LMFDB - Embedded newform 630.2.t.c.311.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (of order $6$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.12
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.261236 - 1.71224i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.629881 - 1.61346i) q^{6} +(-2.20349 - 1.46446i) q^{7} +1.00000i q^{8} +(-2.86351 + 0.894597i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.261236 - 1.71224i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.629881 - 1.61346i) q^{6} +(-2.20349 - 1.46446i) q^{7} +1.00000i q^{8} +(-2.86351 + 0.894597i) q^{9} +(0.866025 + 0.500000i) q^{10} -5.67846i q^{11} +(1.35222 - 1.08236i) q^{12} +(-1.57532 - 0.909513i) q^{13} +(-1.17605 - 2.37000i) q^{14} +(-0.261236 - 1.71224i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.85981 - 4.95334i) q^{17} +(-2.92717 - 0.657012i) q^{18} +(1.07373 - 0.619917i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.93186 + 4.15547i) q^{21} +(2.83923 - 4.91769i) q^{22} +3.48607i q^{23} +(1.71224 - 0.261236i) q^{24} +1.00000 q^{25} +(-0.909513 - 1.57532i) q^{26} +(2.27981 + 4.66931i) q^{27} +(0.166511 - 2.64051i) q^{28} +(-2.25780 + 1.30354i) q^{29} +(0.629881 - 1.61346i) q^{30} +(7.72347 - 4.45915i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-9.72287 + 1.48342i) q^{33} +(4.95334 - 2.85981i) q^{34} +(-2.20349 - 1.46446i) q^{35} +(-2.20650 - 2.03258i) q^{36} +(-2.02715 - 3.51113i) q^{37} +1.23983 q^{38} +(-1.14577 + 2.93492i) q^{39} +1.00000i q^{40} +(-6.21952 + 10.7725i) q^{41} +(-3.75078 + 2.63281i) q^{42} +(-2.45956 - 4.26008i) q^{43} +(4.91769 - 2.83923i) q^{44} +(-2.86351 + 0.894597i) q^{45} +(-1.74303 + 3.01902i) q^{46} +(5.02238 - 8.69903i) q^{47} +(1.61346 + 0.629881i) q^{48} +(2.71074 + 6.45383i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-9.22838 - 3.60268i) q^{51} -1.81903i q^{52} +(-0.844055 - 0.487315i) q^{53} +(-0.360277 + 5.18365i) q^{54} -5.67846i q^{55} +(1.46446 - 2.20349i) q^{56} +(-1.34194 - 1.67653i) q^{57} -2.60709 q^{58} +(5.68540 + 9.84741i) q^{59} +(1.35222 - 1.08236i) q^{60} +(6.45045 + 3.72417i) q^{61} +8.91829 q^{62} +(7.61982 + 2.22225i) q^{63} -1.00000 q^{64} +(-1.57532 - 0.909513i) q^{65} +(-9.16197 - 3.57676i) q^{66} +(0.0344509 + 0.0596708i) q^{67} +5.71962 q^{68} +(5.96898 - 0.910688i) q^{69} +(-1.17605 - 2.37000i) q^{70} -6.62319i q^{71} +(-0.894597 - 2.86351i) q^{72} +(-7.47035 - 4.31301i) q^{73} -4.05430i q^{74} +(-0.261236 - 1.71224i) q^{75} +(1.07373 + 0.619917i) q^{76} +(-8.31586 + 12.5124i) q^{77} +(-2.45973 + 1.96883i) q^{78} +(0.683330 - 1.18356i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.39939 - 5.12338i) q^{81} +(-10.7725 + 6.21952i) q^{82} +(6.04923 + 10.4776i) q^{83} +(-4.56467 + 0.404689i) q^{84} +(2.85981 - 4.95334i) q^{85} -4.91911i q^{86} +(2.82180 + 3.52536i) q^{87} +5.67846 q^{88} +(7.88750 + 13.6615i) q^{89} +(-2.92717 - 0.657012i) q^{90} +(2.13927 + 4.31109i) q^{91} +(-3.01902 + 1.74303i) q^{92} +(-9.65277 - 12.0595i) q^{93} +(8.69903 - 5.02238i) q^{94} +(1.07373 - 0.619917i) q^{95} +(1.08236 + 1.35222i) q^{96} +(1.67919 - 0.969482i) q^{97} +(-0.879348 + 6.94455i) q^{98} +(5.07994 + 16.2603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.261236	−	1.71224i	−0.150825	−	0.988561i
$3$	−0.261236	−	1.71224i	−0.150825	−	0.988561i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.629881	−	1.61346i	0.257148	−	0.658692i
$7$	−2.20349	−	1.46446i	−0.832841	−	0.553512i
$7$	−2.20349	−	1.46446i	−0.832841	−	0.553512i
$8$			1.00000i			0.353553i
$9$	−2.86351	+	0.894597i	−0.954504	+	0.298199i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	5.67846i		−	1.71212i	−0.516876	−	0.856061i	$-0.672905\pi$
$11$		−	5.67846i		−	1.71212i	0.516876	−	0.856061i	$-0.327095\pi$
$12$	1.35222	−	1.08236i	0.390353	−	0.312449i
$13$	−1.57532	−	0.909513i	−0.436916	−	0.252254i	0.265373	−	0.964146i	$-0.414505\pi$
$13$	−1.57532	−	0.909513i	−0.436916	−	0.252254i	−0.702289	+	0.711892i	$0.747838\pi$
$14$	−1.17605	−	2.37000i	−0.314313	−	0.633409i
$15$	−0.261236	−	1.71224i	−0.0674509	−	0.442098i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.85981	−	4.95334i	0.693606	−	1.20136i	−0.277042	−	0.960858i	$-0.589354\pi$
$17$	2.85981	−	4.95334i	0.693606	−	1.20136i	0.970648	−	0.240503i	$-0.0773125\pi$
$18$	−2.92717	−	0.657012i	−0.689941	−	0.154859i
$19$	1.07373	−	0.619917i	0.246330	−	0.142219i	−0.371753	−	0.928332i	$-0.621243\pi$
$19$	1.07373	−	0.619917i	0.246330	−	0.142219i	0.618083	+	0.786113i	$0.287910\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.93186	+	4.15547i	−0.421567	+	0.906797i
$22$	2.83923	−	4.91769i	0.605326	−	1.04846i
$23$			3.48607i			0.726896i	0.931615	+	0.363448i	$0.118401\pi$
$23$			3.48607i			0.726896i	−0.931615	+	0.363448i	$0.881599\pi$
$24$	1.71224	−	0.261236i	0.349509	−	0.0533246i
$25$	1.00000			0.200000
$26$	−0.909513	−	1.57532i	−0.178370	−	0.308946i
$27$	2.27981	+	4.66931i	0.438751	+	0.898609i
$28$	0.166511	−	2.64051i	0.0314677	−	0.499009i
$29$	−2.25780	+	1.30354i	−0.419264	+	0.242062i	−0.694762	−	0.719240i	$-0.744490\pi$
$29$	−2.25780	+	1.30354i	−0.419264	+	0.242062i	0.275499	+	0.961301i	$0.411157\pi$
$30$	0.629881	−	1.61346i	0.115000	−	0.294576i
$31$	7.72347	−	4.45915i	1.38718	−	0.800886i	0.394180	−	0.919033i	$-0.371029\pi$
$31$	7.72347	−	4.45915i	1.38718	−	0.800886i	0.992996	+	0.118147i	$0.0376954\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−9.72287	+	1.48342i	−1.69254	+	0.258230i
$34$	4.95334	−	2.85981i	0.849490	−	0.490454i
$35$	−2.20349	−	1.46446i	−0.372458	−	0.247538i
$36$	−2.20650	−	2.03258i	−0.367750	−	0.338763i
$37$	−2.02715	−	3.51113i	−0.333262	−	0.577226i	0.649888	−	0.760030i	$-0.274816\pi$
$37$	−2.02715	−	3.51113i	−0.333262	−	0.577226i	−0.983149	+	0.182804i	$0.941483\pi$
$38$	1.23983			0.201128
$39$	−1.14577	+	2.93492i	−0.183470	+	0.469964i
$40$			1.00000i			0.158114i
$41$	−6.21952	+	10.7725i	−0.971326	+	1.68239i	−0.279763	+	0.960069i	$0.590256\pi$
$41$	−6.21952	+	10.7725i	−0.971326	+	1.68239i	−0.691563	+	0.722316i	$0.743077\pi$
$42$	−3.75078	+	2.63281i	−0.578757	+	0.406251i
$43$	−2.45956	−	4.26008i	−0.375079	−	0.649656i	0.615260	−	0.788324i	$-0.289051\pi$
$43$	−2.45956	−	4.26008i	−0.375079	−	0.649656i	−0.990339	+	0.138669i	$0.955718\pi$
$44$	4.91769	−	2.83923i	0.741370	−	0.428030i
$45$	−2.86351	+	0.894597i	−0.426867	+	0.133359i
$46$	−1.74303	+	3.01902i	−0.256996	+	0.445131i
$47$	5.02238	−	8.69903i	0.732590	−	1.26888i	−0.223183	−	0.974777i	$-0.571645\pi$
$47$	5.02238	−	8.69903i	0.732590	−	1.26888i	0.955773	−	0.294107i	$-0.0950221\pi$
$48$	1.61346	+	0.629881i	0.232883	+	0.0909155i
$49$	2.71074	+	6.45383i	0.387248	+	0.921976i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−9.22838	−	3.60268i	−1.29223	−	0.504476i
$52$		−	1.81903i		−	0.252254i
$53$	−0.844055	−	0.487315i	−0.115940	−	0.0669379i	0.440909	−	0.897552i	$-0.354656\pi$
$53$	−0.844055	−	0.487315i	−0.115940	−	0.0669379i	−0.556848	+	0.830614i	$0.687990\pi$
$54$	−0.360277	+	5.18365i	−0.0490275	+	0.705405i
$55$		−	5.67846i		−	0.765684i
$56$	1.46446	−	2.20349i	0.195696	−	0.294454i
$57$	−1.34194	−	1.67653i	−0.177745	−	0.222062i
$58$	−2.60709			−0.342327
$59$	5.68540	+	9.84741i	0.740176	+	1.28202i	0.952415	+	0.304805i	$0.0985913\pi$
$59$	5.68540	+	9.84741i	0.740176	+	1.28202i	−0.212238	+	0.977218i	$0.568075\pi$
$60$	1.35222	−	1.08236i	0.174571	−	0.139732i
$61$	6.45045	+	3.72417i	0.825896	+	0.476831i	0.852445	−	0.522816i	$-0.175119\pi$
$61$	6.45045	+	3.72417i	0.825896	+	0.476831i	−0.0265495	+	0.999647i	$0.508452\pi$
$62$	8.91829			1.13262
$63$	7.61982	+	2.22225i	0.960007	+	0.279977i
$64$	−1.00000			−0.125000
$65$	−1.57532	−	0.909513i	−0.195395	−	0.112811i
$66$	−9.16197	−	3.57676i	−1.12776	−	0.440268i
$67$	0.0344509	+	0.0596708i	0.00420885	+	0.00728994i	0.868122	−	0.496351i	$-0.165327\pi$
$67$	0.0344509	+	0.0596708i	0.00420885	+	0.00728994i	−0.863913	+	0.503641i	$0.831994\pi$
$68$	5.71962			0.693606
$69$	5.96898	−	0.910688i	0.718580	−	0.109634i
$70$	−1.17605	−	2.37000i	−0.140565	−	0.283269i
$71$		−	6.62319i		−	0.786028i	−0.919532	−	0.393014i	$-0.871432\pi$
$71$		−	6.62319i		−	0.786028i	0.919532	−	0.393014i	$-0.128568\pi$
$72$	−0.894597	−	2.86351i	−0.105429	−	0.337468i
$73$	−7.47035	−	4.31301i	−0.874339	−	0.504800i	−0.00555117	−	0.999985i	$-0.501767\pi$
$73$	−7.47035	−	4.31301i	−0.874339	−	0.504800i	−0.868788	+	0.495185i	$0.835100\pi$
$74$		−	4.05430i		−	0.471303i
$75$	−0.261236	−	1.71224i	−0.0301650	−	0.197712i
$76$	1.07373	+	0.619917i	0.123165	+	0.0711094i
$77$	−8.31586	+	12.5124i	−0.947680	+	1.42592i
$78$	−2.45973	+	1.96883i	−0.278509	+	0.222927i
$79$	0.683330	−	1.18356i	0.0768806	−	0.133161i	−0.825022	−	0.565101i	$-0.808837\pi$
$79$	0.683330	−	1.18356i	0.0768806	−	0.133161i	0.901903	+	0.431940i	$0.142171\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	7.39939	−	5.12338i	0.822155	−	0.569264i
$82$	−10.7725	+	6.21952i	−1.18963	+	0.686831i
$83$	6.04923	+	10.4776i	0.663989	+	1.15006i	0.979558	+	0.201161i	$0.0644713\pi$
$83$	6.04923	+	10.4776i	0.663989	+	1.15006i	−0.315569	+	0.948903i	$0.602195\pi$
$84$	−4.56467	+	0.404689i	−0.498046	+	0.0441552i
$85$	2.85981	−	4.95334i	0.310190	−	0.537265i
$86$		−	4.91911i		−	0.530442i
$87$	2.82180	+	3.52536i	0.302528	+	0.377958i
$88$	5.67846			0.605326
$89$	7.88750	+	13.6615i	0.836073	+	1.44812i	0.893154	+	0.449752i	$0.148487\pi$
$89$	7.88750	+	13.6615i	0.836073	+	1.44812i	−0.0570806	+	0.998370i	$0.518179\pi$
$90$	−2.92717	−	0.657012i	−0.308551	−	0.0692551i
$91$	2.13927	+	4.31109i	0.224256	+	0.451926i
$92$	−3.01902	+	1.74303i	−0.314755	+	0.181724i
$93$	−9.65277	−	12.0595i	−1.00095	−	1.25051i
$94$	8.69903	−	5.02238i	0.897236	−	0.518019i
$95$	1.07373	−	0.619917i	0.110162	−	0.0636022i
$96$	1.08236	+	1.35222i	0.110467	+	0.138011i
$97$	1.67919	−	0.969482i	0.170496	−	0.0984360i	−0.412324	−	0.911037i	$-0.635283\pi$
$97$	1.67919	−	0.969482i	0.170496	−	0.0984360i	0.582820	+	0.812601i	$0.301949\pi$
$98$	−0.879348	+	6.94455i	−0.0888276	+	0.701505i
$99$	5.07994	+	16.2603i	0.510553	+	1.63423i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	5.51484			0.548747			0.274373	−	0.961623i	$-0.411530\pi$
$101$	5.51484			0.548747			0.274373	+	0.961623i	$0.411530\pi$
$102$	−6.19067	−	7.73420i	−0.612967	−	0.765800i
$103$		−	7.53504i		−	0.742450i	−0.928543	−	0.371225i	$-0.878938\pi$
$103$		−	7.53504i		−	0.742450i	0.928543	−	0.371225i	$-0.121062\pi$
$104$	0.909513	−	1.57532i	0.0891851	−	0.154473i
$105$	−1.93186	+	4.15547i	−0.188531	+	0.405532i
$106$	−0.487315	−	0.844055i	−0.0473322	−	0.0819818i
$107$	−15.6906	+	9.05896i	−1.51686	+	0.875762i	−0.517061	+	0.855949i	$0.672974\pi$
$107$	−15.6906	+	9.05896i	−1.51686	+	0.875762i	−0.999804	+	0.0198138i	$0.993693\pi$
$108$	−2.90383	+	4.30903i	−0.279421	+	0.414637i
$109$	−1.76968	+	3.06518i	−0.169505	+	0.293591i	−0.938246	−	0.345969i	$-0.887550\pi$
$109$	−1.76968	+	3.06518i	−0.169505	+	0.293591i	0.768741	+	0.639560i	$0.220884\pi$
$110$	2.83923	−	4.91769i	0.270710	−	0.468884i
$111$	−5.48232	+	4.38820i	−0.520359	+	0.416509i
$112$	2.37000	−	1.17605i	0.223944	−	0.111126i
$113$	5.41190	+	3.12456i	0.509109	+	0.293934i	0.732467	−	0.680802i	$-0.238369\pi$
$113$	5.41190	+	3.12456i	0.509109	+	0.293934i	−0.223358	+	0.974736i	$0.571702\pi$
$114$	−0.323890	−	2.12289i	−0.0303351	−	0.198827i
$115$			3.48607i			0.325078i
$116$	−2.25780	−	1.30354i	−0.209632	−	0.121031i
$117$	5.32460	+	1.19512i	0.492260	+	0.110489i
$118$			11.3708i			1.04677i
$119$	−13.5555	+	6.72656i	−1.24263	+	0.616623i
$120$	1.71224	−	0.261236i	0.156305	−	0.0238475i
$121$	−21.2449			−1.93136
$122$	3.72417	+	6.45045i	0.337171	+	0.583997i
$123$	20.0699	+	7.83512i	1.80964	+	0.706469i
$124$	7.72347	+	4.45915i	0.693588	+	0.400443i
$125$	1.00000			0.0894427
$126$	5.48783	+	5.73443i	0.488895	+	0.510864i
$127$	19.0703			1.69222			0.846110	−	0.533009i	$-0.178939\pi$
$127$	19.0703			1.69222			0.846110	+	0.533009i	$0.178939\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−6.65174	+	5.32423i	−0.585653	+	0.468772i
$130$	−0.909513	−	1.57532i	−0.0797696	−	0.138165i
$131$	−0.129282			−0.0112954			−0.00564770	−	0.999984i	$-0.501798\pi$
$131$	−0.129282			−0.0112954			−0.00564770	+	0.999984i	$0.501798\pi$
$132$	−6.14612	−	7.67855i	−0.534951	−	0.668332i
$133$	−3.27379	−	0.206446i	−0.283874	−	0.0179012i
$134$			0.0689019i			0.00595221i
$135$	2.27981	+	4.66931i	0.196215	+	0.401870i
$136$	4.95334	+	2.85981i	0.424745	+	0.245227i
$137$		−	7.98369i		−	0.682093i	−0.940047	−	0.341046i	$-0.889219\pi$
$137$		−	7.98369i		−	0.682093i	0.940047	−	0.341046i	$-0.110781\pi$
$138$	5.62463	+	2.19581i	0.478800	+	0.186920i
$139$	4.54379	+	2.62336i	0.385400	+	0.222511i	0.680165	−	0.733059i	$-0.261908\pi$
$139$	4.54379	+	2.62336i	0.385400	+	0.222511i	−0.294765	+	0.955570i	$0.595241\pi$
$140$	0.166511	−	2.64051i	0.0140728	−	0.223164i
$141$	−16.2068	−	6.32701i	−1.36486	−	0.532831i
$142$	3.31160	−	5.73585i	0.277903	−	0.481342i
$143$	−5.16464	+	8.94541i	−0.431889	+	0.748053i
$144$	0.657012	−	2.92717i	0.0547510	−	0.243931i
$145$	−2.25780	+	1.30354i	−0.187500	+	0.108253i
$146$	−4.31301	−	7.47035i	−0.356947	−	0.618251i
$147$	10.3423	−	6.32740i	0.853022	−	0.521875i
$148$	2.02715	−	3.51113i	0.166631	−	0.288613i
$149$			15.9056i			1.30304i	0.758632	+	0.651520i	$0.225868\pi$
$149$			15.9056i			1.30304i	−0.758632	+	0.651520i	$0.774132\pi$
$150$	0.629881	−	1.61346i	0.0514296	−	0.131738i
$151$	19.5824			1.59359			0.796797	−	0.604247i	$-0.206526\pi$
$151$	19.5824			1.59359			0.796797	+	0.604247i	$0.206526\pi$
$152$	0.619917	+	1.07373i	0.0502819	+	0.0870909i
$153$	−3.75786	+	16.7423i	−0.303805	+	1.35354i
$154$	−13.4580	+	6.67816i	−1.08447	+	0.538141i
$155$	7.72347	−	4.45915i	0.620364	−	0.358167i
$156$	−3.11460	+	0.475196i	−0.249368	+	0.0380461i
$157$	14.1700	−	8.18107i	1.13089	−	0.652921i	0.186733	−	0.982411i	$-0.440210\pi$
$157$	14.1700	−	8.18107i	1.13089	−	0.652921i	0.944159	+	0.329490i	$0.106877\pi$
$158$	1.18356	−	0.683330i	0.0941591	−	0.0543628i
$159$	−0.613901	+	1.57253i	−0.0486856	+	0.124709i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	5.10520	−	7.68152i	0.402346	−	0.605389i
$162$	8.96975	−	0.737278i	0.704730	−	0.0579260i
$163$	−6.59007	−	11.4143i	−0.516174	−	0.894040i	−0.999824	−	0.0187781i	$-0.994022\pi$
$163$	−6.59007	−	11.4143i	−0.516174	−	0.894040i	0.483650	−	0.875262i	$-0.339311\pi$
$164$	−12.4390			−0.971326
$165$	−9.72287	+	1.48342i	−0.756925	+	0.115484i
$166$			12.0985i			0.939023i
$167$	2.81257	−	4.87151i	0.217643	−	0.376969i	−0.736444	−	0.676499i	$-0.763497\pi$
$167$	2.81257	−	4.87151i	0.217643	−	0.376969i	0.954087	+	0.299530i	$0.0968298\pi$
$168$	−4.15547	−	1.93186i	−0.320601	−	0.149047i
$169$	−4.84557	−	8.39278i	−0.372736	−	0.645598i
$170$	4.95334	−	2.85981i	0.379904	−	0.219337i
$171$	−2.52006	+	2.73569i	−0.192714	+	0.209204i
$172$	2.45956	−	4.26008i	0.187539	−	0.324828i
$173$	−3.98019	+	6.89389i	−0.302608	+	0.524133i	−0.976726	−	0.214491i	$-0.931191\pi$
$173$	−3.98019	+	6.89389i	−0.302608	+	0.524133i	0.674118	+	0.738624i	$0.264524\pi$
$174$	0.681066	+	4.46395i	0.0516315	+	0.338411i
$175$	−2.20349	−	1.46446i	−0.166568	−	0.110702i
$176$	4.91769	+	2.83923i	0.370685	+	0.214015i
$177$	15.3759	−	12.3073i	1.15572	−	0.925070i
$178$			15.7750i			1.18239i
$179$	−5.99647	−	3.46206i	−0.448197	−	0.258767i	0.258871	−	0.965912i	$-0.416649\pi$
$179$	−5.99647	−	3.46206i	−0.448197	−	0.258767i	−0.707068	+	0.707145i	$0.749983\pi$
$180$	−2.20650	−	2.03258i	−0.164463	−	0.151499i
$181$		−	2.78183i		−	0.206772i	−0.994641	−	0.103386i	$-0.967032\pi$
$181$		−	2.78183i		−	0.206772i	0.994641	−	0.103386i	$-0.0329676\pi$
$182$	−0.302888	+	4.80315i	−0.0224516	+	0.356033i
$183$	4.69157	−	12.0176i	0.346811	−	0.888366i
$184$	−3.48607			−0.256996
$185$	−2.02715	−	3.51113i	−0.149039	−	0.258143i
$186$	−2.32978	−	15.2702i	−0.170828	−	1.11967i
$187$	−28.1273	−	16.2393i	−2.05688	−	1.18754i
$188$	10.0448			0.732590
$189$	1.81445	−	13.6275i	0.131982	−	0.991252i
$190$	1.23983			0.0899471
$191$	2.62400	+	1.51497i	0.189866	+	0.109619i	0.591920	−	0.805997i	$-0.298370\pi$
$191$	2.62400	+	1.51497i	0.189866	+	0.109619i	−0.402054	+	0.915616i	$0.631704\pi$
$192$	0.261236	+	1.71224i	0.0188531	+	0.123570i
$193$	1.76305	+	3.05370i	0.126907	+	0.219810i	0.922477	−	0.386052i	$-0.126162\pi$
$193$	1.76305	+	3.05370i	0.126907	+	0.219810i	−0.795570	+	0.605862i	$0.792828\pi$
$194$	1.93896			0.139210
$195$	−1.14577	+	2.93492i	−0.0820503	+	0.210174i
$196$	−4.23381	+	5.57448i	−0.302415	+	0.398177i
$197$			9.09265i			0.647825i	0.946087	+	0.323912i	$0.104998\pi$
$197$			9.09265i			0.647825i	−0.946087	+	0.323912i	$0.895002\pi$
$198$	−3.73082	+	16.6218i	−0.265138	+	1.18126i
$199$	−12.5241	−	7.23082i	−0.887813	−	0.512579i	−0.0145863	−	0.999894i	$-0.504643\pi$
$199$	−12.5241	−	7.23082i	−0.887813	−	0.512579i	−0.873226	+	0.487315i	$0.837976\pi$
$200$			1.00000i			0.0707107i
$201$	0.0931707	−	0.0745763i	0.00657175	−	0.00526021i
$202$	4.77599	+	2.75742i	0.336037	+	0.194011i
$203$	6.88403	+	0.434109i	0.483164	+	0.0304685i
$204$	−1.49417	−	9.79335i	−0.104613	−	0.685672i
$205$	−6.21952	+	10.7725i	−0.434390	+	0.752386i
$206$	3.76752	−	6.52554i	0.262496	−	0.454656i
$207$	−3.11863	−	9.98240i	−0.216760	−	0.693825i
$208$	1.57532	−	0.909513i	0.109229	−	0.0630634i
$209$	−3.52018	−	6.09713i	−0.243496	−	0.421747i
$210$	−3.75078	+	2.63281i	−0.258828	+	0.181681i
$211$	−6.72807	+	11.6534i	−0.463179	+	0.802250i	−0.999117	−	0.0420072i	$-0.986625\pi$
$211$	−6.72807	+	11.6534i	−0.463179	+	0.802250i	0.535938	+	0.844257i	$0.319958\pi$
$212$		−	0.974630i		−	0.0669379i
$213$	−11.3405	+	1.73022i	−0.777036	+	0.118553i
$214$	−18.1179			−1.23851
$215$	−2.45956	−	4.26008i	−0.167740	−	0.290535i
$216$	−4.66931	+	2.27981i	−0.317706	+	0.155122i
$217$	−23.5488	−	1.48500i	−1.59860	−	0.100808i
$218$	−3.06518	+	1.76968i	−0.207600	+	0.119858i
$219$	−5.43337	+	13.9177i	−0.367153	+	0.940473i
$220$	4.91769	−	2.83923i	0.331551	−	0.191421i
$221$	−9.01025	+	5.20207i	−0.606095	+	0.349929i
$222$	−6.94193	+	1.05913i	−0.465912	+	0.0710842i
$223$	9.11125	−	5.26038i	0.610135	−	0.352261i	−0.162884	−	0.986645i	$-0.552079\pi$
$223$	9.11125	−	5.26038i	0.610135	−	0.352261i	0.773018	+	0.634384i	$0.218746\pi$
$224$	2.64051	+	0.166511i	0.176426	+	0.0111255i
$225$	−2.86351	+	0.894597i	−0.190901	+	0.0596398i
$226$	3.12456	+	5.41190i	0.207843	+	0.359994i
$227$	−29.0780			−1.92997			−0.964987	−	0.262299i	$-0.915519\pi$
$227$	−29.0780			−1.92997			−0.964987	+	0.262299i	$0.915519\pi$
$228$	0.780949	−	2.00042i	0.0517196	−	0.132481i
$229$		−	8.50862i		−	0.562265i	−0.959669	−	0.281133i	$-0.909290\pi$
$229$		−	8.50862i		−	0.562265i	0.959669	−	0.281133i	$-0.0907101\pi$
$230$	−1.74303	+	3.01902i	−0.114932	+	0.199069i
$231$	23.5967	+	10.9700i	1.55255	+	0.721774i
$232$	−1.30354	−	2.25780i	−0.0855818	−	0.148232i
$233$	22.5702	−	13.0309i	1.47863	−	0.853685i	0.478917	−	0.877860i	$-0.341029\pi$
$233$	22.5702	−	13.0309i	1.47863	−	0.853685i	0.999708	+	0.0241753i	$0.00769599\pi$
$234$	4.01368	+	3.69731i	0.262382	+	0.241701i
$235$	5.02238	−	8.69903i	0.327624	−	0.567462i
$236$	−5.68540	+	9.84741i	−0.370088	+	0.641012i
$237$	−2.20505	−	0.860833i	−0.143233	−	0.0559171i
$238$	−15.1027	−	0.952381i	−0.978963	−	0.0617337i
$239$	−13.6870	−	7.90222i	−0.885341	−	0.511152i	−0.0129256	−	0.999916i	$-0.504114\pi$
$239$	−13.6870	−	7.90222i	−0.885341	−	0.511152i	−0.872416	+	0.488764i	$0.837448\pi$
$240$	1.61346	+	0.629881i	0.104148	+	0.0406587i
$241$		−	4.85681i		−	0.312855i	−0.987689	−	0.156427i	$-0.950002\pi$
$241$		−	4.85681i		−	0.312855i	0.987689	−	0.156427i	$-0.0499977\pi$
$242$	−18.3987	−	10.6225i	−1.18271	−	0.682838i
$243$	−10.7054	−	11.3311i	−0.686753	−	0.726891i
$244$			7.44834i			0.476831i
$245$	2.71074	+	6.45383i	0.173183	+	0.412320i
$246$	13.4635	+	16.8203i	0.858399	+	1.07243i
$247$	−2.25529			−0.143501
$248$	4.45915	+	7.72347i	0.283156	+	0.490441i
$249$	16.3598	−	13.0948i	1.03676	−	0.829852i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	21.6259			1.36502			0.682508	−	0.730879i	$-0.260889\pi$
$251$	21.6259			1.36502			0.682508	+	0.730879i	$0.260889\pi$
$252$	1.88538	+	7.71008i	0.118768	+	0.485689i
$253$	19.7955			1.24453
$254$	16.5154	+	9.53517i	1.03627	+	0.598290i
$255$	−9.22838	−	3.60268i	−0.577903	−	0.225609i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.88168			0.304511			0.152255	−	0.988341i	$-0.451346\pi$
$257$	4.88168			0.304511			0.152255	+	0.988341i	$0.451346\pi$
$258$	−8.42269	+	1.28505i	−0.524374	+	0.0800038i
$259$	−0.675087	+	10.7054i	−0.0419479	+	0.665202i
$260$		−	1.81903i		−	0.112811i
$261$	5.29910	−	5.75254i	0.328006	−	0.356073i
$262$	−0.111961	−	0.0646409i	−0.00691699	−	0.00399353i
$263$			14.2417i			0.878178i	0.898444	+	0.439089i	$0.144699\pi$
$263$			14.2417i			0.878178i	−0.898444	+	0.439089i	$0.855301\pi$
$264$	−1.48342	−	9.72287i	−0.0912982	−	0.598402i
$265$	−0.844055	−	0.487315i	−0.0518499	−	0.0299355i
$266$	−2.73196	−	1.81568i	−0.167507	−	0.111327i
$267$	21.3313	−	17.0742i	1.30545	−	1.04492i
$268$	−0.0344509	+	0.0596708i	−0.00210443	+	0.00364497i
$269$	−11.3169	+	19.6014i	−0.690003	+	1.19512i	0.281834	+	0.959463i	$0.409057\pi$
$269$	−11.3169	+	19.6014i	−0.690003	+	1.19512i	−0.971836	+	0.235656i	$0.924276\pi$
$270$	−0.360277	+	5.18365i	−0.0219257	+	0.315467i
$271$	6.61815	−	3.82099i	0.402024	−	0.232109i	−0.285333	−	0.958428i	$-0.592104\pi$
$271$	6.61815	−	3.82099i	0.402024	−	0.232109i	0.687357	+	0.726320i	$0.258771\pi$
$272$	2.85981	+	4.95334i	0.173402	+	0.300340i
$273$	6.82276	−	4.78915i	0.412932	−	0.289852i
$274$	3.99184	−	6.91408i	0.241156	−	0.417695i
$275$		−	5.67846i		−	0.342424i
$276$	3.77317	+	4.71394i	0.227118	+	0.283746i
$277$	−12.5255			−0.752585			−0.376293	−	0.926501i	$-0.622801\pi$
$277$	−12.5255			−0.752585			−0.376293	+	0.926501i	$0.622801\pi$
$278$	2.62336	+	4.54379i	0.157339	+	0.272519i
$279$	−18.1271	+	19.6782i	−1.08524	+	1.17810i
$280$	1.46446	−	2.20349i	0.0875180	−	0.131684i
$281$	18.6742	−	10.7815i	1.11401	−	0.643172i	0.174143	−	0.984720i	$-0.444284\pi$
$281$	18.6742	−	10.7815i	1.11401	−	0.643172i	0.939864	+	0.341548i	$0.110951\pi$
$282$	−10.8720	−	13.5828i	−0.647419	−	0.808842i
$283$	23.7654	−	13.7209i	1.41270	−	0.815625i	0.417061	−	0.908878i	$-0.363060\pi$
$283$	23.7654	−	13.7209i	1.41270	−	0.815625i	0.995642	+	0.0932534i	$0.0297267\pi$
$284$	5.73585	−	3.31160i	0.340360	−	0.196507i
$285$	−1.34194	−	1.67653i	−0.0794898	−	0.0993092i
$286$	−8.94541	+	5.16464i	−0.528953	+	0.305391i
$287$	29.4805	−	14.6289i	1.74018	−	0.863519i
$288$	2.03258	−	2.20650i	0.119771	−	0.130019i
$289$	−7.85704	−	13.6088i	−0.462179	−	0.800517i
$290$	−2.60709			−0.153093
$291$	−2.09865	−	2.62191i	−0.123025	−	0.153699i
$292$		−	8.62602i		−	0.504800i
$293$	11.5161	−	19.9464i	0.672776	−	1.16528i	−0.304337	−	0.952564i	$-0.598435\pi$
$293$	11.5161	−	19.9464i	0.672776	−	1.16528i	0.977114	−	0.212718i	$-0.0682316\pi$
$294$	12.1204	−	0.308516i	0.706878	−	0.0179930i
$295$	5.68540	+	9.84741i	0.331017	+	0.573338i
$296$	3.51113	−	2.02715i	0.204080	−	0.117826i
$297$	26.5145	−	12.9458i	1.53853	−	0.751194i
$298$	−7.95281	+	13.7747i	−0.460694	+	0.797946i
$299$	3.17063	−	5.49169i	0.183362	−	0.317592i
$300$	1.35222	−	1.08236i	0.0780706	−	0.0624898i
$301$	−0.819088	+	12.9889i	−0.0472114	+	0.748671i
$302$	16.9589	+	9.79120i	0.975873	+	0.563421i
$303$	−1.44068	−	9.44271i	−0.0827646	−	0.542469i
$304$			1.23983i			0.0711094i
$305$	6.45045	+	3.72417i	0.369352	+	0.213245i
$306$	−11.6256	+	12.6203i	−0.664589	+	0.721457i
$307$		−	14.6153i		−	0.834137i	−0.908875	−	0.417069i	$-0.863057\pi$
$307$		−	14.6153i		−	0.834137i	0.908875	−	0.417069i	$-0.136943\pi$
$308$	−14.9940	−	0.945528i	−0.854363	−	0.0538765i
$309$	−12.9018	+	1.96843i	−0.733957	+	0.111980i
$310$	8.91829			0.506525
$311$	2.16654	+	3.75256i	0.122853	+	0.212788i	0.920892	−	0.389818i	$-0.127462\pi$
$311$	2.16654	+	3.75256i	0.122853	+	0.212788i	−0.798038	+	0.602607i	$0.794129\pi$
$312$	−2.93492	−	1.14577i	−0.166157	−	0.0648665i
$313$	7.82466	+	4.51757i	0.442276	+	0.255348i	0.704563	−	0.709642i	$-0.251143\pi$
$313$	7.82466	+	4.51757i	0.442276	+	0.255348i	−0.262286	+	0.964990i	$0.584477\pi$
$314$	16.3621			0.923370
$315$	7.61982	+	2.22225i	0.429328	+	0.125210i
$316$	1.36666			0.0768806
$317$	−16.7850	−	9.69080i	−0.942737	−	0.544289i	−0.0519198	−	0.998651i	$-0.516534\pi$
$317$	−16.7850	−	9.69080i	−0.942737	−	0.544289i	−0.890817	+	0.454362i	$0.849867\pi$
$318$	−1.31792	+	1.05490i	−0.0739051	+	0.0591557i
$319$	7.40212	+	12.8209i	0.414439	+	0.717830i
$320$	−1.00000			−0.0559017
$321$	19.6100	+	24.4994i	1.09452	+	1.36743i
$322$	8.26199	−	4.09979i	0.460423	−	0.228473i
$323$		−	7.09139i		−	0.394575i
$324$	8.13667	+	3.84637i	0.452037	+	0.213687i
$325$	−1.57532	−	0.909513i	−0.0873832	−	0.0504507i
$326$		−	13.1801i		−	0.729980i
$327$	5.71063	+	2.22938i	0.315798	+	0.123285i
$328$	−10.7725	−	6.21952i	−0.594813	−	0.343416i
$329$	−23.8061	+	11.8132i	−1.31247	+	0.651280i
$330$	−9.16197	−	3.57676i	−0.504350	−	0.196894i
$331$	−4.17736	+	7.23540i	−0.229608	+	0.397693i	−0.957692	−	0.287795i	$-0.907078\pi$
$331$	−4.17736	+	7.23540i	−0.229608	+	0.397693i	0.728084	+	0.685488i	$0.240411\pi$
$332$	−6.04923	+	10.4776i	−0.331995	+	0.575032i
$333$	8.94581	+	8.24067i	0.490228	+	0.451586i
$334$	4.87151	−	2.81257i	0.266557	−	0.153897i
$335$	0.0344509	+	0.0596708i	0.00188226	+	0.00326016i
$336$	−2.63281	−	3.75078i	−0.143631	−	0.204622i
$337$	−16.8897	+	29.2538i	−0.920039	+	1.59355i	−0.120688	+	0.992690i	$0.538510\pi$
$337$	−16.8897	+	29.2538i	−0.920039	+	1.59355i	−0.799351	+	0.600864i	$0.794823\pi$
$338$		−	9.69114i		−	0.527129i
$339$	3.93621	−	10.0827i	0.213785	−	0.547618i
$340$	5.71962			0.310190
$341$	−25.3211	−	43.8574i	−1.37121	−	2.37501i
$342$	−3.55028	+	1.10915i	−0.191977	+	0.0599761i
$343$	3.47827	−	18.1907i	0.187809	−	0.982206i
$344$	4.26008	−	2.45956i	0.229688	−	0.132610i
$345$	5.96898	−	0.910688i	0.321359	−	0.0490298i
$346$	−6.89389	+	3.98019i	−0.370618	+	0.213976i
$347$	−9.80690	+	5.66202i	−0.526462	+	0.303953i	−0.739575	−	0.673075i	$-0.764973\pi$
$347$	−9.80690	+	5.66202i	−0.526462	+	0.303953i	0.213113	+	0.977028i	$0.431640\pi$
$348$	−1.64216	+	4.20643i	−0.0880288	+	0.225488i
$349$	3.37360	−	1.94775i	0.180585	−	0.104261i	−0.406983	−	0.913436i	$-0.633419\pi$
$349$	3.37360	−	1.94775i	0.180585	−	0.104261i	0.587567	+	0.809175i	$0.300086\pi$
$350$	−1.17605	−	2.37000i	−0.0628625	−	0.126682i
$351$	0.655353	−	9.42919i	0.0349802	−	0.503293i
$352$	2.83923	+	4.91769i	0.151332	+	0.262114i
$353$	−28.7045			−1.52778			−0.763892	−	0.645344i	$-0.776714\pi$
$353$	−28.7045			−1.52778			−0.763892	+	0.645344i	$0.776714\pi$
$354$	19.4695	−	2.97047i	1.03479	−	0.157879i
$355$		−	6.62319i		−	0.351522i
$356$	−7.88750	+	13.6615i	−0.418037	+	0.724061i
$357$	15.0587	+	21.4530i	0.796989	+	1.13541i
$358$	−3.46206	−	5.99647i	−0.182976	−	0.316923i
$359$	2.00897	−	1.15988i	0.106029	−	0.0612161i	−0.446048	−	0.895009i	$-0.647169\pi$
$359$	2.00897	−	1.15988i	0.106029	−	0.0612161i	0.552077	+	0.833793i	$0.313835\pi$
$360$	−0.894597	−	2.86351i	−0.0471494	−	0.150920i
$361$	−8.73140	+	15.1232i	−0.459548	+	0.795960i
$362$	1.39091	−	2.40913i	0.0731048	−	0.126621i
$363$	5.54995	+	36.3764i	0.291297	+	1.90926i
$364$	−2.66388	+	4.00821i	−0.139625	+	0.210087i
$365$	−7.47035	−	4.31301i	−0.391016	−	0.225753i
$366$	10.0718	−	8.06175i	0.526462	−	0.421395i
$367$		−	13.2712i		−	0.692752i	−0.938096	−	0.346376i	$-0.887412\pi$
$367$		−	13.2712i		−	0.692752i	0.938096	−	0.346376i	$-0.112588\pi$
$368$	−3.01902	−	1.74303i	−0.157378	−	0.0908620i
$369$	8.17260	−	36.4112i	0.425448	−	1.89549i
$370$		−	4.05430i		−	0.210773i
$371$	1.14621	+	2.30988i	0.0595085	+	0.119923i
$372$	5.61747	−	14.3893i	0.291252	−	0.746050i
$373$	−4.14264			−0.214498			−0.107249	−	0.994232i	$-0.534204\pi$
$373$	−4.14264			−0.214498			−0.107249	+	0.994232i	$0.534204\pi$
$374$	−16.2393	−	28.1273i	−0.839716	−	1.45443i
$375$	−0.261236	−	1.71224i	−0.0134902	−	0.0884195i
$376$	8.69903	+	5.02238i	0.448618	+	0.259010i
$377$	4.74236			0.244244
$378$	8.38509	−	10.8945i	0.431283	−	0.560353i
$379$	6.21425			0.319204			0.159602	−	0.987181i	$-0.448979\pi$
$379$	6.21425			0.319204			0.159602	+	0.987181i	$0.448979\pi$
$380$	1.07373	+	0.619917i	0.0550811	+	0.0318011i
$381$	−4.98187	−	32.6529i	−0.255229	−	1.67286i
$382$	1.51497	+	2.62400i	0.0775124	+	0.134255i
$383$	13.6364			0.696787			0.348394	−	0.937348i	$-0.386727\pi$
$383$	13.6364			0.696787			0.348394	+	0.937348i	$0.386727\pi$
$384$	−0.629881	+	1.61346i	−0.0321435	+	0.0823365i
$385$	−8.31586	+	12.5124i	−0.423815	+	0.637693i
$386$			3.52611i			0.179474i
$387$	10.8540	+	9.99847i	0.551741	+	0.508251i
$388$	1.67919	+	0.969482i	0.0852481	+	0.0492180i
$389$		−	29.2993i		−	1.48553i	−0.669551	−	0.742766i	$-0.733513\pi$
$389$		−	29.2993i		−	1.48553i	0.669551	−	0.742766i	$-0.266487\pi$
$390$	−2.45973	+	1.96883i	−0.124553	+	0.0996958i
$391$	17.2677	+	9.96950i	0.873264	+	0.504179i
$392$	−6.45383	+	2.71074i	−0.325968	+	0.136913i
$393$	0.0337731	+	0.221361i	0.00170363	+	0.0111662i
$394$	−4.54633	+	7.87447i	−0.229041	+	0.396710i
$395$	0.683330	−	1.18356i	0.0343820	−	0.0595514i
$396$	−11.5419	+	12.5295i	−0.580002	+	0.629632i
$397$	9.62007	−	5.55415i	0.482817	−	0.278755i	−0.238772	−	0.971076i	$-0.576745\pi$
$397$	9.62007	−	5.55415i	0.482817	−	0.278755i	0.721590	+	0.692321i	$0.243412\pi$
$398$	−7.23082	−	12.5241i	−0.362448	−	0.627778i
$399$	0.501748	+	5.65944i	0.0251188	+	0.283326i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	1.44626i		−	0.0722226i	−0.999348	−	0.0361113i	$-0.988503\pi$
$401$		−	1.44626i		−	0.0722226i	0.999348	−	0.0361113i	$-0.0114971\pi$
$402$	0.117976	−	0.0179997i	0.00588412	−	0.000897742i
$403$	−16.2226			−0.808106
$404$	2.75742	+	4.77599i	0.137187	+	0.237614i
$405$	7.39939	−	5.12338i	0.367679	−	0.254583i
$406$	5.74469	+	3.81796i	0.285104	+	0.189482i
$407$	−19.9378	+	11.5111i	−0.988281	+	0.570584i
$408$	3.60268	−	9.22838i	0.178359	−	0.456873i
$409$	−14.0639	+	8.11979i	−0.695415	+	0.401498i	−0.805637	−	0.592409i	$-0.798177\pi$
$409$	−14.0639	+	8.11979i	−0.695415	+	0.401498i	0.110223	+	0.993907i	$0.464844\pi$
$410$	−10.7725	+	6.21952i	−0.532017	+	0.307160i
$411$	−13.6700	+	2.08563i	−0.674290	+	0.102877i
$412$	6.52554	−	3.76752i	0.321490	−	0.185612i
$413$	1.89337	−	30.0247i	0.0931665	−	1.47742i
$414$	2.29039	−	10.2043i	0.112567	−	0.501515i
$415$	6.04923	+	10.4776i	0.296945	+	0.514324i
$416$	1.81903			0.0891851
$417$	3.30481	−	8.46537i	0.161837	−	0.414551i
$418$		−	7.04036i		−	0.344355i
$419$	−4.24495	+	7.35247i	−0.207379	+	0.359192i	−0.950888	−	0.309534i	$-0.899827\pi$
$419$	−4.24495	+	7.35247i	−0.207379	+	0.359192i	0.743509	+	0.668726i	$0.233160\pi$
$420$	−4.56467	+	0.404689i	−0.222733	+	0.0197468i
$421$	0.808166	+	1.39979i	0.0393876	+	0.0682214i	0.885047	−	0.465501i	$-0.154126\pi$
$421$	0.808166	+	1.39979i	0.0393876	+	0.0682214i	−0.845660	+	0.533723i	$0.820793\pi$
$422$	−11.6534	+	6.72807i	−0.567277	+	0.327517i
$423$	−6.59953	+	29.4028i	−0.320880	+	1.42961i
$424$	0.487315	−	0.844055i	0.0236661	−	0.0409909i
$425$	2.85981	−	4.95334i	0.138721	−	0.240272i
$426$	−10.6862	−	4.17182i	−0.517750	−	0.202126i
$427$	−8.75962	−	17.6526i	−0.423908	−	0.854268i
$428$	−15.6906	−	9.05896i	−0.758432	−	0.437881i
$429$	16.6659	+	6.50622i	0.804635	+	0.314123i
$430$		−	4.91911i		−	0.237221i
$431$	−20.0356	−	11.5676i	−0.965081	−	0.557190i	−0.0673476	−	0.997730i	$-0.521454\pi$
$431$	−20.0356	−	11.5676i	−0.965081	−	0.557190i	−0.897733	+	0.440540i	$0.854787\pi$
$432$	−5.18365	−	0.360277i	−0.249398	−	0.0173338i
$433$			2.88532i			0.138660i	0.997594	+	0.0693299i	$0.0220861\pi$
$433$			2.88532i			0.138660i	−0.997594	+	0.0693299i	$0.977914\pi$
$434$	−19.6514	−	13.0604i	−0.943296	−	0.626922i
$435$	2.82180	+	3.52536i	0.135295	+	0.169028i
$436$	−3.53937			−0.169505
$437$	2.16108	+	3.74309i	0.103378	+	0.179056i
$438$	−11.6643	+	9.33642i	−0.557342	+	0.446112i
$439$	4.48844	+	2.59140i	0.214222	+	0.123681i	0.603272	−	0.797536i	$-0.293863\pi$
$439$	4.48844	+	2.59140i	0.214222	+	0.123681i	−0.389050	+	0.921217i	$0.627197\pi$
$440$	5.67846			0.270710
$441$	−13.5358	−	16.0556i	−0.644562	−	0.764552i
$442$	−10.4041			−0.494875
$443$	−16.2631	−	9.38948i	−0.772681	−	0.446108i	0.0611490	−	0.998129i	$-0.480524\pi$
$443$	−16.2631	−	9.38948i	−0.772681	−	0.446108i	−0.833830	+	0.552021i	$0.813857\pi$
$444$	−6.54145	−	2.55373i	−0.310443	−	0.121195i
$445$	7.88750	+	13.6615i	0.373903	+	0.647619i
$446$	10.5208			0.498173
$447$	27.2342	−	4.15513i	1.28813	−	0.196531i
$448$	2.20349	+	1.46446i	0.104105	+	0.0691890i
$449$			23.1775i			1.09381i	0.837194	+	0.546907i	$0.184195\pi$
$449$			23.1775i			1.09381i	−0.837194	+	0.546907i	$0.815805\pi$
$450$	−2.92717	−	0.657012i	−0.137988	−	0.0309718i
$451$	61.1714	+	35.3173i	2.88045	+	1.66303i
$452$			6.24913i			0.293934i
$453$	−5.11564	−	33.5297i	−0.240354	−	1.57536i
$454$	−25.1823	−	14.5390i	−1.18186	−	0.682349i
$455$	2.13927	+	4.31109i	0.100290	+	0.202107i
$456$	1.67653	−	1.34194i	0.0785108	−	0.0628422i
$457$	−9.87115	+	17.0973i	−0.461753	+	0.799780i	−0.999048	−	0.0436143i	$-0.986113\pi$
$457$	−9.87115	+	17.0973i	−0.461753	+	0.799780i	0.537295	+	0.843394i	$0.319446\pi$
$458$	4.25431	−	7.36868i	0.198791	−	0.344316i
$459$	29.6485	+	2.06065i	1.38387	+	0.0961828i
$460$	−3.01902	+	1.74303i	−0.140763	+	0.0812694i
$461$	−6.37073	−	11.0344i	−0.296714	−	0.513924i	0.678668	−	0.734445i	$-0.262558\pi$
$461$	−6.37073	−	11.0344i	−0.296714	−	0.513924i	−0.975382	+	0.220521i	$0.929224\pi$
$462$	14.9503	+	21.2986i	0.695551	+	0.990903i
$463$	6.41119	−	11.1045i	0.297953	−	0.516070i	−0.677714	−	0.735325i	$-0.737029\pi$
$463$	6.41119	−	11.1045i	0.297953	−	0.516070i	0.975668	+	0.219255i	$0.0703627\pi$
$464$		−	2.60709i		−	0.121031i
$465$	−9.65277	−	12.0595i	−0.447636	−	0.559247i
$466$	26.0619			1.20729
$467$	2.77900	+	4.81337i	0.128597	+	0.222736i	0.923133	−	0.384480i	$-0.125619\pi$
$467$	2.77900	+	4.81337i	0.128597	+	0.222736i	−0.794536	+	0.607217i	$0.792286\pi$
$468$	1.62730	+	5.20880i	0.0752218	+	0.240777i
$469$	0.0114729	−	0.181936i	0.000529771	−	0.00840101i
$470$	8.69903	−	5.02238i	0.401256	−	0.231665i
$471$	−17.7097	−	22.1253i	−0.816018	−	1.01948i
$472$	−9.84741	+	5.68540i	−0.453264	+	0.261692i
$473$	−24.1907	+	13.9665i	−1.11229	+	0.642180i
$474$	−1.47921	−	1.84803i	−0.0679424	−	0.0848827i
$475$	1.07373	−	0.619917i	0.0492660	−	0.0284438i
$476$	−12.6031	−	8.37614i	−0.577664	−	0.383920i
$477$	2.85291	+	0.640344i	0.130626	+	0.0293193i
$478$	−7.90222	−	13.6870i	−0.361439	−	0.626031i
$479$	5.75179			0.262806			0.131403	−	0.991329i	$-0.458052\pi$
$479$	5.75179			0.262806			0.131403	+	0.991329i	$0.458052\pi$
$480$	1.08236	+	1.35222i	0.0494026	+	0.0617202i
$481$			7.37488i			0.336266i
$482$	2.42841	−	4.20612i	0.110611	−	0.191584i
$483$	−14.4862	−	6.73461i	−0.659147	−	0.306436i
$484$	−10.6225	−	18.3987i	−0.482840	−	0.836303i
$485$	1.67919	−	0.969482i	0.0762482	−	0.0440219i
$486$	−3.60562	−	15.1657i	−0.163554	−	0.687932i
$487$	−15.3840	+	26.6459i	−0.697116	+	1.20744i	0.272346	+	0.962199i	$0.412200\pi$
$487$	−15.3840	+	26.6459i	−0.697116	+	1.20744i	−0.969462	+	0.245241i	$0.921133\pi$
$488$	−3.72417	+	6.45045i	−0.168585	+	0.291998i
$489$	−17.8225	+	14.2656i	−0.805961	+	0.645113i
$490$	−0.879348	+	6.94455i	−0.0397249	+	0.313723i
$491$	−12.6416	−	7.29865i	−0.570509	−	0.329383i	0.186844	−	0.982390i	$-0.440174\pi$
$491$	−12.6416	−	7.29865i	−0.570509	−	0.329383i	−0.757353	+	0.653006i	$0.773508\pi$
$492$	3.24953	+	21.2986i	0.146500	+	0.960214i
$493$			14.9116i			0.671583i
$494$	−1.95314	−	1.12765i	−0.0878759	−	0.0507352i
$495$	5.07994	+	16.2603i	0.228326	+	0.730848i
$496$			8.91829i			0.400443i
$497$	−9.69937	+	14.5941i	−0.435076	+	0.654636i
$498$	20.7154	−	3.16056i	0.928281	−	0.141628i
$499$	−14.7776			−0.661537			−0.330768	−	0.943712i	$-0.607308\pi$
$499$	−14.7776			−0.661537			−0.330768	+	0.943712i	$0.607308\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−9.07592	−	3.54317i	−0.405482	−	0.158297i
$502$	18.7286	+	10.8130i	0.835898	+	0.482606i
$503$	−12.4283			−0.554152			−0.277076	−	0.960848i	$-0.589365\pi$
$503$	−12.4283			−0.554152			−0.277076	+	0.960848i	$0.589365\pi$
$504$	−2.22225	+	7.61982i	−0.0989869	+	0.339414i
$505$	5.51484			0.245407
$506$	17.1434	+	9.89776i	0.762118	+	0.440009i
$507$	−13.1046	+	10.4893i	−0.581995	+	0.465845i
$508$	9.53517	+	16.5154i	0.423055	+	0.732752i
$509$	26.1249			1.15796			0.578982	−	0.815340i	$-0.303450\pi$
$509$	26.1249			1.15796			0.578982	+	0.815340i	$0.303450\pi$
$510$	−6.19067	−	7.73420i	−0.274127	−	0.342476i
$511$	10.1446	+	20.4437i	0.448772	+	0.904375i
$512$		−	1.00000i		−	0.0441942i
$513$	5.34249	+	3.60027i	0.235877	+	0.158956i
$514$	4.22766	+	2.44084i	0.186474	+	0.107661i
$515$		−	7.53504i		−	0.332034i
$516$	−7.93679	−	3.09846i	−0.349398	−	0.136402i
$517$	−49.3971	−	28.5194i	−2.17248	−	1.25428i
$518$	−5.93735	+	8.93361i	−0.260872	+	0.392520i
$519$	12.8437	+	5.01409i	0.563778	+	0.220094i
$520$	0.909513	−	1.57532i	0.0398848	−	0.0690825i
$521$	1.65977	−	2.87480i	0.0727157	−	0.125947i	−0.827375	−	0.561650i	$-0.810167\pi$
$521$	1.65977	−	2.87480i	0.0727157	−	0.125947i	0.900091	+	0.435703i	$0.143500\pi$
$522$	7.46542	−	2.33229i	0.326753	−	0.102082i
$523$	−26.8169	+	15.4828i	−1.17262	+	0.677014i	−0.954296	−	0.298862i	$-0.903393\pi$
$523$	−26.8169	+	15.4828i	−1.17262	+	0.677014i	−0.218326	+	0.975876i	$0.570060\pi$
$524$	−0.0646409	−	0.111961i	−0.00282385	−	0.00489105i
$525$	−1.93186	+	4.15547i	−0.0843135	+	0.181359i
$526$	−7.12083	+	12.3336i	−0.310483	+	0.537772i
$527$		−	51.0093i		−	2.22200i
$528$	3.57676	−	9.16197i	0.155658	−	0.398723i
$529$	10.8473			0.471623
$530$	−0.487315	−	0.844055i	−0.0211676	−	0.0366634i
$531$	−25.0897	−	23.1120i	−1.08880	−	1.00298i
$532$	−1.45811	−	2.93841i	−0.0632170	−	0.127396i
$533$	19.5955	−	11.3135i	0.848775	−	0.490041i
$534$	27.0105	−	4.12100i	1.16886	−	0.178333i
$535$	−15.6906	+	9.05896i	−0.678363	+	0.391653i
$536$	−0.0596708	+	0.0344509i	−0.00257738	+	0.00148805i
$537$	−4.36138	+	11.1718i	−0.188207	+	0.482098i
$538$	−19.6014	+	11.3169i	−0.845077	+	0.487906i
$539$	36.6478	−	15.3928i	1.57853	−	0.663016i
$540$	−2.90383	+	4.30903i	−0.124961	+	0.185431i
$541$	−16.6857	−	28.9005i	−0.717375	−	1.24253i	−0.962036	−	0.272921i	$-0.912010\pi$
$541$	−16.6857	−	28.9005i	−0.717375	−	1.24253i	0.244662	−	0.969608i	$-0.421323\pi$
$542$	7.64198			0.328251
$543$	−4.76315	+	0.726714i	−0.204406	+	0.0311863i
$544$			5.71962i			0.245227i
$545$	−1.76968	+	3.06518i	−0.0758049	+	0.131298i
$546$	8.30326	−	0.736141i	0.355347	−	0.0315039i
$547$	0.847928	+	1.46865i	0.0362548	+	0.0627951i	0.883583	−	0.468274i	$-0.155124\pi$
$547$	0.847928	+	1.46865i	0.0362548	+	0.0627951i	−0.847329	+	0.531069i	$0.821791\pi$
$548$	6.91408	−	3.99184i	0.295355	−	0.170523i
$549$	−21.8026	−	4.89365i	−0.930511	−	0.208856i
$550$	2.83923	−	4.91769i	0.121065	−	0.209691i
$551$	−1.61618	+	2.79930i	−0.0688515	+	0.119254i
$552$	0.910688	+	5.96898i	0.0387614	+	0.254057i
$553$	−3.23898	+	1.60726i	−0.137736	+	0.0683476i
$554$	−10.8474	−	6.26276i	−0.460862	−	0.266079i
$555$	−5.48232	+	4.38820i	−0.232711	+	0.186269i
$556$			5.24672i			0.222511i
$557$	28.4998	+	16.4544i	1.20757	+	0.697194i	0.962229	−	0.272242i	$-0.0877651\pi$
$557$	28.4998	+	16.4544i	1.20757	+	0.697194i	0.245346	+	0.969436i	$0.421098\pi$
$558$	−25.5376	+	7.97828i	−1.08109	+	0.337747i
$559$			8.94800i			0.378460i
$560$	2.37000	−	1.17605i	0.100151	−	0.0496972i
$561$	−20.4577	+	52.4030i	−0.863725	+	2.21246i
$562$	21.5631			0.909583
$563$	15.8987	+	27.5373i	0.670048	+	1.16056i	0.977890	+	0.209120i	$0.0670599\pi$
$563$	15.8987	+	27.5373i	0.670048	+	1.16056i	−0.307842	+	0.951438i	$0.599607\pi$
$564$	−2.62406	−	17.1990i	−0.110493	−	0.724210i
$565$	5.41190	+	3.12456i	0.227680	+	0.131451i
$566$	27.4419			1.15347
$567$	−23.8074	+	0.453222i	−0.999819	+	0.0190335i
$568$	6.62319			0.277903
$569$	32.9744	+	19.0378i	1.38236	+	0.798105i	0.992438	−	0.122744i	$-0.0391695\pi$
$569$	32.9744	+	19.0378i	1.38236	+	0.798105i	0.389919	+	0.920849i	$0.372503\pi$
$570$	−0.323890	−	2.12289i	−0.0135663	−	0.0889181i
$571$	0.990801	+	1.71612i	0.0414637	+	0.0718173i	0.886012	−	0.463661i	$-0.153465\pi$
$571$	0.990801	+	1.71612i	0.0414637	+	0.0718173i	−0.844549	+	0.535479i	$0.820131\pi$
$572$	−10.3293			−0.431889
$573$	1.90850	−	4.88867i	0.0797286	−	0.204227i
$574$	32.8454	+	2.07124i	1.37094	+	0.0864519i
$575$			3.48607i			0.145379i
$576$	2.86351	−	0.894597i	0.119313	−	0.0372749i
$577$	−5.04572	−	2.91315i	−0.210056	−	0.121276i	0.391281	−	0.920271i	$-0.372032\pi$
$577$	−5.04572	−	2.91315i	−0.210056	−	0.121276i	−0.601337	+	0.798995i	$0.705365\pi$
$578$		−	15.7141i		−	0.653619i
$579$	4.76808	−	3.81650i	0.198155	−	0.158608i
$580$	−2.25780	−	1.30354i	−0.0937502	−	0.0541267i
$581$	2.01453	−	31.9461i	0.0835768	−	1.32535i
$582$	−0.506528	−	3.31997i	−0.0209963	−	0.137617i
$583$	−2.76720	+	4.79293i	−0.114606	+	0.198503i
$584$	4.31301	−	7.47035i	0.178474	−	0.309125i
$585$	5.32460	+	1.19512i	0.220145	+	0.0494122i
$586$	19.9464	−	11.5161i	0.823979	−	0.475725i
$587$	0.0736389	+	0.127546i	0.00303940	+	0.00526440i	0.867541	−	0.497365i	$-0.165699\pi$
$587$	0.0736389	+	0.127546i	0.00303940	+	0.00526440i	−0.864502	+	0.502630i	$0.832366\pi$
$588$	10.6509	+	5.79303i	0.439234	+	0.238901i
$589$	5.52860	−	9.57582i	0.227802	−	0.394565i
$590$			11.3708i			0.468129i
$591$	15.5688	−	2.37533i	0.640414	−	0.0977081i
$592$	4.05430			0.166631
$593$	5.61919	+	9.73273i	0.230753	+	0.399675i	0.958030	−	0.286669i	$-0.0925479\pi$
$593$	5.61919	+	9.73273i	0.230753	+	0.399675i	−0.727277	+	0.686344i	$0.759215\pi$
$594$	29.4352	+	2.04582i	1.20774	+	0.0839409i
$595$	−13.5555	+	6.72656i	−0.555722	+	0.275762i
$596$	−13.7747	+	7.95281i	−0.564233	+	0.325760i
$597$	−9.10911	+	23.3332i	−0.372811	+	0.954966i
$598$	5.49169	−	3.17063i	0.224572	−	0.129657i
$599$	−18.0050	+	10.3952i	−0.735663	+	0.424735i	−0.820490	−	0.571661i	$-0.806299\pi$
$599$	−18.0050	+	10.3952i	−0.735663	+	0.424735i	0.0848276	+	0.996396i	$0.472966\pi$
$600$	1.71224	−	0.261236i	0.0699018	−	0.0106649i
$601$	−8.15985	+	4.71109i	−0.332847	+	0.192169i	−0.657104	−	0.753800i	$-0.728219\pi$
$601$	−8.15985	+	4.71109i	−0.332847	+	0.192169i	0.324257	+	0.945969i	$0.394886\pi$
$602$	−7.20383	+	10.8392i	−0.293606	+	0.441773i
$603$	−0.152032	−	0.140048i	−0.00619122	−	0.00570320i
$604$	9.79120	+	16.9589i	0.398398	+	0.690046i
$605$	−21.2449			−0.863730
$606$	3.47369	−	8.89796i	0.141109	−	0.361455i
$607$			43.4200i			1.76236i	0.472777	+	0.881182i	$0.343252\pi$
$607$			43.4200i			1.76236i	−0.472777	+	0.881182i	$0.656748\pi$
$608$	−0.619917	+	1.07373i	−0.0251410	+	0.0435454i
$609$	−1.05506	−	11.9005i	−0.0427532	−	0.482232i
$610$	3.72417	+	6.45045i	0.150787	+	0.261171i
$611$	−15.8238	+	9.13585i	−0.640161	+	0.369597i
$612$	−16.3782	+	5.11676i	−0.662050	+	0.206833i
$613$	4.95622	−	8.58442i	0.200180	−	0.346722i	−0.748406	−	0.663240i	$-0.769181\pi$
$613$	4.95622	−	8.58442i	0.200180	−	0.346722i	0.948586	+	0.316519i	$0.102514\pi$
$614$	7.30763	−	12.6572i	0.294912	−	0.510803i
$615$	20.0699	+	7.83512i	0.809296	+	0.315942i
$616$	−12.5124	−	8.31586i	−0.504140	−	0.335056i
$617$	32.9309	+	19.0126i	1.32575	+	0.765420i	0.984639	−	0.174604i	$-0.0558645\pi$
$617$	32.9309	+	19.0126i	1.32575	+	0.765420i	0.341108	+	0.940024i	$0.389198\pi$
$618$	−12.1575	−	4.74618i	−0.489046	−	0.190919i
$619$		−	40.9690i		−	1.64668i	−0.567547	−	0.823341i	$-0.692108\pi$
$619$		−	40.9690i		−	1.64668i	0.567547	−	0.823341i	$-0.307892\pi$
$620$	7.72347	+	4.45915i	0.310182	+	0.179084i
$621$	−16.2775	+	7.94759i	−0.653195	+	0.318926i
$622$			4.33309i			0.173741i
$623$	2.62671	−	41.6540i	0.105237	−	1.66883i
$624$	−1.96883	−	2.45973i	−0.0788164	−	0.0984679i
$625$	1.00000			0.0400000
$626$	4.51757	+	7.82466i	0.180558	+	0.312736i
$627$	−9.52013	+	7.62017i	−0.380197	+	0.304320i
$628$	14.1700	+	8.18107i	0.565446	+	0.326460i
$629$	−23.1891			−0.924609
$630$	5.48783	+	5.73443i	0.218640	+	0.228465i
$631$	47.1379			1.87653			0.938265	−	0.345917i	$-0.112432\pi$
$631$	47.1379			1.87653			0.938265	+	0.345917i	$0.112432\pi$
$632$	1.18356	+	0.683330i	0.0470796	+	0.0271814i
$633$	21.7109	+	8.47577i	0.862932	+	0.336882i
$634$	−9.69080	−	16.7850i	−0.384871	−	0.666616i
$635$	19.0703			0.756784
$636$	−1.66880	+	0.254609i	−0.0661722	+	0.0100959i
$637$	1.59956	−	12.6323i	0.0633768	−	0.500511i
$638$			14.8042i			0.586106i
$639$	5.92509	+	18.9656i	0.234393	+	0.750267i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			31.7699i			1.25484i	0.778682	+	0.627418i	$0.215888\pi$
$641$			31.7699i			1.25484i	−0.778682	+	0.627418i	$0.784112\pi$
$642$	4.73306	+	31.0222i	0.186799	+	1.22435i
$643$	22.8044	+	13.1661i	0.899319	+	0.519222i	0.876979	−	0.480528i	$-0.159555\pi$
$643$	22.8044	+	13.1661i	0.899319	+	0.519222i	0.0223397	+	0.999750i	$0.492888\pi$
$644$	9.20499	+	0.580470i	0.362727	+	0.0228737i
$645$	−6.65174	+	5.32423i	−0.261912	+	0.209641i
$646$	3.54569	−	6.14132i	0.139503	−	0.241627i
$647$	−14.6898	+	25.4435i	−0.577517	+	1.00029i	0.418247	+	0.908333i	$0.362645\pi$
$647$	−14.6898	+	25.4435i	−0.577517	+	1.00029i	−0.995763	+	0.0919545i	$0.970689\pi$
$648$	5.12338	+	7.39939i	0.201265	+	0.290676i
$649$	55.9181	−	32.2843i	2.19498	−	1.26727i
$650$	−0.909513	−	1.57532i	−0.0356740	−	0.0617893i
$651$	3.60914	+	40.7091i	0.141453	+	1.59551i
$652$	6.59007	−	11.4143i	0.258087	−	0.447020i
$653$			18.4817i			0.723246i	0.932324	+	0.361623i	$0.117777\pi$
$653$			18.4817i			0.723246i	−0.932324	+	0.361623i	$0.882223\pi$
$654$	3.83086	+	4.78601i	0.149798	+	0.187148i
$655$	−0.129282			−0.00505146
$656$	−6.21952	−	10.7725i	−0.242831	−	0.420596i
$657$	25.2498	+	5.66740i	0.985090	+	0.221106i
$658$	−26.5233	−	1.67257i	−1.03399	−	0.0652034i
$659$	−26.9328	+	15.5497i	−1.04915	+	0.605729i	−0.922412	−	0.386207i	$-0.873785\pi$
$659$	−26.9328	+	15.5497i	−1.04915	+	0.605729i	−0.126741	+	0.991936i	$0.540452\pi$
$660$	−6.14612	−	7.67855i	−0.239237	−	0.298887i
$661$	−3.48233	+	2.01052i	−0.135447	+	0.0782003i	−0.566192	−	0.824273i	$-0.691584\pi$
$661$	−3.48233	+	2.01052i	−0.135447	+	0.0782003i	0.430745	+	0.902473i	$0.358251\pi$
$662$	−7.23540	+	4.17736i	−0.281212	+	0.162358i
$663$	11.2610	+	14.0687i	0.437340	+	0.546384i
$664$	−10.4776	+	6.04923i	−0.406609	+	0.234756i
$665$	−3.27379	−	0.206446i	−0.126952	−	0.00800565i
$666$	3.62697	+	11.6095i	0.140542	+	0.449860i
$667$	−4.54424	−	7.87086i	−0.175954	−	0.304761i
$668$	5.62513			0.217643
$669$	−11.3872	−	14.2264i	−0.440255	−	0.550025i
$670$			0.0689019i			0.00266191i
$671$	21.1476	−	36.6287i	0.816393	−	1.41403i
$672$	−0.404689	−	4.56467i	−0.0156112	−	0.176086i
$673$	3.92719	+	6.80209i	0.151382	+	0.262201i	0.931736	−	0.363137i	$-0.118294\pi$
$673$	3.92719	+	6.80209i	0.151382	+	0.262201i	−0.780354	+	0.625338i	$0.784961\pi$
$674$	−29.2538	+	16.8897i	−1.12681	+	0.650566i
$675$	2.27981	+	4.66931i	0.0877501	+	0.179722i
$676$	4.84557	−	8.39278i	0.186368	−	0.322799i
$677$	−16.9784	+	29.4075i	−0.652534	+	1.13022i	0.329972	+	0.943991i	$0.392961\pi$
$677$	−16.9784	+	29.4075i	−0.652534	+	1.13022i	−0.982506	+	0.186231i	$0.940373\pi$
$678$	8.45021	−	6.76378i	0.324528	−	0.259761i
$679$	−5.11985	−	0.322859i	−0.196482	−	0.0123902i
$680$	4.95334	+	2.85981i	0.189952	+	0.109669i
$681$	7.59622	+	49.7884i	0.291088	+	1.90790i
$682$		−	50.6422i		−	1.93919i
$683$	−5.22203	−	3.01494i	−0.199815	−	0.115363i	0.396754	−	0.917925i	$-0.370137\pi$
$683$	−5.22203	−	3.01494i	−0.199815	−	0.115363i	−0.596569	+	0.802562i	$0.703470\pi$
$684$	−3.62921	−	0.814586i	−0.138766	−	0.0311465i
$685$		−	7.98369i		−	0.305041i
$686$	12.1076	−	14.0145i	0.462271	−	0.535075i
$687$	−14.5688	+	2.22276i	−0.555833	+	0.0848035i
$688$	4.91911			0.187539
$689$	0.886439	+	1.53536i	0.0337706	+	0.0584925i
$690$	5.62463	+	2.19581i	0.214126	+	0.0835931i
$691$	−15.2895	−	8.82741i	−0.581641	−	0.335811i	0.180144	−	0.983640i	$-0.442344\pi$
$691$	−15.2895	−	8.82741i	−0.581641	−	0.335811i	−0.761785	+	0.647830i	$0.775677\pi$
$692$	−7.96037			−0.302608
$693$	12.6190	−	43.2688i	0.479355	−	1.64365i
$694$	−11.3240			−0.429854
$695$	4.54379	+	2.62336i	0.172356	+	0.0995097i
$696$	−3.52536	+	2.82180i	−0.133629	+	0.106960i
$697$	35.5733	+	61.6148i	1.34743	+	2.33383i
$698$	3.89550			0.147447
$699$	−28.2082	−	35.2414i	−1.06693	−	1.33295i
$700$	0.166511	−	2.64051i	0.00629353	−	0.0998018i
$701$		−	27.1258i		−	1.02453i	−0.858828	−	0.512263i	$-0.828807\pi$
$701$		−	27.1258i		−	1.02453i	0.858828	−	0.512263i	$-0.171193\pi$
$702$	5.28215	−	7.83824i	0.199362	−	0.295835i
$703$	−4.35322	−	2.51333i	−0.164185	−	0.0947921i
$704$			5.67846i			0.214015i
$705$	−16.2068	−	6.32701i	−0.610384	−	0.238289i
$706$	−24.8588	−	14.3522i	−0.935573	−	0.540153i
$707$	−12.1519	−	8.07624i	−0.457019	−	0.303738i
$708$	18.3463	+	7.16226i	0.689497	+	0.269174i
$709$	−10.8583	+	18.8071i	−0.407791	+	0.706315i	−0.994642	−	0.103380i	$-0.967034\pi$
$709$	−10.8583	+	18.8071i	−0.407791	+	0.706315i	0.586851	+	0.809695i	$0.300367\pi$
$710$	3.31160	−	5.73585i	0.124282	−	0.215263i
$711$	−0.897912	+	4.00045i	−0.0336743	+	0.150028i
$712$	−13.6615	+	7.88750i	−0.511988	+	0.295596i
$713$	15.5449	+	26.9245i	0.582161	+	1.00833i
$714$	2.31467	+	26.1082i	0.0866244	+	0.977075i
$715$	−5.16464	+	8.94541i	−0.193146	+	0.334540i
$716$		−	6.92412i		−	0.258767i
$717$	−9.95492	+	25.4998i	−0.371773	+	0.952308i
$718$	2.31976			0.0865726
$719$	13.2510	+	22.9514i	0.494178	+	0.855941i	0.999977	−	0.00670969i	$-0.00213578\pi$
$719$	13.2510	+	22.9514i	0.494178	+	0.855941i	−0.505800	+	0.862651i	$0.668802\pi$
$720$	0.657012	−	2.92717i	0.0244854	−	0.109089i
$721$	−11.0347	+	16.6034i	−0.410955	+	0.618343i
$722$	−15.1232	+	8.73140i	−0.562829	+	0.324949i
$723$	−8.31602	+	1.26878i	−0.309276	+	0.0471863i
$724$	2.40913	−	1.39091i	0.0895347	−	0.0516929i
$725$	−2.25780	+	1.30354i	−0.0838527	+	0.0484124i
$726$	−13.3818	+	34.2778i	−0.496645	+	1.27217i
$727$	−6.52916	+	3.76961i	−0.242153	+	0.139807i	−0.616166	−	0.787616i	$-0.711315\pi$
$727$	−6.52916	+	3.76961i	−0.242153	+	0.139807i	0.374013	+	0.927424i	$0.377982\pi$
$728$	−4.31109	+	2.13927i	−0.159780	+	0.0792865i
$729$	−16.6049	+	21.2903i	−0.614996	+	0.788530i
$730$	−4.31301	−	7.47035i	−0.159632	−	0.276490i
$731$	−28.1355			−1.04063
$732$	12.7533	−	1.94578i	0.471376	−	0.0719180i
$733$			21.1837i			0.782436i	0.920298	+	0.391218i	$0.127946\pi$
$733$			21.1837i			0.782436i	−0.920298	+	0.391218i	$0.872054\pi$
$734$	6.63561	−	11.4932i	0.244925	−	0.424222i
$735$	10.3423	−	6.32740i	0.381483	−	0.233390i
$736$	−1.74303	−	3.01902i	−0.0642491	−	0.111283i
$737$	0.338838	−	0.195628i	0.0124813	−	0.00720606i
$738$	25.2833	−	27.4467i	0.930690	−	1.01033i
$739$	−23.0621	+	39.9448i	−0.848355	+	1.46939i	0.0343210	+	0.999411i	$0.489073\pi$
$739$	−23.0621	+	39.9448i	−0.848355	+	1.46939i	−0.882676	+	0.469983i	$0.844260\pi$
$740$	2.02715	−	3.51113i	0.0745195	−	0.129072i
$741$	0.589164	+	3.86159i	0.0216435	+	0.141859i
$742$	−0.162287	+	2.57352i	−0.00595774	+	0.0944768i
$743$	−33.6453	−	19.4252i	−1.23433	−	0.712640i	−0.266399	−	0.963863i	$-0.585834\pi$
$743$	−33.6453	−	19.4252i	−1.23433	−	0.712640i	−0.967929	+	0.251223i	$0.919167\pi$
$744$	12.0595	−	9.65277i	0.442123	−	0.353888i
$745$			15.9056i			0.582737i
$746$	−3.58763	−	2.07132i	−0.131352	−	0.0758364i
$747$	−26.6952	−	24.5910i	−0.976728	−	0.899739i
$748$		−	32.4787i		−	1.18754i
$749$	47.8405	+	3.01684i	1.74805	+	0.110233i
$750$	0.629881	−	1.61346i	0.0230000	−	0.0589152i
$751$	−17.0559			−0.622379			−0.311190	−	0.950348i	$-0.600727\pi$
$751$	−17.0559			−0.622379			−0.311190	+	0.950348i	$0.600727\pi$
$752$	5.02238	+	8.69903i	0.183148	+	0.317221i
$753$	−5.64947	−	37.0287i	−0.205878	−	1.34940i
$754$	4.10700	+	2.37118i	0.149568	+	0.0863533i
$755$	19.5824			0.712677
$756$	12.7090	−	5.24237i	0.462220	−	0.190663i
$757$	3.74105			0.135971			0.0679854	−	0.997686i	$-0.478343\pi$
$757$	3.74105			0.135971			0.0679854	+	0.997686i	$0.478343\pi$
$758$	5.38170	+	3.10712i	0.195472	+	0.112856i
$759$	−5.17131	−	33.8946i	−0.187707	−	1.23030i
$760$	0.619917	+	1.07373i	0.0224868	+	0.0389482i
$761$	24.1220			0.874421			0.437210	−	0.899359i	$-0.355967\pi$
$761$	24.1220			0.874421			0.437210	+	0.899359i	$0.355967\pi$
$762$	12.0121	−	30.7692i	0.435151	−	1.11465i
$763$	8.38831	−	4.16247i	0.303677	−	0.150692i
$764$			3.02993i			0.109619i
$765$	−3.75786	+	16.7423i	−0.135866	+	0.605320i
$766$	11.8095	+	6.81820i	0.426693	+	0.246351i
$767$		−	20.6838i		−	0.746849i
$768$	−1.35222	+	1.08236i	−0.0487941	+	0.0390561i
$769$	11.7667	+	6.79354i	0.424320	+	0.244981i	0.696924	−	0.717145i	$-0.254552\pi$
$769$	11.7667	+	6.79354i	0.424320	+	0.244981i	−0.272604	+	0.962126i	$0.587885\pi$
$770$	−13.4580	+	6.67816i	−0.484991	+	0.240664i
$771$	−1.27527	−	8.35859i	−0.0459278	−	0.301027i
$772$	−1.76305	+	3.05370i	−0.0634537	+	0.109905i
$773$	−9.03034	+	15.6410i	−0.324799	+	0.562568i	−0.981472	−	0.191608i	$-0.938630\pi$
$773$	−9.03034	+	15.6410i	−0.324799	+	0.562568i	0.656673	+	0.754175i	$0.271963\pi$
$774$	4.40062	+	14.0859i	0.158177	+	0.506308i
$775$	7.72347	−	4.45915i	0.277435	−	0.160177i
$776$	0.969482	+	1.67919i	0.0348024	+	0.0602795i
$777$	18.5066	−	1.64073i	0.663919	−	0.0588610i
$778$	14.6496	−	25.3739i	0.525215	−	0.909699i
$779$			15.4224i			0.552563i
$780$	−3.11460	+	0.475196i	−0.111521	+	0.0170147i
$781$	−37.6095			−1.34578
$782$	9.96950	+	17.2677i	0.356509	+	0.617491i
$783$	−11.2340	−	7.57054i	−0.401471	−	0.270549i
$784$	−6.94455	−	0.879348i	−0.248020	−	0.0314053i
$785$	14.1700	−	8.18107i	0.505750	−	0.291995i
$786$	−0.0814322	+	0.208591i	−0.00290459	+	0.00744019i
$787$	28.8427	−	16.6523i	1.02813	−	0.593592i	0.111683	−	0.993744i	$-0.464376\pi$
$787$	28.8427	−	16.6523i	1.02813	−	0.593592i	0.916449	+	0.400152i	$0.131043\pi$
$788$	−7.87447	+	4.54633i	−0.280516	+	0.161956i
$789$	24.3851	−	3.72044i	0.868132	−	0.132451i
$790$	1.18356	−	0.683330i	0.0421092	−	0.0243118i
$791$	−7.34929	−	14.8104i	−0.261311	−	0.526599i
$792$	−16.2603	+	5.07994i	−0.577786	+	0.180508i
$793$	−6.77436	−	11.7335i	−0.240565	−	0.416670i
$794$	11.1083			0.394219
$795$	−0.613901	+	1.57253i	−0.0217728	+	0.0557718i
$796$		−	14.4616i		−	0.512579i
$797$	3.47393	−	6.01703i	0.123053	−	0.213134i	−0.797917	−	0.602767i	$-0.794065\pi$
$797$	3.47393	−	6.01703i	0.123053	−	0.213134i	0.920970	+	0.389633i	$0.127398\pi$
$798$	−2.39519	+	5.15209i	−0.0847889	+	0.182382i
$799$	−28.7261	−	49.7551i	−1.01626	−	1.76021i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−34.8075	−	32.0639i	−1.22986	−	1.13292i
$802$	0.723128	−	1.25249i	0.0255345	−	0.0442271i
$803$	−24.4913	+	42.4201i	−0.864278	+	1.49697i
$804$	0.111170	+	0.0434000i	0.00392067	+	0.00153060i
$805$	5.10520	−	7.68152i	0.179935	−	0.270738i
$806$	−14.0492	−	8.11131i	−0.494862	−	0.285709i
$807$	36.5187	+	14.2566i	1.28552	+	0.501856i
$808$			5.51484i			0.194011i
$809$	−4.12744	−	2.38298i	−0.145113	−	0.0837810i	0.425686	−	0.904871i	$-0.360033\pi$
$809$	−4.12744	−	2.38298i	−0.145113	−	0.0837810i	−0.570799	+	0.821090i	$0.693366\pi$
$810$	8.96975	−	0.737278i	0.315165	−	0.0259053i
$811$		−	28.2422i		−	0.991716i	−0.868404	−	0.495858i	$-0.834854\pi$
$811$		−	28.2422i		−	0.991716i	0.868404	−	0.495858i	$-0.165146\pi$
$812$	3.06607	+	6.17880i	0.107598	+	0.216833i
$813$	−8.27134	−	10.3337i	−0.290089	−	0.362417i
$814$	−23.0222			−0.806928
$815$	−6.59007	−	11.4143i	−0.230840	−	0.399827i
$816$	7.73420	−	6.19067i	0.270751	−	0.216717i
$817$	−5.28179	−	3.04944i	−0.184786	−	0.106687i
$818$	−16.2396			−0.567804
$819$	−9.98251	−	10.4311i	−0.348817	−	0.364492i
$820$	−12.4390			−0.434390
$821$	32.1718	+	18.5744i	1.12280	+	0.648250i	0.942115	−	0.335290i	$-0.108834\pi$
$821$	32.1718	+	18.5744i	1.12280	+	0.648250i	0.180687	+	0.983541i	$0.442168\pi$
$822$	−12.8814	−	5.02878i	−0.449289	−	0.175399i
$823$	2.12316	+	3.67742i	0.0740086	+	0.128187i	0.900655	−	0.434535i	$-0.143087\pi$
$823$	2.12316	+	3.67742i	0.0740086	+	0.128187i	−0.826646	+	0.562722i	$0.809754\pi$
$824$	7.53504			0.262496
$825$	−9.72287	+	1.48342i	−0.338507	+	0.0516461i
$826$	16.6520	−	25.0555i	0.579399	−	0.871791i
$827$			25.2354i			0.877519i	0.898604	+	0.438760i	$0.144582\pi$
$827$			25.2354i			0.877519i	−0.898604	+	0.438760i	$0.855418\pi$
$828$	7.08570	−	7.69201i	0.246245	−	0.267316i
$829$	3.50716	+	2.02486i	0.121809	+	0.0703262i	0.559666	−	0.828718i	$-0.310929\pi$
$829$	3.50716	+	2.02486i	0.121809	+	0.0703262i	−0.437858	+	0.899044i	$0.644263\pi$
$830$			12.0985i			0.419944i
$831$	3.27212	+	21.4466i	0.113509	+	0.743976i
$832$	1.57532	+	0.909513i	0.0546145	+	0.0315317i
$833$	39.7202	+	5.02954i	1.37622	+	0.174263i
$834$	7.09474	−	5.67882i	0.245671	−	0.196641i
$835$	2.81257	−	4.87151i	0.0973329	−	0.168585i
$836$	3.52018	−	6.09713i	0.121748	−	0.210874i
$837$	38.4292	+	25.8972i	1.32831	+	0.895139i
$838$	−7.35247	+	4.24495i	−0.253987	+	0.146639i
$839$	−23.7002	−	41.0500i	−0.818222	−	1.41720i	−0.906991	−	0.421151i	$-0.861626\pi$
$839$	−23.7002	−	41.0500i	−0.818222	−	1.41720i	0.0887683	−	0.996052i	$-0.471707\pi$
$840$	−4.15547	−	1.93186i	−0.143377	−	0.0666557i
$841$	−11.1015	+	19.2284i	−0.382812	+	0.663050i
$842$			1.61633i			0.0557025i
$843$	−23.3389	−	29.1581i	−0.803835	−	1.00426i
$844$	−13.4561			−0.463179
$845$	−4.84557	−	8.39278i	−0.166693	−	0.288720i
$846$	−20.4167	+	22.1638i	−0.701942	+	0.762006i
$847$	46.8130	+	31.1123i	1.60851	+	1.06903i
$848$	0.844055	−	0.487315i	0.0289850	−	0.0167345i
$849$	−29.7019	−	37.1075i	−1.01937	−	1.27353i
$850$	4.95334	−	2.85981i	0.169898	−	0.0980907i
$851$	12.2400	−	7.06679i	0.419583	−	0.242246i
$852$	−7.16865	−	8.95603i	−0.245594	−	0.306828i
$853$	−15.0033	+	8.66216i	−0.513703	+	0.296587i	−0.734354	−	0.678766i	$-0.762515\pi$
$853$	−15.0033	+	8.66216i	−0.513703	+	0.296587i	0.220651	+	0.975353i	$0.429182\pi$
$854$	1.24023	−	19.6674i	0.0424399	−	0.673004i
$855$	−2.52006	+	2.73569i	−0.0861841	+	0.0935588i
$856$	−9.05896	−	15.6906i	−0.309629	−	0.536293i
$857$	28.1875			0.962865			0.481433	−	0.876483i	$-0.340117\pi$
$857$	28.1875			0.962865			0.481433	+	0.876483i	$0.340117\pi$
$858$	11.1799	+	13.9675i	0.381677	+	0.476842i
$859$		−	49.1373i		−	1.67654i	−0.545253	−	0.838272i	$-0.683566\pi$
$859$		−	49.1373i		−	1.67654i	0.545253	−	0.838272i	$-0.316434\pi$
$860$	2.45956	−	4.26008i	0.0838702	−	0.145267i
$861$	−32.7496	−	46.6561i	−1.11610	−	1.59003i
$862$	−11.5676	−	20.0356i	−0.393993	−	0.682415i
$863$	−20.4648	+	11.8154i	−0.696631	+	0.402200i	−0.806092	−	0.591791i	$-0.798421\pi$
$863$	−20.4648	+	11.8154i	−0.696631	+	0.402200i	0.109460	+	0.993991i	$0.465088\pi$
$864$	−4.30903	−	2.90383i	−0.146596	−	0.0987904i
$865$	−3.98019	+	6.89389i	−0.135330	+	0.234399i
$866$	−1.44266	+	2.49876i	−0.0490236	+	0.0849114i
$867$	−21.2489	+	17.0082i	−0.721651	+	0.577629i
$868$	−10.4884	−	21.1364i	−0.355998	−	0.717415i
$869$	−6.72081	−	3.88026i	−0.227988	−	0.131629i
$870$	0.681066	+	4.46395i	0.0230903	+	0.151342i
$871$		−	0.125334i		−	0.00424679i
$872$	−3.06518	−	1.76968i	−0.103800	−	0.0599291i
$873$	−3.94109	+	4.27832i	−0.133386	+	0.144799i
$874$			4.32215i			0.146199i
$875$	−2.20349	−	1.46446i	−0.0744916	−	0.0495077i
$876$	−14.7698	+	2.25343i	−0.499025	+	0.0761363i
$877$	18.9067			0.638435			0.319218	−	0.947681i	$-0.396580\pi$
$877$	18.9067			0.638435			0.319218	+	0.947681i	$0.396580\pi$
$878$	2.59140	+	4.48844i	0.0874557	+	0.151478i
$879$	−37.1614	−	14.5075i	−1.25342	−	0.489326i
$880$	4.91769	+	2.83923i	0.165775	+	0.0957105i
$881$	17.7505			0.598030			0.299015	−	0.954248i	$-0.403342\pi$
$881$	17.7505			0.598030			0.299015	+	0.954248i	$0.403342\pi$
$882$	−3.69455	−	20.6725i	−0.124402	−	0.696078i
$883$	−45.1444			−1.51923			−0.759614	−	0.650374i	$-0.774612\pi$
$883$	−45.1444			−1.51923			−0.759614	+	0.650374i	$0.774612\pi$
$884$	−9.01025	−	5.20207i	−0.303048	−	0.174965i
$885$	15.3759	−	12.3073i	0.516854	−	0.413704i
$886$	−9.38948	−	16.2631i	−0.315446	−	0.546368i
$887$	−27.4427			−0.921437			−0.460718	−	0.887546i	$-0.652408\pi$
$887$	−27.4427			−0.921437			−0.460718	+	0.887546i	$0.652408\pi$
$888$	−4.38820	−	5.48232i	−0.147258	−	0.183975i
$889$	−42.0213	−	27.9277i	−1.40935	−	0.936664i
$890$			15.7750i			0.528779i
$891$	−29.0929	−	42.0172i	−0.974649	−	1.40763i
$892$	9.11125	+	5.26038i	0.305067	+	0.176131i
$893$		−	12.4539i		−	0.416752i
$894$	25.6631	+	10.0187i	0.858302	+	0.335074i
$895$	−5.99647	−	3.46206i	−0.200440	−	0.115724i
$896$	1.17605	+	2.37000i	0.0392891	+	0.0791762i
$897$	−10.2314	−	3.99424i	−0.341615	−	0.133364i
$898$	−11.5887	+	20.0723i	−0.386722	+	0.669821i
$899$	−11.6254	+	20.1358i	−0.387728	+	0.671565i
$900$	−2.20650	−	2.03258i	−0.0735500	−	0.0677525i
$901$	−4.82767	+	2.78726i	−0.160833	+	0.0928571i
$902$	35.3173	+	61.1714i	1.17594	+	2.03678i
$903$	22.4541	−	1.99071i	0.747227	−	0.0662468i
$904$	−3.12456	+	5.41190i	−0.103921	+	0.179997i
$905$		−	2.78183i		−	0.0924711i
$906$	12.3346	−	31.5954i	0.409789	−	1.04969i
$907$	−34.0789			−1.13157			−0.565785	−	0.824553i	$-0.691427\pi$
$907$	−34.0789			−1.13157			−0.565785	+	0.824553i	$0.691427\pi$
$908$	−14.5390	−	25.1823i	−0.482493	−	0.835703i
$909$	−15.7918	+	4.93356i	−0.523781	+	0.163636i
$910$	−0.302888	+	4.80315i	−0.0100407	+	0.159223i
$911$	50.8899	−	29.3813i	1.68606	−	0.973447i	0.728572	−	0.684969i	$-0.240184\pi$
$911$	50.8899	−	29.3813i	1.68606	−	0.973447i	0.957487	−	0.288477i	$-0.0931490\pi$
$912$	2.12289	−	0.323890i	0.0702959	−	0.0107251i
$913$	59.4965	−	34.3503i	1.96905	−	1.13683i
$914$	−17.0973	+	9.87115i	−0.565530	+	0.326509i
$915$	4.69157	−	12.0176i	0.155099	−	0.397289i
$916$	7.36868	−	4.25431i	0.243468	−	0.140566i
$917$	0.284871	+	0.189328i	0.00940728	+	0.00625215i
$918$	24.6460	+	16.6088i	0.813440	+	0.548173i
$919$	25.0699	+	43.4223i	0.826979	+	1.43237i	0.900397	+	0.435068i	$0.143276\pi$
$919$	25.0699	+	43.4223i	0.826979	+	1.43237i	−0.0734186	+	0.997301i	$0.523391\pi$
$920$	−3.48607			−0.114932
$921$	−25.0248	+	3.81804i	−0.824595	+	0.125809i
$922$		−	12.7415i		−	0.419617i
$923$	−6.02388	+	10.4337i	−0.198278	+	0.343428i
$924$	2.29801	+	25.9203i	0.0755991	+	0.852716i
$925$	−2.02715	−	3.51113i	−0.0666523	−	0.115445i
$926$	11.1045	−	6.41119i	0.364917	−	0.210685i
$927$	6.74082	+	21.5767i	0.221398	+	0.708671i
$928$	1.30354	−	2.25780i	0.0427909	−	0.0741160i
$929$	4.56894	−	7.91364i	0.149902	−	0.259638i	−0.781289	−	0.624170i	$-0.785437\pi$
$929$	4.56894	−	7.91364i	0.149902	−	0.259638i	0.931191	+	0.364531i	$0.118771\pi$
$930$	−2.32978	−	15.2702i	−0.0763966	−	0.500731i
$931$	6.91144	+	5.24923i	0.226513	+	0.172036i
$932$	22.5702	+	13.0309i	0.739313	+	0.426842i
$933$	5.85930	−	4.68994i	0.191825	−	0.153542i
$934$			5.55800i			0.181863i
$935$	−28.1273	−	16.2393i	−0.919863	−	0.531083i
$936$	−1.19512	+	5.32460i	−0.0390638	+	0.174040i
$937$		−	12.3801i		−	0.404439i	−0.979340	−	0.202219i	$-0.935185\pi$
$937$		−	12.3801i		−	0.404439i	0.979340	−	0.202219i	$-0.0648154\pi$
$938$	0.100904	−	0.151825i	0.00329462	−	0.00495725i
$939$	5.69107	−	14.5778i	0.185721	−	0.475730i
$940$	10.0448			0.327624
$941$	14.1032	+	24.4275i	0.459751	+	0.796312i	0.998948	−	0.0458677i	$-0.0146053\pi$
$941$	14.1032	+	24.4275i	0.459751	+	0.796312i	−0.539196	+	0.842180i	$0.681272\pi$
$942$	−4.27439	−	28.0159i	−0.139267	−	0.912807i
$943$	−37.5538	−	21.6817i	−1.22292	−	0.706053i
$944$	−11.3708			−0.370088
$945$	1.81445	−	13.6275i	0.0590240	−	0.443301i
$946$	−27.9330			−0.908180
$947$	−6.13947	−	3.54463i	−0.199506	−	0.115185i	0.396919	−	0.917854i	$-0.370079\pi$
$947$	−6.13947	−	3.54463i	−0.199506	−	0.115185i	−0.596425	+	0.802669i	$0.703413\pi$
$948$	−0.357021	−	2.34004i	−0.0115955	−	0.0760011i
$949$	7.84548	+	13.5888i	0.254675	+	0.441110i
$950$	1.23983			0.0402256
$951$	−12.2081	+	31.2714i	−0.395875	+	1.01404i
$952$	−6.72656	−	13.5555i	−0.218009	−	0.439337i
$953$			27.1147i			0.878331i	0.898406	+	0.439165i	$0.144726\pi$
$953$			27.1147i			0.878331i	−0.898406	+	0.439165i	$0.855274\pi$
$954$	2.15052	+	1.98101i	0.0696257	+	0.0641376i
$955$	2.62400	+	1.51497i	0.0849105	+	0.0490231i
$956$		−	15.8044i		−	0.511152i
$957$	20.0186	−	16.0235i	0.647111	−	0.517965i
$958$	4.98120	+	2.87590i	0.160935	+	0.0929160i
$959$	−11.6918	+	17.5920i	−0.377547	+	0.568075i
$960$	0.261236	+	1.71224i	0.00843136	+	0.0552622i
$961$	24.2680	−	42.0334i	0.782838	−	1.35591i
$962$	−3.68744	+	6.38683i	−0.118888	+	0.205920i
$963$	36.8260	−	39.9772i	1.18670	−	1.28825i
$964$	4.20612	−	2.42841i	0.135470	−	0.0782137i
$965$	1.76305	+	3.05370i	0.0567547	+	0.0983020i
$966$	−9.17815	−	13.0755i	−0.295302	−	0.420696i
$967$	−12.5108	+	21.6694i	−0.402321	+	0.696840i	−0.994006	−	0.109329i	$-0.965130\pi$
$967$	−12.5108	+	21.6694i	−0.402321	+	0.696840i	0.591685	+	0.806170i	$0.298463\pi$
$968$		−	21.2449i		−	0.682838i
$969$	−12.1421	+	1.85253i	−0.390062	+	0.0595118i
$970$	1.93896			0.0622564
$971$	21.1676	+	36.6634i	0.679302	+	1.17659i	0.975191	+	0.221363i	$0.0710506\pi$
$971$	21.1676	+	36.6634i	0.679302	+	1.17659i	−0.295890	+	0.955222i	$0.595616\pi$
$972$	4.46031	−	14.9367i	0.143065	−	0.479096i
$973$	−6.17041	−	12.4347i	−0.197814	−	0.398639i
$974$	−26.6459	+	15.3840i	−0.853789	+	0.492935i
$975$	−1.14577	+	2.93492i	−0.0366940	+	0.0939928i
$976$	−6.45045	+	3.72417i	−0.206474	+	0.119208i
$977$	15.9652	−	9.21749i	0.510771	−	0.294894i	−0.222380	−	0.974960i	$-0.571382\pi$
$977$	15.9652	−	9.21749i	0.510771	−	0.294894i	0.733150	+	0.680067i	$0.238049\pi$
$978$	−22.5675	+	3.44313i	−0.721630	+	0.110099i
$979$	77.5766	−	44.7889i	2.47936	−	1.43146i
$980$	−4.23381	+	5.57448i	−0.135244	+	0.178070i
$981$	2.32541	−	10.3603i	0.0742445	−	0.330780i
$982$	−7.29865	−	12.6416i	−0.232909	−	0.403411i
$983$	56.9508			1.81645			0.908224	−	0.418485i	$-0.137439\pi$
$983$	56.9508			1.81645			0.908224	+	0.418485i	$0.137439\pi$
$984$	−7.83512	+	20.0699i	−0.249774	+	0.639804i
$985$			9.09265i			0.289716i
$986$	−7.45578	+	12.9138i	−0.237440	+	0.411259i
$987$	26.4459	+	37.6757i	0.841784	+	1.19923i
$988$	−1.12765	−	1.95314i	−0.0358752	−	0.0621377i
$989$	14.8509	−	8.57419i	0.472232	−	0.272643i
$990$	−3.73082	+	16.6218i	−0.118573	+	0.528277i
$991$	20.5669	−	35.6229i	0.653328	−	1.13160i	−0.328982	−	0.944336i	$-0.606706\pi$
$991$	20.5669	−	35.6229i	0.653328	−	1.13160i	0.982310	−	0.187261i	$-0.0599611\pi$
$992$	−4.45915	+	7.72347i	−0.141578	+	0.245220i
$993$	13.4800	+	5.26248i	0.427775	+	0.167000i
$994$	−15.6970	+	7.78921i	−0.497878	+	0.247059i
$995$	−12.5241	−	7.23082i	−0.397042	−	0.229232i
$996$	19.5204	+	7.62059i	0.618527	+	0.241468i
$997$		−	0.0908950i		−	0.00287867i	−0.999999	−	0.00143934i	$-0.999542\pi$
$997$		−	0.0908950i		−	0.00287867i	0.999999	−	0.00143934i	$-0.000458155\pi$
$998$	−12.7978	−	7.38881i	−0.405107	−	0.233889i
$999$	11.7730	−	17.4701i	0.372482	−	0.552730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.12	✓	32
3.2	odd	2		1890.2.t.c.1151.8		32
7.5	odd	6		630.2.bk.c.131.2	yes	32
9.2	odd	6		630.2.bk.c.101.10	yes	32
9.7	even	3		1890.2.bk.c.521.16		32
21.5	even	6		1890.2.bk.c.341.16		32
63.47	even	6	inner	630.2.t.c.551.12	yes	32
63.61	odd	6		1890.2.t.c.1601.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.12	✓	32	1.1	even	1	trivial
630.2.t.c.551.12	yes	32	63.47	even	6	inner
630.2.bk.c.101.10	yes	32	9.2	odd	6
630.2.bk.c.131.2	yes	32	7.5	odd	6
1890.2.t.c.1151.8		32	3.2	odd	2
1890.2.t.c.1601.8		32	63.61	odd	6
1890.2.bk.c.341.16		32	21.5	even	6
1890.2.bk.c.521.16		32	9.7	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.261236 - 1.71224i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.629881 - 1.61346i) q^{6} +(-2.20349 - 1.46446i) q^{7} +1.00000i q^{8} +(-2.86351 + 0.894597i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.261236 - 1.71224i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.629881 - 1.61346i) q^{6} +(-2.20349 - 1.46446i) q^{7} +1.00000i q^{8} +(-2.86351 + 0.894597i) q^{9} +(0.866025 + 0.500000i) q^{10} -5.67846i q^{11} +(1.35222 - 1.08236i) q^{12} +(-1.57532 - 0.909513i) q^{13} +(-1.17605 - 2.37000i) q^{14} +(-0.261236 - 1.71224i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.85981 - 4.95334i) q^{17} +(-2.92717 - 0.657012i) q^{18} +(1.07373 - 0.619917i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.93186 + 4.15547i) q^{21} +(2.83923 - 4.91769i) q^{22} +3.48607i q^{23} +(1.71224 - 0.261236i) q^{24} +1.00000 q^{25} +(-0.909513 - 1.57532i) q^{26} +(2.27981 + 4.66931i) q^{27} +(0.166511 - 2.64051i) q^{28} +(-2.25780 + 1.30354i) q^{29} +(0.629881 - 1.61346i) q^{30} +(7.72347 - 4.45915i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-9.72287 + 1.48342i) q^{33} +(4.95334 - 2.85981i) q^{34} +(-2.20349 - 1.46446i) q^{35} +(-2.20650 - 2.03258i) q^{36} +(-2.02715 - 3.51113i) q^{37} +1.23983 q^{38} +(-1.14577 + 2.93492i) q^{39} +1.00000i q^{40} +(-6.21952 + 10.7725i) q^{41} +(-3.75078 + 2.63281i) q^{42} +(-2.45956 - 4.26008i) q^{43} +(4.91769 - 2.83923i) q^{44} +(-2.86351 + 0.894597i) q^{45} +(-1.74303 + 3.01902i) q^{46} +(5.02238 - 8.69903i) q^{47} +(1.61346 + 0.629881i) q^{48} +(2.71074 + 6.45383i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-9.22838 - 3.60268i) q^{51} -1.81903i q^{52} +(-0.844055 - 0.487315i) q^{53} +(-0.360277 + 5.18365i) q^{54} -5.67846i q^{55} +(1.46446 - 2.20349i) q^{56} +(-1.34194 - 1.67653i) q^{57} -2.60709 q^{58} +(5.68540 + 9.84741i) q^{59} +(1.35222 - 1.08236i) q^{60} +(6.45045 + 3.72417i) q^{61} +8.91829 q^{62} +(7.61982 + 2.22225i) q^{63} -1.00000 q^{64} +(-1.57532 - 0.909513i) q^{65} +(-9.16197 - 3.57676i) q^{66} +(0.0344509 + 0.0596708i) q^{67} +5.71962 q^{68} +(5.96898 - 0.910688i) q^{69} +(-1.17605 - 2.37000i) q^{70} -6.62319i q^{71} +(-0.894597 - 2.86351i) q^{72} +(-7.47035 - 4.31301i) q^{73} -4.05430i q^{74} +(-0.261236 - 1.71224i) q^{75} +(1.07373 + 0.619917i) q^{76} +(-8.31586 + 12.5124i) q^{77} +(-2.45973 + 1.96883i) q^{78} +(0.683330 - 1.18356i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.39939 - 5.12338i) q^{81} +(-10.7725 + 6.21952i) q^{82} +(6.04923 + 10.4776i) q^{83} +(-4.56467 + 0.404689i) q^{84} +(2.85981 - 4.95334i) q^{85} -4.91911i q^{86} +(2.82180 + 3.52536i) q^{87} +5.67846 q^{88} +(7.88750 + 13.6615i) q^{89} +(-2.92717 - 0.657012i) q^{90} +(2.13927 + 4.31109i) q^{91} +(-3.01902 + 1.74303i) q^{92} +(-9.65277 - 12.0595i) q^{93} +(8.69903 - 5.02238i) q^{94} +(1.07373 - 0.619917i) q^{95} +(1.08236 + 1.35222i) q^{96} +(1.67919 - 0.969482i) q^{97} +(-0.879348 + 6.94455i) q^{98} +(5.07994 + 16.2603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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