LMFDB - Embedded newform 966.2.h.a.827.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.14
Character	$\chi$	$=$	966.827
Dual form			966.2.h.a.827.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.33692 + 1.10121i) q^{3} -1.00000 q^{4} -0.136871 q^{5} +(-1.10121 - 1.33692i) q^{6} -1.00000i q^{7} -1.00000i q^{8} +(0.574695 - 2.94444i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.33692 + 1.10121i) q^{3} -1.00000 q^{4} -0.136871 q^{5} +(-1.10121 - 1.33692i) q^{6} -1.00000i q^{7} -1.00000i q^{8} +(0.574695 - 2.94444i) q^{9} -0.136871i q^{10} +1.44430 q^{11} +(1.33692 - 1.10121i) q^{12} +0.583733 q^{13} +1.00000 q^{14} +(0.182985 - 0.150723i) q^{15} +1.00000 q^{16} +4.60532 q^{17} +(2.94444 + 0.574695i) q^{18} +7.52773i q^{19} +0.136871 q^{20} +(1.10121 + 1.33692i) q^{21} +1.44430i q^{22} +(1.80844 - 4.44180i) q^{23} +(1.10121 + 1.33692i) q^{24} -4.98127 q^{25} +0.583733i q^{26} +(2.47411 + 4.56933i) q^{27} +1.00000i q^{28} +1.43093i q^{29} +(0.150723 + 0.182985i) q^{30} +8.86017 q^{31} +1.00000i q^{32} +(-1.93091 + 1.59047i) q^{33} +4.60532i q^{34} +0.136871i q^{35} +(-0.574695 + 2.94444i) q^{36} +2.06950i q^{37} -7.52773 q^{38} +(-0.780403 + 0.642810i) q^{39} +0.136871i q^{40} +4.66319i q^{41} +(-1.33692 + 1.10121i) q^{42} +11.8820i q^{43} -1.44430 q^{44} +(-0.0786588 + 0.403007i) q^{45} +(4.44180 + 1.80844i) q^{46} -11.3237i q^{47} +(-1.33692 + 1.10121i) q^{48} -1.00000 q^{49} -4.98127i q^{50} +(-6.15693 + 5.07140i) q^{51} -0.583733 q^{52} -7.34859 q^{53} +(-4.56933 + 2.47411i) q^{54} -0.197683 q^{55} -1.00000 q^{56} +(-8.28958 - 10.0640i) q^{57} -1.43093 q^{58} +8.60638i q^{59} +(-0.182985 + 0.150723i) q^{60} -12.4175i q^{61} +8.86017i q^{62} +(-2.94444 - 0.574695i) q^{63} -1.00000 q^{64} -0.0798960 q^{65} +(-1.59047 - 1.93091i) q^{66} +11.2359i q^{67} -4.60532 q^{68} +(2.47359 + 7.92978i) q^{69} -0.136871 q^{70} +3.92611i q^{71} +(-2.94444 - 0.574695i) q^{72} +10.7313 q^{73} -2.06950 q^{74} +(6.65954 - 5.48540i) q^{75} -7.52773i q^{76} -1.44430i q^{77} +(-0.642810 - 0.780403i) q^{78} +4.84919i q^{79} -0.136871 q^{80} +(-8.33945 - 3.38431i) q^{81} -4.66319 q^{82} +16.0249 q^{83} +(-1.10121 - 1.33692i) q^{84} -0.630333 q^{85} -11.8820 q^{86} +(-1.57574 - 1.91303i) q^{87} -1.44430i q^{88} -8.79924 q^{89} +(-0.403007 - 0.0786588i) q^{90} -0.583733i q^{91} +(-1.80844 + 4.44180i) q^{92} +(-11.8453 + 9.75686i) q^{93} +11.3237 q^{94} -1.03033i q^{95} +(-1.10121 - 1.33692i) q^{96} +11.0494i q^{97} -1.00000i q^{98} +(0.830033 - 4.25266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.33692	+	1.10121i	−0.771869	+	0.635781i
$3$	−1.33692	+	1.10121i	−0.771869	+	0.635781i
$4$	−1.00000			−0.500000
$5$	−0.136871			−0.0612104			−0.0306052	−	0.999532i	$-0.509743\pi$
$5$	−0.136871			−0.0612104			−0.0306052	+	0.999532i	$0.509743\pi$
$6$	−1.10121	−	1.33692i	−0.449565	−	0.545794i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	0.574695	−	2.94444i	0.191565	−	0.981480i
$10$		−	0.136871i		−	0.0432823i
$11$	1.44430			0.435474			0.217737	−	0.976008i	$-0.430133\pi$
$11$	1.44430			0.435474			0.217737	+	0.976008i	$0.430133\pi$
$12$	1.33692	−	1.10121i	0.385935	−	0.317891i
$13$	0.583733			0.161899			0.0809493	−	0.996718i	$-0.474205\pi$
$13$	0.583733			0.161899			0.0809493	+	0.996718i	$0.474205\pi$
$14$	1.00000			0.267261
$15$	0.182985	−	0.150723i	0.0472465	−	0.0389164i
$16$	1.00000			0.250000
$17$	4.60532			1.11695			0.558477	−	0.829520i	$-0.311386\pi$
$17$	4.60532			1.11695			0.558477	+	0.829520i	$0.311386\pi$
$18$	2.94444	+	0.574695i	0.694011	+	0.135457i
$19$			7.52773i			1.72698i	0.504366	+	0.863490i	$0.331726\pi$
$19$			7.52773i			1.72698i	−0.504366	+	0.863490i	$0.668274\pi$
$20$	0.136871			0.0306052
$21$	1.10121	+	1.33692i	0.240303	+	0.291739i
$22$			1.44430i			0.307926i
$23$	1.80844	−	4.44180i	0.377086	−	0.926178i
$23$	1.80844	−	4.44180i	0.377086	−	0.926178i
$24$	1.10121	+	1.33692i	0.224783	+	0.272897i
$25$	−4.98127			−0.996253
$26$			0.583733i			0.114480i
$27$	2.47411	+	4.56933i	0.476143	+	0.879368i
$28$			1.00000i			0.188982i
$29$			1.43093i			0.265716i	0.991135	+	0.132858i	$0.0424155\pi$
$29$			1.43093i			0.265716i	−0.991135	+	0.132858i	$0.957585\pi$
$30$	0.150723	+	0.182985i	0.0275181	+	0.0334083i
$31$	8.86017			1.59133			0.795667	−	0.605735i	$-0.207121\pi$
$31$	8.86017			1.59133			0.795667	+	0.605735i	$0.207121\pi$
$32$			1.00000i			0.176777i
$33$	−1.93091	+	1.59047i	−0.336129	+	0.276866i
$34$			4.60532i			0.789806i
$35$			0.136871i			0.0231354i
$36$	−0.574695	+	2.94444i	−0.0957824	+	0.490740i
$37$			2.06950i			0.340223i	0.985425	+	0.170112i	$0.0544128\pi$
$37$			2.06950i			0.340223i	−0.985425	+	0.170112i	$0.945587\pi$
$38$	−7.52773			−1.22116
$39$	−0.780403	+	0.642810i	−0.124965	+	0.102932i
$40$			0.136871i			0.0216412i
$41$			4.66319i			0.728268i	0.931347	+	0.364134i	$0.118635\pi$
$41$			4.66319i			0.728268i	−0.931347	+	0.364134i	$0.881365\pi$
$42$	−1.33692	+	1.10121i	−0.206291	+	0.169920i
$43$			11.8820i			1.81199i	0.423292	+	0.905993i	$0.360874\pi$
$43$			11.8820i			1.81199i	−0.423292	+	0.905993i	$0.639126\pi$
$44$	−1.44430			−0.217737
$45$	−0.0786588	+	0.403007i	−0.0117258	+	0.0600768i
$46$	4.44180	+	1.80844i	0.654907	+	0.266640i
$47$		−	11.3237i		−	1.65173i	−0.563868	−	0.825865i	$-0.690687\pi$
$47$		−	11.3237i		−	1.65173i	0.563868	−	0.825865i	$-0.309313\pi$
$48$	−1.33692	+	1.10121i	−0.192967	+	0.158945i
$49$	−1.00000			−0.142857
$50$		−	4.98127i		−	0.704457i
$51$	−6.15693	+	5.07140i	−0.862143	+	0.710138i
$52$	−0.583733			−0.0809493
$53$	−7.34859			−1.00941			−0.504703	−	0.863293i	$-0.668398\pi$
$53$	−7.34859			−1.00941			−0.504703	+	0.863293i	$0.668398\pi$
$54$	−4.56933	+	2.47411i	−0.621807	+	0.336684i
$55$	−0.197683			−0.0266555
$56$	−1.00000			−0.133631
$57$	−8.28958	−	10.0640i	−1.09798	−	1.33300i
$58$	−1.43093			−0.187890
$59$			8.60638i			1.12046i	0.828339	+	0.560228i	$0.189286\pi$
$59$			8.60638i			1.12046i	−0.828339	+	0.560228i	$0.810714\pi$
$60$	−0.182985	+	0.150723i	−0.0236232	+	0.0194582i
$61$		−	12.4175i		−	1.58990i	−0.606675	−	0.794950i	$-0.707497\pi$
$61$		−	12.4175i		−	1.58990i	0.606675	−	0.794950i	$-0.292503\pi$
$62$			8.86017i			1.12524i
$63$	−2.94444	−	0.574695i	−0.370965	−	0.0724047i
$64$	−1.00000			−0.125000
$65$	−0.0798960			−0.00990988
$66$	−1.59047	−	1.93091i	−0.195774	−	0.237679i
$67$			11.2359i			1.37269i	0.727277	+	0.686344i	$0.240785\pi$
$67$			11.2359i			1.37269i	−0.727277	+	0.686344i	$0.759215\pi$
$68$	−4.60532			−0.558477
$69$	2.47359	+	7.92978i	0.297786	+	0.954633i
$70$	−0.136871			−0.0163592
$71$			3.92611i			0.465944i	0.972483	+	0.232972i	$0.0748450\pi$
$71$			3.92611i			0.465944i	−0.972483	+	0.232972i	$0.925155\pi$
$72$	−2.94444	−	0.574695i	−0.347006	−	0.0677284i
$73$	10.7313			1.25600			0.628002	−	0.778212i	$-0.283873\pi$
$73$	10.7313			1.25600			0.628002	+	0.778212i	$0.283873\pi$
$74$	−2.06950			−0.240574
$75$	6.65954	−	5.48540i	0.768977	−	0.633399i
$76$		−	7.52773i		−	0.863490i
$77$		−	1.44430i		−	0.164594i
$78$	−0.642810	−	0.780403i	−0.0727839	−	0.0883633i
$79$			4.84919i			0.545577i	0.962074	+	0.272788i	$0.0879459\pi$
$79$			4.84919i			0.545577i	−0.962074	+	0.272788i	$0.912054\pi$
$80$	−0.136871			−0.0153026
$81$	−8.33945	−	3.38431i	−0.926606	−	0.376034i
$82$	−4.66319			−0.514963
$83$	16.0249			1.75896			0.879482	−	0.475933i	$-0.157890\pi$
$83$	16.0249			1.75896			0.879482	+	0.475933i	$0.157890\pi$
$84$	−1.10121	−	1.33692i	−0.120151	−	0.145870i
$85$	−0.630333			−0.0683692
$86$	−11.8820			−1.28127
$87$	−1.57574	−	1.91303i	−0.168937	−	0.205098i
$88$		−	1.44430i		−	0.153963i
$89$	−8.79924			−0.932718			−0.466359	−	0.884596i	$-0.654434\pi$
$89$	−8.79924			−0.932718			−0.466359	+	0.884596i	$0.654434\pi$
$90$	−0.403007	−	0.0786588i	−0.0424807	−	0.00829137i
$91$		−	0.583733i		−	0.0611919i
$92$	−1.80844	+	4.44180i	−0.188543	+	0.463089i
$93$	−11.8453	+	9.75686i	−1.22830	+	1.01174i
$94$	11.3237			1.16795
$95$		−	1.03033i		−	0.105709i
$96$	−1.10121	−	1.33692i	−0.112391	−	0.136449i
$97$			11.0494i			1.12190i	0.827851	+	0.560949i	$0.189563\pi$
$97$			11.0494i			1.12190i	−0.827851	+	0.560949i	$0.810437\pi$
$98$		−	1.00000i		−	0.101015i
$99$	0.830033	−	4.25266i	0.0834215	−	0.427409i
$100$	4.98127			0.498127
$101$		−	0.358483i		−	0.0356704i	−0.999841	−	0.0178352i	$-0.994323\pi$
$101$		−	0.358483i		−	0.0356704i	0.999841	−	0.0178352i	$-0.00567743\pi$
$102$	−5.07140	−	6.15693i	−0.502144	−	0.609627i
$103$			6.59411i			0.649737i	0.945759	+	0.324869i	$0.105320\pi$
$103$			6.59411i			0.649737i	−0.945759	+	0.324869i	$0.894680\pi$
$104$		−	0.583733i		−	0.0572398i
$105$	−0.150723	−	0.182985i	−0.0147090	−	0.0178575i
$106$		−	7.34859i		−	0.713758i
$107$	−2.49235			−0.240944			−0.120472	−	0.992717i	$-0.538441\pi$
$107$	−2.49235			−0.240944			−0.120472	+	0.992717i	$0.538441\pi$
$108$	−2.47411	−	4.56933i	−0.238072	−	0.439684i
$109$			4.31321i			0.413130i	0.978433	+	0.206565i	$0.0662286\pi$
$109$			4.31321i			0.413130i	−0.978433	+	0.206565i	$0.933771\pi$
$110$		−	0.197683i		−	0.0188483i
$111$	−2.27894	−	2.76675i	−0.216308	−	0.262608i
$112$		−	1.00000i		−	0.0944911i
$113$	20.5000			1.92847			0.964237	−	0.265041i	$-0.0853856\pi$
$113$	20.5000			1.92847			0.964237	+	0.265041i	$0.0853856\pi$
$114$	10.0640	−	8.28958i	0.942575	−	0.776390i
$115$	−0.247522	+	0.607951i	−0.0230816	+	0.0566918i
$116$		−	1.43093i		−	0.132858i
$117$	0.335468	−	1.71877i	0.0310141	−	0.158900i
$118$	−8.60638			−0.792282
$119$		−	4.60532i		−	0.422169i
$120$	−0.150723	−	0.182985i	−0.0137590	−	0.0167041i
$121$	−8.91399			−0.810363
$122$	12.4175			1.12423
$123$	−5.13513	−	6.23430i	−0.463019	−	0.562128i
$124$	−8.86017			−0.795667
$125$	1.36614			0.122191
$126$	0.574695	−	2.94444i	0.0511979	−	0.262312i
$127$	13.9032			1.23371			0.616855	−	0.787077i	$-0.288407\pi$
$127$	13.9032			1.23371			0.616855	+	0.787077i	$0.288407\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−13.0845	−	15.8852i	−1.15203	−	1.39862i
$130$		−	0.0798960i		−	0.00700734i
$131$		−	9.55139i		−	0.834509i	−0.908790	−	0.417255i	$-0.862992\pi$
$131$		−	9.55139i		−	0.834509i	0.908790	−	0.417255i	$-0.137008\pi$
$132$	1.93091	−	1.59047i	0.168064	−	0.138433i
$133$	7.52773			0.652737
$134$	−11.2359			−0.970637
$135$	−0.338633	−	0.625407i	−0.0291449	−	0.0538265i
$136$		−	4.60532i		−	0.394903i
$137$	13.8847			1.18625			0.593124	−	0.805111i	$-0.297894\pi$
$137$	13.8847			1.18625			0.593124	+	0.805111i	$0.297894\pi$
$138$	−7.92978	+	2.47359i	−0.675027	+	0.210566i
$139$	6.91724			0.586712			0.293356	−	0.956003i	$-0.405228\pi$
$139$	6.91724			0.586712			0.293356	+	0.956003i	$0.405228\pi$
$140$		−	0.136871i		−	0.0115677i
$141$	12.4697	+	15.1388i	1.05014	+	1.27492i
$142$	−3.92611			−0.329472
$143$	0.843088			0.0705026
$144$	0.574695	−	2.94444i	0.0478912	−	0.245370i
$145$		−	0.195852i		−	0.0162646i
$146$			10.7313i			0.888129i
$147$	1.33692	−	1.10121i	0.110267	−	0.0908259i
$148$		−	2.06950i		−	0.170112i
$149$	4.18429			0.342790			0.171395	−	0.985202i	$-0.445172\pi$
$149$	4.18429			0.342790			0.171395	+	0.985202i	$0.445172\pi$
$150$	5.48540	+	6.65954i	0.447881	+	0.543749i
$151$	−9.01508			−0.733637			−0.366818	−	0.930293i	$-0.619553\pi$
$151$	−9.01508			−0.733637			−0.366818	+	0.930293i	$0.619553\pi$
$152$	7.52773			0.610580
$153$	2.64665	−	13.5601i	0.213969	−	1.09627i
$154$	1.44430			0.116385
$155$	−1.21270			−0.0974062
$156$	0.780403	−	0.642810i	0.0624823	−	0.0514660i
$157$			16.8453i			1.34440i	0.740371	+	0.672199i	$0.234650\pi$
$157$			16.8453i			1.34440i	−0.740371	+	0.672199i	$0.765350\pi$
$158$	−4.84919			−0.385781
$159$	9.82446	−	8.09231i	0.779130	−	0.641762i
$160$		−	0.136871i		−	0.0108206i
$161$	−4.44180	−	1.80844i	−0.350063	−	0.142525i
$162$	3.38431	−	8.33945i	0.265896	−	0.655209i
$163$	−5.55114			−0.434799			−0.217399	−	0.976083i	$-0.569757\pi$
$163$	−5.55114			−0.434799			−0.217399	+	0.976083i	$0.569757\pi$
$164$		−	4.66319i		−	0.364134i
$165$	0.264285	−	0.217689i	0.0205746	−	0.0169471i
$166$			16.0249i			1.24377i
$167$			21.1439i			1.63617i	0.575100	+	0.818083i	$0.304963\pi$
$167$			21.1439i			1.63617i	−0.575100	+	0.818083i	$0.695037\pi$
$168$	1.33692	−	1.10121i	0.103145	−	0.0849598i
$169$	−12.6593			−0.973789
$170$		−	0.630333i		−	0.0483443i
$171$	22.1650	+	4.32615i	1.69500	+	0.330829i
$172$		−	11.8820i		−	0.905993i
$173$		−	16.0711i		−	1.22186i	−0.791683	−	0.610932i	$-0.790795\pi$
$173$		−	16.0711i		−	1.22186i	0.791683	−	0.610932i	$-0.209205\pi$
$174$	1.91303	−	1.57574i	0.145026	−	0.119457i
$175$			4.98127i			0.376548i
$176$	1.44430			0.108868
$177$	−9.47739	−	11.5060i	−0.712365	−	0.864846i
$178$		−	8.79924i		−	0.659531i
$179$		−	14.1093i		−	1.05458i	−0.849685	−	0.527291i	$-0.823208\pi$
$179$		−	14.1093i		−	1.05458i	0.849685	−	0.527291i	$-0.176792\pi$
$180$	0.0786588	−	0.403007i	0.00586288	−	0.0300384i
$181$		−	12.0652i		−	0.896796i	−0.893834	−	0.448398i	$-0.851995\pi$
$181$		−	12.0652i		−	0.896796i	0.893834	−	0.448398i	$-0.148005\pi$
$182$	0.583733			0.0432692
$183$	13.6742	+	16.6012i	1.01083	+	1.22719i
$184$	−4.44180	−	1.80844i	−0.327454	−	0.133320i
$185$		−	0.283253i		−	0.0208252i
$186$	−9.75686	−	11.8453i	−0.715408	−	0.868540i
$187$	6.65148			0.486404
$188$			11.3237i			0.825865i
$189$	4.56933	−	2.47411i	0.332370	−	0.179965i
$190$	1.03033			0.0747477
$191$	20.0981			1.45425			0.727125	−	0.686505i	$-0.240856\pi$
$191$	20.0981			1.45425			0.727125	+	0.686505i	$0.240856\pi$
$192$	1.33692	−	1.10121i	0.0964837	−	0.0794726i
$193$	6.21411			0.447301			0.223651	−	0.974669i	$-0.428203\pi$
$193$	6.21411			0.447301			0.223651	+	0.974669i	$0.428203\pi$
$194$	−11.0494			−0.793301
$195$	0.106814	−	0.0879819i	0.00764913	−	0.00630051i
$196$	1.00000			0.0714286
$197$		−	26.3813i		−	1.87959i	−0.341737	−	0.939796i	$-0.611015\pi$
$197$		−	26.3813i		−	1.87959i	0.341737	−	0.939796i	$-0.388985\pi$
$198$	4.25266	+	0.830033i	0.302224	+	0.0589879i
$199$		−	13.3080i		−	0.943376i	−0.881765	−	0.471688i	$-0.843645\pi$
$199$		−	13.3080i		−	0.943376i	0.881765	−	0.471688i	$-0.156355\pi$
$200$			4.98127i			0.352229i
$201$	−12.3731	−	15.0215i	−0.872729	−	1.05954i
$202$	0.358483			0.0252228
$203$	1.43093			0.100431
$204$	6.15693	−	5.07140i	0.431071	−	0.355069i
$205$		−	0.638254i		−	0.0445776i
$206$	−6.59411			−0.459433
$207$	−12.0393	−	7.87752i	−0.836789	−	0.547525i
$208$	0.583733			0.0404746
$209$			10.8723i			0.752054i
$210$	0.182985	−	0.150723i	0.0126271	−	0.0104009i
$211$	−15.4432			−1.06315			−0.531575	−	0.847011i	$-0.678400\pi$
$211$	−15.4432			−1.06315			−0.531575	+	0.847011i	$0.678400\pi$
$212$	7.34859			0.504703
$213$	−4.32346	−	5.24889i	−0.296238	−	0.359648i
$214$		−	2.49235i		−	0.170373i
$215$		−	1.62630i		−	0.110912i
$216$	4.56933	−	2.47411i	0.310903	−	0.168342i
$217$		−	8.86017i		−	0.601467i
$218$	−4.31321			−0.292127
$219$	−14.3469	+	11.8174i	−0.969471	+	0.798544i
$220$	0.197683			0.0133278
$221$	2.68828			0.180833
$222$	2.76675	−	2.27894i	0.185692	−	0.152953i
$223$	23.5613			1.57778			0.788889	−	0.614536i	$-0.210657\pi$
$223$	23.5613			1.57778			0.788889	+	0.614536i	$0.210657\pi$
$224$	1.00000			0.0668153
$225$	−2.86271	+	14.6670i	−0.190847	+	0.977803i
$226$			20.5000i			1.36364i
$227$	3.23814			0.214923			0.107461	−	0.994209i	$-0.465728\pi$
$227$	3.23814			0.214923			0.107461	+	0.994209i	$0.465728\pi$
$228$	8.28958	+	10.0640i	0.548991	+	0.666501i
$229$			17.7542i			1.17323i	0.809866	+	0.586615i	$0.199540\pi$
$229$			17.7542i			1.17323i	−0.809866	+	0.586615i	$0.800460\pi$
$230$	−0.607951	−	0.247522i	−0.0400871	−	0.0163211i
$231$	1.59047	+	1.93091i	0.104645	+	0.127045i
$232$	1.43093			0.0939449
$233$		−	4.04278i		−	0.264851i	−0.991193	−	0.132426i	$-0.957723\pi$
$233$		−	4.04278i		−	0.264851i	0.991193	−	0.132426i	$-0.0422766\pi$
$234$	1.71877	+	0.335468i	0.112359	+	0.0219303i
$235$			1.54988i			0.101103i
$236$		−	8.60638i		−	0.560228i
$237$	−5.33995	−	6.48297i	−0.346867	−	0.421114i
$238$	4.60532			0.298519
$239$			4.23417i			0.273886i	0.990579	+	0.136943i	$0.0437277\pi$
$239$			4.23417i			0.273886i	−0.990579	+	0.136943i	$0.956272\pi$
$240$	0.182985	−	0.150723i	0.0118116	−	0.00972911i
$241$		−	24.7339i		−	1.59325i	−0.604472	−	0.796626i	$-0.706616\pi$
$241$		−	24.7339i		−	1.59325i	0.604472	−	0.796626i	$-0.293384\pi$
$242$		−	8.91399i		−	0.573013i
$243$	14.8760	−	4.65891i	0.954294	−	0.298869i
$244$			12.4175i			0.794950i
$245$	0.136871			0.00874435
$246$	6.23430	−	5.13513i	0.397484	−	0.327404i
$247$			4.39419i			0.279596i
$248$		−	8.86017i		−	0.562621i
$249$	−21.4240	+	17.6467i	−1.35769	+	1.11832i
$250$			1.36614i			0.0864024i
$251$	28.7592			1.81526			0.907632	−	0.419767i	$-0.137888\pi$
$251$	28.7592			1.81526			0.907632	+	0.419767i	$0.137888\pi$
$252$	2.94444	+	0.574695i	0.185482	+	0.0362024i
$253$	2.61193	−	6.41530i	0.164211	−	0.403326i
$254$			13.9032i			0.872364i
$255$	0.842703	−	0.694126i	0.0527721	−	0.0434679i
$256$	1.00000			0.0625000
$257$		−	3.30630i		−	0.206242i	−0.994669	−	0.103121i	$-0.967117\pi$
$257$		−	3.30630i		−	0.206242i	0.994669	−	0.103121i	$-0.0328828\pi$
$258$	15.8852	−	13.0845i	0.988971	−	0.814606i
$259$	2.06950			0.128592
$260$	0.0798960			0.00495494
$261$	4.21328	+	0.822346i	0.260795	+	0.0509019i
$262$	9.55139			0.590087
$263$	0.648912			0.0400136			0.0200068	−	0.999800i	$-0.493631\pi$
$263$	0.648912			0.0400136			0.0200068	+	0.999800i	$0.493631\pi$
$264$	1.59047	+	1.93091i	0.0978869	+	0.118839i
$265$	1.00581			0.0617862
$266$			7.52773i			0.461555i
$267$	11.7639	−	9.68977i	0.719936	−	0.593004i
$268$		−	11.2359i		−	0.686344i
$269$			18.8210i			1.14754i	0.819018	+	0.573768i	$0.194519\pi$
$269$			18.8210i			1.14754i	−0.819018	+	0.573768i	$0.805481\pi$
$270$	0.625407	−	0.338633i	0.0380611	−	0.0206086i
$271$	−18.3134			−1.11246			−0.556231	−	0.831028i	$-0.687753\pi$
$271$	−18.3134			−1.11246			−0.556231	+	0.831028i	$0.687753\pi$
$272$	4.60532			0.279239
$273$	0.642810	+	0.780403i	0.0389046	+	0.0472322i
$274$			13.8847i			0.838804i
$275$	−7.19446			−0.433842
$276$	−2.47359	−	7.92978i	−0.148893	−	0.477316i
$277$	−18.6594			−1.12113			−0.560567	−	0.828109i	$-0.689417\pi$
$277$	−18.6594			−1.12113			−0.560567	+	0.828109i	$0.689417\pi$
$278$			6.91724i			0.414868i
$279$	5.09189	−	26.0882i	0.304844	−	1.56186i
$280$	0.136871			0.00817959
$281$	−20.4331			−1.21894			−0.609468	−	0.792810i	$-0.708617\pi$
$281$	−20.4331			−1.21894			−0.609468	+	0.792810i	$0.708617\pi$
$282$	−15.1388	+	12.4697i	−0.901505	+	0.742560i
$283$			18.6039i			1.10589i	0.833219	+	0.552944i	$0.186496\pi$
$283$			18.6039i			1.10589i	−0.833219	+	0.552944i	$0.813504\pi$
$284$		−	3.92611i		−	0.232972i
$285$	1.13460	+	1.37746i	0.0672079	+	0.0815937i
$286$			0.843088i			0.0498528i
$287$	4.66319			0.275259
$288$	2.94444	+	0.574695i	0.173503	+	0.0338642i
$289$	4.20897			0.247586
$290$	0.195852			0.0115008
$291$	−12.1677	−	14.7721i	−0.713281	−	0.865958i
$292$	−10.7313			−0.628002
$293$	−22.6982			−1.32604			−0.663021	−	0.748601i	$-0.730726\pi$
$293$	−22.6982			−1.32604			−0.663021	+	0.748601i	$0.730726\pi$
$294$	1.10121	+	1.33692i	0.0642236	+	0.0779706i
$295$		−	1.17796i		−	0.0685836i
$296$	2.06950			0.120287
$297$	3.57337	+	6.59949i	0.207348	+	0.382942i
$298$			4.18429i			0.242389i
$299$	1.05565	−	2.59282i	0.0610496	−	0.149947i
$300$	−6.65954	+	5.48540i	−0.384489	+	0.316699i
$301$	11.8820			0.684866
$302$		−	9.01508i		−	0.518759i
$303$	0.394764	+	0.479263i	0.0226786	+	0.0275329i
$304$			7.52773i			0.431745i
$305$			1.69959i			0.0973184i
$306$	13.5601	+	2.64665i	0.775179	+	0.151299i
$307$	6.21291			0.354589			0.177295	−	0.984158i	$-0.443265\pi$
$307$	6.21291			0.354589			0.177295	+	0.984158i	$0.443265\pi$
$308$			1.44430i			0.0822968i
$309$	−7.26147	−	8.81578i	−0.413090	−	0.501512i
$310$		−	1.21270i		−	0.0688766i
$311$			5.35894i			0.303878i	0.988390	+	0.151939i	$0.0485517\pi$
$311$			5.35894i			0.303878i	−0.988390	+	0.151939i	$0.951448\pi$
$312$	0.642810	+	0.780403i	0.0363920	+	0.0441816i
$313$		−	18.3202i		−	1.03552i	−0.855526	−	0.517760i	$-0.826766\pi$
$313$		−	18.3202i		−	1.03552i	0.855526	−	0.517760i	$-0.173234\pi$
$314$	−16.8453			−0.950633
$315$	0.403007	+	0.0786588i	0.0227069	+	0.00443192i
$316$		−	4.84919i		−	0.272788i
$317$		−	2.64552i		−	0.148587i	−0.997236	−	0.0742935i	$-0.976330\pi$
$317$		−	2.64552i		−	0.148587i	0.997236	−	0.0742935i	$-0.0236702\pi$
$318$	8.09231	+	9.82446i	0.453794	+	0.550928i
$319$			2.06669i			0.115712i
$320$	0.136871			0.00765130
$321$	3.33206	−	2.74458i	0.185978	−	0.153188i
$322$	1.80844	−	4.44180i	0.100780	−	0.247532i
$323$			34.6676i			1.92896i
$324$	8.33945	+	3.38431i	0.463303	+	0.188017i
$325$	−2.90773			−0.161292
$326$		−	5.55114i		−	0.307449i
$327$	−4.74973	−	5.76640i	−0.262661	−	0.318883i
$328$	4.66319			0.257482
$329$	−11.3237			−0.624295
$330$	0.217689	+	0.264285i	0.0119834	+	0.0145484i
$331$	7.99157			0.439257			0.219628	−	0.975584i	$-0.429516\pi$
$331$	7.99157			0.439257			0.219628	+	0.975584i	$0.429516\pi$
$332$	−16.0249			−0.879482
$333$	6.09351	+	1.18933i	0.333922	+	0.0651748i
$334$	−21.1439			−1.15694
$335$		−	1.53787i		−	0.0840228i
$336$	1.10121	+	1.33692i	0.0600757	+	0.0729348i
$337$		−	25.1402i		−	1.36947i	−0.728791	−	0.684736i	$-0.759918\pi$
$337$		−	25.1402i		−	1.36947i	0.728791	−	0.684736i	$-0.240082\pi$
$338$		−	12.6593i		−	0.688573i
$339$	−27.4067	+	22.5747i	−1.48853	+	1.22609i
$340$	0.630333			0.0341846
$341$	12.7968			0.692984
$342$	−4.32615	+	22.1650i	−0.233931	+	1.19854i
$343$			1.00000i			0.0539949i
$344$	11.8820			0.640634
$345$	−0.338562	−	1.08535i	−0.0182276	−	0.0584335i
$346$	16.0711			0.863988
$347$		−	28.1621i		−	1.51182i	−0.654676	−	0.755909i	$-0.727195\pi$
$347$		−	28.1621i		−	1.51182i	0.654676	−	0.755909i	$-0.272805\pi$
$348$	1.57574	+	1.91303i	0.0844687	+	0.102549i
$349$	−14.1592			−0.757925			−0.378963	−	0.925412i	$-0.623719\pi$
$349$	−14.1592			−0.757925			−0.378963	+	0.925412i	$0.623719\pi$
$350$	−4.98127			−0.266260
$351$	1.44422	+	2.66727i	0.0770869	+	0.142368i
$352$			1.44430i			0.0769816i
$353$			9.59456i			0.510667i	0.966853	+	0.255333i	$0.0821853\pi$
$353$			9.59456i			0.510667i	−0.966853	+	0.255333i	$0.917815\pi$
$354$	11.5060	−	9.47739i	0.611538	−	0.503718i
$355$		−	0.537370i		−	0.0285206i
$356$	8.79924			0.466359
$357$	5.07140	+	6.15693i	0.268407	+	0.325859i
$358$	14.1093			0.745702
$359$	−29.9075			−1.57846			−0.789228	−	0.614101i	$-0.789519\pi$
$359$	−29.9075			−1.57846			−0.789228	+	0.614101i	$0.789519\pi$
$360$	0.403007	+	0.0786588i	0.0212404	+	0.00414568i
$361$	−37.6667			−1.98246
$362$	12.0652			0.634131
$363$	11.9173	−	9.81613i	0.625494	−	0.515213i
$364$			0.583733i			0.0305959i
$365$	−1.46880			−0.0768805
$366$	−16.6012	+	13.6742i	−0.867758	+	0.714763i
$367$		−	19.4738i		−	1.01652i	−0.861203	−	0.508261i	$-0.830289\pi$
$367$		−	19.4738i		−	1.01652i	0.861203	−	0.508261i	$-0.169711\pi$
$368$	1.80844	−	4.44180i	0.0942714	−	0.231545i
$369$	13.7305	+	2.67991i	0.714780	+	0.139511i
$370$	0.283253			0.0147256
$371$			7.34859i			0.381520i
$372$	11.8453	−	9.75686i	0.614151	−	0.505870i
$373$		−	8.03802i		−	0.416193i	−0.978108	−	0.208097i	$-0.933273\pi$
$373$		−	8.03802i		−	0.416193i	0.978108	−	0.208097i	$-0.0667268\pi$
$374$			6.65148i			0.343940i
$375$	−1.82642	+	1.50440i	−0.0943159	+	0.0776870i
$376$	−11.3237			−0.583975
$377$			0.835279i			0.0430191i
$378$	2.47411	+	4.56933i	0.127255	+	0.235021i
$379$			13.5465i			0.695838i	0.937525	+	0.347919i	$0.113112\pi$
$379$			13.5465i			0.695838i	−0.937525	+	0.347919i	$0.886888\pi$
$380$			1.03033i			0.0528546i
$381$	−18.5874	+	15.3103i	−0.952262	+	0.784369i
$382$			20.0981i			1.02831i
$383$	−2.64368			−0.135086			−0.0675429	−	0.997716i	$-0.521516\pi$
$383$	−2.64368			−0.135086			−0.0675429	+	0.997716i	$0.521516\pi$
$384$	1.10121	+	1.33692i	0.0561956	+	0.0682243i
$385$			0.197683i			0.0100748i
$386$			6.21411i			0.316290i
$387$	34.9858	+	6.82852i	1.77843	+	0.347113i
$388$		−	11.0494i		−	0.560949i
$389$	−2.20235			−0.111664			−0.0558318	−	0.998440i	$-0.517781\pi$
$389$	−2.20235			−0.111664			−0.0558318	+	0.998440i	$0.517781\pi$
$390$	0.0879819	+	0.106814i	0.00445513	+	0.00540875i
$391$	8.32844	−	20.4559i	0.421187	−	1.03450i
$392$			1.00000i			0.0505076i
$393$	10.5180	+	12.7694i	0.530565	+	0.644132i
$394$	26.3813			1.32907
$395$		−	0.663712i		−	0.0333950i
$396$	−0.830033	+	4.25266i	−0.0417107	+	0.213704i
$397$	4.66525			0.234142			0.117071	−	0.993124i	$-0.462649\pi$
$397$	4.66525			0.234142			0.117071	+	0.993124i	$0.462649\pi$
$398$	13.3080			0.667068
$399$	−10.0640	+	8.28958i	−0.503828	+	0.414998i
$400$	−4.98127			−0.249063
$401$	−11.8866			−0.593590			−0.296795	−	0.954941i	$-0.595918\pi$
$401$	−11.8866			−0.593590			−0.296795	+	0.954941i	$0.595918\pi$
$402$	15.0215	−	12.3731i	0.749205	−	0.617112i
$403$	5.17198			0.257635
$404$			0.358483i			0.0178352i
$405$	1.14143	+	0.463212i	0.0567179	+	0.0230172i
$406$			1.43093i			0.0710157i
$407$			2.98898i			0.148158i
$408$	5.07140	+	6.15693i	0.251072	+	0.304813i
$409$	19.6843			0.973324			0.486662	−	0.873590i	$-0.338214\pi$
$409$	19.6843			0.973324			0.486662	+	0.873590i	$0.338214\pi$
$410$	0.638254			0.0315211
$411$	−18.5627	+	15.2899i	−0.915629	+	0.754194i
$412$		−	6.59411i		−	0.324869i
$413$	8.60638			0.423492
$414$	7.87752	−	12.0393i	0.387159	−	0.591699i
$415$	−2.19334			−0.107667
$416$			0.583733i			0.0286199i
$417$	−9.24777	+	7.61730i	−0.452865	+	0.373021i
$418$	−10.8723			−0.531783
$419$	−32.8919			−1.60687			−0.803437	−	0.595390i	$-0.796998\pi$
$419$	−32.8919			−1.60687			−0.803437	+	0.595390i	$0.796998\pi$
$420$	0.150723	+	0.182985i	0.00735451	+	0.00892874i
$421$		−	3.36061i		−	0.163786i	−0.996641	−	0.0818931i	$-0.973903\pi$
$421$		−	3.36061i		−	0.163786i	0.996641	−	0.0818931i	$-0.0260966\pi$
$422$		−	15.4432i		−	0.751761i
$423$	−33.3419	−	6.50767i	−1.62114	−	0.316414i
$424$			7.34859i			0.356879i
$425$	−22.9403			−1.11277
$426$	5.24889	−	4.32346i	0.254309	−	0.209472i
$427$	−12.4175			−0.600926
$428$	2.49235			0.120472
$429$	−1.12714	+	0.928413i	−0.0544188	+	0.0448242i
$430$	1.62630			0.0784269
$431$	−32.0006			−1.54142			−0.770708	−	0.637189i	$-0.780097\pi$
$431$	−32.0006			−1.54142			−0.770708	+	0.637189i	$0.780097\pi$
$432$	2.47411	+	4.56933i	0.119036	+	0.219842i
$433$			32.4391i			1.55892i	0.626449	+	0.779462i	$0.284508\pi$
$433$			32.4391i			1.55892i	−0.626449	+	0.779462i	$0.715492\pi$
$434$	8.86017			0.425302
$435$	0.215673	+	0.261838i	0.0103407	+	0.0125542i
$436$		−	4.31321i		−	0.206565i
$437$	33.4366	+	13.6134i	1.59949	+	0.651219i
$438$	−11.8174	−	14.3469i	−0.564656	−	0.685520i
$439$	−13.2858			−0.634096			−0.317048	−	0.948409i	$-0.602692\pi$
$439$	−13.2858			−0.634096			−0.317048	+	0.948409i	$0.602692\pi$
$440$			0.197683i			0.00942415i
$441$	−0.574695	+	2.94444i	−0.0273664	+	0.140211i
$442$			2.68828i			0.127868i
$443$		−	7.36139i		−	0.349750i	−0.984591	−	0.174875i	$-0.944048\pi$
$443$		−	7.36139i		−	0.349750i	0.984591	−	0.174875i	$-0.0559522\pi$
$444$	2.27894	+	2.76675i	0.108154	+	0.131304i
$445$	1.20436			0.0570920
$446$			23.5613i			1.11566i
$447$	−5.59405	+	4.60776i	−0.264589	+	0.217940i
$448$			1.00000i			0.0472456i
$449$			14.0512i			0.663118i	0.943434	+	0.331559i	$0.107575\pi$
$449$			14.0512i			0.663118i	−0.943434	+	0.331559i	$0.892425\pi$
$450$	−14.6670	−	2.86271i	−0.691411	−	0.134949i
$451$			6.73506i			0.317142i
$452$	−20.5000			−0.964237
$453$	12.0524	−	9.92745i	0.566272	−	0.466432i
$454$			3.23814i			0.151973i
$455$			0.0798960i			0.00374558i
$456$	−10.0640	+	8.28958i	−0.471288	+	0.388195i
$457$		−	26.4623i		−	1.23785i	−0.785448	−	0.618927i	$-0.787567\pi$
$457$		−	26.4623i		−	1.23785i	0.785448	−	0.618927i	$-0.212433\pi$
$458$	−17.7542			−0.829599
$459$	11.3941	+	21.0432i	0.531830	+	0.982213i
$460$	0.247522	−	0.607951i	0.0115408	−	0.0283459i
$461$		−	30.1379i		−	1.40366i	−0.712344	−	0.701830i	$-0.752367\pi$
$461$		−	30.1379i		−	1.40366i	0.712344	−	0.701830i	$-0.247633\pi$
$462$	−1.93091	+	1.59047i	−0.0898342	+	0.0739955i
$463$	−33.7207			−1.56713			−0.783566	−	0.621308i	$-0.786602\pi$
$463$	−33.7207			−1.56713			−0.783566	+	0.621308i	$0.786602\pi$
$464$			1.43093i			0.0664291i
$465$	1.62128	−	1.33543i	0.0751848	−	0.0619290i
$466$	4.04278			0.187278
$467$	5.47544			0.253373			0.126686	−	0.991943i	$-0.459566\pi$
$467$	5.47544			0.253373			0.126686	+	0.991943i	$0.459566\pi$
$468$	−0.335468	+	1.71877i	−0.0155070	+	0.0794501i
$469$	11.2359			0.518827
$470$	−1.54988			−0.0714907
$471$	−18.5501	−	22.5207i	−0.854743	−	1.03770i
$472$	8.60638			0.396141
$473$			17.1612i			0.789072i
$474$	6.48297	−	5.33995i	0.297773	−	0.245272i
$475$		−	37.4976i		−	1.72051i
$476$			4.60532i			0.211084i
$477$	−4.22320	+	21.6375i	−0.193367	+	0.990713i
$478$	−4.23417			−0.193667
$479$	32.7012			1.49416			0.747078	−	0.664736i	$-0.231456\pi$
$479$	32.7012			1.49416			0.747078	+	0.664736i	$0.231456\pi$
$480$	0.150723	+	0.182985i	0.00687952	+	0.00835207i
$481$			1.20804i			0.0550817i
$482$	24.7339			1.12660
$483$	7.92978	−	2.47359i	0.360817	−	0.112552i
$484$	8.91399			0.405181
$485$		−	1.51234i		−	0.0686718i
$486$	4.65891	+	14.8760i	0.211332	+	0.674788i
$487$	22.7090			1.02904			0.514521	−	0.857478i	$-0.327970\pi$
$487$	22.7090			1.02904			0.514521	+	0.857478i	$0.327970\pi$
$488$	−12.4175			−0.562114
$489$	7.42142	−	6.11295i	0.335608	−	0.276437i
$490$			0.136871i			0.00618319i
$491$		−	15.4987i		−	0.699447i	−0.936853	−	0.349723i	$-0.886276\pi$
$491$		−	15.4987i		−	0.699447i	0.936853	−	0.349723i	$-0.113724\pi$
$492$	5.13513	+	6.23430i	0.231509	+	0.281064i
$493$			6.58987i			0.296793i
$494$	−4.39419			−0.197704
$495$	−0.113607	+	0.582065i	−0.00510626	+	0.0261619i
$496$	8.86017			0.397833
$497$	3.92611			0.176110
$498$	−17.6467	−	21.4240i	−0.790768	−	0.960032i
$499$	28.7631			1.28761			0.643806	−	0.765189i	$-0.277355\pi$
$499$	28.7631			1.28761			0.643806	+	0.765189i	$0.277355\pi$
$500$	−1.36614			−0.0610957
$501$	−23.2838	−	28.2677i	−1.04024	−	1.26291i
$502$			28.7592i			1.28359i
$503$	−9.98768			−0.445329			−0.222664	−	0.974895i	$-0.571475\pi$
$503$	−9.98768			−0.445329			−0.222664	+	0.974895i	$0.571475\pi$
$504$	−0.574695	+	2.94444i	−0.0255989	+	0.131156i
$505$			0.0490659i			0.00218340i
$506$	6.41530	+	2.61193i	0.285195	+	0.116115i
$507$	16.9244	−	13.9404i	0.751638	−	0.619117i
$508$	−13.9032			−0.616855
$509$			20.7758i			0.920873i	0.887693	+	0.460436i	$0.152307\pi$
$509$			20.7758i			0.920873i	−0.887693	+	0.460436i	$0.847693\pi$
$510$	0.694126	+	0.842703i	0.0307364	+	0.0373155i
$511$		−	10.7313i		−	0.474725i
$512$			1.00000i			0.0441942i
$513$	−34.3967	+	18.6245i	−1.51865	+	0.822290i
$514$	3.30630			0.145835
$515$		−	0.902540i		−	0.0397707i
$516$	13.0845	+	15.8852i	0.576013	+	0.699308i
$517$		−	16.3548i		−	0.719285i
$518$			2.06950i			0.0909285i
$519$	17.6976	+	21.4857i	0.776838	+	0.943119i
$520$			0.0798960i			0.00350367i
$521$	−9.46889			−0.414840			−0.207420	−	0.978252i	$-0.566507\pi$
$521$	−9.46889			−0.414840			−0.207420	+	0.978252i	$0.566507\pi$
$522$	−0.822346	+	4.21328i	−0.0359931	+	0.184410i
$523$			5.01624i			0.219345i	0.993968	+	0.109672i	$0.0349802\pi$
$523$			5.01624i			0.219345i	−0.993968	+	0.109672i	$0.965020\pi$
$524$			9.55139i			0.417255i
$525$	−5.48540	−	6.65954i	−0.239402	−	0.290646i
$526$			0.648912i			0.0282939i
$527$	40.8039			1.77745
$528$	−1.93091	+	1.59047i	−0.0840322	+	0.0692165i
$529$	−16.4591	−	16.0654i	−0.715613	−	0.698497i
$530$			1.00581i			0.0436895i
$531$	25.3410	+	4.94604i	1.09970	+	0.214640i
$532$	−7.52773			−0.326369
$533$			2.72206i			0.117906i
$534$	9.68977	+	11.7639i	0.419317	+	0.509072i
$535$	0.341129			0.0147483
$536$	11.2359			0.485318
$537$	15.5373	+	18.8630i	0.670483	+	0.814000i
$538$	−18.8210			−0.811431
$539$	−1.44430			−0.0622105
$540$	0.338633	+	0.625407i	0.0145725	+	0.0269132i
$541$	20.9287			0.899796			0.449898	−	0.893080i	$-0.351460\pi$
$541$	20.9287			0.899796			0.449898	+	0.893080i	$0.351460\pi$
$542$		−	18.3134i		−	0.786629i
$543$	13.2862	+	16.1301i	0.570166	+	0.692210i
$544$			4.60532i			0.197451i
$545$		−	0.590352i		−	0.0252879i
$546$	−0.780403	+	0.642810i	−0.0333982	+	0.0275097i
$547$	−25.3979			−1.08594			−0.542968	−	0.839753i	$-0.682700\pi$
$547$	−25.3979			−1.08594			−0.542968	+	0.839753i	$0.682700\pi$
$548$	−13.8847			−0.593124
$549$	−36.5626	−	7.13628i	−1.56045	−	0.304569i
$550$		−	7.19446i		−	0.306773i
$551$	−10.7716			−0.458887
$552$	7.92978	−	2.47359i	0.337514	−	0.105283i
$553$	4.84919			0.206209
$554$		−	18.6594i		−	0.792761i
$555$	0.311920	+	0.378686i	0.0132403	+	0.0160743i
$556$	−6.91724			−0.293356
$557$	−15.8882			−0.673206			−0.336603	−	0.941647i	$-0.609278\pi$
$557$	−15.8882			−0.673206			−0.336603	+	0.941647i	$0.609278\pi$
$558$	26.0882	+	5.09189i	1.10440	+	0.215557i
$559$			6.93591i			0.293358i
$560$			0.136871i			0.00578384i
$561$	−8.89247	+	7.32464i	−0.375440	+	0.309247i
$562$		−	20.4331i		−	0.861918i
$563$	−29.8113			−1.25640			−0.628198	−	0.778054i	$-0.716207\pi$
$563$	−29.8113			−1.25640			−0.628198	+	0.778054i	$0.716207\pi$
$564$	−12.4697	−	15.1388i	−0.525069	−	0.637460i
$565$	−2.80584			−0.118043
$566$	−18.6039			−0.781980
$567$	−3.38431	+	8.33945i	−0.142128	+	0.350224i
$568$	3.92611			0.164736
$569$	−29.1893			−1.22368			−0.611840	−	0.790981i	$-0.709570\pi$
$569$	−29.1893			−1.22368			−0.611840	+	0.790981i	$0.709570\pi$
$570$	−1.37746	+	1.13460i	−0.0576954	+	0.0475231i
$571$			6.19818i			0.259386i	0.991554	+	0.129693i	$0.0413991\pi$
$571$			6.19818i			0.259386i	−0.991554	+	0.129693i	$0.958601\pi$
$572$	−0.843088			−0.0352513
$573$	−26.8695	+	22.1322i	−1.12249	+	0.924584i
$574$			4.66319i			0.194638i
$575$	−9.00832	+	22.1258i	−0.375673	+	0.922708i
$576$	−0.574695	+	2.94444i	−0.0239456	+	0.122685i
$577$	5.81832			0.242220			0.121110	−	0.992639i	$-0.461355\pi$
$577$	5.81832			0.242220			0.121110	+	0.992639i	$0.461355\pi$
$578$			4.20897i			0.175070i
$579$	−8.30775	+	6.84301i	−0.345258	+	0.284386i
$580$			0.195852i			0.00813230i
$581$		−	16.0249i		−	0.664826i
$582$	14.7721	−	12.1677i	0.612325	−	0.504366i
$583$	−10.6136			−0.439570
$584$		−	10.7313i		−	0.444064i
$585$	−0.0459158	+	0.235249i	−0.00189838	+	0.00972635i
$586$		−	22.6982i		−	0.937653i
$587$			22.0666i			0.910787i	0.890290	+	0.455393i	$0.150501\pi$
$587$			22.0666i			0.910787i	−0.890290	+	0.455393i	$0.849499\pi$
$588$	−1.33692	+	1.10121i	−0.0551335	+	0.0454129i
$589$			66.6970i			2.74820i
$590$	1.17796			0.0484959
$591$	29.0512	+	35.2696i	1.19501	+	1.45080i
$592$			2.06950i			0.0850558i
$593$			11.9705i			0.491568i	0.969325	+	0.245784i	$0.0790454\pi$
$593$			11.9705i			0.491568i	−0.969325	+	0.245784i	$0.920955\pi$
$594$	−6.59949	+	3.57337i	−0.270781	+	0.146617i
$595$			0.630333i			0.0258411i
$596$	−4.18429			−0.171395
$597$	14.6548	+	17.7916i	0.599781	+	0.728163i
$598$	2.59282	+	1.05565i	0.106028	+	0.0431686i
$599$		−	27.4925i		−	1.12331i	−0.827370	−	0.561657i	$-0.810164\pi$
$599$		−	27.4925i		−	1.12331i	0.827370	−	0.561657i	$-0.189836\pi$
$600$	−5.48540	−	6.65954i	−0.223940	−	0.271875i
$601$	−25.2682			−1.03071			−0.515356	−	0.856976i	$-0.672340\pi$
$601$	−25.2682			−1.03071			−0.515356	+	0.856976i	$0.672340\pi$
$602$			11.8820i			0.484274i
$603$	33.0835	+	6.45723i	1.34727	+	0.262959i
$604$	9.01508			0.366818
$605$	1.22006			0.0496026
$606$	−0.479263	+	0.394764i	−0.0194687	+	0.0160362i
$607$	−14.4130			−0.585008			−0.292504	−	0.956264i	$-0.594488\pi$
$607$	−14.4130			−0.585008			−0.292504	+	0.956264i	$0.594488\pi$
$608$	−7.52773			−0.305290
$609$	−1.91303	+	1.57574i	−0.0775199	+	0.0638523i
$610$	−1.69959			−0.0688145
$611$		−	6.61002i		−	0.267413i
$612$	−2.64665	+	13.5601i	−0.106985	+	0.548134i
$613$		−	20.2365i		−	0.817343i	−0.912682	−	0.408671i	$-0.865992\pi$
$613$		−	20.2365i		−	0.817343i	0.912682	−	0.408671i	$-0.134008\pi$
$614$			6.21291i			0.250732i
$615$	0.702848	+	0.853292i	0.0283416	+	0.0344081i
$616$	−1.44430			−0.0581926
$617$	23.1317			0.931245			0.465623	−	0.884983i	$-0.345830\pi$
$617$	23.1317			0.931245			0.465623	+	0.884983i	$0.345830\pi$
$618$	8.81578	−	7.26147i	0.354623	−	0.292099i
$619$		−	7.23849i		−	0.290939i	−0.989363	−	0.145470i	$-0.953531\pi$
$619$		−	7.23849i		−	0.290939i	0.989363	−	0.145470i	$-0.0464693\pi$
$620$	1.21270			0.0487031
$621$	24.7703	−	2.72615i	0.993998	−	0.109397i
$622$	−5.35894			−0.214874
$623$			8.79924i			0.352534i
$624$	−0.780403	+	0.642810i	−0.0312411	+	0.0257330i
$625$	24.7193			0.988774
$626$	18.3202			0.732223
$627$	−11.9727	−	14.5354i	−0.478142	−	0.580488i
$628$		−	16.8453i		−	0.672199i
$629$			9.53070i			0.380014i
$630$	−0.0786588	+	0.403007i	−0.00313384	+	0.0160562i
$631$			15.7583i			0.627327i	0.949534	+	0.313664i	$0.101556\pi$
$631$			15.7583i			0.627327i	−0.949534	+	0.313664i	$0.898444\pi$
$632$	4.84919			0.192890
$633$	20.6462	−	17.0061i	0.820613	−	0.675931i
$634$	2.64552			0.105067
$635$	−1.90294			−0.0755158
$636$	−9.82446	+	8.09231i	−0.389565	+	0.320881i
$637$	−0.583733			−0.0231284
$638$	−2.06669			−0.0818211
$639$	11.5602	+	2.25632i	0.457315	+	0.0892585i
$640$			0.136871i			0.00541029i
$641$	4.55427			0.179883			0.0899414	−	0.995947i	$-0.471332\pi$
$641$	4.55427			0.179883			0.0899414	+	0.995947i	$0.471332\pi$
$642$	2.74458	+	3.33206i	0.108320	+	0.131506i
$643$			43.3447i			1.70935i	0.519165	+	0.854674i	$0.326243\pi$
$643$			43.3447i			1.70935i	−0.519165	+	0.854674i	$0.673757\pi$
$644$	4.44180	+	1.80844i	0.175031	+	0.0712625i
$645$	1.79089	+	2.17422i	0.0705160	+	0.0856099i
$646$	−34.6676			−1.36398
$647$		−	4.95867i		−	0.194945i	−0.995238	−	0.0974727i	$-0.968924\pi$
$647$		−	4.95867i		−	0.194945i	0.995238	−	0.0974727i	$-0.0310759\pi$
$648$	−3.38431	+	8.33945i	−0.132948	+	0.327605i
$649$			12.4302i			0.487929i
$650$		−	2.90773i		−	0.114051i
$651$	9.75686	+	11.8453i	0.382402	+	0.464254i
$652$	5.55114			0.217399
$653$		−	0.410840i		−	0.0160774i	−0.999968	−	0.00803870i	$-0.997441\pi$
$653$		−	0.410840i		−	0.0160774i	0.999968	−	0.00803870i	$-0.00255883\pi$
$654$	5.76640	−	4.74973i	0.225484	−	0.185729i
$655$			1.30731i			0.0510807i
$656$			4.66319i			0.182067i
$657$	6.16722	−	31.5977i	0.240606	−	1.23274i
$658$		−	11.3237i		−	0.441444i
$659$	−15.8332			−0.616773			−0.308386	−	0.951261i	$-0.599789\pi$
$659$	−15.8332			−0.616773			−0.308386	+	0.951261i	$0.599789\pi$
$660$	−0.264285	+	0.217689i	−0.0102873	+	0.00847354i
$661$		−	14.0569i		−	0.546751i	−0.961907	−	0.273376i	$-0.911860\pi$
$661$		−	14.0569i		−	0.546751i	0.961907	−	0.273376i	$-0.0881402\pi$
$662$			7.99157i			0.310601i
$663$	−3.59401	+	2.96035i	−0.139580	+	0.114970i
$664$		−	16.0249i		−	0.621887i
$665$	−1.03033			−0.0399543
$666$	−1.18933	+	6.09351i	−0.0460856	+	0.236119i
$667$	6.35588	+	2.58774i	0.246101	+	0.100198i
$668$		−	21.1439i		−	0.818083i
$669$	−31.4994	+	25.9458i	−1.21784	+	1.00312i
$670$	1.53787			0.0594131
$671$		−	17.9346i		−	0.692359i
$672$	−1.33692	+	1.10121i	−0.0515727	+	0.0424799i
$673$	−0.450122			−0.0173509			−0.00867546	−	0.999962i	$-0.502762\pi$
$673$	−0.450122			−0.0173509			−0.00867546	+	0.999962i	$0.502762\pi$
$674$	25.1402			0.968363
$675$	−12.3242	−	22.7610i	−0.474359	−	0.876073i
$676$	12.6593			0.486894
$677$	28.0633			1.07856			0.539280	−	0.842127i	$-0.318697\pi$
$677$	28.0633			1.07856			0.539280	+	0.842127i	$0.318697\pi$
$678$	−22.5747	−	27.4067i	−0.866975	−	1.05255i
$679$	11.0494			0.424037
$680$			0.630333i			0.0241722i
$681$	−4.32912	+	3.56586i	−0.165892	+	0.136644i
$682$			12.7968i			0.490014i
$683$			4.44473i			0.170073i	0.996378	+	0.0850363i	$0.0271006\pi$
$683$			4.44473i			0.170073i	−0.996378	+	0.0850363i	$0.972899\pi$
$684$	−22.1650	−	4.32615i	−0.847498	−	0.165414i
$685$	−1.90041			−0.0726108
$686$	−1.00000			−0.0381802
$687$	−19.5510	−	23.7359i	−0.745918	−	0.905581i
$688$			11.8820i			0.452997i
$689$	−4.28962			−0.163422
$690$	1.08535	−	0.338562i	0.0413187	−	0.0128889i
$691$	5.63538			0.214380			0.107190	−	0.994239i	$-0.465815\pi$
$691$	5.63538			0.214380			0.107190	+	0.994239i	$0.465815\pi$
$692$			16.0711i			0.610932i
$693$	−4.25266	−	0.830033i	−0.161545	−	0.0315304i
$694$	28.1621			1.06902
$695$	−0.946767			−0.0359129
$696$	−1.91303	+	1.57574i	−0.0725132	+	0.0597284i
$697$			21.4755i			0.813442i
$698$		−	14.1592i		−	0.535934i
$699$	4.45193	+	5.40486i	0.168387	+	0.204431i
$700$		−	4.98127i		−	0.188274i
$701$	39.8840			1.50640			0.753198	−	0.657793i	$-0.228510\pi$
$701$	39.8840			1.50640			0.753198	+	0.657793i	$0.228510\pi$
$702$	−2.66727	+	1.44422i	−0.100670	+	0.0545087i
$703$	−15.5786			−0.587559
$704$	−1.44430			−0.0544342
$705$	−1.70674	−	2.07206i	−0.0642794	−	0.0780384i
$706$	−9.59456			−0.361096
$707$	−0.358483			−0.0134822
$708$	9.47739	+	11.5060i	0.356182	+	0.432423i
$709$			9.90560i			0.372013i	0.982549	+	0.186006i	$0.0595545\pi$
$709$			9.90560i			0.372013i	−0.982549	+	0.186006i	$0.940445\pi$
$710$	0.537370			0.0201671
$711$	14.2782	+	2.78680i	0.535473	+	0.104513i
$712$			8.79924i			0.329765i
$713$	16.0231	−	39.3551i	0.600069	−	1.47386i
$714$	−6.15693	+	5.07140i	−0.230417	+	0.189792i
$715$	−0.115394			−0.00431549
$716$			14.1093i			0.527291i
$717$	−4.66269	−	5.66074i	−0.174131	−	0.211404i
$718$		−	29.9075i		−	1.11614i
$719$		−	40.7021i		−	1.51793i	−0.651129	−	0.758967i	$-0.725704\pi$
$719$		−	40.7021i		−	1.51793i	0.651129	−	0.758967i	$-0.274296\pi$
$720$	−0.0786588	+	0.403007i	−0.00293144	+	0.0150192i
$721$	6.59411			0.245578
$722$		−	37.6667i		−	1.40181i
$723$	27.2371	+	33.0672i	1.01296	+	1.22978i
$724$			12.0652i			0.448398i
$725$		−	7.12782i		−	0.264721i
$726$	9.81613	+	11.9173i	0.364311	+	0.442291i
$727$		−	16.1426i		−	0.598695i	−0.954144	−	0.299348i	$-0.903231\pi$
$727$		−	16.1426i		−	0.598695i	0.954144	−	0.299348i	$-0.0967690\pi$
$728$	−0.583733			−0.0216346
$729$	−14.7575	+	22.6101i	−0.546575	+	0.837410i
$730$		−	1.46880i		−	0.0543627i
$731$			54.7204i			2.02391i
$732$	−13.6742	−	16.6012i	−0.505414	−	0.613597i
$733$			11.2047i			0.413855i	0.978356	+	0.206928i	$0.0663464\pi$
$733$			11.2047i			0.413855i	−0.978356	+	0.206928i	$0.933654\pi$
$734$	19.4738			0.718789
$735$	−0.182985	+	0.150723i	−0.00674949	+	0.00555949i
$736$	4.44180	+	1.80844i	0.163727	+	0.0666600i
$737$			16.2281i			0.597769i
$738$	−2.67991	+	13.7305i	−0.0986489	+	0.505426i
$739$	45.7068			1.68135			0.840675	−	0.541540i	$-0.182158\pi$
$739$	45.7068			1.68135			0.840675	+	0.541540i	$0.182158\pi$
$740$			0.283253i			0.0104126i
$741$	−4.83890	−	5.87467i	−0.177762	−	0.215811i
$742$	−7.34859			−0.269775
$743$	11.1584			0.409363			0.204682	−	0.978829i	$-0.434384\pi$
$743$	11.1584			0.409363			0.204682	+	0.978829i	$0.434384\pi$
$744$	9.75686	+	11.8453i	0.357704	+	0.434270i
$745$	−0.572707			−0.0209823
$746$	8.03802			0.294293
$747$	9.20943	−	47.1844i	0.336956	−	1.72639i
$748$	−6.65148			−0.243202
$749$			2.49235i			0.0910684i
$750$	−1.50440	−	1.82642i	−0.0549330	−	0.0666914i
$751$		−	43.7364i		−	1.59596i	−0.602682	−	0.797981i	$-0.705901\pi$
$751$		−	43.7364i		−	1.59596i	0.602682	−	0.797981i	$-0.294099\pi$
$752$		−	11.3237i		−	0.412933i
$753$	−38.4487	+	31.6698i	−1.40115	+	1.15411i
$754$	−0.835279			−0.0304191
$755$	1.23390			0.0449062
$756$	−4.56933	+	2.47411i	−0.166185	+	0.0899826i
$757$		−	34.9544i		−	1.27044i	−0.772331	−	0.635220i	$-0.780909\pi$
$757$		−	34.9544i		−	1.27044i	0.772331	−	0.635220i	$-0.219091\pi$
$758$	−13.5465			−0.492032
$759$	3.57262	+	11.4530i	0.129678	+	0.415717i
$760$	−1.03033			−0.0373738
$761$		−	21.0859i		−	0.764364i	−0.924087	−	0.382182i	$-0.875173\pi$
$761$		−	21.0859i		−	0.764364i	0.924087	−	0.382182i	$-0.124827\pi$
$762$	−15.3103	−	18.5874i	−0.554633	−	0.673351i
$763$	4.31321			0.156149
$764$	−20.0981			−0.727125
$765$	−0.362249	+	1.85598i	−0.0130971	+	0.0671030i
$766$		−	2.64368i		−	0.0955200i
$767$			5.02383i			0.181400i
$768$	−1.33692	+	1.10121i	−0.0482418	+	0.0397363i
$769$		−	20.4339i		−	0.736865i	−0.929654	−	0.368433i	$-0.879895\pi$
$769$		−	20.4339i		−	0.736865i	0.929654	−	0.368433i	$-0.120105\pi$
$770$	−0.197683			−0.00712399
$771$	3.64092	+	4.42026i	0.131125	+	0.159192i
$772$	−6.21411			−0.223651
$773$	21.5230			0.774128			0.387064	−	0.922053i	$-0.373489\pi$
$773$	21.5230			0.774128			0.387064	+	0.922053i	$0.373489\pi$
$774$	−6.82852	+	34.9858i	−0.245446	+	1.25754i
$775$	−44.1349			−1.58537
$776$	11.0494			0.396651
$777$	−2.76675	+	2.27894i	−0.0992565	+	0.0817566i
$778$		−	2.20235i		−	0.0789581i
$779$	−35.1032			−1.25770
$780$	−0.106814	+	0.0879819i	−0.00382457	+	0.00315026i
$781$			5.67050i			0.202906i
$782$	20.4559	+	8.32844i	0.731501	+	0.297824i
$783$	−6.53837	+	3.54027i	−0.233662	+	0.126519i
$784$	−1.00000			−0.0357143
$785$		−	2.30562i		−	0.0822911i
$786$	−12.7694	+	10.5180i	−0.455470	+	0.375166i
$787$		−	8.02490i		−	0.286057i	−0.989719	−	0.143028i	$-0.954316\pi$
$787$		−	8.02490i		−	0.286057i	0.989719	−	0.143028i	$-0.0456840\pi$
$788$			26.3813i			0.939796i
$789$	−0.867541	+	0.714585i	−0.0308853	+	0.0254399i
$790$	0.663712			0.0236138
$791$		−	20.5000i		−	0.728895i
$792$	−4.25266	−	0.830033i	−0.151112	−	0.0294939i
$793$		−	7.24852i		−	0.257402i
$794$			4.66525i			0.165563i
$795$	−1.34468	+	1.10760i	−0.0476909	+	0.0392825i
$796$			13.3080i			0.471688i
$797$	24.9547			0.883940			0.441970	−	0.897030i	$-0.354280\pi$
$797$	24.9547			0.883940			0.441970	+	0.897030i	$0.354280\pi$
$798$	−8.28958	−	10.0640i	−0.293448	−	0.356260i
$799$		−	52.1492i		−	1.84491i
$800$		−	4.98127i		−	0.176114i
$801$	−5.05688	+	25.9088i	−0.178676	+	0.915444i
$802$		−	11.8866i		−	0.419732i
$803$	15.4993			0.546957
$804$	12.3731	+	15.0215i	0.436364	+	0.529768i
$805$	0.607951	+	0.247522i	0.0214275	+	0.00872401i
$806$			5.17198i			0.182175i
$807$	−20.7258	−	25.1621i	−0.729582	−	0.885749i
$808$	−0.358483			−0.0126114
$809$			22.5116i			0.791466i	0.918366	+	0.395733i	$0.129509\pi$
$809$			22.5116i			0.791466i	−0.918366	+	0.395733i	$0.870491\pi$
$810$	−0.463212	+	1.14143i	−0.0162756	+	0.0401056i
$811$	4.41367			0.154985			0.0774924	−	0.996993i	$-0.475309\pi$
$811$	4.41367			0.154985			0.0774924	+	0.996993i	$0.475309\pi$
$812$	−1.43093			−0.0502157
$813$	24.4835	−	20.1668i	0.858675	−	0.707282i
$814$	−2.98898			−0.104764
$815$	0.759788			0.0266142
$816$	−6.15693	+	5.07140i	−0.215536	+	0.177535i
$817$	−89.4444			−3.12926
$818$			19.6843i			0.688244i
$819$	−1.71877	−	0.335468i	−0.0600586	−	0.0117222i
$820$			0.638254i			0.0222888i
$821$		−	43.9235i		−	1.53294i	−0.642279	−	0.766471i	$-0.722011\pi$
$821$		−	43.9235i		−	1.53294i	0.642279	−	0.766471i	$-0.277989\pi$
$822$	−15.2899	−	18.5627i	−0.533296	−	0.647447i
$823$	18.0143			0.627938			0.313969	−	0.949433i	$-0.398341\pi$
$823$	18.0143			0.627938			0.313969	+	0.949433i	$0.398341\pi$
$824$	6.59411			0.229717
$825$	9.61839	−	7.92257i	0.334869	−	0.275829i
$826$			8.60638i			0.299454i
$827$	−0.870316			−0.0302639			−0.0151319	−	0.999886i	$-0.504817\pi$
$827$	−0.870316			−0.0302639			−0.0151319	+	0.999886i	$0.504817\pi$
$828$	12.0393	+	7.87752i	0.418395	+	0.273763i
$829$	−12.0910			−0.419937			−0.209969	−	0.977708i	$-0.567336\pi$
$829$	−12.0910			−0.419937			−0.209969	+	0.977708i	$0.567336\pi$
$830$		−	2.19334i		−	0.0761320i
$831$	24.9460	−	20.5478i	0.865369	−	0.712796i
$832$	−0.583733			−0.0202373
$833$	−4.60532			−0.159565
$834$	−7.61730	−	9.24777i	−0.263765	−	0.320224i
$835$		−	2.89398i		−	0.100150i
$836$		−	10.8723i		−	0.376027i
$837$	21.9211	+	40.4850i	0.757703	+	1.39937i
$838$		−	32.8919i		−	1.13623i
$839$	4.74122			0.163685			0.0818426	−	0.996645i	$-0.473920\pi$
$839$	4.74122			0.163685			0.0818426	+	0.996645i	$0.473920\pi$
$840$	−0.182985	+	0.150723i	−0.00631357	+	0.00520043i
$841$	26.9525			0.929395
$842$	3.36061			0.115814
$843$	27.3174	−	22.5010i	0.940860	−	0.774977i
$844$	15.4432			0.531575
$845$	1.73268			0.0596060
$846$	6.50767	−	33.3419i	0.223738	−	1.14632i
$847$			8.91399i			0.306288i
$848$	−7.34859			−0.252352
$849$	−20.4867	−	24.8719i	−0.703102	−	0.853601i
$850$		−	22.9403i		−	0.786847i
$851$	9.19229	+	3.74256i	0.315107	+	0.128293i
$852$	4.32346	+	5.24889i	0.148119	+	0.179824i
$853$	41.4396			1.41886			0.709432	−	0.704774i	$-0.248951\pi$
$853$	41.4396			1.41886			0.709432	+	0.704774i	$0.248951\pi$
$854$		−	12.4175i		−	0.424919i
$855$	−3.03373	−	0.592122i	−0.103751	−	0.0202502i
$856$			2.49235i			0.0851867i
$857$			30.7161i			1.04924i	0.851336	+	0.524621i	$0.175793\pi$
$857$			30.7161i			1.04924i	−0.851336	+	0.524621i	$0.824207\pi$
$858$	−0.928413	−	1.12714i	−0.0316955	−	0.0384799i
$859$	−12.3909			−0.422772			−0.211386	−	0.977403i	$-0.567798\pi$
$859$	−12.3909			−0.422772			−0.211386	+	0.977403i	$0.567798\pi$
$860$			1.62630i			0.0554562i
$861$	−6.23430	+	5.13513i	−0.212464	+	0.175005i
$862$		−	32.0006i		−	1.08995i
$863$		−	26.8036i		−	0.912405i	−0.889876	−	0.456203i	$-0.849209\pi$
$863$		−	26.8036i		−	0.912405i	0.889876	−	0.456203i	$-0.150791\pi$
$864$	−4.56933	+	2.47411i	−0.155452	+	0.0841710i
$865$			2.19966i			0.0747908i
$866$	−32.4391			−1.10233
$867$	−5.62704	+	4.63494i	−0.191104	+	0.157411i
$868$			8.86017i			0.300734i
$869$			7.00370i			0.237584i
$870$	−0.261838	+	0.215673i	−0.00887713	+	0.00731200i
$871$			6.55879i			0.222236i
$872$	4.31321			0.146064
$873$	32.5343	+	6.35003i	1.10112	+	0.214916i
$874$	−13.6134	+	33.4366i	−0.460482	+	1.13101i
$875$		−	1.36614i		−	0.0461840i
$876$	14.3469	−	11.8174i	0.484736	−	0.399272i
$877$	15.2537			0.515080			0.257540	−	0.966268i	$-0.417088\pi$
$877$	15.2537			0.515080			0.257540	+	0.966268i	$0.417088\pi$
$878$		−	13.2858i		−	0.448374i
$879$	30.3456	−	24.9954i	1.02353	−	0.843072i
$880$	−0.197683			−0.00666388
$881$	15.3571			0.517395			0.258698	−	0.965958i	$-0.416707\pi$
$881$	15.3571			0.517395			0.258698	+	0.965958i	$0.416707\pi$
$882$	−2.94444	−	0.574695i	−0.0991444	−	0.0193510i
$883$	−36.6191			−1.23233			−0.616166	−	0.787616i	$-0.711315\pi$
$883$	−36.6191			−1.23233			−0.616166	+	0.787616i	$0.711315\pi$
$884$	−2.68828			−0.0904166
$885$	1.29718	+	1.57484i	0.0436041	+	0.0529376i
$886$	7.36139			0.247311
$887$			36.3690i			1.22115i	0.791958	+	0.610576i	$0.209062\pi$
$887$			36.3690i			1.22115i	−0.791958	+	0.610576i	$0.790938\pi$
$888$	−2.76675	+	2.27894i	−0.0928459	+	0.0764763i
$889$		−	13.9032i		−	0.466298i
$890$			1.20436i			0.0403702i
$891$	−12.0447	−	4.88797i	−0.403512	−	0.163753i
$892$	−23.5613			−0.788889
$893$	85.2417			2.85251
$894$	−4.60776	−	5.59405i	−0.154107	−	0.187093i
$895$			1.93116i			0.0645514i
$896$	−1.00000			−0.0334077
$897$	1.44392	+	4.62888i	0.0482111	+	0.154554i
$898$	−14.0512			−0.468895
$899$			12.6782i			0.422843i
$900$	2.86271	−	14.6670i	0.0954236	−	0.488901i
$901$	−33.8426			−1.12746
$902$	−6.73506			−0.224253
$903$	−15.8852	+	13.0845i	−0.528628	+	0.435425i
$904$		−	20.5000i		−	0.681819i
$905$			1.65137i			0.0548933i
$906$	9.92745	+	12.0524i	0.329817	+	0.400415i
$907$		−	34.8645i		−	1.15766i	−0.815450	−	0.578828i	$-0.803510\pi$
$907$		−	34.8645i		−	1.15766i	0.815450	−	0.578828i	$-0.196490\pi$
$908$	−3.23814			−0.107461
$909$	−1.05553	−	0.206018i	−0.0350098	−	0.00683320i
$910$	−0.0798960			−0.00264853
$911$	27.4387			0.909083			0.454542	−	0.890725i	$-0.349803\pi$
$911$	27.4387			0.909083			0.454542	+	0.890725i	$0.349803\pi$
$912$	−8.28958	−	10.0640i	−0.274495	−	0.333251i
$913$	23.1448			0.765982
$914$	26.4623			0.875296
$915$	−1.87160	−	2.27221i	−0.0618732	−	0.0751171i
$916$		−	17.7542i		−	0.586615i
$917$	−9.55139			−0.315415
$918$	−21.0432	+	11.3941i	−0.694530	+	0.376061i
$919$		−	3.06053i		−	0.100957i	−0.998725	−	0.0504787i	$-0.983925\pi$
$919$		−	3.06053i		−	0.100957i	0.998725	−	0.0504787i	$-0.0160747\pi$
$920$	0.607951	+	0.247522i	0.0200436	+	0.00816057i
$921$	−8.30614	+	6.84168i	−0.273697	+	0.225441i
$922$	30.1379			0.992538
$923$			2.29180i			0.0754356i
$924$	−1.59047	−	1.93091i	−0.0523227	−	0.0635224i
$925$		−	10.3087i		−	0.338949i
$926$		−	33.7207i		−	1.10813i
$927$	19.4160	+	3.78960i	0.637704	+	0.124467i
$928$	−1.43093			−0.0469724
$929$		−	28.3761i		−	0.930989i	−0.885051	−	0.465495i	$-0.845876\pi$
$929$		−	28.3761i		−	0.930989i	0.885051	−	0.465495i	$-0.154124\pi$
$930$	1.33543	+	1.62128i	0.0437904	+	0.0531637i
$931$		−	7.52773i		−	0.246711i
$932$			4.04278i			0.132426i
$933$	−5.90129	−	7.16446i	−0.193200	−	0.234554i
$934$			5.47544i			0.179162i
$935$	−0.910392			−0.0297730
$936$	−1.71877	−	0.335468i	−0.0561797	−	0.0109651i
$937$		−	9.15261i		−	0.299003i	−0.988762	−	0.149501i	$-0.952233\pi$
$937$		−	9.15261i		−	0.299003i	0.988762	−	0.149501i	$-0.0477668\pi$
$938$			11.2359i			0.366866i
$939$	20.1743	+	24.4926i	0.658364	+	0.799286i
$940$		−	1.54988i		−	0.0505516i
$941$	10.5373			0.343507			0.171754	−	0.985140i	$-0.445057\pi$
$941$	10.5373			0.343507			0.171754	+	0.985140i	$0.445057\pi$
$942$	22.5207	−	18.5501i	0.733764	−	0.604394i
$943$	20.7129	+	8.43310i	0.674506	+	0.274619i
$944$			8.60638i			0.280114i
$945$	−0.625407	+	0.338633i	−0.0203445	+	0.0110157i
$946$	−17.1612			−0.557958
$947$		−	25.2620i		−	0.820903i	−0.911882	−	0.410452i	$-0.865371\pi$
$947$		−	25.2620i		−	0.820903i	0.911882	−	0.410452i	$-0.134629\pi$
$948$	5.33995	+	6.48297i	0.173434	+	0.210557i
$949$	6.26422			0.203345
$950$	37.4976			1.21658
$951$	2.91326	+	3.53684i	0.0944688	+	0.114690i
$952$	−4.60532			−0.149259
$953$	−35.7700			−1.15870			−0.579351	−	0.815078i	$-0.696694\pi$
$953$	−35.7700			−1.15870			−0.579351	+	0.815078i	$0.696694\pi$
$954$	−21.6375	−	4.22320i	−0.700540	−	0.136731i
$955$	−2.75084			−0.0890152
$956$		−	4.23417i		−	0.136943i
$957$	−2.27585	−	2.76299i	−0.0735678	−	0.0893149i
$958$			32.7012i			1.05653i
$959$		−	13.8847i		−	0.448360i
$960$	−0.182985	+	0.150723i	−0.00590581	+	0.00486455i
$961$	47.5026			1.53234
$962$	−1.20804			−0.0389486
$963$	−1.43234	+	7.33856i	−0.0461565	+	0.236482i
$964$			24.7339i			0.796626i
$965$	−0.850529			−0.0273795
$966$	2.47359	+	7.92978i	0.0795866	+	0.255136i
$967$	1.65650			0.0532694			0.0266347	−	0.999645i	$-0.491521\pi$
$967$	1.65650			0.0532694			0.0266347	+	0.999645i	$0.491521\pi$
$968$			8.91399i			0.286506i
$969$	−38.1761	−	46.3477i	−1.22639	−	1.48890i
$970$	1.51234			0.0485583
$971$	−41.3159			−1.32589			−0.662944	−	0.748669i	$-0.730693\pi$
$971$	−41.3159			−1.32589			−0.662944	+	0.748669i	$0.730693\pi$
$972$	−14.8760	+	4.65891i	−0.477147	+	0.149435i
$973$		−	6.91724i		−	0.221756i
$974$			22.7090i			0.727643i
$975$	3.88740	−	3.20201i	0.124496	−	0.102546i
$976$		−	12.4175i		−	0.397475i
$977$	2.29729			0.0734969			0.0367484	−	0.999325i	$-0.488300\pi$
$977$	2.29729			0.0734969			0.0367484	+	0.999325i	$0.488300\pi$
$978$	6.11295	+	7.42142i	0.195470	+	0.237311i
$979$	−12.7088			−0.406174
$980$	−0.136871			−0.00437217
$981$	12.7000	+	2.47878i	0.405479	+	0.0791413i
$982$	15.4987			0.494583
$983$	13.4830			0.430041			0.215020	−	0.976610i	$-0.431018\pi$
$983$	13.4830			0.430041			0.215020	+	0.976610i	$0.431018\pi$
$984$	−6.23430	+	5.13513i	−0.198742	+	0.163702i
$985$			3.61083i			0.115051i
$986$	−6.58987			−0.209864
$987$	15.1388	−	12.4697i	0.481875	−	0.396915i
$988$		−	4.39419i		−	0.139798i
$989$	52.7774	+	21.4879i	1.67822	+	0.683274i
$990$	−0.582065	−	0.113607i	−0.0184992	−	0.00361067i
$991$	−37.0168			−1.17588			−0.587939	−	0.808905i	$-0.700061\pi$
$991$	−37.0168			−1.17588			−0.587939	+	0.808905i	$0.700061\pi$
$992$			8.86017i			0.281311i
$993$	−10.6841	+	8.80036i	−0.339049	+	0.279271i
$994$			3.92611i			0.124529i
$995$			1.82147i			0.0577445i
$996$	21.4240	−	17.6467i	0.678845	−	0.559158i
$997$	7.72316			0.244595			0.122297	−	0.992493i	$-0.460974\pi$
$997$	7.72316			0.244595			0.122297	+	0.992493i	$0.460974\pi$
$998$			28.7631i			0.910479i
$999$	−9.45622	+	5.12017i	−0.299181	+	0.161995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.a.827.14	yes	24
3.2	odd	2		966.2.h.b.827.2	yes	24
23.22	odd	2		966.2.h.b.827.14	yes	24
69.68	even	2	inner	966.2.h.a.827.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.2	✓	24	69.68	even	2	inner
966.2.h.a.827.14	yes	24	1.1	even	1	trivial
966.2.h.b.827.2	yes	24	3.2	odd	2
966.2.h.b.827.14	yes	24	23.22	odd	2

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.33692 + 1.10121i) q^{3} -1.00000 q^{4} -0.136871 q^{5} +(-1.10121 - 1.33692i) q^{6} -1.00000i q^{7} -1.00000i q^{8} +(0.574695 - 2.94444i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.33692 + 1.10121i) q^{3} -1.00000 q^{4} -0.136871 q^{5} +(-1.10121 - 1.33692i) q^{6} -1.00000i q^{7} -1.00000i q^{8} +(0.574695 - 2.94444i) q^{9} -0.136871i q^{10} +1.44430 q^{11} +(1.33692 - 1.10121i) q^{12} +0.583733 q^{13} +1.00000 q^{14} +(0.182985 - 0.150723i) q^{15} +1.00000 q^{16} +4.60532 q^{17} +(2.94444 + 0.574695i) q^{18} +7.52773i q^{19} +0.136871 q^{20} +(1.10121 + 1.33692i) q^{21} +1.44430i q^{22} +(1.80844 - 4.44180i) q^{23} +(1.10121 + 1.33692i) q^{24} -4.98127 q^{25} +0.583733i q^{26} +(2.47411 + 4.56933i) q^{27} +1.00000i q^{28} +1.43093i q^{29} +(0.150723 + 0.182985i) q^{30} +8.86017 q^{31} +1.00000i q^{32} +(-1.93091 + 1.59047i) q^{33} +4.60532i q^{34} +0.136871i q^{35} +(-0.574695 + 2.94444i) q^{36} +2.06950i q^{37} -7.52773 q^{38} +(-0.780403 + 0.642810i) q^{39} +0.136871i q^{40} +4.66319i q^{41} +(-1.33692 + 1.10121i) q^{42} +11.8820i q^{43} -1.44430 q^{44} +(-0.0786588 + 0.403007i) q^{45} +(4.44180 + 1.80844i) q^{46} -11.3237i q^{47} +(-1.33692 + 1.10121i) q^{48} -1.00000 q^{49} -4.98127i q^{50} +(-6.15693 + 5.07140i) q^{51} -0.583733 q^{52} -7.34859 q^{53} +(-4.56933 + 2.47411i) q^{54} -0.197683 q^{55} -1.00000 q^{56} +(-8.28958 - 10.0640i) q^{57} -1.43093 q^{58} +8.60638i q^{59} +(-0.182985 + 0.150723i) q^{60} -12.4175i q^{61} +8.86017i q^{62} +(-2.94444 - 0.574695i) q^{63} -1.00000 q^{64} -0.0798960 q^{65} +(-1.59047 - 1.93091i) q^{66} +11.2359i q^{67} -4.60532 q^{68} +(2.47359 + 7.92978i) q^{69} -0.136871 q^{70} +3.92611i q^{71} +(-2.94444 - 0.574695i) q^{72} +10.7313 q^{73} -2.06950 q^{74} +(6.65954 - 5.48540i) q^{75} -7.52773i q^{76} -1.44430i q^{77} +(-0.642810 - 0.780403i) q^{78} +4.84919i q^{79} -0.136871 q^{80} +(-8.33945 - 3.38431i) q^{81} -4.66319 q^{82} +16.0249 q^{83} +(-1.10121 - 1.33692i) q^{84} -0.630333 q^{85} -11.8820 q^{86} +(-1.57574 - 1.91303i) q^{87} -1.44430i q^{88} -8.79924 q^{89} +(-0.403007 - 0.0786588i) q^{90} -0.583733i q^{91} +(-1.80844 + 4.44180i) q^{92} +(-11.8453 + 9.75686i) q^{93} +11.3237 q^{94} -1.03033i q^{95} +(-1.10121 - 1.33692i) q^{96} +11.0494i q^{97} -1.00000i q^{98} +(0.830033 - 4.25266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

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