LMFDB - Embedded newform 1596.2.r.h.457.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1596,2,Mod(457,1596)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1596, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1596.457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1596.r (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.7441241626$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 8 x^{12} + 7 x^{11} - 57 x^{10} + 47 x^{9} + 645 x^{8} - 2490 x^{7} + 4515 x^{6} + \cdots + 823543 $ x^14 - 3x^13 + 8x^12 + 7x^11 - 57x^10 + 47x^9 + 645x^8 - 2490x^7 + 4515x^6 + 2303x^5 - 19551x^4 + 16807x^3 + 134456x^2 - 352947*x + 823543
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.6
Root			$0.945388 - 2.47108i$ of defining polynomial
Character	$\chi$	$=$	1596.457
Dual form			1596.2.r.h.1369.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +(1.63640 - 2.83433i) q^{5} +(2.61271 + 0.416811i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.13831 + 5.43571i) q^{11} +0.420881 q^{13} +3.27280 q^{15} +(1.10807 + 1.91924i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(0.945388 + 2.47108i) q^{21} +(-0.126876 + 0.219756i) q^{23} +(-2.85560 - 4.94605i) q^{25} -1.00000 q^{27} -3.47207 q^{29} +(0.478289 + 0.828420i) q^{31} +(-3.13831 + 5.43571i) q^{33} +(5.45682 - 6.72321i) q^{35} +(-5.50965 + 9.54300i) q^{37} +(0.210441 + 0.364494i) q^{39} -2.31396 q^{41} +8.97549 q^{43} +(1.63640 + 2.83433i) q^{45} +(1.00273 - 1.73679i) q^{47} +(6.65254 + 2.17801i) q^{49} +(-1.10807 + 1.91924i) q^{51} +(-4.06236 - 7.03621i) q^{53} +20.5421 q^{55} -1.00000 q^{57} +(-7.35306 - 12.7359i) q^{59} +(6.52421 - 11.3003i) q^{61} +(-1.66733 + 2.05427i) q^{63} +(0.688729 - 1.19291i) q^{65} +(2.09328 + 3.62567i) q^{67} -0.253753 q^{69} +6.28208 q^{71} +(-5.80501 - 10.0546i) q^{73} +(2.85560 - 4.94605i) q^{75} +(5.93383 + 15.5100i) q^{77} +(-4.97790 + 8.62198i) q^{79} +(-0.500000 - 0.866025i) q^{81} -9.40488 q^{83} +7.25298 q^{85} +(-1.73603 - 3.00690i) q^{87} +(1.98310 - 3.43483i) q^{89} +(1.09964 + 0.175428i) q^{91} +(-0.478289 + 0.828420i) q^{93} +(1.63640 + 2.83433i) q^{95} -0.0778529 q^{97} -6.27661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 7 q^{3} + 2 q^{5} - 7 q^{9} - 4 q^{11} - 12 q^{13} + 4 q^{15} + 18 q^{17} - 7 q^{19} + 3 q^{21} + 2 q^{23} - 15 q^{25} - 14 q^{27} - 8 q^{29} + q^{31} + 4 q^{33} + 22 q^{35} - 7 q^{37} - 6 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) $ 14 * q + 7 * q^3 + 2 * q^5 - 7 * q^9 - 4 * q^11 - 12 * q^13 + 4 * q^15 + 18 * q^17 - 7 * q^19 + 3 * q^21 + 2 * q^23 - 15 * q^25 - 14 * q^27 - 8 * q^29 + q^31 + 4 * q^33 + 22 * q^35 - 7 * q^37 - 6 * q^39 - 30 * q^41 + 6 * q^43 + 2 * q^45 + 2 * q^47 + 26 * q^49 - 18 * q^51 - 24 * q^53 - 8 * q^55 - 14 * q^57 + 15 * q^59 + 5 * q^61 + 3 * q^63 - 5 * q^65 - 9 * q^67 + 4 * q^69 - 32 * q^71 + q^73 + 15 * q^75 + 47 * q^77 - 13 * q^79 - 7 * q^81 - 22 * q^83 + 22 * q^85 - 4 * q^87 + 7 * q^89 + 39 * q^91 - q^93 + 2 * q^95 - 82 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1596\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	1.63640	−	2.83433i	0.731820	−	1.26755i	−0.224285	−	0.974524i	$-0.572005\pi$
$5$	1.63640	−	2.83433i	0.731820	−	1.26755i	0.956105	−	0.293025i	$-0.0946620\pi$
$6$		0			0
$7$	2.61271	+	0.416811i	0.987513	+	0.157540i
$7$	2.61271	+	0.416811i	0.987513	+	0.157540i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.13831	+	5.43571i	0.946235	+	1.63893i	0.753260	+	0.657723i	$0.228480\pi$
$11$	3.13831	+	5.43571i	0.946235	+	1.63893i	0.192975	+	0.981204i	$0.438186\pi$
$12$		0			0
$13$	0.420881			0.116731			0.0583657	−	0.998295i	$-0.481411\pi$
$13$	0.420881			0.116731			0.0583657	+	0.998295i	$0.481411\pi$
$14$		0			0
$15$	3.27280			0.845033
$16$		0			0
$17$	1.10807	+	1.91924i	0.268747	+	0.465483i	0.968538	−	0.248864i	$-0.0800572\pi$
$17$	1.10807	+	1.91924i	0.268747	+	0.465483i	−0.699792	+	0.714347i	$0.746724\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$		0			0
$21$	0.945388	+	2.47108i	0.206301	+	0.539234i
$22$		0			0
$23$	−0.126876	+	0.219756i	−0.0264555	+	0.0458224i	−0.878950	−	0.476914i	$-0.841755\pi$
$23$	−0.126876	+	0.219756i	−0.0264555	+	0.0458224i	0.852495	+	0.522736i	$0.175089\pi$
$24$		0			0
$25$	−2.85560	−	4.94605i	−0.571120	−	0.989209i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.47207			−0.644747			−0.322373	−	0.946613i	$-0.604481\pi$
$29$	−3.47207			−0.644747			−0.322373	+	0.946613i	$0.604481\pi$
$30$		0			0
$31$	0.478289	+	0.828420i	0.0859032	+	0.148789i	0.905776	−	0.423757i	$-0.139289\pi$
$31$	0.478289	+	0.828420i	0.0859032	+	0.148789i	−0.819873	+	0.572546i	$0.805956\pi$
$32$		0			0
$33$	−3.13831	+	5.43571i	−0.546309	+	0.946235i
$34$		0			0
$35$	5.45682	−	6.72321i	0.922370	−	1.13643i
$36$		0			0
$37$	−5.50965	+	9.54300i	−0.905781	+	1.56886i	−0.0859160	+	0.996302i	$0.527382\pi$
$37$	−5.50965	+	9.54300i	−0.905781	+	1.56886i	−0.819865	+	0.572557i	$0.805952\pi$
$38$		0			0
$39$	0.210441	+	0.364494i	0.0336975	+	0.0583657i
$40$		0			0
$41$	−2.31396			−0.361380			−0.180690	−	0.983540i	$-0.557833\pi$
$41$	−2.31396			−0.361380			−0.180690	+	0.983540i	$0.557833\pi$
$42$		0			0
$43$	8.97549			1.36875			0.684375	−	0.729131i	$-0.260075\pi$
$43$	8.97549			1.36875			0.684375	+	0.729131i	$0.260075\pi$
$44$		0			0
$45$	1.63640	+	2.83433i	0.243940	+	0.422516i
$46$		0			0
$47$	1.00273	−	1.73679i	0.146264	−	0.253336i	−0.783580	−	0.621291i	$-0.786608\pi$
$47$	1.00273	−	1.73679i	0.146264	−	0.253336i	0.929844	+	0.367955i	$0.119942\pi$
$48$		0			0
$49$	6.65254	+	2.17801i	0.950363	+	0.311145i
$50$		0			0
$51$	−1.10807	+	1.91924i	−0.155161	+	0.268747i
$52$		0			0
$53$	−4.06236	−	7.03621i	−0.558008	−	0.966498i	−0.997663	−	0.0683309i	$-0.978233\pi$
$53$	−4.06236	−	7.03621i	−0.558008	−	0.966498i	0.439655	−	0.898167i	$-0.355101\pi$
$54$		0			0
$55$	20.5421			2.76989
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	−7.35306	−	12.7359i	−0.957287	−	1.65807i	−0.729045	−	0.684466i	$-0.760035\pi$
$59$	−7.35306	−	12.7359i	−0.957287	−	1.65807i	−0.228243	−	0.973604i	$-0.573298\pi$
$60$		0			0
$61$	6.52421	−	11.3003i	0.835339	−	1.44685i	−0.0584143	−	0.998292i	$-0.518604\pi$
$61$	6.52421	−	11.3003i	0.835339	−	1.44685i	0.893754	−	0.448558i	$-0.148062\pi$
$62$		0			0
$63$	−1.66733	+	2.05427i	−0.210063	+	0.258814i
$64$		0			0
$65$	0.688729	−	1.19291i	0.0854264	−	0.147963i
$66$		0			0
$67$	2.09328	+	3.62567i	0.255735	+	0.442946i	0.965095	−	0.261900i	$-0.0843491\pi$
$67$	2.09328	+	3.62567i	0.255735	+	0.442946i	−0.709360	+	0.704847i	$0.751016\pi$
$68$		0			0
$69$	−0.253753			−0.0305482
$70$		0			0
$71$	6.28208			0.745546			0.372773	−	0.927923i	$-0.378407\pi$
$71$	6.28208			0.745546			0.372773	+	0.927923i	$0.378407\pi$
$72$		0			0
$73$	−5.80501	−	10.0546i	−0.679425	−	1.17680i	−0.975154	−	0.221526i	$-0.928896\pi$
$73$	−5.80501	−	10.0546i	−0.679425	−	1.17680i	0.295730	−	0.955272i	$-0.404437\pi$
$74$		0			0
$75$	2.85560	−	4.94605i	0.329736	−	0.571120i
$76$		0			0
$77$	5.93383	+	15.5100i	0.676223	+	1.76753i
$78$		0			0
$79$	−4.97790	+	8.62198i	−0.560058	+	0.970049i	0.437433	+	0.899251i	$0.355888\pi$
$79$	−4.97790	+	8.62198i	−0.560058	+	0.970049i	−0.997491	+	0.0707978i	$0.977445\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−9.40488			−1.03232			−0.516160	−	0.856492i	$-0.672639\pi$
$83$	−9.40488			−1.03232			−0.516160	+	0.856492i	$0.672639\pi$
$84$		0			0
$85$	7.25298			0.786696
$86$		0			0
$87$	−1.73603	−	3.00690i	−0.186122	−	0.322373i
$88$		0			0
$89$	1.98310	−	3.43483i	0.210208	−	0.364092i	−0.741571	−	0.670874i	$-0.765919\pi$
$89$	1.98310	−	3.43483i	0.210208	−	0.364092i	0.951780	+	0.306783i	$0.0992524\pi$
$90$		0			0
$91$	1.09964	+	0.175428i	0.115274	+	0.0183898i
$92$		0			0
$93$	−0.478289	+	0.828420i	−0.0495962	+	0.0859032i
$94$		0			0
$95$	1.63640	+	2.83433i	0.167891	+	0.290796i
$96$		0			0
$97$	−0.0778529			−0.00790476			−0.00395238	−	0.999992i	$-0.501258\pi$
$97$	−0.0778529			−0.00790476			−0.00395238	+	0.999992i	$0.501258\pi$
$98$		0			0
$99$	−6.27661			−0.630823
$100$		0			0
$101$	3.33732	+	5.78040i	0.332075	+	0.575172i	0.982919	−	0.184041i	$-0.0589178\pi$
$101$	3.33732	+	5.78040i	0.332075	+	0.575172i	−0.650843	+	0.759212i	$0.725584\pi$
$102$		0			0
$103$	1.09558	−	1.89760i	0.107951	−	0.186976i	−0.806989	−	0.590566i	$-0.798904\pi$
$103$	1.09558	−	1.89760i	0.107951	−	0.186976i	0.914940	+	0.403590i	$0.132238\pi$
$104$		0			0
$105$	8.55088	+	1.36414i	0.834480	+	0.133126i
$106$		0			0
$107$	9.81726	−	17.0040i	0.949070	−	1.64384i	0.201681	−	0.979451i	$-0.435360\pi$
$107$	9.81726	−	17.0040i	0.949070	−	1.64384i	0.747389	−	0.664386i	$-0.231307\pi$
$108$		0			0
$109$	4.37516	+	7.57800i	0.419064	+	0.725841i	0.995846	−	0.0910579i	$-0.0290248\pi$
$109$	4.37516	+	7.57800i	0.419064	+	0.725841i	−0.576781	+	0.816899i	$0.695692\pi$
$110$		0			0
$111$	−11.0193			−1.04591
$112$		0			0
$113$	1.62281			0.152661			0.0763307	−	0.997083i	$-0.475680\pi$
$113$	1.62281			0.152661			0.0763307	+	0.997083i	$0.475680\pi$
$114$		0			0
$115$	0.415241	+	0.719218i	0.0387214	+	0.0670674i
$116$		0			0
$117$	−0.210441	+	0.364494i	−0.0194552	+	0.0336975i
$118$		0			0
$119$	2.09511	+	5.47627i	0.192059	+	0.502008i
$120$		0			0
$121$	−14.1979	+	24.5915i	−1.29072	+	2.23559i
$122$		0			0
$123$	−1.15698	−	2.00395i	−0.104322	−	0.180690i
$124$		0			0
$125$	−2.32762			−0.208189
$126$		0			0
$127$	13.1608			1.16783			0.583916	−	0.811814i	$-0.301520\pi$
$127$	13.1608			1.16783			0.583916	+	0.811814i	$0.301520\pi$
$128$		0			0
$129$	4.48774	+	7.77300i	0.395124	+	0.684375i
$130$		0			0
$131$	1.36809	−	2.36960i	0.119530	−	0.207033i	−0.800051	−	0.599932i	$-0.795194\pi$
$131$	1.36809	−	2.36960i	0.119530	−	0.207033i	0.919582	+	0.392899i	$0.128528\pi$
$132$		0			0
$133$	−1.66733	+	2.05427i	−0.144575	+	0.178128i
$134$		0			0
$135$	−1.63640	+	2.83433i	−0.140839	+	0.243940i
$136$		0			0
$137$	−4.71172	−	8.16094i	−0.402550	−	0.697237i	0.591483	−	0.806317i	$-0.298543\pi$
$137$	−4.71172	−	8.16094i	−0.402550	−	0.697237i	−0.994033	+	0.109081i	$0.965209\pi$
$138$		0			0
$139$	−2.59847			−0.220400			−0.110200	−	0.993909i	$-0.535149\pi$
$139$	−2.59847			−0.220400			−0.110200	+	0.993909i	$0.535149\pi$
$140$		0			0
$141$	2.00547			0.168891
$142$		0			0
$143$	1.32085	+	2.28779i	0.110455	+	0.191314i
$144$		0			0
$145$	−5.68169	+	9.84097i	−0.471838	+	0.817248i
$146$		0			0
$147$	1.44005	+	6.85027i	0.118774	+	0.565001i
$148$		0			0
$149$	1.10014	−	1.90550i	0.0901269	−	0.156104i	−0.817437	−	0.576017i	$-0.804606\pi$
$149$	1.10014	−	1.90550i	0.0901269	−	0.156104i	0.907564	+	0.419913i	$0.137939\pi$
$150$		0			0
$151$	−0.183463	−	0.317767i	−0.0149300	−	0.0258595i	0.858464	−	0.512874i	$-0.171419\pi$
$151$	−0.183463	−	0.317767i	−0.0149300	−	0.0258595i	−0.873394	+	0.487014i	$0.838086\pi$
$152$		0			0
$153$	−2.21614			−0.179164
$154$		0			0
$155$	3.13068			0.251463
$156$		0			0
$157$	10.2059	+	17.6771i	0.814518	+	1.41079i	0.909673	+	0.415325i	$0.136332\pi$
$157$	10.2059	+	17.6771i	0.814518	+	1.41079i	−0.0951547	+	0.995463i	$0.530335\pi$
$158$		0			0
$159$	4.06236	−	7.03621i	0.322166	−	0.558008i
$160$		0			0
$161$	−0.423088	+	0.521277i	−0.0333440	+	0.0410824i
$162$		0			0
$163$	−6.93411	+	12.0102i	−0.543122	+	0.940714i	0.455601	+	0.890184i	$0.349424\pi$
$163$	−6.93411	+	12.0102i	−0.543122	+	0.940714i	−0.998723	+	0.0505302i	$0.983909\pi$
$164$		0			0
$165$	10.2710	+	17.7900i	0.799599	+	1.38495i
$166$		0			0
$167$	−0.755925			−0.0584952			−0.0292476	−	0.999572i	$-0.509311\pi$
$167$	−0.755925			−0.0584952			−0.0292476	+	0.999572i	$0.509311\pi$
$168$		0			0
$169$	−12.8229			−0.986374
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$		0			0
$173$	−4.74309	+	8.21527i	−0.360610	+	0.624595i	−0.988061	−	0.154061i	$-0.950765\pi$
$173$	−4.74309	+	8.21527i	−0.360610	+	0.624595i	0.627451	+	0.778656i	$0.284098\pi$
$174$		0			0
$175$	−5.39930	−	14.1128i	−0.408149	−	1.06683i
$176$		0			0
$177$	7.35306	−	12.7359i	0.552690	−	0.957287i
$178$		0			0
$179$	−11.4115	−	19.7653i	−0.852935	−	1.47733i	−0.878548	−	0.477654i	$-0.841487\pi$
$179$	−11.4115	−	19.7653i	−0.852935	−	1.47733i	0.0256132	−	0.999672i	$-0.491846\pi$
$180$		0			0
$181$	−7.43029			−0.552289			−0.276144	−	0.961116i	$-0.589057\pi$
$181$	−7.43029			−0.552289			−0.276144	+	0.961116i	$0.589057\pi$
$182$		0			0
$183$	13.0484			0.964567
$184$		0			0
$185$	18.0320	+	31.2323i	1.32574	+	2.29624i
$186$		0			0
$187$	−6.95493	+	12.0463i	−0.508595	+	0.880912i
$188$		0			0
$189$	−2.61271	−	0.416811i	−0.190047	−	0.0303185i
$190$		0			0
$191$	−7.26755	+	12.5878i	−0.525862	+	0.910819i	0.473685	+	0.880695i	$0.342924\pi$
$191$	−7.26755	+	12.5878i	−0.525862	+	0.910819i	−0.999546	+	0.0301244i	$0.990410\pi$
$192$		0			0
$193$	−12.8931	−	22.3316i	−0.928068	−	1.60746i	−0.786550	−	0.617526i	$-0.788135\pi$
$193$	−12.8931	−	22.3316i	−0.928068	−	1.60746i	−0.141518	−	0.989936i	$-0.545198\pi$
$194$		0			0
$195$	1.37746			0.0986419
$196$		0			0
$197$	5.86081			0.417565			0.208783	−	0.977962i	$-0.433050\pi$
$197$	5.86081			0.417565			0.208783	+	0.977962i	$0.433050\pi$
$198$		0			0
$199$	−3.70715	−	6.42097i	−0.262793	−	0.455171i	0.704190	−	0.710011i	$-0.251310\pi$
$199$	−3.70715	−	6.42097i	−0.262793	−	0.455171i	−0.966983	+	0.254841i	$0.917977\pi$
$200$		0			0
$201$	−2.09328	+	3.62567i	−0.147649	+	0.255735i
$202$		0			0
$203$	−9.07151	−	1.44719i	−0.636696	−	0.101573i
$204$		0			0
$205$	−3.78657	+	6.55853i	−0.264465	+	0.458067i
$206$		0			0
$207$	−0.126876	−	0.219756i	−0.00881852	−	0.0152741i
$208$		0			0
$209$	−6.27661			−0.434162
$210$		0			0
$211$	−14.9018			−1.02588			−0.512942	−	0.858423i	$-0.671445\pi$
$211$	−14.9018			−1.02588			−0.512942	+	0.858423i	$0.671445\pi$
$212$		0			0
$213$	3.14104	+	5.44044i	0.215221	+	0.372773i
$214$		0			0
$215$	14.6875	−	25.4395i	1.00168	−	1.73496i
$216$		0			0
$217$	0.904337	+	2.36378i	0.0613904	+	0.160464i
$218$		0			0
$219$	5.80501	−	10.0546i	0.392266	−	0.679425i
$220$		0			0
$221$	0.466366	+	0.807770i	0.0313712	+	0.0543365i
$222$		0			0
$223$	17.6877			1.18446			0.592228	−	0.805770i	$-0.298249\pi$
$223$	17.6877			1.18446			0.592228	+	0.805770i	$0.298249\pi$
$224$		0			0
$225$	5.71120			0.380747
$226$		0			0
$227$	−10.3376	−	17.9052i	−0.686129	−	1.18841i	−0.973081	−	0.230465i	$-0.925975\pi$
$227$	−10.3376	−	17.9052i	−0.686129	−	1.18841i	0.286952	−	0.957945i	$-0.407358\pi$
$228$		0			0
$229$	9.32671	−	16.1543i	0.616326	−	1.06751i	−0.373824	−	0.927500i	$-0.621954\pi$
$229$	9.32671	−	16.1543i	0.616326	−	1.06751i	0.990150	−	0.140009i	$-0.0447131\pi$
$230$		0			0
$231$	−10.4652	+	12.8939i	−0.688557	+	0.848354i
$232$		0			0
$233$	13.7503	−	23.8161i	0.900809	−	1.56025i	0.0743639	−	0.997231i	$-0.476307\pi$
$233$	13.7503	−	23.8161i	0.900809	−	1.56025i	0.826446	−	0.563017i	$-0.190359\pi$
$234$		0			0
$235$	−3.28175	−	5.68415i	−0.214078	−	0.370793i
$236$		0			0
$237$	−9.95581			−0.646699
$238$		0			0
$239$	−12.2845			−0.794620			−0.397310	−	0.917685i	$-0.630056\pi$
$239$	−12.2845			−0.794620			−0.397310	+	0.917685i	$0.630056\pi$
$240$		0			0
$241$	−2.93854	−	5.08970i	−0.189288	−	0.327857i	0.755725	−	0.654889i	$-0.227285\pi$
$241$	−2.93854	−	5.08970i	−0.189288	−	0.327857i	−0.945013	+	0.327033i	$0.893951\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	17.0594	−	15.2914i	1.08989	−	0.976929i
$246$		0			0
$247$	−0.210441	+	0.364494i	−0.0133900	+	0.0231922i
$248$		0			0
$249$	−4.70244	−	8.14487i	−0.298005	−	0.516160i
$250$		0			0
$251$	−7.67667			−0.484547			−0.242274	−	0.970208i	$-0.577893\pi$
$251$	−7.67667			−0.484547			−0.242274	+	0.970208i	$0.577893\pi$
$252$		0			0
$253$	−1.59271			−0.100133
$254$		0			0
$255$	3.62649	+	6.28127i	0.227100	+	0.393348i
$256$		0			0
$257$	9.15770	−	15.8616i	0.571242	−	0.989420i	−0.425197	−	0.905101i	$-0.639795\pi$
$257$	9.15770	−	15.8616i	0.571242	−	0.989420i	0.996439	−	0.0843190i	$-0.0268715\pi$
$258$		0			0
$259$	−18.3728	+	22.6366i	−1.14163	+	1.40657i
$260$		0			0
$261$	1.73603	−	3.00690i	0.107458	−	0.186122i
$262$		0			0
$263$	−11.5461	−	19.9984i	−0.711964	−	1.23316i	−0.964119	−	0.265470i	$-0.914473\pi$
$263$	−11.5461	−	19.9984i	−0.711964	−	1.23316i	0.252155	−	0.967687i	$-0.418861\pi$
$264$		0			0
$265$	−26.5905			−1.63344
$266$		0			0
$267$	3.96620			0.242728
$268$		0			0
$269$	0.977577	+	1.69321i	0.0596039	+	0.103237i	0.894288	−	0.447493i	$-0.147683\pi$
$269$	0.977577	+	1.69321i	0.0596039	+	0.103237i	−0.834684	+	0.550730i	$0.814350\pi$
$270$		0			0
$271$	0.722937	−	1.25216i	0.0439153	−	0.0760635i	−0.843232	−	0.537549i	$-0.819350\pi$
$271$	0.722937	−	1.25216i	0.0439153	−	0.0760635i	0.887148	+	0.461486i	$0.152684\pi$
$272$		0			0
$273$	0.397896	+	1.04003i	0.0240818	+	0.0629456i
$274$		0			0
$275$	17.9235	−	31.0444i	1.08083	−	1.87205i
$276$		0			0
$277$	8.61874	+	14.9281i	0.517850	+	0.896942i	0.999785	+	0.0207355i	$0.00660079\pi$
$277$	8.61874	+	14.9281i	0.517850	+	0.896942i	−0.481935	+	0.876207i	$0.660066\pi$
$278$		0			0
$279$	−0.956577			−0.0572688
$280$		0			0
$281$	7.32424			0.436928			0.218464	−	0.975845i	$-0.429895\pi$
$281$	7.32424			0.436928			0.218464	+	0.975845i	$0.429895\pi$
$282$		0			0
$283$	3.53353	+	6.12025i	0.210046	+	0.363811i	0.951729	−	0.306940i	$-0.0993052\pi$
$283$	3.53353	+	6.12025i	0.210046	+	0.363811i	−0.741682	+	0.670751i	$0.765972\pi$
$284$		0			0
$285$	−1.63640	+	2.83433i	−0.0969319	+	0.167891i
$286$		0			0
$287$	−6.04572	−	0.964485i	−0.356868	−	0.0569318i
$288$		0			0
$289$	6.04436	−	10.4691i	0.355550	−	0.615831i
$290$		0			0
$291$	−0.0389264	−	0.0674226i	−0.00228191	−	0.00395238i
$292$		0			0
$293$	−18.5528			−1.08386			−0.541932	−	0.840422i	$-0.682307\pi$
$293$	−18.5528			−1.08386			−0.541932	+	0.840422i	$0.682307\pi$
$294$		0			0
$295$	−48.1302			−2.80225
$296$		0			0
$297$	−3.13831	−	5.43571i	−0.182103	−	0.315412i
$298$		0			0
$299$	−0.0533999	+	0.0924913i	−0.00308819	+	0.00534891i
$300$		0			0
$301$	23.4504	+	3.74108i	1.35166	+	0.215632i
$302$		0			0
$303$	−3.33732	+	5.78040i	−0.191724	+	0.332075i
$304$		0			0
$305$	−21.3524	−	36.9835i	−1.22264	−	2.11767i
$306$		0			0
$307$	2.96218			0.169061			0.0845304	−	0.996421i	$-0.473061\pi$
$307$	2.96218			0.169061			0.0845304	+	0.996421i	$0.473061\pi$
$308$		0			0
$309$	2.19116			0.124651
$310$		0			0
$311$	6.82435	+	11.8201i	0.386973	+	0.670257i	0.992041	−	0.125917i	$-0.0401872\pi$
$311$	6.82435	+	11.8201i	0.386973	+	0.670257i	−0.605068	+	0.796174i	$0.706854\pi$
$312$		0			0
$313$	−5.74049	+	9.94282i	−0.324472	+	0.562001i	−0.981405	−	0.191947i	$-0.938520\pi$
$313$	−5.74049	+	9.94282i	−0.324472	+	0.562001i	0.656934	+	0.753948i	$0.271853\pi$
$314$		0			0
$315$	3.09406	+	8.08735i	0.174331	+	0.455670i
$316$		0			0
$317$	−16.6588	+	28.8539i	−0.935650	+	1.62059i	−0.162181	+	0.986761i	$0.551853\pi$
$317$	−16.6588	+	28.8539i	−0.935650	+	1.62059i	−0.773470	+	0.633833i	$0.781481\pi$
$318$		0			0
$319$	−10.8964	−	18.8731i	−0.610082	−	1.05669i
$320$		0			0
$321$	19.6345			1.09589
$322$		0			0
$323$	−2.21614			−0.123309
$324$		0			0
$325$	−1.20187	−	2.08170i	−0.0666677	−	0.115472i
$326$		0			0
$327$	−4.37516	+	7.57800i	−0.241947	+	0.419064i
$328$		0			0
$329$	3.34377	−	4.11978i	0.184348	−	0.227131i
$330$		0			0
$331$	8.50547	−	14.7319i	0.467503	−	0.809738i	−0.531808	−	0.846865i	$-0.678487\pi$
$331$	8.50547	−	14.7319i	0.467503	−	0.809738i	0.999311	+	0.0371266i	$0.0118205\pi$
$332$		0			0
$333$	−5.50965	−	9.54300i	−0.301927	−	0.522953i
$334$		0			0
$335$	13.7018			0.748608
$336$		0			0
$337$	−19.2432			−1.04824			−0.524121	−	0.851644i	$-0.675606\pi$
$337$	−19.2432			−1.04824			−0.524121	+	0.851644i	$0.675606\pi$
$338$		0			0
$339$	0.811407	+	1.40540i	0.0440696	+	0.0763307i
$340$		0			0
$341$	−3.00203	+	5.19967i	−0.162569	+	0.281578i
$342$		0			0
$343$	16.4734	+	8.46337i	0.889477	+	0.456979i
$344$		0			0
$345$	−0.415241	+	0.719218i	−0.0223558	+	0.0387214i
$346$		0			0
$347$	10.2550	+	17.7622i	0.550519	+	0.953527i	0.998237	+	0.0593520i	$0.0189034\pi$
$347$	10.2550	+	17.7622i	0.550519	+	0.953527i	−0.447718	+	0.894175i	$0.647763\pi$
$348$		0			0
$349$	−3.86395			−0.206833			−0.103416	−	0.994638i	$-0.532977\pi$
$349$	−3.86395			−0.206833			−0.103416	+	0.994638i	$0.532977\pi$
$350$		0			0
$351$	−0.420881			−0.0224650
$352$		0			0
$353$	−5.36488	−	9.29224i	−0.285544	−	0.494576i	0.687197	−	0.726471i	$-0.258841\pi$
$353$	−5.36488	−	9.29224i	−0.285544	−	0.494576i	−0.972741	+	0.231895i	$0.925508\pi$
$354$		0			0
$355$	10.2800	−	17.8055i	0.545605	−	0.945016i
$356$		0			0
$357$	−3.69503	+	4.55255i	−0.195562	+	0.240947i
$358$		0			0
$359$	13.3916	−	23.1949i	0.706780	−	1.22418i	−0.259266	−	0.965806i	$-0.583481\pi$
$359$	13.3916	−	23.1949i	0.706780	−	1.22418i	0.966045	−	0.258372i	$-0.0831861\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	−28.3959			−1.49040
$364$		0			0
$365$	−37.9972			−1.98887
$366$		0			0
$367$	−2.27724	−	3.94430i	−0.118871	−	0.205891i	0.800449	−	0.599400i	$-0.204594\pi$
$367$	−2.27724	−	3.94430i	−0.118871	−	0.205891i	−0.919321	+	0.393509i	$0.871261\pi$
$368$		0			0
$369$	1.15698	−	2.00395i	0.0602301	−	0.104322i
$370$		0			0
$371$	−7.68100	−	20.0768i	−0.398778	−	1.04234i
$372$		0			0
$373$	−9.16386	+	15.8723i	−0.474487	+	0.821835i	−0.999573	−	0.0292140i	$-0.990700\pi$
$373$	−9.16386	+	15.8723i	−0.474487	+	0.821835i	0.525087	+	0.851049i	$0.324033\pi$
$374$		0			0
$375$	−1.16381	−	2.01578i	−0.0600989	−	0.104094i
$376$		0			0
$377$	−1.46133			−0.0752622
$378$		0			0
$379$	18.4090			0.945609			0.472804	−	0.881167i	$-0.343242\pi$
$379$	18.4090			0.945609			0.472804	+	0.881167i	$0.343242\pi$
$380$		0			0
$381$	6.58040	+	11.3976i	0.337124	+	0.583916i
$382$		0			0
$383$	6.22205	−	10.7769i	0.317932	−	0.550674i	−0.662125	−	0.749394i	$-0.730345\pi$
$383$	6.22205	−	10.7769i	0.317932	−	0.550674i	0.980056	+	0.198720i	$0.0636784\pi$
$384$		0			0
$385$	53.6706	+	8.56216i	2.73530	+	0.436368i
$386$		0			0
$387$	−4.48774	+	7.77300i	−0.228125	+	0.395124i
$388$		0			0
$389$	−2.89186	−	5.00885i	−0.146623	−	0.253959i	0.783354	−	0.621576i	$-0.213507\pi$
$389$	−2.89186	−	5.00885i	−0.146623	−	0.253959i	−0.929977	+	0.367617i	$0.880174\pi$
$390$		0			0
$391$	−0.562352			−0.0284394
$392$		0			0
$393$	2.73618			0.138022
$394$		0			0
$395$	16.2917	+	28.2180i	0.819723	+	1.41980i
$396$		0			0
$397$	8.08827	−	14.0093i	0.405939	−	0.703107i	−0.588491	−	0.808503i	$-0.700278\pi$
$397$	8.08827	−	14.0093i	0.405939	−	0.703107i	0.994430	+	0.105397i	$0.0336113\pi$
$398$		0			0
$399$	−2.61271	−	0.416811i	−0.130799	−	0.0208666i
$400$		0			0
$401$	−13.5072	+	23.3952i	−0.674520	+	1.16830i	0.302090	+	0.953280i	$0.402316\pi$
$401$	−13.5072	+	23.3952i	−0.674520	+	1.16830i	−0.976609	+	0.215023i	$0.931017\pi$
$402$		0			0
$403$	0.201303	+	0.348666i	0.0100276	+	0.0173683i
$404$		0			0
$405$	−3.27280			−0.162627
$406$		0			0
$407$	−69.1639			−3.42833
$408$		0			0
$409$	12.5679	+	21.7682i	0.621442	+	1.07637i	0.989217	+	0.146455i	$0.0467863\pi$
$409$	12.5679	+	21.7682i	0.621442	+	1.07637i	−0.367775	+	0.929915i	$0.619880\pi$
$410$		0			0
$411$	4.71172	−	8.16094i	0.232412	−	0.402550i
$412$		0			0
$413$	−13.9030	−	36.3400i	−0.684122	−	1.78818i
$414$		0			0
$415$	−15.3901	+	26.6565i	−0.755472	+	1.30852i
$416$		0			0
$417$	−1.29924	−	2.25034i	−0.0636239	−	0.110200i
$418$		0			0
$419$	8.95289			0.437377			0.218689	−	0.975795i	$-0.429822\pi$
$419$	8.95289			0.437377			0.218689	+	0.975795i	$0.429822\pi$
$420$		0			0
$421$	8.95392			0.436387			0.218194	−	0.975905i	$-0.429984\pi$
$421$	8.95392			0.436387			0.218194	+	0.975905i	$0.429984\pi$
$422$		0			0
$423$	1.00273	+	1.73679i	0.0487546	+	0.0844455i
$424$		0			0
$425$	6.32842	−	10.9611i	0.306973	−	0.531693i
$426$		0			0
$427$	21.7560	−	26.8050i	1.05284	−	1.29718i
$428$		0			0
$429$	−1.32085	+	2.28779i	−0.0637714	+	0.110455i
$430$		0			0
$431$	−10.1351	−	17.5546i	−0.488193	−	0.845575i	0.511715	−	0.859155i	$-0.329010\pi$
$431$	−10.1351	−	17.5546i	−0.488193	−	0.845575i	−0.999908	+	0.0135806i	$0.995677\pi$
$432$		0			0
$433$	11.5672			0.555884			0.277942	−	0.960598i	$-0.410348\pi$
$433$	11.5672			0.555884			0.277942	+	0.960598i	$0.410348\pi$
$434$		0			0
$435$	−11.3634			−0.544832
$436$		0			0
$437$	−0.126876	−	0.219756i	−0.00606932	−	0.0105124i
$438$		0			0
$439$	11.2215	−	19.4363i	0.535575	−	0.927643i	−0.463560	−	0.886065i	$-0.653428\pi$
$439$	11.2215	−	19.4363i	0.535575	−	0.927643i	0.999135	−	0.0415775i	$-0.0132384\pi$
$440$		0			0
$441$	−5.21248	+	4.67226i	−0.248214	+	0.222489i
$442$		0			0
$443$	1.58400	−	2.74357i	0.0752580	−	0.130351i	−0.825940	−	0.563757i	$-0.809355\pi$
$443$	1.58400	−	2.74357i	0.0752580	−	0.130351i	0.901198	+	0.433407i	$0.142689\pi$
$444$		0			0
$445$	−6.49029	−	11.2415i	−0.307669	−	0.532899i
$446$		0			0
$447$	2.20028			0.104070
$448$		0			0
$449$	−29.8178			−1.40719			−0.703594	−	0.710602i	$-0.748423\pi$
$449$	−29.8178			−1.40719			−0.703594	+	0.710602i	$0.748423\pi$
$450$		0			0
$451$	−7.26193	−	12.5780i	−0.341951	−	0.592276i
$452$		0			0
$453$	0.183463	−	0.317767i	0.00861985	−	0.0149300i
$454$		0			0
$455$	2.29667	−	2.82967i	0.107670	−	0.132657i
$456$		0			0
$457$	−11.6123	+	20.1131i	−0.543200	+	0.940850i	0.455518	+	0.890227i	$0.349454\pi$
$457$	−11.6123	+	20.1131i	−0.543200	+	0.940850i	−0.998718	+	0.0506232i	$0.983879\pi$
$458$		0			0
$459$	−1.10807	−	1.91924i	−0.0517203	−	0.0895822i
$460$		0			0
$461$	−24.4000			−1.13642			−0.568210	−	0.822884i	$-0.692364\pi$
$461$	−24.4000			−1.13642			−0.568210	+	0.822884i	$0.692364\pi$
$462$		0			0
$463$	−41.3837			−1.92326			−0.961631	−	0.274344i	$-0.911539\pi$
$463$	−41.3837			−1.92326			−0.961631	+	0.274344i	$0.911539\pi$
$464$		0			0
$465$	1.56534	+	2.71125i	0.0725910	+	0.125731i
$466$		0			0
$467$	5.86328	−	10.1555i	0.271320	−	0.469940i	−0.697880	−	0.716215i	$-0.745873\pi$
$467$	5.86328	−	10.1555i	0.271320	−	0.469940i	0.969200	+	0.246274i	$0.0792065\pi$
$468$		0			0
$469$	3.95793	+	10.3453i	0.182760	+	0.477704i
$470$		0			0
$471$	−10.2059	+	17.6771i	−0.470262	+	0.814518i
$472$		0			0
$473$	28.1678	+	48.7881i	1.29516	+	2.24328i
$474$		0			0
$475$	5.71120			0.262048
$476$		0			0
$477$	8.12471			0.372005
$478$		0			0
$479$	20.2681	+	35.1054i	0.926074	+	1.60401i	0.789825	+	0.613332i	$0.210171\pi$
$479$	20.2681	+	35.1054i	0.926074	+	1.60401i	0.136248	+	0.990675i	$0.456496\pi$
$480$		0			0
$481$	−2.31891	+	4.01647i	−0.105733	+	0.183135i
$482$		0			0
$483$	−0.662983	−	0.105767i	−0.0301668	−	0.00481256i
$484$		0			0
$485$	−0.127398	+	0.220660i	−0.00578486	+	0.0100197i
$486$		0			0
$487$	14.6524	+	25.3787i	0.663962	+	1.15002i	0.979566	+	0.201125i	$0.0644598\pi$
$487$	14.6524	+	25.3787i	0.663962	+	1.15002i	−0.315603	+	0.948891i	$0.602207\pi$
$488$		0			0
$489$	−13.8682			−0.627143
$490$		0			0
$491$	−39.4962			−1.78244			−0.891219	−	0.453572i	$-0.850149\pi$
$491$	−39.4962			−1.78244			−0.891219	+	0.453572i	$0.850149\pi$
$492$		0			0
$493$	−3.84730	−	6.66371i	−0.173274	−	0.300119i
$494$		0			0
$495$	−10.2710	+	17.7900i	−0.461649	+	0.799599i
$496$		0			0
$497$	16.4133	+	2.61844i	0.736236	+	0.117453i
$498$		0			0
$499$	−7.36336	+	12.7537i	−0.329629	+	0.570935i	−0.982438	−	0.186588i	$-0.940257\pi$
$499$	−7.36336	+	12.7537i	−0.329629	+	0.570935i	0.652809	+	0.757523i	$0.273590\pi$
$500$		0			0
$501$	−0.377962	−	0.654650i	−0.0168861	−	0.0292476i
$502$		0			0
$503$	36.4721			1.62621			0.813105	−	0.582118i	$-0.197776\pi$
$503$	36.4721			1.62621			0.813105	+	0.582118i	$0.197776\pi$
$504$		0			0
$505$	21.8447			0.972077
$506$		0			0
$507$	−6.41143	−	11.1049i	−0.284742	−	0.493187i
$508$		0			0
$509$	−18.3932	+	31.8579i	−0.815263	+	1.41208i	0.0938764	+	0.995584i	$0.470074\pi$
$509$	−18.3932	+	31.8579i	−0.815263	+	1.41208i	−0.909139	+	0.416493i	$0.863259\pi$
$510$		0			0
$511$	−10.9760	−	28.6893i	−0.485548	−	1.26914i
$512$		0			0
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$		0			0
$515$	−3.58562	−	6.21047i	−0.158001	−	0.273666i
$516$		0			0
$517$	12.5876			0.553600
$518$		0			0
$519$	−9.48617			−0.416397
$520$		0			0
$521$	−10.8936	−	18.8683i	−0.477257	−	0.826634i	0.522403	−	0.852699i	$-0.325036\pi$
$521$	−10.8936	−	18.8683i	−0.477257	−	0.826634i	−0.999660	+	0.0260649i	$0.991702\pi$
$522$		0			0
$523$	−18.3923	+	31.8564i	−0.804239	+	1.39298i	0.112565	+	0.993644i	$0.464093\pi$
$523$	−18.3923	+	31.8564i	−0.804239	+	1.39298i	−0.916804	+	0.399338i	$0.869240\pi$
$524$		0			0
$525$	9.52243	−	11.7324i	0.415593	−	0.512042i
$526$		0			0
$527$	−1.05996	+	1.83590i	−0.0461724	+	0.0799729i
$528$		0			0
$529$	11.4678	+	19.8628i	0.498600	+	0.863601i
$530$		0			0
$531$	14.7061			0.638192
$532$		0			0
$533$	−0.973904			−0.0421845
$534$		0			0
$535$	−32.1299	−	55.6506i	−1.38910	−	2.40599i
$536$		0			0
$537$	11.4115	−	19.7653i	0.492442	−	0.852935i
$538$		0			0
$539$	9.03866	+	42.9965i	0.389323	+	1.85199i
$540$		0			0
$541$	6.32874	−	10.9617i	0.272094	−	0.471280i	−0.697304	−	0.716775i	$-0.745617\pi$
$541$	6.32874	−	10.9617i	0.272094	−	0.471280i	0.969398	+	0.245495i	$0.0789506\pi$
$542$		0			0
$543$	−3.71514	−	6.43482i	−0.159432	−	0.276144i
$544$		0			0
$545$	28.6380			1.22672
$546$		0			0
$547$	−35.1888			−1.50457			−0.752283	−	0.658840i	$-0.771047\pi$
$547$	−35.1888			−1.50457			−0.752283	+	0.658840i	$0.771047\pi$
$548$		0			0
$549$	6.52421	+	11.3003i	0.278446	+	0.482283i
$550$		0			0
$551$	1.73603	−	3.00690i	0.0739575	−	0.128098i
$552$		0			0
$553$	−16.5996	+	20.4519i	−0.705886	+	0.869704i
$554$		0			0
$555$	−18.0320	+	31.2323i	−0.765415	+	1.32574i
$556$		0			0
$557$	2.81114	+	4.86904i	0.119112	+	0.206308i	0.919416	−	0.393286i	$-0.128662\pi$
$557$	2.81114	+	4.86904i	0.119112	+	0.206308i	−0.800304	+	0.599594i	$0.795329\pi$
$558$		0			0
$559$	3.77761			0.159776
$560$		0			0
$561$	−13.9099			−0.587275
$562$		0			0
$563$	−13.2341	−	22.9222i	−0.557752	−	0.966054i	−0.997684	−	0.0680233i	$-0.978331\pi$
$563$	−13.2341	−	22.9222i	−0.557752	−	0.966054i	0.439932	−	0.898031i	$-0.355003\pi$
$564$		0			0
$565$	2.65557	−	4.59958i	0.111721	−	0.193506i
$566$		0			0
$567$	−0.945388	−	2.47108i	−0.0397026	−	0.103776i
$568$		0			0
$569$	14.9454	−	25.8862i	0.626544	−	1.08521i	−0.361696	−	0.932296i	$-0.617802\pi$
$569$	14.9454	−	25.8862i	0.626544	−	1.08521i	0.988240	−	0.152911i	$-0.0488646\pi$
$570$		0			0
$571$	11.8719	+	20.5628i	0.496825	+	0.860526i	0.999993	−	0.00366246i	$-0.00116580\pi$
$571$	11.8719	+	20.5628i	0.496825	+	0.860526i	−0.503168	+	0.864188i	$0.667832\pi$
$572$		0			0
$573$	−14.5351			−0.607213
$574$		0			0
$575$	1.44923			0.0604372
$576$		0			0
$577$	−2.71595	−	4.70416i	−0.113066	−	0.195837i	0.803939	−	0.594712i	$-0.202734\pi$
$577$	−2.71595	−	4.70416i	−0.113066	−	0.195837i	−0.917005	+	0.398875i	$0.869401\pi$
$578$		0			0
$579$	12.8931	−	22.3316i	0.535821	−	0.928068i
$580$		0			0
$581$	−24.5723	−	3.92006i	−1.01943	−	0.162631i
$582$		0			0
$583$	25.4978	−	44.1636i	1.05601	−	1.82907i
$584$		0			0
$585$	0.688729	+	1.19291i	0.0284755	+	0.0493209i
$586$		0			0
$587$	−9.48287			−0.391400			−0.195700	−	0.980664i	$-0.562698\pi$
$587$	−9.48287			−0.391400			−0.195700	+	0.980664i	$0.562698\pi$
$588$		0			0
$589$	−0.956577			−0.0394151
$590$		0			0
$591$	2.93041	+	5.07561i	0.120541	+	0.208783i
$592$		0			0
$593$	−22.1085	+	38.2930i	−0.907886	+	1.57250i	−0.0908905	+	0.995861i	$0.528971\pi$
$593$	−22.1085	+	38.2930i	−0.907886	+	1.57250i	−0.816996	+	0.576644i	$0.804362\pi$
$594$		0			0
$595$	18.9500	+	3.02312i	0.776873	+	0.123936i
$596$		0			0
$597$	3.70715	−	6.42097i	0.151724	−	0.262793i
$598$		0			0
$599$	−2.89174	−	5.00864i	−0.118153	−	0.204648i	0.800883	−	0.598821i	$-0.204364\pi$
$599$	−2.89174	−	5.00864i	−0.118153	−	0.204648i	−0.919036	+	0.394174i	$0.871031\pi$
$600$		0			0
$601$	−24.2188			−0.987907			−0.493954	−	0.869488i	$-0.664449\pi$
$601$	−24.2188			−0.987907			−0.493954	+	0.869488i	$0.664449\pi$
$602$		0			0
$603$	−4.18657			−0.170490
$604$		0			0
$605$	46.4669	+	80.4831i	1.88915	+	3.27210i
$606$		0			0
$607$	−17.5821	+	30.4531i	−0.713636	+	1.23605i	0.249847	+	0.968285i	$0.419620\pi$
$607$	−17.5821	+	30.4531i	−0.713636	+	1.23605i	−0.963483	+	0.267769i	$0.913714\pi$
$608$		0			0
$609$	−3.28245	−	8.57976i	−0.133012	−	0.347669i
$610$		0			0
$611$	0.422032	−	0.730981i	0.0170736	−	0.0295723i
$612$		0			0
$613$	−4.19151	−	7.25991i	−0.169293	−	0.293225i	0.768878	−	0.639395i	$-0.220815\pi$
$613$	−4.19151	−	7.25991i	−0.169293	−	0.293225i	−0.938172	+	0.346170i	$0.887482\pi$
$614$		0			0
$615$	−7.57313			−0.305378
$616$		0			0
$617$	−19.3402			−0.778609			−0.389304	−	0.921109i	$-0.627285\pi$
$617$	−19.3402			−0.778609			−0.389304	+	0.921109i	$0.627285\pi$
$618$		0			0
$619$	11.3219	+	19.6101i	0.455065	+	0.788196i	0.998692	−	0.0511313i	$-0.0162827\pi$
$619$	11.3219	+	19.6101i	0.455065	+	0.788196i	−0.543627	+	0.839327i	$0.682949\pi$
$620$		0			0
$621$	0.126876	−	0.219756i	0.00509137	−	0.00881852i
$622$		0			0
$623$	6.61295	−	8.14765i	0.264942	−	0.326429i
$624$		0			0
$625$	10.4691	−	18.1330i	0.418764	−	0.725320i
$626$		0			0
$627$	−3.13831	−	5.43571i	−0.125332	−	0.217081i
$628$		0			0
$629$	−24.4203			−0.973703
$630$		0			0
$631$	6.29494			0.250597			0.125299	−	0.992119i	$-0.460011\pi$
$631$	6.29494			0.250597			0.125299	+	0.992119i	$0.460011\pi$
$632$		0			0
$633$	−7.45092	−	12.9054i	−0.296147	−	0.512942i
$634$		0			0
$635$	21.5363	−	37.3020i	0.854643	−	1.48029i
$636$		0			0
$637$	2.79993	+	0.916685i	0.110937	+	0.0363204i
$638$		0			0
$639$	−3.14104	+	5.44044i	−0.124258	+	0.215221i
$640$		0			0
$641$	15.3158	+	26.5278i	0.604938	+	1.04778i	0.992061	+	0.125756i	$0.0401356\pi$
$641$	15.3158	+	26.5278i	0.604938	+	1.04778i	−0.387123	+	0.922028i	$0.626531\pi$
$642$		0			0
$643$	−17.8273			−0.703041			−0.351521	−	0.936180i	$-0.614335\pi$
$643$	−17.8273			−0.703041			−0.351521	+	0.936180i	$0.614335\pi$
$644$		0			0
$645$	29.3750			1.15664
$646$		0			0
$647$	6.04299	+	10.4668i	0.237575	+	0.411491i	0.960018	−	0.279939i	$-0.0903143\pi$
$647$	6.04299	+	10.4668i	0.237575	+	0.411491i	−0.722443	+	0.691430i	$0.756981\pi$
$648$		0			0
$649$	46.1523	−	79.9382i	1.81164	−	3.13785i
$650$		0			0
$651$	−1.59493	+	1.96507i	−0.0625101	+	0.0770171i
$652$		0			0
$653$	8.79486	−	15.2331i	0.344170	−	0.596119i	−0.641033	−	0.767513i	$-0.721494\pi$
$653$	8.79486	−	15.2331i	0.344170	−	0.596119i	0.985203	+	0.171394i	$0.0548272\pi$
$654$		0			0
$655$	−4.47748	−	7.75522i	−0.174949	−	0.303021i
$656$		0			0
$657$	11.6100			0.452950
$658$		0			0
$659$	16.6255			0.647637			0.323819	−	0.946119i	$-0.395033\pi$
$659$	16.6255			0.647637			0.323819	+	0.946119i	$0.395033\pi$
$660$		0			0
$661$	−3.25706	−	5.64140i	−0.126685	−	0.219425i	0.795705	−	0.605684i	$-0.207100\pi$
$661$	−3.25706	−	5.64140i	−0.126685	−	0.219425i	−0.922390	+	0.386259i	$0.873767\pi$
$662$		0			0
$663$	−0.466366	+	0.807770i	−0.0181122	+	0.0313712i
$664$		0			0
$665$	3.09406	+	8.08735i	0.119983	+	0.313614i
$666$		0			0
$667$	0.440523	−	0.763009i	0.0170571	−	0.0295438i
$668$		0			0
$669$	8.84385	+	15.3180i	0.341923	+	0.592228i
$670$		0			0
$671$	81.8999			3.16171
$672$		0			0
$673$	23.0466			0.888382			0.444191	−	0.895932i	$-0.353491\pi$
$673$	23.0466			0.888382			0.444191	+	0.895932i	$0.353491\pi$
$674$		0			0
$675$	2.85560	+	4.94605i	0.109912	+	0.190373i
$676$		0			0
$677$	−22.7549	+	39.4127i	−0.874544	+	1.51475i	−0.0172954	+	0.999850i	$0.505506\pi$
$677$	−22.7549	+	39.4127i	−0.874544	+	1.51475i	−0.857248	+	0.514903i	$0.827828\pi$
$678$		0			0
$679$	−0.203407	−	0.0324499i	−0.00780605	−	0.00124531i
$680$		0			0
$681$	10.3376	−	17.9052i	0.396137	−	0.686129i
$682$		0			0
$683$	3.57645	+	6.19459i	0.136849	+	0.237030i	0.926302	−	0.376781i	$-0.122969\pi$
$683$	3.57645	+	6.19459i	0.136849	+	0.237030i	−0.789453	+	0.613811i	$0.789636\pi$
$684$		0			0
$685$	−30.8410			−1.17838
$686$		0			0
$687$	18.6534			0.711672
$688$		0			0
$689$	−1.70977	−	2.96141i	−0.0651370	−	0.112821i
$690$		0			0
$691$	20.0603	−	34.7455i	0.763132	−	1.32178i	−0.178097	−	0.984013i	$-0.556994\pi$
$691$	20.0603	−	34.7455i	0.763132	−	1.32178i	0.941229	−	0.337770i	$-0.109673\pi$
$692$		0			0
$693$	−16.3990	−	2.61616i	−0.622946	−	0.0993797i
$694$		0			0
$695$	−4.25214	+	7.36492i	−0.161293	+	0.279367i
$696$		0			0
$697$	−2.56404	−	4.44104i	−0.0971198	−	0.168216i
$698$		0			0
$699$	27.5005			1.04017
$700$		0			0
$701$	−43.6226			−1.64760			−0.823801	−	0.566879i	$-0.808151\pi$
$701$	−43.6226			−1.64760			−0.823801	+	0.566879i	$0.808151\pi$
$702$		0			0
$703$	−5.50965	−	9.54300i	−0.207800	−	0.359921i
$704$		0			0
$705$	3.28175	−	5.68415i	0.123598	−	0.214078i
$706$		0			0
$707$	6.31012	+	16.4936i	0.237316	+	0.620304i
$708$		0			0
$709$	−9.90382	+	17.1539i	−0.371946	+	0.644229i	−0.989865	−	0.142013i	$-0.954643\pi$
$709$	−9.90382	+	17.1539i	−0.371946	+	0.644229i	0.617919	+	0.786242i	$0.287976\pi$
$710$		0			0
$711$	−4.97790	−	8.62198i	−0.186686	−	0.323350i
$712$		0			0
$713$	−0.242734			−0.00909046
$714$		0			0
$715$	8.64577			0.323334
$716$		0			0
$717$	−6.14226	−	10.6387i	−0.229387	−	0.397310i
$718$		0			0
$719$	18.4966	−	32.0371i	0.689808	−	1.19478i	−0.282091	−	0.959388i	$-0.591028\pi$
$719$	18.4966	−	32.0371i	0.689808	−	1.19478i	0.971900	−	0.235396i	$-0.0756386\pi$
$720$		0			0
$721$	3.65338	−	4.50124i	0.136059	−	0.167635i
$722$		0			0
$723$	2.93854	−	5.08970i	0.109286	−	0.189288i
$724$		0			0
$725$	9.91484	+	17.1730i	0.368228	+	0.637789i
$726$		0			0
$727$	38.0975			1.41296			0.706479	−	0.707734i	$-0.250282\pi$
$727$	38.0975			1.41296			0.706479	+	0.707734i	$0.250282\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.94548	+	17.2261i	0.367847	+	0.637129i
$732$		0			0
$733$	9.06019	−	15.6927i	0.334646	−	0.579623i	−0.648771	−	0.760984i	$-0.724717\pi$
$733$	9.06019	−	15.6927i	0.334646	−	0.579623i	0.983417	+	0.181360i	$0.0580501\pi$
$734$		0			0
$735$	21.7724	+	7.12820i	0.803087	+	0.262928i
$736$		0			0
$737$	−13.1387	+	22.7569i	−0.483971	+	0.838263i
$738$		0			0
$739$	−24.7602	−	42.8859i	−0.910818	−	1.57758i	−0.812912	−	0.582387i	$-0.802119\pi$
$739$	−24.7602	−	42.8859i	−0.910818	−	1.57758i	−0.0979056	−	0.995196i	$-0.531214\pi$
$740$		0			0
$741$	−0.420881			−0.0154615
$742$		0			0
$743$	31.0074			1.13755			0.568776	−	0.822492i	$-0.307417\pi$
$743$	31.0074			1.13755			0.568776	+	0.822492i	$0.307417\pi$
$744$		0			0
$745$	−3.60053	−	6.23630i	−0.131913	−	0.228480i
$746$		0			0
$747$	4.70244	−	8.14487i	0.172053	−	0.298005i
$748$		0			0
$749$	32.7371	−	40.3346i	1.19619	−	1.47379i
$750$		0			0
$751$	9.22382	−	15.9761i	0.336582	−	0.582977i	−0.647205	−	0.762316i	$-0.724062\pi$
$751$	9.22382	−	15.9761i	0.336582	−	0.582977i	0.983787	+	0.179338i	$0.0573957\pi$
$752$		0			0
$753$	−3.83834	−	6.64819i	−0.139877	−	0.242274i
$754$		0			0
$755$	−1.20088			−0.0437043
$756$		0			0
$757$	−30.9924			−1.12644			−0.563219	−	0.826307i	$-0.690437\pi$
$757$	−30.9924			−1.12644			−0.563219	+	0.826307i	$0.690437\pi$
$758$		0			0
$759$	−0.796354	−	1.37932i	−0.0289058	−	0.0500663i
$760$		0			0
$761$	−2.62953	+	4.55449i	−0.0953205	+	0.165100i	−0.909742	−	0.415173i	$-0.863721\pi$
$761$	−2.62953	+	4.55449i	−0.0953205	+	0.165100i	0.814422	+	0.580273i	$0.197054\pi$
$762$		0			0
$763$	8.27244	+	21.6227i	0.299483	+	0.782796i
$764$		0			0
$765$	−3.62649	+	6.28127i	−0.131116	+	0.227100i
$766$		0			0
$767$	−3.09477	−	5.36029i	−0.111746	−	0.193549i
$768$		0			0
$769$	42.5320			1.53374			0.766872	−	0.641801i	$-0.221812\pi$
$769$	42.5320			1.53374			0.766872	+	0.641801i	$0.221812\pi$
$770$		0			0
$771$	18.3154			0.659613
$772$		0			0
$773$	2.74873	+	4.76093i	0.0988648	+	0.171239i	0.911215	−	0.411931i	$-0.135146\pi$
$773$	2.74873	+	4.76093i	0.0988648	+	0.171239i	−0.812350	+	0.583170i	$0.801812\pi$
$774$		0			0
$775$	2.73160	−	4.73128i	0.0981221	−	0.169952i
$776$		0			0
$777$	−28.7903	−	4.59296i	−1.03285	−	0.164772i
$778$		0			0
$779$	1.15698	−	2.00395i	0.0414532	−	0.0717990i
$780$		0			0
$781$	19.7151	+	34.1475i	0.705462	+	1.22190i
$782$		0			0
$783$	3.47207			0.124082
$784$		0			0
$785$	66.8036			2.38432
$786$		0			0
$787$	21.8095	+	37.7752i	0.777425	+	1.34654i	0.933421	+	0.358782i	$0.116808\pi$
$787$	21.8095	+	37.7752i	0.777425	+	1.34654i	−0.155996	+	0.987758i	$0.549859\pi$
$788$		0			0
$789$	11.5461	−	19.9984i	0.411052	−	0.711964i
$790$		0			0
$791$	4.23995	+	0.676406i	0.150755	+	0.0240502i
$792$		0			0
$793$	2.74592	−	4.75607i	0.0975104	−	0.168893i
$794$		0			0
$795$	−13.2953	−	23.0281i	−0.471535	−	0.816722i
$796$		0			0
$797$	−34.4889			−1.22166			−0.610830	−	0.791762i	$-0.709164\pi$
$797$	−34.4889			−1.22166			−0.610830	+	0.791762i	$0.709164\pi$
$798$		0			0
$799$	4.44440			0.157232
$800$		0			0
$801$	1.98310	+	3.43483i	0.0700695	+	0.121364i
$802$		0			0
$803$	36.4358	−	63.1086i	1.28579	−	2.22705i
$804$		0			0
$805$	0.785127	+	2.05219i	0.0276721	+	0.0723301i
$806$		0			0
$807$	−0.977577	+	1.69321i	−0.0344124	+	0.0596039i
$808$		0			0
$809$	−5.11195	−	8.85416i	−0.179727	−	0.311296i	0.762060	−	0.647506i	$-0.224188\pi$
$809$	−5.11195	−	8.85416i	−0.179727	−	0.311296i	−0.941787	+	0.336210i	$0.890855\pi$
$810$		0			0
$811$	−15.4434			−0.542290			−0.271145	−	0.962539i	$-0.587402\pi$
$811$	−15.4434			−0.542290			−0.271145	+	0.962539i	$0.587402\pi$
$812$		0			0
$813$	1.44587			0.0507090
$814$		0			0
$815$	22.6940	+	39.3071i	0.794934	+	1.37687i
$816$		0			0
$817$	−4.48774	+	7.77300i	−0.157006	+	0.271943i
$818$		0			0
$819$	−0.701746	+	0.864604i	−0.0245210	+	0.0302117i
$820$		0			0
$821$	5.76225	−	9.98052i	0.201104	−	0.348322i	−0.747780	−	0.663946i	$-0.768880\pi$
$821$	5.76225	−	9.98052i	0.201104	−	0.348322i	0.948884	+	0.315624i	$0.102214\pi$
$822$		0			0
$823$	3.19618	+	5.53594i	0.111412	+	0.192971i	0.916340	−	0.400402i	$-0.131129\pi$
$823$	3.19618	+	5.53594i	0.111412	+	0.192971i	−0.804928	+	0.593373i	$0.797796\pi$
$824$		0			0
$825$	35.8470			1.24803
$826$		0			0
$827$	−13.6848			−0.475867			−0.237933	−	0.971281i	$-0.576470\pi$
$827$	−13.6848			−0.475867			−0.237933	+	0.971281i	$0.576470\pi$
$828$		0			0
$829$	13.3621	+	23.1438i	0.464084	+	0.803818i	0.999160	−	0.0409866i	$-0.0130501\pi$
$829$	13.3621	+	23.1438i	0.464084	+	0.803818i	−0.535075	+	0.844804i	$0.679717\pi$
$830$		0			0
$831$	−8.61874	+	14.9281i	−0.298981	+	0.517850i
$832$		0			0
$833$	3.19136	+	15.1812i	0.110574	+	0.525997i
$834$		0			0
$835$	−1.23699	+	2.14254i	−0.0428080	+	0.0741456i
$836$		0			0
$837$	−0.478289	−	0.828420i	−0.0165321	−	0.0286344i
$838$		0			0
$839$	39.8194			1.37472			0.687359	−	0.726318i	$-0.258770\pi$
$839$	39.8194			1.37472			0.687359	+	0.726318i	$0.258770\pi$
$840$		0			0
$841$	−16.9447			−0.584302
$842$		0			0
$843$	3.66212	+	6.34298i	0.126130	+	0.218464i
$844$		0			0
$845$	−20.9833	+	36.3442i	−0.721848	+	1.25028i
$846$		0			0
$847$	−47.3451	+	58.3328i	−1.62680	+	2.00434i
$848$		0			0
$849$	−3.53353	+	6.12025i	−0.121270	+	0.210046i
$850$		0			0
$851$	−1.39809	−	2.42156i	−0.0479259	−	0.0830100i
$852$		0			0
$853$	−47.4962			−1.62624			−0.813119	−	0.582097i	$-0.802232\pi$
$853$	−47.4962			−1.62624			−0.813119	+	0.582097i	$0.802232\pi$
$854$		0			0
$855$	−3.27280			−0.111927
$856$		0			0
$857$	0.602011	+	1.04271i	0.0205643	+	0.0356184i	0.876124	−	0.482085i	$-0.160120\pi$
$857$	0.602011	+	1.04271i	0.0205643	+	0.0356184i	−0.855560	+	0.517703i	$0.826787\pi$
$858$		0			0
$859$	−18.3996	+	31.8691i	−0.627787	+	1.08736i	0.360207	+	0.932872i	$0.382706\pi$
$859$	−18.3996	+	31.8691i	−0.627787	+	1.08736i	−0.987995	+	0.154487i	$0.950627\pi$
$860$		0			0
$861$	−2.18759	−	5.71799i	−0.0745530	−	0.194869i
$862$		0			0
$863$	−21.9939	+	38.0946i	−0.748683	+	1.29676i	0.199772	+	0.979842i	$0.435980\pi$
$863$	−21.9939	+	38.0946i	−0.748683	+	1.29676i	−0.948454	+	0.316914i	$0.897353\pi$
$864$		0			0
$865$	15.5232	+	26.8869i	0.527803	+	0.914182i
$866$		0			0
$867$	12.0887			0.410554
$868$		0			0
$869$	−62.4888			−2.11979
$870$		0			0
$871$	0.881023	+	1.52598i	0.0298523	+	0.0517058i
$872$		0			0
$873$	0.0389264	−	0.0674226i	0.00131746	−	0.00228191i
$874$		0			0
$875$	−6.08141	−	0.970178i	−0.205589	−	0.0327980i
$876$		0			0
$877$	8.64524	−	14.9740i	0.291929	−	0.505636i	−0.682337	−	0.731038i	$-0.739036\pi$
$877$	8.64524	−	14.9740i	0.291929	−	0.505636i	0.974266	+	0.225402i	$0.0723696\pi$
$878$		0			0
$879$	−9.27638	−	16.0672i	−0.312885	−	0.541932i
$880$		0			0
$881$	19.8899			0.670106			0.335053	−	0.942199i	$-0.391246\pi$
$881$	19.8899			0.670106			0.335053	+	0.942199i	$0.391246\pi$
$882$		0			0
$883$	−7.98050			−0.268565			−0.134283	−	0.990943i	$-0.542873\pi$
$883$	−7.98050			−0.268565			−0.134283	+	0.990943i	$0.542873\pi$
$884$		0			0
$885$	−24.0651	−	41.6820i	−0.808939	−	1.40112i
$886$		0			0
$887$	−5.00488	+	8.66871i	−0.168047	+	0.291067i	−0.937733	−	0.347356i	$-0.887080\pi$
$887$	−5.00488	+	8.66871i	−0.168047	+	0.291067i	0.769686	+	0.638423i	$0.220413\pi$
$888$		0			0
$889$	34.3854	+	5.48557i	1.15325	+	0.183980i
$890$		0			0
$891$	3.13831	−	5.43571i	0.105137	−	0.182103i
$892$		0			0
$893$	1.00273	+	1.73679i	0.0335552	+	0.0581194i
$894$		0			0
$895$	−74.6950			−2.49678
$896$		0			0
$897$	−0.106800			−0.00356594
$898$		0			0
$899$	−1.66065	−	2.87633i	−0.0553858	−	0.0959310i
$900$		0			0
$901$	9.00276	−	15.5932i	0.299925	−	0.519486i
$902$		0			0
$903$	8.48532	+	22.1792i	0.282374	+	0.738076i
$904$		0			0
$905$	−12.1589	+	21.0599i	−0.404176	+	0.700053i
$906$		0			0
$907$	11.6222	+	20.1303i	0.385909	+	0.668415i	0.991895	−	0.127061i	$-0.0405544\pi$
$907$	11.6222	+	20.1303i	0.385909	+	0.668415i	−0.605986	+	0.795476i	$0.707221\pi$
$908$		0			0
$909$	−6.67463			−0.221384
$910$		0			0
$911$	39.6369			1.31323			0.656615	−	0.754226i	$-0.271988\pi$
$911$	39.6369			1.31323			0.656615	+	0.754226i	$0.271988\pi$
$912$		0			0
$913$	−29.5154	−	51.1222i	−0.976817	−	1.69190i
$914$		0			0
$915$	21.3524	−	36.9835i	0.705889	−	1.22264i
$916$		0			0
$917$	4.56210	−	5.62085i	0.150654	−	0.185617i
$918$		0			0
$919$	−17.9992	+	31.1756i	−0.593739	+	1.02839i	0.399984	+	0.916522i	$0.369016\pi$
$919$	−17.9992	+	31.1756i	−0.593739	+	1.02839i	−0.993723	+	0.111865i	$0.964318\pi$
$920$		0			0
$921$	1.48109	+	2.56533i	0.0488036	+	0.0845304i
$922$		0			0
$923$	2.64401			0.0870286
$924$		0			0
$925$	62.9335			2.06924
$926$		0			0
$927$	1.09558	+	1.89760i	0.0359836	+	0.0623255i
$928$		0			0
$929$	9.78275	−	16.9442i	0.320962	−	0.555922i	−0.659725	−	0.751507i	$-0.729327\pi$
$929$	9.78275	−	16.9442i	0.320962	−	0.555922i	0.980687	+	0.195585i	$0.0626606\pi$
$930$		0			0
$931$	−5.21248	+	4.67226i	−0.170832	+	0.153127i
$932$		0			0
$933$	−6.82435	+	11.8201i	−0.223419	+	0.386973i
$934$		0			0
$935$	22.7621	+	39.4251i	0.744400	+	1.28934i
$936$		0			0
$937$	1.83137			0.0598282			0.0299141	−	0.999552i	$-0.490477\pi$
$937$	1.83137			0.0598282			0.0299141	+	0.999552i	$0.490477\pi$
$938$		0			0
$939$	−11.4810			−0.374668
$940$		0			0
$941$	6.85385	+	11.8712i	0.223429	+	0.386991i	0.955847	−	0.293865i	$-0.0949416\pi$
$941$	6.85385	+	11.8712i	0.223429	+	0.386991i	−0.732418	+	0.680855i	$0.761608\pi$
$942$		0			0
$943$	0.293587	−	0.508508i	0.00956052	−	0.0165593i
$944$		0			0
$945$	−5.45682	+	6.72321i	−0.177510	+	0.218706i
$946$		0			0
$947$	2.49755	−	4.32588i	0.0811594	−	0.140572i	−0.822589	−	0.568637i	$-0.807471\pi$
$947$	2.49755	−	4.32588i	0.0811594	−	0.140572i	0.903748	+	0.428064i	$0.140804\pi$
$948$		0			0
$949$	−2.44322	−	4.23178i	−0.0793102	−	0.137369i
$950$		0			0
$951$	−33.3176			−1.08040
$952$		0			0
$953$	−0.412533			−0.0133632			−0.00668162	−	0.999978i	$-0.502127\pi$
$953$	−0.412533			−0.0133632			−0.00668162	+	0.999978i	$0.502127\pi$
$954$		0			0
$955$	23.7852	+	41.1972i	0.769672	+	1.33311i
$956$		0			0
$957$	10.8964	−	18.8731i	0.352231	−	0.610082i
$958$		0			0
$959$	−8.90881	−	23.2861i	−0.287681	−	0.751947i
$960$		0			0
$961$	15.0425	−	26.0543i	0.485241	−	0.840463i
$962$		0			0
$963$	9.81726	+	17.0040i	0.316357	+	0.547946i
$964$		0			0
$965$	−84.3933			−2.71672
$966$		0			0
$967$	24.3369			0.782623			0.391311	−	0.920258i	$-0.372022\pi$
$967$	24.3369			0.782623			0.391311	+	0.920258i	$0.372022\pi$
$968$		0			0
$969$	−1.10807	−	1.91924i	−0.0355964	−	0.0616547i
$970$		0			0
$971$	−9.98385	+	17.2925i	−0.320397	+	0.554944i	−0.980570	−	0.196170i	$-0.937150\pi$
$971$	−9.98385	+	17.2925i	−0.320397	+	0.554944i	0.660173	+	0.751114i	$0.270483\pi$
$972$		0			0
$973$	−6.78907	−	1.08307i	−0.217647	−	0.0347217i
$974$		0			0
$975$	1.20187	−	2.08170i	0.0384906	−	0.0666677i
$976$		0			0
$977$	21.4523	+	37.1564i	0.686319	+	1.18874i	0.973020	+	0.230720i	$0.0741081\pi$
$977$	21.4523	+	37.1564i	0.686319	+	1.18874i	−0.286701	+	0.958020i	$0.592559\pi$
$978$		0			0
$979$	24.8943			0.795626
$980$		0			0
$981$	−8.75032			−0.279376
$982$		0			0
$983$	15.2393	+	26.3953i	0.486060	+	0.841880i	0.999872	−	0.0160229i	$-0.00510046\pi$
$983$	15.2393	+	26.3953i	0.486060	+	0.841880i	−0.513812	+	0.857903i	$0.671767\pi$
$984$		0			0
$985$	9.59062	−	16.6114i	0.305583	−	0.529285i
$986$		0			0
$987$	5.23972	+	0.835901i	0.166782	+	0.0266070i
$988$		0			0
$989$	−1.13878	+	1.97242i	−0.0362110	+	0.0627193i
$990$		0			0
$991$	−6.59097	−	11.4159i	−0.209369	−	0.362638i	0.742147	−	0.670237i	$-0.233808\pi$
$991$	−6.59097	−	11.4159i	−0.209369	−	0.362638i	−0.951516	+	0.307599i	$0.900474\pi$
$992$		0			0
$993$	17.0109			0.539826
$994$		0			0
$995$	−24.2655			−0.769268
$996$		0			0
$997$	26.7125	+	46.2675i	0.845995	+	1.46531i	0.884755	+	0.466057i	$0.154326\pi$
$997$	26.7125	+	46.2675i	0.845995	+	1.46531i	−0.0387599	+	0.999249i	$0.512341\pi$
$998$		0			0
$999$	5.50965	−	9.54300i	0.174318	−	0.301927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1596.2.r.h.457.6	✓	14
7.4	even	3	inner	1596.2.r.h.1369.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1596.2.r.h.457.6	✓	14	1.1	even	1	trivial
1596.2.r.h.1369.6	yes	14	7.4	even	3	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:	\( N \)	\(=\)	\( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1596.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(1.63640 - 2.83433i) q^{5} +(2.61271 + 0.416811i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.13831 + 5.43571i) q^{11} +0.420881 q^{13} +3.27280 q^{15} +(1.10807 + 1.91924i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(0.945388 + 2.47108i) q^{21} +(-0.126876 + 0.219756i) q^{23} +(-2.85560 - 4.94605i) q^{25} -1.00000 q^{27} -3.47207 q^{29} +(0.478289 + 0.828420i) q^{31} +(-3.13831 + 5.43571i) q^{33} +(5.45682 - 6.72321i) q^{35} +(-5.50965 + 9.54300i) q^{37} +(0.210441 + 0.364494i) q^{39} -2.31396 q^{41} +8.97549 q^{43} +(1.63640 + 2.83433i) q^{45} +(1.00273 - 1.73679i) q^{47} +(6.65254 + 2.17801i) q^{49} +(-1.10807 + 1.91924i) q^{51} +(-4.06236 - 7.03621i) q^{53} +20.5421 q^{55} -1.00000 q^{57} +(-7.35306 - 12.7359i) q^{59} +(6.52421 - 11.3003i) q^{61} +(-1.66733 + 2.05427i) q^{63} +(0.688729 - 1.19291i) q^{65} +(2.09328 + 3.62567i) q^{67} -0.253753 q^{69} +6.28208 q^{71} +(-5.80501 - 10.0546i) q^{73} +(2.85560 - 4.94605i) q^{75} +(5.93383 + 15.5100i) q^{77} +(-4.97790 + 8.62198i) q^{79} +(-0.500000 - 0.866025i) q^{81} -9.40488 q^{83} +7.25298 q^{85} +(-1.73603 - 3.00690i) q^{87} +(1.98310 - 3.43483i) q^{89} +(1.09964 + 0.175428i) q^{91} +(-0.478289 + 0.828420i) q^{93} +(1.63640 + 2.83433i) q^{95} -0.0778529 q^{97} -6.27661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 7 q^{3} + 2 q^{5} - 7 q^{9} - 4 q^{11} - 12 q^{13} + 4 q^{15} + 18 q^{17} - 7 q^{19} + 3 q^{21} + 2 q^{23} - 15 q^{25} - 14 q^{27} - 8 q^{29} + q^{31} + 4 q^{33} + 22 q^{35} - 7 q^{37} - 6 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) \) 14 * q + 7 * q^3 + 2 * q^5 - 7 * q^9 - 4 * q^11 - 12 * q^13 + 4 * q^15 + 18 * q^17 - 7 * q^19 + 3 * q^21 + 2 * q^23 - 15 * q^25 - 14 * q^27 - 8 * q^29 + q^31 + 4 * q^33 + 22 * q^35 - 7 * q^37 - 6 * q^39 - 30 * q^41 + 6 * q^43 + 2 * q^45 + 2 * q^47 + 26 * q^49 - 18 * q^51 - 24 * q^53 - 8 * q^55 - 14 * q^57 + 15 * q^59 + 5 * q^61 + 3 * q^63 - 5 * q^65 - 9 * q^67 + 4 * q^69 - 32 * q^71 + q^73 + 15 * q^75 + 47 * q^77 - 13 * q^79 - 7 * q^81 - 22 * q^83 + 22 * q^85 - 4 * q^87 + 7 * q^89 + 39 * q^91 - q^93 + 2 * q^95 - 82 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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