LMFDB - Embedded newform 370.2.m.d.249.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.3
Root			$-1.76701i$ of defining polynomial
Character	$\chi$	$=$	370.249
Dual form			370.2.m.d.159.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.53027 + 0.883503i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.209495 - 2.22623i) q^{5} +1.76701i q^{6} +(-3.45647 + 1.99560i) q^{7} -1.00000 q^{8} +(0.0611550 - 0.105924i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.53027 + 0.883503i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.209495 - 2.22623i) q^{5} +1.76701i q^{6} +(-3.45647 + 1.99560i) q^{7} -1.00000 q^{8} +(0.0611550 - 0.105924i) q^{9} +(-1.82323 - 1.29454i) q^{10} -1.12438 q^{11} +(1.53027 + 0.883503i) q^{12} +(2.88034 + 4.98889i) q^{13} +3.99119i q^{14} +(1.64630 + 3.59183i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.376657 - 0.652389i) q^{17} +(-0.0611550 - 0.105924i) q^{18} +(-6.09832 + 3.52087i) q^{19} +(-2.03272 + 0.931689i) q^{20} +(3.52623 - 6.10761i) q^{21} +(-0.562188 + 0.973738i) q^{22} -5.65184 q^{23} +(1.53027 - 0.883503i) q^{24} +(-4.91222 - 0.932768i) q^{25} +5.76068 q^{26} -5.08490i q^{27} +(3.45647 + 1.99560i) q^{28} -2.65900i q^{29} +(3.93377 + 0.370178i) q^{30} +2.29410i q^{31} +(0.500000 + 0.866025i) q^{32} +(1.72060 - 0.993390i) q^{33} +(-0.376657 - 0.652389i) q^{34} +(3.71855 + 8.11298i) q^{35} -0.122310 q^{36} +(-3.94471 + 4.63026i) q^{37} +7.04173i q^{38} +(-8.81540 - 5.08958i) q^{39} +(-0.209495 + 2.22623i) q^{40} +(2.08716 + 3.61506i) q^{41} +(-3.52623 - 6.10761i) q^{42} +8.57454 q^{43} +(0.562188 + 0.973738i) q^{44} +(-0.222999 - 0.158336i) q^{45} +(-2.82592 + 4.89463i) q^{46} -11.1824i q^{47} -1.76701i q^{48} +(4.46480 - 7.73327i) q^{49} +(-3.26391 + 3.78773i) q^{50} +1.33111i q^{51} +(2.88034 - 4.98889i) q^{52} +(-0.361962 - 0.208979i) q^{53} +(-4.40365 - 2.54245i) q^{54} +(-0.235551 + 2.50312i) q^{55} +(3.45647 - 1.99560i) q^{56} +(6.22139 - 10.7758i) q^{57} +(-2.30276 - 1.32950i) q^{58} +(-8.60234 - 4.96656i) q^{59} +(2.28747 - 3.22165i) q^{60} +(-5.28723 + 3.05258i) q^{61} +(1.98675 + 1.14705i) q^{62} +0.488163i q^{63} +1.00000 q^{64} +(11.7099 - 5.36716i) q^{65} -1.98678i q^{66} +(-4.92123 + 2.84128i) q^{67} -0.753314 q^{68} +(8.64885 - 4.99341i) q^{69} +(8.88532 + 0.836134i) q^{70} +(-0.469529 - 0.813247i) q^{71} +(-0.0611550 + 0.105924i) q^{72} -8.97127i q^{73} +(2.03757 + 5.73134i) q^{74} +(8.34114 - 2.91258i) q^{75} +(6.09832 + 3.52087i) q^{76} +(3.88638 - 2.24380i) q^{77} +(-8.81540 + 5.08958i) q^{78} +(2.97626 - 1.71834i) q^{79} +(1.82323 + 1.29454i) q^{80} +(4.67599 + 8.09904i) q^{81} +4.17431 q^{82} +(8.58455 + 4.95629i) q^{83} -7.05246 q^{84} +(-1.37346 - 0.975198i) q^{85} +(4.28727 - 7.42577i) q^{86} +(2.34923 + 4.06899i) q^{87} +1.12438 q^{88} +(0.639228 + 0.369058i) q^{89} +(-0.248622 + 0.113955i) q^{90} +(-19.9116 - 11.4960i) q^{91} +(2.82592 + 4.89463i) q^{92} +(-2.02684 - 3.51059i) q^{93} +(-9.68424 - 5.59120i) q^{94} +(6.56070 + 14.3139i) q^{95} +(-1.53027 - 0.883503i) q^{96} -1.90949 q^{97} +(-4.46480 - 7.73327i) q^{98} +(-0.0687613 + 0.119098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9	$ 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} + 9 q^{15} - 8 q^{16} - 13 q^{18} - 3 q^{19} - 6 q^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{28} - 9 q^{30} + 8 q^{32} + 6 q^{33} + 18 q^{35} - 26 q^{36} + 16 q^{37} + 15 q^{39} + 7 q^{41} + 6 q^{42} - 22 q^{43} + 3 q^{44} + 4 q^{45} - 11 q^{46} + 4 q^{49} + 6 q^{50} - 6 q^{52} + 3 q^{53} + 9 q^{54} - 35 q^{55} + 12 q^{56} + 18 q^{57} + 36 q^{58} + 15 q^{59} - 18 q^{60} + 12 q^{61} - 33 q^{62} + 16 q^{64} + 46 q^{65} + 24 q^{67} + 42 q^{69} + 12 q^{70} - 4 q^{71} - 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} - 24 q^{77} + 15 q^{78} + 6 q^{80} + 10 q^{81} + 14 q^{82} + 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} + 50 q^{87} + 6 q^{88} + 9 q^{89} - q^{90} - 24 q^{91} + 11 q^{92} - 25 q^{93} - 27 q^{94} - 53 q^{95} - 3 q^{96} + 68 q^{97} - 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 + 3 * q^12 - 6 * q^13 + 9 * q^15 - 8 * q^16 - 13 * q^18 - 3 * q^19 - 6 * q^20 - 6 * q^21 - 3 * q^22 - 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 + 12 * q^28 - 9 * q^30 + 8 * q^32 + 6 * q^33 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 7 * q^41 + 6 * q^42 - 22 * q^43 + 3 * q^44 + 4 * q^45 - 11 * q^46 + 4 * q^49 + 6 * q^50 - 6 * q^52 + 3 * q^53 + 9 * q^54 - 35 * q^55 + 12 * q^56 + 18 * q^57 + 36 * q^58 + 15 * q^59 - 18 * q^60 + 12 * q^61 - 33 * q^62 + 16 * q^64 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * q^70 - 4 * q^71 - 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 - 24 * q^77 + 15 * q^78 + 6 * q^80 + 10 * q^81 + 14 * q^82 + 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 + 50 * q^87 + 6 * q^88 + 9 * q^89 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.53027	+	0.883503i	−0.883503	+	0.510091i	−0.871812	−	0.489841i	$-0.837055\pi$
$3$	−1.53027	+	0.883503i	−0.883503	+	0.510091i	−0.0116912	+	0.999932i	$0.503722\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.209495	−	2.22623i	0.0936889	−	0.995602i
$5$	0.209495	−	2.22623i	0.0936889	−	0.995602i
$6$			1.76701i			0.721377i
$7$	−3.45647	+	1.99560i	−1.30642	+	0.754264i	−0.981497	−	0.191475i	$-0.938673\pi$
$7$	−3.45647	+	1.99560i	−1.30642	+	0.754264i	−0.324926	+	0.945739i	$0.605340\pi$
$8$	−1.00000			−0.353553
$9$	0.0611550	−	0.105924i	0.0203850	−	0.0353079i
$10$	−1.82323	−	1.29454i	−0.576555	−	0.409371i
$11$	−1.12438			−0.339012			−0.169506	−	0.985529i	$-0.554217\pi$
$11$	−1.12438			−0.339012			−0.169506	+	0.985529i	$0.554217\pi$
$12$	1.53027	+	0.883503i	0.441751	+	0.255045i
$13$	2.88034	+	4.98889i	0.798862	+	1.38367i	0.920358	+	0.391078i	$0.127898\pi$
$13$	2.88034	+	4.98889i	0.798862	+	1.38367i	−0.121495	+	0.992592i	$0.538769\pi$
$14$			3.99119i			1.06669i
$15$	1.64630	+	3.59183i	0.425073	+	0.927407i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.376657	−	0.652389i	0.0913527	−	0.158228i	−0.816728	−	0.577023i	$-0.804214\pi$
$17$	0.376657	−	0.652389i	0.0913527	−	0.158228i	0.908081	+	0.418796i	$0.137548\pi$
$18$	−0.0611550	−	0.105924i	−0.0144144	−	0.0249664i
$19$	−6.09832	+	3.52087i	−1.39905	+	0.807742i	−0.994293	−	0.106682i	$-0.965977\pi$
$19$	−6.09832	+	3.52087i	−1.39905	+	0.807742i	−0.404757	+	0.914424i	$0.632644\pi$
$20$	−2.03272	+	0.931689i	−0.454530	+	0.208332i
$21$	3.52623	−	6.10761i	0.769486	−	1.33279i
$22$	−0.562188	+	0.973738i	−0.119859	+	0.207602i
$23$	−5.65184			−1.17849			−0.589245	−	0.807955i	$-0.700575\pi$
$23$	−5.65184			−1.17849			−0.589245	+	0.807955i	$0.700575\pi$
$24$	1.53027	−	0.883503i	0.312365	−	0.180344i
$25$	−4.91222	−	0.932768i	−0.982445	−	0.186554i
$26$	5.76068			1.12976
$27$		−	5.08490i		−	0.978589i
$28$	3.45647	+	1.99560i	0.653212	+	0.377132i
$29$		−	2.65900i		−	0.493764i	−0.969046	−	0.246882i	$-0.920594\pi$
$29$		−	2.65900i		−	0.493764i	0.969046	−	0.246882i	$-0.0794059\pi$
$30$	3.93377	+	0.370178i	0.718204	+	0.0675850i
$31$			2.29410i			0.412032i	0.978549	+	0.206016i	$0.0660498\pi$
$31$			2.29410i			0.412032i	−0.978549	+	0.206016i	$0.933950\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.72060	−	0.993390i	0.299518	−	0.172927i
$34$	−0.376657	−	0.652389i	−0.0645961	−	0.111884i
$35$	3.71855	+	8.11298i	0.628549	+	1.37134i
$36$	−0.122310			−0.0203850
$37$	−3.94471	+	4.63026i	−0.648506	+	0.761210i
$37$	−3.94471	+	4.63026i	−0.648506	+	0.761210i
$38$			7.04173i			1.14232i
$39$	−8.81540	−	5.08958i	−1.41159	−	0.814984i
$40$	−0.209495	+	2.22623i	−0.0331240	+	0.351998i
$41$	2.08716	+	3.61506i	0.325959	+	0.564578i	0.981706	−	0.190403i	$-0.0609795\pi$
$41$	2.08716	+	3.61506i	0.325959	+	0.564578i	−0.655747	+	0.754981i	$0.727646\pi$
$42$	−3.52623	−	6.10761i	−0.544109	−	0.942424i
$43$	8.57454			1.30760			0.653802	−	0.756665i	$-0.273173\pi$
$43$	8.57454			1.30760			0.653802	+	0.756665i	$0.273173\pi$
$44$	0.562188	+	0.973738i	0.0847531	+	0.146797i
$45$	−0.222999	−	0.158336i	−0.0332427	−	0.0236033i
$46$	−2.82592	+	4.89463i	−0.416659	+	0.721674i
$47$		−	11.1824i		−	1.63112i	−0.578672	−	0.815560i	$-0.696429\pi$
$47$		−	11.1824i		−	1.63112i	0.578672	−	0.815560i	$-0.303571\pi$
$48$		−	1.76701i		−	0.255045i
$49$	4.46480	−	7.73327i	0.637829	−	1.10475i
$50$	−3.26391	+	3.78773i	−0.461587	+	0.535665i
$51$			1.33111i			0.186393i
$52$	2.88034	−	4.98889i	0.399431	−	0.691835i
$53$	−0.361962	−	0.208979i	−0.0497194	−	0.0287055i	0.474934	−	0.880021i	$-0.342472\pi$
$53$	−0.361962	−	0.208979i	−0.0497194	−	0.0287055i	−0.524654	+	0.851316i	$0.675805\pi$
$54$	−4.40365	−	2.54245i	−0.599261	−	0.345983i
$55$	−0.235551	+	2.50312i	−0.0317617	+	0.337521i
$56$	3.45647	−	1.99560i	0.461891	−	0.266673i
$57$	6.22139	−	10.7758i	0.824044	−	1.42729i
$58$	−2.30276	−	1.32950i	−0.302367	−	0.174572i
$59$	−8.60234	−	4.96656i	−1.11993	−	0.646591i	−0.178546	−	0.983932i	$-0.557139\pi$
$59$	−8.60234	−	4.96656i	−1.11993	−	0.646591i	−0.941383	+	0.337340i	$0.890473\pi$
$60$	2.28747	−	3.22165i	0.295311	−	0.415914i
$61$	−5.28723	+	3.05258i	−0.676960	+	0.390843i	−0.798709	−	0.601718i	$-0.794483\pi$
$61$	−5.28723	+	3.05258i	−0.676960	+	0.390843i	0.121749	+	0.992561i	$0.461150\pi$
$62$	1.98675	+	1.14705i	0.252317	+	0.145675i
$63$			0.488163i			0.0615027i
$64$	1.00000			0.125000
$65$	11.7099	−	5.36716i	1.45243	−	0.665714i
$66$		−	1.98678i		−	0.244556i
$67$	−4.92123	+	2.84128i	−0.601224	+	0.347117i	−0.769523	−	0.638619i	$-0.779506\pi$
$67$	−4.92123	+	2.84128i	−0.601224	+	0.347117i	0.168299	+	0.985736i	$0.446173\pi$
$68$	−0.753314			−0.0913527
$69$	8.64885	−	4.99341i	1.04120	−	0.601136i
$70$	8.88532	+	0.836134i	1.06200	+	0.0999371i
$71$	−0.469529	−	0.813247i	−0.0557228	−	0.0965147i	0.836818	−	0.547480i	$-0.184413\pi$
$71$	−0.469529	−	0.813247i	−0.0557228	−	0.0965147i	−0.892541	+	0.450966i	$0.851080\pi$
$72$	−0.0611550	+	0.105924i	−0.00720719	+	0.0124832i
$73$		−	8.97127i		−	1.05001i	−0.851100	−	0.525004i	$-0.824064\pi$
$73$		−	8.97127i		−	1.05001i	0.851100	−	0.525004i	$-0.175936\pi$
$74$	2.03757	+	5.73134i	0.236863	+	0.666255i
$75$	8.34114	−	2.91258i	0.963152	−	0.336315i
$76$	6.09832	+	3.52087i	0.699525	+	0.403871i
$77$	3.88638	−	2.24380i	0.442894	−	0.255705i
$78$	−8.81540	+	5.08958i	−0.998148	+	0.576281i
$79$	2.97626	−	1.71834i	0.334855	−	0.193329i	−0.323139	−	0.946351i	$-0.604738\pi$
$79$	2.97626	−	1.71834i	0.334855	−	0.193329i	0.657995	+	0.753023i	$0.271405\pi$
$80$	1.82323	+	1.29454i	0.203843	+	0.144734i
$81$	4.67599	+	8.09904i	0.519554	+	0.899894i
$82$	4.17431			0.460976
$83$	8.58455	+	4.95629i	0.942276	+	0.544023i	0.890673	−	0.454644i	$-0.150234\pi$
$83$	8.58455	+	4.95629i	0.942276	+	0.544023i	0.0516032	+	0.998668i	$0.483567\pi$
$84$	−7.05246			−0.769486
$85$	−1.37346	−	0.975198i	−0.148973	−	0.105775i
$86$	4.28727	−	7.42577i	0.462308	−	0.800741i
$87$	2.34923	+	4.06899i	0.251864	+	0.436242i
$88$	1.12438			0.119859
$89$	0.639228	+	0.369058i	0.0677580	+	0.0391201i	0.533496	−	0.845802i	$-0.320878\pi$
$89$	0.639228	+	0.369058i	0.0677580	+	0.0391201i	−0.465738	+	0.884923i	$0.654211\pi$
$90$	−0.248622	+	0.113955i	−0.0262071	+	0.0120119i
$91$	−19.9116	−	11.4960i	−2.08731	−	1.20511i
$92$	2.82592	+	4.89463i	0.294622	+	0.510301i
$93$	−2.02684	−	3.51059i	−0.210174	−	0.364031i
$94$	−9.68424	−	5.59120i	−0.998854	−	0.576688i
$95$	6.56070	+	14.3139i	0.673114	+	1.46857i
$96$	−1.53027	−	0.883503i	−0.156183	−	0.0901721i
$97$	−1.90949			−0.193879			−0.0969395	−	0.995290i	$-0.530905\pi$
$97$	−1.90949			−0.193879			−0.0969395	+	0.995290i	$0.530905\pi$
$98$	−4.46480	−	7.73327i	−0.451013	−	0.781178i
$99$	−0.0687613	+	0.119098i	−0.00691077	+	0.0119698i
$100$	1.64831	+	4.72049i	0.164831	+	0.472049i
$101$	−3.66042			−0.364226			−0.182113	−	0.983278i	$-0.558294\pi$
$101$	−3.66042			−0.364226			−0.182113	+	0.983278i	$0.558294\pi$
$102$	1.15277	+	0.665555i	0.114142	+	0.0658997i
$103$	15.5340			1.53061			0.765304	−	0.643669i	$-0.222589\pi$
$103$	15.5340			1.53061			0.765304	+	0.643669i	$0.222589\pi$
$104$	−2.88034	−	4.98889i	−0.282440	−	0.489201i
$105$	−12.8582	−	9.12972i	−1.25483	−	0.890969i
$106$	−0.361962	+	0.208979i	−0.0351569	+	0.0202978i
$107$	−11.2563	+	6.49882i	−1.08819	+	0.628264i	−0.933093	−	0.359635i	$-0.882901\pi$
$107$	−11.2563	+	6.49882i	−1.08819	+	0.628264i	−0.155093	+	0.987900i	$0.549568\pi$
$108$	−4.40365	+	2.54245i	−0.423741	+	0.244647i
$109$	−13.2003	−	7.62117i	−1.26435	−	0.729976i	−0.290441	−	0.956893i	$-0.593802\pi$
$109$	−13.2003	−	7.62117i	−1.26435	−	0.729976i	−0.973914	+	0.226917i	$0.927135\pi$
$110$	2.04999	+	1.45555i	0.195459	+	0.138782i
$111$	1.94562	−	10.5707i	0.184670	−	1.00333i
$112$		−	3.99119i		−	0.377132i
$113$	−3.12438	+	5.41158i	−0.293917	+	0.509078i	−0.974732	−	0.223376i	$-0.928292\pi$
$113$	−3.12438	+	5.41158i	−0.293917	+	0.509078i	0.680816	+	0.732455i	$0.261625\pi$
$114$	−6.22139	−	10.7758i	−0.582687	−	1.00924i
$115$	−1.18403	+	12.5823i	−0.110411	+	1.17331i
$116$	−2.30276	+	1.32950i	−0.213806	+	0.123441i
$117$	0.704589			0.0651393
$118$	−8.60234	+	4.96656i	−0.791909	+	0.457209i
$119$			3.00662i			0.275616i
$120$	−1.64630	−	3.59183i	−0.150286	−	0.327888i
$121$	−9.73578			−0.885071
$122$			6.10516i			0.552735i
$123$	−6.38783	−	3.68802i	−0.575972	−	0.332537i
$124$	1.98675	−	1.14705i	0.178415	−	0.103008i
$125$	−3.10564	+	10.7403i	−0.277777	+	0.960646i
$126$	0.422761	+	0.244081i	0.0376626	+	0.0217445i
$127$	14.9059	+	8.60590i	1.32268	+	0.763650i	0.984155	−	0.177308i	$-0.0567388\pi$
$127$	14.9059	+	8.60590i	1.32268	+	0.763650i	0.338525	+	0.940957i	$0.390072\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−13.1214	+	7.57563i	−1.15527	+	0.666997i
$130$	1.20683	−	12.8246i	0.105846	−	1.12479i
$131$	9.49301	+	5.48079i	0.829408	+	0.478859i	0.853650	−	0.520847i	$-0.174384\pi$
$131$	9.49301	+	5.48079i	0.829408	+	0.478859i	−0.0242418	+	0.999706i	$0.507717\pi$
$132$	−1.72060	−	0.993390i	−0.149759	−	0.0864635i
$133$	14.0525	−	24.3396i	1.21850	−	2.11051i
$134$			5.68255i			0.490898i
$135$	−11.3202	−	1.06526i	−0.974284	−	0.0916829i
$136$	−0.376657	+	0.652389i	−0.0322981	+	0.0559419i
$137$			23.1827i			1.98063i	0.138833	+	0.990316i	$0.455665\pi$
$137$			23.1827i			1.98063i	−0.138833	+	0.990316i	$0.544335\pi$
$138$		−	9.98683i		−	0.850135i
$139$	−0.122224	+	0.211698i	−0.0103669	+	0.0179560i	−0.871162	−	0.490995i	$-0.836633\pi$
$139$	−0.122224	+	0.211698i	−0.0103669	+	0.0179560i	0.860795	+	0.508951i	$0.169967\pi$
$140$	5.16677	−	7.27685i	0.436672	−	0.615006i
$141$	9.87969	+	17.1121i	0.832020	+	1.44110i
$142$	−0.939057			−0.0788039
$143$	−3.23859	−	5.60939i	−0.270824	−	0.469081i
$144$	0.0611550	+	0.105924i	0.00509625	+	0.00882697i
$145$	−5.91955	−	0.557046i	−0.491592	−	0.0462602i
$146$	−7.76935	−	4.48564i	−0.642996	−	0.371234i
$147$			15.7787i			1.30140i
$148$	5.98227	+	1.10109i	0.491740	+	0.0905087i
$149$	16.5549			1.35623			0.678117	−	0.734954i	$-0.262796\pi$
$149$	16.5549			1.35623			0.678117	+	0.734954i	$0.262796\pi$
$150$	1.64821	−	8.67993i	0.134576	−	0.708713i
$151$	10.0750	+	17.4504i	0.819891	+	1.42009i	0.905762	+	0.423786i	$0.139299\pi$
$151$	10.0750	+	17.4504i	0.819891	+	1.42009i	−0.0858716	+	0.996306i	$0.527367\pi$
$152$	6.09832	−	3.52087i	0.494639	−	0.285580i
$153$	−0.0460689	−	0.0797937i	−0.00372445	−	0.00645094i
$154$		−	4.48760i		−	0.361621i
$155$	5.10719	+	0.480601i	0.410219	+	0.0386028i
$156$			10.1792i			0.814984i
$157$	−18.3795	−	10.6114i	−1.46685	−	0.846884i	−0.467535	−	0.883975i	$-0.654858\pi$
$157$	−18.3795	−	10.6114i	−1.46685	−	0.846884i	−0.999312	+	0.0370902i	$0.988191\pi$
$158$		−	3.43669i		−	0.273408i
$159$	0.738534			0.0585696
$160$	2.03272	−	0.931689i	0.160701	−	0.0736565i
$161$	19.5354	−	11.2788i	1.53961	−	0.888892i
$162$	9.35197			0.734760
$163$	−0.295353	+	0.511567i	−0.0231339	+	0.0400690i	−0.877361	−	0.479832i	$-0.840698\pi$
$163$	−0.295353	+	0.511567i	−0.0231339	+	0.0400690i	0.854227	+	0.519901i	$0.174031\pi$
$164$	2.08716	−	3.61506i	0.162980	−	0.282289i
$165$	−1.85106	−	4.03857i	−0.144105	−	0.314402i
$166$	8.58455	−	4.95629i	0.666290	−	0.384683i
$167$	1.67520	+	2.90153i	0.129631	+	0.224527i	0.923534	−	0.383518i	$-0.125287\pi$
$167$	1.67520	+	2.90153i	0.129631	+	0.224527i	−0.793903	+	0.608045i	$0.791954\pi$
$168$	−3.52623	+	6.10761i	−0.272054	+	0.471212i
$169$	−10.0927	+	17.4811i	−0.776362	+	1.34470i
$170$	−1.53128	+	0.701854i	−0.117444	+	0.0538297i
$171$			0.861275i			0.0658633i
$172$	−4.28727	−	7.42577i	−0.326901	−	0.566209i
$173$	−15.1720	−	8.75957i	−1.15351	−	0.665978i	−0.203768	−	0.979019i	$-0.565319\pi$
$173$	−15.1720	−	8.75957i	−1.15351	−	0.665978i	−0.949740	+	0.313041i	$0.898652\pi$
$174$	4.69847			0.356190
$175$	18.8404	−	6.57872i	1.42420	−	0.497305i
$176$	0.562188	−	0.973738i	0.0423765	−	0.0733983i
$177$	17.5519			1.31928
$178$	0.639228	−	0.369058i	0.0479121	−	0.0276621i
$179$			10.5351i			0.787432i	0.919232	+	0.393716i	$0.128811\pi$
$179$			10.5351i			0.787432i	−0.919232	+	0.393716i	$0.871189\pi$
$180$	−0.0256233	+	0.272291i	−0.00190985	+	0.0202953i
$181$	−1.36123	−	2.35772i	−0.101179	−	0.175248i	0.810991	−	0.585058i	$-0.198928\pi$
$181$	−1.36123	−	2.35772i	−0.101179	−	0.175248i	−0.912171	+	0.409810i	$0.865595\pi$
$182$	−19.9116	+	11.4960i	−1.47595	+	0.852139i
$183$	5.39393	−	9.34256i	0.398731	−	0.690622i
$184$	5.65184			0.416659
$185$	9.48164	+	9.75185i	0.697104	+	0.716970i
$186$	−4.05368			−0.297230
$187$	−0.423504	+	0.733530i	−0.0309697	+	0.0536411i
$188$	−9.68424	+	5.59120i	−0.706296	+	0.407780i
$189$	10.1474	+	17.5758i	0.738114	+	1.27845i
$190$	15.6765	+	1.47521i	1.13730	+	0.107023i
$191$			6.53981i			0.473204i	0.971607	+	0.236602i	$0.0760337\pi$
$191$			6.53981i			0.473204i	−0.971607	+	0.236602i	$0.923966\pi$
$192$	−1.53027	+	0.883503i	−0.110438	+	0.0637613i
$193$	−16.1690			−1.16387			−0.581936	−	0.813235i	$-0.697704\pi$
$193$	−16.1690			−1.16387			−0.581936	+	0.813235i	$0.697704\pi$
$194$	−0.954744	+	1.65366i	−0.0685466	+	0.118726i
$195$	−13.1774	+	18.5589i	−0.943650	+	1.32903i
$196$	−8.92961			−0.637829
$197$	10.6879	+	6.17064i	0.761479	+	0.439640i	0.829826	−	0.558022i	$-0.188439\pi$
$197$	10.6879	+	6.17064i	0.761479	+	0.439640i	−0.0683477	+	0.997662i	$0.521773\pi$
$198$	0.0687613	+	0.119098i	0.00488665	+	0.00846393i
$199$		−	9.41652i		−	0.667520i	−0.942658	−	0.333760i	$-0.891683\pi$
$199$		−	9.41652i		−	0.667520i	0.942658	−	0.333760i	$-0.108317\pi$
$200$	4.91222	+	0.932768i	0.347347	+	0.0659567i
$201$	5.02055	−	8.69585i	0.354122	−	0.613358i
$202$	−1.83021	+	3.17002i	−0.128773	+	0.223042i
$203$	5.30629	+	9.19076i	0.372428	+	0.645065i
$204$	1.15277	−	0.665555i	0.0807104	−	0.0465982i
$205$	8.48521	−	3.88916i	0.592633	−	0.271631i
$206$	7.76698	−	13.4528i	0.541151	−	0.937302i
$207$	−0.345638	+	0.598663i	−0.0240235	+	0.0416100i
$208$	−5.76068			−0.399431
$209$	6.85681	−	3.95878i	0.474295	−	0.273835i
$210$	−14.3357	+	6.57070i	−0.989256	+	0.453421i
$211$	−17.9571			−1.23622			−0.618110	−	0.786092i	$-0.712101\pi$
$211$	−17.9571			−1.23622			−0.618110	+	0.786092i	$0.712101\pi$
$212$			0.417958i			0.0287055i
$213$	1.43701	+	0.829660i	0.0984625	+	0.0568474i
$214$			12.9976i			0.888500i
$215$	1.79632	−	19.0889i	0.122508	−	1.30185i
$216$			5.08490i			0.345983i
$217$	−4.57809	−	7.92948i	−0.310781	−	0.538288i
$218$	−13.2003	+	7.62117i	−0.894034	+	0.516171i
$219$	7.92615	+	13.7285i	0.535599	+	0.927685i
$220$	2.28554	−	1.04757i	0.154091	−	0.0706271i
$221$	4.33960			0.291913
$222$	−8.18170	−	6.97032i	−0.549119	−	0.467817i
$223$			18.1664i			1.21651i	0.793741	+	0.608255i	$0.208130\pi$
$223$			18.1664i			1.21651i	−0.793741	+	0.608255i	$0.791870\pi$
$224$	−3.45647	−	1.99560i	−0.230945	−	0.133336i
$225$	−0.399209	+	0.463277i	−0.0266140	+	0.0308851i
$226$	3.12438	+	5.41158i	0.207830	+	0.359973i
$227$	−3.14423	−	5.44597i	−0.208690	−	0.361462i	0.742612	−	0.669722i	$-0.233587\pi$
$227$	−3.14423	−	5.44597i	−0.208690	−	0.361462i	−0.951302	+	0.308260i	$0.900253\pi$
$228$	−12.4428			−0.824044
$229$	−4.26079	−	7.37991i	−0.281561	−	0.487678i	0.690208	−	0.723611i	$-0.257519\pi$
$229$	−4.26079	−	7.37991i	−0.281561	−	0.487678i	−0.971769	+	0.235933i	$0.924186\pi$
$230$	10.3046	+	7.31655i	0.679464	+	0.482439i
$231$	−3.96481	+	6.86725i	−0.260865	+	0.451832i
$232$			2.65900i			0.174572i
$233$			0.321449i			0.0210588i	0.999945	+	0.0105294i	$0.00335168\pi$
$233$			0.321449i			0.0210588i	−0.999945	+	0.0105294i	$0.996648\pi$
$234$	0.352294	−	0.610192i	0.0230302	−	0.0398895i
$235$	−24.8946	−	2.34265i	−1.62395	−	0.152818i
$236$			9.93312i			0.646591i
$237$	−3.03632	+	5.25907i	−0.197230	+	0.341613i
$238$	2.60381	+	1.50331i	0.168780	+	0.0974451i
$239$	−20.1752	−	11.6482i	−1.30503	−	0.753457i	−0.323764	−	0.946138i	$-0.604948\pi$
$239$	−20.1752	−	11.6482i	−1.30503	−	0.753457i	−0.981261	+	0.192681i	$0.938282\pi$
$240$	−3.93377	−	0.370178i	−0.253924	−	0.0238949i
$241$	19.9282	−	11.5055i	1.28369	−	0.741136i	0.306166	−	0.951978i	$-0.400954\pi$
$241$	19.9282	−	11.5055i	1.28369	−	0.741136i	0.977520	+	0.210842i	$0.0676205\pi$
$242$	−4.86789	+	8.43143i	−0.312920	+	0.541993i
$243$	−1.10011	−	0.635151i	−0.0705723	−	0.0407449i
$244$	5.28723	+	3.05258i	0.338480	+	0.195421i
$245$	−16.2807	−	11.5598i	−1.04014	−	0.738527i
$246$	−6.38783	+	3.68802i	−0.407273	+	0.235139i
$247$	−35.1305	−	20.2826i	−2.23530	−	1.29055i
$248$		−	2.29410i		−	0.145675i
$249$	−17.5156			−1.11001
$250$	7.74859	+	8.05974i	0.490064	+	0.509743i
$251$			7.45541i			0.470581i	0.971925	+	0.235291i	$0.0756042\pi$
$251$			7.45541i			0.470581i	−0.971925	+	0.235291i	$0.924396\pi$
$252$	0.422761	−	0.244081i	0.0266315	−	0.0153757i
$253$	6.35479			0.399522
$254$	14.9059	−	8.60590i	0.935276	−	0.539982i
$255$	2.96336	+	0.278860i	0.185573	+	0.0174629i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.60820	+	4.51754i	−0.162695	+	0.281796i	−0.935834	−	0.352440i	$-0.885352\pi$
$257$	−2.60820	+	4.51754i	−0.162695	+	0.281796i	0.773139	+	0.634236i	$0.218685\pi$
$258$			15.1513i			0.943276i
$259$	4.39464	−	23.8764i	0.273070	−	1.48361i
$260$	−10.5030	−	7.45745i	−0.651370	−	0.462492i
$261$	−0.281651	−	0.162611i	−0.0174337	−	0.0100654i
$262$	9.49301	−	5.48079i	0.586480	−	0.338605i
$263$	20.2665	−	11.7008i	1.24968	−	0.721505i	0.278637	−	0.960396i	$-0.410117\pi$
$263$	20.2665	−	11.7008i	1.24968	−	0.721505i	0.971046	+	0.238892i	$0.0767840\pi$
$264$	−1.72060	+	0.993390i	−0.105896	+	0.0611389i
$265$	−0.541065	+	0.762032i	−0.0332374	+	0.0468113i
$266$	−14.0525	−	24.3396i	−0.861611	−	1.49235i
$267$	−1.30426			−0.0798192
$268$	4.92123	+	2.84128i	0.300612	+	0.173559i
$269$	15.2189			0.927915			0.463958	−	0.885857i	$-0.346429\pi$
$269$	15.2189			0.927915			0.463958	+	0.885857i	$0.346429\pi$
$270$	−6.58262	+	9.27092i	−0.400606	+	0.564210i
$271$	1.48941	−	2.57974i	0.0904755	−	0.156708i	−0.817236	−	0.576303i	$-0.804495\pi$
$271$	1.48941	−	2.57974i	0.0904755	−	0.156708i	0.907711	+	0.419595i	$0.137828\pi$
$272$	0.376657	+	0.652389i	0.0228382	+	0.0395569i
$273$	40.6269			2.45885
$274$	20.0768	+	11.5913i	1.21288	+	0.700259i
$275$	5.52319	+	1.04878i	0.333061	+	0.0632440i
$276$	−8.64885	−	4.99341i	−0.520599	−	0.300568i
$277$	7.70564	+	13.3466i	0.462987	+	0.801917i	0.999108	−	0.0422243i	$-0.0134444\pi$
$277$	7.70564	+	13.3466i	0.462987	+	0.801917i	−0.536121	+	0.844141i	$0.680111\pi$
$278$	0.122224	+	0.211698i	0.00733051	+	0.0126968i
$279$	0.242999	+	0.140295i	0.0145480	+	0.00839927i
$280$	−3.71855	−	8.11298i	−0.222226	−	0.484843i
$281$	−10.1817	−	5.87838i	−0.607387	−	0.350675i	0.164555	−	0.986368i	$-0.447381\pi$
$281$	−10.1817	−	5.87838i	−0.607387	−	0.350675i	−0.771942	+	0.635693i	$0.780714\pi$
$282$	19.7594			1.17665
$283$	6.86014	+	11.8821i	0.407793	+	0.706318i	0.994642	−	0.103378i	$-0.0329653\pi$
$283$	6.86014	+	11.8821i	0.407793	+	0.706318i	−0.586849	+	0.809696i	$0.699632\pi$
$284$	−0.469529	+	0.813247i	−0.0278614	+	0.0482574i
$285$	−22.6860	−	16.1077i	−1.34380	−	0.954140i
$286$	−6.47717			−0.383003
$287$	−14.4284	−	8.33024i	−0.851681	−	0.491718i
$288$	0.122310			0.00720719
$289$	8.21626	+	14.2310i	0.483309	+	0.837116i
$290$	−3.44219	+	4.84796i	−0.202132	+	0.284682i
$291$	2.92204	−	1.68704i	0.171293	−	0.0988959i
$292$	−7.76935	+	4.48564i	−0.454667	+	0.262502i
$293$	−16.2133	+	9.36075i	−0.947190	+	0.546861i	−0.892207	−	0.451627i	$-0.850844\pi$
$293$	−16.2133	+	9.36075i	−0.947190	+	0.546861i	−0.0549833	+	0.998487i	$0.517511\pi$
$294$	13.6647	+	7.88933i	0.796943	+	0.460115i
$295$	−12.8589	+	18.1103i	−0.748672	+	1.05442i
$296$	3.94471	−	4.63026i	0.229281	−	0.269128i
$297$			5.71734i			0.331753i
$298$	8.27747	−	14.3370i	0.479501	−	0.830520i
$299$	−16.2792	−	28.1964i	−0.941451	−	1.63064i
$300$	−6.69294	−	5.76735i	−0.386417	−	0.332978i
$301$	−29.6377	+	17.1113i	−1.70829	+	0.986279i
$302$	20.1500			1.15950
$303$	5.60144	−	3.23399i	0.321794	−	0.185788i
$304$		−	7.04173i		−	0.403871i
$305$	5.68811	+	12.4101i	0.325700	+	0.710600i
$306$	−0.0921378			−0.00526717
$307$		−	4.40733i		−	0.251540i	−0.992059	−	0.125770i	$-0.959860\pi$
$307$		−	4.40733i		−	0.251540i	0.992059	−	0.125770i	$-0.0401401\pi$
$308$	−3.88638	−	2.24380i	−0.221447	−	0.127852i
$309$	−23.7712	+	13.7243i	−1.35230	+	0.780749i
$310$	2.96981	−	4.18266i	0.168674	−	0.237559i
$311$	23.3952	+	13.5073i	1.32662	+	0.765926i	0.984776	−	0.173830i	$-0.0556142\pi$
$311$	23.3952	+	13.5073i	1.32662	+	0.765926i	0.341847	+	0.939756i	$0.388948\pi$
$312$	8.81540	+	5.08958i	0.499074	+	0.288141i
$313$	−3.20475	+	5.55078i	−0.181143	+	0.313749i	−0.942270	−	0.334854i	$-0.891313\pi$
$313$	−3.20475	+	5.55078i	−0.181143	+	0.313749i	0.761127	+	0.648603i	$0.224646\pi$
$314$	−18.3795	+	10.6114i	−1.03722	+	0.598838i
$315$	1.08676	+	0.102268i	0.0612322	+	0.00576212i
$316$	−2.97626	−	1.71834i	−0.167428	−	0.0966644i
$317$	−8.12713	−	4.69220i	−0.456465	−	0.263540i	0.254092	−	0.967180i	$-0.418224\pi$
$317$	−8.12713	−	4.69220i	−0.456465	−	0.263540i	−0.710557	+	0.703640i	$0.751557\pi$
$318$	0.369267	−	0.639590i	0.0207075	−	0.0358664i
$319$			2.98972i			0.167392i
$320$	0.209495	−	2.22623i	0.0117111	−	0.124450i
$321$	11.4835	−	19.8899i	0.640944	−	1.11015i
$322$		−	22.5576i		−	1.25708i
$323$			5.30463i			0.295158i
$324$	4.67599	−	8.09904i	0.259777	−	0.449947i
$325$	−9.49539	−	27.1932i	−0.526709	−	1.50841i
$326$	0.295353	+	0.511567i	0.0163581	+	0.0283331i
$327$	26.9333			1.48941
$328$	−2.08716	−	3.61506i	−0.115244	−	0.199608i
$329$	22.3156	+	38.6517i	1.23030	+	2.13094i
$330$	−4.42303	−	0.416220i	−0.243480	−	0.0229121i
$331$	−13.3301	−	7.69616i	−0.732691	−	0.423019i	0.0867151	−	0.996233i	$-0.472363\pi$
$331$	−13.3301	−	7.69616i	−0.732691	−	0.423019i	−0.819406	+	0.573214i	$0.805696\pi$
$332$		−	9.91258i		−	0.544023i
$333$	0.249215	+	0.701001i	0.0136569	+	0.0384146i
$334$	3.35040			0.183326
$335$	5.29437	+	11.5510i	0.289262	+	0.631101i
$336$	3.52623	+	6.10761i	0.192372	+	0.333197i
$337$	−5.02764	+	2.90271i	−0.273873	+	0.158121i	−0.630647	−	0.776070i	$-0.717210\pi$
$337$	−5.02764	+	2.90271i	−0.273873	+	0.158121i	0.356773	+	0.934191i	$0.383877\pi$
$338$	10.0927	+	17.4811i	0.548971	+	0.950845i
$339$		−	11.0416i		−	0.599696i
$340$	−0.157815	+	1.67705i	−0.00855873	+	0.0909509i
$341$		−	2.57943i		−	0.139684i
$342$	0.745886	+	0.430637i	0.0403329	+	0.0232862i
$343$			7.70143i			0.415838i
$344$	−8.57454			−0.462308
$345$	−9.30461	−	20.3004i	−0.500944	−	1.09294i
$346$	−15.1720	+	8.75957i	−0.815653	+	0.470917i
$347$	−2.99524			−0.160793			−0.0803966	−	0.996763i	$-0.525619\pi$
$347$	−2.99524			−0.160793			−0.0803966	+	0.996763i	$0.525619\pi$
$348$	2.34923	−	4.06899i	0.125932	−	0.218121i
$349$	16.1132	−	27.9089i	0.862520	−	1.49393i	−0.00696887	−	0.999976i	$-0.502218\pi$
$349$	16.1132	−	27.9089i	0.862520	−	1.49393i	0.869489	−	0.493953i	$-0.164448\pi$
$350$	3.72286	−	19.6056i	0.198995	−	1.04796i
$351$	25.3680	−	14.6462i	1.35404	−	0.781757i
$352$	−0.562188	−	0.973738i	−0.0299647	−	0.0519004i
$353$	4.35239	−	7.53855i	0.231654	−	0.401237i	−0.726641	−	0.687017i	$-0.758920\pi$
$353$	4.35239	−	7.53855i	0.231654	−	0.401237i	0.958295	+	0.285781i	$0.0922529\pi$
$354$	8.77594	−	15.2004i	0.466436	−	0.807891i
$355$	−1.90884	+	0.874909i	−0.101311	+	0.0464353i
$356$		−	0.738116i		−	0.0391201i
$357$	−2.65636	−	4.60094i	−0.140589	−	0.243508i
$358$	9.12369	+	5.26756i	0.482202	+	0.278399i
$359$	25.8462			1.36411			0.682056	−	0.731300i	$-0.261086\pi$
$359$	25.8462			1.36411			0.682056	+	0.731300i	$0.261086\pi$
$360$	0.222999	+	0.158336i	0.0117531	+	0.00834503i
$361$	15.2930	−	26.4883i	0.804895	−	1.39412i
$362$	−2.72246			−0.143089
$363$	14.8984	−	8.60159i	0.781963	−	0.451466i
$364$			22.9920i			1.20511i
$365$	−19.9721	−	1.87943i	−1.04539	−	0.0983741i
$366$	−5.39393	−	9.34256i	−0.281945	−	0.488343i
$367$	12.8318	−	7.40844i	0.669814	−	0.386718i	−0.126192	−	0.992006i	$-0.540276\pi$
$367$	12.8318	−	7.40844i	0.669814	−	0.386718i	0.796006	+	0.605288i	$0.206942\pi$
$368$	2.82592	−	4.89463i	0.147311	−	0.255150i
$369$	0.510560			0.0265787
$370$	13.1862	−	3.33542i	0.685516	−	0.173400i
$371$	1.66815			0.0866061
$372$	−2.02684	+	3.51059i	−0.105087	+	0.182016i
$373$	−18.1268	+	10.4655i	−0.938571	+	0.541884i	−0.889512	−	0.456912i	$-0.848956\pi$
$373$	−18.1268	+	10.4655i	−0.938571	+	0.541884i	−0.0490590	+	0.998796i	$0.515622\pi$
$374$	0.423504	+	0.733530i	0.0218989	+	0.0379300i
$375$	−4.73665	−	19.1795i	−0.244599	−	0.990425i
$376$			11.1824i			0.576688i
$377$	13.2655	−	7.65882i	0.683206	−	0.394449i
$378$	20.2948			1.04385
$379$	3.24827	−	5.62616i	0.166852	−	0.288997i	−0.770459	−	0.637489i	$-0.779973\pi$
$379$	3.24827	−	5.62616i	0.166852	−	0.288997i	0.937311	+	0.348493i	$0.113306\pi$
$380$	9.11584	−	12.8387i	0.467632	−	0.658610i
$381$	−30.4133			−1.55812
$382$	5.66364	+	3.26990i	0.289777	+	0.167303i
$383$	−13.9034	−	24.0813i	−0.710428	−	1.23050i	−0.964697	−	0.263364i	$-0.915168\pi$
$383$	−13.9034	−	24.0813i	−0.710428	−	1.23050i	0.254269	−	0.967134i	$-0.418165\pi$
$384$			1.76701i			0.0901721i
$385$	−4.18105	−	9.12204i	−0.213086	−	0.464902i
$386$	−8.08451	+	14.0028i	−0.411491	+	0.712723i
$387$	0.524376	−	0.908246i	0.0266555	−	0.0461687i
$388$	0.954744	+	1.65366i	0.0484698	+	0.0839521i
$389$	15.8121	−	9.12913i	0.801706	−	0.462865i	−0.0423611	−	0.999102i	$-0.513488\pi$
$389$	15.8121	−	9.12913i	0.801706	−	0.462865i	0.844067	+	0.536237i	$0.180155\pi$
$390$	9.48380	+	20.6914i	0.480231	+	1.04775i
$391$	−2.12880	+	3.68719i	−0.107658	+	0.186469i
$392$	−4.46480	+	7.73327i	−0.225507	+	0.390589i
$393$	−19.3692			−0.977046
$394$	10.6879	−	6.17064i	0.538447	−	0.310872i
$395$	−3.20192	−	6.98583i	−0.161106	−	0.351495i
$396$	0.137523			0.00691077
$397$			12.3519i			0.619923i	0.950749	+	0.309961i	$0.100316\pi$
$397$			12.3519i			0.619923i	−0.950749	+	0.309961i	$0.899684\pi$
$398$	−8.15495	−	4.70826i	−0.408771	−	0.236004i
$399$			49.6615i			2.48619i
$400$	3.26391	−	3.78773i	0.163196	−	0.189386i
$401$			8.52882i			0.425909i	0.977062	+	0.212954i	$0.0683086\pi$
$401$			8.52882i			0.425909i	−0.977062	+	0.212954i	$0.931691\pi$
$402$	−5.02055	−	8.69585i	−0.250402	−	0.433709i
$403$	−11.4450	+	6.60777i	−0.570116	+	0.329157i
$404$	1.83021	+	3.17002i	0.0910564	+	0.157714i
$405$	19.0100	−	8.71312i	0.944612	−	0.432959i
$406$	10.6126			0.526693
$407$	4.43533	−	5.20615i	0.219851	−	0.258059i
$408$		−	1.33111i		−	0.0658997i
$409$	15.7176	+	9.07457i	0.777186	+	0.448708i	0.835432	−	0.549594i	$-0.185218\pi$
$409$	15.7176	+	9.07457i	0.777186	+	0.448708i	−0.0582462	+	0.998302i	$0.518551\pi$
$410$	0.874496	−	9.29299i	0.0431883	−	0.458948i
$411$	−20.4820	−	35.4758i	−1.01030	−	1.74989i
$412$	−7.76698	−	13.4528i	−0.382652	−	0.662772i
$413$	39.6450			1.95080
$414$	0.345638	+	0.598663i	0.0169872	+	0.0294227i
$415$	12.8323	−	18.0729i	0.629911	−	0.887163i
$416$	−2.88034	+	4.98889i	−0.141220	+	0.244601i
$417$		−	0.431941i		−	0.0211523i
$418$		−	7.91756i		−	0.387260i
$419$	−0.982935	+	1.70249i	−0.0480195	+	0.0831723i	−0.889036	−	0.457837i	$-0.848624\pi$
$419$	−0.982935	+	1.70249i	−0.0480195	+	0.0831723i	0.841017	+	0.541009i	$0.181958\pi$
$420$	−1.47745	+	15.7004i	−0.0720923	+	0.766102i
$421$			5.71401i			0.278484i	0.990258	+	0.139242i	$0.0444666\pi$
$421$			5.71401i			0.278484i	−0.990258	+	0.139242i	$0.955533\pi$
$422$	−8.97857	+	15.5513i	−0.437070	+	0.757027i
$423$	−1.18448	−	0.683860i	−0.0575914	−	0.0332504i
$424$	0.361962	+	0.208979i	0.0175784	+	0.0101489i
$425$	−2.45875	+	2.85335i	−0.119267	+	0.138408i
$426$	1.43701	−	0.829660i	0.0696235	−	0.0401972i
$427$	12.1834	−	21.1023i	0.589598	−	1.02121i
$428$	11.2563	+	6.49882i	0.544093	+	0.314132i
$429$	9.91183	+	5.72260i	0.478548	+	0.276290i
$430$	−15.6333	−	11.1001i	−0.753906	−	0.535295i
$431$	−25.7488	+	14.8661i	−1.24028	+	0.716074i	−0.969150	−	0.246470i	$-0.920729\pi$
$431$	−25.7488	+	14.8661i	−1.24028	+	0.716074i	−0.271126	+	0.962544i	$0.587396\pi$
$432$	4.40365	+	2.54245i	0.211871	+	0.122324i
$433$			8.82129i			0.423924i	0.977278	+	0.211962i	$0.0679853\pi$
$433$			8.82129i			0.423924i	−0.977278	+	0.211962i	$0.932015\pi$
$434$	−9.15617			−0.439510
$435$	9.55067	−	4.37751i	0.457920	−	0.209885i
$436$			15.2423i			0.729976i
$437$	34.4667	−	19.8994i	1.64877	−	0.951916i
$438$	15.8523			0.757452
$439$	27.7357	−	16.0132i	1.32375	−	0.764270i	0.339429	−	0.940632i	$-0.389766\pi$
$439$	27.7357	−	16.0132i	1.32375	−	0.764270i	0.984325	+	0.176362i	$0.0564328\pi$
$440$	0.235551	−	2.50312i	0.0112294	−	0.119332i
$441$	−0.546090	−	0.945856i	−0.0260043	−	0.0450408i
$442$	2.16980	−	3.75820i	0.103207	−	0.178759i
$443$			19.6970i			0.935831i	0.883773	+	0.467916i	$0.154995\pi$
$443$			19.6970i			0.935831i	−0.883773	+	0.467916i	$0.845005\pi$
$444$	−10.1273	+	3.60040i	−0.480621	+	0.170867i
$445$	0.955524	−	1.34575i	0.0452962	−	0.0637948i
$446$	15.7325	+	9.08319i	0.744958	+	0.430101i
$447$	−25.3336	+	14.6263i	−1.19824	+	0.691802i
$448$	−3.45647	+	1.99560i	−0.163303	+	0.0942830i
$449$	−9.02589	+	5.21110i	−0.425958	+	0.245927i	−0.697623	−	0.716465i	$-0.745759\pi$
$449$	−9.02589	+	5.21110i	−0.425958	+	0.245927i	0.271665	+	0.962392i	$0.412426\pi$
$450$	0.201605	+	0.577364i	0.00950375	+	0.0272172i
$451$	−2.34675	−	4.06469i	−0.110504	−	0.191399i
$452$	6.24875			0.293917
$453$	−30.8349	−	17.8026i	−1.44875	−	0.836437i
$454$	−6.28846			−0.295132
$455$	−29.7641	+	41.9196i	−1.39536	+	1.96522i
$456$	−6.22139	+	10.7758i	−0.291343	+	0.504622i
$457$	20.2592	+	35.0899i	0.947685	+	1.64144i	0.750285	+	0.661115i	$0.229916\pi$
$457$	20.2592	+	35.0899i	0.947685	+	1.64144i	0.197400	+	0.980323i	$0.436750\pi$
$458$	−8.52158			−0.398187
$459$	−3.31733	−	1.91526i	−0.154840	−	0.0893967i
$460$	11.4886	−	5.26575i	0.535659	−	0.245517i
$461$	0.172837	+	0.0997876i	0.00804983	+	0.00464757i	0.504020	−	0.863692i	$-0.331854\pi$
$461$	0.172837	+	0.0997876i	0.00804983	+	0.00464757i	−0.495970	+	0.868340i	$0.665187\pi$
$462$	3.96481	+	6.86725i	0.184460	+	0.319493i
$463$	−10.5797	−	18.3246i	−0.491680	−	0.851615i	0.508274	−	0.861195i	$-0.330284\pi$
$463$	−10.5797	−	18.3246i	−0.491680	−	0.851615i	−0.999954	+	0.00958066i	$0.996950\pi$
$464$	2.30276	+	1.32950i	0.106903	+	0.0617205i
$465$	−8.24000	+	3.77677i	−0.382121	+	0.175143i
$466$	0.278383	+	0.160724i	0.0128958	+	0.00744541i
$467$	−38.6513			−1.78857			−0.894283	−	0.447501i	$-0.852314\pi$
$467$	−38.6513			−1.78857			−0.894283	+	0.447501i	$0.852314\pi$
$468$	−0.352294	−	0.610192i	−0.0162848	−	0.0282061i
$469$	11.3401	−	19.6416i	0.523636	−	0.906964i
$470$	−14.4761	+	20.3881i	−0.667733	+	0.940431i
$471$	37.5009			1.72795
$472$	8.60234	+	4.96656i	0.395955	+	0.228605i
$473$	−9.64101			−0.443294
$474$	3.03632	+	5.25907i	0.139463	+	0.241557i
$475$	33.2405	−	11.6070i	1.52518	−	0.532564i
$476$	2.60381	−	1.50331i	0.119345	−	0.0689041i
$477$	−0.0442716	+	0.0255602i	−0.00202706	+	0.00117032i
$478$	−20.1752	+	11.6482i	−0.922792	+	0.532774i
$479$	−9.67769	−	5.58742i	−0.442185	−	0.255296i	0.262339	−	0.964976i	$-0.415506\pi$
$479$	−9.67769	−	5.58742i	−0.442185	−	0.255296i	−0.704524	+	0.709680i	$0.748839\pi$
$480$	−2.28747	+	3.22165i	−0.104408	+	0.147048i
$481$	−34.4620	−	6.34300i	−1.57133	−	0.289216i
$482$		−	23.0111i		−	1.04813i
$483$	−19.9297	+	34.5192i	−0.906831	+	1.57068i
$484$	4.86789	+	8.43143i	0.221268	+	0.383247i
$485$	−0.400028	+	4.25096i	−0.0181643	+	0.193026i
$486$	−1.10011	+	0.635151i	−0.0499022	+	0.0288110i
$487$	−11.6266			−0.526851			−0.263425	−	0.964680i	$-0.584852\pi$
$487$	−11.6266			−0.526851			−0.263425	+	0.964680i	$0.584852\pi$
$488$	5.28723	−	3.05258i	0.239341	−	0.138184i
$489$		−	1.04378i		−	0.0472015i
$490$	−18.1514	+	8.31961i	−0.819997	+	0.375842i
$491$	−13.0950			−0.590970			−0.295485	−	0.955347i	$-0.595481\pi$
$491$	−13.0950			−0.590970			−0.295485	+	0.955347i	$0.595481\pi$
$492$			7.37603i			0.332537i
$493$	−1.73470	−	1.00153i	−0.0781270	−	0.0451066i
$494$	−35.1305	+	20.2826i	−1.58059	+	0.912556i
$495$	0.250735	+	0.178029i	0.0112697	+	0.00800181i
$496$	−1.98675	−	1.14705i	−0.0892075	−	0.0515040i
$497$	3.24583	+	1.87398i	0.145595	+	0.0840594i
$498$	−8.75779	+	15.1689i	−0.392446	+	0.679737i
$499$	−12.3985	+	7.15828i	−0.555033	+	0.320448i	−0.751149	−	0.660132i	$-0.770500\pi$
$499$	−12.3985	+	7.15828i	−0.555033	+	0.320448i	0.196117	+	0.980581i	$0.437167\pi$
$500$	10.8542	−	2.68061i	0.485416	−	0.119880i
$501$	−5.12702	−	2.96009i	−0.229059	−	0.132247i
$502$	6.45658	+	3.72771i	0.288171	+	0.166376i
$503$	15.0547	−	26.0755i	0.671255	−	1.16265i	−0.306293	−	0.951937i	$-0.599089\pi$
$503$	15.0547	−	26.0755i	0.671255	−	1.16265i	0.977548	−	0.210711i	$-0.0675779\pi$
$504$		−	0.488163i		−	0.0217445i
$505$	−0.766839	+	8.14895i	−0.0341239	+	0.362624i
$506$	3.17740	−	5.50341i	0.141252	−	0.244656i
$507$		−	35.6677i		−	1.58406i
$508$		−	17.2118i		−	0.763650i
$509$	−18.1189	+	31.3829i	−0.803107	+	1.39102i	0.114455	+	0.993428i	$0.463488\pi$
$509$	−18.1189	+	31.3829i	−0.803107	+	1.39102i	−0.917562	+	0.397593i	$0.869846\pi$
$510$	1.72318	−	2.42691i	0.0763037	−	0.107466i
$511$	17.9030	+	31.0090i	0.791984	+	1.37176i
$512$	−1.00000			−0.0441942
$513$	17.9032	+	31.0093i	0.790447	+	1.36909i
$514$	2.60820	+	4.51754i	0.115043	+	0.199260i
$515$	3.25428	−	34.5822i	0.143401	−	1.52388i
$516$	13.1214	+	7.57563i	0.577636	+	0.333498i
$517$			12.5732i			0.552970i
$518$	−18.4802	−	15.7441i	−0.811976	−	0.691755i
$519$	30.9564			1.35884
$520$	−11.7099	+	5.36716i	−0.513511	+	0.235365i
$521$	−20.5166	−	35.5358i	−0.898849	−	1.55685i	−0.828967	−	0.559297i	$-0.811071\pi$
$521$	−20.5166	−	35.5358i	−0.898849	−	1.55685i	−0.0698821	−	0.997555i	$-0.522262\pi$
$522$	−0.281651	+	0.162611i	−0.0123275	+	0.00711730i
$523$	−7.21437	−	12.4957i	−0.315462	−	0.546397i	0.664073	−	0.747667i	$-0.268826\pi$
$523$	−7.21437	−	12.4957i	−0.315462	−	0.546397i	−0.979536	+	0.201271i	$0.935493\pi$
$524$		−	10.9616i		−	0.478859i
$525$	−23.0186	+	26.7128i	−1.00461	+	1.16584i
$526$		−	23.4017i		−	1.02036i
$527$	1.49664	+	0.864087i	0.0651947	+	0.0376402i
$528$			1.98678i			0.0864635i
$529$	8.94326			0.388837
$530$	0.389407	+	0.849592i	0.0169148	+	0.0369039i
$531$	−1.05215	+	0.607461i	−0.0456595	+	0.0263615i
$532$	−28.1049			−1.21850
$533$	−12.0234	+	20.8252i	−0.520793	+	0.902040i
$534$	−0.652128	+	1.12952i	−0.0282203	+	0.0488791i
$535$	12.1097	+	26.4206i	0.523550	+	1.14226i
$536$	4.92123	−	2.84128i	0.212565	−	0.122724i
$537$	−9.30782	−	16.1216i	−0.401662	−	0.695699i
$538$	7.60947	−	13.1800i	0.328068	−	0.568230i
$539$	−5.02012	+	8.69510i	−0.216232	+	0.374525i
$540$	4.73754	+	10.3362i	0.203871	+	0.444798i
$541$			11.5162i			0.495119i	0.968873	+	0.247559i	$0.0796286\pi$
$541$			11.5162i			0.495119i	−0.968873	+	0.247559i	$0.920371\pi$
$542$	−1.48941	−	2.57974i	−0.0639758	−	0.110809i
$543$	4.16610	+	2.40530i	0.178785	+	0.103221i
$544$	0.753314			0.0322981
$545$	−19.7319	+	27.7902i	−0.845221	+	1.19040i
$546$	20.3135	−	35.1840i	0.869336	−	1.50573i
$547$	−18.5360			−0.792543			−0.396271	−	0.918133i	$-0.629696\pi$
$547$	−18.5360			−0.792543			−0.396271	+	0.918133i	$0.629696\pi$
$548$	20.0768	−	11.5913i	0.857639	−	0.495158i
$549$			0.746723i			0.0318694i
$550$	3.66987	−	4.25883i	0.156484	−	0.181597i
$551$	9.36198	+	16.2154i	0.398834	+	0.690800i
$552$	−8.64885	+	4.99341i	−0.368119	+	0.212534i
$553$	−6.85824	+	11.8788i	−0.291642	+	0.505139i
$554$	15.4113			0.654762
$555$	−23.1253	−	6.54592i	−0.981613	−	0.277859i
$556$	0.244448			0.0103669
$557$	4.50635	−	7.80523i	0.190940	−	0.330718i	−0.754622	−	0.656160i	$-0.772180\pi$
$557$	4.50635	−	7.80523i	0.190940	−	0.330718i	0.945562	+	0.325442i	$0.105513\pi$
$558$	0.242999	−	0.140295i	0.0102870	−	0.00593918i
$559$	24.6976	+	42.7774i	1.04460	+	1.80929i
$560$	−8.88532	−	0.836134i	−0.375473	−	0.0353331i
$561$		−	1.49667i		−	0.0631894i
$562$	−10.1817	+	5.87838i	−0.429487	+	0.247965i
$563$	−38.7581			−1.63346			−0.816730	−	0.577021i	$-0.804215\pi$
$563$	−38.7581			−1.63346			−0.816730	+	0.577021i	$0.804215\pi$
$564$	9.87969	−	17.1121i	0.416010	−	0.720550i
$565$	11.3929	+	8.08929i	0.479303	+	0.340319i
$566$	13.7203			0.576706
$567$	−32.3248	−	18.6628i	−1.35752	−	0.783762i
$568$	0.469529	+	0.813247i	0.0197010	+	0.0341231i
$569$			8.08920i			0.339117i	0.985520	+	0.169559i	$0.0542342\pi$
$569$			8.08920i			0.339117i	−0.985520	+	0.169559i	$0.945766\pi$
$570$	−25.2927	+	11.5928i	−1.05940	+	0.485569i
$571$	−15.6120	+	27.0408i	−0.653343	+	1.13162i	0.328963	+	0.944343i	$0.393301\pi$
$571$	−15.6120	+	27.0408i	−0.653343	+	1.13162i	−0.982306	+	0.187281i	$0.940033\pi$
$572$	−3.23859	+	5.60939i	−0.135412	+	0.234541i
$573$	−5.77794	−	10.0077i	−0.241377	−	0.418077i
$574$	−14.4284	+	8.33024i	−0.602230	+	0.347697i
$575$	27.7631	+	5.27185i	1.15780	+	0.219851i
$576$	0.0611550	−	0.105924i	0.00254813	−	0.00441348i
$577$	2.36064	−	4.08875i	0.0982748	−	0.170217i	−0.812696	−	0.582688i	$-0.802001\pi$
$577$	2.36064	−	4.08875i	0.0982748	−	0.170217i	0.910971	+	0.412471i	$0.135334\pi$
$578$	16.4325			0.683503
$579$	24.7430	−	14.2854i	1.02828	−	0.593680i
$580$	2.47736	+	5.40500i	0.102867	+	0.224431i
$581$	−39.5630			−1.64135
$582$		−	3.37408i		−	0.139860i
$583$	0.406982	+	0.234971i	0.0168555	+	0.00973151i
$584$			8.97127i			0.371234i
$585$	0.147608	−	1.56858i	0.00610283	−	0.0648528i
$586$			18.7215i			0.773378i
$587$	−10.4048	−	18.0217i	−0.429453	−	0.743834i	0.567372	−	0.823462i	$-0.307960\pi$
$587$	−10.4048	−	18.0217i	−0.429453	−	0.743834i	−0.996825	+	0.0796274i	$0.974627\pi$
$588$	13.6647	−	7.88933i	0.563524	−	0.325351i
$589$	−8.07721	−	13.9901i	−0.332815	−	0.576453i
$590$	9.25458	+	20.1913i	0.381005	+	0.831262i
$591$	−21.8071			−0.897025
$592$	−2.03757	−	5.73134i	−0.0837436	−	0.235557i
$593$		−	45.0711i		−	1.85085i	−0.378931	−	0.925425i	$-0.623708\pi$
$593$		−	45.0711i		−	1.85085i	0.378931	−	0.925425i	$-0.376292\pi$
$594$	4.95136	+	2.85867i	0.203157	+	0.117293i
$595$	6.69343	+	0.629871i	0.274404	+	0.0258222i
$596$	−8.27747	−	14.3370i	−0.339058	−	0.587266i
$597$	8.31952	+	14.4098i	0.340495	+	0.589755i
$598$	−32.5584			−1.33141
$599$	1.68917	+	2.92573i	0.0690176	+	0.119542i	0.898469	−	0.439037i	$-0.144680\pi$
$599$	1.68917	+	2.92573i	0.0690176	+	0.119542i	−0.829452	+	0.558579i	$0.811347\pi$
$600$	−8.34114	+	2.91258i	−0.340526	+	0.118905i
$601$	10.8586	−	18.8076i	0.442931	−	0.767179i	−0.554974	−	0.831867i	$-0.687272\pi$
$601$	10.8586	−	18.8076i	0.442931	−	0.767179i	0.997906	+	0.0646882i	$0.0206053\pi$
$602$			34.2226i			1.39481i
$603$			0.695033i			0.0283039i
$604$	10.0750	−	17.4504i	0.409945	−	0.710046i
$605$	−2.03959	+	21.6741i	−0.0829213	+	0.881178i
$606$		−	6.46799i		−	0.262744i
$607$	−0.992390	+	1.71887i	−0.0402799	+	0.0697668i	−0.885463	−	0.464711i	$-0.846158\pi$
$607$	−0.992390	+	1.71887i	−0.0402799	+	0.0697668i	0.845183	+	0.534478i	$0.179492\pi$
$608$	−6.09832	−	3.52087i	−0.247320	−	0.142790i
$609$	−16.2401	−	9.37624i	−0.658083	−	0.379944i
$610$	13.5915	+	1.27900i	0.550304	+	0.0517852i
$611$	55.7878	−	32.2091i	2.25693	−	1.30304i
$612$	−0.0460689	+	0.0797937i	−0.00186223	+	0.00322547i
$613$	25.1987	+	14.5485i	1.01777	+	0.587608i	0.913456	−	0.406937i	$-0.133403\pi$
$613$	25.1987	+	14.5485i	1.01777	+	0.587608i	0.104310	+	0.994545i	$0.466737\pi$
$614$	−3.81686	−	2.20367i	−0.154036	−	0.0889327i
$615$	−9.54860	+	13.4482i	−0.385037	+	0.542283i
$616$	−3.88638	+	2.24380i	−0.156587	+	0.0904053i
$617$	7.57750	+	4.37487i	0.305059	+	0.176126i	0.644713	−	0.764425i	$-0.276977\pi$
$617$	7.57750	+	4.37487i	0.305059	+	0.176126i	−0.339654	+	0.940550i	$0.610310\pi$
$618$			27.4486i			1.10415i
$619$	−1.50546			−0.0605094			−0.0302547	−	0.999542i	$-0.509632\pi$
$619$	−1.50546			−0.0605094			−0.0302547	+	0.999542i	$0.509632\pi$
$620$	−2.13738	−	4.66326i	−0.0858394	−	0.187281i
$621$			28.7390i			1.15326i
$622$	23.3952	−	13.5073i	0.938064	−	0.541591i
$623$	−2.94596			−0.118028
$624$	8.81540	−	5.08958i	0.352899	−	0.203746i
$625$	23.2599	+	9.16393i	0.930396	+	0.366557i
$626$	3.20475	+	5.55078i	0.128087	+	0.221854i
$627$	−6.99519	+	12.1160i	−0.279361	+	0.483867i
$628$			21.2229i			0.846884i
$629$	1.53493	+	4.31750i	0.0612016	+	0.172150i
$630$	0.631948	−	0.890032i	0.0251774	−	0.0354597i
$631$	7.86491	+	4.54081i	0.313097	+	0.180767i	0.648312	−	0.761375i	$-0.275475\pi$
$631$	7.86491	+	4.54081i	0.313097	+	0.180767i	−0.335214	+	0.942142i	$0.608809\pi$
$632$	−2.97626	+	1.71834i	−0.118389	+	0.0683520i
$633$	27.4793	−	15.8652i	1.09220	−	0.630584i
$634$	−8.12713	+	4.69220i	−0.322770	+	0.186351i
$635$	22.2814	−	31.3810i	0.884211	−	1.24532i
$636$	−0.369267	−	0.639590i	−0.0146424	−	0.0253614i
$637$	51.4406			2.03815
$638$	2.58917	+	1.49486i	0.102506	+	0.0591820i
$639$	−0.114856			−0.00454364
$640$	−1.82323	−	1.29454i	−0.0720694	−	0.0511713i
$641$	−3.26546	+	5.65594i	−0.128978	+	0.223396i	−0.923281	−	0.384126i	$-0.874503\pi$
$641$	−3.26546	+	5.65594i	−0.128978	+	0.223396i	0.794303	+	0.607522i	$0.207836\pi$
$642$	−11.4835	−	19.8899i	−0.453216	−	0.784992i
$643$	−6.69746			−0.264122			−0.132061	−	0.991242i	$-0.542160\pi$
$643$	−6.69746			−0.264122			−0.132061	+	0.991242i	$0.542160\pi$
$644$	−19.5354	−	11.2788i	−0.769803	−	0.444446i
$645$	14.1163	+	30.7983i	0.555827	+	1.21268i
$646$	4.59395	+	2.65232i	0.180746	+	0.104354i
$647$	−6.84571	−	11.8571i	−0.269132	−	0.466151i	0.699506	−	0.714627i	$-0.253404\pi$
$647$	−6.84571	−	11.8571i	−0.269132	−	0.466151i	−0.968638	+	0.248476i	$0.920070\pi$
$648$	−4.67599	−	8.09904i	−0.183690	−	0.318160i
$649$	9.67226	+	5.58428i	0.379670	+	0.219202i
$650$	−28.2977	−	5.37338i	−1.10993	−	0.210761i
$651$	14.0114	+	8.08951i	0.549152	+	0.317053i
$652$	0.590707			0.0231339
$653$	−5.32021	−	9.21488i	−0.208196	−	0.360606i	0.742950	−	0.669347i	$-0.233426\pi$
$653$	−5.32021	−	9.21488i	−0.208196	−	0.360606i	−0.951146	+	0.308741i	$0.900093\pi$
$654$	13.4667	−	23.3249i	0.526588	−	0.912077i
$655$	14.1903	−	19.9855i	0.554459	−	0.780896i
$656$	−4.17431			−0.162980
$657$	−0.950270	−	0.548638i	−0.0370736	−	0.0214044i
$658$	44.6311			1.73990
$659$	6.31258	+	10.9337i	0.245903	+	0.425917i	0.962385	−	0.271689i	$-0.0875822\pi$
$659$	6.31258	+	10.9337i	0.245903	+	0.425917i	−0.716482	+	0.697606i	$0.754249\pi$
$660$	−2.57197	+	3.62235i	−0.100114	+	0.141000i
$661$	−38.4672	+	22.2090i	−1.49620	+	0.863831i	−0.999990	−	0.00437267i	$-0.998608\pi$
$661$	−38.4672	+	22.2090i	−1.49620	+	0.863831i	−0.496208	+	0.868203i	$0.665275\pi$
$662$	−13.3301	+	7.69616i	−0.518090	+	0.299120i
$663$	−6.64076	+	3.83405i	−0.257906	+	0.148902i
$664$	−8.58455	−	4.95629i	−0.333145	−	0.192341i
$665$	−51.2416	−	36.3830i	−1.98706	−	1.41087i
$666$	0.731692	+	0.134674i	0.0283525	+	0.00521850i
$667$			15.0282i			0.581895i
$668$	1.67520	−	2.90153i	0.0648154	−	0.112264i
$669$	−16.0500	−	27.7995i	−0.620531	−	1.07479i
$670$	12.6507	+	1.19046i	0.488738	+	0.0459917i
$671$	5.94483	−	3.43225i	0.229498	−	0.132501i
$672$	7.05246			0.272054
$673$	−33.3043	+	19.2282i	−1.28379	+	0.741194i	−0.977538	−	0.210757i	$-0.932407\pi$
$673$	−33.3043	+	19.2282i	−1.28379	+	0.741194i	−0.306248	+	0.951952i	$0.599074\pi$
$674$			5.80542i			0.223617i
$675$	−4.74303	+	24.9781i	−0.182559	+	0.961409i
$676$	20.1854			0.776362
$677$			8.06447i			0.309943i	0.987919	+	0.154971i	$0.0495285\pi$
$677$			8.06447i			0.309943i	−0.987919	+	0.154971i	$0.950471\pi$
$678$	−9.56229	−	5.52079i	−0.367238	−	0.212025i
$679$	6.60009	−	3.81056i	0.253288	−	0.146236i
$680$	1.37346	+	0.975198i	0.0526698	+	0.0373971i
$681$	9.62306	+	5.55588i	0.368756	+	0.212902i
$682$	−2.23385	−	1.28971i	−0.0855385	−	0.0493857i
$683$	−13.4194	+	23.2430i	−0.513478	+	0.889370i	0.486400	+	0.873736i	$0.338310\pi$
$683$	−13.4194	+	23.2430i	−0.513478	+	0.889370i	−0.999878	+	0.0156333i	$0.995024\pi$
$684$	0.745886	−	0.430637i	0.0285197	−	0.0164658i
$685$	51.6101	+	4.85665i	1.97192	+	0.185563i
$686$	6.66963	+	3.85072i	0.254648	+	0.147021i
$687$	13.0403	+	7.52884i	0.497520	+	0.287243i
$688$	−4.28727	+	7.42577i	−0.163451	+	0.283105i
$689$		−	2.40772i		−	0.0917269i
$690$	−22.2330	−	2.09219i	−0.846396	−	0.0796482i
$691$	−4.51646	+	7.82274i	−0.171814	+	0.297591i	−0.939054	−	0.343769i	$-0.888296\pi$
$691$	−4.51646	+	7.82274i	−0.171814	+	0.297591i	0.767240	+	0.641360i	$0.221630\pi$
$692$			17.5191i			0.665978i
$693$		−	0.548879i		−	0.0208502i
$694$	−1.49762	+	2.59396i	−0.0568489	+	0.0984653i
$695$	0.445684	+	0.316449i	0.0169058	+	0.0120036i
$696$	−2.34923	−	4.06899i	−0.0890475	−	0.154235i
$697$	3.14457			0.119109
$698$	−16.1132	−	27.9089i	−0.609894	−	1.05637i
$699$	−0.284001	−	0.491904i	−0.0107419	−	0.0186055i
$700$	−15.1175	−	13.0269i	−0.571389	−	0.492371i
$701$	32.6055	+	18.8248i	1.23149	+	0.711004i	0.967341	−	0.253477i	$-0.0815743\pi$
$701$	32.6055	+	18.8248i	1.23149	+	0.711004i	0.264153	+	0.964481i	$0.414908\pi$
$702$		−	29.2924i		−	1.10557i
$703$	7.75355	−	42.1256i	0.292431	−	1.58880i
$704$	−1.12438			−0.0423765
$705$	40.1653	−	18.4096i	1.51271	−	0.693345i
$706$	−4.35239	−	7.53855i	−0.163804	−	0.283717i
$707$	12.6522	−	7.30472i	0.475833	−	0.274722i
$708$	−8.77594	−	15.2004i	−0.329820	−	0.571265i
$709$		−	29.4137i		−	1.10465i	−0.833628	−	0.552327i	$-0.813740\pi$
$709$		−	29.4137i		−	1.10465i	0.833628	−	0.552327i	$-0.186260\pi$
$710$	−0.196728	+	2.09056i	−0.00738305	+	0.0784573i
$711$		−	0.420341i		−	0.0157640i
$712$	−0.639228	−	0.369058i	−0.0239561	−	0.0138310i
$713$		−	12.9659i		−	0.485575i
$714$	−5.31271			−0.198823
$715$	−13.1663	+	6.03471i	−0.492391	+	0.225685i
$716$	9.12369	−	5.26756i	0.340968	−	0.196858i
$717$	41.1647			1.53732
$718$	12.9231	−	22.3835i	0.482287	−	0.835345i
$719$	1.36520	−	2.36459i	0.0509133	−	0.0881844i	−0.839446	−	0.543444i	$-0.817120\pi$
$719$	1.36520	−	2.36459i	0.0509133	−	0.0881844i	0.890359	+	0.455259i	$0.150453\pi$
$720$	0.248622	−	0.113955i	0.00926561	−	0.00424685i
$721$	−53.6927	+	30.9995i	−1.99962	+	1.15448i
$722$	−15.2930	−	26.4883i	−0.569147	−	0.985791i
$723$	−20.3303	+	35.2132i	−0.756094	+	1.30959i
$724$	−1.36123	+	2.35772i	−0.0505897	+	0.0876239i
$725$	−2.48023	+	13.0616i	−0.0921134	+	0.485095i
$726$		−	17.2032i		−	0.638470i
$727$	18.7699	+	32.5104i	0.696136	+	1.20574i	0.969796	+	0.243917i	$0.0784323\pi$
$727$	18.7699	+	32.5104i	0.696136	+	1.20574i	−0.273660	+	0.961826i	$0.588234\pi$
$728$	19.9116	+	11.4960i	0.737974	+	0.426069i
$729$	−25.8113			−0.955973
$730$	−11.6137	+	16.3567i	−0.429843	+	0.605387i
$731$	3.22966	−	5.59393i	0.119453	−	0.206899i
$732$	−10.7879			−0.398731
$733$	−25.6263	+	14.7953i	−0.946528	+	0.546478i	−0.892001	−	0.452034i	$-0.850698\pi$
$733$	−25.6263	+	14.7953i	−0.946528	+	0.546478i	−0.0545272	+	0.998512i	$0.517365\pi$
$734$		−	14.8169i		−	0.546901i
$735$	35.1270	+	3.30555i	1.29568	+	0.121927i
$736$	−2.82592	−	4.89463i	−0.104165	−	0.180419i
$737$	5.53332	−	3.19466i	0.203822	−	0.117677i
$738$	0.255280	−	0.442158i	0.00939699	−	0.0162761i
$739$	−53.4401			−1.96582			−0.982912	−	0.184074i	$-0.941071\pi$
$739$	−53.4401			−1.96582			−0.982912	+	0.184074i	$0.941071\pi$
$740$	3.70453	−	13.0873i	0.136181	−	0.481097i
$741$	71.6789			2.63319
$742$	0.834075	−	1.44466i	0.0306199	−	0.0530352i
$743$	−1.25633	+	0.725343i	−0.0460903	+	0.0266102i	−0.522868	−	0.852414i	$-0.675138\pi$
$743$	−1.25633	+	0.725343i	−0.0460903	+	0.0266102i	0.476778	+	0.879024i	$0.341805\pi$
$744$	2.02684	+	3.51059i	0.0743076	+	0.128704i
$745$	3.46817	−	36.8551i	0.127064	−	1.35027i
$746$			20.9310i			0.766340i
$747$	1.04998	−	0.606204i	0.0384166	−	0.0221799i
$748$	0.847008			0.0309697
$749$	25.9380	−	44.9260i	0.947755	−	1.64156i
$750$	−18.9783	−	5.48769i	−0.692988	−	0.200382i
$751$	−15.9125			−0.580654			−0.290327	−	0.956928i	$-0.593764\pi$
$751$	−15.9125			−0.580654			−0.290327	+	0.956928i	$0.593764\pi$
$752$	9.68424	+	5.59120i	0.353148	+	0.203890i
$753$	−6.58688	−	11.4088i	−0.240039	−	0.415760i
$754$		−	15.3176i		−	0.557835i
$755$	40.9593	−	18.7735i	1.49066	−	0.683238i
$756$	10.1474	−	17.5758i	0.369057	−	0.639226i
$757$	−2.39331	+	4.14533i	−0.0869863	+	0.150665i	−0.906236	−	0.422772i	$-0.861057\pi$
$757$	−2.39331	+	4.14533i	−0.0869863	+	0.150665i	0.819250	+	0.573437i	$0.194390\pi$
$758$	−3.24827	−	5.62616i	−0.117982	−	0.204351i
$759$	−9.72456	+	5.61448i	−0.352979	+	0.203793i
$760$	−6.56070	−	14.3139i	−0.237982	−	0.519219i
$761$	4.63171	−	8.02237i	0.167900	−	0.290811i	−0.769782	−	0.638307i	$-0.779635\pi$
$761$	4.63171	−	8.02237i	0.167900	−	0.290811i	0.937681	+	0.347497i	$0.112968\pi$
$762$	−15.2067	+	26.3387i	−0.550880	+	0.954151i
$763$	60.8351			2.20238
$764$	5.66364	−	3.26990i	0.204903	−	0.118301i
$765$	−0.187291	+	0.0858438i	−0.00677150	+	0.00310369i
$766$	−27.8067			−1.00470
$767$		−	57.2215i		−	2.06615i
$768$	1.53027	+	0.883503i	0.0552189	+	0.0318807i
$769$			35.9197i			1.29530i	0.761940	+	0.647648i	$0.224247\pi$
$769$			35.9197i			1.29530i	−0.761940	+	0.647648i	$0.775753\pi$
$770$	−9.99044	−	0.940129i	−0.360031	−	0.0338799i
$771$		−	9.21742i		−	0.331957i
$772$	8.08451	+	14.0028i	0.290968	+	0.503971i
$773$	9.41162	−	5.43380i	0.338512	−	0.195440i	−0.321102	−	0.947045i	$-0.604053\pi$
$773$	9.41162	−	5.43380i	0.338512	−	0.195440i	0.659614	+	0.751605i	$0.270720\pi$
$774$	−0.524376	−	0.908246i	−0.0188483	−	0.0326462i
$775$	2.13986	−	11.2691i	0.0768660	−	0.404798i
$776$	1.90949			0.0685466
$777$	14.3699	+	40.4201i	0.515516	+	1.45006i
$778$		−	18.2583i		−	0.654591i
$779$	−25.4563	−	14.6972i	−0.912066	−	0.526582i
$780$	22.6612	+	2.13248i	0.811400	+	0.0763550i
$781$	0.527927	+	0.914396i	0.0188907	+	0.0327197i
$782$	2.12880	+	3.68719i	0.0761258	+	0.131854i
$783$	−13.5207			−0.483191
$784$	4.46480	+	7.73327i	0.159457	+	0.276188i
$785$	−27.4739	+	38.6941i	−0.980587	+	1.38105i
$786$	−9.68459	+	16.7742i	−0.345438	+	0.598316i
$787$			26.5706i			0.947140i	0.880756	+	0.473570i	$0.157035\pi$
$787$			26.5706i			0.947140i	−0.880756	+	0.473570i	$0.842965\pi$
$788$		−	12.3413i		−	0.439640i
$789$	−20.6755	+	35.8110i	−0.736066	+	1.27490i
$790$	−7.65086	−	0.719968i	−0.272206	−	0.0256153i
$791$		−	24.9400i		−	0.886763i
$792$	0.0687613	−	0.119098i	0.00244333	−	0.00423196i
$793$	−30.4580	−	17.5849i	−1.08160	−	0.624459i
$794$	10.6970	+	6.17594i	0.379624	+	0.219176i
$795$	0.154719	−	1.64415i	0.00548732	−	0.0583120i
$796$	−8.15495	+	4.70826i	−0.289044	+	0.166880i
$797$	6.97209	−	12.0760i	0.246964	−	0.427755i	−0.715718	−	0.698390i	$-0.753900\pi$
$797$	6.97209	−	12.0760i	0.246964	−	0.427755i	0.962682	+	0.270635i	$0.0872336\pi$
$798$	43.0082	+	24.8308i	1.52247	+	0.879000i
$799$	−7.29527	−	4.21193i	−0.258088	−	0.149007i
$800$	−1.64831	−	4.72049i	−0.0582766	−	0.166895i
$801$	0.0781840	−	0.0451395i	0.00276249	−	0.00159493i
$802$	7.38617	+	4.26441i	0.260815	+	0.150582i
$803$			10.0871i			0.355966i
$804$	−10.0411			−0.354122
$805$	−21.0166	−	45.8532i	−0.740739	−	1.61611i
$806$			13.2155i			0.465498i
$807$	−23.2891	+	13.4460i	−0.819816	+	0.473321i
$808$	3.66042			0.128773
$809$	−14.3319	+	8.27453i	−0.503883	+	0.290917i	−0.730316	−	0.683110i	$-0.760627\pi$
$809$	−14.3319	+	8.27453i	−0.503883	+	0.290917i	0.226433	+	0.974027i	$0.427294\pi$
$810$	1.95919	−	20.8197i	0.0688389	−	0.731528i
$811$	1.32946	+	2.30269i	0.0466837	+	0.0808585i	0.888423	−	0.459026i	$-0.151801\pi$
$811$	1.32946	+	2.30269i	0.0466837	+	0.0808585i	−0.841739	+	0.539884i	$0.818468\pi$
$812$	5.30629	−	9.19076i	0.186214	−	0.322532i
$813$			5.26361i			0.184603i
$814$	−2.29099	−	6.44419i	−0.0802993	−	0.225869i
$815$	1.07699	+	0.764696i	0.0377254	+	0.0267861i
$816$	−1.15277	−	0.665555i	−0.0403552	−	0.0232991i
$817$	−52.2903	+	30.1898i	−1.82940	+	1.05621i
$818$	15.7176	−	9.07457i	0.549553	−	0.317285i
$819$	−2.43539	+	1.40607i	−0.0850995	+	0.0491322i
$820$	−7.61072	−	5.40383i	−0.265778	−	0.188710i
$821$	−24.4954	−	42.4272i	−0.854894	−	1.48072i	−0.876743	−	0.480959i	$-0.840289\pi$
$821$	−24.4954	−	42.4272i	−0.854894	−	1.48072i	0.0218486	−	0.999761i	$-0.493045\pi$
$822$	−40.9640			−1.42878
$823$	26.2415	+	15.1505i	0.914721	+	0.528115i	0.881947	−	0.471348i	$-0.156232\pi$
$823$	26.2415	+	15.1505i	0.914721	+	0.528115i	0.0327742	+	0.999463i	$0.489566\pi$
$824$	−15.5340			−0.541151
$825$	−9.37858	+	3.27483i	−0.326520	+	0.114015i
$826$	19.8225	−	34.3336i	0.689713	−	1.19462i
$827$	23.4746	+	40.6592i	0.816291	+	1.41386i	0.908397	+	0.418108i	$0.137307\pi$
$827$	23.4746	+	40.6592i	0.816291	+	1.41386i	−0.0921062	+	0.995749i	$0.529360\pi$
$828$	0.691277			0.0240235
$829$	7.99309	+	4.61481i	0.277611	+	0.160279i	0.632342	−	0.774690i	$-0.282094\pi$
$829$	7.99309	+	4.61481i	0.277611	+	0.160279i	−0.354730	+	0.934969i	$0.615427\pi$
$830$	−9.23544	−	20.1495i	−0.320567	−	0.699400i
$831$	−23.5834	−	13.6159i	−0.818100	−	0.472330i
$832$	2.88034	+	4.98889i	0.0998578	+	0.172959i
$833$	−3.36340	−	5.82557i	−0.116535	−	0.201844i
$834$	−0.374072	−	0.215971i	−0.0129531	−	0.00747845i
$835$	6.81043	−	3.12153i	0.235685	−	0.108025i
$836$	−6.85681	−	3.95878i	−0.237148	−	0.136917i
$837$	11.6652			0.403210
$838$	0.982935	+	1.70249i	0.0339549	+	0.0588117i
$839$	0.776431	−	1.34482i	0.0268054	−	0.0464283i	−0.852312	−	0.523034i	$-0.824800\pi$
$839$	0.776431	−	1.34482i	0.0268054	−	0.0464283i	0.879117	+	0.476606i	$0.158133\pi$
$840$	12.8582	+	9.12972i	0.443651	+	0.315005i
$841$	21.9297			0.756197
$842$	4.94848	+	2.85700i	0.170536	+	0.0984589i
$843$	20.7743			0.715504
$844$	8.97857	+	15.5513i	0.309055	+	0.535299i
$845$	36.8026	+	26.1309i	1.26605	+	0.898930i
$846$	−1.18448	+	0.683860i	−0.0407233	+	0.0235116i
$847$	33.6515	−	19.4287i	1.15628	−	0.667577i
$848$	0.361962	−	0.208979i	0.0124298	−	0.00717637i
$849$	−20.9957	−	12.1219i	−0.720572	−	0.416023i
$850$	1.24170	+	3.55601i	0.0425898	+	0.121970i
$851$	22.2948	−	26.1695i	0.764257	−	0.897078i
$852$		−	1.65932i		−	0.0568474i
$853$	−8.67374	+	15.0234i	−0.296983	+	0.514390i	−0.975444	−	0.220246i	$-0.929314\pi$
$853$	−8.67374	+	15.0234i	−0.296983	+	0.514390i	0.678461	+	0.734636i	$0.262647\pi$
$854$	−12.1834	−	21.1023i	−0.416909	−	0.722107i
$855$	1.91740	+	0.180433i	0.0655736	+	0.00617066i
$856$	11.2563	−	6.49882i	0.384732	−	0.222125i
$857$	14.7315			0.503218			0.251609	−	0.967829i	$-0.419040\pi$
$857$	14.7315			0.503218			0.251609	+	0.967829i	$0.419040\pi$
$858$	9.91183	−	5.72260i	0.338384	−	0.195366i
$859$			1.90770i			0.0650899i	0.999470	+	0.0325449i	$0.0103612\pi$
$859$			1.90770i			0.0650899i	−0.999470	+	0.0325449i	$0.989639\pi$
$860$	−17.4296	+	7.98880i	−0.594346	+	0.272416i
$861$	29.4392			1.00328
$862$			29.7322i			1.01268i
$863$	47.6480	+	27.5096i	1.62196	+	0.936437i	0.986396	+	0.164385i	$0.0525639\pi$
$863$	47.6480	+	27.5096i	1.62196	+	0.936437i	0.635560	+	0.772052i	$0.280769\pi$
$864$	4.40365	−	2.54245i	0.149815	−	0.0864958i
$865$	−22.6793	+	31.9414i	−0.771119	+	1.08604i
$866$	7.63946	+	4.41064i	0.259599	+	0.149880i
$867$	−25.1462	−	14.5182i	−0.854011	−	0.493063i
$868$	−4.57809	+	7.92948i	−0.155390	+	0.269144i
$869$	−3.34643	+	1.93206i	−0.113520	+	0.0655408i
$870$	0.984304	−	10.4599i	0.0333710	−	0.354623i
$871$	−28.3496	−	16.3677i	−0.960591	−	0.554597i
$872$	13.2003	+	7.62117i	0.447017	+	0.258085i
$873$	−0.116775	+	0.202260i	−0.00395223	+	0.00684546i
$874$		−	39.7987i		−	1.34621i
$875$	−10.6988	−	43.3213i	−0.361686	−	1.46453i
$876$	7.92615	−	13.7285i	0.267800	−	0.463843i
$877$			27.2837i			0.921306i	0.887580	+	0.460653i	$0.152385\pi$
$877$			27.2837i			0.921306i	−0.887580	+	0.460653i	$0.847615\pi$
$878$		−	32.0265i		−	1.08084i
$879$	16.5405	−	28.6490i	0.557897	−	0.966306i
$880$	−2.04999	−	1.45555i	−0.0691052	−	0.0490667i
$881$	6.66001	+	11.5355i	0.224381	+	0.388640i	0.956134	−	0.292931i	$-0.0946305\pi$
$881$	6.66001	+	11.5355i	0.224381	+	0.388640i	−0.731752	+	0.681571i	$0.761297\pi$
$882$	−1.09218			−0.0367756
$883$	1.02963	+	1.78337i	0.0346499	+	0.0600153i	0.882830	−	0.469692i	$-0.155635\pi$
$883$	1.02963	+	1.78337i	0.0346499	+	0.0600153i	−0.848180	+	0.529707i	$0.822302\pi$
$884$	−2.16980	−	3.75820i	−0.0729782	−	0.126402i
$885$	3.67703	−	39.0746i	0.123602	−	1.31348i
$886$	17.0581	+	9.84848i	0.573077	+	0.330866i
$887$		−	50.7096i		−	1.70266i	−0.524630	−	0.851330i	$-0.675796\pi$
$887$		−	50.7096i		−	1.70266i	0.524630	−	0.851330i	$-0.324204\pi$
$888$	−1.94562	+	10.5707i	−0.0652909	+	0.354730i
$889$	−68.6956			−2.30398
$890$	−0.687695	−	1.50039i	−0.0230516	−	0.0502930i
$891$	−5.25757	−	9.10637i	−0.176135	−	0.305075i
$892$	15.7325	−	9.08319i	0.526765	−	0.304128i
$893$	39.3718	+	68.1939i	1.31753	+	2.28202i
$894$			29.2527i			0.978356i
$895$	23.4536	+	2.20705i	0.783969	+	0.0737737i
$896$			3.99119i			0.133336i
$897$	49.8232	+	28.7655i	1.66355	+	0.960451i
$898$			10.4222i			0.347793i
$899$	6.10000			0.203446
$900$	0.600814	+	0.114087i	0.0200271	+	0.00380290i
$901$	−0.272671	+	0.157427i	−0.00908399	+	0.00524465i
$902$	−4.69350			−0.156276
$903$	30.2358	−	52.3699i	1.00618	−	1.74276i
$904$	3.12438	−	5.41158i	0.103915	−	0.179986i
$905$	−5.53400	+	2.53648i	−0.183956	+	0.0843155i
$906$	−30.8349	+	17.8026i	−1.02442	+	0.591450i
$907$	−11.5434	−	19.9938i	−0.383293	−	0.663883i	0.608238	−	0.793755i	$-0.291877\pi$
$907$	−11.5434	−	19.9938i	−0.383293	−	0.663883i	−0.991531	+	0.129872i	$0.958543\pi$
$908$	−3.14423	+	5.44597i	−0.104345	+	0.180731i
$909$	−0.223853	+	0.387725i	−0.00742474	+	0.0128600i
$910$	21.4214	+	46.7363i	0.710111	+	1.54929i
$911$		−	37.6751i		−	1.24823i	−0.781331	−	0.624116i	$-0.785459\pi$
$911$		−	37.6751i		−	1.24823i	0.781331	−	0.624116i	$-0.214541\pi$
$912$	6.22139	+	10.7758i	0.206011	+	0.356821i
$913$	−9.65226	−	5.57274i	−0.319443	−	0.184431i
$914$	40.5184			1.34023
$915$	−19.6687	−	13.9654i	−0.650227	−	0.461680i
$916$	−4.26079	+	7.37991i	−0.140781	+	0.243839i
$917$	−43.7498			−1.44475
$918$	−3.31733	+	1.91526i	−0.109488	+	0.0632130i
$919$			36.4837i			1.20349i	0.798690	+	0.601743i	$0.205527\pi$
$919$			36.4837i			1.20349i	−0.798690	+	0.601743i	$0.794473\pi$
$920$	1.18403	−	12.5823i	0.0390363	−	0.414826i
$921$	3.89389	+	6.74441i	0.128308	+	0.222236i
$922$	0.172837	−	0.0997876i	0.00569209	−	0.00328633i
$923$	2.70480	−	4.68486i	0.0890297	−	0.154204i
$924$	7.92962			0.260865
$925$	23.6962	−	19.0654i	0.779127	−	0.626866i
$926$	−21.1594			−0.695340
$927$	0.949980	−	1.64541i	0.0312015	−	0.0540425i
$928$	2.30276	−	1.32950i	0.0755918	−	0.0436430i
$929$	−9.07242	−	15.7139i	−0.297656	−	0.515556i	0.677943	−	0.735115i	$-0.262872\pi$
$929$	−9.07242	−	15.7139i	−0.297656	−	0.515556i	−0.975599	+	0.219558i	$0.929538\pi$
$930$	−0.849225	+	9.02444i	−0.0278472	+	0.295923i
$931$			62.8799i			2.06081i
$932$	0.278383	−	0.160724i	0.00911873	−	0.00526470i
$933$	−47.7348			−1.56277
$934$	−19.3256	+	33.4730i	−0.632354	+	1.09527i
$935$	1.54429	+	1.09649i	0.0505036	+	0.0358590i
$936$	−0.704589			−0.0230302
$937$	−3.73106	−	2.15413i	−0.121888	−	0.0703723i	0.437816	−	0.899064i	$-0.355752\pi$
$937$	−3.73106	−	2.15413i	−0.121888	−	0.0703723i	−0.559705	+	0.828692i	$0.689085\pi$
$938$	−11.3401	−	19.6416i	−0.370266	−	0.641320i
$939$		−	11.3256i		−	0.369597i
$940$	10.4185	+	22.7307i	0.339815	+	0.741394i
$941$	−28.6354	+	49.5980i	−0.933488	+	1.61685i	−0.156179	+	0.987729i	$0.549918\pi$
$941$	−28.6354	+	49.5980i	−0.933488	+	1.61685i	−0.777309	+	0.629119i	$0.783416\pi$
$942$	18.7505	−	32.4768i	0.610923	−	1.05815i
$943$	−11.7963	−	20.4317i	−0.384139	−	0.665349i
$944$	8.60234	−	4.96656i	0.279982	−	0.161648i
$945$	41.2537	−	18.9084i	1.34198	−	0.615091i
$946$	−4.82050	+	8.34936i	−0.156728	+	0.271461i
$947$	11.5548	−	20.0135i	0.375480	−	0.650351i	−0.614918	−	0.788591i	$-0.710811\pi$
$947$	11.5548	−	20.0135i	0.375480	−	0.650351i	0.990399	+	0.138240i	$0.0441444\pi$
$948$	6.07265			0.197230
$949$	44.7567	−	25.8403i	1.45286	−	0.838812i
$950$	6.56830	−	34.5906i	0.213104	−	1.12227i
$951$	16.5823			0.537718
$952$		−	3.00662i		−	0.0974451i
$953$	−52.4700	−	30.2936i	−1.69967	−	0.981305i	−0.946064	−	0.323980i	$-0.894979\pi$
$953$	−52.4700	−	30.2936i	−1.69967	−	0.981305i	−0.753607	−	0.657325i	$-0.771688\pi$
$954$			0.0511205i			0.00165509i
$955$	14.5591	+	1.37005i	0.471122	+	0.0443339i
$956$			23.2963i			0.753457i
$957$	−2.64142	−	4.57508i	−0.0853851	−	0.147891i
$958$	−9.67769	+	5.58742i	−0.312672	+	0.180521i
$959$	−46.2633	−	80.1304i	−1.49392	−	2.58754i
$960$	1.64630	+	3.59183i	0.0531341	+	0.115926i
$961$	25.7371			0.830230
$962$	−22.7242	+	26.6734i	−0.732657	+	0.859986i
$963$			1.58974i			0.0512287i
$964$	−19.9282	−	11.5055i	−0.641843	−	0.370568i
$965$	−3.38732	+	35.9960i	−0.109042	+	1.15875i
$966$	19.9297	+	34.5192i	0.641227	+	1.11064i
$967$	−2.42170	−	4.19451i	−0.0778768	−	0.134886i	0.824457	−	0.565925i	$-0.191481\pi$
$967$	−2.42170	−	4.19451i	−0.0778768	−	0.134886i	−0.902334	+	0.431038i	$0.858147\pi$
$968$	9.73578			0.312920
$969$	−4.68666	−	8.11753i	−0.150557	−	0.260773i
$970$	3.48143	+	2.47192i	0.111782	+	0.0793684i
$971$	−19.2489	+	33.3400i	−0.617726	+	1.06993i	0.372174	+	0.928163i	$0.378613\pi$
$971$	−19.2489	+	33.3400i	−0.617726	+	1.06993i	−0.989900	+	0.141770i	$0.954721\pi$
$972$			1.27030i			0.0407449i
$973$		−	0.975639i		−	0.0312776i
$974$	−5.81329	+	10.0689i	−0.186270	+	0.322629i
$975$	38.5558	+	33.2239i	1.23478	+	1.06402i
$976$		−	6.10516i		−	0.195421i
$977$	15.2341	−	26.3861i	0.487380	−	0.844168i	−0.512514	−	0.858679i	$-0.671286\pi$
$977$	15.2341	−	26.3861i	0.487380	−	0.844168i	0.999895	+	0.0145110i	$0.00461916\pi$
$978$	−0.903942	−	0.521891i	−0.0289049	−	0.0166882i
$979$	−0.718732	−	0.414960i	−0.0229708	−	0.0132622i
$980$	−1.87071	+	19.8794i	−0.0597575	+	0.635024i
$981$	−1.61452	+	0.932146i	−0.0515478	+	0.0297611i
$982$	−6.54751	+	11.3406i	−0.208939	+	0.361894i
$983$	−39.4371	−	22.7690i	−1.25785	−	0.726218i	−0.285191	−	0.958471i	$-0.592057\pi$
$983$	−39.4371	−	22.7690i	−1.25785	−	0.726218i	−0.972656	+	0.232252i	$0.925390\pi$
$984$	6.38783	+	3.68802i	0.203637	+	0.117570i
$985$	15.9763	−	22.5010i	0.509048	−	0.716940i
$986$	−1.73470	+	1.00153i	−0.0552441	+	0.0318952i
$987$	−68.2977	−	39.4317i	−2.17394	−	1.25513i
$988$			40.5652i			1.29055i
$989$	−48.4619			−1.54100
$990$	0.279545	−	0.128128i	0.00888452	−	0.00407218i
$991$		−	45.1994i		−	1.43581i	−0.696143	−	0.717903i	$-0.745102\pi$
$991$		−	45.1994i		−	1.43581i	0.696143	−	0.717903i	$-0.254898\pi$
$992$	−1.98675	+	1.14705i	−0.0630792	+	0.0364188i
$993$	27.1983			0.863112
$994$	3.24583	−	1.87398i	0.102951	−	0.0594390i
$995$	−20.9634	−	1.97271i	−0.664583	−	0.0625392i
$996$	8.75779	+	15.1689i	0.277501	+	0.480646i
$997$	−1.77135	+	3.06806i	−0.0560991	+	0.0971666i	−0.892711	−	0.450629i	$-0.851200\pi$
$997$	−1.77135	+	3.06806i	−0.0560991	+	0.0971666i	0.836612	+	0.547796i	$0.184533\pi$
$998$			14.3166i			0.453182i
$999$	23.5444	+	20.0584i	0.744911	+	0.634620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.d.249.3	yes	16
5.4	even	2		370.2.m.c.249.6	yes	16
37.11	even	6		370.2.m.c.159.6	✓	16
185.159	even	6	inner	370.2.m.d.159.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.6	✓	16	37.11	even	6
370.2.m.c.249.6	yes	16	5.4	even	2
370.2.m.d.159.3	yes	16	185.159	even	6	inner
370.2.m.d.249.3	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.53027 + 0.883503i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.209495 - 2.22623i) q^{5} +1.76701i q^{6} +(-3.45647 + 1.99560i) q^{7} -1.00000 q^{8} +(0.0611550 - 0.105924i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.53027 + 0.883503i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.209495 - 2.22623i) q^{5} +1.76701i q^{6} +(-3.45647 + 1.99560i) q^{7} -1.00000 q^{8} +(0.0611550 - 0.105924i) q^{9} +(-1.82323 - 1.29454i) q^{10} -1.12438 q^{11} +(1.53027 + 0.883503i) q^{12} +(2.88034 + 4.98889i) q^{13} +3.99119i q^{14} +(1.64630 + 3.59183i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.376657 - 0.652389i) q^{17} +(-0.0611550 - 0.105924i) q^{18} +(-6.09832 + 3.52087i) q^{19} +(-2.03272 + 0.931689i) q^{20} +(3.52623 - 6.10761i) q^{21} +(-0.562188 + 0.973738i) q^{22} -5.65184 q^{23} +(1.53027 - 0.883503i) q^{24} +(-4.91222 - 0.932768i) q^{25} +5.76068 q^{26} -5.08490i q^{27} +(3.45647 + 1.99560i) q^{28} -2.65900i q^{29} +(3.93377 + 0.370178i) q^{30} +2.29410i q^{31} +(0.500000 + 0.866025i) q^{32} +(1.72060 - 0.993390i) q^{33} +(-0.376657 - 0.652389i) q^{34} +(3.71855 + 8.11298i) q^{35} -0.122310 q^{36} +(-3.94471 + 4.63026i) q^{37} +7.04173i q^{38} +(-8.81540 - 5.08958i) q^{39} +(-0.209495 + 2.22623i) q^{40} +(2.08716 + 3.61506i) q^{41} +(-3.52623 - 6.10761i) q^{42} +8.57454 q^{43} +(0.562188 + 0.973738i) q^{44} +(-0.222999 - 0.158336i) q^{45} +(-2.82592 + 4.89463i) q^{46} -11.1824i q^{47} -1.76701i q^{48} +(4.46480 - 7.73327i) q^{49} +(-3.26391 + 3.78773i) q^{50} +1.33111i q^{51} +(2.88034 - 4.98889i) q^{52} +(-0.361962 - 0.208979i) q^{53} +(-4.40365 - 2.54245i) q^{54} +(-0.235551 + 2.50312i) q^{55} +(3.45647 - 1.99560i) q^{56} +(6.22139 - 10.7758i) q^{57} +(-2.30276 - 1.32950i) q^{58} +(-8.60234 - 4.96656i) q^{59} +(2.28747 - 3.22165i) q^{60} +(-5.28723 + 3.05258i) q^{61} +(1.98675 + 1.14705i) q^{62} +0.488163i q^{63} +1.00000 q^{64} +(11.7099 - 5.36716i) q^{65} -1.98678i q^{66} +(-4.92123 + 2.84128i) q^{67} -0.753314 q^{68} +(8.64885 - 4.99341i) q^{69} +(8.88532 + 0.836134i) q^{70} +(-0.469529 - 0.813247i) q^{71} +(-0.0611550 + 0.105924i) q^{72} -8.97127i q^{73} +(2.03757 + 5.73134i) q^{74} +(8.34114 - 2.91258i) q^{75} +(6.09832 + 3.52087i) q^{76} +(3.88638 - 2.24380i) q^{77} +(-8.81540 + 5.08958i) q^{78} +(2.97626 - 1.71834i) q^{79} +(1.82323 + 1.29454i) q^{80} +(4.67599 + 8.09904i) q^{81} +4.17431 q^{82} +(8.58455 + 4.95629i) q^{83} -7.05246 q^{84} +(-1.37346 - 0.975198i) q^{85} +(4.28727 - 7.42577i) q^{86} +(2.34923 + 4.06899i) q^{87} +1.12438 q^{88} +(0.639228 + 0.369058i) q^{89} +(-0.248622 + 0.113955i) q^{90} +(-19.9116 - 11.4960i) q^{91} +(2.82592 + 4.89463i) q^{92} +(-2.02684 - 3.51059i) q^{93} +(-9.68424 - 5.59120i) q^{94} +(6.56070 + 14.3139i) q^{95} +(-1.53027 - 0.883503i) q^{96} -1.90949 q^{97} +(-4.46480 - 7.73327i) q^{98} +(-0.0687613 + 0.119098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} + 9 q^{15} - 8 q^{16} - 13 q^{18} - 3 q^{19} - 6 q^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{28} - 9 q^{30} + 8 q^{32} + 6 q^{33} + 18 q^{35} - 26 q^{36} + 16 q^{37} + 15 q^{39} + 7 q^{41} + 6 q^{42} - 22 q^{43} + 3 q^{44} + 4 q^{45} - 11 q^{46} + 4 q^{49} + 6 q^{50} - 6 q^{52} + 3 q^{53} + 9 q^{54} - 35 q^{55} + 12 q^{56} + 18 q^{57} + 36 q^{58} + 15 q^{59} - 18 q^{60} + 12 q^{61} - 33 q^{62} + 16 q^{64} + 46 q^{65} + 24 q^{67} + 42 q^{69} + 12 q^{70} - 4 q^{71} - 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} - 24 q^{77} + 15 q^{78} + 6 q^{80} + 10 q^{81} + 14 q^{82} + 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} + 50 q^{87} + 6 q^{88} + 9 q^{89} - q^{90} - 24 q^{91} + 11 q^{92} - 25 q^{93} - 27 q^{94} - 53 q^{95} - 3 q^{96} + 68 q^{97} - 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 + 3 * q^12 - 6 * q^13 + 9 * q^15 - 8 * q^16 - 13 * q^18 - 3 * q^19 - 6 * q^20 - 6 * q^21 - 3 * q^22 - 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 + 12 * q^28 - 9 * q^30 + 8 * q^32 + 6 * q^33 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 7 * q^41 + 6 * q^42 - 22 * q^43 + 3 * q^44 + 4 * q^45 - 11 * q^46 + 4 * q^49 + 6 * q^50 - 6 * q^52 + 3 * q^53 + 9 * q^54 - 35 * q^55 + 12 * q^56 + 18 * q^57 + 36 * q^58 + 15 * q^59 - 18 * q^60 + 12 * q^61 - 33 * q^62 + 16 * q^64 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * q^70 - 4 * q^71 - 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 - 24 * q^77 + 15 * q^78 + 6 * q^80 + 10 * q^81 + 14 * q^82 + 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 + 50 * q^87 + 6 * q^88 + 9 * q^89 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

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