LMFDB - Embedded newform 784.2.m.l.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.2
Character	$\chi$	$=$	784.197
Dual form			784.2.m.l.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40713 - 0.141372i) q^{2} +(1.51592 - 1.51592i) q^{3} +(1.96003 + 0.397858i) q^{4} +(0.583934 + 0.583934i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} -1.59603i q^{9} +O(q^{10})$	\(q+(-1.40713 - 0.141372i) q^{2} +(1.51592 - 1.51592i) q^{3} +(1.96003 + 0.397858i) q^{4} +(0.583934 + 0.583934i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} -1.59603i q^{9} +(-0.739119 - 0.904223i) q^{10} +(0.754851 + 0.754851i) q^{11} +(3.57437 - 2.36812i) q^{12} +(-2.93078 + 2.93078i) q^{13} +1.77039 q^{15} +(3.68342 + 1.55963i) q^{16} +4.90431 q^{17} +(-0.225634 + 2.24582i) q^{18} +(4.71106 - 4.71106i) q^{19} +(0.912204 + 1.37685i) q^{20} +(-0.955458 - 1.16889i) q^{22} -5.90297i q^{23} +(-5.36438 + 2.82694i) q^{24} -4.31804i q^{25} +(4.53832 - 3.70966i) q^{26} +(2.12831 + 2.12831i) q^{27} +(3.32371 - 3.32371i) q^{29} +(-2.49117 - 0.250285i) q^{30} +3.48460 q^{31} +(-4.96256 - 2.71533i) q^{32} +2.28859 q^{33} +(-6.90100 - 0.693333i) q^{34} +(0.634992 - 3.12825i) q^{36} +(4.97708 + 4.97708i) q^{37} +(-7.29508 + 5.96305i) q^{38} +8.88566i q^{39} +(-1.08894 - 2.06637i) q^{40} +3.86206i q^{41} +(5.89641 + 5.89641i) q^{43} +(1.17921 + 1.77985i) q^{44} +(0.931974 - 0.931974i) q^{45} +(-0.834516 + 8.30625i) q^{46} -6.21296 q^{47} +(7.94803 - 3.21950i) q^{48} +(-0.610451 + 6.07604i) q^{50} +(7.43454 - 7.43454i) q^{51} +(-6.91045 + 4.57838i) q^{52} +(-9.42504 - 9.42504i) q^{53} +(-2.69393 - 3.29570i) q^{54} +0.881566i q^{55} -14.2832i q^{57} +(-5.14677 + 4.20701i) q^{58} +(-4.26676 - 4.26676i) q^{59} +(3.47002 + 0.704366i) q^{60} +(-6.88524 + 6.88524i) q^{61} +(-4.90328 - 0.492626i) q^{62} +(6.59909 + 4.52239i) q^{64} -3.42277 q^{65} +(-3.22034 - 0.323543i) q^{66} +(8.72771 - 8.72771i) q^{67} +(9.61258 + 1.95122i) q^{68} +(-8.94843 - 8.94843i) q^{69} +0.135373i q^{71} +(-1.33576 + 4.31209i) q^{72} +7.56806i q^{73} +(-6.29978 - 7.70702i) q^{74} +(-6.54581 - 6.54581i) q^{75} +(11.1081 - 7.35947i) q^{76} +(1.25618 - 12.5033i) q^{78} +6.79297 q^{79} +(1.24015 + 3.06159i) q^{80} +11.2408 q^{81} +(0.545988 - 5.43442i) q^{82} +(-5.63027 + 5.63027i) q^{83} +(2.86379 + 2.86379i) q^{85} +(-7.46342 - 9.13060i) q^{86} -10.0770i q^{87} +(-1.40767 - 2.67119i) q^{88} +5.58422i q^{89} +(-1.44316 + 1.17965i) q^{90} +(2.34855 - 11.5700i) q^{92} +(5.28237 - 5.28237i) q^{93} +(8.74245 + 0.878340i) q^{94} +5.50189 q^{95} +(-11.6391 + 3.40662i) q^{96} -6.15204 q^{97} +(1.20476 - 1.20476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 8 q^{11} + 32 q^{15} + 36 q^{16} + 20 q^{18} - 28 q^{22} - 16 q^{29} + 96 q^{30} + 40 q^{32} + 40 q^{36} - 16 q^{37} + 8 q^{43} + 4 q^{44} + 64 q^{46} - 28 q^{50} + 16 q^{53} - 20 q^{58} + 8 q^{60} + 44 q^{64} + 40 q^{67} - 196 q^{72} - 28 q^{74} + 56 q^{78} + 80 q^{79} - 48 q^{81} - 108 q^{86} - 100 q^{88} - 128 q^{95} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 8 * q^11 + 32 * q^15 + 36 * q^16 + 20 * q^18 - 28 * q^22 - 16 * q^29 + 96 * q^30 + 40 * q^32 + 40 * q^36 - 16 * q^37 + 8 * q^43 + 4 * q^44 + 64 * q^46 - 28 * q^50 + 16 * q^53 - 20 * q^58 + 8 * q^60 + 44 * q^64 + 40 * q^67 - 196 * q^72 - 28 * q^74 + 56 * q^78 + 80 * q^79 - 48 * q^81 - 108 * q^86 - 100 * q^88 - 128 * q^95 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−1.40713	−	0.141372i	−0.994991	−	0.0999652i
$2$	−1.40713	−	0.141372i	−0.994991	−	0.0999652i
$3$	1.51592	−	1.51592i	0.875217	−	0.875217i	−0.117818	−	0.993035i	$-0.537590\pi$
$3$	1.51592	−	1.51592i	0.875217	−	0.875217i	0.993035	+	0.117818i	$0.0375901\pi$
$4$	1.96003	+	0.397858i	0.980014	+	0.198929i
$5$	0.583934	+	0.583934i	0.261143	+	0.261143i	0.825518	−	0.564375i	$-0.190883\pi$
$5$	0.583934	+	0.583934i	0.261143	+	0.261143i	−0.564375	+	0.825518i	$0.690883\pi$
$6$	−2.34740	+	1.91879i	−0.958324	+	0.783341i
$7$		0			0
$7$		0			0
$8$	−2.70177	−	0.836931i	−0.955219	−	0.295900i
$9$		−	1.59603i		−	0.532009i
$10$	−0.739119	−	0.904223i	−0.233730	−	0.285940i
$11$	0.754851	+	0.754851i	0.227596	+	0.227596i	0.811688	−	0.584092i	$-0.198549\pi$
$11$	0.754851	+	0.754851i	0.227596	+	0.227596i	−0.584092	+	0.811688i	$0.698549\pi$
$12$	3.57437	−	2.36812i	1.03183	−	0.683619i
$13$	−2.93078	+	2.93078i	−0.812852	+	0.812852i	−0.985061	−	0.172208i	$-0.944910\pi$
$13$	−2.93078	+	2.93078i	−0.812852	+	0.812852i	0.172208	+	0.985061i	$0.444910\pi$
$14$		0			0
$15$	1.77039			0.457114
$16$	3.68342	+	1.55963i	0.920854	+	0.389906i
$17$	4.90431			1.18947			0.594735	−	0.803922i	$-0.297257\pi$
$17$	4.90431			1.18947			0.594735	+	0.803922i	$0.297257\pi$
$18$	−0.225634	+	2.24582i	−0.0531824	+	0.529344i
$19$	4.71106	−	4.71106i	1.08079	−	1.08079i	0.0843545	−	0.996436i	$-0.473117\pi$
$19$	4.71106	−	4.71106i	1.08079	−	1.08079i	0.996436	−	0.0843545i	$-0.0268828\pi$
$20$	0.912204	+	1.37685i	0.203975	+	0.307873i
$21$		0			0
$22$	−0.955458	−	1.16889i	−0.203704	−	0.249208i
$23$		−	5.90297i		−	1.23085i	−0.788194	−	0.615427i	$-0.788983\pi$
$23$		−	5.90297i		−	1.23085i	0.788194	−	0.615427i	$-0.211017\pi$
$24$	−5.36438	+	2.82694i	−1.09500	+	0.577047i
$25$		−	4.31804i		−	0.863608i
$26$	4.53832	−	3.70966i	0.890038	−	0.727524i
$27$	2.12831	+	2.12831i	0.409594	+	0.409594i
$28$		0			0
$29$	3.32371	−	3.32371i	0.617198	−	0.617198i	−0.327614	−	0.944812i	$-0.606245\pi$
$29$	3.32371	−	3.32371i	0.617198	−	0.617198i	0.944812	+	0.327614i	$0.106245\pi$
$30$	−2.49117	−	0.250285i	−0.454824	−	0.0456955i
$31$	3.48460			0.625853			0.312926	−	0.949777i	$-0.398691\pi$
$31$	3.48460			0.625853			0.312926	+	0.949777i	$0.398691\pi$
$32$	−4.96256	−	2.71533i	−0.877265	−	0.480007i
$33$	2.28859			0.398392
$34$	−6.90100	−	0.693333i	−1.18351	−	0.118906i
$35$		0			0
$36$	0.634992	−	3.12825i	0.105832	−	0.521376i
$37$	4.97708	+	4.97708i	0.818227	+	0.818227i	0.985851	−	0.167624i	$-0.0536095\pi$
$37$	4.97708	+	4.97708i	0.818227	+	0.818227i	−0.167624	+	0.985851i	$0.553609\pi$
$38$	−7.29508	+	5.96305i	−1.18342	+	0.967335i
$39$			8.88566i			1.42284i
$40$	−1.08894	−	2.06637i	−0.172177	−	0.326721i
$41$			3.86206i			0.603152i	0.953442	+	0.301576i	$0.0975127\pi$
$41$			3.86206i			0.603152i	−0.953442	+	0.301576i	$0.902487\pi$
$42$		0			0
$43$	5.89641	+	5.89641i	0.899194	+	0.899194i	0.995365	−	0.0961708i	$-0.0306595\pi$
$43$	5.89641	+	5.89641i	0.899194	+	0.899194i	−0.0961708	+	0.995365i	$0.530659\pi$
$44$	1.17921	+	1.77985i	0.177772	+	0.268323i
$45$	0.931974	−	0.931974i	0.138930	−	0.138930i
$46$	−0.834516	+	8.30625i	−0.123043	+	1.22469i
$47$	−6.21296			−0.906254			−0.453127	−	0.891446i	$-0.649692\pi$
$47$	−6.21296			−0.906254			−0.453127	+	0.891446i	$0.649692\pi$
$48$	7.94803	−	3.21950i	1.14720	−	0.464695i
$49$		0			0
$50$	−0.610451	+	6.07604i	−0.0863308	+	0.859283i
$51$	7.43454	−	7.43454i	1.04104	−	1.04104i
$52$	−6.91045	+	4.57838i	−0.958306	+	0.634907i
$53$	−9.42504	−	9.42504i	−1.29463	−	1.29463i	−0.931891	−	0.362738i	$-0.881842\pi$
$53$	−9.42504	−	9.42504i	−1.29463	−	1.29463i	−0.362738	−	0.931891i	$-0.618158\pi$
$54$	−2.69393	−	3.29570i	−0.366597	−	0.448487i
$55$			0.881566i			0.118870i
$56$		0			0
$57$		−	14.2832i		−	1.89185i
$58$	−5.14677	+	4.20701i	−0.675804	+	0.552408i
$59$	−4.26676	−	4.26676i	−0.555485	−	0.555485i	0.372534	−	0.928019i	$-0.378489\pi$
$59$	−4.26676	−	4.26676i	−0.555485	−	0.555485i	−0.928019	+	0.372534i	$0.878489\pi$
$60$	3.47002	+	0.704366i	0.447978	+	0.0909332i
$61$	−6.88524	+	6.88524i	−0.881565	+	0.881565i	−0.993694	−	0.112129i	$-0.964233\pi$
$61$	−6.88524	+	6.88524i	−0.881565	+	0.881565i	0.112129	+	0.993694i	$0.464233\pi$
$62$	−4.90328	−	0.492626i	−0.622718	−	0.0625635i
$63$		0			0
$64$	6.59909	+	4.52239i	0.824886	+	0.565298i
$65$	−3.42277			−0.424542
$66$	−3.22034	−	0.323543i	−0.396396	−	0.0398253i
$67$	8.72771	−	8.72771i	1.06626	−	1.06626i	0.0686169	−	0.997643i	$-0.478141\pi$
$67$	8.72771	−	8.72771i	1.06626	−	1.06626i	0.997643	−	0.0686169i	$-0.0218586\pi$
$68$	9.61258	+	1.95122i	1.16570	+	0.236620i
$69$	−8.94843	−	8.94843i	−1.07726	−	1.07726i
$70$		0			0
$71$			0.135373i			0.0160659i	0.999968	+	0.00803293i	$0.00255699\pi$
$71$			0.135373i			0.0160659i	−0.999968	+	0.00803293i	$0.997443\pi$
$72$	−1.33576	+	4.31209i	−0.157421	+	0.508185i
$73$			7.56806i			0.885775i	0.896577	+	0.442887i	$0.146046\pi$
$73$			7.56806i			0.885775i	−0.896577	+	0.442887i	$0.853954\pi$
$74$	−6.29978	−	7.70702i	−0.732334	−	0.895923i
$75$	−6.54581	−	6.54581i	−0.755845	−	0.755845i
$76$	11.1081	−	7.35947i	1.27419	−	0.844189i
$77$		0			0
$78$	1.25618	−	12.5033i	0.142235	−	1.41572i
$79$	6.79297			0.764269			0.382135	−	0.924107i	$-0.375189\pi$
$79$	6.79297			0.764269			0.382135	+	0.924107i	$0.375189\pi$
$80$	1.24015	+	3.06159i	0.138654	+	0.342296i
$81$	11.2408			1.24898
$82$	0.545988	−	5.43442i	0.0602942	−	0.600131i
$83$	−5.63027	+	5.63027i	−0.618003	+	0.618003i	−0.945019	−	0.327016i	$-0.893957\pi$
$83$	−5.63027	+	5.63027i	−0.618003	+	0.618003i	0.327016	+	0.945019i	$0.393957\pi$
$84$		0			0
$85$	2.86379	+	2.86379i	0.310622	+	0.310622i
$86$	−7.46342	−	9.13060i	−0.804802	−	0.984578i
$87$		−	10.0770i		−	1.08036i
$88$	−1.40767	−	2.67119i	−0.150058	−	0.284750i
$89$			5.58422i			0.591926i	0.955199	+	0.295963i	$0.0956406\pi$
$89$			5.58422i			0.591926i	−0.955199	+	0.295963i	$0.904359\pi$
$90$	−1.44316	+	1.17965i	−0.152123	+	0.124346i
$91$		0			0
$92$	2.34855	−	11.5700i	0.244853	−	1.20625i
$93$	5.28237	−	5.28237i	0.547757	−	0.547757i
$94$	8.74245	+	0.878340i	0.901714	+	0.0905939i
$95$	5.50189			0.564482
$96$	−11.6391	+	3.40662i	−1.18791	+	0.347687i
$97$	−6.15204			−0.624645			−0.312322	−	0.949976i	$-0.601107\pi$
$97$	−6.15204			−0.624645			−0.312322	+	0.949976i	$0.601107\pi$
$98$		0			0
$99$	1.20476	−	1.20476i	0.121083	−	0.121083i
$100$	1.71797	−	8.46348i	0.171797	−	0.846348i
$101$	−5.18720	−	5.18720i	−0.516146	−	0.516146i	0.400257	−	0.916403i	$-0.368921\pi$
$101$	−5.18720	−	5.18720i	−0.516146	−	0.516146i	−0.916403	+	0.400257i	$0.868921\pi$
$102$	−11.5124	+	9.41033i	−1.13990	+	0.931761i
$103$			14.0254i			1.38197i	0.722871	+	0.690983i	$0.242822\pi$
$103$			14.0254i			1.38197i	−0.722871	+	0.690983i	$0.757178\pi$
$104$	10.3711	−	5.46542i	1.01697	−	0.535929i
$105$		0			0
$106$	11.9298	+	14.5947i	1.15873	+	1.41756i
$107$	3.38984	+	3.38984i	0.327708	+	0.327708i	0.851714	−	0.524006i	$-0.175563\pi$
$107$	3.38984	+	3.38984i	0.327708	+	0.327708i	−0.524006	+	0.851714i	$0.675563\pi$
$108$	3.32479	+	5.01832i	0.319928	+	0.482888i
$109$	4.04374	−	4.04374i	0.387320	−	0.387320i	−0.486410	−	0.873731i	$-0.661694\pi$
$109$	4.04374	−	4.04374i	0.387320	−	0.387320i	0.873731	+	0.486410i	$0.161694\pi$
$110$	0.124629	−	1.24048i	0.0118829	−	0.118275i
$111$	15.0897			1.43225
$112$		0			0
$113$	−18.9549			−1.78313			−0.891565	−	0.452893i	$-0.850392\pi$
$113$	−18.9549			−1.78313			−0.891565	+	0.452893i	$0.850392\pi$
$114$	−2.01924	+	20.0983i	−0.189119	+	1.88238i
$115$	3.44695	−	3.44695i	0.321429	−	0.321429i
$116$	7.83693	−	5.19220i	0.727641	−	0.482084i
$117$	4.67760	+	4.67760i	0.432444	+	0.432444i
$118$	5.40069	+	6.60709i	0.497174	+	0.608232i
$119$		0			0
$120$	−4.78319	−	1.48170i	−0.436644	−	0.135260i
$121$		−	9.86040i		−	0.896400i
$122$	10.6618	−	8.71505i	0.965275	−	0.789023i
$123$	5.85457	+	5.85457i	0.527889	+	0.527889i
$124$	6.82991	+	1.38638i	0.613344	+	0.124500i
$125$	5.44112	−	5.44112i	0.486669	−	0.486669i
$126$		0			0
$127$	−13.0124			−1.15467			−0.577333	−	0.816509i	$-0.695907\pi$
$127$	−13.0124			−1.15467			−0.577333	+	0.816509i	$0.695907\pi$
$128$	−8.64644	−	7.29651i	−0.764244	−	0.644927i
$129$	17.8770			1.57398
$130$	4.81627	+	0.483884i	0.422415	+	0.0424394i
$131$	8.75650	−	8.75650i	0.765059	−	0.765059i	−0.212173	−	0.977232i	$-0.568054\pi$
$131$	8.75650	−	8.75650i	0.765059	−	0.765059i	0.977232	+	0.212173i	$0.0680542\pi$
$132$	4.48569	+	0.910533i	0.390430	+	0.0792517i
$133$		0			0
$134$	−13.5149	+	11.0472i	−1.16751	+	0.954330i
$135$			2.48559i			0.213925i
$136$	−13.2503	−	4.10457i	−1.13620	−	0.351964i
$137$		−	10.6783i		−	0.912305i	−0.889902	−	0.456153i	$-0.849227\pi$
$137$		−	10.6783i		−	0.912305i	0.889902	−	0.456153i	$-0.150773\pi$
$138$	11.3265	+	13.8567i	0.964180	+	1.17956i
$139$	−0.564966	−	0.564966i	−0.0479198	−	0.0479198i	0.682741	−	0.730661i	$-0.260788\pi$
$139$	−0.564966	−	0.564966i	−0.0479198	−	0.0479198i	−0.730661	+	0.682741i	$0.760788\pi$
$140$		0			0
$141$	−9.41835	+	9.41835i	−0.793169	+	0.793169i
$142$	0.0191380	−	0.190488i	0.00160603	−	0.0159854i
$143$	−4.42460			−0.370004
$144$	2.48920	−	5.87883i	0.207434	−	0.489903i
$145$	3.88166			0.322354
$146$	1.06991	−	10.6492i	0.0885467	−	0.881338i
$147$		0			0
$148$	7.77504	+	11.7354i	0.639105	+	0.964643i
$149$	4.82246	+	4.82246i	0.395071	+	0.395071i	0.876490	−	0.481419i	$-0.159879\pi$
$149$	4.82246	+	4.82246i	0.395071	+	0.395071i	−0.481419	+	0.876490i	$0.659879\pi$
$150$	8.28540	+	10.1362i	0.676500	+	0.827617i
$151$			18.6097i			1.51444i	0.653160	+	0.757220i	$0.273443\pi$
$151$			18.6097i			1.51444i	−0.653160	+	0.757220i	$0.726557\pi$
$152$	−16.6710	+	8.78535i	−1.35220	+	0.712586i
$153$		−	7.82741i		−	0.632808i
$154$		0			0
$155$	2.03478	+	2.03478i	0.163437	+	0.163437i
$156$	−3.53523	+	17.4161i	−0.283045	+	1.39441i
$157$	0.486767	−	0.486767i	0.0388482	−	0.0388482i	−0.687416	−	0.726264i	$-0.741255\pi$
$157$	0.486767	−	0.486767i	0.0388482	−	0.0388482i	0.726264	+	0.687416i	$0.241255\pi$
$158$	−9.55860	−	0.960338i	−0.760441	−	0.0764004i
$159$	−28.5752			−2.26616
$160$	−1.31223	−	4.48338i	−0.103741	−	0.354442i
$161$		0			0
$162$	−15.8172	−	1.58913i	−1.24272	−	0.124854i
$163$	−8.73635	+	8.73635i	−0.684284	+	0.684284i	−0.960963	−	0.276679i	$-0.910766\pi$
$163$	−8.73635	+	8.73635i	−0.684284	+	0.684284i	0.276679	+	0.960963i	$0.410766\pi$
$164$	−1.53655	+	7.56974i	−0.119984	+	0.591097i
$165$	1.33638	+	1.33638i	0.104037	+	0.104037i
$166$	8.71849	−	7.12656i	0.676686	−	0.553129i
$167$			18.6633i			1.44421i	0.691783	+	0.722106i	$0.256826\pi$
$167$			18.6633i			1.44421i	−0.691783	+	0.722106i	$0.743174\pi$
$168$		0			0
$169$		−	4.17895i		−	0.321457i
$170$	−3.62487	−	4.43459i	−0.278015	−	0.340118i
$171$	−7.51897	−	7.51897i	−0.574990	−	0.574990i
$172$	9.21119	+	13.9031i	0.702347	+	1.06010i
$173$	−6.56968	+	6.56968i	−0.499484	+	0.499484i	−0.911277	−	0.411794i	$-0.864902\pi$
$173$	−6.56968	+	6.56968i	−0.499484	+	0.499484i	0.411794	+	0.911277i	$0.364902\pi$
$174$	−1.42460	+	14.1796i	−0.107999	+	1.07495i
$175$		0			0
$176$	1.60315	+	3.95772i	0.120842	+	0.298324i
$177$	−12.9361			−0.972340
$178$	0.789454	−	7.85773i	0.0591721	−	0.588961i
$179$	0.251536	−	0.251536i	0.0188007	−	0.0188007i	−0.697644	−	0.716445i	$-0.745768\pi$
$179$	0.251536	−	0.251536i	0.0188007	−	0.0188007i	0.716445	+	0.697644i	$0.245768\pi$
$180$	2.19749	−	1.45590i	0.163791	−	0.108516i
$181$	−16.5200	−	16.5200i	−1.22792	−	1.22792i	−0.964750	−	0.263170i	$-0.915232\pi$
$181$	−16.5200	−	16.5200i	−1.22792	−	1.22792i	−0.263170	−	0.964750i	$-0.584768\pi$
$182$		0			0
$183$			20.8750i			1.54312i
$184$	−4.94038	+	15.9485i	−0.364210	+	1.17574i
$185$			5.81257i			0.427349i
$186$	−8.17976	+	6.68620i	−0.599769	+	0.490256i
$187$	3.70202	+	3.70202i	0.270719	+	0.270719i
$188$	−12.1776	−	2.47188i	−0.888141	−	0.180280i
$189$		0			0
$190$	−7.74188	−	0.777815i	−0.561655	−	0.0564286i
$191$	−20.3852			−1.47502			−0.737511	−	0.675335i	$-0.763999\pi$
$191$	−20.3852			−1.47502			−0.737511	+	0.675335i	$0.763999\pi$
$192$	16.8593	−	3.14812i	1.21671	−	0.227196i
$193$	−19.1125			−1.37575			−0.687873	−	0.725831i	$-0.741455\pi$
$193$	−19.1125			−1.37575			−0.687873	+	0.725831i	$0.741455\pi$
$194$	8.65671	+	0.869727i	0.621516	+	0.0624428i
$195$	−5.18864	+	5.18864i	−0.371566	+	0.371566i
$196$		0			0
$197$	6.69173	+	6.69173i	0.476766	+	0.476766i	0.904096	−	0.427330i	$-0.140546\pi$
$197$	6.69173	+	6.69173i	0.476766	+	0.476766i	−0.427330	+	0.904096i	$0.640546\pi$
$198$	−1.86558	+	1.52494i	−0.132581	+	0.108372i
$199$			7.96463i			0.564597i	0.959327	+	0.282299i	$0.0910969\pi$
$199$			7.96463i			0.564597i	−0.959327	+	0.282299i	$0.908903\pi$
$200$	−3.61390	+	11.6663i	−0.255542	+	0.824935i
$201$		−	26.4610i		−	1.86642i
$202$	6.56574	+	8.03240i	0.461964	+	0.565157i
$203$		0			0
$204$	17.5298	−	11.6140i	1.22733	−	0.813144i
$205$	−2.25519	+	2.25519i	−0.157509	+	0.157509i
$206$	1.98281	−	19.7356i	0.138149	−	1.37504i
$207$	−9.42130			−0.654825
$208$	−15.3662	+	6.22437i	−1.06545	+	0.431582i
$209$	7.11229			0.491967
$210$		0			0
$211$	9.30887	−	9.30887i	0.640849	−	0.640849i	−0.309915	−	0.950764i	$-0.600301\pi$
$211$	9.30887	−	9.30887i	0.640849	−	0.640849i	0.950764	+	0.309915i	$0.100301\pi$
$212$	−14.7235	−	22.2232i	−1.01122	−	1.52629i
$213$	0.205215	+	0.205215i	0.0140611	+	0.0140611i
$214$	−4.29071	−	5.24917i	−0.293307	−	0.358826i
$215$			6.88623i			0.469637i
$216$	−3.96895	−	7.53146i	−0.270053	−	0.512451i
$217$		0			0
$218$	−6.26174	+	5.11840i	−0.424099	+	0.346662i
$219$	11.4726	+	11.4726i	0.775245	+	0.775245i
$220$	−0.350738	+	1.72789i	−0.0236468	+	0.116495i
$221$	−14.3735	+	14.3735i	−0.966863	+	0.966863i
$222$	−21.2332	−	2.13327i	−1.42508	−	0.143175i
$223$	3.87218			0.259301			0.129650	−	0.991560i	$-0.458615\pi$
$223$	3.87218			0.259301			0.129650	+	0.991560i	$0.458615\pi$
$224$		0			0
$225$	−6.89171			−0.459447
$226$	26.6720	+	2.67970i	1.77420	+	0.178251i
$227$	−4.33092	+	4.33092i	−0.287453	+	0.287453i	−0.836072	−	0.548619i	$-0.815154\pi$
$227$	−4.33092	+	4.33092i	−0.287453	+	0.287453i	0.548619	+	0.836072i	$0.315154\pi$
$228$	5.68267	−	27.9954i	0.376344	−	1.85404i
$229$	19.0540	+	19.0540i	1.25912	+	1.25912i	0.951513	+	0.307610i	$0.0995292\pi$
$229$	19.0540	+	19.0540i	1.25912	+	1.25912i	0.307610	+	0.951513i	$0.400471\pi$
$230$	−5.33760	+	4.36300i	−0.351951	+	0.287688i
$231$		0			0
$232$	−11.7616	+	6.19818i	−0.772188	+	0.406930i
$233$		−	13.6982i		−	0.897397i	−0.893683	−	0.448699i	$-0.851888\pi$
$233$		−	13.6982i		−	0.897397i	0.893683	−	0.448699i	$-0.148112\pi$
$234$	−5.92071	−	7.24327i	−0.387049	−	0.473508i
$235$	−3.62796	−	3.62796i	−0.236662	−	0.236662i
$236$	−6.66541	−	10.0605i	−0.433881	−	0.654885i
$237$	10.2976	−	10.2976i	0.668901	−	0.668901i
$238$		0			0
$239$	−1.05904			−0.0685033			−0.0342517	−	0.999413i	$-0.510905\pi$
$239$	−1.05904			−0.0685033			−0.0342517	+	0.999413i	$0.510905\pi$
$240$	6.52110	+	2.76115i	0.420935	+	0.178232i
$241$	−4.95723			−0.319323			−0.159662	−	0.987172i	$-0.551040\pi$
$241$	−4.95723			−0.319323			−0.159662	+	0.987172i	$0.551040\pi$
$242$	−1.39399	+	13.8749i	−0.0896089	+	0.891910i
$243$	10.6552	−	10.6552i	0.683530	−	0.683530i
$244$	−16.2346	+	10.7559i	−1.03932	+	0.688577i
$245$		0			0
$246$	−7.41046	−	9.06581i	−0.472474	−	0.578015i
$247$			27.6141i			1.75705i
$248$	−9.41458	−	2.91637i	−0.597826	−	0.185190i
$249$			17.0701i			1.08177i
$250$	−8.42559	+	6.88714i	−0.532881	+	0.435581i
$251$	20.0251	+	20.0251i	1.26397	+	1.26397i	0.949151	+	0.314822i	$0.101945\pi$
$251$	20.0251	+	20.0251i	1.26397	+	1.26397i	0.314822	+	0.949151i	$0.398055\pi$
$252$		0			0
$253$	4.45586	−	4.45586i	0.280138	−	0.280138i
$254$	18.3102	+	1.83960i	1.14888	+	0.115426i
$255$	8.68256			0.543723
$256$	11.1351	+	11.4895i	0.695946	+	0.718094i
$257$	−20.9118			−1.30444			−0.652220	−	0.758030i	$-0.726162\pi$
$257$	−20.9118			−1.30444			−0.652220	+	0.758030i	$0.726162\pi$
$258$	−25.1552	−	2.52731i	−1.56610	−	0.157343i
$259$		0			0
$260$	−6.70871	−	1.36177i	−0.416057	−	0.0844537i
$261$	−5.30473	−	5.30473i	−0.328355	−	0.328355i
$262$	−13.5595	+	11.0836i	−0.837706	+	0.684747i
$263$		−	12.2051i		−	0.752597i	−0.926499	−	0.376298i	$-0.877197\pi$
$263$		−	12.2051i		−	0.752597i	0.926499	−	0.376298i	$-0.122803\pi$
$264$	−6.18323	−	1.91539i	−0.380551	−	0.117884i
$265$		−	11.0072i		−	0.676167i
$266$		0			0
$267$	8.46523	+	8.46523i	0.518064	+	0.518064i
$268$	20.5790	−	13.6342i	1.25706	−	0.832840i
$269$	4.01199	−	4.01199i	0.244615	−	0.244615i	−0.574141	−	0.818756i	$-0.694664\pi$
$269$	4.01199	−	4.01199i	0.244615	−	0.244615i	0.818756	+	0.574141i	$0.194664\pi$
$270$	0.351393	−	3.49754i	0.0213851	−	0.212854i
$271$	−2.94585			−0.178947			−0.0894737	−	0.995989i	$-0.528519\pi$
$271$	−2.94585			−0.178947			−0.0894737	+	0.995989i	$0.528519\pi$
$272$	18.0646	+	7.64889i	1.09533	+	0.463782i
$273$		0			0
$274$	−1.50961	+	15.0257i	−0.0911988	+	0.907736i
$275$	3.25948	−	3.25948i	0.196554	−	0.196554i
$276$	−13.9790	−	21.0994i	−0.841435	−	1.27003i
$277$	−9.45207	−	9.45207i	−0.567920	−	0.567920i	0.363625	−	0.931545i	$-0.381539\pi$
$277$	−9.45207	−	9.45207i	−0.567920	−	0.567920i	−0.931545	+	0.363625i	$0.881539\pi$
$278$	0.715110	+	0.874851i	0.0428895	+	0.0524701i
$279$		−	5.56151i		−	0.332959i
$280$		0			0
$281$		−	5.24743i		−	0.313036i	−0.987675	−	0.156518i	$-0.949973\pi$
$281$		−	5.24743i		−	0.313036i	0.987675	−	0.156518i	$-0.0500269\pi$
$282$	14.5843	−	11.9214i	0.868485	−	0.709906i
$283$	3.81900	+	3.81900i	0.227016	+	0.227016i	0.811445	−	0.584429i	$-0.198681\pi$
$283$	3.81900	+	3.81900i	0.227016	+	0.227016i	−0.584429	+	0.811445i	$0.698681\pi$
$284$	−0.0538594	+	0.265335i	−0.00319597	+	0.0157448i
$285$	8.34043	−	8.34043i	0.494044	−	0.494044i
$286$	6.22599	+	0.625516i	0.368151	+	0.0369875i
$287$		0			0
$288$	−4.33373	+	7.92037i	−0.255368	+	0.466712i
$289$	7.05226			0.414839
$290$	−5.46199	−	0.548758i	−0.320739	−	0.0322242i
$291$	−9.32600	+	9.32600i	−0.546700	+	0.546700i
$292$	−3.01101	+	14.8336i	−0.176206	+	0.868071i
$293$	1.49974	+	1.49974i	0.0876160	+	0.0876160i	0.749556	−	0.661940i	$-0.230267\pi$
$293$	1.49974	+	1.49974i	0.0876160	+	0.0876160i	−0.661940	+	0.749556i	$0.730267\pi$
$294$		0			0
$295$		−	4.98302i		−	0.290122i
$296$	−9.28144	−	17.6124i	−0.539473	−	1.02370i
$297$			3.21312i			0.186444i
$298$	−6.10406	−	7.46758i	−0.353599	−	0.432585i
$299$	17.3003	+	17.3003i	1.00050	+	1.00050i
$300$	−10.2257	−	15.4343i	−0.590379	−	0.891098i
$301$		0			0
$302$	2.63090	−	26.1863i	0.151391	−	1.50685i
$303$	−15.7268			−0.903480
$304$	24.7003	−	10.0053i	1.41666	−	0.573843i
$305$	−8.04106			−0.460430
$306$	−1.10658	+	11.0142i	−0.0632588	+	0.629638i
$307$	−6.27283	+	6.27283i	−0.358010	+	0.358010i	−0.863079	−	0.505069i	$-0.831467\pi$
$307$	−6.27283	+	6.27283i	−0.358010	+	0.358010i	0.505069	+	0.863079i	$0.331467\pi$
$308$		0			0
$309$	21.2614	+	21.2614i	1.20952	+	1.20952i
$310$	−2.57553	−	3.15085i	−0.146280	−	0.178957i
$311$		−	11.0790i		−	0.628232i	−0.949385	−	0.314116i	$-0.898292\pi$
$311$		−	11.0790i		−	0.628232i	0.949385	−	0.314116i	$-0.101708\pi$
$312$	7.43668	−	24.0070i	0.421019	−	1.35913i
$313$		−	12.7771i		−	0.722202i	−0.932527	−	0.361101i	$-0.882401\pi$
$313$		−	12.7771i		−	0.722202i	0.932527	−	0.361101i	$-0.117599\pi$
$314$	−0.753760	+	0.616129i	−0.0425371	+	0.0347702i
$315$		0			0
$316$	13.3144	+	2.70264i	0.748995	+	0.152035i
$317$	−16.2677	+	16.2677i	−0.913687	+	0.913687i	−0.996560	−	0.0828735i	$-0.973590\pi$
$317$	−16.2677	+	16.2677i	−0.913687	+	0.913687i	0.0828735	+	0.996560i	$0.473590\pi$
$318$	40.2090	+	4.03974i	2.25481	+	0.226537i
$319$	5.01781			0.280944
$320$	1.21266	+	6.49421i	0.0677897	+	0.363037i
$321$	10.2774			0.573631
$322$		0			0
$323$	23.1045	−	23.1045i	1.28557	−	1.28557i
$324$	22.0322	+	4.47223i	1.22401	+	0.248457i
$325$	12.6552	+	12.6552i	0.701986	+	0.701986i
$326$	13.5283	−	11.0581i	0.749261	−	0.612452i
$327$		−	12.2600i		−	0.677978i
$328$	3.23228	−	10.4344i	0.178473	−	0.576142i
$329$		0			0
$330$	−1.69154	−	2.06939i	−0.0931161	−	0.113916i
$331$	−7.95536	−	7.95536i	−0.437266	−	0.437266i	0.453825	−	0.891091i	$-0.350059\pi$
$331$	−7.95536	−	7.95536i	−0.437266	−	0.437266i	−0.891091	+	0.453825i	$0.850059\pi$
$332$	−13.2755	+	8.79544i	−0.728590	+	0.482713i
$333$	7.94355	−	7.94355i	0.435304	−	0.435304i
$334$	2.63848	−	26.2617i	0.144371	−	1.43698i
$335$	10.1928			0.556893
$336$		0			0
$337$	1.61885			0.0881844			0.0440922	−	0.999027i	$-0.485960\pi$
$337$	1.61885			0.0881844			0.0440922	+	0.999027i	$0.485960\pi$
$338$	−0.590787	+	5.88032i	−0.0321346	+	0.319847i
$339$	−28.7342	+	28.7342i	−1.56063	+	1.56063i
$340$	4.47373	+	6.75250i	0.242622	+	0.366206i
$341$	2.63035	+	2.63035i	0.142442	+	0.142442i
$342$	9.51719	+	11.6431i	0.514631	+	0.629589i
$343$		0			0
$344$	−10.9958	−	20.8656i	−0.592856	−	1.12500i
$345$		−	10.4506i		−	0.562641i
$346$	10.1732	−	8.31562i	0.546913	−	0.447051i
$347$	9.17301	+	9.17301i	0.492433	+	0.492433i	0.909072	−	0.416639i	$-0.136792\pi$
$347$	9.17301	+	9.17301i	0.492433	+	0.492433i	−0.416639	+	0.909072i	$0.636792\pi$
$348$	4.00920	−	19.7511i	0.214916	−	1.05877i
$349$	0.267623	−	0.267623i	0.0143255	−	0.0143255i	−0.699908	−	0.714233i	$-0.746776\pi$
$349$	0.267623	−	0.267623i	0.0143255	−	0.0143255i	0.714233	+	0.699908i	$0.246776\pi$
$350$		0			0
$351$	−12.4752			−0.665879
$352$	−1.69632	−	5.79566i	−0.0904144	−	0.308910i
$353$	−33.9839			−1.80878			−0.904391	−	0.426706i	$-0.859674\pi$
$353$	−33.9839			−1.80878			−0.904391	+	0.426706i	$0.859674\pi$
$354$	18.2028	+	1.82881i	0.967469	+	0.0972002i
$355$	−0.0790491	+	0.0790491i	−0.00419549	+	0.00419549i
$356$	−2.22173	+	10.9452i	−0.117751	+	0.580096i
$357$		0			0
$358$	−0.389503	+	0.318383i	−0.0205859	+	0.0168271i
$359$			2.57851i			0.136089i	0.997682	+	0.0680444i	$0.0216760\pi$
$359$			2.57851i			0.136089i	−0.997682	+	0.0680444i	$0.978324\pi$
$360$	−3.29797	+	1.73798i	−0.173819	+	0.0915995i
$361$		−	25.3881i		−	1.33622i
$362$	20.9103	+	25.5812i	1.09902	+	1.34452i
$363$	−14.9476	−	14.9476i	−0.784544	−	0.784544i
$364$		0			0
$365$	−4.41925	+	4.41925i	−0.231314	+	0.231314i
$366$	2.95114	−	29.3738i	0.154258	−	1.53539i
$367$	9.29284			0.485082			0.242541	−	0.970141i	$-0.422019\pi$
$367$	9.29284			0.485082			0.242541	+	0.970141i	$0.422019\pi$
$368$	9.20643	−	21.7431i	0.479918	−	1.13344i
$369$	6.16394			0.320882
$370$	0.821736	−	8.17904i	0.0427200	−	0.425208i
$371$		0			0
$372$	12.4552	−	8.25196i	0.645774	−	0.427844i
$373$	7.77679	+	7.77679i	0.402667	+	0.402667i	0.879172	−	0.476505i	$-0.158097\pi$
$373$	7.77679	+	7.77679i	0.402667	+	0.402667i	−0.476505	+	0.879172i	$0.658097\pi$
$374$	−4.68586	−	5.73259i	−0.242300	−	0.296425i
$375$		−	16.4966i		−	0.851881i
$376$	16.7860	+	5.19982i	0.865671	+	0.268160i
$377$			19.4821i			1.00338i
$378$		0			0
$379$	−13.2670	−	13.2670i	−0.681482	−	0.681482i	0.278852	−	0.960334i	$-0.410046\pi$
$379$	−13.2670	−	13.2670i	−0.681482	−	0.681482i	−0.960334	+	0.278852i	$0.910046\pi$
$380$	10.7839	+	2.18897i	0.553200	+	0.112292i
$381$	−19.7258	+	19.7258i	−1.01058	+	1.01058i
$382$	28.6846	+	2.88190i	1.46763	+	0.147451i
$383$	18.5796			0.949375			0.474687	−	0.880154i	$-0.342561\pi$
$383$	18.5796			0.949375			0.474687	+	0.880154i	$0.342561\pi$
$384$	−24.1682	+	2.04638i	−1.23333	+	0.104429i
$385$		0			0
$386$	26.8937	+	2.70197i	1.36885	+	0.137527i
$387$	9.41082	−	9.41082i	0.478379	−	0.478379i
$388$	−12.0582	−	2.44764i	−0.612161	−	0.124260i
$389$	21.9834	+	21.9834i	1.11460	+	1.11460i	0.992520	+	0.122084i	$0.0389577\pi$
$389$	21.9834	+	21.9834i	1.11460	+	1.11460i	0.122084	+	0.992520i	$0.461042\pi$
$390$	8.03461	−	6.56756i	0.406849	−	0.332561i
$391$		−	28.9500i		−	1.46406i
$392$		0			0
$393$		−	26.5483i		−	1.33918i
$394$	−8.47010	−	10.3622i	−0.426718	−	0.522038i
$395$	3.96665	+	3.96665i	0.199584	+	0.199584i
$396$	2.84069	−	1.88204i	0.142750	−	0.0945762i
$397$	21.8736	−	21.8736i	1.09780	−	1.09780i	0.103136	−	0.994667i	$-0.467112\pi$
$397$	21.8736	−	21.8736i	1.09780	−	1.09780i	0.994667	−	0.103136i	$-0.0328876\pi$
$398$	1.12598	−	11.2073i	0.0564401	−	0.561769i
$399$		0			0
$400$	6.73453	−	15.9052i	0.336726	−	0.795258i
$401$	−7.11092			−0.355103			−0.177551	−	0.984112i	$-0.556818\pi$
$401$	−7.11092			−0.355103			−0.177551	+	0.984112i	$0.556818\pi$
$402$	−3.74085	+	37.2341i	−0.186577	+	1.85707i
$403$	−10.2126	+	10.2126i	−0.508726	+	0.508726i
$404$	−8.10329	−	12.2308i	−0.403154	−	0.608507i
$405$	6.56387	+	6.56387i	0.326162	+	0.326162i
$406$		0			0
$407$			7.51391i			0.372451i
$408$	−26.3086	+	13.8642i	−1.30247	+	0.686380i
$409$			34.8286i			1.72216i	0.508468	+	0.861081i	$0.330212\pi$
$409$			34.8286i			1.72216i	−0.508468	+	0.861081i	$0.669788\pi$
$410$	3.49216	−	2.85452i	0.172466	−	0.140975i
$411$	−16.1874	−	16.1874i	−0.798465	−	0.798465i
$412$	−5.58013	+	27.4902i	−0.274913	+	1.35435i
$413$		0			0
$414$	13.2570	+	1.33191i	0.651545	+	0.0654598i
$415$	−6.57542			−0.322775
$416$	22.5022	−	6.58614i	1.10326	−	0.322912i
$417$	−1.71289			−0.0838804
$418$	−10.0079	−	1.00548i	−0.489503	−	0.0491796i
$419$	0.653529	−	0.653529i	0.0319270	−	0.0319270i	−0.690963	−	0.722890i	$-0.742813\pi$
$419$	0.653529	−	0.653529i	0.0319270	−	0.0319270i	0.722890	+	0.690963i	$0.242813\pi$
$420$		0			0
$421$	−9.48036	−	9.48036i	−0.462045	−	0.462045i	0.437280	−	0.899325i	$-0.355942\pi$
$421$	−9.48036	−	9.48036i	−0.462045	−	0.462045i	−0.899325	+	0.437280i	$0.855942\pi$
$422$	−14.4148	+	11.7828i	−0.701701	+	0.573576i
$423$			9.91605i			0.482135i
$424$	17.5762	+	33.3524i	0.853574	+	1.61973i
$425$		−	21.1770i		−	1.02724i
$426$	−0.259753	−	0.317776i	−0.0125851	−	0.0153963i
$427$		0			0
$428$	5.29550	+	7.99285i	0.255968	+	0.386349i
$429$	−6.70735	+	6.70735i	−0.323834	+	0.323834i
$430$	0.973521	−	9.68982i	0.0469474	−	0.467285i
$431$	13.5941			0.654806			0.327403	−	0.944885i	$-0.393827\pi$
$431$	13.5941			0.654806			0.327403	+	0.944885i	$0.393827\pi$
$432$	4.52009	+	11.1588i	0.217473	+	0.536880i
$433$	−6.65932			−0.320027			−0.160013	−	0.987115i	$-0.551154\pi$
$433$	−6.65932			−0.320027			−0.160013	+	0.987115i	$0.551154\pi$
$434$		0			0
$435$	5.88428	−	5.88428i	0.282130	−	0.282130i
$436$	9.53468	−	6.31701i	0.456628	−	0.302530i
$437$	−27.8092	−	27.8092i	−1.33030	−	1.33030i
$438$	−14.5215	−	17.7653i	−0.693864	−	0.848859i
$439$		−	6.08041i		−	0.290202i	−0.989417	−	0.145101i	$-0.953649\pi$
$439$		−	6.08041i		−	0.290202i	0.989417	−	0.145101i	$-0.0463508\pi$
$440$	0.737810	−	2.38179i	0.0351737	−	0.113547i
$441$		0			0
$442$	22.2573	−	18.1933i	1.05867	−	0.865367i
$443$	−13.7361	−	13.7361i	−0.652621	−	0.652621i	0.301002	−	0.953623i	$-0.402679\pi$
$443$	−13.7361	−	13.7361i	−0.652621	−	0.652621i	−0.953623	+	0.301002i	$0.902679\pi$
$444$	29.5762	+	6.00356i	1.40363	+	0.284916i
$445$	−3.26082	+	3.26082i	−0.154578	+	0.154578i
$446$	−5.44866	−	0.547419i	−0.258002	−	0.0259210i
$447$	14.6209			0.691545
$448$		0			0
$449$	16.7810			0.791946			0.395973	−	0.918262i	$-0.370407\pi$
$449$	16.7810			0.791946			0.395973	+	0.918262i	$0.370407\pi$
$450$	9.69752	+	0.974296i	0.457146	+	0.0459287i
$451$	−2.91528	+	2.91528i	−0.137275	+	0.137275i
$452$	−37.1522	−	7.54137i	−1.74749	−	0.354716i
$453$	28.2109	+	28.2109i	1.32546	+	1.32546i
$454$	6.70644	−	5.48189i	0.314749	−	0.257278i
$455$		0			0
$456$	−11.9540	+	38.5898i	−0.559799	+	1.80713i
$457$			39.4714i			1.84639i	0.384328	+	0.923197i	$0.374433\pi$
$457$			39.4714i			1.84639i	−0.384328	+	0.923197i	$0.625567\pi$
$458$	−24.1177	−	29.5051i	−1.12695	−	1.37868i
$459$	10.4379	+	10.4379i	0.487200	+	0.487200i
$460$	8.12751	−	5.38472i	0.378947	−	0.251064i
$461$	1.46832	−	1.46832i	0.0683865	−	0.0683865i	−0.672086	−	0.740473i	$-0.734602\pi$
$461$	1.46832	−	1.46832i	0.0683865	−	0.0683865i	0.740473	+	0.672086i	$0.234602\pi$
$462$		0			0
$463$	−23.8476			−1.10829			−0.554145	−	0.832420i	$-0.686955\pi$
$463$	−23.8476			−1.10829			−0.554145	+	0.832420i	$0.686955\pi$
$464$	17.4264	−	7.05887i	0.808999	−	0.327700i
$465$	6.16912			0.286086
$466$	−1.93654	+	19.2751i	−0.0897085	+	0.892902i
$467$	25.1221	−	25.1221i	1.16251	−	1.16251i	0.178586	−	0.983924i	$-0.442848\pi$
$467$	25.1221	−	25.1221i	1.16251	−	1.16251i	0.983924	−	0.178586i	$-0.0571522\pi$
$468$	7.30721	+	11.0292i	0.337776	+	0.509827i
$469$		0			0
$470$	4.59212	+	5.61790i	0.211819	+	0.259135i
$471$		−	1.47580i		−	0.0680012i
$472$	7.95681	+	15.0988i	0.366242	+	0.694978i
$473$			8.90182i			0.409306i
$474$	−15.9459	+	13.0343i	−0.732418	+	0.598684i
$475$	−20.3425	−	20.3425i	−0.933380	−	0.933380i
$476$		0			0
$477$	−15.0426	+	15.0426i	−0.688754	+	0.688754i
$478$	1.49020	+	0.149718i	0.0681602	+	0.00684795i
$479$	−26.9126			−1.22967			−0.614834	−	0.788656i	$-0.710777\pi$
$479$	−26.9126			−1.22967			−0.614834	+	0.788656i	$0.710777\pi$
$480$	−8.78569	−	4.80720i	−0.401010	−	0.219418i
$481$	−29.1735			−1.33020
$482$	6.97547	+	0.700815i	0.317724	+	0.0319212i
$483$		0			0
$484$	3.92304	−	19.3267i	0.178320	−	0.878484i
$485$	−3.59238	−	3.59238i	−0.163122	−	0.163122i
$486$	−16.4996	+	13.4869i	−0.748436	+	0.611777i
$487$		−	26.7754i		−	1.21331i	−0.794966	−	0.606654i	$-0.792511\pi$
$487$		−	26.7754i		−	1.21331i	0.794966	−	0.606654i	$-0.207489\pi$
$488$	24.3648	−	12.8398i	1.10294	−	0.581233i
$489$			26.4872i			1.19779i
$490$		0			0
$491$	6.87914	+	6.87914i	0.310451	+	0.310451i	0.845084	−	0.534633i	$-0.179550\pi$
$491$	6.87914	+	6.87914i	0.310451	+	0.310451i	−0.534633	+	0.845084i	$0.679550\pi$
$492$	9.14583	+	13.8044i	0.412326	+	0.622351i
$493$	16.3005	−	16.3005i	0.734138	−	0.734138i
$494$	3.90387	−	38.8567i	0.175643	−	1.74824i
$495$	1.40700			0.0632401
$496$	12.8352	+	5.43467i	0.576319	+	0.244024i
$497$		0			0
$498$	2.41324	−	24.0198i	0.108140	−	1.07635i
$499$	14.7221	−	14.7221i	0.659054	−	0.659054i	−0.296103	−	0.955156i	$-0.595687\pi$
$499$	14.7221	−	14.7221i	0.659054	−	0.659054i	0.955156	+	0.296103i	$0.0956870\pi$
$500$	12.8295	−	8.49996i	0.573755	−	0.380130i
$501$	28.2921	+	28.2921i	1.26400	+	1.26400i
$502$	−25.3469	−	31.0089i	−1.13129	−	1.38399i
$503$		−	19.2528i		−	0.858438i	−0.903200	−	0.429219i	$-0.858789\pi$
$503$		−	19.2528i		−	0.858438i	0.903200	−	0.429219i	$-0.141211\pi$
$504$		0			0
$505$		−	6.05797i		−	0.269576i
$506$	−6.89991	+	5.64004i	−0.306739	+	0.250730i
$507$	−6.33495	−	6.33495i	−0.281345	−	0.281345i
$508$	−25.5047	−	5.17710i	−1.13159	−	0.229697i
$509$	−23.4626	+	23.4626i	−1.03996	+	1.03996i	−0.0407957	+	0.999168i	$0.512989\pi$
$509$	−23.4626	+	23.4626i	−1.03996	+	1.03996i	−0.999168	+	0.0407957i	$0.987011\pi$
$510$	−12.2175	−	1.22747i	−0.541000	−	0.0543534i
$511$		0			0
$512$	−14.0443	−	17.7414i	−0.620675	−	0.784068i
$513$	20.0532			0.885370
$514$	29.4256	+	2.95634i	1.29791	+	0.130399i
$515$	−8.18993	+	8.18993i	−0.360891	+	0.360891i
$516$	35.0394	+	7.11250i	1.54252	+	0.313110i
$517$	−4.68986	−	4.68986i	−0.206260	−	0.206260i
$518$		0			0
$519$			19.9182i			0.874313i
$520$	9.24751	+	2.86462i	0.405530	+	0.125622i
$521$		−	32.7494i		−	1.43478i	−0.696673	−	0.717389i	$-0.745337\pi$
$521$		−	32.7494i		−	1.43478i	0.696673	−	0.717389i	$-0.254663\pi$
$522$	6.71450	+	8.21438i	0.293886	+	0.359534i
$523$	27.0864	+	27.0864i	1.18440	+	1.18440i	0.978591	+	0.205813i	$0.0659840\pi$
$523$	27.0864	+	27.0864i	1.18440	+	1.18440i	0.205813	+	0.978591i	$0.434016\pi$
$524$	20.6468	−	13.6791i	0.901960	−	0.597576i
$525$		0			0
$526$	−1.72546	+	17.1741i	−0.0752335	+	0.748827i
$527$	17.0896			0.744433
$528$	8.42982	+	3.56934i	0.366861	+	0.155336i
$529$	−11.8451			−0.515003
$530$	−1.55611	+	15.4886i	−0.0675932	+	0.672780i
$531$	−6.80986	+	6.80986i	−0.295523	+	0.295523i
$532$		0			0
$533$	−11.3188	−	11.3188i	−0.490273	−	0.490273i
$534$	−10.7149	−	13.1084i	−0.463680	−	0.567257i
$535$			3.95888i			0.171157i
$536$	−30.8847	+	16.2758i	−1.33402	+	0.703005i
$537$		−	0.762616i		−	0.0329093i
$538$	−6.21257	+	5.07820i	−0.267843	+	0.218937i
$539$		0			0
$540$	−0.988911	+	4.87182i	−0.0425560	+	0.209650i
$541$	21.5865	−	21.5865i	0.928074	−	0.928074i	−0.0695074	−	0.997581i	$-0.522143\pi$
$541$	21.5865	−	21.5865i	0.928074	−	0.928074i	0.997581	+	0.0695074i	$0.0221427\pi$
$542$	4.14519	+	0.416461i	0.178051	+	0.0178885i
$543$	−50.0859			−2.14939
$544$	−24.3379	−	13.3168i	−1.04348	−	0.570954i
$545$	4.72256			0.202292
$546$		0			0
$547$	−10.1273	+	10.1273i	−0.433010	+	0.433010i	−0.889651	−	0.456641i	$-0.849052\pi$
$547$	−10.1273	+	10.1273i	−0.433010	+	0.433010i	0.456641	+	0.889651i	$0.349052\pi$
$548$	4.24843	−	20.9297i	0.181484	−	0.894072i
$549$	10.9890	+	10.9890i	0.469000	+	0.469000i
$550$	−5.04731	+	4.12571i	−0.215218	+	0.175921i
$551$		−	31.3164i		−	1.33412i
$552$	16.6874	+	31.6658i	0.710261	+	1.34779i
$553$		0			0
$554$	11.9640	+	14.6366i	0.508303	+	0.621848i
$555$	8.81139	+	8.81139i	0.374023	+	0.374023i
$556$	−0.882573	−	1.33213i	−0.0374294	−	0.0564947i
$557$	16.1864	−	16.1864i	0.685838	−	0.685838i	−0.275471	−	0.961309i	$-0.588834\pi$
$557$	16.1864	−	16.1864i	0.685838	−	0.685838i	0.961309	+	0.275471i	$0.0888338\pi$
$558$	−0.786243	+	7.82577i	−0.0332843	+	0.331291i
$559$	−34.5622			−1.46182
$560$		0			0
$561$	11.2239			0.473875
$562$	−0.741841	+	7.38382i	−0.0312927	+	0.311468i
$563$	−6.30467	+	6.30467i	−0.265710	+	0.265710i	−0.827369	−	0.561659i	$-0.810163\pi$
$563$	−6.30467	+	6.30467i	−0.265710	+	0.265710i	0.561659	+	0.827369i	$0.310163\pi$
$564$	−22.2074	+	14.7131i	−0.935100	+	0.619532i
$565$	−11.0684	−	11.0684i	−0.465652	−	0.465652i
$566$	−4.83393	−	5.91373i	−0.203185	−	0.248572i
$567$		0			0
$568$	0.113298	−	0.365747i	0.00475389	−	0.0153464i
$569$		−	2.60882i		−	0.109367i	−0.998504	−	0.0546837i	$-0.982585\pi$
$569$		−	2.60882i		−	0.109367i	0.998504	−	0.0546837i	$-0.0174151\pi$
$570$	−12.9152	+	10.5570i	−0.540957	+	0.442182i
$571$	−21.1488	−	21.1488i	−0.885048	−	0.885048i	0.108994	−	0.994042i	$-0.465237\pi$
$571$	−21.1488	−	21.1488i	−0.885048	−	0.885048i	−0.994042	+	0.108994i	$0.965237\pi$
$572$	−8.67235	−	1.76036i	−0.362609	−	0.0736045i
$573$	−30.9024	+	30.9024i	−1.29096	+	1.29096i
$574$		0			0
$575$	−25.4893			−1.06298
$576$	7.21785	−	10.5323i	0.300744	−	0.438847i
$577$	−29.9676			−1.24757			−0.623785	−	0.781596i	$-0.714406\pi$
$577$	−29.9676			−1.24757			−0.623785	+	0.781596i	$0.714406\pi$
$578$	−9.92344	−	0.996993i	−0.412761	−	0.0414694i
$579$	−28.9730	+	28.9730i	−1.20408	+	1.20408i
$580$	7.60816	+	1.54435i	0.315911	+	0.0641256i
$581$		0			0
$582$	14.4413	−	11.8044i	0.598612	−	0.489310i
$583$		−	14.2290i		−	0.589305i
$584$	6.33395	−	20.4471i	0.262101	−	0.846109i
$585$			5.46282i			0.225860i
$586$	−1.89831	−	2.32236i	−0.0784186	−	0.0959357i
$587$	−6.58566	−	6.58566i	−0.271819	−	0.271819i	0.558013	−	0.829832i	$-0.311564\pi$
$587$	−6.58566	−	6.58566i	−0.271819	−	0.271819i	−0.829832	+	0.558013i	$0.811564\pi$
$588$		0			0
$589$	16.4161	−	16.4161i	0.676415	−	0.676415i
$590$	−0.704460	+	7.01175i	−0.0290022	+	0.288669i
$591$	20.2882			0.834547
$592$	10.5703	+	26.0950i	0.434436	+	1.07250i
$593$	−18.5097			−0.760102			−0.380051	−	0.924965i	$-0.624094\pi$
$593$	−18.5097			−0.760102			−0.380051	+	0.924965i	$0.624094\pi$
$594$	0.454245	−	4.52127i	0.0186379	−	0.185510i
$595$		0			0
$596$	7.53349	+	11.3708i	0.308584	+	0.465766i
$597$	12.0737	+	12.0737i	0.494145	+	0.494145i
$598$	−21.8980	−	26.7896i	−0.895476	−	1.09551i
$599$			16.4660i			0.672782i	0.941722	+	0.336391i	$0.109206\pi$
$599$			16.4660i			0.672782i	−0.941722	+	0.336391i	$0.890794\pi$
$600$	12.2069	+	23.1636i	0.498343	+	0.945651i
$601$			41.7312i			1.70225i	0.524962	+	0.851126i	$0.324079\pi$
$601$			41.7312i			1.70225i	−0.524962	+	0.851126i	$0.675921\pi$
$602$		0			0
$603$	−13.9297	−	13.9297i	−0.567259	−	0.567259i
$604$	−7.40404	+	36.4756i	−0.301266	+	1.48417i
$605$	5.75782	−	5.75782i	0.234089	−	0.234089i
$606$	22.1296	+	2.22333i	0.898954	+	0.0903166i
$607$	−33.6334			−1.36514			−0.682569	−	0.730821i	$-0.739137\pi$
$607$	−33.6334			−1.36514			−0.682569	+	0.730821i	$0.739137\pi$
$608$	−36.1710	+	10.5868i	−1.46693	+	0.429353i
$609$		0			0
$610$	11.3148	+	1.13678i	0.458123	+	0.0460270i
$611$	18.2088	−	18.2088i	0.736650	−	0.736650i
$612$	3.11420	−	15.3419i	0.125884	−	0.620161i
$613$	10.8552	+	10.8552i	0.438436	+	0.438436i	0.891486	−	0.453049i	$-0.149664\pi$
$613$	10.8552	+	10.8552i	0.438436	+	0.438436i	−0.453049	+	0.891486i	$0.649664\pi$
$614$	9.71350	−	7.93989i	0.392005	−	0.320428i
$615$			6.83737i			0.275709i
$616$		0			0
$617$			46.1375i			1.85743i	0.370797	+	0.928714i	$0.379085\pi$
$617$			46.1375i			1.85743i	−0.370797	+	0.928714i	$0.620915\pi$
$618$	−26.9118	−	32.9234i	−1.08255	−	1.32437i
$619$	14.7872	+	14.7872i	0.594347	+	0.594347i	0.938803	−	0.344455i	$-0.111936\pi$
$619$	14.7872	+	14.7872i	0.594347	+	0.594347i	−0.344455	+	0.938803i	$0.611936\pi$
$620$	3.17867	+	4.79777i	0.127658	+	0.192683i
$621$	12.5634	−	12.5634i	0.504151	−	0.504151i
$622$	−1.56626	+	15.5896i	−0.0628013	+	0.625085i
$623$		0			0
$624$	−13.8583	+	32.7296i	−0.554776	+	1.31023i
$625$	−15.2357			−0.609428
$626$	−1.80632	+	17.9790i	−0.0721951	+	0.718584i
$627$	10.7817	−	10.7817i	0.430578	−	0.430578i
$628$	1.14774	−	0.760413i	0.0457998	−	0.0303438i
$629$	24.4091	+	24.4091i	0.973256	+	0.973256i
$630$		0			0
$631$		−	6.87207i		−	0.273573i	−0.990601	−	0.136786i	$-0.956323\pi$
$631$		−	6.87207i		−	0.273573i	0.990601	−	0.136786i	$-0.0436774\pi$
$632$	−18.3530	−	5.68525i	−0.730045	−	0.226147i
$633$		−	28.2230i		−	1.12176i
$634$	25.1906	−	20.5910i	1.00045	−	0.817773i
$635$	−7.59840	−	7.59840i	−0.301533	−	0.301533i
$636$	−56.0082	−	11.3689i	−2.22087	−	0.450805i
$637$		0			0
$638$	−7.06071	−	0.709379i	−0.279536	−	0.0280846i
$639$	0.216059			0.00854717
$640$	−0.788267	−	9.30963i	−0.0311590	−	0.367996i
$641$	−13.7195			−0.541887			−0.270944	−	0.962595i	$-0.587336\pi$
$641$	−13.7195			−0.541887			−0.270944	+	0.962595i	$0.587336\pi$
$642$	−14.4617	−	1.45294i	−0.570758	−	0.0573432i
$643$	22.2363	−	22.2363i	0.876913	−	0.876913i	−0.116301	−	0.993214i	$-0.537104\pi$
$643$	22.2363	−	22.2363i	0.876913	−	0.876913i	0.993214	+	0.116301i	$0.0371039\pi$
$644$		0			0
$645$	10.4390	+	10.4390i	0.411034	+	0.411034i
$646$	−35.7773	+	29.2447i	−1.40764	+	1.15062i
$647$		−	36.1497i		−	1.42119i	−0.703601	−	0.710595i	$-0.748426\pi$
$647$		−	36.1497i		−	1.42119i	0.703601	−	0.710595i	$-0.251574\pi$
$648$	−30.3700	−	9.40776i	−1.19305	−	0.369572i
$649$		−	6.44154i		−	0.252853i
$650$	−16.0185	−	19.5967i	−0.628295	−	0.768644i
$651$		0			0
$652$	−20.5993	+	13.6477i	−0.806732	+	0.534484i
$653$	−35.1317	+	35.1317i	−1.37481	+	1.37481i	−0.521649	+	0.853160i	$0.674683\pi$
$653$	−35.1317	+	35.1317i	−1.37481	+	1.37481i	−0.853160	+	0.521649i	$0.825317\pi$
$654$	−1.73322	+	17.2514i	−0.0677743	+	0.674582i
$655$	10.2264			0.399580
$656$	−6.02336	+	14.2256i	−0.235173	+	0.555415i
$657$	12.0788			0.471240
$658$		0			0
$659$	4.01002	−	4.01002i	0.156208	−	0.156208i	−0.624676	−	0.780884i	$-0.714769\pi$
$659$	4.01002	−	4.01002i	0.156208	−	0.156208i	0.780884	+	0.624676i	$0.214769\pi$
$660$	2.08766	+	3.15104i	0.0812620	+	0.122654i
$661$	−6.14168	−	6.14168i	−0.238884	−	0.238884i	0.577504	−	0.816388i	$-0.304027\pi$
$661$	−6.14168	−	6.14168i	−0.238884	−	0.238884i	−0.816388	+	0.577504i	$0.804027\pi$
$662$	10.0696	+	12.3189i	0.391364	+	0.478787i
$663$			43.5780i			1.69243i
$664$	19.9238	−	10.4995i	0.773195	−	0.407461i
$665$		0			0
$666$	−12.3006	+	10.0546i	−0.476639	+	0.389608i
$667$	−19.6198	−	19.6198i	−0.759681	−	0.759681i
$668$	−7.42535	+	36.5806i	−0.287296	+	1.41535i
$669$	5.86992	−	5.86992i	0.226944	−	0.226944i
$670$	−14.3426	−	1.44098i	−0.554104	−	0.0556700i
$671$	−10.3947			−0.401282
$672$		0			0
$673$	−17.2802			−0.666105			−0.333052	−	0.942908i	$-0.608079\pi$
$673$	−17.2802			−0.666105			−0.333052	+	0.942908i	$0.608079\pi$
$674$	−2.27793	−	0.228861i	−0.0877427	−	0.00881538i
$675$	9.19014	−	9.19014i	0.353729	−	0.353729i
$676$	1.66263	−	8.19085i	0.0639472	−	0.315033i
$677$	3.08834	+	3.08834i	0.118695	+	0.118695i	0.763959	−	0.645265i	$-0.223253\pi$
$677$	3.08834	+	3.08834i	0.118695	+	0.118695i	−0.645265	+	0.763959i	$0.723253\pi$
$678$	44.4949	−	36.3705i	1.70882	−	1.39680i
$679$		0			0
$680$	−5.34051	−	10.1341i	−0.204799	−	0.388625i
$681$			13.1307i			0.503168i
$682$	−3.32939	−	4.07311i	−0.127489	−	0.155967i
$683$	−10.0744	−	10.0744i	−0.385487	−	0.385487i	0.487587	−	0.873074i	$-0.337877\pi$
$683$	−10.0744	−	10.0744i	−0.385487	−	0.385487i	−0.873074	+	0.487587i	$0.837877\pi$
$684$	−11.7459	−	17.7289i	−0.449116	−	0.677880i
$685$	6.23540	−	6.23540i	0.238242	−	0.238242i
$686$		0			0
$687$	57.7686			2.20401
$688$	12.5227	+	30.9151i	0.477425	+	1.17863i
$689$	55.2455			2.10468
$690$	−1.47742	+	14.7053i	−0.0562445	+	0.559822i
$691$	−13.1835	+	13.1835i	−0.501522	+	0.501522i	−0.911911	−	0.410389i	$-0.865393\pi$
$691$	−13.1835	+	13.1835i	−0.501522	+	0.501522i	0.410389	+	0.911911i	$0.365393\pi$
$692$	−15.4906	+	10.2630i	−0.588863	+	0.390139i
$693$		0			0
$694$	−11.6108	−	14.2044i	−0.440740	−	0.539193i
$695$		−	0.659806i		−	0.0250279i
$696$	−8.43372	+	27.2256i	−0.319679	+	1.03198i
$697$			18.9407i			0.717431i
$698$	−0.414415	+	0.338746i	−0.0156858	+	0.0128217i
$699$	−20.7653	−	20.7653i	−0.785417	−	0.785417i
$700$		0			0
$701$	−5.24919	+	5.24919i	−0.198259	+	0.198259i	−0.799253	−	0.600994i	$-0.794771\pi$
$701$	−5.24919	+	5.24919i	−0.198259	+	0.198259i	0.600994	+	0.799253i	$0.294771\pi$
$702$	17.5543	+	1.76365i	0.662543	+	0.0665647i
$703$	46.8946			1.76866
$704$	1.56760	+	8.39506i	0.0590812	+	0.316401i
$705$	−10.9994			−0.414261
$706$	47.8198	+	4.80438i	1.79972	+	0.180815i
$707$		0			0
$708$	−25.3552	−	5.14675i	−0.952907	−	0.193427i
$709$	−3.52800	−	3.52800i	−0.132497	−	0.132497i	0.637748	−	0.770245i	$-0.279866\pi$
$709$	−3.52800	−	3.52800i	−0.132497	−	0.132497i	−0.770245	+	0.637748i	$0.779866\pi$
$710$	0.122408	−	0.100057i	0.00459388	−	0.00375507i
$711$		−	10.8418i		−	0.406598i
$712$	4.67361	−	15.0873i	0.175151	−	0.565419i
$713$		−	20.5695i		−	0.770334i
$714$		0			0
$715$	−2.58368	−	2.58368i	−0.0966240	−	0.0966240i
$716$	0.593092	−	0.392941i	0.0221649	−	0.0146849i
$717$	−1.60541	+	1.60541i	−0.0599553	+	0.0599553i
$718$	0.364530	−	3.62830i	0.0136041	−	0.135407i
$719$	39.3448			1.46731			0.733657	−	0.679520i	$-0.237812\pi$
$719$	39.3448			1.46731			0.733657	+	0.679520i	$0.237812\pi$
$720$	4.88638	−	1.97932i	0.182105	−	0.0737649i
$721$		0			0
$722$	−3.58917	+	35.7243i	−0.133575	+	1.32952i
$723$	−7.51477	+	7.51477i	−0.279477	+	0.279477i
$724$	−25.8070	−	38.9522i	−0.959109	−	1.44765i
$725$	−14.3519	−	14.3519i	−0.533017	−	0.533017i
$726$	18.9200	+	23.1463i	0.702187	+	0.859042i
$727$		−	44.4513i		−	1.64861i	−0.566148	−	0.824304i	$-0.691567\pi$
$727$		−	44.4513i		−	1.64861i	0.566148	−	0.824304i	$-0.308433\pi$
$728$		0			0
$729$			1.41753i			0.0525012i
$730$	6.84322	−	5.59370i	0.253279	−	0.207032i
$731$	28.9178	+	28.9178i	1.06956	+	1.06956i
$732$	−8.30527	+	40.9155i	−0.306972	+	1.51228i
$733$	−28.9619	+	28.9619i	−1.06973	+	1.06973i	−0.0723549	+	0.997379i	$0.523051\pi$
$733$	−28.9619	+	28.9619i	−1.06973	+	1.06973i	−0.997379	+	0.0723549i	$0.976949\pi$
$734$	−13.0762	−	1.31375i	−0.482652	−	0.0484914i
$735$		0			0
$736$	−16.0285	+	29.2938i	−0.590819	+	1.07979i
$737$	13.1762			0.485353
$738$	−8.67347	−	0.871410i	−0.319275	−	0.0320771i
$739$	−4.00996	+	4.00996i	−0.147509	+	0.147509i	−0.777004	−	0.629495i	$-0.783262\pi$
$739$	−4.00996	+	4.00996i	−0.147509	+	0.147509i	0.629495	+	0.777004i	$0.283262\pi$
$740$	−2.31258	+	11.3928i	−0.0850121	+	0.418808i
$741$	41.8608	+	41.8608i	1.53780	+	1.53780i
$742$		0			0
$743$		−	41.4130i		−	1.51930i	−0.650335	−	0.759648i	$-0.725371\pi$
$743$		−	41.4130i		−	1.51930i	0.650335	−	0.759648i	$-0.274629\pi$
$744$	−18.6927	+	9.85076i	−0.685309	+	0.361146i
$745$			5.63199i			0.206340i
$746$	−9.84353	−	12.0424i	−0.360397	−	0.440903i
$747$	8.98606	+	8.98606i	0.328783	+	0.328783i
$748$	5.78319	+	8.72895i	0.211454	+	0.319162i
$749$		0			0
$750$	−2.33216	+	23.2129i	−0.0851585	+	0.847614i
$751$	−30.6754			−1.11936			−0.559680	−	0.828709i	$-0.689076\pi$
$751$	−30.6754			−1.11936			−0.559680	+	0.828709i	$0.689076\pi$
$752$	−22.8849	−	9.68990i	−0.834528	−	0.353354i
$753$	60.7129			2.21250
$754$	2.75423	−	27.4139i	0.100303	−	0.998355i
$755$	−10.8669	+	10.8669i	−0.395486	+	0.395486i
$756$		0			0
$757$	14.1660	+	14.1660i	0.514873	+	0.514873i	0.916016	−	0.401143i	$-0.131387\pi$
$757$	14.1660	+	14.1660i	0.514873	+	0.514873i	−0.401143	+	0.916016i	$0.631387\pi$
$758$	16.7928	+	20.5440i	0.609944	+	0.746193i
$759$		−	13.5095i		−	0.490362i
$760$	−14.8648	−	4.60471i	−0.539204	−	0.167030i
$761$			38.7778i			1.40569i	0.711341	+	0.702847i	$0.248088\pi$
$761$			38.7778i			1.40569i	−0.711341	+	0.702847i	$0.751912\pi$
$762$	30.5454	−	24.9681i	1.10654	−	0.904498i
$763$		0			0
$764$	−39.9556	−	8.11042i	−1.44554	−	0.293425i
$765$	4.57069	−	4.57069i	0.165254	−	0.165254i
$766$	−26.1440	−	2.62664i	−0.944619	−	0.0949045i
$767$	25.0099			0.903055
$768$	34.2971	+	0.537199i	1.23759	+	0.0193845i
$769$	−0.129416			−0.00466687			−0.00233344	−	0.999997i	$-0.500743\pi$
$769$	−0.129416			−0.00466687			−0.00233344	+	0.999997i	$0.500743\pi$
$770$		0			0
$771$	−31.7005	+	31.7005i	−1.14167	+	1.14167i
$772$	−37.4610	−	7.60405i	−1.34825	−	0.273676i
$773$	3.08315	+	3.08315i	0.110893	+	0.110893i	0.760376	−	0.649483i	$-0.225015\pi$
$773$	3.08315	+	3.08315i	0.110893	+	0.110893i	−0.649483	+	0.760376i	$0.725015\pi$
$774$	−14.5727	+	11.9118i	−0.523804	+	0.428161i
$775$		−	15.0466i		−	0.540491i
$776$	16.6214	+	5.14883i	0.596673	+	0.184832i
$777$		0			0
$778$	−27.8257	−	34.0414i	−0.997599	−	1.22044i
$779$	18.1944	+	18.1944i	0.651881	+	0.651881i
$780$	−12.2342	+	8.10553i	−0.438055	+	0.290225i
$781$	−0.102187	+	0.102187i	−0.00365653	+	0.00365653i
$782$	−4.09273	+	40.7364i	−0.146356	+	1.45673i
$783$	14.1478			0.505601
$784$		0			0
$785$	0.568480			0.0202899
$786$	−3.75319	+	37.3569i	−0.133872	+	1.33248i
$787$	30.1492	−	30.1492i	1.07470	−	1.07470i	0.0777274	−	0.996975i	$-0.475234\pi$
$787$	30.1492	−	30.1492i	1.07470	−	1.07470i	0.996975	−	0.0777274i	$-0.0247664\pi$
$788$	10.4536	+	15.7783i	0.372395	+	0.562080i
$789$	−18.5019	−	18.5019i	−0.658685	−	0.658685i
$790$	−5.02082	−	6.14236i	−0.178633	−	0.218536i
$791$		0			0
$792$	−4.26329	+	2.24668i	−0.151489	+	0.0798324i
$793$		−	40.3583i		−	1.43316i
$794$	−33.8713	+	27.6866i	−1.20205	+	0.982562i
$795$	−16.6860	−	16.6860i	−0.591793	−	0.591793i
$796$	−3.16879	+	15.6109i	−0.112315	+	0.553313i
$797$	18.9375	−	18.9375i	0.670800	−	0.670800i	−0.287100	−	0.957901i	$-0.592691\pi$
$797$	18.9375	−	18.9375i	0.670800	−	0.670800i	0.957901	+	0.287100i	$0.0926913\pi$
$798$		0			0
$799$	−30.4703			−1.07796
$800$	−11.7249	+	21.4285i	−0.414538	+	0.757613i
$801$	8.91256			0.314910
$802$	10.0060	+	1.00529i	0.353324	+	0.0354979i
$803$	−5.71276	+	5.71276i	−0.201599	+	0.201599i
$804$	10.5277	−	51.8644i	0.371285	−	1.82911i
$805$		0			0
$806$	15.8142	−	12.9267i	0.557032	−	0.455322i
$807$		−	12.1637i		−	0.428183i
$808$	9.67329	+	18.3560i	0.340305	+	0.645760i
$809$			5.71379i			0.200886i	0.994943	+	0.100443i	$0.0320261\pi$
$809$			5.71379i			0.200886i	−0.994943	+	0.100443i	$0.967974\pi$
$810$	−8.30827	−	10.1642i	−0.291923	−	0.357133i
$811$	20.8976	+	20.8976i	0.733815	+	0.733815i	0.971373	−	0.237559i	$-0.0763472\pi$
$811$	20.8976	+	20.8976i	0.733815	+	0.733815i	−0.237559	+	0.971373i	$0.576347\pi$
$812$		0			0
$813$	−4.46567	+	4.46567i	−0.156618	+	0.156618i
$814$	1.06226	−	10.5730i	0.0372321	−	0.370585i
$815$	−10.2029			−0.357392
$816$	38.9796	−	15.7894i	1.36456	−	0.552740i
$817$	55.5566			1.94368
$818$	4.92379	−	49.0083i	0.172156	−	1.71354i
$819$		0			0
$820$	−5.31747	+	3.52298i	−0.185694	+	0.123028i
$821$	5.02789	+	5.02789i	0.175475	+	0.175475i	0.789380	−	0.613905i	$-0.210402\pi$
$821$	5.02789	+	5.02789i	0.175475	+	0.175475i	−0.613905	+	0.789380i	$0.710402\pi$
$822$	20.4893	+	25.0662i	0.714647	+	0.874284i
$823$		−	26.2711i		−	0.915752i	−0.889016	−	0.457876i	$-0.848610\pi$
$823$		−	26.2711i		−	0.915752i	0.889016	−	0.457876i	$-0.151390\pi$
$824$	11.7383	−	37.8934i	0.408924	−	1.32008i
$825$		−	9.88221i		−	0.344055i
$826$		0			0
$827$	9.59215	+	9.59215i	0.333552	+	0.333552i	0.853934	−	0.520382i	$-0.174210\pi$
$827$	9.59215	+	9.59215i	0.333552	+	0.333552i	−0.520382	+	0.853934i	$0.674210\pi$
$828$	−18.4660	−	3.74834i	−0.641738	−	0.130264i
$829$	20.7941	−	20.7941i	0.722209	−	0.722209i	−0.246846	−	0.969055i	$-0.579394\pi$
$829$	20.7941	−	20.7941i	0.722209	−	0.722209i	0.969055	+	0.246846i	$0.0793940\pi$
$830$	9.25247	+	0.929581i	0.321158	+	0.0322662i
$831$	−28.6572			−0.994106
$832$	−32.5946	+	6.08636i	−1.13001	+	0.211007i
$833$		0			0
$834$	2.41025	+	0.242155i	0.0834603	+	0.00838513i
$835$	−10.8982	+	10.8982i	−0.377146	+	0.377146i
$836$	13.9403	+	2.82968i	0.482135	+	0.0978666i
$837$	7.41632	+	7.41632i	0.256345	+	0.256345i
$838$	−1.01199	+	0.827210i	−0.0349587	+	0.0285755i
$839$			9.21526i			0.318146i	0.987267	+	0.159073i	$0.0508505\pi$
$839$			9.21526i			0.318146i	−0.987267	+	0.159073i	$0.949149\pi$
$840$		0			0
$841$			6.90588i			0.238134i
$842$	11.9998	+	14.6804i	0.413542	+	0.505919i
$843$	−7.95469	−	7.95469i	−0.273974	−	0.273974i
$844$	21.9492	−	14.5420i	0.755524	−	0.500557i
$845$	2.44023	−	2.44023i	0.0839464	−	0.0839464i
$846$	1.40185	−	13.9532i	0.0481967	−	0.479720i
$847$		0			0
$848$	−20.0168	−	49.4159i	−0.687381	−	1.69695i
$849$	11.5786			0.397376
$850$	−2.99384	+	29.7988i	−0.102688	+	1.02209i
$851$	29.3796	−	29.3796i	1.00712	−	1.00712i
$852$	0.320581	+	0.483874i	0.0109829	+	0.0165772i
$853$	−27.5443	−	27.5443i	−0.943099	−	0.943099i	0.0553669	−	0.998466i	$-0.482367\pi$
$853$	−27.5443	−	27.5443i	−0.943099	−	0.943099i	−0.998466	+	0.0553669i	$0.982367\pi$
$854$		0			0
$855$		−	8.78116i		−	0.300309i
$856$	−6.32149	−	11.9956i	−0.216064	−	0.410002i
$857$			0.806719i			0.0275570i	0.999905	+	0.0137785i	$0.00438597\pi$
$857$			0.806719i			0.0275570i	−0.999905	+	0.0137785i	$0.995614\pi$
$858$	10.3863	−	8.48987i	0.354584	−	0.289839i
$859$	−0.223923	−	0.223923i	−0.00764015	−	0.00764015i	0.703276	−	0.710917i	$-0.251720\pi$
$859$	−0.223923	−	0.223923i	−0.00764015	−	0.00764015i	−0.710917	+	0.703276i	$0.751720\pi$
$860$	−2.73974	+	13.4972i	−0.0934244	+	0.460251i
$861$		0			0
$862$	−19.1287	−	1.92183i	−0.651526	−	0.0654578i
$863$	25.8195			0.878905			0.439452	−	0.898266i	$-0.355172\pi$
$863$	25.8195			0.878905			0.439452	+	0.898266i	$0.355172\pi$
$864$	−4.78281	−	16.3409i	−0.162714	−	0.555930i
$865$	−7.67252			−0.260874
$866$	9.37053	+	0.941443i	0.318424	+	0.0319915i
$867$	10.6907	−	10.6907i	0.363074	−	0.363074i
$868$		0			0
$869$	5.12768	+	5.12768i	0.173945	+	0.173945i
$870$	−9.11182	+	7.44807i	−0.308920	+	0.252513i
$871$			51.1580i			1.73342i
$872$	−14.3096	+	7.54091i	−0.484584	+	0.255368i
$873$			9.81881i			0.332316i
$874$	35.1997	+	43.0626i	1.19065	+	1.45662i
$875$		0			0
$876$	17.9221	+	27.0510i	0.605532	+	0.913969i
$877$	34.7532	−	34.7532i	1.17353	−	1.17353i	0.192169	−	0.981362i	$-0.438448\pi$
$877$	34.7532	−	34.7532i	1.17353	−	1.17353i	0.981362	−	0.192169i	$-0.0615522\pi$
$878$	−0.859601	+	8.55593i	−0.0290101	+	0.288749i
$879$	4.54699			0.153366
$880$	−1.37491	+	3.24718i	−0.0463483	+	0.109462i
$881$	29.7995			1.00397			0.501985	−	0.864876i	$-0.332603\pi$
$881$	29.7995			1.00397			0.501985	+	0.864876i	$0.332603\pi$
$882$		0			0
$883$	18.4638	−	18.4638i	0.621356	−	0.621356i	−0.324522	−	0.945878i	$-0.605203\pi$
$883$	18.4638	−	18.4638i	0.621356	−	0.621356i	0.945878	+	0.324522i	$0.105203\pi$
$884$	−33.8910	+	22.4538i	−1.13988	+	0.755202i
$885$	−7.55385	−	7.55385i	−0.253920	−	0.253920i
$886$	17.3865	+	21.2703i	0.584112	+	0.714591i
$887$			54.5072i			1.83017i	0.403260	+	0.915086i	$0.367877\pi$
$887$			54.5072i			1.83017i	−0.403260	+	0.915086i	$0.632123\pi$
$888$	−40.7689	−	12.6290i	−1.36811	−	0.423803i
$889$		0			0
$890$	5.04938	−	4.12740i	0.169256	−	0.138351i
$891$	8.48511	+	8.48511i	0.284262	+	0.284262i
$892$	7.58959	+	1.54058i	0.254118	+	0.0515824i
$893$	−29.2696	+	29.2696i	−0.979470	+	0.979470i
$894$	−20.5735	−	2.06699i	−0.688081	−	0.0691305i
$895$	0.293760			0.00981933
$896$		0			0
$897$	52.4518			1.75131
$898$	−23.6131	−	2.37237i	−0.787979	−	0.0791671i
$899$	11.5818	−	11.5818i	0.386275	−	0.386275i
$900$	−13.5079	−	2.74192i	−0.450265	−	0.0913974i
$901$	−46.2233	−	46.2233i	−1.53992	−	1.53992i
$902$	4.51431	−	3.69003i	0.150310	−	0.122865i
$903$		0			0
$904$	51.2118	+	15.8640i	1.70328	+	0.527628i
$905$		−	19.2931i		−	0.641326i
$906$	−35.7081	−	43.6846i	−1.18632	−	1.45132i
$907$	−19.0469	−	19.0469i	−0.632441	−	0.632441i	0.316239	−	0.948680i	$-0.397580\pi$
$907$	−19.0469	−	19.0469i	−0.632441	−	0.632441i	−0.948680	+	0.316239i	$0.897580\pi$
$908$	−10.2118	+	6.76563i	−0.338891	+	0.224525i
$909$	−8.27891	+	8.27891i	−0.274594	+	0.274594i
$910$		0			0
$911$	38.1287			1.26326			0.631629	−	0.775270i	$-0.282386\pi$
$911$	38.1287			1.26326			0.631629	+	0.775270i	$0.282386\pi$
$912$	22.2764	−	52.6109i	0.737645	−	1.74212i
$913$	−8.50004			−0.281310
$914$	5.58016	−	55.5414i	0.184575	−	1.83714i
$915$	−12.1896	+	12.1896i	−0.402976	+	0.402976i
$916$	29.7656	+	44.9271i	0.983481	+	1.48443i
$917$		0			0
$918$	−13.2119	−	16.1631i	−0.436056	−	0.533462i
$919$			16.1447i			0.532565i	0.963895	+	0.266282i	$0.0857953\pi$
$919$			16.1447i			0.532565i	−0.963895	+	0.266282i	$0.914205\pi$
$920$	−12.1977	+	6.42799i	−0.402146	+	0.211925i
$921$			19.0182i			0.626672i
$922$	−2.27370	+	1.85854i	−0.0748802	+	0.0612076i
$923$	−0.396749	−	0.396749i	−0.0130592	−	0.0130592i
$924$		0			0
$925$	21.4912	−	21.4912i	0.706628	−	0.706628i
$926$	33.5566	+	3.37138i	1.10274	+	0.110791i
$927$	22.3849			0.735218
$928$	−25.5191	+	7.46915i	−0.837705	+	0.245187i
$929$	−28.3807			−0.931142			−0.465571	−	0.885011i	$-0.654151\pi$
$929$	−28.3807			−0.931142			−0.465571	+	0.885011i	$0.654151\pi$
$930$	−8.68075	−	0.872142i	−0.284653	−	0.0285986i
$931$		0			0
$932$	5.44993	−	26.8488i	0.178518	−	0.879462i
$933$	−16.7949	−	16.7949i	−0.549839	−	0.549839i
$934$	−38.9016	+	31.7984i	−1.27290	+	1.04048i
$935$			4.32347i			0.141393i
$936$	−8.72296	−	16.5526i	−0.285119	−	0.541039i
$937$		−	18.2863i		−	0.597387i	−0.954349	−	0.298693i	$-0.903449\pi$
$937$		−	18.2863i		−	0.597387i	0.954349	−	0.298693i	$-0.0965508\pi$
$938$		0			0
$939$	−19.3690	−	19.3690i	−0.632083	−	0.632083i
$940$	−5.66749	−	8.55432i	−0.184853	−	0.279011i
$941$	9.68063	−	9.68063i	0.315580	−	0.315580i	−0.531487	−	0.847067i	$-0.678367\pi$
$941$	9.68063	−	9.68063i	0.315580	−	0.315580i	0.847067	+	0.531487i	$0.178367\pi$
$942$	−0.208637	+	2.07664i	−0.00679776	+	0.0676606i
$943$	22.7976			0.742393
$944$	−9.06172	−	22.3708i	−0.294934	−	0.728108i
$945$		0			0
$946$	1.25847	−	12.5260i	0.0409164	−	0.407256i
$947$	−9.28454	+	9.28454i	−0.301707	+	0.301707i	−0.841681	−	0.539974i	$-0.818434\pi$
$947$	−9.28454	+	9.28454i	−0.301707	+	0.301707i	0.539974	+	0.841681i	$0.318434\pi$
$948$	24.2806	−	16.0866i	0.788597	−	0.522469i
$949$	−22.1803	−	22.1803i	−0.720004	−	0.720004i
$950$	25.7487	+	31.5005i	0.835399	+	1.02201i
$951$			49.3211i			1.59935i
$952$		0			0
$953$			28.4500i			0.921586i	0.887508	+	0.460793i	$0.152435\pi$
$953$			28.4500i			0.921586i	−0.887508	+	0.460793i	$0.847565\pi$
$954$	23.2935	−	19.0403i	0.754155	−	0.616452i
$955$	−11.9036	−	11.9036i	−0.385192	−	0.385192i
$956$	−2.07574	−	0.421346i	−0.0671342	−	0.0136273i
$957$	7.60660	−	7.60660i	0.245887	−	0.245887i
$958$	37.8695	+	3.80469i	1.22351	+	0.122924i
$959$		0			0
$960$	11.6830	+	8.00641i	0.377067	+	0.258406i
$961$	−18.8576			−0.608309
$962$	41.0508	+	4.12432i	1.32353	+	0.132973i
$963$	5.41027	−	5.41027i	0.174343	−	0.174343i
$964$	−9.71631	−	1.97228i	−0.312941	−	0.0635227i
$965$	−11.1604	−	11.1604i	−0.359267	−	0.359267i
$966$		0			0
$967$			4.34118i			0.139603i	0.997561	+	0.0698015i	$0.0222366\pi$
$967$			4.34118i			0.139603i	−0.997561	+	0.0698015i	$0.977763\pi$
$968$	−8.25248	+	26.6405i	−0.265245	+	0.856258i
$969$		−	70.0491i		−	2.25030i
$970$	4.54709	+	5.56281i	0.145998	+	0.178611i
$971$	−4.37363	−	4.37363i	−0.140357	−	0.140357i	0.633437	−	0.773794i	$-0.281643\pi$
$971$	−4.37363	−	4.37363i	−0.140357	−	0.140357i	−0.773794	+	0.633437i	$0.781643\pi$
$972$	25.1237	−	16.6452i	0.805843	−	0.533895i
$973$		0			0
$974$	−3.78530	+	37.6765i	−0.121289	+	1.20723i
$975$	38.3686			1.22878
$976$	−36.0996	+	14.6228i	−1.15552	+	0.468065i
$977$	43.2290			1.38302			0.691509	−	0.722367i	$-0.256946\pi$
$977$	43.2290			1.38302			0.691509	+	0.722367i	$0.256946\pi$
$978$	3.74456	−	37.2710i	0.119738	−	1.19179i
$979$	−4.21526	+	4.21526i	−0.134720	+	0.134720i
$980$		0			0
$981$	−6.45392	−	6.45392i	−0.206058	−	0.206058i
$982$	−8.70732	−	10.6524i	−0.277862	−	0.339930i
$983$			32.0422i			1.02199i	0.859584	+	0.510994i	$0.170723\pi$
$983$			32.0422i			1.02199i	−0.859584	+	0.510994i	$0.829277\pi$
$984$	−10.9178	−	20.7176i	−0.348047	−	0.660452i
$985$			7.81505i			0.249008i
$986$	−25.2414	+	20.6325i	−0.803849	+	0.657072i
$987$		0			0
$988$	−10.9865	+	54.1245i	−0.349527	+	1.72193i
$989$	34.8063	−	34.8063i	1.10678	−	1.10678i
$990$	−1.97984	−	0.198911i	−0.0629233	−	0.00632181i
$991$	−10.6987			−0.339857			−0.169928	−	0.985456i	$-0.554354\pi$
$991$	−10.6987			−0.339857			−0.169928	+	0.985456i	$0.554354\pi$
$992$	−17.2925	−	9.46183i	−0.549038	−	0.300413i
$993$	−24.1194			−0.765405
$994$		0			0
$995$	−4.65082	+	4.65082i	−0.147441	+	0.147441i
$996$	−6.79147	+	33.4579i	−0.215196	+	1.06015i
$997$	−19.3163	−	19.3163i	−0.611753	−	0.611753i	0.331650	−	0.943403i	$-0.392395\pi$
$997$	−19.3163	−	19.3163i	−0.611753	−	0.611753i	−0.943403	+	0.331650i	$0.892395\pi$
$998$	−22.7973	+	18.6347i	−0.721635	+	0.589870i
$999$			21.1856i			0.670281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.l.197.2	yes	48
7.2	even	3		784.2.x.p.165.16		96
7.3	odd	6		784.2.x.p.373.18		96
7.4	even	3		784.2.x.p.373.17		96
7.5	odd	6		784.2.x.p.165.15		96
7.6	odd	2	inner	784.2.m.l.197.1	✓	48
16.13	even	4	inner	784.2.m.l.589.2	yes	48
112.13	odd	4	inner	784.2.m.l.589.1	yes	48
112.45	odd	12		784.2.x.p.765.15		96
112.61	odd	12		784.2.x.p.557.18		96
112.93	even	12		784.2.x.p.557.17		96
112.109	even	12		784.2.x.p.765.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.1	✓	48	7.6	odd	2	inner
784.2.m.l.197.2	yes	48	1.1	even	1	trivial
784.2.m.l.589.1	yes	48	112.13	odd	4	inner
784.2.m.l.589.2	yes	48	16.13	even	4	inner
784.2.x.p.165.15		96	7.5	odd	6
784.2.x.p.165.16		96	7.2	even	3
784.2.x.p.373.17		96	7.4	even	3
784.2.x.p.373.18		96	7.3	odd	6
784.2.x.p.557.17		96	112.93	even	12
784.2.x.p.557.18		96	112.61	odd	12
784.2.x.p.765.15		96	112.45	odd	12
784.2.x.p.765.16		96	112.109	even	12

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40713 - 0.141372i) q^{2} +(1.51592 - 1.51592i) q^{3} +(1.96003 + 0.397858i) q^{4} +(0.583934 + 0.583934i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} -1.59603i q^{9} +O(q^{10})\)	\(q+(-1.40713 - 0.141372i) q^{2} +(1.51592 - 1.51592i) q^{3} +(1.96003 + 0.397858i) q^{4} +(0.583934 + 0.583934i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} -1.59603i q^{9} +(-0.739119 - 0.904223i) q^{10} +(0.754851 + 0.754851i) q^{11} +(3.57437 - 2.36812i) q^{12} +(-2.93078 + 2.93078i) q^{13} +1.77039 q^{15} +(3.68342 + 1.55963i) q^{16} +4.90431 q^{17} +(-0.225634 + 2.24582i) q^{18} +(4.71106 - 4.71106i) q^{19} +(0.912204 + 1.37685i) q^{20} +(-0.955458 - 1.16889i) q^{22} -5.90297i q^{23} +(-5.36438 + 2.82694i) q^{24} -4.31804i q^{25} +(4.53832 - 3.70966i) q^{26} +(2.12831 + 2.12831i) q^{27} +(3.32371 - 3.32371i) q^{29} +(-2.49117 - 0.250285i) q^{30} +3.48460 q^{31} +(-4.96256 - 2.71533i) q^{32} +2.28859 q^{33} +(-6.90100 - 0.693333i) q^{34} +(0.634992 - 3.12825i) q^{36} +(4.97708 + 4.97708i) q^{37} +(-7.29508 + 5.96305i) q^{38} +8.88566i q^{39} +(-1.08894 - 2.06637i) q^{40} +3.86206i q^{41} +(5.89641 + 5.89641i) q^{43} +(1.17921 + 1.77985i) q^{44} +(0.931974 - 0.931974i) q^{45} +(-0.834516 + 8.30625i) q^{46} -6.21296 q^{47} +(7.94803 - 3.21950i) q^{48} +(-0.610451 + 6.07604i) q^{50} +(7.43454 - 7.43454i) q^{51} +(-6.91045 + 4.57838i) q^{52} +(-9.42504 - 9.42504i) q^{53} +(-2.69393 - 3.29570i) q^{54} +0.881566i q^{55} -14.2832i q^{57} +(-5.14677 + 4.20701i) q^{58} +(-4.26676 - 4.26676i) q^{59} +(3.47002 + 0.704366i) q^{60} +(-6.88524 + 6.88524i) q^{61} +(-4.90328 - 0.492626i) q^{62} +(6.59909 + 4.52239i) q^{64} -3.42277 q^{65} +(-3.22034 - 0.323543i) q^{66} +(8.72771 - 8.72771i) q^{67} +(9.61258 + 1.95122i) q^{68} +(-8.94843 - 8.94843i) q^{69} +0.135373i q^{71} +(-1.33576 + 4.31209i) q^{72} +7.56806i q^{73} +(-6.29978 - 7.70702i) q^{74} +(-6.54581 - 6.54581i) q^{75} +(11.1081 - 7.35947i) q^{76} +(1.25618 - 12.5033i) q^{78} +6.79297 q^{79} +(1.24015 + 3.06159i) q^{80} +11.2408 q^{81} +(0.545988 - 5.43442i) q^{82} +(-5.63027 + 5.63027i) q^{83} +(2.86379 + 2.86379i) q^{85} +(-7.46342 - 9.13060i) q^{86} -10.0770i q^{87} +(-1.40767 - 2.67119i) q^{88} +5.58422i q^{89} +(-1.44316 + 1.17965i) q^{90} +(2.34855 - 11.5700i) q^{92} +(5.28237 - 5.28237i) q^{93} +(8.74245 + 0.878340i) q^{94} +5.50189 q^{95} +(-11.6391 + 3.40662i) q^{96} -6.15204 q^{97} +(1.20476 - 1.20476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 8 q^{11} + 32 q^{15} + 36 q^{16} + 20 q^{18} - 28 q^{22} - 16 q^{29} + 96 q^{30} + 40 q^{32} + 40 q^{36} - 16 q^{37} + 8 q^{43} + 4 q^{44} + 64 q^{46} - 28 q^{50} + 16 q^{53} - 20 q^{58} + 8 q^{60} + 44 q^{64} + 40 q^{67} - 196 q^{72} - 28 q^{74} + 56 q^{78} + 80 q^{79} - 48 q^{81} - 108 q^{86} - 100 q^{88} - 128 q^{95} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 8 * q^11 + 32 * q^15 + 36 * q^16 + 20 * q^18 - 28 * q^22 - 16 * q^29 + 96 * q^30 + 40 * q^32 + 40 * q^36 - 16 * q^37 + 8 * q^43 + 4 * q^44 + 64 * q^46 - 28 * q^50 + 16 * q^53 - 20 * q^58 + 8 * q^60 + 44 * q^64 + 40 * q^67 - 196 * q^72 - 28 * q^74 + 56 * q^78 + 80 * q^79 - 48 * q^81 - 108 * q^86 - 100 * q^88 - 128 * q^95 - 40 * q^99

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