LMFDB - Embedded newform 740.2.bf.a.97.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(97,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("740.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.bf (of order $12$, degree $4$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.19
Character	$\chi$	$=$	740.97
Dual form			740.2.bf.a.473.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.843267 - 3.14712i) q^{3} +(-2.00134 - 0.997312i) q^{5} +(0.336984 - 1.25764i) q^{7} +(-6.59517 - 3.80772i) q^{9} +0.753951i q^{11} +(0.257348 + 0.445740i) q^{13} +(-4.82632 + 5.45745i) q^{15} +(-4.71154 - 2.72021i) q^{17} +(8.35912 + 2.23982i) q^{19} +(-3.67377 - 2.12105i) q^{21} -7.75662 q^{23} +(3.01074 + 3.99193i) q^{25} +(-10.6333 + 10.6333i) q^{27} +(1.51569 + 1.51569i) q^{29} +(5.02996 - 5.02996i) q^{31} +(2.37277 + 0.635783i) q^{33} +(-1.92868 + 2.18089i) q^{35} +(-3.80792 - 4.74339i) q^{37} +(1.61981 - 0.434026i) q^{39} +(5.29441 - 3.05673i) q^{41} -6.78856 q^{43} +(9.40169 + 14.1980i) q^{45} +(1.96762 + 1.96762i) q^{47} +(4.59408 + 2.65239i) q^{49} +(-12.5339 + 12.5339i) q^{51} +(-0.0508139 - 0.189640i) q^{53} +(0.751925 - 1.50891i) q^{55} +(14.0979 - 24.4183i) q^{57} +(-2.50761 - 9.35852i) q^{59} +(-9.48560 - 2.54166i) q^{61} +(-7.01120 + 7.01120i) q^{63} +(-0.0704995 - 1.14873i) q^{65} +(0.679656 + 0.182113i) q^{67} +(-6.54090 + 24.4110i) q^{69} +(3.51261 + 6.08402i) q^{71} +(2.33866 + 2.33866i) q^{73} +(15.1019 - 6.10888i) q^{75} +(0.948199 + 0.254069i) q^{77} +(-13.2069 - 3.53879i) q^{79} +(13.0743 + 22.6454i) q^{81} +(0.350447 + 1.30789i) q^{83} +(6.71650 + 10.1429i) q^{85} +(6.04818 - 3.49192i) q^{87} +(8.40884 - 2.25314i) q^{89} +(0.647302 - 0.173444i) q^{91} +(-11.5883 - 20.0715i) q^{93} +(-14.4956 - 12.8193i) q^{95} -3.58048i q^{97} +(2.87084 - 4.97244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} + 8 q^{13} + 2 q^{15} + 12 q^{19} - 4 q^{23} + 2 q^{25} + 28 q^{27} - 6 q^{29} + 16 q^{31} - 6 q^{33} + 20 q^{35} - 22 q^{37} + 8 q^{39} + 54 q^{41} - 16 q^{43} + 38 q^{45} + 8 q^{47} - 36 q^{49}+ \cdots - 70 q^{95}+O(q^{100}) $ 76 * q - 2 * q^3 + 8 * q^13 + 2 * q^15 + 12 * q^19 - 4 * q^23 + 2 * q^25 + 28 * q^27 - 6 * q^29 + 16 * q^31 - 6 * q^33 + 20 * q^35 - 22 * q^37 + 8 * q^39 + 54 * q^41 - 16 * q^43 + 38 * q^45 + 8 * q^47 - 36 * q^49 - 24 * q^53 + 18 * q^55 - 16 * q^59 - 28 * q^61 - 6 * q^65 - 34 * q^67 + 64 * q^69 - 8 * q^71 + 4 * q^73 + 24 * q^75 - 2 * q^77 - 40 * q^79 + 2 * q^81 - 62 * q^83 + 108 * q^87 - 2 * q^89 - 20 * q^91 - 30 * q^93 - 70 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.843267	−	3.14712i	0.486861	−	1.81699i	−0.0846714	−	0.996409i	$-0.526984\pi$
$3$	0.843267	−	3.14712i	0.486861	−	1.81699i	0.571532	−	0.820580i	$-0.306349\pi$
$4$		0			0
$5$	−2.00134	−	0.997312i	−0.895027	−	0.446012i
$5$	−2.00134	−	0.997312i	−0.895027	−	0.446012i
$6$		0			0
$7$	0.336984	−	1.25764i	0.127368	−	0.475343i	−0.872545	−	0.488533i	$-0.837532\pi$
$7$	0.336984	−	1.25764i	0.127368	−	0.475343i	0.999913	+	0.0131903i	$0.00419871\pi$
$8$		0			0
$9$	−6.59517	−	3.80772i	−2.19839	−	1.26924i
$10$		0			0
$11$			0.753951i			0.227325i	0.993519	+	0.113662i	$0.0362582\pi$
$11$			0.753951i			0.227325i	−0.993519	+	0.113662i	$0.963742\pi$
$12$		0			0
$13$	0.257348	+	0.445740i	0.0713755	+	0.123626i	0.899504	−	0.436912i	$-0.143928\pi$
$13$	0.257348	+	0.445740i	0.0713755	+	0.123626i	−0.828129	+	0.560538i	$0.810594\pi$
$14$		0			0
$15$	−4.82632	+	5.45745i	−1.24615	+	1.40911i
$16$		0			0
$17$	−4.71154	−	2.72021i	−1.14272	−	0.659747i	−0.195614	−	0.980681i	$-0.562670\pi$
$17$	−4.71154	−	2.72021i	−1.14272	−	0.659747i	−0.947102	+	0.320934i	$0.896003\pi$
$18$		0			0
$19$	8.35912	+	2.23982i	1.91771	+	0.513850i	0.990112	+	0.140276i	$0.0447989\pi$
$19$	8.35912	+	2.23982i	1.91771	+	0.513850i	0.927600	+	0.373574i	$0.121868\pi$
$20$		0			0
$21$	−3.67377	−	2.12105i	−0.801683	−	0.462852i
$22$		0			0
$23$	−7.75662			−1.61737			−0.808683	−	0.588245i	$-0.799819\pi$
$23$	−7.75662			−1.61737			−0.808683	+	0.588245i	$0.799819\pi$
$24$		0			0
$25$	3.01074	+	3.99193i	0.602147	+	0.798385i
$26$		0			0
$27$	−10.6333	+	10.6333i	−2.04638	+	2.04638i
$28$		0			0
$29$	1.51569	+	1.51569i	0.281456	+	0.281456i	0.833690	−	0.552233i	$-0.186224\pi$
$29$	1.51569	+	1.51569i	0.281456	+	0.281456i	−0.552233	+	0.833690i	$0.686224\pi$
$30$		0			0
$31$	5.02996	−	5.02996i	0.903408	−	0.903408i	−0.0923213	−	0.995729i	$-0.529429\pi$
$31$	5.02996	−	5.02996i	0.903408	−	0.903408i	0.995729	+	0.0923213i	$0.0294287\pi$
$32$		0			0
$33$	2.37277	+	0.635783i	0.413047	+	0.110676i
$34$		0			0
$35$	−1.92868	+	2.18089i	−0.326006	+	0.368637i
$36$		0			0
$37$	−3.80792	−	4.74339i	−0.626018	−	0.779809i
$37$	−3.80792	−	4.74339i	−0.626018	−	0.779809i
$38$		0			0
$39$	1.61981	−	0.434026i	0.259377	−	0.0694999i
$40$		0			0
$41$	5.29441	−	3.05673i	0.826849	−	0.477381i	−0.0259238	−	0.999664i	$-0.508253\pi$
$41$	5.29441	−	3.05673i	0.826849	−	0.477381i	0.852772	+	0.522283i	$0.174919\pi$
$42$		0			0
$43$	−6.78856			−1.03525			−0.517623	−	0.855609i	$-0.673183\pi$
$43$	−6.78856			−1.03525			−0.517623	+	0.855609i	$0.673183\pi$
$44$		0			0
$45$	9.40169	+	14.1980i	1.40152	+	2.11651i
$46$		0			0
$47$	1.96762	+	1.96762i	0.287007	+	0.287007i	0.835896	−	0.548888i	$-0.184949\pi$
$47$	1.96762	+	1.96762i	0.287007	+	0.287007i	−0.548888	+	0.835896i	$0.684949\pi$
$48$		0			0
$49$	4.59408	+	2.65239i	0.656297	+	0.378913i
$50$		0			0
$51$	−12.5339	+	12.5339i	−1.75510	+	1.75510i
$52$		0			0
$53$	−0.0508139	−	0.189640i	−0.00697983	−	0.0260491i	0.962348	−	0.271820i	$-0.0876256\pi$
$53$	−0.0508139	−	0.189640i	−0.00697983	−	0.0260491i	−0.969328	+	0.245771i	$0.920959\pi$
$54$		0			0
$55$	0.751925	−	1.50891i	0.101390	−	0.203462i
$56$		0			0
$57$	14.0979	−	24.4183i	1.86732	−	3.23429i
$58$		0			0
$59$	−2.50761	−	9.35852i	−0.326463	−	1.21838i	−0.912833	−	0.408333i	$-0.866110\pi$
$59$	−2.50761	−	9.35852i	−0.326463	−	1.21838i	0.586370	−	0.810043i	$-0.300556\pi$
$60$		0			0
$61$	−9.48560	−	2.54166i	−1.21451	−	0.325426i	−0.405978	−	0.913883i	$-0.633069\pi$
$61$	−9.48560	−	2.54166i	−1.21451	−	0.325426i	−0.808529	+	0.588457i	$0.799736\pi$
$62$		0			0
$63$	−7.01120	+	7.01120i	−0.883329	+	0.883329i
$64$		0			0
$65$	−0.0704995	−	1.14873i	−0.00874438	−	0.142483i
$66$		0			0
$67$	0.679656	+	0.182113i	0.0830331	+	0.0222487i	0.300096	−	0.953909i	$-0.402981\pi$
$67$	0.679656	+	0.182113i	0.0830331	+	0.0222487i	−0.217063	+	0.976158i	$0.569648\pi$
$68$		0			0
$69$	−6.54090	+	24.4110i	−0.787432	+	2.93874i
$70$		0			0
$71$	3.51261	+	6.08402i	0.416871	+	0.722041i	0.995623	−	0.0934625i	$-0.0297935\pi$
$71$	3.51261	+	6.08402i	0.416871	+	0.722041i	−0.578752	+	0.815503i	$0.696460\pi$
$72$		0			0
$73$	2.33866	+	2.33866i	0.273719	+	0.273719i	0.830596	−	0.556876i	$-0.188000\pi$
$73$	2.33866	+	2.33866i	0.273719	+	0.273719i	−0.556876	+	0.830596i	$0.688000\pi$
$74$		0			0
$75$	15.1019	−	6.10888i	1.74382	−	0.705393i
$76$		0			0
$77$	0.948199	+	0.254069i	0.108057	+	0.0289539i
$78$		0			0
$79$	−13.2069	−	3.53879i	−1.48590	−	0.398145i	−0.577548	−	0.816357i	$-0.695990\pi$
$79$	−13.2069	−	3.53879i	−1.48590	−	0.398145i	−0.908350	+	0.418212i	$0.862657\pi$
$80$		0			0
$81$	13.0743	+	22.6454i	1.45270	+	2.51615i
$82$		0			0
$83$	0.350447	+	1.30789i	0.0384666	+	0.143559i	0.982488	−	0.186324i	$-0.0596574\pi$
$83$	0.350447	+	1.30789i	0.0384666	+	0.143559i	−0.944022	+	0.329883i	$0.892991\pi$
$84$		0			0
$85$	6.71650	+	10.1429i	0.728507	+	1.10016i
$86$		0			0
$87$	6.04818	−	3.49192i	0.648433	−	0.374373i
$88$		0			0
$89$	8.40884	−	2.25314i	0.891335	−	0.238832i	0.216044	−	0.976384i	$-0.430685\pi$
$89$	8.40884	−	2.25314i	0.891335	−	0.238832i	0.675291	+	0.737551i	$0.264018\pi$
$90$		0			0
$91$	0.647302	−	0.173444i	0.0678557	−	0.0181819i
$92$		0			0
$93$	−11.5883	−	20.0715i	−1.20165	−	2.08132i
$94$		0			0
$95$	−14.4956	−	12.8193i	−1.48722	−	1.31523i
$96$		0			0
$97$		−	3.58048i		−	0.363543i	−0.983341	−	0.181772i	$-0.941817\pi$
$97$		−	3.58048i		−	0.363543i	0.983341	−	0.181772i	$-0.0581831\pi$
$98$		0			0
$99$	2.87084	−	4.97244i	0.288530	−	0.499749i
$100$		0			0
$101$		−	4.51410i		−	0.449169i	−0.974455	−	0.224585i	$-0.927897\pi$
$101$		−	4.51410i		−	0.449169i	0.974455	−	0.224585i	$-0.0721025\pi$
$102$		0			0
$103$		−	8.78656i		−	0.865766i	−0.901450	−	0.432883i	$-0.857496\pi$
$103$		−	8.78656i		−	0.865766i	0.901450	−	0.432883i	$-0.142504\pi$
$104$		0			0
$105$	5.23712	+	7.90885i	0.511091	+	0.771825i
$106$		0			0
$107$	1.62511	−	6.06499i	0.157105	−	0.586325i	−0.841811	−	0.539773i	$-0.818510\pi$
$107$	1.62511	−	6.06499i	0.157105	−	0.586325i	0.998916	−	0.0465518i	$-0.0148232\pi$
$108$		0			0
$109$	−4.06748	−	15.1800i	−0.389594	−	1.45398i	−0.830797	−	0.556576i	$-0.812115\pi$
$109$	−4.06748	−	15.1800i	−0.389594	−	1.45398i	0.441203	−	0.897407i	$-0.354552\pi$
$110$		0			0
$111$	−18.1391	+	7.98401i	−1.72169	+	0.757809i
$112$		0			0
$113$	−0.0331903	−	0.0191624i	−0.00312228	−	0.00180265i	0.498438	−	0.866925i	$-0.333907\pi$
$113$	−0.0331903	−	0.0191624i	−0.00312228	−	0.00180265i	−0.501560	+	0.865123i	$0.667240\pi$
$114$		0			0
$115$	15.5236	+	7.73577i	1.44759	+	0.721364i
$116$		0			0
$117$		−	3.91964i		−	0.362371i
$118$		0			0
$119$	−5.00875	+	5.00875i	−0.459151	+	0.459151i
$120$		0			0
$121$	10.4316			0.948323
$122$		0			0
$123$	−5.15528	−	19.2398i	−0.464836	−	1.73479i
$124$		0			0
$125$	−2.04432	−	10.9919i	−0.182849	−	0.983141i
$126$		0			0
$127$	−7.33510	+	1.96543i	−0.650884	+	0.174404i	−0.569129	−	0.822248i	$-0.692719\pi$
$127$	−7.33510	+	1.96543i	−0.650884	+	0.174404i	−0.0817557	+	0.996652i	$0.526053\pi$
$128$		0			0
$129$	−5.72457	+	21.3644i	−0.504021	+	1.88103i
$130$		0			0
$131$	−4.85667	−	18.1254i	−0.424330	−	1.58362i	−0.765383	−	0.643576i	$-0.777450\pi$
$131$	−4.85667	−	18.1254i	−0.424330	−	1.58362i	0.341053	−	0.940044i	$-0.389216\pi$
$132$		0			0
$133$	5.63377	−	9.75798i	0.488510	−	0.846124i
$134$		0			0
$135$	31.8855	−	10.6761i	2.74427	−	0.918855i
$136$		0			0
$137$	−10.7920	−	10.7920i	−0.922025	−	0.922025i	0.0751471	−	0.997172i	$-0.476057\pi$
$137$	−10.7920	−	10.7920i	−0.922025	−	0.922025i	−0.997172	+	0.0751471i	$0.976057\pi$
$138$		0			0
$139$	−0.628806	+	1.08912i	−0.0533346	+	0.0923783i	−0.891460	−	0.453099i	$-0.850318\pi$
$139$	−0.628806	+	1.08912i	−0.0533346	+	0.0923783i	0.838125	+	0.545477i	$0.183652\pi$
$140$		0			0
$141$	7.85157	−	4.53310i	0.661221	−	0.381756i
$142$		0			0
$143$	−0.336066	+	0.194028i	−0.0281033	+	0.0162254i
$144$		0			0
$145$	−1.52180	−	4.54503i	−0.126378	−	0.377444i
$146$		0			0
$147$	12.2214	−	12.2214i	1.00801	−	1.00801i
$148$		0			0
$149$			17.0103i			1.39354i	0.717295	+	0.696769i	$0.245380\pi$
$149$			17.0103i			1.39354i	−0.717295	+	0.696769i	$0.754620\pi$
$150$		0			0
$151$	11.7599	−	6.78958i	0.957007	−	0.552528i	0.0617565	−	0.998091i	$-0.480330\pi$
$151$	11.7599	−	6.78958i	0.957007	−	0.552528i	0.895251	+	0.445563i	$0.146996\pi$
$152$		0			0
$153$	20.7156	+	35.8804i	1.67476	+	2.90076i
$154$		0			0
$155$	−15.0831	+	5.05023i	−1.21151	+	0.405644i
$156$		0			0
$157$	5.00541	−	1.34119i	0.399475	−	0.107039i	−0.0534876	−	0.998569i	$-0.517034\pi$
$157$	5.00541	−	1.34119i	0.399475	−	0.107039i	0.452963	+	0.891530i	$0.350367\pi$
$158$		0			0
$159$	−0.639669			−0.0507291
$160$		0			0
$161$	−2.61385	+	9.75503i	−0.206000	+	0.768804i
$162$		0			0
$163$	19.4362	+	11.2215i	1.52236	+	0.878934i	0.999651	+	0.0264223i	$0.00841145\pi$
$163$	19.4362	+	11.2215i	1.52236	+	0.878934i	0.522708	+	0.852512i	$0.324922\pi$
$164$		0			0
$165$	−4.11466	−	3.63881i	−0.320326	−	0.283281i
$166$		0			0
$167$	−6.65984	+	3.84506i	−0.515354	+	0.297540i	−0.735032	−	0.678033i	$-0.762833\pi$
$167$	−6.65984	+	3.84506i	−0.515354	+	0.297540i	0.219678	+	0.975572i	$0.429499\pi$
$168$		0			0
$169$	6.36754	−	11.0289i	0.489811	−	0.848378i
$170$		0			0
$171$	−46.6012	−	46.6012i	−3.56368	−	3.56368i
$172$		0			0
$173$	4.47400	−	1.19881i	0.340152	−	0.0911435i	−0.0846993	−	0.996407i	$-0.526993\pi$
$173$	4.47400	−	1.19881i	0.340152	−	0.0911435i	0.424852	+	0.905263i	$0.360326\pi$
$174$		0			0
$175$	6.03497	−	2.44121i	0.456201	−	0.184538i
$176$		0			0
$177$	−31.5669			−2.37272
$178$		0			0
$179$	−0.0394269	−	0.0394269i	−0.00294691	−	0.00294691i	0.705632	−	0.708579i	$-0.250663\pi$
$179$	−0.0394269	−	0.0394269i	−0.00294691	−	0.00294691i	−0.708579	+	0.705632i	$0.750663\pi$
$180$		0			0
$181$	1.38206	+	2.39380i	0.102728	+	0.177929i	0.912808	−	0.408390i	$-0.133910\pi$
$181$	1.38206	+	2.39380i	0.102728	+	0.177929i	−0.810080	+	0.586319i	$0.800576\pi$
$182$		0			0
$183$	−15.9978	+	27.7090i	−1.18259	+	2.04831i
$184$		0			0
$185$	2.89030	+	13.2908i	0.212499	+	0.977161i
$186$		0			0
$187$	2.05090	−	3.55227i	0.149977	−	0.259768i
$188$		0			0
$189$	9.78960	+	16.9561i	0.712089	+	1.23337i
$190$		0			0
$191$	−13.5132	−	13.5132i	−0.977783	−	0.977783i	0.0219752	−	0.999759i	$-0.493005\pi$
$191$	−13.5132	−	13.5132i	−0.977783	−	0.977783i	−0.999759	+	0.0219752i	$0.993005\pi$
$192$		0			0
$193$	17.9898			1.29493			0.647467	−	0.762093i	$-0.275828\pi$
$193$	17.9898			1.29493			0.647467	+	0.762093i	$0.275828\pi$
$194$		0			0
$195$	−3.67465	−	0.746820i	−0.263147	−	0.0534809i
$196$		0			0
$197$	1.02074	−	0.273507i	0.0727249	−	0.0194866i	−0.222273	−	0.974984i	$-0.571348\pi$
$197$	1.02074	−	0.273507i	0.0727249	−	0.0194866i	0.294998	+	0.955498i	$0.404681\pi$
$198$		0			0
$199$	18.2309	+	18.2309i	1.29235	+	1.29235i	0.933328	+	0.359024i	$0.116890\pi$
$199$	18.2309	+	18.2309i	1.29235	+	1.29235i	0.359024	+	0.933328i	$0.383110\pi$
$200$		0			0
$201$	1.14626	−	1.98539i	0.0808511	−	0.140038i
$202$		0			0
$203$	2.41695	−	1.39543i	0.169637	−	0.0979399i
$204$		0			0
$205$	−13.6444	+	0.837380i	−0.952970	+	0.0584851i
$206$		0			0
$207$	51.1562	+	29.5350i	3.55560	+	2.05283i
$208$		0			0
$209$	−1.68871	+	6.30237i	−0.116811	+	0.435944i
$210$		0			0
$211$	5.17023			0.355933			0.177967	−	0.984037i	$-0.443048\pi$
$211$	5.17023			0.355933			0.177967	+	0.984037i	$0.443048\pi$
$212$		0			0
$213$	22.1092	−	5.92414i	1.51490	−	0.405916i
$214$		0			0
$215$	13.5862	+	6.77032i	0.926574	+	0.461732i
$216$		0			0
$217$	−4.63087	−	8.02090i	−0.314364	−	0.544494i
$218$		0			0
$219$	9.33215	−	5.38792i	0.630608	−	0.364082i
$220$		0			0
$221$		−	2.80016i		−	0.188359i
$222$		0			0
$223$	3.17253	−	3.17253i	0.212448	−	0.212448i	−0.592858	−	0.805307i	$-0.702001\pi$
$223$	3.17253	−	3.17253i	0.212448	−	0.212448i	0.805307	+	0.592858i	$0.202001\pi$
$224$		0			0
$225$	−4.65617	−	37.7915i	−0.310411	−	2.51943i
$226$		0			0
$227$	7.65611	−	4.42026i	0.508154	−	0.293383i	−0.223920	−	0.974607i	$-0.571886\pi$
$227$	7.65611	−	4.42026i	0.508154	−	0.293383i	0.732075	+	0.681225i	$0.238552\pi$
$228$		0			0
$229$	5.31204	−	3.06691i	0.351030	−	0.202667i	−0.314109	−	0.949387i	$-0.601706\pi$
$229$	5.31204	−	3.06691i	0.351030	−	0.202667i	0.665139	+	0.746720i	$0.268372\pi$
$230$		0			0
$231$	1.59917	−	2.76985i	0.105218	−	0.182242i
$232$		0			0
$233$	13.2535	+	13.2535i	0.868262	+	0.868262i	0.992280	−	0.124018i	$-0.0395779\pi$
$233$	13.2535	+	13.2535i	0.868262	+	0.868262i	−0.124018	+	0.992280i	$0.539578\pi$
$234$		0			0
$235$	−1.97555	−	5.90022i	−0.128871	−	0.384888i
$236$		0			0
$237$	−22.2740	+	38.5797i	−1.44685	+	2.50602i
$238$		0			0
$239$	2.67258	+	9.97420i	0.172875	+	0.645177i	0.996904	+	0.0786298i	$0.0250545\pi$
$239$	2.67258	+	9.97420i	0.172875	+	0.645177i	−0.824029	+	0.566547i	$0.808279\pi$
$240$		0			0
$241$	−2.32393	+	8.67301i	−0.149697	+	0.558678i	0.849804	+	0.527099i	$0.176720\pi$
$241$	−2.32393	+	8.67301i	−0.149697	+	0.558678i	−0.999501	+	0.0315789i	$0.989946\pi$
$242$		0			0
$243$	38.7168	−	10.3741i	2.48369	−	0.665501i
$244$		0			0
$245$	−6.54906	−	9.89007i	−0.418404	−	0.631854i
$246$		0			0
$247$	1.15283	+	4.30240i	0.0733526	+	0.273755i
$248$		0			0
$249$	4.41159			0.279573
$250$		0			0
$251$	10.4423	−	10.4423i	0.659111	−	0.659111i	−0.296059	−	0.955170i	$-0.595672\pi$
$251$	10.4423	−	10.4423i	0.659111	−	0.659111i	0.955170	+	0.296059i	$0.0956725\pi$
$252$		0			0
$253$		−	5.84811i		−	0.367668i
$254$		0			0
$255$	37.5848	−	12.5844i	2.35365	−	0.788066i
$256$		0			0
$257$	10.0055	+	5.77665i	0.624123	+	0.360338i	0.778472	−	0.627679i	$-0.215995\pi$
$257$	10.0055	+	5.77665i	0.624123	+	0.360338i	−0.154350	+	0.988016i	$0.549328\pi$
$258$		0			0
$259$	−7.24868	+	3.19054i	−0.450411	+	0.198251i
$260$		0			0
$261$	−4.22490	−	15.7675i	−0.261515	−	0.975986i
$262$		0			0
$263$	−0.0322467	+	0.120346i	−0.00198841	+	0.00742086i	−0.966913	−	0.255107i	$-0.917889\pi$
$263$	−0.0322467	+	0.120346i	−0.00198841	+	0.00742086i	0.964924	+	0.262528i	$0.0845561\pi$
$264$		0			0
$265$	−0.0874344	+	0.430212i	−0.00537105	+	0.0264277i
$266$		0			0
$267$		−	28.3636i		−	1.73582i
$268$		0			0
$269$			19.4827i			1.18788i	0.804510	+	0.593940i	$0.202428\pi$
$269$			19.4827i			1.18788i	−0.804510	+	0.593940i	$0.797572\pi$
$270$		0			0
$271$	−11.5488	+	20.0031i	−0.701541	+	1.21510i	0.266385	+	0.963867i	$0.414171\pi$
$271$	−11.5488	+	20.0031i	−0.701541	+	1.21510i	−0.967926	+	0.251237i	$0.919163\pi$
$272$		0			0
$273$		−	2.18340i		−	0.132145i
$274$		0			0
$275$	−3.00972	+	2.26995i	−0.181493	+	0.136883i
$276$		0			0
$277$	3.16913	+	5.48909i	0.190415	+	0.329808i	0.945388	−	0.325948i	$-0.105683\pi$
$277$	3.16913	+	5.48909i	0.190415	+	0.329808i	−0.754973	+	0.655756i	$0.772350\pi$
$278$		0			0
$279$	−52.3261	+	14.0207i	−3.13268	+	0.839400i
$280$		0			0
$281$	10.9155	−	2.92479i	0.651163	−	0.174479i	0.0819083	−	0.996640i	$-0.473899\pi$
$281$	10.9155	−	2.92479i	0.651163	−	0.174479i	0.569255	+	0.822161i	$0.307232\pi$
$282$		0			0
$283$	−6.34817	+	3.66512i	−0.377360	+	0.217869i	−0.676669	−	0.736288i	$-0.736577\pi$
$283$	−6.34817	+	3.66512i	−0.377360	+	0.217869i	0.299309	+	0.954156i	$0.403244\pi$
$284$		0			0
$285$	−52.5675	+	34.8094i	−3.11383	+	2.06193i
$286$		0			0
$287$	−2.06014	−	7.68853i	−0.121606	−	0.453840i
$288$		0			0
$289$	6.29905	+	10.9103i	0.370533	+	0.641781i
$290$		0			0
$291$	−11.2682	−	3.01931i	−0.660554	−	0.176995i
$292$		0			0
$293$	7.41855	+	1.98779i	0.433396	+	0.116128i	0.468920	−	0.883241i	$-0.344643\pi$
$293$	7.41855	+	1.98779i	0.433396	+	0.116128i	−0.0355238	+	0.999369i	$0.511310\pi$
$294$		0			0
$295$	−4.31479	+	21.2305i	−0.251217	+	1.23609i
$296$		0			0
$297$	−8.01698	−	8.01698i	−0.465192	−	0.465192i
$298$		0			0
$299$	−1.99615	−	3.45743i	−0.115440	−	0.199949i
$300$		0			0
$301$	−2.28763	+	8.53757i	−0.131857	+	0.492097i
$302$		0			0
$303$	−14.2064	−	3.80659i	−0.816135	−	0.218683i
$304$		0			0
$305$	16.4491	+	14.5468i	0.941873	+	0.832949i
$306$		0			0
$307$	−21.7666	+	21.7666i	−1.24229	+	1.24229i	−0.283234	+	0.959051i	$0.591407\pi$
$307$	−21.7666	+	21.7666i	−1.24229	+	1.24229i	−0.959051	+	0.283234i	$0.908593\pi$
$308$		0			0
$309$	−27.6523	−	7.40942i	−1.57309	−	0.421507i
$310$		0			0
$311$	−0.626820	−	2.33932i	−0.0355437	−	0.132651i	0.945874	−	0.324534i	$-0.105207\pi$
$311$	−0.626820	−	2.33932i	−0.0355437	−	0.132651i	−0.981418	+	0.191883i	$0.938541\pi$
$312$		0			0
$313$	8.06952	−	13.9768i	0.456116	−	0.790016i	−0.542636	−	0.839968i	$-0.682574\pi$
$313$	8.06952	−	13.9768i	0.456116	−	0.790016i	0.998752	+	0.0499522i	$0.0159069\pi$
$314$		0			0
$315$	21.0242	−	7.03945i	1.18458	−	0.396628i
$316$		0			0
$317$	−3.46889	−	12.9461i	−0.194832	−	0.727123i	−0.992310	−	0.123776i	$-0.960500\pi$
$317$	−3.46889	−	12.9461i	−0.194832	−	0.727123i	0.797478	−	0.603348i	$-0.206167\pi$
$318$		0			0
$319$	−1.14276	+	1.14276i	−0.0639820	+	0.0639820i
$320$		0			0
$321$	−17.7168	−	10.2288i	−0.988857	−	0.570917i
$322$		0			0
$323$	−33.2915	−	33.2915i	−1.85239	−	1.85239i
$324$		0			0
$325$	−1.00455	+	2.36932i	−0.0557226	+	0.131426i
$326$		0			0
$327$	−51.2033			−2.83155
$328$		0			0
$329$	3.13762	−	1.81150i	0.172982	−	0.0998714i
$330$		0			0
$331$	−13.4650	+	3.60793i	−0.740101	+	0.198310i	−0.609123	−	0.793076i	$-0.708478\pi$
$331$	−13.4650	+	3.60793i	−0.740101	+	0.198310i	−0.130978	+	0.991385i	$0.541812\pi$
$332$		0			0
$333$	7.05233	+	45.7830i	0.386465	+	2.50889i
$334$		0			0
$335$	−1.17860	−	1.04230i	−0.0643938	−	0.0569469i
$336$		0			0
$337$	−10.4763	−	2.80712i	−0.570681	−	0.152913i	−0.0380719	−	0.999275i	$-0.512122\pi$
$337$	−10.4763	−	2.80712i	−0.570681	−	0.152913i	−0.532609	+	0.846362i	$0.678788\pi$
$338$		0			0
$339$	−0.0882947	+	0.0882947i	−0.00479551	+	0.00479551i
$340$		0			0
$341$	3.79235	+	3.79235i	0.205367	+	0.205367i
$342$		0			0
$343$	11.3285	−	11.3285i	0.611680	−	0.611680i
$344$		0			0
$345$	37.4359	−	42.3314i	2.01548	−	2.27904i
$346$		0			0
$347$	−24.3833			−1.30896			−0.654482	−	0.756078i	$-0.727113\pi$
$347$	−24.3833			−1.30896			−0.654482	+	0.756078i	$0.727113\pi$
$348$		0			0
$349$	−27.8464	−	16.0771i	−1.49058	−	0.860588i	−0.490640	−	0.871362i	$-0.663237\pi$
$349$	−27.8464	−	16.0771i	−1.49058	−	0.860588i	−0.999942	+	0.0107744i	$0.996570\pi$
$350$		0			0
$351$	−7.47613	−	2.00322i	−0.399047	−	0.106924i
$352$		0			0
$353$	1.81044	+	1.04526i	0.0963598	+	0.0556334i	0.547406	−	0.836867i	$-0.315616\pi$
$353$	1.81044	+	1.04526i	0.0963598	+	0.0556334i	−0.451046	+	0.892501i	$0.648949\pi$
$354$		0			0
$355$	−0.962266	−	15.6794i	−0.0510718	−	0.832175i
$356$		0			0
$357$	11.5394	+	19.9868i	0.610730	+	1.05782i
$358$		0			0
$359$			6.88791i			0.363530i	0.983342	+	0.181765i	$0.0581810\pi$
$359$			6.88791i			0.363530i	−0.983342	+	0.181765i	$0.941819\pi$
$360$		0			0
$361$	48.4036	+	27.9458i	2.54756	+	1.47083i
$362$		0			0
$363$	8.79659	−	32.8293i	0.461701	−	1.72309i
$364$		0			0
$365$	−2.34808	−	7.01283i	−0.122904	−	0.367068i
$366$		0			0
$367$	3.16441	−	11.8097i	0.165181	−	0.616463i	−0.832836	−	0.553519i	$-0.813284\pi$
$367$	3.16441	−	11.8097i	0.165181	−	0.616463i	0.998017	−	0.0629438i	$-0.0200489\pi$
$368$		0			0
$369$	−46.5567			−2.42365
$370$		0			0
$371$	−0.255622			−0.0132713
$372$		0			0
$373$	3.22643	−	12.0412i	0.167058	−	0.623469i	−0.830711	−	0.556704i	$-0.812066\pi$
$373$	3.22643	−	12.0412i	0.167058	−	0.623469i	0.997769	−	0.0667647i	$-0.0212677\pi$
$374$		0			0
$375$	−36.3165	−	2.83537i	−1.87538	−	0.146418i
$376$		0			0
$377$	−0.285543	+	1.06566i	−0.0147062	+	0.0548844i
$378$		0			0
$379$	−5.31835	−	3.07055i	−0.273186	−	0.157724i	0.357149	−	0.934047i	$-0.383749\pi$
$379$	−5.31835	−	3.07055i	−0.273186	−	0.157724i	−0.630334	+	0.776324i	$0.717082\pi$
$380$		0			0
$381$			24.7418i			1.26756i
$382$		0			0
$383$	12.0712	+	20.9079i	0.616809	+	1.06834i	0.990064	+	0.140615i	$0.0449081\pi$
$383$	12.0712	+	20.9079i	0.616809	+	1.06834i	−0.373256	+	0.927728i	$0.621759\pi$
$384$		0			0
$385$	−1.64428	−	1.45413i	−0.0838005	−	0.0741093i
$386$		0			0
$387$	44.7717	+	25.8490i	2.27587	+	1.31398i
$388$		0			0
$389$	3.49899	+	0.937553i	0.177406	+	0.0475358i	0.346428	−	0.938076i	$-0.387394\pi$
$389$	3.49899	+	0.937553i	0.177406	+	0.0475358i	−0.169022	+	0.985612i	$0.554061\pi$
$390$		0			0
$391$	36.5456	+	21.0996i	1.84819	+	1.06705i
$392$		0			0
$393$	−61.1381			−3.08401
$394$		0			0
$395$	22.9023	+	20.2538i	1.15234	+	1.01908i
$396$		0			0
$397$	21.1870	−	21.1870i	1.06334	−	1.06334i	0.0654899	−	0.997853i	$-0.479139\pi$
$397$	21.1870	−	21.1870i	1.06334	−	1.06334i	0.997853	−	0.0654899i	$-0.0208610\pi$
$398$		0			0
$399$	−25.9587	−	25.9587i	−1.29956	−	1.29956i
$400$		0			0
$401$	16.8262	−	16.8262i	0.840263	−	0.840263i	−0.148630	−	0.988893i	$-0.547486\pi$
$401$	16.8262	−	16.8262i	0.840263	−	0.840263i	0.988893	+	0.148630i	$0.0474864\pi$
$402$		0			0
$403$	3.53651	+	0.947604i	0.176166	+	0.0472035i
$404$		0			0
$405$	−3.58166	−	58.3603i	−0.177974	−	2.89995i
$406$		0			0
$407$	3.57629	−	2.87098i	0.177270	−	0.142309i
$408$		0			0
$409$	−16.9415	+	4.53946i	−0.837702	+	0.224462i	−0.652071	−	0.758158i	$-0.726100\pi$
$409$	−16.9415	+	4.53946i	−0.837702	+	0.224462i	−0.185631	+	0.982619i	$0.559433\pi$
$410$		0			0
$411$	−43.0643	+	24.8632i	−2.12421	+	1.22641i
$412$		0			0
$413$	−12.6147			−0.620727
$414$		0			0
$415$	0.603007	−	2.96703i	0.0296004	−	0.145646i
$416$		0			0
$417$	2.89735	+	2.89735i	0.141884	+	0.141884i
$418$		0			0
$419$	−25.8588	−	14.9296i	−1.26329	−	0.729359i	−0.289577	−	0.957155i	$-0.593515\pi$
$419$	−25.8588	−	14.9296i	−1.26329	−	0.729359i	−0.973709	+	0.227796i	$0.926848\pi$
$420$		0			0
$421$	−13.8065	+	13.8065i	−0.672887	+	0.672887i	−0.958381	−	0.285494i	$-0.907842\pi$
$421$	−13.8065	+	13.8065i	−0.672887	+	0.672887i	0.285494	+	0.958381i	$0.407842\pi$
$422$		0			0
$423$	−5.48464	−	20.4689i	−0.266672	−	0.995234i
$424$		0			0
$425$	−3.32633	−	26.9979i	−0.161351	−	1.30959i
$426$		0			0
$427$	−6.39298	+	11.0730i	−0.309378	+	0.535859i
$428$		0			0
$429$	0.327235	+	1.22126i	0.0157990	+	0.0589628i
$430$		0			0
$431$	3.04036	+	0.814662i	0.146449	+	0.0392409i	0.331299	−	0.943526i	$-0.392513\pi$
$431$	3.04036	+	0.814662i	0.146449	+	0.0392409i	−0.184850	+	0.982767i	$0.559180\pi$
$432$		0			0
$433$	23.0806	−	23.0806i	1.10918	−	1.10918i	0.115926	−	0.993258i	$-0.463016\pi$
$433$	23.0806	−	23.0806i	1.10918	−	1.10918i	0.993258	−	0.115926i	$-0.0369836\pi$
$434$		0			0
$435$	−15.5870	+	0.956597i	−0.747340	+	0.0458653i
$436$		0			0
$437$	−64.8385	−	17.3734i	−3.10164	−	0.831083i
$438$		0			0
$439$	−5.08845	+	18.9904i	−0.242859	+	0.906361i	0.731589	+	0.681746i	$0.238779\pi$
$439$	−5.08845	+	18.9904i	−0.242859	+	0.906361i	−0.974448	+	0.224615i	$0.927888\pi$
$440$		0			0
$441$	−20.1991	−	34.9859i	−0.961864	−	1.66600i
$442$		0			0
$443$	23.2565	+	23.2565i	1.10495	+	1.10495i	0.993804	+	0.111144i	$0.0354516\pi$
$443$	23.2565	+	23.2565i	1.10495	+	1.10495i	0.111144	+	0.993804i	$0.464548\pi$
$444$		0			0
$445$	−19.0760	−	3.87693i	−0.904291	−	0.183784i
$446$		0			0
$447$	53.5334	+	14.3442i	2.53204	+	0.678459i
$448$		0			0
$449$	7.82037	+	2.09546i	0.369066	+	0.0988909i	0.438585	−	0.898690i	$-0.355480\pi$
$449$	7.82037	+	2.09546i	0.369066	+	0.0988909i	−0.0695191	+	0.997581i	$0.522146\pi$
$450$		0			0
$451$	2.30463	+	3.99173i	0.108521	+	0.187963i
$452$		0			0
$453$	−11.4509	−	42.7352i	−0.538009	−	2.00788i
$454$		0			0
$455$	−1.46845	−	0.298442i	−0.0688420	−	0.0139912i
$456$		0			0
$457$	16.6277	−	9.60001i	0.777811	−	0.449069i	−0.0578430	−	0.998326i	$-0.518422\pi$
$457$	16.6277	−	9.60001i	0.777811	−	0.449069i	0.835654	+	0.549256i	$0.185089\pi$
$458$		0			0
$459$	79.0239	−	21.1744i	3.68852	−	0.988335i
$460$		0			0
$461$	27.4968	−	7.36773i	1.28065	−	0.343150i	0.446549	−	0.894759i	$-0.352653\pi$
$461$	27.4968	−	7.36773i	1.28065	−	0.343150i	0.834103	+	0.551609i	$0.185986\pi$
$462$		0			0
$463$	6.38352	+	11.0566i	0.296667	+	0.513843i	0.975371	−	0.220569i	$-0.0707915\pi$
$463$	6.38352	+	11.0566i	0.296667	+	0.513843i	−0.678704	+	0.734412i	$0.737458\pi$
$464$		0			0
$465$	3.17456	+	51.7270i	0.147217	+	2.39878i
$466$		0			0
$467$			32.7112i			1.51369i	0.653592	+	0.756847i	$0.273261\pi$
$467$			32.7112i			1.51369i	−0.653592	+	0.756847i	$0.726739\pi$
$468$		0			0
$469$	0.458065	−	0.793393i	0.0211515	−	0.0366355i
$470$		0			0
$471$		−	16.8836i		−	0.777955i
$472$		0			0
$473$		−	5.11825i		−	0.235337i
$474$		0			0
$475$	16.2259	+	40.1125i	0.744496	+	1.84049i
$476$		0			0
$477$	−0.386970	+	1.44419i	−0.0177182	+	0.0661251i
$478$		0			0
$479$	4.68641	+	17.4899i	0.214127	+	0.799135i	0.986472	+	0.163931i	$0.0524173\pi$
$479$	4.68641	+	17.4899i	0.214127	+	0.799135i	−0.772344	+	0.635204i	$0.780916\pi$
$480$		0			0
$481$	1.13436	−	2.91804i	0.0517223	−	0.133051i
$482$		0			0
$483$	28.4960	+	16.4522i	1.29661	+	0.748601i
$484$		0			0
$485$	−3.57086	+	7.16577i	−0.162144	+	0.325381i
$486$		0			0
$487$			37.4831i			1.69852i	0.527972	+	0.849262i	$0.322953\pi$
$487$			37.4831i			1.69852i	−0.527972	+	0.849262i	$0.677047\pi$
$488$		0			0
$489$	51.7052	−	51.7052i	2.33819	−	2.33819i
$490$		0			0
$491$	−28.0295			−1.26495			−0.632476	−	0.774580i	$-0.717961\pi$
$491$	−28.0295			−1.26495			−0.632476	+	0.774580i	$0.717961\pi$
$492$		0			0
$493$	−3.01824	−	11.2642i	−0.135935	−	0.507315i
$494$		0			0
$495$	−10.7046	+	7.08842i	−0.481136	+	0.318601i
$496$		0			0
$497$	8.83520	−	2.36739i	0.396313	−	0.106192i
$498$		0			0
$499$	−0.445108	+	1.66116i	−0.0199258	+	0.0743639i	−0.975173	−	0.221445i	$-0.928923\pi$
$499$	−0.445108	+	1.66116i	−0.0199258	+	0.0743639i	0.955247	+	0.295809i	$0.0955893\pi$
$500$		0			0
$501$	6.48483	+	24.2017i	0.289721	+	1.08125i
$502$		0			0
$503$	−12.8565	+	22.2680i	−0.573241	+	0.992883i	0.422989	+	0.906135i	$0.360981\pi$
$503$	−12.8565	+	22.2680i	−0.573241	+	0.992883i	−0.996230	+	0.0867480i	$0.972353\pi$
$504$		0			0
$505$	−4.50196	+	9.03425i	−0.200335	+	0.402019i
$506$		0			0
$507$	−29.3397	−	29.3397i	−1.30302	−	1.30302i
$508$		0			0
$509$	−15.7219	+	27.2312i	−0.696863	+	1.20700i	0.272686	+	0.962103i	$0.412088\pi$
$509$	−15.7219	+	27.2312i	−0.696863	+	1.20700i	−0.969549	+	0.244899i	$0.921245\pi$
$510$		0			0
$511$	3.72928	−	2.15310i	0.164974	−	0.0952476i
$512$		0			0
$513$	−112.702	+	65.0682i	−4.97589	+	2.87283i
$514$		0			0
$515$	−8.76295	+	17.5849i	−0.386142	+	0.774884i
$516$		0			0
$517$	−1.48349	+	1.48349i	−0.0652439	+	0.0652439i
$518$		0			0
$519$		−	15.0911i		−	0.662427i
$520$		0			0
$521$	32.4896	−	18.7579i	1.42340	−	0.821799i	0.426810	−	0.904341i	$-0.359637\pi$
$521$	32.4896	−	18.7579i	1.42340	−	0.821799i	0.996588	+	0.0825427i	$0.0263041\pi$
$522$		0			0
$523$	−2.14658	−	3.71799i	−0.0938635	−	0.162576i	0.815270	−	0.579081i	$-0.196588\pi$
$523$	−2.14658	−	3.71799i	−0.0938635	−	0.162576i	−0.909134	+	0.416504i	$0.863255\pi$
$524$		0			0
$525$	−2.59367	−	21.0514i	−0.113197	−	0.918756i
$526$		0			0
$527$	−37.3814	+	10.0163i	−1.62836	+	0.436318i
$528$		0			0
$529$	37.1651			1.61587
$530$		0			0
$531$	−19.0966	+	71.2693i	−0.828720	+	3.09282i
$532$		0			0
$533$	2.72501	+	1.57329i	0.118033	+	0.0681467i
$534$		0			0
$535$	−9.30109	+	10.5174i	−0.402121	+	0.454706i
$536$		0			0
$537$	−0.157328	+	0.0908336i	−0.00678923	+	0.00391976i
$538$		0			0
$539$	−1.99978	+	3.46371i	−0.0861364	+	0.149193i
$540$		0			0
$541$	−8.80718	−	8.80718i	−0.378650	−	0.378650i	0.491965	−	0.870615i	$-0.336279\pi$
$541$	−8.80718	−	8.80718i	−0.378650	−	0.378650i	−0.870615	+	0.491965i	$0.836279\pi$
$542$		0			0
$543$	8.69900	−	2.33089i	0.373310	−	0.100028i
$544$		0			0
$545$	−6.99882	+	34.4370i	−0.299797	+	1.47512i
$546$		0			0
$547$	21.3774			0.914033			0.457016	−	0.889458i	$-0.348918\pi$
$547$	21.3774			0.914033			0.457016	+	0.889458i	$0.348918\pi$
$548$		0			0
$549$	52.8812	+	52.8812i	2.25691	+	2.25691i
$550$		0			0
$551$	9.27495	+	16.0647i	0.395126	+	0.684379i
$552$		0			0
$553$	−8.90105	+	15.4171i	−0.378511	+	0.655600i
$554$		0			0
$555$	44.2651	+	2.11162i	1.87895	+	0.0896331i
$556$		0			0
$557$	13.5980	−	23.5525i	0.576167	−	0.997951i	−0.419746	−	0.907641i	$-0.637881\pi$
$557$	13.5980	−	23.5525i	0.576167	−	0.997951i	0.995914	−	0.0903098i	$-0.0287857\pi$
$558$		0			0
$559$	−1.74702	−	3.02593i	−0.0738912	−	0.127983i
$560$		0			0
$561$	−9.44995	−	9.44995i	−0.398977	−	0.398977i
$562$		0			0
$563$	10.9821			0.462841			0.231420	−	0.972854i	$-0.425663\pi$
$563$	10.9821			0.462841			0.231420	+	0.972854i	$0.425663\pi$
$564$		0			0
$565$	0.0473142	+	0.0714516i	0.00199052	+	0.00300599i
$566$		0			0
$567$	32.8856	−	8.81166i	1.38106	−	0.370055i
$568$		0			0
$569$	−25.1669	−	25.1669i	−1.05505	−	1.05505i	−0.998394	−	0.0566573i	$-0.981956\pi$
$569$	−25.1669	−	25.1669i	−1.05505	−	1.05505i	−0.0566573	−	0.998394i	$-0.518044\pi$
$570$		0			0
$571$	13.9041	−	24.0826i	0.581869	−	1.00783i	−0.413389	−	0.910555i	$-0.635655\pi$
$571$	13.9041	−	24.0826i	0.581869	−	1.00783i	0.995258	−	0.0972719i	$-0.0310117\pi$
$572$		0			0
$573$	−53.9230	+	31.1325i	−2.25267	+	1.30058i
$574$		0			0
$575$	−23.3531	−	30.9638i	−0.973893	−	1.29128i
$576$		0			0
$577$	−1.39081	−	0.802984i	−0.0579002	−	0.0334287i	0.470770	−	0.882256i	$-0.343976\pi$
$577$	−1.39081	−	0.802984i	−0.0579002	−	0.0334287i	−0.528671	+	0.848827i	$0.677309\pi$
$578$		0			0
$579$	15.1702	−	56.6160i	0.630453	−	2.35288i
$580$		0			0
$581$	1.76295			0.0731393
$582$		0			0
$583$	0.142979	−	0.0383112i	0.00592160	−	0.00158669i
$584$		0			0
$585$	−3.90910	+	7.84454i	−0.161622	+	0.324332i
$586$		0			0
$587$	−10.6945	−	18.5234i	−0.441408	−	0.764542i	0.556386	−	0.830924i	$-0.312188\pi$
$587$	−10.6945	−	18.5234i	−0.441408	−	0.764542i	−0.997794	+	0.0663823i	$0.978854\pi$
$588$		0			0
$589$	53.3123	−	30.7798i	2.19669	−	1.26826i
$590$		0			0
$591$		−	3.44304i		−	0.141628i
$592$		0			0
$593$	−9.10270	+	9.10270i	−0.373803	+	0.373803i	−0.868860	−	0.495057i	$-0.835147\pi$
$593$	−9.10270	+	9.10270i	−0.373803	+	0.373803i	0.495057	+	0.868860i	$0.335147\pi$
$594$		0			0
$595$	15.0195	−	5.02893i	0.615740	−	0.206166i
$596$		0			0
$597$	72.7482	−	42.0012i	2.97739	−	1.71899i
$598$		0			0
$599$	8.66526	−	5.00289i	0.354053	−	0.204413i	−0.312416	−	0.949945i	$-0.601138\pi$
$599$	8.66526	−	5.00289i	0.354053	−	0.204413i	0.666469	+	0.745533i	$0.267805\pi$
$600$		0			0
$601$	−14.7811	+	25.6017i	−0.602935	+	1.04431i	0.389439	+	0.921052i	$0.372669\pi$
$601$	−14.7811	+	25.6017i	−0.602935	+	1.04431i	−0.992374	+	0.123262i	$0.960664\pi$
$602$		0			0
$603$	−3.78901	−	3.78901i	−0.154300	−	0.154300i
$604$		0			0
$605$	−20.8771	−	10.4035i	−0.848775	−	0.422963i
$606$		0			0
$607$	−9.09854	+	15.7591i	−0.369298	+	0.639643i	−0.989456	−	0.144834i	$-0.953735\pi$
$607$	−9.09854	+	15.7591i	−0.369298	+	0.639643i	0.620158	+	0.784477i	$0.287069\pi$
$608$		0			0
$609$	−2.35344	−	8.78315i	−0.0953661	−	0.355911i
$610$		0			0
$611$	−0.370684	+	1.38341i	−0.0149963	+	0.0559668i
$612$		0			0
$613$	36.8312	−	9.86890i	1.48760	−	0.398601i	0.578674	−	0.815559i	$-0.303571\pi$
$613$	36.8312	−	9.86890i	1.48760	−	0.398601i	0.908926	+	0.416958i	$0.136904\pi$
$614$		0			0
$615$	−8.87059	+	43.6468i	−0.357697	+	1.76001i
$616$		0			0
$617$	10.9184	+	40.7482i	0.439560	+	1.64046i	0.729913	+	0.683541i	$0.239561\pi$
$617$	10.9184	+	40.7482i	0.439560	+	1.64046i	−0.290353	+	0.956920i	$0.593773\pi$
$618$		0			0
$619$	−22.0237			−0.885206			−0.442603	−	0.896718i	$-0.645945\pi$
$619$	−22.0237			−0.885206			−0.442603	+	0.896718i	$0.645945\pi$
$620$		0			0
$621$	82.4783	−	82.4783i	3.30974	−	3.30974i
$622$		0			0
$623$		−	11.3346i		−	0.454109i
$624$		0			0
$625$	−6.87093	+	24.0373i	−0.274837	+	0.961491i
$626$		0			0
$627$	18.4103	+	10.6292i	0.735235	+	0.424488i
$628$		0			0
$629$	5.03813	+	32.7070i	0.200883	+	1.30411i
$630$		0			0
$631$	3.15476	+	11.7737i	0.125589	+	0.468705i	0.999860	−	0.0167336i	$-0.00532672\pi$
$631$	3.15476	+	11.7737i	0.125589	+	0.468705i	−0.874271	+	0.485438i	$0.838660\pi$
$632$		0			0
$633$	4.35988	−	16.2713i	0.173290	−	0.646727i
$634$		0			0
$635$	16.6402	+	3.38188i	0.660345	+	0.134206i
$636$		0			0
$637$			2.73035i			0.108180i
$638$		0			0
$639$		−	53.5002i		−	2.11644i
$640$		0			0
$641$	4.64384	−	8.04337i	0.183421	−	0.317694i	−0.759623	−	0.650364i	$-0.774616\pi$
$641$	4.64384	−	8.04337i	0.183421	−	0.317694i	0.943043	+	0.332670i	$0.107950\pi$
$642$		0			0
$643$			26.1310i			1.03051i	0.857038	+	0.515253i	$0.172302\pi$
$643$			26.1310i			1.03051i	−0.857038	+	0.515253i	$0.827698\pi$
$644$		0			0
$645$	32.7638	−	37.0483i	1.29007	−	1.45877i
$646$		0			0
$647$	−17.6918	−	30.6431i	−0.695537	−	1.20470i	−0.969999	−	0.243107i	$-0.921833\pi$
$647$	−17.6918	−	30.6431i	−0.695537	−	1.20470i	0.274463	−	0.961598i	$-0.411500\pi$
$648$		0			0
$649$	7.05587	−	1.89062i	0.276967	−	0.0742131i
$650$		0			0
$651$	−29.1478	+	7.81012i	−1.14239	+	0.306103i
$652$		0			0
$653$	41.1928	−	23.7827i	1.61200	−	0.930689i	0.623094	−	0.782147i	$-0.285875\pi$
$653$	41.1928	−	23.7827i	1.61200	−	0.930689i	0.988906	−	0.148542i	$-0.0474580\pi$
$654$		0			0
$655$	−8.35678	+	41.1187i	−0.326526	+	1.60664i
$656$		0			0
$657$	−6.51889	−	24.3288i	−0.254326	−	0.949157i
$658$		0			0
$659$	17.6445	+	30.5611i	0.687331	+	1.19049i	0.972698	+	0.232074i	$0.0745511\pi$
$659$	17.6445	+	30.5611i	0.687331	+	1.19049i	−0.285367	+	0.958418i	$0.592116\pi$
$660$		0			0
$661$	2.03679	+	0.545758i	0.0792221	+	0.0212275i	0.298212	−	0.954500i	$-0.403610\pi$
$661$	2.03679	+	0.545758i	0.0792221	+	0.0212275i	−0.218990	+	0.975727i	$0.570276\pi$
$662$		0			0
$663$	−8.81243	−	2.36128i	−0.342246	−	0.0917047i
$664$		0			0
$665$	−21.0068	+	13.9104i	−0.814611	+	0.539423i
$666$		0			0
$667$	−11.7566	−	11.7566i	−0.455218	−	0.455218i
$668$		0			0
$669$	−7.30903	−	12.6596i	−0.282583	−	0.489449i
$670$		0			0
$671$	1.91629	−	7.15168i	0.0739775	−	0.276088i
$672$		0			0
$673$	6.14444	+	1.64640i	0.236851	+	0.0634640i	0.375292	−	0.926907i	$-0.377542\pi$
$673$	6.14444	+	1.64640i	0.236851	+	0.0634640i	−0.138441	+	0.990371i	$0.544209\pi$
$674$		0			0
$675$	−74.4613	−	10.4333i	−2.86602	−	0.401576i
$676$		0			0
$677$	6.44730	−	6.44730i	0.247790	−	0.247790i	−0.572273	−	0.820063i	$-0.693938\pi$
$677$	6.44730	−	6.44730i	0.247790	−	0.247790i	0.820063	+	0.572273i	$0.193938\pi$
$678$		0			0
$679$	−4.50296	−	1.20656i	−0.172808	−	0.0463037i
$680$		0			0
$681$	−7.45492	−	27.8221i	−0.285673	−	1.06615i
$682$		0			0
$683$	−18.5957	+	32.2087i	−0.711545	+	1.23243i	0.252733	+	0.967536i	$0.418671\pi$
$683$	−18.5957	+	32.2087i	−0.711545	+	1.23243i	−0.964277	+	0.264895i	$0.914663\pi$
$684$		0			0
$685$	10.8355	+	32.3616i	0.414004	+	1.23647i
$686$		0			0
$687$	−5.17245	−	19.3038i	−0.197341	−	0.736487i
$688$		0			0
$689$	0.0714533	−	0.0714533i	0.00272215	−	0.00272215i
$690$		0			0
$691$	−7.79684	−	4.50151i	−0.296606	−	0.171245i	0.344311	−	0.938856i	$-0.388112\pi$
$691$	−7.79684	−	4.50151i	−0.296606	−	0.171245i	−0.640917	+	0.767610i	$0.721446\pi$
$692$		0			0
$693$	−5.28611	−	5.28611i	−0.200803	−	0.200803i
$694$		0			0
$695$	2.34465	−	1.55259i	0.0889377	−	0.0588932i
$696$		0			0
$697$	−33.2598			−1.25980
$698$		0			0
$699$	52.8864	−	30.5340i	2.00035	−	1.15490i
$700$		0			0
$701$	−19.7448	+	5.29059i	−0.745749	+	0.199823i	−0.611632	−	0.791143i	$-0.709487\pi$
$701$	−19.7448	+	5.29059i	−0.745749	+	0.199823i	−0.134117	+	0.990965i	$0.542820\pi$
$702$		0			0
$703$	−21.2065	−	48.1796i	−0.799818	−	1.81713i
$704$		0			0
$705$	−20.2346	+	1.24183i	−0.762079	+	0.0467699i
$706$		0			0
$707$	−5.67711	−	1.52118i	−0.213510	−	0.0572097i
$708$		0			0
$709$	5.78446	−	5.78446i	0.217240	−	0.217240i	−0.590094	−	0.807334i	$-0.700909\pi$
$709$	5.78446	−	5.78446i	0.217240	−	0.217240i	0.807334	+	0.590094i	$0.200909\pi$
$710$		0			0
$711$	73.6273	+	73.6273i	2.76124	+	2.76124i
$712$		0			0
$713$	−39.0155	+	39.0155i	−1.46114	+	1.46114i
$714$		0			0
$715$	0.866090	−	0.0531532i	0.0323899	−	0.00198782i
$716$		0			0
$717$	33.6437			1.25645
$718$		0			0
$719$	17.1252	+	9.88723i	0.638662	+	0.368731i	0.784099	−	0.620636i	$-0.213126\pi$
$719$	17.1252	+	9.88723i	0.638662	+	0.368731i	−0.145437	+	0.989367i	$0.546459\pi$
$720$		0			0
$721$	−11.0503	−	2.96093i	−0.411536	−	0.110271i
$722$		0			0
$723$	25.3353	+	14.6273i	0.942229	+	0.543996i
$724$		0			0
$725$	−1.48718	+	10.6139i	−0.0552324	+	0.394189i
$726$		0			0
$727$	15.9327	+	27.5963i	0.590911	+	1.02349i	0.994110	+	0.108376i	$0.0345650\pi$
$727$	15.9327	+	27.5963i	0.590911	+	1.02349i	−0.403199	+	0.915112i	$0.632102\pi$
$728$		0			0
$729$		−	52.1486i		−	1.93143i
$730$		0			0
$731$	31.9846	+	18.4663i	1.18299	+	0.683001i
$732$		0			0
$733$	−2.78935	+	10.4100i	−0.103027	+	0.384503i	−0.998114	−	0.0613895i	$-0.980447\pi$
$733$	−2.78935	+	10.4100i	−0.103027	+	0.384503i	0.895087	+	0.445892i	$0.147113\pi$
$734$		0			0
$735$	−36.6478	+	12.2707i	−1.35178	+	0.452610i
$736$		0			0
$737$	−0.137304	+	0.512427i	−0.00505768	+	0.0188755i
$738$		0			0
$739$	12.8027			0.470956			0.235478	−	0.971880i	$-0.424334\pi$
$739$	12.8027			0.470956			0.235478	+	0.971880i	$0.424334\pi$
$740$		0			0
$741$	14.5123			0.533123
$742$		0			0
$743$	8.58431	−	32.0371i	0.314928	−	1.17533i	−0.609129	−	0.793071i	$-0.708481\pi$
$743$	8.58431	−	32.0371i	0.314928	−	1.17533i	0.924057	−	0.382255i	$-0.124852\pi$
$744$		0			0
$745$	16.9646	−	34.0434i	0.621534	−	1.24725i
$746$		0			0
$747$	2.66881	−	9.96014i	0.0976467	−	0.364422i
$748$		0			0
$749$	−7.07994	−	4.08760i	−0.258695	−	0.149358i
$750$		0			0
$751$		−	43.1364i		−	1.57407i	−0.616909	−	0.787035i	$-0.711615\pi$
$751$		−	43.1364i		−	1.57407i	0.616909	−	0.787035i	$-0.288385\pi$
$752$		0			0
$753$	−24.0574	−	41.6687i	−0.876702	−	1.51849i
$754$		0			0
$755$	−30.3069	+	1.85998i	−1.10298	+	0.0676916i
$756$		0			0
$757$	−5.91601	−	3.41561i	−0.215021	−	0.124142i	0.388622	−	0.921397i	$-0.372951\pi$
$757$	−5.91601	−	3.41561i	−0.215021	−	0.124142i	−0.603643	+	0.797255i	$0.706285\pi$
$758$		0			0
$759$	−18.4047	−	4.93152i	−0.668048	−	0.179003i
$760$		0			0
$761$	20.8355	+	12.0294i	0.755287	+	0.436065i	0.827601	−	0.561317i	$-0.189705\pi$
$761$	20.8355	+	12.0294i	0.755287	+	0.436065i	−0.0723142	+	0.997382i	$0.523038\pi$
$762$		0			0
$763$	−20.4617			−0.740763
$764$		0			0
$765$	−5.67495	−	92.4689i	−0.205178	−	3.34322i
$766$		0			0
$767$	3.52614	−	3.52614i	0.127321	−	0.127321i
$768$		0			0
$769$	6.18779	+	6.18779i	0.223138	+	0.223138i	0.809818	−	0.586681i	$-0.199566\pi$
$769$	6.18779	+	6.18779i	0.223138	+	0.223138i	−0.586681	+	0.809818i	$0.699566\pi$
$770$		0			0
$771$	26.6171	−	26.6171i	0.958590	−	0.958590i
$772$		0			0
$773$	−13.8332	−	3.70659i	−0.497544	−	0.133317i	0.00131571	−	0.999999i	$-0.499581\pi$
$773$	−13.8332	−	3.70659i	−0.497544	−	0.133317i	−0.498860	+	0.866683i	$0.666248\pi$
$774$		0			0
$775$	35.2231	+	4.93534i	1.26525	+	0.177283i
$776$		0			0
$777$	3.92843	+	25.5029i	0.140932	+	0.914913i
$778$		0			0
$779$	51.1032	−	13.6930i	1.83096	−	0.490604i
$780$		0			0
$781$	−4.58706	+	2.64834i	−0.164138	+	0.0947651i
$782$		0			0
$783$	−32.2335			−1.15193
$784$		0			0
$785$	−11.3551	−	2.30776i	−0.405282	−	0.0823677i
$786$		0			0
$787$	−31.3313	−	31.3313i	−1.11684	−	1.11684i	−0.992202	−	0.124638i	$-0.960223\pi$
$787$	−31.3313	−	31.3313i	−1.11684	−	1.11684i	−0.124638	−	0.992202i	$-0.539777\pi$
$788$		0			0
$789$	0.351551	+	0.202968i	0.0125155	+	0.00722585i
$790$		0			0
$791$	−0.0352840	+	0.0352840i	−0.00125455	+	0.00125455i
$792$		0			0
$793$	−1.30818	−	4.88220i	−0.0464549	−	0.173372i
$794$		0			0
$795$	1.28020	+	0.637950i	0.0454039	+	0.0226258i
$796$		0			0
$797$	−5.47530	+	9.48350i	−0.193945	+	0.335923i	−0.946554	−	0.322545i	$-0.895462\pi$
$797$	−5.47530	+	9.48350i	−0.193945	+	0.335923i	0.752609	+	0.658468i	$0.228795\pi$
$798$		0			0
$799$	−3.91818	−	14.6229i	−0.138615	−	0.517320i
$800$		0			0
$801$	−64.0370	−	17.1587i	−2.26264	−	0.606272i
$802$		0			0
$803$	−1.76324	+	1.76324i	−0.0622232	+	0.0622232i
$804$		0			0
$805$	14.9600	−	16.9163i	0.527271	−	0.596222i
$806$		0			0
$807$	61.3142	+	16.4291i	2.15836	+	0.578332i
$808$		0			0
$809$	8.59459	−	32.0755i	0.302170	−	1.12771i	−0.633184	−	0.774001i	$-0.718253\pi$
$809$	8.59459	−	32.0755i	0.302170	−	1.12771i	0.935354	−	0.353712i	$-0.115081\pi$
$810$		0			0
$811$	−0.563337	−	0.975729i	−0.0197814	−	0.0342625i	0.855965	−	0.517033i	$-0.172964\pi$
$811$	−0.563337	−	0.975729i	−0.0197814	−	0.0342625i	−0.875747	+	0.482771i	$0.839630\pi$
$812$		0			0
$813$	53.2135	+	53.2135i	1.86628	+	1.86628i
$814$		0			0
$815$	−27.7071	−	41.8420i	−0.970538	−	1.46566i
$816$		0			0
$817$	−56.7464	−	15.2052i	−1.98531	−	0.531961i
$818$		0			0
$819$	−4.92949	−	1.32085i	−0.172250	−	0.0461544i
$820$		0			0
$821$	7.07122	+	12.2477i	0.246787	+	0.427448i	0.962633	−	0.270811i	$-0.0872918\pi$
$821$	7.07122	+	12.2477i	0.246787	+	0.427448i	−0.715845	+	0.698259i	$0.753958\pi$
$822$		0			0
$823$	−8.87451	−	33.1201i	−0.309346	−	1.15449i	−0.929139	−	0.369730i	$-0.879450\pi$
$823$	−8.87451	−	33.1201i	−0.309346	−	1.15449i	0.619793	−	0.784765i	$-0.287216\pi$
$824$		0			0
$825$	4.60580	+	11.3861i	0.160353	+	0.396413i
$826$		0			0
$827$	27.2681	−	15.7432i	0.948204	−	0.547446i	0.0556815	−	0.998449i	$-0.482267\pi$
$827$	27.2681	−	15.7432i	0.948204	−	0.547446i	0.892523	+	0.451003i	$0.148934\pi$
$828$		0			0
$829$	−48.7282	+	13.0567i	−1.69240	+	0.453477i	−0.971007	−	0.239050i	$-0.923164\pi$
$829$	−48.7282	+	13.0567i	−1.69240	+	0.453477i	−0.721392	+	0.692527i	$0.756497\pi$
$830$		0			0
$831$	19.9472	−	5.34485i	0.691962	−	0.185411i
$832$		0			0
$833$	−14.4301	−	24.9937i	−0.499974	−	0.865980i
$834$		0			0
$835$	17.1633	−	1.05334i	0.593962	−	0.0364523i
$836$		0			0
$837$			106.970i			3.69743i
$838$		0			0
$839$	20.9590	−	36.3021i	0.723585	−	1.25329i	−0.235968	−	0.971761i	$-0.575826\pi$
$839$	20.9590	−	36.3021i	0.723585	−	1.25329i	0.959554	−	0.281526i	$-0.0908406\pi$
$840$		0			0
$841$		−	24.4054i		−	0.841565i
$842$		0			0
$843$		−	36.8187i		−	1.26810i
$844$		0			0
$845$	−23.7429	+	15.7222i	−0.816781	+	0.540860i
$846$		0			0
$847$	3.51526	−	13.1191i	0.120786	−	0.450779i
$848$		0			0
$849$	6.18135	+	23.0691i	0.212143	+	0.791730i
$850$		0			0
$851$	29.5365	+	36.7927i	1.01250	+	1.26124i
$852$		0			0
$853$	−36.3669	−	20.9964i	−1.24518	−	0.718904i	−0.275034	−	0.961434i	$-0.588689\pi$
$853$	−36.3669	−	20.9964i	−1.24518	−	0.718904i	−0.970144	+	0.242531i	$0.922022\pi$
$854$		0			0
$855$	46.7889	+	139.741i	1.60015	+	4.77903i
$856$		0			0
$857$			24.4991i			0.836873i	0.908246	+	0.418436i	$0.137422\pi$
$857$			24.4991i			0.836873i	−0.908246	+	0.418436i	$0.862578\pi$
$858$		0			0
$859$	−27.4252	+	27.4252i	−0.935736	+	0.935736i	−0.998056	−	0.0623205i	$-0.980150\pi$
$859$	−27.4252	+	27.4252i	−0.935736	+	0.935736i	0.0623205	+	0.998056i	$0.480150\pi$
$860$		0			0
$861$	−25.9340			−0.883827
$862$		0			0
$863$	−2.71023	−	10.1147i	−0.0922571	−	0.344308i	0.904332	−	0.426829i	$-0.140370\pi$
$863$	−2.71023	−	10.1147i	−0.0922571	−	0.344308i	−0.996589	+	0.0825210i	$0.973703\pi$
$864$		0			0
$865$	−10.1496	−	2.06276i	−0.345097	−	0.0701359i
$866$		0			0
$867$	39.6477	−	10.6236i	1.34651	−	0.360795i
$868$		0			0
$869$	2.66808	−	9.95740i	0.0905083	−	0.337782i
$870$		0			0
$871$	0.0937329	+	0.349816i	0.00317602	+	0.0118531i
$872$		0			0
$873$	−13.6335	+	23.6139i	−0.461424	+	0.799209i
$874$		0			0
$875$	−14.5127	−	1.13306i	−0.490618	−	0.0383044i
$876$		0			0
$877$	3.38914	+	3.38914i	0.114443	+	0.114443i	0.762009	−	0.647566i	$-0.224213\pi$
$877$	3.38914	+	3.38914i	0.114443	+	0.114443i	−0.647566	+	0.762009i	$0.724213\pi$
$878$		0			0
$879$	12.5116	−	21.6708i	0.422007	−	0.730938i
$880$		0			0
$881$	32.1757	−	18.5767i	1.08403	−	0.625864i	0.152048	−	0.988373i	$-0.451413\pi$
$881$	32.1757	−	18.5767i	1.08403	−	0.625864i	0.931980	+	0.362509i	$0.118080\pi$
$882$		0			0
$883$	18.2110	−	10.5141i	0.612850	−	0.353829i	−0.161230	−	0.986917i	$-0.551546\pi$
$883$	18.2110	−	10.5141i	0.612850	−	0.353829i	0.774080	+	0.633088i	$0.218213\pi$
$884$		0			0
$885$	63.1762	+	31.4821i	2.12365	+	1.05826i
$886$		0			0
$887$	−1.83076	+	1.83076i	−0.0614710	+	0.0614710i	−0.737174	−	0.675703i	$-0.763840\pi$
$887$	−1.83076	+	1.83076i	−0.0614710	+	0.0614710i	0.675703	+	0.737174i	$0.263840\pi$
$888$		0			0
$889$			9.88723i			0.331607i
$890$		0			0
$891$	−17.0735	+	9.85740i	−0.571985	+	0.330235i
$892$		0			0
$893$	12.0405	+	20.8547i	0.402919	+	0.697876i
$894$		0			0
$895$	0.0395858	+	0.118228i	0.00132321	+	0.00395191i
$896$		0			0
$897$	−12.5642	+	3.36658i	−0.419508	+	0.112407i
$898$		0			0
$899$	15.2477			0.508540
$900$		0			0
$901$	−0.276449	+	1.03172i	−0.00920984	+	0.0343716i
$902$		0			0
$903$	24.9396	+	14.3989i	0.829939	+	0.479166i
$904$		0			0
$905$	−0.378609	−	6.16915i	−0.0125854	−	0.205069i
$906$		0			0
$907$	18.5126	−	10.6883i	0.614701	−	0.354898i	−0.160102	−	0.987101i	$-0.551182\pi$
$907$	18.5126	−	10.6883i	0.614701	−	0.354898i	0.774803	+	0.632202i	$0.217849\pi$
$908$		0			0
$909$	−17.1884	+	29.7712i	−0.570104	+	0.987449i
$910$		0			0
$911$	−23.0946	−	23.0946i	−0.765158	−	0.765158i	0.212092	−	0.977250i	$-0.431972\pi$
$911$	−23.0946	−	23.0946i	−0.765158	−	0.765158i	−0.977250	+	0.212092i	$0.931972\pi$
$912$		0			0
$913$	−0.986083	+	0.264220i	−0.0326346	+	0.00874441i
$914$		0			0
$915$	59.6516	−	39.5004i	1.97202	−	1.30584i
$916$		0			0
$917$	−24.4318			−0.806809
$918$		0			0
$919$	−7.25445	−	7.25445i	−0.239302	−	0.239302i	0.577259	−	0.816561i	$-0.304122\pi$
$919$	−7.25445	−	7.25445i	−0.239302	−	0.239302i	−0.816561	+	0.577259i	$0.804122\pi$
$920$		0			0
$921$	50.1470	+	86.8571i	1.65240	+	2.86204i
$922$		0			0
$923$	−1.80793	+	3.13142i	−0.0595087	+	0.103072i
$924$		0			0
$925$	7.47063	−	29.4820i	0.245633	−	0.969363i
$926$		0			0
$927$	−33.4568	+	57.9488i	−1.09886	+	1.90329i
$928$		0			0
$929$	8.22373	+	14.2439i	0.269812	+	0.467328i	0.968813	−	0.247793i	$-0.0797052\pi$
$929$	8.22373	+	14.2439i	0.269812	+	0.467328i	−0.699001	+	0.715120i	$0.746372\pi$
$930$		0			0
$931$	32.4616	+	32.4616i	1.06388	+	1.06388i
$932$		0			0
$933$	−7.89070			−0.258330
$934$		0			0
$935$	−7.64728	+	5.06391i	−0.250093	+	0.165608i
$936$		0			0
$937$	40.0915	−	10.7425i	1.30973	−	0.350942i	0.464611	−	0.885515i	$-0.346194\pi$
$937$	40.0915	−	10.7425i	1.30973	−	0.350942i	0.845122	+	0.534573i	$0.179528\pi$
$938$		0			0
$939$	−37.1819	−	37.1819i	−1.21339	−	1.21339i
$940$		0			0
$941$	−10.6572	+	18.4589i	−0.347416	+	0.601743i	−0.985790	−	0.167984i	$-0.946274\pi$
$941$	−10.6572	+	18.4589i	−0.347416	+	0.601743i	0.638373	+	0.769727i	$0.279608\pi$
$942$		0			0
$943$	−41.0667	+	23.7099i	−1.33732	+	0.772100i
$944$		0			0
$945$	−2.68182	−	43.6982i	−0.0872397	−	1.42150i
$946$		0			0
$947$	−14.5748	−	8.41475i	−0.473616	−	0.273443i	0.244136	−	0.969741i	$-0.421496\pi$
$947$	−14.5748	−	8.41475i	−0.473616	−	0.273443i	−0.717752	+	0.696298i	$0.754829\pi$
$948$		0			0
$949$	−0.440584	+	1.64428i	−0.0143020	+	0.0533757i
$950$		0			0
$951$	−43.6680			−1.41603
$952$		0			0
$953$	−26.2583	+	7.03588i	−0.850589	+	0.227915i	−0.657676	−	0.753301i	$-0.728460\pi$
$953$	−26.2583	+	7.03588i	−0.850589	+	0.227915i	−0.192913	+	0.981216i	$0.561794\pi$
$954$		0			0
$955$	13.5677	+	40.5215i	0.439040	+	1.31125i
$956$		0			0
$957$	2.63274	+	4.56003i	0.0851043	+	0.147405i
$958$		0			0
$959$	−17.2092	+	9.93575i	−0.555715	+	0.320842i
$960$		0			0
$961$		−	19.6011i		−	0.632292i
$962$		0			0
$963$	−33.8117	+	33.8117i	−1.08957	+	1.08957i
$964$		0			0
$965$	−36.0038	−	17.9415i	−1.15900	−	0.577556i
$966$		0			0
$967$	37.7826	−	21.8138i	1.21501	−	0.701484i	0.251160	−	0.967946i	$-0.419188\pi$
$967$	37.7826	−	21.8138i	1.21501	−	0.701484i	0.963845	+	0.266462i	$0.0858546\pi$
$968$		0			0
$969$	−132.846	+	76.6986i	−4.26763	+	2.46392i
$970$		0			0
$971$	12.0260	−	20.8296i	0.385931	−	0.668453i	−0.605967	−	0.795490i	$-0.707213\pi$
$971$	12.0260	−	20.8296i	0.385931	−	0.668453i	0.991898	+	0.127037i	$0.0405468\pi$
$972$		0			0
$973$	1.15783	+	1.15783i	0.0371183	+	0.0371183i
$974$		0			0
$975$	6.60942	+	5.15942i	0.211671	+	0.165234i
$976$		0			0
$977$	22.3270	−	38.6716i	0.714305	−	1.23721i	−0.248921	−	0.968524i	$-0.580076\pi$
$977$	22.3270	−	38.6716i	0.714305	−	1.23721i	0.963227	−	0.268690i	$-0.0865906\pi$
$978$		0			0
$979$	1.69876	+	6.33985i	0.0542926	+	0.202623i
$980$		0			0
$981$	−30.9756	+	115.603i	−0.988976	+	3.69091i
$982$		0			0
$983$	16.9411	−	4.53936i	0.540338	−	0.144783i	0.0216802	−	0.999765i	$-0.493098\pi$
$983$	16.9411	−	4.53936i	0.540338	−	0.144783i	0.518658	+	0.854982i	$0.326432\pi$
$984$		0			0
$985$	−2.31563	−	0.470618i	−0.0737820	−	0.0149951i
$986$		0			0
$987$	−3.05516	−	11.4020i	−0.0972469	−	0.362930i
$988$		0			0
$989$	52.6563			1.67437
$990$		0			0
$991$	−8.44357	+	8.44357i	−0.268219	+	0.268219i	−0.828382	−	0.560163i	$-0.810738\pi$
$991$	−8.44357	+	8.44357i	−0.268219	+	0.268219i	0.560163	+	0.828382i	$0.310738\pi$
$992$		0			0
$993$			45.4182i			1.44130i
$994$		0			0
$995$	−18.3043	−	54.6681i	−0.580286	−	1.73309i
$996$		0			0
$997$	−25.0588	−	14.4677i	−0.793621	−	0.458197i	0.0476146	−	0.998866i	$-0.484838\pi$
$997$	−25.0588	−	14.4677i	−0.793621	−	0.458197i	−0.841236	+	0.540668i	$0.818171\pi$
$998$		0			0
$999$	90.9285	+	9.94718i	2.87685	+	0.314715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.bf.a.97.19	✓	76
5.3	odd	4		740.2.bi.a.393.19	yes	76
37.29	odd	12		740.2.bi.a.177.19	yes	76
185.103	even	12	inner	740.2.bf.a.473.19	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.bf.a.97.19	✓	76	1.1	even	1	trivial
740.2.bf.a.473.19	yes	76	185.103	even	12	inner
740.2.bi.a.177.19	yes	76	37.29	odd	12
740.2.bi.a.393.19	yes	76	5.3	odd	4

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.843267 - 3.14712i) q^{3} +(-2.00134 - 0.997312i) q^{5} +(0.336984 - 1.25764i) q^{7} +(-6.59517 - 3.80772i) q^{9} +0.753951i q^{11} +(0.257348 + 0.445740i) q^{13} +(-4.82632 + 5.45745i) q^{15} +(-4.71154 - 2.72021i) q^{17} +(8.35912 + 2.23982i) q^{19} +(-3.67377 - 2.12105i) q^{21} -7.75662 q^{23} +(3.01074 + 3.99193i) q^{25} +(-10.6333 + 10.6333i) q^{27} +(1.51569 + 1.51569i) q^{29} +(5.02996 - 5.02996i) q^{31} +(2.37277 + 0.635783i) q^{33} +(-1.92868 + 2.18089i) q^{35} +(-3.80792 - 4.74339i) q^{37} +(1.61981 - 0.434026i) q^{39} +(5.29441 - 3.05673i) q^{41} -6.78856 q^{43} +(9.40169 + 14.1980i) q^{45} +(1.96762 + 1.96762i) q^{47} +(4.59408 + 2.65239i) q^{49} +(-12.5339 + 12.5339i) q^{51} +(-0.0508139 - 0.189640i) q^{53} +(0.751925 - 1.50891i) q^{55} +(14.0979 - 24.4183i) q^{57} +(-2.50761 - 9.35852i) q^{59} +(-9.48560 - 2.54166i) q^{61} +(-7.01120 + 7.01120i) q^{63} +(-0.0704995 - 1.14873i) q^{65} +(0.679656 + 0.182113i) q^{67} +(-6.54090 + 24.4110i) q^{69} +(3.51261 + 6.08402i) q^{71} +(2.33866 + 2.33866i) q^{73} +(15.1019 - 6.10888i) q^{75} +(0.948199 + 0.254069i) q^{77} +(-13.2069 - 3.53879i) q^{79} +(13.0743 + 22.6454i) q^{81} +(0.350447 + 1.30789i) q^{83} +(6.71650 + 10.1429i) q^{85} +(6.04818 - 3.49192i) q^{87} +(8.40884 - 2.25314i) q^{89} +(0.647302 - 0.173444i) q^{91} +(-11.5883 - 20.0715i) q^{93} +(-14.4956 - 12.8193i) q^{95} -3.58048i q^{97} +(2.87084 - 4.97244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} + 8 q^{13} + 2 q^{15} + 12 q^{19} - 4 q^{23} + 2 q^{25} + 28 q^{27} - 6 q^{29} + 16 q^{31} - 6 q^{33} + 20 q^{35} - 22 q^{37} + 8 q^{39} + 54 q^{41} - 16 q^{43} + 38 q^{45} + 8 q^{47} - 36 q^{49}+ \cdots - 70 q^{95}+O(q^{100}) \) 76 * q - 2 * q^3 + 8 * q^13 + 2 * q^15 + 12 * q^19 - 4 * q^23 + 2 * q^25 + 28 * q^27 - 6 * q^29 + 16 * q^31 - 6 * q^33 + 20 * q^35 - 22 * q^37 + 8 * q^39 + 54 * q^41 - 16 * q^43 + 38 * q^45 + 8 * q^47 - 36 * q^49 - 24 * q^53 + 18 * q^55 - 16 * q^59 - 28 * q^61 - 6 * q^65 - 34 * q^67 + 64 * q^69 - 8 * q^71 + 4 * q^73 + 24 * q^75 - 2 * q^77 - 40 * q^79 + 2 * q^81 - 62 * q^83 + 108 * q^87 - 2 * q^89 - 20 * q^91 - 30 * q^93 - 70 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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