-0.943211\pi$
$503$	−1.30982	−	12.4621i	−0.0584019	−	0.555657i	0.925726	−	0.378195i	$-0.123455\pi$
$504$	−3.41270	−	2.47947i	−0.152014	−	0.110445i
$505$	2.56292	−	24.3846i	0.114049	−	1.08510i
$506$	38.7563	−	43.0433i	1.72293	−	1.91351i
$507$	−2.00253	−	0.891583i	−0.0889354	−	0.0395966i
$508$	−24.8512	−	5.28228i	−1.10259	−	0.234363i
$509$	25.8296	−	5.49025i	1.14488	−	0.243351i	0.403848	−	0.914826i	$-0.367672\pi$
$509$	25.8296	−	5.49025i	1.14488	−	0.243351i	0.741027	+	0.671475i	$0.234339\pi$
$510$	4.40086	−	1.95939i	0.194873	−	0.0867632i
$511$	−1.23192	+	3.79144i	−0.0544967	+	0.167724i
$512$	−5.32449	+	16.3871i	−0.235311	+	0.724214i
$513$	4.85111	−	2.15986i	0.214182	−	0.0953599i
$514$	0.187276	−	0.0398068i	0.00826041	−	0.00175580i
$515$	−21.7317	−	4.61921i	−0.957611	−	0.203547i
$516$	0.659142	+	0.293469i	0.0290171	+	0.0129193i
$517$	−20.2431	+	22.4822i	−0.890291	+	0.988768i
$518$	1.06146	−	10.0992i	0.0466381	−	0.443732i
$519$	1.18007	+	0.857368i	0.0517991	+	0.0376343i
$520$	−0.430195	−	4.09303i	−0.0188653	−	0.179491i
$521$	12.1247	−	21.0006i	0.531193	−	0.920053i	−0.468144	−	0.883652i	$-0.655077\pi$
$521$	12.1247	−	21.0006i	0.531193	−	0.920053i	0.999337	−	0.0364011i	$-0.0115894\pi$
$522$	9.63717	+	16.6921i	0.421808	+	0.730592i
$523$	−29.0062	+	21.0742i	−1.26835	+	0.921512i	−0.999136	−	0.0415670i	$-0.986765\pi$
$523$	−29.0062	+	21.0742i	−1.26835	+	0.921512i	−0.269217	+	0.963079i	$0.586765\pi$
$524$	4.54778	+	5.05083i	0.198671	+	0.220646i
$525$	−0.0672403	−	0.206944i	−0.00293461	−	0.00903179i
$526$	−42.8327			−1.86759
$527$		0			0
$528$	5.06323			0.220349
$529$	3.95754	+	12.1801i	0.172067	+	0.529568i
$530$	−2.70328	−	3.00230i	−0.117423	−	0.130411i
$531$	7.34887	−	5.33927i	0.318914	−	0.231705i
$532$	−3.06504	−	5.30881i	−0.132887	−	0.230166i
$533$	6.51434	−	11.2832i	0.282168	−	0.488729i
$534$	−0.0317350	−	0.301939i	−0.00137331	−	0.0130662i
$535$	0.588330	+	0.427447i	0.0254357	+	0.0184801i
$536$	−1.12633	+	10.7163i	−0.0486502	+	0.462876i
$537$	−1.70354	+	1.89197i	−0.0735131	+	0.0816445i
$538$	−4.24409	−	1.88959i	−0.182976	−	0.0814661i
$539$	−30.9513	−	6.57890i	−1.33317	−	0.283373i
$540$	−3.43293	+	0.729691i	−0.147730	+	0.0314009i
$541$	13.7372	−	6.11619i	0.590608	−	0.262955i	−0.0895966	−	0.995978i	$-0.528558\pi$
$541$	13.7372	−	6.11619i	0.590608	−	0.262955i	0.680204	+	0.733023i	$0.261891\pi$
$542$	16.1990	−	49.8554i	0.695807	−	2.14147i
$543$	1.23795	−	3.81002i	0.0531256	−	0.163504i
$544$	32.1123	−	14.2973i	1.37680	−	0.612992i
$545$	5.27344	−	1.12090i	0.225889	−	0.0480143i
$546$	0.436989	+	0.0928848i	0.0187014	+	0.00397510i
$547$	−36.9975	−	16.4724i	−1.58190	−	0.704307i	−0.587425	−	0.809279i	$-0.699858\pi$
$547$	−36.9975	−	16.4724i	−1.58190	−	0.704307i	−0.994475	+	0.104971i	$0.966525\pi$
$548$	3.67030	−	4.07628i	0.156787	−	0.174130i
$549$	−2.82630	+	26.8904i	−0.120623	+	1.14766i
$550$	−8.48039	−	6.16137i	−0.361605	−	0.262722i
$551$	−1.75851	−	16.7311i	−0.0749150	−	0.712768i
$552$	−0.772976	+	1.33883i	−0.0329000	+	0.0569845i
$553$	4.47698	+	7.75435i	0.190380	+	0.329748i
$554$	17.5465	−	12.7483i	0.745478	−	0.541622i
$555$	1.68737	+	1.87402i	0.0716250	+	0.0795476i
$556$	−2.59673	−	7.99190i	−0.110126	−	0.338932i
$557$	32.3465			1.37057			0.685284	−	0.728276i	$-0.259678\pi$
$557$	32.3465			1.37057			0.685284	+	0.728276i	$0.259678\pi$
$558$		0			0
$559$	−3.72966			−0.157748
$560$	−3.95955	−	12.1863i	−0.167322	−	0.514963i
$561$	−3.89306	−	4.32368i	−0.164365	−	0.182546i
$562$	−45.4101	+	32.9924i	−1.91551	+	1.39170i
$563$	−14.3093	−	24.7844i	−0.603064	−	1.04454i	−0.992354	−	0.123422i	$-0.960613\pi$
$563$	−14.3093	−	24.7844i	−0.603064	−	1.04454i	0.389290	−	0.921115i	$-0.372720\pi$
$564$	−0.672196	+	1.16428i	−0.0283045	+	0.0490249i
$565$	2.73473	+	26.0193i	0.115051	+	1.09464i
$566$	8.36813	+	6.07980i	0.351739	+	0.255553i
$567$	0.953866	−	9.07543i	0.0400586	−	0.381132i
$568$	5.49354	−	6.10120i	0.230504	−	0.256001i
$569$	−34.1208	−	15.1916i	−1.43042	−	0.636863i	−0.462155	−	0.886799i	$-0.652924\pi$
$569$	−34.1208	−	15.1916i	−1.43042	−	0.636863i	−0.968262	+	0.249936i	$0.919590\pi$
$570$	3.87238	+	0.823101i	0.162196	+	0.0344759i
$571$	−9.76259	+	2.07510i	−0.408552	+	0.0868404i	−0.407603	−	0.913159i	$-0.633635\pi$
$571$	−9.76259	+	2.07510i	−0.408552	+	0.0868404i	−0.000948665		1.00000i	$0.500302\pi$
$572$	7.56014	−	3.36599i	0.316105	−	0.140739i
$573$	0.446522	−	1.37425i	0.0186537	−	0.0574103i
$574$	6.19085	−	19.0535i	0.258401	−	0.795277i
$575$	5.92002	−	2.63576i	0.246882	−	0.109919i
$576$	−3.74614	+	0.796267i	−0.156089	+	0.0331778i
$577$	37.5925	+	7.99053i	1.56500	+	0.332650i	0.907251	−	0.420590i	$-0.138177\pi$
$577$	37.5925	+	7.99053i	1.56500	+	0.332650i	0.657746	+	0.753240i	$0.271510\pi$
$578$	−25.0200	−	11.1396i	−1.04069	−	0.463347i
$579$	−1.63912	+	1.82043i	−0.0681195	+	0.0756544i
$580$	−1.16223	+	11.0579i	−0.0482591	+	0.459154i
$581$	−11.2643	−	8.18402i	−0.467324	−	0.339530i
$582$	0.310968	+	2.95867i	0.0128901	+	0.122641i
$583$	−2.43963	+	4.22556i	−0.101039	+	0.175005i
$584$	−2.56297	−	4.43920i	−0.106057	−	0.183695i
$585$	7.29364	−	5.29914i	0.301555	−	0.219092i
$586$	−1.54276	−	1.71341i	−0.0637310	−	0.0707805i
$587$	9.36540	+	28.8237i	0.386551	+	1.18968i	0.935349	+	0.353728i	$0.115086\pi$
$587$	9.36540	+	28.8237i	0.386551	+	1.18968i	−0.548797	+	0.835956i	$0.684914\pi$
$588$	−1.40616			−0.0579890
$589$		0			0
$590$	13.6276			0.561040
$591$	−1.04578	−	3.21858i	−0.0430176	−	0.132395i
$592$	17.6898	+	19.6465i	0.727047	+	0.807467i
$593$	−1.75119	+	1.27231i	−0.0719126	+	0.0522476i	−0.623161	−	0.782094i	$-0.714152\pi$
$593$	−1.75119	+	1.27231i	−0.0719126	+	0.0522476i	0.551248	+	0.834341i	$0.314152\pi$
$594$	5.51165	+	9.54645i	0.226146	+	0.391696i
$595$	−7.36185	+	12.7511i	−0.301806	+	0.522744i
$596$	−0.289554	−	2.75492i	−0.0118606	−	0.112846i
$597$	−0.0362278	−	0.0263211i	−0.00148271	−	0.00107725i
$598$	−1.39074	+	13.2320i	−0.0568717	+	0.541098i
$599$	−17.7151	+	19.6746i	−0.723820	+	0.803883i	−0.986976	−	0.160870i	$-0.948570\pi$
$599$	−17.7151	+	19.6746i	−0.723820	+	0.803883i	0.263156	+	0.964753i	$0.415237\pi$
$600$	0.255595	+	0.113798i	0.0104346	+	0.00464579i
$601$	40.1743	+	8.53931i	1.63874	+	0.348326i	0.932926	−	0.360068i	$-0.117247\pi$
$601$	40.1743	+	8.53931i	1.63874	+	0.348326i	0.705817	+	0.708394i	$0.250580\pi$
$602$	−5.60972	+	1.19238i	−0.228635	+	0.0485979i
$603$	−21.5635	+	9.60068i	−0.878133	+	0.390970i
$604$	−1.83217	+	5.63883i	−0.0745498	+	0.229441i
$605$	−13.5909	+	41.8283i	−0.552547	+	1.70056i
$606$	−3.12638	+	1.39196i	−0.127001	+	0.0565443i
$607$	−38.3633	+	8.15437i	−1.55712	+	0.330976i	−0.904421	−	0.426642i	$-0.859696\pi$
$607$	−38.3633	+	8.15437i	−1.55712	+	0.330976i	−0.652698	+	0.757618i	$0.726363\pi$
$608$	28.2561	+	6.00602i	1.14594	+	0.243576i
$609$	0.662260	+	0.294857i	0.0268361	+	0.0119482i
$610$	−27.1426	+	30.1449i	−1.09897	+	1.22053i
$611$	0.726409	−	6.91132i	0.0293873	−	0.279602i
$612$	16.9977	+	12.3495i	0.687090	+	0.499200i
$613$	2.27184	+	21.6151i	0.0917587	+	0.873026i	0.939485	+	0.342591i	$0.111305\pi$
$613$	2.27184	+	21.6151i	0.0917587	+	0.873026i	−0.847726	+	0.530435i	$0.822029\pi$
$614$	−14.1446	+	24.4991i	−0.570829	+	0.988704i
$615$	2.48752	+	4.30852i	0.100307	+	0.173736i
$616$	−6.18342	+	4.49252i	−0.249137	+	0.181009i
$617$	−9.06416	−	10.0668i	−0.364909	−	0.405273i	0.532530	−	0.846411i	$-0.321241\pi$
$617$	−9.06416	−	10.0668i	−0.364909	−	0.405273i	−0.897439	+	0.441138i	$0.854575\pi$
$618$	0.958257	+	2.94921i	0.0385467	+	0.118635i
$619$	42.3785			1.70334			0.851668	−	0.524082i	$-0.175592\pi$
$619$	42.3785			1.70334			0.851668	+	0.524082i	$0.175592\pi$
$620$		0			0
$621$	−6.81469			−0.273464
$622$	−15.2946	−	47.0719i	−0.613256	−	1.88741i
$623$	0.620905	+	0.689584i	0.0248760	+	0.0276276i
$624$	−0.940947	+	0.683638i	−0.0376680	+	0.0273674i
$625$	14.6210	+	25.3243i	0.584840	+	1.01297i
$626$	11.5443	−	19.9953i	0.461402	−	0.799171i
$627$	−0.499784	−	4.75512i	−0.0199594	−	0.189901i
$628$	−4.09242	−	2.97331i	−0.163305	−	0.118648i
$629$	3.17541	−	30.2120i	0.126612	−	1.20463i
$630$	9.27608	−	10.3021i	0.369568	−	0.410447i
$631$	20.9058	+	9.30788i	0.832248	+	0.370541i	0.778215	−	0.627998i	$-0.216126\pi$
$631$	20.9058	+	9.30788i	0.832248	+	0.370541i	0.0540336	+	0.998539i	$0.482792\pi$
$632$	−11.2615	−	2.39370i	−0.447957	−	0.0952161i
$633$	−3.05886	+	0.650181i	−0.121579	+	0.0258424i
$634$	15.6822	−	6.98216i	0.622819	−	0.277297i
$635$	−15.4968	+	47.6943i	−0.614972	+	1.89269i
$636$	−0.0670032	+	0.206215i	−0.00265685	+	0.00817694i
$637$	6.64026	−	2.95643i	0.263097	−	0.117138i
$638$	34.1597	−	7.26087i	1.35240	−	0.287461i
$639$	17.5915	+	3.73918i	0.695908	+	0.147920i
$640$	22.6686	+	10.0927i	0.896056	+	0.398950i
$641$	15.6932	−	17.4290i	0.619842	−	0.688405i	−0.348705	−	0.937232i	$-0.613379\pi$
$641$	15.6932	−	17.4290i	0.619842	−	0.688405i	0.968548	+	0.248828i	$0.0800453\pi$
$642$	0.0106098	−	0.100946i	0.000418737	−	0.00398401i
$643$	−11.7586	−	8.54309i	−0.463712	−	0.336907i	0.331273	−	0.943535i	$-0.392522\pi$
$643$	−11.7586	−	8.54309i	−0.463712	−	0.336907i	−0.794986	+	0.606628i	$0.792522\pi$
$644$	0.822311	+	7.82376i	0.0324036	+	0.308299i
$645$	0.712092	−	1.23338i	0.0280386	−	0.0485643i
$646$	−23.8457	−	41.3019i	−0.938195	−	1.62500i
$647$	3.99958	−	2.90587i	0.157240	−	0.114241i	−0.506383	−	0.862309i	$-0.669018\pi$
$647$	3.99958	−	2.90587i	0.157240	−	0.114241i	0.663623	+	0.748067i	$0.269018\pi$
$648$	7.85126	+	8.71971i	0.308427	+	0.342542i
$649$	−5.08599	−	15.6531i	−0.199643	−	0.614437i
$650$	2.40790			0.0944456
$651$		0			0
$652$	−1.35484			−0.0530595
$653$	4.89446	+	15.0636i	0.191535	+	0.589484i	1.00000		0.000939296i	$0.000298987\pi$
$653$	4.89446	+	15.0636i	0.191535	+	0.589484i	−0.808465	+	0.588545i	$0.799701\pi$
$654$	−0.503514	−	0.559209i	−0.0196889	−	0.0218668i
$655$	10.8533	−	7.88542i	0.424075	−	0.308109i
$656$	26.0783	+	45.1690i	1.01819	+	1.76355i
$657$	5.61436	−	9.72435i	0.219037	−	0.379383i
$658$	−1.11699	−	10.6274i	−0.0435447	−	0.414300i
$659$	−19.2714	−	14.0015i	−0.750708	−	0.545421i	0.145339	−	0.989382i	$-0.453573\pi$
$659$	−19.2714	−	14.0015i	−0.750708	−	0.545421i	−0.896046	+	0.443961i	$0.853573\pi$
$660$	−0.330317	+	3.14275i	−0.0128576	+	0.122332i
$661$	27.5748	−	30.6250i	1.07254	−	1.19117i	0.0918126	−	0.995776i	$-0.470734\pi$
$661$	27.5748	−	30.6250i	1.07254	−	1.19117i	0.980724	−	0.195397i	$-0.0625994\pi$
$662$	−35.5430	−	15.8248i	−1.38142	−	0.615047i
$663$	1.30727	+	0.277869i	0.0507701	+	0.0107915i
$664$	17.5117	−	3.72222i	0.679585	−	0.144450i
$665$	−11.0539	+	4.92150i	−0.428650	+	0.190847i
$666$	−8.83862	+	27.2025i	−0.342490	+	1.05408i
$667$	−6.67155	+	20.5329i	−0.258323	+	0.795038i
$668$	−12.7276	+	5.66668i	−0.492445	+	0.219251i
$669$	1.83011	−	0.389002i	0.0707562	−	0.0150397i
$670$	−34.6378	−	7.36248i	−1.33817	−	0.284437i
$671$	44.7552	+	19.9263i	1.72776	+	0.769247i
$672$	−0.832927	+	0.925059i	−0.0321309	+	0.0356849i
$673$	−4.20284	+	39.9874i	−0.162008	+	1.54140i	0.547563	+	0.836765i	$0.315556\pi$
$673$	−4.20284	+	39.9874i	−0.162008	+	1.54140i	−0.709570	+	0.704635i	$0.751111\pi$
$674$	−6.63262	−	4.81888i	−0.255479	−	0.185616i
$675$	0.128916	+	1.22655i	0.00496198	+	0.0472101i
$676$	7.17133	−	12.4211i	0.275820	−	0.477735i
$677$	15.8290	+	27.4165i	0.608356	+	1.05370i	0.991511	+	0.130020i	$0.0415040\pi$
$677$	15.8290	+	27.4165i	0.608356	+	1.05370i	−0.383155	+	0.923684i	$0.625163\pi$
$678$	2.95426	−	2.14640i	0.113458	−	0.0824319i
$679$	−6.08419	−	6.75717i	−0.233490	−	0.259317i
$680$	−5.85026	−	18.0052i	−0.224347	−	0.690469i
$681$	−0.275503			−0.0105573
$682$		0			0
$683$	10.8397			0.414771			0.207386	−	0.978259i	$-0.433505\pi$
$683$	10.8397			0.414771			0.207386	+	0.978259i	$0.433505\pi$
$684$	5.33557	+	16.4212i	0.204011	+	0.627880i
$685$	−7.24467	−	8.04602i	−0.276804	−	0.307422i
$686$	19.7833	−	14.3734i	0.755328	−	0.548778i
$687$	2.65998	+	4.60722i	0.101484	+	0.175776i
$688$	7.46532	−	12.9303i	0.284613	−	0.492964i
$689$	−0.117157	−	1.11467i	−0.00446332	−	0.0424657i
$690$	−4.11023	−	2.98626i	−0.156474	−	0.113685i
$691$	2.76749	−	26.3309i	0.105280	−	1.00168i	−0.806566	−	0.591144i	$-0.798676\pi$
$691$	2.76749	−	26.3309i	0.105280	−	1.00168i	0.911846	−	0.410532i	$-0.134657\pi$
$692$	−6.38617	+	7.09256i	−0.242766	+	0.269619i
$693$	−15.2953	−	6.80990i	−0.581019	−	0.258687i
$694$	51.8210	+	11.0149i	1.96710	+	0.418119i
$695$	−16.2243	+	3.44858i	−0.615422	+	0.130812i
$696$	−0.851538	+	0.379129i	−0.0322775	+	0.0143708i
$697$	18.5202	−	56.9992i	0.701502	−	2.15900i
$698$	3.76076	−	11.5744i	0.142347	−	0.438098i
$699$	−2.66544	+	1.18673i	−0.100816	+	0.0448863i
$700$	1.39262	−	0.296010i	0.0526360	−	0.0111881i
$701$	−10.4923	−	2.23020i	−0.396287	−	0.0842334i	0.00545771	−	0.999985i	$-0.498263\pi$
$701$	−10.4923	−	2.23020i	−0.396287	−	0.0842334i	−0.401745	+	0.915752i	$0.631596\pi$
$702$	−2.31324	−	1.02992i	−0.0873078	−	0.0388719i
$703$	16.7049	−	18.5527i	0.630037	−	0.699726i
$704$	−0.725344	+	6.90119i	−0.0273374	+	0.260098i
$705$	2.14684	+	1.55977i	0.0808548	+	0.0587445i
$706$	1.46609	+	13.9489i	0.0551771	+	0.524975i
$707$	5.22988	−	9.05842i	0.196690	−	0.340677i
$708$	−0.365698	−	0.633408i	−0.0137438	−	0.0238049i
$709$	27.1529	−	19.7278i	1.01975	−	0.740892i	0.0535184	−	0.998567i	$-0.482956\pi$
$709$	27.1529	−	19.7278i	1.01975	−	0.740892i	0.966232	+	0.257675i	$0.0829564\pi$
$710$	18.0537	+	20.0506i	0.677542	+	0.752487i
$711$	−7.79343	−	23.9857i	−0.292276	−	0.899534i
$712$	−1.19313			−0.0447146
$713$		0			0
$714$	2.05508			0.0769093
$715$	−5.04776	−	15.5354i	−0.188776	−	0.580992i
$716$	−11.1463	−	12.3793i	−0.416559	−	0.462635i
$717$	−0.704196	+	0.511628i	−0.0262987	+	0.0191071i
$718$	2.33204	+	4.03922i	0.0870311	+	0.150742i
$719$	4.62689	−	8.01401i	0.172554	−	0.298872i	−0.766758	−	0.641936i	$-0.778131\pi$
$719$	4.62689	−	8.01401i	0.172554	−	0.298872i	0.939312	+	0.343064i	$0.111465\pi$
$720$	3.77251	+	35.8930i	0.140593	+	1.33765i
$721$	−7.66773	−	5.57093i	−0.285561	−	0.207472i
$722$	0.516648	−	4.91558i	0.0192276	−	0.182939i
$723$	−1.02488	+	1.13824i	−0.0381155	+	0.0423316i
$724$	23.9460	+	10.6614i	0.889945	+	0.396229i
$725$	3.82186	+	0.812362i	0.141940	+	0.0301704i
$726$	6.00454	−	1.27630i	0.222849	−	0.0473681i
$727$	41.6620	−	18.5491i	1.54516	−	0.687949i	0.555516	−	0.831506i	$-0.312521\pi$
$727$	41.6620	−	18.5491i	1.54516	−	0.687949i	0.989642	+	0.143557i	$0.0458539\pi$
$728$	0.542542	−	1.66977i	0.0201080	−	0.0618859i
$729$	−7.74106	+	23.8245i	−0.286706	+	0.882390i
$730$	15.3892	−	6.85173i	0.569581	−	0.253594i
$731$	−16.7817	+	3.56706i	−0.620694	+	0.131933i
$732$	2.12950	+	0.452639i	0.0787086	+	0.0167300i
$733$	34.6873	+	15.4438i	1.28120	+	0.570429i	0.930581	−	0.366087i	$-0.119303\pi$
$733$	34.6873	+	15.4438i	1.28120	+	0.570429i	0.350624	+	0.936516i	$0.385969\pi$
$734$	42.4918	−	47.1919i	1.56840	−	1.74189i
$735$	−0.290125	+	2.76036i	−0.0107014	+	0.101817i
$736$	−29.9916	−	21.7902i	−1.10551	−	0.803197i
$737$	4.47047	+	42.5337i	0.164672	+	1.56675i
$738$	−28.2143	+	48.8686i	−1.03858	+	1.79888i
$739$	−13.1610	−	22.7955i	−0.484134	−	0.838545i	0.515700	−	0.856769i	$-0.327532\pi$
$739$	−13.1610	−	22.7955i	−0.484134	−	0.838545i	−0.999834	+	0.0182243i	$0.994199\pi$
$740$	−13.3487	+	9.69839i	−0.490708	+	0.356520i
$741$	0.734917	+	0.816209i	0.0269979	+	0.0299842i
$742$	−0.532578	−	1.63911i	−0.0195515	−	0.0601735i
$743$	−53.3973			−1.95896			−0.979479	−	0.201545i	$-0.935404\pi$
$743$	−53.3973			−1.95896			−0.979479	+	0.201545i	$0.935404\pi$
$744$		0			0
$745$	−5.46780			−0.200325
$746$	−3.72382	−	11.4607i	−0.136339	−	0.419607i
$747$	26.2416	+	29.1443i	0.960130	+	1.06633i
$748$	30.7978	−	22.3759i	1.12608	−	0.818143i
$749$	0.155115	+	0.268667i	0.00566778	+	0.00981688i
$750$	1.66285	−	2.88015i	0.0607188	−	0.105168i
$751$	−0.929006	−	8.83890i	−0.0338999	−	0.322536i	−0.998309	−	0.0581230i	$-0.981488\pi$
$751$	−0.929006	−	8.83890i	−0.0338999	−	0.322536i	0.964410	−	0.264413i	$-0.0851782\pi$
$752$	22.5068	+	16.3521i	0.820737	+	0.596300i
$753$	0.235622	−	2.24179i	0.00858654	−	0.0816955i
$754$	−5.36786	+	5.96161i	−0.195486	+	0.217109i
$755$	10.6913	+	4.76007i	0.389096	+	0.173237i
$756$	−1.46449	−	0.311286i	−0.0532628	−	0.0113214i
$757$	−38.2830	+	8.13731i	−1.39142	+	0.295755i	−0.841859	−	0.539698i	$-0.818538\pi$
$757$	−38.2830	+	8.13731i	−1.39142	+	0.295755i	−0.549561	+	0.835453i	$0.685205\pi$
$758$	−28.9488	+	12.8888i	−1.05147	+	0.468143i
$759$	−1.89611	+	5.83564i	−0.0688246	+	0.211820i
$760$	4.80775	−	14.7967i	0.174395	−	0.536734i
$761$	15.3052	−	6.81432i	0.554813	−	0.247019i	−0.110124	−	0.993918i	$-0.535125\pi$
$761$	15.3052	−	6.81432i	0.554813	−	0.247019i	0.664937	+	0.746899i	$0.268458\pi$
$762$	6.84661	−	1.45529i	0.248026	−	0.0527196i
$763$	2.24965	+	0.478178i	0.0814428	+	0.0173112i
$764$	8.63717	+	3.84552i	0.312482	+	0.139126i
$765$	27.7498	−	30.8192i	1.00330	−	1.11427i
$766$	6.13853	−	58.4042i	0.221794	−	2.11023i
$767$	3.05866	+	2.22225i	0.110442	+	0.0802406i
$768$	−0.413620	−	3.93533i	−0.0149252	−	0.142004i
$769$	−8.61075	+	14.9142i	−0.310511	+	0.537822i	−0.978473	−	0.206374i	$-0.933834\pi$
$769$	−8.61075	+	14.9142i	−0.310511	+	0.537822i	0.667962	+	0.744196i	$0.267167\pi$
$770$	−12.5590	−	21.7528i	−0.452594	−	0.783915i
$771$	−0.0164092	+	0.0119220i	−0.000590962	+	0.000429359i
$772$	−10.7249	−	11.9112i	−0.385996	−	0.428692i
$773$	9.11444	+	28.0514i	0.327824	+	1.00894i	0.970150	+	0.242506i	$0.0779694\pi$
$773$	9.11444	+	28.0514i	0.327824	+	1.00894i	−0.642326	+	0.766431i	$0.722031\pi$
$774$	16.1536			0.580628
$775$		0			0
$776$	11.6914			0.419697
$777$	0.332432	+	1.02312i	0.0119259	+	0.0367043i
$778$	−10.1176	−	11.2368i	−0.362734	−	0.402857i
$779$	39.8462	−	28.9500i	1.42764	−	1.03724i
$780$	−0.362950	−	0.628647i	−0.0129957	−	0.0225092i
$781$	16.2929	−	28.2201i	0.583005	−	1.00979i
$782$	6.39747	+	60.8679i	0.228773	+	2.17663i
$783$	−3.32416	−	2.41514i	−0.118796	−	0.0863101i
$784$	−3.04157	+	28.9386i	−0.108628	+	1.03352i
$785$	−6.68113	+	7.42015i	−0.238460	+	0.264837i
$786$	−1.71059	−	0.761606i	−0.0610149	−	0.0271656i
$787$	14.7749	+	3.14051i	0.526670	+	0.111947i	0.463570	−	0.886060i	$-0.346568\pi$
$787$	14.7749	+	3.14051i	0.526670	+	0.111947i	0.0630995	+	0.998007i	$0.479901\pi$
$788$	21.6592	−	4.60381i	0.771579	−	0.164004i
$789$	4.14529	−	1.84560i	0.147576	−	0.0657052i
$790$	11.6919	−	35.9840i	0.415979	−	1.28025i
$791$	−3.44892	+	10.6147i	−0.122630	+	0.377415i
$792$	19.6668	−	8.75620i	0.698828	−	0.311138i
$793$	−11.0077	+	2.33977i	−0.390896	+	0.0830876i
$794$	46.2854	+	9.83826i	1.64261	+	0.349147i
$795$	0.390985	+	0.174078i	0.0138668	+	0.00617390i
$796$	0.196054	−	0.217740i	0.00694896	−	0.00771760i
$797$	−4.31272	+	41.0328i	−0.152764	+	1.45346i	0.602543	+	0.798086i	$0.294154\pi$
$797$	−4.31272	+	41.0328i	−0.152764	+	1.45346i	−0.755308	+	0.655371i	$0.772512\pi$
$798$	1.36632	+	0.992690i	0.0483672	+	0.0351408i
$799$	−3.34151	−	31.7924i	−0.118214	−	1.12473i
$800$	−3.35458	+	5.81031i	−0.118602	+	0.205426i
$801$	−1.30682	−	2.26348i	−0.0461742	−	0.0799760i
$802$	3.92045	−	2.84837i	0.138436	−	0.100579i
$803$	−13.6135	−	15.1194i	−0.480411	−	0.533551i
$804$	0.587301	+	1.80753i	0.0207125	+	0.0637465i
$805$	15.5281			0.547294
$806$		0			0
$807$	0.492158			0.0173248
$808$	4.15604	+	12.7910i	0.146209	+	0.449985i
$809$	−13.0141	−	14.4536i	−0.457550	−	0.508161i	0.469585	−	0.882887i	$-0.344403\pi$
$809$	−13.0141	−	14.4536i	−0.457550	−	0.508161i	−0.927136	+	0.374726i	$0.877737\pi$
$810$	−31.1960	+	22.6652i	−1.09612	+	0.796375i
$811$	−8.01689	−	13.8857i	−0.281511	−	0.487591i	0.690246	−	0.723575i	$-0.257502\pi$
$811$	−8.01689	−	13.8857i	−0.281511	−	0.487591i	−0.971757	+	0.235983i	$0.924169\pi$
$812$	−2.37164	+	4.10781i	−0.0832283	+	0.144156i
$813$	0.580485	+	5.52294i	0.0203585	+	0.193698i
$814$	41.9266	+	30.4615i	1.46953	+	1.06767i
$815$	−0.279537	+	2.65961i	−0.00979174	+	0.0931622i
$816$	−3.57998	+	3.97597i	−0.125324	+	0.139187i
$817$	−12.8804	−	5.73472i	−0.450628	−	0.200632i
$818$	5.45816	+	1.16017i	0.190840	+	0.0405643i
$819$	3.76194	−	0.799625i	0.131453	−	0.0279412i
$820$	−29.7378	+	13.2401i	−1.03849	+	0.462365i
$821$	6.34275	−	19.5210i	0.221364	−	0.681287i	−0.777277	−	0.629159i	$-0.783400\pi$
$821$	6.34275	−	19.5210i	0.221364	−	0.681287i	0.998640	−	0.0521282i	$-0.0166004\pi$
$822$	−0.466983	+	1.43722i	−0.0162879	+	0.0501290i
$823$	−24.3481	+	10.8405i	−0.848720	+	0.377875i	−0.784551	−	0.620064i	$-0.787106\pi$
$823$	−24.3481	+	10.8405i	−0.848720	+	0.377875i	−0.0641693	+	0.997939i	$0.520440\pi$
$824$	11.9204	−	2.53375i	0.415265	−	0.0882673i
$825$	1.08621	+	0.230881i	0.0378169	+	0.00803823i
$826$	5.31093	+	2.36458i	0.184791	+	0.0822742i
$827$	−17.1362	+	19.0317i	−0.595886	+	0.661798i	−0.963353	−	0.268239i	$-0.913558\pi$
$827$	−17.1362	+	19.0317i	−0.595886	+	0.661798i	0.367467	+	0.930037i	$0.380225\pi$
$828$	2.31615	−	22.0367i	0.0804919	−	0.765829i
$829$	−28.5293	−	20.7277i	−0.990863	−	0.719904i	−0.0307533	−	0.999527i	$-0.509791\pi$
$829$	−28.5293	−	20.7277i	−0.990863	−	0.719904i	−0.960110	+	0.279623i	$0.909791\pi$
$830$	6.14994	+	58.5128i	0.213468	+	2.03101i
$831$	−1.14882	+	1.98982i	−0.0398522	+	0.0690260i
$832$	−0.797003	−	1.38045i	−0.0276311	−	0.0478585i
$833$	27.0504	−	19.6533i	0.937242	−	0.680946i
$834$	1.54911	+	1.72046i	0.0536414	+	0.0595748i
$835$	8.49797	+	26.1541i	0.294084	+	0.905099i
$836$	31.2844			1.08199
$837$		0			0
$838$	−58.9095			−2.03499
$839$	6.60260	+	20.3207i	0.227947	+	0.701549i	0.997979	+	0.0635436i	$0.0202402\pi$
$839$	6.60260	+	20.3207i	0.227947	+	0.701549i	−0.770032	+	0.638005i	$0.779760\pi$
$840$	0.448599	+	0.498220i	0.0154782	+	0.0171902i
$841$	12.9302	−	9.39437i	0.445870	−	0.323944i
$842$	12.2889	+	21.2850i	0.423504	+	0.733530i
$843$	2.97314	−	5.14963i	0.102400	−	0.177363i
$844$	−2.13880	−	20.3494i	−0.0736206	−	0.700454i
$845$	−22.9036	−	16.6405i	−0.787909	−	0.572449i
$846$	−3.14615	+	29.9336i	−0.108167	+	1.02914i
$847$	−12.5544	+	13.9431i	−0.431374	+	0.479090i
$848$	4.09895	+	1.82497i	0.140758	+	0.0626697i
$849$	−1.07183	−	0.227824i	−0.0367851	−	0.00781890i
$850$	10.8344	−	2.30292i	0.371617	−	0.0789896i
$851$	−29.2683	+	13.0311i	−1.00330	+	0.446700i
$852$	0.447476	−	1.37719i	0.0153303	−	0.0471817i
$853$	5.52630	−	17.0082i	0.189217	−	0.582349i	−0.810779	−	0.585353i	$-0.800956\pi$
$853$	5.52630	−	17.0082i	0.189217	−	0.582349i	0.999995	+	0.00300347i	$0.000956035\pi$
$854$	−15.8085	+	7.03841i	−0.540956	+	0.240849i
$855$	33.3365	−	7.08589i	1.14008	−	0.242332i
$856$	−0.390179	−	0.0829351i	−0.0133360	−	0.00283466i
$857$	−18.7380	−	8.34268i	−0.640077	−	0.284981i	0.0609225	−	0.998143i	$-0.480596\pi$
$857$	−18.7380	−	8.34268i	−0.640077	−	0.284981i	−0.700999	+	0.713162i	$0.747262\pi$
$858$	−1.52559	+	1.69434i	−0.0520829	+	0.0578439i
$859$	2.91636	−	27.7474i	0.0995051	−	0.946728i	−0.824891	−	0.565293i	$-0.808763\pi$
$859$	2.91636	−	27.7474i	0.0995051	−	0.946728i	0.924396	−	0.381435i	$-0.124570\pi$
$860$	7.53885	+	5.47729i	0.257073	+	0.186774i
$861$	0.221847	+	2.11073i	0.00756051	+	0.0719334i
$862$	25.0807	−	43.4410i	0.854252	−	1.47961i
$863$	18.0809	+	31.3170i	0.615480	+	1.06604i	0.990300	+	0.138945i	$0.0443710\pi$
$863$	18.0809	+	31.3170i	0.615480	+	1.06604i	−0.374820	+	0.927097i	$0.622296\pi$
$864$	5.70794	−	4.14706i	0.194188	−	0.141086i
$865$	12.6054	+	13.9997i	0.428597	+	0.476006i
$866$	−1.18571	−	3.64924i	−0.0402921	−	0.124006i
$867$	2.90140			0.0985366
$868$		0			0
$869$	−45.6958			−1.55012
$870$	−0.946605	−	2.91335i	−0.0320929	−	0.0987719i
$871$	−6.57370	−	7.30083i	−0.222741	−	0.247379i
$872$	−2.39245	+	1.73822i	−0.0810187	+	0.0588635i
$873$	12.8054	+	22.1796i	0.433397	+	0.750666i
$874$	−25.1484	+	43.5584i	−0.850658	+	1.47338i
$875$	1.06250	+	10.1090i	0.0359190	+	0.341747i
$876$	−0.731438	−	0.531420i	−0.0247130	−	0.0179550i
$877$	1.92306	−	18.2967i	0.0649371	−	0.617835i	−0.912859	−	0.408275i	$-0.866130\pi$
$877$	1.92306	−	18.2967i	0.0649371	−	0.617835i	0.977796	−	0.209560i	$-0.0672030\pi$
$878$	−11.3381	+	12.5922i	−0.382641	+	0.424966i
$879$	0.223136	+	0.0993464i	0.00752618	+	0.00335087i
$880$	63.9631	+	13.5958i	2.15620	+	0.458314i
$881$	−32.5643	+	6.92175i	−1.09712	+	0.233200i	−0.720698	−	0.693250i	$-0.756178\pi$
$881$	−32.5643	+	6.92175i	−1.09712	+	0.233200i	−0.376420	+	0.926449i	$0.622845\pi$
$882$	−28.7596	+	12.8046i	−0.968388	+	0.431154i
$883$	1.62460	−	5.00001i	0.0546722	−	0.168264i	−0.919992	−	0.391937i	$-0.871805\pi$
$883$	1.62460	−	5.00001i	0.0546722	−	0.168264i	0.974664	+	0.223674i	$0.0718050\pi$
$884$	−2.70224	+	8.31664i	−0.0908862	+	0.279719i
$885$	−1.31886	+	0.587196i	−0.0443331	+	0.0197384i
$886$	55.3804	−	11.7715i	1.86054	−	0.395470i
$887$	−35.4363	−	7.53222i	−1.18983	−	0.252907i	−0.429882	−	0.902885i	$-0.641445\pi$
$887$	−35.4363	−	7.53222i	−1.18983	−	0.252907i	−0.759953	+	0.649978i	$0.774778\pi$
$888$	−1.26365	−	0.562613i	−0.0424053	−	0.0188801i
$889$	−14.3150	+	15.8984i	−0.480110	+	0.533216i
$890$	0.409861	−	3.89957i	0.0137386	−	0.130714i
$891$	37.6766	+	27.3737i	1.26222	+	0.917053i
$892$	1.27964	+	12.1750i	0.0428456	+	0.407649i
$893$	13.1355	−	22.7513i	0.439561	−	0.761343i
$894$	0.381587	+	0.660928i	0.0127622	+	0.0221047i
$895$	−26.6009	+	19.3267i	−0.889170	+	0.646020i
$896$	7.08315	+	7.86663i	0.236631	+	0.262806i
$897$	−0.435557	−	1.34051i	−0.0145428	−	0.0447582i
$898$	43.4706			1.45063
$899$		0			0
$900$	−4.01014			−0.133671
$901$	−1.59323	−	4.90345i	−0.0530781	−	0.163358i
$902$	68.4133	+	75.9806i	2.27791	+	2.52988i
$903$	0.491524	−	0.357113i	0.0163569	−	0.0118840i
$904$	−7.17541	−	12.4282i	−0.238651	−	0.413355i
$905$	25.8696	−	44.8074i	0.859934	−	1.48945i
$906$	−0.170744	−	1.62452i	−0.00567259	−	0.0539710i
$907$	14.1026	+	10.2462i	0.468270	+	0.340218i	0.796767	−	0.604287i	$-0.206542\pi$
$907$	14.1026	+	10.2462i	0.468270	+	0.340218i	−0.328496	+	0.944505i	$0.606542\pi$
$908$	0.188426	−	1.79276i	0.00625314	−	0.0594947i
$909$	−19.7135	+	21.8941i	−0.653857	+	0.726181i
$910$	5.27101	+	2.34681i	0.174732	+	0.0777959i
$911$	−17.9829	−	3.82237i	−0.595799	−	0.126641i	−0.0998645	−	0.995001i	$-0.531841\pi$
$911$	−17.9829	−	3.82237i	−0.595799	−	0.126641i	−0.495934	+	0.868360i	$0.665174\pi$
$912$	−4.30072	+	0.914146i	−0.142411	+	0.0302704i
$913$	64.9142	−	28.9017i	2.14835	−	0.956506i
$914$	−2.06448	+	6.35383i	−0.0682870	+	0.210166i
$915$	1.32792	−	4.08692i	0.0438998	−	0.135110i
$916$	−31.7994	+	14.1580i	−1.05068	+	0.467794i
$917$	5.59798	−	1.18989i	0.184862	−	0.0392935i
$918$	−11.3935	−	2.42177i	−0.376042	−	0.0799302i
$919$	35.4800	+	15.7967i	1.17038	+	0.521085i	0.897522	−	0.440970i	$-0.145366\pi$
$919$	35.4800	+	15.7967i	1.17038	+	0.521085i	0.272854	+	0.962055i	$0.412032\pi$
$920$	−13.3599	+	14.8377i	−0.440464	+	0.489185i
$921$	0.313260	−	2.98047i	0.0103223	−	0.0982097i
$922$	24.8979	+	18.0894i	0.819969	+	0.595742i
$923$	0.782425	+	7.44427i	0.0257538	+	0.245031i
$924$	−0.674042	+	1.16747i	−0.0221743	+	0.0384071i
$925$	2.89910	+	5.02139i	0.0953219	+	0.165102i
$926$	7.16415	−	5.20506i	0.235429	−	0.171049i
$927$	17.8629	+	19.8387i	0.586694	+	0.651590i
$928$	−6.90721	−	21.2582i	−0.226740	−	0.697835i
$929$	−45.3781			−1.48881			−0.744404	−	0.667729i	$-0.767266\pi$
$929$	−45.3781			−1.48881			−0.744404	+	0.667729i	$0.767266\pi$
$930$		0			0
$931$	27.4779			0.900552
$932$	−5.89933	−	18.1563i	−0.193239	−	0.594728i
$933$	3.50846	+	3.89653i	0.114862	+	0.127567i
$934$	−3.74868	+	2.72358i	−0.122661	+	0.0891182i
$935$	−37.5706	−	65.0743i	−1.22869	−	2.12816i
$936$	−2.47259	+	4.28266i	−0.0808192	+	0.139983i
$937$	2.72289	+	25.9066i	0.0889530	+	0.846331i	0.944479	+	0.328571i	$0.106567\pi$
$937$	2.72289	+	25.9066i	0.0889530	+	0.846331i	−0.855526	+	0.517760i	$0.826766\pi$
$938$	−12.2215	−	8.87942i	−0.399045	−	0.289923i
$939$	−0.255671	+	2.43255i	−0.00834350	+	0.0793831i
$940$	−11.6181	+	12.9032i	−0.378940	+	0.420856i
$941$	37.3711	+	16.6387i	1.21826	+	0.542405i	0.912255	−	0.409624i	$-0.134340\pi$
$941$	37.3711	+	16.6387i	1.21826	+	0.542405i	0.306008	+	0.952029i	$0.401007\pi$
$942$	1.36318	+	0.289754i	0.0444149	+	0.00944069i
$943$	−61.8256	+	13.1414i	−2.01332	+	0.427944i
$944$	−13.8265	+	6.15596i	−0.450014	+	0.200359i
$945$	−0.913230	+	2.81063i	−0.0297074	+	0.0914299i
$946$	9.04442	−	27.8359i	0.294060	−	0.905022i
$947$	−35.6777	+	15.8847i	−1.15937	+	0.516184i	−0.894046	−	0.447975i	$-0.852145\pi$
$947$	−35.6777	+	15.8847i	−1.15937	+	0.516184i	−0.265323	+	0.964160i	$0.585479\pi$
$948$	−1.98628	+	0.422197i	−0.0645113	+	0.0137123i
$949$	4.57135	+	0.971671i	0.148392	+	0.0315418i
$950$	8.31568	+	3.70238i	0.269796	+	0.120121i
$951$	−1.21685	+	1.35145i	−0.0394591	+	0.0438238i
$952$	0.844205	−	8.03207i	0.0273608	−	0.260321i
$953$	6.40158	+	4.65102i	0.207368	+	0.150661i	0.686622	−	0.727015i	$-0.259093\pi$
$953$	6.40158	+	4.65102i	0.207368	+	0.150661i	−0.479254	+	0.877676i	$0.659093\pi$
$954$	0.507419	+	4.82777i	0.0164283	+	0.156305i
$955$	9.33101	−	16.1618i	0.301944	−	0.522983i
$956$	−2.84765	−	4.93228i	−0.0920996	−	0.159521i
$957$	−2.99307	+	2.17460i	−0.0967524	+	0.0702947i
$958$	−2.47660	−	2.75055i	−0.0800154	−	0.0888661i
$959$	−1.42728	−	4.39273i	−0.0460894	−	0.141849i
$960$	0.608676			0.0196449
$961$		0			0
$962$	−11.9045			−0.383818
$963$	−0.270021	−	0.831040i	−0.00870131	−	0.0267799i
$964$	−6.70582	−	7.44757i	−0.215980	−	0.239870i
$965$	−25.5950	+	18.5959i	−0.823933	+	0.598623i
$966$	−1.08368	−	1.87698i	−0.0348667	−	0.0603909i
$967$	−5.71906	+	9.90569i	−0.183912	+	0.318546i	−0.943210	−	0.332198i	$-0.892210\pi$
$967$	−5.71906	+	9.90569i	−0.183912	+	0.318546i	0.759297	+	0.650744i	$0.225543\pi$
$968$	−2.52171	−	23.9925i	−0.0810508	−	0.771147i
$969$	4.08740	+	2.96967i	0.131306	+	0.0953996i
$970$	−4.01619	+	38.2115i	−0.128952	+	1.22690i
$971$	−21.3696	+	23.7333i	−0.685782	+	0.761638i	−0.981045	−	0.193778i	$-0.937926\pi$
$971$	−21.3696	+	23.7333i	−0.685782	+	0.761638i	0.295263	+	0.955416i	$0.404593\pi$
$972$	5.79053	+	2.57811i	0.185731	+	0.0826929i
$973$	−6.92128	−	1.47116i	−0.221886	−	0.0471633i
$974$	−31.2295	+	6.63804i	−1.00066	+	0.212696i
$975$	−0.233034	+	0.103753i	−0.00746305	+	0.00332277i
$976$	13.9215	−	42.8459i	0.445615	−	1.37146i
$977$	−3.63699	+	11.1935i	−0.116358	+	0.358112i	−0.992228	−	0.124435i	$-0.960288\pi$
$977$	−3.63699	+	11.1935i	−0.116358	+	0.358112i	0.875870	+	0.482547i	$0.160288\pi$
$978$	0.340993	−	0.151820i	0.0109037	−	0.00485466i
$979$	−4.63212	+	0.984588i	−0.148043	+	0.0314676i
$980$	−17.7638	−	3.77582i	−0.567445	−	0.120614i
$981$	−5.91796	−	2.63485i	−0.188946	−	0.0841242i
$982$	−27.1057	+	30.1039i	−0.864977	+	0.960654i
$983$	5.57810	−	53.0720i	0.177914	−	1.69273i	−0.433284	−	0.901257i	$-0.642645\pi$
$983$	5.57810	−	53.0720i	0.177914	−	1.69273i	0.611198	−	0.791478i	$-0.290688\pi$
$984$	−2.20776	−	1.60403i	−0.0703807	−	0.0511346i
$985$	−4.56868	−	43.4681i	−0.145570	−	1.38501i
$986$	−18.4511	+	31.9582i	−0.587602	+	1.01776i
$987$	0.566023	+	0.980380i	0.0180167	+	0.0312058i
$988$	−5.81388	+	4.22403i	−0.184964	+	0.134384i
$989$	12.1072	+	13.4464i	0.384987	+	0.427571i
$990$	21.8624	+	67.2855i	0.694833	+	2.13847i
$991$	−11.6584			−0.370343			−0.185171	−	0.982706i	$-0.559284\pi$
$991$	−11.6584			−0.370343			−0.185171	+	0.982706i	$0.559284\pi$
$992$		0			0
$993$	4.12168			0.130798
$994$	3.55679	+	10.9467i	0.112814	+	0.347207i
$995$	−0.386985	−	0.429790i	−0.0122682	−	0.0136253i
$996$	2.55462	−	1.85604i	0.0809464	−	0.0588110i
$997$	−13.0744	−	22.6455i	−0.414071	−	0.717191i	0.581260	−	0.813718i	$-0.302560\pi$
$997$	−13.0744	−	22.6455i	−0.414071	−	0.717191i	−0.995330	+	0.0965266i	$0.969227\pi$
$998$	−18.0267	+	31.2231i	−0.570624	+	0.988350i
$999$	−0.637354	−	6.06402i	−0.0201650	−	0.191857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.v.547.4		96
31.2	even	5	inner	961.2.g.v.235.10		96
31.3	odd	30		961.2.c.k.521.4		24
31.4	even	5	inner	961.2.g.v.816.9		96
31.5	even	3		961.2.d.r.531.4		48
31.6	odd	6	inner	961.2.g.v.844.4		96
31.7	even	15	inner	961.2.g.v.732.10		96
31.8	even	5	inner	961.2.g.v.846.3		96
31.9	even	15		961.2.d.r.628.4		48
31.10	even	15		961.2.d.r.388.9		48
31.11	odd	30		961.2.d.r.374.10		48
31.12	odd	30	inner	961.2.g.v.338.10		96
31.13	odd	30		961.2.a.k.1.3	✓	12
31.14	even	15	inner	961.2.g.v.448.4		96
31.15	odd	10		961.2.c.k.439.4		24
31.16	even	5		961.2.c.k.439.3		24
31.17	odd	30	inner	961.2.g.v.448.3		96
31.18	even	15		961.2.a.k.1.4	yes	12
31.19	even	15	inner	961.2.g.v.338.9		96
31.20	even	15		961.2.d.r.374.9		48
31.21	odd	30		961.2.d.r.388.10		48
31.22	odd	30		961.2.d.r.628.3		48
31.23	odd	10	inner	961.2.g.v.846.4		96
31.24	odd	30	inner	961.2.g.v.732.9		96
31.25	even	3	inner	961.2.g.v.844.3		96
31.26	odd	6		961.2.d.r.531.3		48
31.27	odd	10	inner	961.2.g.v.816.10		96
31.28	even	15		961.2.c.k.521.3		24
31.29	odd	10	inner	961.2.g.v.235.9		96
31.30	odd	2	inner	961.2.g.v.547.3		96
93.44	even	30		8649.2.a.bp.1.9		12
93.80	odd	30		8649.2.a.bp.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.3	✓	12	31.13	odd	30
961.2.a.k.1.4	yes	12	31.18	even	15
961.2.c.k.439.3		24	31.16	even	5
961.2.c.k.439.4		24	31.15	odd	10
961.2.c.k.521.3		24	31.28	even	15
961.2.c.k.521.4		24	31.3	odd	30
961.2.d.r.374.9		48	31.20	even	15
961.2.d.r.374.10		48	31.11	odd	30
961.2.d.r.388.9		48	31.10	even	15
961.2.d.r.388.10		48	31.21	odd	30
961.2.d.r.531.3		48	31.26	odd	6
961.2.d.r.531.4		48	31.5	even	3
961.2.d.r.628.3		48	31.22	odd	30
961.2.d.r.628.4		48	31.9	even	15
961.2.g.v.235.9		96	31.29	odd	10	inner
961.2.g.v.235.10		96	31.2	even	5	inner
961.2.g.v.338.9		96	31.19	even	15	inner
961.2.g.v.338.10		96	31.12	odd	30	inner
961.2.g.v.448.3		96	31.17	odd	30	inner
961.2.g.v.448.4		96	31.14	even	15	inner
961.2.g.v.547.3		96	31.30	odd	2	inner
961.2.g.v.547.4		96	1.1	even	1	trivial
961.2.g.v.732.9		96	31.24	odd	30	inner
961.2.g.v.732.10		96	31.7	even	15	inner
961.2.g.v.816.9		96	31.4	even	5	inner
961.2.g.v.816.10		96	31.27	odd	10	inner
961.2.g.v.844.3		96	31.25	even	3	inner
961.2.g.v.844.4		96	31.6	odd	6	inner
961.2.g.v.846.3		96	31.8	even	5	inner
961.2.g.v.846.4		96	31.23	odd	10	inner
8649.2.a.bp.1.9		12	93.44	even	30
8649.2.a.bp.1.10		12	93.80	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.557046 - 1.71441i) q^{2} +(0.127782 + 0.141916i) q^{3} +(-1.01088 + 0.734444i) q^{4} +(1.23318 + 2.13593i) q^{5} +(0.172123 - 0.298125i) q^{6} +(0.109980 + 1.04639i) q^{7} +(-1.09449 - 0.795192i) q^{8} +(0.309773 - 2.94730i) q^{9} +(2.97493 - 3.30400i) q^{10} +(-4.90535 - 2.18400i) q^{11} +(-0.233401 - 0.0496110i) q^{12} +(1.20649 - 0.256448i) q^{13} +(1.73268 - 0.771437i) q^{14} +(-0.145545 + 0.447943i) q^{15} +(-1.52585 + 4.69607i) q^{16} +(5.18337 - 2.30778i) q^{17} +(-5.22544 + 1.11070i) q^{18} +(4.56093 + 0.969455i) q^{19} +(-2.81532 - 1.25346i) q^{20} +(-0.134446 + 0.149317i) q^{21} +(-1.01177 + 9.62638i) q^{22} +(-4.84106 - 3.51724i) q^{23} +(-0.0270052 - 0.256937i) q^{24} +(-0.541477 + 0.937865i) q^{25} +(-1.11173 - 1.92557i) q^{26} +(0.921341 - 0.669393i) q^{27} +(-0.879689 - 0.976993i) q^{28} +(-1.11492 - 3.43137i) q^{29} +0.849035 q^{30} +6.19525 q^{32} +(-0.316870 - 0.975226i) q^{33} +(-6.84387 - 7.60089i) q^{34} +(-2.09939 + 1.52530i) q^{35} +(1.85148 + 3.20686i) q^{36} +(2.67703 - 4.63676i) q^{37} +(-0.878602 - 8.35934i) q^{38} +(0.190562 + 0.138451i) q^{39} +(0.348775 - 3.31837i) q^{40} +(7.06792 - 7.84972i) q^{41} +(0.330884 + 0.147319i) q^{42} +(-2.95770 - 0.628679i) q^{43} +(6.56272 - 1.39495i) q^{44} +(6.67724 - 2.97290i) q^{45} +(-3.33330 + 10.2588i) q^{46} +(1.74104 - 5.35837i) q^{47} +(-0.861426 + 0.383532i) q^{48} +(5.76420 - 1.22522i) q^{49} +(1.90952 + 0.405880i) q^{50} +(0.989854 + 0.440711i) q^{51} +(-1.03127 + 1.14534i) q^{52} +(0.0949835 - 0.903708i) q^{53} +(-1.66085 - 1.20668i) q^{54} +(-1.38430 - 13.1708i) q^{55} +(0.711707 - 1.23271i) q^{56} +(0.445223 + 0.771149i) q^{57} +(-5.26172 + 3.82286i) q^{58} +(2.05099 + 2.27786i) q^{59} +(-0.181861 - 0.559710i) q^{60} -9.12376 q^{61} +3.11808 q^{63} +(-0.399349 - 1.22907i) q^{64} +(2.03558 + 2.26074i) q^{65} +(-1.49543 + 1.08649i) q^{66} +(-3.98244 - 6.89779i) q^{67} +(-3.54480 + 6.13978i) q^{68} +(-0.119447 - 1.13647i) q^{69} +(3.78444 + 2.74956i) q^{70} +(-0.634341 + 6.03535i) q^{71} +(-2.68271 + 2.97945i) q^{72} +(3.46139 + 1.54111i) q^{73} +(-9.44055 - 2.00665i) q^{74} +(-0.202290 + 0.0429980i) q^{75} +(-5.32254 + 2.36975i) q^{76} +(1.74582 - 5.37309i) q^{77} +(0.131211 - 0.403826i) q^{78} +(7.77440 - 3.46139i) q^{79} +(-11.9122 + 2.53201i) q^{80} +(-8.48358 - 1.80324i) q^{81} +(-17.3948 - 7.74468i) q^{82} +(-8.85485 + 9.83430i) q^{83} +(0.0262429 - 0.249684i) q^{84} +(11.3213 + 8.22541i) q^{85} +(0.569762 + 5.42092i) q^{86} +(0.344501 - 0.596693i) q^{87} +(3.63214 + 6.29106i) q^{88} +(0.713499 - 0.518388i) q^{89} +(-8.81631 - 9.79150i) q^{90} +(0.401033 + 1.23425i) q^{91} +7.47693 q^{92} -10.1563 q^{94} +(3.55376 + 10.9374i) q^{95} +(0.791642 + 0.879208i) q^{96} +(-6.99151 + 5.07963i) q^{97} +(-5.31146 - 9.19972i) q^{98} +(-7.95645 + 13.7810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) \) 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

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