LMFDB - Embedded newform 784.2.bp.c.255.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(47,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 5]))

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

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

chi := DirichletCharacter("784.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bp (of order $42$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			255.8
Character	$\chi$	$=$	784.255
Dual form			784.2.bp.c.495.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30128 - 0.887199i) q^{3} +(-3.55166 + 0.266160i) q^{5} +(2.60649 - 0.454131i) q^{7} +(-0.189810 + 0.483628i) q^{9} +O(q^{10})$	\(q+(1.30128 - 0.887199i) q^{3} +(-3.55166 + 0.266160i) q^{5} +(2.60649 - 0.454131i) q^{7} +(-0.189810 + 0.483628i) q^{9} +(3.28740 - 1.29021i) q^{11} +(1.33630 + 1.06566i) q^{13} +(-4.38557 + 3.49738i) q^{15} +(4.60104 - 4.95874i) q^{17} +(1.26170 + 2.18533i) q^{19} +(2.98887 - 2.90342i) q^{21} +(-4.90853 - 5.29013i) q^{23} +(7.59929 - 1.14541i) q^{25} +(1.23345 + 5.40412i) q^{27} +(0.815942 - 3.57488i) q^{29} +(2.53827 - 4.39641i) q^{31} +(3.13316 - 4.59550i) q^{33} +(-9.13648 + 2.30666i) q^{35} +(-2.30934 + 0.712338i) q^{37} +(2.68436 + 0.201165i) q^{39} +(3.85892 - 8.01313i) q^{41} +(-0.185940 - 0.386109i) q^{43} +(0.545418 - 1.76820i) q^{45} +(12.8599 + 1.93832i) q^{47} +(6.58753 - 2.36737i) q^{49} +(1.58786 - 10.5348i) q^{51} +(-3.74376 - 1.15480i) q^{53} +(-11.3323 + 5.45735i) q^{55} +(3.58065 + 1.72435i) q^{57} +(-0.392828 + 5.24192i) q^{59} +(3.85033 + 12.4825i) q^{61} +(-0.275107 + 1.34677i) q^{63} +(-5.02972 - 3.42921i) q^{65} +(-8.82791 - 5.09679i) q^{67} +(-11.0808 - 2.52912i) q^{69} +(-11.4127 + 2.60487i) q^{71} +(0.665073 + 4.41247i) q^{73} +(8.87261 - 8.23258i) q^{75} +(7.98262 - 4.85581i) q^{77} +(-5.38475 + 3.10889i) q^{79} +(5.25704 + 4.87782i) q^{81} +(5.83732 + 7.31977i) q^{83} +(-15.0215 + 18.8364i) q^{85} +(-2.10986 - 5.37583i) q^{87} +(-7.37597 - 2.89485i) q^{89} +(3.96700 + 2.17078i) q^{91} +(-0.597487 - 7.97291i) q^{93} +(-5.06277 - 7.42573i) q^{95} -5.29761i q^{97} +1.83477i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{5} + 12 q^{9}+O(q^{10}) $ 120 * q + 6 * q^5 + 12 * q^9	$ 120 q + 6 q^{5} + 12 q^{9} - 32 q^{17} - 14 q^{21} - 8 q^{25} - 28 q^{29} + 42 q^{33} + 28 q^{37} + 56 q^{41} + 186 q^{45} + 84 q^{49} + 128 q^{53} - 70 q^{57} + 8 q^{61} + 4 q^{65} - 56 q^{69} + 60 q^{73} + 84 q^{77} + 34 q^{81} + 12 q^{85} + 22 q^{89} - 112 q^{93}+O(q^{100}) $ 120 * q + 6 * q^5 + 12 * q^9 - 32 * q^17 - 14 * q^21 - 8 * q^25 - 28 * q^29 + 42 * q^33 + 28 * q^37 + 56 * q^41 + 186 * q^45 + 84 * q^49 + 128 * q^53 - 70 * q^57 + 8 * q^61 + 4 * q^65 - 56 * q^69 + 60 * q^73 + 84 * q^77 + 34 * q^81 + 12 * q^85 + 22 * q^89 - 112 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{42}\right)$

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			0
$2$		0			0
$3$	1.30128	−	0.887199i	0.751296	−	0.512225i	−0.126085	−	0.992019i	$-0.540241\pi$
$3$	1.30128	−	0.887199i	0.751296	−	0.512225i	0.877381	+	0.479795i	$0.159289\pi$
$4$		0			0
$5$	−3.55166	+	0.266160i	−1.58835	+	0.119030i	−0.839369	−	0.543561i	$-0.817076\pi$
$5$	−3.55166	+	0.266160i	−1.58835	+	0.119030i	−0.748981	+	0.662592i	$0.769456\pi$
$6$		0			0
$7$	2.60649	−	0.454131i	0.985159	−	0.171645i
$7$	2.60649	−	0.454131i	0.985159	−	0.171645i
$8$		0			0
$9$	−0.189810	+	0.483628i	−0.0632701	+	0.161209i
$10$		0			0
$11$	3.28740	−	1.29021i	0.991187	−	0.389012i	0.186334	−	0.982486i	$-0.440339\pi$
$11$	3.28740	−	1.29021i	0.991187	−	0.389012i	0.804853	+	0.593474i	$0.202244\pi$
$12$		0			0
$13$	1.33630	+	1.06566i	0.370623	+	0.295562i	0.791035	−	0.611771i	$-0.209543\pi$
$13$	1.33630	+	1.06566i	0.370623	+	0.295562i	−0.420411	+	0.907334i	$0.638114\pi$
$14$		0			0
$15$	−4.38557	+	3.49738i	−1.13235	+	0.903019i
$16$		0			0
$17$	4.60104	−	4.95874i	1.11592	−	1.20267i	0.138719	−	0.990332i	$-0.455701\pi$
$17$	4.60104	−	4.95874i	1.11592	−	1.20267i	0.977196	−	0.212339i	$-0.0681081\pi$
$18$		0			0
$19$	1.26170	+	2.18533i	0.289454	+	0.501349i	0.973679	−	0.227922i	$-0.0731930\pi$
$19$	1.26170	+	2.18533i	0.289454	+	0.501349i	−0.684226	+	0.729270i	$0.739860\pi$
$20$		0			0
$21$	2.98887	−	2.90342i	0.652224	−	0.633579i
$22$		0			0
$23$	−4.90853	−	5.29013i	−1.02350	−	1.10307i	−0.994631	−	0.103486i	$-0.967000\pi$
$23$	−4.90853	−	5.29013i	−1.02350	−	1.10307i	−0.0288676	−	0.999583i	$-0.509190\pi$
$24$		0			0
$25$	7.59929	−	1.14541i	1.51986	−	0.229082i
$26$		0			0
$27$	1.23345	+	5.40412i	0.237378	+	1.04002i
$28$		0			0
$29$	0.815942	−	3.57488i	0.151517	−	0.663838i	−0.840928	−	0.541147i	$-0.817990\pi$
$29$	0.815942	−	3.57488i	0.151517	−	0.663838i	0.992445	−	0.122691i	$-0.0391525\pi$
$30$		0			0
$31$	2.53827	−	4.39641i	0.455886	−	0.789618i	−0.542853	−	0.839828i	$-0.682656\pi$
$31$	2.53827	−	4.39641i	0.455886	−	0.789618i	0.998739	+	0.0502101i	$0.0159891\pi$
$32$		0			0
$33$	3.13316	−	4.59550i	0.545413	−	0.799974i
$34$		0			0
$35$	−9.13648	+	2.30666i	−1.54435	+	0.389897i
$36$		0			0
$37$	−2.30934	+	0.712338i	−0.379654	+	0.117108i	−0.478708	−	0.877974i	$-0.658895\pi$
$37$	−2.30934	+	0.712338i	−0.379654	+	0.117108i	0.0990538	+	0.995082i	$0.468418\pi$
$38$		0			0
$39$	2.68436	+	0.201165i	0.429842	+	0.0322122i
$40$		0			0
$41$	3.85892	−	8.01313i	0.602662	−	1.25144i	−0.346912	−	0.937898i	$-0.612770\pi$
$41$	3.85892	−	8.01313i	0.602662	−	1.25144i	0.949574	−	0.313543i	$-0.101516\pi$
$42$		0			0
$43$	−0.185940	−	0.386109i	−0.0283556	−	0.0588811i	0.886310	−	0.463093i	$-0.153260\pi$
$43$	−0.185940	−	0.386109i	−0.0283556	−	0.0588811i	−0.914666	+	0.404212i	$0.867546\pi$
$44$		0			0
$45$	0.545418	−	1.76820i	0.0813062	−	0.263588i
$46$		0			0
$47$	12.8599	+	1.93832i	1.87581	+	0.282733i	0.985119	−	0.171873i	$-0.0549819\pi$
$47$	12.8599	+	1.93832i	1.87581	+	0.282733i	0.890693	+	0.454606i	$0.150220\pi$
$48$		0			0
$49$	6.58753	−	2.36737i	0.941076	−	0.338196i
$50$		0			0
$51$	1.58786	−	10.5348i	0.222345	−	1.47516i
$52$		0			0
$53$	−3.74376	−	1.15480i	−0.514245	−	0.158624i	0.0267618	−	0.999642i	$-0.491480\pi$
$53$	−3.74376	−	1.15480i	−0.514245	−	0.158624i	−0.541007	+	0.841018i	$0.681957\pi$
$54$		0			0
$55$	−11.3323	+	5.45735i	−1.52805	+	0.735869i
$56$		0			0
$57$	3.58065	+	1.72435i	0.474268	+	0.228396i
$58$		0			0
$59$	−0.392828	+	5.24192i	−0.0511418	+	0.682440i	0.911437	+	0.411439i	$0.134974\pi$
$59$	−0.392828	+	5.24192i	−0.0511418	+	0.682440i	−0.962579	+	0.271001i	$0.912645\pi$
$60$		0			0
$61$	3.85033	+	12.4825i	0.492984	+	1.59822i	0.770463	+	0.637484i	$0.220025\pi$
$61$	3.85033	+	12.4825i	0.492984	+	1.59822i	−0.277479	+	0.960732i	$0.589499\pi$
$62$		0			0
$63$	−0.275107	+	1.34677i	−0.0346602	+	0.169677i
$64$		0			0
$65$	−5.02972	−	3.42921i	−0.623861	−	0.425341i
$66$		0			0
$67$	−8.82791	−	5.09679i	−1.07850	−	0.622672i	−0.148009	−	0.988986i	$-0.547286\pi$
$67$	−8.82791	−	5.09679i	−1.07850	−	0.622672i	−0.930491	+	0.366314i	$0.880620\pi$
$68$		0			0
$69$	−11.0808	−	2.52912i	−1.33397	−	0.304470i
$70$		0			0
$71$	−11.4127	+	2.60487i	−1.35444	+	0.309142i	−0.837292	−	0.546755i	$-0.815863\pi$
$71$	−11.4127	+	2.60487i	−1.35444	+	0.309142i	−0.517146	+	0.855897i	$0.673006\pi$
$72$		0			0
$73$	0.665073	+	4.41247i	0.0778409	+	0.516440i	0.993441	+	0.114349i	$0.0364784\pi$
$73$	0.665073	+	4.41247i	0.0778409	+	0.516440i	−0.915600	+	0.402091i	$0.868284\pi$
$74$		0			0
$75$	8.87261	−	8.23258i	1.02452	−	0.950616i
$76$		0			0
$77$	7.98262	−	4.85581i	0.909704	−	0.553371i
$78$		0			0
$79$	−5.38475	+	3.10889i	−0.605832	+	0.349777i	−0.771332	−	0.636432i	$-0.780409\pi$
$79$	−5.38475	+	3.10889i	−0.605832	+	0.349777i	0.165500	+	0.986210i	$0.447076\pi$
$80$		0			0
$81$	5.25704	+	4.87782i	0.584116	+	0.541980i
$82$		0			0
$83$	5.83732	+	7.31977i	0.640729	+	0.803449i	0.991094	−	0.133164i	$-0.0425138\pi$
$83$	5.83732	+	7.31977i	0.640729	+	0.803449i	−0.350365	+	0.936613i	$0.613942\pi$
$84$		0			0
$85$	−15.0215	+	18.8364i	−1.62931	+	2.04309i
$86$		0			0
$87$	−2.10986	−	5.37583i	−0.226200	−	0.576349i
$88$		0			0
$89$	−7.37597	−	2.89485i	−0.781851	−	0.306854i	−0.0593621	−	0.998237i	$-0.518907\pi$
$89$	−7.37597	−	2.89485i	−0.781851	−	0.306854i	−0.722489	+	0.691383i	$0.757002\pi$
$90$		0			0
$91$	3.96700	+	2.17078i	0.415855	+	0.227560i
$92$		0			0
$93$	−0.597487	−	7.97291i	−0.0619565	−	0.826753i
$94$		0			0
$95$	−5.06277	−	7.42573i	−0.519430	−	0.761863i
$96$		0			0
$97$		−	5.29761i		−	0.537891i	−0.963155	−	0.268945i	$-0.913325\pi$
$97$		−	5.29761i		−	0.537891i	0.963155	−	0.268945i	$-0.0866751\pi$
$98$		0			0
$99$			1.83477i			0.184402i
$100$		0			0
$101$	−6.88842	−	10.1035i	−0.685423	−	1.00533i	−0.998454	−	0.0555881i	$-0.982297\pi$
$101$	−6.88842	−	10.1035i	−0.685423	−	1.00533i	0.313031	−	0.949743i	$-0.398656\pi$
$102$		0			0
$103$	0.889060	+	11.8637i	0.0876017	+	1.16896i	0.851759	+	0.523934i	$0.175536\pi$
$103$	0.889060	+	11.8637i	0.0876017	+	1.16896i	−0.764157	+	0.645030i	$0.776845\pi$
$104$		0			0
$105$	−9.84266	+	11.1075i	−0.960546	+	1.08398i
$106$		0			0
$107$	2.47400	+	0.970972i	0.239170	+	0.0938674i	0.481899	−	0.876227i	$-0.339947\pi$
$107$	2.47400	+	0.970972i	0.239170	+	0.0938674i	−0.242729	+	0.970094i	$0.578042\pi$
$108$		0			0
$109$	2.43709	+	6.20959i	0.233431	+	0.594771i	0.998808	−	0.0488103i	$-0.0155430\pi$
$109$	2.43709	+	6.20959i	0.233431	+	0.594771i	−0.765378	+	0.643582i	$0.777448\pi$
$110$		0			0
$111$	−2.37312	+	2.97580i	−0.225247	+	0.282451i
$112$		0			0
$113$	8.36228	+	10.4860i	0.786657	+	0.986437i	0.999955	+	0.00944959i	$0.00300794\pi$
$113$	8.36228	+	10.4860i	0.786657	+	0.986437i	−0.213298	+	0.976987i	$0.568421\pi$
$114$		0			0
$115$	18.8414	+	17.4823i	1.75697	+	1.63023i
$116$		0			0
$117$	−0.769029	+	0.443999i	−0.0710968	+	0.0410478i
$118$		0			0
$119$	9.74062	−	15.0144i	0.892921	−	1.37636i
$120$		0			0
$121$	1.07876	−	1.00094i	0.0980691	−	0.0909948i
$122$		0			0
$123$	−2.08770	−	13.8510i	−0.188241	−	1.24890i
$124$		0			0
$125$	−9.32361	+	2.12805i	−0.833929	+	0.190339i
$126$		0			0
$127$	11.3211	+	2.58396i	1.00458	+	0.229289i	0.693006	−	0.720932i	$-0.256286\pi$
$127$	11.3211	+	2.58396i	1.00458	+	0.229289i	0.311576	+	0.950221i	$0.399143\pi$
$128$		0			0
$129$	−0.584516	−	0.337471i	−0.0514638	−	0.0297126i
$130$		0			0
$131$	3.08172	+	2.10108i	0.269251	+	0.183572i	0.690417	−	0.723411i	$-0.257427\pi$
$131$	3.08172	+	2.10108i	0.269251	+	0.183572i	−0.421167	+	0.906983i	$0.638379\pi$
$132$		0			0
$133$	4.28103	+	5.12305i	0.371212	+	0.444225i
$134$		0			0
$135$	−5.81917	−	18.8653i	−0.500834	−	1.62366i
$136$		0			0
$137$	0.624269	−	8.33029i	0.0533349	−	0.711704i	−0.904882	−	0.425662i	$-0.860041\pi$
$137$	0.624269	−	8.33029i	0.0533349	−	0.711704i	0.958217	−	0.286042i	$-0.0923397\pi$
$138$		0			0
$139$	−14.6728	−	7.06605i	−1.24453	−	0.599334i	−0.308490	−	0.951228i	$-0.599824\pi$
$139$	−14.6728	−	7.06605i	−1.24453	−	0.599334i	−0.936040	+	0.351893i	$0.885538\pi$
$140$		0			0
$141$	18.4541	−	8.88701i	1.55411	−	0.748421i
$142$		0			0
$143$	5.76788	+	1.77916i	0.482334	+	0.148780i
$144$		0			0
$145$	−1.94646	+	12.9139i	−0.161645	+	1.07244i
$146$		0			0
$147$	6.47191	−	8.92507i	0.533794	−	0.736127i
$148$		0			0
$149$	−1.30993	−	0.197440i	−0.107313	−	0.0161749i	0.0951660	−	0.995461i	$-0.469662\pi$
$149$	−1.30993	−	0.197440i	−0.107313	−	0.0161749i	−0.202479	+	0.979287i	$0.564900\pi$
$150$		0			0
$151$	−6.67155	+	21.6286i	−0.542923	+	1.76011i	0.100855	+	0.994901i	$0.467842\pi$
$151$	−6.67155	+	21.6286i	−0.542923	+	1.76011i	−0.643778	+	0.765212i	$0.722634\pi$
$152$		0			0
$153$	1.52486	+	3.16641i	0.123278	+	0.255989i
$154$		0			0
$155$	−7.84491	+	16.2901i	−0.630118	+	1.30845i
$156$		0			0
$157$	−0.542763	−	0.0406744i	−0.0433172	−	0.00324617i	0.0530539	−	0.998592i	$-0.483104\pi$
$157$	−0.542763	−	0.0406744i	−0.0433172	−	0.00324617i	−0.0963711	+	0.995345i	$0.530724\pi$
$158$		0			0
$159$	−5.89622	+	1.81874i	−0.467601	+	0.144236i
$160$		0			0
$161$	−15.1964	−	11.5595i	−1.19765	−	0.911019i
$162$		0			0
$163$	3.28737	−	4.82169i	0.257487	−	0.377664i	−0.675628	−	0.737243i	$-0.736127\pi$
$163$	3.28737	−	4.82169i	0.257487	−	0.377664i	0.933115	+	0.359579i	$0.117080\pi$
$164$		0			0
$165$	−9.90477	+	17.1556i	−0.771085	+	1.33556i
$166$		0			0
$167$	0.555158	−	2.43231i	0.0429594	−	0.188218i	−0.948895	−	0.315591i	$-0.897797\pi$
$167$	0.555158	−	2.43231i	0.0429594	−	0.188218i	0.991855	+	0.127373i	$0.0406545\pi$
$168$		0			0
$169$	−2.24271	−	9.82596i	−0.172516	−	0.755843i
$170$		0			0
$171$	−1.29637	+	0.195396i	−0.0991359	+	0.0149423i
$172$		0			0
$173$	−5.95821	−	6.42142i	−0.452994	−	0.488212i	0.464717	−	0.885459i	$-0.346156\pi$
$173$	−5.95821	−	6.42142i	−0.452994	−	0.488212i	−0.917712	+	0.397247i	$0.869965\pi$
$174$		0			0
$175$	19.2873	−	6.43656i	1.45798	−	0.486558i
$176$		0			0
$177$	4.13945	+	7.16973i	0.311140	+	0.538910i
$178$		0			0
$179$	−6.64626	+	7.16296i	−0.496765	+	0.535385i	−0.930809	−	0.365507i	$-0.880896\pi$
$179$	−6.64626	+	7.16296i	−0.496765	+	0.535385i	0.434044	+	0.900892i	$0.357086\pi$
$180$		0			0
$181$	1.59003	−	1.26800i	0.118186	−	0.0942500i	−0.562613	−	0.826720i	$-0.690204\pi$
$181$	1.59003	−	1.26800i	0.118186	−	0.0942500i	0.680799	+	0.732470i	$0.261633\pi$
$182$		0			0
$183$	16.0848	+	12.8272i	1.18902	+	0.948214i
$184$		0			0
$185$	8.01241	−	3.14464i	0.589084	−	0.231198i
$186$		0			0
$187$	8.72762	−	22.2376i	0.638227	−	1.62618i
$188$		0			0
$189$	5.66916	+	13.5256i	0.412370	+	0.983842i
$190$		0			0
$191$	−3.06050	+	0.229353i	−0.221450	+	0.0165954i	−0.184993	−	0.982740i	$-0.559226\pi$
$191$	−3.06050	+	0.229353i	−0.221450	+	0.0165954i	−0.0364569	+	0.999335i	$0.511607\pi$
$192$		0			0
$193$	−9.46724	+	6.45465i	−0.681467	+	0.464616i	−0.853922	−	0.520401i	$-0.825782\pi$
$193$	−9.46724	+	6.45465i	−0.681467	+	0.464616i	0.172455	+	0.985017i	$0.444830\pi$
$194$		0			0
$195$	−9.58748			−0.686574
$196$		0			0
$197$	−19.1900			−1.36723			−0.683617	−	0.729841i	$-0.739594\pi$
$197$	−19.1900			−1.36723			−0.683617	+	0.729841i	$0.739594\pi$
$198$		0			0
$199$	0.245318	−	0.167255i	0.0173901	−	0.0118564i	−0.554594	−	0.832121i	$-0.687126\pi$
$199$	0.245318	−	0.167255i	0.0173901	−	0.0118564i	0.571984	+	0.820265i	$0.306174\pi$
$200$		0			0
$201$	−16.0095	+	1.19974i	−1.12922	+	0.0846234i
$202$		0			0
$203$	0.503279	−	9.68841i	0.0353233	−	0.679993i
$204$		0			0
$205$	−11.5728	+	29.4870i	−0.808279	+	2.05946i
$206$		0			0
$207$	3.49015	−	1.36978i	0.242582	−	0.0952064i
$208$		0			0
$209$	6.96723	+	5.55618i	0.481933	+	0.384329i
$210$		0			0
$211$	0.216716	−	0.172825i	0.0149194	−	0.0118978i	−0.616002	−	0.787745i	$-0.711249\pi$
$211$	0.216716	−	0.172825i	0.0149194	−	0.0118978i	0.630921	+	0.775847i	$0.282677\pi$
$212$		0			0
$213$	−12.5401	+	13.5150i	−0.859234	+	0.926034i
$214$		0			0
$215$	0.763163	+	1.32184i	0.0520473	+	0.0901486i
$216$		0			0
$217$	4.61941	−	12.6119i	0.313586	−	0.856150i
$218$		0			0
$219$	4.78019	+	5.15182i	0.323015	+	0.348127i
$220$		0			0
$221$	11.4327	−	1.72321i	0.769048	−	0.115915i
$222$		0			0
$223$	−5.36963	−	23.5259i	−0.359577	−	1.57541i	−0.754250	−	0.656587i	$-0.771999\pi$
$223$	−5.36963	−	23.5259i	−0.359577	−	1.57541i	0.394673	−	0.918822i	$-0.370858\pi$
$224$		0			0
$225$	−0.888470	+	3.89264i	−0.0592313	+	0.259509i
$226$		0			0
$227$	−9.87817	+	17.1095i	−0.655637	+	1.13560i	0.326097	+	0.945336i	$0.394267\pi$
$227$	−9.87817	+	17.1095i	−0.655637	+	1.13560i	−0.981734	+	0.190260i	$0.939067\pi$
$228$		0			0
$229$	14.8131	−	21.7268i	0.978876	−	1.43575i	0.0803806	−	0.996764i	$-0.474386\pi$
$229$	14.8131	−	21.7268i	0.978876	−	1.43575i	0.898495	−	0.438983i	$-0.144661\pi$
$230$		0			0
$231$	6.07957	−	13.4010i	0.400006	−	0.881719i
$232$		0			0
$233$	−18.2835	+	5.63970i	−1.19779	+	0.369469i	−0.828576	−	0.559876i	$-0.810849\pi$
$233$	−18.2835	+	5.63970i	−1.19779	+	0.369469i	−0.369212	+	0.929345i	$0.620373\pi$
$234$		0			0
$235$	−46.1899	−	3.46146i	−3.01310	−	0.225801i
$236$		0			0
$237$	−4.24888	+	8.82289i	−0.275994	+	0.573108i
$238$		0			0
$239$	11.6427	+	24.1762i	0.753101	+	1.56383i	0.824159	+	0.566358i	$0.191648\pi$
$239$	11.6427	+	24.1762i	0.753101	+	1.56383i	−0.0710585	+	0.997472i	$0.522638\pi$
$240$		0			0
$241$	0.273352	−	0.886186i	0.0176082	−	0.0570843i	−0.946342	−	0.323166i	$-0.895253\pi$
$241$	0.273352	−	0.886186i	0.0176082	−	0.0570843i	0.963951	+	0.266082i	$0.0857290\pi$
$242$		0			0
$243$	−5.27504	−	0.795085i	−0.338394	−	0.0510047i
$244$		0			0
$245$	−22.7666	+	10.1614i	−1.45450	+	0.649190i
$246$		0			0
$247$	−0.642816	+	4.26481i	−0.0409014	+	0.271363i
$248$		0			0
$249$	14.0901	+	4.34622i	0.892924	+	0.275430i
$250$		0			0
$251$	−28.0939	+	13.5293i	−1.77327	+	0.853961i	−0.809545	+	0.587057i	$0.800286\pi$
$251$	−28.0939	+	13.5293i	−1.77327	+	0.853961i	−0.963723	+	0.266904i	$0.913999\pi$
$252$		0			0
$253$	−22.9616	−	11.0577i	−1.44359	−	0.695194i
$254$		0			0
$255$	−2.83560	+	37.8385i	−0.177572	+	2.36954i
$256$		0			0
$257$	8.25124	+	26.7499i	0.514698	+	1.66861i	0.723240	+	0.690597i	$0.242652\pi$
$257$	8.25124	+	26.7499i	0.514698	+	1.66861i	−0.208542	+	0.978013i	$0.566872\pi$
$258$		0			0
$259$	−5.69578	+	2.90544i	−0.353918	+	0.180535i
$260$		0			0
$261$	1.57404	+	1.07316i	0.0974305	+	0.0664270i
$262$		0			0
$263$	−10.0646	−	5.81082i	−0.620612	−	0.358311i	0.156495	−	0.987679i	$-0.449980\pi$
$263$	−10.0646	−	5.81082i	−0.620612	−	0.358311i	−0.777107	+	0.629368i	$0.783314\pi$
$264$		0			0
$265$	13.6039	+	3.10501i	0.835682	+	0.190739i
$266$		0			0
$267$	−12.1665	+	2.77693i	−0.744579	+	0.169945i
$268$		0			0
$269$	−0.0717249	−	0.475864i	−0.00437315	−	0.0290139i	0.986538	−	0.163533i	$-0.0522891\pi$
$269$	−0.0717249	−	0.475864i	−0.00437315	−	0.0290139i	−0.990911	+	0.134519i	$0.957051\pi$
$270$		0			0
$271$	−0.509332	+	0.472591i	−0.0309397	+	0.0287078i	−0.695491	−	0.718535i	$-0.744813\pi$
$271$	−0.509332	+	0.472591i	−0.0309397	+	0.0287078i	0.664551	+	0.747243i	$0.268623\pi$
$272$		0			0
$273$	7.08811	−	0.694718i	0.428992	−	0.0420463i
$274$		0			0
$275$	23.5040	−	13.5701i	1.41735	−	0.818306i
$276$		0			0
$277$	−11.8139	−	10.9617i	−0.709828	−	0.658624i	0.240223	−	0.970718i	$-0.422779\pi$
$277$	−11.8139	−	10.9617i	−0.709828	−	0.658624i	−0.950051	+	0.312093i	$0.898970\pi$
$278$		0			0
$279$	1.64444	+	2.06206i	0.0984499	+	0.123452i
$280$		0			0
$281$	4.16927	−	5.22809i	0.248718	−	0.311882i	−0.641763	−	0.766903i	$-0.721797\pi$
$281$	4.16927	−	5.22809i	0.248718	−	0.311882i	0.890481	+	0.455021i	$0.150368\pi$
$282$		0			0
$283$	6.31133	+	16.0810i	0.375169	+	0.955916i	0.986385	+	0.164452i	$0.0525856\pi$
$283$	6.31133	+	16.0810i	0.375169	+	0.955916i	−0.611216	+	0.791464i	$0.709319\pi$
$284$		0			0
$285$	−13.1762	−	5.17128i	−0.780490	−	0.306320i
$286$		0			0
$287$	6.41921	−	22.6386i	0.378914	−	1.33631i
$288$		0			0
$289$	−2.14913	−	28.6782i	−0.126420	−	1.68695i
$290$		0			0
$291$	−4.70003	−	6.89368i	−0.275521	−	0.404115i
$292$		0			0
$293$			8.46030i			0.494256i	0.968983	+	0.247128i	$0.0794868\pi$
$293$			8.46030i			0.494256i	−0.968983	+	0.247128i	$0.920513\pi$
$294$		0			0
$295$		−	18.7221i		−	1.09004i
$296$		0			0
$297$	11.0273	+	16.1741i	0.639868	+	0.938514i
$298$		0			0
$299$	−0.921762	−	12.3001i	−0.0533069	−	0.711331i
$300$		0			0
$301$	−0.659995	−	0.921946i	−0.0380415	−	0.0531401i
$302$		0			0
$303$	−17.9276	−	7.03604i	−1.02991	−	0.404210i
$304$		0			0
$305$	−16.9974	−	43.3087i	−0.973268	−	2.47985i
$306$		0			0
$307$	−2.47927	+	3.10891i	−0.141499	+	0.177435i	−0.847531	−	0.530745i	$-0.821912\pi$
$307$	−2.47927	+	3.10891i	−0.141499	+	0.177435i	0.706032	+	0.708180i	$0.250484\pi$
$308$		0			0
$309$	11.6824	+	14.6492i	0.664587	+	0.833365i
$310$		0			0
$311$	−4.06319	−	3.77009i	−0.230402	−	0.213782i	0.556520	−	0.830834i	$-0.312136\pi$
$311$	−4.06319	−	3.77009i	−0.230402	−	0.213782i	−0.786922	+	0.617052i	$0.788327\pi$
$312$		0			0
$313$	12.0395	−	6.95103i	0.680515	−	0.392895i	−0.119534	−	0.992830i	$-0.538140\pi$
$313$	12.0395	−	6.95103i	0.680515	−	0.392895i	0.800049	+	0.599935i	$0.204807\pi$
$314$		0			0
$315$	0.618629	−	4.85649i	0.0348558	−	0.273632i
$316$		0			0
$317$	24.1796	−	22.4353i	1.35806	−	1.26009i	0.422757	−	0.906243i	$-0.361062\pi$
$317$	24.1796	−	22.4353i	1.35806	−	1.26009i	0.935302	−	0.353852i	$-0.115128\pi$
$318$		0			0
$319$	−1.93001	−	12.8048i	−0.108060	−	0.716929i
$320$		0			0
$321$	4.08081	−	0.931419i	0.227769	−	0.0519867i
$322$		0			0
$323$	16.6416	+	3.79834i	0.925963	+	0.211345i
$324$		0			0
$325$	11.3756	+	6.56768i	0.631003	+	0.364309i
$326$		0			0
$327$	8.68048	+	5.91825i	0.480032	+	0.327280i
$328$		0			0
$329$	34.3994	−	0.787883i	1.89650	−	0.0434374i
$330$		0			0
$331$	6.80412	+	22.0584i	0.373988	+	1.21244i	0.925653	+	0.378374i	$0.123517\pi$
$331$	6.80412	+	22.0584i	0.373988	+	1.21244i	−0.551665	+	0.834066i	$0.686007\pi$
$332$		0			0
$333$	0.0938299	−	1.25207i	0.00514185	−	0.0686132i
$334$		0			0
$335$	32.7103	+	15.7524i	1.78715	+	0.860648i
$336$		0			0
$337$	20.4737	−	9.85964i	1.11528	−	0.537089i	0.216846	−	0.976206i	$-0.430423\pi$
$337$	20.4737	−	9.85964i	1.11528	−	0.537089i	0.898430	+	0.439117i	$0.144709\pi$
$338$		0			0
$339$	20.1848	+	6.22619i	1.09629	+	0.338160i
$340$		0			0
$341$	2.67201	−	17.7276i	0.144697	−	0.960004i
$342$		0			0
$343$	16.0952	−	9.16212i	0.869059	−	0.494708i
$344$		0			0
$345$	40.0283	+	6.03330i	2.15505	+	0.324822i
$346$		0			0
$347$	3.30059	−	10.7003i	0.177185	−	0.574420i	−0.822796	−	0.568336i	$-0.807587\pi$
$347$	3.30059	−	10.7003i	0.177185	−	0.574420i	0.999981	−	0.00608367i	$-0.00193650\pi$
$348$		0			0
$349$	2.05126	+	4.25949i	0.109801	+	0.228005i	0.948628	−	0.316394i	$-0.102472\pi$
$349$	2.05126	+	4.25949i	0.109801	+	0.228005i	−0.838826	+	0.544399i	$0.816758\pi$
$350$		0			0
$351$	−4.11071	+	8.53598i	−0.219413	+	0.455617i
$352$		0			0
$353$	−22.9450	−	1.71949i	−1.22124	−	0.0915191i	−0.551537	−	0.834150i	$-0.685959\pi$
$353$	−22.9450	−	1.71949i	−1.22124	−	0.0915191i	−0.669701	+	0.742631i	$0.733578\pi$
$354$		0			0
$355$	39.8407	−	12.2892i	2.11453	−	0.652245i
$356$		0			0
$357$	−0.645428	−	28.1798i	−0.0341597	−	1.49143i
$358$		0			0
$359$	5.54511	−	8.13319i	0.292660	−	0.429253i	−0.651546	−	0.758609i	$-0.725879\pi$
$359$	5.54511	−	8.13319i	0.292660	−	0.429253i	0.944206	+	0.329356i	$0.106832\pi$
$360$		0			0
$361$	6.31623	−	10.9400i	0.332433	−	0.575791i
$362$		0			0
$363$	0.515736	−	2.25958i	0.0270691	−	0.118597i
$364$		0			0
$365$	−3.53653	−	15.4946i	−0.185111	−	0.811023i
$366$		0			0
$367$	11.1288	−	1.67740i	0.580920	−	0.0875596i	0.147993	−	0.988988i	$-0.452719\pi$
$367$	11.1288	−	1.67740i	0.580920	−	0.0875596i	0.432927	+	0.901429i	$0.357481\pi$
$368$		0			0
$369$	3.14291	+	3.38726i	0.163614	+	0.176333i
$370$		0			0
$371$	−10.2825	−	1.30980i	−0.533840	−	0.0680016i
$372$		0			0
$373$	12.7075	+	22.0101i	0.657972	+	1.13964i	0.981140	+	0.193299i	$0.0619188\pi$
$373$	12.7075	+	22.0101i	0.657972	+	1.13964i	−0.323168	+	0.946342i	$0.604748\pi$
$374$		0			0
$375$	−10.2446	+	11.0411i	−0.529031	+	0.570160i
$376$		0			0
$377$	4.89996	−	3.90759i	0.252361	−	0.201251i
$378$		0			0
$379$	−17.1095	−	13.6444i	−0.878856	−	0.700864i	0.0762629	−	0.997088i	$-0.475701\pi$
$379$	−17.1095	−	13.6444i	−0.878856	−	0.700864i	−0.955119	+	0.296224i	$0.904273\pi$
$380$		0			0
$381$	17.0244	−	6.68158i	0.872186	−	0.342308i
$382$		0			0
$383$	−9.98296	+	25.4362i	−0.510106	+	1.29973i	0.411433	+	0.911440i	$0.365029\pi$
$383$	−9.98296	+	25.4362i	−0.510106	+	1.29973i	−0.921538	+	0.388288i	$0.873067\pi$
$384$		0			0
$385$	−27.0591	+	19.3709i	−1.37906	+	0.987230i
$386$		0			0
$387$	0.222027	−	0.0166386i	0.0112862	−	0.000845787i
$388$		0			0
$389$	−9.47411	+	6.45934i	−0.480357	+	0.327502i	−0.779173	−	0.626809i	$-0.784361\pi$
$389$	−9.47411	+	6.45934i	−0.480357	+	0.327502i	0.298816	+	0.954311i	$0.403408\pi$
$390$		0			0
$391$	−48.8167			−2.46877
$392$		0			0
$393$	5.87426			0.296317
$394$		0			0
$395$	18.2973	−	12.4749i	0.920639	−	0.627681i
$396$		0			0
$397$	16.2364	−	1.21675i	0.814883	−	0.0610670i	0.339234	−	0.940702i	$-0.389832\pi$
$397$	16.2364	−	1.21675i	0.814883	−	0.0610670i	0.475649	+	0.879635i	$0.342213\pi$
$398$		0			0
$399$	10.1160	+	2.86841i	0.506433	+	0.143600i
$400$		0			0
$401$	8.29814	−	21.1433i	0.414389	−	1.05585i	−0.559502	−	0.828829i	$-0.689007\pi$
$401$	8.29814	−	21.1433i	0.414389	−	1.05585i	0.973891	−	0.227017i	$-0.0728973\pi$
$402$		0			0
$403$	8.07699	−	3.16998i	0.402343	−	0.157908i
$404$		0			0
$405$	−19.9695	−	15.9252i	−0.992293	−	0.791327i
$406$		0			0
$407$	−6.67266	+	5.32127i	−0.330752	+	0.263766i
$408$		0			0
$409$	−11.6711	+	12.5784i	−0.577098	+	0.621964i	−0.952368	−	0.304952i	$-0.901360\pi$
$409$	−11.6711	+	12.5784i	−0.577098	+	0.621964i	0.375270	+	0.926916i	$0.377550\pi$
$410$		0			0
$411$	−6.57827	−	11.3939i	−0.324482	−	0.562020i
$412$		0			0
$413$	1.35662	+	13.8414i	0.0667548	+	0.681090i
$414$		0			0
$415$	−22.6804	−	24.4437i	−1.11334	−	1.19989i
$416$		0			0
$417$	−25.3624	+	3.82277i	−1.24200	+	0.187202i
$418$		0			0
$419$	−1.10535	−	4.84287i	−0.0540000	−	0.236590i	0.940725	−	0.339172i	$-0.110147\pi$
$419$	−1.10535	−	4.84287i	−0.0540000	−	0.236590i	−0.994725	+	0.102582i	$0.967290\pi$
$420$		0			0
$421$	4.52323	−	19.8176i	0.220449	−	0.965850i	−0.736692	−	0.676228i	$-0.763613\pi$
$421$	4.52323	−	19.8176i	0.220449	−	0.965850i	0.957141	−	0.289622i	$-0.0935295\pi$
$422$		0			0
$423$	−3.37837	+	5.85151i	−0.164262	+	0.284510i
$424$		0			0
$425$	29.2848	−	42.9529i	1.42052	−	2.08352i
$426$		0			0
$427$	15.7045	+	30.7868i	0.759994	+	1.48988i
$428$		0			0
$429$	9.08410	−	2.80208i	0.438585	−	0.135285i
$430$		0			0
$431$	−20.4586	−	1.53316i	−0.985458	−	0.0738499i	−0.427759	−	0.903893i	$-0.640697\pi$
$431$	−20.4586	−	1.53316i	−0.985458	−	0.0738499i	−0.557699	+	0.830043i	$0.688316\pi$
$432$		0			0
$433$	−9.10273	+	18.9020i	−0.437449	+	0.908373i	0.559388	+	0.828906i	$0.311036\pi$
$433$	−9.10273	+	18.9020i	−0.437449	+	0.908373i	−0.996837	+	0.0794673i	$0.974678\pi$
$434$		0			0
$435$	8.92432	+	18.5315i	0.427888	+	0.888519i
$436$		0			0
$437$	5.36759	−	17.4013i	0.256767	−	0.832417i
$438$		0			0
$439$	29.4443	+	4.43801i	1.40530	+	0.211815i	0.807517	−	0.589844i	$-0.200811\pi$
$439$	29.4443	+	4.43801i	1.40530	+	0.211815i	0.597782	+	0.801659i	$0.296049\pi$
$440$		0			0
$441$	−0.105452	+	3.63527i	−0.00502153	+	0.173108i
$442$		0			0
$443$	0.983142	−	6.52272i	0.0467105	−	0.309904i	−0.953259	−	0.302153i	$-0.902295\pi$
$443$	0.983142	−	6.52272i	0.0467105	−	0.309904i	0.999970	−	0.00775087i	$-0.00246720\pi$
$444$		0			0
$445$	26.9674	+	8.31834i	1.27838	+	0.394327i
$446$		0			0
$447$	−1.87975	+	0.905241i	−0.0889092	+	0.0428164i
$448$		0			0
$449$	−29.4178	−	14.1668i	−1.38831	−	0.668575i	−0.417556	−	0.908651i	$-0.637113\pi$
$449$	−29.4178	−	14.1668i	−1.38831	−	0.668575i	−0.970754	+	0.240077i	$0.922827\pi$
$450$		0			0
$451$	2.34719	−	31.3211i	0.110525	−	1.47485i
$452$		0			0
$453$	10.5073	+	34.0640i	0.493678	+	1.60046i
$454$		0			0
$455$	−14.6672	−	6.65403i	−0.687610	−	0.311946i
$456$		0			0
$457$	−22.4381	−	15.2980i	−1.04961	−	0.715612i	−0.0897138	−	0.995968i	$-0.528595\pi$
$457$	−22.4381	−	15.2980i	−1.04961	−	0.715612i	−0.959896	+	0.280356i	$0.909548\pi$
$458$		0			0
$459$	32.4728	+	18.7482i	1.51570	+	0.875089i
$460$		0			0
$461$	18.8477	+	4.30187i	0.877825	+	0.200358i	0.637608	−	0.770361i	$-0.279924\pi$
$461$	18.8477	+	4.30187i	0.877825	+	0.200358i	0.240217	+	0.970719i	$0.422781\pi$
$462$		0			0
$463$	2.95266	−	0.673925i	0.137222	−	0.0313199i	−0.153358	−	0.988171i	$-0.549009\pi$
$463$	2.95266	−	0.673925i	0.137222	−	0.0313199i	0.290580	+	0.956851i	$0.406152\pi$
$464$		0			0
$465$	4.24414	+	28.1580i	0.196817	+	1.30580i
$466$		0			0
$467$	−11.6095	+	10.7720i	−0.537223	+	0.498470i	−0.901475	−	0.432830i	$-0.857515\pi$
$467$	−11.6095	+	10.7720i	−0.537223	+	0.498470i	0.364253	+	0.931300i	$0.381324\pi$
$468$		0			0
$469$	−25.3244	−	9.27569i	−1.16937	−	0.428312i
$470$		0			0
$471$	−0.742374	+	0.428610i	−0.0342068	+	0.0197493i
$472$		0			0
$473$	−1.10942	−	1.02939i	−0.0510112	−	0.0473315i
$474$		0			0
$475$	12.0911	+	15.1618i	0.554778	+	0.695670i
$476$		0			0
$477$	1.26910	−	1.59140i	0.0581079	−	0.0728650i
$478$		0			0
$479$	−1.01058	−	2.57491i	−0.0461746	−	0.117651i	0.905926	−	0.423436i	$-0.139176\pi$
$479$	−1.01058	−	2.57491i	−0.0461746	−	0.117651i	−0.952100	+	0.305785i	$0.901081\pi$
$480$		0			0
$481$	−3.84509	−	1.50909i	−0.175321	−	0.0688085i
$482$		0			0
$483$	−30.0304	−	1.55998i	−1.36643	−	0.0709814i
$484$		0			0
$485$	1.41001	+	18.8153i	0.0640253	+	0.854359i
$486$		0			0
$487$	21.6192	+	31.7095i	0.979658	+	1.43689i	0.897878	+	0.440244i	$0.145108\pi$
$487$	21.6192	+	31.7095i	0.979658	+	1.43689i	0.0817802	+	0.996650i	$0.473939\pi$
$488$		0			0
$489$		−	9.19094i		−	0.415629i
$490$		0			0
$491$			33.8831i			1.52912i	0.644551	+	0.764561i	$0.277044\pi$
$491$			33.8831i			1.52912i	−0.644551	+	0.764561i	$0.722956\pi$
$492$		0			0
$493$	−13.9727	−	20.4942i	−0.629299	−	0.923011i
$494$		0			0
$495$	−0.488343	−	6.51648i	−0.0219494	−	0.292894i
$496$		0			0
$497$	−28.5641	+	11.9724i	−1.28127	+	0.537037i
$498$		0			0
$499$	−30.7013	−	12.0494i	−1.37438	−	0.539404i	−0.440745	−	0.897632i	$-0.645286\pi$
$499$	−30.7013	−	12.0494i	−1.37438	−	0.539404i	−0.933634	+	0.358228i	$0.883381\pi$
$500$		0			0
$501$	−1.43552	−	3.65765i	−0.0641345	−	0.163412i
$502$		0			0
$503$	5.95459	−	7.46682i	0.265502	−	0.332929i	−0.631153	−	0.775658i	$-0.717418\pi$
$503$	5.95459	−	7.46682i	0.265502	−	0.332929i	0.896655	+	0.442729i	$0.145990\pi$
$504$		0			0
$505$	27.1544	+	34.0506i	1.20836	+	1.51523i
$506$		0			0
$507$	−11.6360	−	10.7966i	−0.516772	−	0.479495i
$508$		0			0
$509$	6.46266	−	3.73122i	0.286452	−	0.165383i	−0.349889	−	0.936791i	$-0.613781\pi$
$509$	6.46266	−	3.73122i	0.286452	−	0.165383i	0.636341	+	0.771408i	$0.280447\pi$
$510$		0			0
$511$	3.73734	+	11.1990i	0.165330	+	0.495415i
$512$		0			0
$513$	−10.2535	+	9.51387i	−0.452704	+	0.420048i
$514$		0			0
$515$	−6.31528	−	41.8991i	−0.278284	−	1.84630i
$516$		0			0
$517$	44.7765	−	10.2199i	1.96927	−	0.449472i
$518$		0			0
$519$	−13.4504	−	3.06996i	−0.590407	−	0.134756i
$520$		0			0
$521$	−2.39895	−	1.38503i	−0.105100	−	0.0606794i	0.446529	−	0.894769i	$-0.352660\pi$
$521$	−2.39895	−	1.38503i	−0.105100	−	0.0606794i	−0.551629	+	0.834090i	$0.685993\pi$
$522$		0			0
$523$	15.4215	+	10.5142i	0.674334	+	0.459753i	0.851449	−	0.524437i	$-0.175724\pi$
$523$	15.4215	+	10.5142i	0.674334	+	0.459753i	−0.177115	+	0.984190i	$0.556677\pi$
$524$		0			0
$525$	19.3877	−	25.4874i	0.846147	−	1.11236i
$526$		0			0
$527$	−10.1220	−	32.8146i	−0.440920	−	1.42943i
$528$		0			0
$529$	−2.17309	+	28.9978i	−0.0944821	+	1.26078i
$530$		0			0
$531$	−2.46058	−	1.18495i	−0.106780	−	0.0514225i
$532$		0			0
$533$	13.6960	−	6.59564i	0.593239	−	0.285689i
$534$		0			0
$535$	−9.04522	−	2.79008i	−0.391059	−	0.120626i
$536$		0			0
$537$	−2.29368	+	15.2176i	−0.0989797	+	0.656688i
$538$		0			0
$539$	18.6014	−	16.2818i	0.801220	−	0.701305i
$540$		0			0
$541$	10.9373	+	1.64853i	0.470231	+	0.0708759i	0.379883	−	0.925034i	$-0.375964\pi$
$541$	10.9373	+	1.64853i	0.470231	+	0.0708759i	0.0903474	+	0.995910i	$0.471202\pi$
$542$		0			0
$543$	0.944101	−	3.06070i	0.0405152	−	0.131347i
$544$		0			0
$545$	−10.3084	−	21.4057i	−0.441565	−	0.916920i
$546$		0			0
$547$	−8.20100	+	17.0295i	−0.350649	+	0.728131i	−0.999461	−	0.0328178i	$-0.989552\pi$
$547$	−8.20100	+	17.0295i	−0.350649	+	0.728131i	0.648812	+	0.760949i	$0.275266\pi$
$548$		0			0
$549$	−6.76771	−	0.507170i	−0.288839	−	0.0216455i
$550$		0			0
$551$	8.84175	−	2.72732i	0.376671	−	0.116188i
$552$		0			0
$553$	−12.6234	+	10.5487i	−0.536803	+	0.448574i
$554$		0			0
$555$	7.63648	−	11.2007i	0.324151	−	0.475442i
$556$		0			0
$557$	−11.4347	+	19.8054i	−0.484502	+	0.839183i	−0.999842	−	0.0178037i	$-0.994333\pi$
$557$	−11.4347	+	19.8054i	−0.484502	+	0.839183i	0.515339	+	0.856986i	$0.327666\pi$
$558$		0			0
$559$	0.162990	−	0.714108i	0.00689376	−	0.0302035i
$560$		0			0
$561$	−8.37210	−	36.6806i	−0.353470	−	1.54865i
$562$		0			0
$563$	10.8046	−	1.62853i	0.455358	−	0.0686342i	0.0826413	−	0.996579i	$-0.473664\pi$
$563$	10.8046	−	1.62853i	0.455358	−	0.0686342i	0.372717	+	0.927945i	$0.378426\pi$
$564$		0			0
$565$	−32.4909	−	35.0169i	−1.36690	−	1.47317i
$566$		0			0
$567$	15.9176	+	10.3266i	0.668475	+	0.433676i
$568$		0			0
$569$	−2.81437	−	4.87463i	−0.117984	−	0.204355i	0.800984	−	0.598685i	$-0.204310\pi$
$569$	−2.81437	−	4.87463i	−0.117984	−	0.204355i	−0.918969	+	0.394330i	$0.870977\pi$
$570$		0			0
$571$	22.2051	−	23.9314i	0.929255	−	1.00150i	−0.0707373	−	0.997495i	$-0.522535\pi$
$571$	22.2051	−	23.9314i	0.929255	−	1.00150i	0.999992	−	0.00400343i	$-0.00127433\pi$
$572$		0			0
$573$	−3.77909	+	3.01372i	−0.157874	+	0.125900i
$574$		0			0
$575$	−43.3607	−	34.5790i	−1.80826	−	1.44204i
$576$		0			0
$577$	−3.20066	+	1.25617i	−0.133245	+	0.0522949i	−0.431027	−	0.902339i	$-0.641849\pi$
$577$	−3.20066	+	1.25617i	−0.133245	+	0.0522949i	0.297782	+	0.954634i	$0.403753\pi$
$578$		0			0
$579$	−6.59298	+	16.7986i	−0.273995	+	0.698128i
$580$		0			0
$581$	18.5390	+	16.4280i	0.769128	+	0.681547i
$582$		0			0
$583$	−13.7971	+	1.03395i	−0.571419	+	0.0428220i
$584$		0			0
$585$	2.61316	−	1.78162i	0.108041	−	0.0736609i
$586$		0			0
$587$	4.50362			0.185884			0.0929421	−	0.995672i	$-0.470373\pi$
$587$	4.50362			0.185884			0.0929421	+	0.995672i	$0.470373\pi$
$588$		0			0
$589$	12.8101			0.527832
$590$		0			0
$591$	−24.9717	+	17.0254i	−1.02720	+	0.700331i
$592$		0			0
$593$	−22.1208	+	1.65772i	−0.908391	+	0.0680745i	−0.520724	−	0.853725i	$-0.674338\pi$
$593$	−22.1208	+	1.65772i	−0.908391	+	0.0680745i	−0.387667	+	0.921800i	$0.626719\pi$
$594$		0			0
$595$	−30.5991	+	55.9184i	−1.25444	+	2.29243i
$596$		0			0
$597$	0.170839	−	0.435292i	0.00699199	−	0.0178153i
$598$		0			0
$599$	−4.36118	+	1.71164i	−0.178193	+	0.0699355i	−0.452760	−	0.891632i	$-0.649561\pi$
$599$	−4.36118	+	1.71164i	−0.178193	+	0.0699355i	0.274567	+	0.961568i	$0.411465\pi$
$600$		0			0
$601$	15.4581	+	12.3275i	0.630550	+	0.502847i	0.885824	−	0.464022i	$-0.153594\pi$
$601$	15.4581	+	12.3275i	0.630550	+	0.502847i	−0.255273	+	0.966869i	$0.582165\pi$
$602$		0			0
$603$	4.14058	−	3.30200i	0.168617	−	0.134468i
$604$		0			0
$605$	−3.56498	+	3.84213i	−0.144937	+	0.156205i
$606$		0			0
$607$	16.5186	+	28.6111i	0.670470	+	1.16129i	0.977771	+	0.209676i	$0.0672409\pi$
$607$	16.5186	+	28.6111i	0.670470	+	1.16129i	−0.307301	+	0.951612i	$0.599426\pi$
$608$		0			0
$609$	−7.94064	−	13.0539i	−0.321771	−	0.528969i
$610$		0			0
$611$	15.1191	+	16.2945i	0.611654	+	0.659207i
$612$		0			0
$613$	27.3112	−	4.11650i	1.10309	−	0.166264i	0.427841	−	0.903854i	$-0.359274\pi$
$613$	27.3112	−	4.11650i	1.10309	−	0.166264i	0.675249	+	0.737590i	$0.264036\pi$
$614$		0			0
$615$	11.1014	+	48.6383i	0.447650	+	1.96128i
$616$		0			0
$617$	−4.25471	+	18.6411i	−0.171288	+	0.750463i	0.814181	+	0.580611i	$0.197186\pi$
$617$	−4.25471	+	18.6411i	−0.171288	+	0.750463i	−0.985470	+	0.169852i	$0.945671\pi$
$618$		0			0
$619$	17.7456	−	30.7363i	0.713256	−	1.23540i	−0.250373	−	0.968150i	$-0.580553\pi$
$619$	17.7456	−	30.7363i	0.713256	−	1.23540i	0.963628	−	0.267246i	$-0.0861136\pi$
$620$		0			0
$621$	22.5340	−	33.0514i	0.904260	−	1.32631i
$622$		0			0
$623$	−20.5400	−	4.19574i	−0.822917	−	0.168099i
$624$		0			0
$625$	−4.17059	+	1.28646i	−0.166824	+	0.0514583i
$626$		0			0
$627$	13.9958	+	1.04884i	0.558937	+	0.0418866i
$628$		0			0
$629$	−7.09308	+	14.7289i	−0.282819	+	0.587281i
$630$		0			0
$631$	−9.71542	−	20.1743i	−0.386765	−	0.803126i	−0.999913	−	0.0131580i	$-0.995812\pi$
$631$	−9.71542	−	20.1743i	−0.386765	−	0.803126i	0.613148	−	0.789968i	$-0.289903\pi$
$632$		0			0
$633$	0.128678	−	0.417165i	0.00511451	−	0.0165808i
$634$		0			0
$635$	−40.8963	−	6.16413i	−1.62292	−	0.244616i
$636$		0			0
$637$	11.3258	+	3.85658i	0.448743	+	0.152803i
$638$		0			0
$639$	0.906455	−	6.01394i	0.0358588	−	0.237908i
$640$		0			0
$641$	31.4722	+	9.70789i	1.24308	+	0.383439i	0.845424	−	0.534097i	$-0.179348\pi$
$641$	31.4722	+	9.70789i	1.24308	+	0.383439i	0.397654	+	0.917535i	$0.369824\pi$
$642$		0			0
$643$	−17.6790	+	8.51375i	−0.697191	+	0.335749i	−0.748687	−	0.662924i	$-0.769315\pi$
$643$	−17.6790	+	8.51375i	−0.697191	+	0.335749i	0.0514960	+	0.998673i	$0.483601\pi$
$644$		0			0
$645$	2.16582	+	1.04301i	0.0852792	+	0.0410683i
$646$		0			0
$647$	3.74351	−	49.9537i	0.147173	−	1.96388i	−0.100213	−	0.994966i	$-0.531953\pi$
$647$	3.74351	−	49.9537i	0.147173	−	1.96388i	0.247386	−	0.968917i	$-0.420428\pi$
$648$		0			0
$649$	5.47178	+	17.7391i	0.214786	+	0.696320i
$650$		0			0
$651$	−5.17809	−	20.5099i	−0.202945	−	0.803848i
$652$		0			0
$653$	−4.72140	−	3.21899i	−0.184763	−	0.125969i	0.467407	−	0.884042i	$-0.345188\pi$
$653$	−4.72140	−	3.21899i	−0.184763	−	0.125969i	−0.652169	+	0.758073i	$0.726141\pi$
$654$		0			0
$655$	−11.5044	−	6.64209i	−0.449515	−	0.259528i
$656$		0			0
$657$	−2.26023	−	0.515883i	−0.0881801	−	0.0201265i
$658$		0			0
$659$	−5.79992	+	1.32379i	−0.225933	+	0.0515677i	−0.333988	−	0.942577i	$-0.608395\pi$
$659$	−5.79992	+	1.32379i	−0.225933	+	0.0515677i	0.108056	+	0.994145i	$0.465538\pi$
$660$		0			0
$661$	−1.58827	−	10.5375i	−0.0617764	−	0.409859i	−0.998251	−	0.0591233i	$-0.981170\pi$
$661$	−1.58827	−	10.5375i	−0.0617764	−	0.409859i	0.936474	−	0.350736i	$-0.114069\pi$
$662$		0			0
$663$	13.3484	−	12.3855i	0.518408	−	0.481012i
$664$		0			0
$665$	−16.5683	−	17.0559i	−0.642491	−	0.661399i
$666$		0			0
$667$	−22.9166	+	13.2309i	−0.887336	+	0.512304i
$668$		0			0
$669$	−27.8595	−	25.8499i	−1.07711	−	0.999414i
$670$		0			0
$671$	28.7625	+	36.0671i	1.11037	+	1.39235i
$672$		0			0
$673$	−28.4019	+	35.6149i	−1.09481	+	1.37285i	−0.173135	+	0.984898i	$0.555390\pi$
$673$	−28.4019	+	35.6149i	−1.09481	+	1.37285i	−0.921678	+	0.387955i	$0.873182\pi$
$674$		0			0
$675$	15.5633	+	39.6546i	0.599031	+	1.52631i
$676$		0			0
$677$	26.9043	+	10.5592i	1.03402	+	0.405822i	0.820820	−	0.571188i	$-0.193517\pi$
$677$	26.9043	+	10.5592i	1.03402	+	0.405822i	0.213197	+	0.977009i	$0.431612\pi$
$678$		0			0
$679$	−2.40581	−	13.8081i	−0.0923265	−	0.529908i
$680$		0			0
$681$	2.32524	+	31.0282i	0.0891034	+	1.18900i
$682$		0			0
$683$	20.1617	+	29.5718i	0.771466	+	1.13153i	0.987878	+	0.155230i	$0.0496120\pi$
$683$	20.1617	+	29.5718i	0.771466	+	1.13153i	−0.216413	+	0.976302i	$0.569436\pi$
$684$		0			0
$685$			29.7525i			1.13678i
$686$		0			0
$687$		−	41.4148i		−	1.58008i
$688$		0			0
$689$	−3.77216	−	5.53275i	−0.143708	−	0.210781i
$690$		0			0
$691$	−1.40657	−	18.7694i	−0.0535085	−	0.714021i	−0.957861	−	0.287234i	$-0.907264\pi$
$691$	−1.40657	−	18.7694i	−0.0535085	−	0.714021i	0.904352	−	0.426787i	$-0.140355\pi$
$692$		0			0
$693$	0.833227	+	4.78231i	0.0316517	+	0.181665i
$694$		0			0
$695$	53.9935	+	21.1909i	2.04809	+	0.803816i
$696$		0			0
$697$	−21.9800	−	56.0041i	−0.832551	−	2.12131i
$698$		0			0
$699$	−18.7884	+	23.5599i	−0.710642	+	0.891117i
$700$		0			0
$701$	−10.3833	−	13.0203i	−0.392172	−	0.491769i	0.546074	−	0.837737i	$-0.316122\pi$
$701$	−10.3833	−	13.0203i	−0.392172	−	0.491769i	−0.938246	+	0.345969i	$0.887550\pi$
$702$		0			0
$703$	−4.47039	−	4.14792i	−0.168604	−	0.156442i
$704$		0			0
$705$	−63.1772	+	36.4753i	−2.37939	+	1.37374i
$706$		0			0
$707$	−22.5428	−	23.2063i	−0.847811	−	0.872761i
$708$		0			0
$709$	0.980841	−	0.910088i	0.0368363	−	0.0341791i	−0.661540	−	0.749910i	$-0.730097\pi$
$709$	0.980841	−	0.910088i	0.0368363	−	0.0341791i	0.698376	+	0.715731i	$0.253906\pi$
$710$		0			0
$711$	−0.481466	−	3.19432i	−0.0180564	−	0.119796i
$712$		0			0
$713$	−35.7167	+	8.15211i	−1.33760	+	0.305299i
$714$		0			0
$715$	−20.9591	−	4.78377i	−0.783825	−	0.178903i
$716$		0			0
$717$	36.5995	+	21.1307i	1.36683	+	0.789142i
$718$		0			0
$719$	8.07862	+	5.50791i	0.301282	+	0.205410i	0.704519	−	0.709685i	$-0.251163\pi$
$719$	8.07862	+	5.50791i	0.301282	+	0.205410i	−0.403237	+	0.915095i	$0.632115\pi$
$720$		0			0
$721$	7.70499	+	30.5188i	0.286949	+	1.13658i
$722$		0			0
$723$	−0.430515	−	1.39570i	−0.0160110	−	0.0519065i
$724$		0			0
$725$	2.10589	−	28.1011i	0.0782106	−	1.04365i
$726$		0			0
$727$	26.2048	+	12.6196i	0.971884	+	0.468034i	0.851306	−	0.524669i	$-0.175811\pi$
$727$	26.2048	+	12.6196i	0.971884	+	0.468034i	0.120578	+	0.992704i	$0.461525\pi$
$728$		0			0
$729$	−26.9535	+	12.9801i	−0.998277	+	0.480745i
$730$		0			0
$731$	−2.77013	−	0.854472i	−0.102457	−	0.0316038i
$732$		0			0
$733$	−6.46457	+	42.8896i	−0.238774	+	1.58416i	0.472552	+	0.881303i	$0.343333\pi$
$733$	−6.46457	+	42.8896i	−0.238774	+	1.58416i	−0.711326	+	0.702862i	$0.751905\pi$
$734$		0			0
$735$	−20.6105	+	33.4214i	−0.760230	+	1.23277i
$736$		0			0
$737$	−35.5967	−	5.36534i	−1.31122	−	0.197635i
$738$		0			0
$739$	6.75574	−	21.9016i	0.248514	−	0.805662i	−0.742257	−	0.670115i	$-0.766245\pi$
$739$	6.75574	−	21.9016i	0.248514	−	0.805662i	0.990771	−	0.135547i	$-0.0432791\pi$
$740$		0			0
$741$	2.94725	+	6.12002i	0.108270	+	0.224825i
$742$		0			0
$743$	−4.34466	+	9.02179i	−0.159390	+	0.330977i	−0.965335	−	0.261013i	$-0.915943\pi$
$743$	−4.34466	+	9.02179i	−0.159390	+	0.330977i	0.805945	+	0.591990i	$0.201658\pi$
$744$		0			0
$745$	4.70496	+	0.352588i	0.172376	+	0.0129178i
$746$		0			0
$747$	−4.64803	+	1.43373i	−0.170063	+	0.0524574i
$748$		0			0
$749$	6.88938	+	1.40731i	0.251733	+	0.0514218i
$750$		0			0
$751$	−10.7004	+	15.6947i	−0.390464	+	0.572706i	−0.970263	−	0.242054i	$-0.922179\pi$
$751$	−10.7004	+	15.6947i	−0.390464	+	0.572706i	0.579798	+	0.814760i	$0.303131\pi$
$752$		0			0
$753$	−24.5549	+	42.5303i	−0.894829	+	1.54989i
$754$		0			0
$755$	17.9384	−	78.5932i	0.652845	−	2.86030i
$756$		0			0
$757$	2.84508	+	12.4651i	0.103406	+	0.453052i	0.999949	+	0.0100949i	$0.00321336\pi$
$757$	2.84508	+	12.4651i	0.103406	+	0.453052i	−0.896543	+	0.442957i	$0.853929\pi$
$758$		0			0
$759$	−39.6900	+	5.98230i	−1.44066	+	0.217144i
$760$		0			0
$761$	−11.5297	−	12.4260i	−0.417950	−	0.450443i	0.488621	−	0.872496i	$-0.337500\pi$
$761$	−11.5297	−	12.4260i	−0.417950	−	0.450443i	−0.906571	+	0.422053i	$0.861310\pi$
$762$		0			0
$763$	9.17220	+	15.0785i	0.332056	+	0.545877i
$764$		0			0
$765$	−6.25857	−	10.8402i	−0.226279	−	0.391927i
$766$		0			0
$767$	−6.11107	+	6.58616i	−0.220658	+	0.237813i
$768$		0			0
$769$	−33.2688	+	26.5310i	−1.19970	+	0.956732i	−0.999734	−	0.0230699i	$-0.992656\pi$
$769$	−33.2688	+	26.5310i	−1.19970	+	0.956732i	−0.199970	+	0.979802i	$0.564085\pi$
$770$		0			0
$771$	34.4696	+	27.4886i	1.24139	+	0.989979i
$772$		0			0
$773$	−21.4078	+	8.40196i	−0.769987	+	0.302198i	−0.717624	−	0.696431i	$-0.754770\pi$
$773$	−21.4078	+	8.40196i	−0.769987	+	0.302198i	−0.0523626	+	0.998628i	$0.516675\pi$
$774$		0			0
$775$	14.2533	−	36.3169i	0.511995	−	1.30454i
$776$		0			0
$777$	−4.83410	+	8.83409i	−0.173423	+	0.316921i
$778$		0			0
$779$	22.3801	−	1.67716i	0.801851	−	0.0600904i
$780$		0			0
$781$	−34.1572	+	23.2880i	−1.22224	+	0.833310i
$782$		0			0
$783$	20.3255			0.726373
$784$		0			0
$785$	1.93853			0.0691892
$786$		0			0
$787$	6.56143	−	4.47351i	0.233890	−	0.159463i	−0.440704	−	0.897652i	$-0.645271\pi$
$787$	6.56143	−	4.47351i	0.233890	−	0.159463i	0.674594	+	0.738189i	$0.264319\pi$
$788$		0			0
$789$	−18.2523	+	1.36782i	−0.649799	+	0.0486957i
$790$		0			0
$791$	26.5582	+	23.5339i	0.944299	+	0.836771i
$792$		0			0
$793$	−8.15692	+	20.7835i	−0.289661	+	0.738044i
$794$		0			0
$795$	20.4573	−	8.02890i	0.725545	−	0.284756i
$796$		0			0
$797$	−21.2011	−	16.9073i	−0.750983	−	0.598889i	0.171384	−	0.985204i	$-0.445176\pi$
$797$	−21.2011	−	16.9073i	−0.750983	−	0.598889i	−0.922367	+	0.386316i	$0.873748\pi$
$798$		0			0
$799$	68.7806	−	54.8507i	2.43328	−	1.94048i
$800$		0			0
$801$	2.80007	−	3.01775i	0.0989355	−	0.106627i
$802$		0			0
$803$	7.87936	+	13.6474i	0.278056	+	0.481608i
$804$		0			0
$805$	57.0492	+	37.0109i	2.01072	+	1.30446i
$806$		0			0
$807$	−0.515520	−	0.555599i	−0.0181472	−	0.0195580i
$808$		0			0
$809$	7.42560	−	1.11923i	0.261070	−	0.0393500i	−0.0172029	−	0.999852i	$-0.505476\pi$
$809$	7.42560	−	1.11923i	0.261070	−	0.0393500i	0.278273	+	0.960502i	$0.410238\pi$
$810$		0			0
$811$	−3.17813	−	13.9243i	−0.111599	−	0.488948i	−0.999578	−	0.0290630i	$-0.990748\pi$
$811$	−3.17813	−	13.9243i	−0.111599	−	0.488948i	0.887978	−	0.459885i	$-0.152109\pi$
$812$		0			0
$813$	−0.243502	+	1.06685i	−0.00853999	+	0.0374161i
$814$		0			0
$815$	−10.3923	+	18.0000i	−0.364026	+	0.630512i
$816$		0			0
$817$	0.609174	−	0.893494i	0.0213123	−	0.0312594i
$818$		0			0
$819$	−1.80283	+	1.50652i	−0.0629960	+	0.0526420i
$820$		0			0
$821$	−28.9379	+	8.92617i	−1.00994	+	0.311525i	−0.755207	−	0.655486i	$-0.772464\pi$
$821$	−28.9379	+	8.92617i	−1.00994	+	0.311525i	−0.254733	+	0.967011i	$0.581988\pi$
$822$		0			0
$823$	−8.87393	−	0.665009i	−0.309326	−	0.0231808i	−0.0808370	−	0.996727i	$-0.525759\pi$
$823$	−8.87393	−	0.665009i	−0.309326	−	0.0231808i	−0.228489	+	0.973547i	$0.573378\pi$
$824$		0			0
$825$	18.5460	−	38.5113i	0.645690	−	1.34079i
$826$		0			0
$827$	7.29764	+	15.1537i	0.253764	+	0.526946i	0.988466	−	0.151444i	$-0.0483923\pi$
$827$	7.29764	+	15.1537i	0.253764	+	0.526946i	−0.734702	+	0.678390i	$0.762678\pi$
$828$		0			0
$829$	4.37598	−	14.1866i	0.151984	−	0.492721i	−0.847277	−	0.531151i	$-0.821760\pi$
$829$	4.37598	−	14.1866i	0.151984	−	0.492721i	0.999261	+	0.0384305i	$0.0122358\pi$
$830$		0			0
$831$	−25.0984	−	3.78298i	−0.870654	−	0.131230i
$832$		0			0
$833$	18.5703	−	43.5582i	0.643423	−	1.50920i
$834$		0			0
$835$	−1.32435	+	8.78649i	−0.0458310	+	0.304069i
$836$		0			0
$837$	26.8895	+	8.29432i	0.929438	+	0.286694i
$838$		0			0
$839$	27.5284	−	13.2570i	0.950387	−	0.457682i	0.106565	−	0.994306i	$-0.466015\pi$
$839$	27.5284	−	13.2570i	0.950387	−	0.457682i	0.843822	+	0.536623i	$0.180300\pi$
$840$		0			0
$841$	14.0141	+	6.74884i	0.483246	+	0.232719i
$842$		0			0
$843$	0.787031	−	10.5022i	0.0271068	−	0.361715i
$844$		0			0
$845$	10.5806	+	34.3016i	0.363985	+	1.18001i
$846$		0			0
$847$	2.35721	−	3.09884i	0.0809948	−	0.106477i
$848$		0			0
$849$	22.4799	+	15.3265i	0.771507	+	0.526005i
$850$		0			0
$851$	15.1038	+	8.72021i	0.517753	+	0.298925i
$852$		0			0
$853$	−48.2537	−	11.0136i	−1.65217	−	0.377098i	−0.707914	−	0.706298i	$-0.750364\pi$
$853$	−48.2537	−	11.0136i	−1.65217	−	0.377098i	−0.944260	+	0.329200i	$0.893221\pi$
$854$		0			0
$855$	4.55226	−	1.03902i	0.155684	−	0.0355338i
$856$		0			0
$857$	3.44894	+	22.8822i	0.117814	+	0.781643i	0.967227	+	0.253914i	$0.0817180\pi$
$857$	3.44894	+	22.8822i	0.117814	+	0.781643i	−0.849413	+	0.527728i	$0.823044\pi$
$858$		0			0
$859$	−10.9159	+	10.1285i	−0.372445	+	0.345579i	−0.844082	−	0.536214i	$-0.819854\pi$
$859$	−10.9159	+	10.1285i	−0.372445	+	0.345579i	0.471637	+	0.881793i	$0.343663\pi$
$860$		0			0
$861$	−11.7317	−	35.1543i	−0.399816	−	1.19805i
$862$		0			0
$863$	−22.3064	+	12.8786i	−0.759319	+	0.438393i	−0.829051	−	0.559173i	$-0.811119\pi$
$863$	−22.3064	+	12.8786i	−0.759319	+	0.438393i	0.0697325	+	0.997566i	$0.477785\pi$
$864$		0			0
$865$	22.8707	+	21.2209i	0.777625	+	0.721531i
$866$		0			0
$867$	−28.2399	−	35.4117i	−0.959078	−	1.20265i
$868$		0			0
$869$	−13.6907	+	17.1676i	−0.464425	+	0.582371i
$870$		0			0
$871$	−6.36527	−	16.2184i	−0.215679	−	0.549541i
$872$		0			0
$873$	2.56207	+	1.00554i	0.0867131	+	0.0340324i
$874$		0			0
$875$	−23.3354	+	9.78088i	−0.788882	+	0.330654i
$876$		0			0
$877$	−4.17044	−	55.6506i	−0.140826	−	1.87919i	−0.404447	−	0.914562i	$-0.632536\pi$
$877$	−4.17044	−	55.6506i	−0.140826	−	1.87919i	0.263621	−	0.964626i	$-0.415083\pi$
$878$		0			0
$879$	7.50597	+	11.0092i	0.253170	+	0.371332i
$880$		0			0
$881$		−	15.9782i		−	0.538319i	−0.963096	−	0.269159i	$-0.913254\pi$
$881$		−	15.9782i		−	0.538319i	0.963096	−	0.269159i	$-0.0867458\pi$
$882$		0			0
$883$			14.1392i			0.475822i	0.971287	+	0.237911i	$0.0764626\pi$
$883$			14.1392i			0.475822i	−0.971287	+	0.237911i	$0.923537\pi$
$884$		0			0
$885$	−16.6102	−	24.3627i	−0.558346	−	0.818943i
$886$		0			0
$887$	0.963813	+	12.8612i	0.0323617	+	0.431836i	0.989728	+	0.142961i	$0.0456623\pi$
$887$	0.963813	+	12.8612i	0.0323617	+	0.431836i	−0.957367	+	0.288875i	$0.906719\pi$
$888$		0			0
$889$	30.6816	+	1.59381i	1.02903	+	0.0534545i
$890$		0			0
$891$	23.5754	+	9.25266i	0.789805	+	0.309976i
$892$		0			0
$893$	11.9895	+	30.5487i	0.401213	+	1.02227i
$894$		0			0
$895$	21.6987	−	27.2094i	0.725309	−	0.909509i
$896$		0			0
$897$	−12.1121	−	15.1881i	−0.404410	−	0.507115i
$898$		0			0
$899$	−13.6455	−	12.6612i	−0.455104	−	0.422275i
$900$		0			0
$901$	−22.9515	+	13.2511i	−0.764626	+	0.441457i
$902$		0			0
$903$	−1.67679	−	0.614165i	−0.0558000	−	0.0204381i
$904$		0			0
$905$	−5.30974	+	4.92672i	−0.176502	+	0.163770i
$906$		0			0
$907$	2.65498	+	17.6147i	0.0881573	+	0.584886i	0.988676	+	0.150068i	$0.0479492\pi$
$907$	2.65498	+	17.6147i	0.0881573	+	0.584886i	−0.900518	+	0.434818i	$0.856813\pi$
$908$		0			0
$909$	6.19381	−	1.41370i	0.205436	−	0.0468893i
$910$		0			0
$911$	9.37522	+	2.13983i	0.310615	+	0.0708959i	0.374987	−	0.927030i	$-0.377647\pi$
$911$	9.37522	+	2.13983i	0.310615	+	0.0708959i	−0.0643718	+	0.997926i	$0.520504\pi$
$912$		0			0
$913$	28.6336	+	16.5316i	0.947634	+	0.547117i
$914$		0			0
$915$	−60.5418	−	41.2767i	−2.00145	−	1.36457i
$916$		0			0
$917$	8.98661	+	4.07693i	0.296764	+	0.134632i
$918$		0			0
$919$	8.44895	+	27.3908i	0.278705	+	0.903539i	0.981388	+	0.192036i	$0.0615091\pi$
$919$	8.44895	+	27.3908i	0.278705	+	0.903539i	−0.702683	+	0.711503i	$0.748015\pi$
$920$		0			0
$921$	−0.468011	+	6.24517i	−0.0154215	+	0.205785i
$922$		0			0
$923$	−18.0267	−	8.68122i	−0.593357	−	0.285746i
$924$		0			0
$925$	−16.7334	+	8.05840i	−0.550192	+	0.264959i
$926$		0			0
$927$	−5.90637	−	1.82187i	−0.193991	−	0.0598382i
$928$		0			0
$929$	3.81476	−	25.3093i	0.125158	−	0.830370i	−0.834866	−	0.550453i	$-0.814455\pi$
$929$	3.81476	−	25.3093i	0.125158	−	0.830370i	0.960024	−	0.279917i	$-0.0903070\pi$
$930$		0			0
$931$	13.4850	+	11.4090i	0.441952	+	0.373915i
$932$		0			0
$933$	−8.63217	−	1.30109i	−0.282604	−	0.0425958i
$934$		0			0
$935$	−25.0788	+	81.3034i	−0.820164	+	2.65891i
$936$		0			0
$937$	−10.9204	−	22.6765i	−0.356754	−	0.740808i	0.642930	−	0.765925i	$-0.277719\pi$
$937$	−10.9204	−	22.6765i	−0.356754	−	0.740808i	−0.999685	+	0.0251168i	$0.992004\pi$
$938$		0			0
$939$	9.49989	−	19.7267i	0.310017	−	0.643757i
$940$		0			0
$941$	−9.72641	−	0.728893i	−0.317072	−	0.0237612i	−0.0847562	−	0.996402i	$-0.527011\pi$
$941$	−9.72641	−	0.728893i	−0.317072	−	0.0237612i	−0.232316	+	0.972640i	$0.574630\pi$
$942$		0			0
$943$	−61.3321	+	18.9185i	−1.99725	+	0.616070i
$944$		0			0
$945$	−23.7349	−	46.5294i	−0.772096	−	1.51360i
$946$		0			0
$947$	−21.6860	+	31.8075i	−0.704700	+	1.03361i	0.292309	+	0.956324i	$0.405576\pi$
$947$	−21.6860	+	31.8075i	−0.704700	+	1.03361i	−0.997009	+	0.0772817i	$0.975376\pi$
$948$		0			0
$949$	−3.81348	+	6.60513i	−0.123791	+	0.214412i
$950$		0			0
$951$	11.5598	−	50.6468i	0.374852	−	1.64233i
$952$		0			0
$953$	6.52746	+	28.5987i	0.211445	+	0.926402i	0.963586	+	0.267400i	$0.0861643\pi$
$953$	6.52746	+	28.5987i	0.211445	+	0.926402i	−0.752140	+	0.659003i	$0.770979\pi$
$954$		0			0
$955$	10.8088	−	1.62916i	0.349764	−	0.0527185i
$956$		0			0
$957$	−13.8719	−	14.9503i	−0.448414	−	0.483275i
$958$		0			0
$959$	−2.15589	−	21.9963i	−0.0696174	−	0.710296i
$960$		0			0
$961$	2.61441	+	4.52828i	0.0843356	+	0.146074i
$962$		0			0
$963$	−0.939179	+	1.01219i	−0.0302646	+	0.0326175i
$964$		0			0
$965$	31.9064	−	25.4445i	1.02710	−	0.819088i
$966$		0			0
$967$	−32.0616	−	25.5682i	−1.03103	−	0.822219i	−0.0467629	−	0.998906i	$-0.514891\pi$
$967$	−32.0616	−	25.5682i	−1.03103	−	0.822219i	−0.984267	+	0.176687i	$0.943462\pi$
$968$		0			0
$969$	25.0253	−	9.82170i	0.803928	−	0.315519i
$970$		0			0
$971$	−14.4150	+	36.7287i	−0.462598	+	1.17868i	0.489259	+	0.872139i	$0.337267\pi$
$971$	−14.4150	+	36.7287i	−0.462598	+	1.17868i	−0.951857	+	0.306542i	$0.900828\pi$
$972$		0			0
$973$	−41.4533	−	11.7542i	−1.32893	−	0.376822i
$974$		0			0
$975$	20.6297	−	1.54598i	0.660678	−	0.0495110i
$976$		0			0
$977$	31.2622	−	21.3142i	1.00017	−	0.681901i	0.0516611	−	0.998665i	$-0.483548\pi$
$977$	31.2622	−	21.3142i	1.00017	−	0.681901i	0.948505	+	0.316763i	$0.102596\pi$
$978$		0			0
$979$	−27.9827			−0.894330
$980$		0			0
$981$	−3.46572			−0.110652
$982$		0			0
$983$	−26.2902	+	17.9243i	−0.838526	+	0.571697i	−0.904670	−	0.426113i	$-0.859883\pi$
$983$	−26.2902	+	17.9243i	−0.838526	+	0.571697i	0.0661444	+	0.997810i	$0.478930\pi$
$984$		0			0
$985$	68.1565	−	5.10762i	2.17165	−	0.162742i
$986$		0			0
$987$	44.0644	−	31.5444i	1.40258	−	1.00407i
$988$		0			0
$989$	−1.12988	+	2.87887i	−0.0359279	+	0.0915429i
$990$		0			0
$991$	23.9420	−	9.39653i	0.760542	−	0.298491i	0.0468043	−	0.998904i	$-0.485096\pi$
$991$	23.9420	−	9.39653i	0.760542	−	0.298491i	0.713737	+	0.700414i	$0.247001\pi$
$992$		0			0
$993$	28.4243	+	22.6676i	0.902017	+	0.719335i
$994$		0			0
$995$	−0.826769	+	0.659326i	−0.0262103	+	0.0209021i
$996$		0			0
$997$	−16.3579	+	17.6297i	−0.518061	+	0.558337i	−0.936843	−	0.349750i	$-0.886267\pi$
$997$	−16.3579	+	17.6297i	−0.518061	+	0.558337i	0.418782	+	0.908087i	$0.362457\pi$
$998$		0			0
$999$	−6.69803	−	11.6013i	−0.211916	−	0.367050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bp.c.255.8	yes	120
4.3	odd	2	inner	784.2.bp.c.255.3	✓	120
49.5	odd	42	inner	784.2.bp.c.495.3	yes	120
196.103	even	42	inner	784.2.bp.c.495.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bp.c.255.3	✓	120	4.3	odd	2	inner
784.2.bp.c.255.8	yes	120	1.1	even	1	trivial
784.2.bp.c.495.3	yes	120	49.5	odd	42	inner
784.2.bp.c.495.8	yes	120	196.103	even	42	inner

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.bp (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30128 - 0.887199i) q^{3} +(-3.55166 + 0.266160i) q^{5} +(2.60649 - 0.454131i) q^{7} +(-0.189810 + 0.483628i) q^{9} +O(q^{10})\)	\(q+(1.30128 - 0.887199i) q^{3} +(-3.55166 + 0.266160i) q^{5} +(2.60649 - 0.454131i) q^{7} +(-0.189810 + 0.483628i) q^{9} +(3.28740 - 1.29021i) q^{11} +(1.33630 + 1.06566i) q^{13} +(-4.38557 + 3.49738i) q^{15} +(4.60104 - 4.95874i) q^{17} +(1.26170 + 2.18533i) q^{19} +(2.98887 - 2.90342i) q^{21} +(-4.90853 - 5.29013i) q^{23} +(7.59929 - 1.14541i) q^{25} +(1.23345 + 5.40412i) q^{27} +(0.815942 - 3.57488i) q^{29} +(2.53827 - 4.39641i) q^{31} +(3.13316 - 4.59550i) q^{33} +(-9.13648 + 2.30666i) q^{35} +(-2.30934 + 0.712338i) q^{37} +(2.68436 + 0.201165i) q^{39} +(3.85892 - 8.01313i) q^{41} +(-0.185940 - 0.386109i) q^{43} +(0.545418 - 1.76820i) q^{45} +(12.8599 + 1.93832i) q^{47} +(6.58753 - 2.36737i) q^{49} +(1.58786 - 10.5348i) q^{51} +(-3.74376 - 1.15480i) q^{53} +(-11.3323 + 5.45735i) q^{55} +(3.58065 + 1.72435i) q^{57} +(-0.392828 + 5.24192i) q^{59} +(3.85033 + 12.4825i) q^{61} +(-0.275107 + 1.34677i) q^{63} +(-5.02972 - 3.42921i) q^{65} +(-8.82791 - 5.09679i) q^{67} +(-11.0808 - 2.52912i) q^{69} +(-11.4127 + 2.60487i) q^{71} +(0.665073 + 4.41247i) q^{73} +(8.87261 - 8.23258i) q^{75} +(7.98262 - 4.85581i) q^{77} +(-5.38475 + 3.10889i) q^{79} +(5.25704 + 4.87782i) q^{81} +(5.83732 + 7.31977i) q^{83} +(-15.0215 + 18.8364i) q^{85} +(-2.10986 - 5.37583i) q^{87} +(-7.37597 - 2.89485i) q^{89} +(3.96700 + 2.17078i) q^{91} +(-0.597487 - 7.97291i) q^{93} +(-5.06277 - 7.42573i) q^{95} -5.29761i q^{97} +1.83477i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{5} + 12 q^{9}+O(q^{10}) \) 120 * q + 6 * q^5 + 12 * q^9	\( 120 q + 6 q^{5} + 12 q^{9} - 32 q^{17} - 14 q^{21} - 8 q^{25} - 28 q^{29} + 42 q^{33} + 28 q^{37} + 56 q^{41} + 186 q^{45} + 84 q^{49} + 128 q^{53} - 70 q^{57} + 8 q^{61} + 4 q^{65} - 56 q^{69} + 60 q^{73} + 84 q^{77} + 34 q^{81} + 12 q^{85} + 22 q^{89} - 112 q^{93}+O(q^{100}) \) 120 * q + 6 * q^5 + 12 * q^9 - 32 * q^17 - 14 * q^21 - 8 * q^25 - 28 * q^29 + 42 * q^33 + 28 * q^37 + 56 * q^41 + 186 * q^45 + 84 * q^49 + 128 * q^53 - 70 * q^57 + 8 * q^61 + 4 * q^65 - 56 * q^69 + 60 * q^73 + 84 * q^77 + 34 * q^81 + 12 * q^85 + 22 * q^89 - 112 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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