LMFDB - Embedded newform 370.2.c.a.369.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(369,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("370.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.c (of order $2$, degree $1$, 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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			369.8
Root			$1.76216i$ of defining polynomial
Character	$\chi$	$=$	370.369
Dual form			370.2.c.a.369.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.76216i q^{3} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.76216i q^{6} -1.22131i q^{7} -1.00000 q^{8} -0.105209 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.76216i q^{3} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.76216i q^{6} -1.22131i q^{7} -1.00000 q^{8} -0.105209 q^{9} +(1.62868 + 1.53213i) q^{10} +1.87120 q^{11} +1.76216i q^{12} +6.50491 q^{13} +1.22131i q^{14} +(2.69985 - 2.86999i) q^{15} +1.00000 q^{16} -0.765994 q^{17} +0.105209 q^{18} +3.34507i q^{19} +(-1.62868 - 1.53213i) q^{20} +2.15215 q^{21} -1.87120 q^{22} +1.38964 q^{23} -1.76216i q^{24} +(0.305180 + 4.99068i) q^{25} -6.50491 q^{26} +5.10109i q^{27} -1.22131i q^{28} -1.72909i q^{29} +(-2.69985 + 2.86999i) q^{30} +4.11288i q^{31} -1.00000 q^{32} +3.29736i q^{33} +0.765994 q^{34} +(-1.87120 + 1.98912i) q^{35} -0.105209 q^{36} +(1.76599 - 5.82076i) q^{37} -3.34507i q^{38} +11.4627i q^{39} +(1.62868 + 1.53213i) q^{40} +3.73892 q^{41} -2.15215 q^{42} +4.91814 q^{43} +1.87120 q^{44} +(0.171351 + 0.161193i) q^{45} -1.38964 q^{46} -6.30775i q^{47} +1.76216i q^{48} +5.50840 q^{49} +(-0.305180 - 4.99068i) q^{50} -1.34980i q^{51} +6.50491 q^{52} -2.57768i q^{53} -5.10109i q^{54} +(-3.04759 - 2.86692i) q^{55} +1.22131i q^{56} -5.89455 q^{57} +1.72909i q^{58} +10.5664i q^{59} +(2.69985 - 2.86999i) q^{60} -11.1550i q^{61} -4.11288i q^{62} +0.128493i q^{63} +1.00000 q^{64} +(-10.5944 - 9.96634i) q^{65} -3.29736i q^{66} -11.1219i q^{67} -0.765994 q^{68} +2.44877i q^{69} +(1.87120 - 1.98912i) q^{70} +0.963126 q^{71} +0.105209 q^{72} +9.03119i q^{73} +(-1.76599 + 5.82076i) q^{74} +(-8.79437 + 0.537776i) q^{75} +3.34507i q^{76} -2.28532i q^{77} -11.4627i q^{78} +10.3333i q^{79} +(-1.62868 - 1.53213i) q^{80} -9.30456 q^{81} -3.73892 q^{82} -0.00656819i q^{83} +2.15215 q^{84} +(1.24756 + 1.17360i) q^{85} -4.91814 q^{86} +3.04694 q^{87} -1.87120 q^{88} -4.70144i q^{89} +(-0.171351 - 0.161193i) q^{90} -7.94452i q^{91} +1.38964 q^{92} -7.24756 q^{93} +6.30775i q^{94} +(5.12507 - 5.44804i) q^{95} -1.76216i q^{96} -0.403430 q^{97} -5.50840 q^{98} -0.196867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.76216i			1.01738i	0.860949	+	0.508692i	$0.169871\pi$
$3$			1.76216i			1.01738i	−0.860949	+	0.508692i	$0.830129\pi$
$4$	1.00000			0.500000
$5$	−1.62868	−	1.53213i	−0.728367	−	0.685188i
$5$	−1.62868	−	1.53213i	−0.728367	−	0.685188i
$6$		−	1.76216i		−	0.719399i
$7$		−	1.22131i		−	0.461612i	−0.973000	−	0.230806i	$-0.925864\pi$
$7$		−	1.22131i		−	0.461612i	0.973000	−	0.230806i	$-0.0741363\pi$
$8$	−1.00000			−0.353553
$9$	−0.105209			−0.0350696
$10$	1.62868	+	1.53213i	0.515033	+	0.484501i
$11$	1.87120			0.564189			0.282094	−	0.959387i	$-0.408971\pi$
$11$	1.87120			0.564189			0.282094	+	0.959387i	$0.408971\pi$
$12$			1.76216i			0.508692i
$13$	6.50491			1.80414			0.902069	−	0.431592i	$-0.142048\pi$
$13$	6.50491			1.80414			0.902069	+	0.431592i	$0.142048\pi$
$14$			1.22131i			0.326409i
$15$	2.69985	−	2.86999i	0.697099	−	0.741028i
$16$	1.00000			0.250000
$17$	−0.765994			−0.185781			−0.0928904	−	0.995676i	$-0.529611\pi$
$17$	−0.765994			−0.185781			−0.0928904	+	0.995676i	$0.529611\pi$
$18$	0.105209			0.0247979
$19$			3.34507i			0.767412i	0.923455	+	0.383706i	$0.125352\pi$
$19$			3.34507i			0.767412i	−0.923455	+	0.383706i	$0.874648\pi$
$20$	−1.62868	−	1.53213i	−0.364183	−	0.342594i
$21$	2.15215			0.469637
$22$	−1.87120			−0.398942
$23$	1.38964			0.289760			0.144880	−	0.989449i	$-0.453720\pi$
$23$	1.38964			0.289760			0.144880	+	0.989449i	$0.453720\pi$
$24$		−	1.76216i		−	0.359699i
$25$	0.305180	+	4.99068i	0.0610360	+	0.998136i
$26$	−6.50491			−1.27572
$27$			5.10109i			0.981704i
$28$		−	1.22131i		−	0.230806i
$29$		−	1.72909i		−	0.321084i	−0.987029	−	0.160542i	$-0.948676\pi$
$29$		−	1.72909i		−	0.321084i	0.987029	−	0.160542i	$-0.0513243\pi$
$30$	−2.69985	+	2.86999i	−0.492923	+	0.523986i
$31$			4.11288i			0.738695i	0.929291	+	0.369348i	$0.120419\pi$
$31$			4.11288i			0.738695i	−0.929291	+	0.369348i	$0.879581\pi$
$32$	−1.00000			−0.176777
$33$			3.29736i			0.573996i
$34$	0.765994			0.131367
$35$	−1.87120	+	1.98912i	−0.316291	+	0.336223i
$36$	−0.105209			−0.0175348
$37$	1.76599	−	5.82076i	0.290328	−	0.956927i
$37$	1.76599	−	5.82076i	0.290328	−	0.956927i
$38$		−	3.34507i		−	0.542642i
$39$			11.4627i			1.83550i
$40$	1.62868	+	1.53213i	0.257517	+	0.242250i
$41$	3.73892			0.583921			0.291960	−	0.956430i	$-0.405692\pi$
$41$	3.73892			0.583921			0.291960	+	0.956430i	$0.405692\pi$
$42$	−2.15215			−0.332083
$43$	4.91814			0.750009			0.375005	−	0.927023i	$-0.377641\pi$
$43$	4.91814			0.750009			0.375005	+	0.927023i	$0.377641\pi$
$44$	1.87120			0.282094
$45$	0.171351	+	0.161193i	0.0255435	+	0.0240292i
$46$	−1.38964			−0.204891
$47$		−	6.30775i		−	0.920080i	−0.887898	−	0.460040i	$-0.847835\pi$
$47$		−	6.30775i		−	0.920080i	0.887898	−	0.460040i	$-0.152165\pi$
$48$			1.76216i			0.254346i
$49$	5.50840			0.786914
$50$	−0.305180	−	4.99068i	−0.0431590	−	0.705788i
$51$		−	1.34980i		−	0.189010i
$52$	6.50491			0.902069
$53$		−	2.57768i		−	0.354072i	−0.984204	−	0.177036i	$-0.943349\pi$
$53$		−	2.57768i		−	0.354072i	0.984204	−	0.177036i	$-0.0566509\pi$
$54$		−	5.10109i		−	0.694170i
$55$	−3.04759	−	2.86692i	−0.410936	−	0.386575i
$56$			1.22131i			0.163205i
$57$	−5.89455			−0.780752
$58$			1.72909i			0.227041i
$59$			10.5664i			1.37563i	0.725887	+	0.687814i	$0.241429\pi$
$59$			10.5664i			1.37563i	−0.725887	+	0.687814i	$0.758571\pi$
$60$	2.69985	−	2.86999i	0.348549	−	0.370514i
$61$		−	11.1550i		−	1.42825i	−0.700020	−	0.714123i	$-0.746826\pi$
$61$		−	11.1550i		−	1.42825i	0.700020	−	0.714123i	$-0.253174\pi$
$62$		−	4.11288i		−	0.522337i
$63$			0.128493i			0.0161886i
$64$	1.00000			0.125000
$65$	−10.5944	−	9.96634i	−1.31407	−	1.23617i
$66$		−	3.29736i		−	0.405877i
$67$		−	11.1219i		−	1.35875i	−0.733789	−	0.679377i	$-0.762250\pi$
$67$		−	11.1219i		−	1.35875i	0.733789	−	0.679377i	$-0.237750\pi$
$68$	−0.765994			−0.0928904
$69$			2.44877i			0.294797i
$70$	1.87120	−	1.98912i	0.223651	−	0.237746i
$71$	0.963126			0.114302			0.0571510	−	0.998366i	$-0.481798\pi$
$71$	0.963126			0.114302			0.0571510	+	0.998366i	$0.481798\pi$
$72$	0.105209			0.0123990
$73$			9.03119i			1.05702i	0.848927	+	0.528511i	$0.177249\pi$
$73$			9.03119i			1.05702i	−0.848927	+	0.528511i	$0.822751\pi$
$74$	−1.76599	+	5.82076i	−0.205293	+	0.676650i
$75$	−8.79437	+	0.537776i	−1.01549	+	0.0620971i
$76$			3.34507i			0.383706i
$77$		−	2.28532i		−	0.260436i
$78$		−	11.4627i		−	1.29789i
$79$			10.3333i			1.16259i	0.813694	+	0.581293i	$0.197453\pi$
$79$			10.3333i			1.16259i	−0.813694	+	0.581293i	$0.802547\pi$
$80$	−1.62868	−	1.53213i	−0.182092	−	0.171297i
$81$	−9.30456			−1.03384
$82$	−3.73892			−0.412894
$83$		−	0.00656819i		−	0.000720953i	−1.00000		0.000360477i	$-0.999885\pi$
$83$		−	0.00656819i		−	0.000720953i	1.00000		0.000360477i	$-0.000114743\pi$
$84$	2.15215			0.234818
$85$	1.24756	+	1.17360i	0.135317	+	0.127295i
$86$	−4.91814			−0.530337
$87$	3.04694			0.326666
$88$	−1.87120			−0.199471
$89$		−	4.70144i		−	0.498352i	−0.968458	−	0.249176i	$-0.919840\pi$
$89$		−	4.70144i		−	0.498352i	0.968458	−	0.249176i	$-0.0801598\pi$
$90$	−0.171351	−	0.161193i	−0.0180620	−	0.0169912i
$91$		−	7.94452i		−	0.832812i
$92$	1.38964			0.144880
$93$	−7.24756			−0.751537
$94$			6.30775i			0.650595i
$95$	5.12507	−	5.44804i	0.525821	−	0.558957i
$96$		−	1.76216i		−	0.179850i
$97$	−0.403430			−0.0409621			−0.0204811	−	0.999790i	$-0.506520\pi$
$97$	−0.403430			−0.0409621			−0.0204811	+	0.999790i	$0.506520\pi$
$98$	−5.50840			−0.556432
$99$	−0.196867			−0.0197859
$100$	0.305180	+	4.99068i	0.0305180	+	0.499068i
$101$	−19.3724			−1.92762			−0.963812	−	0.266582i	$-0.914106\pi$
$101$	−19.3724			−1.92762			−0.963812	+	0.266582i	$0.914106\pi$
$102$			1.34980i			0.133650i
$103$	−5.56165			−0.548005			−0.274003	−	0.961729i	$-0.588348\pi$
$103$	−5.56165			−0.548005			−0.274003	+	0.961729i	$0.588348\pi$
$104$	−6.50491			−0.637859
$105$	−3.50515	−	3.29736i	−0.342068	−	0.321789i
$106$			2.57768i			0.250367i
$107$			1.93484i			0.187048i	0.995617	+	0.0935241i	$0.0298132\pi$
$107$			1.93484i			0.187048i	−0.995617	+	0.0935241i	$0.970187\pi$
$108$			5.10109i			0.490852i
$109$		−	8.70619i		−	0.833901i	−0.908929	−	0.416951i	$-0.863099\pi$
$109$		−	8.70619i		−	0.833901i	0.908929	−	0.416951i	$-0.136901\pi$
$110$	3.04759	+	2.86692i	0.290576	+	0.273350i
$111$	10.2571	+	3.11196i	0.973562	+	0.295375i
$112$		−	1.22131i		−	0.115403i
$113$	−14.7585			−1.38837			−0.694183	−	0.719798i	$-0.744234\pi$
$113$	−14.7585			−1.38837			−0.694183	+	0.719798i	$0.744234\pi$
$114$	5.89455			0.552075
$115$	−2.26327	−	2.12910i	−0.211051	−	0.198540i
$116$		−	1.72909i		−	0.160542i
$117$	−0.684374			−0.0632704
$118$		−	10.5664i		−	0.972715i
$119$			0.935517i			0.0857587i
$120$	−2.69985	+	2.86999i	−0.246462	+	0.261993i
$121$	−7.49860			−0.681691
$122$			11.1550i			1.00992i
$123$			6.58857i			0.594072i
$124$			4.11288i			0.369348i
$125$	7.14931	−	8.59578i	0.639453	−	0.768830i
$126$		−	0.128493i		−	0.0114470i
$127$			11.1280i			0.987453i	0.869617	+	0.493727i	$0.164366\pi$
$127$			11.1280i			0.987453i	−0.869617	+	0.493727i	$0.835634\pi$
$128$	−1.00000			−0.0883883
$129$			8.66655i			0.763047i
$130$	10.5944	+	9.96634i	0.929191	+	0.874106i
$131$		−	12.8363i		−	1.12152i	−0.827980	−	0.560758i	$-0.810510\pi$
$131$		−	12.8363i		−	1.12152i	0.827980	−	0.560758i	$-0.189490\pi$
$132$			3.29736i			0.286998i
$133$	4.08537			0.354247
$134$			11.1219i			0.960785i
$135$	7.81551	−	8.30802i	0.672652	−	0.715041i
$136$	0.765994			0.0656834
$137$		−	12.0355i		−	1.02826i	−0.857713	−	0.514129i	$-0.828115\pi$
$137$		−	12.0355i		−	1.02826i	0.857713	−	0.514129i	$-0.171885\pi$
$138$		−	2.44877i		−	0.208453i
$139$	−9.78562			−0.830005			−0.415003	−	0.909820i	$-0.636219\pi$
$139$	−9.78562			−0.830005			−0.415003	+	0.909820i	$0.636219\pi$
$140$	−1.87120	+	1.98912i	−0.158145	+	0.168111i
$141$	11.1153			0.936075
$142$	−0.963126			−0.0808237
$143$	12.1720			1.01787
$144$	−0.105209			−0.00876740
$145$	−2.64919	+	2.81613i	−0.220003	+	0.233867i
$146$		−	9.03119i		−	0.747427i
$147$			9.70668i			0.800594i
$148$	1.76599	−	5.82076i	0.145164	−	0.478464i
$149$	−11.8876			−0.973868			−0.486934	−	0.873439i	$-0.661885\pi$
$149$	−11.8876			−0.973868			−0.486934	+	0.873439i	$0.661885\pi$
$150$	8.79437	−	0.537776i	0.718058	−	0.0439093i
$151$	21.3141			1.73452			0.867259	−	0.497857i	$-0.165880\pi$
$151$	21.3141			1.73452			0.867259	+	0.497857i	$0.165880\pi$
$152$		−	3.34507i		−	0.271321i
$153$	0.0805893			0.00651526
$154$			2.28532i			0.184156i
$155$	6.30145	−	6.69856i	0.506145	−	0.538041i
$156$			11.4627i			0.917750i
$157$			15.3009i			1.22115i	0.791960	+	0.610573i	$0.209061\pi$
$157$			15.3009i			1.22115i	−0.791960	+	0.610573i	$0.790939\pi$
$158$		−	10.3333i		−	0.822072i
$159$	4.54229			0.360227
$160$	1.62868	+	1.53213i	0.128758	+	0.121125i
$161$		−	1.69718i		−	0.133757i
$162$	9.30456			0.731035
$163$	−14.9177			−1.16844			−0.584221	−	0.811595i	$-0.698600\pi$
$163$	−14.9177			−1.16844			−0.584221	+	0.811595i	$0.698600\pi$
$164$	3.73892			0.291960
$165$	5.05197	−	5.37033i	0.393295	−	0.418080i
$166$			0.00656819i			0.000509791i
$167$	17.3041			1.33903			0.669514	−	0.742800i	$-0.266502\pi$
$167$	17.3041			1.33903			0.669514	+	0.742800i	$0.266502\pi$
$168$	−2.15215			−0.166042
$169$	29.3139			2.25491
$170$	−1.24756	−	1.17360i	−0.0956832	−	0.0900109i
$171$		−	0.351931i		−	0.0269128i
$172$	4.91814			0.375005
$173$			19.7322i			1.50021i	0.661317	+	0.750107i	$0.269998\pi$
$173$			19.7322i			1.50021i	−0.661317	+	0.750107i	$0.730002\pi$
$174$	−3.04694			−0.230988
$175$	6.09517	−	0.372720i	0.460752	−	0.0281750i
$176$	1.87120			0.141047
$177$	−18.6197			−1.39954
$178$			4.70144i			0.352388i
$179$		−	3.70357i		−	0.276818i	−0.990375	−	0.138409i	$-0.955801\pi$
$179$		−	3.70357i		−	0.276818i	0.990375	−	0.138409i	$-0.0441988\pi$
$180$	0.171351	+	0.161193i	0.0127718	+	0.0120146i
$181$	−10.4093			−0.773714			−0.386857	−	0.922140i	$-0.626439\pi$
$181$	−10.4093			−0.773714			−0.386857	+	0.922140i	$0.626439\pi$
$182$			7.94452i			0.588887i
$183$	19.6568			1.45307
$184$	−1.38964			−0.102446
$185$	−11.7944	+	6.77442i	−0.867140	+	0.498065i
$186$	7.24756			0.531417
$187$	−1.43333			−0.104815
$188$		−	6.30775i		−	0.460040i
$189$	6.23001			0.453167
$190$	−5.12507	+	5.44804i	−0.371812	+	0.395242i
$191$			23.0954i			1.67113i	0.549395	+	0.835563i	$0.314858\pi$
$191$			23.0954i			1.67113i	−0.549395	+	0.835563i	$0.685142\pi$
$192$			1.76216i			0.127173i
$193$	−12.4951			−0.899418			−0.449709	−	0.893175i	$-0.648472\pi$
$193$	−12.4951			−0.899418			−0.449709	+	0.893175i	$0.648472\pi$
$194$	0.403430			0.0289646
$195$	17.5623	−	18.6690i	1.25766	−	1.33692i
$196$	5.50840			0.393457
$197$		−	5.51302i		−	0.392786i	−0.980525	−	0.196393i	$-0.937077\pi$
$197$		−	5.51302i		−	0.392786i	0.980525	−	0.196393i	$-0.0629229\pi$
$198$	0.196867			0.0139907
$199$		−	18.8033i		−	1.33293i	−0.745537	−	0.666464i	$-0.767807\pi$
$199$		−	18.8033i		−	1.33293i	0.745537	−	0.666464i	$-0.232193\pi$
$200$	−0.305180	−	4.99068i	−0.0215795	−	0.352894i
$201$	19.5985			1.38237
$202$	19.3724			1.36304
$203$	−2.11176			−0.148216
$204$		−	1.34980i		−	0.0945052i
$205$	−6.08949	−	5.72849i	−0.425309	−	0.400095i
$206$	5.56165			0.387498
$207$	−0.146202			−0.0101618
$208$	6.50491			0.451034
$209$			6.25931i			0.432965i
$210$	3.50515	+	3.29736i	0.241878	+	0.227539i
$211$	−26.6632			−1.83557			−0.917784	−	0.397081i	$-0.870023\pi$
$211$	−26.6632			−1.83557			−0.917784	+	0.397081i	$0.870023\pi$
$212$		−	2.57768i		−	0.177036i
$213$			1.69718i			0.116289i
$214$		−	1.93484i		−	0.132263i
$215$	−8.01006	−	7.53521i	−0.546282	−	0.513897i
$216$		−	5.10109i		−	0.347085i
$217$	5.02311			0.340991
$218$			8.70619i			0.589657i
$219$	−15.9144			−1.07540
$220$	−3.04759	−	2.86692i	−0.205468	−	0.193288i
$221$	−4.98272			−0.335174
$222$	−10.2571	−	3.11196i	−0.688412	−	0.208861i
$223$			10.8630i			0.727441i	0.931508	+	0.363721i	$0.118494\pi$
$223$			10.8630i			0.727441i	−0.931508	+	0.363721i	$0.881506\pi$
$224$			1.22131i			0.0816023i
$225$	−0.0321076	−	0.525063i	−0.00214051	−	0.0350042i
$226$	14.7585			0.981723
$227$	6.82427			0.452942			0.226471	−	0.974018i	$-0.427281\pi$
$227$	6.82427			0.452942			0.226471	+	0.974018i	$0.427281\pi$
$228$	−5.89455			−0.390376
$229$	2.56189			0.169294			0.0846471	−	0.996411i	$-0.473024\pi$
$229$	2.56189			0.169294			0.0846471	+	0.996411i	$0.473024\pi$
$230$	2.26327	+	2.12910i	0.149236	+	0.140389i
$231$	4.02710			0.264964
$232$			1.72909i			0.113520i
$233$			23.3423i			1.52921i	0.644502	+	0.764603i	$0.277065\pi$
$233$			23.3423i			1.52921i	−0.644502	+	0.764603i	$0.722935\pi$
$234$	0.684374			0.0447389
$235$	−9.66427	+	10.2733i	−0.630428	+	0.670156i
$236$			10.5664i			0.687814i
$237$	−18.2089			−1.18280
$238$		−	0.935517i		−	0.0606405i
$239$		−	5.19256i		−	0.335879i	−0.985797	−	0.167940i	$-0.946289\pi$
$239$		−	5.19256i		−	0.335879i	0.985797	−	0.167940i	$-0.0537113\pi$
$240$	2.69985	−	2.86999i	0.174275	−	0.185257i
$241$		−	15.5243i		−	1.00001i	−0.866022	−	0.500005i	$-0.833331\pi$
$241$		−	15.5243i		−	1.00001i	0.866022	−	0.500005i	$-0.166669\pi$
$242$	7.49860			0.482028
$243$		−	1.09286i		−	0.0701072i
$244$		−	11.1550i		−	0.714123i
$245$	−8.97140	−	8.43956i	−0.573162	−	0.539184i
$246$		−	6.58857i		−	0.420072i
$247$			21.7594i			1.38452i
$248$		−	4.11288i		−	0.261168i
$249$	0.0115742			0.000733486
$250$	−7.14931	+	8.59578i	−0.452162	+	0.543645i
$251$			3.85199i			0.243136i	0.992583	+	0.121568i	$0.0387922\pi$
$251$			3.85199i			0.243136i	−0.992583	+	0.121568i	$0.961208\pi$
$252$			0.128493i			0.00809428i
$253$	2.60030			0.163479
$254$		−	11.1280i		−	0.698235i
$255$	−2.06807	+	2.19840i	−0.129508	+	0.137669i
$256$	1.00000			0.0625000
$257$	3.34529			0.208673			0.104337	−	0.994542i	$-0.466728\pi$
$257$	3.34529			0.208673			0.104337	+	0.994542i	$0.466728\pi$
$258$		−	8.66655i		−	0.539556i
$259$	−7.10896	−	2.15683i	−0.441729	−	0.134019i
$260$	−10.5944	−	9.96634i	−0.657037	−	0.618086i
$261$			0.181916i			0.0112603i
$262$			12.8363i			0.793031i
$263$			1.14405i			0.0705454i	0.999378	+	0.0352727i	$0.0112300\pi$
$263$			1.14405i			0.0705454i	−0.999378	+	0.0352727i	$0.988770\pi$
$264$		−	3.29736i		−	0.202938i
$265$	−3.94934	+	4.19821i	−0.242606	+	0.257894i
$266$	−4.08537			−0.250490
$267$	8.28470			0.507015
$268$		−	11.1219i		−	0.679377i
$269$	15.1344			0.922760			0.461380	−	0.887203i	$-0.347355\pi$
$269$	15.1344			0.922760			0.461380	+	0.887203i	$0.347355\pi$
$270$	−7.81551	+	8.30802i	−0.475637	+	0.505610i
$271$	−18.2842			−1.11069			−0.555344	−	0.831621i	$-0.687413\pi$
$271$	−18.2842			−1.11069			−0.555344	+	0.831621i	$0.687413\pi$
$272$	−0.765994			−0.0464452
$273$	13.9995			0.847289
$274$			12.0355i			0.727088i
$275$	0.571054	+	9.33857i	0.0344359	+	0.563137i
$276$			2.44877i			0.147398i
$277$	2.58352			0.155229			0.0776145	−	0.996983i	$-0.475270\pi$
$277$	2.58352			0.155229			0.0776145	+	0.996983i	$0.475270\pi$
$278$	9.78562			0.586902
$279$		−	0.432711i		−	0.0259057i
$280$	1.87120	−	1.98912i	0.111826	−	0.118873i
$281$			19.3056i			1.15168i	0.817563	+	0.575839i	$0.195325\pi$
$281$			19.3056i			1.15168i	−0.817563	+	0.575839i	$0.804675\pi$
$282$	−11.1153			−0.661905
$283$	9.02942			0.536743			0.268372	−	0.963315i	$-0.413514\pi$
$283$	9.02942			0.536743			0.268372	+	0.963315i	$0.413514\pi$
$284$	0.963126			0.0571510
$285$	9.60032	+	9.03119i	0.568674	+	0.534962i
$286$	−12.1720			−0.719746
$287$		−	4.56638i		−	0.269545i
$288$	0.105209			0.00619949
$289$	−16.4133			−0.965485
$290$	2.64919	−	2.81613i	0.155566	−	0.165369i
$291$		−	0.710909i		−	0.0416742i
$292$			9.03119i			0.528511i
$293$		−	13.0845i		−	0.764405i	−0.924079	−	0.382203i	$-0.875166\pi$
$293$		−	13.0845i		−	0.764405i	0.924079	−	0.382203i	$-0.124834\pi$
$294$		−	9.70668i		−	0.566105i
$295$	16.1890	−	17.2092i	0.942563	−	1.00196i
$296$	−1.76599	+	5.82076i	−0.102646	+	0.338325i
$297$			9.54517i			0.553867i
$298$	11.8876			0.688629
$299$	9.03948			0.522767
$300$	−8.79437	+	0.537776i	−0.507743	+	0.0310485i
$301$		−	6.00658i		−	0.346213i
$302$	−21.3141			−1.22649
$303$		−	34.1373i		−	1.96113i
$304$			3.34507i			0.191853i
$305$	−17.0908	+	18.1678i	−0.978616	+	1.04029i
$306$	−0.0805893			−0.00460698
$307$			7.60942i			0.434293i	0.976139	+	0.217146i	$0.0696749\pi$
$307$			7.60942i			0.434293i	−0.976139	+	0.217146i	$0.930325\pi$
$308$		−	2.28532i		−	0.130218i
$309$		−	9.80051i		−	0.557532i
$310$	−6.30145	+	6.69856i	−0.357898	+	0.380453i
$311$			15.2359i			0.863950i	0.901886	+	0.431975i	$0.142183\pi$
$311$			15.2359i			0.863950i	−0.901886	+	0.431975i	$0.857817\pi$
$312$		−	11.4627i		−	0.648947i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		−	15.3009i		−	0.863480i
$315$	0.196867	−	0.209273i	0.0110922	−	0.0117912i
$316$			10.3333i			0.581293i
$317$		−	34.1403i		−	1.91751i	−0.284230	−	0.958756i	$-0.591738\pi$
$317$		−	34.1403i		−	1.91751i	0.284230	−	0.958756i	$-0.408262\pi$
$318$	−4.54229			−0.254719
$319$		−	3.23548i		−	0.181152i
$320$	−1.62868	−	1.53213i	−0.0910458	−	0.0856484i
$321$	−3.40950			−0.190300
$322$			1.69718i			0.0945803i
$323$		−	2.56230i		−	0.142570i
$324$	−9.30456			−0.516920
$325$	1.98517	+	32.4639i	0.110117	+	1.80077i
$326$	14.9177			0.826213
$327$	15.3417			0.848398
$328$	−3.73892			−0.206447
$329$	−7.70373			−0.424720
$330$	−5.05197	+	5.37033i	−0.278102	+	0.295627i
$331$		−	27.2567i		−	1.49817i	−0.662476	−	0.749083i	$-0.730494\pi$
$331$		−	27.2567i		−	1.49817i	0.662476	−	0.749083i	$-0.269506\pi$
$332$		−	0.00656819i		−	0.000360477i
$333$	−0.185798	+	0.612395i	−0.0101817	+	0.0335590i
$334$	−17.3041			−0.946836
$335$	−17.0401	+	18.1140i	−0.931002	+	0.989672i
$336$	2.15215			0.117409
$337$		−	22.5315i		−	1.22737i	−0.789552	−	0.613683i	$-0.789687\pi$
$337$		−	22.5315i		−	1.22737i	0.789552	−	0.613683i	$-0.210313\pi$
$338$	−29.3139			−1.59446
$339$		−	26.0069i		−	1.41250i
$340$	1.24756	+	1.17360i	0.0676583	+	0.0636473i
$341$			7.69603i			0.416764i
$342$			0.351931i			0.0190302i
$343$		−	15.2766i		−	0.824861i
$344$	−4.91814			−0.265168
$345$	3.75182	−	3.98825i	0.201991	−	0.214720i
$346$		−	19.7322i		−	1.06081i
$347$	−34.7252			−1.86415			−0.932073	−	0.362272i	$-0.882001\pi$
$347$	−34.7252			−1.86415			−0.932073	+	0.362272i	$0.882001\pi$
$348$	3.04694			0.163333
$349$	15.9343			0.852942			0.426471	−	0.904501i	$-0.359757\pi$
$349$	15.9343			0.852942			0.426471	+	0.904501i	$0.359757\pi$
$350$	−6.09517	+	0.372720i	−0.325801	+	0.0199227i
$351$			33.1821i			1.77113i
$352$	−1.87120			−0.0997354
$353$	20.1925			1.07474			0.537370	−	0.843347i	$-0.319418\pi$
$353$	20.1925			1.07474			0.537370	+	0.843347i	$0.319418\pi$
$354$	18.6197			0.989625
$355$	−1.56862	−	1.47563i	−0.0832538	−	0.0783183i
$356$		−	4.70144i		−	0.249176i
$357$	−1.64853			−0.0872495
$358$			3.70357i			0.195740i
$359$	−30.8657			−1.62903			−0.814515	−	0.580143i	$-0.802997\pi$
$359$	−30.8657			−1.62903			−0.814515	+	0.580143i	$0.802997\pi$
$360$	−0.171351	−	0.161193i	−0.00903100	−	0.00849562i
$361$	7.81050			0.411079
$362$	10.4093			0.547099
$363$		−	13.2137i		−	0.693541i
$364$		−	7.94452i		−	0.416406i
$365$	13.8369	−	14.7089i	0.724258	−	0.769899i
$366$	−19.6568			−1.02748
$367$			28.9254i			1.50989i	0.655786	+	0.754947i	$0.272337\pi$
$367$			28.9254i			1.50989i	−0.655786	+	0.754947i	$0.727663\pi$
$368$	1.38964			0.0724400
$369$	−0.393367			−0.0204779
$370$	11.7944	−	6.77442i	0.613160	−	0.352185i
$371$	−3.14815			−0.163444
$372$	−7.24756			−0.375768
$373$		−	27.8899i		−	1.44408i	−0.691849	−	0.722042i	$-0.743204\pi$
$373$		−	27.8899i		−	1.44408i	0.691849	−	0.722042i	$-0.256796\pi$
$374$	1.43333			0.0741157
$375$	15.1471	+	12.5982i	0.782195	+	0.650570i
$376$			6.30775i			0.325298i
$377$		−	11.2476i		−	0.579280i
$378$	−6.23001			−0.320437
$379$	−5.73365			−0.294518			−0.147259	−	0.989098i	$-0.547045\pi$
$379$	−5.73365			−0.294518			−0.147259	+	0.989098i	$0.547045\pi$
$380$	5.12507	−	5.44804i	0.262911	−	0.279479i
$381$	−19.6094			−1.00462
$382$		−	23.0954i		−	1.18166i
$383$	17.8363			0.911391			0.455696	−	0.890136i	$-0.349391\pi$
$383$	17.8363			0.911391			0.455696	+	0.890136i	$0.349391\pi$
$384$		−	1.76216i		−	0.0899249i
$385$	−3.50140	+	3.72205i	−0.178448	+	0.189693i
$386$	12.4951			0.635985
$387$	−0.517431			−0.0263025
$388$	−0.403430			−0.0204811
$389$		−	29.8974i		−	1.51586i	−0.652337	−	0.757929i	$-0.726211\pi$
$389$		−	29.8974i		−	1.51586i	0.652337	−	0.757929i	$-0.273789\pi$
$390$	−17.5623	+	18.6690i	−0.889301	+	0.945343i
$391$	−1.06446			−0.0538318
$392$	−5.50840			−0.278216
$393$	22.6197			1.14101
$394$			5.51302i			0.277742i
$395$	15.8319	−	16.8296i	0.796589	−	0.846789i
$396$	−0.196867			−0.00989293
$397$		−	13.2064i		−	0.662812i	−0.943488	−	0.331406i	$-0.892477\pi$
$397$		−	13.2064i		−	0.662812i	0.943488	−	0.331406i	$-0.107523\pi$
$398$			18.8033i			0.942523i
$399$			7.19908i			0.360405i
$400$	0.305180	+	4.99068i	0.0152590	+	0.249534i
$401$			23.0269i			1.14991i	0.818185	+	0.574954i	$0.194980\pi$
$401$			23.0269i			1.14991i	−0.818185	+	0.574954i	$0.805020\pi$
$402$	−19.5985			−0.977487
$403$			26.7539i			1.33271i
$404$	−19.3724			−0.963812
$405$	15.1541	+	14.2558i	0.753014	+	0.708374i
$406$	2.11176			0.104805
$407$	3.30453	−	10.8918i	0.163800	−	0.539888i
$408$			1.34980i			0.0668252i
$409$		−	9.77049i		−	0.483120i	−0.970386	−	0.241560i	$-0.922341\pi$
$409$		−	9.77049i		−	0.483120i	0.970386	−	0.241560i	$-0.0776590\pi$
$410$	6.08949	+	5.72849i	0.300739	+	0.282910i
$411$	21.2084			1.04613
$412$	−5.56165			−0.274003
$413$	12.9049			0.635006
$414$	0.146202			0.00718545
$415$	−0.0100633	+	0.0106975i	−0.000493988	+	0.000525118i
$416$	−6.50491			−0.318930
$417$		−	17.2438i		−	0.844434i
$418$		−	6.25931i		−	0.306153i
$419$	2.06109			0.100691			0.0503455	−	0.998732i	$-0.483968\pi$
$419$	2.06109			0.100691			0.0503455	+	0.998732i	$0.483968\pi$
$420$	−3.50515	−	3.29736i	−0.171034	−	0.160895i
$421$			12.8910i			0.628271i	0.949378	+	0.314135i	$0.101715\pi$
$421$			12.8910i			0.628271i	−0.949378	+	0.314135i	$0.898285\pi$
$422$	26.6632			1.29794
$423$			0.663631i			0.0322668i
$424$			2.57768i			0.125183i
$425$	−0.233766	−	3.82283i	−0.0113393	−	0.185434i
$426$		−	1.69718i		−	0.0822288i
$427$	−13.6237			−0.659296
$428$			1.93484i			0.0935241i
$429$			21.4490i			1.03557i
$430$	8.01006	+	7.53521i	0.386280	+	0.363380i
$431$		−	9.41662i		−	0.453582i	−0.973943	−	0.226791i	$-0.927176\pi$
$431$		−	9.41662i		−	0.453582i	0.973943	−	0.226791i	$-0.0728235\pi$
$432$			5.10109i			0.245426i
$433$		−	3.07581i		−	0.147814i	−0.997265	−	0.0739069i	$-0.976453\pi$
$433$		−	3.07581i		−	0.147814i	0.997265	−	0.0739069i	$-0.0235468\pi$
$434$	−5.02311			−0.241117
$435$	−4.96248	−	4.66829i	−0.237933	−	0.223827i
$436$		−	8.70619i		−	0.416951i
$437$			4.64844i			0.222365i
$438$	15.9144			0.760420
$439$			1.93763i			0.0924780i	0.998930	+	0.0462390i	$0.0147236\pi$
$439$			1.93763i			0.0924780i	−0.998930	+	0.0462390i	$0.985276\pi$
$440$	3.04759	+	2.86692i	0.145288	+	0.136675i
$441$	−0.579532			−0.0275968
$442$	4.98272			0.237004
$443$			26.5690i			1.26233i	0.775649	+	0.631165i	$0.217423\pi$
$443$			26.5690i			1.26233i	−0.775649	+	0.631165i	$0.782577\pi$
$444$	10.2571	+	3.11196i	0.486781	+	0.147687i
$445$	−7.20320	+	7.65713i	−0.341465	+	0.362983i
$446$		−	10.8630i		−	0.514379i
$447$		−	20.9478i		−	0.990798i
$448$		−	1.22131i		−	0.0577015i
$449$		−	0.777045i		−	0.0366710i	−0.999832	−	0.0183355i	$-0.994163\pi$
$449$		−	0.777045i		−	0.0366710i	0.999832	−	0.0183355i	$-0.00583670\pi$
$450$	0.0321076	+	0.525063i	0.00151357	+	0.0247517i
$451$	6.99627			0.329442
$452$	−14.7585			−0.694183
$453$			37.5589i			1.76467i
$454$	−6.82427			−0.320279
$455$	−12.1720	+	12.9391i	−0.570633	+	0.606593i
$456$	5.89455			0.276038
$457$	21.1753			0.990537			0.495268	−	0.868740i	$-0.335070\pi$
$457$	21.1753			0.990537			0.495268	+	0.868740i	$0.335070\pi$
$458$	−2.56189			−0.119709
$459$		−	3.90740i		−	0.182382i
$460$	−2.26327	−	2.12910i	−0.105526	−	0.0992699i
$461$			23.9797i			1.11685i	0.829556	+	0.558424i	$0.188594\pi$
$461$			23.9797i			1.11685i	−0.829556	+	0.558424i	$0.811406\pi$
$462$	−4.02710			−0.187358
$463$	−25.1591			−1.16924			−0.584622	−	0.811306i	$-0.698757\pi$
$463$	−25.1591			−1.16924			−0.584622	+	0.811306i	$0.698757\pi$
$464$		−	1.72909i		−	0.0802711i
$465$	11.8039	+	11.1042i	0.547394	+	0.514944i
$466$		−	23.3423i		−	1.08131i
$467$	15.6162			0.722632			0.361316	−	0.932443i	$-0.382328\pi$
$467$	15.6162			0.722632			0.361316	+	0.932443i	$0.382328\pi$
$468$	−0.684374			−0.0316352
$469$	−13.5833			−0.627218
$470$	9.66427	−	10.2733i	0.445780	−	0.473872i
$471$	−26.9626			−1.24237
$472$		−	10.5664i		−	0.486358i
$473$	9.20284			0.423147
$474$	18.2089			0.836363
$475$	−16.6942	+	1.02085i	−0.765981	+	0.0468398i
$476$			0.935517i			0.0428793i
$477$			0.271195i			0.0124172i
$478$			5.19256i			0.237502i
$479$			31.4974i			1.43915i	0.694414	+	0.719576i	$0.255664\pi$
$479$			31.4974i			1.43915i	−0.694414	+	0.719576i	$0.744336\pi$
$480$	−2.69985	+	2.86999i	−0.123231	+	0.130997i
$481$	11.4876	−	37.8635i	0.523791	−	1.72643i
$482$			15.5243i			0.707114i
$483$	2.99071			0.136082
$484$	−7.49860			−0.340845
$485$	0.657058	+	0.618106i	0.0298355	+	0.0280667i
$486$			1.09286i			0.0495733i
$487$	24.2768			1.10009			0.550043	−	0.835137i	$-0.314611\pi$
$487$	24.2768			1.10009			0.550043	+	0.835137i	$0.314611\pi$
$488$			11.1550i			0.504961i
$489$		−	26.2873i		−	1.18875i
$490$	8.97140	+	8.43956i	0.405287	+	0.381260i
$491$	16.5129			0.745218			0.372609	−	0.927988i	$-0.378463\pi$
$491$	16.5129			0.745218			0.372609	+	0.927988i	$0.378463\pi$
$492$			6.58857i			0.297036i
$493$			1.32447i			0.0596513i
$494$		−	21.7594i		−	0.979001i
$495$	0.320633	+	0.301625i	0.0144114	+	0.0135570i
$496$			4.11288i			0.184674i
$497$		−	1.17628i		−	0.0527632i
$498$	−0.0115742			−0.000518653
$499$		−	22.8436i		−	1.02262i	−0.859397	−	0.511310i	$-0.829161\pi$
$499$		−	22.8436i		−	1.02262i	0.859397	−	0.511310i	$-0.170839\pi$
$500$	7.14931	−	8.59578i	0.319727	−	0.384415i
$501$			30.4925i			1.36231i
$502$		−	3.85199i		−	0.171923i
$503$	−37.0666			−1.65272			−0.826359	−	0.563144i	$-0.809592\pi$
$503$	−37.0666			−1.65272			−0.826359	+	0.563144i	$0.809592\pi$
$504$		−	0.128493i		−	0.00572352i
$505$	31.5514	+	29.6809i	1.40402	+	1.32078i
$506$	−2.60030			−0.115597
$507$			51.6557i			2.29411i
$508$			11.1280i			0.493727i
$509$	20.0939			0.890645			0.445323	−	0.895370i	$-0.353089\pi$
$509$	20.0939			0.890645			0.445323	+	0.895370i	$0.353089\pi$
$510$	2.06807	−	2.19840i	0.0915757	−	0.0973466i
$511$	11.0299			0.487934
$512$	−1.00000			−0.0441942
$513$	−17.0635			−0.753372
$514$	−3.34529			−0.147554
$515$	9.05813	+	8.52114i	0.399149	+	0.375486i
$516$			8.66655i			0.381524i
$517$		−	11.8031i		−	0.519099i
$518$	7.10896	+	2.15683i	0.312350	+	0.0947656i
$519$	−34.7713			−1.52629
$520$	10.5944	+	9.96634i	0.464595	+	0.437053i
$521$	32.3101			1.41553			0.707766	−	0.706447i	$-0.249703\pi$
$521$	32.3101			1.41553			0.707766	+	0.706447i	$0.249703\pi$
$522$		−	0.181916i		−	0.00796223i
$523$	−38.5348			−1.68501			−0.842505	−	0.538688i	$-0.818920\pi$
$523$	−38.5348			−1.68501			−0.842505	+	0.538688i	$0.818920\pi$
$524$		−	12.8363i		−	0.560758i
$525$	0.656792	+	10.7407i	0.0286648	+	0.468761i
$526$		−	1.14405i		−	0.0498831i
$527$		−	3.15044i		−	0.137235i
$528$			3.29736i			0.143499i
$529$	−21.0689			−0.916039
$530$	3.94934	−	4.19821i	0.171548	−	0.182359i
$531$		−	1.11168i		−	0.0482427i
$532$	4.08537			0.177123
$533$	24.3213			1.05347
$534$	−8.28470			−0.358514
$535$	2.96442	−	3.15123i	0.128163	−	0.136240i
$536$			11.1219i			0.480392i
$537$	6.52628			0.281630
$538$	−15.1344			−0.652490
$539$	10.3073			0.443968
$540$	7.81551	−	8.30802i	0.336326	−	0.357520i
$541$		−	40.6354i		−	1.74705i	−0.486776	−	0.873527i	$-0.661827\pi$
$541$		−	40.6354i		−	1.74705i	0.486776	−	0.873527i	$-0.338173\pi$
$542$	18.2842			0.785374
$543$		−	18.3428i		−	0.787164i
$544$	0.765994			0.0328417
$545$	−13.3390	+	14.1796i	−0.571379	+	0.607386i
$546$	−13.9995			−0.599124
$547$	−26.6260			−1.13845			−0.569223	−	0.822183i	$-0.692756\pi$
$547$	−26.6260			−1.13845			−0.569223	+	0.822183i	$0.692756\pi$
$548$		−	12.0355i		−	0.514129i
$549$			1.17360i			0.0500880i
$550$	−0.571054	−	9.33857i	−0.0243498	−	0.398198i
$551$	5.78394			0.246404
$552$		−	2.44877i		−	0.104226i
$553$	12.6202			0.536664
$554$	−2.58352			−0.109763
$555$	−11.9376	−	20.7836i	−0.506723	−	0.882214i
$556$	−9.78562			−0.415003
$557$	−31.8613			−1.35001			−0.675004	−	0.737814i	$-0.735858\pi$
$557$	−31.8613			−1.35001			−0.675004	+	0.737814i	$0.735858\pi$
$558$			0.432711i			0.0183181i
$559$	31.9921			1.35312
$560$	−1.87120	+	1.98912i	−0.0790727	+	0.0840557i
$561$		−	2.52576i		−	0.106638i
$562$		−	19.3056i		−	0.814360i
$563$	−0.477178			−0.0201107			−0.0100553	−	0.999949i	$-0.503201\pi$
$563$	−0.477178			−0.0201107			−0.0100553	+	0.999949i	$0.503201\pi$
$564$	11.1153			0.468037
$565$	24.0369	+	22.6119i	1.01124	+	0.951291i
$566$	−9.02942			−0.379535
$567$			11.3638i			0.477233i
$568$	−0.963126			−0.0404119
$569$		−	10.3567i		−	0.434175i	−0.976152	−	0.217087i	$-0.930344\pi$
$569$		−	10.3567i		−	0.434175i	0.976152	−	0.217087i	$-0.0696557\pi$
$570$	−9.60032	−	9.03119i	−0.402113	−	0.378275i
$571$	−1.56306			−0.0654119			−0.0327059	−	0.999465i	$-0.510412\pi$
$571$	−1.56306			−0.0654119			−0.0327059	+	0.999465i	$0.510412\pi$
$572$	12.1720			0.508937
$573$	−40.6978			−1.70018
$574$			4.56638i			0.190597i
$575$	0.424091	+	6.93524i	0.0176858	+	0.289220i
$576$	−0.105209			−0.00438370
$577$	−19.1344			−0.796575			−0.398287	−	0.917261i	$-0.630395\pi$
$577$	−19.1344			−0.796575			−0.398287	+	0.917261i	$0.630395\pi$
$578$	16.4133			0.682701
$579$		−	22.0184i		−	0.915053i
$580$	−2.64919	+	2.81613i	−0.110001	+	0.116934i
$581$	−0.00802181			−0.000332801
$582$			0.710909i			0.0294681i
$583$		−	4.82337i		−	0.199763i
$584$		−	9.03119i		−	0.373713i
$585$	1.11462	+	1.04855i	0.0460840	+	0.0433521i
$586$			13.0845i			0.540516i
$587$	7.16828			0.295867			0.147933	−	0.988997i	$-0.452738\pi$
$587$	7.16828			0.295867			0.147933	+	0.988997i	$0.452738\pi$
$588$			9.70668i			0.400297i
$589$	−13.7579			−0.566884
$590$	−16.1890	+	17.2092i	−0.666492	+	0.708493i
$591$	9.71482			0.399614
$592$	1.76599	−	5.82076i	0.0725819	−	0.239232i
$593$			36.6287i			1.50416i	0.659071	+	0.752081i	$0.270950\pi$
$593$			36.6287i			1.50416i	−0.659071	+	0.752081i	$0.729050\pi$
$594$		−	9.54517i		−	0.391643i
$595$	1.43333	−	1.52366i	0.0587608	−	0.0624638i
$596$	−11.8876			−0.486934
$597$	33.1344			1.35610
$598$	−9.03948			−0.369652
$599$	38.3505			1.56696			0.783480	−	0.621417i	$-0.213443\pi$
$599$	38.3505			1.56696			0.783480	+	0.621417i	$0.213443\pi$
$600$	8.79437	−	0.537776i	0.359029	−	0.0219546i
$601$	−20.5311			−0.837480			−0.418740	−	0.908106i	$-0.637528\pi$
$601$	−20.5311			−0.837480			−0.418740	+	0.908106i	$0.637528\pi$
$602$			6.00658i			0.244810i
$603$			1.17012i			0.0476510i
$604$	21.3141			0.867259
$605$	12.2128	+	11.4888i	0.496521	+	0.467086i
$606$			34.1373i			1.38673i
$607$	−35.3953			−1.43665			−0.718326	−	0.695706i	$-0.755091\pi$
$607$	−35.3953			−1.43665			−0.718326	+	0.695706i	$0.755091\pi$
$608$		−	3.34507i		−	0.135661i
$609$		−	3.72126i		−	0.150793i
$610$	17.0908	−	18.1678i	0.691986	−	0.735594i
$611$		−	41.0314i		−	1.65995i
$612$	0.0805893			0.00325763
$613$		−	10.3293i		−	0.417198i	−0.978001	−	0.208599i	$-0.933110\pi$
$613$		−	10.3293i		−	0.417198i	0.978001	−	0.208599i	$-0.0668904\pi$
$614$		−	7.60942i		−	0.307091i
$615$	10.0945	−	10.7307i	0.407050	−	0.432702i
$616$			2.28532i			0.0920782i
$617$		−	2.91338i		−	0.117288i	−0.998279	−	0.0586441i	$-0.981322\pi$
$617$		−	2.91338i		−	0.117288i	0.998279	−	0.0586441i	$-0.0186777\pi$
$618$			9.80051i			0.394234i
$619$	30.7715			1.23681			0.618405	−	0.785860i	$-0.287779\pi$
$619$	30.7715			1.23681			0.618405	+	0.785860i	$0.287779\pi$
$620$	6.30145	−	6.69856i	0.253072	−	0.269021i
$621$			7.08867i			0.284459i
$622$		−	15.2359i		−	0.610905i
$623$	−5.74193			−0.230045
$624$			11.4627i			0.458875i
$625$	−24.8137	+	3.04611i	−0.992549	+	0.121844i
$626$	10.0000			0.399680
$627$	−11.0299			−0.440492
$628$			15.3009i			0.610573i
$629$	−1.35274	+	4.45867i	−0.0539373	+	0.177779i
$630$	−0.196867	+	0.209273i	−0.00784337	+	0.00833764i
$631$		−	12.8167i		−	0.510225i	−0.966911	−	0.255113i	$-0.917887\pi$
$631$		−	12.8167i		−	0.510225i	0.966911	−	0.255113i	$-0.0821126\pi$
$632$		−	10.3333i		−	0.411036i
$633$		−	46.9847i		−	1.86748i
$634$			34.1403i			1.35589i
$635$	17.0495	−	18.1240i	0.676591	−	0.719228i
$636$	4.54229			0.180114
$637$	35.8316			1.41970
$638$			3.23548i			0.128094i
$639$	−0.101329			−0.00400853
$640$	1.62868	+	1.53213i	0.0643791	+	0.0605626i
$641$	39.8277			1.57310			0.786550	−	0.617527i	$-0.211865\pi$
$641$	39.8277			1.57310			0.786550	+	0.617527i	$0.211865\pi$
$642$	3.40950			0.134562
$643$	−15.9821			−0.630273			−0.315137	−	0.949046i	$-0.602050\pi$
$643$	−15.9821			−0.630273			−0.315137	+	0.949046i	$0.602050\pi$
$644$		−	1.69718i		−	0.0668784i
$645$	13.2782	−	14.1150i	0.522830	−	0.555778i
$646$			2.56230i			0.100812i
$647$	37.8647			1.48861			0.744307	−	0.667838i	$-0.232780\pi$
$647$	37.8647			1.48861			0.744307	+	0.667838i	$0.232780\pi$
$648$	9.30456			0.365518
$649$			19.7719i			0.776113i
$650$	−1.98517	−	32.4639i	−0.0778648	−	1.27334i
$651$			8.85152i			0.346919i
$652$	−14.9177			−0.584221
$653$	−9.60006			−0.375679			−0.187840	−	0.982200i	$-0.560149\pi$
$653$	−9.60006			−0.375679			−0.187840	+	0.982200i	$0.560149\pi$
$654$	−15.3417			−0.599908
$655$	−19.6669	+	20.9062i	−0.768449	+	0.816875i
$656$	3.73892			0.145980
$657$		−	0.950161i		−	0.0370693i
$658$	7.70373			0.300323
$659$	30.3448			1.18207			0.591033	−	0.806647i	$-0.298720\pi$
$659$	30.3448			1.18207			0.591033	+	0.806647i	$0.298720\pi$
$660$	5.05197	−	5.37033i	0.196648	−	0.209040i
$661$			28.0304i			1.09026i	0.838353	+	0.545128i	$0.183519\pi$
$661$			28.0304i			1.09026i	−0.838353	+	0.545128i	$0.816481\pi$
$662$			27.2567i			1.05936i
$663$		−	8.78035i		−	0.341001i
$664$			0.00656819i			0.000254895i
$665$	−6.65375	−	6.25931i	−0.258022	−	0.242725i
$666$	0.185798	−	0.612395i	0.00719953	−	0.0237298i
$667$		−	2.40281i		−	0.0930374i
$668$	17.3041			0.669514
$669$	−19.1424			−0.740087
$670$	17.0401	−	18.1140i	0.658318	−	0.699804i
$671$		−	20.8732i		−	0.805800i
$672$	−2.15215			−0.0830208
$673$			1.70175i			0.0655975i	0.999462	+	0.0327987i	$0.0104420\pi$
$673$			1.70175i			0.0655975i	−0.999462	+	0.0327987i	$0.989558\pi$
$674$			22.5315i			0.867879i
$675$	−25.4579	+	1.55675i	−0.979874	+	0.0599194i
$676$	29.3139			1.12746
$677$		−	3.49272i		−	0.134236i	−0.997745	−	0.0671180i	$-0.978620\pi$
$677$		−	3.49272i		−	0.134236i	0.997745	−	0.0671180i	$-0.0213804\pi$
$678$			26.0069i			0.998789i
$679$			0.492714i			0.0189086i
$680$	−1.24756	−	1.17360i	−0.0478416	−	0.0450055i
$681$			12.0254i			0.460816i
$682$		−	7.69603i		−	0.294696i
$683$	−18.9186			−0.723901			−0.361950	−	0.932197i	$-0.617889\pi$
$683$	−18.9186			−0.723901			−0.361950	+	0.932197i	$0.617889\pi$
$684$		−	0.351931i		−	0.0134564i
$685$	−18.4398	+	19.6019i	−0.704550	+	0.748949i
$686$			15.2766i			0.583265i
$687$			4.51446i			0.172237i
$688$	4.91814			0.187502
$689$		−	16.7676i		−	0.638795i
$690$	−3.75182	+	3.98825i	−0.142829	+	0.151830i
$691$	4.56018			0.173477			0.0867386	−	0.996231i	$-0.472355\pi$
$691$	4.56018			0.173477			0.0867386	+	0.996231i	$0.472355\pi$
$692$			19.7322i			0.750107i
$693$			0.240436i			0.00913340i
$694$	34.7252			1.31815
$695$	15.9376	+	14.9928i	0.604548	+	0.568709i
$696$	−3.04694			−0.115494
$697$	−2.86399			−0.108481
$698$	−15.9343			−0.603121
$699$	−41.1329			−1.55579
$700$	6.09517	−	0.372720i	0.230376	−	0.0140875i
$701$		−	18.9895i		−	0.717224i	−0.933487	−	0.358612i	$-0.883250\pi$
$701$		−	18.9895i		−	0.717224i	0.933487	−	0.358612i	$-0.116750\pi$
$702$		−	33.1821i		−	1.25238i
$703$	19.4709	+	5.90737i	0.734357	+	0.222801i
$704$	1.87120			0.0705236
$705$	−18.1032	−	17.0300i	−0.681806	−	0.641387i
$706$	−20.1925			−0.759956
$707$			23.6597i			0.889815i
$708$	−18.6197			−0.699770
$709$		−	10.8195i		−	0.406336i	−0.979144	−	0.203168i	$-0.934876\pi$
$709$		−	10.8195i		−	0.406336i	0.979144	−	0.203168i	$-0.0651238\pi$
$710$	1.56862	+	1.47563i	0.0588693	+	0.0553794i
$711$		−	1.08715i		−	0.0407714i
$712$			4.70144i			0.176194i
$713$			5.71542i			0.214044i
$714$	1.64853			0.0616947
$715$	−19.8243	−	18.6490i	−0.741386	−	0.697435i
$716$		−	3.70357i		−	0.138409i
$717$	9.15013			0.341718
$718$	30.8657			1.15190
$719$	−8.43399			−0.314535			−0.157267	−	0.987556i	$-0.550268\pi$
$719$	−8.43399			−0.314535			−0.157267	+	0.987556i	$0.550268\pi$
$720$	0.171351	+	0.161193i	0.00638588	+	0.00600731i
$721$			6.79250i			0.252966i
$722$	−7.81050			−0.290677
$723$	27.3564			1.01739
$724$	−10.4093			−0.386857
$725$	8.62934	−	0.527685i	0.320486	−	0.0195977i
$726$			13.2137i			0.490408i
$727$	−16.7156			−0.619947			−0.309974	−	0.950745i	$-0.600320\pi$
$727$	−16.7156			−0.619947			−0.309974	+	0.950745i	$0.600320\pi$
$728$			7.94452i			0.294444i
$729$	−25.9879			−0.962514
$730$	−13.8369	+	14.7089i	−0.512128	+	0.544401i
$731$	−3.76726			−0.139337
$732$	19.6568			0.726537
$733$		−	10.4157i		−	0.384711i	−0.981325	−	0.192356i	$-0.938387\pi$
$733$		−	10.4157i		−	0.384711i	0.981325	−	0.192356i	$-0.0616127\pi$
$734$		−	28.9254i		−	1.06766i
$735$	14.8719	−	15.8091i	0.548557	−	0.583126i
$736$	−1.38964			−0.0512228
$737$		−	20.8113i		−	0.766594i
$738$	0.393367			0.0144800
$739$	−19.7975			−0.728261			−0.364131	−	0.931348i	$-0.618634\pi$
$739$	−19.7975			−0.728261			−0.364131	+	0.931348i	$0.618634\pi$
$740$	−11.7944	+	6.77442i	−0.433570	+	0.249033i
$741$	−38.3435			−1.40858
$742$	3.14815			0.115572
$743$		−	34.4142i		−	1.26253i	−0.775566	−	0.631267i	$-0.782535\pi$
$743$		−	34.4142i		−	1.26253i	0.775566	−	0.631267i	$-0.217465\pi$
$744$	7.24756			0.265708
$745$	19.3610	+	18.2133i	0.709333	+	0.667282i
$746$			27.8899i			1.02112i
$747$		0	0.000691032i		0	2.52835e-5i
$748$	−1.43333			−0.0524077
$749$	2.36304			0.0863437
$750$	−15.1471	−	12.5982i	−0.553095	−	0.460022i
$751$	−40.7020			−1.48524			−0.742618	−	0.669715i	$-0.766416\pi$
$751$	−40.7020			−1.48524			−0.742618	+	0.669715i	$0.766416\pi$
$752$		−	6.30775i		−	0.230020i
$753$	−6.78783			−0.247362
$754$			11.2476i			0.409613i
$755$	−34.7138	−	32.6559i	−1.26337	−	1.18847i
$756$	6.23001			0.226583
$757$	2.06470			0.0750426			0.0375213	−	0.999296i	$-0.488054\pi$
$757$	2.06470			0.0750426			0.0375213	+	0.999296i	$0.488054\pi$
$758$	5.73365			0.208256
$759$			4.58214i			0.166321i
$760$	−5.12507	+	5.44804i	−0.185906	+	0.197621i
$761$	9.07263			0.328883			0.164441	−	0.986387i	$-0.447418\pi$
$761$	9.07263			0.328883			0.164441	+	0.986387i	$0.447418\pi$
$762$	19.6094			0.710373
$763$	−10.6330			−0.384939
$764$			23.0954i			0.835563i
$765$	−0.131254	−	0.123473i	−0.00474550	−	0.00446417i
$766$	−17.8363			−0.644451
$767$			68.7335i			2.48182i
$768$			1.76216i			0.0635865i
$769$			50.9991i			1.83907i	0.393002	+	0.919537i	$0.371436\pi$
$769$			50.9991i			1.83907i	−0.393002	+	0.919537i	$0.628564\pi$
$770$	3.50140	−	3.72205i	0.126182	−	0.134133i
$771$			5.89493i			0.212301i
$772$	−12.4951			−0.449709
$773$			40.9981i			1.47460i	0.675565	+	0.737300i	$0.263900\pi$
$773$			40.9981i			1.47460i	−0.675565	+	0.737300i	$0.736100\pi$
$774$	0.517431			0.0185987
$775$	−20.5261	+	1.25517i	−0.737318	+	0.0450870i
$776$	0.403430			0.0144823
$777$	3.80068	−	12.5271i	0.136349	−	0.449408i
$778$			29.8974i			1.07187i
$779$			12.5069i			0.448108i
$780$	17.5623	−	18.6690i	0.628831	−	0.668459i
$781$	1.80220			0.0644879
$782$	1.06446			0.0380648
$783$	8.82025			0.315210
$784$	5.50840			0.196729
$785$	23.4429	−	24.9202i	0.836713	−	0.889441i
$786$	−22.6197			−0.806817
$787$		−	30.4357i		−	1.08492i	−0.840083	−	0.542458i	$-0.817494\pi$
$787$		−	30.4357i		−	1.08492i	0.840083	−	0.542458i	$-0.182506\pi$
$788$		−	5.51302i		−	0.196393i
$789$	−2.01601			−0.0717718
$790$	−15.8319	+	16.8296i	−0.563274	+	0.598770i
$791$			18.0248i			0.640887i
$792$	0.196867			0.00699536
$793$		−	72.5620i		−	2.57675i
$794$			13.2064i			0.468679i
$795$	−7.39793	−	6.95936i	−0.262377	−	0.246823i
$796$		−	18.8033i		−	0.666464i
$797$	0.999495			0.0354039			0.0177020	−	0.999843i	$-0.494365\pi$
$797$	0.999495			0.0354039			0.0177020	+	0.999843i	$0.494365\pi$
$798$		−	7.19908i		−	0.254845i
$799$			4.83170i			0.170933i
$800$	−0.305180	−	4.99068i	−0.0107898	−	0.176447i
$801$			0.494633i			0.0174770i
$802$		−	23.0269i		−	0.813108i
$803$			16.8992i			0.596360i
$804$	19.5985			0.691187
$805$	−2.60030	+	2.76416i	−0.0916484	+	0.0974239i
$806$		−	26.7539i		−	0.942367i
$807$			26.6692i			0.938801i
$808$	19.3724			0.681518
$809$		−	21.8030i		−	0.766552i	−0.923634	−	0.383276i	$-0.874796\pi$
$809$		−	21.8030i		−	0.766552i	0.923634	−	0.383276i	$-0.125204\pi$
$810$	−15.1541	−	14.2558i	−0.532462	−	0.500896i
$811$	−40.9653			−1.43848			−0.719242	−	0.694759i	$-0.755511\pi$
$811$	−40.9653			−1.43848			−0.719242	+	0.694759i	$0.755511\pi$
$812$	−2.11176			−0.0741082
$813$		−	32.2197i		−	1.12999i
$814$	−3.30453	+	10.8918i	−0.115824	+	0.381758i
$815$	24.2961	+	22.8557i	0.851054	+	0.800601i
$816$		−	1.34980i		−	0.0472526i
$817$			16.4515i			0.575566i
$818$			9.77049i			0.341617i
$819$			0.835833i			0.0292064i
$820$	−6.08949	−	5.72849i	−0.212654	−	0.200048i
$821$	36.2693			1.26581			0.632904	−	0.774230i	$-0.281863\pi$
$821$	36.2693			1.26581			0.632904	+	0.774230i	$0.281863\pi$
$822$	−21.2084			−0.739728
$823$		−	48.5397i		−	1.69199i	−0.533194	−	0.845993i	$-0.679008\pi$
$823$		−	48.5397i		−	1.69199i	0.533194	−	0.845993i	$-0.320992\pi$
$824$	5.56165			0.193749
$825$	−16.4561	+	1.00629i	−0.572926	+	0.0350345i
$826$	−12.9049			−0.449017
$827$	−39.6895			−1.38014			−0.690069	−	0.723743i	$-0.742420\pi$
$827$	−39.6895			−1.38014			−0.690069	+	0.723743i	$0.742420\pi$
$828$	−0.146202			−0.00508088
$829$			53.4506i			1.85641i	0.372064	+	0.928207i	$0.378650\pi$
$829$			53.4506i			1.85641i	−0.372064	+	0.928207i	$0.621350\pi$
$830$	0.0100633	−	0.0106975i	0.000349302	−	0.000371315i
$831$			4.55258i			0.157927i
$832$	6.50491			0.225517
$833$	−4.21940			−0.146194
$834$			17.2438i			0.597105i
$835$	−28.1827	−	26.5120i	−0.975303	−	0.917485i
$836$			6.25931i			0.216483i
$837$	−20.9802			−0.725181
$838$	−2.06109			−0.0711993
$839$	−33.5857			−1.15951			−0.579753	−	0.814792i	$-0.696851\pi$
$839$	−33.5857			−1.15951			−0.579753	+	0.814792i	$0.696851\pi$
$840$	3.50515	+	3.29736i	0.120939	+	0.113770i
$841$	26.0102			0.896905
$842$		−	12.8910i		−	0.444255i
$843$	−34.0196			−1.17170
$844$	−26.6632			−0.917784
$845$	−47.7428	−	44.9125i	−1.64240	−	1.54504i
$846$		−	0.663631i		−	0.0228161i
$847$			9.15813i			0.314677i
$848$		−	2.57768i		−	0.0885180i
$849$			15.9113i			0.546074i
$850$	0.233766	+	3.82283i	0.00801811	+	0.131122i
$851$	2.45409	−	8.08876i	0.0841253	−	0.277279i
$852$			1.69718i			0.0581445i
$853$	−0.641846			−0.0219764			−0.0109882	−	0.999940i	$-0.503498\pi$
$853$	−0.641846			−0.0219764			−0.0109882	+	0.999940i	$0.503498\pi$
$854$	13.6237			0.466192
$855$	−0.539202	+	0.573182i	−0.0184403	+	0.0196024i
$856$		−	1.93484i		−	0.0661315i
$857$	−20.5938			−0.703470			−0.351735	−	0.936100i	$-0.614408\pi$
$857$	−20.5938			−0.703470			−0.351735	+	0.936100i	$0.614408\pi$
$858$		−	21.4490i		−	0.732258i
$859$		−	6.18892i		−	0.211163i	−0.994411	−	0.105582i	$-0.966330\pi$
$859$		−	6.18892i		−	0.211163i	0.994411	−	0.105582i	$-0.0336704\pi$
$860$	−8.01006	−	7.53521i	−0.273141	−	0.256949i
$861$	8.04670			0.274231
$862$			9.41662i			0.320731i
$863$		−	48.8873i		−	1.66414i	−0.554669	−	0.832071i	$-0.687155\pi$
$863$		−	48.8873i		−	1.66414i	0.554669	−	0.832071i	$-0.312845\pi$
$864$		−	5.10109i		−	0.173542i
$865$	30.2323	−	32.1374i	1.02793	−	1.09271i
$866$			3.07581i			0.104520i
$867$		−	28.9228i		−	0.982269i
$868$	5.02311			0.170495
$869$			19.3357i			0.655918i
$870$	4.96248	+	4.66829i	0.168244	+	0.158270i
$871$		−	72.3469i		−	2.45138i
$872$			8.70619i			0.294829i
$873$	0.0424444			0.00143653
$874$		−	4.64844i		−	0.157236i
$875$	−10.4981	−	8.73153i	−0.354901	−	0.295180i
$876$	−15.9144			−0.537698
$877$		−	2.65696i		−	0.0897190i	−0.998993	−	0.0448595i	$-0.985716\pi$
$877$		−	2.65696i		−	0.0897190i	0.998993	−	0.0448595i	$-0.0142840\pi$
$878$		−	1.93763i		−	0.0653918i
$879$	23.0570			0.777693
$880$	−3.04759	−	2.86692i	−0.102734	−	0.0966438i
$881$	−1.97718			−0.0666130			−0.0333065	−	0.999445i	$-0.510604\pi$
$881$	−1.97718			−0.0666130			−0.0333065	+	0.999445i	$0.510604\pi$
$882$	0.579532			0.0195139
$883$	35.6965			1.20128			0.600641	−	0.799519i	$-0.294912\pi$
$883$	35.6965			1.20128			0.600641	+	0.799519i	$0.294912\pi$
$884$	−4.98272			−0.167587
$885$	30.3254	+	28.5277i	1.01938	+	0.958948i
$886$		−	26.5690i		−	0.892602i
$887$		−	0.181192i		−	0.00608382i	−0.999995	−	0.00304191i	$-0.999032\pi$
$887$		−	0.181192i		−	0.00608382i	0.999995	−	0.00304191i	$-0.000968271\pi$
$888$	−10.2571	−	3.11196i	−0.344206	−	0.104431i
$889$	13.5908			0.455820
$890$	7.20320	−	7.65713i	0.241452	−	0.256668i
$891$	−17.4107			−0.583281
$892$			10.8630i			0.363721i
$893$	21.0999			0.706081
$894$			20.9478i			0.700600i
$895$	−5.67434	+	6.03192i	−0.189672	+	0.201625i
$896$			1.22131i			0.0408011i
$897$			15.9290i			0.531854i
$898$			0.777045i			0.0259303i
$899$	7.11155			0.237184
$900$	−0.0321076	−	0.525063i	−0.00107025	−	0.0175021i
$901$			1.97449i			0.0657798i
$902$	−6.99627			−0.232950
$903$	10.5846			0.352232
$904$	14.7585			0.490862
$905$	16.9533	+	15.9483i	0.563548	+	0.530139i
$906$		−	37.5589i		−	1.24781i
$907$	28.0542			0.931525			0.465762	−	0.884910i	$-0.345780\pi$
$907$	28.0542			0.931525			0.465762	+	0.884910i	$0.345780\pi$
$908$	6.82427			0.226471
$909$	2.03814			0.0676010
$910$	12.1720	−	12.9391i	0.403498	−	0.428926i
$911$			33.0379i			1.09459i	0.836939	+	0.547297i	$0.184343\pi$
$911$			33.0379i			1.09459i	−0.836939	+	0.547297i	$0.815657\pi$
$912$	−5.89455			−0.195188
$913$		−	0.0122904i		−	0.000406754i
$914$	−21.1753			−0.700415
$915$	−32.0146	−	30.1167i	−1.05837	−	0.995628i
$916$	2.56189			0.0846471
$917$	−15.6772			−0.517705
$918$			3.90740i			0.128963i
$919$			24.1489i			0.796600i	0.917255	+	0.398300i	$0.130400\pi$
$919$			24.1489i			0.796600i	−0.917255	+	0.398300i	$0.869600\pi$
$920$	2.26327	+	2.12910i	0.0746180	+	0.0701944i
$921$	−13.4090			−0.441842
$922$		−	23.9797i		−	0.789731i
$923$	6.26505			0.206217
$924$	4.02710			0.132482
$925$	29.5885	+	7.03712i	0.972864	+	0.231379i
$926$	25.1591			0.826781
$927$	0.585134			0.0192183
$928$			1.72909i			0.0567602i
$929$	30.9086			1.01408			0.507039	−	0.861923i	$-0.330740\pi$
$929$	30.9086			1.01408			0.507039	+	0.861923i	$0.330740\pi$
$930$	−11.8039	−	11.1042i	−0.387066	−	0.364120i
$931$			18.4260i			0.603887i
$932$			23.3423i			0.764603i
$933$	−26.8481			−0.878969
$934$	−15.6162			−0.510978
$935$	2.33443	+	2.19604i	0.0763441	+	0.0718182i
$936$	0.684374			0.0223695
$937$			33.6530i			1.09940i	0.835363	+	0.549698i	$0.185257\pi$
$937$			33.6530i			1.09940i	−0.835363	+	0.549698i	$0.814743\pi$
$938$	13.5833			0.443510
$939$		−	17.6216i		−	0.575059i
$940$	−9.66427	+	10.2733i	−0.315214	+	0.335078i
$941$	−33.8242			−1.10264			−0.551319	−	0.834294i	$-0.685875\pi$
$941$	−33.8242			−1.10264			−0.551319	+	0.834294i	$0.685875\pi$
$942$	26.9626			0.878490
$943$	5.19575			0.169197
$944$			10.5664i			0.343907i
$945$	−10.1467	−	9.54517i	−0.330072	−	0.310504i
$946$	−9.20284			−0.299210
$947$	17.3591			0.564095			0.282048	−	0.959400i	$-0.408986\pi$
$947$	17.3591			0.564095			0.282048	+	0.959400i	$0.408986\pi$
$948$	−18.2089			−0.591398
$949$			58.7471i			1.90701i
$950$	16.6942	−	1.02085i	0.541630	−	0.0331207i
$951$	60.1607			1.95085
$952$		−	0.935517i		−	0.0303203i
$953$			15.0520i			0.487582i	0.969828	+	0.243791i	$0.0783911\pi$
$953$			15.0520i			0.487582i	−0.969828	+	0.243791i	$0.921609\pi$
$954$		−	0.271195i		−	0.00878026i
$955$	35.3851	−	37.6150i	1.14503	−	1.21719i
$956$		−	5.19256i		−	0.167940i
$957$	5.70144			0.184301
$958$		−	31.4974i		−	1.01763i
$959$	−14.6990			−0.474657
$960$	2.69985	−	2.86999i	0.0871373	−	0.0926285i
$961$	14.0842			0.454329
$962$	−11.4876	+	37.8635i	−0.370376	+	1.22077i
$963$		−	0.203562i		−	0.00655970i
$964$		−	15.5243i		−	0.500005i
$965$	20.3505	+	19.1441i	0.655106	+	0.616270i
$966$	−2.99071			−0.0962244
$967$	23.3045			0.749423			0.374712	−	0.927141i	$-0.377742\pi$
$967$	23.3045			0.749423			0.374712	+	0.927141i	$0.377742\pi$
$968$	7.49860			0.241014
$969$	4.51519			0.145049
$970$	−0.657058	−	0.618106i	−0.0210969	−	0.0198462i
$971$	−40.7911			−1.30905			−0.654524	−	0.756041i	$-0.727131\pi$
$971$	−40.7911			−1.30905			−0.654524	+	0.756041i	$0.727131\pi$
$972$		−	1.09286i		−	0.0350536i
$973$			11.9513i			0.383140i
$974$	−24.2768			−0.777878
$975$	−57.2066	+	3.49819i	−1.83208	+	0.112032i
$976$		−	11.1550i		−	0.357061i
$977$	−2.64739			−0.0846976			−0.0423488	−	0.999103i	$-0.513484\pi$
$977$	−2.64739			−0.0846976			−0.0423488	+	0.999103i	$0.513484\pi$
$978$			26.2873i			0.840575i
$979$		−	8.79735i		−	0.281165i
$980$	−8.97140	−	8.43956i	−0.286581	−	0.269592i
$981$			0.915967i			0.0292446i
$982$	−16.5129			−0.526949
$983$		−	27.8528i		−	0.888367i	−0.895936	−	0.444183i	$-0.853494\pi$
$983$		−	27.8528i		−	0.888367i	0.895936	−	0.444183i	$-0.146506\pi$
$984$		−	6.58857i		−	0.210036i
$985$	−8.44664	+	8.97893i	−0.269132	+	0.286093i
$986$		−	1.32447i		−	0.0421798i
$987$		−	13.5752i		−	0.432104i
$988$			21.7594i			0.692258i
$989$	6.83444			0.217323
$990$	−0.320633	−	0.301625i	−0.0101904	−	0.00958627i
$991$		−	47.8484i		−	1.51995i	−0.649950	−	0.759977i	$-0.725210\pi$
$991$		−	47.8484i		−	1.51995i	0.649950	−	0.759977i	$-0.274790\pi$
$992$		−	4.11288i		−	0.130584i
$993$	48.0307			1.52421
$994$			1.17628i			0.0373092i
$995$	−28.8090	+	30.6245i	−0.913306	+	0.970861i
$996$	0.0115742			0.000366743
$997$	−3.95282			−0.125187			−0.0625936	−	0.998039i	$-0.519937\pi$
$997$	−3.95282			−0.125187			−0.0625936	+	0.998039i	$0.519937\pi$
$998$			22.8436i			0.723101i
$999$	29.6922	+	9.00849i	0.939420	+	0.285016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.c.a.369.8	yes	10
3.2	odd	2		3330.2.e.d.739.8		10
5.2	odd	4		1850.2.d.i.1701.8		20
5.3	odd	4		1850.2.d.i.1701.13		20
5.4	even	2		370.2.c.b.369.3	yes	10
15.14	odd	2		3330.2.e.c.739.4		10
37.36	even	2		370.2.c.b.369.8	yes	10
111.110	odd	2		3330.2.e.c.739.3		10
185.73	odd	4		1850.2.d.i.1701.3		20
185.147	odd	4		1850.2.d.i.1701.18		20
185.184	even	2	inner	370.2.c.a.369.3	✓	10
555.554	odd	2		3330.2.e.d.739.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.3	✓	10	185.184	even	2	inner
370.2.c.a.369.8	yes	10	1.1	even	1	trivial
370.2.c.b.369.3	yes	10	5.4	even	2
370.2.c.b.369.8	yes	10	37.36	even	2
1850.2.d.i.1701.3		20	185.73	odd	4
1850.2.d.i.1701.8		20	5.2	odd	4
1850.2.d.i.1701.13		20	5.3	odd	4
1850.2.d.i.1701.18		20	185.147	odd	4
3330.2.e.c.739.3		10	111.110	odd	2
3330.2.e.c.739.4		10	15.14	odd	2
3330.2.e.d.739.7		10	555.554	odd	2
3330.2.e.d.739.8		10	3.2	odd	2

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.76216i q^{3} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.76216i q^{6} -1.22131i q^{7} -1.00000 q^{8} -0.105209 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.76216i q^{3} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.76216i q^{6} -1.22131i q^{7} -1.00000 q^{8} -0.105209 q^{9} +(1.62868 + 1.53213i) q^{10} +1.87120 q^{11} +1.76216i q^{12} +6.50491 q^{13} +1.22131i q^{14} +(2.69985 - 2.86999i) q^{15} +1.00000 q^{16} -0.765994 q^{17} +0.105209 q^{18} +3.34507i q^{19} +(-1.62868 - 1.53213i) q^{20} +2.15215 q^{21} -1.87120 q^{22} +1.38964 q^{23} -1.76216i q^{24} +(0.305180 + 4.99068i) q^{25} -6.50491 q^{26} +5.10109i q^{27} -1.22131i q^{28} -1.72909i q^{29} +(-2.69985 + 2.86999i) q^{30} +4.11288i q^{31} -1.00000 q^{32} +3.29736i q^{33} +0.765994 q^{34} +(-1.87120 + 1.98912i) q^{35} -0.105209 q^{36} +(1.76599 - 5.82076i) q^{37} -3.34507i q^{38} +11.4627i q^{39} +(1.62868 + 1.53213i) q^{40} +3.73892 q^{41} -2.15215 q^{42} +4.91814 q^{43} +1.87120 q^{44} +(0.171351 + 0.161193i) q^{45} -1.38964 q^{46} -6.30775i q^{47} +1.76216i q^{48} +5.50840 q^{49} +(-0.305180 - 4.99068i) q^{50} -1.34980i q^{51} +6.50491 q^{52} -2.57768i q^{53} -5.10109i q^{54} +(-3.04759 - 2.86692i) q^{55} +1.22131i q^{56} -5.89455 q^{57} +1.72909i q^{58} +10.5664i q^{59} +(2.69985 - 2.86999i) q^{60} -11.1550i q^{61} -4.11288i q^{62} +0.128493i q^{63} +1.00000 q^{64} +(-10.5944 - 9.96634i) q^{65} -3.29736i q^{66} -11.1219i q^{67} -0.765994 q^{68} +2.44877i q^{69} +(1.87120 - 1.98912i) q^{70} +0.963126 q^{71} +0.105209 q^{72} +9.03119i q^{73} +(-1.76599 + 5.82076i) q^{74} +(-8.79437 + 0.537776i) q^{75} +3.34507i q^{76} -2.28532i q^{77} -11.4627i q^{78} +10.3333i q^{79} +(-1.62868 - 1.53213i) q^{80} -9.30456 q^{81} -3.73892 q^{82} -0.00656819i q^{83} +2.15215 q^{84} +(1.24756 + 1.17360i) q^{85} -4.91814 q^{86} +3.04694 q^{87} -1.87120 q^{88} -4.70144i q^{89} +(-0.171351 - 0.161193i) q^{90} -7.94452i q^{91} +1.38964 q^{92} -7.24756 q^{93} +6.30775i q^{94} +(5.12507 - 5.44804i) q^{95} -1.76216i q^{96} -0.403430 q^{97} -5.50840 q^{98} -0.196867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Introduction

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