LMFDB - Embedded newform 572.2.n.b.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	572.157
Dual form			572.2.n.b.521.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.288033 + 0.886474i) q^{3} +(-2.56853 - 1.86615i) q^{5} +(-0.780072 + 2.40081i) q^{7} +(1.72418 - 1.25269i) q^{9} +O(q^{10})$	\(q+(0.288033 + 0.886474i) q^{3} +(-2.56853 - 1.86615i) q^{5} +(-0.780072 + 2.40081i) q^{7} +(1.72418 - 1.25269i) q^{9} +(3.31569 - 0.0787964i) q^{11} +(0.809017 - 0.587785i) q^{13} +(0.914469 - 2.81445i) q^{15} +(2.29379 + 1.66654i) q^{17} +(2.68517 + 8.26410i) q^{19} -2.35295 q^{21} +5.07051 q^{23} +(1.56976 + 4.83122i) q^{25} +(3.86933 + 2.81124i) q^{27} +(-0.125810 + 0.387203i) q^{29} +(-3.27610 + 2.38022i) q^{31} +(1.02488 + 2.91658i) q^{33} +(6.48391 - 4.71084i) q^{35} +(2.80590 - 8.63568i) q^{37} +(0.754080 + 0.547871i) q^{39} +(0.885358 + 2.72485i) q^{41} -4.20497 q^{43} -6.76630 q^{45} +(0.403553 + 1.24201i) q^{47} +(0.507721 + 0.368881i) q^{49} +(-0.816655 + 2.51341i) q^{51} +(0.446679 - 0.324531i) q^{53} +(-8.66349 - 5.98517i) q^{55} +(-6.55249 + 4.76066i) q^{57} +(3.34056 - 10.2812i) q^{59} +(-1.63334 - 1.18669i) q^{61} +(1.66249 + 5.11662i) q^{63} -3.17488 q^{65} -7.10489 q^{67} +(1.46047 + 4.49488i) q^{69} +(1.10920 + 0.805877i) q^{71} +(-2.29640 + 7.06760i) q^{73} +(-3.83061 + 2.78310i) q^{75} +(-2.39730 + 8.02182i) q^{77} +(11.4604 - 8.32649i) q^{79} +(0.598140 - 1.84089i) q^{81} +(-0.527172 - 0.383013i) q^{83} +(-2.78167 - 8.56111i) q^{85} -0.379483 q^{87} +9.85313 q^{89} +(0.780072 + 2.40081i) q^{91} +(-3.05363 - 2.21859i) q^{93} +(8.52508 - 26.2375i) q^{95} +(-15.3326 + 11.1398i) q^{97} +(5.61813 - 4.28938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.288033	+	0.886474i	0.166296	+	0.511806i	0.999129	−	0.0417175i	$-0.0132829\pi$
$3$	0.288033	+	0.886474i	0.166296	+	0.511806i	−0.832834	+	0.553523i	$0.813283\pi$
$4$		0			0
$5$	−2.56853	−	1.86615i	−1.14868	−	0.834566i	−0.160377	−	0.987056i	$-0.551271\pi$
$5$	−2.56853	−	1.86615i	−1.14868	−	0.834566i	−0.988305	+	0.152490i	$0.951271\pi$
$6$		0			0
$7$	−0.780072	+	2.40081i	−0.294839	+	0.907423i	0.688436	+	0.725297i	$0.258298\pi$
$7$	−0.780072	+	2.40081i	−0.294839	+	0.907423i	−0.983275	+	0.182125i	$0.941702\pi$
$8$		0			0
$9$	1.72418	−	1.25269i	0.574726	−	0.417563i
$10$		0			0
$11$	3.31569	−	0.0787964i	0.999718	−	0.0237580i
$11$	3.31569	−	0.0787964i	0.999718	−	0.0237580i
$12$		0			0
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$		0			0
$15$	0.914469	−	2.81445i	0.236115	−	0.726687i
$16$		0			0
$17$	2.29379	+	1.66654i	0.556327	+	0.404195i	0.830113	−	0.557596i	$-0.188276\pi$
$17$	2.29379	+	1.66654i	0.556327	+	0.404195i	−0.273786	+	0.961791i	$0.588276\pi$
$18$		0			0
$19$	2.68517	+	8.26410i	0.616020	+	1.89591i	0.384729	+	0.923030i	$0.374295\pi$
$19$	2.68517	+	8.26410i	0.616020	+	1.89591i	0.231291	+	0.972885i	$0.425705\pi$
$20$		0			0
$21$	−2.35295			−0.513455
$22$		0			0
$23$	5.07051			1.05728			0.528638	−	0.848848i	$-0.322703\pi$
$23$	5.07051			1.05728			0.528638	+	0.848848i	$0.322703\pi$
$24$		0			0
$25$	1.56976	+	4.83122i	0.313952	+	0.966245i
$26$		0			0
$27$	3.86933	+	2.81124i	0.744654	+	0.541023i
$28$		0			0
$29$	−0.125810	+	0.387203i	−0.0233623	+	0.0719018i	−0.962058	−	0.272845i	$-0.912035\pi$
$29$	−0.125810	+	0.387203i	−0.0233623	+	0.0719018i	0.938696	+	0.344747i	$0.112035\pi$
$30$		0			0
$31$	−3.27610	+	2.38022i	−0.588404	+	0.427501i	−0.841744	−	0.539877i	$-0.818471\pi$
$31$	−3.27610	+	2.38022i	−0.588404	+	0.427501i	0.253340	+	0.967377i	$0.418471\pi$
$32$		0			0
$33$	1.02488	+	2.91658i	0.178408	+	0.507711i
$34$		0			0
$35$	6.48391	−	4.71084i	1.09598	−	0.796277i
$36$		0			0
$37$	2.80590	−	8.63568i	0.461288	−	1.41970i	−0.402304	−	0.915506i	$-0.631791\pi$
$37$	2.80590	−	8.63568i	0.461288	−	1.41970i	0.863592	−	0.504191i	$-0.168209\pi$
$38$		0			0
$39$	0.754080	+	0.547871i	0.120749	+	0.0877296i
$40$		0			0
$41$	0.885358	+	2.72485i	0.138270	+	0.425550i	0.996084	−	0.0884090i	$-0.0281782\pi$
$41$	0.885358	+	2.72485i	0.138270	+	0.425550i	−0.857815	+	0.513959i	$0.828178\pi$
$42$		0			0
$43$	−4.20497			−0.641251			−0.320626	−	0.947206i	$-0.603893\pi$
$43$	−4.20497			−0.641251			−0.320626	+	0.947206i	$0.603893\pi$
$44$		0			0
$45$	−6.76630			−1.00866
$46$		0			0
$47$	0.403553	+	1.24201i	0.0588642	+	0.181166i	0.976165	−	0.217029i	$-0.0696368\pi$
$47$	0.403553	+	1.24201i	0.0588642	+	0.181166i	−0.917301	+	0.398195i	$0.869637\pi$
$48$		0			0
$49$	0.507721	+	0.368881i	0.0725316	+	0.0526973i
$50$		0			0
$51$	−0.816655	+	2.51341i	−0.114355	+	0.351947i
$52$		0			0
$53$	0.446679	−	0.324531i	0.0613561	−	0.0445778i	−0.556684	−	0.830724i	$-0.687927\pi$
$53$	0.446679	−	0.324531i	0.0613561	−	0.0445778i	0.618041	+	0.786146i	$0.287927\pi$
$54$		0			0
$55$	−8.66349	−	5.98517i	−1.16819	−	0.807040i
$56$		0			0
$57$	−6.55249	+	4.76066i	−0.867899	+	0.630565i
$58$		0			0
$59$	3.34056	−	10.2812i	0.434904	−	1.33850i	−0.458281	−	0.888807i	$-0.651535\pi$
$59$	3.34056	−	10.2812i	0.434904	−	1.33850i	0.893185	−	0.449690i	$-0.148465\pi$
$60$		0			0
$61$	−1.63334	−	1.18669i	−0.209128	−	0.151940i	0.478291	−	0.878201i	$-0.341256\pi$
$61$	−1.63334	−	1.18669i	−0.209128	−	0.151940i	−0.687419	+	0.726261i	$0.741256\pi$
$62$		0			0
$63$	1.66249	+	5.11662i	0.209454	+	0.644633i
$64$		0			0
$65$	−3.17488			−0.393795
$66$		0			0
$67$	−7.10489			−0.868000			−0.434000	−	0.900913i	$-0.642898\pi$
$67$	−7.10489			−0.868000			−0.434000	+	0.900913i	$0.642898\pi$
$68$		0			0
$69$	1.46047	+	4.49488i	0.175820	+	0.541120i
$70$		0			0
$71$	1.10920	+	0.805877i	0.131637	+	0.0956400i	0.651655	−	0.758515i	$-0.274075\pi$
$71$	1.10920	+	0.805877i	0.131637	+	0.0956400i	−0.520018	+	0.854155i	$0.674075\pi$
$72$		0			0
$73$	−2.29640	+	7.06760i	−0.268774	+	0.827200i	0.722026	+	0.691866i	$0.243211\pi$
$73$	−2.29640	+	7.06760i	−0.268774	+	0.827200i	−0.990800	+	0.135335i	$0.956789\pi$
$74$		0			0
$75$	−3.83061	+	2.78310i	−0.442321	+	0.321365i
$76$		0			0
$77$	−2.39730	+	8.02182i	−0.273198	+	0.914171i
$78$		0			0
$79$	11.4604	−	8.32649i	1.28940	−	0.936803i	0.289605	−	0.957146i	$-0.406476\pi$
$79$	11.4604	−	8.32649i	1.28940	−	0.936803i	0.999793	+	0.0203433i	$0.00647592\pi$
$80$		0			0
$81$	0.598140	−	1.84089i	0.0664600	−	0.204543i
$82$		0			0
$83$	−0.527172	−	0.383013i	−0.0578647	−	0.0420411i	0.558477	−	0.829520i	$-0.311386\pi$
$83$	−0.527172	−	0.383013i	−0.0578647	−	0.0420411i	−0.616342	+	0.787479i	$0.711386\pi$
$84$		0			0
$85$	−2.78167	−	8.56111i	−0.301715	−	0.928583i
$86$		0			0
$87$	−0.379483			−0.0406848
$88$		0			0
$89$	9.85313			1.04443			0.522215	−	0.852814i	$-0.325106\pi$
$89$	9.85313			1.04443			0.522215	+	0.852814i	$0.325106\pi$
$90$		0			0
$91$	0.780072	+	2.40081i	0.0817738	+	0.251674i
$92$		0			0
$93$	−3.05363	−	2.21859i	−0.316646	−	0.230057i
$94$		0			0
$95$	8.52508	−	26.2375i	0.874655	−	2.69191i
$96$		0			0
$97$	−15.3326	+	11.1398i	−1.55679	+	1.13108i	−0.618216	+	0.786008i	$0.712144\pi$
$97$	−15.3326	+	11.1398i	−1.55679	+	1.13108i	−0.938577	+	0.345069i	$0.887856\pi$
$98$		0			0
$99$	5.61813	−	4.28938i	0.564643	−	0.431099i
$100$		0			0
$101$	3.36005	−	2.44122i	0.334337	−	0.242910i	−0.407932	−	0.913013i	$-0.633750\pi$
$101$	3.36005	−	2.44122i	0.334337	−	0.242910i	0.742269	+	0.670102i	$0.233750\pi$
$102$		0			0
$103$	1.06379	−	3.27402i	0.104819	−	0.322599i	−0.884869	−	0.465840i	$-0.845752\pi$
$103$	1.06379	−	3.27402i	0.104819	−	0.322599i	0.989688	+	0.143241i	$0.0457524\pi$
$104$		0			0
$105$	6.04361	+	4.39094i	0.589796	+	0.428512i
$106$		0			0
$107$	−0.427878	−	1.31687i	−0.0413646	−	0.127307i	0.928242	−	0.371978i	$-0.121320\pi$
$107$	−0.427878	−	1.31687i	−0.0413646	−	0.127307i	−0.969606	+	0.244671i	$0.921320\pi$
$108$		0			0
$109$	−9.42159			−0.902425			−0.451212	−	0.892417i	$-0.649008\pi$
$109$	−9.42159			−0.902425			−0.451212	+	0.892417i	$0.649008\pi$
$110$		0			0
$111$	8.46350			0.803320
$112$		0			0
$113$	2.05838	+	6.33505i	0.193636	+	0.595952i	0.999990	+	0.00451752i	$0.00143798\pi$
$113$	2.05838	+	6.33505i	0.193636	+	0.595952i	−0.806353	+	0.591434i	$0.798562\pi$
$114$		0			0
$115$	−13.0238	−	9.46232i	−1.21447	−	0.882366i
$116$		0			0
$117$	0.658577	−	2.02689i	0.0608855	−	0.187386i
$118$		0			0
$119$	−5.79038	+	4.20695i	−0.530803	+	0.385651i
$120$		0			0
$121$	10.9876	−	0.522528i	0.998871	−	0.0475026i
$122$		0			0
$123$	−2.16050	+	1.56969i	−0.194806	+	0.141534i
$124$		0			0
$125$	0.0783406	−	0.241108i	0.00700700	−	0.0215653i
$126$		0			0
$127$	0.148842	+	0.108140i	0.0132075	+	0.00959584i	0.594369	−	0.804192i	$-0.297402\pi$
$127$	0.148842	+	0.108140i	0.0132075	+	0.00959584i	−0.581162	+	0.813788i	$0.697402\pi$
$128$		0			0
$129$	−1.21117	−	3.72759i	−0.106637	−	0.328196i
$130$		0			0
$131$	1.86254			0.162731			0.0813655	−	0.996684i	$-0.474072\pi$
$131$	1.86254			0.162731			0.0813655	+	0.996684i	$0.474072\pi$
$132$		0			0
$133$	−21.9352			−1.90202
$134$		0			0
$135$	−4.69232	−	14.4415i	−0.403851	−	1.24293i
$136$		0			0
$137$	−11.5969	−	8.42563i	−0.990789	−	0.719850i	−0.0306953	−	0.999529i	$-0.509772\pi$
$137$	−11.5969	−	8.42563i	−0.990789	−	0.719850i	−0.960094	+	0.279678i	$0.909772\pi$
$138$		0			0
$139$	4.95968	−	15.2643i	0.420675	−	1.29470i	−0.486401	−	0.873736i	$-0.661690\pi$
$139$	4.95968	−	15.2643i	0.420675	−	1.29470i	0.907076	−	0.420968i	$-0.138310\pi$
$140$		0			0
$141$	−0.984771	+	0.715478i	−0.0829327	+	0.0602541i
$142$		0			0
$143$	2.63613	−	2.01266i	0.220445	−	0.168307i
$144$		0			0
$145$	1.04572	−	0.759763i	0.0868427	−	0.0630949i
$146$		0			0
$147$	−0.180763	+	0.556331i	−0.0149091	+	0.0458854i
$148$		0			0
$149$	−14.8054	−	10.7567i	−1.21290	−	0.881227i	−0.217413	−	0.976080i	$-0.569762\pi$
$149$	−14.8054	−	10.7567i	−1.21290	−	0.881227i	−0.995491	+	0.0948530i	$0.969762\pi$
$150$		0			0
$151$	3.88540	+	11.9580i	0.316190	+	0.973132i	0.975262	+	0.221052i	$0.0709492\pi$
$151$	3.88540	+	11.9580i	0.316190	+	0.973132i	−0.659072	+	0.752080i	$0.729051\pi$
$152$		0			0
$153$	6.04256			0.488512
$154$		0			0
$155$	12.8566			1.03267
$156$		0			0
$157$	−0.332944	−	1.02470i	−0.0265719	−	0.0817798i	0.936891	−	0.349621i	$-0.113690\pi$
$157$	−0.332944	−	1.02470i	−0.0265719	−	0.0817798i	−0.963463	+	0.267841i	$0.913690\pi$
$158$		0			0
$159$	0.416347	+	0.302494i	0.0330184	+	0.0239893i
$160$		0			0
$161$	−3.95537	+	12.1734i	−0.311726	+	0.959395i
$162$		0			0
$163$	−18.7489	+	13.6219i	−1.46853	+	1.06695i	−0.487490	+	0.873129i	$0.662087\pi$
$163$	−18.7489	+	13.6219i	−1.46853	+	1.06695i	−0.981037	+	0.193818i	$0.937913\pi$
$164$		0			0
$165$	2.81033	−	9.40388i	0.218784	−	0.732091i
$166$		0			0
$167$	−13.0740	+	9.49884i	−1.01170	+	0.735042i	−0.964565	−	0.263846i	$-0.915009\pi$
$167$	−13.0740	+	9.49884i	−1.01170	+	0.735042i	−0.0471341	+	0.998889i	$0.515009\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$		0			0
$171$	14.9821	+	10.8851i	1.14571	+	0.832404i
$172$		0			0
$173$	6.44369	+	19.8316i	0.489904	+	1.50777i	0.824750	+	0.565498i	$0.191316\pi$
$173$	6.44369	+	19.8316i	0.489904	+	1.50777i	−0.334846	+	0.942273i	$0.608684\pi$
$174$		0			0
$175$	−12.8234			−0.969358
$176$		0			0
$177$	10.0762			0.757373
$178$		0			0
$179$	−5.51401	−	16.9704i	−0.412136	−	1.26842i	−0.914788	−	0.403935i	$-0.867642\pi$
$179$	−5.51401	−	16.9704i	−0.412136	−	1.26842i	0.502651	−	0.864489i	$-0.332358\pi$
$180$		0			0
$181$	−21.6510	−	15.7304i	−1.60931	−	1.16923i	−0.865621	−	0.500700i	$-0.833076\pi$
$181$	−21.6510	−	15.7304i	−1.60931	−	1.16923i	−0.743686	−	0.668529i	$-0.766924\pi$
$182$		0			0
$183$	0.581515	−	1.78972i	0.0429868	−	0.132300i
$184$		0			0
$185$	−23.3225	+	16.9448i	−1.71470	+	1.24581i
$186$		0			0
$187$	7.73682	+	5.34498i	0.565773	+	0.390864i
$188$		0			0
$189$	−9.76762	+	7.09659i	−0.710489	+	0.516201i
$190$		0			0
$191$	−6.73229	+	20.7198i	−0.487131	+	1.49924i	0.341739	+	0.939795i	$0.388984\pi$
$191$	−6.73229	+	20.7198i	−0.487131	+	1.49924i	−0.828870	+	0.559441i	$0.811016\pi$
$192$		0			0
$193$	−15.3808	−	11.1748i	−1.10713	−	0.804380i	−0.124924	−	0.992166i	$-0.539869\pi$
$193$	−15.3808	−	11.1748i	−1.10713	−	0.804380i	−0.982210	+	0.187787i	$0.939869\pi$
$194$		0			0
$195$	−0.914469	−	2.81445i	−0.0654865	−	0.201547i
$196$		0			0
$197$	11.2245			0.799712			0.399856	−	0.916578i	$-0.369060\pi$
$197$	11.2245			0.799712			0.399856	+	0.916578i	$0.369060\pi$
$198$		0			0
$199$	−0.388299			−0.0275258			−0.0137629	−	0.999905i	$-0.504381\pi$
$199$	−0.388299			−0.0275258			−0.0137629	+	0.999905i	$0.504381\pi$
$200$		0			0
$201$	−2.04644	−	6.29830i	−0.144345	−	0.444248i
$202$		0			0
$203$	−0.831462	−	0.604093i	−0.0583572	−	0.0423990i
$204$		0			0
$205$	2.81090	−	8.65107i	0.196322	−	0.604217i
$206$		0			0
$207$	8.74247	−	6.35177i	0.607644	−	0.441479i
$208$		0			0
$209$	9.55436	+	27.1896i	0.660889	+	1.88074i
$210$		0			0
$211$	5.28777	−	3.84179i	0.364025	−	0.264480i	−0.390704	−	0.920516i	$-0.627768\pi$
$211$	5.28777	−	3.84179i	0.364025	−	0.264480i	0.754729	+	0.656037i	$0.227768\pi$
$212$		0			0
$213$	−0.394905	+	1.21539i	−0.0270584	+	0.0832773i
$214$		0			0
$215$	10.8006	+	7.84708i	0.736594	+	0.535167i
$216$		0			0
$217$	−3.15888	−	9.72204i	−0.214439	−	0.659975i
$218$		0			0
$219$	−6.92669			−0.468062
$220$		0			0
$221$	2.83529			0.190722
$222$		0			0
$223$	0.991337	+	3.05102i	0.0663849	+	0.204312i	0.978747	−	0.205073i	$-0.0657433\pi$
$223$	0.991337	+	3.05102i	0.0663849	+	0.204312i	−0.912362	+	0.409385i	$0.865743\pi$
$224$		0			0
$225$	8.75857	+	6.36347i	0.583904	+	0.424231i
$226$		0			0
$227$	5.05033	−	15.5433i	0.335202	−	1.03165i	−0.631421	−	0.775441i	$-0.717528\pi$
$227$	5.05033	−	15.5433i	0.335202	−	1.03165i	0.966623	−	0.256205i	$-0.0824721\pi$
$228$		0			0
$229$	16.8739	−	12.2596i	1.11506	−	0.810138i	0.131606	−	0.991302i	$-0.457987\pi$
$229$	16.8739	−	12.2596i	1.11506	−	0.810138i	0.983453	+	0.181164i	$0.0579865\pi$
$230$		0			0
$231$	−7.80163	+	0.185404i	−0.513310	+	0.0121987i
$232$		0			0
$233$	11.1377	−	8.09199i	0.729653	−	0.530124i	−0.159801	−	0.987149i	$-0.551085\pi$
$233$	11.1377	−	8.09199i	0.729653	−	0.530124i	0.889454	+	0.457026i	$0.151085\pi$
$234$		0			0
$235$	1.28123	−	3.94322i	0.0835783	−	0.257228i
$236$		0			0
$237$	10.6822	+	7.76107i	0.693883	+	0.504135i
$238$		0			0
$239$	−3.30945	−	10.1854i	−0.214070	−	0.658841i	−0.999218	−	0.0395325i	$-0.987413\pi$
$239$	−3.30945	−	10.1854i	−0.214070	−	0.658841i	0.785148	−	0.619308i	$-0.212587\pi$
$240$		0			0
$241$	26.7787			1.72497			0.862485	−	0.506082i	$-0.168907\pi$
$241$	26.7787			1.72497			0.862485	+	0.506082i	$0.168907\pi$
$242$		0			0
$243$	16.1525			1.03618
$244$		0			0
$245$	−0.615711	−	1.89496i	−0.0393364	−	0.121065i
$246$		0			0
$247$	7.02986	+	5.10749i	0.447299	+	0.324982i
$248$		0			0
$249$	0.187688	−	0.577645i	0.0118943	−	0.0366067i
$250$		0			0
$251$	12.3029	−	8.93855i	0.776549	−	0.564196i	−0.127392	−	0.991852i	$-0.540661\pi$
$251$	12.3029	−	8.93855i	0.776549	−	0.564196i	0.903941	+	0.427656i	$0.140661\pi$
$252$		0			0
$253$	16.8122	−	0.399538i	1.05698	−	0.0251187i
$254$		0			0
$255$	6.78799	−	4.93176i	0.425080	−	0.308839i
$256$		0			0
$257$	0.970364	−	2.98647i	0.0605297	−	0.186291i	−0.916219	−	0.400677i	$-0.868775\pi$
$257$	0.970364	−	2.98647i	0.0605297	−	0.186291i	0.976749	+	0.214386i	$0.0687750\pi$
$258$		0			0
$259$	18.5439	+	13.4729i	1.15226	+	0.837166i
$260$		0			0
$261$	0.268126	+	0.825208i	0.0165966	+	0.0510791i
$262$		0			0
$263$	−26.1369			−1.61167			−0.805834	−	0.592142i	$-0.798283\pi$
$263$	−26.1369			−1.61167			−0.805834	+	0.592142i	$0.798283\pi$
$264$		0			0
$265$	−1.75293			−0.107682
$266$		0			0
$267$	2.83803	+	8.73455i	0.173684	+	0.534546i
$268$		0			0
$269$	−2.94180	−	2.13734i	−0.179364	−	0.130316i	0.494480	−	0.869189i	$-0.335358\pi$
$269$	−2.94180	−	2.13734i	−0.179364	−	0.130316i	−0.673845	+	0.738873i	$0.735358\pi$
$270$		0			0
$271$	−6.41068	+	19.7301i	−0.389421	+	1.19852i	0.543800	+	0.839215i	$0.316985\pi$
$271$	−6.41068	+	19.7301i	−0.389421	+	1.19852i	−0.933222	+	0.359301i	$0.883015\pi$
$272$		0			0
$273$	−1.90357	+	1.38303i	−0.115209	+	0.0837046i
$274$		0			0
$275$	5.58552	+	15.8951i	0.336819	+	0.958513i
$276$		0			0
$277$	−14.3976	+	10.4605i	−0.865068	+	0.628509i	−0.929259	−	0.369429i	$-0.879553\pi$
$277$	−14.3976	+	10.4605i	−0.865068	+	0.628509i	0.0641908	+	0.997938i	$0.479553\pi$
$278$		0			0
$279$	−2.66689	+	8.20785i	−0.159663	+	0.491391i
$280$		0			0
$281$	20.7630	+	15.0852i	1.23861	+	0.899906i	0.997505	−	0.0705916i	$-0.0224887\pi$
$281$	20.7630	+	15.0852i	1.23861	+	0.899906i	0.241109	+	0.970498i	$0.422489\pi$
$282$		0			0
$283$	−2.63303	−	8.10362i	−0.156517	−	0.481710i	0.841794	−	0.539798i	$-0.181500\pi$
$283$	−2.63303	−	8.10362i	−0.156517	−	0.481710i	−0.998311	+	0.0580882i	$0.981500\pi$
$284$		0			0
$285$	25.7144			1.52319
$286$		0			0
$287$	−7.23251			−0.426921
$288$		0			0
$289$	−2.76915	−	8.52257i	−0.162891	−	0.501327i
$290$		0			0
$291$	−14.2915	−	10.3834i	−0.837780	−	0.608683i
$292$		0			0
$293$	5.52381	−	17.0005i	0.322704	−	0.993182i	−0.649762	−	0.760138i	$-0.725131\pi$
$293$	5.52381	−	17.0005i	0.322704	−	0.993182i	0.972466	−	0.233044i	$-0.0748687\pi$
$294$		0			0
$295$	−27.7665	+	20.1736i	−1.61663	+	1.17455i
$296$		0			0
$297$	13.0510	+	9.01629i	0.757297	+	0.523178i
$298$		0			0
$299$	4.10213	−	2.98037i	0.237232	−	0.172359i
$300$		0			0
$301$	3.28018	−	10.0953i	0.189066	−	0.581886i
$302$		0			0
$303$	3.13188	+	2.27544i	0.179922	+	0.130721i
$304$		0			0
$305$	1.98074	+	6.09610i	0.113417	+	0.349062i
$306$		0			0
$307$	22.7969			1.30108			0.650542	−	0.759470i	$-0.274542\pi$
$307$	22.7969			1.30108			0.650542	+	0.759470i	$0.274542\pi$
$308$		0			0
$309$	3.20874			0.182539
$310$		0			0
$311$	1.67690	+	5.16098i	0.0950884	+	0.292652i	0.987277	−	0.159012i	$-0.0508307\pi$
$311$	1.67690	+	5.16098i	0.0950884	+	0.292652i	−0.892188	+	0.451664i	$0.850831\pi$
$312$		0			0
$313$	5.98268	+	4.34667i	0.338161	+	0.245689i	0.743886	−	0.668307i	$-0.232981\pi$
$313$	5.98268	+	4.34667i	0.338161	+	0.245689i	−0.405724	+	0.913995i	$0.632981\pi$
$314$		0			0
$315$	5.27820	−	16.2446i	0.297393	−	0.915282i
$316$		0			0
$317$	0.660509	−	0.479888i	0.0370979	−	0.0269532i	−0.569082	−	0.822281i	$-0.692701\pi$
$317$	0.660509	−	0.479888i	0.0370979	−	0.0269532i	0.606180	+	0.795328i	$0.292701\pi$
$318$		0			0
$319$	−0.386636	+	1.29376i	−0.0216475	+	0.0724366i
$320$		0			0
$321$	1.04413	−	0.758606i	0.0582777	−	0.0423413i
$322$		0			0
$323$	−7.61322	+	23.4311i	−0.423611	+	1.30374i
$324$		0			0
$325$	4.10969	+	2.98586i	0.227964	+	0.165626i
$326$		0			0
$327$	−2.71373	−	8.35199i	−0.150069	−	0.461866i
$328$		0			0
$329$	−3.29663			−0.181749
$330$		0			0
$331$	−27.9408			−1.53576			−0.767882	−	0.640592i	$-0.778689\pi$
$331$	−27.9408			−1.53576			−0.767882	+	0.640592i	$0.778689\pi$
$332$		0			0
$333$	−5.97994	−	18.4044i	−0.327699	−	1.00855i
$334$		0			0
$335$	18.2491	+	13.2588i	0.997056	+	0.724403i
$336$		0			0
$337$	3.85801	−	11.8737i	0.210159	−	0.646804i	−0.789303	−	0.614005i	$-0.789558\pi$
$337$	3.85801	−	11.8737i	0.210159	−	0.646804i	0.999462	−	0.0327997i	$-0.0104423\pi$
$338$		0			0
$339$	−5.02298	+	3.64941i	−0.272811	+	0.198209i
$340$		0			0
$341$	−10.6750	+	8.15022i	−0.578081	+	0.441359i
$342$		0			0
$343$	−15.5775	+	11.3177i	−0.841104	+	0.611098i
$344$		0			0
$345$	4.63683	−	14.2707i	0.249638	−	0.768308i
$346$		0			0
$347$	16.6140	+	12.0708i	0.891889	+	0.647995i	0.936370	−	0.351015i	$-0.114163\pi$
$347$	16.6140	+	12.0708i	0.891889	+	0.647995i	−0.0444810	+	0.999010i	$0.514163\pi$
$348$		0			0
$349$	6.33079	+	19.4842i	0.338879	+	1.04296i	0.964779	+	0.263060i	$0.0847318\pi$
$349$	6.33079	+	19.4842i	0.338879	+	1.04296i	−0.625900	+	0.779903i	$0.715268\pi$
$350$		0			0
$351$	4.78276			0.255285
$352$		0			0
$353$	−26.0531			−1.38666			−0.693332	−	0.720618i	$-0.743858\pi$
$353$	−26.0531			−1.38666			−0.693332	+	0.720618i	$0.743858\pi$
$354$		0			0
$355$	−1.34512	−	4.13984i	−0.0713913	−	0.219720i
$356$		0			0
$357$	−5.39717	−	3.92128i	−0.285649	−	0.207536i
$358$		0			0
$359$	2.11268	−	6.50215i	0.111503	−	0.343171i	−0.879699	−	0.475531i	$-0.842256\pi$
$359$	2.11268	−	6.50215i	0.111503	−	0.343171i	0.991202	+	0.132361i	$0.0422558\pi$
$360$		0			0
$361$	−45.7139	+	33.2131i	−2.40599	+	1.74806i
$362$		0			0
$363$	3.62799	+	9.58970i	0.190420	+	0.503329i
$364$		0			0
$365$	19.0876	−	13.8679i	0.999089	−	0.725881i
$366$		0			0
$367$	−4.51896	+	13.9079i	−0.235888	+	0.725987i	0.761115	+	0.648617i	$0.224652\pi$
$367$	−4.51896	+	13.9079i	−0.235888	+	0.725987i	−0.997002	+	0.0773702i	$0.975348\pi$
$368$		0			0
$369$	4.93991	+	3.58905i	0.257161	+	0.186839i
$370$		0			0
$371$	0.430698	+	1.32555i	0.0223607	+	0.0688192i
$372$		0			0
$373$	−3.81475			−0.197520			−0.0987600	−	0.995111i	$-0.531488\pi$
$373$	−3.81475			−0.197520			−0.0987600	+	0.995111i	$0.531488\pi$
$374$		0			0
$375$	0.236300			0.0122025
$376$		0			0
$377$	0.125810	+	0.387203i	0.00647954	+	0.0199420i
$378$		0			0
$379$	13.7738	+	10.0072i	0.707511	+	0.514037i	0.882370	−	0.470557i	$-0.155947\pi$
$379$	13.7738	+	10.0072i	0.707511	+	0.514037i	−0.174859	+	0.984593i	$0.555947\pi$
$380$		0			0
$381$	−0.0529918	+	0.163092i	−0.00271485	+	0.00835545i
$382$		0			0
$383$	27.0214	−	19.6322i	1.38073	−	1.00316i	0.383918	−	0.923367i	$-0.374574\pi$
$383$	27.0214	−	19.6322i	1.38073	−	1.00316i	0.996812	−	0.0797920i	$-0.0254256\pi$
$384$		0			0
$385$	21.1274	−	16.1306i	1.07675	−	0.822090i
$386$		0			0
$387$	−7.25011	+	5.26751i	−0.368544	+	0.267763i
$388$		0			0
$389$	9.39401	−	28.9118i	0.476295	−	1.46589i	−0.367908	−	0.929862i	$-0.619926\pi$
$389$	9.39401	−	28.9118i	0.476295	−	1.46589i	0.844203	−	0.536024i	$-0.180074\pi$
$390$		0			0
$391$	11.6307	+	8.45021i	0.588190	+	0.427345i
$392$		0			0
$393$	0.536473	+	1.65109i	0.0270615	+	0.0832867i
$394$		0			0
$395$	−44.9749			−2.26293
$396$		0			0
$397$	−19.2545			−0.966357			−0.483178	−	0.875522i	$-0.660518\pi$
$397$	−19.2545			−0.966357			−0.483178	+	0.875522i	$0.660518\pi$
$398$		0			0
$399$	−6.31806	−	19.4450i	−0.316298	−	0.973466i
$400$		0			0
$401$	−21.5278	−	15.6408i	−1.07504	−	0.781066i	−0.0982327	−	0.995163i	$-0.531319\pi$
$401$	−21.5278	−	15.6408i	−1.07504	−	0.781066i	−0.976812	+	0.214098i	$0.931319\pi$
$402$		0			0
$403$	−1.25136	+	3.85128i	−0.0623345	+	0.191846i
$404$		0			0
$405$	−4.97170	+	3.61215i	−0.247046	+	0.179489i
$406$		0			0
$407$	8.62304	−	28.8543i	0.427428	−	1.43026i
$408$		0			0
$409$	13.1314	−	9.54050i	0.649304	−	0.471747i	−0.213730	−	0.976893i	$-0.568561\pi$
$409$	13.1314	−	9.54050i	0.649304	−	0.471747i	0.863034	+	0.505146i	$0.168561\pi$
$410$		0			0
$411$	4.12882	−	12.7072i	0.203660	−	0.626800i
$412$		0			0
$413$	22.0774	+	16.0401i	1.08636	+	0.789283i
$414$		0			0
$415$	0.639299	+	1.96756i	0.0313820	+	0.0965838i
$416$		0			0
$417$	14.9600			0.732594
$418$		0			0
$419$	−14.4843			−0.707603			−0.353801	−	0.935321i	$-0.615111\pi$
$419$	−14.4843			−0.707603			−0.353801	+	0.935321i	$0.615111\pi$
$420$		0			0
$421$	3.03793	+	9.34978i	0.148059	+	0.455680i	0.997392	−	0.0721784i	$-0.0229951\pi$
$421$	3.03793	+	9.34978i	0.148059	+	0.455680i	−0.849332	+	0.527859i	$0.822995\pi$
$422$		0			0
$423$	2.25165	+	1.63592i	0.109479	+	0.0795410i
$424$		0			0
$425$	−4.45072	+	13.6979i	−0.215892	+	0.664446i
$426$		0			0
$427$	4.12315	−	2.99564i	0.199533	−	0.144969i
$428$		0			0
$429$	2.54346	+	1.75715i	0.122800	+	0.0848360i
$430$		0			0
$431$	18.5065	−	13.4457i	0.891425	−	0.647658i	−0.0448241	−	0.998995i	$-0.514273\pi$
$431$	18.5065	−	13.4457i	0.891425	−	0.647658i	0.936249	+	0.351337i	$0.114273\pi$
$432$		0			0
$433$	−5.59811	+	17.2292i	−0.269028	+	0.827983i	0.721710	+	0.692196i	$0.243356\pi$
$433$	−5.59811	+	17.2292i	−0.269028	+	0.827983i	−0.990738	+	0.135788i	$0.956644\pi$
$434$		0			0
$435$	0.974713	+	0.708171i	0.0467339	+	0.0339542i
$436$		0			0
$437$	13.6152	+	41.9032i	0.651303	+	2.00450i
$438$		0			0
$439$	−9.74243			−0.464981			−0.232490	−	0.972599i	$-0.574687\pi$
$439$	−9.74243			−0.464981			−0.232490	+	0.972599i	$0.574687\pi$
$440$		0			0
$441$	1.33749			0.0636902
$442$		0			0
$443$	−4.19940	−	12.9244i	−0.199519	−	0.614057i	−0.999894	−	0.0145573i	$-0.995366\pi$
$443$	−4.19940	−	12.9244i	−0.199519	−	0.614057i	0.800375	−	0.599500i	$-0.204634\pi$
$444$		0			0
$445$	−25.3081	−	18.3874i	−1.19972	−	0.871646i
$446$		0			0
$447$	5.27113	−	16.2229i	0.249316	−	0.767316i
$448$		0			0
$449$	20.8122	−	15.1210i	0.982190	−	0.713603i	0.0239929	−	0.999712i	$-0.492362\pi$
$449$	20.8122	−	15.1210i	0.982190	−	0.713603i	0.958197	+	0.286109i	$0.0923621\pi$
$450$		0			0
$451$	3.15028	+	8.96500i	0.148341	+	0.422145i
$452$		0			0
$453$	−9.48137	+	6.88862i	−0.445474	+	0.323656i
$454$		0			0
$455$	2.47663	−	7.62229i	0.116106	−	0.357339i
$456$		0			0
$457$	−13.4505	−	9.77234i	−0.629186	−	0.457131i	0.226932	−	0.973911i	$-0.427131\pi$
$457$	−13.4505	−	9.77234i	−0.629186	−	0.457131i	−0.856118	+	0.516780i	$0.827131\pi$
$458$		0			0
$459$	4.19042	+	12.8968i	0.195592	+	0.601971i
$460$		0			0
$461$	−22.5289			−1.04928			−0.524638	−	0.851325i	$-0.675799\pi$
$461$	−22.5289			−1.04928			−0.524638	+	0.851325i	$0.675799\pi$
$462$		0			0
$463$	15.0683			0.700282			0.350141	−	0.936697i	$-0.386134\pi$
$463$	15.0683			0.700282			0.350141	+	0.936697i	$0.386134\pi$
$464$		0			0
$465$	3.70312	+	11.3970i	0.171728	+	0.528525i
$466$		0			0
$467$	18.4699	+	13.4191i	0.854684	+	0.620964i	0.926433	−	0.376459i	$-0.122858\pi$
$467$	18.4699	+	13.4191i	0.854684	+	0.620964i	−0.0717498	+	0.997423i	$0.522858\pi$
$468$		0			0
$469$	5.54232	−	17.0575i	0.255921	−	0.787643i
$470$		0			0
$471$	0.812469	−	0.590293i	0.0374366	−	0.0271993i
$472$		0			0
$473$	−13.9424	+	0.331336i	−0.641070	+	0.0152348i
$474$		0			0
$475$	−35.7106	+	25.9453i	−1.63852	+	1.19045i
$476$		0			0
$477$	0.363617	−	1.11910i	0.0166489	−	0.0512401i
$478$		0			0
$479$	−15.7347	−	11.4319i	−0.718936	−	0.522337i	0.167108	−	0.985939i	$-0.446557\pi$
$479$	−15.7347	−	11.4319i	−0.718936	−	0.522337i	−0.886044	+	0.463601i	$0.846557\pi$
$480$		0			0
$481$	−2.80590	−	8.63568i	−0.127938	−	0.393753i
$482$		0			0
$483$	−11.9306			−0.542863
$484$		0			0
$485$	60.1709			2.73222
$486$		0			0
$487$	−3.69497	−	11.3719i	−0.167435	−	0.515312i	0.831772	−	0.555117i	$-0.187326\pi$
$487$	−3.69497	−	11.3719i	−0.167435	−	0.515312i	−0.999207	+	0.0398046i	$0.987326\pi$
$488$		0			0
$489$	−17.4757	−	12.6969i	−0.790280	−	0.574172i
$490$		0			0
$491$	−4.16376	+	12.8147i	−0.187908	+	0.578321i	−0.999986	−	0.00522720i	$-0.998336\pi$
$491$	−4.16376	+	12.8147i	−0.187908	+	0.578321i	0.812078	+	0.583548i	$0.198336\pi$
$492$		0			0
$493$	−0.933871	+	0.678497i	−0.0420594	+	0.0305580i
$494$		0			0
$495$	−22.4350	+	0.533160i	−1.00838	+	0.0239638i
$496$		0			0
$497$	−2.80001	+	2.03433i	−0.125598	+	0.0912521i
$498$		0			0
$499$	2.73674	−	8.42283i	0.122513	−	0.377057i	−0.870926	−	0.491413i	$-0.836480\pi$
$499$	2.73674	−	8.42283i	0.122513	−	0.377057i	0.993440	+	0.114356i	$0.0364804\pi$
$500$		0			0
$501$	−12.1862	−	8.85381i	−0.544440	−	0.395559i
$502$		0			0
$503$	5.36873	+	16.5233i	0.239380	+	0.736735i	0.996510	+	0.0834716i	$0.0266008\pi$
$503$	5.36873	+	16.5233i	0.239380	+	0.736735i	−0.757130	+	0.653264i	$0.773399\pi$
$504$		0			0
$505$	−13.1861			−0.586772
$506$		0			0
$507$	0.932094			0.0413957
$508$		0			0
$509$	−10.0061	−	30.7955i	−0.443510	−	1.36498i	−0.884109	−	0.467280i	$-0.845234\pi$
$509$	−10.0061	−	30.7955i	−0.443510	−	1.36498i	0.440599	−	0.897704i	$-0.354766\pi$
$510$		0			0
$511$	−15.1766	−	11.0265i	−0.671375	−	0.487783i
$512$		0			0
$513$	−12.8425	+	39.5252i	−0.567011	+	1.74508i
$514$		0			0
$515$	−8.84218	+	6.42422i	−0.389633	+	0.283085i
$516$		0			0
$517$	1.43592	+	4.08631i	0.0631518	+	0.179716i
$518$		0			0
$519$	−15.7242	+	11.4243i	−0.690217	+	0.501472i
$520$		0			0
$521$	6.69706	−	20.6114i	0.293403	−	0.903003i	−0.690350	−	0.723476i	$-0.742543\pi$
$521$	6.69706	−	20.6114i	0.293403	−	0.903003i	0.983753	−	0.179527i	$-0.0574567\pi$
$522$		0			0
$523$	−2.89877	−	2.10608i	−0.126754	−	0.0920925i	0.522602	−	0.852577i	$-0.324962\pi$
$523$	−2.89877	−	2.10608i	−0.126754	−	0.0920925i	−0.649356	+	0.760484i	$0.724962\pi$
$524$		0			0
$525$	−3.69356	−	11.3676i	−0.161200	−	0.496123i
$526$		0			0
$527$	−11.4814			−0.500139
$528$		0			0
$529$	2.71011			0.117831
$530$		0			0
$531$	−7.11941	−	21.9113i	−0.308956	−	0.950869i
$532$		0			0
$533$	2.31790	+	1.68405i	0.100399	+	0.0729443i
$534$		0			0
$535$	−1.35846	+	4.18092i	−0.0587314	+	0.180757i
$536$		0			0
$537$	13.4556	−	9.77604i	0.580651	−	0.421867i
$538$		0			0
$539$	1.71251	+	1.18309i	0.0737631	+	0.0509592i
$540$		0			0
$541$	19.4468	−	14.1289i	0.836084	−	0.607451i	−0.0851899	−	0.996365i	$-0.527150\pi$
$541$	19.4468	−	14.1289i	0.836084	−	0.607451i	0.921274	+	0.388914i	$0.127150\pi$
$542$		0			0
$543$	7.70837	−	23.7239i	0.330798	−	1.01809i
$544$		0			0
$545$	24.1996	+	17.5821i	1.03660	+	0.753133i
$546$		0			0
$547$	7.29293	+	22.4453i	0.311823	+	0.959693i	0.977042	+	0.213045i	$0.0683381\pi$
$547$	7.29293	+	22.4453i	0.311823	+	0.959693i	−0.665219	+	0.746648i	$0.731662\pi$
$548$		0			0
$549$	−4.30272			−0.183636
$550$		0			0
$551$	−3.53771			−0.150711
$552$		0			0
$553$	11.0504	+	34.0096i	0.469910	+	1.44624i
$554$		0			0
$555$	−21.7387	−	15.7941i	−0.922759	−	0.670423i
$556$		0			0
$557$	12.8898	−	39.6708i	0.546159	−	1.68091i	−0.172058	−	0.985087i	$-0.555042\pi$
$557$	12.8898	−	39.6708i	0.546159	−	1.68091i	0.718217	−	0.695819i	$-0.244958\pi$
$558$		0			0
$559$	−3.40189	+	2.47162i	−0.143885	+	0.104538i
$560$		0			0
$561$	−2.50973	+	8.39802i	−0.105961	+	0.354565i
$562$		0			0
$563$	−30.7711	+	22.3565i	−1.29685	+	0.942214i	−0.999920	−	0.0126856i	$-0.995962\pi$
$563$	−30.7711	+	22.3565i	−1.29685	+	0.942214i	−0.296927	+	0.954900i	$0.595962\pi$
$564$		0			0
$565$	6.53512	−	20.1130i	0.274934	−	0.846161i
$566$		0			0
$567$	3.95303	+	2.87205i	0.166012	+	0.120615i
$568$		0			0
$569$	−13.3482	−	41.0816i	−0.559587	−	1.72223i	−0.683512	−	0.729940i	$-0.739548\pi$
$569$	−13.3482	−	41.0816i	−0.559587	−	1.72223i	0.123925	−	0.992292i	$-0.460452\pi$
$570$		0			0
$571$	−30.6353			−1.28205			−0.641023	−	0.767521i	$-0.721490\pi$
$571$	−30.6353			−1.28205			−0.641023	+	0.767521i	$0.721490\pi$
$572$		0			0
$573$	−20.3067			−0.848325
$574$		0			0
$575$	7.95949	+	24.4968i	0.331934	+	1.02159i
$576$		0			0
$577$	−8.42117	−	6.11834i	−0.350578	−	0.254710i	0.398533	−	0.917154i	$-0.369519\pi$
$577$	−8.42117	−	6.11834i	−0.350578	−	0.254710i	−0.749111	+	0.662444i	$0.769519\pi$
$578$		0			0
$579$	5.47599	−	16.8534i	0.227575	−	0.700402i
$580$		0			0
$581$	1.33078	−	0.966865i	0.0552099	−	0.0401123i
$582$		0			0
$583$	1.45548	−	1.11124i	0.0602797	−	0.0460229i
$584$		0			0
$585$	−5.47405	+	3.97713i	−0.226324	+	0.164434i
$586$		0			0
$587$	14.3549	−	44.1800i	0.592492	−	1.82350i	0.0256575	−	0.999671i	$-0.491832\pi$
$587$	14.3549	−	44.1800i	0.592492	−	1.82350i	0.566834	−	0.823832i	$-0.308168\pi$
$588$		0			0
$589$	−28.4673	−	20.6827i	−1.17297	−	0.852215i
$590$		0			0
$591$	3.23302	+	9.95022i	0.132989	+	0.409297i
$592$		0			0
$593$	−39.1041			−1.60581			−0.802907	−	0.596105i	$-0.796714\pi$
$593$	−39.1041			−1.60581			−0.802907	+	0.596105i	$0.796714\pi$
$594$		0			0
$595$	22.7235			0.931575
$596$		0			0
$597$	−0.111843	−	0.344217i	−0.00457742	−	0.0140879i
$598$		0			0
$599$	22.7884	+	16.5568i	0.931109	+	0.676491i	0.946264	−	0.323395i	$-0.104824\pi$
$599$	22.7884	+	16.5568i	0.931109	+	0.676491i	−0.0151548	+	0.999885i	$0.504824\pi$
$600$		0			0
$601$	1.49466	−	4.60009i	0.0609685	−	0.187642i	−0.915933	−	0.401331i	$-0.868548\pi$
$601$	1.49466	−	4.60009i	0.0609685	−	0.187642i	0.976902	+	0.213689i	$0.0685479\pi$
$602$		0			0
$603$	−12.2501	+	8.90021i	−0.498862	+	0.362445i
$604$		0			0
$605$	−29.1971	−	19.1623i	−1.18703	−	0.779059i
$606$		0			0
$607$	−0.00270616	+	0.00196614i	−0.000109840	+	7.98032e-5i	−0.587840	−	0.808977i	$-0.700022\pi$
$607$	−0.00270616	+	0.00196614i	−0.000109840	+	7.98032e-5i	0.587730	+	0.809057i	$0.300022\pi$
$608$		0			0
$609$	0.296024	−	0.911068i	0.0119955	−	0.0369183i
$610$		0			0
$611$	1.05652	+	0.767603i	0.0427420	+	0.0310539i
$612$		0			0
$613$	−13.8811	−	42.7216i	−0.560652	−	1.72551i	−0.680528	−	0.732722i	$-0.738250\pi$
$613$	−13.8811	−	42.7216i	−0.560652	−	1.72551i	0.119876	−	0.992789i	$-0.461750\pi$
$614$		0			0
$615$	8.47858			0.341889
$616$		0			0
$617$	−11.9703			−0.481906			−0.240953	−	0.970537i	$-0.577460\pi$
$617$	−11.9703			−0.481906			−0.240953	+	0.970537i	$0.577460\pi$
$618$		0			0
$619$	−11.3078	−	34.8018i	−0.454499	−	1.39880i	−0.871723	−	0.490000i	$-0.836997\pi$
$619$	−11.3078	−	34.8018i	−0.454499	−	1.39880i	0.417224	−	0.908804i	$-0.363003\pi$
$620$		0			0
$621$	19.6195	+	14.2544i	0.787304	+	0.572010i
$622$		0			0
$623$	−7.68615	+	23.6555i	−0.307939	+	0.947739i
$624$		0			0
$625$	19.8973	−	14.4562i	0.795891	−	0.578248i
$626$		0			0
$627$	−21.3509	+	16.3012i	−0.852673	+	0.651007i
$628$		0			0
$629$	20.8279	−	15.1323i	0.830461	−	0.603365i
$630$		0			0
$631$	−13.6688	+	42.0682i	−0.544145	+	1.67471i	0.178869	+	0.983873i	$0.442756\pi$
$631$	−13.6688	+	42.0682i	−0.544145	+	1.67471i	−0.723014	+	0.690834i	$0.757244\pi$
$632$		0			0
$633$	4.92870	+	3.58091i	0.195898	+	0.142328i
$634$		0			0
$635$	−0.180499	−	0.555520i	−0.00716290	−	0.0220451i
$636$		0			0
$637$	0.627578			0.0248655
$638$		0			0
$639$	2.92196			0.115591
$640$		0			0
$641$	6.75570	+	20.7919i	0.266834	+	0.821230i	0.991265	+	0.131883i	$0.0421025\pi$
$641$	6.75570	+	20.7919i	0.266834	+	0.821230i	−0.724431	+	0.689347i	$0.757898\pi$
$642$		0			0
$643$	−20.5488	−	14.9295i	−0.810364	−	0.588764i	0.103572	−	0.994622i	$-0.466973\pi$
$643$	−20.5488	−	14.9295i	−0.810364	−	0.588764i	−0.913936	+	0.405858i	$0.866973\pi$
$644$		0			0
$645$	−3.84531	+	11.8347i	−0.151409	+	0.465989i
$646$		0			0
$647$	2.75233	−	1.99969i	0.108205	−	0.0786158i	−0.532367	−	0.846514i	$-0.678697\pi$
$647$	2.75233	−	1.99969i	0.108205	−	0.0786158i	0.640572	+	0.767898i	$0.278697\pi$
$648$		0			0
$649$	10.2661	−	34.3525i	0.402981	−	1.34845i
$650$		0			0
$651$	7.70847	−	5.60053i	0.302119	−	0.219502i
$652$		0			0
$653$	3.56806	−	10.9814i	0.139629	−	0.429733i	−0.856652	−	0.515894i	$-0.827460\pi$
$653$	3.56806	−	10.9814i	0.139629	−	0.429733i	0.996281	+	0.0861606i	$0.0274598\pi$
$654$		0			0
$655$	−4.78400	−	3.47578i	−0.186926	−	0.135810i
$656$		0			0
$657$	4.89410	+	15.0625i	0.190937	+	0.587644i
$658$		0			0
$659$	−9.96372			−0.388131			−0.194066	−	0.980989i	$-0.562167\pi$
$659$	−9.96372			−0.388131			−0.194066	+	0.980989i	$0.562167\pi$
$660$		0			0
$661$	47.0753			1.83102			0.915508	−	0.402300i	$-0.131789\pi$
$661$	47.0753			1.83102			0.915508	+	0.402300i	$0.131789\pi$
$662$		0			0
$663$	0.816655	+	2.51341i	0.0317163	+	0.0976126i
$664$		0			0
$665$	56.3412	+	40.9343i	2.18482	+	1.58736i
$666$		0			0
$667$	−0.637921	+	1.96332i	−0.0247004	+	0.0760200i
$668$		0			0
$669$	−2.41911	+	1.75759i	−0.0935284	+	0.0679523i
$670$		0			0
$671$	−5.50915	−	3.80599i	−0.212678	−	0.146929i
$672$		0			0
$673$	19.7695	−	14.3634i	0.762058	−	0.553668i	−0.137483	−	0.990504i	$-0.543901\pi$
$673$	19.7695	−	14.3634i	0.762058	−	0.553668i	0.899541	+	0.436837i	$0.143901\pi$
$674$		0			0
$675$	−7.50779	+	23.1066i	−0.288975	+	0.889373i
$676$		0			0
$677$	−25.0914	−	18.2300i	−0.964341	−	0.700635i	−0.0101862	−	0.999948i	$-0.503242\pi$
$677$	−25.0914	−	18.2300i	−0.964341	−	0.700635i	−0.954155	+	0.299313i	$0.903242\pi$
$678$		0			0
$679$	−14.7841	−	45.5007i	−0.567360	−	1.74616i
$680$		0			0
$681$	15.2334			0.583745
$682$		0			0
$683$	4.80590			0.183893			0.0919463	−	0.995764i	$-0.470691\pi$
$683$	4.80590			0.183893			0.0919463	+	0.995764i	$0.470691\pi$
$684$		0			0
$685$	14.0635	+	43.2830i	0.537338	+	1.65376i
$686$		0			0
$687$	15.7281	+	11.4271i	0.600063	+	0.435971i
$688$		0			0
$689$	0.170616	−	0.525103i	0.00649996	−	0.0200048i
$690$		0			0
$691$	−24.7682	+	17.9952i	−0.942227	+	0.684568i	−0.948956	−	0.315409i	$-0.897858\pi$
$691$	−24.7682	+	17.9952i	−0.942227	+	0.684568i	0.00672860	+	0.999977i	$0.497858\pi$
$692$		0			0
$693$	5.91547	+	16.8341i	0.224710	+	0.639475i
$694$		0			0
$695$	−41.2246	+	29.9514i	−1.56374	+	1.13612i
$696$		0			0
$697$	−2.51024	+	7.72573i	−0.0950822	+	0.292633i
$698$		0			0
$699$	10.3813	+	7.54249i	0.392659	+	0.285283i
$700$		0			0
$701$	2.89910	+	8.92250i	0.109497	+	0.336998i	0.990760	−	0.135629i	$-0.0433056\pi$
$701$	2.89910	+	8.92250i	0.109497	+	0.336998i	−0.881262	+	0.472627i	$0.843306\pi$
$702$		0			0
$703$	78.9004			2.97579
$704$		0			0
$705$	3.86460			0.145549
$706$		0			0
$707$	3.23983	+	9.97118i	0.121846	+	0.375005i
$708$		0			0
$709$	5.75588	+	4.18189i	0.216166	+	0.157054i	0.690599	−	0.723238i	$-0.257347\pi$
$709$	5.75588	+	4.18189i	0.216166	+	0.157054i	−0.474433	+	0.880292i	$0.657347\pi$
$710$		0			0
$711$	9.32932	−	28.7127i	0.349877	−	1.07681i
$712$		0			0
$713$	−16.6115	+	12.0689i	−0.622105	+	0.451986i
$714$		0			0
$715$	−10.5269	+	0.250169i	−0.393684	+	0.00935578i
$716$		0			0
$717$	8.07589	−	5.86748i	0.301600	−	0.219125i
$718$		0			0
$719$	4.82473	−	14.8490i	0.179932	−	0.553773i	−0.819892	−	0.572518i	$-0.805967\pi$
$719$	4.82473	−	14.8490i	0.179932	−	0.553773i	0.999824	+	0.0187442i	$0.00596680\pi$
$720$		0			0
$721$	7.03048	+	5.10794i	0.261829	+	0.190230i
$722$		0			0
$723$	7.71316	+	23.7387i	0.286855	+	0.882850i
$724$		0			0
$725$	−2.06816			−0.0768094
$726$		0			0
$727$	−34.7615			−1.28923			−0.644616	−	0.764507i	$-0.722983\pi$
$727$	−34.7615			−1.28923			−0.644616	+	0.764507i	$0.722983\pi$
$728$		0			0
$729$	2.85802	+	8.79608i	0.105853	+	0.325781i
$730$		0			0
$731$	−9.64533	−	7.00774i	−0.356745	−	0.259191i
$732$		0			0
$733$	−9.19672	+	28.3046i	−0.339688	+	1.04545i	0.624678	+	0.780883i	$0.285230\pi$
$733$	−9.19672	+	28.3046i	−0.339688	+	1.04545i	−0.964366	+	0.264571i	$0.914770\pi$
$734$		0			0
$735$	1.50249	−	1.09162i	0.0554202	−	0.0402652i
$736$		0			0
$737$	−23.5576	+	0.559839i	−0.867755	+	0.0206219i
$738$		0			0
$739$	25.6477	−	18.6342i	0.943468	−	0.685469i	−0.00578522	−	0.999983i	$-0.501842\pi$
$739$	25.6477	−	18.6342i	0.943468	−	0.685469i	0.949253	+	0.314514i	$0.101842\pi$
$740$		0			0
$741$	−2.50283	+	7.70291i	−0.0919437	+	0.282974i
$742$		0			0
$743$	−8.74104	−	6.35074i	−0.320678	−	0.232986i	0.415787	−	0.909462i	$-0.363506\pi$
$743$	−8.74104	−	6.35074i	−0.320678	−	0.232986i	−0.736465	+	0.676476i	$0.763506\pi$
$744$		0			0
$745$	17.9544	+	55.2580i	0.657799	+	2.02450i
$746$		0			0
$747$	−1.38873			−0.0508111
$748$		0			0
$749$	3.49535			0.127717
$750$		0			0
$751$	1.60249	+	4.93197i	0.0584758	+	0.179970i	0.976028	−	0.217646i	$-0.0698377\pi$
$751$	1.60249	+	4.93197i	0.0584758	+	0.179970i	−0.917552	+	0.397616i	$0.869838\pi$
$752$		0			0
$753$	11.4674	+	8.33156i	0.417896	+	0.303619i
$754$		0			0
$755$	12.3357	−	37.9653i	0.448942	−	1.38170i
$756$		0			0
$757$	−15.7830	+	11.4671i	−0.573645	+	0.416777i	−0.836427	−	0.548078i	$-0.815360\pi$
$757$	−15.7830	+	11.4671i	−0.573645	+	0.416777i	0.262783	+	0.964855i	$0.415360\pi$
$758$		0			0
$759$	5.19666	+	14.7885i	0.188627	+	0.536790i
$760$		0			0
$761$	34.0364	−	24.7289i	1.23382	−	0.896422i	0.236649	−	0.971595i	$-0.423951\pi$
$761$	34.0364	−	24.7289i	1.23382	−	0.896422i	0.997171	+	0.0751727i	$0.0239508\pi$
$762$		0			0
$763$	7.34952	−	22.6195i	0.266070	−	0.818880i
$764$		0			0
$765$	−15.5205	−	11.2763i	−0.561145	−	0.407696i
$766$		0			0
$767$	−3.34056	−	10.2812i	−0.120621	−	0.371232i
$768$		0			0
$769$	12.7508			0.459805			0.229902	−	0.973214i	$-0.426159\pi$
$769$	12.7508			0.459805			0.229902	+	0.973214i	$0.426159\pi$
$770$		0			0
$771$	2.92693			0.105411
$772$		0			0
$773$	5.05293	+	15.5513i	0.181741	+	0.559342i	0.999877	−	0.0156833i	$-0.00499237\pi$
$773$	5.05293	+	15.5513i	0.181741	+	0.559342i	−0.818136	+	0.575025i	$0.804992\pi$
$774$		0			0
$775$	−16.6421	−	12.0912i	−0.597801	−	0.434328i
$776$		0			0
$777$	−6.60214	+	20.3193i	−0.236850	+	0.728950i
$778$		0			0
$779$	−20.1411	+	14.6334i	−0.721630	+	0.524295i
$780$		0			0
$781$	3.74125	+	2.58464i	0.133872	+	0.0924856i
$782$		0			0
$783$	−1.57532	+	1.14454i	−0.0562973	+	0.0409024i
$784$		0			0
$785$	−1.05706	+	3.25329i	−0.0377280	+	0.116115i
$786$		0			0
$787$	17.8334	+	12.9567i	0.635691	+	0.461857i	0.858367	−	0.513036i	$-0.171479\pi$
$787$	17.8334	+	12.9567i	0.635691	+	0.461857i	−0.222676	+	0.974893i	$0.571479\pi$
$788$		0			0
$789$	−7.52827	−	23.1696i	−0.268014	−	0.824861i
$790$		0			0
$791$	−16.8150			−0.597872
$792$		0			0
$793$	−2.01892			−0.0716939
$794$		0			0
$795$	−0.504902	−	1.55393i	−0.0179070	−	0.0551122i
$796$		0			0
$797$	−42.4546	−	30.8451i	−1.50382	−	1.09259i	−0.968829	−	0.247729i	$-0.920316\pi$
$797$	−42.4546	−	30.8451i	−1.50382	−	1.09259i	−0.534989	−	0.844859i	$-0.679684\pi$
$798$		0			0
$799$	−1.14419	+	3.52145i	−0.0404785	+	0.124580i
$800$		0			0
$801$	16.9886	−	12.3429i	0.600261	−	0.436115i
$802$		0			0
$803$	−7.05726	+	23.6149i	−0.249045	+	0.833353i
$804$		0			0
$805$	32.8768	−	23.8864i	1.15875	−	0.841883i
$806$		0			0
$807$	1.04736	−	3.22345i	0.0368689	−	0.113471i
$808$		0			0
$809$	−0.447482	−	0.325115i	−0.0157326	−	0.0114304i	0.579891	−	0.814694i	$-0.303095\pi$
$809$	−0.447482	−	0.325115i	−0.0157326	−	0.0114304i	−0.595624	+	0.803264i	$0.703095\pi$
$810$		0			0
$811$	11.9027	+	36.6328i	0.417961	+	1.28635i	0.909575	+	0.415539i	$0.136407\pi$
$811$	11.9027	+	36.6328i	0.417961	+	1.28635i	−0.491614	+	0.870813i	$0.663593\pi$
$812$		0			0
$813$	−19.3367			−0.678167
$814$		0			0
$815$	73.5775			2.57731
$816$		0			0
$817$	−11.2910	−	34.7503i	−0.395024	−	1.21576i
$818$		0			0
$819$	4.35246	+	3.16224i	0.152087	+	0.110498i
$820$		0			0
$821$	−15.2865	+	47.0471i	−0.533503	+	1.64195i	0.213358	+	0.976974i	$0.431560\pi$
$821$	−15.2865	+	47.0471i	−0.533503	+	1.64195i	−0.746861	+	0.664980i	$0.768440\pi$
$822$		0			0
$823$	31.1304	−	22.6175i	1.08514	−	0.788398i	0.106565	−	0.994306i	$-0.466015\pi$
$823$	31.1304	−	22.6175i	1.08514	−	0.788398i	0.978571	+	0.205908i	$0.0660147\pi$
$824$		0			0
$825$	−12.4818	+	9.52974i	−0.434561	+	0.331783i
$826$		0			0
$827$	−37.1586	+	26.9973i	−1.29213	+	0.938788i	−0.999846	−	0.0175428i	$-0.994416\pi$
$827$	−37.1586	+	26.9973i	−1.29213	+	0.938788i	−0.292285	+	0.956331i	$0.594416\pi$
$828$		0			0
$829$	−5.65212	+	17.3954i	−0.196306	+	0.604168i	0.803653	+	0.595099i	$0.202887\pi$
$829$	−5.65212	+	17.3954i	−0.196306	+	0.604168i	−0.999959	+	0.00906965i	$0.997113\pi$
$830$		0			0
$831$	−13.4199	−	9.75014i	−0.465532	−	0.338229i
$832$		0			0
$833$	0.549853	+	1.69227i	0.0190513	+	0.0586338i
$834$		0			0
$835$	51.3073			1.77556
$836$		0			0
$837$	−19.3677			−0.669445
$838$		0			0
$839$	8.42059	+	25.9159i	0.290711	+	0.894716i	0.984629	+	0.174662i	$0.0558832\pi$
$839$	8.42059	+	25.9159i	0.290711	+	0.894716i	−0.693918	+	0.720054i	$0.744117\pi$
$840$		0			0
$841$	23.3274	+	16.9483i	0.804393	+	0.584426i
$842$		0			0
$843$	−7.39220	+	22.7509i	−0.254601	+	0.783581i
$844$		0			0
$845$	−2.56853	+	1.86615i	−0.0883601	+	0.0641974i
$846$		0			0
$847$	−7.31661	+	26.7868i	−0.251402	+	0.920404i
$848$		0			0
$849$	6.42525	−	4.66822i	0.220514	−	0.160213i
$850$		0			0
$851$	14.2274	−	43.7873i	0.487708	−	1.50101i
$852$		0			0
$853$	−14.3496	−	10.4256i	−0.491322	−	0.356966i	0.314371	−	0.949300i	$-0.398207\pi$
$853$	−14.3496	−	10.4256i	−0.491322	−	0.356966i	−0.805692	+	0.592334i	$0.798207\pi$
$854$		0			0
$855$	−18.1687	−	55.9174i	−0.621355	−	1.91233i
$856$		0			0
$857$	−39.0900			−1.33529			−0.667644	−	0.744481i	$-0.732697\pi$
$857$	−39.0900			−1.33529			−0.667644	+	0.744481i	$0.732697\pi$
$858$		0			0
$859$	−15.6074			−0.532517			−0.266258	−	0.963902i	$-0.585787\pi$
$859$	−15.6074			−0.532517			−0.266258	+	0.963902i	$0.585787\pi$
$860$		0			0
$861$	−2.08320	−	6.41143i	−0.0709952	−	0.218501i
$862$		0			0
$863$	32.1076	+	23.3275i	1.09296	+	0.794079i	0.979896	−	0.199510i	$-0.0639349\pi$
$863$	32.1076	+	23.3275i	1.09296	+	0.794079i	0.113060	+	0.993588i	$0.463935\pi$
$864$		0			0
$865$	20.4579	−	62.9630i	0.695590	−	2.14081i
$866$		0			0
$867$	6.75743	−	4.90956i	0.229494	−	0.166737i
$868$		0			0
$869$	37.3431	−	28.5111i	1.26678	−	0.967172i
$870$		0			0
$871$	−5.74797	+	4.17615i	−0.194763	+	0.141503i
$872$		0			0
$873$	−12.4815	+	38.4140i	−0.422434	+	1.30012i
$874$		0			0
$875$	0.517743	+	0.376163i	0.0175029	+	0.0127166i
$876$		0			0
$877$	5.54258	+	17.0583i	0.187160	+	0.576019i	0.999979	−	0.00649761i	$-0.00206827\pi$
$877$	5.54258	+	17.0583i	0.187160	+	0.576019i	−0.812819	+	0.582516i	$0.802068\pi$
$878$		0			0
$879$	16.6616			0.561981
$880$		0			0
$881$	−42.5530			−1.43365			−0.716823	−	0.697255i	$-0.754404\pi$
$881$	−42.5530			−1.43365			−0.716823	+	0.697255i	$0.754404\pi$
$882$		0			0
$883$	−1.51108	−	4.65063i	−0.0508519	−	0.156506i	0.922406	−	0.386222i	$-0.126220\pi$
$883$	−1.51108	−	4.65063i	−0.0508519	−	0.156506i	−0.973258	+	0.229716i	$0.926220\pi$
$884$		0			0
$885$	−25.8810	−	18.8037i	−0.869981	−	0.632078i
$886$		0			0
$887$	2.69486	−	8.29393i	0.0904846	−	0.278483i	−0.895566	−	0.444929i	$-0.853229\pi$
$887$	2.69486	−	8.29393i	0.0904846	−	0.278483i	0.986051	+	0.166446i	$0.0532290\pi$
$888$		0			0
$889$	−0.375730	+	0.272984i	−0.0126016	+	0.00915559i
$890$		0			0
$891$	1.83819	−	6.15094i	0.0615817	−	0.206064i
$892$		0			0
$893$	−9.18047	+	6.67000i	−0.307213	+	0.223203i
$894$		0			0
$895$	−17.5063	+	53.8788i	−0.585171	+	1.80097i
$896$		0			0
$897$	3.82357	+	2.77799i	0.127665	+	0.0927543i
$898$		0			0
$899$	−0.509464	−	1.56797i	−0.0169916	−	0.0522947i
$900$		0			0
$901$	1.56543			0.0521522
$902$		0			0
$903$	9.89406			0.329254
$904$		0			0
$905$	26.2561	+	80.8079i	0.872781	+	2.68615i
$906$		0			0
$907$	19.7709	+	14.3644i	0.656483	+	0.476963i	0.865473	−	0.500955i	$-0.167018\pi$
$907$	19.7709	+	14.3644i	0.656483	+	0.476963i	−0.208991	+	0.977918i	$0.567018\pi$
$908$		0			0
$909$	2.73523	−	8.41819i	0.0907220	−	0.279214i
$910$		0			0
$911$	−1.01430	+	0.736933i	−0.0336053	+	0.0244157i	−0.604461	−	0.796635i	$-0.706612\pi$
$911$	−1.01430	+	0.736933i	−0.0336053	+	0.0244157i	0.570856	+	0.821050i	$0.306612\pi$
$912$		0			0
$913$	−1.77812	−	1.22841i	−0.0588471	−	0.0406545i
$914$		0			0
$915$	−4.83351	+	3.51175i	−0.159791	+	0.116095i
$916$		0			0
$917$	−1.45292	+	4.47162i	−0.0479795	+	0.147666i
$918$		0			0
$919$	−4.06610	−	2.95419i	−0.134128	−	0.0974499i	0.518698	−	0.854957i	$-0.326417\pi$
$919$	−4.06610	−	2.95419i	−0.134128	−	0.0974499i	−0.652826	+	0.757508i	$0.726417\pi$
$920$		0			0
$921$	6.56624	+	20.2088i	0.216365	+	0.665903i
$922$		0			0
$923$	1.37104			0.0451283
$924$		0			0
$925$	46.1255			1.51660
$926$		0			0
$927$	−2.26716	−	6.97759i	−0.0744632	−	0.229174i
$928$		0			0
$929$	−1.32828	−	0.965054i	−0.0435796	−	0.0316624i	0.565782	−	0.824555i	$-0.308574\pi$
$929$	−1.32828	−	0.965054i	−0.0435796	−	0.0316624i	−0.609362	+	0.792892i	$0.708574\pi$
$930$		0			0
$931$	−1.68515	+	5.18637i	−0.0552286	+	0.169976i
$932$		0			0
$933$	−4.09207	+	2.97306i	−0.133968	+	0.0973337i
$934$		0			0
$935$	−9.89775	−	28.1668i	−0.323691	−	0.921153i
$936$		0			0
$937$	28.4382	−	20.6616i	0.929036	−	0.674984i	−0.0167208	−	0.999860i	$-0.505323\pi$
$937$	28.4382	−	20.6616i	0.929036	−	0.674984i	0.945757	+	0.324876i	$0.105323\pi$
$938$		0			0
$939$	−2.13000	+	6.55548i	−0.0695101	+	0.213930i
$940$		0			0
$941$	−20.0380	−	14.5584i	−0.653219	−	0.474591i	0.211147	−	0.977454i	$-0.432280\pi$
$941$	−20.0380	−	14.5584i	−0.653219	−	0.474591i	−0.864366	+	0.502863i	$0.832280\pi$
$942$		0			0
$943$	4.48922	+	13.8164i	0.146189	+	0.449924i
$944$		0			0
$945$	38.3317			1.24693
$946$		0			0
$947$	52.3126			1.69993			0.849965	−	0.526839i	$-0.176623\pi$
$947$	52.3126			1.69993			0.849965	+	0.526839i	$0.176623\pi$
$948$		0			0
$949$	2.29640	+	7.06760i	0.0745444	+	0.229424i
$950$		0			0
$951$	0.615656	+	0.447300i	0.0199640	+	0.0145047i
$952$		0			0
$953$	2.20186	−	6.77662i	0.0713252	−	0.219516i	−0.909039	−	0.416710i	$-0.863183\pi$
$953$	2.20186	−	6.77662i	0.0713252	−	0.219516i	0.980364	+	0.197194i	$0.0631829\pi$
$954$		0			0
$955$	55.9583	−	40.6561i	1.81077	−	1.31560i
$956$		0			0
$957$	−1.25825	+	0.0299019i	−0.0406733	+	0.000966590i
$958$		0			0
$959$	29.2748	−	21.2694i	0.945332	−	0.686824i
$960$		0			0
$961$	−4.51219	+	13.8871i	−0.145554	+	0.447970i
$962$		0			0
$963$	−2.38737	−	1.73453i	−0.0769320	−	0.0558944i
$964$		0			0
$965$	18.6522	+	57.4056i	0.600436	+	1.84795i
$966$		0			0
$967$	0.888668			0.0285777			0.0142888	−	0.999898i	$-0.495452\pi$
$967$	0.888668			0.0285777			0.0142888	+	0.999898i	$0.495452\pi$
$968$		0			0
$969$	−22.9639			−0.737707
$970$		0			0
$971$	−11.3164	−	34.8282i	−0.363159	−	1.11769i	−0.951126	−	0.308804i	$-0.900071\pi$
$971$	−11.3164	−	34.8282i	−0.363159	−	1.11769i	0.587966	−	0.808885i	$-0.299929\pi$
$972$		0			0
$973$	32.7779	+	23.8146i	1.05081	+	0.763460i
$974$		0			0
$975$	−1.46316	+	4.50315i	−0.0468587	+	0.144216i
$976$		0			0
$977$	−5.66562	+	4.11631i	−0.181259	+	0.131692i	−0.674715	−	0.738078i	$-0.735733\pi$
$977$	−5.66562	+	4.11631i	−0.181259	+	0.131692i	0.493456	+	0.869771i	$0.335733\pi$
$978$		0			0
$979$	32.6699	−	0.776391i	1.04414	−	0.0248136i
$980$		0			0
$981$	−16.2445	+	11.8023i	−0.518647	+	0.376819i
$982$		0			0
$983$	−9.33831	+	28.7404i	−0.297846	+	0.916676i	0.684405	+	0.729102i	$0.260062\pi$
$983$	−9.33831	+	28.7404i	−0.297846	+	0.916676i	−0.982251	+	0.187573i	$0.939938\pi$
$984$		0			0
$985$	−28.8304	−	20.9465i	−0.918615	−	0.667413i
$986$		0			0
$987$	−0.949538	−	2.92238i	−0.0302241	−	0.0930203i
$988$		0			0
$989$	−21.3213			−0.677979
$990$		0			0
$991$	0.795394			0.0252665			0.0126333	−	0.999920i	$-0.495979\pi$
$991$	0.795394			0.0252665			0.0126333	+	0.999920i	$0.495979\pi$
$992$		0			0
$993$	−8.04786	−	24.7688i	−0.255391	−	0.786013i
$994$		0			0
$995$	0.997358	+	0.724623i	0.0316184	+	0.0229721i
$996$		0			0
$997$	−6.41600	+	19.7464i	−0.203197	+	0.625376i	0.796586	+	0.604526i	$0.206637\pi$
$997$	−6.41600	+	19.7464i	−0.203197	+	0.625376i	−0.999783	+	0.0208502i	$0.993363\pi$
$998$		0			0
$999$	35.1339	−	25.5263i	1.11159	−	0.807616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.157.4	✓	28
11.2	odd	10		6292.2.a.y.1.9		14
11.4	even	5	inner	572.2.n.b.521.4	yes	28
11.9	even	5		6292.2.a.z.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.157.4	✓	28	1.1	even	1	trivial
572.2.n.b.521.4	yes	28	11.4	even	5	inner
6292.2.a.y.1.9		14	11.2	odd	10
6292.2.a.z.1.9		14	11.9	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.288033 + 0.886474i) q^{3} +(-2.56853 - 1.86615i) q^{5} +(-0.780072 + 2.40081i) q^{7} +(1.72418 - 1.25269i) q^{9} +O(q^{10})\)	\(q+(0.288033 + 0.886474i) q^{3} +(-2.56853 - 1.86615i) q^{5} +(-0.780072 + 2.40081i) q^{7} +(1.72418 - 1.25269i) q^{9} +(3.31569 - 0.0787964i) q^{11} +(0.809017 - 0.587785i) q^{13} +(0.914469 - 2.81445i) q^{15} +(2.29379 + 1.66654i) q^{17} +(2.68517 + 8.26410i) q^{19} -2.35295 q^{21} +5.07051 q^{23} +(1.56976 + 4.83122i) q^{25} +(3.86933 + 2.81124i) q^{27} +(-0.125810 + 0.387203i) q^{29} +(-3.27610 + 2.38022i) q^{31} +(1.02488 + 2.91658i) q^{33} +(6.48391 - 4.71084i) q^{35} +(2.80590 - 8.63568i) q^{37} +(0.754080 + 0.547871i) q^{39} +(0.885358 + 2.72485i) q^{41} -4.20497 q^{43} -6.76630 q^{45} +(0.403553 + 1.24201i) q^{47} +(0.507721 + 0.368881i) q^{49} +(-0.816655 + 2.51341i) q^{51} +(0.446679 - 0.324531i) q^{53} +(-8.66349 - 5.98517i) q^{55} +(-6.55249 + 4.76066i) q^{57} +(3.34056 - 10.2812i) q^{59} +(-1.63334 - 1.18669i) q^{61} +(1.66249 + 5.11662i) q^{63} -3.17488 q^{65} -7.10489 q^{67} +(1.46047 + 4.49488i) q^{69} +(1.10920 + 0.805877i) q^{71} +(-2.29640 + 7.06760i) q^{73} +(-3.83061 + 2.78310i) q^{75} +(-2.39730 + 8.02182i) q^{77} +(11.4604 - 8.32649i) q^{79} +(0.598140 - 1.84089i) q^{81} +(-0.527172 - 0.383013i) q^{83} +(-2.78167 - 8.56111i) q^{85} -0.379483 q^{87} +9.85313 q^{89} +(0.780072 + 2.40081i) q^{91} +(-3.05363 - 2.21859i) q^{93} +(8.52508 - 26.2375i) q^{95} +(-15.3326 + 11.1398i) q^{97} +(5.61813 - 4.28938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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