LMFDB - Embedded newform 630.2.i.i.151.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

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.i (of order $3$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.7
Root			$1.67659 - 0.434811i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.i.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.21485 - 1.23456i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.21485 + 1.23456i) q^{6} +(-1.09594 + 2.40809i) q^{7} -1.00000 q^{8} +(-0.0482768 - 2.99961i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.21485 - 1.23456i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.21485 + 1.23456i) q^{6} +(-1.09594 + 2.40809i) q^{7} -1.00000 q^{8} +(-0.0482768 - 2.99961i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.554785 - 0.960915i) q^{11} +(1.21485 - 1.23456i) q^{12} +(-1.64072 - 2.84181i) q^{13} +(1.09594 - 2.40809i) q^{14} +(-0.461735 - 1.66937i) q^{15} +1.00000 q^{16} +(2.19747 - 3.80613i) q^{17} +(0.0482768 + 2.99961i) q^{18} +(-0.622647 - 1.07846i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.64153 + 4.27848i) q^{21} +(0.554785 + 0.960915i) q^{22} +(3.14773 - 5.45204i) q^{23} +(-1.21485 + 1.23456i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.64072 + 2.84181i) q^{26} +(-3.76185 - 3.58448i) q^{27} +(-1.09594 + 2.40809i) q^{28} +(3.26879 - 5.66171i) q^{29} +(0.461735 + 1.66937i) q^{30} +3.10957 q^{31} -1.00000 q^{32} +(-1.86029 - 0.482453i) q^{33} +(-2.19747 + 3.80613i) q^{34} +(1.53750 + 2.15316i) q^{35} +(-0.0482768 - 2.99961i) q^{36} +(0.659906 + 1.14299i) q^{37} +(0.622647 + 1.07846i) q^{38} +(-5.50161 - 1.42680i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.60559 + 6.24507i) q^{41} +(-1.64153 - 4.27848i) q^{42} +(-4.88416 + 8.45961i) q^{43} +(-0.554785 - 0.960915i) q^{44} +(-2.62188 - 1.45800i) q^{45} +(-3.14773 + 5.45204i) q^{46} -11.4617 q^{47} +(1.21485 - 1.23456i) q^{48} +(-4.59781 - 5.27827i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.02930 - 7.33678i) q^{51} +(-1.64072 - 2.84181i) q^{52} +(2.73283 - 4.73340i) q^{53} +(3.76185 + 3.58448i) q^{54} -1.10957 q^{55} +(1.09594 - 2.40809i) q^{56} +(-2.08784 - 0.541468i) q^{57} +(-3.26879 + 5.66171i) q^{58} +6.46993 q^{59} +(-0.461735 - 1.66937i) q^{60} +4.40470 q^{61} -3.10957 q^{62} +(7.27625 + 3.17115i) q^{63} +1.00000 q^{64} -3.28143 q^{65} +(1.86029 + 0.482453i) q^{66} -5.23241 q^{67} +(2.19747 - 3.80613i) q^{68} +(-2.90684 - 10.5095i) q^{69} +(-1.53750 - 2.15316i) q^{70} +16.3046 q^{71} +(0.0482768 + 2.99961i) q^{72} +(-0.731993 + 1.26785i) q^{73} +(-0.659906 - 1.14299i) q^{74} +(-1.67659 - 0.434811i) q^{75} +(-0.622647 - 1.07846i) q^{76} +(2.92199 - 0.282863i) q^{77} +(5.50161 + 1.42680i) q^{78} +3.41668 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.99534 + 0.289623i) q^{81} +(-3.60559 - 6.24507i) q^{82} +(-4.06648 + 7.04336i) q^{83} +(1.64153 + 4.27848i) q^{84} +(-2.19747 - 3.80613i) q^{85} +(4.88416 - 8.45961i) q^{86} +(-3.01863 - 10.9136i) q^{87} +(0.554785 + 0.960915i) q^{88} +(-1.42132 - 2.46180i) q^{89} +(2.62188 + 1.45800i) q^{90} +(8.64146 - 0.836537i) q^{91} +(3.14773 - 5.45204i) q^{92} +(3.77766 - 3.83895i) q^{93} +11.4617 q^{94} -1.24529 q^{95} +(-1.21485 + 1.23456i) q^{96} +(-8.54592 + 14.8020i) q^{97} +(4.59781 + 5.27827i) q^{98} +(-2.85559 + 1.71053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.21485	−	1.23456i	0.701394	−	0.712774i
$3$	1.21485	−	1.23456i	0.701394	−	0.712774i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.21485	+	1.23456i	−0.495961	+	0.504007i
$7$	−1.09594	+	2.40809i	−0.414228	+	0.910173i
$7$	−1.09594	+	2.40809i	−0.414228	+	0.910173i
$8$	−1.00000			−0.353553
$9$	−0.0482768	−	2.99961i	−0.0160923	−	0.999871i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.554785	−	0.960915i	−0.167274	−	0.289727i	0.770187	−	0.637819i	$-0.220163\pi$
$11$	−0.554785	−	0.960915i	−0.167274	−	0.289727i	−0.937460	+	0.348092i	$0.886830\pi$
$12$	1.21485	−	1.23456i	0.350697	−	0.356387i
$13$	−1.64072	−	2.84181i	−0.455053	−	0.788175i	0.543638	−	0.839320i	$-0.317046\pi$
$13$	−1.64072	−	2.84181i	−0.455053	−	0.788175i	−0.998691	+	0.0511446i	$0.983713\pi$
$14$	1.09594	−	2.40809i	0.292903	−	0.643590i
$15$	−0.461735	−	1.66937i	−0.119219	−	0.431030i
$16$	1.00000			0.250000
$17$	2.19747	−	3.80613i	0.532964	−	0.923121i	−0.466294	−	0.884630i	$-0.654411\pi$
$17$	2.19747	−	3.80613i	0.532964	−	0.923121i	0.999259	−	0.0384919i	$-0.0122554\pi$
$18$	0.0482768	+	2.99961i	0.0113789	+	0.707015i
$19$	−0.622647	−	1.07846i	−0.142845	−	0.247415i	0.785722	−	0.618580i	$-0.212292\pi$
$19$	−0.622647	−	1.07846i	−0.142845	−	0.247415i	−0.928567	+	0.371165i	$0.878958\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	1.64153	+	4.27848i	0.358210	+	0.933641i
$22$	0.554785	+	0.960915i	0.118281	+	0.204868i
$23$	3.14773	−	5.45204i	0.656348	−	1.13683i	−0.325206	−	0.945643i	$-0.605434\pi$
$23$	3.14773	−	5.45204i	0.656348	−	1.13683i	0.981554	−	0.191185i	$-0.0612330\pi$
$24$	−1.21485	+	1.23456i	−0.247980	+	0.252004i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.64072	+	2.84181i	0.321771	+	0.557324i
$27$	−3.76185	−	3.58448i	−0.723968	−	0.689833i
$28$	−1.09594	+	2.40809i	−0.207114	+	0.455087i
$29$	3.26879	−	5.66171i	0.606999	−	1.05135i	−0.384733	−	0.923028i	$-0.625707\pi$
$29$	3.26879	−	5.66171i	0.606999	−	1.05135i	0.991732	−	0.128325i	$-0.0409601\pi$
$30$	0.461735	+	1.66937i	0.0843009	+	0.304784i
$31$	3.10957			0.558495			0.279248	−	0.960219i	$-0.409915\pi$
$31$	3.10957			0.558495			0.279248	+	0.960219i	$0.409915\pi$
$32$	−1.00000			−0.176777
$33$	−1.86029	−	0.482453i	−0.323835	−	0.0839844i
$34$	−2.19747	+	3.80613i	−0.376863	+	0.652745i
$35$	1.53750	+	2.15316i	0.259884	+	0.363951i
$36$	−0.0482768	−	2.99961i	−0.00804613	−	0.499935i
$37$	0.659906	+	1.14299i	0.108488	+	0.187907i	0.915158	−	0.403096i	$-0.132066\pi$
$37$	0.659906	+	1.14299i	0.108488	+	0.187907i	−0.806670	+	0.591002i	$0.798732\pi$
$38$	0.622647	+	1.07846i	0.101007	+	0.174949i
$39$	−5.50161	−	1.42680i	−0.880962	−	0.228472i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	3.60559	+	6.24507i	0.563099	+	0.975317i	0.997224	+	0.0744637i	$0.0237245\pi$
$41$	3.60559	+	6.24507i	0.563099	+	0.975317i	−0.434124	+	0.900853i	$0.642942\pi$
$42$	−1.64153	−	4.27848i	−0.253293	−	0.660184i
$43$	−4.88416	+	8.45961i	−0.744827	+	1.29008i	0.205448	+	0.978668i	$0.434135\pi$
$43$	−4.88416	+	8.45961i	−0.744827	+	1.29008i	−0.950275	+	0.311411i	$0.899198\pi$
$44$	−0.554785	−	0.960915i	−0.0836370	−	0.144863i
$45$	−2.62188	−	1.45800i	−0.390847	−	0.217345i
$46$	−3.14773	+	5.45204i	−0.464108	+	0.803859i
$47$	−11.4617			−1.67186			−0.835929	−	0.548838i	$-0.815070\pi$
$47$	−11.4617			−1.67186			−0.835929	+	0.548838i	$0.815070\pi$
$48$	1.21485	−	1.23456i	0.175349	−	0.178193i
$49$	−4.59781	−	5.27827i	−0.656830	−	0.754038i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−2.02930	−	7.33678i	−0.284158	−	1.02736i
$52$	−1.64072	−	2.84181i	−0.227527	−	0.394088i
$53$	2.73283	−	4.73340i	0.375383	−	0.650182i	−0.615002	−	0.788526i	$-0.710845\pi$
$53$	2.73283	−	4.73340i	0.375383	−	0.650182i	0.990384	+	0.138344i	$0.0441779\pi$
$54$	3.76185	+	3.58448i	0.511923	+	0.487786i
$55$	−1.10957			−0.149614
$56$	1.09594	−	2.40809i	0.146452	−	0.321795i
$57$	−2.08784	−	0.541468i	−0.276541	−	0.0717191i
$58$	−3.26879	+	5.66171i	−0.429213	+	0.743419i
$59$	6.46993			0.842313			0.421157	−	0.906988i	$-0.361624\pi$
$59$	6.46993			0.842313			0.421157	+	0.906988i	$0.361624\pi$
$60$	−0.461735	−	1.66937i	−0.0596097	−	0.215515i
$61$	4.40470			0.563964			0.281982	−	0.959420i	$-0.409008\pi$
$61$	4.40470			0.563964			0.281982	+	0.959420i	$0.409008\pi$
$62$	−3.10957			−0.394916
$63$	7.27625	+	3.17115i	0.916721	+	0.399528i
$64$	1.00000			0.125000
$65$	−3.28143			−0.407012
$66$	1.86029	+	0.482453i	0.228986	+	0.0593859i
$67$	−5.23241			−0.639241			−0.319620	−	0.947546i	$-0.603555\pi$
$67$	−5.23241			−0.639241			−0.319620	+	0.947546i	$0.603555\pi$
$68$	2.19747	−	3.80613i	0.266482	−	0.461561i
$69$	−2.90684	−	10.5095i	−0.349942	−	1.26519i
$70$	−1.53750	−	2.15316i	−0.183766	−	0.257352i
$71$	16.3046			1.93501			0.967503	−	0.252860i	$-0.0813713\pi$
$71$	16.3046			1.93501			0.967503	+	0.252860i	$0.0813713\pi$
$72$	0.0482768	+	2.99961i	0.00568947	+	0.353508i
$73$	−0.731993	+	1.26785i	−0.0856733	+	0.148391i	−0.905678	−	0.423966i	$-0.860637\pi$
$73$	−0.731993	+	1.26785i	−0.0856733	+	0.148391i	0.820005	+	0.572357i	$0.193971\pi$
$74$	−0.659906	−	1.14299i	−0.0767126	−	0.132870i
$75$	−1.67659	−	0.434811i	−0.193595	−	0.0502077i
$76$	−0.622647	−	1.07846i	−0.0714225	−	0.123707i
$77$	2.92199	−	0.282863i	0.332991	−	0.0322352i
$78$	5.50161	+	1.42680i	0.622934	+	0.161554i
$79$	3.41668			0.384407			0.192204	−	0.981355i	$-0.438437\pi$
$79$	3.41668			0.384407			0.192204	+	0.981355i	$0.438437\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.99534	+	0.289623i	−0.999482	+	0.0321804i
$82$	−3.60559	−	6.24507i	−0.398171	−	0.689653i
$83$	−4.06648	+	7.04336i	−0.446355	+	0.773109i	−0.998145	−	0.0608736i	$-0.980611\pi$
$83$	−4.06648	+	7.04336i	−0.446355	+	0.773109i	0.551791	+	0.833983i	$0.313945\pi$
$84$	1.64153	+	4.27848i	0.179105	+	0.466820i
$85$	−2.19747	−	3.80613i	−0.238349	−	0.412832i
$86$	4.88416	−	8.45961i	0.526672	−	0.912223i
$87$	−3.01863	−	10.9136i	−0.323631	−	1.17007i
$88$	0.554785	+	0.960915i	0.0591403	+	0.102434i
$89$	−1.42132	−	2.46180i	−0.150660	−	0.260950i	0.780810	−	0.624768i	$-0.214806\pi$
$89$	−1.42132	−	2.46180i	−0.150660	−	0.260950i	−0.931470	+	0.363818i	$0.881473\pi$
$90$	2.62188	+	1.45800i	0.276370	+	0.153686i
$91$	8.64146	−	0.836537i	0.905872	−	0.0876929i
$92$	3.14773	−	5.45204i	0.328174	−	0.568414i
$93$	3.77766	−	3.83895i	0.391725	−	0.398081i
$94$	11.4617			1.18218
$95$	−1.24529			−0.127764
$96$	−1.21485	+	1.23456i	−0.123990	+	0.126002i
$97$	−8.54592	+	14.8020i	−0.867707	+	1.50291i	−0.00337237	+	0.999994i	$0.501073\pi$
$97$	−8.54592	+	14.8020i	−0.867707	+	1.50291i	−0.864334	+	0.502918i	$0.832260\pi$
$98$	4.59781	+	5.27827i	0.464449	+	0.533186i
$99$	−2.85559	+	1.71053i	−0.286998	+	0.171915i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.73642	−	6.47167i	−0.371788	−	0.643955i	0.618053	−	0.786136i	$-0.287922\pi$
$101$	−3.73642	−	6.47167i	−0.371788	−	0.643955i	−0.989841	+	0.142181i	$0.954588\pi$
$102$	2.02930	+	7.33678i	0.200930	+	0.726450i
$103$	2.48518	−	4.30445i	0.244872	−	0.424130i	−0.717224	−	0.696843i	$-0.754587\pi$
$103$	2.48518	−	4.30445i	0.244872	−	0.424130i	0.962096	+	0.272713i	$0.0879208\pi$
$104$	1.64072	+	2.84181i	0.160886	+	0.278662i
$105$	4.52604	+	0.717638i	0.441696	+	0.0700343i
$106$	−2.73283	+	4.73340i	−0.265436	+	0.459748i
$107$	−3.51531	−	6.08870i	−0.339838	−	0.588617i	0.644564	−	0.764550i	$-0.277039\pi$
$107$	−3.51531	−	6.08870i	−0.339838	−	0.588617i	−0.984402	+	0.175934i	$0.943706\pi$
$108$	−3.76185	−	3.58448i	−0.361984	−	0.344917i
$109$	−5.12829	+	8.88245i	−0.491201	+	0.850785i	−0.999949	−	0.0101309i	$-0.996775\pi$
$109$	−5.12829	+	8.88245i	−0.491201	+	0.850785i	0.508748	+	0.860916i	$0.330109\pi$
$110$	1.10957			0.105793
$111$	2.21278	+	0.573870i	0.210028	+	0.0544693i
$112$	−1.09594	+	2.40809i	−0.103557	+	0.227543i
$113$	3.64304	+	6.30993i	0.342708	+	0.593588i	0.984935	−	0.172927i	$-0.0553224\pi$
$113$	3.64304	+	6.30993i	0.342708	+	0.593588i	−0.642226	+	0.766515i	$0.721989\pi$
$114$	2.08784	+	0.541468i	0.195544	+	0.0507131i
$115$	−3.14773	−	5.45204i	−0.293528	−	0.508405i
$116$	3.26879	−	5.66171i	0.303499	−	0.525677i
$117$	−8.44510	+	5.05871i	−0.780750	+	0.467678i
$118$	−6.46993			−0.595605
$119$	6.75720	+	9.46301i	0.619432	+	0.867473i
$120$	0.461735	+	1.66937i	0.0421505	+	0.152392i
$121$	4.88443	−	8.46008i	0.444039	−	0.769098i
$122$	−4.40470			−0.398783
$123$	12.0902	+	3.13551i	1.09013	+	0.282719i
$124$	3.10957			0.279248
$125$	−1.00000			−0.0894427
$126$	−7.27625	−	3.17115i	−0.648220	−	0.282509i
$127$	20.9242			1.85673			0.928363	−	0.371674i	$-0.121216\pi$
$127$	20.9242			1.85673			0.928363	+	0.371674i	$0.121216\pi$
$128$	−1.00000			−0.0883883
$129$	4.51038	+	16.3070i	0.397116	+	1.43575i
$130$	3.28143			0.287801
$131$	−7.41195	+	12.8379i	−0.647585	+	1.12165i	0.336113	+	0.941822i	$0.390888\pi$
$131$	−7.41195	+	12.8379i	−0.647585	+	1.12165i	−0.983698	+	0.179828i	$0.942446\pi$
$132$	−1.86029	−	0.482453i	−0.161917	−	0.0419922i
$133$	3.27941	−	0.317463i	0.284361	−	0.0275275i
$134$	5.23241			0.452011
$135$	−4.98517	+	1.46562i	−0.429056	+	0.126140i
$136$	−2.19747	+	3.80613i	−0.188431	+	0.326373i
$137$	−6.20268	−	10.7434i	−0.529931	−	0.917867i	−0.999390	−	0.0349133i	$-0.988884\pi$
$137$	−6.20268	−	10.7434i	−0.529931	−	0.917867i	0.469459	−	0.882954i	$-0.344449\pi$
$138$	2.90684	+	10.5095i	0.247447	+	0.894626i
$139$	11.5310	+	19.9723i	0.978047	+	1.69403i	0.669491	+	0.742820i	$0.266512\pi$
$139$	11.5310	+	19.9723i	0.978047	+	1.69403i	0.308555	+	0.951206i	$0.400155\pi$
$140$	1.53750	+	2.15316i	0.129942	+	0.181975i
$141$	−13.9242	+	14.1501i	−1.17263	+	1.19166i
$142$	−16.3046			−1.36826
$143$	−1.82049	+	3.15318i	−0.152237	+	0.263682i
$144$	−0.0482768	−	2.99961i	−0.00402306	−	0.249968i
$145$	−3.26879	−	5.66171i	−0.271458	−	0.470179i
$146$	0.731993	−	1.26785i	0.0605802	−	0.104928i
$147$	−12.1020	−	0.736033i	−0.998156	−	0.0607070i
$148$	0.659906	+	1.14299i	0.0542440	+	0.0939533i
$149$	−1.37460	+	2.38087i	−0.112611	+	0.195048i	−0.916822	−	0.399295i	$-0.869255\pi$
$149$	−1.37460	+	2.38087i	−0.112611	+	0.195048i	0.804211	+	0.594344i	$0.202588\pi$
$150$	1.67659	+	0.434811i	0.136893	+	0.0355022i
$151$	9.23849	+	16.0015i	0.751818	+	1.30219i	0.946941	+	0.321408i	$0.104156\pi$
$151$	9.23849	+	16.0015i	0.751818	+	1.30219i	−0.195123	+	0.980779i	$0.562511\pi$
$152$	0.622647	+	1.07846i	0.0505033	+	0.0874743i
$153$	−11.5230	−	6.40780i	−0.931579	−	0.518040i
$154$	−2.92199	+	0.282863i	−0.235460	+	0.0227937i
$155$	1.55478	−	2.69297i	0.124883	−	0.216304i
$156$	−5.50161	−	1.42680i	−0.440481	−	0.114236i
$157$	−4.29934			−0.343124			−0.171562	−	0.985173i	$-0.554881\pi$
$157$	−4.29934			−0.343124			−0.171562	+	0.985173i	$0.554881\pi$
$158$	−3.41668			−0.271817
$159$	−2.52368	−	9.12421i	−0.200141	−	0.723597i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	9.67926	+	13.5552i	0.762833	+	1.06830i
$162$	8.99534	−	0.289623i	0.706741	−	0.0227549i
$163$	6.23750	+	10.8037i	0.488558	+	0.846208i	0.999913	−	0.0131616i	$-0.00418959\pi$
$163$	6.23750	+	10.8037i	0.488558	+	0.846208i	−0.511355	+	0.859370i	$0.670856\pi$
$164$	3.60559	+	6.24507i	0.281550	+	0.487658i
$165$	−1.34796	+	1.36983i	−0.104939	+	0.106641i
$166$	4.06648	−	7.04336i	0.315620	−	0.546671i
$167$	3.40584	+	5.89909i	0.263552	+	0.456486i	0.967183	−	0.254080i	$-0.0817726\pi$
$167$	3.40584	+	5.89909i	0.263552	+	0.456486i	−0.703631	+	0.710565i	$0.748439\pi$
$168$	−1.64153	−	4.27848i	−0.126646	−	0.330092i
$169$	1.11609	−	1.93313i	0.0858534	−	0.148702i
$170$	2.19747	+	3.80613i	0.168538	+	0.291917i
$171$	−3.20489	+	1.91976i	−0.245084	+	0.146808i
$172$	−4.88416	+	8.45961i	−0.372414	+	0.645039i
$173$	−8.41334			−0.639655			−0.319827	−	0.947476i	$-0.603625\pi$
$173$	−8.41334			−0.639655			−0.319827	+	0.947476i	$0.603625\pi$
$174$	3.01863	+	10.9136i	0.228842	+	0.827361i
$175$	2.63344	−	0.254930i	0.199069	−	0.0192709i
$176$	−0.554785	−	0.960915i	−0.0418185	−	0.0724317i
$177$	7.86000	−	7.98752i	0.590794	−	0.600379i
$178$	1.42132	+	2.46180i	0.106533	+	0.184520i
$179$	−11.0539	+	19.1459i	−0.826205	+	1.43103i	0.0747893	+	0.997199i	$0.476172\pi$
$179$	−11.0539	+	19.1459i	−0.826205	+	1.43103i	−0.900995	+	0.433830i	$0.857162\pi$
$180$	−2.62188	−	1.45800i	−0.195423	−	0.108673i
$181$	6.82038			0.506955			0.253477	−	0.967341i	$-0.418426\pi$
$181$	6.82038			0.506955			0.253477	+	0.967341i	$0.418426\pi$
$182$	−8.64146	+	0.836537i	−0.640548	+	0.0620082i
$183$	5.35105	−	5.43786i	0.395561	−	0.401978i
$184$	−3.14773	+	5.45204i	−0.232054	+	0.401929i
$185$	1.31981			0.0970346
$186$	−3.77766	+	3.83895i	−0.276992	+	0.281485i
$187$	−4.87649			−0.356604
$188$	−11.4617			−0.835929
$189$	12.7545	−	5.13049i	0.927756	−	0.373188i
$190$	1.24529			0.0903431
$191$	3.93174			0.284491			0.142245	−	0.989831i	$-0.454568\pi$
$191$	3.93174			0.284491			0.142245	+	0.989831i	$0.454568\pi$
$192$	1.21485	−	1.23456i	0.0876743	−	0.0890967i
$193$	5.85359			0.421351			0.210675	−	0.977556i	$-0.432434\pi$
$193$	5.85359			0.421351			0.210675	+	0.977556i	$0.432434\pi$
$194$	8.54592	−	14.8020i	0.613561	−	1.06272i
$195$	−3.98645	+	4.05113i	−0.285476	+	0.290107i
$196$	−4.59781	−	5.27827i	−0.328415	−	0.377019i
$197$	1.71845			0.122435			0.0612174	−	0.998124i	$-0.480502\pi$
$197$	1.71845			0.122435			0.0612174	+	0.998124i	$0.480502\pi$
$198$	2.85559	−	1.71053i	0.202938	−	0.121562i
$199$	2.00694	−	3.47612i	0.142268	−	0.246415i	−0.786082	−	0.618122i	$-0.787894\pi$
$199$	2.00694	−	3.47612i	0.142268	−	0.246415i	0.928350	+	0.371706i	$0.121227\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−6.35660	+	6.45972i	−0.448360	+	0.455634i
$202$	3.73642	+	6.47167i	0.262893	+	0.455345i
$203$	10.0515	+	14.0765i	0.705477	+	0.987974i
$204$	−2.02930	−	7.33678i	−0.142079	−	0.513678i
$205$	7.21119			0.503651
$206$	−2.48518	+	4.30445i	−0.173150	+	0.299905i
$207$	−16.5060	−	9.17877i	−1.14724	−	0.637969i
$208$	−1.64072	−	2.84181i	−0.113763	−	0.197044i
$209$	−0.690870	+	1.19662i	−0.0477885	+	0.0827720i
$210$	−4.52604	−	0.717638i	−0.312326	−	0.0495217i
$211$	−2.32892	−	4.03380i	−0.160329	−	0.277698i	0.774657	−	0.632381i	$-0.217922\pi$
$211$	−2.32892	−	4.03380i	−0.160329	−	0.277698i	−0.934987	+	0.354683i	$0.884589\pi$
$212$	2.73283	−	4.73340i	0.187691	−	0.325091i
$213$	19.8077	−	20.1291i	1.35720	−	1.37922i
$214$	3.51531	+	6.08870i	0.240302	+	0.416215i
$215$	4.88416	+	8.45961i	0.333097	+	0.576941i
$216$	3.76185	+	3.58448i	0.255961	+	0.243893i
$217$	−3.40792	+	7.48813i	−0.231344	+	0.508327i
$218$	5.12829	−	8.88245i	0.347331	−	0.601596i
$219$	0.675974	+	2.44394i	0.0456781	+	0.165146i
$220$	−1.10957			−0.0748072
$221$	−14.4217			−0.970108
$222$	−2.21278	−	0.573870i	−0.148512	−	0.0385156i
$223$	13.3981	−	23.2061i	0.897201	−	1.55400i	0.0661434	−	0.997810i	$-0.478931\pi$
$223$	13.3981	−	23.2061i	0.897201	−	1.55400i	0.831057	−	0.556187i	$-0.187736\pi$
$224$	1.09594	−	2.40809i	0.0732259	−	0.160897i
$225$	−2.57360	+	1.54161i	−0.171573	+	0.102774i
$226$	−3.64304	−	6.30993i	−0.242331	−	0.419730i
$227$	−6.05706	−	10.4911i	−0.402021	−	0.696322i	0.591948	−	0.805976i	$-0.298359\pi$
$227$	−6.05706	−	10.4911i	−0.402021	−	0.696322i	−0.993970	+	0.109654i	$0.965026\pi$
$228$	−2.08784	−	0.541468i	−0.138271	−	0.0358596i
$229$	8.07886	−	13.9930i	0.533866	−	0.924683i	−0.465351	−	0.885126i	$-0.654072\pi$
$229$	8.07886	−	13.9930i	0.533866	−	0.924683i	0.999217	−	0.0395568i	$-0.0125946\pi$
$230$	3.14773	+	5.45204i	0.207555	+	0.359497i
$231$	3.20056	−	3.95100i	0.210582	−	0.259957i
$232$	−3.26879	+	5.66171i	−0.214607	+	0.371709i
$233$	8.65151	+	14.9849i	0.566779	+	0.981691i	0.996882	+	0.0789105i	$0.0251441\pi$
$233$	8.65151	+	14.9849i	0.566779	+	0.981691i	−0.430102	+	0.902780i	$0.641523\pi$
$234$	8.44510	−	5.05871i	0.552074	−	0.330698i
$235$	−5.73084	+	9.92610i	−0.373839	+	0.647508i
$236$	6.46993			0.421157
$237$	4.15076	−	4.21810i	0.269621	−	0.273995i
$238$	−6.75720	−	9.46301i	−0.438004	−	0.613396i
$239$	0.644644	+	1.11656i	0.0416985	+	0.0722240i	0.886121	−	0.463453i	$-0.153390\pi$
$239$	0.644644	+	1.11656i	0.0416985	+	0.0722240i	−0.844423	+	0.535677i	$0.820056\pi$
$240$	−0.461735	−	1.66937i	−0.0298049	−	0.107757i
$241$	0.200516	+	0.347304i	0.0129164	+	0.0223718i	0.872411	−	0.488772i	$-0.162555\pi$
$241$	0.200516	+	0.347304i	0.0129164	+	0.0223718i	−0.859495	+	0.511144i	$0.829222\pi$
$242$	−4.88443	+	8.46008i	−0.313983	+	0.543834i
$243$	−10.5704	+	11.4571i	−0.678094	+	0.734975i
$244$	4.40470			0.281982
$245$	−6.87002	+	1.34269i	−0.438910	+	0.0857811i
$246$	−12.0902	−	3.13551i	−0.770842	−	0.199913i
$247$	−2.04317	+	3.53888i	−0.130004	+	0.225174i
$248$	−3.10957			−0.197458
$249$	3.75528	+	13.5769i	0.237981	+	0.860404i
$250$	1.00000			0.0632456
$251$	6.00739			0.379183			0.189592	−	0.981863i	$-0.439284\pi$
$251$	6.00739			0.379183			0.189592	+	0.981863i	$0.439284\pi$
$252$	7.27625	+	3.17115i	0.458361	+	0.199764i
$253$	−6.98526			−0.439160
$254$	−20.9242			−1.31290
$255$	−7.36849	−	1.91097i	−0.461433	−	0.119669i
$256$	1.00000			0.0625000
$257$	12.2294	−	21.1819i	0.762848	−	1.32129i	−0.178528	−	0.983935i	$-0.557134\pi$
$257$	12.2294	−	21.1819i	0.762848	−	1.32129i	0.941377	−	0.337357i	$-0.109533\pi$
$258$	−4.51038	−	16.3070i	−0.280804	−	1.01523i
$259$	−3.47565	+	0.336460i	−0.215966	+	0.0209066i
$260$	−3.28143			−0.203506
$261$	−17.1407	−	9.53177i	−1.06098	−	0.590002i
$262$	7.41195	−	12.8379i	0.457912	−	0.793126i
$263$	12.0119	+	20.8052i	0.740684	+	1.28290i	0.952184	+	0.305524i	$0.0988317\pi$
$263$	12.0119	+	20.8052i	0.740684	+	1.28290i	−0.211500	+	0.977378i	$0.567835\pi$
$264$	1.86029	+	0.482453i	0.114493	+	0.0296930i
$265$	−2.73283	−	4.73340i	−0.167876	−	0.290770i
$266$	−3.27941	+	0.317463i	−0.201073	+	0.0194649i
$267$	−4.76593	−	1.23601i	−0.291670	−	0.0756428i
$268$	−5.23241			−0.319620
$269$	−8.24890	+	14.2875i	−0.502944	+	0.871125i	0.497050	+	0.867722i	$0.334417\pi$
$269$	−8.24890	+	14.2875i	−0.502944	+	0.871125i	−0.999994	+	0.00340330i	$0.998917\pi$
$270$	4.98517	−	1.46562i	0.303388	−	0.0891947i
$271$	−14.6982	−	25.4580i	−0.892852	−	1.54646i	−0.836441	−	0.548057i	$-0.815368\pi$
$271$	−14.6982	−	25.4580i	−0.892852	−	1.54646i	−0.0564111	−	0.998408i	$-0.517966\pi$
$272$	2.19747	−	3.80613i	0.133241	−	0.230780i
$273$	9.46533	−	11.6847i	0.572868	−	0.707189i
$274$	6.20268	+	10.7434i	0.374718	+	0.649030i
$275$	−0.554785	+	0.960915i	−0.0334548	+	0.0579454i
$276$	−2.90684	−	10.5095i	−0.174971	−	0.632596i
$277$	4.86992	+	8.43495i	0.292605	+	0.506807i	0.974425	−	0.224713i	$-0.0721445\pi$
$277$	4.86992	+	8.43495i	0.292605	+	0.506807i	−0.681820	+	0.731520i	$0.738811\pi$
$278$	−11.5310	−	19.9723i	−0.691583	−	1.19786i
$279$	−0.150120	−	9.32750i	−0.00898745	−	0.558423i
$280$	−1.53750	−	2.15316i	−0.0918830	−	0.128676i
$281$	11.2140	−	19.4232i	0.668970	−	1.15869i	−0.309223	−	0.950990i	$-0.600069\pi$
$281$	11.2140	−	19.4232i	0.668970	−	1.15869i	0.978193	−	0.207700i	$-0.0665979\pi$
$282$	13.9242	−	14.1501i	0.829175	−	0.842628i
$283$	−18.4120			−1.09448			−0.547240	−	0.836976i	$-0.684322\pi$
$283$	−18.4120			−1.09448			−0.547240	+	0.836976i	$0.684322\pi$
$284$	16.3046			0.967503
$285$	−1.51285	+	1.53739i	−0.0896132	+	0.0910671i
$286$	1.82049	−	3.15318i	0.107648	−	0.186452i
$287$	−18.9902	+	1.83835i	−1.12096	+	0.108514i
$288$	0.0482768	+	2.99961i	0.00284474	+	0.176754i
$289$	−1.15774	−	2.00526i	−0.0681021	−	0.117956i
$290$	3.26879	+	5.66171i	0.191950	+	0.332467i
$291$	7.89190	+	28.5326i	0.462631	+	1.67261i
$292$	−0.731993	+	1.26785i	−0.0428366	+	0.0741953i
$293$	−9.32830	−	16.1571i	−0.544965	−	0.943907i	−0.998609	−	0.0527239i	$-0.983210\pi$
$293$	−9.32830	−	16.1571i	−0.544965	−	0.943907i	0.453644	−	0.891183i	$-0.350124\pi$
$294$	12.1020	+	0.736033i	0.705803	+	0.0429263i
$295$	3.23497	−	5.60312i	0.188347	−	0.326226i
$296$	−0.659906	−	1.14299i	−0.0383563	−	0.0664350i
$297$	−1.35736	+	5.60343i	−0.0787623	+	0.325144i
$298$	1.37460	−	2.38087i	0.0796282	−	0.137920i
$299$	−20.6582			−1.19469
$300$	−1.67659	−	0.434811i	−0.0967977	−	0.0251038i
$301$	−15.0188	−	21.0328i	−0.865667	−	1.21231i
$302$	−9.23849	−	16.0015i	−0.531616	−	0.920785i
$303$	−12.5289	−	3.24927i	−0.719764	−	0.186666i
$304$	−0.622647	−	1.07846i	−0.0357112	−	0.0618537i
$305$	2.20235	−	3.81458i	0.126106	−	0.218422i
$306$	11.5230	+	6.40780i	0.658725	+	0.366310i
$307$	25.9429			1.48064			0.740320	−	0.672255i	$-0.234674\pi$
$307$	25.9429			1.48064			0.740320	+	0.672255i	$0.234674\pi$
$308$	2.92199	−	0.282863i	0.166496	−	0.0161176i
$309$	−2.29499	−	8.29737i	−0.130557	−	0.472021i
$310$	−1.55478	+	2.69297i	−0.0883058	+	0.152950i
$311$	9.38608			0.532236			0.266118	−	0.963940i	$-0.414259\pi$
$311$	9.38608			0.532236			0.266118	+	0.963940i	$0.414259\pi$
$312$	5.50161	+	1.42680i	0.311467	+	0.0807769i
$313$	0.317071			0.0179219			0.00896097	−	0.999960i	$-0.497148\pi$
$313$	0.317071			0.0179219			0.00896097	+	0.999960i	$0.497148\pi$
$314$	4.29934			0.242626
$315$	6.38442	−	4.71584i	0.359721	−	0.265707i
$316$	3.41668			0.192204
$317$	4.25665			0.239077			0.119539	−	0.992830i	$-0.461859\pi$
$317$	4.25665			0.239077			0.119539	+	0.992830i	$0.461859\pi$
$318$	2.52368	+	9.12421i	0.141521	+	0.511660i
$319$	−7.25390			−0.406140
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−11.7874	−	3.05700i	−0.657911	−	0.170625i
$322$	−9.67926	−	13.5552i	−0.539404	−	0.755400i
$323$	−5.47299			−0.304525
$324$	−8.99534	+	0.289623i	−0.499741	+	0.0160902i
$325$	−1.64072	+	2.84181i	−0.0910106	+	0.157635i
$326$	−6.23750	−	10.8037i	−0.345463	−	0.598359i
$327$	4.73582	+	17.1220i	0.261891	+	0.946850i
$328$	−3.60559	−	6.24507i	−0.199086	−	0.344827i
$329$	12.5614	−	27.6008i	0.692530	−	1.52168i
$330$	1.34796	−	1.36983i	0.0742028	−	0.0754067i
$331$	6.77455			0.372363			0.186181	−	0.982515i	$-0.440389\pi$
$331$	6.77455			0.372363			0.186181	+	0.982515i	$0.440389\pi$
$332$	−4.06648	+	7.04336i	−0.223177	+	0.386554i
$333$	3.39667	−	2.03464i	0.186136	−	0.111498i
$334$	−3.40584	−	5.89909i	−0.186359	−	0.322784i
$335$	−2.61620	+	4.53140i	−0.142939	+	0.247577i
$336$	1.64153	+	4.27848i	0.0895525	+	0.233410i
$337$	7.69796	+	13.3333i	0.419335	+	0.726309i	0.995873	−	0.0907613i	$-0.0289300\pi$
$337$	7.69796	+	13.3333i	0.419335	+	0.726309i	−0.576538	+	0.817070i	$0.695597\pi$
$338$	−1.11609	+	1.93313i	−0.0607075	+	0.105148i
$339$	12.2157	+	3.16807i	0.663467	+	0.172066i
$340$	−2.19747	−	3.80613i	−0.119174	−	0.206416i
$341$	−1.72514	−	2.98803i	−0.0934217	−	0.161811i
$342$	3.20489	−	1.91976i	0.173301	−	0.103809i
$343$	17.7495	−	5.28726i	0.958383	−	0.285485i
$344$	4.88416	−	8.45961i	0.263336	−	0.456112i
$345$	−10.5549	−	2.73734i	−0.568256	−	0.147374i
$346$	8.41334			0.452304
$347$	−4.27257			−0.229363			−0.114682	−	0.993402i	$-0.536585\pi$
$347$	−4.27257			−0.229363			−0.114682	+	0.993402i	$0.536585\pi$
$348$	−3.01863	−	10.9136i	−0.161816	−	0.585033i
$349$	3.08538	−	5.34404i	0.165157	−	0.286060i	−0.771554	−	0.636164i	$-0.780520\pi$
$349$	3.08538	−	5.34404i	0.165157	−	0.286060i	0.936711	+	0.350104i	$0.113854\pi$
$350$	−2.63344	+	0.254930i	−0.140763	+	0.0136266i
$351$	−4.01426	+	16.5716i	−0.214265	+	0.884525i
$352$	0.554785	+	0.960915i	0.0295701	+	0.0512170i
$353$	6.21075	+	10.7573i	0.330565	+	0.572555i	0.982623	−	0.185614i	$-0.0594275\pi$
$353$	6.21075	+	10.7573i	0.330565	+	0.572555i	−0.652058	+	0.758169i	$0.726094\pi$
$354$	−7.86000	+	7.98752i	−0.417754	+	0.424532i
$355$	8.15232	−	14.1202i	0.432680	−	0.749424i
$356$	−1.42132	−	2.46180i	−0.0753299	−	0.130475i
$357$	19.8916	+	3.15397i	1.05278	+	0.166926i
$358$	11.0539	−	19.1459i	0.584215	−	1.01189i
$359$	11.9318	+	20.6665i	0.629738	+	1.09074i	0.987604	+	0.156965i	$0.0501709\pi$
$359$	11.9318	+	20.6665i	0.629738	+	1.09074i	−0.357867	+	0.933773i	$0.616496\pi$
$360$	2.62188	+	1.45800i	0.138185	+	0.0768432i
$361$	8.72462	−	15.1115i	0.459191	−	0.795342i
$362$	−6.82038			−0.358471
$363$	−4.51062	−	16.3078i	−0.236746	−	0.855940i
$364$	8.64146	−	0.836537i	0.452936	−	0.0438464i
$365$	0.731993	+	1.26785i	0.0383143	+	0.0663622i
$366$	−5.35105	+	5.43786i	−0.279704	+	0.284242i
$367$	−3.98627	−	6.90443i	−0.208082	−	0.360408i	0.743028	−	0.669260i	$-0.233389\pi$
$367$	−3.98627	−	6.90443i	−0.208082	−	0.360408i	−0.951110	+	0.308852i	$0.900055\pi$
$368$	3.14773	−	5.45204i	0.164087	−	0.284207i
$369$	18.5587	−	11.1169i	0.966129	−	0.578721i
$370$	−1.31981			−0.0686138
$371$	8.40343	+	11.7684i	0.436284	+	0.610987i
$372$	3.77766	−	3.83895i	0.195863	−	0.199040i
$373$	2.25724	−	3.90965i	0.116875	−	0.202434i	−0.801653	−	0.597790i	$-0.796046\pi$
$373$	2.25724	−	3.90965i	0.116875	−	0.202434i	0.918528	+	0.395356i	$0.129379\pi$
$374$	4.87649			0.252157
$375$	−1.21485	+	1.23456i	−0.0627346	+	0.0637524i
$376$	11.4617			0.591091
$377$	−21.4526			−1.10487
$378$	−12.7545	+	5.13049i	−0.656022	+	0.263884i
$379$	−7.52115			−0.386336			−0.193168	−	0.981166i	$-0.561876\pi$
$379$	−7.52115			−0.386336			−0.193168	+	0.981166i	$0.561876\pi$
$380$	−1.24529			−0.0638822
$381$	25.4198	−	25.8322i	1.30230	−	1.32343i
$382$	−3.93174			−0.201165
$383$	−8.53489	+	14.7829i	−0.436113	+	0.755369i	−0.997386	−	0.0722614i	$-0.976978\pi$
$383$	−8.53489	+	14.7829i	−0.436113	+	0.755369i	0.561273	+	0.827631i	$0.310312\pi$
$384$	−1.21485	+	1.23456i	−0.0619951	+	0.0630009i
$385$	1.21603	−	2.67195i	0.0619744	−	0.136175i
$386$	−5.85359			−0.297940
$387$	25.6113	+	14.2422i	1.30190	+	0.723971i
$388$	−8.54592	+	14.8020i	−0.433853	+	0.751456i
$389$	−18.3046	−	31.7044i	−0.928078	−	1.60748i	−0.786535	−	0.617545i	$-0.788127\pi$
$389$	−18.3046	−	31.7044i	−0.928078	−	1.60748i	−0.141542	−	0.989932i	$-0.545206\pi$
$390$	3.98645	−	4.05113i	0.201862	−	0.205137i
$391$	−13.8341	−	23.9614i	−0.699620	−	1.21178i
$392$	4.59781	+	5.27827i	0.232225	+	0.266593i
$393$	6.84471	+	24.7466i	0.345270	+	1.24830i
$394$	−1.71845			−0.0865745
$395$	1.70834	−	2.95894i	0.0859560	−	0.148880i
$396$	−2.85559	+	1.71053i	−0.143499	+	0.0859573i
$397$	3.55157	+	6.15150i	0.178248	+	0.308735i	0.941281	−	0.337625i	$-0.109624\pi$
$397$	3.55157	+	6.15150i	0.178248	+	0.308735i	−0.763032	+	0.646360i	$0.776290\pi$
$398$	−2.00694	+	3.47612i	−0.100599	+	0.174242i
$399$	3.59206	−	4.43429i	0.179828	−	0.221992i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	14.8674	−	25.7511i	0.742442	−	1.28595i	−0.208939	−	0.977929i	$-0.567001\pi$
$401$	14.8674	−	25.7511i	0.742442	−	1.28595i	0.951381	−	0.308018i	$-0.0996657\pi$
$402$	6.35660	−	6.45972i	0.317038	−	0.322182i
$403$	−5.10192	−	8.83679i	−0.254145	−	0.440192i
$404$	−3.73642	−	6.47167i	−0.185894	−	0.321977i
$405$	−4.24685	+	7.93500i	−0.211028	+	0.394293i
$406$	−10.0515	−	14.0765i	−0.498848	−	0.698603i
$407$	0.732212	−	1.26823i	0.0362944	−	0.0628638i
$408$	2.02930	+	7.33678i	0.100465	+	0.363225i
$409$	−34.4783			−1.70484			−0.852422	−	0.522855i	$-0.824867\pi$
$409$	−34.4783			−1.70484			−0.852422	+	0.522855i	$0.824867\pi$
$410$	−7.21119			−0.356135
$411$	−20.7987	−	5.39399i	−1.02592	−	0.266066i
$412$	2.48518	−	4.30445i	0.122436	−	0.212065i
$413$	−7.09068	+	15.5802i	−0.348910	+	0.766651i
$414$	16.5060	+	9.17877i	0.811223	+	0.451112i
$415$	4.06648	+	7.04336i	0.199616	+	0.345745i
$416$	1.64072	+	2.84181i	0.0804428	+	0.139331i
$417$	38.6654	+	10.0276i	1.89345	+	0.491055i
$418$	0.690870	−	1.19662i	0.0337915	−	0.0585287i
$419$	−6.08528	−	10.5400i	−0.297285	−	0.514913i	0.678229	−	0.734851i	$-0.262748\pi$
$419$	−6.08528	−	10.5400i	−0.297285	−	0.514913i	−0.975514	+	0.219938i	$0.929415\pi$
$420$	4.52604	+	0.717638i	0.220848	+	0.0350171i
$421$	−4.27799	+	7.40969i	−0.208496	+	0.361126i	−0.951241	−	0.308449i	$-0.900190\pi$
$421$	−4.27799	+	7.40969i	−0.208496	+	0.361126i	0.742745	+	0.669575i	$0.233524\pi$
$422$	2.32892	+	4.03380i	0.113370	+	0.196362i
$423$	0.553333	+	34.3806i	0.0269040	+	1.67164i
$424$	−2.73283	+	4.73340i	−0.132718	+	0.229874i
$425$	−4.39494			−0.213186
$426$	−19.8077	+	20.1291i	−0.959687	+	0.975256i
$427$	−4.82730	+	10.6069i	−0.233610	+	0.513305i
$428$	−3.51531	−	6.08870i	−0.169919	−	0.294308i
$429$	1.68117	+	6.07815i	0.0811676	+	0.293456i
$430$	−4.88416	−	8.45961i	−0.235535	−	0.407959i
$431$	−12.6727	+	21.9497i	−0.610422	+	1.05728i	0.380747	+	0.924679i	$0.375667\pi$
$431$	−12.6727	+	21.9497i	−0.610422	+	1.05728i	−0.991169	+	0.132603i	$0.957667\pi$
$432$	−3.76185	−	3.58448i	−0.180992	−	0.172458i
$433$	−17.9795			−0.864041			−0.432020	−	0.901864i	$-0.642199\pi$
$433$	−17.9795			−0.864041			−0.432020	+	0.901864i	$0.642199\pi$
$434$	3.40792	−	7.48813i	0.163585	−	0.359442i
$435$	−10.9608	−	2.84261i	−0.525531	−	0.136293i
$436$	−5.12829	+	8.88245i	−0.245600	+	0.425392i
$437$	−7.83971			−0.375024
$438$	−0.675974	−	2.44394i	−0.0322993	−	0.116776i
$439$	−4.23398			−0.202077			−0.101038	−	0.994883i	$-0.532217\pi$
$439$	−4.23398			−0.202077			−0.101038	+	0.994883i	$0.532217\pi$
$440$	1.10957			0.0528967
$441$	−15.6108	+	14.0465i	−0.743371	+	0.668879i
$442$	14.4217			0.685970
$443$	−21.7581			−1.03376			−0.516879	−	0.856059i	$-0.672906\pi$
$443$	−21.7581			−1.03376			−0.516879	+	0.856059i	$0.672906\pi$
$444$	2.21278	+	0.573870i	0.105014	+	0.0272346i
$445$	−2.84264			−0.134754
$446$	−13.3981	+	23.2061i	−0.634417	+	1.09884i
$447$	1.26940	+	4.58942i	0.0600405	+	0.217072i
$448$	−1.09594	+	2.40809i	−0.0517785	+	0.113772i
$449$	−29.3888			−1.38694			−0.693471	−	0.720485i	$-0.743919\pi$
$449$	−29.3888			−1.38694			−0.693471	+	0.720485i	$0.743919\pi$
$450$	2.57360	−	1.54161i	0.121321	−	0.0726724i
$451$	4.00066	−	6.92934i	0.188384	−	0.326290i
$452$	3.64304	+	6.30993i	0.171354	+	0.296794i
$453$	30.9782	+	8.03400i	1.45549	+	0.377470i
$454$	6.05706	+	10.4911i	0.284272	+	0.492374i
$455$	3.59627	−	7.90200i	0.168596	−	0.370451i
$456$	2.08784	+	0.541468i	0.0977721	+	0.0253565i
$457$	27.7640			1.29875			0.649373	−	0.760470i	$-0.275032\pi$
$457$	27.7640			1.29875			0.649373	+	0.760470i	$0.275032\pi$
$458$	−8.07886	+	13.9930i	−0.377500	+	0.653850i
$459$	−21.9095	+	6.44130i	−1.02265	+	0.300654i
$460$	−3.14773	−	5.45204i	−0.146764	−	0.254202i
$461$	−4.36929	+	7.56783i	−0.203498	+	0.352469i	−0.949653	−	0.313303i	$-0.898564\pi$
$461$	−4.36929	+	7.56783i	−0.203498	+	0.352469i	0.746155	+	0.665772i	$0.231898\pi$
$462$	−3.20056	+	3.95100i	−0.148904	+	0.183817i
$463$	17.2947	+	29.9553i	0.803753	+	1.39214i	0.917129	+	0.398590i	$0.130500\pi$
$463$	17.2947	+	29.9553i	0.803753	+	1.39214i	−0.113376	+	0.993552i	$0.536166\pi$
$464$	3.26879	−	5.66171i	0.151750	−	0.262838i
$465$	−1.43580	−	5.19103i	−0.0665835	−	0.240728i
$466$	−8.65151	−	14.9849i	−0.400774	−	0.694160i
$467$	−17.2500	−	29.8779i	−0.798236	−	1.38259i	−0.920764	−	0.390121i	$-0.872433\pi$
$467$	−17.2500	−	29.8779i	−0.798236	−	1.38259i	0.122527	−	0.992465i	$-0.460900\pi$
$468$	−8.44510	+	5.05871i	−0.390375	+	0.233839i
$469$	5.73443	−	12.6001i	0.264791	−	0.581820i
$470$	5.73084	−	9.92610i	0.264344	−	0.457857i
$471$	−5.22305	+	5.30779i	−0.240665	+	0.244570i
$472$	−6.46993			−0.297803
$473$	10.8386			0.498361
$474$	−4.15076	+	4.21810i	−0.190651	+	0.193744i
$475$	−0.622647	+	1.07846i	−0.0285690	+	0.0494829i
$476$	6.75720	+	9.46301i	0.309716	+	0.433736i
$477$	−14.3303	−	7.96891i	−0.656139	−	0.364871i
$478$	−0.644644	−	1.11656i	−0.0294853	−	0.0510701i
$479$	−1.60798	−	2.78510i	−0.0734703	−	0.127254i	0.826950	−	0.562276i	$-0.190074\pi$
$479$	−1.60798	−	2.78510i	−0.0734703	−	0.127254i	−0.900420	+	0.435022i	$0.856741\pi$
$480$	0.461735	+	1.66937i	0.0210752	+	0.0761960i
$481$	2.16544	−	3.75065i	0.0987356	−	0.171015i
$482$	−0.200516	−	0.347304i	−0.00913326	−	0.0158193i
$483$	28.4935	+	4.51787i	1.29650	+	0.205570i
$484$	4.88443	−	8.46008i	0.222019	−	0.384549i
$485$	8.54592	+	14.8020i	0.388050	+	0.672123i
$486$	10.5704	−	11.4571i	0.479485	−	0.519706i
$487$	−7.44719	+	12.8989i	−0.337465	+	0.584506i	−0.983955	−	0.178416i	$-0.942903\pi$
$487$	−7.44719	+	12.8989i	−0.337465	+	0.584506i	0.646491	+	0.762922i	$0.276236\pi$
$488$	−4.40470			−0.199391
$489$	20.9154	+	5.42427i	0.945827	+	0.245294i
$490$	6.87002	−	1.34269i	0.310356	−	0.0606564i
$491$	21.6718	+	37.5367i	0.978035	+	1.69401i	0.669532	+	0.742783i	$0.266495\pi$
$491$	21.6718	+	37.5367i	0.978035	+	1.69401i	0.308503	+	0.951223i	$0.400172\pi$
$492$	12.0902	+	3.13551i	0.545067	+	0.141360i
$493$	−14.3661	−	24.8829i	−0.647018	−	1.12067i
$494$	2.04317	−	3.53888i	0.0919268	−	0.159222i
$495$	0.0535664	+	3.32828i	0.00240763	+	0.149595i
$496$	3.10957			0.139624
$497$	−17.8690	+	39.2631i	−0.801534	+	1.76119i
$498$	−3.75528	−	13.5769i	−0.168278	−	0.608397i
$499$	−21.8828	+	37.9022i	−0.979611	+	1.69674i	−0.315817	+	0.948820i	$0.602278\pi$
$499$	−21.8828	+	37.9022i	−0.979611	+	1.69674i	−0.663794	+	0.747915i	$0.731055\pi$
$500$	−1.00000			−0.0447214
$501$	11.4204	+	2.96180i	0.510225	+	0.132323i
$502$	−6.00739			−0.268123
$503$	−22.8379			−1.01829			−0.509147	−	0.860680i	$-0.670039\pi$
$503$	−22.8379			−1.01829			−0.509147	+	0.860680i	$0.670039\pi$
$504$	−7.27625	−	3.17115i	−0.324110	−	0.141254i
$505$	−7.47284			−0.332537
$506$	6.98526			0.310533
$507$	−1.03068	−	3.72635i	−0.0457741	−	0.165493i
$508$	20.9242			0.928363
$509$	−8.35737	+	14.4754i	−0.370434	+	0.641610i	−0.989632	−	0.143624i	$-0.954124\pi$
$509$	−8.35737	+	14.4754i	−0.370434	+	0.641610i	0.619198	+	0.785235i	$0.287458\pi$
$510$	7.36849	+	1.91097i	0.326282	+	0.0846191i
$511$	−2.25087	−	3.15220i	−0.0995728	−	0.139445i
$512$	−1.00000			−0.0441942
$513$	−1.52340	+	6.28885i	−0.0672597	+	0.277660i
$514$	−12.2294	+	21.1819i	−0.539415	+	0.934295i
$515$	−2.48518	−	4.30445i	−0.109510	−	0.189677i
$516$	4.51038	+	16.3070i	0.198558	+	0.717874i
$517$	6.35876	+	11.0137i	0.279658	+	0.484382i
$518$	3.47565	−	0.336460i	0.152711	−	0.0147832i
$519$	−10.2210	+	10.3868i	−0.448650	+	0.455929i
$520$	3.28143			0.143900
$521$	9.95880	−	17.2491i	0.436303	−	0.755699i	−0.561098	−	0.827749i	$-0.689621\pi$
$521$	9.95880	−	17.2491i	0.436303	−	0.755699i	0.997401	+	0.0720506i	$0.0229543\pi$
$522$	17.1407	+	9.53177i	0.750230	+	0.417194i
$523$	−10.8121	−	18.7270i	−0.472778	−	0.818876i	0.526736	−	0.850029i	$-0.323416\pi$
$523$	−10.8121	−	18.7270i	−0.472778	−	0.818876i	−0.999515	+	0.0311527i	$0.990082\pi$
$524$	−7.41195	+	12.8379i	−0.323792	+	0.560825i
$525$	2.88451	−	3.56084i	0.125890	−	0.155408i
$526$	−12.0119	−	20.8052i	−0.523743	−	0.907149i
$527$	6.83318	−	11.8354i	0.297658	−	0.515559i
$528$	−1.86029	−	0.482453i	−0.0809587	−	0.0209961i
$529$	−8.31647	−	14.4045i	−0.361585	−	0.626284i
$530$	2.73283	+	4.73340i	0.118706	+	0.205606i
$531$	−0.312347	−	19.4073i	−0.0135547	−	0.842204i
$532$	3.27941	−	0.317463i	0.142180	−	0.0137638i
$533$	11.8315	−	20.4928i	0.512480	−	0.887642i
$534$	4.76593	+	1.23601i	0.206242	+	0.0534875i
$535$	−7.03063			−0.303960
$536$	5.23241			0.226006
$537$	10.2079	+	36.9060i	0.440504	+	1.59261i
$538$	8.24890	−	14.2875i	0.355635	−	0.615979i
$539$	−2.52117	+	7.34641i	−0.108595	+	0.316432i
$540$	−4.98517	+	1.46562i	−0.214528	+	0.0630701i
$541$	4.89248	+	8.47403i	0.210344	+	0.364327i	0.951822	−	0.306650i	$-0.0992082\pi$
$541$	4.89248	+	8.47403i	0.210344	+	0.364327i	−0.741478	+	0.670977i	$0.765875\pi$
$542$	14.6982	+	25.4580i	0.631342	+	1.09352i
$543$	8.28574	−	8.42017i	0.355575	−	0.361344i
$544$	−2.19747	+	3.80613i	−0.0942157	+	0.163186i
$545$	5.12829	+	8.88245i	0.219672	+	0.380482i
$546$	−9.46533	+	11.6847i	−0.405079	+	0.500058i
$547$	−7.90117	+	13.6852i	−0.337830	+	0.585138i	−0.984024	−	0.178034i	$-0.943026\pi$
$547$	−7.90117	+	13.6852i	−0.337830	+	0.585138i	0.646194	+	0.763173i	$0.276360\pi$
$548$	−6.20268	−	10.7434i	−0.264965	−	0.458934i
$549$	−0.212645	−	13.2124i	−0.00907545	−	0.563891i
$550$	0.554785	−	0.960915i	0.0236561	−	0.0409736i
$551$	−8.14120			−0.346827
$552$	2.90684	+	10.5095i	0.123723	+	0.447313i
$553$	−3.74450	+	8.22769i	−0.159232	+	0.349877i
$554$	−4.86992	−	8.43495i	−0.206903	−	0.358367i
$555$	1.60338	−	1.62939i	0.0680595	−	0.0691637i
$556$	11.5310	+	19.9723i	0.489023	+	0.847013i
$557$	22.5882	−	39.1239i	0.957093	−	1.65773i	0.227589	−	0.973757i	$-0.426916\pi$
$557$	22.5882	−	39.1239i	0.957093	−	1.65773i	0.729504	−	0.683976i	$-0.239751\pi$
$558$	0.150120	+	9.32750i	0.00635509	+	0.394865i
$559$	32.0541			1.35574
$560$	1.53750	+	2.15316i	0.0649711	+	0.0909877i
$561$	−5.92420	+	6.02032i	−0.250120	+	0.254178i
$562$	−11.2140	+	19.4232i	−0.473033	+	0.819318i
$563$	15.1412			0.638128			0.319064	−	0.947733i	$-0.396632\pi$
$563$	15.1412			0.638128			0.319064	+	0.947733i	$0.396632\pi$
$564$	−13.9242	+	14.1501i	−0.586316	+	0.595828i
$565$	7.28608			0.306528
$566$	18.4120			0.773914
$567$	9.16095	−	21.9790i	0.384724	−	0.923032i
$568$	−16.3046			−0.684128
$569$	−24.5423			−1.02887			−0.514434	−	0.857530i	$-0.671998\pi$
$569$	−24.5423			−1.02887			−0.514434	+	0.857530i	$0.671998\pi$
$570$	1.51285	−	1.53739i	0.0633661	−	0.0643941i
$571$	9.54361			0.399387			0.199694	−	0.979858i	$-0.436005\pi$
$571$	9.54361			0.399387			0.199694	+	0.979858i	$0.436005\pi$
$572$	−1.82049	+	3.15318i	−0.0761185	+	0.131841i
$573$	4.77647	−	4.85397i	0.199540	−	0.202777i
$574$	18.9902	−	1.83835i	0.792637	−	0.0767313i
$575$	−6.29547			−0.262539
$576$	−0.0482768	−	2.99961i	−0.00201153	−	0.124984i
$577$	−7.75559	+	13.4331i	−0.322869	+	0.559226i	−0.981079	−	0.193609i	$-0.937981\pi$
$577$	−7.75559	+	13.4331i	−0.322869	+	0.559226i	0.658210	+	0.752835i	$0.271314\pi$
$578$	1.15774	+	2.00526i	0.0481555	+	0.0834078i
$579$	7.11124	−	7.22661i	0.295533	−	0.300328i
$580$	−3.26879	−	5.66171i	−0.135729	−	0.235090i
$581$	−12.5044	−	17.5116i	−0.518770	−	0.726503i
$582$	−7.89190	−	28.5326i	−0.327130	−	1.18272i
$583$	−6.06452			−0.251167
$584$	0.731993	−	1.26785i	0.0302901	−	0.0524640i
$585$	0.158417	+	9.84303i	0.00654974	+	0.406959i
$586$	9.32830	+	16.1571i	0.385348	+	0.667443i
$587$	5.40254	−	9.35747i	0.222987	−	0.386224i	−0.732727	−	0.680523i	$-0.761753\pi$
$587$	5.40254	−	9.35747i	0.222987	−	0.386224i	0.955713	+	0.294299i	$0.0950861\pi$
$588$	−12.1020	−	0.736033i	−0.499078	−	0.0303535i
$589$	−1.93616	−	3.35353i	−0.0797782	−	0.138180i
$590$	−3.23497	+	5.60312i	−0.133181	+	0.230677i
$591$	2.08766	−	2.12153i	0.0858750	−	0.0872683i
$592$	0.659906	+	1.14299i	0.0271220	+	0.0469767i
$593$	3.55908	+	6.16452i	0.146154	+	0.253146i	0.929803	−	0.368058i	$-0.119977\pi$
$593$	3.55908	+	6.16452i	0.146154	+	0.253146i	−0.783649	+	0.621204i	$0.786644\pi$
$594$	1.35736	−	5.60343i	0.0556933	−	0.229912i
$595$	11.5738	−	1.12040i	0.474480	−	0.0459320i
$596$	−1.37460	+	2.38087i	−0.0563056	+	0.0975242i
$597$	−1.85335	−	6.70065i	−0.0758524	−	0.274239i
$598$	20.6582			0.844775
$599$	−22.4482			−0.917208			−0.458604	−	0.888641i	$-0.651650\pi$
$599$	−22.4482			−0.917208			−0.458604	+	0.888641i	$0.651650\pi$
$600$	1.67659	+	0.434811i	0.0684463	+	0.0177511i
$601$	−7.16754	+	12.4145i	−0.292370	+	0.506400i	−0.974370	−	0.224953i	$-0.927777\pi$
$601$	−7.16754	+	12.4145i	−0.292370	+	0.506400i	0.682000	+	0.731353i	$0.261111\pi$
$602$	15.0188	+	21.0328i	0.612119	+	0.857232i
$603$	0.252604	+	15.6952i	0.0102868	+	0.639158i
$604$	9.23849	+	16.0015i	0.375909	+	0.651093i
$605$	−4.88443	−	8.46008i	−0.198580	−	0.343951i
$606$	12.5289	+	3.24927i	0.508950	+	0.131993i
$607$	16.8347	−	29.1586i	0.683300	−	1.18351i	−0.290667	−	0.956824i	$-0.593877\pi$
$607$	16.8347	−	29.1586i	0.683300	−	1.18351i	0.973968	−	0.226687i	$-0.0727893\pi$
$608$	0.622647	+	1.07846i	0.0252517	+	0.0437371i
$609$	29.5893	+	4.69161i	1.19902	+	0.190114i
$610$	−2.20235	+	3.81458i	−0.0891705	+	0.154448i
$611$	18.8054	+	32.5719i	0.760784	+	1.31772i
$612$	−11.5230	−	6.40780i	−0.465789	−	0.259020i
$613$	2.64921	−	4.58857i	0.107001	−	0.185331i	−0.807553	−	0.589795i	$-0.799209\pi$
$613$	2.64921	−	4.58857i	0.107001	−	0.185331i	0.914554	+	0.404464i	$0.132542\pi$
$614$	−25.9429			−1.04697
$615$	8.76052	−	8.90265i	0.353258	−	0.358989i
$616$	−2.92199	+	0.282863i	−0.117730	+	0.0113969i
$617$	2.92877	+	5.07278i	0.117908	+	0.204222i	0.918938	−	0.394401i	$-0.129048\pi$
$617$	2.92877	+	5.07278i	0.117908	+	0.204222i	−0.801031	+	0.598623i	$0.795715\pi$
$618$	2.29499	+	8.29737i	0.0923179	+	0.333769i
$619$	−13.9169	−	24.1049i	−0.559369	−	0.968856i	−0.997549	−	0.0699689i	$-0.977710\pi$
$619$	−13.9169	−	24.1049i	−0.559369	−	0.968856i	0.438180	−	0.898887i	$-0.355623\pi$
$620$	1.55478	−	2.69297i	0.0624417	−	0.108152i
$621$	−31.3840	+	9.22675i	−1.25940	+	0.370257i
$622$	−9.38608			−0.376347
$623$	7.48593	−	0.724676i	0.299918	−	0.0290335i
$624$	−5.50161	−	1.42680i	−0.220240	−	0.0571179i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−0.317071			−0.0126727
$627$	0.637998	+	2.30664i	0.0254792	+	0.0921182i
$628$	−4.29934			−0.171562
$629$	5.80049			0.231281
$630$	−6.38442	+	4.71584i	−0.254361	+	0.187884i
$631$	27.1850			1.08222			0.541109	−	0.840952i	$-0.318005\pi$
$631$	27.1850			1.08222			0.541109	+	0.840952i	$0.318005\pi$
$632$	−3.41668			−0.135908
$633$	−7.80926	−	2.02528i	−0.310390	−	0.0804976i
$634$	−4.25665			−0.169053
$635$	10.4621	−	18.1209i	0.415177	−	0.719107i
$636$	−2.52368	−	9.12421i	−0.100071	−	0.361798i
$637$	−7.45611	+	21.7262i	−0.295422	+	0.860825i
$638$	7.25390			0.287185
$639$	−0.787136	−	48.9076i	−0.0311386	−	1.93476i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−6.21099	−	10.7578i	−0.245319	−	0.424906i	0.716902	−	0.697174i	$-0.245560\pi$
$641$	−6.21099	−	10.7578i	−0.245319	−	0.424906i	−0.962221	+	0.272268i	$0.912226\pi$
$642$	11.7874	+	3.05700i	0.465213	+	0.120650i
$643$	15.6754	+	27.1506i	0.618177	+	1.07071i	0.989818	+	0.142337i	$0.0454618\pi$
$643$	15.6754	+	27.1506i	0.618177	+	1.07071i	−0.371641	+	0.928376i	$0.621205\pi$
$644$	9.67926	+	13.5552i	0.381416	+	0.534148i
$645$	16.3774	+	4.24738i	0.644860	+	0.167240i
$646$	5.47299			0.215332
$647$	0.918400	−	1.59071i	0.0361060	−	0.0625374i	−0.847408	−	0.530943i	$-0.821838\pi$
$647$	0.918400	−	1.59071i	0.0361060	−	0.0625374i	0.883514	+	0.468405i	$0.155171\pi$
$648$	8.99534	−	0.289623i	0.353370	−	0.0113775i
$649$	−3.58942	−	6.21706i	−0.140897	−	0.244041i
$650$	1.64072	−	2.84181i	0.0643542	−	0.111465i
$651$	5.10444	+	13.3042i	0.200059	+	0.521434i
$652$	6.23750	+	10.8037i	0.244279	+	0.423104i
$653$	−7.84443	+	13.5870i	−0.306976	+	0.531699i	−0.977699	−	0.210009i	$-0.932651\pi$
$653$	−7.84443	+	13.5870i	−0.306976	+	0.531699i	0.670723	+	0.741708i	$0.265984\pi$
$654$	−4.73582	−	17.1220i	−0.185185	−	0.669524i
$655$	7.41195	+	12.8379i	0.289609	+	0.501617i
$656$	3.60559	+	6.24507i	0.140775	+	0.243829i
$657$	3.83839	+	2.13449i	0.149750	+	0.0832743i
$658$	−12.5614	+	27.6008i	−0.489693	+	1.07599i
$659$	7.26080	−	12.5761i	0.282841	−	0.489894i	−0.689243	−	0.724531i	$-0.742057\pi$
$659$	7.26080	−	12.5761i	0.282841	−	0.489894i	0.972083	+	0.234636i	$0.0753899\pi$
$660$	−1.34796	+	1.36983i	−0.0524693	+	0.0533206i
$661$	−48.7637			−1.89669			−0.948344	−	0.317244i	$-0.897242\pi$
$661$	−48.7637			−1.89669			−0.948344	+	0.317244i	$0.897242\pi$
$662$	−6.77455			−0.263300
$663$	−17.5202	+	17.8045i	−0.680428	+	0.691468i
$664$	4.06648	−	7.04336i	0.157810	−	0.273335i
$665$	1.36477	−	2.99878i	0.0529236	−	0.116288i
$666$	−3.39667	+	2.03464i	−0.131618	+	0.0788408i
$667$	−20.5786	−	35.6431i	−0.796805	−	1.38011i
$668$	3.40584	+	5.89909i	0.131776	+	0.228243i
$669$	−12.3727	−	44.7327i	−0.478357	−	1.72947i
$670$	2.61620	−	4.53140i	0.101073	−	0.175063i
$671$	−2.44366	−	4.23254i	−0.0943364	−	0.163395i
$672$	−1.64153	−	4.27848i	−0.0633232	−	0.165046i
$673$	−19.7658	+	34.2354i	−0.761915	+	1.31968i	0.179947	+	0.983676i	$0.442407\pi$
$673$	−19.7658	+	34.2354i	−0.761915	+	1.31968i	−0.941862	+	0.335999i	$0.890926\pi$
$674$	−7.69796	−	13.3333i	−0.296514	−	0.513578i
$675$	−1.22332	+	5.05010i	−0.0470858	+	0.194378i
$676$	1.11609	−	1.93313i	0.0429267	−	0.0743512i
$677$	44.9411			1.72723			0.863614	−	0.504153i	$-0.168195\pi$
$677$	44.9411			1.72723			0.863614	+	0.504153i	$0.168195\pi$
$678$	−12.2157	−	3.16807i	−0.469142	−	0.121669i
$679$	−26.2786	−	36.8015i	−1.00848	−	1.41231i
$680$	2.19747	+	3.80613i	0.0842691	+	0.145958i
$681$	−20.3104	−	5.26736i	−0.778295	−	0.201846i
$682$	1.72514	+	2.98803i	0.0660591	+	0.114418i
$683$	17.3244	−	30.0068i	0.662900	−	1.14818i	−0.316950	−	0.948442i	$-0.602659\pi$
$683$	17.3244	−	30.0068i	0.662900	−	1.14818i	0.979850	−	0.199734i	$-0.0640079\pi$
$684$	−3.20489	+	1.91976i	−0.122542	+	0.0734039i
$685$	−12.4054			−0.473985
$686$	−17.7495	+	5.28726i	−0.677679	+	0.201869i
$687$	−7.46058	−	26.9732i	−0.284639	−	1.02909i
$688$	−4.88416	+	8.45961i	−0.186207	+	0.322520i
$689$	−17.9352			−0.683276
$690$	10.5549	+	2.73734i	0.401818	+	0.104209i
$691$	45.7430			1.74015			0.870073	−	0.492923i	$-0.164071\pi$
$691$	45.7430			1.74015			0.870073	+	0.492923i	$0.164071\pi$
$692$	−8.41334			−0.319827
$693$	−0.989543	−	8.75117i	−0.0375896	−	0.332429i
$694$	4.27257			0.162184
$695$	23.0620			0.874791
$696$	3.01863	+	10.9136i	0.114421	+	0.413681i
$697$	31.6927			1.20045
$698$	−3.08538	+	5.34404i	−0.116783	+	0.202275i
$699$	29.0100	+	7.52355i	1.09726	+	0.284567i
$700$	2.63344	−	0.254930i	0.0995347	−	0.00963546i
$701$	24.6901			0.932533			0.466267	−	0.884644i	$-0.345599\pi$
$701$	24.6901			0.932533			0.466267	+	0.884644i	$0.345599\pi$
$702$	4.01426	−	16.5716i	0.151509	−	0.625453i
$703$	0.821777	−	1.42336i	0.0309939	−	0.0536830i
$704$	−0.554785	−	0.960915i	−0.0209092	−	0.0362159i
$705$	5.29226	+	19.1338i	0.199318	+	0.720620i
$706$	−6.21075	−	10.7573i	−0.233745	−	0.404857i
$707$	19.6793	−	1.90505i	0.740115	−	0.0716469i
$708$	7.86000	−	7.98752i	0.295397	−	0.300189i
$709$	−36.8564			−1.38417			−0.692086	−	0.721815i	$-0.743308\pi$
$709$	−36.8564			−1.38417			−0.692086	+	0.721815i	$0.743308\pi$
$710$	−8.15232	+	14.1202i	−0.305951	+	0.529923i
$711$	−0.164947	−	10.2487i	−0.00618598	−	0.384357i
$712$	1.42132	+	2.46180i	0.0532663	+	0.0922599i
$713$	9.78810	−	16.9535i	0.366567	−	0.634913i
$714$	−19.8916	−	3.15397i	−0.744426	−	0.118034i
$715$	1.82049	+	3.15318i	0.0680825	+	0.117922i
$716$	−11.0539	+	19.1459i	−0.413103	+	0.715515i
$717$	2.16160	+	0.560597i	0.0807265	+	0.0209359i
$718$	−11.9318	−	20.6665i	−0.445292	−	0.771268i
$719$	−20.1527	−	34.9055i	−0.751569	−	1.30176i	−0.947062	−	0.321051i	$-0.895964\pi$
$719$	−20.1527	−	34.9055i	−0.751569	−	1.30176i	0.195492	−	0.980705i	$-0.437369\pi$
$720$	−2.62188	−	1.45800i	−0.0977116	−	0.0543363i
$721$	7.64190	+	10.7020i	0.284599	+	0.398562i
$722$	−8.72462	+	15.1115i	−0.324697	+	0.562391i
$723$	0.672365	+	0.174373i	0.0250055	+	0.00648501i
$724$	6.82038			0.253477
$725$	−6.53758			−0.242800
$726$	4.51062	+	16.3078i	0.167405	+	0.605241i
$727$	−6.90054	+	11.9521i	−0.255927	+	0.443278i	−0.965147	−	0.261709i	$-0.915714\pi$
$727$	−6.90054	+	11.9521i	−0.255927	+	0.443278i	0.709220	+	0.704987i	$0.249047\pi$
$728$	−8.64146	+	0.836537i	−0.320274	+	0.0310041i
$729$	1.30302	+	26.9685i	0.0482601	+	0.998835i
$730$	−0.731993	−	1.26785i	−0.0270923	−	0.0469252i
$731$	21.4656	+	37.1795i	0.793933	+	1.37513i
$732$	5.35105	−	5.43786i	0.197780	−	0.200989i
$733$	−14.8346	+	25.6942i	−0.547928	+	0.949038i	0.450489	+	0.892782i	$0.351250\pi$
$733$	−14.8346	+	25.6942i	−0.547928	+	0.949038i	−0.998416	+	0.0562563i	$0.982084\pi$
$734$	3.98627	+	6.90443i	0.147136	+	0.254847i
$735$	−6.68842	+	10.1126i	−0.246706	+	0.373010i
$736$	−3.14773	+	5.45204i	−0.116027	+	0.200965i
$737$	2.90286	+	5.02790i	0.106928	+	0.185205i
$738$	−18.5587	+	11.1169i	−0.683156	+	0.409218i
$739$	22.7417	−	39.3898i	0.836568	−	1.44898i	−0.0561788	−	0.998421i	$-0.517892\pi$
$739$	22.7417	−	39.3898i	0.836568	−	1.44898i	0.892747	−	0.450558i	$-0.148775\pi$
$740$	1.31981			0.0485173
$741$	1.88681	+	6.82163i	0.0693137	+	0.250599i
$742$	−8.40343	−	11.7684i	−0.308499	−	0.432033i
$743$	−16.8783	−	29.2341i	−0.619206	−	1.07250i	−0.989631	−	0.143634i	$-0.954121\pi$
$743$	−16.8783	−	29.2341i	−0.619206	−	1.07250i	0.370424	−	0.928863i	$-0.379212\pi$
$744$	−3.77766	+	3.83895i	−0.138496	+	0.140743i
$745$	1.37460	+	2.38087i	0.0503613	+	0.0872283i
$746$	−2.25724	+	3.90965i	−0.0826433	+	0.143142i
$747$	21.3237	+	11.8578i	0.780192	+	0.433856i
$748$	−4.87649			−0.178302
$749$	18.5147	−	1.79232i	0.676514	−	0.0654899i
$750$	1.21485	−	1.23456i	0.0443601	−	0.0450798i
$751$	16.2454	−	28.1379i	0.592805	−	1.02677i	−0.401048	−	0.916057i	$-0.631354\pi$
$751$	16.2454	−	28.1379i	0.592805	−	1.02677i	0.993853	−	0.110711i	$-0.0353127\pi$
$752$	−11.4617			−0.417964
$753$	7.29808	−	7.41648i	0.265957	−	0.270272i
$754$	21.4526			0.781259
$755$	18.4770			0.672446
$756$	12.7545	−	5.13049i	0.463878	−	0.186594i
$757$	18.6647			0.678382			0.339191	−	0.940718i	$-0.389847\pi$
$757$	18.6647			0.678382			0.339191	+	0.940718i	$0.389847\pi$
$758$	7.52115			0.273181
$759$	−8.48605	+	8.62372i	−0.308024	+	0.313021i
$760$	1.24529			0.0451715
$761$	−16.4080	+	28.4195i	−0.594789	+	1.03021i	0.398787	+	0.917044i	$0.369431\pi$
$761$	−16.4080	+	28.4195i	−0.594789	+	1.03021i	−0.993577	+	0.113162i	$0.963902\pi$
$762$	−25.4198	+	25.8322i	−0.920863	+	0.935803i
$763$	−15.7694	−	22.0841i	−0.570892	−	0.799497i
$764$	3.93174			0.142245
$765$	−11.3108	+	6.77530i	−0.408943	+	0.244961i
$766$	8.53489	−	14.7829i	0.308378	−	0.534127i
$767$	−10.6153	−	18.3863i	−0.383297	−	0.663890i
$768$	1.21485	−	1.23456i	0.0438371	−	0.0445483i
$769$	13.2690	+	22.9826i	0.478493	+	0.828775i	0.999696	−	0.0246581i	$-0.00784972\pi$
$769$	13.2690	+	22.9826i	0.478493	+	0.828775i	−0.521203	+	0.853433i	$0.674516\pi$
$770$	−1.21603	+	2.67195i	−0.0438226	+	0.0962902i
$771$	−11.2935	−	40.8308i	−0.406725	−	1.47048i
$772$	5.85359			0.210675
$773$	24.6606	−	42.7135i	0.886981	−	1.53630i	0.0435555	−	0.999051i	$-0.486131\pi$
$773$	24.6606	−	42.7135i	0.886981	−	1.53630i	0.843426	−	0.537246i	$-0.180535\pi$
$774$	−25.6113	−	14.2422i	−0.920581	−	0.511925i
$775$	−1.55478	−	2.69297i	−0.0558495	−	0.0967342i
$776$	8.54592	−	14.8020i	0.306781	−	0.531360i
$777$	−3.80701	+	4.69965i	−0.136576	+	0.168599i
$778$	18.3046	+	31.7044i	0.656250	+	1.13666i
$779$	4.49002	−	7.77695i	0.160872	−	0.278638i
$780$	−3.98645	+	4.05113i	−0.142738	+	0.145054i
$781$	−9.04557	−	15.6674i	−0.323676	−	0.560623i
$782$	13.8341	+	23.9614i	0.494706	+	0.856856i
$783$	−32.5910	+	9.58159i	−1.16471	+	0.342418i
$784$	−4.59781	−	5.27827i	−0.164208	−	0.188510i
$785$	−2.14967	+	3.72333i	−0.0767249	+	0.132891i
$786$	−6.84471	−	24.7466i	−0.244143	−	0.882681i
$787$	−40.4417			−1.44159			−0.720795	−	0.693149i	$-0.756223\pi$
$787$	−40.4417			−1.44159			−0.720795	+	0.693149i	$0.756223\pi$
$788$	1.71845			0.0612174
$789$	40.2779	+	10.4458i	1.43393	+	0.371880i
$790$	−1.70834	+	2.95894i	−0.0607801	+	0.105274i
$791$	−19.1875	+	1.85744i	−0.682227	+	0.0660430i
$792$	2.85559	−	1.71053i	0.101469	−	0.0607810i
$793$	−7.22686	−	12.5173i	−0.256633	−	0.444502i
$794$	−3.55157	−	6.15150i	−0.126041	−	0.218309i
$795$	−9.16364	−	2.37653i	−0.325001	−	0.0842868i
$796$	2.00694	−	3.47612i	0.0711340	−	0.123208i
$797$	−21.8594	−	37.8616i	−0.774300	−	1.34113i	−0.935187	−	0.354154i	$-0.884769\pi$
$797$	−21.8594	−	37.8616i	−0.774300	−	1.34113i	0.160887	−	0.986973i	$-0.448565\pi$
$798$	−3.59206	+	4.43429i	−0.127158	+	0.156972i
$799$	−25.1867	+	43.6246i	−0.891041	+	1.54333i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−7.31583	+	4.38226i	−0.258492	+	0.154840i
$802$	−14.8674	+	25.7511i	−0.524986	+	0.909302i
$803$	1.62439			0.0573236
$804$	−6.35660	+	6.45972i	−0.224180	+	0.227817i
$805$	16.5787	−	1.60491i	0.584324	−	0.0565655i
$806$	5.10192	+	8.83679i	0.179708	+	0.311263i
$807$	7.61762	+	27.5410i	0.268153	+	0.969488i
$808$	3.73642	+	6.47167i	0.131447	+	0.227672i
$809$	−3.41634	+	5.91727i	−0.120112	+	0.208040i	−0.919812	−	0.392360i	$-0.871659\pi$
$809$	−3.41634	+	5.91727i	−0.120112	+	0.208040i	0.799700	+	0.600400i	$0.204992\pi$
$810$	4.24685	−	7.93500i	0.149219	−	0.278808i
$811$	−43.5544			−1.52940			−0.764701	−	0.644386i	$-0.777113\pi$
$811$	−43.5544			−1.52940			−0.764701	+	0.644386i	$0.777113\pi$
$812$	10.0515	+	14.0765i	0.352739	+	0.493987i
$813$	−49.2856	−	12.7819i	−1.72852	−	0.448280i
$814$	−0.732212	+	1.26823i	−0.0256640	+	0.0444514i
$815$	12.4750			0.436980
$816$	−2.02930	−	7.33678i	−0.0710396	−	0.256839i
$817$	12.1644			0.425579
$818$	34.4783			1.20551
$819$	−2.92647	−	25.8806i	−0.102259	−	0.904343i
$820$	7.21119			0.251826
$821$	4.94619			0.172623			0.0863116	−	0.996268i	$-0.472492\pi$
$821$	4.94619			0.172623			0.0863116	+	0.996268i	$0.472492\pi$
$822$	20.7987	+	5.39399i	0.725436	+	0.188137i
$823$	49.7275			1.73339			0.866696	−	0.498836i	$-0.166239\pi$
$823$	49.7275			1.73339			0.866696	+	0.498836i	$0.166239\pi$
$824$	−2.48518	+	4.30445i	−0.0865752	+	0.149953i
$825$	0.512327	+	1.85228i	0.0178369	+	0.0644882i
$826$	7.09068	−	15.5802i	0.246716	−	0.542104i
$827$	−34.5238			−1.20051			−0.600255	−	0.799808i	$-0.704934\pi$
$827$	−34.5238			−1.20051			−0.600255	+	0.799808i	$0.704934\pi$
$828$	−16.5060	−	9.17877i	−0.573622	−	0.318984i
$829$	−12.9897	+	22.4988i	−0.451150	+	0.781414i	−0.998458	−	0.0555170i	$-0.982319\pi$
$829$	−12.9897	+	22.4988i	−0.451150	+	0.781414i	0.547308	+	0.836931i	$0.315653\pi$
$830$	−4.06648	−	7.04336i	−0.141150	−	0.244478i
$831$	16.3297	+	4.23500i	0.566470	+	0.146910i
$832$	−1.64072	−	2.84181i	−0.0568816	−	0.0985219i
$833$	−30.1933	+	5.90103i	−1.04614	+	0.204458i
$834$	−38.6654	−	10.0276i	−1.33887	−	0.347228i
$835$	6.81169			0.235728
$836$	−0.690870	+	1.19662i	−0.0238942	+	0.0413860i
$837$	−11.6977	−	11.1462i	−0.404333	−	0.385269i
$838$	6.08528	+	10.5400i	0.210212	+	0.364098i
$839$	−12.0636	+	20.8948i	−0.416483	+	0.721370i	−0.995583	−	0.0938866i	$-0.970071\pi$
$839$	−12.0636	+	20.8948i	−0.416483	+	0.721370i	0.579100	+	0.815257i	$0.303404\pi$
$840$	−4.52604	−	0.717638i	−0.156163	−	0.0247609i
$841$	−6.86997	−	11.8991i	−0.236895	−	0.410315i
$842$	4.27799	−	7.40969i	0.147429	−	0.255355i
$843$	−10.3558	−	37.4406i	−0.356672	−	1.28952i
$844$	−2.32892	−	4.03380i	−0.0801646	−	0.138849i
$845$	−1.11609	−	1.93313i	−0.0383948	−	0.0665017i
$846$	−0.553333	−	34.3806i	−0.0190240	−	1.18203i
$847$	15.0196	+	21.0339i	0.516079	+	0.722734i
$848$	2.73283	−	4.73340i	0.0938457	−	0.162545i
$849$	−22.3678	+	22.7307i	−0.767662	+	0.780117i
$850$	4.39494			0.150745
$851$	8.30884			0.284823
$852$	19.8077	−	20.1291i	0.678601	−	0.689610i
$853$	2.39457	−	4.14752i	0.0819886	−	0.142008i	−0.822115	−	0.569321i	$-0.807206\pi$
$853$	2.39457	−	4.14752i	0.0819886	−	0.142008i	0.904104	+	0.427312i	$0.140540\pi$
$854$	4.82730	−	10.6069i	0.165187	−	0.362961i
$855$	0.0601187	+	3.73540i	0.00205602	+	0.127748i
$856$	3.51531	+	6.08870i	0.120151	+	0.208107i
$857$	14.5259	+	25.1597i	0.496197	+	0.859438i	0.999990	−	0.00438620i	$-0.00139618\pi$
$857$	14.5259	+	25.1597i	0.496197	+	0.859438i	−0.503794	+	0.863824i	$0.668063\pi$
$858$	−1.68117	−	6.07815i	−0.0573941	−	0.207505i
$859$	−10.8654	+	18.8194i	−0.370722	+	0.642109i	−0.989677	−	0.143318i	$-0.954223\pi$
$859$	−10.8654	+	18.8194i	−0.370722	+	0.642109i	0.618955	+	0.785426i	$0.287556\pi$
$860$	4.88416	+	8.45961i	0.166548	+	0.288470i
$861$	−20.8008	+	25.6779i	−0.708888	+	0.875101i
$862$	12.6727	−	21.9497i	0.431633	−	0.747611i
$863$	−2.46678	−	4.27259i	−0.0839703	−	0.145441i	0.820982	−	0.570955i	$-0.193427\pi$
$863$	−2.46678	−	4.27259i	−0.0839703	−	0.145441i	−0.904952	+	0.425514i	$0.860093\pi$
$864$	3.76185	+	3.58448i	0.127981	+	0.121946i
$865$	−4.20667	+	7.28617i	−0.143031	+	0.247737i
$866$	17.9795			0.610969
$867$	−3.88209	−	1.00679i	−0.131843	−	0.0341925i
$868$	−3.40792	+	7.48813i	−0.115672	+	0.254164i
$869$	−1.89552	−	3.28315i	−0.0643013	−	0.111373i
$870$	10.9608	+	2.84261i	0.371606	+	0.0963736i
$871$	8.58490	+	14.8695i	0.290888	+	0.503833i
$872$	5.12829	−	8.88245i	0.173666	−	0.300798i
$873$	44.8127	+	24.9198i	1.51668	+	0.843409i
$874$	7.83971			0.265182
$875$	1.09594	−	2.40809i	0.0370497	−	0.0814084i
$876$	0.675974	+	2.44394i	0.0228390	+	0.0825730i
$877$	13.0736	−	22.6442i	0.441465	−	0.764639i	−0.556334	−	0.830959i	$-0.687792\pi$
$877$	13.0736	−	22.6442i	0.441465	−	0.764639i	0.997798	+	0.0663196i	$0.0211257\pi$
$878$	4.23398			0.142890
$879$	−31.2794	−	8.11210i	−1.05503	−	0.273614i
$880$	−1.10957			−0.0374036
$881$	39.6778			1.33678			0.668389	−	0.743812i	$-0.266984\pi$
$881$	39.6778			1.33678			0.668389	+	0.743812i	$0.266984\pi$
$882$	15.6108	−	14.0465i	0.525643	−	0.472969i
$883$	−26.5578			−0.893742			−0.446871	−	0.894598i	$-0.647462\pi$
$883$	−26.5578			−0.893742			−0.446871	+	0.894598i	$0.647462\pi$
$884$	−14.4217			−0.485054
$885$	−2.98739	−	10.8007i	−0.100420	−	0.363062i
$886$	21.7581			0.730977
$887$	−17.4629	+	30.2467i	−0.586348	+	1.01558i	0.408358	+	0.912822i	$0.366101\pi$
$887$	−17.4629	+	30.2467i	−0.586348	+	1.01558i	−0.994706	+	0.102762i	$0.967232\pi$
$888$	−2.21278	−	0.573870i	−0.0742560	−	0.0192578i
$889$	−22.9318	+	50.3875i	−0.769108	+	1.68994i
$890$	2.84264			0.0952856
$891$	5.26878	+	8.48308i	0.176511	+	0.284194i
$892$	13.3981	−	23.2061i	0.448600	−	0.776999i
$893$	7.13657	+	12.3609i	0.238816	+	0.413642i
$894$	−1.26940	−	4.58942i	−0.0424550	−	0.153493i
$895$	11.0539	+	19.1459i	0.369490	+	0.639976i
$896$	1.09594	−	2.40809i	0.0366129	−	0.0804487i
$897$	−25.0966	+	25.5038i	−0.837951	+	0.851545i
$898$	29.3888			0.980716
$899$	10.1645	−	17.6055i	0.339006	−	0.587176i
$900$	−2.57360	+	1.54161i	−0.0857867	+	0.0513872i
$901$	−12.0106	−	20.8030i	−0.400131	−	0.693048i
$902$	−4.00066	+	6.92934i	−0.133207	+	0.230722i
$903$	−44.2118	−	7.01011i	−1.47128	−	0.233282i
$904$	−3.64304	−	6.30993i	−0.121166	−	0.209865i
$905$	3.41019	−	5.90662i	0.113359	−	0.196343i
$906$	−30.9782	−	8.03400i	−1.02918	−	0.266912i
$907$	23.8443	+	41.2996i	0.791737	+	1.37133i	0.924890	+	0.380234i	$0.124157\pi$
$907$	23.8443	+	41.2996i	0.791737	+	1.37133i	−0.133153	+	0.991096i	$0.542510\pi$
$908$	−6.05706	−	10.4911i	−0.201011	−	0.348161i
$909$	−19.2321	+	11.5202i	−0.637889	+	0.382102i
$910$	−3.59627	+	7.90200i	−0.119215	+	0.261949i
$911$	12.1806	−	21.0974i	0.403561	−	0.698989i	−0.590592	−	0.806971i	$-0.701106\pi$
$911$	12.1806	−	21.0974i	0.403561	−	0.698989i	0.994153	+	0.107982i	$0.0344389\pi$
$912$	−2.08784	−	0.541468i	−0.0691353	−	0.0179298i
$913$	9.02409			0.298654
$914$	−27.7640			−0.918352
$915$	−2.03380	−	7.35307i	−0.0672355	−	0.243085i
$916$	8.07886	−	13.9930i	0.266933	−	0.462341i
$917$	−22.7917	−	31.9182i	−0.752648	−	1.05403i
$918$	21.9095	−	6.44130i	0.723122	−	0.212595i
$919$	−14.7746	−	25.5904i	−0.487369	−	0.844149i	0.512525	−	0.858672i	$-0.328710\pi$
$919$	−14.7746	−	25.5904i	−0.487369	−	0.844149i	−0.999895	+	0.0145236i	$0.995377\pi$
$920$	3.14773	+	5.45204i	0.103778	+	0.179748i
$921$	31.5167	−	32.0281i	1.03851	−	1.05536i
$922$	4.36929	−	7.56783i	0.143895	−	0.249233i
$923$	−26.7513	−	46.3346i	−0.880530	−	1.52512i
$924$	3.20056	−	3.95100i	0.105291	−	0.129978i
$925$	0.659906	−	1.14299i	0.0216976	−	0.0375813i
$926$	−17.2947	−	29.9553i	−0.568339	−	0.984393i
$927$	−13.0317	−	7.24676i	−0.428016	−	0.238015i
$928$	−3.26879	+	5.66171i	−0.107303	+	0.185855i
$929$	21.3312			0.699854			0.349927	−	0.936777i	$-0.386206\pi$
$929$	21.3312			0.699854			0.349927	+	0.936777i	$0.386206\pi$
$930$	1.43580	+	5.19103i	0.0470817	+	0.170220i
$931$	−2.82957	+	8.24503i	−0.0927353	+	0.270220i
$932$	8.65151	+	14.9849i	0.283390	+	0.490845i
$933$	11.4027	−	11.5877i	0.373307	−	0.379364i
$934$	17.2500	+	29.8779i	0.564438	+	0.977636i
$935$	−2.43824	+	4.22316i	−0.0797391	+	0.138112i
$936$	8.44510	−	5.05871i	0.276037	−	0.165349i
$937$	5.48745			0.179267			0.0896337	−	0.995975i	$-0.471430\pi$
$937$	5.48745			0.179267			0.0896337	+	0.995975i	$0.471430\pi$
$938$	−5.73443	+	12.6001i	−0.187236	+	0.411409i
$939$	0.385194	−	0.391444i	0.0125703	−	0.0127743i
$940$	−5.73084	+	9.92610i	−0.186919	+	0.323754i
$941$	−23.8907			−0.778813			−0.389407	−	0.921066i	$-0.627320\pi$
$941$	−23.8907			−0.778813			−0.389407	+	0.921066i	$0.627320\pi$
$942$	5.22305	−	5.30779i	0.170176	−	0.172937i
$943$	45.3978			1.47836
$944$	6.46993			0.210578
$945$	1.93413	−	13.6110i	0.0629173	−	0.442766i
$946$	−10.8386			−0.352394
$947$	6.18056			0.200841			0.100421	−	0.994945i	$-0.467981\pi$
$947$	6.18056			0.200841			0.100421	+	0.994945i	$0.467981\pi$
$948$	4.15076	−	4.21810i	0.134810	−	0.136998i
$949$	4.80397			0.155944
$950$	0.622647	−	1.07846i	0.0202013	−	0.0349897i
$951$	5.17119	−	5.25508i	0.167687	−	0.170408i
$952$	−6.75720	−	9.46301i	−0.219002	−	0.306698i
$953$	5.30086			0.171712			0.0858558	−	0.996308i	$-0.472638\pi$
$953$	5.30086			0.171712			0.0858558	+	0.996308i	$0.472638\pi$
$954$	14.3303	+	7.96891i	0.463960	+	0.258003i
$955$	1.96587	−	3.40499i	0.0636140	−	0.110183i
$956$	0.644644	+	1.11656i	0.0208493	+	0.0361120i
$957$	−8.81240	+	8.95537i	−0.284864	+	0.289486i
$958$	1.60798	+	2.78510i	0.0519513	+	0.0899824i
$959$	32.6688	−	3.16250i	1.05493	−	0.102123i
$960$	−0.461735	−	1.66937i	−0.0149024	−	0.0538787i
$961$	−21.3306			−0.688083
$962$	−2.16544	+	3.75065i	−0.0698166	+	0.120926i
$963$	−18.0940	+	10.8385i	−0.583072	+	0.349266i
$964$	0.200516	+	0.347304i	0.00645819	+	0.0111859i
$965$	2.92679	−	5.06936i	0.0942169	−	0.163188i
$966$	−28.4935	−	4.51787i	−0.916764	−	0.145360i
$967$	3.99630	+	6.92180i	0.128512	+	0.222590i	0.923100	−	0.384559i	$-0.125646\pi$
$967$	3.99630	+	6.92180i	0.128512	+	0.222590i	−0.794588	+	0.607149i	$0.792313\pi$
$968$	−4.88443	+	8.46008i	−0.156991	+	0.271917i
$969$	−6.64886	+	6.75673i	−0.213592	+	0.217057i
$970$	−8.54592	−	14.8020i	−0.274393	−	0.475263i
$971$	−10.4036	−	18.0196i	−0.333869	−	0.578278i	0.649398	−	0.760449i	$-0.275021\pi$
$971$	−10.4036	−	18.0196i	−0.333869	−	0.578278i	−0.983267	+	0.182171i	$0.941688\pi$
$972$	−10.5704	+	11.4571i	−0.339047	+	0.367488i
$973$	−60.7324	+	5.87920i	−1.94699	+	0.188479i
$974$	7.44719	−	12.8989i	0.238624	−	0.413308i
$975$	1.51515	+	5.47793i	0.0485237	+	0.175434i
$976$	4.40470			0.140991
$977$	37.8435			1.21072			0.605360	−	0.795952i	$-0.293029\pi$
$977$	37.8435			1.21072			0.605360	+	0.795952i	$0.293029\pi$
$978$	−20.9154	−	5.42427i	−0.668800	−	0.173449i
$979$	−1.57706	+	2.73154i	−0.0504029	+	0.0873004i
$980$	−6.87002	+	1.34269i	−0.219455	+	0.0428906i
$981$	26.8915	+	14.9541i	0.858579	+	0.477446i
$982$	−21.6718	−	37.5367i	−0.691575	−	1.19784i
$983$	10.9759	+	19.0108i	0.350077	+	0.606351i	0.986263	−	0.165185i	$-0.0528222\pi$
$983$	10.9759	+	19.0108i	0.350077	+	0.606351i	−0.636186	+	0.771536i	$0.719489\pi$
$984$	−12.0902	−	3.13551i	−0.385421	−	0.0999563i
$985$	0.859227	−	1.48822i	0.0273772	−	0.0474188i
$986$	14.3661	+	24.8829i	0.457511	+	0.792432i
$987$	−18.8146	−	49.0386i	−0.598876	−	1.56091i
$988$	−2.04317	+	3.53888i	−0.0650020	+	0.112587i
$989$	30.7481	+	53.2572i	0.977732	+	1.69348i
$990$	−0.0535664	−	3.32828i	−0.00170245	−	0.105780i
$991$	26.5988	−	46.0704i	0.844938	−	1.46348i	−0.0407375	−	0.999170i	$-0.512971\pi$
$991$	26.5988	−	46.0704i	0.844938	−	1.46348i	0.885675	−	0.464305i	$-0.153696\pi$
$992$	−3.10957			−0.0987289
$993$	8.23006	−	8.36358i	0.261173	−	0.265410i
$994$	17.8690	−	39.2631i	0.566770	−	1.24535i
$995$	−2.00694	−	3.47612i	−0.0636242	−	0.110200i
$996$	3.75528	+	13.5769i	0.118991	+	0.430202i
$997$	19.4525	+	33.6927i	0.616067	+	1.06706i	0.990196	+	0.139683i	$0.0446083\pi$
$997$	19.4525	+	33.6927i	0.616067	+	1.06706i	−0.374129	+	0.927377i	$0.622058\pi$
$998$	21.8828	−	37.9022i	0.692689	−	1.19977i
$999$	1.61456	−	6.66518i	0.0510824	−	0.210877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.i.151.7	yes	16
3.2	odd	2		1890.2.i.i.991.3		16
7.2	even	3		630.2.l.i.331.5	yes	16
9.4	even	3		630.2.l.i.571.5	yes	16
9.5	odd	6		1890.2.l.i.361.3		16
21.2	odd	6		1890.2.l.i.1801.3		16
63.23	odd	6		1890.2.i.i.1171.3		16
63.58	even	3	inner	630.2.i.i.121.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.7	✓	16	63.58	even	3	inner
630.2.i.i.151.7	yes	16	1.1	even	1	trivial
630.2.l.i.331.5	yes	16	7.2	even	3
630.2.l.i.571.5	yes	16	9.4	even	3
1890.2.i.i.991.3		16	3.2	odd	2
1890.2.i.i.1171.3		16	63.23	odd	6
1890.2.l.i.361.3		16	9.5	odd	6
1890.2.l.i.1801.3		16	21.2	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.21485 - 1.23456i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.21485 + 1.23456i) q^{6} +(-1.09594 + 2.40809i) q^{7} -1.00000 q^{8} +(-0.0482768 - 2.99961i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.21485 - 1.23456i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.21485 + 1.23456i) q^{6} +(-1.09594 + 2.40809i) q^{7} -1.00000 q^{8} +(-0.0482768 - 2.99961i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.554785 - 0.960915i) q^{11} +(1.21485 - 1.23456i) q^{12} +(-1.64072 - 2.84181i) q^{13} +(1.09594 - 2.40809i) q^{14} +(-0.461735 - 1.66937i) q^{15} +1.00000 q^{16} +(2.19747 - 3.80613i) q^{17} +(0.0482768 + 2.99961i) q^{18} +(-0.622647 - 1.07846i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.64153 + 4.27848i) q^{21} +(0.554785 + 0.960915i) q^{22} +(3.14773 - 5.45204i) q^{23} +(-1.21485 + 1.23456i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.64072 + 2.84181i) q^{26} +(-3.76185 - 3.58448i) q^{27} +(-1.09594 + 2.40809i) q^{28} +(3.26879 - 5.66171i) q^{29} +(0.461735 + 1.66937i) q^{30} +3.10957 q^{31} -1.00000 q^{32} +(-1.86029 - 0.482453i) q^{33} +(-2.19747 + 3.80613i) q^{34} +(1.53750 + 2.15316i) q^{35} +(-0.0482768 - 2.99961i) q^{36} +(0.659906 + 1.14299i) q^{37} +(0.622647 + 1.07846i) q^{38} +(-5.50161 - 1.42680i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.60559 + 6.24507i) q^{41} +(-1.64153 - 4.27848i) q^{42} +(-4.88416 + 8.45961i) q^{43} +(-0.554785 - 0.960915i) q^{44} +(-2.62188 - 1.45800i) q^{45} +(-3.14773 + 5.45204i) q^{46} -11.4617 q^{47} +(1.21485 - 1.23456i) q^{48} +(-4.59781 - 5.27827i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.02930 - 7.33678i) q^{51} +(-1.64072 - 2.84181i) q^{52} +(2.73283 - 4.73340i) q^{53} +(3.76185 + 3.58448i) q^{54} -1.10957 q^{55} +(1.09594 - 2.40809i) q^{56} +(-2.08784 - 0.541468i) q^{57} +(-3.26879 + 5.66171i) q^{58} +6.46993 q^{59} +(-0.461735 - 1.66937i) q^{60} +4.40470 q^{61} -3.10957 q^{62} +(7.27625 + 3.17115i) q^{63} +1.00000 q^{64} -3.28143 q^{65} +(1.86029 + 0.482453i) q^{66} -5.23241 q^{67} +(2.19747 - 3.80613i) q^{68} +(-2.90684 - 10.5095i) q^{69} +(-1.53750 - 2.15316i) q^{70} +16.3046 q^{71} +(0.0482768 + 2.99961i) q^{72} +(-0.731993 + 1.26785i) q^{73} +(-0.659906 - 1.14299i) q^{74} +(-1.67659 - 0.434811i) q^{75} +(-0.622647 - 1.07846i) q^{76} +(2.92199 - 0.282863i) q^{77} +(5.50161 + 1.42680i) q^{78} +3.41668 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.99534 + 0.289623i) q^{81} +(-3.60559 - 6.24507i) q^{82} +(-4.06648 + 7.04336i) q^{83} +(1.64153 + 4.27848i) q^{84} +(-2.19747 - 3.80613i) q^{85} +(4.88416 - 8.45961i) q^{86} +(-3.01863 - 10.9136i) q^{87} +(0.554785 + 0.960915i) q^{88} +(-1.42132 - 2.46180i) q^{89} +(2.62188 + 1.45800i) q^{90} +(8.64146 - 0.836537i) q^{91} +(3.14773 - 5.45204i) q^{92} +(3.77766 - 3.83895i) q^{93} +11.4617 q^{94} -1.24529 q^{95} +(-1.21485 + 1.23456i) q^{96} +(-8.54592 + 14.8020i) q^{97} +(4.59781 + 5.27827i) q^{98} +(-2.85559 + 1.71053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

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