LMFDB - Embedded newform 702.2.bb.a.197.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.8
Character	$\chi$	$=$	702.197
Dual form			702.2.bb.a.449.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.891175 + 3.32591i) q^{5} +(-0.00737496 + 0.0275237i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.98193 + 1.72162i) q^{10} +(-3.07674 + 3.07674i) q^{11} +(-3.57728 - 0.450627i) q^{13} +(-0.0246771 + 0.0142473i) q^{14} -1.00000 q^{16} +(3.35521 - 5.81139i) q^{17} +(-0.521462 - 1.94612i) q^{19} +(-3.32591 - 0.891175i) q^{20} -4.35116 q^{22} +(-0.264071 + 0.457384i) q^{23} +(-5.93735 - 3.42793i) q^{25} +(-2.21088 - 2.84816i) q^{26} +(-0.0275237 - 0.00737496i) q^{28} +8.30696i q^{29} +(1.39364 + 0.373424i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.48176 - 1.73678i) q^{34} +(-0.0849690 - 0.0490569i) q^{35} +(-2.09857 + 7.83198i) q^{37} +(1.00739 - 1.74484i) q^{38} +(-1.72162 - 2.98193i) q^{40} +(-4.85352 + 1.30050i) q^{41} +(7.58793 - 4.38090i) q^{43} +(-3.07674 - 3.07674i) q^{44} +(-0.510146 + 0.136693i) q^{46} +(0.207869 + 0.775777i) q^{47} +(6.06147 + 3.49959i) q^{49} +(-1.77443 - 6.62226i) q^{50} +(0.450627 - 3.57728i) q^{52} +5.06566i q^{53} +(-7.49104 - 12.9749i) q^{55} +(-0.0142473 - 0.0246771i) q^{56} +(-5.87391 + 5.87391i) q^{58} +(-10.1180 + 10.1180i) q^{59} +(0.0107467 + 0.0186139i) q^{61} +(0.721399 + 1.24950i) q^{62} -1.00000i q^{64} +(4.68673 - 11.4961i) q^{65} +(-0.244574 - 0.912763i) q^{67} +(5.81139 + 3.35521i) q^{68} +(-0.0253937 - 0.0947706i) q^{70} +(-9.32969 + 2.49988i) q^{71} +(6.53713 + 6.53713i) q^{73} +(-7.02196 + 4.05413i) q^{74} +(1.94612 - 0.521462i) q^{76} +(-0.0619924 - 0.107374i) q^{77} +(1.40950 - 2.44132i) q^{79} +(0.891175 - 3.32591i) q^{80} +(-4.35155 - 2.51237i) q^{82} +(14.1896 - 3.80210i) q^{83} +(16.3381 + 16.3381i) q^{85} +(8.46324 + 2.26772i) q^{86} -4.35116i q^{88} +(10.8696 + 2.91249i) q^{89} +(0.0387852 - 0.0951367i) q^{91} +(-0.457384 - 0.264071i) q^{92} +(-0.401572 + 0.695542i) q^{94} +6.93734 q^{95} +(-0.455998 - 0.122184i) q^{97} +(1.81152 + 6.76070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.891175	+	3.32591i	−0.398545	+	1.48739i	0.417111	+	0.908855i	$0.363043\pi$
$5$	−0.891175	+	3.32591i	−0.398545	+	1.48739i	−0.815657	+	0.578536i	$0.803624\pi$
$6$		0			0
$7$	−0.00737496	+	0.0275237i	−0.00278747	+	0.0104030i	−0.967306	−	0.253614i	$-0.918381\pi$
$7$	−0.00737496	+	0.0275237i	−0.00278747	+	0.0104030i	0.964518	+	0.264017i	$0.0850474\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.98193	+	1.72162i	−0.942969	+	0.544423i
$11$	−3.07674	+	3.07674i	−0.927671	+	0.927671i	−0.997555	−	0.0698842i	$-0.977737\pi$
$11$	−3.07674	+	3.07674i	−0.927671	+	0.927671i	0.0698842	+	0.997555i	$0.477737\pi$
$12$		0			0
$13$	−3.57728	−	0.450627i	−0.992159	−	0.124981i
$13$	−3.57728	−	0.450627i	−0.992159	−	0.124981i
$14$	−0.0246771	+	0.0142473i	−0.00659523	+	0.00380776i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.35521	−	5.81139i	0.813757	−	1.40947i	−0.0964602	−	0.995337i	$-0.530752\pi$
$17$	3.35521	−	5.81139i	0.813757	−	1.40947i	0.910217	−	0.414131i	$-0.135915\pi$
$18$		0			0
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	0.879960	−	0.475048i	$-0.157569\pi$
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	−0.999592	+	0.0285767i	$0.990903\pi$
$20$	−3.32591	−	0.891175i	−0.743696	−	0.199273i
$21$		0			0
$22$	−4.35116			−0.927671
$23$	−0.264071	+	0.457384i	−0.0550626	+	0.0953712i	−0.892243	−	0.451556i	$-0.850869\pi$
$23$	−0.264071	+	0.457384i	−0.0550626	+	0.0953712i	0.837180	+	0.546927i	$0.184202\pi$
$24$		0			0
$25$	−5.93735	−	3.42793i	−1.18747	−	0.685587i
$26$	−2.21088	−	2.84816i	−0.433589	−	0.558570i
$27$		0			0
$28$	−0.0275237	−	0.00737496i	−0.00520149	−	0.00139374i
$29$			8.30696i			1.54256i	0.636493	+	0.771282i	$0.280384\pi$
$29$			8.30696i			1.54256i	−0.636493	+	0.771282i	$0.719616\pi$
$30$		0			0
$31$	1.39364	+	0.373424i	0.250305	+	0.0670689i	0.381790	−	0.924249i	$-0.375308\pi$
$31$	1.39364	+	0.373424i	0.250305	+	0.0670689i	−0.131485	+	0.991318i	$0.541975\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	6.48176	−	1.73678i	1.11161	−	0.297856i
$35$	−0.0849690	−	0.0490569i	−0.0143624	−	0.00829212i
$36$		0			0
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	0.547605	+	0.836737i	$0.315540\pi$
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	−0.892608	+	0.450833i	$0.851127\pi$
$38$	1.00739	−	1.74484i	0.163420	−	0.283051i
$39$		0			0
$40$	−1.72162	−	2.98193i	−0.272212	−	0.471484i
$41$	−4.85352	+	1.30050i	−0.757992	+	0.203103i	−0.617060	−	0.786916i	$-0.711677\pi$
$41$	−4.85352	+	1.30050i	−0.757992	+	0.203103i	−0.140932	+	0.990019i	$0.545010\pi$
$42$		0			0
$43$	7.58793	−	4.38090i	1.15715	−	0.668080i	0.206530	−	0.978440i	$-0.433783\pi$
$43$	7.58793	−	4.38090i	1.15715	−	0.668080i	0.950619	+	0.310360i	$0.100450\pi$
$44$	−3.07674	−	3.07674i	−0.463835	−	0.463835i
$45$		0			0
$46$	−0.510146	+	0.136693i	−0.0752169	+	0.0201543i
$47$	0.207869	+	0.775777i	0.0303208	+	0.113159i	0.979428	−	0.201795i	$-0.0646776\pi$
$47$	0.207869	+	0.775777i	0.0303208	+	0.113159i	−0.949107	+	0.314954i	$0.898011\pi$
$48$		0			0
$49$	6.06147	+	3.49959i	0.865925	+	0.499942i
$50$	−1.77443	−	6.62226i	−0.250942	−	0.936529i
$51$		0			0
$52$	0.450627	−	3.57728i	0.0624907	−	0.496080i
$53$			5.06566i			0.695822i	0.937527	+	0.347911i	$0.113109\pi$
$53$			5.06566i			0.695822i	−0.937527	+	0.347911i	$0.886891\pi$
$54$		0			0
$55$	−7.49104	−	12.9749i	−1.01009	−	1.74953i
$56$	−0.0142473	−	0.0246771i	−0.00190388	−	0.00329761i
$57$		0			0
$58$	−5.87391	+	5.87391i	−0.771282	+	0.771282i
$59$	−10.1180	+	10.1180i	−1.31725	+	1.31725i	−0.401298	+	0.915948i	$0.631441\pi$
$59$	−10.1180	+	10.1180i	−1.31725	+	1.31725i	−0.915948	+	0.401298i	$0.868559\pi$
$60$		0			0
$61$	0.0107467	+	0.0186139i	0.00137598	+	0.00238327i	0.866713	−	0.498808i	$-0.166229\pi$
$61$	0.0107467	+	0.0186139i	0.00137598	+	0.00238327i	−0.865337	+	0.501191i	$0.832895\pi$
$62$	0.721399	+	1.24950i	0.0916178	+	0.158687i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	4.68673	−	11.4961i	0.581317	−	1.42592i
$66$		0			0
$67$	−0.244574	−	0.912763i	−0.0298795	−	0.111512i	0.949376	−	0.314143i	$-0.101717\pi$
$67$	−0.244574	−	0.912763i	−0.0298795	−	0.111512i	−0.979255	+	0.202632i	$0.935051\pi$
$68$	5.81139	+	3.35521i	0.704734	+	0.406878i
$69$		0			0
$70$	−0.0253937	−	0.0947706i	−0.00303513	−	0.0113273i
$71$	−9.32969	+	2.49988i	−1.10723	+	0.296682i	−0.765706	−	0.643191i	$-0.777610\pi$
$71$	−9.32969	+	2.49988i	−1.10723	+	0.296682i	−0.341525	+	0.939873i	$0.610943\pi$
$72$		0			0
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	0.977242	−	0.212129i	$-0.0680396\pi$
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	−0.212129	+	0.977242i	$0.568040\pi$
$74$	−7.02196	+	4.05413i	−0.816286	+	0.471283i
$75$		0			0
$76$	1.94612	−	0.521462i	0.223235	−	0.0598158i
$77$	−0.0619924	−	0.107374i	−0.00706469	−	0.0122364i
$78$		0			0
$79$	1.40950	−	2.44132i	0.158581	−	0.274670i	−0.775776	−	0.631008i	$-0.782641\pi$
$79$	1.40950	−	2.44132i	0.158581	−	0.274670i	0.934357	+	0.356338i	$0.115975\pi$
$80$	0.891175	−	3.32591i	0.0996364	−	0.371848i
$81$		0			0
$82$	−4.35155	−	2.51237i	−0.480548	−	0.277444i
$83$	14.1896	−	3.80210i	1.55752	−	0.417335i	0.625640	−	0.780112i	$-0.284838\pi$
$83$	14.1896	−	3.80210i	1.55752	−	0.417335i	0.931876	+	0.362777i	$0.118171\pi$
$84$		0			0
$85$	16.3381	+	16.3381i	1.77211	+	1.77211i
$86$	8.46324	+	2.26772i	0.912615	+	0.244534i
$87$		0			0
$88$		−	4.35116i		−	0.463835i
$89$	10.8696	+	2.91249i	1.15217	+	0.308724i	0.783835	−	0.620969i	$-0.213261\pi$
$89$	10.8696	+	2.91249i	1.15217	+	0.308724i	0.368337	+	0.929692i	$0.379927\pi$
$90$		0			0
$91$	0.0387852	−	0.0951367i	0.00406579	−	0.00997303i
$92$	−0.457384	−	0.264071i	−0.0476856	−	0.0275313i
$93$		0			0
$94$	−0.401572	+	0.695542i	−0.0414189	+	0.0717397i
$95$	6.93734			0.711756
$96$		0			0
$97$	−0.455998	−	0.122184i	−0.0462996	−	0.0124059i	0.235595	−	0.971851i	$-0.424296\pi$
$97$	−0.455998	−	0.122184i	−0.0462996	−	0.0124059i	−0.281895	+	0.959445i	$0.590963\pi$
$98$	1.81152	+	6.76070i	0.182991	+	0.682933i
$99$		0			0
$100$	3.42793	−	5.93735i	0.342793	−	0.593735i
$101$	5.49087			0.546362			0.273181	−	0.961963i	$-0.411924\pi$
$101$	5.49087			0.546362			0.273181	+	0.961963i	$0.411924\pi$
$102$		0			0
$103$	−3.62390	+	2.09226i	−0.357073	+	0.206156i	−0.667796	−	0.744344i	$-0.732762\pi$
$103$	−3.62390	+	2.09226i	−0.357073	+	0.206156i	0.310723	+	0.950501i	$0.399429\pi$
$104$	2.84816	−	2.21088i	0.279285	−	0.216794i
$105$		0			0
$106$	−3.58197	+	3.58197i	−0.347911	+	0.347911i
$107$	−2.85234	+	1.64680i	−0.275746	+	0.159202i	−0.631496	−	0.775379i	$-0.717559\pi$
$107$	−2.85234	+	1.64680i	−0.275746	+	0.159202i	0.355750	+	0.934581i	$0.384226\pi$
$108$		0			0
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	−0.916823	−	0.399294i	$-0.869255\pi$
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	0.399294	+	0.916823i	$0.369255\pi$
$110$	3.87765	−	14.4716i	0.369719	−	1.37981i
$111$		0			0
$112$	0.00737496	−	0.0275237i	0.000696868	−	0.00260075i
$113$			0.581902i			0.0547407i	0.999625	+	0.0273704i	$0.00871334\pi$
$113$			0.581902i			0.0547407i	−0.999625	+	0.0273704i	$0.991287\pi$
$114$		0			0
$115$	−1.28588	−	1.28588i	−0.119909	−	0.119909i
$116$	−8.30696			−0.771282
$117$		0			0
$118$	−14.3089			−1.31725
$119$	0.135206	+	0.135206i	0.0123944	+	0.0123944i
$120$		0			0
$121$		−	7.93261i		−	0.721147i
$122$	−0.00556292	+	0.0207611i	−0.000503644	+	0.00187962i
$123$		0			0
$124$	−0.373424	+	1.39364i	−0.0335345	+	0.125152i
$125$	4.51854	−	4.51854i	0.404150	−	0.404150i
$126$		0			0
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	−0.0694101	−	0.997588i	$-0.522112\pi$
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	0.829232	+	0.558905i	$0.188778\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	11.4430	−	4.81497i	1.00362	−	0.422301i
$131$	15.6965	−	9.06236i	1.37141	−	0.791782i	0.380301	−	0.924863i	$-0.375820\pi$
$131$	15.6965	−	9.06236i	1.37141	−	0.791782i	0.991105	+	0.133081i	$0.0424871\pi$
$132$		0			0
$133$	0.0574102			0.00497810
$134$	0.472481	−	0.818361i	0.0408161	−	0.0706956i
$135$		0			0
$136$	1.73678	+	6.48176i	0.148928	+	0.555806i
$137$	−16.1465	−	4.32643i	−1.37948	−	0.369632i	−0.508551	−	0.861032i	$-0.669819\pi$
$137$	−16.1465	−	4.32643i	−1.37948	−	0.369632i	−0.870934	+	0.491400i	$0.836485\pi$
$138$		0			0
$139$	5.08483			0.431289			0.215645	−	0.976472i	$-0.430815\pi$
$139$	5.08483			0.431289			0.215645	+	0.976472i	$0.430815\pi$
$140$	0.0490569	−	0.0849690i	0.00414606	−	0.00718119i
$141$		0			0
$142$	−8.36477	−	4.82940i	−0.701956	−	0.405275i
$143$	12.3928	−	9.61989i	1.03634	−	0.804456i
$144$		0			0
$145$	−27.6282	−	7.40295i	−2.29440	−	0.614782i
$146$			9.24490i			0.765113i
$147$		0			0
$148$	−7.83198	−	2.09857i	−0.643785	−	0.172502i
$149$	−3.73867	−	3.73867i	−0.306284	−	0.306284i	0.537182	−	0.843466i	$-0.319489\pi$
$149$	−3.73867	−	3.73867i	−0.306284	−	0.306284i	−0.843466	+	0.537182i	$0.819489\pi$
$150$		0			0
$151$	9.40508	−	2.52008i	0.765375	−	0.205082i	0.145047	−	0.989425i	$-0.453667\pi$
$151$	9.40508	−	2.52008i	0.765375	−	0.205082i	0.620327	+	0.784343i	$0.287000\pi$
$152$	1.74484	+	1.00739i	0.141526	+	0.0817098i
$153$		0			0
$154$	0.0320896	−	0.119760i	0.00258586	−	0.00965055i
$155$	−2.48395	+	4.30232i	−0.199515	+	0.345571i
$156$		0			0
$157$	4.81339	+	8.33703i	0.384150	+	0.665368i	0.991651	−	0.128952i	$-0.0411612\pi$
$157$	4.81339	+	8.33703i	0.384150	+	0.665368i	−0.607501	+	0.794319i	$0.707828\pi$
$158$	2.72294	−	0.729610i	0.216626	−	0.0580446i
$159$		0			0
$160$	2.98193	−	1.72162i	0.235742	−	0.136106i
$161$	−0.0106414	−	0.0106414i	−0.000838659	−	0.000838659i
$162$		0			0
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.186142	−	0.982523i	$-0.440402\pi$
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.652465	+	0.757819i	$0.273735\pi$
$164$	−1.30050	−	4.85352i	−0.101552	−	0.378996i
$165$		0			0
$166$	12.7221	+	7.34510i	0.987425	+	0.570090i
$167$	−3.86269	−	14.4157i	−0.298904	−	1.11552i	−0.938067	−	0.346453i	$-0.887386\pi$
$167$	−3.86269	−	14.4157i	−0.298904	−	1.11552i	0.639164	−	0.769071i	$-0.279281\pi$
$168$		0			0
$169$	12.5939	+	3.22404i	0.968759	+	0.248003i
$170$			23.1055i			1.77211i
$171$		0			0
$172$	4.38090	+	7.58793i	0.334040	+	0.578574i
$173$	9.53013	+	16.5067i	0.724562	+	1.25498i	0.959154	+	0.282884i	$0.0912913\pi$
$173$	9.53013	+	16.5067i	0.724562	+	1.25498i	−0.234592	+	0.972094i	$0.575375\pi$
$174$		0			0
$175$	0.138137	−	0.138137i	0.0104422	−	0.0104422i
$176$	3.07674	−	3.07674i	0.231918	−	0.231918i
$177$		0			0
$178$	5.62650	+	9.74539i	0.421724	+	0.730448i
$179$	−12.0533	−	20.8769i	−0.900906	−	1.56041i	−0.826320	−	0.563200i	$-0.809570\pi$
$179$	−12.0533	−	20.8769i	−0.900906	−	1.56041i	−0.0745856	−	0.997215i	$-0.523763\pi$
$180$		0			0
$181$		−	1.16505i		−	0.0865977i	−0.999062	−	0.0432988i	$-0.986213\pi$
$181$		−	1.16505i		−	0.0865977i	0.999062	−	0.0432988i	$-0.0137868\pi$
$182$	0.0946971	−	0.0398465i	0.00701941	−	0.00295362i
$183$		0			0
$184$	−0.136693	−	0.510146i	−0.0100771	−	0.0376084i
$185$	−24.1783	−	13.9593i	−1.77762	−	1.02631i
$186$		0			0
$187$	7.55702	+	28.2032i	0.552624	+	2.06242i
$188$	−0.775777	+	0.207869i	−0.0565793	+	0.0151604i
$189$		0			0
$190$	4.90544	+	4.90544i	0.355878	+	0.355878i
$191$	10.0152	−	5.78229i	0.724676	−	0.418392i	−0.0917955	−	0.995778i	$-0.529261\pi$
$191$	10.0152	−	5.78229i	0.724676	−	0.418392i	0.816471	+	0.577386i	$0.195927\pi$
$192$		0			0
$193$	1.39097	−	0.372710i	0.100124	−	0.0268283i	−0.208409	−	0.978042i	$-0.566829\pi$
$193$	1.39097	−	0.372710i	0.100124	−	0.0268283i	0.308533	+	0.951214i	$0.400162\pi$
$194$	−0.236042	−	0.408837i	−0.0169468	−	0.0293528i
$195$		0			0
$196$	−3.49959	+	6.06147i	−0.249971	+	0.432962i
$197$	−1.07594	+	4.01546i	−0.0766575	+	0.286090i	−0.993604	−	0.112920i	$-0.963980\pi$
$197$	−1.07594	+	4.01546i	−0.0766575	+	0.286090i	0.916947	+	0.399010i	$0.130646\pi$
$198$		0			0
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	0.561910	−	0.827198i	$-0.310067\pi$
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	−0.435419	+	0.900228i	$0.643400\pi$
$200$	6.62226	−	1.77443i	0.468264	−	0.125471i
$201$		0			0
$202$	3.88263	+	3.88263i	0.273181	+	0.273181i
$203$	−0.228638	−	0.0612635i	−0.0160473	−	0.00429985i
$204$		0			0
$205$		−	17.3013i		−	1.20838i
$206$	−4.04193	−	1.08303i	−0.281615	−	0.0754585i
$207$		0			0
$208$	3.57728	+	0.450627i	0.248040	+	0.0312453i
$209$	7.59210	+	4.38330i	0.525157	+	0.303199i
$210$		0			0
$211$	−9.57481	+	16.5841i	−0.659157	+	1.14169i	0.321677	+	0.946849i	$0.395753\pi$
$211$	−9.57481	+	16.5841i	−0.659157	+	1.14169i	−0.980834	+	0.194844i	$0.937580\pi$
$212$	−5.06566			−0.347911
$213$		0			0
$214$	−3.18137	−	0.852446i	−0.217474	−	0.0582720i
$215$	7.80829	+	29.1409i	0.532521	+	1.98739i
$216$		0			0
$217$	−0.0205560	+	0.0356041i	−0.00139543	+	0.00241696i
$218$	−7.64122			−0.517529
$219$		0			0
$220$	12.9749	−	7.49104i	0.874765	−	0.505046i
$221$	−14.6213	+	19.2770i	−0.983534	+	1.29671i
$222$		0			0
$223$	18.6817	−	18.6817i	1.25102	−	1.25102i	0.295754	−	0.955264i	$-0.404429\pi$
$223$	18.6817	−	18.6817i	1.25102	−	1.25102i	0.955264	−	0.295754i	$-0.0955710\pi$
$224$	0.0246771	−	0.0142473i	0.00164881	−	0.000951939i
$225$		0			0
$226$	−0.411467	+	0.411467i	−0.0273704	+	0.0273704i
$227$	−1.32881	+	4.95918i	−0.0881962	+	0.329153i	−0.995900	−	0.0904584i	$-0.971167\pi$
$227$	−1.32881	+	4.95918i	−0.0881962	+	0.329153i	0.907704	+	0.419611i	$0.137833\pi$
$228$		0			0
$229$	2.05522	−	7.67020i	0.135813	−	0.506861i	−0.864180	−	0.503182i	$-0.832162\pi$
$229$	2.05522	−	7.67020i	0.135813	−	0.506861i	0.999993	−	0.00367870i	$-0.00117097\pi$
$230$		−	1.81852i		−	0.119909i
$231$		0			0
$232$	−5.87391	−	5.87391i	−0.385641	−	0.385641i
$233$	−0.240333			−0.0157448			−0.00787238	−	0.999969i	$-0.502506\pi$
$233$	−0.240333			−0.0157448			−0.00787238	+	0.999969i	$0.502506\pi$
$234$		0			0
$235$	−2.76541			−0.180395
$236$	−10.1180	−	10.1180i	−0.658623	−	0.658623i
$237$		0			0
$238$			0.191211i			0.0123944i
$239$	1.74060	−	6.49603i	0.112590	−	0.420193i	−0.886505	−	0.462719i	$-0.846874\pi$
$239$	1.74060	−	6.49603i	0.112590	−	0.420193i	0.999095	+	0.0425261i	$0.0135406\pi$
$240$		0			0
$241$	−6.71652	+	25.0664i	−0.432649	+	1.61467i	0.313980	+	0.949430i	$0.398337\pi$
$241$	−6.71652	+	25.0664i	−0.432649	+	1.61467i	−0.746630	+	0.665240i	$0.768329\pi$
$242$	5.60920	−	5.60920i	0.360573	−	0.360573i
$243$		0			0
$244$	−0.0186139	+	0.0107467i	−0.00119163	+	0.000687990i
$245$	−17.0412	+	17.0412i	−1.08872	+	1.08872i
$246$		0			0
$247$	0.988441	+	7.19681i	0.0628930	+	0.457922i
$248$	−1.24950	+	0.721399i	−0.0793434	+	0.0458089i
$249$		0			0
$250$	6.39018			0.404150
$251$	10.2804	−	17.8061i	0.648892	−	1.12391i	−0.334496	−	0.942397i	$-0.608566\pi$
$251$	10.2804	−	17.8061i	0.648892	−	1.12391i	0.983388	−	0.181517i	$-0.0581007\pi$
$252$		0			0
$253$	−0.594774	−	2.21973i	−0.0373931	−	0.139553i
$254$	9.55051	+	2.55905i	0.599252	+	0.160569i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.71905	+	13.3698i	−0.481501	+	0.833984i	−0.999775	−	0.0212306i	$-0.993242\pi$
$257$	−7.71905	+	13.3698i	−0.481501	+	0.833984i	0.518274	+	0.855215i	$0.326575\pi$
$258$		0			0
$259$	−0.200088	−	0.115521i	−0.0124329	−	0.00717813i
$260$	11.4961	+	4.68673i	0.712959	+	0.290658i
$261$		0			0
$262$	17.5071	+	4.69102i	1.08159	+	0.289812i
$263$			12.6233i			0.778388i	0.921156	+	0.389194i	$0.127246\pi$
$263$			12.6233i			0.778388i	−0.921156	+	0.389194i	$0.872754\pi$
$264$		0			0
$265$	−16.8479	−	4.51439i	−1.03496	−	0.277317i
$266$	0.0405952	+	0.0405952i	0.00248905	+	0.00248905i
$267$		0			0
$268$	0.912763	−	0.244574i	0.0557559	−	0.0149397i
$269$	−13.5676	−	7.83325i	−0.827230	−	0.477602i	0.0256732	−	0.999670i	$-0.491827\pi$
$269$	−13.5676	−	7.83325i	−0.827230	−	0.477602i	−0.852903	+	0.522069i	$0.825160\pi$
$270$		0			0
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	0.690537	+	0.723297i	$0.257374\pi$
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	−0.959671	+	0.281126i	$0.909292\pi$
$272$	−3.35521	+	5.81139i	−0.203439	+	0.352367i
$273$		0			0
$274$	−8.35802	−	14.4765i	−0.504926	−	0.874558i
$275$	28.8145	−	7.72083i	1.73758	−	0.465583i
$276$		0			0
$277$	−16.9335	+	9.77658i	−1.01744	+	0.587418i	−0.913361	−	0.407151i	$-0.866522\pi$
$277$	−16.9335	+	9.77658i	−1.01744	+	0.587418i	−0.104077	+	0.994569i	$0.533189\pi$
$278$	3.59552	+	3.59552i	0.215645	+	0.215645i
$279$		0			0
$280$	0.0947706	−	0.0253937i	0.00566363	−	0.00151756i
$281$	−7.92083	−	29.5609i	−0.472517	−	1.76346i	−0.630679	−	0.776044i	$-0.717223\pi$
$281$	−7.92083	−	29.5609i	−0.472517	−	1.76346i	0.158162	−	0.987413i	$-0.449443\pi$
$282$		0			0
$283$	−20.4545	−	11.8094i	−1.21589	−	0.701995i	−0.251855	−	0.967765i	$-0.581041\pi$
$283$	−20.4545	−	11.8094i	−1.21589	−	0.701995i	−0.964036	+	0.265770i	$0.914374\pi$
$284$	−2.49988	−	9.32969i	−0.148341	−	0.553615i
$285$		0			0
$286$	15.5653	+	1.96075i	0.920397	+	0.115942i
$287$		−	0.143178i		−	0.00845153i
$288$		0			0
$289$	−14.0148	−	24.2744i	−0.824401	−	1.42790i
$290$	−14.3014	−	24.7708i	−0.839808	−	1.45459i
$291$		0			0
$292$	−6.53713	+	6.53713i	−0.382557	+	0.382557i
$293$	15.6173	−	15.6173i	0.912375	−	0.912375i	−0.0840837	−	0.996459i	$-0.526796\pi$
$293$	15.6173	−	15.6173i	0.912375	−	0.912375i	0.996459	+	0.0840837i	$0.0267963\pi$
$294$		0			0
$295$	−24.6345	−	42.6683i	−1.43428	−	2.48424i
$296$	−4.05413	−	7.02196i	−0.235642	−	0.408143i
$297$		0			0
$298$		−	5.28728i		−	0.306284i
$299$	1.15076	−	1.51719i	0.0665504	−	0.0877416i
$300$		0			0
$301$	0.0646178	+	0.241157i	0.00372451	+	0.0139001i
$302$	8.43236	+	4.86843i	0.485228	+	0.280147i
$303$		0			0
$304$	0.521462	+	1.94612i	0.0299079	+	0.111618i
$305$	−0.0714854	+	0.0191545i	−0.00409324	+	0.00109678i
$306$		0			0
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	0.787461	−	0.616364i	$-0.211395\pi$
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	−0.616364	+	0.787461i	$0.711395\pi$
$308$	0.107374	−	0.0619924i	0.00611820	−	0.00353234i
$309$		0			0
$310$	−4.79862	+	1.28579i	−0.272543	+	0.0730277i
$311$	15.1300	+	26.2059i	0.857943	+	1.48600i	0.873888	+	0.486128i	$0.161591\pi$
$311$	15.1300	+	26.2059i	0.857943	+	1.48600i	−0.0159450	+	0.999873i	$0.505076\pi$
$312$		0			0
$313$	−16.7332	+	28.9828i	−0.945817	+	1.63820i	−0.191710	+	0.981452i	$0.561403\pi$
$313$	−16.7332	+	28.9828i	−0.945817	+	1.63820i	−0.754107	+	0.656751i	$0.771930\pi$
$314$	−2.49159	+	9.29875i	−0.140609	+	0.524759i
$315$		0			0
$316$	2.44132	+	1.40950i	0.137335	+	0.0792905i
$317$	−10.7787	+	2.88814i	−0.605392	+	0.162214i	−0.548478	−	0.836165i	$-0.684793\pi$
$317$	−10.7787	+	2.88814i	−0.605392	+	0.162214i	−0.0569135	+	0.998379i	$0.518126\pi$
$318$		0			0
$319$	−25.5583	−	25.5583i	−1.43099	−	1.43099i
$320$	3.32591	+	0.891175i	0.185924	+	0.0498182i
$321$		0			0
$322$		−	0.0150492i		−	0.000838659i
$323$	−13.0593	−	3.49922i	−0.726638	−	0.194702i
$324$		0			0
$325$	19.6949	+	14.9382i	1.09247	+	0.828623i
$326$	9.59929	+	5.54215i	0.531655	+	0.306951i
$327$		0			0
$328$	2.51237	−	4.35155i	0.138722	−	0.240274i
$329$	−0.0228853			−0.00126171
$330$		0			0
$331$	−3.99853	−	1.07140i	−0.219779	−	0.0588897i	0.147249	−	0.989099i	$-0.452958\pi$
$331$	−3.99853	−	1.07140i	−0.219779	−	0.0588897i	−0.367028	+	0.930210i	$0.619625\pi$
$332$	3.80210	+	14.1896i	0.208668	+	0.778758i
$333$		0			0
$334$	7.46214	−	12.9248i	0.408310	−	0.707213i
$335$	3.25372			0.177770
$336$		0			0
$337$	14.3966	−	8.31187i	0.784232	−	0.452777i	−0.0536959	−	0.998557i	$-0.517100\pi$
$337$	14.3966	−	8.31187i	0.784232	−	0.452777i	0.837928	+	0.545781i	$0.183767\pi$
$338$	6.62547	+	11.1849i	0.360378	+	0.608381i
$339$		0			0
$340$	−16.3381	+	16.3381i	−0.886056	+	0.886056i
$341$	−5.43678	+	3.13893i	−0.294418	+	0.169982i
$342$		0			0
$343$	−0.282066	+	0.282066i	−0.0152301	+	0.0152301i
$344$	−2.26772	+	8.46324i	−0.122267	+	0.456307i
$345$		0			0
$346$	−4.93316	+	18.4108i	−0.265208	+	0.989770i
$347$		−	20.3538i		−	1.09265i	−0.837574	−	0.546324i	$-0.816027\pi$
$347$		−	20.3538i		−	1.09265i	0.837574	−	0.546324i	$-0.183973\pi$
$348$		0			0
$349$	−13.8299	−	13.8299i	−0.740298	−	0.740298i	0.232337	−	0.972635i	$-0.425363\pi$
$349$	−13.8299	−	13.8299i	−0.740298	−	0.740298i	−0.972635	+	0.232337i	$0.925363\pi$
$350$	0.195355			0.0104422
$351$		0			0
$352$	4.35116			0.231918
$353$	7.15642	+	7.15642i	0.380898	+	0.380898i	0.871426	−	0.490528i	$-0.163196\pi$
$353$	7.15642	+	7.15642i	0.380898	+	0.380898i	−0.490528	+	0.871426i	$0.663196\pi$
$354$		0			0
$355$		−	33.2575i		−	1.76513i
$356$	−2.91249	+	10.8696i	−0.154362	+	0.576086i
$357$		0			0
$358$	6.23925	−	23.2852i	0.329754	−	1.23066i
$359$	−1.10596	+	1.10596i	−0.0583705	+	0.0583705i	−0.735689	−	0.677319i	$-0.763142\pi$
$359$	−1.10596	+	1.10596i	−0.0583705	+	0.0583705i	0.677319	+	0.735689i	$0.263142\pi$
$360$		0			0
$361$	12.9390	−	7.47034i	0.681001	−	0.393176i
$362$	0.823817	−	0.823817i	0.0432988	−	0.0432988i
$363$		0			0
$364$	0.0951367	+	0.0387852i	0.00498652	+	0.00203290i
$365$	−27.5676	+	15.9162i	−1.44296	+	0.833091i
$366$		0			0
$367$	−6.23361			−0.325392			−0.162696	−	0.986676i	$-0.552019\pi$
$367$	−6.23361			−0.325392			−0.162696	+	0.986676i	$0.552019\pi$
$368$	0.264071	−	0.457384i	0.0137656	−	0.0238428i
$369$		0			0
$370$	−7.22588	−	26.9673i	−0.375656	−	1.40197i
$371$	−0.139426	−	0.0373590i	−0.00723863	−	0.00193958i
$372$		0			0
$373$	−21.1091			−1.09299			−0.546493	−	0.837463i	$-0.684038\pi$
$373$	−21.1091			−1.09299			−0.546493	+	0.837463i	$0.684038\pi$
$374$	−14.5990	+	25.2863i	−0.754899	+	1.30752i
$375$		0			0
$376$	−0.695542	−	0.401572i	−0.0358699	−	0.0207095i
$377$	3.74334	−	29.7163i	0.192792	−	1.53047i
$378$		0			0
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	0.291769	−	0.956489i	$-0.405756\pi$
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	−0.225565	+	0.974228i	$0.572423\pi$
$380$			6.93734i			0.355878i
$381$		0			0
$382$	11.1705	+	2.99313i	0.571534	+	0.153142i
$383$	18.2839	+	18.2839i	0.934261	+	0.934261i	0.997969	−	0.0637072i	$-0.0202924\pi$
$383$	18.2839	+	18.2839i	0.934261	+	0.934261i	−0.0637072	+	0.997969i	$0.520292\pi$
$384$		0			0
$385$	0.412362	−	0.110492i	0.0210159	−	0.00563120i
$386$	1.24711	+	0.720021i	0.0634764	+	0.0366481i
$387$		0			0
$388$	0.122184	−	0.455998i	0.00620297	−	0.0231498i
$389$	7.30331	−	12.6497i	0.370292	−	0.641365i	−0.619318	−	0.785140i	$-0.712591\pi$
$389$	7.30331	−	12.6497i	0.370292	−	0.641365i	0.989610	+	0.143775i	$0.0459242\pi$
$390$		0			0
$391$	1.77202	+	3.06924i	0.0896151	+	0.155218i
$392$	−6.76070	+	1.81152i	−0.341467	+	0.0914957i
$393$		0			0
$394$	−3.60016	+	2.07856i	−0.181374	+	0.104716i
$395$	6.86351	+	6.86351i	0.345341	+	0.345341i
$396$		0			0
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	−0.185772	−	0.982593i	$-0.559479\pi$
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	0.330413	+	0.943837i	$0.392812\pi$
$398$	0.533275	+	1.99021i	0.0267307	+	0.0997601i
$399$		0			0
$400$	5.93735	+	3.42793i	0.296868	+	0.171397i
$401$	−2.86637	−	10.6974i	−0.143140	−	0.534205i	−0.999831	−	0.0183755i	$-0.994151\pi$
$401$	−2.86637	−	10.6974i	−0.143140	−	0.534205i	0.856691	−	0.515829i	$-0.172516\pi$
$402$		0			0
$403$	−4.81715	−	1.96385i	−0.239960	−	0.0978264i
$404$			5.49087i			0.273181i
$405$		0			0
$406$	−0.118352	−	0.204992i	−0.00587371	−	0.0101736i
$407$	−17.6402	−	30.5537i	−0.874391	−	1.51449i
$408$		0			0
$409$	10.3795	−	10.3795i	0.513233	−	0.513233i	−0.402283	−	0.915515i	$-0.631783\pi$
$409$	10.3795	−	10.3795i	0.513233	−	0.513233i	0.915515	+	0.402283i	$0.131783\pi$
$410$	12.2339	−	12.2339i	0.604189	−	0.604189i
$411$		0			0
$412$	−2.09226	−	3.62390i	−0.103078	−	0.178537i
$413$	−0.203864	−	0.353103i	−0.0100315	−	0.0173751i
$414$		0			0
$415$			50.5818i			2.48296i
$416$	2.21088	+	2.84816i	0.108397	+	0.139643i
$417$		0			0
$418$	2.26896	+	8.46789i	0.110979	+	0.414178i
$419$	−24.3908	−	14.0820i	−1.19157	−	0.687953i	−0.232907	−	0.972499i	$-0.574824\pi$
$419$	−24.3908	−	14.0820i	−1.19157	−	0.687953i	−0.958662	+	0.284546i	$0.908157\pi$
$420$		0			0
$421$	−1.88397	−	7.03106i	−0.0918189	−	0.342673i	0.904699	−	0.426051i	$-0.140096\pi$
$421$	−1.88397	−	7.03106i	−0.0918189	−	0.342673i	−0.996518	+	0.0833784i	$0.973429\pi$
$422$	−18.4971	+	4.95629i	−0.900425	+	0.241268i
$423$		0			0
$424$	−3.58197	−	3.58197i	−0.173956	−	0.173956i
$425$	−39.8421	+	23.0028i	−1.93262	+	1.11580i
$426$		0			0
$427$	−0.000591581	0	0.000158514i	−2.86286e−5	0	7.67101e-6i
$428$	−1.64680	−	2.85234i	−0.0796011	−	0.137873i
$429$		0			0
$430$	−15.0845	+	26.1270i	−0.727437	+	1.25996i
$431$	−4.90556	+	18.3078i	−0.236292	+	0.881855i	0.741270	+	0.671207i	$0.234224\pi$
$431$	−4.90556	+	18.3078i	−0.236292	+	0.881855i	−0.977562	+	0.210648i	$0.932443\pi$
$432$		0			0
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.982381	−	0.186890i	$-0.0598407\pi$
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.329339	+	0.944212i	$0.393174\pi$
$434$	−0.0397112	+	0.0106406i	−0.00190620	+	0.000510764i
$435$		0			0
$436$	−5.40316	−	5.40316i	−0.258764	−	0.258764i
$437$	1.02783	+	0.275406i	0.0491677	+	0.0131744i
$438$		0			0
$439$		−	12.8872i		−	0.615072i	−0.951536	−	0.307536i	$-0.900495\pi$
$439$		−	12.8872i		−	0.615072i	0.951536	−	0.307536i	$-0.0995045\pi$
$440$	14.4716	+	3.87765i	0.689905	+	0.184860i
$441$		0			0
$442$	−23.9697	+	3.29210i	−1.14012	+	0.156589i
$443$	10.9018	+	6.29415i	0.517959	+	0.299044i	0.736099	−	0.676874i	$-0.236666\pi$
$443$	10.9018	+	6.29415i	0.517959	+	0.299044i	−0.218140	+	0.975917i	$0.569999\pi$
$444$		0			0
$445$	−19.3734	+	33.5557i	−0.918386	+	1.59069i
$446$	26.4199			1.25102
$447$		0			0
$448$	0.0275237	+	0.00737496i	0.00130037	+	0.000348434i
$449$	−1.16977	−	4.36565i	−0.0552050	−	0.206028i	0.932814	−	0.360357i	$-0.117345\pi$
$449$	−1.16977	−	4.36565i	−0.0552050	−	0.206028i	−0.988020	+	0.154329i	$0.950678\pi$
$450$		0			0
$451$	10.9317	−	18.9343i	0.514754	−	0.891581i
$452$	−0.581902			−0.0273704
$453$		0			0
$454$	−4.44628	+	2.56706i	−0.208674	+	0.120478i
$455$	0.281852	+	0.213779i	0.0132134	+	0.0100221i
$456$		0			0
$457$	7.19189	−	7.19189i	0.336422	−	0.336422i	−0.518597	−	0.855019i	$-0.673545\pi$
$457$	7.19189	−	7.19189i	0.336422	−	0.336422i	0.855019	+	0.518597i	$0.173545\pi$
$458$	6.87691	−	3.97039i	0.321337	−	0.185524i
$459$		0			0
$460$	1.28588	−	1.28588i	0.0599547	−	0.0599547i
$461$	−7.04174	+	26.2801i	−0.327966	+	1.22399i	0.583330	+	0.812236i	$0.301750\pi$
$461$	−7.04174	+	26.2801i	−0.327966	+	1.22399i	−0.911296	+	0.411752i	$0.864917\pi$
$462$		0			0
$463$	−3.06727	+	11.4472i	−0.142548	+	0.531996i	0.857304	+	0.514810i	$0.172138\pi$
$463$	−3.06727	+	11.4472i	−0.142548	+	0.531996i	−0.999852	+	0.0171864i	$0.994529\pi$
$464$		−	8.30696i		−	0.385641i
$465$		0			0
$466$	−0.169941	−	0.169941i	−0.00787238	−	0.00787238i
$467$	−0.615879			−0.0284995			−0.0142497	−	0.999898i	$-0.504536\pi$
$467$	−0.615879			−0.0284995			−0.0142497	+	0.999898i	$0.504536\pi$
$468$		0			0
$469$	0.0269263			0.00124334
$470$	−1.95544	−	1.95544i	−0.0901977	−	0.0901977i
$471$		0			0
$472$		−	14.3089i		−	0.658623i
$473$	−9.86721	+	36.8249i	−0.453695	+	1.69321i
$474$		0			0
$475$	−3.57507	+	13.3423i	−0.164036	+	0.612189i
$476$	−0.135206	+	0.135206i	−0.00619718	+	0.00619718i
$477$		0			0
$478$	5.82418	−	3.36259i	0.266392	−	0.153801i
$479$	14.1707	−	14.1707i	0.647474	−	0.647474i	−0.304908	−	0.952382i	$-0.598626\pi$
$479$	14.1707	−	14.1707i	0.647474	−	0.647474i	0.952382	+	0.304908i	$0.0986257\pi$
$480$		0			0
$481$	11.0365	−	27.0715i	0.503220	−	1.23436i
$482$	−22.4739	+	12.9753i	−1.02366	+	0.591010i
$483$		0			0
$484$	7.93261			0.360573
$485$	0.812748	−	1.40772i	0.0369050	−	0.0639213i
$486$		0			0
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	−0.971845	−	0.235620i	$-0.924288\pi$
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	0.723833	−	0.689975i	$-0.242379\pi$
$488$	−0.0207611	−	0.00556292i	−0.000939812	−	0.000251822i
$489$		0			0
$490$	−24.0998			−1.08872
$491$	9.87564	−	17.1051i	0.445681	−	0.771943i	−0.552418	−	0.833567i	$-0.686295\pi$
$491$	9.87564	−	17.1051i	0.445681	−	0.771943i	0.998099	+	0.0616246i	$0.0196282\pi$
$492$		0			0
$493$	48.2750	+	27.8716i	2.17420	+	1.25527i
$494$	−4.38998	+	5.78784i	−0.197514	+	0.260407i
$495$		0			0
$496$	−1.39364	−	0.373424i	−0.0625761	−	0.0167672i
$497$		−	0.275224i		−	0.0123455i
$498$		0			0
$499$	5.12859	+	1.37420i	0.229587	+	0.0615177i	0.371778	−	0.928321i	$-0.378748\pi$
$499$	5.12859	+	1.37420i	0.229587	+	0.0615177i	−0.142191	+	0.989839i	$0.545415\pi$
$500$	4.51854	+	4.51854i	0.202075	+	0.202075i
$501$		0			0
$502$	19.8602	−	5.32152i	0.886403	−	0.237511i
$503$	−16.2322	−	9.37164i	−0.723756	−	0.417861i	0.0923776	−	0.995724i	$-0.470553\pi$
$503$	−16.2322	−	9.37164i	−0.723756	−	0.417861i	−0.816134	+	0.577863i	$0.803887\pi$
$504$		0			0
$505$	−4.89333	+	18.2621i	−0.217750	+	0.812654i
$506$	1.14901	−	1.99015i	0.0510799	−	0.0884731i
$507$		0			0
$508$	4.94371	+	8.56275i	0.219342	+	0.379911i
$509$	16.5036	−	4.42212i	0.731509	−	0.196007i	0.126208	−	0.992004i	$-0.459719\pi$
$509$	16.5036	−	4.42212i	0.731509	−	0.196007i	0.605301	+	0.795997i	$0.293053\pi$
$510$		0			0
$511$	−0.228137	+	0.131715i	−0.0100922	+	0.00582673i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−14.9121	+	3.99567i	−0.657743	+	0.176242i
$515$	−3.72914	−	13.9173i	−0.164325	−	0.613271i
$516$		0			0
$517$	−3.02642	−	1.74730i	−0.133102	−	0.0768463i
$518$	−0.0597981	−	0.223169i	−0.00262738	−	0.00980550i
$519$		0			0
$520$	4.81497	+	11.4430i	0.211150	+	0.501809i
$521$		−	6.18564i		−	0.270998i	−0.990777	−	0.135499i	$-0.956736\pi$
$521$		−	6.18564i		−	0.270998i	0.990777	−	0.135499i	$-0.0432637\pi$
$522$		0			0
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	0.929453	−	0.368941i	$-0.120280\pi$
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	−0.784239	+	0.620459i	$0.786946\pi$
$524$	9.06236	+	15.6965i	0.395891	+	0.685703i
$525$		0			0
$526$	−8.92605	+	8.92605i	−0.389194	+	0.389194i
$527$	6.84605	−	6.84605i	0.298219	−	0.298219i
$528$		0			0
$529$	11.3605	+	19.6770i	0.493936	+	0.855523i
$530$	−8.72113	−	15.1054i	−0.378822	−	0.656139i
$531$		0			0
$532$			0.0574102i			0.00248905i
$533$	17.9484	−	2.46512i	0.777433	−	0.106776i
$534$		0			0
$535$	−2.93517	−	10.9542i	−0.126899	−	0.473592i
$536$	0.818361	+	0.472481i	0.0353478	+	0.0204081i
$537$		0			0
$538$	−4.05479	−	15.1327i	−0.174814	−	0.652416i
$539$	−29.4169	+	7.88223i	−1.26708	+	0.339512i
$540$		0			0
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	0.794273	−	0.607561i	$-0.207852\pi$
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	−0.607561	+	0.794273i	$0.707852\pi$
$542$	−14.8248	+	8.55909i	−0.636779	+	0.367644i
$543$		0			0
$544$	−6.48176	+	1.73678i	−0.277903	+	0.0744639i
$545$	−13.1553	−	22.7856i	−0.563509	−	0.976027i
$546$		0			0
$547$	−16.4189	+	28.4384i	−0.702022	+	1.21594i	0.265733	+	0.964047i	$0.414386\pi$
$547$	−16.4189	+	28.4384i	−0.702022	+	1.21594i	−0.967755	+	0.251892i	$0.918947\pi$
$548$	4.32643	−	16.1465i	0.184816	−	0.689742i
$549$		0			0
$550$	25.8344	+	14.9155i	1.10158	+	0.635999i
$551$	16.1664	−	4.33176i	0.688710	−	0.184539i
$552$		0			0
$553$	0.0567993	+	0.0567993i	0.00241535	+	0.00241535i
$554$	−18.8869	−	5.06073i	−0.802428	−	0.215010i
$555$		0			0
$556$			5.08483i			0.215645i
$557$	−7.73861	−	2.07355i	−0.327895	−	0.0878593i	0.0911160	−	0.995840i	$-0.470957\pi$
$557$	−7.73861	−	2.07355i	−0.327895	−	0.0878593i	−0.419011	+	0.907981i	$0.637623\pi$
$558$		0			0
$559$	−29.1183	+	12.2524i	−1.23157	+	0.518220i
$560$	0.0849690	+	0.0490569i	0.00359059	+	0.00207303i
$561$		0			0
$562$	15.3019	−	26.5036i	0.645470	−	1.11799i
$563$	−14.8846			−0.627313			−0.313656	−	0.949537i	$-0.601554\pi$
$563$	−14.8846			−0.627313			−0.313656	+	0.949537i	$0.601554\pi$
$564$		0			0
$565$	−1.93535	−	0.518576i	−0.0814209	−	0.0218167i
$566$	−6.11299	−	22.8140i	−0.256948	−	0.958943i
$567$		0			0
$568$	4.82940	−	8.36477i	0.202637	−	0.350978i
$569$	8.90454			0.373298			0.186649	−	0.982427i	$-0.440237\pi$
$569$	8.90454			0.373298			0.186649	+	0.982427i	$0.440237\pi$
$570$		0			0
$571$	−0.862884	+	0.498186i	−0.0361106	+	0.0208484i	−0.517947	−	0.855413i	$-0.673303\pi$
$571$	−0.862884	+	0.498186i	−0.0361106	+	0.0208484i	0.481836	+	0.876261i	$0.339970\pi$
$572$	9.61989	+	12.3928i	0.402228	+	0.518169i
$573$		0			0
$574$	0.101242	−	0.101242i	0.00422576	−	0.00422576i
$575$	3.13576	−	1.81043i	0.130770	−	0.0755003i
$576$		0			0
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	−0.948247	−	0.317534i	$-0.897145\pi$
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	0.317534	+	0.948247i	$0.397145\pi$
$578$	7.25460	−	27.0745i	0.301752	−	1.12615i
$579$		0			0
$580$	7.40295	−	27.6282i	0.307391	−	1.14720i
$581$			0.418592i			0.0173661i
$582$		0			0
$583$	−15.5857	−	15.5857i	−0.645494	−	0.645494i
$584$	−9.24490			−0.382557
$585$		0			0
$586$	22.0863			0.912375
$587$	4.52599	+	4.52599i	0.186808	+	0.186808i	0.794314	−	0.607507i	$-0.207830\pi$
$587$	4.52599	+	4.52599i	0.186808	+	0.186808i	−0.607507	+	0.794314i	$0.707830\pi$
$588$		0			0
$589$		−	2.90691i		−	0.119777i
$590$	12.7518	−	47.5903i	0.524982	−	1.95926i
$591$		0			0
$592$	2.09857	−	7.83198i	0.0862508	−	0.321892i
$593$	24.4287	−	24.4287i	1.00317	−	1.00317i	0.00317304	−	0.999995i	$-0.498990\pi$
$593$	24.4287	−	24.4287i	1.00317	−	1.00317i	0.999995	−	0.00317304i	$-0.00101001\pi$
$594$		0			0
$595$	−0.570177	+	0.329192i	−0.0233750	+	0.0134955i
$596$	3.73867	−	3.73867i	0.153142	−	0.153142i
$597$		0			0
$598$	1.88653	−	0.259104i	0.0771460	−	0.0105956i
$599$	−36.9806	+	21.3507i	−1.51099	+	0.872368i	−0.511068	+	0.859540i	$0.670750\pi$
$599$	−36.9806	+	21.3507i	−1.51099	+	0.872368i	−0.999918	+	0.0128274i	$0.995917\pi$
$600$		0			0
$601$	−27.0330			−1.10270			−0.551349	−	0.834275i	$-0.685887\pi$
$601$	−27.0330			−1.10270			−0.551349	+	0.834275i	$0.685887\pi$
$602$	−0.124832	+	0.216215i	−0.00508777	+	0.00881228i
$603$		0			0
$604$	2.52008	+	9.40508i	0.102541	+	0.382687i
$605$	26.3831	+	7.06934i	1.07263	+	0.287410i
$606$		0			0
$607$	47.0756			1.91074			0.955370	−	0.295412i	$-0.0954569\pi$
$607$	47.0756			1.91074			0.955370	+	0.295412i	$0.0954569\pi$
$608$	−1.00739	+	1.74484i	−0.0408549	+	0.0707628i
$609$		0			0
$610$	−0.0640921	−	0.0370036i	−0.00259501	−	0.00149823i
$611$	−0.394019	−	2.86884i	−0.0159403	−	0.116061i
$612$		0			0
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.687217	−	0.726452i	$-0.258832\pi$
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.231922	+	0.972734i	$0.425499\pi$
$614$			4.23961i			0.171097i
$615$		0			0
$616$	0.119760	+	0.0320896i	0.00482527	+	0.00129293i
$617$	3.43163	+	3.43163i	0.138152	+	0.138152i	0.772801	−	0.634649i	$-0.218855\pi$
$617$	3.43163	+	3.43163i	0.138152	+	0.138152i	−0.634649	+	0.772801i	$0.718855\pi$
$618$		0			0
$619$	24.6854	−	6.61442i	0.992188	−	0.265856i	0.274019	−	0.961724i	$-0.411647\pi$
$619$	24.6854	−	6.61442i	0.992188	−	0.265856i	0.718170	+	0.695868i	$0.244980\pi$
$620$	−4.30232	−	2.48395i	−0.172785	−	0.0997577i
$621$		0			0
$622$	−7.83186	+	29.2289i	−0.314029	+	1.17197i
$623$	−0.160325	+	0.277691i	−0.00642329	+	0.0111255i
$624$		0			0
$625$	−6.13822	−	10.6317i	−0.245529	−	0.425268i
$626$	−32.3261	+	8.66175i	−1.29201	+	0.346193i
$627$		0			0
$628$	−8.33703	+	4.81339i	−0.332684	+	0.192075i
$629$	38.4735	+	38.4735i	1.53404	+	1.53404i
$630$		0			0
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.136440	−	0.990648i	$-0.456434\pi$
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.613484	+	0.789707i	$0.289767\pi$
$632$	0.729610	+	2.72294i	0.0290223	+	0.108313i
$633$		0			0
$634$	−9.66391	−	5.57946i	−0.383803	−	0.221589i
$635$	8.81142	+	32.8847i	0.349670	+	1.30499i
$636$		0			0
$637$	−20.1066	−	15.2505i	−0.796652	−	0.604246i
$638$		−	36.1449i		−	1.43099i
$639$		0			0
$640$	1.72162	+	2.98193i	0.0680529	+	0.117871i
$641$	11.4390	+	19.8130i	0.451814	+	0.782566i	0.998499	−	0.0547731i	$-0.0174436\pi$
$641$	11.4390	+	19.8130i	0.451814	+	0.782566i	−0.546684	+	0.837339i	$0.684110\pi$
$642$		0			0
$643$	9.35496	−	9.35496i	0.368924	−	0.368924i	−0.498161	−	0.867085i	$-0.665991\pi$
$643$	9.35496	−	9.35496i	0.368924	−	0.368924i	0.867085	+	0.498161i	$0.165991\pi$
$644$	0.0106414	−	0.0106414i	0.000419330	−	0.000419330i
$645$		0			0
$646$	−6.75998	−	11.7086i	−0.265968	−	0.460670i
$647$	5.87399	+	10.1741i	0.230930	+	0.399983i	0.958082	−	0.286493i	$-0.0924897\pi$
$647$	5.87399	+	10.1741i	0.230930	+	0.399983i	−0.727152	+	0.686477i	$0.759156\pi$
$648$		0			0
$649$		−	62.2606i		−	2.44394i
$650$	3.36346	+	24.4893i	0.131926	+	0.960548i
$651$		0			0
$652$	2.86883	+	10.7066i	0.112352	+	0.419303i
$653$	7.98654	+	4.61103i	0.312537	+	0.180444i	0.648061	−	0.761588i	$-0.275580\pi$
$653$	7.98654	+	4.61103i	0.312537	+	0.180444i	−0.335524	+	0.942032i	$0.608913\pi$
$654$		0			0
$655$	16.1523	+	60.2811i	0.631122	+	2.35538i
$656$	4.85352	−	1.30050i	0.189498	−	0.0507759i
$657$		0			0
$658$	−0.0161823	−	0.0161823i	−0.000630853	−	0.000630853i
$659$	−3.69702	+	2.13448i	−0.144015	+	0.0831474i	−0.570276	−	0.821453i	$-0.693164\pi$
$659$	−3.69702	+	2.13448i	−0.144015	+	0.0831474i	0.426261	+	0.904600i	$0.359831\pi$
$660$		0			0
$661$	43.1340	−	11.5577i	1.67772	−	0.449543i	0.710543	−	0.703654i	$-0.248449\pi$
$661$	43.1340	−	11.5577i	1.67772	−	0.449543i	0.967175	+	0.254110i	$0.0817827\pi$
$662$	−2.06979	−	3.58499i	−0.0804448	−	0.139335i
$663$		0			0
$664$	−7.34510	+	12.7221i	−0.285045	+	0.493713i
$665$	−0.0511626	+	0.190941i	−0.00198400	+	0.00740438i
$666$		0			0
$667$	−3.79947	−	2.19363i	−0.147116	−	0.0849375i
$668$	14.4157	−	3.86269i	0.557762	−	0.149452i
$669$		0			0
$670$	2.30073	+	2.30073i	0.0888850	+	0.0888850i
$671$	−0.0903350	−	0.0242052i	−0.00348734	−	0.000934431i
$672$		0			0
$673$			5.63994i			0.217404i	0.994074	+	0.108702i	$0.0346694\pi$
$673$			5.63994i			0.217404i	−0.994074	+	0.108702i	$0.965331\pi$
$674$	16.0573	+	4.30254i	0.618504	+	0.165728i
$675$		0			0
$676$	−3.22404	+	12.5939i	−0.124001	+	0.484380i
$677$	21.2676	+	12.2789i	0.817381	+	0.471915i	0.849512	−	0.527569i	$-0.176896\pi$
$677$	21.2676	+	12.2789i	0.817381	+	0.471915i	−0.0321318	+	0.999484i	$0.510230\pi$
$678$		0			0
$679$	0.00672593	−	0.0116497i	0.000258118	−	0.000447073i
$680$	−23.1055			−0.886056
$681$		0			0
$682$	−6.06394	−	1.62483i	−0.232200	−	0.0622179i
$683$	7.16139	+	26.7267i	0.274023	+	1.02267i	0.956493	+	0.291755i	$0.0942391\pi$
$683$	7.16139	+	26.7267i	0.274023	+	1.02267i	−0.682470	+	0.730913i	$0.739094\pi$
$684$		0			0
$685$	28.7786	−	49.8460i	1.09957	−	1.90452i
$686$	−0.398902			−0.0152301
$687$		0			0
$688$	−7.58793	+	4.38090i	−0.289287	+	0.167020i
$689$	2.28272	−	18.1213i	0.0869648	−	0.690367i
$690$		0			0
$691$	−5.58645	+	5.58645i	−0.212518	+	0.212518i	−0.805336	−	0.592818i	$-0.798015\pi$
$691$	−5.58645	+	5.58645i	−0.212518	+	0.212518i	0.592818	+	0.805336i	$0.298015\pi$
$692$	−16.5067	+	9.53013i	−0.627489	+	0.362281i
$693$		0			0
$694$	14.3923	−	14.3923i	0.546324	−	0.546324i
$695$	−4.53147	+	16.9117i	−0.171888	+	0.641496i
$696$		0			0
$697$	−8.72687	+	32.5691i	−0.330554	+	1.23364i
$698$		−	19.5584i		−	0.740298i
$699$		0			0
$700$	0.138137	+	0.138137i	0.00522109	+	0.00522109i
$701$	39.9569			1.50915			0.754575	−	0.656214i	$-0.227843\pi$
$701$	39.9569			1.50915			0.754575	+	0.656214i	$0.227843\pi$
$702$		0			0
$703$	16.3363			0.616136
$704$	3.07674	+	3.07674i	0.115959	+	0.115959i
$705$		0			0
$706$			10.1207i			0.380898i
$707$	−0.0404949	+	0.151129i	−0.00152297	+	0.00568380i
$708$		0			0
$709$	−13.1727	+	49.1613i	−0.494712	+	1.84629i	0.0369258	+	0.999318i	$0.488243\pi$
$709$	−13.1727	+	49.1613i	−0.494712	+	1.84629i	−0.531638	+	0.846972i	$0.678423\pi$
$710$	23.5166	−	23.5166i	0.882564	−	0.882564i
$711$		0			0
$712$	−9.74539	+	5.62650i	−0.365224	+	0.210862i
$713$	−0.538817	+	0.538817i	−0.0201789	+	0.0201789i
$714$		0			0
$715$	20.9507	+	49.7904i	0.783513	+	1.86205i
$716$	20.8769	−	12.0533i	0.780207	−	0.450453i
$717$		0			0
$718$	−1.56407			−0.0583705
$719$	−0.750575	+	1.30003i	−0.0279917	+	0.0484831i	−0.879682	−	0.475563i	$-0.842245\pi$
$719$	−0.750575	+	1.30003i	−0.0279917	+	0.0484831i	0.851690	+	0.524046i	$0.175578\pi$
$720$		0			0
$721$	−0.0308606	−	0.115173i	−0.00114931	−	0.00428928i
$722$	14.4316	+	3.86693i	0.537088	+	0.143912i
$723$		0			0
$724$	1.16505			0.0432988
$725$	28.4757	−	49.3214i	1.05756	−	1.83175i
$726$		0			0
$727$	−41.9032	−	24.1928i	−1.55410	−	0.897261i	−0.997801	−	0.0662809i	$-0.978887\pi$
$727$	−41.9032	−	24.1928i	−1.55410	−	0.897261i	−0.556301	−	0.830981i	$-0.687780\pi$
$728$	0.0398465	+	0.0946971i	0.00147681	+	0.00350971i
$729$		0			0
$730$	−30.7477	−	8.23882i	−1.13802	−	0.304932i
$731$		−	58.7952i		−	2.17462i
$732$		0			0
$733$	22.9793	+	6.15729i	0.848761	+	0.227425i	0.656882	−	0.753994i	$-0.271875\pi$
$733$	22.9793	+	6.15729i	0.848761	+	0.227425i	0.191879	+	0.981419i	$0.438542\pi$
$734$	−4.40783	−	4.40783i	−0.162696	−	0.162696i
$735$		0			0
$736$	0.510146	−	0.136693i	0.0188042	−	0.00503857i
$737$	3.56082	+	2.05584i	0.131164	+	0.0757279i
$738$		0			0
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	−0.282786	−	0.959183i	$-0.591259\pi$
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	0.724491	−	0.689284i	$-0.242075\pi$
$740$	13.9593	−	24.1783i	0.513155	−	0.888811i
$741$		0			0
$742$	−0.0721721	−	0.125006i	−0.00264952	−	0.00458911i
$743$	34.8450	−	9.33669i	1.27834	−	0.342530i	0.445119	−	0.895471i	$-0.353161\pi$
$743$	34.8450	−	9.33669i	1.27834	−	0.342530i	0.833220	+	0.552941i	$0.186495\pi$
$744$		0			0
$745$	15.7663	−	9.10267i	0.577632	−	0.333496i
$746$	−14.9264	−	14.9264i	−0.546493	−	0.546493i
$747$		0			0
$748$	−28.2032	+	7.55702i	−1.03121	+	0.276312i
$749$	−0.0242902	−	0.0906521i	−0.000887543	−	0.00331236i
$750$		0			0
$751$	−15.1601	−	8.75269i	−0.553200	−	0.319390i	0.197212	−	0.980361i	$-0.436811\pi$
$751$	−15.1601	−	8.75269i	−0.553200	−	0.319390i	−0.750412	+	0.660971i	$0.770145\pi$
$752$	−0.207869	−	0.775777i	−0.00758019	−	0.0282897i
$753$		0			0
$754$	23.6596	−	18.3657i	0.861630	−	0.668839i
$755$			33.5263i			1.22015i
$756$		0			0
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	0.880484	−	0.474076i	$-0.157218\pi$
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	−0.850804	+	0.525483i	$0.823885\pi$
$758$	0.667158	+	1.15555i	0.0242323	+	0.0419715i
$759$		0			0
$760$	−4.90544	+	4.90544i	−0.177939	+	0.177939i
$761$	−12.5216	+	12.5216i	−0.453909	+	0.453909i	−0.896650	−	0.442741i	$-0.854006\pi$
$761$	−12.5216	+	12.5216i	−0.453909	+	0.453909i	0.442741	+	0.896650i	$0.354006\pi$
$762$		0			0
$763$	−0.108867	−	0.188563i	−0.00394125	−	0.00682644i
$764$	5.78229	+	10.0152i	0.209196	+	0.362338i
$765$		0			0
$766$			25.8573i			0.934261i
$767$	40.7542	−	31.6353i	1.47155	−	1.14229i
$768$		0			0
$769$	5.30157	+	19.7857i	0.191179	+	0.713492i	0.993223	+	0.116226i	$0.0370796\pi$
$769$	5.30157	+	19.7857i	0.191179	+	0.713492i	−0.802043	+	0.597266i	$0.796254\pi$
$770$	0.369714	+	0.213454i	0.0133236	+	0.00769236i
$771$		0			0
$772$	0.372710	+	1.39097i	0.0134141	+	0.0500622i
$773$	8.74973	−	2.34448i	0.314706	−	0.0843252i	−0.0980088	−	0.995186i	$-0.531247\pi$
$773$	8.74973	−	2.34448i	0.314706	−	0.0843252i	0.412715	+	0.910860i	$0.364581\pi$
$774$		0			0
$775$	−6.99444	−	6.99444i	−0.251248	−	0.251248i
$776$	0.408837	−	0.236042i	0.0146764	−	0.00847342i
$777$		0			0
$778$	14.1089	−	3.78047i	0.505829	−	0.135536i
$779$	5.06185	+	8.76738i	0.181360	+	0.314124i
$780$		0			0
$781$	21.0135	−	36.3965i	0.751923	−	1.30237i
$782$	−0.917267	+	3.42329i	−0.0328014	+	0.122416i
$783$		0			0
$784$	−6.06147	−	3.49959i	−0.216481	−	0.124986i
$785$	−32.0178	+	8.57914i	−1.14276	+	0.306203i
$786$		0			0
$787$	−13.3787	−	13.3787i	−0.476900	−	0.476900i	0.427239	−	0.904139i	$-0.359486\pi$
$787$	−13.3787	−	13.3787i	−0.476900	−	0.476900i	−0.904139	+	0.427239i	$0.859486\pi$
$788$	−4.01546	−	1.07594i	−0.143045	−	0.0383288i
$789$		0			0
$790$			9.70646i			0.345341i
$791$	−0.0160161	−	0.00429150i	−0.000569467	−	0.000152588i
$792$		0			0
$793$	−0.0300562	−	0.0714299i	−0.00106733	−	0.00253655i
$794$	2.58388	+	1.49180i	0.0916983	+	0.0529421i
$795$		0			0
$796$	−1.03021	+	1.78437i	−0.0365147	+	0.0632454i
$797$	−33.7072			−1.19397			−0.596986	−	0.802252i	$-0.703635\pi$
$797$	−33.7072			−1.19397			−0.596986	+	0.802252i	$0.703635\pi$
$798$		0			0
$799$	5.20578	+	1.39488i	0.184167	+	0.0493475i
$800$	1.77443	+	6.62226i	0.0627355	+	0.234132i
$801$		0			0
$802$	5.53740	−	9.59106i	0.195533	−	0.338672i
$803$	−40.2260			−1.41955
$804$		0			0
$805$	0.0448757	−	0.0259090i	0.00158166	−	0.000913171i
$806$	−2.01759	−	4.79490i	−0.0710666	−	0.168893i
$807$		0			0
$808$	−3.88263	+	3.88263i	−0.136591	+	0.136591i
$809$	−9.20764	+	5.31603i	−0.323723	+	0.186902i	−0.653051	−	0.757314i	$-0.726511\pi$
$809$	−9.20764	+	5.31603i	−0.323723	+	0.186902i	0.329328	+	0.944216i	$0.393178\pi$
$810$		0			0
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	−0.559874	−	0.828578i	$-0.689151\pi$
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	0.828578	+	0.559874i	$0.189151\pi$
$812$	0.0612635	−	0.228638i	0.00214993	−	0.00802363i
$813$		0			0
$814$	9.13123	−	34.0782i	0.320049	−	1.19444i
$815$			38.1659i			1.33689i
$816$		0			0
$817$	−12.4826	−	12.4826i	−0.436710	−	0.436710i
$818$	14.6788			0.513233
$819$		0			0
$820$	17.3013			0.604189
$821$	−10.8656	−	10.8656i	−0.379212	−	0.379212i	0.491606	−	0.870818i	$-0.336410\pi$
$821$	−10.8656	−	10.8656i	−0.379212	−	0.379212i	−0.870818	+	0.491606i	$0.836410\pi$
$822$		0			0
$823$			15.2209i			0.530567i	0.964170	+	0.265284i	$0.0854656\pi$
$823$			15.2209i			0.530567i	−0.964170	+	0.265284i	$0.914534\pi$
$824$	1.08303	−	4.04193i	0.0377292	−	0.140807i
$825$		0			0
$826$	0.105528	−	0.393835i	0.00367178	−	0.0137033i
$827$	16.9790	−	16.9790i	0.590418	−	0.590418i	−0.347326	−	0.937744i	$-0.612910\pi$
$827$	16.9790	−	16.9790i	0.590418	−	0.590418i	0.937744	+	0.347326i	$0.112910\pi$
$828$		0			0
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	−0.732335	−	0.680944i	$-0.761570\pi$
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	0.223547	+	0.974693i	$0.428236\pi$
$830$	−35.7667	+	35.7667i	−1.24148	+	1.24148i
$831$		0			0
$832$	−0.450627	+	3.57728i	−0.0156227	+	0.124020i
$833$	40.6750	−	23.4837i	1.40930	−	0.813662i
$834$		0			0
$835$	51.3878			1.77835
$836$	−4.38330	+	7.59210i	−0.151600	+	0.262578i
$837$		0			0
$838$	−7.28940	−	27.2044i	−0.251808	−	0.939761i
$839$	−22.8417	−	6.12041i	−0.788583	−	0.211300i	−0.158017	−	0.987436i	$-0.550510\pi$
$839$	−22.8417	−	6.12041i	−0.788583	−	0.211300i	−0.630565	+	0.776136i	$0.717177\pi$
$840$		0			0
$841$	−40.0056			−1.37950
$842$	3.63954	−	6.30387i	0.125427	−	0.217246i
$843$		0			0
$844$	−16.5841	−	9.57481i	−0.570847	−	0.329579i
$845$	−21.9462	+	39.0129i	−0.754972	+	1.34208i
$846$		0			0
$847$	0.218335	+	0.0585027i	0.00750208	+	0.00201018i
$848$		−	5.06566i		−	0.173956i
$849$		0			0
$850$	−44.4381	−	11.9071i	−1.52421	−	0.408412i
$851$	−3.02805	−	3.02805i	−0.103800	−	0.103800i
$852$		0			0
$853$	55.3955	−	14.8432i	1.89671	−	0.508221i	0.899208	−	0.437522i	$-0.144144\pi$
$853$	55.3955	−	14.8432i	1.89671	−	0.508221i	0.997498	−	0.0706986i	$-0.0225229\pi$
$854$	−0.000530397	0	0.000306225i	−1.81498e−5	0	1.04788e-5i
$855$		0			0
$856$	0.852446	−	3.18137i	0.0291360	−	0.108737i
$857$	9.63613	−	16.6903i	0.329164	−	0.570129i	−0.653182	−	0.757201i	$-0.726566\pi$
$857$	9.63613	−	16.6903i	0.329164	−	0.570129i	0.982346	+	0.187072i	$0.0598998\pi$
$858$		0			0
$859$	−21.1198	−	36.5805i	−0.720597	−	1.24811i	−0.960761	−	0.277378i	$-0.910534\pi$
$859$	−21.1198	−	36.5805i	−0.720597	−	1.24811i	0.240164	−	0.970732i	$-0.422799\pi$
$860$	−29.1409	+	7.80829i	−0.993697	+	0.266260i
$861$		0			0
$862$	−16.4143	+	9.47681i	−0.559074	+	0.322781i
$863$	4.51248	+	4.51248i	0.153607	+	0.153607i	0.779727	−	0.626120i	$-0.215358\pi$
$863$	4.51248	+	4.51248i	0.153607	+	0.153607i	−0.626120	+	0.779727i	$0.715358\pi$
$864$		0			0
$865$	−63.3927	+	16.9860i	−2.15542	+	0.577542i
$866$	8.15738	+	30.4438i	0.277199	+	1.03452i
$867$		0			0
$868$	−0.0356041	−	0.0205560i	−0.00120848	−	0.000697717i
$869$	3.17465	+	11.8480i	0.107693	+	0.401914i
$870$		0			0
$871$	0.463595	+	3.37542i	0.0157083	+	0.114372i
$872$		−	7.64122i		−	0.258764i
$873$		0			0
$874$	0.532043	+	0.921525i	0.0179966	+	0.0311711i
$875$	0.0910429	+	0.157691i	0.00307781	+	0.00533093i
$876$		0			0
$877$	−8.53740	+	8.53740i	−0.288288	+	0.288288i	−0.836403	−	0.548115i	$-0.815346\pi$
$877$	−8.53740	+	8.53740i	−0.288288	+	0.288288i	0.548115	+	0.836403i	$0.315346\pi$
$878$	9.11262	−	9.11262i	0.307536	−	0.307536i
$879$		0			0
$880$	7.49104	+	12.9749i	0.252523	+	0.437382i
$881$	−23.1313	−	40.0646i	−0.779314	−	1.34981i	−0.932337	−	0.361589i	$-0.882234\pi$
$881$	−23.1313	−	40.0646i	−0.779314	−	1.34981i	0.153023	−	0.988223i	$-0.451099\pi$
$882$		0			0
$883$			5.00836i			0.168545i	0.996443	+	0.0842723i	$0.0268566\pi$
$883$			5.00836i			0.168545i	−0.996443	+	0.0842723i	$0.973143\pi$
$884$	−19.2770	−	14.6213i	−0.648356	−	0.491767i
$885$		0			0
$886$	3.25809	+	12.1594i	0.109458	+	0.408502i
$887$	18.7915	+	10.8493i	0.630958	+	0.364284i	0.781123	−	0.624377i	$-0.214647\pi$
$887$	18.7915	+	10.8493i	0.630958	+	0.364284i	−0.150165	+	0.988661i	$0.547981\pi$
$888$		0			0
$889$	0.0729193	+	0.272138i	0.00244563	+	0.00912723i
$890$	−37.4265	+	10.0284i	−1.25454	+	0.336153i
$891$		0			0
$892$	18.6817	+	18.6817i	0.625509	+	0.625509i
$893$	1.40136	−	0.809076i	0.0468947	−	0.0270747i
$894$		0			0
$895$	80.1764	−	21.4832i	2.68000	−	0.718104i
$896$	0.0142473	+	0.0246771i	0.000475970	+	0.000824403i
$897$		0			0
$898$	2.25983	−	3.91414i	0.0754115	−	0.130616i
$899$	−3.10202	+	11.5769i	−0.103458	+	0.386111i
$900$		0			0
$901$	29.4385	+	16.9963i	0.980740	+	0.566230i
$902$	21.1185	−	5.65867i	0.703167	−	0.188413i
$903$		0			0
$904$	−0.411467	−	0.411467i	−0.0136852	−	0.0136852i
$905$	3.87486	+	1.03827i	0.128805	+	0.0345131i
$906$		0			0
$907$		−	30.7861i		−	1.02224i	−0.859511	−	0.511118i	$-0.829232\pi$
$907$		−	30.7861i		−	1.02224i	0.859511	−	0.511118i	$-0.170768\pi$
$908$	−4.95918	−	1.32881i	−0.164576	−	0.0440981i
$909$		0			0
$910$	0.0481342	+	0.350464i	0.00159563	+	0.0116178i
$911$	−13.1044	−	7.56582i	−0.434168	−	0.250667i	0.266953	−	0.963710i	$-0.413983\pi$
$911$	−13.1044	−	7.56582i	−0.434168	−	0.250667i	−0.701120	+	0.713043i	$0.747316\pi$
$912$		0			0
$913$	−31.9597	+	55.3559i	−1.05771	+	1.83201i
$914$	10.1709			0.336422
$915$		0			0
$916$	7.67020	+	2.05522i	0.253431	+	0.0679065i
$917$	0.133669	+	0.498859i	0.00441414	+	0.0164738i
$918$		0			0
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.0323673	+	0.999476i	$0.510305\pi$
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.849388	+	0.527769i	$0.823029\pi$
$920$	1.81852			0.0599547
$921$		0			0
$922$	−23.5621	+	13.6036i	−0.775977	+	0.448011i
$923$	34.5014	−	4.73858i	1.13563	−	0.155972i
$924$		0			0
$925$	39.3075	−	39.3075i	1.29242	−	1.29242i
$926$	−10.2633	+	5.92551i	−0.337272	+	0.194724i
$927$		0			0
$928$	5.87391	−	5.87391i	0.192821	−	0.192821i
$929$	13.9078	−	51.9045i	0.456299	−	1.70293i	−0.227940	−	0.973675i	$-0.573199\pi$
$929$	13.9078	−	51.9045i	0.456299	−	1.70293i	0.684239	−	0.729257i	$-0.260134\pi$
$930$		0			0
$931$	3.64981	−	13.6213i	0.119618	−	0.446419i
$932$		−	0.240333i		−	0.00787238i
$933$		0			0
$934$	−0.435492	−	0.435492i	−0.0142497	−	0.0142497i
$935$	−100.536			−3.28787
$936$		0			0
$937$	−2.41921			−0.0790323			−0.0395162	−	0.999219i	$-0.512582\pi$
$937$	−2.41921			−0.0790323			−0.0395162	+	0.999219i	$0.512582\pi$
$938$	0.0190398	+	0.0190398i	0.000621671	+	0.000621671i
$939$		0			0
$940$		−	2.76541i		−	0.0901977i
$941$	0.0115889	−	0.0432503i	0.000377786	−	0.00140992i	−0.965737	−	0.259524i	$-0.916434\pi$
$941$	0.0115889	−	0.0432503i	0.000377786	−	0.00140992i	0.966114	+	0.258114i	$0.0831010\pi$
$942$		0			0
$943$	0.686846	−	2.56335i	0.0223668	−	0.0834740i
$944$	10.1180	−	10.1180i	0.329311	−	0.329311i
$945$		0			0
$946$	−33.0163	+	19.0620i	−1.07345	+	0.619759i
$947$	−16.6276	+	16.6276i	−0.540323	+	0.540323i	−0.923624	−	0.383301i	$-0.874787\pi$
$947$	−16.6276	+	16.6276i	−0.540323	+	0.540323i	0.383301	+	0.923624i	$0.374787\pi$
$948$		0			0
$949$	−20.4393	−	26.3309i	−0.663489	−	0.854739i
$950$	−11.9624	+	6.90651i	−0.388112	+	0.224077i
$951$		0			0
$952$	−0.191211			−0.00619718
$953$	−13.8021	+	23.9060i	−0.447095	+	0.774392i	−0.998196	−	0.0600474i	$-0.980875\pi$
$953$	−13.8021	+	23.9060i	−0.447095	+	0.774392i	0.551100	+	0.834439i	$0.314208\pi$
$954$		0			0
$955$	10.3061	+	38.4627i	0.333496	+	1.24462i
$956$	6.49603	+	1.74060i	0.210096	+	0.0562952i
$957$		0			0
$958$	20.0403			0.647474
$959$	0.238159	−	0.412503i	0.00769055	−	0.0133204i
$960$		0			0
$961$	−25.0440	−	14.4592i	−0.807871	−	0.466425i
$962$	26.9464	−	11.3385i	0.868788	−	0.365567i
$963$		0			0
$964$	−25.0664	−	6.71652i	−0.807335	−	0.216325i
$965$			4.95840i			0.159617i
$966$		0			0
$967$	31.0146	+	8.31034i	0.997363	+	0.267243i	0.720340	−	0.693621i	$-0.243986\pi$
$967$	31.0146	+	8.31034i	0.997363	+	0.267243i	0.277023	+	0.960863i	$0.410652\pi$
$968$	5.60920	+	5.60920i	0.180287	+	0.180287i
$969$		0			0
$970$	1.57011	−	0.420710i	0.0504132	−	0.0135082i
$971$	16.6187	+	9.59478i	0.533318	+	0.307911i	0.742366	−	0.669994i	$-0.233703\pi$
$971$	16.6187	+	9.59478i	0.533318	+	0.307911i	−0.209049	+	0.977905i	$0.567037\pi$
$972$		0			0
$973$	−0.0375004	+	0.139953i	−0.00120221	+	0.00448670i
$974$	10.5733	−	18.3135i	0.338791	−	0.586804i
$975$		0			0
$976$	−0.0107467	−	0.0186139i	−0.000343995	−	0.000595817i
$977$	−29.5657	+	7.92211i	−0.945891	+	0.253451i	−0.698618	−	0.715495i	$-0.746201\pi$
$977$	−29.5657	+	7.92211i	−0.945891	+	0.253451i	−0.247273	+	0.968946i	$0.579535\pi$
$978$		0			0
$979$	−42.4038	+	24.4818i	−1.35523	+	0.782443i
$980$	−17.0412	−	17.0412i	−0.544360	−	0.544360i
$981$		0			0
$982$	19.0783	−	5.11201i	0.608812	−	0.163131i
$983$	5.86347	+	21.8828i	0.187016	+	0.697952i	0.994190	+	0.107639i	$0.0343290\pi$
$983$	5.86347	+	21.8828i	0.187016	+	0.697952i	−0.807175	+	0.590313i	$0.799004\pi$
$984$		0			0
$985$	−12.3962	−	7.15696i	−0.394976	−	0.228040i
$986$	14.4274	+	53.8437i	0.459462	+	1.71473i
$987$		0			0
$988$	−7.19681	+	0.988441i	−0.228961	+	0.0314465i
$989$			4.62747i			0.147145i
$990$		0			0
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	−0.995997	−	0.0893845i	$-0.971510\pi$
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	0.420589	−	0.907251i	$-0.361823\pi$
$992$	−0.721399	−	1.24950i	−0.0229045	−	0.0396717i
$993$		0			0
$994$	0.194613	−	0.194613i	0.00617275	−	0.00617275i
$995$	−5.01657	+	5.01657i	−0.159036	+	0.159036i
$996$		0			0
$997$	8.88423	+	15.3879i	0.281366	+	0.487341i	0.971722	−	0.236130i	$-0.0758790\pi$
$997$	8.88423	+	15.3879i	0.281366	+	0.487341i	−0.690355	+	0.723471i	$0.742546\pi$
$998$	2.65476	+	4.59817i	0.0840348	+	0.145553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.197.8		56
3.2	odd	2		234.2.y.a.119.3	yes	56
9.4	even	3		234.2.z.a.41.2	yes	56
9.5	odd	6		702.2.bc.a.665.8		56
13.7	odd	12		702.2.bc.a.683.8		56
39.20	even	12		234.2.z.a.137.2	yes	56
117.59	even	12	inner	702.2.bb.a.449.8		56
117.85	odd	12		234.2.y.a.59.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.3	✓	56	117.85	odd	12
234.2.y.a.119.3	yes	56	3.2	odd	2
234.2.z.a.41.2	yes	56	9.4	even	3
234.2.z.a.137.2	yes	56	39.20	even	12
702.2.bb.a.197.8		56	1.1	even	1	trivial
702.2.bb.a.449.8		56	117.59	even	12	inner
702.2.bc.a.665.8		56	9.5	odd	6
702.2.bc.a.683.8		56	13.7	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.891175 + 3.32591i) q^{5} +(-0.00737496 + 0.0275237i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.98193 + 1.72162i) q^{10} +(-3.07674 + 3.07674i) q^{11} +(-3.57728 - 0.450627i) q^{13} +(-0.0246771 + 0.0142473i) q^{14} -1.00000 q^{16} +(3.35521 - 5.81139i) q^{17} +(-0.521462 - 1.94612i) q^{19} +(-3.32591 - 0.891175i) q^{20} -4.35116 q^{22} +(-0.264071 + 0.457384i) q^{23} +(-5.93735 - 3.42793i) q^{25} +(-2.21088 - 2.84816i) q^{26} +(-0.0275237 - 0.00737496i) q^{28} +8.30696i q^{29} +(1.39364 + 0.373424i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.48176 - 1.73678i) q^{34} +(-0.0849690 - 0.0490569i) q^{35} +(-2.09857 + 7.83198i) q^{37} +(1.00739 - 1.74484i) q^{38} +(-1.72162 - 2.98193i) q^{40} +(-4.85352 + 1.30050i) q^{41} +(7.58793 - 4.38090i) q^{43} +(-3.07674 - 3.07674i) q^{44} +(-0.510146 + 0.136693i) q^{46} +(0.207869 + 0.775777i) q^{47} +(6.06147 + 3.49959i) q^{49} +(-1.77443 - 6.62226i) q^{50} +(0.450627 - 3.57728i) q^{52} +5.06566i q^{53} +(-7.49104 - 12.9749i) q^{55} +(-0.0142473 - 0.0246771i) q^{56} +(-5.87391 + 5.87391i) q^{58} +(-10.1180 + 10.1180i) q^{59} +(0.0107467 + 0.0186139i) q^{61} +(0.721399 + 1.24950i) q^{62} -1.00000i q^{64} +(4.68673 - 11.4961i) q^{65} +(-0.244574 - 0.912763i) q^{67} +(5.81139 + 3.35521i) q^{68} +(-0.0253937 - 0.0947706i) q^{70} +(-9.32969 + 2.49988i) q^{71} +(6.53713 + 6.53713i) q^{73} +(-7.02196 + 4.05413i) q^{74} +(1.94612 - 0.521462i) q^{76} +(-0.0619924 - 0.107374i) q^{77} +(1.40950 - 2.44132i) q^{79} +(0.891175 - 3.32591i) q^{80} +(-4.35155 - 2.51237i) q^{82} +(14.1896 - 3.80210i) q^{83} +(16.3381 + 16.3381i) q^{85} +(8.46324 + 2.26772i) q^{86} -4.35116i q^{88} +(10.8696 + 2.91249i) q^{89} +(0.0387852 - 0.0951367i) q^{91} +(-0.457384 - 0.264071i) q^{92} +(-0.401572 + 0.695542i) q^{94} +6.93734 q^{95} +(-0.455998 - 0.122184i) q^{97} +(1.81152 + 6.76070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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