LMFDB - Embedded newform 950.2.bb.e.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.e.507.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(0.684861 - 1.46869i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.52279 - 0.554250i) q^{6} +(3.13506 + 0.840038i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.240351 + 0.286439i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.684861 - 1.46869i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.52279 - 0.554250i) q^{6} +(3.13506 + 0.840038i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.240351 + 0.286439i) q^{9} +(-1.40883 + 2.44017i) q^{11} +(-0.419421 + 1.56530i) q^{12} +(1.06751 - 0.497786i) q^{13} +(0.563602 - 3.19635i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.952583 - 0.0833402i) q^{17} +(0.264401 - 0.264401i) q^{18} +(4.34670 - 0.325943i) q^{19} +(3.38084 - 4.02912i) q^{21} +(2.55367 + 1.19080i) q^{22} +(4.61545 - 6.59154i) q^{23} +(1.59590 + 0.281400i) q^{24} +(-0.588931 - 1.02006i) q^{26} +(5.28120 - 1.41509i) q^{27} +(-3.23331 - 0.282878i) q^{28} +(3.52334 - 2.95643i) q^{29} +(-7.77127 + 4.48674i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(2.61899 + 3.74031i) q^{33} +(-0.166046 - 0.941694i) q^{34} +(-0.286439 - 0.240351i) q^{36} +(0.707105 + 0.707105i) q^{37} +(-0.703542 - 4.30175i) q^{38} -1.90875i q^{39} +(2.33341 + 6.41100i) q^{41} +(-4.30845 - 3.01681i) q^{42} +(-9.51246 + 6.66069i) q^{43} +(0.963698 - 2.64774i) q^{44} +(-6.96872 - 4.02339i) q^{46} +(0.652086 - 7.45338i) q^{47} +(0.141238 - 1.61435i) q^{48} +(3.06078 + 1.76714i) q^{49} +(0.529986 - 1.45612i) q^{51} +(-0.964848 + 0.675594i) q^{52} +(-0.155432 - 0.108835i) q^{53} +(-1.86999 - 5.13777i) q^{54} +3.24566i q^{56} +(2.49817 - 6.60717i) q^{57} +(-3.25226 - 3.25226i) q^{58} +(2.18825 + 1.83616i) q^{59} +(-1.86064 - 10.5522i) q^{61} +(5.14698 + 7.35065i) q^{62} +(0.512895 + 1.09991i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(3.49782 - 2.93502i) q^{66} +(-1.15233 - 0.100816i) q^{67} +(-0.923639 + 0.247488i) q^{68} +(-6.51998 - 11.2929i) q^{69} +(-1.83802 - 0.324092i) q^{71} +(-0.214471 + 0.306297i) q^{72} +(-3.32726 - 1.55153i) q^{73} +(0.642786 - 0.766043i) q^{74} +(-4.22406 + 1.07579i) q^{76} +(-6.46661 + 6.46661i) q^{77} +(-1.90148 + 0.166358i) q^{78} +(2.91615 - 1.06139i) q^{79} +(1.34376 - 7.62086i) q^{81} +(6.18323 - 2.88329i) q^{82} +(2.82113 - 10.5286i) q^{83} +(-2.62982 + 4.55499i) q^{84} +(7.46441 + 8.89574i) q^{86} +(-1.92908 - 7.19943i) q^{87} +(-2.72165 - 0.729265i) q^{88} +(-9.52932 - 3.46839i) q^{89} +(3.76486 - 0.663846i) q^{91} +(-3.40072 + 7.29286i) q^{92} +(1.26739 + 14.4864i) q^{93} -7.48185 q^{94} -1.62052 q^{96} +(1.69156 + 19.3347i) q^{97} +(1.49365 - 3.20315i) q^{98} +(-1.03757 + 0.182952i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	0.684861	−	1.46869i	0.395405	−	0.847948i	−0.603322	−	0.797498i	$-0.706157\pi$
$3$	0.684861	−	1.46869i	0.395405	−	0.847948i	0.998727	−	0.0504501i	$-0.0160656\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−1.52279	−	0.554250i	−0.621676	−	0.226272i
$7$	3.13506	+	0.840038i	1.18494	+	0.317504i	0.796885	−	0.604131i	$-0.206480\pi$
$7$	3.13506	+	0.840038i	1.18494	+	0.317504i	0.388057	+	0.921635i	$0.373146\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	0.240351	+	0.286439i	0.0801169	+	0.0954796i
$10$		0			0
$11$	−1.40883	+	2.44017i	−0.424779	+	0.735739i	−0.996400	−	0.0847793i	$-0.972981\pi$
$11$	−1.40883	+	2.44017i	−0.424779	+	0.735739i	0.571621	+	0.820518i	$0.306315\pi$
$12$	−0.419421	+	1.56530i	−0.121076	+	0.451863i
$13$	1.06751	−	0.497786i	0.296073	−	0.138061i	−0.268906	−	0.963166i	$-0.586662\pi$
$13$	1.06751	−	0.497786i	0.296073	−	0.138061i	0.564979	+	0.825105i	$0.308884\pi$
$14$	0.563602	−	3.19635i	0.150629	−	0.854260i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	0.952583	−	0.0833402i	0.231035	−	0.0202130i	0.0289498	−	0.999581i	$-0.490784\pi$
$17$	0.952583	−	0.0833402i	0.231035	−	0.0202130i	0.202085	+	0.979368i	$0.435228\pi$
$18$	0.264401	−	0.264401i	0.0623199	−	0.0623199i
$19$	4.34670	−	0.325943i	0.997200	−	0.0747763i
$19$	4.34670	−	0.325943i	0.997200	−	0.0747763i
$20$		0			0
$21$	3.38084	−	4.02912i	0.737759	−	0.879227i
$22$	2.55367	+	1.19080i	0.544444	+	0.253879i
$23$	4.61545	−	6.59154i	0.962387	−	1.37443i	0.0353857	−	0.999374i	$-0.488734\pi$
$23$	4.61545	−	6.59154i	0.962387	−	1.37443i	0.927002	−	0.375058i	$-0.122377\pi$
$24$	1.59590	+	0.281400i	0.325762	+	0.0574406i
$25$		0			0
$26$	−0.588931	−	1.02006i	−0.115499	−	0.200050i
$27$	5.28120	−	1.41509i	1.01637	−	0.272335i
$28$	−3.23331	−	0.282878i	−0.611037	−	0.0534588i
$29$	3.52334	−	2.95643i	0.654267	−	0.548995i	−0.254095	−	0.967179i	$-0.581778\pi$
$29$	3.52334	−	2.95643i	0.654267	−	0.548995i	0.908362	+	0.418184i	$0.137333\pi$
$30$		0			0
$31$	−7.77127	+	4.48674i	−1.39576	+	0.805843i	−0.993945	−	0.109878i	$-0.964954\pi$
$31$	−7.77127	+	4.48674i	−1.39576	+	0.805843i	−0.401815	+	0.915721i	$0.631621\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	2.61899	+	3.74031i	0.455908	+	0.651105i
$34$	−0.166046	−	0.941694i	−0.0284767	−	0.161499i
$35$		0			0
$36$	−0.286439	−	0.240351i	−0.0477398	−	0.0400584i
$37$	0.707105	+	0.707105i	0.116247	+	0.116247i	0.762838	−	0.646590i	$-0.223806\pi$
$37$	0.707105	+	0.707105i	0.116247	+	0.116247i	−0.646590	+	0.762838i	$0.723806\pi$
$38$	−0.703542	−	4.30175i	−0.114130	−	0.697836i
$39$		−	1.90875i		−	0.305644i
$40$		0			0
$41$	2.33341	+	6.41100i	0.364418	+	1.00123i	0.977449	+	0.211171i	$0.0677277\pi$
$41$	2.33341	+	6.41100i	0.364418	+	1.00123i	−0.613031	+	0.790059i	$0.710050\pi$
$42$	−4.30845	−	3.01681i	−0.664808	−	0.465504i
$43$	−9.51246	+	6.66069i	−1.45064	+	1.01575i	−0.458757	+	0.888562i	$0.651705\pi$
$43$	−9.51246	+	6.66069i	−1.45064	+	1.01575i	−0.991879	+	0.127184i	$0.959406\pi$
$44$	0.963698	−	2.64774i	0.145283	−	0.399162i
$45$		0			0
$46$	−6.96872	−	4.02339i	−1.02748	−	0.593217i
$47$	0.652086	−	7.45338i	0.0951165	−	1.08719i	−0.787253	−	0.616630i	$-0.788497\pi$
$47$	0.652086	−	7.45338i	0.0951165	−	1.08719i	0.882370	−	0.470557i	$-0.155947\pi$
$48$	0.141238	−	1.61435i	0.0203859	−	0.233012i
$49$	3.06078	+	1.76714i	0.437254	+	0.252449i
$50$		0			0
$51$	0.529986	−	1.45612i	0.0742128	−	0.203898i
$52$	−0.964848	+	0.675594i	−0.133800	+	0.0936880i
$53$	−0.155432	−	0.108835i	−0.0213502	−	0.0149496i	0.562853	−	0.826557i	$-0.309704\pi$
$53$	−0.155432	−	0.108835i	−0.0213502	−	0.0149496i	−0.584203	+	0.811608i	$0.698593\pi$
$54$	−1.86999	−	5.13777i	−0.254474	−	0.699162i
$55$		0			0
$56$			3.24566i			0.433719i
$57$	2.49817	−	6.60717i	0.330891	−	0.875141i
$58$	−3.25226	−	3.25226i	−0.427043	−	0.427043i
$59$	2.18825	+	1.83616i	0.284886	+	0.239048i	0.774020	−	0.633161i	$-0.218243\pi$
$59$	2.18825	+	1.83616i	0.284886	+	0.239048i	−0.489134	+	0.872208i	$0.662687\pi$
$60$		0			0
$61$	−1.86064	−	10.5522i	−0.238231	−	1.35107i	−0.835702	−	0.549183i	$-0.814939\pi$
$61$	−1.86064	−	10.5522i	−0.238231	−	1.35107i	0.597472	−	0.801890i	$-0.296172\pi$
$62$	5.14698	+	7.35065i	0.653667	+	0.933533i
$63$	0.512895	+	1.09991i	0.0646187	+	0.138575i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	3.49782	−	2.93502i	0.430552	−	0.361276i
$67$	−1.15233	−	0.100816i	−0.140780	−	0.0123166i	0.0165481	−	0.999863i	$-0.494732\pi$
$67$	−1.15233	−	0.100816i	−0.140780	−	0.0123166i	−0.157328	+	0.987546i	$0.550288\pi$
$68$	−0.923639	+	0.247488i	−0.112008	+	0.0300124i
$69$	−6.51998	−	11.2929i	−0.784914	−	1.35951i
$70$		0			0
$71$	−1.83802	−	0.324092i	−0.218132	−	0.0384626i	0.0635138	−	0.997981i	$-0.479769\pi$
$71$	−1.83802	−	0.324092i	−0.218132	−	0.0384626i	−0.281646	+	0.959518i	$0.590880\pi$
$72$	−0.214471	+	0.306297i	−0.0252757	+	0.0360974i
$73$	−3.32726	−	1.55153i	−0.389426	−	0.181592i	0.218037	−	0.975941i	$-0.430035\pi$
$73$	−3.32726	−	1.55153i	−0.389426	−	0.181592i	−0.607463	+	0.794348i	$0.707813\pi$
$74$	0.642786	−	0.766043i	0.0747224	−	0.0890506i
$75$		0			0
$76$	−4.22406	+	1.07579i	−0.484533	+	0.123401i
$77$	−6.46661	+	6.46661i	−0.736939	+	0.736939i
$78$	−1.90148	+	0.166358i	−0.215301	+	0.0188364i
$79$	2.91615	−	1.06139i	0.328093	−	0.119416i	−0.172722	−	0.984971i	$-0.555256\pi$
$79$	2.91615	−	1.06139i	0.328093	−	0.119416i	0.500815	+	0.865555i	$0.333034\pi$
$80$		0			0
$81$	1.34376	−	7.62086i	0.149307	−	0.846763i
$82$	6.18323	−	2.88329i	0.682824	−	0.318406i
$83$	2.82113	−	10.5286i	0.309659	−	1.15566i	−0.619200	−	0.785233i	$-0.712543\pi$
$83$	2.82113	−	10.5286i	0.309659	−	1.15566i	0.928860	−	0.370431i	$-0.120790\pi$
$84$	−2.62982	+	4.55499i	−0.286937	+	0.496990i
$85$		0			0
$86$	7.46441	+	8.89574i	0.804908	+	0.959252i
$87$	−1.92908	−	7.19943i	−0.206819	−	0.771860i
$88$	−2.72165	−	0.729265i	−0.290129	−	0.0777399i
$89$	−9.52932	−	3.46839i	−1.01011	−	0.367649i	−0.216633	−	0.976253i	$-0.569507\pi$
$89$	−9.52932	−	3.46839i	−1.01011	−	0.367649i	−0.793474	+	0.608605i	$0.791730\pi$
$90$		0			0
$91$	3.76486	−	0.663846i	0.394664	−	0.0695899i
$92$	−3.40072	+	7.29286i	−0.354549	+	0.760334i
$93$	1.26739	+	14.4864i	0.131422	+	1.50217i
$94$	−7.48185			−0.771694
$95$		0			0
$96$	−1.62052			−0.165393
$97$	1.69156	+	19.3347i	0.171752	+	1.96314i	0.255953	+	0.966689i	$0.417611\pi$
$97$	1.69156	+	19.3347i	0.171752	+	1.96314i	−0.0842004	+	0.996449i	$0.526834\pi$
$98$	1.49365	−	3.20315i	0.150882	−	0.323567i
$99$	−1.03757	+	0.182952i	−0.104280	+	0.0183874i
$100$		0			0
$101$	−0.481715	−	0.175330i	−0.0479324	−	0.0174460i	0.317943	−	0.948110i	$-0.397008\pi$
$101$	−0.481715	−	0.175330i	−0.0479324	−	0.0174460i	−0.365875	+	0.930664i	$0.619230\pi$
$102$	−1.49677	−	0.401059i	−0.148203	−	0.0397108i
$103$	1.18751	+	4.43186i	0.117009	+	0.436684i	0.999429	−	0.0337781i	$-0.0107540\pi$
$103$	1.18751	+	4.43186i	0.117009	+	0.436684i	−0.882420	+	0.470462i	$0.844087\pi$
$104$	0.757115	+	0.902295i	0.0742413	+	0.0884773i
$105$		0			0
$106$	−0.0948738	+	0.164326i	−0.00921495	+	0.0159608i
$107$	2.25163	−	8.40321i	0.217674	−	0.812369i	−0.767535	−	0.641007i	$-0.778517\pi$
$107$	2.25163	−	8.40321i	0.217674	−	0.812369i	0.985208	−	0.171361i	$-0.0548166\pi$
$108$	−4.95524	+	2.31066i	−0.476818	+	0.222344i
$109$	−1.97889	+	11.2229i	−0.189544	+	1.07495i	0.730434	+	0.682983i	$0.239318\pi$
$109$	−1.97889	+	11.2229i	−0.189544	+	1.07495i	−0.919977	+	0.391971i	$0.871793\pi$
$110$		0			0
$111$	1.52279	−	0.554249i	0.144536	−	0.0526070i
$112$	3.23331	−	0.282878i	0.305519	−	0.0267294i
$113$	2.32073	−	2.32073i	0.218316	−	0.218316i	−0.589472	−	0.807788i	$-0.700664\pi$
$113$	2.32073	−	2.32073i	0.218316	−	0.218316i	0.807788	+	0.589472i	$0.200664\pi$
$114$	−6.79976	−	1.91281i	−0.636855	−	0.179151i
$115$		0			0
$116$	−2.95643	+	3.52334i	−0.274498	+	0.327134i
$117$	0.399161	+	0.186132i	0.0369024	+	0.0172079i
$118$	1.63845	−	2.33995i	0.150832	−	0.215410i
$119$	3.05642	+	0.538929i	0.280181	+	0.0494035i
$120$		0			0
$121$	1.53038	+	2.65070i	0.139126	+	0.240973i
$122$	−10.3499	+	2.77325i	−0.937035	+	0.251078i
$123$	11.0138	+	0.963585i	0.993083	+	0.0868835i
$124$	6.87409	−	5.76804i	0.617311	−	0.517986i
$125$		0			0
$126$	1.05102	−	0.606807i	0.0936323	−	0.0540586i
$127$	0.513549	+	1.10131i	0.0455701	+	0.0977255i	0.927775	−	0.373141i	$-0.121719\pi$
$127$	0.513549	+	1.10131i	0.0455701	+	0.0977255i	−0.882205	+	0.470866i	$0.843941\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	3.26778	+	18.5325i	0.287712	+	1.63169i
$130$		0			0
$131$	−10.2562	−	8.60598i	−0.896089	−	0.751908i	0.0733328	−	0.997308i	$-0.476636\pi$
$131$	−10.2562	−	8.60598i	−0.896089	−	0.751908i	−0.969422	+	0.245399i	$0.921081\pi$
$132$	−3.22870	−	3.22870i	−0.281023	−	0.281023i
$133$	13.9010	+	2.62954i	1.20537	+	0.228010i
$134$			1.15673i			0.0999265i
$135$		0			0
$136$	0.327047	+	0.898554i	0.0280440	+	0.0770504i
$137$	−15.9313	−	11.1552i	−1.36110	−	0.953055i	−0.999788	−	0.0206115i	$-0.993439\pi$
$137$	−15.9313	−	11.1552i	−1.36110	−	0.953055i	−0.361316	−	0.932443i	$-0.617672\pi$
$138$	−10.6817	+	7.47942i	−0.909288	+	0.636690i
$139$	2.76982	−	7.61001i	0.234933	−	0.645473i	−0.765066	−	0.643952i	$-0.777294\pi$
$139$	2.76982	−	7.61001i	0.234933	−	0.645473i	0.999999	−	0.00152088i	$-0.000484110\pi$
$140$		0			0
$141$	−10.5001	−	6.06224i	−0.884268	−	0.510533i
$142$	−0.162665	+	1.85927i	−0.0136505	+	0.156026i
$143$	−0.289254	+	3.30619i	−0.0241887	+	0.276478i
$144$	0.323824	+	0.186960i	0.0269853	+	0.0155800i
$145$		0			0
$146$	−1.25563	+	3.44982i	−0.103917	+	0.285509i
$147$	4.69159	−	3.28509i	0.386956	−	0.270949i
$148$	−0.819150	−	0.573575i	−0.0673337	−	0.0471476i
$149$	3.82887	+	10.5197i	0.313673	+	0.861810i	0.991907	+	0.126964i	$0.0405232\pi$
$149$	3.82887	+	10.5197i	0.313673	+	0.861810i	−0.678234	+	0.734846i	$0.737255\pi$
$150$		0			0
$151$			23.1471i			1.88368i	0.336061	+	0.941840i	$0.390905\pi$
$151$			23.1471i			1.88368i	−0.336061	+	0.941840i	$0.609095\pi$
$152$	1.43984	+	4.11423i	0.116787	+	0.333708i
$153$	0.252826	+	0.252826i	0.0204397	+	0.0204397i
$154$	7.00561	+	5.87840i	0.564528	+	0.473695i
$155$		0			0
$156$	0.331451	+	1.87975i	0.0265373	+	0.150500i
$157$	−0.753125	−	1.07557i	−0.0601059	−	0.0858401i	0.787974	−	0.615709i	$-0.211130\pi$
$157$	−0.753125	−	1.07557i	−0.0601059	−	0.0858401i	−0.848080	+	0.529869i	$0.822241\pi$
$158$	−1.31151	−	2.81255i	−0.104338	−	0.223755i
$159$	−0.266294	+	0.153745i	−0.0211185	+	0.0121927i
$160$		0			0
$161$	20.0069	−	16.7877i	1.57676	−	1.32306i
$162$	−7.70898	−	0.674448i	−0.605675	−	0.0529897i
$163$	−1.30285	+	0.349097i	−0.102047	+	0.0273434i	−0.309481	−	0.950906i	$-0.600155\pi$
$163$	−1.30285	+	0.349097i	−0.102047	+	0.0273434i	0.207434	+	0.978249i	$0.433489\pi$
$164$	−3.41122	−	5.90841i	−0.266372	−	0.461369i
$165$		0			0
$166$	−10.7344	−	1.89277i	−0.833152	−	0.146907i
$167$	2.34443	−	3.34820i	0.181418	−	0.259091i	−0.718135	−	0.695904i	$-0.755004\pi$
$167$	2.34443	−	3.34820i	0.181418	−	0.259091i	0.899552	+	0.436813i	$0.143893\pi$
$168$	4.76686	+	2.22282i	0.367771	+	0.171494i
$169$	−7.46446	+	8.89580i	−0.574189	+	0.684292i
$170$		0			0
$171$	1.13809	+	1.16672i	0.0870322	+	0.0892214i
$172$	8.21132	−	8.21132i	0.626107	−	0.626107i
$173$	−2.26658	+	0.198300i	−0.172325	+	0.0150765i	−0.172992	−	0.984923i	$-0.555343\pi$
$173$	−2.26658	+	0.198300i	−0.172325	+	0.0150765i	0.000666560		1.00000i	$0.499788\pi$
$174$	−7.00390	+	2.54921i	−0.530965	+	0.193255i
$175$		0			0
$176$	−0.489282	+	2.77486i	−0.0368810	+	0.209163i
$177$	4.19539	−	1.95634i	0.315345	−	0.147048i
$178$	−2.62466	+	9.79535i	−0.196726	+	0.734193i
$179$	−3.15617	+	5.46665i	−0.235903	+	0.408597i	−0.959535	−	0.281590i	$-0.909138\pi$
$179$	−3.15617	+	5.46665i	−0.235903	+	0.408597i	0.723631	+	0.690187i	$0.242472\pi$
$180$		0			0
$181$	7.11002	+	8.47339i	0.528484	+	0.629822i	0.962565	−	0.271051i	$-0.0873713\pi$
$181$	7.11002	+	8.47339i	0.528484	+	0.629822i	−0.434081	+	0.900874i	$0.642927\pi$
$182$	−0.989449	−	3.69267i	−0.0733428	−	0.273719i
$183$	−16.7722	−	4.49410i	−1.23984	−	0.332213i
$184$	7.56151	+	2.75216i	0.557442	+	0.202892i
$185$		0			0
$186$	14.3208	−	2.52514i	1.05005	−	0.185152i
$187$	−1.13866	+	2.44187i	−0.0832674	+	0.178568i
$188$	0.652086	+	7.45338i	0.0475583	+	0.543594i
$189$	17.7456			1.29080
$190$		0			0
$191$	18.5084			1.33922			0.669609	−	0.742714i	$-0.266462\pi$
$191$	18.5084			1.33922			0.669609	+	0.742714i	$0.266462\pi$
$192$	0.141238	+	1.61435i	0.0101929	+	0.116506i
$193$	10.3911	−	22.2837i	0.747966	−	1.60402i	−0.0481245	−	0.998841i	$-0.515324\pi$
$193$	10.3911	−	22.2837i	0.747966	−	1.60402i	0.796091	−	0.605177i	$-0.206898\pi$
$194$	19.1137	−	3.37025i	1.37228	−	0.241970i
$195$		0			0
$196$	−3.32114	−	1.20880i	−0.237224	−	0.0863426i
$197$	−14.8809	−	3.98733i	−1.06022	−	0.284085i	−0.313752	−	0.949505i	$-0.601586\pi$
$197$	−14.8809	−	3.98733i	−1.06022	−	0.284085i	−0.746470	+	0.665420i	$0.768253\pi$
$198$	0.272686	+	1.01768i	0.0193790	+	0.0723233i
$199$	−1.14904	−	1.36937i	−0.0814532	−	0.0970721i	0.723779	−	0.690032i	$-0.242404\pi$
$199$	−1.14904	−	1.36937i	−0.0814532	−	0.0970721i	−0.805232	+	0.592960i	$0.797959\pi$
$200$		0			0
$201$	−0.937254	+	1.62337i	−0.0661088	+	0.114504i
$202$	−0.132678	+	0.495163i	−0.00933522	+	0.0348395i
$203$	13.5294	−	6.30886i	0.949578	−	0.442795i
$204$	−0.269081	+	1.52603i	−0.0188394	+	0.106844i
$205$		0			0
$206$	4.31149	−	1.56926i	0.300396	−	0.109335i
$207$	2.99740	−	0.262238i	0.208334	−	0.0182268i
$208$	0.832874	−	0.832874i	0.0577494	−	0.0577494i
$209$	−5.32841	+	11.0659i	−0.368574	+	0.765442i
$210$		0			0
$211$	14.8594	−	17.7087i	1.02296	−	1.21912i	0.0475159	−	0.998870i	$-0.484870\pi$
$211$	14.8594	−	17.7087i	1.02296	−	1.21912i	0.975444	−	0.220246i	$-0.0706860\pi$
$212$	0.171970	+	0.0801908i	0.0118109	+	0.00550752i
$213$	−1.73478	+	2.47752i	−0.118865	+	0.169757i
$214$	−8.56748	−	1.51068i	−0.585661	−	0.103268i
$215$		0			0
$216$	2.73375	+	4.73499i	0.186008	+	0.322175i
$217$	−28.1324	+	7.53806i	−1.90975	+	0.511717i
$218$	11.3526	+	0.993226i	0.768897	+	0.0672698i
$219$	−4.55741	+	3.82412i	−0.307962	+	0.258410i
$220$		0			0
$221$	0.975402	−	0.563149i	0.0656126	−	0.0378815i
$222$	−0.684859	−	1.46869i	−0.0459647	−	0.0985717i
$223$	4.26883	+	6.09652i	0.285862	+	0.408253i	0.936242	−	0.351356i	$-0.114279\pi$
$223$	4.26883	+	6.09652i	0.285862	+	0.408253i	−0.650380	+	0.759609i	$0.725390\pi$
$224$	−0.563602	−	3.19635i	−0.0376573	−	0.213565i
$225$		0			0
$226$	−2.51417	−	2.10963i	−0.167240	−	0.140331i
$227$	14.2873	+	14.2873i	0.948280	+	0.948280i	0.998727	−	0.0504463i	$-0.0160644\pi$
$227$	14.2873	+	14.2873i	0.948280	+	0.948280i	−0.0504463	+	0.998727i	$0.516064\pi$
$228$	−1.31290	+	6.94059i	−0.0869488	+	0.459652i
$229$			13.2858i			0.877951i	0.898499	+	0.438976i	$0.144659\pi$
$229$			13.2858i			0.877951i	−0.898499	+	0.438976i	$0.855341\pi$
$230$		0			0
$231$	5.06871	+	13.9262i	0.333497	+	0.916274i
$232$	3.76760	+	2.63810i	0.247355	+	0.173200i
$233$	−19.7773	+	13.8482i	−1.29565	+	0.907224i	−0.998861	−	0.0477184i	$-0.984805\pi$
$233$	−19.7773	+	13.8482i	−1.29565	+	0.907224i	−0.296790	+	0.954943i	$0.595916\pi$
$234$	0.150634	−	0.413864i	0.00984727	−	0.0270552i
$235$		0			0
$236$	−2.47385	−	1.42828i	−0.161034	−	0.0929730i
$237$	0.438303	−	5.00983i	0.0284709	−	0.325423i
$238$	0.270494	−	3.09176i	0.0175335	−	0.200409i
$239$	−22.3391	−	12.8975i	−1.44499	−	0.834267i	−0.446816	−	0.894626i	$-0.647442\pi$
$239$	−22.3391	−	12.8975i	−1.44499	−	0.834267i	−0.998177	+	0.0603584i	$0.980776\pi$
$240$		0			0
$241$	−9.32526	+	25.6210i	−0.600693	+	1.65039i	0.149181	+	0.988810i	$0.452336\pi$
$241$	−9.32526	+	25.6210i	−0.600693	+	1.65039i	−0.749874	+	0.661581i	$0.769886\pi$
$242$	2.50724	−	1.75559i	0.161171	−	0.112853i
$243$	3.16376	+	2.21529i	0.202955	+	0.142111i
$244$	3.66475	+	10.0688i	0.234611	+	0.644589i
$245$		0			0
$246$		−	11.0559i		−	0.704898i
$247$	4.47787	−	2.51167i	0.284920	−	0.159814i
$248$	−6.34521	−	6.34521i	−0.402921	−	0.402921i
$249$	−13.5312	−	11.3540i	−0.857502	−	0.719530i
$250$		0			0
$251$	−0.726792	−	4.12184i	−0.0458747	−	0.260169i	0.953241	−	0.302211i	$-0.0977247\pi$
$251$	−0.726792	−	4.12184i	−0.0458747	−	0.260169i	−0.999116	+	0.0420423i	$0.986614\pi$
$252$	−0.696100	−	0.994134i	−0.0438502	−	0.0626245i
$253$	9.58208	+	20.5488i	0.602420	+	1.29189i
$254$	1.05236	−	0.607581i	0.0660310	−	0.0381230i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	15.6032	+	1.36511i	0.973303	+	0.0851530i	0.562700	−	0.826661i	$-0.309763\pi$
$257$	15.6032	+	1.36511i	0.973303	+	0.0851530i	0.410603	+	0.911814i	$0.365318\pi$
$258$	18.1772	−	4.87055i	1.13166	−	0.303227i
$259$	1.62282	+	2.81081i	0.100837	+	0.174655i
$260$		0			0
$261$	1.69367	+	0.298640i	0.104836	+	0.0184854i
$262$	−7.67935	+	10.9672i	−0.474432	+	0.677559i
$263$	−3.44685	−	1.60729i	−0.212542	−	0.0991100i	0.313432	−	0.949611i	$-0.398521\pi$
$263$	−3.44685	−	1.60729i	−0.212542	−	0.0991100i	−0.525974	+	0.850501i	$0.676299\pi$
$264$	−2.93502	+	3.49782i	−0.180638	+	0.215276i
$265$		0			0
$266$	1.40798	−	14.0772i	0.0863289	−	0.863132i
$267$	−11.6202	+	11.6202i	−0.711147	+	0.711147i
$268$	1.15233	−	0.100816i	0.0703898	−	0.00615831i
$269$	1.86490	−	0.678766i	0.113705	−	0.0413851i	−0.284541	−	0.958664i	$-0.591841\pi$
$269$	1.86490	−	0.678766i	0.113705	−	0.0413851i	0.398246	+	0.917279i	$0.369619\pi$
$270$		0			0
$271$	−1.06841	+	6.05925i	−0.0649012	+	0.368073i	0.935008	+	0.354626i	$0.115392\pi$
$271$	−1.06841	+	6.05925i	−0.0649012	+	0.368073i	−0.999910	+	0.0134475i	$0.995719\pi$
$272$	0.866631	−	0.404117i	0.0525472	−	0.0245032i
$273$	1.60342	−	5.98404i	0.0970434	−	0.362171i
$274$	−9.72427	+	16.8429i	−0.587465	+	1.01752i
$275$		0			0
$276$	8.38193	+	9.98919i	0.504533	+	0.601279i
$277$	−1.29567	−	4.83550i	−0.0778492	−	0.290537i	0.916015	−	0.401144i	$-0.131387\pi$
$277$	−1.29567	−	4.83550i	−0.0778492	−	0.290537i	−0.993864	+	0.110607i	$0.964721\pi$
$278$	−7.82246	−	2.09602i	−0.469160	−	0.125711i
$279$	−3.15301	−	1.14760i	−0.188765	−	0.0687050i
$280$		0			0
$281$	−30.6240	+	5.39983i	−1.82687	+	0.322127i	−0.978338	−	0.207013i	$-0.933626\pi$
$281$	−30.6240	+	5.39983i	−1.82687	+	0.322127i	−0.848534	+	0.529140i	$0.822515\pi$
$282$	−5.12403	+	10.9885i	−0.305131	+	0.654356i
$283$	−2.60412	−	29.7653i	−0.154799	−	1.76936i	−0.535377	−	0.844613i	$-0.679830\pi$
$283$	−2.60412	−	29.7653i	−0.154799	−	1.76936i	0.380578	−	0.924749i	$-0.375725\pi$
$284$	1.86637			0.110749
$285$		0			0
$286$	3.31882			0.196246
$287$	1.92992	+	22.0590i	0.113919	+	1.30210i
$288$	0.158025	−	0.338886i	0.00931172	−	0.0199690i
$289$	−15.8413	+	2.79324i	−0.931839	+	0.164308i
$290$		0			0
$291$	29.5551	+	10.7572i	1.73255	+	0.630597i
$292$	3.54613	+	0.950182i	0.207521	+	0.0556052i
$293$	3.13382	+	11.6956i	0.183080	+	0.683264i	0.995033	+	0.0995416i	$0.0317376\pi$
$293$	3.13382	+	11.6956i	0.183080	+	0.683264i	−0.811953	+	0.583722i	$0.801596\pi$
$294$	−3.68148	−	4.38742i	−0.214708	−	0.255880i
$295$		0			0
$296$	−0.499999	+	0.866023i	−0.0290618	+	0.0503366i
$297$	−3.98726	+	14.8806i	−0.231364	+	0.863462i
$298$	10.1460	−	4.73115i	0.587741	−	0.274068i
$299$	1.64584	−	9.33401i	0.0951813	−	0.539800i
$300$		0			0
$301$	−35.4174	+	12.8909i	−2.04142	+	0.743018i
$302$	23.0590	−	2.01740i	1.32689	−	0.116088i
$303$	−0.587412	+	0.587412i	−0.0337460	+	0.0337460i
$304$	3.97308	−	1.79294i	0.227872	−	0.102832i
$305$		0			0
$306$	0.229828	−	0.273899i	0.0131384	−	0.0156578i
$307$	20.6608	+	9.63428i	1.17917	+	0.549857i	0.910554	−	0.413389i	$-0.135655\pi$
$307$	20.6608	+	9.63428i	1.17917	+	0.549857i	0.268618	+	0.963247i	$0.413433\pi$
$308$	5.24545	−	7.49128i	0.298887	−	0.426855i
$309$	7.32230	+	1.29112i	0.416551	+	0.0734492i
$310$		0			0
$311$	12.4243	+	21.5196i	0.704520	+	1.22026i	0.966865	+	0.255290i	$0.0821709\pi$
$311$	12.4243	+	21.5196i	0.704520	+	1.22026i	−0.262345	+	0.964974i	$0.584496\pi$
$312$	1.84371	−	0.494020i	0.104379	−	0.0279684i
$313$	−26.8720	−	2.35099i	−1.51889	−	0.132886i	−0.703043	−	0.711147i	$-0.748176\pi$
$313$	−26.8720	−	2.35099i	−1.51889	−	0.132886i	−0.815852	+	0.578261i	$0.803731\pi$
$314$	−1.00584	+	0.844001i	−0.0567629	+	0.0476297i
$315$		0			0
$316$	−2.68754	+	1.55165i	−0.151186	+	0.0872873i
$317$	−9.88351	−	21.1952i	−0.555113	−	1.19044i	−0.961007	−	0.276524i	$-0.910818\pi$
$317$	−9.88351	−	21.1952i	−0.555113	−	1.19044i	0.405894	−	0.913920i	$-0.366960\pi$
$318$	0.176369	+	0.251881i	0.00989026	+	0.0141248i
$319$	2.25040	+	12.7627i	0.125998	+	0.714571i
$320$		0			0
$321$	−10.7996	−	9.06198i	−0.602777	−	0.505790i
$322$	−18.4676	−	18.4676i	−1.02916	−	1.02916i
$323$	4.11342	−	0.672742i	0.228877	−	0.0374323i
$324$			7.73843i			0.429913i
$325$		0			0
$326$	0.461319	+	1.26746i	0.0255501	+	0.0701984i
$327$	15.1276	+	10.5925i	0.836559	+	0.585765i
$328$	−5.58862	+	3.91319i	−0.308580	+	0.216070i
$329$	8.30545	−	22.8190i	0.457894	−	1.25805i
$330$		0			0
$331$	−21.0222	−	12.1372i	−1.15549	−	0.667120i	−0.205268	−	0.978706i	$-0.565807\pi$
$331$	−21.0222	−	12.1372i	−1.15549	−	0.667120i	−0.950218	+	0.311586i	$0.899140\pi$
$332$	−0.949999	+	10.8585i	−0.0521380	+	0.595940i
$333$	−0.0325891	+	0.372495i	−0.00178587	+	0.0204126i
$334$	−3.53979	−	2.04370i	−0.193689	−	0.111826i
$335$		0			0
$336$	1.79890	−	4.94245i	0.0981383	−	0.269633i
$337$	−1.26342	+	0.884657i	−0.0688229	+	0.0481903i	−0.607482	−	0.794334i	$-0.707820\pi$
$337$	−1.26342	+	0.884657i	−0.0688229	+	0.0481903i	0.538659	+	0.842524i	$0.318931\pi$
$338$	9.51252	+	6.66074i	0.517413	+	0.362296i
$339$	−1.81905	−	4.99781i	−0.0987974	−	0.271444i
$340$		0			0
$341$		−	25.2843i		−	1.36922i
$342$	1.06309	−	1.23545i	0.0574853	−	0.0668054i
$343$	−7.95391	−	7.95391i	−0.429471	−	0.429471i
$344$	−8.89574	−	7.46441i	−0.479626	−	0.402454i
$345$		0			0
$346$	0.395092	+	2.24068i	0.0212403	+	0.120459i
$347$	9.21689	+	13.1631i	0.494789	+	0.706632i	0.986433	−	0.164165i	$-0.0524928\pi$
$347$	9.21689	+	13.1631i	0.494789	+	0.706632i	−0.491644	+	0.870796i	$0.663604\pi$
$348$	3.14994	+	6.75507i	0.168855	+	0.362110i
$349$	20.0099	−	11.5527i	1.07111	−	0.618404i	0.142623	−	0.989777i	$-0.454446\pi$
$349$	20.0099	−	11.5527i	1.07111	−	0.618404i	0.928484	+	0.371373i	$0.121113\pi$
$350$		0			0
$351$	4.93330	−	4.13953i	0.263320	−	0.220952i
$352$	2.80694	+	0.245576i	0.149611	+	0.0130892i
$353$	−12.5467	+	3.36187i	−0.667792	+	0.178934i	−0.576760	−	0.816914i	$-0.695683\pi$
$353$	−12.5467	+	3.36187i	−0.667792	+	0.178934i	−0.0910321	+	0.995848i	$0.529017\pi$
$354$	−2.31455	−	4.00892i	−0.123017	−	0.213072i
$355$		0			0
$356$	9.98683	+	1.76095i	0.529301	+	0.0933300i
$357$	2.88474	−	4.11983i	0.152676	−	0.218045i
$358$	5.72093	+	2.66771i	0.302360	+	0.140993i
$359$	10.5413	−	12.5626i	0.556347	−	0.663028i	−0.412422	−	0.910993i	$-0.635317\pi$
$359$	10.5413	−	12.5626i	0.556347	−	0.663028i	0.968769	+	0.247965i	$0.0797617\pi$
$360$		0			0
$361$	18.7875	−	2.83355i	0.988817	−	0.149134i
$362$	7.82147	−	7.82147i	0.411087	−	0.411087i
$363$	4.94116	−	0.432295i	0.259344	−	0.0226896i
$364$	−3.59238	+	1.30752i	−0.188292	+	0.0685327i
$365$		0			0
$366$	−3.01520	+	17.1001i	−0.157607	+	0.893834i
$367$	−17.5387	+	8.17845i	−0.915515	+	0.426912i	−0.822508	−	0.568754i	$-0.807426\pi$
$367$	−17.5387	+	8.17845i	−0.915515	+	0.426912i	−0.0930070	+	0.995665i	$0.529648\pi$
$368$	2.08266	−	7.77260i	0.108566	−	0.405175i
$369$	−1.27552	+	2.20927i	−0.0664010	+	0.115010i
$370$		0			0
$371$	−0.395864	−	0.471772i	−0.0205522	−	0.0244932i
$372$	−3.76367	−	14.0462i	−0.195137	−	0.728262i
$373$	−19.9144	−	5.33606i	−1.03113	−	0.276291i	−0.296698	−	0.954971i	$-0.595885\pi$
$373$	−19.9144	−	5.33606i	−1.03113	−	0.276291i	−0.734433	+	0.678681i	$0.762552\pi$
$374$	2.53182	+	0.921508i	0.130917	+	0.0476501i
$375$		0			0
$376$	7.36818	−	1.29921i	0.379985	−	0.0670016i
$377$	2.28951	−	4.90988i	0.117916	−	0.252871i
$378$	−1.54663	−	17.6781i	−0.0795502	−	0.909263i
$379$	22.7837			1.17032			0.585161	−	0.810917i	$-0.301031\pi$
$379$	22.7837			1.17032			0.585161	+	0.810917i	$0.301031\pi$
$380$		0			0
$381$	1.96919			0.100885
$382$	−1.61311	−	18.4379i	−0.0825339	−	0.943366i
$383$	−14.5352	+	31.1709i	−0.742716	+	1.59276i	0.0612761	+	0.998121i	$0.480483\pi$
$383$	−14.5352	+	31.1709i	−0.742716	+	1.59276i	−0.803992	+	0.594639i	$0.797295\pi$
$384$	1.59590	−	0.281400i	0.0814404	−	0.0143601i
$385$		0			0
$386$	−23.1046	−	8.40938i	−1.17599	−	0.428026i
$387$	−4.19421	−	1.12383i	−0.213203	−	0.0571277i
$388$	−5.02330	−	18.7472i	−0.255019	−	0.951745i
$389$	−18.8672	−	22.4850i	−0.956605	−	1.14004i	−0.990067	−	0.140597i	$-0.955098\pi$
$389$	−18.8672	−	22.4850i	−0.956605	−	1.14004i	0.0334623	−	0.999440i	$-0.489347\pi$
$390$		0			0
$391$	3.84725	−	6.66364i	0.194564	−	0.336995i
$392$	−0.914740	+	3.41386i	−0.0462013	+	0.172426i
$393$	−19.6636	+	9.16928i	−0.991897	+	0.462529i
$394$	−2.67520	+	15.1718i	−0.134775	+	0.764345i
$395$		0			0
$396$	0.990040	−	0.360345i	0.0497514	−	0.0181080i
$397$	−23.9784	+	2.09784i	−1.20344	+	0.105288i	−0.671182	−	0.741292i	$-0.734213\pi$
$397$	−23.9784	+	2.09784i	−1.20344	+	0.105288i	−0.532261	+	0.846580i	$0.678658\pi$
$398$	−1.26401	+	1.26401i	−0.0633593	+	0.0633593i
$399$	13.3822	−	18.6153i	0.669948	−	0.931932i
$400$		0			0
$401$	−1.35617	+	1.61622i	−0.0677238	+	0.0807101i	−0.798843	−	0.601540i	$-0.794554\pi$
$401$	−1.35617	+	1.61622i	−0.0677238	+	0.0807101i	0.731119	+	0.682250i	$0.238998\pi$
$402$	1.69888	+	0.792201i	0.0847325	+	0.0395114i
$403$	−6.06243	+	8.65805i	−0.301991	+	0.431288i
$404$	0.504842	+	0.0890173i	0.0251168	+	0.00442877i
$405$		0			0
$406$	−7.46402	−	12.9281i	−0.370433	−	0.641609i
$407$	−2.72165	+	0.729263i	−0.134907	+	0.0361482i
$408$	1.54368	+	0.135054i	0.0764235	+	0.00668619i
$409$	−3.55332	+	2.98159i	−0.175700	+	0.147430i	−0.726397	−	0.687275i	$-0.758807\pi$
$409$	−3.55332	+	2.98159i	−0.175700	+	0.147430i	0.550697	+	0.834705i	$0.314362\pi$
$410$		0			0
$411$	−27.2943	+	15.7584i	−1.34633	+	0.777303i
$412$	−1.93906	−	4.15832i	−0.0955304	−	0.204866i
$413$	5.31786	+	7.59469i	0.261675	+	0.373710i
$414$	−0.522481	−	2.96314i	−0.0256785	−	0.145630i
$415$		0			0
$416$	−0.902295	−	0.757115i	−0.0442386	−	0.0371206i
$417$	−9.27980	−	9.27980i	−0.454434	−	0.454434i
$418$	11.4882	+	4.34368i	0.561904	+	0.212456i
$419$			3.11186i			0.152024i	0.997107	+	0.0760122i	$0.0242188\pi$
$419$			3.11186i			0.152024i	−0.997107	+	0.0760122i	$0.975781\pi$
$420$		0			0
$421$	−2.86185	−	7.86288i	−0.139478	−	0.383213i	0.850212	−	0.526441i	$-0.176474\pi$
$421$	−2.86185	−	7.86288i	−0.139478	−	0.383213i	−0.989690	+	0.143228i	$0.954252\pi$
$422$	−18.9364	−	13.2594i	−0.921809	−	0.645457i
$423$	2.29167	−	1.60464i	0.111425	−	0.0780203i
$424$	0.0648975	−	0.178304i	0.00315170	−	0.00865922i
$425$		0			0
$426$	2.61928	+	1.51224i	0.126905	+	0.0732685i
$427$	3.03103	−	34.6449i	0.146682	−	1.67658i
$428$	−0.758224	+	8.66654i	−0.0366501	+	0.418913i
$429$	4.65767	+	2.68910i	0.224874	+	0.129831i
$430$		0			0
$431$	10.3779	−	28.5131i	0.499887	−	1.37343i	−0.391498	−	0.920179i	$-0.628043\pi$
$431$	10.3779	−	28.5131i	0.499887	−	1.37343i	0.891384	−	0.453248i	$-0.149735\pi$
$432$	4.47871	−	3.13603i	0.215482	−	0.150882i
$433$	−12.5758	−	8.80566i	−0.604354	−	0.423173i	0.230947	−	0.972966i	$-0.425818\pi$
$433$	−12.5758	−	8.80566i	−0.604354	−	0.423173i	−0.835301	+	0.549793i	$0.814706\pi$
$434$	9.96128	+	27.3684i	0.478157	+	1.31373i
$435$		0			0
$436$		−	11.3960i		−	0.545769i
$437$	17.9135	−	30.1558i	0.856918	−	1.44255i
$438$	4.20678	+	4.20678i	0.201008	+	0.201008i
$439$	7.88512	+	6.61640i	0.376336	+	0.315784i	0.811262	−	0.584683i	$-0.198781\pi$
$439$	7.88512	+	6.61640i	0.376336	+	0.315784i	−0.434926	+	0.900466i	$0.643225\pi$
$440$		0			0
$441$	0.229482	+	1.30146i	0.0109277	+	0.0619742i
$442$	−0.646017	−	0.922609i	−0.0307279	−	0.0438840i
$443$	−0.262054	−	0.561978i	−0.0124506	−	0.0267004i	0.899984	−	0.435923i	$-0.143578\pi$
$443$	−0.262054	−	0.561978i	−0.0124506	−	0.0267004i	−0.912435	+	0.409222i	$0.865800\pi$
$444$	−1.40341	+	0.810257i	−0.0666027	+	0.0384531i
$445$		0			0
$446$	5.70127	−	4.78393i	0.269963	−	0.226526i
$447$	18.0724	+	1.58113i	0.854797	+	0.0747851i
$448$	−3.13506	+	0.840038i	−0.148118	+	0.0396880i
$449$	11.0436	+	19.1281i	0.521181	+	0.902713i	0.999697	+	0.0246333i	$0.00784180\pi$
$449$	11.0436	+	19.1281i	0.521181	+	0.902713i	−0.478515	+	0.878079i	$0.658825\pi$
$450$		0			0
$451$	−18.9313	−	3.33810i	−0.891440	−	0.157185i
$452$	−1.88248	+	2.68846i	−0.0885446	+	0.126455i
$453$	33.9958	+	15.8525i	1.59726	+	0.744816i
$454$	12.9877	−	15.4781i	0.609543	−	0.726425i
$455$		0			0
$456$	7.02861	+	0.702989i	0.329145	+	0.0329205i
$457$	6.26952	−	6.26952i	0.293276	−	0.293276i	−0.545097	−	0.838373i	$-0.683507\pi$
$457$	6.26952	−	6.26952i	0.293276	−	0.293276i	0.838373	+	0.545097i	$0.183507\pi$
$458$	13.2353	−	1.15793i	0.618443	−	0.0541067i
$459$	4.91284	−	1.78813i	0.229312	−	0.0834627i
$460$		0			0
$461$	−2.47947	+	14.0618i	−0.115481	+	0.654923i	0.871031	+	0.491229i	$0.163452\pi$
$461$	−2.47947	+	14.0618i	−0.115481	+	0.654923i	−0.986511	+	0.163694i	$0.947659\pi$
$462$	13.4314	−	6.26317i	0.624886	−	0.291389i
$463$	−0.695552	+	2.59584i	−0.0323250	+	0.120639i	−0.980203	−	0.197995i	$-0.936557\pi$
$463$	−0.695552	+	2.59584i	−0.0323250	+	0.120639i	0.947878	+	0.318633i	$0.103224\pi$
$464$	2.29970	−	3.98319i	0.106761	−	0.184915i
$465$		0			0
$466$	15.5192	+	18.4950i	0.718912	+	0.856766i
$467$	−5.00025	−	18.6612i	−0.231384	−	0.863537i	−0.979746	−	0.200246i	$-0.935826\pi$
$467$	−5.00025	−	18.6612i	−0.231384	−	0.863537i	0.748362	−	0.663291i	$-0.230841\pi$
$468$	−0.425418	−	0.113990i	−0.0196650	−	0.00526921i
$469$	−3.52794	−	1.28407i	−0.162905	−	0.0592927i
$470$		0			0
$471$	−2.09547	+	0.369488i	−0.0965541	+	0.0170251i
$472$	−1.20723	+	2.58892i	−0.0555674	+	0.119165i
$473$	−2.85176	−	32.5958i	−0.131124	−	1.49876i
$474$	−5.02897			−0.230988
$475$		0			0
$476$	−3.10357			−0.142252
$477$	−0.00618372	−	0.0706802i	−0.000283133	−	0.00323623i
$478$	−10.9014	+	23.3781i	−0.498619	+	1.06929i
$479$	6.38735	−	1.12626i	0.291845	−	0.0514602i	−0.0258086	−	0.999667i	$-0.508216\pi$
$479$	6.38735	−	1.12626i	0.291845	−	0.0514602i	0.317654	+	0.948207i	$0.397105\pi$
$480$		0			0
$481$	1.10683	+	0.402852i	0.0504669	+	0.0183685i
$482$	26.3362	+	7.05677i	1.19958	+	0.321427i
$483$	−10.9541	−	40.8811i	−0.498427	−	1.86016i
$484$	−1.96742	−	2.34469i	−0.0894284	−	0.106577i
$485$		0			0
$486$	1.93112	−	3.34479i	0.0875972	−	0.151723i
$487$	−5.75650	+	21.4835i	−0.260852	+	0.973512i	0.703889	+	0.710310i	$0.251445\pi$
$487$	−5.75650	+	21.4835i	−0.260852	+	0.973512i	−0.964741	+	0.263202i	$0.915221\pi$
$488$	9.71109	−	4.52835i	0.439600	−	0.204989i
$489$	−0.379555	+	2.15256i	−0.0171641	+	0.0973422i
$490$		0			0
$491$	3.81981	−	1.39030i	0.172386	−	0.0627433i	−0.254385	−	0.967103i	$-0.581873\pi$
$491$	3.81981	−	1.39030i	0.172386	−	0.0627433i	0.426771	+	0.904360i	$0.359651\pi$
$492$	−11.0138	+	0.963585i	−0.496541	+	0.0434417i
$493$	3.10988	−	3.10988i	0.140062	−	0.140062i
$494$	−2.89238	−	4.24193i	−0.130135	−	0.190853i
$495$		0			0
$496$	−5.76804	+	6.87409i	−0.258993	+	0.308656i
$497$	−5.49005	−	2.56005i	−0.246262	−	0.114834i
$498$	−10.1315	+	14.4692i	−0.454002	+	0.648382i
$499$	−11.7334	−	2.06892i	−0.525260	−	0.0926176i	−0.0952707	−	0.995451i	$-0.530372\pi$
$499$	−11.7334	−	2.06892i	−0.525260	−	0.0926176i	−0.429990	+	0.902834i	$0.641483\pi$
$500$		0			0
$501$	−3.31185	−	5.73629i	−0.147962	−	0.256279i
$502$	−4.04282	+	1.08327i	−0.180440	+	0.0483487i
$503$	13.7836	+	1.20591i	0.614581	+	0.0537689i	0.390196	−	0.920732i	$-0.372407\pi$
$503$	13.7836	+	1.20591i	0.614581	+	0.0537689i	0.224385	+	0.974501i	$0.427963\pi$
$504$	−0.929682	+	0.780095i	−0.0414113	+	0.0347482i
$505$		0			0
$506$	19.6355	−	11.3366i	0.872905	−	0.503972i
$507$	7.95304	+	17.0554i	0.353207	+	0.757455i
$508$	−0.696988	−	0.995402i	−0.0309238	−	0.0441638i
$509$	−2.39466	−	13.5808i	−0.106141	−	0.601957i	−0.990758	−	0.135639i	$-0.956691\pi$
$509$	−2.39466	−	13.5808i	−0.106141	−	0.601957i	0.884617	−	0.466318i	$-0.154420\pi$
$510$		0			0
$511$	−9.12782	−	7.65915i	−0.403791	−	0.338821i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	22.4945	−	7.87234i	0.993157	−	0.347573i
$514$		−	15.6628i		−	0.690858i
$515$		0			0
$516$	−6.43626	−	17.6835i	−0.283341	−	0.778472i
$517$	17.2688	+	12.0918i	0.759482	+	0.531795i
$518$	2.65868	−	1.86163i	0.116816	−	0.0817952i
$519$	−1.26105	+	3.46471i	−0.0553541	+	0.152084i
$520$		0			0
$521$	−16.8081	−	9.70414i	−0.736375	−	0.425146i	0.0843749	−	0.996434i	$-0.473111\pi$
$521$	−16.8081	−	9.70414i	−0.736375	−	0.425146i	−0.820750	+	0.571288i	$0.806444\pi$
$522$	0.149890	−	1.71326i	0.00656053	−	0.0749872i
$523$	0.742850	−	8.49081i	0.0324826	−	0.371277i	−0.962504	−	0.271268i	$-0.912557\pi$
$523$	0.742850	−	8.49081i	0.0324826	−	0.371277i	0.994986	−	0.100010i	$-0.0318873\pi$
$524$	11.5948	+	6.69427i	0.506522	+	0.292440i
$525$		0			0
$526$	−1.30076	+	3.57382i	−0.0567160	+	0.155826i
$527$	−7.02885	+	4.92165i	−0.306181	+	0.214391i
$528$	3.74031	+	2.61899i	0.162776	+	0.113977i
$529$	−14.2796	−	39.2329i	−0.620852	−	1.70578i
$530$		0			0
$531$			1.06812i			0.0463525i
$532$	−14.1464	−	0.175711i	−0.613324	−	0.00761804i
$533$	5.68224	+	5.68224i	0.246125	+	0.246125i
$534$	12.5888	+	10.5633i	0.544771	+	0.457117i
$535$		0			0
$536$	−0.200865	−	1.13916i	−0.00867603	−	0.0492042i
$537$	5.86727	+	8.37933i	0.253191	+	0.361595i
$538$	−0.838720	−	1.79864i	−0.0361598	−	0.0775449i
$539$	−8.62425	+	4.97921i	−0.371473	+	0.214470i
$540$		0			0
$541$	3.34990	−	2.81090i	0.144024	−	0.120850i	−0.567929	−	0.823077i	$-0.692255\pi$
$541$	3.34990	−	2.81090i	0.144024	−	0.120850i	0.711953	+	0.702227i	$0.247811\pi$
$542$	6.12931	+	0.536245i	0.263276	+	0.0230337i
$543$	17.3142	−	4.63931i	0.743021	−	0.199092i
$544$	−0.478111	−	0.828112i	−0.0204988	−	0.0355050i
$545$		0			0
$546$	−6.10102	−	1.07577i	−0.261100	−	0.0460389i
$547$	−8.04878	+	11.4948i	−0.344141	+	0.491484i	−0.953493	−	0.301416i	$-0.902541\pi$
$547$	−8.04878	+	11.4948i	−0.344141	+	0.491484i	0.609352	+	0.792900i	$0.291430\pi$
$548$	17.6264	+	8.21931i	0.752961	+	0.351111i
$549$	2.57536	−	3.06919i	0.109914	−	0.130990i
$550$		0			0
$551$	14.3512	−	13.9991i	0.611384	−	0.596382i
$552$	9.22065	−	9.22065i	0.392457	−	0.392457i
$553$	10.0339	−	0.877856i	0.426686	−	0.0373302i
$554$	−4.70417	+	1.71218i	−0.199861	+	0.0727435i
$555$		0			0
$556$	−1.40627	+	7.97537i	−0.0596393	+	0.338231i
$557$	−7.76356	+	3.62021i	−0.328953	+	0.153393i	−0.580077	−	0.814562i	$-0.696978\pi$
$557$	−7.76356	+	3.62021i	−0.328953	+	0.153393i	0.251124	+	0.967955i	$0.419200\pi$
$558$	−0.868431	+	3.24103i	−0.0367636	+	0.137204i
$559$	−6.83900	+	11.8455i	−0.289259	+	0.501011i
$560$		0			0
$561$	2.80653	+	3.34469i	0.118492	+	0.141213i
$562$	8.04834	+	30.0368i	0.339499	+	1.26703i
$563$	−7.00107	−	1.87593i	−0.295060	−	0.0790611i	0.108252	−	0.994123i	$-0.465475\pi$
$563$	−7.00107	−	1.87593i	−0.295060	−	0.0790611i	−0.403312	+	0.915062i	$0.632141\pi$
$564$	11.3933	+	4.14682i	0.479744	+	0.174612i
$565$		0			0
$566$	−29.4250	+	5.18843i	−1.23683	+	0.218086i
$567$	10.6146	−	22.7631i	0.445771	−	0.955959i
$568$	−0.162665	−	1.85927i	−0.00682527	−	0.0780132i
$569$	−19.2597			−0.807409			−0.403704	−	0.914889i	$-0.632278\pi$
$569$	−19.2597			−0.807409			−0.403704	+	0.914889i	$0.632278\pi$
$570$		0			0
$571$	−0.818210			−0.0342410			−0.0171205	−	0.999853i	$-0.505450\pi$
$571$	−0.818210			−0.0342410			−0.0171205	+	0.999853i	$0.505450\pi$
$572$	−0.289254	−	3.30619i	−0.0120943	−	0.138239i
$573$	12.6756	−	27.1830i	0.529533	−	1.13559i
$574$	21.8069	−	3.84514i	0.910202	−	0.160493i
$575$		0			0
$576$	−0.351369	−	0.127888i	−0.0146404	−	0.00532866i
$577$	13.1893	+	3.53406i	0.549078	+	0.147125i	0.522684	−	0.852527i	$-0.324931\pi$
$577$	13.1893	+	3.53406i	0.549078	+	0.147125i	0.0263942	+	0.999652i	$0.491598\pi$
$578$	4.16327	+	15.5375i	0.173169	+	0.646276i
$579$	−25.6114	−	30.5225i	−1.06437	−	1.26847i
$580$		0			0
$581$	17.6888	−	30.6380i	0.733857	−	1.27108i
$582$	8.14034	−	30.3802i	0.337428	−	1.25930i
$583$	0.484553	−	0.225951i	0.0200681	−	0.00935792i
$584$	0.637501	−	3.61545i	0.0263800	−	0.149608i
$585$		0			0
$586$	11.3780	−	4.14124i	0.470019	−	0.171073i
$587$	−37.9328	+	3.31869i	−1.56566	+	0.136977i	−0.836730	−	0.547616i	$-0.815535\pi$
$587$	−37.9328	+	3.31869i	−1.56566	+	0.136977i	−0.728925	+	0.684593i	$0.759980\pi$
$588$	−4.04986	+	4.04986i	−0.167014	+	0.167014i
$589$	−32.3169	+	22.0355i	−1.33159	+	0.907956i
$590$		0			0
$591$	−16.0475	+	19.1247i	−0.660106	+	0.786684i
$592$	0.906306	+	0.422617i	0.0372489	+	0.0173695i
$593$	−12.9331	+	18.4704i	−0.531099	+	0.758487i	−0.991624	−	0.129159i	$-0.958772\pi$
$593$	−12.9331	+	18.4704i	−0.531099	+	0.758487i	0.460525	+	0.887647i	$0.347661\pi$
$594$	15.1715	+	2.67515i	0.622495	+	0.109763i
$595$		0			0
$596$	−5.59743	−	9.69503i	−0.229280	−	0.397124i
$597$	−2.79811	+	0.749752i	−0.114519	+	0.0306853i
$598$	−9.44194	−	0.826063i	−0.386110	−	0.0337802i
$599$	28.7371	−	24.1133i	1.17416	−	0.985241i	0.174164	−	0.984717i	$-0.444278\pi$
$599$	28.7371	−	24.1133i	1.17416	−	0.985241i	1.00000		0.000524215i	$-0.000166863\pi$
$600$		0			0
$601$	−38.9733	+	22.5013i	−1.58975	+	0.917845i	−0.596408	+	0.802681i	$0.703406\pi$
$601$	−38.9733	+	22.5013i	−1.58975	+	0.917845i	−0.993346	+	0.115164i	$0.963261\pi$
$602$	15.9286	+	34.1591i	0.649203	+	1.39222i
$603$	−0.248086	−	0.354304i	−0.0101028	−	0.0144284i
$604$	−4.01944	−	22.7954i	−0.163549	−	0.927532i
$605$		0			0
$606$	0.636373	+	0.533981i	0.0258509	+	0.0216915i
$607$	16.1710	+	16.1710i	0.656359	+	0.656359i	0.954517	−	0.298158i	$-0.0963722\pi$
$607$	16.1710	+	16.1710i	0.656359	+	0.656359i	−0.298158	+	0.954517i	$0.596372\pi$
$608$	−2.13240	−	3.80169i	−0.0864801	−	0.154179i
$609$		−	24.1912i		−	0.980276i
$610$		0			0
$611$	−3.01408	−	8.28112i	−0.121937	−	0.335018i
$612$	−0.292887	−	0.205082i	−0.0118393	−	0.00828995i
$613$	−17.6923	+	12.3883i	−0.714584	+	0.500357i	−0.873432	−	0.486946i	$-0.838111\pi$
$613$	−17.6923	+	12.3883i	−0.714584	+	0.500357i	0.158848	+	0.987303i	$0.449222\pi$
$614$	7.79691	−	21.4218i	0.314658	−	0.864515i
$615$		0			0
$616$	−7.91995	−	4.57258i	−0.319104	−	0.184235i
$617$	−0.563698	+	6.44309i	−0.0226936	+	0.259389i	0.976369	+	0.216109i	$0.0693365\pi$
$617$	−0.563698	+	6.44309i	−0.0226936	+	0.259389i	−0.999063	+	0.0432806i	$0.986219\pi$
$618$	0.648025	−	7.40696i	0.0260674	−	0.297952i
$619$	−7.80487	−	4.50615i	−0.313704	−	0.181117i	0.334879	−	0.942261i	$-0.391305\pi$
$619$	−7.80487	−	4.50615i	−0.313704	−	0.181117i	−0.648583	+	0.761144i	$0.724638\pi$
$620$		0			0
$621$	15.0474	−	41.3425i	0.603833	−	1.65902i
$622$	20.3548	−	14.2526i	0.816155	−	0.571478i
$623$	−26.9614	−	18.8786i	−1.08019	−	0.756356i
$624$	−0.652830	−	1.79364i	−0.0261341	−	0.0718029i
$625$		0			0
$626$			26.9746i			1.07812i
$627$	12.6031	+	15.4044i	0.503319	+	0.615191i
$628$	0.928454	+	0.928454i	0.0370494	+	0.0370494i
$629$	0.732506	+	0.614646i	0.0292069	+	0.0245075i
$630$		0			0
$631$	6.00407	+	34.0507i	0.239018	+	1.35554i	0.833984	+	0.551788i	$0.186054\pi$
$631$	6.00407	+	34.0507i	0.239018	+	1.35554i	−0.594966	+	0.803751i	$0.702835\pi$
$632$	1.77998	+	2.54208i	0.0708040	+	0.101119i
$633$	−15.8320	−	33.9518i	−0.629264	−	1.34946i
$634$	−20.2532	+	11.6932i	−0.804357	+	0.464396i
$635$		0			0
$636$	0.235551	−	0.197650i	0.00934019	−	0.00783735i
$637$	4.14706	+	0.362820i	0.164312	+	0.0143755i
$638$	12.5180	−	3.35417i	0.495590	−	0.132793i
$639$	−0.348936	−	0.604375i	−0.0138037	−	0.0239087i
$640$		0			0
$641$	20.7905	+	3.66592i	0.821175	+	0.144795i	0.568424	−	0.822736i	$-0.307553\pi$
$641$	20.7905	+	3.66592i	0.821175	+	0.144795i	0.252751	+	0.967531i	$0.418665\pi$
$642$	−8.08624	+	11.5484i	−0.319139	+	0.455777i
$643$	−39.9139	−	18.6122i	−1.57405	−	0.733992i	−0.577455	−	0.816423i	$-0.695954\pi$
$643$	−39.9139	−	18.6122i	−1.57405	−	0.733992i	−0.996597	+	0.0824304i	$0.973732\pi$
$644$	−16.7877	+	20.0069i	−0.661530	+	0.788381i
$645$		0			0
$646$	−1.02869	−	4.03914i	−0.0404733	−	0.158918i
$647$	20.6662	−	20.6662i	0.812472	−	0.812472i	−0.172532	−	0.985004i	$-0.555195\pi$
$647$	20.6662	−	20.6662i	0.812472	−	0.812472i	0.985004	+	0.172532i	$0.0551947\pi$
$648$	7.70898	−	0.674448i	0.302837	−	0.0264948i
$649$	−7.56341	+	2.75286i	−0.296890	+	0.108059i
$650$		0			0
$651$	−8.19573	+	46.4803i	−0.321216	+	1.82171i
$652$	1.22244	−	0.570031i	0.0478743	−	0.0223241i
$653$	−2.19514	+	8.19238i	−0.0859025	+	0.320592i	−0.995484	−	0.0949341i	$-0.969736\pi$
$653$	−2.19514	+	8.19238i	−0.0859025	+	0.320592i	0.909581	+	0.415526i	$0.136403\pi$
$654$	9.23371	−	15.9933i	0.361067	−	0.625386i
$655$		0			0
$656$	4.38538	+	5.22629i	0.171220	+	0.204052i
$657$	−0.355291	−	1.32597i	−0.0138612	−	0.0517308i
$658$	−23.4561	−	6.28504i	−0.914413	−	0.245016i
$659$	−11.2571	−	4.09726i	−0.438515	−	0.159606i	0.113322	−	0.993558i	$-0.463851\pi$
$659$	−11.2571	−	4.09726i	−0.438515	−	0.159606i	−0.551837	+	0.833952i	$0.686073\pi$
$660$		0			0
$661$	−35.9339	+	6.33611i	−1.39767	+	0.246446i	−0.821184	−	0.570664i	$-0.806686\pi$
$661$	−35.9339	+	6.33611i	−1.39767	+	0.246446i	−0.576482	+	0.817110i	$0.695575\pi$
$662$	−10.2588	+	22.0000i	−0.398719	+	0.855056i
$663$	−0.159075	−	1.81824i	−0.00617798	−	0.0706146i
$664$	10.9000			0.423003
$665$		0			0
$666$	0.373918			0.0144890
$667$	−3.22566	−	36.8695i	−0.124898	−	1.42759i
$668$	−1.72741	+	3.70444i	−0.0668354	+	0.143329i
$669$	11.8774	−	2.09431i	0.459209	−	0.0809709i
$670$		0			0
$671$	28.3705	+	10.3260i	1.09523	+	0.398632i
$672$	−5.08043	−	1.36130i	−0.195982	−	0.0525132i
$673$	1.31189	+	4.89604i	0.0505696	+	0.188728i	0.986590	−	0.163217i	$-0.0521870\pi$
$673$	1.31189	+	4.89604i	0.0505696	+	0.188728i	−0.936021	+	0.351945i	$0.885520\pi$
$674$	0.991405	+	1.18151i	0.0381875	+	0.0455101i
$675$		0			0
$676$	5.80632	−	10.0568i	0.223320	−	0.386802i
$677$	5.59167	−	20.8684i	0.214905	−	0.802038i	−0.771295	−	0.636478i	$-0.780390\pi$
$677$	5.59167	−	20.8684i	0.214905	−	0.802038i	0.986200	−	0.165559i	$-0.0529429\pi$
$678$	−4.82025	+	2.24772i	−0.185121	+	0.0863231i
$679$	−10.9387	+	62.0364i	−0.419788	+	2.38074i
$680$		0			0
$681$	30.7684	−	11.1988i	1.17905	−	0.429138i
$682$	−25.1881	+	2.20367i	−0.964500	+	0.0843828i
$683$	18.4087	−	18.4087i	0.704388	−	0.704388i	−0.260961	−	0.965349i	$-0.584039\pi$
$683$	18.4087	−	18.4087i	0.704388	−	0.704388i	0.965349	+	0.260961i	$0.0840394\pi$
$684$	−1.32340	−	0.951368i	−0.0506016	−	0.0363765i
$685$		0			0
$686$	−7.23041	+	8.61687i	−0.276058	+	0.328994i
$687$	19.5127	+	9.09893i	0.744457	+	0.347146i
$688$	−6.66069	+	9.51246i	−0.253937	+	0.362659i
$689$	−0.220101	−	0.0388097i	−0.00838518	−	0.00147853i
$690$		0			0
$691$	−5.73435	−	9.93218i	−0.218145	−	0.377838i	0.736096	−	0.676877i	$-0.236667\pi$
$691$	−5.73435	−	9.93218i	−0.218145	−	0.377838i	−0.954241	+	0.299039i	$0.903334\pi$
$692$	2.19771	−	0.588876i	0.0835446	−	0.0223857i
$693$	−3.40654	−	0.298034i	−0.129404	−	0.0113214i
$694$	12.3097	−	10.3291i	0.467270	−	0.392086i
$695$		0			0
$696$	6.45483	−	3.72670i	0.244670	−	0.141260i
$697$	2.75706	+	5.91254i	0.104431	+	0.223953i
$698$	−13.2528	−	18.9269i	−0.501624	−	0.716394i
$699$	6.79400	+	38.5307i	0.256973	+	1.45736i
$700$		0			0
$701$	29.0134	+	24.3451i	1.09582	+	0.919503i	0.997137	−	0.0756156i	$-0.0240922\pi$
$701$	29.0134	+	24.3451i	1.09582	+	0.919503i	0.0986842	+	0.995119i	$0.468537\pi$
$702$	−4.55374	−	4.55374i	−0.171870	−	0.171870i
$703$	3.30405	+	2.84309i	0.124614	+	0.107229i
$704$		−	2.81766i		−	0.106195i
$705$		0			0
$706$	4.44259	+	12.2059i	0.167199	+	0.459376i
$707$	−1.36292	−	0.954328i	−0.0512580	−	0.0358912i
$708$	−3.79194	+	2.65514i	−0.142510	+	0.0997864i
$709$	7.64849	−	21.0141i	0.287245	−	0.789199i	−0.709204	−	0.705003i	$-0.750946\pi$
$709$	7.64849	−	21.0141i	0.287245	−	0.789199i	0.996449	−	0.0841961i	$-0.0268322\pi$
$710$		0			0
$711$	1.00492	+	0.580193i	0.0376876	+	0.0217589i
$712$	0.883837	−	10.1023i	0.0331232	−	0.378600i
$713$	−6.29332	+	71.9329i	−0.235687	+	2.69391i
$714$	−4.35558	−	2.51469i	−0.163003	−	0.0941100i
$715$		0			0
$716$	2.15895	−	5.93166i	0.0806837	−	0.221677i
$717$	−34.2415	+	23.9762i	−1.27877	+	0.895406i
$718$	−13.4335	−	9.40625i	−0.501334	−	0.351038i
$719$	8.24828	+	22.6620i	0.307609	+	0.845149i	0.993122	+	0.117088i	$0.0373560\pi$
$719$	8.24828	+	22.6620i	0.307609	+	0.845149i	−0.685512	+	0.728061i	$0.740422\pi$
$720$		0			0
$721$			14.8917i			0.554596i
$722$	−4.46020	−	18.4691i	−0.165992	−	0.687348i
$723$	31.2427	+	31.2427i	1.16193	+	1.16193i
$724$	−8.47339	−	7.11002i	−0.314911	−	0.264242i
$725$		0			0
$726$	−0.861301	−	4.88468i	−0.0319659	−	0.181287i
$727$	−5.13661	−	7.33585i	−0.190507	−	0.272071i	0.712524	−	0.701648i	$-0.247552\pi$
$727$	−5.13661	−	7.33585i	−0.190507	−	0.272071i	−0.903031	+	0.429576i	$0.858663\pi$
$728$	1.61564	+	3.46476i	0.0598797	+	0.128412i
$729$	25.5253	−	14.7370i	0.945382	−	0.545817i
$730$		0			0
$731$	−8.50630	+	7.13763i	−0.314617	+	0.263995i
$732$	17.2978	+	1.51336i	0.639344	+	0.0559354i
$733$	11.7137	−	3.13868i	0.432656	−	0.115930i	−0.0359165	−	0.999355i	$-0.511435\pi$
$733$	11.7137	−	3.13868i	0.432656	−	0.115930i	0.468573	+	0.883425i	$0.344768\pi$
$734$	9.67593	+	16.7592i	0.357145	+	0.618593i
$735$		0			0
$736$	−7.92454	−	1.39731i	−0.292102	−	0.0515055i
$737$	1.86945	−	2.66985i	0.0688620	−	0.0983452i
$738$	2.31203	+	1.07812i	0.0851070	+	0.0396860i
$739$	11.0708	−	13.1937i	0.407247	−	0.485338i	−0.522968	−	0.852352i	$-0.675175\pi$
$739$	11.0708	−	13.1937i	0.407247	−	0.485338i	0.930215	+	0.367014i	$0.119620\pi$
$740$		0			0
$741$	−0.622142	−	8.29674i	−0.0228550	−	0.304789i
$742$	−0.435475	+	0.435475i	−0.0159868	+	0.0159868i
$743$	13.6857	−	1.19734i	0.502079	−	0.0439263i	0.166697	−	0.986008i	$-0.446690\pi$
$743$	13.6857	−	1.19734i	0.502079	−	0.0439263i	0.335383	+	0.942082i	$0.391134\pi$
$744$	−13.6647	+	4.97355i	−0.500973	+	0.182339i
$745$		0			0
$746$	−3.58010	+	20.3037i	−0.131077	+	0.743373i
$747$	3.69386	−	1.72248i	0.135151	−	0.0630221i
$748$	0.697339	−	2.60250i	0.0254972	−	0.0951570i
$749$	14.1180	−	24.4531i	0.515861	−	0.893498i
$750$		0			0
$751$	−14.3326	−	17.0809i	−0.523002	−	0.623290i	0.438286	−	0.898836i	$-0.355586\pi$
$751$	−14.3326	−	17.0809i	−0.523002	−	0.623290i	−0.961288	+	0.275546i	$0.911141\pi$
$752$	−1.93645	−	7.22691i	−0.0706149	−	0.263538i
$753$	−6.55146	−	1.75546i	−0.238748	−	0.0639724i
$754$	−5.09074	−	1.85288i	−0.185394	−	0.0674778i
$755$		0			0
$756$	−17.4760	+	3.08149i	−0.635597	+	0.112073i
$757$	9.51981	−	20.4153i	0.346003	−	0.742007i	−0.653890	−	0.756589i	$-0.726864\pi$
$757$	9.51981	−	20.4153i	0.346003	−	0.742007i	0.999894	+	0.0145828i	$0.00464200\pi$
$758$	−1.98573	−	22.6970i	−0.0721251	−	0.824393i
$759$	36.7422			1.33366
$760$		0			0
$761$	−40.1885			−1.45683			−0.728416	−	0.685135i	$-0.759743\pi$
$761$	−40.1885			−1.45683			−0.728416	+	0.685135i	$0.759743\pi$
$762$	−0.171626	−	1.96170i	−0.00621737	−	0.0710648i
$763$	−15.6316	+	33.5220i	−0.565901	+	1.21358i
$764$	−18.2272	+	3.21394i	−0.659436	+	0.116276i
$765$		0			0
$766$	32.3191	+	11.7632i	1.16774	+	0.425022i
$767$	3.24998	+	0.870830i	0.117350	+	0.0314439i
$768$	−0.419421	−	1.56530i	−0.0151346	−	0.0564829i
$769$	20.2981	+	24.1904i	0.731970	+	0.872328i	0.995735	−	0.0922593i	$-0.0294089\pi$
$769$	20.2981	+	24.1904i	0.731970	+	0.872328i	−0.263765	+	0.964587i	$0.584964\pi$
$770$		0			0
$771$	12.6910	−	21.9814i	0.457054	−	0.791641i
$772$	−6.36368	+	23.7496i	−0.229034	+	0.854766i
$773$	6.31844	−	2.94634i	0.227259	−	0.105972i	−0.305654	−	0.952143i	$-0.598875\pi$
$773$	6.31844	−	2.94634i	0.227259	−	0.105972i	0.532913	+	0.846170i	$0.321097\pi$
$774$	−0.754008	+	4.27619i	−0.0271023	+	0.153705i
$775$		0			0
$776$	−18.2380	+	6.63811i	−0.654708	+	0.238294i
$777$	5.23962	−	0.458407i	0.187970	−	0.0164453i
$778$	−20.7551	+	20.7551i	−0.744106	+	0.744106i
$779$	12.2322	+	27.1061i	0.438266	+	0.971177i
$780$		0			0
$781$	3.38029	−	4.02848i	0.120956	−	0.144150i
$782$	−6.97359	−	3.25184i	−0.249375	−	0.116286i
$783$	14.4238	−	20.5993i	0.515465	−	0.736161i
$784$	3.48059	+	0.613722i	0.124307	+	0.0219186i
$785$		0			0
$786$	10.8482	+	18.7896i	0.386942	+	0.670203i
$787$	−9.70610	+	2.60074i	−0.345985	+	0.0927064i	−0.427627	−	0.903955i	$-0.640650\pi$
$787$	−9.70610	+	2.60074i	−0.345985	+	0.0927064i	0.0816419	+	0.996662i	$0.473984\pi$
$788$	15.3472	+	1.34271i	0.546723	+	0.0478320i
$789$	−4.72123	+	3.96158i	−0.168080	+	0.141036i
$790$		0			0
$791$	9.22514	−	5.32614i	0.328008	−	0.189376i
$792$	−0.445262	−	0.954867i	−0.0158217	−	0.0339297i
$793$	−7.23899	−	10.3383i	−0.257064	−	0.367125i
$794$	4.17972	+	23.7044i	0.148333	+	0.841236i
$795$		0			0
$796$	1.36937	+	1.14904i	0.0485361	+	0.0407266i
$797$	31.6153	+	31.6153i	1.11987	+	1.11987i	0.991760	+	0.128114i	$0.0408922\pi$
$797$	31.6153	+	31.6153i	1.11987	+	1.11987i	0.128114	+	0.991760i	$0.459108\pi$
$798$	−19.7108	−	11.7088i	−0.697756	−	0.414489i
$799$		−	7.15431i		−	0.253101i
$800$		0			0
$801$	−1.29690	−	3.56320i	−0.0458236	−	0.125899i
$802$	1.72827	+	1.21015i	0.0610272	+	0.0427317i
$803$	8.47353	−	5.93323i	0.299024	−	0.209379i
$804$	0.641119	−	1.76146i	0.0226105	−	0.0621219i
$805$		0			0
$806$	9.15348	+	5.28476i	0.322418	+	0.186148i
$807$	0.280297	−	3.20381i	0.00986693	−	0.112780i
$808$	0.0446787	−	0.510679i	0.00157179	−	0.0179656i
$809$	−2.02964	−	1.17181i	−0.0713583	−	0.0411988i	0.463896	−	0.885890i	$-0.346451\pi$
$809$	−2.02964	−	1.17181i	−0.0713583	−	0.0411988i	−0.535255	+	0.844691i	$0.679784\pi$
$810$		0			0
$811$	6.19403	−	17.0180i	0.217502	−	0.597582i	−0.782173	−	0.623061i	$-0.785889\pi$
$811$	6.19403	−	17.0180i	0.217502	−	0.597582i	0.999675	+	0.0254791i	$0.00811112\pi$
$812$	−12.2283	+	8.56237i	−0.429130	+	0.300480i
$813$	8.16744	+	5.71890i	0.286445	+	0.200571i
$814$	0.963696	+	2.64773i	0.0337775	+	0.0928029i
$815$		0			0
$816$		−	1.54957i		−	0.0542460i
$817$	−39.1767	+	32.0525i	−1.37062	+	1.12138i
$818$	3.27993	+	3.27993i	0.114680	+	0.114680i
$819$	1.09504	+	0.918845i	0.0382637	+	0.0321070i
$820$		0			0
$821$	3.31439	+	18.7968i	0.115673	+	0.656014i	0.986415	+	0.164274i	$0.0525280\pi$
$821$	3.31439	+	18.7968i	0.115673	+	0.656014i	−0.870742	+	0.491740i	$0.836361\pi$
$822$	18.0772	+	25.8170i	0.630516	+	0.900471i
$823$	10.6994	+	22.9448i	0.372956	+	0.799807i	0.999787	+	0.0206513i	$0.00657397\pi$
$823$	10.6994	+	22.9448i	0.372956	+	0.799807i	−0.626831	+	0.779155i	$0.715648\pi$
$824$	−3.97349	+	2.29410i	−0.138423	+	0.0799187i
$825$		0			0
$826$	7.10230	−	5.95954i	0.247121	−	0.207359i
$827$	−30.2405	−	2.64570i	−1.05156	−	0.0920000i	−0.451754	−	0.892142i	$-0.649202\pi$
$827$	−30.2405	−	2.64570i	−1.05156	−	0.0920000i	−0.599810	+	0.800142i	$0.704757\pi$
$828$	−2.90632	+	0.778747i	−0.101002	+	0.0270633i
$829$	23.0042	+	39.8444i	0.798969	+	1.38385i	0.920288	+	0.391241i	$0.127954\pi$
$829$	23.0042	+	39.8444i	0.798969	+	1.38385i	−0.121320	+	0.992613i	$0.538713\pi$
$830$		0			0
$831$	−7.98920	−	1.40871i	−0.277142	−	0.0488676i
$832$	−0.675594	+	0.964848i	−0.0234220	+	0.0334501i
$833$	3.06292	+	1.42826i	0.106124	+	0.0494864i
$834$	−8.43570	+	10.0533i	−0.292104	+	0.348116i
$835$		0			0
$836$	3.32589	−	11.8230i	0.115028	−	0.408908i
$837$	−34.6924	+	34.6924i	−1.19915	+	1.19915i
$838$	3.10002	−	0.271217i	0.107088	−	0.00936902i
$839$	−16.7995	+	6.11453i	−0.579984	+	0.211097i	−0.615319	−	0.788278i	$-0.710973\pi$
$839$	−16.7995	+	6.11453i	−0.579984	+	0.211097i	0.0353342	+	0.999376i	$0.488750\pi$
$840$		0			0
$841$	−1.36238	+	7.72642i	−0.0469785	+	0.266428i
$842$	−7.58353	+	3.53626i	−0.261346	+	0.121868i
$843$	−13.0425	+	48.6752i	−0.449207	+	1.67646i
$844$	−11.5585	+	20.0200i	−0.397861	+	0.689115i
$845$		0			0
$846$	−1.79827	−	2.14309i	−0.0618257	−	0.0736810i
$847$	2.57116	+	9.59571i	0.0883462	+	0.329712i
$848$	−0.183282	−	0.0491103i	−0.00629393	−	0.00168645i
$849$	−45.4994	−	16.5604i	−1.56154	−	0.568352i
$850$		0			0
$851$	7.92452	−	1.39731i	0.271649	−	0.0478990i
$852$	1.27820	−	2.74112i	0.0437905	−	0.0939091i
$853$	−2.32176	−	26.5378i	−0.0794955	−	0.908638i	−0.926313	−	0.376755i	$-0.877040\pi$
$853$	−2.32176	−	26.5378i	−0.0794955	−	0.908638i	0.846818	−	0.531884i	$-0.178516\pi$
$854$	−34.7772			−1.19005
$855$		0			0
$856$	8.69964			0.297348
$857$	−0.228741	−	2.61453i	−0.00781366	−	0.0893105i	0.991287	−	0.131723i	$-0.0420511\pi$
$857$	−0.228741	−	2.61453i	−0.00781366	−	0.0893105i	−0.999100	+	0.0424129i	$0.986496\pi$
$858$	2.27293	−	4.87431i	0.0775965	−	0.166406i
$859$	−7.24643	+	1.27774i	−0.247245	+	0.0435959i	−0.295897	−	0.955220i	$-0.595619\pi$
$859$	−7.24643	+	1.27774i	−0.247245	+	0.0435959i	0.0486522	+	0.998816i	$0.484507\pi$
$860$		0			0
$861$	33.7196	+	12.2729i	1.14916	+	0.418260i
$862$	−29.3091	−	7.85335i	−0.998271	−	0.267486i
$863$	−9.51872	−	35.5243i	−0.324021	−	1.20926i	−0.915292	−	0.402790i	$-0.868040\pi$
$863$	−9.51872	−	35.5243i	−0.324021	−	1.20926i	0.591271	−	0.806473i	$-0.298626\pi$
$864$	−3.51444	−	4.18835i	−0.119564	−	0.142490i
$865$		0			0
$866$	−7.67610	+	13.2954i	−0.260844	+	0.451796i
$867$	−6.74666	+	25.1789i	−0.229128	+	0.855119i
$868$	26.3961	−	12.3087i	0.895941	−	0.417784i
$869$	−1.51839	+	8.61123i	−0.0515080	+	0.292116i
$870$		0			0
$871$	−1.28031	+	0.465993i	−0.0433815	+	0.0157896i
$872$	−11.3526	+	0.993226i	−0.384448	+	0.0336349i
$873$	−5.13163	+	5.13163i	−0.173679	+	0.173679i
$874$	−31.6023	−	15.2171i	−1.06896	−	0.514725i
$875$		0			0
$876$	3.82412	−	4.55741i	0.129205	−	0.153981i
$877$	22.0625	+	10.2879i	0.744999	+	0.347399i	0.757772	−	0.652520i	$-0.226288\pi$
$877$	22.0625	+	10.2879i	0.744999	+	0.347399i	−0.0127729	+	0.999918i	$0.504066\pi$
$878$	5.90399	−	8.43178i	0.199250	−	0.284559i
$879$	19.3234	+	3.40724i	0.651763	+	0.114923i
$880$		0			0
$881$	8.54272	+	14.7964i	0.287811	+	0.498504i	0.973287	−	0.229591i	$-0.0737390\pi$
$881$	8.54272	+	14.7964i	0.287811	+	0.498504i	−0.685476	+	0.728096i	$0.740406\pi$
$882$	1.27651	−	0.342039i	0.0429822	−	0.0115170i
$883$	48.8873	+	4.27709i	1.64519	+	0.143935i	0.871755	−	0.489941i	$-0.162982\pi$
$883$	48.8873	+	4.27709i	1.64519	+	0.143935i	0.773434	+	0.633877i	$0.218537\pi$
$884$	−0.862794	+	0.723970i	−0.0290189	+	0.0243497i
$885$		0			0
$886$	−0.537000	+	0.310037i	−0.0180409	+	0.0104159i
$887$	−18.8817	−	40.4920i	−0.633987	−	1.35959i	−0.916387	−	0.400292i	$-0.868909\pi$
$887$	−18.8817	−	40.4920i	−0.633987	−	1.35959i	0.282401	−	0.959297i	$-0.408869\pi$
$888$	0.929489	+	1.32745i	0.0311916	+	0.0445462i
$889$	0.684868	+	3.88408i	0.0229697	+	0.130268i
$890$		0			0
$891$	16.7031	+	14.0155i	0.559573	+	0.469538i
$892$	−5.26263	−	5.26263i	−0.176206	−	0.176206i
$893$	0.405047	−	32.6101i	0.0135544	−	1.09126i
$894$		−	18.1415i		−	0.606742i
$895$		0			0
$896$	1.11008	+	3.04992i	0.0370852	+	0.101891i
$897$	−12.5816	−	8.80972i	−0.420087	−	0.294148i
$898$	18.0928	−	12.6687i	0.603766	−	0.422761i
$899$	−14.1160	+	38.7835i	−0.470797	+	1.29350i
$900$		0			0
$901$	−0.157132	−	0.0907203i	−0.00523483	−	0.00302233i
$902$	−1.67542	+	19.1502i	−0.0557855	+	0.637632i
$903$	−5.32330	+	60.8456i	−0.177148	+	2.02481i
$904$	2.84230	+	1.64100i	0.0945336	+	0.0545790i
$905$		0			0
$906$	12.8293	−	35.2481i	0.426223	−	1.17104i
$907$	19.8089	−	13.8704i	0.657744	−	0.460558i	−0.196448	−	0.980514i	$-0.562941\pi$
$907$	19.8089	−	13.8704i	0.657744	−	0.460558i	0.854193	+	0.519957i	$0.174052\pi$
$908$	−16.5512	−	11.5893i	−0.549271	−	0.384603i
$909$	−0.0655592	−	0.180122i	−0.00217446	−	0.00597428i
$910$		0			0
$911$		−	2.06286i		−	0.0683457i	−0.999416	−	0.0341729i	$-0.989120\pi$
$911$		−	2.06286i		−	0.0683457i	0.999416	−	0.0341729i	$-0.0108797\pi$
$912$	0.0877305	−	7.06313i	0.00290505	−	0.233884i
$913$	21.7171	+	21.7171i	0.718730	+	0.718730i
$914$	−6.79208	−	5.69924i	−0.224662	−	0.188514i
$915$		0			0
$916$	−2.30706	−	13.0840i	−0.0762273	−	0.432307i
$917$	−24.9245	−	35.5959i	−0.823080	−	1.17548i
$918$	−2.20951	−	4.73830i	−0.0729246	−	0.156387i
$919$	17.8675	−	10.3158i	0.589393	−	0.340286i	−0.175464	−	0.984486i	$-0.556143\pi$
$919$	17.8675	−	10.3158i	0.589393	−	0.340286i	0.764858	+	0.644199i	$0.222809\pi$
$920$		0			0
$921$	28.2995	−	23.7461i	0.932501	−	0.782461i
$922$	14.2244	+	1.24447i	0.468455	+	0.0409845i
$923$	−2.12342	+	0.568969i	−0.0698933	+	0.0187278i
$924$	−7.40996	−	12.8344i	−0.243770	−	0.422222i
$925$		0			0
$926$	2.64658	+	0.466663i	0.0869720	+	0.0153355i
$927$	−0.984036	+	1.40535i	−0.0323200	+	0.0461577i
$928$	−4.16846	−	1.94379i	−0.136837	−	0.0638079i
$929$	−12.9972	+	15.4895i	−0.426424	+	0.508193i	−0.935887	−	0.352300i	$-0.885400\pi$
$929$	−12.9972	+	15.4895i	−0.426424	+	0.508193i	0.509463	+	0.860493i	$0.329844\pi$
$930$		0			0
$931$	13.8803	+	6.68359i	0.454907	+	0.219046i
$932$	17.0721	−	17.0721i	0.559215	−	0.559215i
$933$	40.1145	−	3.50957i	1.31329	−	0.114898i
$934$	−18.1544	+	6.60765i	−0.594030	+	0.216209i
$935$		0			0
$936$	−0.0764790	+	0.433734i	−0.00249980	+	0.0141770i
$937$	9.99296	−	4.65979i	0.326456	−	0.152229i	−0.252480	−	0.967602i	$-0.581246\pi$
$937$	9.99296	−	4.65979i	0.326456	−	0.152229i	0.578935	+	0.815373i	$0.303468\pi$
$938$	−0.971699	+	3.62643i	−0.0317271	+	0.118407i
$939$	−21.8564	+	37.8565i	−0.713258	+	1.23540i
$940$		0			0
$941$	6.51252	+	7.76131i	0.212302	+	0.253012i	0.861678	−	0.507456i	$-0.169414\pi$
$941$	6.51252	+	7.76131i	0.212302	+	0.253012i	−0.649376	+	0.760468i	$0.724970\pi$
$942$	0.550714	+	2.05529i	0.0179432	+	0.0669650i
$943$	53.0281	+	14.2088i	1.72683	+	0.462703i
$944$	2.68429	+	0.977000i	0.0873660	+	0.0317986i
$945$		0			0
$946$	−32.2232	+	5.68182i	−1.04767	+	0.184732i
$947$	5.10321	−	10.9439i	0.165832	−	0.355628i	−0.805777	−	0.592218i	$-0.798252\pi$
$947$	5.10321	−	10.9439i	0.165832	−	0.355628i	0.971609	+	0.236591i	$0.0760300\pi$
$948$	0.438303	+	5.00983i	0.0142354	+	0.162712i
$949$	−4.32419			−0.140369
$950$		0			0
$951$	−37.8980			−1.22893
$952$	0.270494	+	3.09176i	0.00876675	+	0.100204i
$953$	−13.5627	+	29.0853i	−0.439339	+	0.942166i	0.554588	+	0.832125i	$0.312876\pi$
$953$	−13.5627	+	29.0853i	−0.439339	+	0.942166i	−0.993927	+	0.110041i	$0.964902\pi$
$954$	−0.0698723	+	0.0123204i	−0.00226220	+	0.000398887i
$955$		0			0
$956$	24.2393	+	8.82238i	0.783955	+	0.285336i
$957$	20.2856	+	5.43550i	0.655739	+	0.175705i
$958$	−1.67867	−	6.26488i	−0.0542354	−	0.202409i
$959$	−40.5748	−	48.3552i	−1.31023	−	1.56147i
$960$		0			0
$961$	24.7617	−	42.8885i	0.798765	−	1.38350i
$962$	0.304852	−	1.13772i	0.00982884	−	0.0366817i
$963$	2.94819	−	1.37476i	0.0950040	−	0.0443011i
$964$	4.73456	−	26.8510i	0.152490	−	0.864813i
$965$		0			0
$966$	−39.7708	+	14.4754i	−1.27961	+	0.465738i
$967$	11.3734	−	0.995047i	0.365745	−	0.0319986i	0.0971980	−	0.995265i	$-0.469012\pi$
$967$	11.3734	−	0.995047i	0.365745	−	0.0319986i	0.268547	+	0.963266i	$0.413456\pi$
$968$	−2.16429	+	2.16429i	−0.0695629	+	0.0695629i
$969$	1.82907	−	6.50207i	0.0587583	−	0.208877i
$970$		0			0
$971$	21.5084	−	25.6328i	0.690239	−	0.822594i	−0.301146	−	0.953578i	$-0.597369\pi$
$971$	21.5084	−	25.6328i	0.690239	−	0.822594i	0.991385	+	0.130984i	$0.0418135\pi$
$972$	−3.50037	−	1.63225i	−0.112274	−	0.0523544i
$973$	15.0762	−	21.5311i	0.483322	−	0.690256i
$974$	21.9035	+	3.86218i	0.701834	+	0.123752i
$975$		0			0
$976$	−5.35750	−	9.27946i	−0.171489	−	0.297028i
$977$	32.0726	−	8.59383i	1.02609	−	0.274941i	0.293754	−	0.955881i	$-0.405095\pi$
$977$	32.0726	−	8.59383i	1.02609	−	0.274941i	0.732339	+	0.680940i	$0.238429\pi$
$978$	2.17745	+	0.190502i	0.0696272	+	0.00609159i
$979$	21.8887	−	18.3668i	0.699565	−	0.587005i
$980$		0			0
$981$	−3.69029	+	2.13059i	−0.117822	+	0.0680245i
$982$	−1.71793	−	3.68410i	−0.0548212	−	0.117564i
$983$	−12.2871	−	17.5478i	−0.391898	−	0.559688i	0.573920	−	0.818912i	$-0.305422\pi$
$983$	−12.2871	−	17.5478i	−0.391898	−	0.559688i	−0.965817	+	0.259224i	$0.916533\pi$
$984$	1.91984	+	10.8879i	0.0612021	+	0.347094i
$985$		0			0
$986$	−3.36909	−	2.82700i	−0.107294	−	0.0900301i
$987$	−27.8260	−	27.8260i	−0.885711	−	0.885711i
$988$	−3.97370	+	3.25109i	−0.126420	+	0.103431i
$989$			93.4438i			2.97134i
$990$		0			0
$991$	−5.75998	−	15.8254i	−0.182972	−	0.502711i	0.813966	−	0.580913i	$-0.197304\pi$
$991$	−5.75998	−	15.8254i	−0.182972	−	0.502711i	−0.996938	+	0.0782020i	$0.975082\pi$
$992$	7.35065	+	5.14698i	0.233383	+	0.163417i
$993$	−32.2230	+	22.5628i	−1.02257	+	0.716009i
$994$	−2.07182	+	5.69228i	−0.0657141	+	0.180548i
$995$		0			0
$996$	15.2972	+	8.83184i	0.484710	+	0.279847i
$997$	1.38136	−	15.7891i	0.0437482	−	0.500044i	−0.942435	−	0.334388i	$-0.891470\pi$
$997$	1.38136	−	15.7891i	0.0437482	−	0.500044i	0.986184	−	0.165656i	$-0.0529741\pi$
$998$	−1.03841	+	11.8691i	−0.0328703	+	0.375710i
$999$	4.73498	+	2.73374i	0.149808	+	0.0864918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.193.4		120
5.2	odd	4	inner	950.2.bb.e.307.7		120
5.3	odd	4		190.2.r.a.117.4	yes	120
5.4	even	2		190.2.r.a.3.7	✓	120
19.13	odd	18	inner	950.2.bb.e.393.7		120
95.13	even	36		190.2.r.a.127.7	yes	120
95.32	even	36	inner	950.2.bb.e.507.4		120
95.89	odd	18		190.2.r.a.13.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.3.7	✓	120	5.4	even	2
190.2.r.a.13.4	yes	120	95.89	odd	18
190.2.r.a.117.4	yes	120	5.3	odd	4
190.2.r.a.127.7	yes	120	95.13	even	36
950.2.bb.e.193.4		120	1.1	even	1	trivial
950.2.bb.e.307.7		120	5.2	odd	4	inner
950.2.bb.e.393.7		120	19.13	odd	18	inner
950.2.bb.e.507.4		120	95.32	even	36	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.684861 - 1.46869i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.52279 - 0.554250i) q^{6} +(3.13506 + 0.840038i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.240351 + 0.286439i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.684861 - 1.46869i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.52279 - 0.554250i) q^{6} +(3.13506 + 0.840038i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.240351 + 0.286439i) q^{9} +(-1.40883 + 2.44017i) q^{11} +(-0.419421 + 1.56530i) q^{12} +(1.06751 - 0.497786i) q^{13} +(0.563602 - 3.19635i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.952583 - 0.0833402i) q^{17} +(0.264401 - 0.264401i) q^{18} +(4.34670 - 0.325943i) q^{19} +(3.38084 - 4.02912i) q^{21} +(2.55367 + 1.19080i) q^{22} +(4.61545 - 6.59154i) q^{23} +(1.59590 + 0.281400i) q^{24} +(-0.588931 - 1.02006i) q^{26} +(5.28120 - 1.41509i) q^{27} +(-3.23331 - 0.282878i) q^{28} +(3.52334 - 2.95643i) q^{29} +(-7.77127 + 4.48674i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(2.61899 + 3.74031i) q^{33} +(-0.166046 - 0.941694i) q^{34} +(-0.286439 - 0.240351i) q^{36} +(0.707105 + 0.707105i) q^{37} +(-0.703542 - 4.30175i) q^{38} -1.90875i q^{39} +(2.33341 + 6.41100i) q^{41} +(-4.30845 - 3.01681i) q^{42} +(-9.51246 + 6.66069i) q^{43} +(0.963698 - 2.64774i) q^{44} +(-6.96872 - 4.02339i) q^{46} +(0.652086 - 7.45338i) q^{47} +(0.141238 - 1.61435i) q^{48} +(3.06078 + 1.76714i) q^{49} +(0.529986 - 1.45612i) q^{51} +(-0.964848 + 0.675594i) q^{52} +(-0.155432 - 0.108835i) q^{53} +(-1.86999 - 5.13777i) q^{54} +3.24566i q^{56} +(2.49817 - 6.60717i) q^{57} +(-3.25226 - 3.25226i) q^{58} +(2.18825 + 1.83616i) q^{59} +(-1.86064 - 10.5522i) q^{61} +(5.14698 + 7.35065i) q^{62} +(0.512895 + 1.09991i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(3.49782 - 2.93502i) q^{66} +(-1.15233 - 0.100816i) q^{67} +(-0.923639 + 0.247488i) q^{68} +(-6.51998 - 11.2929i) q^{69} +(-1.83802 - 0.324092i) q^{71} +(-0.214471 + 0.306297i) q^{72} +(-3.32726 - 1.55153i) q^{73} +(0.642786 - 0.766043i) q^{74} +(-4.22406 + 1.07579i) q^{76} +(-6.46661 + 6.46661i) q^{77} +(-1.90148 + 0.166358i) q^{78} +(2.91615 - 1.06139i) q^{79} +(1.34376 - 7.62086i) q^{81} +(6.18323 - 2.88329i) q^{82} +(2.82113 - 10.5286i) q^{83} +(-2.62982 + 4.55499i) q^{84} +(7.46441 + 8.89574i) q^{86} +(-1.92908 - 7.19943i) q^{87} +(-2.72165 - 0.729265i) q^{88} +(-9.52932 - 3.46839i) q^{89} +(3.76486 - 0.663846i) q^{91} +(-3.40072 + 7.29286i) q^{92} +(1.26739 + 14.4864i) q^{93} -7.48185 q^{94} -1.62052 q^{96} +(1.69156 + 19.3347i) q^{97} +(1.49365 - 3.20315i) q^{98} +(-1.03757 + 0.182952i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Database

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