LMFDB - Embedded newform 684.2.z.b.467.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(467,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("684.467");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.z (of order $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			467.13
Character	$\chi$	$=$	684.467
Dual form			684.2.z.b.539.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.472184 + 1.33306i) q^{2} +(-1.55408 - 1.25890i) q^{4} +(-0.367115 - 0.211954i) q^{5} +1.57832i q^{7} +(2.41200 - 1.47725i) q^{8} +(0.455893 - 0.389305i) q^{10} +3.34264 q^{11} +(-3.20044 - 5.54332i) q^{13} +(-2.10399 - 0.745256i) q^{14} +(0.830358 + 3.91286i) q^{16} +(6.19487 + 3.57661i) q^{17} +(1.01008 - 4.24025i) q^{19} +(0.303700 + 0.791555i) q^{20} +(-1.57834 + 4.45593i) q^{22} +(1.83920 + 3.18559i) q^{23} +(-2.41015 - 4.17450i) q^{25} +(8.90077 - 1.64890i) q^{26} +(1.98694 - 2.45284i) q^{28} +(-0.235912 + 0.136204i) q^{29} +8.66745i q^{31} +(-5.60815 - 0.740676i) q^{32} +(-7.69295 + 6.56930i) q^{34} +(0.334531 - 0.579425i) q^{35} +8.28095 q^{37} +(5.17556 + 3.34867i) q^{38} +(-1.19859 + 0.0310900i) q^{40} +(5.15907 + 2.97859i) q^{41} +(8.84091 + 5.10430i) q^{43} +(-5.19474 - 4.20804i) q^{44} +(-5.11501 + 0.947576i) q^{46} +(1.72091 + 2.98070i) q^{47} +4.50892 q^{49} +(6.70289 - 1.24174i) q^{50} +(-2.00472 + 12.6438i) q^{52} +(-1.31406 + 0.758673i) q^{53} +(-1.22713 - 0.708486i) q^{55} +(2.33157 + 3.80689i) q^{56} +(-0.0701736 - 0.378797i) q^{58} +(7.16435 - 12.4090i) q^{59} +(0.562485 + 0.974253i) q^{61} +(-11.5542 - 4.09263i) q^{62} +(3.63544 - 7.12626i) q^{64} +2.71339i q^{65} +(-6.64652 + 3.83737i) q^{67} +(-5.12477 - 13.3571i) q^{68} +(0.614446 + 0.719544i) q^{70} +(-3.51052 + 6.08040i) q^{71} +(2.01357 - 3.48761i) q^{73} +(-3.91013 + 11.0390i) q^{74} +(-6.90779 + 5.31813i) q^{76} +5.27574i q^{77} +(-10.7532 - 6.20835i) q^{79} +(0.524511 - 1.61247i) q^{80} +(-6.40666 + 5.47089i) q^{82} -13.3559 q^{83} +(-1.51616 - 2.62606i) q^{85} +(-10.9789 + 9.37527i) q^{86} +(8.06243 - 4.93792i) q^{88} +(-4.41659 + 2.54992i) q^{89} +(8.74912 - 5.05131i) q^{91} +(1.15205 - 7.26603i) q^{92} +(-4.78603 + 0.886631i) q^{94} +(-1.26955 + 1.34257i) q^{95} +(7.15088 - 12.3857i) q^{97} +(-2.12904 + 6.01064i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{4} + 12 q^{10} + 4 q^{13} + 20 q^{16} + 28 q^{25} - 20 q^{34} - 40 q^{37} - 40 q^{40} - 32 q^{46} - 32 q^{49} - 8 q^{52} + 96 q^{58} + 28 q^{61} + 48 q^{64} - 72 q^{70} - 20 q^{73} - 36 q^{76}+ \cdots - 112 q^{94}+O(q^{100}) $ 72 * q - 12 * q^4 + 12 * q^10 + 4 * q^13 + 20 * q^16 + 28 * q^25 - 20 * q^34 - 40 * q^37 - 40 * q^40 - 32 * q^46 - 32 * q^49 - 8 * q^52 + 96 * q^58 + 28 * q^61 + 48 * q^64 - 72 * q^70 - 20 * q^73 - 36 * q^76 - 4 * q^82 + 48 * q^85 - 56 * q^88 - 112 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.472184	+	1.33306i	−0.333884	+	0.942614i
$2$	−0.472184	+	1.33306i	−0.333884	+	0.942614i
$3$		0			0
$3$		0			0
$4$	−1.55408	−	1.25890i	−0.777042	−	0.629448i
$5$	−0.367115	−	0.211954i	−0.164179	−	0.0947888i	0.415659	−	0.909520i	$-0.363551\pi$
$5$	−0.367115	−	0.211954i	−0.164179	−	0.0947888i	−0.579838	+	0.814732i	$0.696884\pi$
$6$		0			0
$7$			1.57832i			0.596548i	0.954480	+	0.298274i	$0.0964109\pi$
$7$			1.57832i			0.596548i	−0.954480	+	0.298274i	$0.903589\pi$
$8$	2.41200	−	1.47725i	0.852769	−	0.522288i
$9$		0			0
$10$	0.455893	−	0.389305i	0.144166	−	0.123109i
$11$	3.34264			1.00784			0.503922	−	0.863749i	$-0.331890\pi$
$11$	3.34264			1.00784			0.503922	+	0.863749i	$0.331890\pi$
$12$		0			0
$13$	−3.20044	−	5.54332i	−0.887642	−	1.53744i	−0.842655	−	0.538454i	$-0.819009\pi$
$13$	−3.20044	−	5.54332i	−0.887642	−	1.53744i	−0.0449872	−	0.998988i	$-0.514325\pi$
$14$	−2.10399	−	0.745256i	−0.562314	−	0.199178i
$15$		0			0
$16$	0.830358	+	3.91286i	0.207590	+	0.978216i
$17$	6.19487	+	3.57661i	1.50248	+	0.867456i	0.999996	+	0.00286757i	$0.000912778\pi$
$17$	6.19487	+	3.57661i	1.50248	+	0.867456i	0.502481	+	0.864588i	$0.332421\pi$
$18$		0			0
$19$	1.01008	−	4.24025i	0.231728	−	0.972781i
$19$	1.01008	−	4.24025i	0.231728	−	0.972781i
$20$	0.303700	+	0.791555i	0.0679094	+	0.176997i
$21$		0			0
$22$	−1.57834	+	4.45593i	−0.336503	+	0.950007i
$23$	1.83920	+	3.18559i	0.383500	+	0.664241i	0.991560	−	0.129650i	$-0.0413854\pi$
$23$	1.83920	+	3.18559i	0.383500	+	0.664241i	−0.608060	+	0.793891i	$0.708052\pi$
$24$		0			0
$25$	−2.41015	−	4.17450i	−0.482030	−	0.834901i
$26$	8.90077	−	1.64890i	1.74558	−	0.323376i
$27$		0			0
$28$	1.98694	−	2.45284i	0.375496	−	0.463543i
$29$	−0.235912	+	0.136204i	−0.0438077	+	0.0252924i	−0.521744	−	0.853102i	$-0.674718\pi$
$29$	−0.235912	+	0.136204i	−0.0438077	+	0.0252924i	0.477936	+	0.878395i	$0.341385\pi$
$30$		0			0
$31$			8.66745i			1.55672i	0.627818	+	0.778360i	$0.283948\pi$
$31$			8.66745i			1.55672i	−0.627818	+	0.778360i	$0.716052\pi$
$32$	−5.60815	−	0.740676i	−0.991391	−	0.130934i
$33$		0			0
$34$	−7.69295	+	6.56930i	−1.31933	+	1.12663i
$35$	0.334531	−	0.579425i	0.0565460	−	0.0979406i
$36$		0			0
$37$	8.28095			1.36138			0.680690	−	0.732571i	$-0.261680\pi$
$37$	8.28095			1.36138			0.680690	+	0.732571i	$0.261680\pi$
$38$	5.17556	+	3.34867i	0.839586	+	0.543226i
$39$		0			0
$40$	−1.19859	+	0.0310900i	−0.189514	+	0.00491576i
$41$	5.15907	+	2.97859i	0.805711	+	0.465178i	0.845464	−	0.534032i	$-0.179324\pi$
$41$	5.15907	+	2.97859i	0.805711	+	0.465178i	−0.0397529	+	0.999210i	$0.512657\pi$
$42$		0			0
$43$	8.84091	+	5.10430i	1.34823	+	0.778399i	0.987998	−	0.154466i	$-0.0493657\pi$
$43$	8.84091	+	5.10430i	1.34823	+	0.778399i	0.360228	+	0.932864i	$0.382699\pi$
$44$	−5.19474	−	4.20804i	−0.783137	−	0.634385i
$45$		0			0
$46$	−5.11501	+	0.947576i	−0.754167	+	0.139712i
$47$	1.72091	+	2.98070i	0.251020	+	0.434780i	0.963807	−	0.266601i	$-0.0859005\pi$
$47$	1.72091	+	2.98070i	0.251020	+	0.434780i	−0.712787	+	0.701381i	$0.752567\pi$
$48$		0			0
$49$	4.50892			0.644131
$50$	6.70289	−	1.24174i	0.947932	−	0.175608i
$51$		0			0
$52$	−2.00472	+	12.6438i	−0.278004	+	1.75338i
$53$	−1.31406	+	0.758673i	−0.180500	+	0.104212i	−0.587528	−	0.809204i	$-0.699899\pi$
$53$	−1.31406	+	0.758673i	−0.180500	+	0.104212i	0.407028	+	0.913416i	$0.366565\pi$
$54$		0			0
$55$	−1.22713	−	0.708486i	−0.165467	−	0.0955323i
$56$	2.33157	+	3.80689i	0.311570	+	0.508718i
$57$		0			0
$58$	−0.0701736	−	0.378797i	−0.00921425	−	0.0497385i
$59$	7.16435	−	12.4090i	0.932719	−	1.61552i	0.154067	−	0.988060i	$-0.450763\pi$
$59$	7.16435	−	12.4090i	0.932719	−	1.61552i	0.778652	−	0.627456i	$-0.215904\pi$
$60$		0			0
$61$	0.562485	+	0.974253i	0.0720188	+	0.124740i	0.899786	−	0.436331i	$-0.143722\pi$
$61$	0.562485	+	0.974253i	0.0720188	+	0.124740i	−0.827767	+	0.561072i	$0.810389\pi$
$62$	−11.5542	−	4.09263i	−1.46739	−	0.519765i
$63$		0			0
$64$	3.63544	−	7.12626i	0.454431	−	0.890782i
$65$			2.71339i			0.336554i
$66$		0			0
$67$	−6.64652	+	3.83737i	−0.812001	+	0.468809i	−0.847650	−	0.530555i	$-0.821983\pi$
$67$	−6.64652	+	3.83737i	−0.812001	+	0.468809i	0.0356490	+	0.999364i	$0.488650\pi$
$68$	−5.12477	−	13.3571i	−0.621470	−	1.61978i
$69$		0			0
$70$	0.614446	+	0.719544i	0.0734404	+	0.0860019i
$71$	−3.51052	+	6.08040i	−0.416622	+	0.721610i	−0.995597	−	0.0937347i	$-0.970119\pi$
$71$	−3.51052	+	6.08040i	−0.416622	+	0.721610i	0.578975	+	0.815345i	$0.303453\pi$
$72$		0			0
$73$	2.01357	−	3.48761i	0.235671	−	0.408193i	−0.723797	−	0.690013i	$-0.757605\pi$
$73$	2.01357	−	3.48761i	0.235671	−	0.408193i	0.959467	+	0.281820i	$0.0909381\pi$
$74$	−3.91013	+	11.0390i	−0.454544	+	1.28326i
$75$		0			0
$76$	−6.90779	+	5.31813i	−0.792377	+	0.610031i
$77$			5.27574i			0.601227i
$78$		0			0
$79$	−10.7532	−	6.20835i	−1.20983	−	0.698494i	−0.247105	−	0.968989i	$-0.579479\pi$
$79$	−10.7532	−	6.20835i	−1.20983	−	0.698494i	−0.962721	+	0.270495i	$0.912813\pi$
$80$	0.524511	−	1.61247i	0.0586421	−	0.180280i
$81$		0			0
$82$	−6.40666	+	5.47089i	−0.707498	+	0.604159i
$83$	−13.3559			−1.46600			−0.733000	−	0.680229i	$-0.761880\pi$
$83$	−13.3559			−1.46600			−0.733000	+	0.680229i	$0.761880\pi$
$84$		0			0
$85$	−1.51616	−	2.62606i	−0.164450	−	0.284836i
$86$	−10.9789	+	9.37527i	−1.18388	+	1.01096i
$87$		0			0
$88$	8.06243	−	4.93792i	0.859458	−	0.526385i
$89$	−4.41659	+	2.54992i	−0.468157	+	0.270291i	−0.715468	−	0.698645i	$-0.753787\pi$
$89$	−4.41659	+	2.54992i	−0.468157	+	0.270291i	0.247311	+	0.968936i	$0.420453\pi$
$90$		0			0
$91$	8.74912	−	5.05131i	0.917157	−	0.529521i
$92$	1.15205	−	7.26603i	0.120110	−	0.757536i
$93$		0			0
$94$	−4.78603	+	0.886631i	−0.493642	+	0.0914491i
$95$	−1.26955	+	1.34257i	−0.130254	+	0.137745i
$96$		0			0
$97$	7.15088	−	12.3857i	0.726062	−	1.25758i	−0.232473	−	0.972603i	$-0.574682\pi$
$97$	7.15088	−	12.3857i	0.726062	−	1.25758i	0.958535	−	0.284973i	$-0.0919848\pi$
$98$	−2.12904	+	6.01064i	−0.215065	+	0.607167i
$99$		0			0
$100$	−1.50969	+	9.52166i	−0.150969	+	0.952166i
$101$	10.5619	−	6.09791i	1.05095	−	0.606764i	0.128032	−	0.991770i	$-0.459134\pi$
$101$	10.5619	−	6.09791i	1.05095	−	0.606764i	0.922914	+	0.385006i	$0.125801\pi$
$102$		0			0
$103$		−	1.59364i		−	0.157026i	−0.996913	−	0.0785132i	$-0.974983\pi$
$103$		−	1.59364i		−	0.157026i	0.996913	−	0.0785132i	$-0.0250173\pi$
$104$	−15.9083	−	8.64261i	−1.55994	−	0.847478i
$105$		0			0
$106$	−0.390876	−	2.10995i	−0.0379653	−	0.204936i
$107$	3.35104			0.323958			0.161979	−	0.986794i	$-0.448212\pi$
$107$	3.35104			0.323958			0.161979	+	0.986794i	$0.448212\pi$
$108$		0			0
$109$	−0.586616	+	1.01605i	−0.0561877	+	0.0973199i	−0.892751	−	0.450550i	$-0.851228\pi$
$109$	−0.586616	+	1.01605i	−0.0561877	+	0.0973199i	0.836563	+	0.547870i	$0.184561\pi$
$110$	1.52389	−	1.30130i	0.145297	−	0.124075i
$111$		0			0
$112$	−6.17574	+	1.31057i	−0.583553	+	0.123837i
$113$		−	7.55037i		−	0.710279i	−0.934813	−	0.355140i	$-0.884433\pi$
$113$		−	7.55037i		−	0.710279i	0.934813	−	0.355140i	$-0.115567\pi$
$114$		0			0
$115$		−	1.55930i		−	0.145406i
$116$	0.538093	+	0.0853164i	0.0499607	+	0.00792143i
$117$		0			0
$118$	13.1590	+	15.4098i	1.21139	+	1.41859i
$119$	−5.64503	+	9.77747i	−0.517479	+	0.896299i
$120$		0			0
$121$	0.173233			0.0157484
$122$	−1.56433	+	0.289798i	−0.141628	+	0.0262371i
$123$		0			0
$124$	10.9114	−	13.4700i	0.979875	−	1.20964i
$125$			4.16291i			0.372342i
$126$		0			0
$127$	2.83879	−	1.63897i	0.251901	−	0.145435i	−0.368733	−	0.929535i	$-0.620208\pi$
$127$	2.83879	−	1.63897i	0.251901	−	0.145435i	0.620635	+	0.784100i	$0.286875\pi$
$128$	7.78311	+	8.21116i	0.687936	+	0.725771i
$129$		0			0
$130$	−3.61710	−	1.28122i	−0.317241	−	0.112370i
$131$	−3.52862	+	6.11175i	−0.308297	+	0.533986i	−0.977990	−	0.208652i	$-0.933092\pi$
$131$	−3.52862	+	6.11175i	−0.308297	+	0.533986i	0.669693	+	0.742638i	$0.266426\pi$
$132$		0			0
$133$	6.69246	+	1.59422i	0.580310	+	0.138237i
$134$	−1.97705	−	10.6721i	−0.170791	−	0.921932i
$135$		0			0
$136$	20.2256	−	0.524626i	1.73433	−	0.0449863i
$137$	8.54085	−	4.93106i	0.729694	−	0.421289i	−0.0886164	−	0.996066i	$-0.528245\pi$
$137$	8.54085	−	4.93106i	0.729694	−	0.421289i	0.818310	+	0.574777i	$0.194911\pi$
$138$		0			0
$139$	−7.06929	+	4.08146i	−0.599609	+	0.346185i	−0.768888	−	0.639384i	$-0.779190\pi$
$139$	−7.06929	+	4.08146i	−0.599609	+	0.346185i	0.169279	+	0.985568i	$0.445856\pi$
$140$	−1.24932	+	0.479335i	−0.105587	+	0.0405112i
$141$		0			0
$142$	−6.44791	−	7.55079i	−0.541096	−	0.633648i
$143$	−10.6979	−	18.5293i	−0.894604	−	1.54950i
$144$		0			0
$145$	0.115476			0.00958974
$146$	3.69840	+	4.33100i	0.306082	+	0.358436i
$147$		0			0
$148$	−12.8693	−	10.4249i	−1.05785	−	0.856919i
$149$	−13.5843	−	7.84293i	−1.11287	−	0.642517i	−0.173301	−	0.984869i	$-0.555443\pi$
$149$	−13.5843	−	7.84293i	−1.11287	−	0.642517i	−0.939572	+	0.342351i	$0.888777\pi$
$150$		0			0
$151$		−	18.3715i		−	1.49505i	−0.664232	−	0.747526i	$-0.731241\pi$
$151$		−	18.3715i		−	1.49505i	0.664232	−	0.747526i	$-0.268759\pi$
$152$	−3.82763	−	11.7196i	−0.310461	−	0.950586i
$153$		0			0
$154$	−7.03287	−	2.49112i	−0.566725	−	0.200740i
$155$	1.83710	−	3.18196i	0.147560	−	0.255581i
$156$		0			0
$157$	1.03762	−	1.79721i	0.0828112	−	0.143433i	−0.821645	−	0.569999i	$-0.806943\pi$
$157$	1.03762	−	1.79721i	0.0828112	−	0.143433i	0.904456	+	0.426566i	$0.140277\pi$
$158$	13.3536	−	11.4031i	1.06235	−	0.907183i
$159$		0			0
$160$	1.90185	+	1.46059i	0.150354	+	0.115469i
$161$	−5.02787	+	2.90284i	−0.396251	+	0.228776i
$162$		0			0
$163$			3.43636i			0.269157i	0.990903	+	0.134578i	$0.0429680\pi$
$163$			3.43636i			0.269157i	−0.990903	+	0.134578i	$0.957032\pi$
$164$	−4.26789	−	11.1237i	−0.333267	−	0.868617i
$165$		0			0
$166$	6.30644	−	17.8042i	0.489474	−	1.38187i
$167$	3.89876	+	6.75286i	0.301695	+	0.522552i	0.976520	−	0.215426i	$-0.0691141\pi$
$167$	3.89876	+	6.75286i	0.301695	+	0.522552i	−0.674825	+	0.737978i	$0.735781\pi$
$168$		0			0
$169$	−13.9856	+	24.2238i	−1.07582	+	1.86337i
$170$	4.21659	−	0.781140i	0.323398	−	0.0599107i
$171$		0			0
$172$	−7.31373	−	19.0623i	−0.557667	−	1.45349i
$173$	12.8677	+	7.42919i	0.978316	+	0.564831i	0.901761	−	0.432235i	$-0.142275\pi$
$173$	12.8677	+	7.42919i	0.978316	+	0.564831i	0.0765545	+	0.997065i	$0.475608\pi$
$174$		0			0
$175$	6.58869	−	3.80398i	0.498058	−	0.287554i
$176$	2.77559	+	13.0793i	0.209218	+	0.985889i
$177$		0			0
$178$	−1.31375	−	7.09160i	−0.0984694	−	0.531538i
$179$	−2.28060			−0.170460			−0.0852300	−	0.996361i	$-0.527162\pi$
$179$	−2.28060			−0.170460			−0.0852300	+	0.996361i	$0.527162\pi$
$180$		0			0
$181$	−5.70296	−	9.87782i	−0.423898	−	0.734213i	0.572419	−	0.819961i	$-0.306005\pi$
$181$	−5.70296	−	9.87782i	−0.423898	−	0.734213i	−0.996317	+	0.0857487i	$0.972672\pi$
$182$	2.60249	+	14.0482i	0.192909	+	1.04132i
$183$		0			0
$184$	9.14206	+	4.96666i	0.673962	+	0.366147i
$185$	−3.04007	−	1.75518i	−0.223510	−	0.129044i
$186$		0			0
$187$	20.7072	+	11.9553i	1.51426	+	0.874259i
$188$	1.07796	−	6.79871i	0.0786181	−	0.495847i
$189$		0			0
$190$	−1.19026	−	2.32633i	−0.0863507	−	0.168770i
$191$	−5.64189			−0.408233			−0.204116	−	0.978947i	$-0.565432\pi$
$191$	−5.64189			−0.408233			−0.204116	+	0.978947i	$0.565432\pi$
$192$		0			0
$193$	−0.536055	+	0.928475i	−0.0385861	+	0.0668331i	−0.884674	−	0.466211i	$-0.845619\pi$
$193$	−0.536055	+	0.928475i	−0.0385861	+	0.0668331i	0.846087	+	0.533044i	$0.178952\pi$
$194$	13.1343	+	15.3809i	0.942988	+	1.10428i
$195$		0			0
$196$	−7.00724	−	5.67626i	−0.500517	−	0.405447i
$197$			23.1797i			1.65148i	0.564048	+	0.825742i	$0.309243\pi$
$197$			23.1797i			1.65148i	−0.564048	+	0.825742i	$0.690757\pi$
$198$		0			0
$199$	14.1971	−	8.19667i	1.00640	−	0.581047i	0.0962663	−	0.995356i	$-0.469310\pi$
$199$	14.1971	−	8.19667i	1.00640	−	0.581047i	0.910136	+	0.414309i	$0.135977\pi$
$200$	−11.9801	−	6.50848i	−0.847119	−	0.460219i
$201$		0			0
$202$	3.14171	+	16.9589i	0.221050	+	1.19323i
$203$	−0.214973	−	0.372343i	−0.0150881	−	0.0261334i
$204$		0			0
$205$	−1.26265	−	2.18697i	−0.0881873	−	0.152745i
$206$	2.12442	+	0.752493i	0.148015	+	0.0524287i
$207$		0			0
$208$	19.0328	−	17.1258i	1.31968	−	1.18746i
$209$	3.37632	−	14.1736i	0.233545	−	0.980411i
$210$		0			0
$211$	−16.0919	−	9.29068i	−1.10781	−	0.639597i	−0.169552	−	0.985521i	$-0.554232\pi$
$211$	−16.0919	−	9.29068i	−1.10781	−	0.639597i	−0.938262	+	0.345924i	$0.887565\pi$
$212$	2.99725	+	0.475224i	0.205852	+	0.0326385i
$213$		0			0
$214$	−1.58231	+	4.46713i	−0.108164	+	0.305367i
$215$	−2.16376	−	3.74773i	−0.147567	−	0.255593i
$216$		0			0
$217$	−13.6800			−0.928658
$218$	−1.07746	−	1.26176i	−0.0729749	−	0.0854569i
$219$		0			0
$220$	1.01516	+	2.64588i	0.0684420	+	0.178385i
$221$		−	45.7869i		−	3.07996i
$222$		0			0
$223$	−0.286804	−	0.165586i	−0.0192058	−	0.0110885i	0.490366	−	0.871516i	$-0.336863\pi$
$223$	−0.286804	−	0.165586i	−0.0192058	−	0.0110885i	−0.509572	+	0.860428i	$0.670196\pi$
$224$	1.16902	−	8.85145i	0.0781086	−	0.591412i
$225$		0			0
$226$	10.0651	+	3.56517i	0.669519	+	0.237151i
$227$	19.9650			1.32513			0.662563	−	0.749006i	$-0.269469\pi$
$227$	19.9650			1.32513			0.662563	+	0.749006i	$0.269469\pi$
$228$		0			0
$229$	−2.10239			−0.138930			−0.0694650	−	0.997584i	$-0.522129\pi$
$229$	−2.10239			−0.138930			−0.0694650	+	0.997584i	$0.522129\pi$
$230$	2.07864	+	0.736278i	0.137062	+	0.0485488i
$231$		0			0
$232$	−0.367811	+	0.677024i	−0.0241479	+	0.0444488i
$233$	−4.37924	−	2.52836i	−0.286894	−	0.165638i	0.349646	−	0.936882i	$-0.386302\pi$
$233$	−4.37924	−	2.52836i	−0.286894	−	0.165638i	−0.636540	+	0.771244i	$0.719635\pi$
$234$		0			0
$235$		−	1.45902i		−	0.0951757i
$236$	−26.7557	+	10.2655i	−1.74165	+	0.668226i
$237$		0			0
$238$	−10.3684	−	12.1419i	−0.672086	−	0.787043i
$239$	−10.9317			−0.707110			−0.353555	−	0.935414i	$-0.615027\pi$
$239$	−10.9317			−0.707110			−0.353555	+	0.935414i	$0.615027\pi$
$240$		0			0
$241$	−0.384451	−	0.665889i	−0.0247647	−	0.0428937i	0.853377	−	0.521294i	$-0.174550\pi$
$241$	−0.384451	−	0.665889i	−0.0247647	−	0.0428937i	−0.878142	+	0.478400i	$0.841217\pi$
$242$	−0.0817978	+	0.230929i	−0.00525816	+	0.0148447i
$243$		0			0
$244$	0.352334	−	2.22218i	0.0225559	−	0.142261i
$245$	−1.65529	−	0.955683i	−0.105753	−	0.0610564i
$246$		0			0
$247$	−26.7378	+	7.97149i	−1.70128	+	0.507214i
$248$	12.8040	+	20.9059i	0.813056	+	1.32752i
$249$		0			0
$250$	−5.54940	−	1.96566i	−0.350975	−	0.124319i
$251$	8.07339	+	13.9835i	0.509588	+	0.882632i	0.999938	+	0.0111067i	$0.00353544\pi$
$251$	8.07339	+	13.9835i	0.509588	+	0.882632i	−0.490350	+	0.871525i	$0.663131\pi$
$252$		0			0
$253$	6.14778	+	10.6483i	0.386508	+	0.669451i
$254$	0.844417	+	4.55816i	0.0529834	+	0.286004i
$255$		0			0
$256$	−14.6210	+	6.49816i	−0.913813	+	0.406135i
$257$	−18.7642	+	10.8335i	−1.17048	+	0.675776i	−0.953793	−	0.300465i	$-0.902858\pi$
$257$	−18.7642	+	10.8335i	−1.17048	+	0.675776i	−0.216686	+	0.976241i	$0.569525\pi$
$258$		0			0
$259$			13.0700i			0.812128i
$260$	3.41587	−	4.21683i	0.211843	−	0.261517i
$261$		0			0
$262$	−6.48116	−	7.58973i	−0.400407	−	0.468895i
$263$	−9.38270	+	16.2513i	−0.578562	+	1.00210i	0.417083	+	0.908868i	$0.363052\pi$
$263$	−9.38270	+	16.2513i	−0.578562	+	1.00210i	−0.995645	+	0.0932299i	$0.970281\pi$
$264$		0			0
$265$	0.643215			0.0395124
$266$	−5.28526	+	8.16867i	−0.324060	+	0.500853i
$267$		0			0
$268$	15.1601	+	2.40368i	0.926051	+	0.146828i
$269$	−13.8440	−	7.99282i	−0.844082	−	0.487331i	0.0145675	−	0.999894i	$-0.495363\pi$
$269$	−13.8440	−	7.99282i	−0.844082	−	0.487331i	−0.858650	+	0.512563i	$0.828696\pi$
$270$		0			0
$271$	−16.2214	−	9.36544i	−0.985381	−	0.568910i	−0.0814909	−	0.996674i	$-0.525968\pi$
$271$	−16.2214	−	9.36544i	−0.985381	−	0.568910i	−0.903891	+	0.427764i	$0.859301\pi$
$272$	−8.85083	+	27.2096i	−0.536660	+	1.64982i
$273$		0			0
$274$	2.54054	+	13.7138i	0.153479	+	0.828481i
$275$	−8.05626	−	13.9539i	−0.485811	−	0.841449i
$276$		0			0
$277$	−2.24535			−0.134910			−0.0674550	−	0.997722i	$-0.521488\pi$
$277$	−2.24535			−0.134910			−0.0674550	+	0.997722i	$0.521488\pi$
$278$	−2.10281	−	11.3510i	−0.126118	−	0.680786i
$279$		0			0
$280$	−0.0490698	−	1.89176i	−0.00293248	−	0.113054i
$281$	−18.1896	+	10.5018i	−1.08510	+	0.626483i	−0.932268	−	0.361769i	$-0.882173\pi$
$281$	−18.1896	+	10.5018i	−1.08510	+	0.626483i	−0.152833	+	0.988252i	$0.548840\pi$
$282$		0			0
$283$	−2.12081	−	1.22445i	−0.126069	−	0.0727861i	0.435639	−	0.900121i	$-0.356522\pi$
$283$	−2.12081	−	1.22445i	−0.126069	−	0.0727861i	−0.561708	+	0.827335i	$0.689856\pi$
$284$	13.1102	−	5.03007i	0.777949	−	0.298480i
$285$		0			0
$286$	29.7520	−	5.51168i	1.75928	−	0.325913i
$287$	−4.70116	+	8.14265i	−0.277501	+	0.480645i
$288$		0			0
$289$	17.0843	+	29.5909i	1.00496	+	1.74064i
$290$	−0.0545258	+	0.153936i	−0.00320186	+	0.00903942i
$291$		0			0
$292$	−7.51979	+	2.88516i	−0.440063	+	0.168841i
$293$			10.6974i			0.624948i	0.949926	+	0.312474i	$0.101158\pi$
$293$			10.6974i			0.624948i	−0.949926	+	0.312474i	$0.898842\pi$
$294$		0			0
$295$	−5.26029	+	3.03703i	−0.306266	+	0.176823i
$296$	19.9736	−	12.2331i	1.16094	−	0.711033i
$297$		0			0
$298$	16.8694	−	14.4054i	0.977217	−	0.834483i
$299$	11.7725	−	20.3906i	0.680821	−	1.17922i
$300$		0			0
$301$	−8.05620	+	13.9538i	−0.464352	+	0.804281i
$302$	24.4903	+	8.67473i	1.40926	+	0.499175i
$303$		0			0
$304$	17.4303	+	0.431366i	0.999694	+	0.0247405i
$305$		−	0.476884i		−	0.0273063i
$306$		0			0
$307$	11.4535	+	6.61270i	0.653687	+	0.377406i	0.789867	−	0.613278i	$-0.210149\pi$
$307$	11.4535	+	6.61270i	0.653687	+	0.377406i	−0.136180	+	0.990684i	$0.543483\pi$
$308$	6.64162	−	8.19895i	0.378441	−	0.467179i
$309$		0			0
$310$	3.37428	+	3.95143i	0.191646	+	0.224426i
$311$	22.1322			1.25500			0.627501	−	0.778616i	$-0.284078\pi$
$311$	22.1322			1.25500			0.627501	+	0.778616i	$0.284078\pi$
$312$		0			0
$313$	3.55543	+	6.15818i	0.200965	+	0.348081i	0.948840	−	0.315759i	$-0.102259\pi$
$313$	3.55543	+	6.15818i	0.200965	+	0.348081i	−0.747875	+	0.663840i	$0.768926\pi$
$314$	1.90584	+	2.23183i	0.107553	+	0.125949i
$315$		0			0
$316$	8.89567	+	23.1854i	0.500421	+	1.30428i
$317$	−4.80972	+	2.77689i	−0.270141	+	0.155966i	−0.628952	−	0.777445i	$-0.716516\pi$
$317$	−4.80972	+	2.77689i	−0.270141	+	0.155966i	0.358811	+	0.933410i	$0.383182\pi$
$318$		0			0
$319$	−0.788567	+	0.455280i	−0.0441513	+	0.0254908i
$320$	−2.84507	+	1.84561i	−0.159044	+	0.103173i
$321$		0			0
$322$	−1.49558	−	8.07311i	−0.0833451	−	0.449897i
$323$	21.4230	−	22.6552i	1.19201	−	1.26057i
$324$		0			0
$325$	−15.4271	+	26.7205i	−0.855741	+	1.48219i
$326$	−4.58087	−	1.62259i	−0.253711	−	0.0898672i
$327$		0			0
$328$	16.8438	−	0.436907i	0.930043	−	0.0241242i
$329$	−4.70449	+	2.71614i	−0.259367	+	0.149746i
$330$		0			0
$331$		−	11.2542i		−	0.618586i	−0.950967	−	0.309293i	$-0.899908\pi$
$331$		−	11.2542i		−	0.618586i	0.950967	−	0.309293i	$-0.100092\pi$
$332$	20.7562	+	16.8137i	1.13914	+	0.922771i
$333$		0			0
$334$	−10.8429	+	2.00869i	−0.593296	+	0.109910i
$335$	3.25339			0.177751
$336$		0			0
$337$	−9.01521	+	15.6148i	−0.491090	+	0.850592i	−0.999947	−	0.0102584i	$-0.996735\pi$
$337$	−9.01521	+	15.6148i	−0.491090	+	0.850592i	0.508858	+	0.860851i	$0.330068\pi$
$338$	−25.6879	−	30.0817i	−1.39724	−	1.63623i
$339$		0			0
$340$	−0.949702	+	5.98980i	−0.0515048	+	0.324843i
$341$			28.9722i			1.56893i
$342$		0			0
$343$			18.1647i			0.980803i
$344$	28.8646	−	0.748712i	1.55627	−	0.0403678i
$345$		0			0
$346$	−15.9795	+	13.6455i	−0.859062	+	0.733586i
$347$	16.7293	−	28.9760i	0.898077	−	1.55552i	0.0681280	−	0.997677i	$-0.478297\pi$
$347$	16.7293	−	28.9760i	0.898077	−	1.55552i	0.829949	−	0.557839i	$-0.188369\pi$
$348$		0			0
$349$	−7.65195			−0.409599			−0.204800	−	0.978804i	$-0.565654\pi$
$349$	−7.65195			−0.409599			−0.204800	+	0.978804i	$0.565654\pi$
$350$	1.95985	+	10.5793i	0.104759	+	0.565486i
$351$		0			0
$352$	−18.7460	−	2.47581i	−0.999167	−	0.131961i
$353$		−	25.0814i		−	1.33495i	−0.744633	−	0.667474i	$-0.767376\pi$
$353$		−	25.0814i		−	1.33495i	0.744633	−	0.667474i	$-0.232624\pi$
$354$		0			0
$355$	2.57753	−	1.48814i	0.136801	−	0.0789822i
$356$	10.0738	+	1.59724i	0.533912	+	0.0846535i
$357$		0			0
$358$	1.07686	−	3.04017i	0.0569139	−	0.160678i
$359$	−12.7229	+	22.0368i	−0.671491	+	1.16306i	0.305991	+	0.952034i	$0.401012\pi$
$359$	−12.7229	+	22.0368i	−0.671491	+	1.16306i	−0.977481	+	0.211021i	$0.932321\pi$
$360$		0			0
$361$	−16.9595	−	8.56597i	−0.892605	−	0.450840i
$362$	15.8605	−	2.93823i	0.833612	−	0.154430i
$363$		0			0
$364$	−19.9560	−	3.16408i	−1.04598	−	0.165843i
$365$	−1.47843	+	0.853569i	−0.0773843	+	0.0446778i
$366$		0			0
$367$	−16.8899	+	9.75136i	−0.881643	+	0.509017i	−0.871200	−	0.490929i	$-0.836658\pi$
$367$	−16.8899	+	9.75136i	−0.881643	+	0.509017i	−0.0104432	+	0.999945i	$0.503324\pi$
$368$	−10.9376	+	9.84172i	−0.570161	+	0.513035i
$369$		0			0
$370$	3.77523	−	3.22381i	0.196265	−	0.167598i
$371$	−1.19743	−	2.07400i	−0.0621673	−	0.107677i
$372$		0			0
$373$	5.89241			0.305098			0.152549	−	0.988296i	$-0.451252\pi$
$373$	5.89241			0.305098			0.152549	+	0.988296i	$0.451252\pi$
$374$	−25.7147	+	21.9588i	−1.32968	+	1.13546i
$375$		0			0
$376$	8.55408	+	4.64722i	0.441143	+	0.239662i
$377$	1.51004	+	0.871823i	0.0777711	+	0.0449012i
$378$		0			0
$379$			23.7997i			1.22251i	0.791434	+	0.611255i	$0.209335\pi$
$379$			23.7997i			1.22251i	−0.791434	+	0.611255i	$0.790665\pi$
$380$	3.66315	−	0.488233i	0.187916	−	0.0250458i
$381$		0			0
$382$	2.66401	−	7.52096i	0.136303	−	0.384806i
$383$	−8.15336	+	14.1220i	−0.416617	+	0.721603i	−0.995597	−	0.0937396i	$-0.970118\pi$
$383$	−8.15336	+	14.1220i	−0.416617	+	0.721603i	0.578979	+	0.815342i	$0.303451\pi$
$384$		0			0
$385$	1.11822	−	1.93681i	0.0569896	−	0.0987088i
$386$	−0.984594	−	1.15300i	−0.0501145	−	0.0586863i
$387$		0			0
$388$	−26.7054	+	10.2462i	−1.35576	+	0.520171i
$389$	−7.32907	+	4.23144i	−0.371599	+	0.214543i	−0.674157	−	0.738588i	$-0.735493\pi$
$389$	−7.32907	+	4.23144i	−0.371599	+	0.214543i	0.302558	+	0.953131i	$0.402159\pi$
$390$		0			0
$391$			26.3124i			1.33068i
$392$	10.8755	−	6.66081i	0.549295	−	0.336422i
$393$		0			0
$394$	−30.8998	−	10.9451i	−1.55671	−	0.551405i
$395$	2.63177	+	4.55836i	0.132419	+	0.229356i
$396$		0			0
$397$	1.63514	−	2.83215i	0.0820656	−	0.142142i	−0.822071	−	0.569384i	$-0.807182\pi$
$397$	1.63514	−	2.83215i	0.0820656	−	0.142142i	0.904137	+	0.427243i	$0.140515\pi$
$398$	4.22302	+	22.7958i	0.211681	+	1.14265i
$399$		0			0
$400$	14.3330	−	12.8969i	0.716649	−	0.644846i
$401$	−2.77928	−	1.60462i	−0.138791	−	0.0801309i	0.428997	−	0.903306i	$-0.358867\pi$
$401$	−2.77928	−	1.60462i	−0.138791	−	0.0801309i	−0.567788	+	0.823175i	$0.692201\pi$
$402$		0			0
$403$	48.0465	−	27.7397i	2.39337	−	1.38181i
$404$	−24.0907	−	3.81966i	−1.19856	−	0.190035i
$405$		0			0
$406$	0.597862	−	0.110756i	0.0296714	−	0.00549674i
$407$	27.6802			1.37206
$408$		0			0
$409$	−11.7577	−	20.3650i	−0.581383	−	1.00698i	−0.995316	−	0.0966774i	$-0.969179\pi$
$409$	−11.7577	−	20.3650i	−0.581383	−	1.00698i	0.413933	−	0.910307i	$-0.364155\pi$
$410$	3.51156	−	0.650531i	0.173424	−	0.0321274i
$411$		0			0
$412$	−2.00623	+	2.47666i	−0.0988400	+	0.122016i
$413$	19.5854	+	11.3076i	0.963733	+	0.556411i
$414$		0			0
$415$	4.90315	+	2.83084i	0.240686	+	0.138960i
$416$	13.8428	+	33.4583i	0.678697	+	1.64043i
$417$		0			0
$418$	17.3000	+	11.1934i	0.846172	+	0.547487i
$419$	6.33551			0.309510			0.154755	−	0.987953i	$-0.450541\pi$
$419$	6.33551			0.309510			0.154755	+	0.987953i	$0.450541\pi$
$420$		0			0
$421$	−8.94425	+	15.4919i	−0.435916	+	0.755029i	−0.997370	−	0.0724791i	$-0.976909\pi$
$421$	−8.94425	+	15.4919i	−0.435916	+	0.755029i	0.561454	+	0.827508i	$0.310242\pi$
$422$	19.9834	−	17.0646i	0.972775	−	0.830690i
$423$		0			0
$424$	−2.04875	+	3.77111i	−0.0994963	+	0.183141i
$425$		−	34.4807i		−	1.67256i
$426$		0			0
$427$	−1.53768	+	0.887780i	−0.0744135	+	0.0429627i
$428$	−5.20780	−	4.21862i	−0.251729	−	0.203915i
$429$		0			0
$430$	6.01764	−	1.11479i	0.290196	−	0.0537600i
$431$	1.50760	+	2.61123i	0.0726184	+	0.125779i	0.900048	−	0.435791i	$-0.143531\pi$
$431$	1.50760	+	2.61123i	0.0726184	+	0.125779i	−0.827430	+	0.561569i	$0.810198\pi$
$432$		0			0
$433$	4.83380	+	8.37238i	0.232297	+	0.402351i	0.958484	−	0.285147i	$-0.0920424\pi$
$433$	4.83380	+	8.37238i	0.232297	+	0.402351i	−0.726186	+	0.687498i	$0.758709\pi$
$434$	6.45947	−	18.2362i	0.310065	−	0.875366i
$435$		0			0
$436$	2.19075	−	0.840537i	0.104918	−	0.0402544i
$437$	15.3654	−	4.58098i	0.735028	−	0.219138i
$438$		0			0
$439$	−29.5548	−	17.0635i	−1.41058	−	0.814396i	−0.415133	−	0.909761i	$-0.636265\pi$
$439$	−29.5548	−	17.0635i	−1.41058	−	0.814396i	−0.995442	+	0.0953647i	$0.969598\pi$
$440$	−4.00646	+	0.103923i	−0.191000	+	0.00495431i
$441$		0			0
$442$	61.0366	+	21.6198i	2.90321	+	1.02835i
$443$	−14.4822	−	25.0839i	−0.688070	−	1.19177i	−0.972461	−	0.233065i	$-0.925125\pi$
$443$	−14.4822	−	25.0839i	−0.688070	−	1.19177i	0.284391	−	0.958708i	$-0.408209\pi$
$444$		0			0
$445$	2.16186			0.102482
$446$	0.356160	−	0.304139i	0.0168647	−	0.0144014i
$447$		0			0
$448$	11.2475	+	5.73788i	0.531394	+	0.271090i
$449$			25.9744i			1.22581i	0.790158	+	0.612904i	$0.209999\pi$
$449$			25.9744i			1.22581i	−0.790158	+	0.612904i	$0.790001\pi$
$450$		0			0
$451$	17.2449	+	9.95635i	0.812031	+	0.468826i
$452$	−9.50514	+	11.7339i	−0.447084	+	0.551917i
$453$		0			0
$454$	−9.42716	+	26.6145i	−0.442439	+	1.24908i
$455$	−4.28258			−0.200771
$456$		0			0
$457$	35.7570			1.67264			0.836320	−	0.548242i	$-0.184703\pi$
$457$	35.7570			1.67264			0.836320	+	0.548242i	$0.184703\pi$
$458$	0.992715	−	2.80261i	0.0463865	−	0.130957i
$459$		0			0
$460$	−1.96300	+	2.42329i	−0.0915255	+	0.112987i
$461$	−31.0358	−	17.9185i	−1.44548	−	0.834548i	−0.447272	−	0.894398i	$-0.647604\pi$
$461$	−31.0358	−	17.9185i	−1.44548	−	0.834548i	−0.998207	+	0.0598505i	$0.980938\pi$
$462$		0			0
$463$		−	5.93667i		−	0.275900i	−0.990439	−	0.137950i	$-0.955949\pi$
$463$		−	5.93667i		−	0.275900i	0.990439	−	0.137950i	$-0.0440514\pi$
$464$	−0.728838	−	0.809992i	−0.0338354	−	0.0376030i
$465$		0			0
$466$	5.43826	−	4.64393i	0.251922	−	0.215126i
$467$	−21.3841			−0.989536			−0.494768	−	0.869025i	$-0.664747\pi$
$467$	−21.3841			−0.989536			−0.494768	+	0.869025i	$0.664747\pi$
$468$		0			0
$469$	−6.05658	−	10.4903i	−0.279667	−	0.484398i
$470$	1.94495	+	0.688924i	0.0897140	+	0.0317777i
$471$		0			0
$472$	−1.05088	−	40.5140i	−0.0483709	−	1.86481i
$473$	29.5520	+	17.0618i	1.35880	+	0.784504i
$474$		0			0
$475$	−20.1354	+	6.00308i	−0.923875	+	0.275440i
$476$	21.0817	−	8.08852i	0.966277	−	0.370736i
$477$		0			0
$478$	5.16175	−	14.5725i	0.236093	−	0.666532i
$479$	15.0731	+	26.1074i	0.688709	+	1.19288i	0.972256	+	0.233921i	$0.0751557\pi$
$479$	15.0731	+	26.1074i	0.688709	+	1.19288i	−0.283546	+	0.958959i	$0.591511\pi$
$480$		0			0
$481$	−26.5027	−	45.9040i	−1.20842	−	2.09304i
$482$	1.06920	−	0.198074i	0.0487008	−	0.00902200i
$483$		0			0
$484$	−0.269219	−	0.218082i	−0.0122372	−	0.00991284i
$485$	−5.25040	+	3.03132i	−0.238408	+	0.137645i
$486$		0			0
$487$		−	10.9339i		−	0.495464i	−0.968829	−	0.247732i	$-0.920315\pi$
$487$		−	10.9339i		−	0.495464i	0.968829	−	0.247732i	$-0.0796853\pi$
$488$	2.79593	+	1.51896i	0.126566	+	0.0687601i
$489$		0			0
$490$	2.05558	−	1.75534i	0.0928618	−	0.0792982i
$491$	−3.57892	+	6.19887i	−0.161514	+	0.279751i	−0.935412	−	0.353560i	$-0.884971\pi$
$491$	−3.57892	+	6.19887i	−0.161514	+	0.279751i	0.773898	+	0.633311i	$0.218304\pi$
$492$		0			0
$493$	−1.94859			−0.0877601
$494$	1.99870	−	39.4070i	0.0899258	−	1.77301i
$495$		0			0
$496$	−33.9146	+	7.19709i	−1.52281	+	0.323159i
$497$	−9.59679	−	5.54071i	−0.430475	−	0.248535i
$498$		0			0
$499$	−8.42620	−	4.86487i	−0.377209	−	0.217782i	0.299394	−	0.954129i	$-0.403215\pi$
$499$	−8.42620	−	4.86487i	−0.377209	−	0.217782i	−0.676603	+	0.736348i	$0.736549\pi$
$500$	5.24067	−	6.46951i	0.234370	−	0.289325i
$501$		0			0
$502$	−22.4530	+	4.15950i	−1.00212	+	0.185648i
$503$	1.04454	+	1.80920i	0.0465738	+	0.0806681i	0.888373	−	0.459123i	$-0.151836\pi$
$503$	1.04454	+	1.80920i	0.0465738	+	0.0806681i	−0.841799	+	0.539791i	$0.818503\pi$
$504$		0			0
$505$	−5.16991			−0.230058
$506$	−17.0976	+	3.16740i	−0.760083	+	0.140808i
$507$		0			0
$508$	−6.47501	−	1.02663i	−0.287282	−	0.0455495i
$509$	15.0261	−	8.67530i	0.666019	−	0.384526i	−0.128548	−	0.991703i	$-0.541032\pi$
$509$	15.0261	−	8.67530i	0.666019	−	0.384526i	0.794566	+	0.607177i	$0.207698\pi$
$510$		0			0
$511$	5.50455	+	3.17805i	0.243507	+	0.140589i
$512$	−1.75861	−	22.5590i	−0.0777204	−	0.996975i
$513$		0			0
$514$	−5.58155	−	30.1292i	−0.246192	−	1.32894i
$515$	−0.337780	+	0.585052i	−0.0148843	+	0.0257804i
$516$		0			0
$517$	5.75238	+	9.96341i	0.252989	+	0.438190i
$518$	−17.4230	−	6.17143i	−0.765524	−	0.271157i
$519$		0			0
$520$	4.00836	+	6.54468i	0.175778	+	0.287003i
$521$			40.6113i			1.77921i	0.456728	+	0.889606i	$0.349021\pi$
$521$			40.6113i			1.77921i	−0.456728	+	0.889606i	$0.650979\pi$
$522$		0			0
$523$	2.93364	−	1.69374i	0.128279	−	0.0740619i	−0.434487	−	0.900678i	$-0.643070\pi$
$523$	2.93364	−	1.69374i	0.128279	−	0.0740619i	0.562766	+	0.826616i	$0.309737\pi$
$524$	13.1778	−	5.05601i	0.575677	−	0.220873i
$525$		0			0
$526$	−17.2336	−	20.1813i	−0.751419	−	0.879945i
$527$	−31.0001	+	53.6938i	−1.35039	+	2.33894i
$528$		0			0
$529$	4.73469	−	8.20072i	0.205856	−	0.356553i
$530$	−0.303716	+	0.857443i	−0.0131926	+	0.0372449i
$531$		0			0
$532$	−8.39369	−	10.9027i	−0.363913	−	0.472691i
$533$		−	38.1312i		−	1.65165i
$534$		0			0
$535$	−1.23022	−	0.710268i	−0.0531870	−	0.0307075i
$536$	−10.3626	+	19.0743i	−0.447596	+	0.823885i
$537$		0			0
$538$	17.1918	−	14.6807i	0.741191	−	0.632931i
$539$	15.0717			0.649183
$540$		0			0
$541$	−2.18450	−	3.78366i	−0.0939189	−	0.162672i	0.815238	−	0.579126i	$-0.196606\pi$
$541$	−2.18450	−	3.78366i	−0.0939189	−	0.162672i	−0.909157	+	0.416454i	$0.863273\pi$
$542$	20.1442	−	17.2019i	0.865266	−	0.738884i
$543$		0			0
$544$	−32.0927	−	24.6466i	−1.37596	−	1.05671i
$545$	0.430712	−	0.248672i	0.0184497	−	0.0106519i
$546$		0			0
$547$	23.8817	−	13.7881i	1.02111	−	0.589537i	0.106683	−	0.994293i	$-0.465977\pi$
$547$	23.8817	−	13.7881i	1.02111	−	0.589537i	0.914425	+	0.404756i	$0.132644\pi$
$548$	−19.4809	−	3.08876i	−0.832182	−	0.131945i
$549$		0			0
$550$	22.4053	−	4.15068i	0.955367	−	0.176985i
$551$	0.339249	+	1.13790i	0.0144525	+	0.0484762i
$552$		0			0
$553$	9.79874	−	16.9719i	0.416685	−	0.721719i
$554$	1.06022	−	2.99318i	0.0450444	−	0.127168i
$555$		0			0
$556$	16.1244	+	2.55658i	0.683827	+	0.108423i
$557$	−19.2807	+	11.1317i	−0.816949	+	0.471666i	−0.849363	−	0.527809i	$-0.823014\pi$
$557$	−19.2807	+	11.1317i	−0.816949	+	0.471666i	0.0324144	+	0.999475i	$0.489680\pi$
$558$		0			0
$559$		−	65.3440i		−	2.76376i
$560$	2.54499	+	0.827844i	0.107545	+	0.0349828i
$561$		0			0
$562$	−5.41063	−	29.2065i	−0.228234	−	1.23200i
$563$	−24.1341			−1.01713			−0.508565	−	0.861024i	$-0.669824\pi$
$563$	−24.1341			−1.01713			−0.508565	+	0.861024i	$0.669824\pi$
$564$		0			0
$565$	−1.60033	+	2.77186i	−0.0673265	+	0.116613i
$566$	2.63368	−	2.24900i	0.110702	−	0.0945325i
$567$		0			0
$568$	0.514932	+	19.8518i	0.0216061	+	0.832964i
$569$		−	14.0617i		−	0.589498i	−0.955575	−	0.294749i	$-0.904764\pi$
$569$		−	14.0617i		−	0.589498i	0.955575	−	0.294749i	$-0.0952360\pi$
$570$		0			0
$571$			32.7376i			1.37003i	0.728531	+	0.685013i	$0.240203\pi$
$571$			32.7376i			1.37003i	−0.728531	+	0.685013i	$0.759797\pi$
$572$	−6.70105	+	42.2637i	−0.280185	+	1.76713i
$573$		0			0
$574$	−8.63481	−	10.1117i	−0.360410	−	0.422056i
$575$	8.86550	−	15.3555i	0.369717	−	0.640368i
$576$		0			0
$577$	10.7140			0.446030			0.223015	−	0.974815i	$-0.428410\pi$
$577$	10.7140			0.446030			0.223015	+	0.974815i	$0.428410\pi$
$578$	−47.5133	+	8.80202i	−1.97629	+	0.366116i
$579$		0			0
$580$	−0.179459	−	0.145372i	−0.00745163	−	0.00603625i
$581$		−	21.0798i		−	0.874539i
$582$		0			0
$583$	−4.39243	+	2.53597i	−0.181916	+	0.105029i
$584$	−0.295356	−	11.3866i	−0.0122219	−	0.471183i
$585$		0			0
$586$	−14.2602	−	5.05114i	−0.589085	−	0.208661i
$587$	7.30998	−	12.6613i	0.301715	−	0.522586i	−0.674809	−	0.737992i	$-0.735774\pi$
$587$	7.30998	−	12.6613i	0.301715	−	0.522586i	0.976525	+	0.215406i	$0.0691075\pi$
$588$		0			0
$589$	36.7522	+	8.75480i	1.51435	+	0.360735i
$590$	−1.56471	−	8.44630i	−0.0644181	−	0.347729i
$591$		0			0
$592$	6.87616	+	32.4022i	0.282608	+	1.33172i
$593$	30.2950	−	17.4908i	1.24407	−	0.718263i	0.274148	−	0.961688i	$-0.411604\pi$
$593$	30.2950	−	17.4908i	1.24407	−	0.718263i	0.969920	+	0.243425i	$0.0782710\pi$
$594$		0			0
$595$	4.14475	−	2.39297i	0.169918	−	0.0981024i
$596$	11.2378	+	29.2899i	0.460318	+	1.19976i
$597$		0			0
$598$	21.6230	+	25.3215i	0.884230	+	1.03547i
$599$	−12.3891	−	21.4585i	−0.506203	−	0.876769i	−0.999974	−	0.00717732i	$-0.997715\pi$
$599$	−12.3891	−	21.4585i	−0.506203	−	0.876769i	0.493771	−	0.869592i	$-0.335618\pi$
$600$		0			0
$601$	8.27423			0.337513			0.168756	−	0.985658i	$-0.446025\pi$
$601$	8.27423			0.337513			0.168756	+	0.985658i	$0.446025\pi$
$602$	−14.7971	−	17.3281i	−0.603087	−	0.706242i
$603$		0			0
$604$	−23.1278	+	28.5509i	−0.941058	+	1.16172i
$605$	−0.0635965	−	0.0367174i	−0.00258556	−	0.00149278i
$606$		0			0
$607$		−	31.4951i		−	1.27834i	−0.769063	−	0.639172i	$-0.779277\pi$
$607$		−	31.4951i		−	1.27834i	0.769063	−	0.639172i	$-0.220723\pi$
$608$	−8.80532	+	23.0319i	−0.357103	+	0.934065i
$609$		0			0
$610$	0.635714	+	0.225177i	0.0257393	+	0.00911715i
$611$	11.0153	−	19.0791i	0.445633	−	0.771858i
$612$		0			0
$613$	20.2322	−	35.0432i	0.817171	−	1.41538i	−0.0905868	−	0.995889i	$-0.528874\pi$
$613$	20.2322	−	35.0432i	0.817171	−	1.41538i	0.907758	−	0.419494i	$-0.137792\pi$
$614$	−14.2233	+	12.1458i	−0.574005	+	0.490165i
$615$		0			0
$616$	7.79361	+	12.7251i	0.314014	+	0.512708i
$617$	8.90543	−	5.14155i	0.358519	−	0.206991i	−0.309912	−	0.950765i	$-0.600300\pi$
$617$	8.90543	−	5.14155i	0.358519	−	0.206991i	0.668431	+	0.743774i	$0.266966\pi$
$618$		0			0
$619$			31.0081i			1.24632i	0.782094	+	0.623160i	$0.214152\pi$
$619$			31.0081i			1.24632i	−0.782094	+	0.623160i	$0.785848\pi$
$620$	−6.86077	+	2.63231i	−0.275535	+	0.105716i
$621$		0			0
$622$	−10.4505	+	29.5035i	−0.419026	+	1.18298i
$623$	−4.02458	−	6.97078i	−0.161241	−	0.279278i
$624$		0			0
$625$	−11.1684	+	19.3443i	−0.446736	+	0.773770i
$626$	−9.88803	+	1.83180i	−0.395205	+	0.0732133i
$627$		0			0
$628$	−3.87506	+	1.48676i	−0.154632	+	0.0593283i
$629$	51.2995	+	29.6178i	2.04544	+	1.18094i
$630$		0			0
$631$	−23.5977	+	13.6241i	−0.939409	+	0.542368i	−0.889775	−	0.456399i	$-0.849139\pi$
$631$	−23.5977	+	13.6241i	−0.939409	+	0.542368i	−0.0496341	+	0.998767i	$0.515806\pi$
$632$	−35.1079	+	0.910656i	−1.39652	+	0.0362240i
$633$		0			0
$634$	−1.43068	−	7.72283i	−0.0568197	−	0.306713i
$635$	−1.38955			−0.0551426
$636$		0			0
$637$	−14.4305	−	24.9944i	−0.571758	−	0.990313i
$638$	−0.234565	−	1.26618i	−0.00928652	−	0.0501286i
$639$		0			0
$640$	−1.11691	−	4.66411i	−0.0441498	−	0.184365i
$641$	21.0271	+	12.1400i	0.830522	+	0.479502i	0.854031	−	0.520222i	$-0.174151\pi$
$641$	21.0271	+	12.1400i	0.830522	+	0.479502i	−0.0235095	+	0.999724i	$0.507484\pi$
$642$		0			0
$643$	18.9639	+	10.9488i	0.747861	+	0.431778i	0.824921	−	0.565249i	$-0.191220\pi$
$643$	18.9639	+	10.9488i	0.747861	+	0.431778i	−0.0770593	+	0.997027i	$0.524553\pi$
$644$	11.4681	+	1.81831i	0.451907	+	0.0716513i
$645$		0			0
$646$	20.0850	+	39.2555i	0.790235	+	1.54449i
$647$	−20.3200			−0.798863			−0.399432	−	0.916763i	$-0.630793\pi$
$647$	−20.3200			−0.798863			−0.399432	+	0.916763i	$0.630793\pi$
$648$		0			0
$649$	23.9478	−	41.4789i	0.940035	−	1.62819i
$650$	−28.3355	−	33.1822i	−1.11141	−	1.30151i
$651$		0			0
$652$	4.32602	−	5.34040i	0.169420	−	0.209146i
$653$			27.9624i			1.09425i	0.837050	+	0.547127i	$0.184279\pi$
$653$			27.9624i			1.09425i	−0.837050	+	0.547127i	$0.815721\pi$
$654$		0			0
$655$	2.59082	−	1.49581i	0.101232	−	0.0584462i
$656$	−7.37094	+	22.6600i	−0.287787	+	0.884726i
$657$		0			0
$658$	−1.39939	−	7.55388i	−0.0545537	−	0.294481i
$659$	−20.4405	−	35.4041i	−0.796251	−	1.37915i	−0.922042	−	0.387090i	$-0.873480\pi$
$659$	−20.4405	−	35.4041i	−0.796251	−	1.37915i	0.125791	−	0.992057i	$-0.459853\pi$
$660$		0			0
$661$	−20.3817	−	35.3021i	−0.792756	−	1.37309i	−0.924254	−	0.381778i	$-0.875312\pi$
$661$	−20.3817	−	35.3021i	−0.792756	−	1.37309i	0.131498	−	0.991316i	$-0.458021\pi$
$662$	15.0025	+	5.31405i	0.583088	+	0.206536i
$663$		0			0
$664$	−32.2143	+	19.7300i	−1.25016	+	0.765674i
$665$	−2.11900	−	2.00376i	−0.0821715	−	0.0777024i
$666$		0			0
$667$	−0.867777	−	0.501011i	−0.0336005	−	0.0193992i
$668$	2.44214	−	15.4027i	0.0944893	−	0.595947i
$669$		0			0
$670$	−1.53620	+	4.33695i	−0.0593484	+	0.167551i
$671$	1.88018	+	3.25657i	0.0725837	+	0.125719i
$672$		0			0
$673$	−8.88413			−0.342458			−0.171229	−	0.985231i	$-0.554774\pi$
$673$	−8.88413			−0.342458			−0.171229	+	0.985231i	$0.554774\pi$
$674$	−16.5586	−	19.3908i	−0.637813	−	0.746907i
$675$		0			0
$676$	52.2301	−	20.0394i	2.00885	−	0.770746i
$677$		−	17.2567i		−	0.663230i	−0.943415	−	0.331615i	$-0.892407\pi$
$677$		−	17.2567i		−	0.663230i	0.943415	−	0.331615i	$-0.107593\pi$
$678$		0			0
$679$	19.5485	+	11.2864i	0.750204	+	0.433131i
$680$	−7.53631	−	4.09429i	−0.289004	−	0.157009i
$681$		0			0
$682$	−38.6216	−	13.6802i	−1.47890	−	0.523842i
$683$	−31.9696			−1.22328			−0.611642	−	0.791135i	$-0.709491\pi$
$683$	−31.9696			−1.22328			−0.611642	+	0.791135i	$0.709491\pi$
$684$		0			0
$685$	−4.18063			−0.159734
$686$	−24.2146	−	8.57709i	−0.924518	−	0.327475i
$687$		0			0
$688$	−12.6313	+	38.8317i	−0.481564	+	1.48044i
$689$	8.41114	+	4.85617i	0.320439	+	0.185005i
$690$		0			0
$691$		−	3.79632i		−	0.144419i	−0.997389	−	0.0722094i	$-0.976995\pi$
$691$		−	3.79632i		−	0.144419i	0.997389	−	0.0722094i	$-0.0230050\pi$
$692$	−10.6450	−	27.7447i	−0.404661	−	1.05470i
$693$		0			0
$694$	30.7274	+	35.9832i	1.16640	+	1.36590i
$695$	3.46033			0.131258
$696$		0			0
$697$	21.3065	+	36.9040i	0.807042	+	1.39784i
$698$	3.61313	−	10.2005i	0.136759	−	0.386094i
$699$		0			0
$700$	−15.0282	−	2.38277i	−0.568013	−	0.0900602i
$701$	12.5583	+	7.25051i	0.474319	+	0.273848i	0.718046	−	0.695996i	$-0.245037\pi$
$701$	12.5583	+	7.25051i	0.474319	+	0.273848i	−0.243727	+	0.969844i	$0.578370\pi$
$702$		0			0
$703$	8.36440	−	35.1133i	0.315469	−	1.32432i
$704$	12.1520	−	23.8205i	0.457995	−	0.897769i
$705$		0			0
$706$	33.4349	+	11.8430i	1.25834	+	0.445718i
$707$	9.62443	+	16.6700i	0.361964	+	0.626940i
$708$		0			0
$709$	9.49806	+	16.4511i	0.356707	+	0.617835i	0.987409	−	0.158191i	$-0.0505661\pi$
$709$	9.49806	+	16.4511i	0.356707	+	0.617835i	−0.630701	+	0.776026i	$0.717233\pi$
$710$	0.766705	+	4.13867i	0.0287739	+	0.155322i
$711$		0			0
$712$	−6.88592	+	12.6748i	−0.258061	+	0.475009i
$713$	−27.6109	+	15.9412i	−1.03404	+	0.597002i
$714$		0			0
$715$			9.06987i			0.339194i
$716$	3.54424	+	2.87104i	0.132455	+	0.107296i
$717$		0			0
$718$	−23.3687	−	27.3658i	−0.872112	−	1.02128i
$719$	−19.0788	+	33.0455i	−0.711520	+	1.23239i	0.252766	+	0.967527i	$0.418660\pi$
$719$	−19.0788	+	33.0455i	−0.711520	+	1.23239i	−0.964286	+	0.264862i	$0.914674\pi$
$720$		0			0
$721$	2.51528			0.0936738
$722$	19.4269	−	18.5633i	0.722995	−	0.690853i
$723$		0			0
$724$	−3.57227	+	22.5304i	−0.132762	+	0.837336i
$725$	1.13717	+	0.656543i	0.0422333	+	0.0243834i
$726$		0			0
$727$	−12.7406	−	7.35580i	−0.472523	−	0.272812i	0.244772	−	0.969581i	$-0.421287\pi$
$727$	−12.7406	−	7.35580i	−0.472523	−	0.272812i	−0.717295	+	0.696769i	$0.754620\pi$
$728$	13.6408	−	25.1084i	0.505561	−	0.930579i
$729$		0			0
$730$	−0.439768	−	2.37387i	−0.0162765	−	0.0878608i
$731$	36.5122	+	63.2410i	1.35045	+	2.33905i
$732$		0			0
$733$	33.7014			1.24479			0.622394	−	0.782704i	$-0.286160\pi$
$733$	33.7014			1.24479			0.622394	+	0.782704i	$0.286160\pi$
$734$	−5.02401	−	27.1196i	−0.185439	−	1.00100i
$735$		0			0
$736$	−7.95503	−	19.2275i	−0.293226	−	0.708736i
$737$	−22.2169	+	12.8269i	−0.818370	+	0.472486i
$738$		0			0
$739$	−5.64141	−	3.25707i	−0.207523	−	0.119813i	0.392637	−	0.919694i	$-0.371563\pi$
$739$	−5.64141	−	3.25707i	−0.207523	−	0.119813i	−0.600160	+	0.799880i	$0.704896\pi$
$740$	2.51493	+	6.55483i	0.0924505	+	0.240960i
$741$		0			0
$742$	3.33017	−	0.616927i	0.122254	−	0.0226481i
$743$	11.9393	−	20.6794i	0.438009	−	0.758654i	−0.559527	−	0.828812i	$-0.689017\pi$
$743$	11.9393	−	20.6794i	0.438009	−	0.758654i	0.997536	+	0.0701582i	$0.0223504\pi$
$744$		0			0
$745$	3.32468	+	5.75852i	0.121807	+	0.210976i
$746$	−2.78230	+	7.85492i	−0.101867	+	0.287589i
$747$		0			0
$748$	−17.1303	−	44.6478i	−0.626344	−	1.63249i
$749$			5.28901i			0.193256i
$750$		0			0
$751$	−28.3170	+	16.3489i	−1.03330	+	0.596578i	−0.917929	−	0.396744i	$-0.870140\pi$
$751$	−28.3170	+	16.3489i	−1.03330	+	0.596578i	−0.115374	+	0.993322i	$0.536807\pi$
$752$	−10.2341	+	9.20874i	−0.373200	+	0.335808i
$753$		0			0
$754$	−1.87521	+	1.60131i	−0.0682910	+	0.0583163i
$755$	−3.89392	+	6.74447i	−0.141714	+	0.245456i
$756$		0			0
$757$	−1.36677	+	2.36731i	−0.0496761	+	0.0860415i	−0.889794	−	0.456362i	$-0.849152\pi$
$757$	−1.36677	+	2.36731i	−0.0496761	+	0.0860415i	0.840118	+	0.542403i	$0.182486\pi$
$758$	−31.7264	−	11.2379i	−1.15236	−	0.408177i
$759$		0			0
$760$	−1.07884	+	5.11373i	−0.0391336	+	0.185495i
$761$		−	51.7163i		−	1.87471i	−0.348370	−	0.937357i	$-0.613265\pi$
$761$		−	51.7163i		−	1.87471i	0.348370	−	0.937357i	$-0.386735\pi$
$762$		0			0
$763$	−1.60365	−	0.925867i	−0.0580560	−	0.0335186i
$764$	8.76797	+	7.10255i	0.317214	+	0.256961i
$765$		0			0
$766$	−14.9756	−	17.5371i	−0.541091	−	0.633641i
$767$	−91.7163			−3.31168
$768$		0			0
$769$	−0.762207	−	1.32018i	−0.0274859	−	0.0476069i	0.851955	−	0.523615i	$-0.175417\pi$
$769$	−0.762207	−	1.32018i	−0.0274859	−	0.0476069i	−0.879441	+	0.476008i	$0.842083\pi$
$770$	2.05387	+	2.40518i	0.0740164	+	0.0866765i
$771$		0			0
$772$	2.00193	−	0.768091i	0.0720510	−	0.0276442i
$773$	−21.3265	+	12.3129i	−0.767061	+	0.442863i	−0.831825	−	0.555038i	$-0.812704\pi$
$773$	−21.3265	+	12.3129i	−0.767061	+	0.442863i	0.0647639	+	0.997901i	$0.479371\pi$
$774$		0			0
$775$	36.1823	−	20.8899i	1.29971	−	0.750386i
$776$	−1.04891	−	40.4379i	−0.0376537	−	1.45164i
$777$		0			0
$778$	−2.18009	−	11.7681i	−0.0781598	−	0.421907i
$779$	17.8410	−	18.8672i	0.639221	−	0.675986i
$780$		0			0
$781$	−11.7344	+	20.3246i	−0.419890	+	0.727270i
$782$	−35.0760	−	12.4243i	−1.25431	−	0.444292i
$783$		0			0
$784$	3.74402	+	17.6428i	0.133715	+	0.630099i
$785$	−0.761854	+	0.439857i	−0.0271917	+	0.0156992i
$786$		0			0
$787$		−	15.8933i		−	0.566535i	−0.959041	−	0.283268i	$-0.908582\pi$
$787$		−	15.8933i		−	0.566535i	0.959041	−	0.283268i	$-0.0914185\pi$
$788$	29.1808	−	36.0232i	1.03952	−	1.28327i
$789$		0			0
$790$	−7.31923	+	1.35592i	−0.260407	+	0.0482413i
$791$	11.9169			0.423716
$792$		0			0
$793$	3.60040	−	6.23607i	0.127854	−	0.221449i
$794$	3.00333	+	3.51704i	0.106584	+	0.124815i
$795$		0			0
$796$	−32.3822	−	5.13430i	−1.14776	−	0.181980i
$797$			18.7840i			0.665363i	0.943039	+	0.332681i	$0.107953\pi$
$797$			18.7840i			0.665363i	−0.943039	+	0.332681i	$0.892047\pi$
$798$		0			0
$799$			24.6201i			0.870996i
$800$	10.4245	+	25.1964i	0.368563	+	0.890827i
$801$		0			0
$802$	3.45138	−	2.94727i	0.121873	−	0.104072i
$803$	6.73064	−	11.6578i	0.237519	−	0.411395i
$804$		0			0
$805$	2.46108			0.0867416
$806$	14.2918	+	77.1470i	0.503406	+	2.71739i
$807$		0			0
$808$	16.4671	−	30.3107i	0.579309	−	1.06633i
$809$			20.5436i			0.722276i	0.932512	+	0.361138i	$0.117612\pi$
$809$			20.5436i			0.722276i	−0.932512	+	0.361138i	$0.882388\pi$
$810$		0			0
$811$	−34.8986	+	20.1487i	−1.22546	+	0.707518i	−0.966076	−	0.258258i	$-0.916852\pi$
$811$	−34.8986	+	20.1487i	−1.22546	+	0.707518i	−0.259380	+	0.965775i	$0.583518\pi$
$812$	−0.134656	+	0.849281i	−0.00472551	+	0.0298039i
$813$		0			0
$814$	−13.0702	+	36.8993i	−0.458109	+	1.29332i
$815$	0.728351	−	1.26154i	0.0255130	−	0.0441899i
$816$		0			0
$817$	30.5735	−	32.3319i	1.06963	−	1.13115i
$818$	32.6995	−	6.05772i	1.14331	−	0.211803i
$819$		0			0
$820$	−0.790909	+	4.98829i	−0.0276197	+	0.174199i
$821$	5.62962	−	3.25026i	0.196475	−	0.113435i	−0.398535	−	0.917153i	$-0.630481\pi$
$821$	5.62962	−	3.25026i	0.196475	−	0.113435i	0.595010	+	0.803718i	$0.297148\pi$
$822$		0			0
$823$	−8.55192	+	4.93745i	−0.298101	+	0.172109i	−0.641590	−	0.767048i	$-0.721725\pi$
$823$	−8.55192	+	4.93745i	−0.298101	+	0.172109i	0.343488	+	0.939157i	$0.388391\pi$
$824$	−2.35422	−	3.84386i	−0.0820130	−	0.133907i
$825$		0			0
$826$	−24.3216	+	20.7691i	−0.846256	+	0.722651i
$827$	−6.15486	−	10.6605i	−0.214025	−	0.370703i	0.738945	−	0.673766i	$-0.235324\pi$
$827$	−6.15486	−	10.6605i	−0.214025	−	0.370703i	−0.952971	+	0.303063i	$0.901991\pi$
$828$		0			0
$829$	14.6518			0.508879			0.254440	−	0.967089i	$-0.418109\pi$
$829$	14.6518			0.508879			0.254440	+	0.967089i	$0.418109\pi$
$830$	−6.08886	+	5.19951i	−0.211347	+	0.180478i
$831$		0			0
$832$	−51.1382	+	2.65471i	−1.77290	+	0.0920355i
$833$	27.9322	+	16.1266i	0.967792	+	0.558755i
$834$		0			0
$835$		−	3.30544i		−	0.114389i
$836$	−23.0902	+	17.7766i	−0.798592	+	0.614816i
$837$		0			0
$838$	−2.99153	+	8.44560i	−0.103341	+	0.291749i
$839$	16.5294	−	28.6297i	0.570657	−	0.988407i	−0.425841	−	0.904798i	$-0.640022\pi$
$839$	16.5294	−	28.6297i	0.570657	−	0.988407i	0.996499	−	0.0836095i	$-0.0266448\pi$
$840$		0			0
$841$	−14.4629	+	25.0505i	−0.498721	+	0.863809i
$842$	−16.4283	−	19.2382i	−0.566155	−	0.662993i
$843$		0			0
$844$	13.3122	+	34.6966i	0.458226	+	1.19431i
$845$	10.2687	−	5.92862i	0.353253	−	0.203951i
$846$		0			0
$847$			0.273417i			0.00939470i
$848$	−4.05972	−	4.51177i	−0.139411	−	0.154935i
$849$		0			0
$850$	45.9647	+	16.2812i	1.57658	+	0.558442i
$851$	15.2303	+	26.3797i	0.522089	+	0.904285i
$852$		0			0
$853$	19.1816	−	33.2235i	0.656766	−	1.13755i	−0.324682	−	0.945823i	$-0.605257\pi$
$853$	19.1816	−	33.2235i	0.656766	−	1.13755i	0.981448	−	0.191729i	$-0.0614095\pi$
$854$	−0.457394	−	2.46901i	−0.0156517	−	0.0844878i
$855$		0			0
$856$	8.08270	−	4.95034i	0.276261	−	0.169199i
$857$	6.28396	+	3.62804i	0.214656	+	0.123932i	0.603473	−	0.797383i	$-0.293783\pi$
$857$	6.28396	+	3.62804i	0.214656	+	0.123932i	−0.388817	+	0.921315i	$0.627116\pi$
$858$		0			0
$859$	12.2839	−	7.09209i	0.419120	−	0.241979i	−0.275581	−	0.961278i	$-0.588870\pi$
$859$	12.2839	−	7.09209i	0.419120	−	0.241979i	0.694701	+	0.719299i	$0.255537\pi$
$860$	−1.35535	+	8.54824i	−0.0462171	+	0.291493i
$861$		0			0
$862$	−4.19279	+	0.776730i	−0.142807	+	0.0264555i
$863$	−17.8126			−0.606347			−0.303173	−	0.952935i	$-0.598046\pi$
$863$	−17.8126			−0.606347			−0.303173	+	0.952935i	$0.598046\pi$
$864$		0			0
$865$	−3.14930	−	5.45474i	−0.107079	−	0.185467i
$866$	−13.4433	+	2.49042i	−0.456822	+	0.0846281i
$867$		0			0
$868$	21.2599	+	17.2217i	0.721607	+	0.584542i
$869$	−35.9440	−	20.7523i	−1.21932	−	0.703972i
$870$		0			0
$871$	42.5436	+	24.5625i	1.44153	+	0.832270i
$872$	0.0860464	+	3.31729i	0.00291390	+	0.112338i
$873$		0			0
$874$	−1.14860	+	22.6461i	−0.0388518	+	0.766015i
$875$	−6.57039			−0.222120
$876$		0			0
$877$	22.8083	−	39.5051i	0.770181	−	1.33399i	−0.167283	−	0.985909i	$-0.553499\pi$
$877$	22.8083	−	39.5051i	0.770181	−	1.33399i	0.937464	−	0.348083i	$-0.113167\pi$
$878$	36.7019	−	31.3412i	1.23863	−	1.05771i
$879$		0			0
$880$	1.75325	−	5.38991i	0.0591020	−	0.181694i
$881$			8.56330i			0.288505i	0.989541	+	0.144252i	$0.0460777\pi$
$881$			8.56330i			0.288505i	−0.989541	+	0.144252i	$0.953922\pi$
$882$		0			0
$883$	−1.19996	+	0.692799i	−0.0403820	+	0.0233146i	−0.520055	−	0.854133i	$-0.674089\pi$
$883$	−1.19996	+	0.692799i	−0.0403820	+	0.0233146i	0.479673	+	0.877447i	$0.340755\pi$
$884$	−57.6410	+	71.1567i	−1.93868	+	2.39326i
$885$		0			0
$886$	40.2766	−	7.46139i	1.35312	−	0.250670i
$887$	17.9690	+	31.1232i	0.603339	+	1.04501i	0.992312	+	0.123765i	$0.0394969\pi$
$887$	17.9690	+	31.1232i	0.603339	+	1.04501i	−0.388972	+	0.921250i	$0.627170\pi$
$888$		0			0
$889$	2.58682	+	4.48050i	0.0867591	+	0.150271i
$890$	−1.02080	+	2.88189i	−0.0342172	+	0.0966011i
$891$		0			0
$892$	0.237261	+	0.618391i	0.00794410	+	0.0207053i
$893$	14.3772	−	4.28635i	0.481114	−	0.143437i
$894$		0			0
$895$	0.837243	+	0.483382i	0.0279859	+	0.0161577i
$896$	−12.9598	+	12.2842i	−0.432957	+	0.410387i
$897$		0			0
$898$	−34.6254	−	12.2647i	−1.15546	−	0.409278i
$899$	−1.18054	−	2.04475i	−0.0393732	−	0.0681963i
$900$		0			0
$901$	−10.8539			−0.361596
$902$	−21.4152	+	18.2872i	−0.713047	+	0.608898i
$903$		0			0
$904$	−11.1538	−	18.2115i	−0.370970	−	0.605704i
$905$			4.83507i			0.160723i
$906$		0			0
$907$	−24.8911	−	14.3709i	−0.826496	−	0.477178i	0.0261551	−	0.999658i	$-0.491674\pi$
$907$	−24.8911	−	14.3709i	−0.826496	−	0.477178i	−0.852652	+	0.522480i	$0.825007\pi$
$908$	−31.0273	−	25.1339i	−1.02968	−	0.834098i
$909$		0			0
$910$	2.02217	−	5.70893i	0.0670342	−	0.189249i
$911$	21.0396			0.697073			0.348537	−	0.937295i	$-0.386679\pi$
$911$	21.0396			0.697073			0.348537	+	0.937295i	$0.386679\pi$
$912$		0			0
$913$	−44.6439			−1.47750
$914$	−16.8839	+	47.6661i	−0.558468	+	1.57665i
$915$		0			0
$916$	3.26729	+	2.64669i	0.107954	+	0.0874492i
$917$	−9.64628	−	5.56928i	−0.318548	−	0.183914i
$918$		0			0
$919$			34.8764i			1.15046i	0.817990	+	0.575232i	$0.195088\pi$
$919$			34.8764i			1.15046i	−0.817990	+	0.575232i	$0.804912\pi$
$920$	−2.30349	−	3.76103i	−0.0759437	−	0.123998i
$921$		0			0
$922$	38.5410	−	32.9116i	1.26928	−	1.08389i
$923$	44.9408			1.47924
$924$		0			0
$925$	−19.9583	−	34.5689i	−0.656226	−	1.13662i
$926$	7.91392	+	2.80320i	0.260068	+	0.0921189i
$927$		0			0
$928$	1.42391	−	0.589117i	0.0467422	−	0.0193387i
$929$	5.68106	+	3.27996i	0.186389	+	0.107612i	0.590291	−	0.807190i	$-0.299013\pi$
$929$	5.68106	+	3.27996i	0.186389	+	0.107612i	−0.403902	+	0.914802i	$0.632346\pi$
$930$		0			0
$931$	4.55435	−	19.1189i	0.149263	−	0.626598i
$932$	3.62278	+	9.44230i	0.118668	+	0.309293i
$933$		0			0
$934$	10.0972	−	28.5062i	0.330391	−	0.932750i
$935$	−5.06796	−	8.77796i	−0.165740	−	0.287070i
$936$		0			0
$937$	14.2092	+	24.6111i	0.464195	+	0.804009i	0.999165	−	0.0408621i	$-0.0130104\pi$
$937$	14.2092	+	24.6111i	0.464195	+	0.804009i	−0.534970	+	0.844871i	$0.679677\pi$
$938$	16.8440	−	3.12042i	0.549976	−	0.101885i
$939$		0			0
$940$	−1.83675	+	2.26743i	−0.0599082	+	0.0739556i
$941$	23.3438	−	13.4776i	0.760987	−	0.439356i	−0.0686627	−	0.997640i	$-0.521873\pi$
$941$	23.3438	−	13.4776i	0.760987	−	0.439356i	0.829650	+	0.558284i	$0.188540\pi$
$942$		0			0
$943$			21.9129i			0.713582i
$944$	54.5038	+	17.7292i	1.77395	+	0.577036i
$945$		0			0
$946$	−36.6984	+	31.3381i	−1.19317	+	1.01889i
$947$	−0.844072	+	1.46198i	−0.0274286	+	0.0475078i	−0.879414	−	0.476058i	$-0.842065\pi$
$947$	−0.844072	+	1.46198i	−0.0274286	+	0.0475078i	0.851985	+	0.523566i	$0.175399\pi$
$948$		0			0
$949$	−25.7772			−0.836764
$950$	1.50516	−	29.6762i	0.0488338	−	0.962823i
$951$		0			0
$952$	0.828027	+	31.9224i	0.0268365	+	1.03461i
$953$	21.3872	+	12.3479i	0.692800	+	0.399988i	0.804660	−	0.593736i	$-0.202348\pi$
$953$	21.3872	+	12.3479i	0.692800	+	0.399988i	−0.111860	+	0.993724i	$0.535681\pi$
$954$		0			0
$955$	2.07122	+	1.19582i	0.0670232	+	0.0386959i
$956$	16.9887	+	13.7618i	0.549454	+	0.445089i
$957$		0			0
$958$	−41.9200	+	7.76585i	−1.35437	+	0.250903i
$959$	7.78277	+	13.4802i	0.251319	+	0.435297i
$960$		0			0
$961$	−44.1247			−1.42338
$962$	73.7068	−	13.6545i	2.37640	−	0.440238i
$963$		0			0
$964$	−0.240816	+	1.51883i	−0.00775616	+	0.0489183i
$965$	0.393588	−	0.227238i	0.0126701	−	0.00731506i
$966$		0			0
$967$	−7.13840	−	4.12136i	−0.229556	−	0.132534i	0.380811	−	0.924653i	$-0.375645\pi$
$967$	−7.13840	−	4.12136i	−0.229556	−	0.132534i	−0.610367	+	0.792119i	$0.708978\pi$
$968$	0.417837	−	0.255909i	0.0134298	−	0.00822523i
$969$		0			0
$970$	−1.56177	−	8.43042i	−0.0501454	−	0.270685i
$971$	2.00120	−	3.46619i	0.0642217	−	0.111235i	−0.832127	−	0.554585i	$-0.812877\pi$
$971$	2.00120	−	3.46619i	0.0642217	−	0.111235i	0.896348	+	0.443350i	$0.146210\pi$
$972$		0			0
$973$	−6.44183	−	11.1576i	−0.206516	−	0.357696i
$974$	14.5756	+	5.16283i	0.467032	+	0.165428i
$975$		0			0
$976$	−3.34505	+	3.00991i	−0.107073	+	0.0963448i
$977$			13.1093i			0.419403i	0.977765	+	0.209701i	$0.0672492\pi$
$977$			13.1093i			0.419403i	−0.977765	+	0.209701i	$0.932751\pi$
$978$		0			0
$979$	−14.7631	+	8.52346i	−0.471829	+	0.272411i
$980$	1.36936	+	3.56906i	0.0437425	+	0.114009i
$981$		0			0
$982$	−6.57354	−	7.69791i	−0.209770	−	0.245650i
$983$	16.5664	−	28.6939i	0.528386	−	0.915192i	−0.471066	−	0.882098i	$-0.656131\pi$
$983$	16.5664	−	28.6939i	0.528386	−	0.915192i	0.999452	−	0.0330939i	$-0.0105361\pi$
$984$		0			0
$985$	4.91303	−	8.50962i	0.156542	−	0.271139i
$986$	0.920093	−	2.59758i	0.0293017	−	0.0827239i
$987$		0			0
$988$	51.5881	+	21.2717i	1.64123	+	0.676744i
$989$			37.5513i			1.19406i
$990$		0			0
$991$	−44.7495	−	25.8361i	−1.42151	−	0.820711i	−0.425085	−	0.905153i	$-0.639756\pi$
$991$	−44.7495	−	25.8361i	−1.42151	−	0.820711i	−0.996428	+	0.0844418i	$0.973089\pi$
$992$	6.41978	−	48.6084i	0.203828	−	1.54332i
$993$		0			0
$994$	11.9175	−	10.1768i	0.378001	−	0.322790i
$995$	−6.94928			−0.220307
$996$		0			0
$997$	6.03246	+	10.4485i	0.191050	+	0.330908i	0.945598	−	0.325336i	$-0.105477\pi$
$997$	6.03246	+	10.4485i	0.191050	+	0.330908i	−0.754549	+	0.656244i	$0.772144\pi$
$998$	10.4639	−	8.93550i	0.331228	−	0.282848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.z.b.467.13	yes	72
3.2	odd	2	inner	684.2.z.b.467.24	yes	72
4.3	odd	2	inner	684.2.z.b.467.27	yes	72
12.11	even	2	inner	684.2.z.b.467.10	✓	72
19.7	even	3	inner	684.2.z.b.539.10	yes	72
57.26	odd	6	inner	684.2.z.b.539.27	yes	72
76.7	odd	6	inner	684.2.z.b.539.24	yes	72
228.83	even	6	inner	684.2.z.b.539.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.z.b.467.10	✓	72	12.11	even	2	inner
684.2.z.b.467.13	yes	72	1.1	even	1	trivial
684.2.z.b.467.24	yes	72	3.2	odd	2	inner
684.2.z.b.467.27	yes	72	4.3	odd	2	inner
684.2.z.b.539.10	yes	72	19.7	even	3	inner
684.2.z.b.539.13	yes	72	228.83	even	6	inner
684.2.z.b.539.24	yes	72	76.7	odd	6	inner
684.2.z.b.539.27	yes	72	57.26	odd	6	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.472184 + 1.33306i) q^{2} +(-1.55408 - 1.25890i) q^{4} +(-0.367115 - 0.211954i) q^{5} +1.57832i q^{7} +(2.41200 - 1.47725i) q^{8} +(0.455893 - 0.389305i) q^{10} +3.34264 q^{11} +(-3.20044 - 5.54332i) q^{13} +(-2.10399 - 0.745256i) q^{14} +(0.830358 + 3.91286i) q^{16} +(6.19487 + 3.57661i) q^{17} +(1.01008 - 4.24025i) q^{19} +(0.303700 + 0.791555i) q^{20} +(-1.57834 + 4.45593i) q^{22} +(1.83920 + 3.18559i) q^{23} +(-2.41015 - 4.17450i) q^{25} +(8.90077 - 1.64890i) q^{26} +(1.98694 - 2.45284i) q^{28} +(-0.235912 + 0.136204i) q^{29} +8.66745i q^{31} +(-5.60815 - 0.740676i) q^{32} +(-7.69295 + 6.56930i) q^{34} +(0.334531 - 0.579425i) q^{35} +8.28095 q^{37} +(5.17556 + 3.34867i) q^{38} +(-1.19859 + 0.0310900i) q^{40} +(5.15907 + 2.97859i) q^{41} +(8.84091 + 5.10430i) q^{43} +(-5.19474 - 4.20804i) q^{44} +(-5.11501 + 0.947576i) q^{46} +(1.72091 + 2.98070i) q^{47} +4.50892 q^{49} +(6.70289 - 1.24174i) q^{50} +(-2.00472 + 12.6438i) q^{52} +(-1.31406 + 0.758673i) q^{53} +(-1.22713 - 0.708486i) q^{55} +(2.33157 + 3.80689i) q^{56} +(-0.0701736 - 0.378797i) q^{58} +(7.16435 - 12.4090i) q^{59} +(0.562485 + 0.974253i) q^{61} +(-11.5542 - 4.09263i) q^{62} +(3.63544 - 7.12626i) q^{64} +2.71339i q^{65} +(-6.64652 + 3.83737i) q^{67} +(-5.12477 - 13.3571i) q^{68} +(0.614446 + 0.719544i) q^{70} +(-3.51052 + 6.08040i) q^{71} +(2.01357 - 3.48761i) q^{73} +(-3.91013 + 11.0390i) q^{74} +(-6.90779 + 5.31813i) q^{76} +5.27574i q^{77} +(-10.7532 - 6.20835i) q^{79} +(0.524511 - 1.61247i) q^{80} +(-6.40666 + 5.47089i) q^{82} -13.3559 q^{83} +(-1.51616 - 2.62606i) q^{85} +(-10.9789 + 9.37527i) q^{86} +(8.06243 - 4.93792i) q^{88} +(-4.41659 + 2.54992i) q^{89} +(8.74912 - 5.05131i) q^{91} +(1.15205 - 7.26603i) q^{92} +(-4.78603 + 0.886631i) q^{94} +(-1.26955 + 1.34257i) q^{95} +(7.15088 - 12.3857i) q^{97} +(-2.12904 + 6.01064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{4} + 12 q^{10} + 4 q^{13} + 20 q^{16} + 28 q^{25} - 20 q^{34} - 40 q^{37} - 40 q^{40} - 32 q^{46} - 32 q^{49} - 8 q^{52} + 96 q^{58} + 28 q^{61} + 48 q^{64} - 72 q^{70} - 20 q^{73} - 36 q^{76}+ \cdots - 112 q^{94}+O(q^{100}) \) 72 * q - 12 * q^4 + 12 * q^10 + 4 * q^13 + 20 * q^16 + 28 * q^25 - 20 * q^34 - 40 * q^37 - 40 * q^40 - 32 * q^46 - 32 * q^49 - 8 * q^52 + 96 * q^58 + 28 * q^61 + 48 * q^64 - 72 * q^70 - 20 * q^73 - 36 * q^76 - 4 * q^82 + 48 * q^85 - 56 * q^88 - 112 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more