LMFDB - Embedded newform 1155.2.i.d.76.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.d.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40558i q^{2} -1.00000i q^{3} -3.78682 q^{4} -1.00000i q^{5} -2.40558 q^{6} +(1.69010 - 2.03557i) q^{7} +4.29833i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.40558i q^{2} -1.00000i q^{3} -3.78682 q^{4} -1.00000i q^{5} -2.40558 q^{6} +(1.69010 - 2.03557i) q^{7} +4.29833i q^{8} -1.00000 q^{9} -2.40558 q^{10} +(2.71459 - 1.90552i) q^{11} +3.78682i q^{12} -4.65071 q^{13} +(-4.89673 - 4.06568i) q^{14} -1.00000 q^{15} +2.76635 q^{16} +0.659618 q^{17} +2.40558i q^{18} -0.0804002 q^{19} +3.78682i q^{20} +(-2.03557 - 1.69010i) q^{21} +(-4.58388 - 6.53017i) q^{22} -3.80729 q^{23} +4.29833 q^{24} -1.00000 q^{25} +11.1877i q^{26} +1.00000i q^{27} +(-6.40011 + 7.70833i) q^{28} -8.10222i q^{29} +2.40558i q^{30} +3.95104i q^{31} +1.94199i q^{32} +(-1.90552 - 2.71459i) q^{33} -1.58676i q^{34} +(-2.03557 - 1.69010i) q^{35} +3.78682 q^{36} -5.99548 q^{37} +0.193409i q^{38} +4.65071i q^{39} +4.29833 q^{40} +4.39060 q^{41} +(-4.06568 + 4.89673i) q^{42} -5.26124i q^{43} +(-10.2797 + 7.21585i) q^{44} +1.00000i q^{45} +9.15873i q^{46} +7.38022i q^{47} -2.76635i q^{48} +(-1.28710 - 6.88065i) q^{49} +2.40558i q^{50} -0.659618i q^{51} +17.6114 q^{52} -3.67876 q^{53} +2.40558 q^{54} +(-1.90552 - 2.71459i) q^{55} +(8.74956 + 7.26462i) q^{56} +0.0804002i q^{57} -19.4905 q^{58} +6.62923i q^{59} +3.78682 q^{60} +14.5030 q^{61} +9.50455 q^{62} +(-1.69010 + 2.03557i) q^{63} +10.2043 q^{64} +4.65071i q^{65} +(-6.53017 + 4.58388i) q^{66} -6.70622 q^{67} -2.49785 q^{68} +3.80729i q^{69} +(-4.06568 + 4.89673i) q^{70} +14.8253 q^{71} -4.29833i q^{72} +6.71133 q^{73} +14.4226i q^{74} +1.00000i q^{75} +0.304461 q^{76} +(0.709123 - 8.74626i) q^{77} +11.1877 q^{78} -4.24069i q^{79} -2.76635i q^{80} +1.00000 q^{81} -10.5619i q^{82} -2.35068 q^{83} +(7.70833 + 6.40011i) q^{84} -0.659618i q^{85} -12.6563 q^{86} -8.10222 q^{87} +(8.19054 + 11.6682i) q^{88} +10.1884i q^{89} +2.40558 q^{90} +(-7.86018 + 9.46685i) q^{91} +14.4175 q^{92} +3.95104 q^{93} +17.7537 q^{94} +0.0804002i q^{95} +1.94199 q^{96} -4.04513i q^{97} +(-16.5520 + 3.09622i) q^{98} +(-2.71459 + 1.90552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 36 * q^4 - 32 * q^9	$ 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) $ 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$-1$

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 $

$2$		−	2.40558i		−	1.70100i	−0.525973	−	0.850501i	$-0.676299\pi$
$2$		−	2.40558i		−	1.70100i	0.525973	−	0.850501i	$-0.323701\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−3.78682			−1.89341
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.40558			−0.982074
$7$	1.69010	−	2.03557i	0.638799	−	0.769374i
$7$	1.69010	−	2.03557i	0.638799	−	0.769374i
$8$			4.29833i			1.51969i
$9$	−1.00000			−0.333333
$10$	−2.40558			−0.760711
$11$	2.71459	−	1.90552i	0.818480	−	0.574535i
$11$	2.71459	−	1.90552i	0.818480	−	0.574535i
$12$			3.78682i			1.09316i
$13$	−4.65071			−1.28987			−0.644937	−	0.764235i	$-0.723117\pi$
$13$	−4.65071			−1.28987			−0.644937	+	0.764235i	$0.723117\pi$
$14$	−4.89673	−	4.06568i	−1.30871	−	1.08660i
$15$	−1.00000			−0.258199
$16$	2.76635			0.691587
$17$	0.659618			0.159981			0.0799905	−	0.996796i	$-0.474511\pi$
$17$	0.659618			0.159981			0.0799905	+	0.996796i	$0.474511\pi$
$18$			2.40558i			0.567001i
$19$	−0.0804002			−0.0184451			−0.00922253	−	0.999957i	$-0.502936\pi$
$19$	−0.0804002			−0.0184451			−0.00922253	+	0.999957i	$0.502936\pi$
$20$			3.78682i			0.846758i
$21$	−2.03557	−	1.69010i	−0.444198	−	0.368811i
$22$	−4.58388	−	6.53017i	−0.977286	−	1.39224i
$23$	−3.80729			−0.793874			−0.396937	−	0.917846i	$-0.629927\pi$
$23$	−3.80729			−0.793874			−0.396937	+	0.917846i	$0.629927\pi$
$24$	4.29833			0.877393
$25$	−1.00000			−0.200000
$26$			11.1877i			2.19408i
$27$			1.00000i			0.192450i
$28$	−6.40011	+	7.70833i	−1.20951	+	1.45674i
$29$		−	8.10222i		−	1.50455i	−0.658852	−	0.752273i	$-0.728958\pi$
$29$		−	8.10222i		−	1.50455i	0.658852	−	0.752273i	$-0.271042\pi$
$30$			2.40558i			0.439197i
$31$			3.95104i			0.709628i	0.934937	+	0.354814i	$0.115456\pi$
$31$			3.95104i			0.709628i	−0.934937	+	0.354814i	$0.884544\pi$
$32$			1.94199i			0.343299i
$33$	−1.90552	−	2.71459i	−0.331708	−	0.472550i
$34$		−	1.58676i		−	0.272128i
$35$	−2.03557	−	1.69010i	−0.344074	−	0.285680i
$36$	3.78682			0.631136
$37$	−5.99548			−0.985650			−0.492825	−	0.870128i	$-0.664036\pi$
$37$	−5.99548			−0.985650			−0.492825	+	0.870128i	$0.664036\pi$
$38$			0.193409i			0.0313751i
$39$			4.65071i			0.744710i
$40$	4.29833			0.679626
$41$	4.39060			0.685697			0.342849	−	0.939391i	$-0.388608\pi$
$41$	4.39060			0.685697			0.342849	+	0.939391i	$0.388608\pi$
$42$	−4.06568	+	4.89673i	−0.627348	+	0.755582i
$43$		−	5.26124i		−	0.802332i	−0.916005	−	0.401166i	$-0.868605\pi$
$43$		−	5.26124i		−	0.802332i	0.916005	−	0.401166i	$-0.131395\pi$
$44$	−10.2797	+	7.21585i	−1.54972	+	1.08783i
$45$			1.00000i			0.149071i
$46$			9.15873i			1.35038i
$47$			7.38022i			1.07652i	0.842780	+	0.538258i	$0.180917\pi$
$47$			7.38022i			1.07652i	−0.842780	+	0.538258i	$0.819083\pi$
$48$		−	2.76635i		−	0.399288i
$49$	−1.28710	−	6.88065i	−0.183871	−	0.982950i
$50$			2.40558i			0.340200i
$51$		−	0.659618i		−	0.0923650i
$52$	17.6114			2.44226
$53$	−3.67876			−0.505316			−0.252658	−	0.967556i	$-0.581305\pi$
$53$	−3.67876			−0.505316			−0.252658	+	0.967556i	$0.581305\pi$
$54$	2.40558			0.327358
$55$	−1.90552	−	2.71459i	−0.256940	−	0.366035i
$56$	8.74956	+	7.26462i	1.16921	+	0.970776i
$57$			0.0804002i			0.0106493i
$58$	−19.4905			−2.55923
$59$			6.62923i			0.863053i	0.902100	+	0.431526i	$0.142025\pi$
$59$			6.62923i			0.863053i	−0.902100	+	0.431526i	$0.857975\pi$
$60$	3.78682			0.488876
$61$	14.5030			1.85692			0.928459	−	0.371434i	$-0.121134\pi$
$61$	14.5030			1.85692			0.928459	+	0.371434i	$0.121134\pi$
$62$	9.50455			1.20708
$63$	−1.69010	+	2.03557i	−0.212933	+	0.256458i
$64$	10.2043			1.27554
$65$			4.65071i			0.576850i
$66$	−6.53017	+	4.58388i	−0.803808	+	0.564236i
$67$	−6.70622			−0.819295			−0.409648	−	0.912244i	$-0.634348\pi$
$67$	−6.70622			−0.819295			−0.409648	+	0.912244i	$0.634348\pi$
$68$	−2.49785			−0.302909
$69$			3.80729i			0.458343i
$70$	−4.06568	+	4.89673i	−0.485942	+	0.585271i
$71$	14.8253			1.75944			0.879721	−	0.475490i	$-0.157729\pi$
$71$	14.8253			1.75944			0.879721	+	0.475490i	$0.157729\pi$
$72$		−	4.29833i		−	0.506563i
$73$	6.71133			0.785502			0.392751	−	0.919645i	$-0.371523\pi$
$73$	6.71133			0.785502			0.392751	+	0.919645i	$0.371523\pi$
$74$			14.4226i			1.67659i
$75$			1.00000i			0.115470i
$76$	0.304461			0.0349240
$77$	0.709123	−	8.74626i	0.0808120	−	0.996729i
$78$	11.1877			1.26675
$79$		−	4.24069i		−	0.477115i	−0.971128	−	0.238557i	$-0.923326\pi$
$79$		−	4.24069i		−	0.477115i	0.971128	−	0.238557i	$-0.0766745\pi$
$80$		−	2.76635i		−	0.309287i
$81$	1.00000			0.111111
$82$		−	10.5619i		−	1.16637i
$83$	−2.35068			−0.258020			−0.129010	−	0.991643i	$-0.541180\pi$
$83$	−2.35068			−0.258020			−0.129010	+	0.991643i	$0.541180\pi$
$84$	7.70833	+	6.40011i	0.841048	+	0.698309i
$85$		−	0.659618i		−	0.0715456i
$86$	−12.6563			−1.36477
$87$	−8.10222			−0.868649
$88$	8.19054	+	11.6682i	0.873115	+	1.24384i
$89$			10.1884i			1.07996i	0.841676	+	0.539982i	$0.181569\pi$
$89$			10.1884i			1.07996i	−0.841676	+	0.539982i	$0.818431\pi$
$90$	2.40558			0.253570
$91$	−7.86018	+	9.46685i	−0.823971	+	0.992396i
$92$	14.4175			1.50313
$93$	3.95104			0.409704
$94$	17.7537			1.83116
$95$			0.0804002i			0.00824888i
$96$	1.94199			0.198204
$97$		−	4.04513i		−	0.410721i	−0.978686	−	0.205360i	$-0.934163\pi$
$97$		−	4.04513i		−	0.410721i	0.978686	−	0.205360i	$-0.0658366\pi$
$98$	−16.5520	+	3.09622i	−1.67200	+	0.312766i
$99$	−2.71459	+	1.90552i	−0.272827	+	0.191512i
$100$	3.78682			0.378682
$101$	−7.77046			−0.773190			−0.386595	−	0.922250i	$-0.626349\pi$
$101$	−7.77046			−0.773190			−0.386595	+	0.922250i	$0.626349\pi$
$102$	−1.58676			−0.157113
$103$		−	15.0740i		−	1.48528i	−0.669690	−	0.742641i	$-0.733573\pi$
$103$		−	15.0740i		−	1.48528i	0.669690	−	0.742641i	$-0.266427\pi$
$104$		−	19.9903i		−	1.96021i
$105$	−1.69010	+	2.03557i	−0.164937	+	0.198651i
$106$			8.84954i			0.859544i
$107$			9.45278i			0.913834i	0.889509	+	0.456917i	$0.151046\pi$
$107$			9.45278i			0.913834i	−0.889509	+	0.456917i	$0.848954\pi$
$108$		−	3.78682i		−	0.364387i
$109$		−	10.5884i		−	1.01418i	−0.861893	−	0.507091i	$-0.830721\pi$
$109$		−	10.5884i		−	1.01418i	0.861893	−	0.507091i	$-0.169279\pi$
$110$	−6.53017	+	4.58388i	−0.622627	+	0.437055i
$111$			5.99548i			0.569065i
$112$	4.67541	−	5.63109i	0.441785	−	0.532088i
$113$	−1.37754			−0.129588			−0.0647940	−	0.997899i	$-0.520639\pi$
$113$	−1.37754			−0.129588			−0.0647940	+	0.997899i	$0.520639\pi$
$114$	0.193409			0.0181144
$115$			3.80729i			0.355031i
$116$			30.6816i			2.84872i
$117$	4.65071			0.429958
$118$	15.9472			1.46805
$119$	1.11482	−	1.34270i	0.102196	−	0.123085i
$120$		−	4.29833i		−	0.392382i
$121$	3.73800	−	10.3454i	0.339819	−	0.940491i
$122$		−	34.8881i		−	3.15862i
$123$		−	4.39060i		−	0.395887i
$124$		−	14.9619i		−	1.34362i
$125$			1.00000i			0.0894427i
$126$	4.89673	+	4.06568i	0.436235	+	0.362200i
$127$		−	18.8937i		−	1.67655i	−0.545250	−	0.838273i	$-0.683565\pi$
$127$		−	18.8937i		−	1.67655i	0.545250	−	0.838273i	$-0.316435\pi$
$128$		−	20.6633i		−	1.82640i
$129$	−5.26124			−0.463227
$130$	11.1877			0.981222
$131$	−8.64539			−0.755352			−0.377676	−	0.925938i	$-0.623277\pi$
$131$	−8.64539			−0.755352			−0.377676	+	0.925938i	$0.623277\pi$
$132$	7.21585	+	10.2797i	0.628059	+	0.894729i
$133$	−0.135885	+	0.163660i	−0.0117827	+	0.0141911i
$134$			16.1324i			1.39362i
$135$	1.00000			0.0860663
$136$			2.83526i			0.243121i
$137$	14.3876			1.22921			0.614606	−	0.788834i	$-0.289315\pi$
$137$	14.3876			1.22921			0.614606	+	0.788834i	$0.289315\pi$
$138$	9.15873			0.779643
$139$	−16.8889			−1.43249			−0.716247	−	0.697847i	$-0.754142\pi$
$139$	−16.8889			−1.43249			−0.716247	+	0.697847i	$0.754142\pi$
$140$	7.70833	+	6.40011i	0.651473	+	0.540908i
$141$	7.38022			0.621527
$142$		−	35.6635i		−	2.99282i
$143$	−12.6248	+	8.86201i	−1.05574	+	0.741079i
$144$	−2.76635			−0.230529
$145$	−8.10222			−0.672853
$146$		−	16.1446i		−	1.33614i
$147$	−6.88065	+	1.28710i	−0.567507	+	0.106158i
$148$	22.7038			1.86624
$149$			0.839325i			0.0687602i	0.999409	+	0.0343801i	$0.0109457\pi$
$149$			0.839325i			0.0687602i	−0.999409	+	0.0343801i	$0.989054\pi$
$150$	2.40558			0.196415
$151$		−	7.93126i		−	0.645437i	−0.946495	−	0.322718i	$-0.895403\pi$
$151$		−	7.93126i		−	0.645437i	0.946495	−	0.322718i	$-0.104597\pi$
$152$		−	0.345586i		−	0.0280308i
$153$	−0.659618			−0.0533270
$154$	−21.0398	−	1.70585i	−1.69544	−	0.137461i
$155$	3.95104			0.317355
$156$		−	17.6114i		−	1.41004i
$157$		−	3.42988i		−	0.273734i	−0.990589	−	0.136867i	$-0.956297\pi$
$157$		−	3.42988i		−	0.273734i	0.990589	−	0.136867i	$-0.0437033\pi$
$158$	−10.2013			−0.811573
$159$			3.67876i			0.291744i
$160$	1.94199			0.153528
$161$	−6.43471	+	7.75000i	−0.507126	+	0.610786i
$162$		−	2.40558i		−	0.189000i
$163$	−18.0102			−1.41066			−0.705332	−	0.708877i	$-0.749202\pi$
$163$	−18.0102			−1.41066			−0.705332	+	0.708877i	$0.749202\pi$
$164$	−16.6264			−1.29830
$165$	−2.71459	+	1.90552i	−0.211331	+	0.148344i
$166$			5.65475i			0.438893i
$167$	2.82747			0.218796			0.109398	−	0.993998i	$-0.465108\pi$
$167$	2.82747			0.218796			0.109398	+	0.993998i	$0.465108\pi$
$168$	7.26462	−	8.74956i	0.560478	−	0.675043i
$169$	8.62910			0.663777
$170$	−1.58676			−0.121699
$171$	0.0804002			0.00614835
$172$			19.9234i			1.51914i
$173$	−16.4879			−1.25355			−0.626777	−	0.779199i	$-0.715626\pi$
$173$	−16.4879			−1.25355			−0.626777	+	0.779199i	$0.715626\pi$
$174$			19.4905i			1.47757i
$175$	−1.69010	+	2.03557i	−0.127760	+	0.153875i
$176$	7.50950	−	5.27132i	0.566050	−	0.397341i
$177$	6.62923			0.498284
$178$	24.5089			1.83702
$179$	7.60126			0.568145			0.284072	−	0.958803i	$-0.408314\pi$
$179$	7.60126			0.568145			0.284072	+	0.958803i	$0.408314\pi$
$180$		−	3.78682i		−	0.282253i
$181$		−	21.2622i		−	1.58040i	−0.612847	−	0.790202i	$-0.709976\pi$
$181$		−	21.2622i		−	1.58040i	0.612847	−	0.790202i	$-0.290024\pi$
$182$	22.7733	+	18.9083i	1.68807	+	1.40158i
$183$		−	14.5030i		−	1.07209i
$184$		−	16.3650i		−	1.20644i
$185$			5.99548i			0.440796i
$186$		−	9.50455i		−	0.696907i
$187$	1.79059	−	1.25691i	0.130941	−	0.0919147i
$188$		−	27.9476i		−	2.03828i
$189$	2.03557	+	1.69010i	0.148066	+	0.122937i
$190$	0.193409			0.0140314
$191$	22.0784			1.59754			0.798770	−	0.601637i	$-0.205485\pi$
$191$	22.0784			1.59754			0.798770	+	0.601637i	$0.205485\pi$
$192$		−	10.2043i		−	0.736433i
$193$			24.6257i			1.77259i	0.463117	+	0.886297i	$0.346731\pi$
$193$			24.6257i			1.77259i	−0.463117	+	0.886297i	$0.653269\pi$
$194$	−9.73088			−0.698637
$195$	4.65071			0.333044
$196$	4.87401	+	26.0558i	0.348144	+	1.86113i
$197$		−	6.05578i		−	0.431456i	−0.976453	−	0.215728i	$-0.930787\pi$
$197$		−	6.05578i		−	0.431456i	0.976453	−	0.215728i	$-0.0692125\pi$
$198$	4.58388	+	6.53017i	0.325762	+	0.464079i
$199$		−	15.1981i		−	1.07737i	−0.842509	−	0.538683i	$-0.818922\pi$
$199$		−	15.1981i		−	1.07737i	0.842509	−	0.538683i	$-0.181078\pi$
$200$		−	4.29833i		−	0.303938i
$201$			6.70622i			0.473020i
$202$			18.6925i			1.31520i
$203$	−16.4927	−	13.6936i	−1.15756	−	0.961102i
$204$			2.49785i			0.174885i
$205$		−	4.39060i		−	0.306653i
$206$	−36.2616			−2.52647
$207$	3.80729			0.264625
$208$	−12.8655			−0.892060
$209$	−0.218254	+	0.153204i	−0.0150969	+	0.0105973i
$210$	4.89673	+	4.06568i	0.337906	+	0.280559i
$211$			10.3975i			0.715795i	0.933761	+	0.357898i	$0.116506\pi$
$211$			10.3975i			0.715795i	−0.933761	+	0.357898i	$0.883494\pi$
$212$	13.9308			0.956770
$213$		−	14.8253i		−	1.01581i
$214$	22.7394			1.55443
$215$	−5.26124			−0.358814
$216$	−4.29833			−0.292464
$217$	8.04263	+	6.67767i	0.545969	+	0.453310i
$218$	−25.4712			−1.72512
$219$		−	6.71133i		−	0.453510i
$220$	7.21585	+	10.2797i	0.486492	+	0.693054i
$221$	−3.06769			−0.206355
$222$	14.4226			0.967981
$223$			21.4094i			1.43368i	0.697238	+	0.716840i	$0.254412\pi$
$223$			21.4094i			1.43368i	−0.697238	+	0.716840i	$0.745588\pi$
$224$	3.95307	+	3.28217i	0.264125	+	0.219299i
$225$	1.00000			0.0666667
$226$			3.31378i			0.220430i
$227$	0.584050			0.0387648			0.0193824	−	0.999812i	$-0.493830\pi$
$227$	0.584050			0.0387648			0.0193824	+	0.999812i	$0.493830\pi$
$228$		−	0.304461i		−	0.0201634i
$229$			20.8472i			1.37762i	0.724942	+	0.688810i	$0.241867\pi$
$229$			20.8472i			1.37762i	−0.724942	+	0.688810i	$0.758133\pi$
$230$	9.15873			0.603909
$231$	−8.74626	−	0.709123i	−0.575462	−	0.0466568i
$232$	34.8260			2.28644
$233$		−	16.6205i		−	1.08884i	−0.838812	−	0.544422i	$-0.816749\pi$
$233$		−	16.6205i		−	1.08884i	0.838812	−	0.544422i	$-0.183251\pi$
$234$		−	11.1877i		−	0.731360i
$235$	7.38022			0.481433
$236$		−	25.1037i		−	1.63411i
$237$	−4.24069			−0.275462
$238$	−3.22997	−	2.68180i	−0.209368	−	0.173835i
$239$			4.92640i			0.318662i	0.987225	+	0.159331i	$0.0509337\pi$
$239$			4.92640i			0.318662i	−0.987225	+	0.159331i	$0.949066\pi$
$240$	−2.76635			−0.178567
$241$	−6.45040			−0.415507			−0.207753	−	0.978181i	$-0.566615\pi$
$241$	−6.45040			−0.415507			−0.207753	+	0.978181i	$0.566615\pi$
$242$	−24.8867	−	8.99207i	−1.59978	−	0.578032i
$243$		−	1.00000i		−	0.0641500i
$244$	−54.9202			−3.51590
$245$	−6.88065	+	1.28710i	−0.439589	+	0.0822298i
$246$	−10.5619			−0.673405
$247$	0.373918			0.0237918
$248$	−16.9829			−1.07841
$249$			2.35068i			0.148968i
$250$	2.40558			0.152142
$251$		−	24.2009i		−	1.52755i	−0.645483	−	0.763774i	$-0.723344\pi$
$251$		−	24.2009i		−	1.52755i	0.645483	−	0.763774i	$-0.276656\pi$
$252$	6.40011	−	7.70833i	0.403169	−	0.485579i
$253$	−10.3352	+	7.25485i	−0.649770	+	0.456109i
$254$	−45.4504			−2.85181
$255$	−0.659618			−0.0413069
$256$	−29.2986			−1.83116
$257$			2.94681i			0.183817i	0.995767	+	0.0919083i	$0.0292967\pi$
$257$			2.94681i			0.183817i	−0.995767	+	0.0919083i	$0.970703\pi$
$258$			12.6563i			0.787950i
$259$	−10.1330	+	12.2042i	−0.629632	+	0.758333i
$260$		−	17.6114i		−	1.09221i
$261$			8.10222i			0.501515i
$262$			20.7972i			1.28485i
$263$		−	16.3592i		−	1.00875i	−0.863485	−	0.504375i	$-0.831723\pi$
$263$		−	16.3592i		−	1.00875i	0.863485	−	0.504375i	$-0.168277\pi$
$264$	11.6682	−	8.19054i	0.718129	−	0.504093i
$265$			3.67876i			0.225984i
$266$	0.393698	+	0.326881i	0.0241392	+	0.0200424i
$267$	10.1884			0.623518
$268$	25.3952			1.55126
$269$			0.824772i			0.0502872i	0.999684	+	0.0251436i	$0.00800430\pi$
$269$			0.824772i			0.0502872i	−0.999684	+	0.0251436i	$0.991996\pi$
$270$		−	2.40558i		−	0.146399i
$271$	−13.7748			−0.836760			−0.418380	−	0.908272i	$-0.637402\pi$
$271$	−13.7748			−0.836760			−0.418380	+	0.908272i	$0.637402\pi$
$272$	1.82473			0.110641
$273$	9.46685	+	7.86018i	0.572960	+	0.475720i
$274$		−	34.6104i		−	2.09089i
$275$	−2.71459	+	1.90552i	−0.163696	+	0.114907i
$276$		−	14.4175i		−	0.867831i
$277$			3.60665i			0.216703i	0.994113	+	0.108351i	$0.0345572\pi$
$277$			3.60665i			0.216703i	−0.994113	+	0.108351i	$0.965443\pi$
$278$			40.6275i			2.43668i
$279$		−	3.95104i		−	0.236543i
$280$	7.26462	−	8.74956i	0.434144	−	0.522886i
$281$		−	18.2573i		−	1.08914i	−0.838716	−	0.544570i	$-0.816693\pi$
$281$		−	18.2573i		−	1.08914i	0.838716	−	0.544570i	$-0.183307\pi$
$282$		−	17.7537i		−	1.05722i
$283$	30.7240			1.82635			0.913175	−	0.407568i	$-0.133623\pi$
$283$	30.7240			1.82635			0.913175	+	0.407568i	$0.133623\pi$
$284$	−56.1408			−3.33134
$285$	0.0804002			0.00476249
$286$	21.3183	+	30.3699i	1.26058	+	1.79581i
$287$	7.42057	−	8.93738i	0.438023	−	0.527557i
$288$		−	1.94199i		−	0.114433i
$289$	−16.5649			−0.974406
$290$			19.4905i			1.14452i
$291$	−4.04513			−0.237130
$292$	−25.4146			−1.48728
$293$	21.7952			1.27329			0.636645	−	0.771157i	$-0.280322\pi$
$293$	21.7952			1.27329			0.636645	+	0.771157i	$0.280322\pi$
$294$	3.09622	+	16.5520i	0.180575	+	0.965330i
$295$	6.62923			0.385969
$296$		−	25.7705i		−	1.49788i
$297$	1.90552	+	2.71459i	0.110569	+	0.157517i
$298$	2.01906			0.116961
$299$	17.7066			1.02400
$300$		−	3.78682i		−	0.218632i
$301$	−10.7096	−	8.89205i	−0.617293	−	0.512529i
$302$	−19.0793			−1.09789
$303$			7.77046i			0.446401i
$304$	−0.222415			−0.0127564
$305$		−	14.5030i		−	0.830439i
$306$			1.58676i			0.0907093i
$307$	6.13857			0.350346			0.175173	−	0.984538i	$-0.443951\pi$
$307$	6.13857			0.350346			0.175173	+	0.984538i	$0.443951\pi$
$308$	−2.68532	+	33.1205i	−0.153010	+	1.88722i
$309$	−15.0740			−0.857528
$310$		−	9.50455i		−	0.539822i
$311$		−	1.49969i		−	0.0850394i	−0.999096	−	0.0425197i	$-0.986461\pi$
$311$		−	1.49969i		−	0.0850394i	0.999096	−	0.0425197i	$-0.0135385\pi$
$312$	−19.9903			−1.13173
$313$		−	2.89092i		−	0.163404i	−0.996657	−	0.0817022i	$-0.973964\pi$
$313$		−	2.89092i		−	0.163404i	0.996657	−	0.0817022i	$-0.0260356\pi$
$314$	−8.25084			−0.465622
$315$	2.03557	+	1.69010i	0.114691	+	0.0952266i
$316$			16.0587i			0.903373i
$317$	−18.6937			−1.04994			−0.524971	−	0.851120i	$-0.675924\pi$
$317$	−18.6937			−1.04994			−0.524971	+	0.851120i	$0.675924\pi$
$318$	8.84954			0.496258
$319$	−15.4389	−	21.9942i	−0.864414	−	1.23144i
$320$		−	10.2043i		−	0.570438i
$321$	9.45278			0.527603
$322$	18.6433	+	15.4792i	1.03895	+	0.862623i
$323$	−0.0530334			−0.00295086
$324$	−3.78682			−0.210379
$325$	4.65071			0.257975
$326$			43.3249i			2.39954i
$327$	−10.5884			−0.585538
$328$			18.8723i			1.04205i
$329$	15.0230	+	12.4733i	0.828243	+	0.687678i
$330$	4.58388	+	6.53017i	0.252334	+	0.359474i
$331$	5.32284			0.292570			0.146285	−	0.989242i	$-0.453268\pi$
$331$	5.32284			0.292570			0.146285	+	0.989242i	$0.453268\pi$
$332$	8.90159			0.488538
$333$	5.99548			0.328550
$334$		−	6.80172i		−	0.372173i
$335$			6.70622i			0.366400i
$336$	−5.63109	−	4.67541i	−0.307201	−	0.255065i
$337$			6.56922i			0.357848i	0.983863	+	0.178924i	$0.0572617\pi$
$337$			6.56922i			0.357848i	−0.983863	+	0.178924i	$0.942738\pi$
$338$		−	20.7580i		−	1.12909i
$339$			1.37754i			0.0748177i
$340$			2.49785i			0.135465i
$341$	7.52878	+	10.7255i	0.407706	+	0.580816i
$342$		−	0.193409i		−	0.0104584i
$343$	−16.1814	−	9.00903i	−0.873713	−	0.486442i
$344$	22.6146			1.21930
$345$	3.80729			0.204977
$346$			39.6630i			2.13230i
$347$		−	22.6020i		−	1.21334i	−0.794954	−	0.606669i	$-0.792505\pi$
$347$		−	22.6020i		−	1.21334i	0.794954	−	0.606669i	$-0.207495\pi$
$348$	30.6816			1.64471
$349$	−8.23089			−0.440589			−0.220295	−	0.975433i	$-0.570702\pi$
$349$	−8.23089			−0.440589			−0.220295	+	0.975433i	$0.570702\pi$
$350$	4.89673	+	4.06568i	0.261741	+	0.217320i
$351$		−	4.65071i		−	0.248237i
$352$	3.70050	+	5.27172i	0.197237	+	0.280983i
$353$			14.4320i			0.768138i	0.923304	+	0.384069i	$0.125477\pi$
$353$			14.4320i			0.768138i	−0.923304	+	0.384069i	$0.874523\pi$
$354$		−	15.9472i		−	0.847582i
$355$		−	14.8253i		−	0.786847i
$356$		−	38.5815i		−	2.04481i
$357$	−1.34270	−	1.11482i	−0.0710632	−	0.0590027i
$358$		−	18.2854i		−	0.966415i
$359$			18.8093i			0.992715i	0.868118	+	0.496357i	$0.165329\pi$
$359$			18.8093i			0.992715i	−0.868118	+	0.496357i	$0.834671\pi$
$360$	−4.29833			−0.226542
$361$	−18.9935			−0.999660
$362$	−51.1478			−2.68827
$363$	−10.3454	−	3.73800i	−0.542993	−	0.196194i
$364$	29.7651	−	35.8492i	1.56011	−	1.87901i
$365$		−	6.71133i		−	0.351287i
$366$	−34.8881			−1.82363
$367$		−	35.8151i		−	1.86953i	−0.355263	−	0.934766i	$-0.615609\pi$
$367$		−	35.8151i		−	1.86953i	0.355263	−	0.934766i	$-0.384391\pi$
$368$	−10.5323			−0.549033
$369$	−4.39060			−0.228566
$370$	14.4226			0.749795
$371$	−6.21748	+	7.48837i	−0.322795	+	0.388777i
$372$	−14.9619			−0.775737
$373$			13.0010i			0.673165i	0.941654	+	0.336583i	$0.109271\pi$
$373$			13.0010i			0.673165i	−0.941654	+	0.336583i	$0.890729\pi$
$374$	−3.02361	−	4.30742i	−0.156347	−	0.222731i
$375$	1.00000			0.0516398
$376$	−31.7226			−1.63597
$377$			37.6811i			1.94067i
$378$	4.06568	−	4.89673i	0.209116	−	0.251861i
$379$	15.7149			0.807218			0.403609	−	0.914932i	$-0.367756\pi$
$379$	15.7149			0.807218			0.403609	+	0.914932i	$0.367756\pi$
$380$		−	0.304461i		−	0.0156185i
$381$	−18.8937			−0.967955
$382$		−	53.1114i		−	2.71742i
$383$		−	19.4519i		−	0.993944i	−0.867766	−	0.496972i	$-0.834445\pi$
$383$		−	19.4519i		−	0.993944i	0.867766	−	0.496972i	$-0.165555\pi$
$384$	−20.6633			−1.05447
$385$	−8.74626	−	0.709123i	−0.445751	−	0.0361402i
$386$	59.2390			3.01519
$387$			5.26124i			0.267444i
$388$			15.3182i			0.777662i
$389$	28.6741			1.45384			0.726918	−	0.686725i	$-0.240952\pi$
$389$	28.6741			1.45384			0.726918	+	0.686725i	$0.240952\pi$
$390$		−	11.1877i		−	0.566509i
$391$	−2.51136			−0.127005
$392$	29.5753	−	5.53238i	1.49378	−	0.279427i
$393$			8.64539i			0.436102i
$394$	−14.5677			−0.733908
$395$	−4.24069			−0.213372
$396$	10.2797	−	7.21585i	0.516572	−	0.362610i
$397$		−	19.5780i		−	0.982592i	−0.870993	−	0.491296i	$-0.836523\pi$
$397$		−	19.5780i		−	0.982592i	0.870993	−	0.491296i	$-0.163477\pi$
$398$	−36.5603			−1.83260
$399$	0.163660	+	0.135885i	0.00819326	+	0.00680274i
$400$	−2.76635			−0.138317
$401$	−3.58854			−0.179203			−0.0896015	−	0.995978i	$-0.528559\pi$
$401$	−3.58854			−0.179203			−0.0896015	+	0.995978i	$0.528559\pi$
$402$	16.1324			0.804609
$403$		−	18.3752i		−	0.915332i
$404$	29.4253			1.46396
$405$		−	1.00000i		−	0.0496904i
$406$	−32.9410	+	39.6744i	−1.63484	+	1.96901i
$407$	−16.2753	+	11.4245i	−0.806735	+	0.566291i
$408$	2.83526			0.140366
$409$	−14.1578			−0.700060			−0.350030	−	0.936739i	$-0.613829\pi$
$409$	−14.1578			−0.700060			−0.350030	+	0.936739i	$0.613829\pi$
$410$	−10.5619			−0.521617
$411$		−	14.3876i		−	0.709686i
$412$			57.0823i			2.81225i
$413$	13.4943	+	11.2041i	0.664010	+	0.551317i
$414$		−	9.15873i		−	0.450127i
$415$			2.35068i			0.115390i
$416$		−	9.03165i		−	0.442813i
$417$			16.8889i			0.827051i
$418$	0.368544	+	0.525026i	0.0180261	+	0.0256799i
$419$		−	17.7777i		−	0.868500i	−0.900792	−	0.434250i	$-0.857014\pi$
$419$		−	17.7777i		−	0.868500i	0.900792	−	0.434250i	$-0.142986\pi$
$420$	6.40011	−	7.70833i	0.312294	−	0.376128i
$421$	−2.32563			−0.113344			−0.0566721	−	0.998393i	$-0.518049\pi$
$421$	−2.32563			−0.113344			−0.0566721	+	0.998393i	$0.518049\pi$
$422$	25.0121			1.21757
$423$		−	7.38022i		−	0.358839i
$424$		−	15.8125i		−	0.767923i
$425$	−0.659618			−0.0319962
$426$	−35.6635			−1.72790
$427$	24.5116	−	29.5219i	1.18620	−	1.42866i
$428$		−	35.7959i		−	1.73026i
$429$	8.86201	+	12.6248i	0.427862	+	0.609530i
$430$			12.6563i			0.610343i
$431$		−	32.0050i		−	1.54163i	−0.637062	−	0.770813i	$-0.719850\pi$
$431$		−	32.0050i		−	1.54163i	0.637062	−	0.770813i	$-0.280150\pi$
$432$			2.76635i			0.133096i
$433$		−	26.6911i		−	1.28269i	−0.767252	−	0.641346i	$-0.778376\pi$
$433$		−	26.6911i		−	1.28269i	0.767252	−	0.641346i	$-0.221624\pi$
$434$	16.0637	−	19.3472i	0.771081	−	0.928695i
$435$			8.10222i			0.388472i
$436$			40.0962i			1.92026i
$437$	0.306107			0.0146431
$438$	−16.1446			−0.771421
$439$	8.83818			0.421823			0.210912	−	0.977505i	$-0.432357\pi$
$439$	8.83818			0.421823			0.210912	+	0.977505i	$0.432357\pi$
$440$	11.6682	−	8.19054i	0.556260	−	0.390469i
$441$	1.28710	+	6.88065i	0.0612904	+	0.327650i
$442$			7.37958i			0.351011i
$443$	31.0075			1.47321			0.736606	−	0.676322i	$-0.236427\pi$
$443$	31.0075			1.47321			0.736606	+	0.676322i	$0.236427\pi$
$444$		−	22.7038i		−	1.07747i
$445$	10.1884			0.482975
$446$	51.5020			2.43869
$447$	0.839325			0.0396987
$448$	17.2463	−	20.7716i	0.814813	−	0.981366i
$449$	39.0429			1.84255			0.921273	−	0.388915i	$-0.127150\pi$
$449$	39.0429			1.84255			0.921273	+	0.388915i	$0.127150\pi$
$450$		−	2.40558i		−	0.113400i
$451$	11.9187	−	8.36637i	0.561229	−	0.393957i
$452$	5.21649			0.245363
$453$	−7.93126			−0.372643
$454$		−	1.40498i		−	0.0659390i
$455$	9.46685	+	7.86018i	0.443813	+	0.368491i
$456$	−0.345586			−0.0161836
$457$			10.9263i			0.511109i	0.966795	+	0.255554i	$0.0822580\pi$
$457$			10.9263i			0.511109i	−0.966795	+	0.255554i	$0.917742\pi$
$458$	50.1496			2.34334
$459$			0.659618i			0.0307883i
$460$		−	14.4175i		−	0.672219i
$461$	37.6329			1.75274			0.876369	−	0.481641i	$-0.159959\pi$
$461$	37.6329			1.75274			0.876369	+	0.481641i	$0.159959\pi$
$462$	−1.70585	+	21.0398i	−0.0793634	+	0.978862i
$463$	25.5488			1.18736			0.593678	−	0.804703i	$-0.297675\pi$
$463$	25.5488			1.18736			0.593678	+	0.804703i	$0.297675\pi$
$464$		−	22.4136i		−	1.04052i
$465$		−	3.95104i		−	0.183225i
$466$	−39.9819			−1.85212
$467$			12.0398i			0.557136i	0.960417	+	0.278568i	$0.0898597\pi$
$467$			12.0398i			0.557136i	−0.960417	+	0.278568i	$0.910140\pi$
$468$	−17.6114			−0.814087
$469$	−11.3342	+	13.6510i	−0.523365	+	0.630344i
$470$		−	17.7537i		−	0.818918i
$471$	−3.42988			−0.158040
$472$	−28.4946			−1.31157
$473$	−10.0254	−	14.2821i	−0.460968	−	0.656693i
$474$			10.2013i			0.468562i
$475$	0.0804002			0.00368901
$476$	−4.22163	+	5.08456i	−0.193498	+	0.233050i
$477$	3.67876			0.168439
$478$	11.8508			0.542045
$479$	−22.2312			−1.01577			−0.507885	−	0.861425i	$-0.669572\pi$
$479$	−22.2312			−1.01577			−0.507885	+	0.861425i	$0.669572\pi$
$480$		−	1.94199i		−	0.0886395i
$481$	27.8832			1.27137
$482$			15.5169i			0.706778i
$483$	7.75000	+	6.43471i	0.352637	+	0.292789i
$484$	−14.1551	+	39.1761i	−0.643415	+	1.78073i
$485$	−4.04513			−0.183680
$486$	−2.40558			−0.109119
$487$	6.53695			0.296217			0.148109	−	0.988971i	$-0.452681\pi$
$487$	6.53695			0.296217			0.148109	+	0.988971i	$0.452681\pi$
$488$			62.3387i			2.82194i
$489$			18.0102i			0.814447i
$490$	3.09622	+	16.5520i	0.139873	+	0.747741i
$491$			26.4467i			1.19353i	0.802418	+	0.596763i	$0.203547\pi$
$491$			26.4467i			1.19353i	−0.802418	+	0.596763i	$0.796453\pi$
$492$			16.6264i			0.749576i
$493$		−	5.34437i		−	0.240698i
$494$		−	0.899489i		−	0.0404699i
$495$	1.90552	+	2.71459i	0.0856467	+	0.122012i
$496$			10.9300i			0.490769i
$497$	25.0563	−	30.1780i	1.12393	−	1.35367i
$498$	5.65475			0.253395
$499$	35.9400			1.60890			0.804449	−	0.594022i	$-0.202461\pi$
$499$	35.9400			1.60890			0.804449	+	0.594022i	$0.202461\pi$
$500$		−	3.78682i		−	0.169352i
$501$		−	2.82747i		−	0.126322i
$502$	−58.2173			−2.59836
$503$	7.61141			0.339376			0.169688	−	0.985498i	$-0.445724\pi$
$503$	7.61141			0.339376			0.169688	+	0.985498i	$0.445724\pi$
$504$	−8.74956	−	7.26462i	−0.389736	−	0.323592i
$505$			7.77046i			0.345781i
$506$	17.4521	+	24.8622i	0.775842	+	1.10526i
$507$		−	8.62910i		−	0.383232i
$508$			71.5471i			3.17439i
$509$			8.34386i			0.369835i	0.982754	+	0.184917i	$0.0592018\pi$
$509$			8.34386i			0.369835i	−0.982754	+	0.184917i	$0.940798\pi$
$510$			1.58676i			0.0702631i
$511$	11.3428	−	13.6614i	0.501778	−	0.604344i
$512$			29.1536i			1.28842i
$513$		−	0.0804002i		−	0.00354975i
$514$	7.08878			0.312673
$515$	−15.0740			−0.664238
$516$	19.9234			0.877077
$517$	14.0631	+	20.0343i	0.618497	+	0.881107i
$518$	29.3582	+	24.3757i	1.28993	+	1.07101i
$519$			16.4879i			0.723740i
$520$	−19.9903			−0.876632
$521$		−	4.12749i		−	0.180828i	−0.995904	−	0.0904142i	$-0.971181\pi$
$521$		−	4.12749i		−	0.180828i	0.995904	−	0.0904142i	$-0.0288191\pi$
$522$	19.4905			0.853078
$523$	−40.4980			−1.77085			−0.885426	−	0.464780i	$-0.846133\pi$
$523$	−40.4980			−1.77085			−0.885426	+	0.464780i	$0.846133\pi$
$524$	32.7385			1.43019
$525$	2.03557	+	1.69010i	0.0888396	+	0.0737622i
$526$	−39.3533			−1.71589
$527$			2.60618i			0.113527i
$528$	−5.27132	−	7.50950i	−0.229405	−	0.326809i
$529$	−8.50457			−0.369764
$530$	8.84954			0.384400
$531$		−	6.62923i		−	0.287684i
$532$	0.514570	−	0.619751i	0.0223094	−	0.0268696i
$533$	−20.4194			−0.884463
$534$		−	24.5089i		−	1.06061i
$535$	9.45278			0.408679
$536$		−	28.8256i		−	1.24507i
$537$		−	7.60126i		−	0.328019i
$538$	1.98406			0.0855387
$539$	−16.6052	−	16.2256i	−0.715235	−	0.698884i
$540$	−3.78682			−0.162959
$541$			11.9745i			0.514826i	0.966302	+	0.257413i	$0.0828700\pi$
$541$			11.9745i			0.514826i	−0.966302	+	0.257413i	$0.917130\pi$
$542$			33.1364i			1.42333i
$543$	−21.2622			−0.912446
$544$			1.28097i			0.0549213i
$545$	−10.5884			−0.453556
$546$	18.9083	−	22.7733i	0.809200	−	0.974606i
$547$		−	26.9299i		−	1.15144i	−0.817648	−	0.575719i	$-0.804722\pi$
$547$		−	26.9299i		−	1.15144i	0.817648	−	0.575719i	$-0.195278\pi$
$548$	−54.4831			−2.32740
$549$	−14.5030			−0.618973
$550$	4.58388	+	6.53017i	0.195457	+	0.278447i
$551$			0.651420i			0.0277514i
$552$	−16.3650			−0.696540
$553$	−8.63222	−	7.16720i	−0.367079	−	0.304780i
$554$	8.67610			0.368612
$555$	5.99548			0.254494
$556$	63.9550			2.71230
$557$			7.84335i			0.332333i	0.986098	+	0.166167i	$0.0531390\pi$
$557$			7.84335i			0.332333i	−0.986098	+	0.166167i	$0.946861\pi$
$558$	−9.50455			−0.402360
$559$			24.4685i			1.03491i
$560$	−5.63109	−	4.67541i	−0.237957	−	0.197572i
$561$	−1.25691	−	1.79059i	−0.0530670	−	0.0755989i
$562$	−43.9194			−1.85263
$563$	−16.0986			−0.678476			−0.339238	−	0.940701i	$-0.610169\pi$
$563$	−16.0986			−0.678476			−0.339238	+	0.940701i	$0.610169\pi$
$564$	−27.9476			−1.17680
$565$			1.37754i			0.0579535i
$566$		−	73.9089i		−	3.10662i
$567$	1.69010	−	2.03557i	0.0709777	−	0.0854860i
$568$			63.7242i			2.67381i
$569$			46.6884i			1.95728i	0.205583	+	0.978640i	$0.434091\pi$
$569$			46.6884i			1.95728i	−0.205583	+	0.978640i	$0.565909\pi$
$570$		−	0.193409i		−	0.00810101i
$571$		−	33.0059i		−	1.38125i	−0.723211	−	0.690627i	$-0.757335\pi$
$571$		−	33.0059i		−	1.38125i	0.723211	−	0.690627i	$-0.242665\pi$
$572$	47.8077	−	33.5588i	1.99894	−	1.40316i
$573$		−	22.0784i		−	0.922340i
$574$	−21.4996	−	17.8508i	−0.897376	−	0.745077i
$575$	3.80729			0.158775
$576$	−10.2043			−0.425180
$577$			20.8844i			0.869428i	0.900569	+	0.434714i	$0.143150\pi$
$577$			20.8844i			0.869428i	−0.900569	+	0.434714i	$0.856850\pi$
$578$			39.8482i			1.65747i
$579$	24.6257			1.02341
$580$	30.6816			1.27399
$581$	−3.97289	+	4.78497i	−0.164823	+	0.198514i
$582$			9.73088i			0.403358i
$583$	−9.98632	+	7.00994i	−0.413591	+	0.290322i
$584$			28.8475i			1.19372i
$585$		−	4.65071i		−	0.192283i
$586$		−	52.4301i		−	2.16587i
$587$			21.7160i			0.896316i	0.893954	+	0.448158i	$0.147920\pi$
$587$			21.7160i			0.896316i	−0.893954	+	0.448158i	$0.852080\pi$
$588$	26.0558	−	4.87401i	1.07452	−	0.201001i
$589$		−	0.317664i		−	0.0130891i
$590$		−	15.9472i		−	0.656534i
$591$	−6.05578			−0.249101
$592$	−16.5856			−0.681662
$593$	23.9547			0.983701			0.491851	−	0.870680i	$-0.336321\pi$
$593$	23.9547			0.983701			0.491851	+	0.870680i	$0.336321\pi$
$594$	6.53017	−	4.58388i	0.267936	−	0.188079i
$595$	−1.34270	−	1.11482i	−0.0550453	−	0.0457033i
$596$		−	3.17837i		−	0.130191i
$597$	−15.1981			−0.622017
$598$		−	42.5946i		−	1.74182i
$599$	32.8643			1.34280			0.671400	−	0.741095i	$-0.265693\pi$
$599$	32.8643			1.34280			0.671400	+	0.741095i	$0.265693\pi$
$600$	−4.29833			−0.175479
$601$	34.6261			1.41243			0.706214	−	0.707999i	$-0.250402\pi$
$601$	34.6261			1.41243			0.706214	+	0.707999i	$0.250402\pi$
$602$	−21.3905	+	25.7629i	−0.871813	+	1.05002i
$603$	6.70622			0.273098
$604$			30.0342i			1.22208i
$605$	−10.3454	−	3.73800i	−0.420600	−	0.151971i
$606$	18.6925			0.759330
$607$	−11.0252			−0.447501			−0.223751	−	0.974646i	$-0.571830\pi$
$607$	−11.0252			−0.447501			−0.223751	+	0.974646i	$0.571830\pi$
$608$		−	0.156137i		−	0.00633218i
$609$	−13.6936	+	16.4927i	−0.554893	+	0.668316i
$610$	−34.8881			−1.41258
$611$		−	34.3233i		−	1.38857i
$612$	2.49785			0.100970
$613$		−	22.0177i		−	0.889287i	−0.895708	−	0.444644i	$-0.853330\pi$
$613$		−	22.0177i		−	0.889287i	0.895708	−	0.444644i	$-0.146670\pi$
$614$		−	14.7668i		−	0.595940i
$615$	−4.39060			−0.177046
$616$	37.5943	+	3.04804i	1.51472	+	0.122809i
$617$	29.6726			1.19457			0.597286	−	0.802028i	$-0.296246\pi$
$617$	29.6726			1.19457			0.597286	+	0.802028i	$0.296246\pi$
$618$			36.2616i			1.45866i
$619$			37.0099i			1.48755i	0.668429	+	0.743776i	$0.266967\pi$
$619$			37.0099i			1.48755i	−0.668429	+	0.743776i	$0.733033\pi$
$620$	−14.9619			−0.600883
$621$		−	3.80729i		−	0.152781i
$622$	−3.60761			−0.144652
$623$	20.7391	+	17.2194i	0.830896	+	0.689881i
$624$			12.8655i			0.515031i
$625$	1.00000			0.0400000
$626$	−6.95433			−0.277951
$627$	0.153204	+	0.218254i	0.00611838	+	0.00871621i
$628$			12.9883i			0.518290i
$629$	−3.95472			−0.157685
$630$	4.06568	−	4.89673i	0.161981	−	0.195090i
$631$	−7.62738			−0.303641			−0.151821	−	0.988408i	$-0.548514\pi$
$631$	−7.62738			−0.303641			−0.151821	+	0.988408i	$0.548514\pi$
$632$	18.2279			0.725066
$633$	10.3975			0.413265
$634$			44.9691i			1.78595i
$635$	−18.8937			−0.749775
$636$		−	13.9308i		−	0.552391i
$637$	5.98593	+	31.9999i	0.237171	+	1.26788i
$638$	−52.9089	+	37.1396i	−2.09468	+	1.47037i
$639$	−14.8253			−0.586481
$640$	−20.6633			−0.816789
$641$	−10.0894			−0.398507			−0.199254	−	0.979948i	$-0.563852\pi$
$641$	−10.0894			−0.398507			−0.199254	+	0.979948i	$0.563852\pi$
$642$		−	22.7394i		−	0.897453i
$643$		−	48.5452i		−	1.91444i	−0.289365	−	0.957219i	$-0.593444\pi$
$643$		−	48.5452i		−	1.91444i	0.289365	−	0.957219i	$-0.406556\pi$
$644$	24.3671	−	29.3478i	0.960197	−	1.15647i
$645$			5.26124i			0.207161i
$646$			0.127576i			0.00501942i
$647$			9.34167i			0.367259i	0.982996	+	0.183630i	$0.0587847\pi$
$647$			9.34167i			0.367259i	−0.982996	+	0.183630i	$0.941215\pi$
$648$			4.29833i			0.168854i
$649$	12.6321	+	17.9957i	0.495854	+	0.706391i
$650$		−	11.1877i		−	0.438816i
$651$	6.67767	−	8.04263i	0.261719	−	0.315215i
$652$	68.2011			2.67096
$653$	−4.49618			−0.175949			−0.0879745	−	0.996123i	$-0.528039\pi$
$653$	−4.49618			−0.175949			−0.0879745	+	0.996123i	$0.528039\pi$
$654$			25.4712i			0.996001i
$655$			8.64539i			0.337804i
$656$	12.1459			0.474219
$657$	−6.71133			−0.261834
$658$	30.0056	−	36.1390i	1.16974	−	1.40884i
$659$			17.1228i			0.667012i	0.942748	+	0.333506i	$0.108232\pi$
$659$			17.1228i			0.667012i	−0.942748	+	0.333506i	$0.891768\pi$
$660$	10.2797	−	7.21585i	0.400135	−	0.280876i
$661$			34.1063i			1.32658i	0.748361	+	0.663291i	$0.230841\pi$
$661$			34.1063i			1.32658i	−0.748361	+	0.663291i	$0.769159\pi$
$662$		−	12.8045i		−	0.497662i
$663$			3.06769i			0.119139i
$664$		−	10.1040i		−	0.392111i
$665$	0.163660	+	0.135885i	0.00634647	+	0.00526938i
$666$		−	14.4226i		−	0.558864i
$667$			30.8475i			1.19442i
$668$	−10.7071			−0.414271
$669$	21.4094			0.827735
$670$	16.1324			0.623247
$671$	39.3697	−	27.6357i	1.51985	−	1.06687i
$672$	3.28217	−	3.95307i	0.126612	−	0.152493i
$673$			33.8751i			1.30579i	0.757449	+	0.652894i	$0.226445\pi$
$673$			33.8751i			1.30579i	−0.757449	+	0.652894i	$0.773555\pi$
$674$	15.8028			0.608701
$675$		−	1.00000i		−	0.0384900i
$676$	−32.6768			−1.25680
$677$	−21.7921			−0.837540			−0.418770	−	0.908092i	$-0.637539\pi$
$677$	−21.7921			−0.837540			−0.418770	+	0.908092i	$0.637539\pi$
$678$	3.31378			0.127265
$679$	−8.23415	−	6.83669i	−0.315998	−	0.262368i
$680$	2.83526			0.108727
$681$		−	0.584050i		−	0.0223809i
$682$	25.8010	−	18.1111i	0.987970	−	0.693509i
$683$	−16.9983			−0.650422			−0.325211	−	0.945641i	$-0.605435\pi$
$683$	−16.9983			−0.650422			−0.325211	+	0.945641i	$0.605435\pi$
$684$	−0.304461			−0.0116413
$685$		−	14.3876i		−	0.549721i
$686$	−21.6720	+	38.9256i	−0.827439	+	1.48619i
$687$	20.8472			0.795370
$688$		−	14.5544i		−	0.554882i
$689$	17.1088			0.651794
$690$		−	9.15873i		−	0.348667i
$691$			5.11875i			0.194727i	0.995249	+	0.0973633i	$0.0310409\pi$
$691$			5.11875i			0.194727i	−0.995249	+	0.0973633i	$0.968959\pi$
$692$	62.4368			2.37349
$693$	−0.709123	+	8.74626i	−0.0269373	+	0.332243i
$694$	−54.3709			−2.06389
$695$			16.8889i			0.640631i
$696$		−	34.8260i		−	1.32008i
$697$	2.89612			0.109698
$698$			19.8001i			0.749444i
$699$	−16.6205			−0.628644
$700$	6.40011	−	7.70833i	0.241902	−	0.291348i
$701$			0.316921i			0.0119700i	0.999982	+	0.00598498i	$0.00190509\pi$
$701$			0.316921i			0.0119700i	−0.999982	+	0.00598498i	$0.998095\pi$
$702$	−11.1877			−0.422251
$703$	0.482037			0.0181804
$704$	27.7005	−	19.4445i	1.04400	−	0.732842i
$705$		−	7.38022i		−	0.277955i
$706$	34.7173			1.30660
$707$	−13.1329	+	15.8173i	−0.493913	+	0.594872i
$708$	−25.1037			−0.943454
$709$	36.5464			1.37253			0.686264	−	0.727353i	$-0.259250\pi$
$709$	36.5464			1.37253			0.686264	+	0.727353i	$0.259250\pi$
$710$	−35.6635			−1.33843
$711$			4.24069i			0.159038i
$712$	−43.7930			−1.64121
$713$		−	15.0428i		−	0.563356i
$714$	−2.68180	+	3.22997i	−0.100364	+	0.120879i
$715$	8.86201	+	12.6248i	0.331420	+	0.472140i
$716$	−28.7846			−1.07573
$717$	4.92640			0.183980
$718$	45.2472			1.68861
$719$			6.93939i			0.258795i	0.991593	+	0.129398i	$0.0413044\pi$
$719$			6.93939i			0.258795i	−0.991593	+	0.129398i	$0.958696\pi$
$720$			2.76635i			0.103096i
$721$	−30.6841	−	25.4766i	−1.14274	−	0.948797i
$722$			45.6905i			1.70042i
$723$			6.45040i			0.239893i
$724$			80.5159i			2.99235i
$725$			8.10222i			0.300909i
$726$	−8.99207	+	24.8867i	−0.333727	+	0.923632i
$727$			32.0737i			1.18955i	0.803892	+	0.594775i	$0.202759\pi$
$727$			32.0737i			1.18955i	−0.803892	+	0.594775i	$0.797241\pi$
$728$	−40.6917	−	33.7857i	−1.50813	−	1.25218i
$729$	−1.00000			−0.0370370
$730$	−16.1446			−0.597540
$731$		−	3.47041i		−	0.128358i
$732$			54.9202i			2.02991i
$733$	51.0892			1.88702			0.943511	−	0.331342i	$-0.107501\pi$
$733$	51.0892			1.88702			0.943511	+	0.331342i	$0.107501\pi$
$734$	−86.1561			−3.18008
$735$	1.28710	+	6.88065i	0.0474754	+	0.253797i
$736$		−	7.39373i		−	0.272536i
$737$	−18.2046	+	12.7788i	−0.670577	+	0.470714i
$738$			10.5619i			0.388791i
$739$			9.39146i			0.345470i	0.984968	+	0.172735i	$0.0552605\pi$
$739$			9.39146i			0.345470i	−0.984968	+	0.172735i	$0.944740\pi$
$740$		−	22.7038i		−	0.834607i
$741$		−	0.373918i		−	0.0137362i
$742$	18.0139	+	14.9566i	0.661310	+	0.549076i
$743$		−	2.96558i		−	0.108797i	−0.998519	−	0.0543983i	$-0.982676\pi$
$743$		−	2.96558i		−	0.108797i	0.998519	−	0.0543983i	$-0.0173241\pi$
$744$			16.9829i			0.622623i
$745$	0.839325			0.0307505
$746$	31.2749			1.14506
$747$	2.35068			0.0860068
$748$	−6.78065	+	4.75970i	−0.247925	+	0.174032i
$749$	19.2418	+	15.9762i	0.703080	+	0.583757i
$750$		−	2.40558i		−	0.0878394i
$751$	−43.9272			−1.60293			−0.801463	−	0.598045i	$-0.795945\pi$
$751$	−43.9272			−1.60293			−0.801463	+	0.598045i	$0.795945\pi$
$752$			20.4163i			0.744504i
$753$	−24.2009			−0.881931
$754$	90.6449			3.30109
$755$	−7.93126			−0.288648
$756$	−7.70833	−	6.40011i	−0.280349	−	0.232770i
$757$	35.6098			1.29426			0.647129	−	0.762380i	$-0.275969\pi$
$757$	35.6098			1.29426			0.647129	+	0.762380i	$0.275969\pi$
$758$		−	37.8033i		−	1.37308i
$759$	7.25485	+	10.3352i	0.263334	+	0.375145i
$760$	−0.345586			−0.0125357
$761$	41.3593			1.49927			0.749637	−	0.661849i	$-0.230228\pi$
$761$	41.3593			1.49927			0.749637	+	0.661849i	$0.230228\pi$
$762$			45.4504i			1.64649i
$763$	−21.5534	−	17.8954i	−0.780284	−	0.647858i
$764$	−83.6070			−3.02479
$765$			0.659618i			0.0238485i
$766$	−46.7930			−1.69070
$767$		−	30.8306i		−	1.11323i
$768$			29.2986i			1.05722i
$769$	−24.9503			−0.899731			−0.449866	−	0.893096i	$-0.648528\pi$
$769$	−24.9503			−0.899731			−0.449866	+	0.893096i	$0.648528\pi$
$770$	−1.70585	+	21.0398i	−0.0614746	+	0.758223i
$771$	2.94681			0.106127
$772$		−	93.2529i		−	3.35624i
$773$		−	17.7957i		−	0.640067i	−0.947406	−	0.320033i	$-0.896306\pi$
$773$		−	17.7957i		−	0.640067i	0.947406	−	0.320033i	$-0.103694\pi$
$774$	12.6563			0.454923
$775$		−	3.95104i		−	0.141926i
$776$	17.3873			0.624168
$777$	12.2042	+	10.1330i	0.437824	+	0.363518i
$778$		−	68.9779i		−	2.47298i
$779$	−0.353005			−0.0126477
$780$	−17.6114			−0.630589
$781$	40.2447	−	28.2499i	1.44007	−	1.01086i
$782$			6.04127i			0.216035i
$783$	8.10222			0.289550
$784$	−3.56056	−	19.0343i	−0.127163	−	0.679795i
$785$	−3.42988			−0.122418
$786$	20.7972			0.741811
$787$	16.0252			0.571238			0.285619	−	0.958343i	$-0.407801\pi$
$787$	16.0252			0.571238			0.285619	+	0.958343i	$0.407801\pi$
$788$			22.9321i			0.816923i
$789$	−16.3592			−0.582402
$790$			10.2013i			0.362946i
$791$	−2.32818	+	2.80408i	−0.0827807	+	0.0997016i
$792$	−8.19054	−	11.6682i	−0.291038	−	0.414612i
$793$	−67.4492			−2.39519
$794$	−47.0965			−1.67139
$795$	3.67876			0.130472
$796$			57.5525i			2.03989i
$797$		−	14.2424i		−	0.504492i	−0.967663	−	0.252246i	$-0.918831\pi$
$797$		−	14.2424i		−	0.504492i	0.967663	−	0.252246i	$-0.0811692\pi$
$798$	0.326881	−	0.393698i	0.0115715	−	0.0139368i
$799$			4.86813i			0.172222i
$800$		−	1.94199i		−	0.0686598i
$801$		−	10.1884i		−	0.359988i
$802$			8.63252i			0.304825i
$803$	18.2185	−	12.7886i	0.642917	−	0.451298i
$804$		−	25.3952i		−	0.895621i
$805$	7.75000	+	6.43471i	0.273152	+	0.226794i
$806$	−44.2029			−1.55698
$807$	0.824772			0.0290333
$808$		−	33.4000i		−	1.17501i
$809$		−	0.838625i		−	0.0294845i	−0.999891	−	0.0147422i	$-0.995307\pi$
$809$		−	0.838625i		−	0.0294845i	0.999891	−	0.0147422i	$-0.00469277\pi$
$810$	−2.40558			−0.0845235
$811$	−5.78255			−0.203053			−0.101526	−	0.994833i	$-0.532373\pi$
$811$	−5.78255			−0.203053			−0.101526	+	0.994833i	$0.532373\pi$
$812$	62.4546	+	51.8551i	2.19173	+	1.81976i
$813$			13.7748i			0.483104i
$814$	27.4825	+	39.1514i	0.963262	+	1.37226i
$815$			18.0102i			0.630868i
$816$		−	1.82473i		−	0.0638784i
$817$			0.423005i			0.0147991i
$818$			34.0578i			1.19080i
$819$	7.86018	−	9.46685i	0.274657	−	0.330799i
$820$			16.6264i			0.580619i
$821$		−	39.3175i		−	1.37219i	−0.727512	−	0.686095i	$-0.759323\pi$
$821$		−	39.3175i		−	1.37219i	0.727512	−	0.686095i	$-0.240677\pi$
$822$	−34.6104			−1.20718
$823$	45.1536			1.57396			0.786978	−	0.616981i	$-0.211645\pi$
$823$	45.1536			1.57396			0.786978	+	0.616981i	$0.211645\pi$
$824$	64.7929			2.25717
$825$	1.90552	+	2.71459i	0.0663416	+	0.0945099i
$826$	26.9523	−	32.4616i	0.937792	−	1.12948i
$827$			18.3881i			0.639417i	0.947516	+	0.319709i	$0.103585\pi$
$827$			18.3881i			0.639417i	−0.947516	+	0.319709i	$0.896415\pi$
$828$	−14.4175			−0.501043
$829$			28.0628i			0.974662i	0.873217	+	0.487331i	$0.162029\pi$
$829$			28.0628i			0.974662i	−0.873217	+	0.487331i	$0.837971\pi$
$830$	5.65475			0.196279
$831$	3.60665			0.125113
$832$	−47.4573			−1.64529
$833$	−0.848994	−	4.53860i	−0.0294159	−	0.157253i
$834$	40.6275			1.40682
$835$		−	2.82747i		−	0.0978488i
$836$	0.826486	−	0.580155i	0.0285846	−	0.0200651i
$837$	−3.95104			−0.136568
$838$	−42.7658			−1.47732
$839$			20.0231i			0.691273i	0.938368	+	0.345637i	$0.112337\pi$
$839$			20.0231i			0.691273i	−0.938368	+	0.345637i	$0.887663\pi$
$840$	−8.74956	−	7.26462i	−0.301888	−	0.250653i
$841$	−36.6460			−1.26366
$842$			5.59448i			0.192799i
$843$	−18.2573			−0.628815
$844$		−	39.3735i		−	1.35529i
$845$		−	8.62910i		−	0.296850i
$846$	−17.7537			−0.610386
$847$	−14.7412	−	25.0938i	−0.506513	−	0.862232i
$848$	−10.1767			−0.349470
$849$		−	30.7240i		−	1.05444i
$850$			1.58676i			0.0544256i
$851$	22.8265			0.782482
$852$			56.1408i			1.92335i
$853$	−46.8512			−1.60416			−0.802078	−	0.597219i	$-0.796272\pi$
$853$	−46.8512			−1.60416			−0.802078	+	0.597219i	$0.796272\pi$
$854$	−71.0173	−	58.9645i	−2.43016	−	2.01773i
$855$		−	0.0804002i		−	0.00274963i
$856$	−40.6312			−1.38874
$857$	−15.5901			−0.532546			−0.266273	−	0.963898i	$-0.585792\pi$
$857$	−15.5901			−0.532546			−0.266273	+	0.963898i	$0.585792\pi$
$858$	30.3699	−	21.3183i	1.03681	−	0.727794i
$859$		−	3.90336i		−	0.133181i	−0.997780	−	0.0665904i	$-0.978788\pi$
$859$		−	3.90336i		−	0.133181i	0.997780	−	0.0665904i	$-0.0212121\pi$
$860$	19.9234			0.679381
$861$	−8.93738	−	7.42057i	−0.304585	−	0.252892i
$862$	−76.9905			−2.62231
$863$	27.1263			0.923389			0.461695	−	0.887039i	$-0.347242\pi$
$863$	27.1263			0.923389			0.461695	+	0.887039i	$0.347242\pi$
$864$	−1.94199			−0.0660680
$865$			16.4879i			0.560607i
$866$	−64.2075			−2.18186
$867$			16.5649i			0.562574i
$868$	−30.4560	−	25.2871i	−1.03374	−	0.858301i
$869$	−8.08070	−	11.5117i	−0.274119	−	0.390509i
$870$	19.4905			0.660791
$871$	31.1887			1.05679
$872$	45.5123			1.54124
$873$			4.04513i			0.136907i
$874$		−	0.736364i		−	0.0249079i
$875$	2.03557	+	1.69010i	0.0688149	+	0.0571359i
$876$			25.4146i			0.858679i
$877$		−	4.59538i		−	0.155175i	−0.996986	−	0.0775874i	$-0.975278\pi$
$877$		−	4.59538i		−	0.155175i	0.996986	−	0.0775874i	$-0.0247217\pi$
$878$		−	21.2610i		−	0.717522i
$879$		−	21.7952i		−	0.735134i
$880$	−5.27132	−	7.50950i	−0.177696	−	0.253145i
$881$			50.5936i			1.70454i	0.523101	+	0.852271i	$0.324775\pi$
$881$			50.5936i			1.70454i	−0.523101	+	0.852271i	$0.675225\pi$
$882$	16.5520	−	3.09622i	0.557334	−	0.104255i
$883$	−36.5104			−1.22867			−0.614337	−	0.789044i	$-0.710576\pi$
$883$	−36.5104			−1.22867			−0.614337	+	0.789044i	$0.710576\pi$
$884$	11.6168			0.390715
$885$		−	6.62923i		−	0.222839i
$886$		−	74.5911i		−	2.50594i
$887$	−58.3614			−1.95959			−0.979793	−	0.200016i	$-0.935901\pi$
$887$	−58.3614			−1.95959			−0.979793	+	0.200016i	$0.935901\pi$
$888$	−25.7705			−0.864803
$889$	−38.4595	−	31.9324i	−1.28989	−	1.07098i
$890$		−	24.5089i		−	0.821541i
$891$	2.71459	−	1.90552i	0.0909422	−	0.0638372i
$892$		−	81.0735i		−	2.71454i
$893$		−	0.593371i		−	0.0198564i
$894$		−	2.01906i		−	0.0675276i
$895$		−	7.60126i		−	0.254082i
$896$	−42.0616	−	34.9231i	−1.40518	−	1.16670i
$897$		−	17.7066i		−	0.591206i
$898$		−	93.9208i		−	3.13418i
$899$	32.0122			1.06767
$900$	−3.78682			−0.126227
$901$	−2.42657			−0.0808409
$902$	−20.1260	−	28.6714i	−0.670122	−	0.954652i
$903$	−8.89205	+	10.7096i	−0.295909	+	0.356394i
$904$		−	5.92112i		−	0.196934i
$905$	−21.2622			−0.706778
$906$			19.0793i			0.633867i
$907$	−34.8835			−1.15829			−0.579144	−	0.815226i	$-0.696613\pi$
$907$	−34.8835			−1.15829			−0.579144	+	0.815226i	$0.696613\pi$
$908$	−2.21169			−0.0733976
$909$	7.77046			0.257730
$910$	18.9083	−	22.7733i	0.626804	−	0.754927i
$911$	39.9696			1.32425			0.662126	−	0.749393i	$-0.269655\pi$
$911$	39.9696			1.32425			0.662126	+	0.749393i	$0.269655\pi$
$912$			0.222415i			0.00736489i
$913$	−6.38113	+	4.47926i	−0.211185	+	0.148242i
$914$	26.2840			0.869397
$915$	−14.5030			−0.479454
$916$		−	78.9445i		−	2.60840i
$917$	−14.6116	+	17.5983i	−0.482518	+	0.581148i
$918$	1.58676			0.0523710
$919$		−	28.2546i		−	0.932033i	−0.884776	−	0.466017i	$-0.845689\pi$
$919$		−	28.2546i		−	0.932033i	0.884776	−	0.466017i	$-0.154311\pi$
$920$	−16.3650			−0.539537
$921$		−	6.13857i		−	0.202273i
$922$		−	90.5289i		−	2.98141i
$923$	−68.9483			−2.26946
$924$	33.1205	+	2.68532i	1.08958	+	0.0883405i
$925$	5.99548			0.197130
$926$		−	61.4598i		−	2.01969i
$927$			15.0740i			0.495094i
$928$	15.7345			0.516509
$929$			20.0919i			0.659193i	0.944122	+	0.329596i	$0.106913\pi$
$929$			20.0919i			0.659193i	−0.944122	+	0.329596i	$0.893087\pi$
$930$	−9.50455			−0.311666
$931$	0.103483	+	0.553206i	0.00339152	+	0.0181306i
$932$			62.9387i			2.06162i
$933$	−1.49969			−0.0490975
$934$	28.9627			0.947689
$935$	−1.25691	−	1.79059i	−0.0411055	−	0.0585587i
$936$			19.9903i			0.653403i
$937$	33.5978			1.09759			0.548796	−	0.835956i	$-0.315086\pi$
$937$	33.5978			1.09759			0.548796	+	0.835956i	$0.315086\pi$
$938$	32.8386	+	27.2653i	1.07222	+	0.890245i
$939$	−2.89092			−0.0943415
$940$	−27.9476			−0.911549
$941$	23.0918			0.752773			0.376386	−	0.926463i	$-0.377167\pi$
$941$	23.0918			0.752773			0.376386	+	0.926463i	$0.377167\pi$
$942$			8.25084i			0.268827i
$943$	−16.7163			−0.544357
$944$			18.3388i			0.596876i
$945$	1.69010	−	2.03557i	0.0549791	−	0.0662171i
$946$	−34.3568	+	24.1169i	−1.11704	+	0.784108i
$947$	−56.6272			−1.84014			−0.920069	−	0.391757i	$-0.871867\pi$
$947$	−56.6272			−1.84014			−0.920069	+	0.391757i	$0.871867\pi$
$948$	16.0587			0.521562
$949$	−31.2125			−1.01320
$950$		−	0.193409i		−	0.00627502i
$951$			18.6937i			0.606184i
$952$	5.77137	+	4.79188i	0.187051	+	0.155306i
$953$			36.0915i			1.16912i	0.811351	+	0.584559i	$0.198732\pi$
$953$			36.0915i			1.16912i	−0.811351	+	0.584559i	$0.801268\pi$
$954$		−	8.84954i		−	0.286515i
$955$		−	22.0784i		−	0.714441i
$956$		−	18.6554i		−	0.603357i
$957$	−21.9942	+	15.4389i	−0.710972	+	0.499070i
$958$			53.4790i			1.72783i
$959$	24.3165	−	29.2869i	0.785220	−	0.945724i
$960$	−10.2043			−0.329343
$961$	15.3893			0.496428
$962$		−	67.0753i		−	2.16259i
$963$		−	9.45278i		−	0.304611i
$964$	24.4265			0.786724
$965$	24.6257			0.792728
$966$	15.4792	−	18.6433i	0.498035	−	0.599837i
$967$			13.7868i			0.443354i	0.975120	+	0.221677i	$0.0711531\pi$
$967$			13.7868i			0.443354i	−0.975120	+	0.221677i	$0.928847\pi$
$968$	44.4680	+	16.0672i	1.42925	+	0.516419i
$969$			0.0530334i			0.00170368i
$970$			9.73088i			0.312440i
$971$			10.9905i			0.352701i	0.984327	+	0.176350i	$0.0564291\pi$
$971$			10.9905i			0.352701i	−0.984327	+	0.176350i	$0.943571\pi$
$972$			3.78682i			0.121462i
$973$	−28.5439	+	34.3785i	−0.915076	+	1.10212i
$974$		−	15.7251i		−	0.503866i
$975$		−	4.65071i		−	0.148942i
$976$	40.1203			1.28422
$977$	50.3300			1.61020			0.805100	−	0.593139i	$-0.202112\pi$
$977$	50.3300			1.61020			0.805100	+	0.593139i	$0.202112\pi$
$978$	43.3249			1.38538
$979$	19.4141	+	27.6572i	0.620478	+	0.883929i
$980$	26.0558	−	4.87401i	0.832321	−	0.155695i
$981$			10.5884i			0.338060i
$982$	63.6198			2.03019
$983$		−	9.53413i		−	0.304092i	−0.988373	−	0.152046i	$-0.951414\pi$
$983$		−	9.53413i		−	0.304092i	0.988373	−	0.152046i	$-0.0485861\pi$
$984$	18.8723			0.601626
$985$	−6.05578			−0.192953
$986$	−12.8563			−0.409429
$987$	12.4733	−	15.0230i	0.397031	−	0.478186i
$988$	−1.41596			−0.0450476
$989$			20.0311i			0.636951i
$990$	6.53017	−	4.58388i	0.207542	−	0.145685i
$991$	−2.48229			−0.0788525			−0.0394262	−	0.999222i	$-0.512553\pi$
$991$	−2.48229			−0.0788525			−0.0394262	+	0.999222i	$0.512553\pi$
$992$	−7.67290			−0.243615
$993$		−	5.32284i		−	0.168915i
$994$	−72.5956	−	60.2750i	−2.30259	−	1.91181i
$995$	−15.1981			−0.481813
$996$		−	8.90159i		−	0.282058i
$997$	5.32148			0.168533			0.0842664	−	0.996443i	$-0.473145\pi$
$997$	5.32148			0.168533			0.0842664	+	0.996443i	$0.473145\pi$
$998$		−	86.4566i		−	2.73674i
$999$		−	5.99548i		−	0.189688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.d.76.5	✓	32
7.6	odd	2	inner	1155.2.i.d.76.27	yes	32
11.10	odd	2	inner	1155.2.i.d.76.28	yes	32
77.76	even	2	inner	1155.2.i.d.76.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.d.76.5	✓	32	1.1	even	1	trivial
1155.2.i.d.76.6	yes	32	77.76	even	2	inner
1155.2.i.d.76.27	yes	32	7.6	odd	2	inner
1155.2.i.d.76.28	yes	32	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.40558i q^{2} -1.00000i q^{3} -3.78682 q^{4} -1.00000i q^{5} -2.40558 q^{6} +(1.69010 - 2.03557i) q^{7} +4.29833i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.40558i q^{2} -1.00000i q^{3} -3.78682 q^{4} -1.00000i q^{5} -2.40558 q^{6} +(1.69010 - 2.03557i) q^{7} +4.29833i q^{8} -1.00000 q^{9} -2.40558 q^{10} +(2.71459 - 1.90552i) q^{11} +3.78682i q^{12} -4.65071 q^{13} +(-4.89673 - 4.06568i) q^{14} -1.00000 q^{15} +2.76635 q^{16} +0.659618 q^{17} +2.40558i q^{18} -0.0804002 q^{19} +3.78682i q^{20} +(-2.03557 - 1.69010i) q^{21} +(-4.58388 - 6.53017i) q^{22} -3.80729 q^{23} +4.29833 q^{24} -1.00000 q^{25} +11.1877i q^{26} +1.00000i q^{27} +(-6.40011 + 7.70833i) q^{28} -8.10222i q^{29} +2.40558i q^{30} +3.95104i q^{31} +1.94199i q^{32} +(-1.90552 - 2.71459i) q^{33} -1.58676i q^{34} +(-2.03557 - 1.69010i) q^{35} +3.78682 q^{36} -5.99548 q^{37} +0.193409i q^{38} +4.65071i q^{39} +4.29833 q^{40} +4.39060 q^{41} +(-4.06568 + 4.89673i) q^{42} -5.26124i q^{43} +(-10.2797 + 7.21585i) q^{44} +1.00000i q^{45} +9.15873i q^{46} +7.38022i q^{47} -2.76635i q^{48} +(-1.28710 - 6.88065i) q^{49} +2.40558i q^{50} -0.659618i q^{51} +17.6114 q^{52} -3.67876 q^{53} +2.40558 q^{54} +(-1.90552 - 2.71459i) q^{55} +(8.74956 + 7.26462i) q^{56} +0.0804002i q^{57} -19.4905 q^{58} +6.62923i q^{59} +3.78682 q^{60} +14.5030 q^{61} +9.50455 q^{62} +(-1.69010 + 2.03557i) q^{63} +10.2043 q^{64} +4.65071i q^{65} +(-6.53017 + 4.58388i) q^{66} -6.70622 q^{67} -2.49785 q^{68} +3.80729i q^{69} +(-4.06568 + 4.89673i) q^{70} +14.8253 q^{71} -4.29833i q^{72} +6.71133 q^{73} +14.4226i q^{74} +1.00000i q^{75} +0.304461 q^{76} +(0.709123 - 8.74626i) q^{77} +11.1877 q^{78} -4.24069i q^{79} -2.76635i q^{80} +1.00000 q^{81} -10.5619i q^{82} -2.35068 q^{83} +(7.70833 + 6.40011i) q^{84} -0.659618i q^{85} -12.6563 q^{86} -8.10222 q^{87} +(8.19054 + 11.6682i) q^{88} +10.1884i q^{89} +2.40558 q^{90} +(-7.86018 + 9.46685i) q^{91} +14.4175 q^{92} +3.95104 q^{93} +17.7537 q^{94} +0.0804002i q^{95} +1.94199 q^{96} -4.04513i q^{97} +(-16.5520 + 3.09622i) q^{98} +(-2.71459 + 1.90552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 36 * q^4 - 32 * q^9	\( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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