LMFDB - Embedded newform 1155.2.k.b.769.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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, 1, 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("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.11
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69546 q^{2} +1.00000 q^{3} +0.874594 q^{4} +(-2.22547 - 0.217459i) q^{5} -1.69546 q^{6} +(0.698105 - 2.55199i) q^{7} +1.90808 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.69546 q^{2} +1.00000 q^{3} +0.874594 q^{4} +(-2.22547 - 0.217459i) q^{5} -1.69546 q^{6} +(0.698105 - 2.55199i) q^{7} +1.90808 q^{8} +1.00000 q^{9} +(3.77320 + 0.368694i) q^{10} +(3.25064 + 0.658292i) q^{11} +0.874594 q^{12} -5.21239i q^{13} +(-1.18361 + 4.32680i) q^{14} +(-2.22547 - 0.217459i) q^{15} -4.98427 q^{16} -3.07632i q^{17} -1.69546 q^{18} -4.27252 q^{19} +(-1.94638 - 0.190189i) q^{20} +(0.698105 - 2.55199i) q^{21} +(-5.51134 - 1.11611i) q^{22} +6.74583i q^{23} +1.90808 q^{24} +(4.90542 + 0.967898i) q^{25} +8.83741i q^{26} +1.00000 q^{27} +(0.610559 - 2.23195i) q^{28} -0.101717i q^{29} +(3.77320 + 0.368694i) q^{30} +6.52719i q^{31} +4.63448 q^{32} +(3.25064 + 0.658292i) q^{33} +5.21579i q^{34} +(-2.10857 + 5.52756i) q^{35} +0.874594 q^{36} -10.8576i q^{37} +7.24390 q^{38} -5.21239i q^{39} +(-4.24638 - 0.414931i) q^{40} +10.0082 q^{41} +(-1.18361 + 4.32680i) q^{42} -6.80409 q^{43} +(2.84299 + 0.575738i) q^{44} +(-2.22547 - 0.217459i) q^{45} -11.4373i q^{46} -6.68431 q^{47} -4.98427 q^{48} +(-6.02530 - 3.56312i) q^{49} +(-8.31696 - 1.64103i) q^{50} -3.07632i q^{51} -4.55872i q^{52} -2.30571i q^{53} -1.69546 q^{54} +(-7.09104 - 2.17189i) q^{55} +(1.33204 - 4.86941i) q^{56} -4.27252 q^{57} +0.172458i q^{58} -7.18644i q^{59} +(-1.94638 - 0.190189i) q^{60} -4.40985 q^{61} -11.0666i q^{62} +(0.698105 - 2.55199i) q^{63} +2.11096 q^{64} +(-1.13348 + 11.6000i) q^{65} +(-5.51134 - 1.11611i) q^{66} -4.25941i q^{67} -2.69053i q^{68} +6.74583i q^{69} +(3.57499 - 9.37178i) q^{70} -5.83327 q^{71} +1.90808 q^{72} -8.09569i q^{73} +18.4087i q^{74} +(4.90542 + 0.967898i) q^{75} -3.73672 q^{76} +(3.94924 - 7.83604i) q^{77} +8.83741i q^{78} -14.2003i q^{79} +(11.0923 + 1.08388i) q^{80} +1.00000 q^{81} -16.9685 q^{82} +7.09509i q^{83} +(0.610559 - 2.23195i) q^{84} +(-0.668975 + 6.84626i) q^{85} +11.5361 q^{86} -0.101717i q^{87} +(6.20249 + 1.25608i) q^{88} -16.3777i q^{89} +(3.77320 + 0.368694i) q^{90} +(-13.3020 - 3.63880i) q^{91} +5.89986i q^{92} +6.52719i q^{93} +11.3330 q^{94} +(9.50836 + 0.929100i) q^{95} +4.63448 q^{96} +2.98755 q^{97} +(10.2157 + 6.04113i) q^{98} +(3.25064 + 0.658292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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 $

$2$	−1.69546			−1.19887			−0.599437	−	0.800422i	$-0.704609\pi$
$2$	−1.69546			−1.19887			−0.599437	+	0.800422i	$0.704609\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.874594			0.437297
$5$	−2.22547	−	0.217459i	−0.995260	−	0.0972508i
$5$	−2.22547	−	0.217459i	−0.995260	−	0.0972508i
$6$	−1.69546			−0.692170
$7$	0.698105	−	2.55199i	0.263859	−	0.964561i
$7$	0.698105	−	2.55199i	0.263859	−	0.964561i
$8$	1.90808			0.674610
$9$	1.00000			0.333333
$10$	3.77320	+	0.368694i	1.19319	+	0.116591i
$11$	3.25064	+	0.658292i	0.980104	+	0.198483i
$11$	3.25064	+	0.658292i	0.980104	+	0.198483i
$12$	0.874594			0.252473
$13$		−	5.21239i		−	1.44566i	−0.691028	−	0.722828i	$-0.742842\pi$
$13$		−	5.21239i		−	1.44566i	0.691028	−	0.722828i	$-0.257158\pi$
$14$	−1.18361	+	4.32680i	−0.316334	+	1.15639i
$15$	−2.22547	−	0.217459i	−0.574614	−	0.0561477i
$16$	−4.98427			−1.24607
$17$		−	3.07632i		−	0.746118i	−0.927808	−	0.373059i	$-0.878309\pi$
$17$		−	3.07632i		−	0.746118i	0.927808	−	0.373059i	$-0.121691\pi$
$18$	−1.69546			−0.399624
$19$	−4.27252			−0.980184			−0.490092	−	0.871671i	$-0.663037\pi$
$19$	−4.27252			−0.980184			−0.490092	+	0.871671i	$0.663037\pi$
$20$	−1.94638	−	0.190189i	−0.435224	−	0.0425275i
$21$	0.698105	−	2.55199i	0.152339	−	0.556890i
$22$	−5.51134	−	1.11611i	−1.17502	−	0.237955i
$23$			6.74583i			1.40660i	0.710892	+	0.703302i	$0.248292\pi$
$23$			6.74583i			1.40660i	−0.710892	+	0.703302i	$0.751708\pi$
$24$	1.90808			0.389486
$25$	4.90542	+	0.967898i	0.981085	+	0.193580i
$26$			8.83741i			1.73316i
$27$	1.00000			0.192450
$28$	0.610559	−	2.23195i	0.115385	−	0.421800i
$29$		−	0.101717i		−	0.0188884i	−0.999955	−	0.00944422i	$-0.996994\pi$
$29$		−	0.101717i		−	0.0188884i	0.999955	−	0.00944422i	$-0.00300623\pi$
$30$	3.77320	+	0.368694i	0.688889	+	0.0673140i
$31$			6.52719i			1.17232i	0.810196	+	0.586159i	$0.199360\pi$
$31$			6.52719i			1.17232i	−0.810196	+	0.586159i	$0.800640\pi$
$32$	4.63448			0.819268
$33$	3.25064	+	0.658292i	0.565864	+	0.114594i
$34$			5.21579i			0.894501i
$35$	−2.10857	+	5.52756i	−0.356413	+	0.934329i
$36$	0.874594			0.145766
$37$		−	10.8576i		−	1.78498i	−0.451063	−	0.892492i	$-0.648955\pi$
$37$		−	10.8576i		−	1.78498i	0.451063	−	0.892492i	$-0.351045\pi$
$38$	7.24390			1.17512
$39$		−	5.21239i		−	0.834650i
$40$	−4.24638	−	0.414931i	−0.671412	−	0.0656063i
$41$	10.0082			1.56302			0.781509	−	0.623894i	$-0.214450\pi$
$41$	10.0082			1.56302			0.781509	+	0.623894i	$0.214450\pi$
$42$	−1.18361	+	4.32680i	−0.182635	+	0.667640i
$43$	−6.80409			−1.03761			−0.518807	−	0.854892i	$-0.673624\pi$
$43$	−6.80409			−1.03761			−0.518807	+	0.854892i	$0.673624\pi$
$44$	2.84299	+	0.575738i	0.428597	+	0.0867958i
$45$	−2.22547	−	0.217459i	−0.331753	−	0.0324169i
$46$		−	11.4373i		−	1.68634i
$47$	−6.68431			−0.975007			−0.487504	−	0.873121i	$-0.662092\pi$
$47$	−6.68431			−0.975007			−0.487504	+	0.873121i	$0.662092\pi$
$48$	−4.98427			−0.719418
$49$	−6.02530	−	3.56312i	−0.860757	−	0.509016i
$50$	−8.31696	−	1.64103i	−1.17620	−	0.232077i
$51$		−	3.07632i		−	0.430771i
$52$		−	4.55872i		−	0.632181i
$53$		−	2.30571i		−	0.316714i	−0.987382	−	0.158357i	$-0.949380\pi$
$53$		−	2.30571i		−	0.316714i	0.987382	−	0.158357i	$-0.0506197\pi$
$54$	−1.69546			−0.230723
$55$	−7.09104	−	2.17189i	−0.956156	−	0.292858i
$56$	1.33204	−	4.86941i	0.178002	−	0.650702i
$57$	−4.27252			−0.565909
$58$			0.172458i			0.0226448i
$59$		−	7.18644i		−	0.935595i	−0.883836	−	0.467797i	$-0.845048\pi$
$59$		−	7.18644i		−	0.935595i	0.883836	−	0.467797i	$-0.154952\pi$
$60$	−1.94638	−	0.190189i	−0.251277	−	0.0245532i
$61$	−4.40985			−0.564623			−0.282312	−	0.959323i	$-0.591101\pi$
$61$	−4.40985			−0.564623			−0.282312	+	0.959323i	$0.591101\pi$
$62$		−	11.0666i		−	1.40546i
$63$	0.698105	−	2.55199i	0.0879530	−	0.321520i
$64$	2.11096			0.263870
$65$	−1.13348	+	11.6000i	−0.140591	+	1.43880i
$66$	−5.51134	−	1.11611i	−0.678399	−	0.137384i
$67$		−	4.25941i		−	0.520370i	−0.965559	−	0.260185i	$-0.916216\pi$
$67$		−	4.25941i		−	0.520370i	0.965559	−	0.260185i	$-0.0837835\pi$
$68$		−	2.69053i		−	0.326275i
$69$			6.74583i			0.812103i
$70$	3.57499	−	9.37178i	0.427294	−	1.12014i
$71$	−5.83327			−0.692282			−0.346141	−	0.938182i	$-0.612508\pi$
$71$	−5.83327			−0.692282			−0.346141	+	0.938182i	$0.612508\pi$
$72$	1.90808			0.224870
$73$		−	8.09569i		−	0.947529i	−0.880652	−	0.473764i	$-0.842895\pi$
$73$		−	8.09569i		−	0.947529i	0.880652	−	0.473764i	$-0.157105\pi$
$74$			18.4087i			2.13997i
$75$	4.90542	+	0.967898i	0.566429	+	0.111763i
$76$	−3.73672			−0.428631
$77$	3.94924	−	7.83604i	0.450058	−	0.892999i
$78$			8.83741i			1.00064i
$79$		−	14.2003i		−	1.59766i	−0.601555	−	0.798831i	$-0.705452\pi$
$79$		−	14.2003i		−	1.59766i	0.601555	−	0.798831i	$-0.294548\pi$
$80$	11.0923	+	1.08388i	1.24016	+	0.121181i
$81$	1.00000			0.111111
$82$	−16.9685			−1.87386
$83$			7.09509i			0.778787i	0.921071	+	0.389394i	$0.127315\pi$
$83$			7.09509i			0.778787i	−0.921071	+	0.389394i	$0.872685\pi$
$84$	0.610559	−	2.23195i	0.0666174	−	0.243526i
$85$	−0.668975	+	6.84626i	−0.0725605	+	0.742581i
$86$	11.5361			1.24397
$87$		−	0.101717i		−	0.0109052i
$88$	6.20249	+	1.25608i	0.661188	+	0.133898i
$89$		−	16.3777i		−	1.73604i	−0.496533	−	0.868018i	$-0.665394\pi$
$89$		−	16.3777i		−	1.73604i	0.496533	−	0.868018i	$-0.334606\pi$
$90$	3.77320	+	0.368694i	0.397730	+	0.0388638i
$91$	−13.3020	−	3.63880i	−1.39442	−	0.381450i
$92$			5.89986i			0.615103i
$93$			6.52719i			0.676838i
$94$	11.3330			1.16891
$95$	9.50836	+	0.929100i	0.975538	+	0.0953236i
$96$	4.63448			0.473005
$97$	2.98755			0.303340			0.151670	−	0.988431i	$-0.451535\pi$
$97$	2.98755			0.303340			0.151670	+	0.988431i	$0.451535\pi$
$98$	10.2157	+	6.04113i	1.03194	+	0.610246i
$99$	3.25064	+	0.658292i	0.326701	+	0.0661608i
$100$	4.29025	+	0.846517i	0.429025	+	0.0846517i
$101$	−15.2038			−1.51283			−0.756415	−	0.654092i	$-0.773051\pi$
$101$	−15.2038			−1.51283			−0.756415	+	0.654092i	$0.773051\pi$
$102$			5.21579i			0.516440i
$103$	3.93640			0.387865			0.193933	−	0.981015i	$-0.437876\pi$
$103$	3.93640			0.387865			0.193933	+	0.981015i	$0.437876\pi$
$104$		−	9.94568i		−	0.975254i
$105$	−2.10857	+	5.52756i	−0.205775	+	0.539435i
$106$			3.90925i			0.379700i
$107$	−7.59473			−0.734210			−0.367105	−	0.930179i	$-0.619651\pi$
$107$	−7.59473			−0.734210			−0.367105	+	0.930179i	$0.619651\pi$
$108$	0.874594			0.0841578
$109$			8.59953i			0.823686i	0.911255	+	0.411843i	$0.135115\pi$
$109$			8.59953i			0.823686i	−0.911255	+	0.411843i	$0.864885\pi$
$110$	12.0226	+	3.68236i	1.14631	+	0.351099i
$111$		−	10.8576i		−	1.03056i
$112$	−3.47955	+	12.7198i	−0.328786	+	1.20191i
$113$			14.1076i			1.32713i	0.748119	+	0.663565i	$0.230957\pi$
$113$			14.1076i			1.32713i	−0.748119	+	0.663565i	$0.769043\pi$
$114$	7.24390			0.678454
$115$	1.46694	−	15.0126i	0.136793	−	1.39994i
$116$		−	0.0889614i		−	0.00825986i
$117$		−	5.21239i		−	0.481886i
$118$			12.1843i			1.12166i
$119$	−7.85074	−	2.14760i	−0.719676	−	0.196870i
$120$	−4.24638	−	0.414931i	−0.387640	−	0.0378778i
$121$	10.1333	+	4.27974i	0.921209	+	0.389067i
$122$	7.47674			0.676912
$123$	10.0082			0.902409
$124$			5.70864i			0.512651i
$125$	−10.7064	−	3.22076i	−0.957608	−	0.288073i
$126$	−1.18361	+	4.32680i	−0.105445	+	0.385462i
$127$	−10.3710			−0.920282			−0.460141	−	0.887846i	$-0.652201\pi$
$127$	−10.3710			−0.920282			−0.460141	+	0.887846i	$0.652201\pi$
$128$	−12.8480			−1.13561
$129$	−6.80409			−0.599066
$130$	1.92178	−	19.6674i	0.168551	−	1.72494i
$131$	−8.42169			−0.735806			−0.367903	−	0.929864i	$-0.619924\pi$
$131$	−8.42169			−0.735806			−0.367903	+	0.929864i	$0.619924\pi$
$132$	2.84299	+	0.575738i	0.247450	+	0.0501116i
$133$	−2.98267	+	10.9034i	−0.258630	+	0.945447i
$134$			7.22167i			0.623857i
$135$	−2.22547	−	0.217459i	−0.191538	−	0.0187159i
$136$		−	5.86988i		−	0.503338i
$137$		−	8.59604i		−	0.734409i	−0.930140	−	0.367205i	$-0.880315\pi$
$137$		−	8.59604i		−	0.734409i	0.930140	−	0.367205i	$-0.119685\pi$
$138$		−	11.4373i		−	0.973608i
$139$	5.01950			0.425748			0.212874	−	0.977080i	$-0.431718\pi$
$139$	5.01950			0.425748			0.212874	+	0.977080i	$0.431718\pi$
$140$	−1.84414	+	4.83437i	−0.155858	+	0.408579i
$141$	−6.68431			−0.562921
$142$	9.89010			0.829959
$143$	3.43127	−	16.9436i	0.286938	−	1.41689i
$144$	−4.98427			−0.415356
$145$	−0.0221194	+	0.226369i	−0.00183692	+	0.0187989i
$146$			13.7259i			1.13597i
$147$	−6.02530	−	3.56312i	−0.496958	−	0.293881i
$148$		−	9.49602i		−	0.780568i
$149$		−	1.83577i		−	0.150392i	−0.997169	−	0.0751961i	$-0.976042\pi$
$149$		−	1.83577i		−	0.150392i	0.997169	−	0.0751961i	$-0.0239583\pi$
$150$	−8.31696	−	1.64103i	−0.679077	−	0.133990i
$151$		−	18.2332i		−	1.48380i	−0.670510	−	0.741900i	$-0.733925\pi$
$151$		−	18.2332i		−	1.48380i	0.670510	−	0.741900i	$-0.266075\pi$
$152$	−8.15233			−0.661241
$153$		−	3.07632i		−	0.248706i
$154$	−6.69579	+	13.2857i	−0.539562	+	1.07059i
$155$	1.41940	−	14.5260i	0.114009	−	1.16676i
$156$		−	4.55872i		−	0.364990i
$157$	−0.249225			−0.0198903			−0.00994516	−	0.999951i	$-0.503166\pi$
$157$	−0.249225			−0.0198903			−0.00994516	+	0.999951i	$0.503166\pi$
$158$			24.0761i			1.91539i
$159$		−	2.30571i		−	0.182855i
$160$	−10.3139	−	1.00781i	−0.815385	−	0.0796745i
$161$	17.2153	+	4.70930i	1.35675	+	0.371145i
$162$	−1.69546			−0.133208
$163$			6.38148i			0.499836i	0.968267	+	0.249918i	$0.0804037\pi$
$163$			6.38148i			0.499836i	−0.968267	+	0.249918i	$0.919596\pi$
$164$	8.75311			0.683503
$165$	−7.09104	−	2.17189i	−0.552037	−	0.169081i
$166$		−	12.0295i		−	0.933667i
$167$			1.85241i			0.143344i	0.997428	+	0.0716721i	$0.0228335\pi$
$167$			1.85241i			0.143344i	−0.997428	+	0.0716721i	$0.977166\pi$
$168$	1.33204	−	4.86941i	0.102769	−	0.375683i
$169$	−14.1690			−1.08992
$170$	1.13422	−	11.6076i	0.0869909	−	0.890261i
$171$	−4.27252			−0.326728
$172$	−5.95081			−0.453745
$173$		−	1.63810i		−	0.124542i	−0.998059	−	0.0622712i	$-0.980166\pi$
$173$		−	1.63810i		−	0.124542i	0.998059	−	0.0622712i	$-0.0198344\pi$
$174$			0.172458i			0.0130740i
$175$	5.89457	−	11.8429i	0.445587	−	0.895238i
$176$	−16.2021	−	3.28111i	−1.22128	−	0.247323i
$177$		−	7.18644i		−	0.540166i
$178$			27.7678i			2.08129i
$179$	10.9148			0.815812			0.407906	−	0.913024i	$-0.366259\pi$
$179$	10.9148			0.815812			0.407906	+	0.913024i	$0.366259\pi$
$180$	−1.94638	−	0.190189i	−0.145075	−	0.0141758i
$181$		−	22.8005i		−	1.69475i	−0.530997	−	0.847374i	$-0.678183\pi$
$181$		−	22.8005i		−	1.69475i	0.530997	−	0.847374i	$-0.321817\pi$
$182$	22.5530	+	6.16944i	1.67174	+	0.457310i
$183$	−4.40985			−0.325985
$184$			12.8716i			0.948908i
$185$	−2.36109	+	24.1633i	−0.173591	+	1.77652i
$186$		−	11.0666i		−	0.811443i
$187$	2.02512	−	10.0000i	0.148091	−	0.731273i
$188$	−5.84606			−0.426368
$189$	0.698105	−	2.55199i	0.0507797	−	0.185630i
$190$	−16.1211	−	1.57525i	−1.16955	−	0.114281i
$191$	12.7993			0.926128			0.463064	−	0.886325i	$-0.346750\pi$
$191$	12.7993			0.926128			0.463064	+	0.886325i	$0.346750\pi$
$192$	2.11096			0.152345
$193$	15.2983			1.10120			0.550598	−	0.834770i	$-0.314400\pi$
$193$	15.2983			1.10120			0.550598	+	0.834770i	$0.314400\pi$
$194$	−5.06528			−0.363666
$195$	−1.13348	+	11.6000i	−0.0811704	+	0.830694i
$196$	−5.26969	−	3.11628i	−0.376406	−	0.222591i
$197$	−11.7636			−0.838119			−0.419060	−	0.907959i	$-0.637640\pi$
$197$	−11.7636			−0.838119			−0.419060	+	0.907959i	$0.637640\pi$
$198$	−5.51134	−	1.11611i	−0.391674	−	0.0793185i
$199$			1.92230i			0.136268i	0.997676	+	0.0681342i	$0.0217046\pi$
$199$			1.92230i			0.136268i	−0.997676	+	0.0681342i	$0.978295\pi$
$200$	9.35996	+	1.84683i	0.661849	+	0.130591i
$201$		−	4.25941i		−	0.300436i
$202$	25.7774			1.81369
$203$	−0.259582	−	0.0710095i	−0.0182191	−	0.00498389i
$204$		−	2.69053i		−	0.188375i
$205$	−22.2729	−	2.17638i	−1.55561	−	0.152005i
$206$	−6.67402			−0.465001
$207$			6.74583i			0.468868i
$208$			25.9800i			1.80139i
$209$	−13.8884	−	2.81257i	−0.960682	−	0.194549i
$210$	3.57499	−	9.37178i	0.246698	−	0.646714i
$211$		−	23.2254i		−	1.59890i	−0.600733	−	0.799450i	$-0.705124\pi$
$211$		−	23.2254i		−	1.59890i	0.600733	−	0.799450i	$-0.294876\pi$
$212$		−	2.01656i		−	0.138498i
$213$	−5.83327			−0.399689
$214$	12.8766			0.880225
$215$	15.1423	+	1.47961i	1.03270	+	0.100909i
$216$	1.90808			0.129829
$217$	16.6573	+	4.55666i	1.13077	+	0.309327i
$218$		−	14.5802i		−	0.987495i
$219$		−	8.09569i		−	0.547056i
$220$	−6.20178	−	1.89952i	−0.418124	−	0.128066i
$221$	−16.0350			−1.07863
$222$			18.4087i			1.23551i
$223$	−1.61335			−0.108038			−0.0540188	−	0.998540i	$-0.517203\pi$
$223$	−1.61335			−0.108038			−0.0540188	+	0.998540i	$0.517203\pi$
$224$	3.23536	−	11.8271i	0.216171	−	0.790234i
$225$	4.90542	+	0.967898i	0.327028	+	0.0645265i
$226$		−	23.9189i		−	1.59106i
$227$			21.2348i			1.40940i	0.709505	+	0.704700i	$0.248919\pi$
$227$			21.2348i			1.40940i	−0.709505	+	0.704700i	$0.751081\pi$
$228$	−3.73672			−0.247470
$229$			25.4110i			1.67921i	0.543201	+	0.839603i	$0.317212\pi$
$229$			25.4110i			1.67921i	−0.543201	+	0.839603i	$0.682788\pi$
$230$	−2.48715	+	25.4534i	−0.163998	+	1.67835i
$231$	3.94924	−	7.83604i	0.259841	−	0.515573i
$232$		−	0.194085i		−	0.0127423i
$233$	−1.12193			−0.0735002			−0.0367501	−	0.999324i	$-0.511701\pi$
$233$	−1.12193			−0.0735002			−0.0367501	+	0.999324i	$0.511701\pi$
$234$			8.83741i			0.577720i
$235$	14.8757	+	1.45357i	0.970386	+	0.0948202i
$236$		−	6.28521i		−	0.409133i
$237$		−	14.2003i		−	0.922411i
$238$	13.3106	+	3.64117i	0.862801	+	0.236022i
$239$			11.8362i			0.765617i	0.923828	+	0.382809i	$0.125043\pi$
$239$			11.8362i			0.765617i	−0.923828	+	0.382809i	$0.874957\pi$
$240$	11.0923	+	1.08388i	0.716008	+	0.0699639i
$241$	13.8181			0.890101			0.445051	−	0.895505i	$-0.353186\pi$
$241$	13.8181			0.890101			0.445051	+	0.895505i	$0.353186\pi$
$242$	−17.1806	−	7.25614i	−1.10441	−	0.466442i
$243$	1.00000			0.0641500
$244$	−3.85683			−0.246908
$245$	12.6343	+	9.23986i	0.807174	+	0.590313i
$246$	−16.9685			−1.08187
$247$			22.2700i			1.41701i
$248$			12.4544i			0.790857i
$249$			7.09509i			0.449633i
$250$	18.1523	+	5.46067i	1.14805	+	0.345363i
$251$			19.1296i			1.20745i	0.797192	+	0.603726i	$0.206318\pi$
$251$			19.1296i			1.20745i	−0.797192	+	0.603726i	$0.793682\pi$
$252$	0.610559	−	2.23195i	0.0384616	−	0.140600i
$253$	−4.44073	+	21.9283i	−0.279186	+	1.37862i
$254$	17.5837			1.10330
$255$	−0.668975	+	6.84626i	−0.0418928	+	0.428729i
$256$	17.5614			1.09759
$257$	9.95694			0.621097			0.310549	−	0.950558i	$-0.399487\pi$
$257$	9.95694			0.621097			0.310549	+	0.950558i	$0.399487\pi$
$258$	11.5361			0.718205
$259$	−27.7086	−	7.57978i	−1.72173	−	0.470984i
$260$	−0.991337	+	10.1453i	−0.0614801	+	0.629185i
$261$		−	0.101717i		−	0.00629615i
$262$	14.2787			0.882138
$263$	5.34712			0.329718			0.164859	−	0.986317i	$-0.447283\pi$
$263$	5.34712			0.329718			0.164859	+	0.986317i	$0.447283\pi$
$264$	6.20249	+	1.25608i	0.381737	+	0.0773062i
$265$	−0.501399	+	5.13130i	−0.0308007	+	0.315213i
$266$	5.05701	−	18.4864i	0.310065	−	1.13347i
$267$		−	16.3777i		−	1.00230i
$268$		−	3.72525i		−	0.227556i
$269$		−	18.3005i		−	1.11580i	−0.829908	−	0.557900i	$-0.811607\pi$
$269$		−	18.3005i		−	1.11580i	0.829908	−	0.557900i	$-0.188393\pi$
$270$	3.77320	+	0.368694i	0.229630	+	0.0224380i
$271$	−28.7953			−1.74919			−0.874594	−	0.484856i	$-0.838872\pi$
$271$	−28.7953			−1.74919			−0.874594	+	0.484856i	$0.838872\pi$
$272$			15.3332i			0.929714i
$273$	−13.3020	−	3.63880i	−0.805071	−	0.220230i
$274$			14.5743i			0.880464i
$275$	15.3086	+	6.37549i	0.923143	+	0.384456i
$276$			5.89986i			0.355130i
$277$	17.5422			1.05401			0.527005	−	0.849862i	$-0.323315\pi$
$277$	17.5422			1.05401			0.527005	+	0.849862i	$0.323315\pi$
$278$	−8.51037			−0.510418
$279$			6.52719i			0.390772i
$280$	−4.02332	+	10.5471i	−0.240439	+	0.630307i
$281$			12.3263i			0.735324i	0.929960	+	0.367662i	$0.119842\pi$
$281$			12.3263i			0.735324i	−0.929960	+	0.367662i	$0.880158\pi$
$282$	11.3330			0.674870
$283$			6.91029i			0.410774i	0.978681	+	0.205387i	$0.0658453\pi$
$283$			6.91029i			0.410774i	−0.978681	+	0.205387i	$0.934155\pi$
$284$	−5.10175			−0.302733
$285$	9.50836	+	0.929100i	0.563227	+	0.0550351i
$286$	−5.81760	+	28.7272i	−0.344002	+	1.69868i
$287$	6.98678	−	25.5408i	0.412416	−	1.50763i
$288$	4.63448			0.273089
$289$	7.53624			0.443308
$290$	0.0375026	−	0.383800i	0.00220223	−	0.0225375i
$291$	2.98755			0.175133
$292$		−	7.08044i		−	0.414351i
$293$		−	24.3494i		−	1.42250i	−0.702937	−	0.711252i	$-0.748128\pi$
$293$		−	24.3494i		−	1.42250i	0.702937	−	0.711252i	$-0.251872\pi$
$294$	10.2157	+	6.04113i	0.595790	+	0.352326i
$295$	−1.56276	+	15.9932i	−0.0909873	+	0.931160i
$296$		−	20.7173i		−	1.20417i
$297$	3.25064	+	0.658292i	0.188621	+	0.0381980i
$298$			3.11248i			0.180301i
$299$	35.1619			2.03347
$300$	4.29025	+	0.846517i	0.247698	+	0.0488737i
$301$	−4.74997	+	17.3640i	−0.273784	+	1.00084i
$302$			30.9138i			1.77889i
$303$	−15.2038			−0.873433
$304$	21.2954			1.22138
$305$	9.81398	+	0.958963i	0.561947	+	0.0549100i
$306$			5.21579i			0.298167i
$307$			12.5546i			0.716528i	0.933620	+	0.358264i	$0.116631\pi$
$307$			12.5546i			0.716528i	−0.933620	+	0.358264i	$0.883369\pi$
$308$	3.45398	−	6.85335i	0.196809	−	0.390506i
$309$	3.93640			0.223934
$310$	−2.40654	+	24.6284i	−0.136682	+	1.39880i
$311$		−	2.57715i		−	0.146137i	−0.997327	−	0.0730683i	$-0.976721\pi$
$311$		−	2.57715i		−	0.146137i	0.997327	−	0.0730683i	$-0.0232791\pi$
$312$		−	9.94568i		−	0.563063i
$313$	13.1184			0.741494			0.370747	−	0.928734i	$-0.379102\pi$
$313$	13.1184			0.741494			0.370747	+	0.928734i	$0.379102\pi$
$314$	0.422552			0.0238460
$315$	−2.10857	+	5.52756i	−0.118804	+	0.311443i
$316$		−	12.4195i		−	0.698653i
$317$		−	12.8246i		−	0.720304i	−0.932894	−	0.360152i	$-0.882725\pi$
$317$		−	12.8246i		−	0.720304i	0.932894	−	0.360152i	$-0.117275\pi$
$318$			3.90925i			0.219220i
$319$	0.0669597	−	0.330646i	0.00374903	−	0.0185126i
$320$	−4.69787	−	0.459047i	−0.262619	−	0.0256615i
$321$	−7.59473			−0.423896
$322$	−29.1879	−	7.98445i	−1.62658	−	0.444956i
$323$			13.1437i			0.731333i
$324$	0.874594			0.0485885
$325$	5.04506	−	25.5690i	0.279850	−	1.41831i
$326$		−	10.8196i		−	0.599240i
$327$			8.59953i			0.475555i
$328$	19.0965			1.05443
$329$	−4.66635	+	17.0583i	−0.257264	+	0.940454i
$330$	12.0226	+	3.68236i	0.661822	+	0.202707i
$331$	−5.60078			−0.307847			−0.153923	−	0.988083i	$-0.549191\pi$
$331$	−5.60078			−0.307847			−0.153923	+	0.988083i	$0.549191\pi$
$332$			6.20532i			0.340561i
$333$		−	10.8576i		−	0.594995i
$334$		−	3.14070i		−	0.171851i
$335$	−0.926248	+	9.47918i	−0.0506063	+	0.517903i
$336$	−3.47955	+	12.7198i	−0.189825	+	0.693923i
$337$	−12.6126			−0.687050			−0.343525	−	0.939144i	$-0.611621\pi$
$337$	−12.6126			−0.687050			−0.343525	+	0.939144i	$0.611621\pi$
$338$	24.0230			1.30668
$339$			14.1076i			0.766219i
$340$	−0.585081	+	5.98770i	−0.0317305	+	0.324728i
$341$	−4.29679	+	21.2175i	−0.232684	+	1.14899i
$342$	7.24390			0.391705
$343$	−13.2993	+	12.8891i	−0.718096	+	0.695944i
$344$	−12.9828			−0.699984
$345$	1.46694	−	15.0126i	0.0789776	−	0.808253i
$346$			2.77733i			0.149310i
$347$	2.35408			0.126374			0.0631869	−	0.998002i	$-0.479874\pi$
$347$	2.35408			0.126374			0.0631869	+	0.998002i	$0.479874\pi$
$348$		−	0.0889614i		−	0.00476883i
$349$	24.6723			1.32068			0.660338	−	0.750969i	$-0.270413\pi$
$349$	24.6723			1.32068			0.660338	+	0.750969i	$0.270413\pi$
$350$	−9.99402	+	20.0792i	−0.534203	+	1.07328i
$351$		−	5.21239i		−	0.278217i
$352$	15.0650	+	3.05084i	0.802968	+	0.162610i
$353$	−31.0238			−1.65123			−0.825615	−	0.564233i	$-0.809172\pi$
$353$	−31.0238			−1.65123			−0.825615	+	0.564233i	$0.809172\pi$
$354$			12.1843i			0.647590i
$355$	12.9818	+	1.26850i	0.689001	+	0.0673250i
$356$		−	14.3239i		−	0.759163i
$357$	−7.85074	−	2.14760i	−0.415505	−	0.113663i
$358$	−18.5057			−0.978055
$359$			28.0789i			1.48195i	0.671534	+	0.740974i	$0.265636\pi$
$359$			28.0789i			1.48195i	−0.671534	+	0.740974i	$0.734364\pi$
$360$	−4.24638	−	0.414931i	−0.223804	−	0.0218688i
$361$	−0.745557			−0.0392398
$362$			38.6574i			2.03179i
$363$	10.1333	+	4.27974i	0.531860	+	0.224628i
$364$	−11.6338	−	3.18247i	−0.609777	−	0.166807i
$365$	−1.76048	+	18.0167i	−0.0921479	+	0.943037i
$366$	7.47674			0.390815
$367$	−17.9322			−0.936055			−0.468027	−	0.883714i	$-0.655035\pi$
$367$	−17.9322			−0.936055			−0.468027	+	0.883714i	$0.655035\pi$
$368$		−	33.6231i		−	1.75272i
$369$	10.0082			0.521006
$370$	4.00315	−	40.9680i	0.208114	−	2.12983i
$371$	−5.88416	−	1.60963i	−0.305490	−	0.0835679i
$372$			5.70864i			0.295979i
$373$	7.85662			0.406800			0.203400	−	0.979096i	$-0.434801\pi$
$373$	7.85662			0.406800			0.203400	+	0.979096i	$0.434801\pi$
$374$	−3.43351	+	16.9547i	−0.177543	+	0.876704i
$375$	−10.7064	−	3.22076i	−0.552875	−	0.166319i
$376$	−12.7542			−0.657749
$377$	−0.530190			−0.0273062
$378$	−1.18361	+	4.32680i	−0.0608784	+	0.222547i
$379$	0.747352			0.0383889			0.0191944	−	0.999816i	$-0.493890\pi$
$379$	0.747352			0.0383889			0.0191944	+	0.999816i	$0.493890\pi$
$380$	8.31596	+	0.812585i	0.426600	+	0.0416847i
$381$	−10.3710			−0.531325
$382$	−21.7008			−1.11031
$383$	17.0599			0.871718			0.435859	−	0.900015i	$-0.356445\pi$
$383$	17.0599			0.871718			0.435859	+	0.900015i	$0.356445\pi$
$384$	−12.8480			−0.655647
$385$	−10.4929	+	16.5801i	−0.534770	+	0.844998i
$386$	−25.9377			−1.32019
$387$	−6.80409			−0.345871
$388$	2.61289			0.132650
$389$	−18.0537			−0.915360			−0.457680	−	0.889117i	$-0.651319\pi$
$389$	−18.0537			−0.915360			−0.457680	+	0.889117i	$0.651319\pi$
$390$	1.92178	−	19.6674i	0.0973130	−	0.995897i
$391$	20.7524			1.04949
$392$	−11.4968	−	6.79872i	−0.580675	−	0.343387i
$393$	−8.42169			−0.424818
$394$	19.9447			1.00480
$395$	−3.08799	+	31.6024i	−0.155374	+	1.59009i
$396$	2.84299	+	0.575738i	0.142866	+	0.0289319i
$397$	11.1730			0.560756			0.280378	−	0.959890i	$-0.409540\pi$
$397$	11.1730			0.560756			0.280378	+	0.959890i	$0.409540\pi$
$398$		−	3.25919i		−	0.163369i
$399$	−2.98267	+	10.9034i	−0.149320	+	0.545854i
$400$	−24.4500	−	4.82427i	−1.22250	−	0.241213i
$401$	27.2031			1.35846			0.679228	−	0.733927i	$-0.262315\pi$
$401$	27.2031			1.35846			0.679228	+	0.733927i	$0.262315\pi$
$402$			7.22167i			0.360184i
$403$	34.0222			1.69477
$404$	−13.2971			−0.661556
$405$	−2.22547	−	0.217459i	−0.110584	−	0.0108056i
$406$	0.440111	+	0.120394i	0.0218423	+	0.00597505i
$407$	7.14750	−	35.2943i	0.354288	−	1.74947i
$408$		−	5.86988i		−	0.290603i
$409$	17.4674			0.863705			0.431853	−	0.901944i	$-0.357860\pi$
$409$	17.4674			0.863705			0.431853	+	0.901944i	$0.357860\pi$
$410$	37.7629	+	3.68996i	1.86498	+	0.182234i
$411$		−	8.59604i		−	0.424011i
$412$	3.44275			0.169612
$413$	−18.3397	−	5.01689i	−0.902438	−	0.246865i
$414$		−	11.4373i		−	0.562113i
$415$	1.54289	−	15.7899i	0.0757376	−	0.775096i
$416$		−	24.1567i		−	1.18438i
$417$	5.01950			0.245806
$418$	23.5473	+	4.76860i	1.15174	+	0.233240i
$419$		−	16.3087i		−	0.796734i	−0.917226	−	0.398367i	$-0.869577\pi$
$419$		−	16.3087i		−	0.796734i	0.917226	−	0.398367i	$-0.130423\pi$
$420$	−1.84414	+	4.83437i	−0.0899848	+	0.235893i
$421$	22.5439			1.09872			0.549361	−	0.835585i	$-0.314871\pi$
$421$	22.5439			1.09872			0.549361	+	0.835585i	$0.314871\pi$
$422$			39.3777i			1.91688i
$423$	−6.68431			−0.325002
$424$		−	4.39950i		−	0.213658i
$425$	2.97757	−	15.0907i	0.144433	−	0.732005i
$426$	9.89010			0.479177
$427$	−3.07854	+	11.2539i	−0.148981	+	0.544614i
$428$	−6.64230			−0.321068
$429$	3.43127	−	16.9436i	0.165663	−	0.818044i
$430$	−25.6732	−	2.50863i	−1.23807	−	0.120977i
$431$			2.82593i			0.136120i	0.997681	+	0.0680602i	$0.0216810\pi$
$431$			2.82593i			0.136120i	−0.997681	+	0.0680602i	$0.978319\pi$
$432$	−4.98427			−0.239806
$433$	1.50782			0.0724614			0.0362307	−	0.999343i	$-0.488465\pi$
$433$	1.50782			0.0724614			0.0362307	+	0.999343i	$0.488465\pi$
$434$	−28.2418	−	7.72565i	−1.35565	−	0.370843i
$435$	−0.0221194	+	0.226369i	−0.00106054	+	0.0108536i
$436$			7.52110i			0.360195i
$437$		−	28.8217i		−	1.37873i
$438$			13.7259i			0.655851i
$439$	−3.65823			−0.174598			−0.0872989	−	0.996182i	$-0.527824\pi$
$439$	−3.65823			−0.174598			−0.0872989	+	0.996182i	$0.527824\pi$
$440$	−13.5303	−	4.14415i	−0.645032	−	0.197565i
$441$	−6.02530	−	3.56312i	−0.286919	−	0.169672i
$442$	27.1867			1.29314
$443$		−	33.2175i		−	1.57821i	−0.614258	−	0.789105i	$-0.710545\pi$
$443$		−	33.2175i		−	1.57821i	0.614258	−	0.789105i	$-0.289455\pi$
$444$		−	9.49602i		−	0.450661i
$445$	−3.56149	+	36.4481i	−0.168831	+	1.72781i
$446$	2.73537			0.129523
$447$		−	1.83577i		−	0.0868289i
$448$	1.47367	−	5.38714i	0.0696244	−	0.254518i
$449$	34.9542			1.64959			0.824794	−	0.565433i	$-0.191291\pi$
$449$	34.9542			1.64959			0.824794	+	0.565433i	$0.191291\pi$
$450$	−8.31696	−	1.64103i	−0.392065	−	0.0773591i
$451$	32.5330	+	6.58832i	1.53192	+	0.310232i
$452$			12.3384i			0.580350i
$453$		−	18.2332i		−	0.856673i
$454$		−	36.0028i		−	1.68969i
$455$	28.8118	+	10.9907i	1.35072	+	0.515250i
$456$	−8.15233			−0.381768
$457$	−35.2276			−1.64788			−0.823939	−	0.566679i	$-0.808228\pi$
$457$	−35.2276			−1.64788			−0.823939	+	0.566679i	$0.808228\pi$
$458$		−	43.0834i		−	2.01315i
$459$		−	3.07632i		−	0.143590i
$460$	1.28298	−	13.1300i	0.0598193	−	0.612188i
$461$	25.1307			1.17045			0.585226	−	0.810870i	$-0.301006\pi$
$461$	25.1307			1.17045			0.585226	+	0.810870i	$0.301006\pi$
$462$	−6.69579	+	13.2857i	−0.311517	+	0.618107i
$463$			7.59548i			0.352992i	0.984301	+	0.176496i	$0.0564763\pi$
$463$			7.59548i			0.352992i	−0.984301	+	0.176496i	$0.943524\pi$
$464$			0.506987i			0.0235363i
$465$	1.41940	−	14.5260i	0.0658230	−	0.673629i
$466$	1.90219			0.0881174
$467$	−31.8136			−1.47216			−0.736078	−	0.676896i	$-0.763325\pi$
$467$	−31.8136			−1.47216			−0.736078	+	0.676896i	$0.763325\pi$
$468$		−	4.55872i		−	0.210727i
$469$	−10.8700	−	2.97352i	−0.501928	−	0.137304i
$470$	−25.2212	−	2.46447i	−1.16337	−	0.113677i
$471$	−0.249225			−0.0114837
$472$		−	13.7123i		−	0.631161i
$473$	−22.1176	−	4.47908i	−1.01697	−	0.205948i
$474$			24.0761i			1.10585i
$475$	−20.9585	−	4.13536i	−0.961643	−	0.189744i
$476$	−6.86621	−	1.87828i	−0.314712	−	0.0860906i
$477$		−	2.30571i		−	0.105571i
$478$		−	20.0678i		−	0.917878i
$479$	−16.8777			−0.771162			−0.385581	−	0.922674i	$-0.625999\pi$
$479$	−16.8777			−0.771162			−0.385581	+	0.922674i	$0.625999\pi$
$480$	−10.3139	−	1.00781i	−0.470763	−	0.0460001i
$481$	−56.5942			−2.58047
$482$	−23.4281			−1.06712
$483$	17.2153	+	4.70930i	0.783323	+	0.214281i
$484$	8.86252	+	3.74303i	0.402842	+	0.170138i
$485$	−6.64870	−	0.649670i	−0.301902	−	0.0295000i
$486$	−1.69546			−0.0769078
$487$			5.64916i			0.255988i	0.991775	+	0.127994i	$0.0408538\pi$
$487$			5.64916i			0.255988i	−0.991775	+	0.127994i	$0.959146\pi$
$488$	−8.41436			−0.380900
$489$			6.38148i			0.288581i
$490$	−21.4209	−	15.6658i	−0.967700	−	0.707710i
$491$			1.29270i			0.0583387i	0.999574	+	0.0291694i	$0.00928621\pi$
$491$			1.29270i			0.0583387i	−0.999574	+	0.0291694i	$0.990714\pi$
$492$	8.75311			0.394621
$493$	−0.312915			−0.0140930
$494$		−	37.7580i		−	1.69881i
$495$	−7.09104	−	2.17189i	−0.318719	−	0.0976192i
$496$		−	32.5333i		−	1.46079i
$497$	−4.07224	+	14.8865i	−0.182665	+	0.667749i
$498$		−	12.0295i		−	0.539053i
$499$	41.9429			1.87762			0.938812	−	0.344430i	$-0.111928\pi$
$499$	41.9429			1.87762			0.938812	+	0.344430i	$0.111928\pi$
$500$	−9.36374	−	2.81685i	−0.418759	−	0.125974i
$501$			1.85241i			0.0827598i
$502$		−	32.4336i		−	1.44758i
$503$			1.84866i			0.0824278i	0.999150	+	0.0412139i	$0.0131225\pi$
$503$			1.84866i			0.0824278i	−0.999150	+	0.0412139i	$0.986877\pi$
$504$	1.33204	−	4.86941i	0.0593340	−	0.216901i
$505$	33.8355	+	3.30620i	1.50566	+	0.147124i
$506$	7.52909	−	37.1786i	0.334709	−	1.65279i
$507$	−14.1690			−0.629267
$508$	−9.07046			−0.402436
$509$		−	13.1479i		−	0.582770i	−0.956606	−	0.291385i	$-0.905884\pi$
$509$		−	13.1479i		−	0.582770i	0.956606	−	0.291385i	$-0.0941160\pi$
$510$	1.13422	−	11.6076i	0.0502242	−	0.513992i
$511$	−20.6601	−	5.65164i	−0.913949	−	0.250014i
$512$	−4.07870			−0.180255
$513$	−4.27252			−0.188636
$514$	−16.8816			−0.744617
$515$	−8.76034	−	0.856007i	−0.386027	−	0.0377202i
$516$	−5.95081			−0.261970
$517$	−21.7283	−	4.40023i	−0.955609	−	0.193522i
$518$	46.9789	+	12.8512i	2.06413	+	0.564651i
$519$		−	1.63810i		−	0.0719045i
$520$	−2.16278	+	22.1338i	−0.0948442	+	0.970631i
$521$			32.1405i			1.40810i	0.710150	+	0.704051i	$0.248627\pi$
$521$			32.1405i			1.40810i	−0.710150	+	0.704051i	$0.751373\pi$
$522$			0.172458i			0.00754828i
$523$		−	21.6013i		−	0.944557i	−0.881449	−	0.472279i	$-0.843432\pi$
$523$		−	21.6013i		−	0.944557i	0.881449	−	0.472279i	$-0.156568\pi$
$524$	−7.36556			−0.321766
$525$	5.89457	−	11.8429i	0.257260	−	0.516866i
$526$	−9.06585			−0.395290
$527$	20.0797			0.874687
$528$	−16.2021	−	3.28111i	−0.705105	−	0.142792i
$529$	−22.5062			−0.978532
$530$	0.850103	−	8.69992i	0.0369261	−	0.377900i
$531$		−	7.18644i		−	0.311865i
$532$	−2.60863	+	9.53607i	−0.113098	+	0.413441i
$533$		−	52.1666i		−	2.25959i
$534$			27.7678i			1.20163i
$535$	16.9018	+	1.65154i	0.730730	+	0.0714025i
$536$		−	8.12731i		−	0.351046i
$537$	10.9148			0.471009
$538$			31.0278i			1.33770i
$539$	−17.2405	−	15.5488i	−0.742601	−	0.669734i
$540$	−1.94638	−	0.190189i	−0.0837589	−	0.00818441i
$541$			7.77783i			0.334395i	0.985923	+	0.167197i	$0.0534717\pi$
$541$			7.77783i			0.334395i	−0.985923	+	0.167197i	$0.946528\pi$
$542$	48.8213			2.09705
$543$		−	22.8005i		−	0.978463i
$544$		−	14.2572i		−	0.611271i
$545$	1.87005	−	19.1380i	0.0801041	−	0.819782i
$546$	22.5530	+	6.16944i	0.965178	+	0.264028i
$547$	9.62307			0.411453			0.205726	−	0.978610i	$-0.434044\pi$
$547$	9.62307			0.411453			0.205726	+	0.978610i	$0.434044\pi$
$548$		−	7.51805i		−	0.321155i
$549$	−4.40985			−0.188208
$550$	−25.9552	−	10.8094i	−1.10673	−	0.460914i
$551$			0.434590i			0.0185141i
$552$			12.8716i			0.547852i
$553$	−36.2391	−	9.91333i	−1.54104	−	0.421558i
$554$	−29.7422			−1.26363
$555$	−2.36109	+	24.1633i	−0.100223	+	1.02568i
$556$	4.39002			0.186178
$557$	23.8241			1.00946			0.504729	−	0.863278i	$-0.331593\pi$
$557$	23.8241			1.00946			0.504729	+	0.863278i	$0.331593\pi$
$558$		−	11.0666i		−	0.468487i
$559$			35.4655i			1.50003i
$560$	10.5097	−	27.5509i	0.444115	−	1.16424i
$561$	2.02512	−	10.0000i	0.0855006	−	0.422201i
$562$		−	20.8987i		−	0.881560i
$563$			9.76389i			0.411499i	0.978605	+	0.205749i	$0.0659632\pi$
$563$			9.76389i			0.411499i	−0.978605	+	0.205749i	$0.934037\pi$
$564$	−5.84606			−0.246163
$565$	3.06782	−	31.3960i	0.129064	−	1.32084i
$566$		−	11.7161i		−	0.492466i
$567$	0.698105	−	2.55199i	0.0293177	−	0.107173i
$568$	−11.1304			−0.467020
$569$		−	27.8924i		−	1.16931i	−0.811282	−	0.584655i	$-0.801230\pi$
$569$		−	27.8924i		−	1.16931i	0.811282	−	0.584655i	$-0.198770\pi$
$570$	−16.1211	−	1.57525i	−0.675238	−	0.0659801i
$571$			40.9925i			1.71548i	0.514082	+	0.857741i	$0.328133\pi$
$571$			40.9925i			1.71548i	−0.514082	+	0.857741i	$0.671867\pi$
$572$	3.00097	−	14.8188i	0.125477	−	0.619604i
$573$	12.7993			0.534700
$574$	−11.8458	+	43.3035i	−0.494435	+	1.80745i
$575$	−6.52928	+	33.0912i	−0.272290	+	1.38000i
$576$	2.11096			0.0879565
$577$	36.4994			1.51949			0.759745	−	0.650221i	$-0.225324\pi$
$577$	36.4994			1.51949			0.759745	+	0.650221i	$0.225324\pi$
$578$	−12.7774			−0.531470
$579$	15.2983			0.635776
$580$	−0.0193455	+	0.197981i	−0.000803277	+	0.00822070i
$581$	18.1066	+	4.95312i	0.751188	+	0.205490i
$582$	−5.06528			−0.209963
$583$	1.51783	−	7.49505i	0.0628622	−	0.310413i
$584$		−	15.4473i		−	0.639212i
$585$	−1.13348	+	11.6000i	−0.0468637	+	0.479601i
$586$			41.2834i			1.70540i
$587$	−2.68144			−0.110675			−0.0553375	−	0.998468i	$-0.517623\pi$
$587$	−2.68144			−0.110675			−0.0553375	+	0.998468i	$0.517623\pi$
$588$	−5.26969	−	3.11628i	−0.217318	−	0.128513i
$589$		−	27.8875i		−	1.14909i
$590$	2.64960	−	27.1159i	0.109082	−	1.11634i
$591$	−11.7636			−0.483888
$592$			54.1174i			2.22421i
$593$		−	4.81046i		−	0.197542i	−0.995110	−	0.0987710i	$-0.968509\pi$
$593$		−	4.81046i		−	0.197542i	0.995110	−	0.0987710i	$-0.0314911\pi$
$594$	−5.51134	−	1.11611i	−0.226133	−	0.0457945i
$595$	17.0046	+	6.48663i	0.697119	+	0.265926i
$596$		−	1.60555i		−	0.0657660i
$597$			1.92230i			0.0786747i
$598$	−59.6157			−2.43787
$599$	−28.4657			−1.16308			−0.581539	−	0.813519i	$-0.697549\pi$
$599$	−28.4657			−1.16308			−0.581539	+	0.813519i	$0.697549\pi$
$600$	9.35996	+	1.84683i	0.382119	+	0.0753965i
$601$	14.8482			0.605672			0.302836	−	0.953043i	$-0.402067\pi$
$601$	14.8482			0.605672			0.302836	+	0.953043i	$0.402067\pi$
$602$	8.05340	−	29.4399i	0.328232	−	1.19988i
$603$		−	4.25941i		−	0.173457i
$604$		−	15.9467i		−	0.648861i
$605$	−21.6207	−	11.7280i	−0.879006	−	0.476811i
$606$	25.7774			1.04713
$607$			17.3804i			0.705450i	0.935727	+	0.352725i	$0.114745\pi$
$607$			17.3804i			0.705450i	−0.935727	+	0.352725i	$0.885255\pi$
$608$	−19.8009			−0.803033
$609$	−0.259582	−	0.0710095i	−0.0105188	−	0.00287745i
$610$	−16.6392	−	1.62589i	−0.673703	−	0.0658302i
$611$			34.8412i			1.40953i
$612$		−	2.69053i		−	0.108758i
$613$	−39.6897			−1.60305			−0.801526	−	0.597960i	$-0.795978\pi$
$613$	−39.6897			−1.60305			−0.801526	+	0.597960i	$0.795978\pi$
$614$		−	21.2858i		−	0.859026i
$615$	−22.2729	−	2.17638i	−0.898131	−	0.0877599i
$616$	7.53549	−	14.9518i	0.303613	−	0.602426i
$617$			20.0629i			0.807703i	0.914825	+	0.403851i	$0.132329\pi$
$617$			20.0629i			0.807703i	−0.914825	+	0.403851i	$0.867671\pi$
$618$	−6.67402			−0.268469
$619$			3.79143i			0.152390i	0.997093	+	0.0761952i	$0.0242772\pi$
$619$			3.79143i			0.152390i	−0.997093	+	0.0761952i	$0.975723\pi$
$620$	1.24140	−	12.7044i	0.0498557	−	0.510221i
$621$			6.74583i			0.270701i
$622$			4.36946i			0.175199i
$623$	−41.7958	−	11.4334i	−1.67451	−	0.458069i
$624$			25.9800i			1.04003i
$625$	23.1263	+	9.49590i	0.925054	+	0.379836i
$626$	−22.2417			−0.888958
$627$	−13.8884	−	2.81257i	−0.554650	−	0.112323i
$628$	−0.217971			−0.00869798
$629$	−33.4016			−1.33181
$630$	3.57499	−	9.37178i	0.142431	−	0.373381i
$631$	−27.9799			−1.11386			−0.556930	−	0.830559i	$-0.688021\pi$
$631$	−27.9799			−1.11386			−0.556930	+	0.830559i	$0.688021\pi$
$632$		−	27.0954i		−	1.07780i
$633$		−	23.2254i		−	0.923125i
$634$			21.7437i			0.863553i
$635$	23.0804	+	2.25528i	0.915920	+	0.0894981i
$636$		−	2.01656i		−	0.0799620i
$637$	−18.5723	+	31.4062i	−0.735863	+	1.24436i
$638$	−0.113528	+	0.560599i	−0.00449461	+	0.0221943i
$639$	−5.83327			−0.230761
$640$	28.5928	+	2.79392i	1.13023	+	0.110439i
$641$	−10.7320			−0.423887			−0.211944	−	0.977282i	$-0.567979\pi$
$641$	−10.7320			−0.423887			−0.211944	+	0.977282i	$0.567979\pi$
$642$	12.8766			0.508198
$643$	30.0170			1.18376			0.591878	−	0.806028i	$-0.298387\pi$
$643$	30.0170			1.18376			0.591878	+	0.806028i	$0.298387\pi$
$644$	15.0564	+	4.11873i	0.593305	+	0.162301i
$645$	15.1423	+	1.47961i	0.596227	+	0.0582597i
$646$		−	22.2846i		−	0.876775i
$647$	36.1461			1.42105			0.710525	−	0.703672i	$-0.248457\pi$
$647$	36.1461			1.42105			0.710525	+	0.703672i	$0.248457\pi$
$648$	1.90808			0.0749566
$649$	4.73077	−	23.3605i	0.185699	−	0.916980i
$650$	−8.55371	+	43.3512i	−0.335504	+	1.70038i
$651$	16.6573	+	4.55666i	0.652851	+	0.178590i
$652$			5.58121i			0.218577i
$653$			36.7293i			1.43733i	0.695357	+	0.718665i	$0.255246\pi$
$653$			36.7293i			1.43733i	−0.695357	+	0.718665i	$0.744754\pi$
$654$		−	14.5802i		−	0.570130i
$655$	18.7422	+	1.83137i	0.732318	+	0.0715577i
$656$	−49.8836			−1.94763
$657$		−	8.09569i		−	0.315843i
$658$	7.91163	−	28.9217i	0.308427	−	1.12749i
$659$		−	14.0230i		−	0.546257i	−0.961978	−	0.273128i	$-0.911942\pi$
$659$		−	14.0230i		−	0.546257i	0.961978	−	0.273128i	$-0.0880584\pi$
$660$	−6.20178	−	1.89952i	−0.241404	−	0.0739388i
$661$		−	23.6065i		−	0.918186i	−0.888388	−	0.459093i	$-0.848174\pi$
$661$		−	23.6065i		−	0.918186i	0.888388	−	0.459093i	$-0.151826\pi$
$662$	9.49591			0.369069
$663$	−16.0350			−0.622747
$664$			13.5380i			0.525377i
$665$	9.00889	−	23.6166i	0.349350	−	0.915814i
$666$			18.4087i			0.713323i
$667$	0.686168			0.0265685
$668$			1.62011i			0.0626840i
$669$	−1.61335			−0.0623756
$670$	1.57042	−	16.0716i	0.0606706	−	0.620900i
$671$	−14.3348	−	2.90297i	−0.553390	−	0.112068i
$672$	3.23536	−	11.8271i	0.124807	−	0.456242i
$673$	30.3169			1.16863			0.584315	−	0.811527i	$-0.301363\pi$
$673$	30.3169			1.16863			0.584315	+	0.811527i	$0.301363\pi$
$674$	21.3841			0.823686
$675$	4.90542	+	0.967898i	0.188810	+	0.0372544i
$676$	−12.3921			−0.476620
$677$		−	20.2672i		−	0.778931i	−0.921041	−	0.389465i	$-0.872660\pi$
$677$		−	20.2672i		−	0.778931i	0.921041	−	0.389465i	$-0.127340\pi$
$678$		−	23.9189i		−	0.918599i
$679$	2.08562	−	7.62419i	0.0800389	−	0.292590i
$680$	−1.27646	+	13.0632i	−0.0489500	+	0.500952i
$681$			21.2348i			0.813718i
$682$	7.28506	−	35.9735i	0.278959	−	1.37750i
$683$			22.7066i			0.868845i	0.900709	+	0.434422i	$0.143048\pi$
$683$			22.7066i			0.868845i	−0.900709	+	0.434422i	$0.856952\pi$
$684$	−3.73672			−0.142877
$685$	−1.86929	+	19.1302i	−0.0714219	+	0.730928i
$686$	22.5485	−	21.8529i	0.860906	−	0.834349i
$687$			25.4110i			0.969490i
$688$	33.9134			1.29294
$689$	−12.0183			−0.457860
$690$	−2.48715	+	25.4534i	−0.0946841	+	0.968993i
$691$			11.0008i			0.418490i	0.977863	+	0.209245i	$0.0671006\pi$
$691$			11.0008i			0.418490i	−0.977863	+	0.209245i	$0.932899\pi$
$692$		−	1.43267i		−	0.0544620i
$693$	3.94924	−	7.83604i	0.150019	−	0.297666i
$694$	−3.99126			−0.151506
$695$	−11.1707	−	1.09154i	−0.423730	−	0.0414043i
$696$		−	0.194085i		−	0.00735678i
$697$		−	30.7884i		−	1.16620i
$698$	−41.8309			−1.58332
$699$	−1.12193			−0.0424353
$700$	5.15535	−	10.3577i	0.194854	−	0.391485i
$701$		−	36.6955i		−	1.38597i	−0.720952	−	0.692985i	$-0.756295\pi$
$701$		−	36.6955i		−	1.38597i	0.720952	−	0.692985i	$-0.243705\pi$
$702$			8.83741i			0.333547i
$703$			46.3895i			1.74961i
$704$	6.86196	+	1.38963i	0.258620	+	0.0523735i
$705$	14.8757	+	1.45357i	0.560252	+	0.0547445i
$706$	52.5997			1.97962
$707$	−10.6138	+	38.7998i	−0.399174	+	1.45922i
$708$		−	6.28521i		−	0.236213i
$709$	46.8048			1.75779			0.878895	−	0.477014i	$-0.158281\pi$
$709$	46.8048			1.75779			0.878895	+	0.477014i	$0.158281\pi$
$710$	−22.0101	−	2.15069i	−0.826025	−	0.0807141i
$711$		−	14.2003i		−	0.532554i
$712$		−	31.2501i		−	1.17115i
$713$	−44.0313			−1.64899
$714$	13.3106	+	3.64117i	0.498138	+	0.136267i
$715$	−11.3207	+	36.9613i	−0.423371	+	1.38227i
$716$	9.54604			0.356752
$717$			11.8362i			0.442029i
$718$		−	47.6067i		−	1.77667i
$719$			7.64661i			0.285170i	0.989783	+	0.142585i	$0.0455415\pi$
$719$			7.64661i			0.285170i	−0.989783	+	0.142585i	$0.954459\pi$
$720$	11.0923	+	1.08388i	0.413387	+	0.0403937i
$721$	2.74802	−	10.0457i	0.102342	−	0.374120i
$722$	1.26406			0.0470436
$723$	13.8181			0.513900
$724$		−	19.9412i		−	0.741108i
$725$	0.0984520	−	0.498967i	0.00365642	−	0.0185312i
$726$	−17.1806	−	7.25614i	−0.637633	−	0.269301i
$727$	−17.9461			−0.665582			−0.332791	−	0.943001i	$-0.607990\pi$
$727$	−17.9461			−0.665582			−0.332791	+	0.943001i	$0.607990\pi$
$728$	−25.3813	−	6.94313i	−0.940692	−	0.257330i
$729$	1.00000			0.0370370
$730$	2.98483	−	30.5466i	0.110474	−	1.13058i
$731$			20.9316i			0.774182i
$732$	−3.85683			−0.142552
$733$			14.6975i			0.542865i	0.962457	+	0.271433i	$0.0874974\pi$
$733$			14.6975i			0.542865i	−0.962457	+	0.271433i	$0.912503\pi$
$734$	30.4034			1.12221
$735$	12.6343	+	9.23986i	0.466022	+	0.340817i
$736$			31.2634i			1.15239i
$737$	2.80394	−	13.8458i	0.103284	−	0.510017i
$738$	−16.9685			−0.624620
$739$		−	36.1709i		−	1.33057i	−0.746590	−	0.665285i	$-0.768310\pi$
$739$		−	36.1709i		−	1.33057i	0.746590	−	0.665285i	$-0.231690\pi$
$740$	−2.06500	+	21.1331i	−0.0759109	+	0.776868i
$741$			22.2700i			0.818111i
$742$	9.97637	+	2.72907i	0.366244	+	0.100187i
$743$	45.5913			1.67258			0.836291	−	0.548286i	$-0.184719\pi$
$743$	45.5913			1.67258			0.836291	+	0.548286i	$0.184719\pi$
$744$			12.4544i			0.456601i
$745$	−0.399205	+	4.08545i	−0.0146257	+	0.149679i
$746$	−13.3206			−0.487702
$747$			7.09509i			0.259596i
$748$	1.77116	−	8.74595i	0.0647599	−	0.319784i
$749$	−5.30192	+	19.3817i	−0.193728	+	0.708191i
$750$	18.1523	+	5.46067i	0.662828	+	0.199396i
$751$	−33.7027			−1.22983			−0.614915	−	0.788594i	$-0.710810\pi$
$751$	−33.7027			−1.22983			−0.614915	+	0.788594i	$0.710810\pi$
$752$	33.3164			1.21493
$753$			19.1296i			0.697123i
$754$	0.898918			0.0327367
$755$	−3.96499	+	40.5775i	−0.144301	+	1.47677i
$756$	0.610559	−	2.23195i	0.0222058	−	0.0811754i
$757$		−	16.2726i		−	0.591436i	−0.955275	−	0.295718i	$-0.904441\pi$
$757$		−	16.2726i		−	0.591436i	0.955275	−	0.295718i	$-0.0955589\pi$
$758$	−1.26711			−0.0460234
$759$	−4.44073	+	21.9283i	−0.161188	+	0.795945i
$760$	18.1428	+	1.77280i	0.658107	+	0.0643062i
$761$	13.2064			0.478733			0.239367	−	0.970929i	$-0.423060\pi$
$761$	13.2064			0.478733			0.239367	+	0.970929i	$0.423060\pi$
$762$	17.5837			0.636991
$763$	21.9459	+	6.00338i	0.794496	+	0.217337i
$764$	11.1942			0.404993
$765$	−0.668975	+	6.84626i	−0.0241868	+	0.247527i
$766$	−28.9244			−1.04508
$767$	−37.4585			−1.35255
$768$	17.5614			0.633693
$769$	−9.25814			−0.333857			−0.166928	−	0.985969i	$-0.553385\pi$
$769$	−9.25814			−0.333857			−0.166928	+	0.985969i	$0.553385\pi$
$770$	17.7904	−	28.1109i	0.641121	−	1.01305i
$771$	9.95694			0.358591
$772$	13.3798			0.481550
$773$	12.1231			0.436038			0.218019	−	0.975944i	$-0.430040\pi$
$773$	12.1231			0.436038			0.218019	+	0.975944i	$0.430040\pi$
$774$	11.5361			0.414656
$775$	−6.31765	+	32.0186i	−0.226937	+	1.15014i
$776$	5.70050			0.204636
$777$	−27.7086	−	7.57978i	−0.994040	−	0.271923i
$778$	30.6094			1.09740
$779$	−42.7602			−1.53204
$780$	−0.991337	+	10.1453i	−0.0354955	+	0.363260i
$781$	−18.9619	−	3.84000i	−0.678509	−	0.137406i
$782$	−35.1848			−1.25821
$783$		−	0.101717i		−	0.00363508i
$784$	30.0317	+	17.7595i	1.07256	+	0.634269i
$785$	0.554642	+	0.0541963i	0.0197960	+	0.00193435i
$786$	14.2787			0.509303
$787$		−	9.15717i		−	0.326418i	−0.986592	−	0.163209i	$-0.947816\pi$
$787$		−	9.15717i		−	0.326418i	0.986592	−	0.163209i	$-0.0521845\pi$
$788$	−10.2883			−0.366507
$789$	5.34712			0.190363
$790$	5.23558	−	53.5807i	0.186274	−	1.90632i
$791$	36.0024	+	9.84858i	1.28010	+	0.350175i
$792$	6.20249	+	1.25608i	0.220396	+	0.0446327i
$793$			22.9858i			0.816251i
$794$	−18.9434			−0.672275
$795$	−0.501399	+	5.13130i	−0.0177828	+	0.181988i
$796$			1.68123i			0.0595898i
$797$	−37.9065			−1.34272			−0.671359	−	0.741133i	$-0.734289\pi$
$797$	−37.9065			−1.34272			−0.671359	+	0.741133i	$0.734289\pi$
$798$	5.05701	−	18.4864i	0.179016	−	0.654410i
$799$			20.5631i			0.727470i
$800$	22.7341	+	4.48570i	0.803771	+	0.158594i
$801$		−	16.3777i		−	0.578679i
$802$	−46.1218			−1.62862
$803$	5.32933	−	26.3162i	0.188068	−	0.928677i
$804$		−	3.72525i		−	0.131380i
$805$	−37.2880	−	14.2240i	−1.31423	−	0.501331i
$806$	−57.6834			−2.03181
$807$		−	18.3005i		−	0.644208i
$808$	−29.0100			−1.02057
$809$		−	14.2322i		−	0.500379i	−0.968197	−	0.250189i	$-0.919507\pi$
$809$		−	14.2322i		−	0.500379i	0.968197	−	0.250189i	$-0.0804929\pi$
$810$	3.77320	+	0.368694i	0.132577	+	0.0129546i
$811$	16.2404			0.570276			0.285138	−	0.958486i	$-0.407961\pi$
$811$	16.2404			0.570276			0.285138	+	0.958486i	$0.407961\pi$
$812$	−0.227028	−	0.0621044i	−0.00796714	−	0.00217944i
$813$	−28.7953			−1.00989
$814$	−12.1183	+	59.8401i	−0.424747	+	2.09739i
$815$	1.38771	−	14.2018i	0.0486095	−	0.497467i
$816$			15.3332i			0.536771i
$817$	29.0706			1.01705
$818$	−29.6153			−1.03547
$819$	−13.3020	−	3.63880i	−0.464808	−	0.127150i
$820$	−19.4798	−	1.90344i	−0.680263	−	0.0664712i
$821$		−	33.9504i		−	1.18488i	−0.805615	−	0.592439i	$-0.798165\pi$
$821$		−	33.9504i		−	1.18488i	0.805615	−	0.592439i	$-0.201835\pi$
$822$			14.5743i			0.508336i
$823$		−	35.6601i		−	1.24303i	−0.783402	−	0.621516i	$-0.786517\pi$
$823$		−	35.6601i		−	1.24303i	0.783402	−	0.621516i	$-0.213483\pi$
$824$	7.51098			0.261658
$825$	15.3086	+	6.37549i	0.532977	+	0.221966i
$826$	31.0943	+	8.50595i	1.08191	+	0.295960i
$827$	33.6366			1.16966			0.584830	−	0.811156i	$-0.301161\pi$
$827$	33.6366			1.16966			0.584830	+	0.811156i	$0.301161\pi$
$828$			5.89986i			0.205034i
$829$			32.2690i			1.12075i	0.828239	+	0.560375i	$0.189343\pi$
$829$			32.2690i			1.12075i	−0.828239	+	0.560375i	$0.810657\pi$
$830$	−2.61592	+	26.7712i	−0.0907998	+	0.929241i
$831$	17.5422			0.608533
$832$		−	11.0031i		−	0.381465i
$833$	−10.9613	+	18.5358i	−0.379786	+	0.642226i
$834$	−8.51037			−0.294690
$835$	0.402825	−	4.12249i	0.0139403	−	0.142665i
$836$	−12.1467	−	2.45985i	−0.420103	−	0.0850758i
$837$			6.52719i			0.225613i
$838$			27.6509i			0.955183i
$839$		−	13.8229i		−	0.477218i	−0.971116	−	0.238609i	$-0.923309\pi$
$839$		−	13.8229i		−	0.477218i	0.971116	−	0.238609i	$-0.0766915\pi$
$840$	−4.02332	+	10.5471i	−0.138818	+	0.363908i
$841$	28.9897			0.999643
$842$	−38.2224			−1.31723
$843$			12.3263i			0.424539i
$844$		−	20.3128i		−	0.699194i
$845$	31.5327	+	3.08118i	1.08476	+	0.105996i
$846$	11.3330			0.389637
$847$	17.9960	−	22.8724i	0.618349	−	0.785904i
$848$			11.4923i			0.394648i
$849$			6.91029i			0.237160i
$850$	−5.04835	+	25.5857i	−0.173157	+	0.877581i
$851$	73.2438			2.51077
$852$	−5.10175			−0.174783
$853$		−	30.0368i		−	1.02844i	−0.857658	−	0.514220i	$-0.828081\pi$
$853$		−	30.0368i		−	1.02844i	0.857658	−	0.514220i	$-0.171919\pi$
$854$	5.21955	−	19.0805i	0.178609	−	0.652923i
$855$	9.50836	+	0.929100i	0.325179	+	0.0317745i
$856$	−14.4914			−0.495305
$857$			5.96899i			0.203897i	0.994790	+	0.101948i	$0.0325077\pi$
$857$			5.96899i			0.203897i	−0.994790	+	0.101948i	$0.967492\pi$
$858$	−5.81760	+	28.7272i	−0.198609	+	0.980731i
$859$			8.60226i			0.293505i	0.989173	+	0.146753i	$0.0468822\pi$
$859$			8.60226i			0.293505i	−0.989173	+	0.146753i	$0.953118\pi$
$860$	13.2433	+	1.29406i	0.451594	+	0.0441271i
$861$	6.98678	−	25.5408i	0.238109	−	0.870428i
$862$		−	4.79126i		−	0.163191i
$863$		−	41.6886i		−	1.41910i	−0.704657	−	0.709548i	$-0.748899\pi$
$863$		−	41.6886i		−	1.41910i	0.704657	−	0.709548i	$-0.251101\pi$
$864$	4.63448			0.157668
$865$	−0.356220	+	3.64554i	−0.0121118	+	0.123952i
$866$	−2.55646			−0.0868721
$867$	7.53624			0.255944
$868$	14.5684	+	3.98523i	0.494483	+	0.135268i
$869$	9.34797	−	46.1602i	0.317108	−	1.56588i
$870$	0.0375026	−	0.383800i	0.00127146	−	0.0130120i
$871$	−22.2017			−0.752276
$872$			16.4086i			0.555666i
$873$	2.98755			0.101113
$874$			48.8661i			1.65292i
$875$	−15.6935	+	25.0742i	−0.530538	+	0.847661i
$876$		−	7.08044i		−	0.239226i
$877$	15.3366			0.517881			0.258940	−	0.965893i	$-0.416627\pi$
$877$	15.3366			0.517881			0.258940	+	0.965893i	$0.416627\pi$
$878$	6.20240			0.209321
$879$		−	24.3494i		−	0.821283i
$880$	35.3437	+	10.8253i	1.19144	+	0.364921i
$881$			0.709323i			0.0238977i	0.999929	+	0.0119488i	$0.00380353\pi$
$881$			0.709323i			0.0238977i	−0.999929	+	0.0119488i	$0.996196\pi$
$882$	10.2157	+	6.04113i	0.343979	+	0.203415i
$883$		−	54.8313i		−	1.84522i	−0.385735	−	0.922609i	$-0.626052\pi$
$883$		−	54.8313i		−	1.84522i	0.385735	−	0.922609i	$-0.373948\pi$
$884$	−14.0241			−0.471682
$885$	−1.56276	+	15.9932i	−0.0525315	+	0.537605i
$886$			56.3190i			1.89207i
$887$			24.5045i			0.822782i	0.911459	+	0.411391i	$0.134957\pi$
$887$			24.5045i			0.822782i	−0.911459	+	0.411391i	$0.865043\pi$
$888$		−	20.7173i		−	0.695227i
$889$	−7.24009	+	26.4668i	−0.242825	+	0.887668i
$890$	6.03837	−	61.7964i	0.202407	−	2.07142i
$891$	3.25064	+	0.658292i	0.108900	+	0.0220536i
$892$	−1.41102			−0.0472445
$893$	28.5589			0.955686
$894$			3.11248i			0.104097i
$895$	−24.2906	−	2.37353i	−0.811945	−	0.0793383i
$896$	−8.96927	+	32.7880i	−0.299642	+	1.09537i
$897$	35.1619			1.17402
$898$	−59.2635			−1.97765
$899$	0.663928			0.0221432
$900$	4.29025	+	0.846517i	0.143008	+	0.0282172i
$901$	−7.09312			−0.236306
$902$	−55.1585	−	11.1702i	−1.83658	−	0.371928i
$903$	−4.74997	+	17.3640i	−0.158069	+	0.577836i
$904$			26.9184i			0.895294i
$905$	−4.95818	+	50.7418i	−0.164815	+	1.68671i
$906$			30.9138i			1.02704i
$907$		−	27.9528i		−	0.928157i	−0.885794	−	0.464079i	$-0.846386\pi$
$907$		−	27.9528i		−	0.928157i	0.885794	−	0.464079i	$-0.153614\pi$
$908$			18.5718i			0.616327i
$909$	−15.2038			−0.504277
$910$	−48.8493	−	18.6343i	−1.61934	−	0.617720i
$911$	28.4151			0.941435			0.470718	−	0.882284i	$-0.343995\pi$
$911$	28.4151			0.941435			0.470718	+	0.882284i	$0.343995\pi$
$912$	21.2954			0.705162
$913$	−4.67064	+	23.0636i	−0.154576	+	0.763293i
$914$	59.7271			1.97560
$915$	9.81398	+	0.958963i	0.324440	+	0.0317023i
$916$			22.2243i			0.734312i
$917$	−5.87923	+	21.4921i	−0.194149	+	0.709730i
$918$			5.21579i			0.172147i
$919$		−	38.1808i		−	1.25947i	−0.776810	−	0.629735i	$-0.783164\pi$
$919$		−	38.1808i		−	1.25947i	0.776810	−	0.629735i	$-0.216836\pi$
$920$	2.79905	−	28.6454i	0.0922820	−	0.944410i
$921$			12.5546i			0.413688i
$922$	−42.6081			−1.40322
$923$			30.4053i			1.00080i
$924$	3.45398	−	6.85335i	0.113628	−	0.225459i
$925$	10.5091	−	53.2613i	0.345537	−	1.75122i
$926$		−	12.8779i		−	0.423193i
$927$	3.93640			0.129288
$928$		−	0.471407i		−	0.0154747i
$929$			20.4152i			0.669800i	0.942254	+	0.334900i	$0.108703\pi$
$929$			20.4152i			0.669800i	−0.942254	+	0.334900i	$0.891297\pi$
$930$	−2.40654	+	24.6284i	−0.0789134	+	0.807596i
$931$	25.7432	+	15.2235i	0.843700	+	0.498930i
$932$	−0.981234			−0.0321414
$933$		−	2.57715i		−	0.0843720i
$934$	53.9387			1.76493
$935$	−6.68143	+	21.8143i	−0.218506	+	0.713405i
$936$		−	9.94568i		−	0.325085i
$937$			18.4928i			0.604133i	0.953287	+	0.302066i	$0.0976764\pi$
$937$			18.4928i			0.604133i	−0.953287	+	0.302066i	$0.902324\pi$
$938$	18.4296	+	5.04149i	0.601749	+	0.164610i
$939$	13.1184			0.428102
$940$	13.0102	+	1.27128i	0.424347	+	0.0414646i
$941$	−22.8138			−0.743708			−0.371854	−	0.928291i	$-0.621278\pi$
$941$	−22.8138			−0.743708			−0.371854	+	0.928291i	$0.621278\pi$
$942$	0.422552			0.0137675
$943$			67.5136i			2.19855i
$944$			35.8192i			1.16581i
$945$	−2.10857	+	5.52756i	−0.0685916	+	0.179812i
$946$	37.4996	+	7.59411i	1.21922	+	0.246906i
$947$			10.9888i			0.357087i	0.983932	+	0.178544i	$0.0571385\pi$
$947$			10.9888i			0.357087i	−0.983932	+	0.178544i	$0.942861\pi$
$948$		−	12.4195i		−	0.403367i
$949$	−42.1979			−1.36980
$950$	35.5344	+	7.01136i	1.15289	+	0.227478i
$951$		−	12.8246i		−	0.415868i
$952$	−14.9799	−	4.09780i	−0.485501	−	0.132810i
$953$	38.0878			1.23378			0.616892	−	0.787048i	$-0.288391\pi$
$953$	38.0878			1.23378			0.616892	+	0.787048i	$0.288391\pi$
$954$			3.90925i			0.126567i
$955$	−28.4845	−	2.78333i	−0.921738	−	0.0900666i
$956$			10.3518i			0.334802i
$957$	0.0669597	−	0.330646i	0.00216450	−	0.0106883i
$958$	28.6155			0.924525
$959$	−21.9370	−	6.00094i	−0.708383	−	0.193781i
$960$	−4.69787	−	0.459047i	−0.151623	−	0.0148157i
$961$	−11.6042			−0.374328
$962$	95.9534			3.09366
$963$	−7.59473			−0.244737
$964$	12.0852			0.389239
$965$	−34.0459	−	3.32676i	−1.09598	−	0.107092i
$966$	−29.1879	−	7.98445i	−0.939105	−	0.256895i
$967$	24.6986			0.794253			0.397126	−	0.917764i	$-0.370007\pi$
$967$	24.6986			0.794253			0.397126	+	0.917764i	$0.370007\pi$
$968$	19.3352	+	8.16610i	0.621457	+	0.262468i
$969$			13.1437i			0.422235i
$970$	11.2726	+	1.10149i	0.361942	+	0.0353668i
$971$		−	23.3634i		−	0.749766i	−0.927072	−	0.374883i	$-0.877683\pi$
$971$		−	23.3634i		−	0.749766i	0.927072	−	0.374883i	$-0.122317\pi$
$972$	0.874594			0.0280526
$973$	3.50414	−	12.8097i	0.112338	−	0.410660i
$974$		−	9.57794i		−	0.306897i
$975$	5.04506	−	25.5690i	0.161571	−	0.818862i
$976$	21.9799			0.703559
$977$			12.9148i			0.413180i	0.978428	+	0.206590i	$0.0662367\pi$
$977$			12.9148i			0.413180i	−0.978428	+	0.206590i	$0.933763\pi$
$978$		−	10.8196i		−	0.345972i
$979$	10.7813	−	53.2381i	0.344573	−	1.70150i
$980$	11.0499	+	8.08112i	0.352975	+	0.258142i
$981$			8.59953i			0.274562i
$982$		−	2.19172i		−	0.0699407i
$983$	45.5860			1.45397			0.726984	−	0.686655i	$-0.240921\pi$
$983$	45.5860			1.45397			0.726984	+	0.686655i	$0.240921\pi$
$984$	19.0965			0.608774
$985$	26.1794	+	2.55810i	0.834146	+	0.0815077i
$986$	0.530537			0.0168957
$987$	−4.66635	+	17.0583i	−0.148532	+	0.542971i
$988$			19.4772i			0.619654i
$989$		−	45.8992i		−	1.45951i
$990$	12.0226	+	3.68236i	0.382103	+	0.117033i
$991$	23.9141			0.759656			0.379828	−	0.925057i	$-0.375983\pi$
$991$	23.9141			0.759656			0.379828	+	0.925057i	$0.375983\pi$
$992$			30.2501i			0.960442i
$993$	−5.60078			−0.177735
$994$	6.90433	−	25.2394i	0.218992	−	0.800546i
$995$	0.418023	−	4.27803i	0.0132522	−	0.135623i
$996$			6.20532i			0.196623i
$997$		−	23.2026i		−	0.734835i	−0.930056	−	0.367418i	$-0.880242\pi$
$997$		−	23.2026i		−	0.734835i	0.930056	−	0.367418i	$-0.119758\pi$
$998$	−71.1127			−2.25103
$999$		−	10.8576i		−	0.343520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.11	yes	48
5.4	even	2		1155.2.k.a.769.38	yes	48
7.6	odd	2		1155.2.k.a.769.12	yes	48
11.10	odd	2	inner	1155.2.k.b.769.38	yes	48
35.34	odd	2	inner	1155.2.k.b.769.37	yes	48
55.54	odd	2		1155.2.k.a.769.11	✓	48
77.76	even	2		1155.2.k.a.769.37	yes	48
385.384	even	2	inner	1155.2.k.b.769.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.11	✓	48	55.54	odd	2
1155.2.k.a.769.12	yes	48	7.6	odd	2
1155.2.k.a.769.37	yes	48	77.76	even	2
1155.2.k.a.769.38	yes	48	5.4	even	2
1155.2.k.b.769.11	yes	48	1.1	even	1	trivial
1155.2.k.b.769.12	yes	48	385.384	even	2	inner
1155.2.k.b.769.37	yes	48	35.34	odd	2	inner
1155.2.k.b.769.38	yes	48	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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.69546 q^{2} +1.00000 q^{3} +0.874594 q^{4} +(-2.22547 - 0.217459i) q^{5} -1.69546 q^{6} +(0.698105 - 2.55199i) q^{7} +1.90808 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.69546 q^{2} +1.00000 q^{3} +0.874594 q^{4} +(-2.22547 - 0.217459i) q^{5} -1.69546 q^{6} +(0.698105 - 2.55199i) q^{7} +1.90808 q^{8} +1.00000 q^{9} +(3.77320 + 0.368694i) q^{10} +(3.25064 + 0.658292i) q^{11} +0.874594 q^{12} -5.21239i q^{13} +(-1.18361 + 4.32680i) q^{14} +(-2.22547 - 0.217459i) q^{15} -4.98427 q^{16} -3.07632i q^{17} -1.69546 q^{18} -4.27252 q^{19} +(-1.94638 - 0.190189i) q^{20} +(0.698105 - 2.55199i) q^{21} +(-5.51134 - 1.11611i) q^{22} +6.74583i q^{23} +1.90808 q^{24} +(4.90542 + 0.967898i) q^{25} +8.83741i q^{26} +1.00000 q^{27} +(0.610559 - 2.23195i) q^{28} -0.101717i q^{29} +(3.77320 + 0.368694i) q^{30} +6.52719i q^{31} +4.63448 q^{32} +(3.25064 + 0.658292i) q^{33} +5.21579i q^{34} +(-2.10857 + 5.52756i) q^{35} +0.874594 q^{36} -10.8576i q^{37} +7.24390 q^{38} -5.21239i q^{39} +(-4.24638 - 0.414931i) q^{40} +10.0082 q^{41} +(-1.18361 + 4.32680i) q^{42} -6.80409 q^{43} +(2.84299 + 0.575738i) q^{44} +(-2.22547 - 0.217459i) q^{45} -11.4373i q^{46} -6.68431 q^{47} -4.98427 q^{48} +(-6.02530 - 3.56312i) q^{49} +(-8.31696 - 1.64103i) q^{50} -3.07632i q^{51} -4.55872i q^{52} -2.30571i q^{53} -1.69546 q^{54} +(-7.09104 - 2.17189i) q^{55} +(1.33204 - 4.86941i) q^{56} -4.27252 q^{57} +0.172458i q^{58} -7.18644i q^{59} +(-1.94638 - 0.190189i) q^{60} -4.40985 q^{61} -11.0666i q^{62} +(0.698105 - 2.55199i) q^{63} +2.11096 q^{64} +(-1.13348 + 11.6000i) q^{65} +(-5.51134 - 1.11611i) q^{66} -4.25941i q^{67} -2.69053i q^{68} +6.74583i q^{69} +(3.57499 - 9.37178i) q^{70} -5.83327 q^{71} +1.90808 q^{72} -8.09569i q^{73} +18.4087i q^{74} +(4.90542 + 0.967898i) q^{75} -3.73672 q^{76} +(3.94924 - 7.83604i) q^{77} +8.83741i q^{78} -14.2003i q^{79} +(11.0923 + 1.08388i) q^{80} +1.00000 q^{81} -16.9685 q^{82} +7.09509i q^{83} +(0.610559 - 2.23195i) q^{84} +(-0.668975 + 6.84626i) q^{85} +11.5361 q^{86} -0.101717i q^{87} +(6.20249 + 1.25608i) q^{88} -16.3777i q^{89} +(3.77320 + 0.368694i) q^{90} +(-13.3020 - 3.63880i) q^{91} +5.89986i q^{92} +6.52719i q^{93} +11.3330 q^{94} +(9.50836 + 0.929100i) q^{95} +4.63448 q^{96} +2.98755 q^{97} +(10.2157 + 6.04113i) q^{98} +(3.25064 + 0.658292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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