LMFDB - Embedded newform 750.2.o.b.229.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.2
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.84358 - 1.26539i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.846010 + 1.16443i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.84358 - 1.26539i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.846010 + 1.16443i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-0.767151 + 2.10035i) q^{10} +(-3.75915 + 0.965185i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(-0.488644 - 1.23417i) q^{13} +(1.33824 + 0.529848i) q^{14} +(-2.04804 - 0.897519i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.36813 + 2.48862i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(-0.522009 + 2.73647i) q^{19} +(2.22515 + 0.220713i) q^{20} +(-0.612832 + 1.30233i) q^{21} +(1.86972 + 3.40102i) q^{22} +(-5.36408 - 0.337479i) q^{23} +(0.809017 + 0.587785i) q^{24} +(1.79760 + 4.66569i) q^{25} +(-1.07388 + 0.780219i) q^{26} +(0.844328 - 0.535827i) q^{27} +(0.180394 - 1.42797i) q^{28} +(-5.66147 - 0.715210i) q^{29} +(-0.359996 + 2.20690i) q^{30} +(-2.11794 - 1.16435i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-3.51171 + 1.65248i) q^{33} +(2.75067 + 0.706252i) q^{34} +(3.03315 - 1.07620i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(7.23571 + 4.59192i) q^{37} +(2.78032 - 0.174923i) q^{38} +(-0.711250 - 1.12075i) q^{39} +(-0.339593 - 2.21013i) q^{40} +(0.225239 + 3.58006i) q^{41} +(1.41382 + 0.269701i) q^{42} +(-7.53110 + 2.44700i) q^{43} +(2.82919 - 2.65678i) q^{44} +(-2.17994 - 0.497858i) q^{45} +(1.00712 + 5.27948i) q^{46} +(0.752616 - 0.801454i) q^{47} +(0.368125 - 0.929776i) q^{48} +(1.52295 + 4.68715i) q^{49} +(4.07206 - 2.90143i) q^{50} +(-0.877574 + 2.70090i) q^{51} +(1.02277 + 0.846109i) q^{52} +(0.401579 + 0.188969i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(8.15164 + 2.97737i) q^{55} +(-1.42797 + 0.180394i) q^{56} +2.78581i q^{57} +(0.715210 + 5.66147i) q^{58} +(-8.28075 - 10.0097i) q^{59} +(2.22709 - 0.200148i) q^{60} +(0.204729 - 3.25407i) q^{61} +(-0.601056 + 2.34096i) q^{62} +(-0.357944 + 1.39410i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-0.660850 + 2.89363i) q^{65} +(2.47389 + 2.99042i) q^{66} +(0.359046 + 2.84214i) q^{67} -2.83989i q^{68} +(-5.33230 + 0.673626i) q^{69} +(-1.79670 - 2.67021i) q^{70} +(1.31429 + 1.23421i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-10.3548 - 8.56621i) q^{73} +(2.64821 - 8.15035i) q^{74} +(2.64002 + 4.24621i) q^{75} +(-0.860863 - 2.64946i) q^{76} +(2.05638 - 5.19383i) q^{77} +(-0.908660 + 0.967625i) q^{78} +(-2.41756 - 12.6733i) q^{79} +(-2.05624 + 0.878561i) q^{80} +(0.728969 - 0.684547i) q^{81} +(3.41157 - 1.10849i) q^{82} +(4.65098 + 0.887222i) q^{83} +(-0.0903755 - 1.43648i) q^{84} +(5.67132 - 2.85676i) q^{85} +(4.24303 + 6.68595i) q^{86} +(-5.69521 + 0.358312i) q^{87} +(-3.27690 - 2.07959i) q^{88} +(5.01267 - 6.05927i) q^{89} +(0.0599126 + 2.23527i) q^{90} +(1.85051 + 0.475130i) q^{91} +(4.86316 - 2.28843i) q^{92} +(-2.29860 - 0.746860i) q^{93} +(-0.963443 - 0.529657i) q^{94} +(4.42505 - 4.38436i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(-2.44716 + 19.3712i) q^{97} +(4.16116 - 2.64075i) q^{98} +(-3.13986 + 2.28124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	−1.84358	−	1.26539i	−0.824475	−	0.565898i
$5$	−1.84358	−	1.26539i	−0.824475	−	0.565898i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	−0.846010	+	1.16443i	−0.319762	+	0.440114i	−0.938394	−	0.345566i	$-0.887687\pi$
$7$	−0.846010	+	1.16443i	−0.319762	+	0.440114i	0.618633	+	0.785680i	$0.287687\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	−0.767151	+	2.10035i	−0.242594	+	0.664190i
$11$	−3.75915	+	0.965185i	−1.13343	+	0.291014i	−0.768392	−	0.639980i	$-0.778943\pi$
$11$	−3.75915	+	0.965185i	−1.13343	+	0.291014i	−0.365034	+	0.930994i	$0.618943\pi$
$12$	−0.770513	+	0.637424i	−0.222428	+	0.184008i
$13$	−0.488644	−	1.23417i	−0.135526	−	0.342298i	0.846126	−	0.532983i	$-0.178929\pi$
$13$	−0.488644	−	1.23417i	−0.135526	−	0.342298i	−0.981651	+	0.190685i	$0.938929\pi$
$14$	1.33824	+	0.529848i	0.357661	+	0.141608i
$15$	−2.04804	−	0.897519i	−0.528801	−	0.231738i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−1.36813	+	2.48862i	−0.331820	+	0.603578i	−0.988611	−	0.150495i	$-0.951913\pi$
$17$	−1.36813	+	2.48862i	−0.331820	+	0.603578i	0.656791	+	0.754073i	$0.271913\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	−0.522009	+	2.73647i	−0.119757	+	0.627789i	0.870905	+	0.491451i	$0.163533\pi$
$19$	−0.522009	+	2.73647i	−0.119757	+	0.627789i	−0.990662	+	0.136338i	$0.956467\pi$
$20$	2.22515	+	0.220713i	0.497558	+	0.0493529i
$21$	−0.612832	+	1.30233i	−0.133731	+	0.284193i
$22$	1.86972	+	3.40102i	0.398627	+	0.725099i
$23$	−5.36408	−	0.337479i	−1.11849	−	0.0703693i	−0.507237	−	0.861807i	$-0.669333\pi$
$23$	−5.36408	−	0.337479i	−1.11849	−	0.0703693i	−0.611250	+	0.791437i	$0.709333\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.79760	+	4.66569i	0.359520	+	0.933137i
$26$	−1.07388	+	0.780219i	−0.210605	+	0.153014i
$27$	0.844328	−	0.535827i	0.162491	−	0.103120i
$28$	0.180394	−	1.42797i	0.0340913	−	0.269861i
$29$	−5.66147	−	0.715210i	−1.05131	−	0.132811i	−0.419359	−	0.907821i	$-0.637745\pi$
$29$	−5.66147	−	0.715210i	−1.05131	−	0.132811i	−0.631950	+	0.775009i	$0.717745\pi$
$30$	−0.359996	+	2.20690i	−0.0657259	+	0.402923i
$31$	−2.11794	−	1.16435i	−0.380393	−	0.209123i	0.280073	−	0.959979i	$-0.409641\pi$
$31$	−2.11794	−	1.16435i	−0.380393	−	0.209123i	−0.660466	+	0.750856i	$0.729641\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	−3.51171	+	1.65248i	−0.611310	+	0.287660i
$34$	2.75067	+	0.706252i	0.471736	+	0.121121i
$35$	3.03315	−	1.07620i	0.512695	−	0.181911i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	7.23571	+	4.59192i	1.18954	+	0.754907i	0.975086	−	0.221826i	$-0.0712017\pi$
$37$	7.23571	+	4.59192i	1.18954	+	0.754907i	0.214457	+	0.976733i	$0.431202\pi$
$38$	2.78032	−	0.174923i	0.451027	−	0.0283762i
$39$	−0.711250	−	1.12075i	−0.113891	−	0.179464i
$40$	−0.339593	−	2.21013i	−0.0536944	−	0.349452i
$41$	0.225239	+	3.58006i	0.0351763	+	0.559112i	0.975662	+	0.219279i	$0.0703705\pi$
$41$	0.225239	+	3.58006i	0.0351763	+	0.559112i	−0.940486	+	0.339833i	$0.889629\pi$
$42$	1.41382	+	0.269701i	0.218158	+	0.0416158i
$43$	−7.53110	+	2.44700i	−1.14848	+	0.373164i	−0.820571	−	0.571544i	$-0.806345\pi$
$43$	−7.53110	+	2.44700i	−1.14848	+	0.373164i	−0.327911	+	0.944709i	$0.606345\pi$
$44$	2.82919	−	2.65678i	0.426516	−	0.400525i
$45$	−2.17994	−	0.497858i	−0.324966	−	0.0742162i
$46$	1.00712	+	5.27948i	0.148491	+	0.778417i
$47$	0.752616	−	0.801454i	0.109780	−	0.116904i	−0.671731	−	0.740795i	$-0.734449\pi$
$47$	0.752616	−	0.801454i	0.109780	−	0.116904i	0.781512	+	0.623891i	$0.214449\pi$
$48$	0.368125	−	0.929776i	0.0531342	−	0.134202i
$49$	1.52295	+	4.68715i	0.217564	+	0.669593i
$50$	4.07206	−	2.90143i	0.575876	−	0.410325i
$51$	−0.877574	+	2.70090i	−0.122885	+	0.378201i
$52$	1.02277	+	0.846109i	0.141833	+	0.117334i
$53$	0.401579	+	0.188969i	0.0551611	+	0.0259569i	0.453162	−	0.891428i	$-0.350296\pi$
$53$	0.401579	+	0.188969i	0.0551611	+	0.0259569i	−0.398001	+	0.917385i	$0.630296\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	8.15164	+	2.97737i	1.09917	+	0.401469i
$56$	−1.42797	+	0.180394i	−0.190820	+	0.0241062i
$57$			2.78581i			0.368990i
$58$	0.715210	+	5.66147i	0.0939116	+	0.743387i
$59$	−8.28075	−	10.0097i	−1.07806	−	1.30315i	−0.950296	−	0.311348i	$-0.899219\pi$
$59$	−8.28075	−	10.0097i	−1.07806	−	1.30315i	−0.127766	−	0.991804i	$-0.540781\pi$
$60$	2.22709	−	0.200148i	0.287516	−	0.0258390i
$61$	0.204729	−	3.25407i	0.0262128	−	0.416641i	−0.962937	−	0.269728i	$-0.913066\pi$
$61$	0.204729	−	3.25407i	0.0262128	−	0.416641i	0.989149	−	0.146913i	$-0.0469337\pi$
$62$	−0.601056	+	2.34096i	−0.0763342	+	0.297302i
$63$	−0.357944	+	1.39410i	−0.0450967	+	0.175640i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−0.660850	+	2.89363i	−0.0819684	+	0.358910i
$66$	2.47389	+	2.99042i	0.304515	+	0.368096i
$67$	0.359046	+	2.84214i	0.0438644	+	0.347223i	0.998739	+	0.0502120i	$0.0159897\pi$
$67$	0.359046	+	2.84214i	0.0438644	+	0.347223i	−0.954874	+	0.297011i	$0.904010\pi$
$68$		−	2.83989i		−	0.344387i
$69$	−5.33230	+	0.673626i	−0.641934	+	0.0810951i
$70$	−1.79670	−	2.67021i	−0.214747	−	0.319152i
$71$	1.31429	+	1.23421i	0.155978	+	0.146473i	0.758607	−	0.651548i	$-0.225880\pi$
$71$	1.31429	+	1.23421i	0.155978	+	0.146473i	−0.602629	+	0.798021i	$0.705880\pi$
$72$	0.904827	+	0.425779i	0.106635	+	0.0501786i
$73$	−10.3548	−	8.56621i	−1.21193	−	1.00260i	−0.999678	−	0.0253845i	$-0.991919\pi$
$73$	−10.3548	−	8.56621i	−1.21193	−	1.00260i	−0.212256	−	0.977214i	$-0.568081\pi$
$74$	2.64821	−	8.15035i	0.307848	−	0.947459i
$75$	2.64002	+	4.24621i	0.304843	+	0.490310i
$76$	−0.860863	−	2.64946i	−0.0987478	−	0.303914i
$77$	2.05638	−	5.19383i	0.234347	−	0.591892i
$78$	−0.908660	+	0.967625i	−0.102885	+	0.109562i
$79$	−2.41756	−	12.6733i	−0.271997	−	1.42586i	−0.811736	−	0.584025i	$-0.801477\pi$
$79$	−2.41756	−	12.6733i	−0.271997	−	1.42586i	0.539739	−	0.841833i	$-0.318523\pi$
$80$	−2.05624	+	0.878561i	−0.229895	+	0.0982261i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	3.41157	−	1.10849i	0.376745	−	0.122412i
$83$	4.65098	+	0.887222i	0.510512	+	0.0973853i	0.436200	−	0.899850i	$-0.356324\pi$
$83$	4.65098	+	0.887222i	0.510512	+	0.0973853i	0.0743117	+	0.997235i	$0.476324\pi$
$84$	−0.0903755	−	1.43648i	−0.00986078	−	0.156733i
$85$	5.67132	−	2.85676i	0.615141	−	0.309859i
$86$	4.24303	+	6.68595i	0.457538	+	0.720965i
$87$	−5.69521	+	0.358312i	−0.610590	+	0.0384151i
$88$	−3.27690	−	2.07959i	−0.349319	−	0.221685i
$89$	5.01267	−	6.05927i	0.531341	−	0.642281i	−0.434729	−	0.900561i	$-0.643156\pi$
$89$	5.01267	−	6.05927i	0.531341	−	0.642281i	0.966070	+	0.258280i	$0.0831557\pi$
$90$	0.0599126	+	2.23527i	0.00631534	+	0.235618i
$91$	1.85051	+	0.475130i	0.193986	+	0.0498072i
$92$	4.86316	−	2.28843i	0.507019	−	0.238585i
$93$	−2.29860	−	0.746860i	−0.238354	−	0.0774458i
$94$	−0.963443	−	0.529657i	−0.0993716	−	0.0546300i
$95$	4.42505	−	4.38436i	0.454001	−	0.449826i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	−2.44716	+	19.3712i	−0.248471	+	1.96685i	0.00678412	+	0.999977i	$0.497841\pi$
$97$	−2.44716	+	19.3712i	−0.248471	+	1.96685i	−0.255255	+	0.966874i	$0.582159\pi$
$98$	4.16116	−	2.64075i	0.420340	−	0.266756i
$99$	−3.13986	+	2.28124i	−0.315568	+	0.229273i
$100$	−3.82296	−	3.22257i	−0.382296	−	0.322257i
$101$	−1.83728	−	1.33486i	−0.182816	−	0.132824i	0.492613	−	0.870248i	$-0.336042\pi$
$101$	−1.83728	−	1.33486i	−0.182816	−	0.132824i	−0.675429	+	0.737425i	$0.736042\pi$
$102$	2.83429	+	0.178318i	0.280636	+	0.0176561i
$103$	1.17229	+	2.13238i	0.115509	+	0.210110i	0.927741	−	0.373224i	$-0.121748\pi$
$103$	1.17229	+	2.13238i	0.115509	+	0.210110i	−0.812232	+	0.583334i	$0.801748\pi$
$104$	0.565175	−	1.20106i	0.0554199	−	0.117773i
$105$	2.77776	−	1.62549i	0.271082	−	0.158632i
$106$	0.0831633	−	0.435957i	0.00807754	−	0.0423439i
$107$	3.07326	+	4.22998i	0.297103	+	0.408928i	0.931305	−	0.364240i	$-0.118671\pi$
$107$	3.07326	+	4.22998i	0.297103	+	0.408928i	−0.634202	+	0.773168i	$0.718671\pi$
$108$	−0.481754	+	0.876307i	−0.0463568	+	0.0843226i
$109$	3.36380	−	5.30050i	0.322194	−	0.507696i	−0.644168	−	0.764884i	$-0.722796\pi$
$109$	3.36380	−	5.30050i	0.322194	−	0.507696i	0.966361	+	0.257188i	$0.0827961\pi$
$110$	0.856604	−	8.63598i	0.0816740	−	0.823408i
$111$	7.96799	+	3.15475i	0.756288	+	0.299436i
$112$	0.529848	+	1.33824i	0.0500660	+	0.126452i
$113$	−3.27025	+	2.70539i	−0.307639	+	0.254501i	−0.778413	−	0.627753i	$-0.783975\pi$
$113$	−3.27025	+	2.70539i	−0.307639	+	0.254501i	0.470773	+	0.882254i	$0.343975\pi$
$114$	2.69829	−	0.692803i	0.252718	−	0.0648870i
$115$	9.46208	+	7.40980i	0.882344	+	0.690967i
$116$	5.30574	−	2.10069i	0.492625	−	0.195044i
$117$	−0.908660	−	0.967625i	−0.0840056	−	0.0894569i
$118$	−7.63589	+	10.5099i	−0.702941	+	0.967515i
$119$	−1.74038	−	3.69849i	−0.159540	−	0.339040i
$120$	−0.747715	−	2.10735i	−0.0682567	−	0.192374i
$121$	3.56025	−	1.95726i	0.323659	−	0.177933i
$122$	−3.20275	+	0.610957i	−0.289963	+	0.0553135i
$123$	0.892086	+	3.47445i	0.0804367	+	0.313280i
$124$	2.41689			0.217043
$125$	2.58987	−	10.8762i	0.231645	−	0.972800i
$126$	1.43932			0.128225
$127$	0.599624	+	2.33538i	0.0532080	+	0.207232i	0.989629	−	0.143647i	$-0.0458830\pi$
$127$	0.599624	+	2.33538i	0.0532080	+	0.207232i	−0.936421	+	0.350879i	$0.885883\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−6.93918	+	3.81485i	−0.610961	+	0.335879i
$130$	2.96707	−	0.0795273i	0.260229	−	0.00697500i
$131$	−7.05700	−	14.9969i	−0.616573	−	1.31028i	−0.932386	−	0.361463i	$-0.882277\pi$
$131$	−7.05700	−	14.9969i	−0.616573	−	1.31028i	0.315813	−	0.948821i	$-0.397723\pi$
$132$	2.28124	−	3.13986i	0.198557	−	0.273290i
$133$	−2.74481	−	2.92292i	−0.238005	−	0.253450i
$134$	2.66356	−	1.05458i	0.230096	−	0.0911016i
$135$	−2.23462	−	0.0805591i	−0.192325	−	0.00693342i
$136$	−2.75067	+	0.706252i	−0.235868	+	0.0605606i
$137$	−5.36261	+	4.43634i	−0.458159	+	0.379022i	−0.837680	−	0.546161i	$-0.816089\pi$
$137$	−5.36261	+	4.43634i	−0.458159	+	0.379022i	0.379521	+	0.925183i	$0.376089\pi$
$138$	1.97855	+	4.99725i	0.168426	+	0.425395i
$139$	−3.76857	−	1.49208i	−0.319646	−	0.126557i	0.202822	−	0.979216i	$-0.434989\pi$
$139$	−3.76857	−	1.49208i	−0.319646	−	0.126557i	−0.522468	+	0.852659i	$0.674989\pi$
$140$	−2.13950	+	2.40431i	−0.180821	+	0.203201i
$141$	0.589107	−	0.928284i	0.0496118	−	0.0781757i
$142$	0.868578	−	1.57994i	0.0728895	−	0.132585i
$143$	3.02809	+	4.16781i	0.253222	+	0.348530i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	9.53237	+	8.48249i	0.791620	+	0.704432i
$146$	−5.72196	+	12.1598i	−0.473553	+	1.00635i
$147$	2.37426	+	4.31876i	0.195825	+	0.356205i
$148$	−8.55288	−	0.538101i	−0.703042	−	0.0442317i
$149$	0.100474	+	0.0729989i	0.00823118	+	0.00598030i	0.591893	−	0.806016i	$-0.298381\pi$
$149$	0.100474	+	0.0729989i	0.00823118	+	0.00598030i	−0.583662	+	0.811997i	$0.698381\pi$
$150$	3.45626	−	3.61307i	0.282202	−	0.295006i
$151$	3.88982	−	2.82612i	0.316549	−	0.229986i	−0.418153	−	0.908377i	$-0.637322\pi$
$151$	3.88982	−	2.82612i	0.316549	−	0.229986i	0.734701	+	0.678391i	$0.237322\pi$
$152$	−2.35214	+	1.49271i	−0.190784	+	0.121075i
$153$	−0.355933	+	2.81750i	−0.0287755	+	0.227781i
$154$	−5.54206	−	0.700125i	−0.446592	−	0.0564177i
$155$	2.43125	+	4.82657i	0.195282	+	0.387680i
$156$	1.16320	+	0.639474i	0.0931305	+	0.0511989i
$157$	−8.67000	−	2.81706i	−0.691942	−	0.224825i	−0.0581256	−	0.998309i	$-0.518512\pi$
$157$	−8.67000	−	2.81706i	−0.691942	−	0.224825i	−0.633816	+	0.773484i	$0.718512\pi$
$158$	−11.6739	+	5.49333i	−0.928727	+	0.437026i
$159$	0.429875	+	0.110373i	0.0340913	+	0.00875316i
$160$	1.36233	+	1.77315i	0.107701	+	0.140180i
$161$	4.93103	−	5.96060i	0.388620	−	0.469761i
$162$	−0.844328	−	0.535827i	−0.0663367	−	0.0420985i
$163$	−5.75008	+	0.361765i	−0.450381	+	0.0283356i	−0.286362	−	0.958122i	$-0.592446\pi$
$163$	−5.75008	+	0.361765i	−0.450381	+	0.0283356i	−0.164019	+	0.986457i	$0.552446\pi$
$164$	−1.92209	−	3.02872i	−0.150090	−	0.236504i
$165$	8.56515	+	1.39717i	0.666796	+	0.108770i
$166$	−0.297304	−	4.72551i	−0.0230752	−	0.366770i
$167$	3.76190	+	0.717620i	0.291104	+	0.0555311i	0.330865	−	0.943678i	$-0.392660\pi$
$167$	3.76190	+	0.717620i	0.291104	+	0.0555311i	−0.0397606	+	0.999209i	$0.512660\pi$
$168$	−1.36887	+	0.444774i	−0.105611	+	0.0343150i
$169$	8.19218	−	7.69297i	0.630168	−	0.591767i
$170$	−4.17741	−	4.78269i	−0.320393	−	0.366816i
$171$	0.522009	+	2.73647i	0.0399190	+	0.209263i
$172$	5.42070	−	5.77246i	0.413325	−	0.440146i
$173$	5.86190	−	14.8055i	0.445672	−	1.12564i	−0.517245	−	0.855838i	$-0.673042\pi$
$173$	5.86190	−	14.8055i	0.445672	−	1.12564i	0.962916	−	0.269801i	$-0.0869578\pi$
$174$	1.76339	+	5.42717i	0.133683	+	0.411433i
$175$	−6.95366	−	1.85404i	−0.525648	−	0.140152i
$176$	−1.19932	+	3.69113i	−0.0904021	+	0.278229i
$177$	−10.0097	−	8.28075i	−0.752375	−	0.622419i
$178$	−7.11551	−	3.34830i	−0.533330	−	0.250966i
$179$	−9.72831	−	9.13549i	−0.727128	−	0.682819i	0.229769	−	0.973245i	$-0.426203\pi$
$179$	−9.72831	−	9.13549i	−0.727128	−	0.682819i	−0.956897	+	0.290426i	$0.906203\pi$
$180$	2.15014	−	0.613918i	0.160262	−	0.0457588i
$181$	12.8014	−	1.61719i	0.951517	−	0.120205i	0.365776	−	0.930703i	$-0.380804\pi$
$181$	12.8014	−	1.61719i	0.951517	−	0.120205i	0.585741	+	0.810498i	$0.300804\pi$
$182$		−	1.91053i		−	0.141618i
$183$	−0.408649	−	3.23479i	−0.0302082	−	0.239123i
$184$	−3.42595	−	4.14126i	−0.252565	−	0.305298i
$185$	−7.52908	−	17.6216i	−0.553549	−	1.29556i
$186$	−0.151758	+	2.41212i	−0.0111274	+	0.176865i
$187$	2.74102	−	10.6756i	0.200443	−	0.780675i
$188$	−0.273419	+	1.06490i	−0.0199411	+	0.0776655i
$189$	−0.0903755	+	1.43648i	−0.00657385	+	0.104488i
$190$	−5.34709	−	3.19569i	−0.387918	−	0.231839i
$191$	−9.29798	−	11.2393i	−0.672778	−	0.813249i	0.318093	−	0.948059i	$-0.396958\pi$
$191$	−9.29798	−	11.2393i	−0.672778	−	0.813249i	−0.990871	+	0.134810i	$0.956958\pi$
$192$	0.125333	+	0.992115i	0.00904515	+	0.0715997i
$193$		−	15.4808i		−	1.11434i	−0.830400	−	0.557168i	$-0.811888\pi$
$193$		−	15.4808i		−	1.11434i	0.830400	−	0.557168i	$-0.188112\pi$
$194$	19.3712	−	2.44716i	1.39077	−	0.175696i
$195$	−0.106933	+	2.96620i	−0.00765765	+	0.212414i
$196$	−3.59262	−	3.37370i	−0.256616	−	0.240978i
$197$	9.64817	+	4.54008i	0.687403	+	0.323468i	0.737567	−	0.675273i	$-0.235974\pi$
$197$	9.64817	+	4.54008i	0.687403	+	0.323468i	−0.0501640	+	0.998741i	$0.515974\pi$
$198$	2.99042	+	2.47389i	0.212520	+	0.175812i
$199$	−8.07115	+	24.8404i	−0.572149	+	1.76089i	0.0735412	+	0.997292i	$0.476570\pi$
$199$	−8.07115	+	24.8404i	−0.572149	+	1.76089i	−0.645690	+	0.763600i	$0.723430\pi$
$200$	−2.17060	+	4.50428i	−0.153485	+	0.318500i
$201$	0.885250	+	2.72452i	0.0624407	+	0.192173i
$202$	−0.836012	+	2.11153i	−0.0588216	+	0.148566i
$203$	5.62247	−	5.98732i	0.394620	−	0.420228i
$204$	−0.532142	−	2.78959i	−0.0372574	−	0.195310i
$205$	4.11492	−	6.88516i	0.287398	−	0.480880i
$206$	1.77385	−	1.66576i	0.123590	−	0.116059i
$207$	−5.11163	+	1.66087i	−0.355283	+	0.115438i
$208$	−1.30388	−	0.248728i	−0.0904076	−	0.0172462i
$209$	−0.678889	−	10.7906i	−0.0469597	−	0.746403i
$210$	−2.26523	−	2.28625i	−0.156315	−	0.157766i
$211$	−6.16899	−	9.72077i	−0.424691	−	0.669205i	0.562852	−	0.826558i	$-0.309704\pi$
$211$	−6.16899	−	9.72077i	−0.424691	−	0.669205i	−0.987542	+	0.157353i	$0.949704\pi$
$212$	−0.442943	+	0.0278676i	−0.0304214	+	0.00191395i
$213$	1.52228	+	0.966070i	0.104305	+	0.0661940i
$214$	3.33280	−	4.02866i	0.227826	−	0.275394i
$215$	16.9806	+	5.01849i	1.15807	+	0.342258i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	3.14760	−	1.48115i	0.213673	−	0.100547i
$218$	−5.97052	−	1.93994i	−0.404375	−	0.131389i
$219$	−11.7765	−	6.47419i	−0.795782	−	0.437485i
$220$	−8.57769	+	1.31799i	−0.578308	+	0.0888588i
$221$	3.73991	+	0.472461i	0.251574	+	0.0317812i
$222$	1.07408	−	8.50221i	0.0720875	−	0.570631i
$223$	−15.7068	+	9.96781i	−1.05180	+	0.667494i	−0.945095	−	0.326796i	$-0.894031\pi$
$223$	−15.7068	+	9.96781i	−1.05180	+	0.667494i	−0.106707	+	0.994290i	$0.534031\pi$
$224$	1.16443	−	0.846010i	0.0778019	−	0.0565264i
$225$	3.38892	+	3.67631i	0.225928	+	0.245087i
$226$	3.43367	+	2.49471i	0.228404	+	0.165946i
$227$	−4.02903	−	0.253485i	−0.267416	−	0.0168244i	−0.0714835	−	0.997442i	$-0.522773\pi$
$227$	−4.02903	−	0.253485i	−0.267416	−	0.0168244i	−0.195932	+	0.980617i	$0.562773\pi$
$228$	−1.34208	−	2.44123i	−0.0888811	−	0.161674i
$229$	10.7800	−	22.9086i	0.712360	−	1.51384i	−0.139584	−	0.990210i	$-0.544576\pi$
$229$	10.7800	−	22.9086i	0.712360	−	1.51384i	0.851944	−	0.523633i	$-0.175424\pi$
$230$	4.82388	−	11.0076i	0.318077	−	0.725817i
$231$	1.04673	−	5.48716i	0.0688699	−	0.361029i
$232$	−3.35418	−	4.61663i	−0.220212	−	0.303096i
$233$	−13.0103	+	23.6656i	−0.852332	+	1.55039i	−0.0175234	+	0.999846i	$0.505578\pi$
$233$	−13.0103	+	23.6656i	−0.852332	+	1.55039i	−0.834809	+	0.550540i	$0.814422\pi$
$234$	−0.711250	+	1.12075i	−0.0464959	+	0.0732658i
$235$	−2.40166	+	0.525199i	−0.156667	+	0.0342602i
$236$	12.0787	+	4.78229i	0.786256	+	0.311301i
$237$	−4.74948	−	11.9958i	−0.308512	−	0.779212i
$238$	−3.14948	+	2.60547i	−0.204150	+	0.168888i
$239$	−2.62054	+	0.672840i	−0.169509	+	0.0435224i	−0.332490	−	0.943107i	$-0.607889\pi$
$239$	−2.62054	+	0.672840i	−0.169509	+	0.0435224i	0.162982	+	0.986629i	$0.447889\pi$
$240$	−1.85519	+	1.24830i	−0.119752	+	0.0805775i
$241$	17.8142	−	7.05314i	1.14751	−	0.454333i	0.284083	−	0.958800i	$-0.408311\pi$
$241$	17.8142	−	7.05314i	1.14751	−	0.454333i	0.863431	+	0.504467i	$0.168311\pi$
$242$	−2.78117	−	2.96164i	−0.178780	−	0.190382i
$243$	0.587785	−	0.809017i	0.0377064	−	0.0518985i
$244$	1.38825	+	2.95019i	0.0888739	+	0.188867i
$245$	3.12337	−	10.5683i	0.199545	−	0.675182i
$246$	3.14344	−	1.72812i	0.200418	−	0.110181i
$247$	3.63236	−	0.692909i	0.231121	−	0.0440887i
$248$	−0.601056	−	2.34096i	−0.0381671	−	0.148651i
$249$	4.73485			0.300059
$250$	−11.1786	+	0.196305i	−0.706998	+	0.0124154i
$251$	6.87277			0.433805			0.216903	−	0.976193i	$-0.430405\pi$
$251$	6.87277			0.433805			0.216903	+	0.976193i	$0.430405\pi$
$252$	−0.357944	−	1.39410i	−0.0225483	−	0.0878200i
$253$	20.4901	−	3.90870i	1.28820	−	0.245738i
$254$	2.11289	−	1.16157i	0.132574	−	0.0728834i
$255$	5.03556	−	3.86886i	0.315339	−	0.242277i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	−16.2202	+	22.3251i	−1.01179	+	1.39260i	−0.0939790	+	0.995574i	$0.529959\pi$
$257$	−16.2202	+	22.3251i	−1.01179	+	1.39260i	−0.917806	+	0.397029i	$0.870041\pi$
$258$	5.42070	+	5.77246i	0.337478	+	0.359378i
$259$	−11.4685	+	4.54069i	−0.712616	+	0.282145i
$260$	−0.814908	−	2.85407i	−0.0505384	−	0.177002i
$261$	−5.52719	+	1.41914i	−0.342124	+	0.0878426i
$262$	−12.7707	+	10.5649i	−0.788979	+	0.652700i
$263$	−0.181320	−	0.457963i	−0.0111807	−	0.0282392i	0.924079	−	0.382202i	$-0.124834\pi$
$263$	−0.181320	−	0.457963i	−0.0111807	−	0.0282392i	−0.935260	+	0.353962i	$0.884834\pi$
$264$	−3.60854	−	1.42872i	−0.222090	−	0.0879317i
$265$	−0.501226	−	0.856532i	−0.0307901	−	0.0526163i
$266$	−2.14849	+	3.38548i	−0.131732	+	0.207577i
$267$	3.78848	−	6.89122i	0.231851	−	0.421736i
$268$	−1.68385	−	2.31762i	−0.102857	−	0.141571i
$269$	−1.15104	+	6.03396i	−0.0701801	+	0.367897i	−1.00000		0.000117857i	$-0.999962\pi$
$269$	−1.15104	+	6.03396i	−0.0701801	+	0.367897i	0.929820	+	0.368015i	$0.119962\pi$
$270$	0.477698	+	2.18445i	0.0290718	+	0.132941i
$271$	−9.48289	+	20.1522i	−0.576044	+	1.22416i	0.378365	+	0.925656i	$0.376486\pi$
$271$	−9.48289	+	20.1522i	−0.576044	+	1.22416i	−0.954410	+	0.298500i	$0.903514\pi$
$272$	1.36813	+	2.48862i	0.0829549	+	0.150894i
$273$	1.90676	+	0.119963i	0.115403	+	0.00726052i
$274$	5.63059	+	4.09086i	0.340156	+	0.247138i
$275$	−11.2607	−	15.8040i	−0.679045	−	0.953017i
$276$	4.34821	−	3.15916i	0.261731	−	0.190159i
$277$	−20.2033	+	12.8214i	−1.21390	+	0.770363i	−0.979434	−	0.201762i	$-0.935333\pi$
$277$	−20.2033	+	12.8214i	−1.21390	+	0.770363i	−0.234463	+	0.972125i	$0.575333\pi$
$278$	−0.508000	+	4.02124i	−0.0304678	+	0.241178i
$279$	−2.39783	−	0.302917i	−0.143554	−	0.0181351i
$280$	2.86085	+	1.47436i	0.170968	+	0.0881098i
$281$	22.9859	+	12.6366i	1.37122	+	0.753836i	0.985644	−	0.168838i	$-0.0540015\pi$
$281$	22.9859	+	12.6366i	1.37122	+	0.753836i	0.385580	+	0.922675i	$0.374002\pi$
$282$	−1.04563	−	0.339744i	−0.0622661	−	0.0202315i
$283$	−5.77852	+	2.71916i	−0.343497	+	0.161637i	−0.589787	−	0.807559i	$-0.700788\pi$
$283$	−5.77852	+	2.71916i	−0.343497	+	0.161637i	0.246290	+	0.969196i	$0.420788\pi$
$284$	−1.74631	−	0.448376i	−0.103624	−	0.0266062i
$285$	3.52513	−	5.13588i	0.208810	−	0.304223i
$286$	3.28382	−	3.96945i	0.194176	−	0.234719i
$287$	−4.35930	−	2.76649i	−0.257321	−	0.163301i
$288$	−0.998027	+	0.0627905i	−0.0588093	+	0.00369997i
$289$	4.78762	+	7.54409i	0.281625	+	0.443770i
$290$	5.84539	−	11.3424i	0.343253	−	0.666049i
$291$	1.22600	+	19.4867i	0.0718692	+	1.14233i
$292$	13.2008	+	2.51818i	0.772516	+	0.147365i
$293$	5.77468	−	1.87631i	0.337361	−	0.109615i	−0.135438	−	0.990786i	$-0.543244\pi$
$293$	5.77468	−	1.87631i	0.337361	−	0.109615i	0.472798	+	0.881171i	$0.343244\pi$
$294$	3.59262	−	3.37370i	0.209526	−	0.196758i
$295$	2.60011	+	28.9321i	0.151384	+	1.68449i
$296$	1.60582	+	8.41799i	0.0933363	+	0.489286i
$297$	−2.65678	+	2.82919i	−0.154162	+	0.164166i
$298$	0.0457185	−	0.115472i	0.00264840	−	0.00668911i
$299$	2.20462	+	6.78512i	0.127496	+	0.392393i
$300$	−4.35909	−	2.44914i	−0.251672	−	0.141401i
$301$	3.52201	−	10.8396i	0.203006	−	0.624787i
$302$	−3.70469	−	3.06479i	−0.213181	−	0.176359i
$303$	−2.05487	−	0.966946i	−0.118049	−	0.0555496i
$304$	2.03077	+	1.90702i	0.116473	+	0.109375i
$305$	−4.49509	+	5.74008i	−0.257388	+	0.328676i
$306$	2.81750	−	0.355933i	0.161066	−	0.0203473i
$307$			20.3467i			1.16125i	0.814173	+	0.580623i	$0.197191\pi$
$307$			20.3467i			1.16125i	−0.814173	+	0.580623i	$0.802809\pi$
$308$	0.700125	+	5.54206i	0.0398933	+	0.315788i
$309$	1.55109	+	1.87494i	0.0882384	+	0.106662i
$310$	4.07031	−	3.55518i	0.231178	−	0.201921i
$311$	−0.940431	+	14.9477i	−0.0533269	+	0.847607i	0.876912	+	0.480652i	$0.159600\pi$
$311$	−0.940431	+	14.9477i	−0.0533269	+	0.847607i	−0.930238	+	0.366956i	$0.880400\pi$
$312$	0.330108	−	1.28569i	0.0186887	−	0.0727876i
$313$	7.72626	−	30.0918i	0.436714	−	1.70089i	−0.245212	−	0.969469i	$-0.578858\pi$
$313$	7.72626	−	30.0918i	0.436714	−	1.70089i	0.681927	−	0.731420i	$-0.261142\pi$
$314$	−0.572410	+	9.09819i	−0.0323030	+	0.513441i
$315$	2.42397	−	2.11720i	0.136575	−	0.119291i
$316$	8.22393	+	9.94103i	0.462632	+	0.559226i
$317$	0.301523	+	2.38680i	0.0169352	+	0.134056i	0.998315	−	0.0580188i	$-0.0184783\pi$
$317$	0.301523	+	2.38680i	0.0169352	+	0.134056i	−0.981380	+	0.192075i	$0.938478\pi$
$318$		−	0.443819i		−	0.0248881i
$319$	21.9726	−	2.77579i	1.23023	−	0.155414i
$320$	1.37865	−	1.76049i	0.0770688	−	0.0984144i
$321$	3.81145	+	3.57919i	0.212734	+	0.199771i
$322$	−6.99963	−	3.29378i	−0.390074	−	0.183555i
$323$	−6.09584	−	5.04292i	−0.339182	−	0.280595i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	4.87989	−	4.49841i	0.270687	−	0.249527i
$326$	1.78039	+	5.47947i	0.0986065	+	0.303480i
$327$	2.31100	−	5.83693i	0.127799	−	0.322783i
$328$	−2.45557	+	2.61491i	−0.135586	+	0.144384i
$329$	0.296519	+	1.55441i	0.0163476	+	0.0856973i
$330$	−0.776790	−	8.64353i	−0.0427609	−	0.475810i
$331$	−1.33502	+	1.25366i	−0.0733791	+	0.0689075i	−0.720369	−	0.693591i	$-0.756028\pi$
$331$	−1.33502	+	1.25366i	−0.0733791	+	0.0689075i	0.646990	+	0.762499i	$0.276028\pi$
$332$	−4.50311	+	1.46315i	−0.247140	+	0.0803007i
$333$	8.41799	+	1.60582i	0.461303	+	0.0879983i
$334$	−0.240471	−	3.82217i	−0.0131580	−	0.209140i
$335$	2.93447	−	5.69405i	0.160327	−	0.311099i
$336$	0.771225	+	1.21526i	0.0420738	+	0.0662977i
$337$	10.4805	−	0.659375i	0.570907	−	0.0359184i	0.225286	−	0.974293i	$-0.427668\pi$
$337$	10.4805	−	0.659375i	0.570907	−	0.0359184i	0.345621	+	0.938374i	$0.387668\pi$
$338$	−9.48859	−	6.02164i	−0.516111	−	0.327534i
$339$	−2.70539	+	3.27025i	−0.146936	+	0.177616i
$340$	−3.59356	+	5.23557i	−0.194888	+	0.283939i
$341$	9.08545	+	2.33275i	0.492005	+	0.126325i
$342$	2.52068	−	1.18614i	0.136303	−	0.0641392i
$343$	−16.3284	−	5.30542i	−0.881651	−	0.286466i
$344$	−6.93918	−	3.81485i	−0.374136	−	0.205683i
$345$	10.6829	+	5.50553i	0.575150	+	0.296408i
$346$	−15.7981	−	1.99577i	−0.849312	−	0.107293i
$347$	−3.67904	+	29.1226i	−0.197501	+	1.56338i	0.512192	+	0.858871i	$0.328834\pi$
$347$	−3.67904	+	29.1226i	−0.197501	+	1.56338i	−0.709693	+	0.704511i	$0.751166\pi$
$348$	4.81813	−	3.05768i	0.258279	−	0.163909i
$349$	23.4771	−	17.0571i	1.25670	−	0.913045i	0.258108	−	0.966116i	$-0.416901\pi$
$349$	23.4771	−	17.0571i	1.25670	−	0.913045i	0.998591	+	0.0530708i	$0.0169009\pi$
$350$	−0.0664811	+	7.19628i	−0.00355357	+	0.384657i
$351$	−1.07388	−	0.780219i	−0.0573195	−	0.0416450i
$352$	3.87342	+	0.243695i	0.206454	+	0.0129890i
$353$	8.74144	+	15.9006i	0.465260	+	0.846305i	0.999999	+	0.00128746i	$0.000409811\pi$
$353$	8.74144	+	15.9006i	0.465260	+	0.846305i	−0.534739	+	0.845017i	$0.679590\pi$
$354$	−5.53128	+	11.7546i	−0.293984	+	0.624748i
$355$	−0.861267	−	3.93845i	−0.0457113	−	0.209031i
$356$	−1.47356	+	7.72465i	−0.0780983	+	0.409406i
$357$	−2.40258	−	3.30686i	−0.127158	−	0.175018i
$358$	−6.42915	+	11.6946i	−0.339791	+	0.618078i
$359$	0.871072	−	1.37259i	0.0459734	−	0.0724425i	−0.820564	−	0.571555i	$-0.806340\pi$
$359$	0.871072	−	1.37259i	0.0459734	−	0.0724425i	0.866537	+	0.499112i	$0.166340\pi$
$360$	−1.12935	−	1.92991i	−0.0595219	−	0.101715i
$361$	10.4500	+	4.13744i	0.549999	+	0.217760i
$362$	−4.74995	−	11.9970i	−0.249652	−	0.630548i
$363$	3.13043	−	2.58972i	0.164305	−	0.135925i
$364$	−1.85051	+	0.475130i	−0.0969931	+	0.0249036i
$365$	8.25032	+	28.8953i	0.431841	+	1.51245i
$366$	−3.03154	+	1.20027i	−0.158461	+	0.0627392i
$367$	−3.13096	−	3.33414i	−0.163435	−	0.174041i	0.642039	−	0.766672i	$-0.278089\pi$
$367$	−3.13096	−	3.33414i	−0.163435	−	0.174041i	−0.805473	+	0.592632i	$0.798089\pi$
$368$	−3.15916	+	4.34821i	−0.164683	+	0.226666i
$369$	1.52733	+	3.24574i	0.0795097	+	0.168967i
$370$	−15.1955	+	11.6748i	−0.789978	+	0.606946i
$371$	−0.559781	+	0.307742i	−0.0290624	+	0.0159772i
$372$	2.37408	−	0.452880i	0.123090	−	0.0234807i
$373$	−2.26058	−	8.80436i	−0.117048	−	0.455873i	0.882857	−	0.469642i	$-0.155617\pi$
$373$	−2.26058	−	8.80436i	−0.117048	−	0.455873i	−0.999905	+	0.0137693i	$0.995617\pi$
$374$	−11.0218			−0.569926
$375$	0.505994	−	11.1689i	0.0261294	−	0.576759i
$376$	1.09944			0.0566991
$377$	1.88375	+	7.33672i	0.0970181	+	0.377861i
$378$	1.41382	−	0.269701i	0.0727192	−	0.0138719i
$379$	−32.1526	+	17.6760i	−1.65157	+	0.907956i	−0.664568	+	0.747228i	$0.731384\pi$
$379$	−32.1526	+	17.6760i	−1.65157	+	0.907956i	−0.986999	+	0.160728i	$0.948616\pi$
$380$	−1.76552	+	5.97383i	−0.0905693	+	0.306451i
$381$	1.02661	+	2.18166i	0.0525948	+	0.111770i
$382$	−8.57391	+	11.8010i	−0.438679	+	0.603790i
$383$	25.4240	+	27.0739i	1.29911	+	1.38341i	0.879641	+	0.475639i	$0.157783\pi$
$383$	25.4240	+	27.0739i	1.29911	+	1.38341i	0.419467	+	0.907770i	$0.362217\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	−10.3633	+	6.97314i	−0.528163	+	0.355384i
$386$	−14.9945	+	3.84993i	−0.763199	+	0.195956i
$387$	−6.10144	+	5.04755i	−0.310153	+	0.256581i
$388$	−7.18770	−	18.1541i	−0.364900	−	0.921633i
$389$	12.0541	+	4.77254i	0.611165	+	0.241978i	0.653257	−	0.757136i	$-0.273402\pi$
$389$	12.0541	+	4.77254i	0.611165	+	0.241978i	−0.0420915	+	0.999114i	$0.513402\pi$
$390$	2.89961	−	0.634091i	0.146827	−	0.0321085i
$391$	8.17860	−	12.8874i	0.413610	−	0.651744i
$392$	−2.37426	+	4.31876i	−0.119918	+	0.218130i
$393$	−9.74214	−	13.4089i	−0.491426	−	0.676390i
$394$	1.99805	−	10.4741i	0.100660	−	0.527679i
$395$	−11.5796	+	26.4234i	−0.582635	+	1.32951i
$396$	1.65248	−	3.51171i	0.0830404	−	0.176470i
$397$	18.6303	+	33.8884i	0.935029	+	1.70081i	0.678995	+	0.734143i	$0.262416\pi$
$397$	18.6303	+	33.8884i	0.935029	+	1.70081i	0.256034	+	0.966668i	$0.417584\pi$
$398$	26.0672	+	1.64001i	1.30663	+	0.0822064i
$399$	−3.24389	−	2.35682i	−0.162398	−	0.117989i
$400$	4.90257	+	0.982238i	0.245129	+	0.0491119i
$401$	−22.1815	+	16.1158i	−1.10769	+	0.804784i	−0.982298	−	0.187323i	$-0.940019\pi$
$401$	−22.1815	+	16.1158i	−1.10769	+	0.804784i	−0.125392	+	0.992107i	$0.540019\pi$
$402$	2.41877	−	1.53500i	0.120637	−	0.0765588i
$403$	−0.402088	+	3.18285i	−0.0200294	+	0.158549i
$404$	2.25310	+	0.284632i	0.112096	+	0.0141610i
$405$	−2.21013	+	0.339593i	−0.109822	+	0.0168745i
$406$	−7.19747	−	3.95684i	−0.357205	−	0.196375i
$407$	−31.6322	−	10.2779i	−1.56795	−	0.509457i
$408$	−2.56961	+	1.20917i	−0.127215	+	0.0598627i
$409$	−4.56367	−	1.17175i	−0.225659	−	0.0579394i	0.134167	−	0.990959i	$-0.457164\pi$
$409$	−4.56367	−	1.17175i	−0.225659	−	0.0579394i	−0.359826	+	0.933019i	$0.617164\pi$
$410$	−7.69219	−	2.27337i	−0.379890	−	0.112274i
$411$	−4.43634	+	5.36261i	−0.218828	+	0.264518i
$412$	−2.05456	−	1.30387i	−0.101221	−	0.0642368i
$413$	18.6612	−	1.17406i	0.918259	−	0.0577719i
$414$	2.87990	+	4.53800i	0.141539	+	0.223030i
$415$	−7.45180	−	7.52095i	−0.365794	−	0.369189i
$416$	0.0833474	+	1.32477i	0.00408644	+	0.0649522i
$417$	−3.98140	−	0.759493i	−0.194970	−	0.0371926i
$418$	−10.2828	+	3.34108i	−0.502948	+	0.163418i
$419$	−11.9405	+	11.2129i	−0.583334	+	0.547787i	−0.919032	−	0.394183i	$-0.871028\pi$
$419$	−11.9405	+	11.2129i	−0.583334	+	0.547787i	0.335698	+	0.941970i	$0.391028\pi$
$420$	−1.65108	+	2.76263i	−0.0805646	+	0.134802i
$421$	0.522827	+	2.74076i	0.0254810	+	0.133576i	0.992755	−	0.120160i	$-0.0383406\pi$
$421$	0.522827	+	2.74076i	0.0254810	+	0.133576i	−0.967274	+	0.253736i	$0.918341\pi$
$422$	−7.88121	+	8.39263i	−0.383651	+	0.408547i
$423$	0.404729	−	1.02223i	0.0196786	−	0.0497025i
$424$	0.137147	+	0.422097i	0.00666047	+	0.0204988i
$425$	−14.0704	−	1.90973i	−0.682517	−	0.0926353i
$426$	0.557143	−	1.71471i	0.0269936	−	0.0830779i
$427$	3.61594	+	2.99137i	0.174988	+	0.144762i
$428$	−4.73093	−	2.22621i	−0.228678	−	0.107608i
$429$	3.75543	+	3.52658i	0.181314	+	0.170265i
$430$	0.637921	−	17.6952i	0.0307633	−	0.853337i
$431$	19.8464	−	2.50718i	0.955967	−	0.120767i	0.368155	−	0.929764i	$-0.379990\pi$
$431$	19.8464	−	2.50718i	0.955967	−	0.120767i	0.587812	+	0.808998i	$0.299990\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	0.441024	+	3.49106i	0.0211943	+	0.167770i	0.999159	−	0.0409995i	$-0.0130542\pi$
$433$	0.441024	+	3.49106i	0.0211943	+	0.167770i	−0.977965	+	0.208769i	$0.933054\pi$
$434$	−2.21739	−	2.68036i	−0.106438	−	0.128662i
$435$	10.9530	+	6.54605i	0.525156	+	0.313859i
$436$	−0.394185	+	6.26539i	−0.0188780	+	0.300058i
$437$	3.72360	−	14.5025i	0.178124	−	0.693747i
$438$	−3.34209	+	13.0166i	−0.159691	+	0.621956i
$439$	1.62568	−	25.8394i	0.0775893	−	1.23325i	−0.745956	−	0.665995i	$-0.768007\pi$
$439$	1.62568	−	25.8394i	0.0775893	−	1.23325i	0.823545	−	0.567251i	$-0.191993\pi$
$440$	3.40977	+	7.98044i	0.162554	+	0.380453i
$441$	3.14146	+	3.79737i	0.149593	+	0.180827i
$442$	−0.472461	−	3.73991i	−0.0224727	−	0.177890i
$443$			29.6219i			1.40738i	0.710507	+	0.703690i	$0.248466\pi$
$443$			29.6219i			1.40738i	−0.710507	+	0.703690i	$0.751534\pi$
$444$	−8.50221	+	1.07408i	−0.403497	+	0.0509735i
$445$	−16.9086	+	4.82782i	−0.801544	+	0.228860i
$446$	13.5608	+	12.7344i	0.642121	+	0.602992i
$447$	0.112373	+	0.0528789i	0.00531508	+	0.00250108i
$448$	−1.10901	−	0.917456i	−0.0523960	−	0.0433457i
$449$	−3.29315	+	10.1353i	−0.155413	+	0.478313i	−0.998203	−	0.0599307i	$-0.980912\pi$
$449$	−3.29315	+	10.1353i	−0.155413	+	0.478313i	0.842789	+	0.538244i	$0.180912\pi$
$450$	2.71802	−	4.19671i	0.128129	−	0.197835i
$451$	−4.30213	−	13.2406i	−0.202579	−	0.623475i
$452$	1.56241	−	3.94620i	0.0734897	−	0.185614i
$453$	3.29136	−	3.50494i	0.154641	−	0.164676i
$454$	0.756457	+	3.96549i	0.0355023	+	0.186110i
$455$	−2.81035	−	3.21755i	−0.131751	−	0.150841i
$456$	−2.03077	+	1.90702i	−0.0950995	+	0.0893044i
$457$	22.2755	−	7.23774i	1.04200	−	0.338567i	0.262478	−	0.964938i	$-0.415460\pi$
$457$	22.2755	−	7.23774i	1.04200	−	0.338567i	0.779525	+	0.626371i	$0.215460\pi$
$458$	−24.8698	−	4.74416i	−1.16209	−	0.221680i
$459$	0.178318	+	2.83429i	0.00832318	+	0.132293i
$460$	−11.8614	−	1.93486i	−0.553040	−	0.0902134i
$461$	−15.9988	−	25.2101i	−0.745139	−	1.17415i	−0.979391	−	0.201976i	$-0.935264\pi$
$461$	−15.9988	−	25.2101i	−0.745139	−	1.17415i	0.234251	−	0.972176i	$-0.424736\pi$
$462$	−5.57509	+	0.350755i	−0.259376	+	0.0163186i
$463$	−0.357116	−	0.226633i	−0.0165966	−	0.0105325i	0.527503	−	0.849553i	$-0.323128\pi$
$463$	−0.357116	−	0.226633i	−0.0165966	−	0.0105325i	−0.544099	+	0.839021i	$0.683128\pi$
$464$	−3.63744	+	4.39691i	−0.168864	+	0.204121i
$465$	3.29259	+	4.28551i	0.152690	+	0.198736i
$466$	26.1577	+	6.71614i	1.21173	+	0.311119i
$467$	19.6777	−	9.25964i	0.910577	−	0.428485i	0.0873373	−	0.996179i	$-0.472164\pi$
$467$	19.6777	−	9.25964i	0.910577	−	0.428485i	0.823240	+	0.567694i	$0.192164\pi$
$468$	1.26242	+	0.410186i	0.0583555	+	0.0189608i
$469$	−3.61324	−	1.98639i	−0.166844	−	0.0917232i
$470$	1.10597	+	2.19559i	0.0510144	+	0.101275i
$471$	−9.04430	−	1.14256i	−0.416739	−	0.0526464i
$472$	1.62820	−	12.8885i	0.0749439	−	0.593242i
$473$	25.9487	−	16.4676i	1.19312	−	0.757179i
$474$	−10.4378	+	7.58350i	−0.479424	+	0.348322i
$475$	−13.7059	+	2.48354i	−0.628868	+	0.113953i
$476$	3.30686	+	2.40258i	0.151570	+	0.110122i
$477$	0.442943	+	0.0278676i	0.0202810	+	0.00127597i
$478$	1.30340	+	2.37088i	0.0596163	+	0.108442i
$479$	−14.5761	+	30.9759i	−0.666001	+	1.41532i	0.230849	+	0.972990i	$0.425850\pi$
$479$	−14.5761	+	30.9759i	−0.666001	+	1.41532i	−0.896850	+	0.442335i	$0.854150\pi$
$480$	1.67045	+	1.48647i	0.0762453	+	0.0678478i
$481$	2.13154	−	11.1739i	0.0971901	−	0.509488i
$482$	−11.2618	−	15.5005i	−0.512959	−	0.706028i
$483$	3.72679	−	6.77900i	0.169575	−	0.308455i
$484$	−2.17695	+	3.43032i	−0.0989522	+	0.155924i
$485$	29.0236	−	32.6159i	1.31789	−	1.48101i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	−7.12955	−	18.0072i	−0.323071	−	0.815984i	−0.997015	−	0.0772021i	$-0.975401\pi$
$487$	−7.12955	−	18.0072i	−0.323071	−	0.815984i	0.673945	−	0.738782i	$-0.264599\pi$
$488$	2.51226	−	2.07832i	0.113725	−	0.0940812i
$489$	−5.58045	+	1.43282i	−0.252357	+	0.0647941i
$490$	−11.0130	−	0.397025i	−0.497517	−	0.0179357i
$491$	−35.5512	+	14.0757i	−1.60440	+	0.635229i	−0.988312	−	0.152445i	$-0.951285\pi$
$491$	−35.5512	+	14.0757i	−1.60440	+	0.635229i	−0.616093	+	0.787673i	$0.711285\pi$
$492$	−2.45557	−	2.61491i	−0.110706	−	0.117889i
$493$	9.52549	−	13.1107i	0.429007	−	0.590477i
$494$	−1.57447	−	3.34592i	−0.0708388	−	0.150540i
$495$	8.67524	−	0.232526i	0.389923	−	0.0104512i
$496$	−2.11794	+	1.16435i	−0.0950982	+	0.0522807i
$497$	−2.54905	+	0.486258i	−0.114341	+	0.0218117i
$498$	−1.17751	−	4.58610i	−0.0527655	−	0.205508i
$499$	18.8225			0.842611			0.421306	−	0.906919i	$-0.361572\pi$
$499$	18.8225			0.842611			0.421306	+	0.906919i	$0.361572\pi$
$500$	2.97015	+	10.7786i	0.132829	+	0.482034i
$501$	3.82973			0.171100
$502$	−1.70919	−	6.65685i	−0.0762848	−	0.297110i
$503$	29.4472	−	5.61736i	1.31299	−	0.250466i	0.517108	−	0.855920i	$-0.327009\pi$
$503$	29.4472	−	5.61736i	1.31299	−	0.250466i	0.795880	+	0.605455i	$0.207009\pi$
$504$	−1.26128	+	0.693397i	−0.0561820	+	0.0308863i
$505$	1.69806	+	4.78580i	0.0755628	+	0.212965i
$506$	−8.88158	−	18.8743i	−0.394834	−	0.839065i
$507$	6.60555	−	9.09177i	0.293363	−	0.403779i
$508$	−1.65053	−	1.75764i	−0.0732305	−	0.0779826i
$509$	−21.9403	+	8.68680i	−0.972488	+	0.385035i	−0.800016	−	0.599979i	$-0.795176\pi$
$509$	−21.9403	+	8.68680i	−0.972488	+	0.385035i	−0.172473	+	0.985014i	$0.555176\pi$
$510$	−4.99960	−	3.91521i	−0.221386	−	0.173368i
$511$	18.7350	−	4.81033i	0.828788	−	0.212797i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	1.02553	+	2.59018i	0.0452781	+	0.114359i
$514$	25.6575	+	10.1585i	1.13170	+	0.448074i
$515$	0.537076	−	5.41461i	0.0236664	−	0.238596i
$516$	4.24303	−	6.68595i	0.186789	−	0.294333i
$517$	−2.05564	+	3.73920i	−0.0904071	+	0.164450i
$518$	7.25013	+	9.97894i	0.318552	+	0.438450i
$519$	2.98380	−	15.6416i	0.130974	−	0.686591i
$520$	−2.56175	+	1.49908i	−0.112340	+	0.0657392i
$521$	−18.1458	+	38.5617i	−0.794980	+	1.68942i	−0.0731777	+	0.997319i	$0.523314\pi$
$521$	−18.1458	+	38.5617i	−0.794980	+	1.68942i	−0.721802	+	0.692099i	$0.756686\pi$
$522$	2.74911	+	5.00061i	0.120325	+	0.218871i
$523$	24.0974	+	1.51608i	1.05370	+	0.0662934i	0.580181	−	0.814488i	$-0.302982\pi$
$523$	24.0974	+	1.51608i	1.05370	+	0.0662934i	0.473523	+	0.880781i	$0.342982\pi$
$524$	13.4089	+	9.74214i	0.585771	+	0.425587i
$525$	−7.17791	−	0.518208i	−0.313270	−	0.0226165i
$526$	−0.398483	+	0.289515i	−0.0173747	+	0.0126234i
$527$	5.79522	−	3.67776i	0.252444	−	0.160206i
$528$	−0.486428	+	3.85048i	−0.0211691	+	0.167571i
$529$	5.84080	+	0.737864i	0.253948	+	0.0320811i
$530$	−0.704973	+	0.698490i	−0.0306221	+	0.0303405i
$531$	−11.3841	−	6.25844i	−0.494026	−	0.271593i
$532$	3.81342	+	1.23906i	0.165333	+	0.0537199i
$533$	4.30836	−	2.02736i	0.186616	−	0.0878148i
$534$	−7.61688	−	1.95568i	−0.329615	−	0.0846307i
$535$	−0.313256	−	11.6872i	−0.0135432	−	0.505281i
$536$	−1.82605	+	2.20731i	−0.0788732	+	0.0953414i
$537$	−11.2678	−	7.15077i	−0.486242	−	0.308579i
$538$	6.13065	−	0.385708i	0.264311	−	0.0166290i
$539$	−10.2490	−	16.1498i	−0.441454	−	0.695620i
$540$	1.99702	−	1.00594i	0.0859380	−	0.0432888i
$541$	−1.63275	−	25.9517i	−0.0701972	−	1.11575i	−0.862644	−	0.505812i	$-0.831193\pi$
$541$	−1.63275	−	25.9517i	−0.0701972	−	1.11575i	0.792447	−	0.609941i	$-0.208807\pi$
$542$	21.8773	+	4.17333i	0.939712	+	0.179260i
$543$	12.2716	−	3.98728i	0.526624	−	0.171110i
$544$	2.07019	−	1.94404i	0.0887587	−	0.0833500i
$545$	−12.9086	+	5.51541i	−0.552945	+	0.236254i
$546$	−0.357998	−	1.87669i	−0.0153209	−	0.0803151i
$547$	−7.70930	+	8.20958i	−0.329626	+	0.351016i	−0.872338	−	0.488903i	$-0.837397\pi$
$547$	−7.70930	+	8.20958i	−0.329626	+	0.351016i	0.542712	+	0.839919i	$0.317397\pi$
$548$	2.56207	−	6.47105i	0.109446	−	0.276430i
$549$	−1.00755	−	3.10092i	−0.0430012	−	0.132344i
$550$	−12.5071	+	14.8372i	−0.533303	+	0.632661i
$551$	4.91249	−	15.1191i	0.209279	−	0.644094i
$552$	−4.14126	−	3.42595i	−0.176264	−	0.145818i
$553$	16.8025	+	7.90665i	0.714514	+	0.336225i
$554$	17.4429	+	16.3800i	0.741079	+	0.695920i
$555$	−10.6977	−	15.8986i	−0.454091	−	0.674859i
$556$	4.02124	−	0.508000i	0.170538	−	0.0215440i
$557$			7.58793i			0.321511i	0.986994	+	0.160755i	$0.0513930\pi$
$557$			7.58793i			0.321511i	−0.986994	+	0.160755i	$0.948607\pi$
$558$	0.302917	+	2.39783i	0.0128235	+	0.101508i
$559$	6.70006	+	8.09898i	0.283382	+	0.342550i
$560$	0.716575	−	3.13763i	0.0302808	−	0.132589i
$561$	0.692067	−	11.0001i	0.0292191	−	0.464424i
$562$	6.52324	−	25.4063i	0.275166	−	1.07170i
$563$	−0.852483	+	3.32020i	−0.0359279	+	0.139930i	−0.984017	−	0.178075i	$-0.943013\pi$
$563$	−0.852483	+	3.32020i	−0.0359279	+	0.139930i	0.948089	+	0.318005i	$0.103013\pi$
$564$	−0.0690342	+	1.09727i	−0.00290686	+	0.0462033i
$565$	9.45234	−	0.849478i	0.397663	−	0.0357378i
$566$	4.07079	+	4.92075i	0.171108	+	0.206834i
$567$	0.180394	+	1.42797i	0.00757585	+	0.0599690i
$568$			1.80295i			0.0756502i
$569$	−20.2518	+	2.55840i	−0.849001	+	0.107254i	−0.537781	−	0.843084i	$-0.680737\pi$
$569$	−20.2518	+	2.55840i	−0.849001	+	0.107254i	−0.311219	+	0.950338i	$0.600737\pi$
$570$	−5.85119	−	2.13714i	−0.245079	−	0.0895149i
$571$	−13.5051	−	12.6821i	−0.565169	−	0.530729i	0.348436	−	0.937333i	$-0.386713\pi$
$571$	−13.5051	−	12.6821i	−0.565169	−	0.530729i	−0.913605	+	0.406604i	$0.866713\pi$
$572$	−4.66140	−	2.19349i	−0.194903	−	0.0917143i
$573$	−11.2393	−	9.29798i	−0.469530	−	0.388429i
$574$	−1.59547	+	4.91034i	−0.0665935	+	0.204954i
$575$	−8.06789	−	25.6338i	−0.336454	−	1.06900i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−8.09170	+	20.4373i	−0.336862	+	0.850816i	0.658317	+	0.752741i	$0.271269\pi$
$577$	−8.09170	+	20.4373i	−0.336862	+	0.850816i	−0.995179	+	0.0980754i	$0.968731\pi$
$578$	6.11644	−	6.51335i	0.254410	−	0.270920i
$579$	−2.90082	−	15.2066i	−0.120554	−	0.631966i
$580$	−12.4398	−	2.84101i	−0.516533	−	0.117966i
$581$	−4.96789	+	4.66516i	−0.206103	+	0.193543i
$582$	18.5696	−	6.03362i	0.769733	−	0.250101i
$583$	−1.69199	−	0.322764i	−0.0700749	−	0.0133675i
$584$	−0.843829	−	13.4123i	−0.0349179	−	0.555004i
$585$	0.450772	+	2.93370i	0.0186371	+	0.121294i
$586$	−3.25347	−	5.12664i	−0.134399	−	0.211780i
$587$	34.6115	−	2.17757i	1.42857	−	0.0898779i	0.670431	−	0.741972i	$-0.266109\pi$
$587$	34.6115	−	2.17757i	1.42857	−	0.0898779i	0.758138	+	0.652094i	$0.226109\pi$
$588$	−4.16116	−	2.64075i	−0.171603	−	0.108903i
$589$	4.29178	−	5.18787i	0.176840	−	0.213762i
$590$	27.3765	−	9.71354i	1.12707	−	0.399900i
$591$	10.3280	+	2.65178i	0.424837	+	0.109080i
$592$	7.75418	−	3.64884i	0.318695	−	0.149966i
$593$	−10.1073	−	3.28406i	−0.415057	−	0.134860i	0.0940420	−	0.995568i	$-0.470021\pi$
$593$	−10.1073	−	3.28406i	−0.415057	−	0.134860i	−0.509099	+	0.860708i	$0.670021\pi$
$594$	3.40102	+	1.86972i	0.139545	+	0.0767157i
$595$	−1.47148	+	9.02071i	−0.0603250	+	0.369813i
$596$	−0.123214	−	0.0155655i	−0.00504704	−	0.000637589i
$597$	−3.27355	+	25.9128i	−0.133978	+	1.06054i
$598$	6.02368	−	3.82275i	0.246327	−	0.156324i
$599$	−12.0370	+	8.74536i	−0.491817	+	0.357326i	−0.805882	−	0.592076i	$-0.798309\pi$
$599$	−12.0370	+	8.74536i	−0.491817	+	0.357326i	0.314066	+	0.949401i	$0.398309\pi$
$600$	−1.28813	+	4.83122i	−0.0525879	+	0.197234i
$601$	−29.7453	−	21.6112i	−1.21334	−	0.881541i	−0.217807	−	0.975992i	$-0.569890\pi$
$601$	−29.7453	−	21.6112i	−1.21334	−	0.881541i	−0.995529	+	0.0944512i	$0.969890\pi$
$602$	−11.3750	−	0.715654i	−0.463610	−	0.0291679i
$603$	1.38009	+	2.51038i	0.0562018	+	0.102231i
$604$	−2.04718	+	4.35048i	−0.0832986	+	0.177019i
$605$	−9.04030	−	0.896709i	−0.367540	−	0.0364564i
$606$	−0.425544	+	2.23078i	−0.0172865	+	0.0906192i
$607$	12.9487	+	17.8224i	0.525573	+	0.723390i	0.986448	−	0.164076i	$-0.0524641\pi$
$607$	12.9487	+	17.8224i	0.525573	+	0.723390i	−0.460874	+	0.887465i	$0.652464\pi$
$608$	1.34208	−	2.44123i	0.0544283	−	0.0990048i
$609$	4.40097	−	6.93482i	0.178336	−	0.281013i
$610$	6.67763	+	2.92636i	0.270369	+	0.118485i
$611$	−1.35690	−	0.537233i	−0.0548941	−	0.0217341i
$612$	−1.04543	−	2.64046i	−0.0422591	−	0.106734i
$613$	−29.9637	+	24.7882i	−1.21022	+	1.00118i	−0.210503	+	0.977593i	$0.567510\pi$
$613$	−29.9637	+	24.7882i	−1.21022	+	1.00118i	−0.999722	+	0.0235914i	$0.992490\pi$
$614$	19.7074	−	5.06001i	0.795327	−	0.204205i
$615$	2.75188	−	7.53426i	0.110966	−	0.303811i
$616$	5.19383	−	2.05638i	0.209265	−	0.0828541i
$617$	−8.19864	−	8.73067i	−0.330065	−	0.351483i	0.542435	−	0.840098i	$-0.317502\pi$
$617$	−8.19864	−	8.73067i	−0.330065	−	0.351483i	−0.872500	+	0.488614i	$0.837502\pi$
$618$	1.43030	−	1.96864i	0.0575351	−	0.0791902i
$619$	3.63154	+	7.71742i	0.145964	+	0.310189i	0.964418	−	0.264383i	$-0.0851683\pi$
$619$	3.63154	+	7.71742i	0.145964	+	0.310189i	−0.818454	+	0.574573i	$0.805168\pi$
$620$	−4.45574	−	3.05830i	−0.178947	−	0.122824i
$621$	−4.70987	+	2.58927i	−0.189001	+	0.103904i
$622$	14.7120	−	2.80646i	0.589897	−	0.112529i
$623$	2.81485	+	10.9631i	0.112775	+	0.439228i
$624$	−1.32739			−0.0531381
$625$	−18.5373	+	16.7741i	−0.741491	+	0.670963i
$626$	−31.0679			−1.24172
$627$	−2.68883	−	10.4723i	−0.107381	−	0.418223i
$628$	8.95471	−	1.70820i	0.357332	−	0.0681647i
$629$	−21.3269	+	11.7246i	−0.850359	+	0.467489i
$630$	−2.65350	−	1.82129i	−0.105718	−	0.0725620i
$631$	−1.31256	−	2.78934i	−0.0522523	−	0.111042i	0.876996	−	0.480498i	$-0.159544\pi$
$631$	−1.31256	−	2.78934i	−0.0522523	−	0.111042i	−0.929248	+	0.369456i	$0.879544\pi$
$632$	7.58350	−	10.4378i	0.301656	−	0.415193i
$633$	−7.88121	−	8.39263i	−0.313250	−	0.333577i
$634$	2.23683	−	0.885624i	0.0888359	−	0.0351726i
$635$	1.84970	−	5.06422i	0.0734031	−	0.200968i
$636$	−0.429875	+	0.110373i	−0.0170457	+	0.00437658i
$637$	5.04059	−	4.16993i	0.199715	−	0.165219i
$638$	−8.15295	−	20.5920i	−0.322778	−	0.815245i
$639$	1.67634	+	0.663711i	0.0663151	+	0.0262560i
$640$	−2.04804	−	0.897519i	−0.0809558	−	0.0354776i
$641$	−6.83715	+	10.7736i	−0.270051	+	0.425533i	−0.952106	−	0.305769i	$-0.901087\pi$
$641$	−6.83715	+	10.7736i	−0.270051	+	0.425533i	0.682055	+	0.731301i	$0.261087\pi$
$642$	2.51887	−	4.58181i	0.0994119	−	0.180830i
$643$	−21.2655	−	29.2694i	−0.838628	−	1.15427i	−0.986255	−	0.165230i	$-0.947164\pi$
$643$	−21.2655	−	29.2694i	−0.838628	−	1.15427i	0.147627	−	0.989043i	$-0.452836\pi$
$644$	−1.44956	+	7.59885i	−0.0571206	+	0.299437i
$645$	17.6202	+	1.74775i	0.693795	+	0.0688176i
$646$	−3.36851	+	7.15845i	−0.132532	+	0.281645i
$647$	−16.0868	−	29.2618i	−0.632439	−	1.15040i	−0.977322	−	0.211756i	$-0.932082\pi$
$647$	−16.0868	−	29.2618i	−0.632439	−	1.15040i	0.344884	−	0.938645i	$-0.387918\pi$
$648$	0.998027	+	0.0627905i	0.0392062	+	0.00246664i
$649$	40.7898	+	29.6355i	1.60114	+	1.16330i
$650$	−5.57066	−	3.60787i	−0.218499	−	0.141512i
$651$	2.81431	−	2.04471i	0.110301	−	0.0801386i
$652$	4.86456	−	3.08714i	0.190511	−	0.120902i
$653$	4.02383	−	31.8519i	0.157465	−	1.24646i	−0.693197	−	0.720748i	$-0.743799\pi$
$653$	4.02383	−	31.8519i	0.157465	−	1.24646i	0.850662	−	0.525713i	$-0.176201\pi$
$654$	−6.22827	−	0.786814i	−0.243545	−	0.0307669i
$655$	−5.96668	+	36.5779i	−0.233138	+	1.42922i
$656$	3.14344	+	1.72812i	0.122731	+	0.0674717i
$657$	−12.7810	−	4.15281i	−0.498636	−	0.162017i
$658$	1.43183	−	0.673769i	0.0558186	−	0.0262663i
$659$	−16.0552	−	4.12229i	−0.625424	−	0.160582i	−0.0773397	−	0.997005i	$-0.524643\pi$
$659$	−16.0552	−	4.12229i	−0.625424	−	0.160582i	−0.548084	+	0.836423i	$0.684643\pi$
$660$	−8.17879	+	2.90194i	−0.318359	+	0.112958i
$661$	9.11306	−	11.0158i	0.354457	−	0.428465i	−0.562903	−	0.826523i	$-0.690316\pi$
$661$	9.11306	−	11.0158i	0.354457	−	0.428465i	0.917360	+	0.398058i	$0.130316\pi$
$662$	1.54628	+	0.981300i	0.0600979	+	0.0381393i
$663$	3.76220	−	0.236698i	0.146112	−	0.00919257i
$664$	2.53706	+	3.99777i	0.0984570	+	0.155143i
$665$	1.36166	+	8.86189i	0.0528028	+	0.343649i
$666$	−0.538101	−	8.55288i	−0.0208510	−	0.331417i
$667$	30.1272	+	5.74707i	1.16653	+	0.222527i
$668$	−3.64229	+	1.18345i	−0.140924	+	0.0457891i
$669$	−13.5608	+	12.7344i	−0.524289	+	0.492341i
$670$	−6.24494	−	1.42623i	−0.241263	−	0.0551000i
$671$	2.37117	+	12.4301i	0.0915382	+	0.479860i
$672$	0.985281	−	1.04922i	0.0380080	−	0.0404744i
$673$	2.45045	−	6.18914i	0.0944581	−	0.238574i	−0.874864	−	0.484369i	$-0.839049\pi$
$673$	2.45045	−	6.18914i	0.0944581	−	0.238574i	0.969322	+	0.245795i	$0.0790491\pi$
$674$	−3.24504	−	9.98722i	−0.124994	−	0.384693i
$675$	4.01776	+	2.97617i	0.154644	+	0.114553i
$676$	−3.47275	+	10.6880i	−0.133567	+	0.411077i
$677$	16.7712	+	13.8743i	0.644570	+	0.533234i	0.901271	−	0.433257i	$-0.142636\pi$
$677$	16.7712	+	13.8743i	0.644570	+	0.533234i	−0.256701	+	0.966491i	$0.582636\pi$
$678$	3.84031	+	1.80711i	0.147486	+	0.0694018i
$679$	−20.4862	−	19.2378i	−0.786187	−	0.738279i
$680$	5.96477	+	2.17862i	0.228739	+	0.0835464i
$681$	−4.00516	+	0.505969i	−0.153478	+	0.0193888i
$682$		−	9.38014i		−	0.359184i
$683$	−1.81834	−	14.3936i	−0.0695769	−	0.550758i	−0.987919	−	0.154970i	$-0.950472\pi$
$683$	−1.81834	−	14.3936i	−0.0695769	−	0.550758i	0.918342	−	0.395787i	$-0.129528\pi$
$684$	−1.77574	−	2.14651i	−0.0678973	−	0.0820737i
$685$	15.5001	−	1.39299i	0.592228	−	0.0532233i
$686$	−1.07803	+	17.1348i	−0.0411595	+	0.654211i
$687$	6.29638	−	24.5228i	0.240222	−	0.935603i
$688$	−1.96929	+	7.66989i	−0.0750786	+	0.292412i
$689$	0.0369911	−	0.587957i	0.00140925	−	0.0223994i
$690$	2.67583	−	11.7165i	0.101867	−	0.446039i
$691$	11.2394	+	13.5861i	0.427566	+	0.516838i	0.939669	−	0.342086i	$-0.111133\pi$
$691$	11.2394	+	13.5861i	0.427566	+	0.516838i	−0.512103	+	0.858924i	$0.671133\pi$
$692$	1.99577	+	15.7981i	0.0758676	+	0.600554i
$693$		−	5.58611i		−	0.212199i
$694$	29.1226	−	3.67904i	1.10548	−	0.139654i
$695$	5.05961	+	7.51947i	0.191922	+	0.285230i
$696$	−4.15983	−	3.90634i	−0.157678	−	0.148070i
$697$	−9.21756	−	4.33745i	−0.349140	−	0.164293i
$698$	−22.3597	−	18.4976i	−0.846328	−	0.700143i
$699$	−8.34534	+	25.6843i	−0.315650	+	0.971470i
$700$	6.98673	−	1.72525i	0.264074	−	0.0652083i
$701$	−14.8103	−	45.5815i	−0.559378	−	1.72159i	−0.684091	−	0.729396i	$-0.739801\pi$
$701$	−14.8103	−	45.5815i	−0.559378	−	1.72159i	0.124713	−	0.992193i	$-0.460199\pi$
$702$	−0.488644	+	1.23417i	−0.0184427	+	0.0465809i
$703$	−16.3428	+	17.4033i	−0.616379	+	0.656377i
$704$	−0.727242	−	3.81234i	−0.0274090	−	0.143683i
$705$	−2.26071	+	0.965922i	−0.0851431	+	0.0363787i
$706$	13.2272	−	12.4211i	0.497811	−	0.467476i
$707$	3.10871	−	1.01008i	0.116915	−	0.0379881i
$708$	12.7609	+	2.43426i	0.479582	+	0.0914852i
$709$	−0.559761	−	8.89715i	−0.0210223	−	0.334139i	−0.994455	−	0.105165i	$-0.966463\pi$
$709$	−0.559761	−	8.89715i	−0.0210223	−	0.334139i	0.973432	−	0.228974i	$-0.0735371\pi$
$710$	−3.60053	+	1.81366i	−0.135125	+	0.0680655i
$711$	−6.91314	−	10.8934i	−0.259263	−	0.408533i
$712$	7.84842	−	0.493781i	0.294132	−	0.0185052i
$713$	10.9678	+	6.96040i	0.410749	+	0.260669i
$714$	−2.60547	+	3.14948i	−0.0975074	+	0.117866i
$715$	−0.308652	−	11.5154i	−0.0115429	−	0.430652i
$716$	12.9260	+	3.31884i	0.483069	+	0.124031i
$717$	−2.44804	+	1.15196i	−0.0914239	+	0.0430208i
$718$	−1.54609	−	0.502356i	−0.0576997	−	0.0187478i
$719$	15.4447	+	8.49078i	0.575989	+	0.316653i	0.742988	−	0.669304i	$-0.233408\pi$
$719$	15.4447	+	8.49078i	0.575989	+	0.316653i	−0.166999	+	0.985957i	$0.553408\pi$
$720$	−1.58843	+	1.57382i	−0.0591971	+	0.0586528i
$721$	−3.47478	−	0.438966i	−0.129407	−	0.0163480i
$722$	1.40865	−	11.1506i	0.0524246	−	0.414983i
$723$	16.1770	−	10.2663i	0.601630	−	0.381806i
$724$	−10.4388	+	7.58425i	−0.387956	+	0.281866i
$725$	−6.84010	−	27.7003i	−0.254035	−	1.02876i
$726$	−3.28686	−	2.38805i	−0.121987	−	0.0886287i
$727$	−43.6423	−	2.74574i	−1.61860	−	0.101834i	−0.772558	−	0.634944i	$-0.781023\pi$
$727$	−43.6423	−	2.74574i	−1.61860	−	0.101834i	−0.846046	+	0.533110i	$0.821023\pi$
$728$	0.920407	+	1.67421i	0.0341125	+	0.0620505i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	25.9357	−	15.1771i	0.959924	−	0.561729i
$731$	4.21386	−	22.0898i	0.155855	−	0.817021i
$732$	1.91647	+	2.63780i	0.0708350	+	0.0974959i
$733$	6.49410	−	11.8127i	0.239865	−	0.436313i	−0.728785	−	0.684743i	$-0.759914\pi$
$733$	6.49410	−	11.8127i	0.239865	−	0.436313i	0.968650	+	0.248430i	$0.0799145\pi$
$734$	−2.45075	+	3.86176i	−0.0904588	+	0.142540i
$735$	1.08775	−	10.9663i	0.0401224	−	0.404500i
$736$	4.99725	+	1.97855i	0.184201	+	0.0729304i
$737$	−4.09290	−	10.3375i	−0.150764	−	0.380786i
$738$	2.76394	−	2.28653i	0.101742	−	0.0841683i
$739$	10.5682	−	2.71345i	0.388757	−	0.0998159i	−0.0492519	−	0.998786i	$-0.515684\pi$
$739$	10.5682	−	2.71345i	0.388757	−	0.0998159i	0.438009	+	0.898970i	$0.355684\pi$
$740$	15.0870	+	11.8147i	0.554611	+	0.434318i
$741$	3.43818	−	1.36127i	0.126305	−	0.0500076i
$742$	0.437286	+	0.465662i	0.0160533	+	0.0170950i
$743$	0.965250	−	1.32855i	0.0354116	−	0.0487399i	−0.790944	−	0.611888i	$-0.790410\pi$
$743$	0.965250	−	1.32855i	0.0354116	−	0.0487399i	0.826356	+	0.563149i	$0.190410\pi$
$744$	−1.02906	−	2.18687i	−0.0377272	−	0.0801744i
$745$	−0.0928611	−	0.261718i	−0.00340217	−	0.00958862i
$746$	−7.96557	+	4.37911i	−0.291640	+	0.160331i
$747$	4.65098	−	0.887222i	0.170171	−	0.0324618i
$748$	2.74102	+	10.6756i	0.100222	+	0.390338i
$749$	−7.52554			−0.274977
$750$	−10.9438	+	2.28749i	−0.399612	+	0.0835274i
$751$	−52.0655			−1.89990			−0.949948	−	0.312409i	$-0.898864\pi$
$751$	−52.0655			−1.89990			−0.949948	+	0.312409i	$0.898864\pi$
$752$	−0.273419	−	1.06490i	−0.00997055	−	0.0388327i
$753$	6.75104	−	1.28783i	0.246021	−	0.0469311i
$754$	6.63776	−	3.64914i	0.241733	−	0.132894i
$755$	−10.7473	+	0.288065i	−0.391136	+	0.0104837i
$756$	−0.612832	−	1.30233i	−0.0222885	−	0.0473654i
$757$	6.98157	−	9.60930i	0.253749	−	0.349256i	−0.663071	−	0.748557i	$-0.730747\pi$
$757$	6.98157	−	9.60930i	0.253749	−	0.349256i	0.916820	+	0.399301i	$0.130747\pi$
$758$	25.1167	+	26.7466i	0.912280	+	0.971480i
$759$	19.3947	−	7.67892i	0.703985	−	0.278727i
$760$	6.22522	+	0.224423i	0.225813	+	0.00814066i
$761$	26.8618	−	6.89695i	0.973741	−	0.250014i	0.271882	−	0.962331i	$-0.412354\pi$
$761$	26.8618	−	6.89695i	0.973741	−	0.250014i	0.701858	+	0.712316i	$0.252354\pi$
$762$	1.85781	−	1.53691i	0.0673013	−	0.0556765i
$763$	3.32627	+	8.40119i	0.120419	+	0.304144i
$764$	13.5625	+	5.36976i	0.490673	+	0.194271i
$765$	4.22141	−	4.74390i	0.152625	−	0.171516i
$766$	19.9006	−	31.3583i	0.719037	−	1.13302i
$767$	−8.30738	+	15.1111i	−0.299962	+	0.545629i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	−1.85133	+	9.70501i	−0.0667607	+	0.349972i	−0.999956	−	0.00939830i	$-0.997008\pi$
$769$	−1.85133	+	9.70501i	−0.0667607	+	0.349972i	0.933195	+	0.359370i	$0.117008\pi$
$770$	9.33132	+	8.30358i	0.336277	+	0.299240i
$771$	−11.7495	+	24.9690i	−0.423149	+	0.899238i
$772$	7.45796	+	13.5660i	0.268418	+	0.488250i
$773$	−10.6792	−	0.671878i	−0.384104	−	0.0241658i	−0.130435	−	0.991457i	$-0.541637\pi$
$773$	−10.6792	−	0.671878i	−0.384104	−	0.0241658i	−0.253669	+	0.967291i	$0.581637\pi$
$774$	6.40634	+	4.65448i	0.230271	+	0.167302i
$775$	1.62527	−	11.9747i	0.0583815	−	0.430142i
$776$	−15.7962	+	11.4766i	−0.567051	+	0.411987i
$777$	−10.4145	+	6.60924i	−0.373618	+	0.237105i
$778$	1.62488	−	12.8622i	0.0582548	−	0.461134i
$779$	−9.91431	−	1.25247i	−0.355217	−	0.0448743i
$780$	−1.33527	−	2.65082i	−0.0478105	−	0.0949146i
$781$	−6.13187	−	3.37102i	−0.219415	−	0.120625i
$782$	−14.5165	−	4.71668i	−0.519108	−	0.168668i
$783$	−5.16336	+	2.42969i	−0.184524	+	0.0868302i
$784$	4.77353	+	1.22563i	0.170483	+	0.0437727i
$785$	12.4192	+	16.1644i	0.443261	+	0.576931i
$786$	−10.5649	+	12.7707i	−0.376836	+	0.455517i
$787$	9.37827	+	5.95163i	0.334299	+	0.212153i	0.692372	−	0.721541i	$-0.256566\pi$
$787$	9.37827	+	5.95163i	0.334299	+	0.212153i	−0.358072	+	0.933694i	$0.616566\pi$
$788$	−10.6420	+	0.669535i	−0.379104	+	0.0238512i
$789$	−0.263922	−	0.415875i	−0.00939589	−	0.0148055i
$790$	28.4730	+	4.64460i	1.01302	+	0.165247i
$791$	−0.383576	−	6.09677i	−0.0136384	−	0.216776i
$792$	−3.81234	−	0.727242i	−0.135465	−	0.0258414i
$793$	−4.11613	+	1.33741i	−0.146168	+	0.0474929i
$794$	28.1906	−	26.4727i	1.00045	−	0.939481i
$795$	−0.652846	−	0.747440i	−0.0231541	−	0.0265090i
$796$	−4.89417	−	25.6561i	−0.173469	−	0.909358i
$797$	9.40220	−	10.0123i	0.333043	−	0.354655i	−0.540550	−	0.841312i	$-0.681784\pi$
$797$	9.40220	−	10.0123i	0.333043	−	0.354655i	0.873593	+	0.486657i	$0.161784\pi$
$798$	−1.47606	+	3.72810i	−0.0522519	+	0.131973i
$799$	0.964837	+	2.96946i	0.0341335	+	0.105052i
$800$	−0.267841	−	4.99282i	−0.00946961	−	0.176523i
$801$	2.43009	−	7.47905i	0.0858631	−	0.264259i
$802$	21.1258	+	17.4768i	0.745978	+	0.617126i
$803$	47.1931	+	22.2074i	1.66541	+	0.783681i
$804$	−2.08830	−	1.96104i	−0.0736486	−	0.0691606i
$805$	−16.6332	+	4.74920i	−0.586244	+	0.167387i
$806$	3.18285	−	0.402088i	0.112111	−	0.0141629i
$807$			6.14277i			0.216236i
$808$	−0.284632	−	2.25310i	−0.0100133	−	0.0792636i
$809$	13.4078	+	16.2073i	0.471394	+	0.569817i	0.951600	−	0.307338i	$-0.0994383\pi$
$809$	13.4078	+	16.2073i	0.471394	+	0.569817i	−0.480207	+	0.877155i	$0.659438\pi$
$810$	0.878561	+	2.05624i	0.0308695	+	0.0722490i
$811$	0.737010	−	11.7144i	0.0258799	−	0.411349i	−0.963664	−	0.267117i	$-0.913929\pi$
$811$	0.737010	−	11.7144i	0.0258799	−	0.411349i	0.989544	−	0.144232i	$-0.0460712\pi$
$812$	−2.04259	+	7.95538i	−0.0716810	+	0.279179i
$813$	−5.53878	+	21.5721i	−0.194254	+	0.756568i
$814$	−2.08842	+	33.1944i	−0.0731989	+	1.16346i
$815$	11.0585	+	6.60913i	0.387363	+	0.231508i
$816$	1.81021	+	2.18817i	0.0633702	+	0.0766014i
$817$	−2.76484	−	21.8860i	−0.0967295	−	0.765693i
$818$			4.71170i			0.164741i
$819$	1.89547	−	0.239453i	0.0662330	−	0.00836718i
$820$	−0.288977	+	8.01589i	−0.0100915	+	0.279927i
$821$	24.8716	+	23.3560i	0.868025	+	0.815130i	0.984009	−	0.178121i	$-0.0570019\pi$
$821$	24.8716	+	23.3560i	0.868025	+	0.815130i	−0.115983	+	0.993251i	$0.537002\pi$
$822$	6.29741	+	2.96333i	0.219647	+	0.103358i
$823$	−17.3376	−	14.3429i	−0.604351	−	0.499963i	0.284185	−	0.958770i	$-0.408277\pi$
$823$	−17.3376	−	14.3429i	−0.604351	−	0.499963i	−0.888536	+	0.458807i	$0.848277\pi$
$824$	−0.751953	+	2.31427i	−0.0261955	+	0.0806215i
$825$	−14.0226	−	13.4140i	−0.488205	−	0.467016i
$826$	−5.77804	−	17.7830i	−0.201044	−	0.618749i
$827$	1.07164	−	2.70664i	0.0372644	−	0.0941192i	−0.909953	−	0.414712i	$-0.863882\pi$
$827$	1.07164	−	2.70664i	0.0372644	−	0.0941192i	0.947217	+	0.320593i	$0.103882\pi$
$828$	3.67922	−	3.91798i	0.127862	−	0.136159i
$829$	1.16245	+	6.09377i	0.0403735	+	0.211645i	0.996757	−	0.0804681i	$-0.0256415\pi$
$829$	1.16245	+	6.09377i	0.0403735	+	0.211645i	−0.956384	+	0.292113i	$0.905642\pi$
$830$	−5.43148	+	9.08807i	−0.188530	+	0.315451i
$831$	−17.4429	+	16.3800i	−0.605089	+	0.568216i
$832$	1.26242	−	0.410186i	0.0437666	−	0.0142206i
$833$	−13.7481	−	2.62259i	−0.476344	−	0.0908674i
$834$	0.254502	+	4.04520i	0.00881270	+	0.140074i
$835$	−6.02730	−	6.08324i	−0.208583	−	0.210519i
$836$	5.79334	+	9.12884i	0.200367	+	0.315728i
$837$	−2.41212	+	0.151758i	−0.0833751	+	0.00524552i
$838$	13.8301	+	8.77687i	0.477754	+	0.303192i
$839$	−1.85926	+	2.24746i	−0.0641888	+	0.0775909i	−0.801630	−	0.597820i	$-0.796034\pi$
$839$	−1.85926	+	2.24746i	−0.0641888	+	0.0775909i	0.737442	+	0.675411i	$0.236034\pi$
$840$	3.08644	+	0.912174i	0.106492	+	0.0314730i
$841$	3.45179	+	0.886268i	0.119027	+	0.0305610i
$842$	2.52463	−	1.18800i	0.0870044	−	0.0409412i
$843$	24.9466	+	8.10565i	0.859207	+	0.279173i
$844$	10.0889	+	5.54644i	0.347276	+	0.190916i
$845$	−24.8375	+	3.81636i	−0.854437	+	0.131287i
$846$	−1.09077	−	0.137796i	−0.0375013	−	0.00473752i
$847$	−0.732904	+	5.80153i	−0.0251829	+	0.199343i
$848$	0.374728	−	0.237810i	0.0128682	−	0.00816643i
$849$	−5.16664	+	3.75379i	−0.177319	+	0.128830i
$850$	1.64945	+	14.1033i	0.0565756	+	0.483740i
$851$	−37.2632	−	27.0733i	−1.27737	−	0.928062i
$852$	−1.79939	−	0.113208i	−0.0616462	−	0.00387845i
$853$	−9.75672	−	17.7474i	−0.334064	−	0.607660i	0.654918	−	0.755700i	$-0.272703\pi$
$853$	−9.75672	−	17.7474i	−0.334064	−	0.607660i	−0.988981	+	0.148041i	$0.952703\pi$
$854$	1.99814	−	4.24626i	0.0683749	−	0.145304i
$855$	2.50032	−	5.70545i	0.0855091	−	0.195122i
$856$	−0.979732	+	5.13593i	−0.0334865	+	0.175543i
$857$	−25.9487	−	35.7153i	−0.886391	−	1.22001i	−0.974610	−	0.223911i	$-0.928117\pi$
$857$	−25.9487	−	35.7153i	−0.886391	−	1.22001i	0.0882189	−	0.996101i	$-0.471883\pi$
$858$	2.48185	−	4.51447i	0.0847290	−	0.154121i
$859$	28.2438	−	44.5051i	0.963667	−	1.51850i	0.112466	−	0.993656i	$-0.464125\pi$
$859$	28.2438	−	44.5051i	0.963667	−	1.51850i	0.851201	−	0.524840i	$-0.175875\pi$
$860$	−17.2979	+	3.78273i	−0.589853	+	0.128990i
$861$	−4.80047	−	1.90064i	−0.163600	−	0.0647737i
$862$	−7.36401	−	18.5994i	−0.250819	−	0.633497i
$863$	−1.23502	+	1.02169i	−0.0420405	+	0.0347789i	−0.658207	−	0.752837i	$-0.728685\pi$
$863$	−1.23502	+	1.02169i	−0.0420405	+	0.0347789i	0.616167	+	0.787616i	$0.288685\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	−29.5415	+	19.8775i	−1.00444	+	0.675857i
$866$	3.27171	−	1.29536i	0.111177	−	0.0440181i
$867$	6.11644	+	6.51335i	0.207725	+	0.221205i
$868$	−2.04471	+	2.81431i	−0.0694021	+	0.0955237i
$869$	21.3201	+	45.3074i	0.723233	+	1.53695i
$870$	3.61650	−	12.2368i	0.122611	−	0.414867i
$871$	3.33225	−	1.83192i	0.112909	−	0.0620723i
$872$	6.16658	−	1.17634i	0.208827	−	0.0398358i
$873$	4.85572	+	18.9118i	0.164341	+	0.640067i
$874$	−14.9729			−0.506465
$875$	10.4736	+	12.2171i	0.354072	+	0.413015i
$876$	13.4388			0.454055
$877$	−11.3365	−	44.1526i	−0.382805	−	1.49093i	−0.809818	−	0.586681i	$-0.800434\pi$
$877$	−11.3365	−	44.1526i	−0.382805	−	1.49093i	0.427013	−	0.904245i	$-0.359566\pi$
$878$	−25.4319	+	4.85139i	−0.858284	+	0.163726i
$879$	5.32081	−	2.92514i	0.179467	−	0.0986626i
$880$	6.88174	−	5.28730i	0.231984	−	0.178235i
$881$	−17.8387	−	37.9091i	−0.601000	−	1.27719i	−0.941522	−	0.336953i	$-0.890604\pi$
$881$	−17.8387	−	37.9091i	−0.601000	−	1.27719i	0.340522	−	0.940237i	$-0.389396\pi$
$882$	2.89682	−	3.98713i	0.0975410	−	0.134254i
$883$	0.756617	+	0.805715i	0.0254622	+	0.0271145i	0.741574	−	0.670871i	$-0.234080\pi$
$883$	0.756617	+	0.805715i	0.0254622	+	0.0271145i	−0.716111	+	0.697986i	$0.754080\pi$
$884$	−3.50492	+	1.38770i	−0.117883	+	0.0466733i
$885$	7.97538	+	27.9324i	0.268090	+	0.938937i
$886$	28.6913	−	7.36667i	0.963903	−	0.247488i
$887$	28.1382	−	23.2780i	0.944790	−	0.781598i	−0.0311778	−	0.999514i	$-0.509926\pi$
$887$	28.1382	−	23.2780i	0.944790	−	0.781598i	0.975968	+	0.217916i	$0.0699258\pi$
$888$	3.15475	+	7.96799i	0.105866	+	0.267388i
$889$	−3.22668	−	1.27753i	−0.108219	−	0.0428471i
$890$	8.88114	+	15.1767i	0.297696	+	0.508725i
$891$	−2.07959	+	3.27690i	−0.0696688	+	0.109780i
$892$	8.96191	−	16.3016i	0.300067	−	0.545820i
$893$	1.80028	+	2.47788i	0.0602441	+	0.0829189i
$894$	0.0232715	−	0.121993i	0.000778315	−	0.00408007i
$895$	6.37503	+	29.1521i	0.213094	+	0.974447i
$896$	−0.612832	+	1.30233i	−0.0204733	+	0.0435079i
$897$	3.43697	+	6.25183i	0.114757	+	0.208742i
$898$	10.6358	+	0.669149i	0.354922	+	0.0223298i
$899$	11.1579	+	8.10667i	0.372136	+	0.270373i
$900$	−4.74081	−	1.58895i	−0.158027	−	0.0529649i
$901$	−1.01968	+	0.740842i	−0.0339705	+	0.0246810i
$902$	−11.7547	+	7.45977i	−0.391389	+	0.248383i
$903$	1.42848	−	11.3076i	0.0475369	−	0.376294i
$904$	−4.21078	−	0.531946i	−0.140049	−	0.0176923i
$905$	−25.6467	−	13.2172i	−0.852526	−	0.439356i
$906$	−4.21335	−	2.31631i	−0.139979	−	0.0769543i
$907$	−25.1612	−	8.17538i	−0.835465	−	0.271459i	−0.140120	−	0.990135i	$-0.544749\pi$
$907$	−25.1612	−	8.17538i	−0.835465	−	0.271459i	−0.695346	+	0.718676i	$0.744749\pi$
$908$	3.65278	−	1.71887i	0.121222	−	0.0570426i
$909$	−2.19966	−	0.564776i	−0.0729580	−	0.0187324i
$910$	−2.41756	+	3.52223i	−0.0801414	+	0.116761i
$911$	25.1500	−	30.4011i	0.833256	−	1.00723i	−0.166519	−	0.986038i	$-0.553253\pi$
$911$	25.1500	−	30.4011i	0.833256	−	1.00723i	0.999775	−	0.0211957i	$-0.00674731\pi$
$912$	2.35214	+	1.49271i	0.0778871	+	0.0494287i
$913$	−18.3401	+	1.15386i	−0.606968	+	0.0381872i
$914$	−12.5500	−	19.7757i	−0.415118	−	0.654122i
$915$	−3.33988	+	6.48071i	−0.110413	+	0.214246i
$916$	1.58974	+	25.2682i	0.0525266	+	0.834886i
$917$	23.4332	+	4.47012i	0.773831	+	0.147616i
$918$	2.70090	−	0.877574i	0.0891429	−	0.0289643i
$919$	23.5664	−	22.1303i	0.777385	−	0.730013i	−0.190424	−	0.981702i	$-0.560986\pi$
$919$	23.5664	−	22.1303i	0.777385	−	0.730013i	0.967808	+	0.251689i	$0.0809861\pi$
$920$	1.07573	+	11.9699i	0.0354658	+	0.394636i
$921$	3.81258	+	19.9863i	0.125629	+	0.658570i
$922$	−20.4393	+	21.7657i	−0.673134	+	0.716815i
$923$	0.881002	−	2.22516i	0.0289985	−	0.0732419i
$924$	1.72620	+	5.31270i	0.0567879	+	0.174775i
$925$	−8.41757	+	42.0140i	−0.276768	+	1.38141i
$926$	−0.130701	+	0.402258i	−0.00429512	+	0.0132190i
$927$	1.87494	+	1.55109i	0.0615813	+	0.0509444i
$928$	5.16336	+	2.42969i	0.169496	+	0.0797586i
$929$	25.5140	+	23.9593i	0.837088	+	0.786078i	0.979013	−	0.203800i	$-0.0653291\pi$
$929$	25.5140	+	23.9593i	0.837088	+	0.786078i	−0.141925	+	0.989877i	$0.545329\pi$
$930$	3.33204	−	4.25491i	0.109262	−	0.139524i
$931$	−13.6212	+	1.72076i	−0.446418	+	0.0563957i
$932$		−	27.0061i		−	0.884614i
$933$	1.87715	+	14.8592i	0.0614551	+	0.486467i
$934$	−13.8624	−	16.7567i	−0.453591	−	0.548298i
$935$	−18.5620	+	16.2129i	−0.607043	+	0.530217i
$936$	0.0833474	−	1.32477i	0.00272430	−	0.0433014i
$937$	0.255620	−	0.995573i	0.00835073	−	0.0325239i	−0.964271	−	0.264917i	$-0.914656\pi$
$937$	0.255620	−	0.995573i	0.00835073	−	0.0325239i	0.972622	+	0.232393i	$0.0746555\pi$
$938$	−1.02541	+	3.99372i	−0.0334809	+	0.130399i
$939$	1.95077	−	31.0066i	0.0636609	−	1.01186i
$940$	1.85157	−	1.61724i	0.0603916	−	0.0527486i
$941$	−2.47067	−	2.98653i	−0.0805416	−	0.0973581i	0.728703	−	0.684830i	$-0.240123\pi$
$941$	−2.47067	−	2.98653i	−0.0805416	−	0.0973581i	−0.809245	+	0.587472i	$0.800123\pi$
$942$	1.14256	+	9.04430i	0.0372266	+	0.294679i
$943$		−	19.2798i		−	0.627835i
$944$	−12.8885	+	1.62820i	−0.419486	+	0.0529934i
$945$	1.98431	−	2.53391i	0.0645497	−	0.0824280i
$946$	−22.4034	−	21.0382i	−0.728397	−	0.684010i
$947$	21.0901	+	9.92424i	0.685336	+	0.322494i	0.736733	−	0.676184i	$-0.236367\pi$
$947$	21.0901	+	9.92424i	0.685336	+	0.322494i	−0.0513974	+	0.998678i	$0.516367\pi$
$948$	9.94103	+	8.22393i	0.322870	+	0.267101i
$949$	−5.51240	+	16.9654i	−0.178940	+	0.550721i
$950$	5.81402	+	12.6576i	0.188632	+	0.410668i
$951$	0.743425	+	2.28803i	0.0241072	+	0.0741943i
$952$	1.50471	−	3.80047i	0.0487680	−	0.123174i
$953$	13.1148	−	13.9659i	0.424832	−	0.452400i	−0.480570	−	0.876957i	$-0.659570\pi$
$953$	13.1148	−	13.9659i	0.424832	−	0.452400i	0.905401	+	0.424557i	$0.139570\pi$
$954$	−0.0831633	−	0.435957i	−0.00269251	−	0.0141146i
$955$	2.91952	+	32.4862i	0.0944734	+	1.05123i
$956$	1.97225	−	1.85207i	0.0637872	−	0.0599002i
$957$	21.0633	−	6.84388i	0.680879	−	0.221231i
$958$	33.6277	+	6.41482i	1.08646	+	0.207253i
$959$	−0.628995	−	9.99758i	−0.0203113	−	0.322839i
$960$	1.02435	−	1.98764i	0.0330606	−	0.0641508i
$961$	−13.4807	−	21.2421i	−0.434860	−	0.685230i
$962$	−11.3530	+	0.714270i	−0.366035	+	0.0230290i
$963$	4.41461	+	2.80160i	0.142259	+	0.0902801i
$964$	−12.2128	+	14.7628i	−0.393349	+	0.475477i
$965$	−19.5892	+	28.5402i	−0.630600	+	0.918743i
$966$	−7.49284	−	1.92383i	−0.241078	−	0.0618984i
$967$	37.2364	−	17.5221i	1.19744	−	0.563474i	0.279484	−	0.960150i	$-0.409837\pi$
$967$	37.2364	−	17.5221i	1.19744	−	0.563474i	0.917958	+	0.396677i	$0.129837\pi$
$968$	3.86394	+	1.25547i	0.124192	+	0.0403523i
$969$	−6.93281	−	3.81135i	−0.222714	−	0.122438i
$970$	−38.8091	−	20.0005i	−1.24608	−	0.642179i
$971$	20.4248	+	2.58025i	0.655462	+	0.0828041i	0.446028	−	0.895019i	$-0.352838\pi$
$971$	20.4248	+	2.58025i	0.655462	+	0.0828041i	0.209433	+	0.977823i	$0.432838\pi$
$972$	−0.125333	+	0.992115i	−0.00402007	+	0.0318221i
$973$	4.92567	−	3.12593i	0.157910	−	0.100213i
$974$	−15.6684	+	11.3838i	−0.502049	+	0.364760i
$975$	3.95053	−	5.33313i	0.126518	−	0.170797i
$976$	−2.63780	−	1.91647i	−0.0844340	−	0.0613449i
$977$	48.5254	+	3.05296i	1.55246	+	0.0976727i	0.815699	−	0.578476i	$-0.196353\pi$
$977$	48.5254	+	3.05296i	1.55246	+	0.0976727i	0.736765	+	0.676149i	$0.236353\pi$
$978$	2.77560	+	5.04880i	0.0887539	+	0.161443i
$979$	−12.9950	+	27.6159i	−0.415323	+	0.882607i
$980$	2.35427	+	10.7657i	0.0752044	+	0.343899i
$981$	1.17634	−	6.16658i	0.0375576	−	0.196884i
$982$	22.4747	+	30.9338i	0.717198	+	0.987138i
$983$	−10.5254	+	19.1456i	−0.335708	+	0.610651i	−0.989249	−	0.146240i	$-0.953283\pi$
$983$	−10.5254	+	19.1456i	−0.335708	+	0.610651i	0.653541	+	0.756891i	$0.273283\pi$
$984$	−1.92209	+	3.02872i	−0.0612739	+	0.0965522i
$985$	−12.0422	−	20.5787i	−0.383698	−	0.655691i
$986$	−15.0677	−	5.96573i	−0.479854	−	0.189988i
$987$	0.582534	+	1.47131i	0.0185423	+	0.0468324i
$988$	−2.84925	+	2.35710i	−0.0906466	+	0.0749894i
$989$	41.2232	−	10.5843i	1.31082	−	0.336562i
$990$	−2.38267	−	8.34487i	−0.0757261	−	0.265217i
$991$	−48.8366	+	19.3358i	−1.55135	+	0.614222i	−0.978648	−	0.205544i	$-0.934104\pi$
$991$	−48.8366	+	19.3358i	−1.55135	+	0.614222i	−0.572699	+	0.819766i	$0.694104\pi$
$992$	1.65447	+	1.76184i	0.0525296	+	0.0559384i
$993$	−1.07646	+	1.48161i	−0.0341603	+	0.0470176i
$994$	1.10491	+	2.34804i	0.0350455	+	0.0744754i
$995$	46.3126	−	35.5823i	1.46821	−	1.12803i
$996$	−4.14918	+	2.28103i	−0.131472	+	0.0722772i
$997$	−31.4925	+	6.00752i	−0.997378	+	0.190260i	−0.660127	−	0.751154i	$-0.729497\pi$
$997$	−31.4925	+	6.00752i	−0.997378	+	0.190260i	−0.337252	+	0.941414i	$0.609497\pi$
$998$	−4.68097	−	18.2312i	−0.148173	−	0.577097i
$999$	8.56979			0.271136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.2	✓	280
125.119	even	50	inner	750.2.o.b.619.2	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.2	✓	280	1.1	even	1	trivial
750.2.o.b.619.2	yes	280	125.119	even	50	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.84358 - 1.26539i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.846010 + 1.16443i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.84358 - 1.26539i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.846010 + 1.16443i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-0.767151 + 2.10035i) q^{10} +(-3.75915 + 0.965185i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(-0.488644 - 1.23417i) q^{13} +(1.33824 + 0.529848i) q^{14} +(-2.04804 - 0.897519i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.36813 + 2.48862i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(-0.522009 + 2.73647i) q^{19} +(2.22515 + 0.220713i) q^{20} +(-0.612832 + 1.30233i) q^{21} +(1.86972 + 3.40102i) q^{22} +(-5.36408 - 0.337479i) q^{23} +(0.809017 + 0.587785i) q^{24} +(1.79760 + 4.66569i) q^{25} +(-1.07388 + 0.780219i) q^{26} +(0.844328 - 0.535827i) q^{27} +(0.180394 - 1.42797i) q^{28} +(-5.66147 - 0.715210i) q^{29} +(-0.359996 + 2.20690i) q^{30} +(-2.11794 - 1.16435i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-3.51171 + 1.65248i) q^{33} +(2.75067 + 0.706252i) q^{34} +(3.03315 - 1.07620i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(7.23571 + 4.59192i) q^{37} +(2.78032 - 0.174923i) q^{38} +(-0.711250 - 1.12075i) q^{39} +(-0.339593 - 2.21013i) q^{40} +(0.225239 + 3.58006i) q^{41} +(1.41382 + 0.269701i) q^{42} +(-7.53110 + 2.44700i) q^{43} +(2.82919 - 2.65678i) q^{44} +(-2.17994 - 0.497858i) q^{45} +(1.00712 + 5.27948i) q^{46} +(0.752616 - 0.801454i) q^{47} +(0.368125 - 0.929776i) q^{48} +(1.52295 + 4.68715i) q^{49} +(4.07206 - 2.90143i) q^{50} +(-0.877574 + 2.70090i) q^{51} +(1.02277 + 0.846109i) q^{52} +(0.401579 + 0.188969i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(8.15164 + 2.97737i) q^{55} +(-1.42797 + 0.180394i) q^{56} +2.78581i q^{57} +(0.715210 + 5.66147i) q^{58} +(-8.28075 - 10.0097i) q^{59} +(2.22709 - 0.200148i) q^{60} +(0.204729 - 3.25407i) q^{61} +(-0.601056 + 2.34096i) q^{62} +(-0.357944 + 1.39410i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-0.660850 + 2.89363i) q^{65} +(2.47389 + 2.99042i) q^{66} +(0.359046 + 2.84214i) q^{67} -2.83989i q^{68} +(-5.33230 + 0.673626i) q^{69} +(-1.79670 - 2.67021i) q^{70} +(1.31429 + 1.23421i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-10.3548 - 8.56621i) q^{73} +(2.64821 - 8.15035i) q^{74} +(2.64002 + 4.24621i) q^{75} +(-0.860863 - 2.64946i) q^{76} +(2.05638 - 5.19383i) q^{77} +(-0.908660 + 0.967625i) q^{78} +(-2.41756 - 12.6733i) q^{79} +(-2.05624 + 0.878561i) q^{80} +(0.728969 - 0.684547i) q^{81} +(3.41157 - 1.10849i) q^{82} +(4.65098 + 0.887222i) q^{83} +(-0.0903755 - 1.43648i) q^{84} +(5.67132 - 2.85676i) q^{85} +(4.24303 + 6.68595i) q^{86} +(-5.69521 + 0.358312i) q^{87} +(-3.27690 - 2.07959i) q^{88} +(5.01267 - 6.05927i) q^{89} +(0.0599126 + 2.23527i) q^{90} +(1.85051 + 0.475130i) q^{91} +(4.86316 - 2.28843i) q^{92} +(-2.29860 - 0.746860i) q^{93} +(-0.963443 - 0.529657i) q^{94} +(4.42505 - 4.38436i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(-2.44716 + 19.3712i) q^{97} +(4.16116 - 2.64075i) q^{98} +(-3.13986 + 2.28124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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