LMFDB - Embedded newform 432.2.u.f.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	432.193
Dual form			432.2.u.f.385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51338 + 0.842423i) q^{3} +(-0.672282 + 3.81270i) q^{5} +(-2.31237 + 1.94030i) q^{7} +(1.58065 - 2.54981i) q^{9} +O(q^{10})$	\(q+(-1.51338 + 0.842423i) q^{3} +(-0.672282 + 3.81270i) q^{5} +(-2.31237 + 1.94030i) q^{7} +(1.58065 - 2.54981i) q^{9} +(-0.624892 - 3.54394i) q^{11} +(-3.29907 + 1.20076i) q^{13} +(-2.19449 - 6.33642i) q^{15} +(3.25033 - 5.62973i) q^{17} +(1.15418 + 1.99910i) q^{19} +(1.86493 - 4.88441i) q^{21} +(0.461596 + 0.387325i) q^{23} +(-9.38628 - 3.41633i) q^{25} +(-0.244098 + 5.19042i) q^{27} +(-3.20886 - 1.16793i) q^{29} +(-2.33017 - 1.95524i) q^{31} +(3.93119 + 4.83690i) q^{33} +(-5.84324 - 10.1208i) q^{35} +(-2.29461 + 3.97438i) q^{37} +(3.98120 - 4.59643i) q^{39} +(-9.50385 + 3.45912i) q^{41} +(1.70541 + 9.67188i) q^{43} +(8.65905 + 7.74073i) q^{45} +(1.11715 - 0.937396i) q^{47} +(0.366713 - 2.07973i) q^{49} +(-0.176369 + 11.2581i) q^{51} -5.64327 q^{53} +13.9321 q^{55} +(-3.43081 - 2.05309i) q^{57} +(1.03250 - 5.85562i) q^{59} +(4.48457 - 3.76300i) q^{61} +(1.29239 + 8.96304i) q^{63} +(-2.36025 - 13.3856i) q^{65} +(-6.06757 + 2.20842i) q^{67} +(-1.02486 - 0.197311i) q^{69} +(-0.397962 + 0.689290i) q^{71} +(-0.747567 - 1.29482i) q^{73} +(17.0830 - 2.73701i) q^{75} +(8.32129 + 6.98239i) q^{77} +(-10.2545 - 3.73232i) q^{79} +(-4.00311 - 8.06071i) q^{81} +(10.5905 + 3.85461i) q^{83} +(19.2794 + 16.1773i) q^{85} +(5.84013 - 0.935696i) q^{87} +(4.55528 + 7.88997i) q^{89} +(5.29881 - 9.17781i) q^{91} +(5.17357 + 0.996041i) q^{93} +(-8.39792 + 3.05659i) q^{95} +(1.96190 + 11.1265i) q^{97} +(-10.0241 - 4.00835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q - 3 * q^7 - 6 * q^9	$ 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) $ 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.51338	+	0.842423i	−0.873751	+	0.486373i
$3$	−1.51338	+	0.842423i	−0.873751	+	0.486373i
$4$		0			0
$5$	−0.672282	+	3.81270i	−0.300654	+	1.70509i	0.342635	+	0.939469i	$0.388681\pi$
$5$	−0.672282	+	3.81270i	−0.300654	+	1.70509i	−0.643288	+	0.765624i	$0.722430\pi$
$6$		0			0
$7$	−2.31237	+	1.94030i	−0.873992	+	0.733366i	−0.964935	−	0.262490i	$-0.915456\pi$
$7$	−2.31237	+	1.94030i	−0.873992	+	0.733366i	0.0909428	+	0.995856i	$0.471012\pi$
$8$		0			0
$9$	1.58065	−	2.54981i	0.526882	−	0.849938i
$10$		0			0
$11$	−0.624892	−	3.54394i	−0.188412	−	1.06854i	−0.921493	−	0.388395i	$-0.873029\pi$
$11$	−0.624892	−	3.54394i	−0.188412	−	1.06854i	0.733081	−	0.680141i	$-0.238082\pi$
$12$		0			0
$13$	−3.29907	+	1.20076i	−0.914998	+	0.333032i	−0.756247	−	0.654287i	$-0.772969\pi$
$13$	−3.29907	+	1.20076i	−0.914998	+	0.333032i	−0.158751	+	0.987319i	$0.550747\pi$
$14$		0			0
$15$	−2.19449	−	6.33642i	−0.566615	−	1.63606i
$16$		0			0
$17$	3.25033	−	5.62973i	0.788320	−	1.36541i	−0.138676	−	0.990338i	$-0.544285\pi$
$17$	3.25033	−	5.62973i	0.788320	−	1.36541i	0.926996	−	0.375072i	$-0.122382\pi$
$18$		0			0
$19$	1.15418	+	1.99910i	0.264788	+	0.458626i	0.967508	−	0.252841i	$-0.0813648\pi$
$19$	1.15418	+	1.99910i	0.264788	+	0.458626i	−0.702720	+	0.711466i	$0.748031\pi$
$20$		0			0
$21$	1.86493	−	4.88441i	0.406962	−	1.06587i
$22$		0			0
$23$	0.461596	+	0.387325i	0.0962494	+	0.0807629i	0.689643	−	0.724150i	$-0.257768\pi$
$23$	0.461596	+	0.387325i	0.0962494	+	0.0807629i	−0.593393	+	0.804913i	$0.702212\pi$
$24$		0			0
$25$	−9.38628	−	3.41633i	−1.87726	−	0.683265i
$26$		0			0
$27$	−0.244098	+	5.19042i	−0.0469768	+	0.998896i
$28$		0			0
$29$	−3.20886	−	1.16793i	−0.595871	−	0.216879i	0.0264387	−	0.999650i	$-0.491583\pi$
$29$	−3.20886	−	1.16793i	−0.595871	−	0.216879i	−0.622310	+	0.782771i	$0.713806\pi$
$30$		0			0
$31$	−2.33017	−	1.95524i	−0.418510	−	0.351172i	0.409086	−	0.912496i	$-0.365848\pi$
$31$	−2.33017	−	1.95524i	−0.418510	−	0.351172i	−0.827596	+	0.561324i	$0.810292\pi$
$32$		0			0
$33$	3.93119	+	4.83690i	0.684333	+	0.841997i
$34$		0			0
$35$	−5.84324	−	10.1208i	−0.987689	−	1.71073i
$36$		0			0
$37$	−2.29461	+	3.97438i	−0.377231	+	0.653383i	−0.990658	−	0.136368i	$-0.956457\pi$
$37$	−2.29461	+	3.97438i	−0.377231	+	0.653383i	0.613427	+	0.789751i	$0.289790\pi$
$38$		0			0
$39$	3.98120	−	4.59643i	0.637503	−	0.736017i
$40$		0			0
$41$	−9.50385	+	3.45912i	−1.48425	+	0.540224i	−0.951929	−	0.306318i	$-0.900903\pi$
$41$	−9.50385	+	3.45912i	−1.48425	+	0.540224i	−0.532323	+	0.846541i	$0.678681\pi$
$42$		0			0
$43$	1.70541	+	9.67188i	0.260073	+	1.47495i	0.782707	+	0.622391i	$0.213839\pi$
$43$	1.70541	+	9.67188i	0.260073	+	1.47495i	−0.522633	+	0.852558i	$0.675050\pi$
$44$		0			0
$45$	8.65905	+	7.74073i	1.29081	+	1.15392i
$46$		0			0
$47$	1.11715	−	0.937396i	0.162952	−	0.136733i	−0.557665	−	0.830066i	$-0.688303\pi$
$47$	1.11715	−	0.937396i	0.162952	−	0.136733i	0.720618	+	0.693333i	$0.243858\pi$
$48$		0			0
$49$	0.366713	−	2.07973i	0.0523876	−	0.297105i
$50$		0			0
$51$	−0.176369	+	11.2581i	−0.0246966	+	1.57645i
$52$		0			0
$53$	−5.64327			−0.775163			−0.387582	−	0.921835i	$-0.626689\pi$
$53$	−5.64327			−0.775163			−0.387582	+	0.921835i	$0.626689\pi$
$54$		0			0
$55$	13.9321			1.87860
$56$		0			0
$57$	−3.43081	−	2.05309i	−0.454422	−	0.271939i
$58$		0			0
$59$	1.03250	−	5.85562i	0.134421	−	0.762337i	−0.840841	−	0.541283i	$-0.817939\pi$
$59$	1.03250	−	5.85562i	0.134421	−	0.762337i	0.975261	−	0.221055i	$-0.0709499\pi$
$60$		0			0
$61$	4.48457	−	3.76300i	0.574191	−	0.481803i	−0.308843	−	0.951113i	$-0.599942\pi$
$61$	4.48457	−	3.76300i	0.574191	−	0.481803i	0.883034	+	0.469310i	$0.155497\pi$
$62$		0			0
$63$	1.29239	+	8.96304i	0.162825	+	1.12924i
$64$		0			0
$65$	−2.36025	−	13.3856i	−0.292753	−	1.66028i
$66$		0			0
$67$	−6.06757	+	2.20842i	−0.741272	+	0.269801i	−0.684928	−	0.728610i	$-0.740167\pi$
$67$	−6.06757	+	2.20842i	−0.741272	+	0.269801i	−0.0563438	+	0.998411i	$0.517944\pi$
$68$		0			0
$69$	−1.02486	−	0.197311i	−0.123379	−	0.0237535i
$70$		0			0
$71$	−0.397962	+	0.689290i	−0.0472294	+	0.0818037i	−0.888674	−	0.458540i	$-0.848373\pi$
$71$	−0.397962	+	0.689290i	−0.0472294	+	0.0818037i	0.841444	+	0.540344i	$0.181706\pi$
$72$		0			0
$73$	−0.747567	−	1.29482i	−0.0874961	−	0.151548i	0.818956	−	0.573856i	$-0.194553\pi$
$73$	−0.747567	−	1.29482i	−0.0874961	−	0.151548i	−0.906452	+	0.422309i	$0.861220\pi$
$74$		0			0
$75$	17.0830	−	2.73701i	1.97258	−	0.316043i
$76$		0			0
$77$	8.32129	+	6.98239i	0.948299	+	0.795718i
$78$		0			0
$79$	−10.2545	−	3.73232i	−1.15372	−	0.419919i	−0.306868	−	0.951752i	$-0.599281\pi$
$79$	−10.2545	−	3.73232i	−1.15372	−	0.419919i	−0.846849	+	0.531834i	$0.821503\pi$
$80$		0			0
$81$	−4.00311	−	8.06071i	−0.444790	−	0.895635i
$82$		0			0
$83$	10.5905	+	3.85461i	1.16245	+	0.423099i	0.849974	−	0.526825i	$-0.176618\pi$
$83$	10.5905	+	3.85461i	1.16245	+	0.423099i	0.312481	+	0.949924i	$0.398840\pi$
$84$		0			0
$85$	19.2794	+	16.1773i	2.09114	+	1.75467i
$86$		0			0
$87$	5.84013	−	0.935696i	0.626127	−	0.100317i
$88$		0			0
$89$	4.55528	+	7.88997i	0.482858	+	0.836335i	0.999806	−	0.0196817i	$-0.00626529\pi$
$89$	4.55528	+	7.88997i	0.482858	+	0.836335i	−0.516948	+	0.856017i	$0.672932\pi$
$90$		0			0
$91$	5.29881	−	9.17781i	0.555466	−	0.962096i
$92$		0			0
$93$	5.17357	+	0.996041i	0.536474	+	0.103285i
$94$		0			0
$95$	−8.39792	+	3.05659i	−0.861609	+	0.313600i
$96$		0			0
$97$	1.96190	+	11.1265i	0.199200	+	1.12972i	0.906309	+	0.422616i	$0.138888\pi$
$97$	1.96190	+	11.1265i	0.199200	+	1.12972i	−0.707108	+	0.707105i	$0.750001\pi$
$98$		0			0
$99$	−10.0241	−	4.00835i	−1.00746	−	0.402855i
$100$		0			0
$101$	4.82470	−	4.04841i	0.480076	−	0.402832i	−0.370378	−	0.928881i	$-0.620772\pi$
$101$	4.82470	−	4.04841i	0.480076	−	0.402832i	0.850454	+	0.526050i	$0.176327\pi$
$102$		0			0
$103$	−2.89093	+	16.3953i	−0.284852	+	1.61548i	0.420961	+	0.907079i	$0.361693\pi$
$103$	−2.89093	+	16.3953i	−0.284852	+	1.61548i	−0.705813	+	0.708398i	$0.749418\pi$
$104$		0			0
$105$	17.3690	+	10.3941i	1.69505	+	1.01436i
$106$		0			0
$107$	−13.4864			−1.30378			−0.651891	−	0.758313i	$-0.726024\pi$
$107$	−13.4864			−1.30378			−0.651891	+	0.758313i	$0.726024\pi$
$108$		0			0
$109$	−9.49508			−0.909464			−0.454732	−	0.890628i	$-0.650265\pi$
$109$	−9.49508			−0.909464			−0.454732	+	0.890628i	$0.650265\pi$
$110$		0			0
$111$	0.124510	−	7.94778i	0.0118179	−	0.754370i
$112$		0			0
$113$	0.642097	−	3.64151i	0.0604034	−	0.342565i	−0.939597	−	0.342284i	$-0.888800\pi$
$113$	0.642097	−	3.64151i	0.0604034	−	0.342565i	1.00000		0.000280663i	$-8.93377e-5\pi$
$114$		0			0
$115$	−1.78708	+	1.49954i	−0.166646	+	0.139833i
$116$		0			0
$117$	−2.15294	+	10.3100i	−0.199039	+	0.953160i
$118$		0			0
$119$	3.40745	+	19.3246i	0.312361	+	1.77148i
$120$		0			0
$121$	−1.83237	+	0.666929i	−0.166579	+	0.0606299i
$122$		0			0
$123$	11.4689	−	13.2412i	1.03412	−	1.19392i
$124$		0			0
$125$	9.65687	−	16.7262i	0.863737	−	1.49604i
$126$		0			0
$127$	−4.87430	−	8.44254i	−0.432524	−	0.749154i	0.564566	−	0.825388i	$-0.309044\pi$
$127$	−4.87430	−	8.44254i	−0.432524	−	0.749154i	−0.997090	+	0.0762341i	$0.975710\pi$
$128$		0			0
$129$	−10.7288	−	13.2006i	−0.944615	−	1.16225i
$130$		0			0
$131$	0.983192	+	0.824996i	0.0859019	+	0.0720802i	0.684727	−	0.728799i	$-0.259921\pi$
$131$	0.983192	+	0.824996i	0.0859019	+	0.0720802i	−0.598826	+	0.800880i	$0.704366\pi$
$132$		0			0
$133$	−6.54776	−	2.38319i	−0.567763	−	0.206649i
$134$		0			0
$135$	−19.6254	−	4.42010i	−1.68909	−	0.380422i
$136$		0			0
$137$	7.26267	+	2.64339i	0.620492	+	0.225840i	0.633088	−	0.774080i	$-0.281787\pi$
$137$	7.26267	+	2.64339i	0.620492	+	0.225840i	−0.0125960	+	0.999921i	$0.504010\pi$
$138$		0			0
$139$	−5.96960	−	5.00909i	−0.506335	−	0.424865i	0.353502	−	0.935434i	$-0.384991\pi$
$139$	−5.96960	−	5.00909i	−0.506335	−	0.424865i	−0.859837	+	0.510568i	$0.829435\pi$
$140$		0			0
$141$	−0.900983	+	2.35975i	−0.0758764	+	0.198727i
$142$		0			0
$143$	6.31699	+	10.9414i	0.528253	+	0.914962i
$144$		0			0
$145$	6.61024	−	11.4493i	0.548950	−	0.950810i
$146$		0			0
$147$	1.19704	+	3.45636i	0.0987301	+	0.285076i
$148$		0			0
$149$	−2.18241	+	0.794333i	−0.178790	+	0.0650743i	−0.429864	−	0.902894i	$-0.641439\pi$
$149$	−2.18241	+	0.794333i	−0.178790	+	0.0650743i	0.251074	+	0.967968i	$0.419216\pi$
$150$		0			0
$151$	1.17145	+	6.64363i	0.0953313	+	0.540651i	0.994645	+	0.103347i	$0.0329553\pi$
$151$	1.17145	+	6.64363i	0.0953313	+	0.540651i	−0.899314	+	0.437303i	$0.855934\pi$
$152$		0			0
$153$	−9.21715	−	17.1863i	−0.745163	−	1.38943i
$154$		0			0
$155$	9.02129	−	7.56976i	0.724607	−	0.608018i
$156$		0			0
$157$	−2.24116	+	12.7102i	−0.178864	+	1.01439i	0.754725	+	0.656042i	$0.227770\pi$
$157$	−2.24116	+	12.7102i	−0.178864	+	1.01439i	−0.933589	+	0.358347i	$0.883341\pi$
$158$		0			0
$159$	8.54043	−	4.75402i	0.677300	−	0.377019i
$160$		0			0
$161$	−1.81891			−0.143350
$162$		0			0
$163$	−23.7600			−1.86102			−0.930512	−	0.366261i	$-0.880638\pi$
$163$	−23.7600			−1.86102			−0.930512	+	0.366261i	$0.880638\pi$
$164$		0			0
$165$	−21.0846	+	11.7367i	−1.64143	+	0.913701i
$166$		0			0
$167$	0.312848	−	1.77425i	0.0242089	−	0.137295i	−0.970308	−	0.241874i	$-0.922238\pi$
$167$	0.312848	−	1.77425i	0.0242089	−	0.137295i	0.994517	+	0.104578i	$0.0333492\pi$
$168$		0			0
$169$	−0.516539	+	0.433428i	−0.0397338	+	0.0333406i
$170$		0			0
$171$	6.92170	+	0.216923i	0.529315	+	0.0165886i
$172$		0			0
$173$	2.66781	+	15.1299i	0.202830	+	1.15030i	0.900819	+	0.434196i	$0.142967\pi$
$173$	2.66781	+	15.1299i	0.202830	+	1.15030i	−0.697989	+	0.716108i	$0.745922\pi$
$174$		0			0
$175$	28.3332	−	10.3124i	2.14179	−	0.779548i
$176$		0			0
$177$	3.37034	+	9.73160i	0.253330	+	0.731472i
$178$		0			0
$179$	3.35006	−	5.80247i	0.250395	−	0.433697i	−0.713239	−	0.700920i	$-0.752773\pi$
$179$	3.35006	−	5.80247i	0.250395	−	0.433697i	0.963635	+	0.267223i	$0.0861061\pi$
$180$		0			0
$181$	2.81554	+	4.87666i	0.209278	+	0.362480i	0.951487	−	0.307688i	$-0.0995554\pi$
$181$	2.81554	+	4.87666i	0.209278	+	0.362480i	−0.742210	+	0.670168i	$0.766222\pi$
$182$		0			0
$183$	−3.61683	+	9.47277i	−0.267364	+	0.700247i
$184$		0			0
$185$	−13.6105	−	11.4206i	−1.00066	−	0.839656i
$186$		0			0
$187$	−21.9825	−	8.00098i	−1.60752	−	0.585089i
$188$		0			0
$189$	−9.50654	−	12.4758i	−0.691499	−	0.907478i
$190$		0			0
$191$	4.57475	+	1.66507i	0.331017	+	0.120480i	0.502182	−	0.864762i	$-0.332531\pi$
$191$	4.57475	+	1.66507i	0.331017	+	0.120480i	−0.171165	+	0.985242i	$0.554753\pi$
$192$		0			0
$193$	15.4554	+	12.9686i	1.11250	+	0.933501i	0.998202	−	0.0599449i	$-0.0190925\pi$
$193$	15.4554	+	12.9686i	1.11250	+	0.933501i	0.114302	+	0.993446i	$0.463537\pi$
$194$		0			0
$195$	14.8483	+	18.2692i	1.06331	+	1.30829i
$196$		0			0
$197$	−12.7126	−	22.0189i	−0.905737	−	1.56878i	−0.819924	−	0.572472i	$-0.805985\pi$
$197$	−12.7126	−	22.0189i	−0.905737	−	1.56878i	−0.0858131	−	0.996311i	$-0.527349\pi$
$198$		0			0
$199$	6.86596	−	11.8922i	0.486715	−	0.843015i	−0.513168	−	0.858288i	$-0.671528\pi$
$199$	6.86596	−	11.8922i	0.486715	−	0.843015i	0.999883	+	0.0152727i	$0.00486166\pi$
$200$		0			0
$201$	7.32213	−	8.45364i	0.516463	−	0.596274i
$202$		0			0
$203$	9.68621	−	3.52549i	0.679838	−	0.247441i
$204$		0			0
$205$	−6.79932	−	38.5609i	−0.474885	−	2.69321i
$206$		0			0
$207$	1.71723	−	0.564760i	0.119356	−	0.0392536i
$208$		0			0
$209$	6.36345	−	5.33957i	0.440169	−	0.369346i
$210$		0			0
$211$	−2.78509	+	15.7950i	−0.191733	+	1.08737i	0.725261	+	0.688474i	$0.241719\pi$
$211$	−2.78509	+	15.7950i	−0.191733	+	1.08737i	−0.916995	+	0.398900i	$0.869392\pi$
$212$		0			0
$213$	0.0215942	−	1.37841i	0.00147961	−	0.0944472i
$214$		0			0
$215$	−38.0225			−2.59312
$216$		0			0
$217$	9.18196			0.623312
$218$		0			0
$219$	2.22214	+	1.32980i	0.150159	+	0.0898593i
$220$		0			0
$221$	−3.96308	+	22.4758i	−0.266586	+	1.51188i
$222$		0			0
$223$	19.2988	−	16.1936i	1.29235	−	1.08441i	0.300932	−	0.953646i	$-0.402702\pi$
$223$	19.2988	−	16.1936i	1.29235	−	1.08441i	0.991414	−	0.130761i	$-0.0417421\pi$
$224$		0			0
$225$	−23.5474	+	18.5333i	−1.56983	+	1.23555i
$226$		0			0
$227$	−0.881993	−	5.00203i	−0.0585399	−	0.331996i	0.941447	−	0.337162i	$-0.109467\pi$
$227$	−0.881993	−	5.00203i	−0.0585399	−	0.331996i	−0.999987	+	0.00516536i	$0.998356\pi$
$228$		0			0
$229$	−10.5248	+	3.83070i	−0.695496	+	0.253140i	−0.665487	−	0.746410i	$-0.731776\pi$
$229$	−10.5248	+	3.83070i	−0.695496	+	0.253140i	−0.0300093	+	0.999550i	$0.509554\pi$
$230$		0			0
$231$	−18.4754	−	3.55698i	−1.21559	−	0.234032i
$232$		0			0
$233$	−9.00600	+	15.5988i	−0.590002	+	1.02191i	0.404229	+	0.914658i	$0.367540\pi$
$233$	−9.00600	+	15.5988i	−0.590002	+	1.02191i	−0.994231	+	0.107256i	$0.965793\pi$
$234$		0			0
$235$	2.82298	+	4.88954i	0.184151	+	0.318958i
$236$		0			0
$237$	18.6631	−	2.99017i	1.21230	−	0.194233i
$238$		0			0
$239$	6.70944	+	5.62989i	0.433998	+	0.364167i	0.833458	−	0.552583i	$-0.186358\pi$
$239$	6.70944	+	5.62989i	0.433998	+	0.364167i	−0.399460	+	0.916751i	$0.630802\pi$
$240$		0			0
$241$	−5.86490	−	2.13465i	−0.377792	−	0.137505i	0.146143	−	0.989264i	$-0.453314\pi$
$241$	−5.86490	−	2.13465i	−0.377792	−	0.137505i	−0.523934	+	0.851759i	$0.675536\pi$
$242$		0			0
$243$	12.8488	+	8.82662i	0.824249	+	0.566228i
$244$		0			0
$245$	7.68287	+	2.79634i	0.490841	+	0.178651i
$246$		0			0
$247$	−6.20818	−	5.20928i	−0.395017	−	0.331459i
$248$		0			0
$249$	−19.2746	+	3.08815i	−1.22148	+	0.195704i
$250$		0			0
$251$	5.65707	+	9.79833i	0.357071	+	0.618465i	0.987470	−	0.157806i	$-0.0504421\pi$
$251$	5.65707	+	9.79833i	0.357071	+	0.618465i	−0.630399	+	0.776271i	$0.717109\pi$
$252$		0			0
$253$	1.08421	−	1.87790i	0.0681636	−	0.118063i
$254$		0			0
$255$	−42.8051	−	8.24105i	−2.68056	−	0.516075i
$256$		0			0
$257$	2.62005	−	0.953620i	0.163434	−	0.0594852i	−0.259007	−	0.965875i	$-0.583395\pi$
$257$	2.62005	−	0.953620i	0.163434	−	0.0594852i	0.422442	+	0.906390i	$0.361173\pi$
$258$		0			0
$259$	−2.40553	−	13.6424i	−0.149472	−	0.847700i
$260$		0			0
$261$	−8.05009	+	6.33592i	−0.498288	+	0.392184i
$262$		0			0
$263$	−3.46935	+	2.91113i	−0.213929	+	0.179508i	−0.743455	−	0.668786i	$-0.766814\pi$
$263$	−3.46935	+	2.91113i	−0.213929	+	0.179508i	0.529526	+	0.848294i	$0.322370\pi$
$264$		0			0
$265$	3.79387	−	21.5161i	0.233056	−	1.32173i
$266$		0			0
$267$	−13.5406	−	8.10306i	−0.828669	−	0.495899i
$268$		0			0
$269$	−21.2355			−1.29475			−0.647377	−	0.762170i	$-0.724134\pi$
$269$	−21.2355			−1.29475			−0.647377	+	0.762170i	$0.724134\pi$
$270$		0			0
$271$	30.1643			1.83235			0.916175	−	0.400778i	$-0.131260\pi$
$271$	30.1643			1.83235			0.916175	+	0.400778i	$0.131260\pi$
$272$		0			0
$273$	−0.287523	+	18.3534i	−0.0174017	+	1.11080i
$274$		0			0
$275$	−6.24183	+	35.3992i	−0.376397	+	2.13465i
$276$		0			0
$277$	7.61239	−	6.38755i	0.457384	−	0.383791i	−0.384783	−	0.923007i	$-0.625724\pi$
$277$	7.61239	−	6.38755i	0.457384	−	0.383791i	0.842167	+	0.539216i	$0.181279\pi$
$278$		0			0
$279$	−8.66868	+	2.85095i	−0.518980	+	0.170682i
$280$		0			0
$281$	2.42744	+	13.7667i	0.144809	+	0.821253i	0.967520	+	0.252793i	$0.0813493\pi$
$281$	2.42744	+	13.7667i	0.144809	+	0.821253i	−0.822711	+	0.568459i	$0.807540\pi$
$282$		0			0
$283$	6.28822	−	2.28873i	0.373796	−	0.136051i	−0.148289	−	0.988944i	$-0.547377\pi$
$283$	6.28822	−	2.28873i	0.373796	−	0.136051i	0.522085	+	0.852893i	$0.325154\pi$
$284$		0			0
$285$	10.1343	−	11.7004i	0.600305	−	0.693072i
$286$		0			0
$287$	15.2646	−	26.4391i	0.901043	−	1.56065i
$288$		0			0
$289$	−12.6292	−	21.8745i	−0.742897	−	1.28673i
$290$		0			0
$291$	−12.3423	−	15.1858i	−0.723518	−	0.890210i
$292$		0			0
$293$	10.6813	+	8.96266i	0.624007	+	0.523604i	0.899060	−	0.437825i	$-0.144251\pi$
$293$	10.6813	+	8.96266i	0.624007	+	0.523604i	−0.275053	+	0.961429i	$0.588695\pi$
$294$		0			0
$295$	21.6316	+	7.87327i	1.25944	+	0.458399i
$296$		0			0
$297$	18.5470	−	2.37838i	1.07621	−	0.138007i
$298$		0			0
$299$	−1.98792	−	0.723545i	−0.114965	−	0.0418437i
$300$		0			0
$301$	−22.7099	−	19.0559i	−1.30898	−	1.09836i
$302$		0			0
$303$	−3.89115	+	10.1912i	−0.223541	+	0.585471i
$304$		0			0
$305$	11.3323	+	19.6281i	0.648887	+	1.12390i
$306$		0			0
$307$	−0.891285	+	1.54375i	−0.0508683	+	0.0881065i	−0.890338	−	0.455299i	$-0.849532\pi$
$307$	−0.891285	+	1.54375i	−0.0508683	+	0.0881065i	0.839470	+	0.543406i	$0.182866\pi$
$308$		0			0
$309$	−9.43669	−	27.2477i	−0.536835	−	1.55007i
$310$		0			0
$311$	−7.98367	+	2.90582i	−0.452712	+	0.164774i	−0.558305	−	0.829636i	$-0.688548\pi$
$311$	−7.98367	+	2.90582i	−0.452712	+	0.164774i	0.105593	+	0.994409i	$0.466326\pi$
$312$		0			0
$313$	4.91976	+	27.9013i	0.278081	+	1.57708i	0.729002	+	0.684512i	$0.239985\pi$
$313$	4.91976	+	27.9013i	0.278081	+	1.57708i	−0.450921	+	0.892564i	$0.648904\pi$
$314$		0			0
$315$	−35.0423	−	1.09821i	−1.97441	−	0.0618772i
$316$		0			0
$317$	15.9825	−	13.4110i	0.897669	−	0.753234i	−0.0720640	−	0.997400i	$-0.522959\pi$
$317$	15.9825	−	13.4110i	0.897669	−	0.753234i	0.969733	+	0.244166i	$0.0785142\pi$
$318$		0			0
$319$	−2.13388	+	12.1018i	−0.119474	+	0.677573i
$320$		0			0
$321$	20.4101	−	11.3613i	1.13918	−	0.634124i
$322$		0			0
$323$	15.0059			0.834949
$324$		0			0
$325$	35.0682			1.94523
$326$		0			0
$327$	14.3697	−	7.99887i	0.794645	−	0.442339i
$328$		0			0
$329$	−0.764414	+	4.33521i	−0.0421435	+	0.239008i
$330$		0			0
$331$	−15.4062	+	12.9274i	−0.846802	+	0.710551i	−0.959083	−	0.283125i	$-0.908629\pi$
$331$	−15.4062	+	12.9274i	−0.846802	+	0.710551i	0.112281	+	0.993677i	$0.464184\pi$
$332$		0			0
$333$	6.50696	+	12.1329i	0.356579	+	0.664879i
$334$		0			0
$335$	−4.34091	−	24.6185i	−0.237169	−	1.34505i
$336$		0			0
$337$	−7.39965	+	2.69325i	−0.403085	+	0.146711i	−0.535603	−	0.844470i	$-0.679916\pi$
$337$	−7.39965	+	2.69325i	−0.403085	+	0.146711i	0.132519	+	0.991181i	$0.457694\pi$
$338$		0			0
$339$	2.09596	+	6.05191i	0.113837	+	0.328695i
$340$		0			0
$341$	−5.47315	+	9.47977i	−0.296388	+	0.513359i
$342$		0			0
$343$	−7.37768	−	12.7785i	−0.398357	−	0.689975i
$344$		0			0
$345$	1.44129	−	3.77485i	0.0775963	−	0.203231i
$346$		0			0
$347$	−18.8318	−	15.8018i	−1.01094	−	0.848283i	−0.0224816	−	0.999747i	$-0.507157\pi$
$347$	−18.8318	−	15.8018i	−1.01094	−	0.848283i	−0.988463	+	0.151464i	$0.951601\pi$
$348$		0			0
$349$	11.2462	+	4.09329i	0.601996	+	0.219109i	0.624998	−	0.780627i	$-0.285100\pi$
$349$	11.2462	+	4.09329i	0.601996	+	0.219109i	−0.0230012	+	0.999735i	$0.507322\pi$
$350$		0			0
$351$	−5.42717	−	17.4167i	−0.289681	−	0.929632i
$352$		0			0
$353$	10.1423	+	3.69148i	0.539818	+	0.196478i	0.597517	−	0.801856i	$-0.296154\pi$
$353$	10.1423	+	3.69148i	0.539818	+	0.196478i	−0.0576987	+	0.998334i	$0.518376\pi$
$354$		0			0
$355$	−2.36052	−	1.98071i	−0.125283	−	0.105125i
$356$		0			0
$357$	−21.4363	−	26.3750i	−1.13453	−	1.39591i
$358$		0			0
$359$	7.61872	+	13.1960i	0.402101	+	0.696459i	0.993979	−	0.109568i	$-0.0349469\pi$
$359$	7.61872	+	13.1960i	0.402101	+	0.696459i	−0.591879	+	0.806027i	$0.701614\pi$
$360$		0			0
$361$	6.83573	−	11.8398i	0.359775	−	0.623149i
$362$		0			0
$363$	2.21124	−	2.55295i	0.116060	−	0.133995i
$364$		0			0
$365$	5.43936	−	1.97976i	0.284709	−	0.103626i
$366$		0			0
$367$	−5.08044	−	28.8126i	−0.265197	−	1.50401i	−0.768474	−	0.639881i	$-0.778984\pi$
$367$	−5.08044	−	28.8126i	−0.265197	−	1.50401i	0.503278	−	0.864125i	$-0.332127\pi$
$368$		0			0
$369$	−6.20212	+	29.7007i	−0.322869	+	1.54616i
$370$		0			0
$371$	13.0493	−	10.9497i	0.677486	−	0.568479i
$372$		0			0
$373$	4.61263	−	26.1595i	0.238833	−	1.35449i	−0.595556	−	0.803314i	$-0.703068\pi$
$373$	4.61263	−	26.1595i	0.238833	−	1.35449i	0.834389	−	0.551176i	$-0.185821\pi$
$374$		0			0
$375$	−0.524000	+	33.4483i	−0.0270592	+	1.72726i
$376$		0			0
$377$	11.9887			0.617448
$378$		0			0
$379$	11.1857			0.574569			0.287285	−	0.957845i	$-0.407247\pi$
$379$	11.1857			0.574569			0.287285	+	0.957845i	$0.407247\pi$
$380$		0			0
$381$	14.4889	+	8.67056i	0.742287	+	0.444206i
$382$		0			0
$383$	−4.81683	+	27.3176i	−0.246128	+	1.39586i	0.571729	+	0.820443i	$0.306273\pi$
$383$	−4.81683	+	27.3176i	−0.246128	+	1.39586i	−0.817857	+	0.575421i	$0.804838\pi$
$384$		0			0
$385$	−32.2161	+	27.0325i	−1.64188	+	1.37770i
$386$		0			0
$387$	27.3572	+	10.9393i	1.39064	+	0.556078i
$388$		0			0
$389$	−0.784714	−	4.45033i	−0.0397866	−	0.225641i	0.958431	−	0.285325i	$-0.0921016\pi$
$389$	−0.784714	−	4.45033i	−0.0397866	−	0.225641i	−0.998217	+	0.0596845i	$0.980991\pi$
$390$		0			0
$391$	3.68087	−	1.33973i	0.186150	−	0.0677530i
$392$		0			0
$393$	−2.18294	−	0.420270i	−0.110115	−	0.0211998i
$394$		0			0
$395$	21.1241	−	36.5880i	1.06287	−	1.84094i
$396$		0			0
$397$	3.00374	+	5.20262i	0.150753	+	0.261112i	0.931505	−	0.363730i	$-0.118497\pi$
$397$	3.00374	+	5.20262i	0.150753	+	0.261112i	−0.780751	+	0.624842i	$0.785163\pi$
$398$		0			0
$399$	11.9169	−	1.90931i	0.596592	−	0.0955850i
$400$		0			0
$401$	17.0605	+	14.3154i	0.851959	+	0.714879i	0.960220	−	0.279244i	$-0.0900838\pi$
$401$	17.0605	+	14.3154i	0.851959	+	0.714879i	−0.108261	+	0.994122i	$0.534528\pi$
$402$		0			0
$403$	10.0352	+	3.65250i	0.499887	+	0.181944i
$404$		0			0
$405$	33.4243	−	9.84360i	1.66087	−	0.489133i
$406$		0			0
$407$	15.5188	+	5.64839i	0.769239	+	0.279980i
$408$		0			0
$409$	8.72621	+	7.32216i	0.431483	+	0.362057i	0.832511	−	0.554008i	$-0.186902\pi$
$409$	8.72621	+	7.32216i	0.431483	+	0.362057i	−0.401028	+	0.916066i	$0.631347\pi$
$410$		0			0
$411$	−13.2180	+	2.11777i	−0.651998	+	0.104462i
$412$		0			0
$413$	8.97417	+	15.5437i	0.441590	+	0.764856i
$414$		0			0
$415$	−21.8163	+	37.7869i	−1.07092	+	1.85489i
$416$		0			0
$417$	13.2541	+	2.55173i	0.649054	+	0.124959i
$418$		0			0
$419$	−1.92660	+	0.701227i	−0.0941208	+	0.0342572i	−0.388651	−	0.921385i	$-0.627059\pi$
$419$	−1.92660	+	0.701227i	−0.0941208	+	0.0342572i	0.294531	+	0.955642i	$0.404837\pi$
$420$		0			0
$421$	3.00569	+	17.0461i	0.146489	+	0.830778i	0.966160	+	0.257944i	$0.0830450\pi$
$421$	3.00569	+	17.0461i	0.146489	+	0.830778i	−0.819671	+	0.572834i	$0.805844\pi$
$422$		0			0
$423$	−0.624375	−	4.33021i	−0.0303581	−	0.210542i
$424$		0			0
$425$	−49.7415	+	41.7380i	−2.41282	+	2.02459i
$426$		0			0
$427$	−3.06860	+	17.4029i	−0.148500	+	0.842184i
$428$		0			0
$429$	−18.7773	−	11.2369i	−0.906575	−	0.542521i
$430$		0			0
$431$	28.0894			1.35302			0.676511	−	0.736433i	$-0.263491\pi$
$431$	28.0894			1.35302			0.676511	+	0.736433i	$0.263491\pi$
$432$		0			0
$433$	−17.4373			−0.837985			−0.418992	−	0.907990i	$-0.637617\pi$
$433$	−17.4373			−0.837985			−0.418992	+	0.907990i	$0.637617\pi$
$434$		0			0
$435$	−0.358684	+	22.8957i	−0.0171976	+	1.09777i
$436$		0			0
$437$	−0.241537	+	1.36982i	−0.0115543	+	0.0655275i
$438$		0			0
$439$	−19.5148	+	16.3748i	−0.931390	+	0.781529i	−0.976066	−	0.217473i	$-0.930219\pi$
$439$	−19.5148	+	16.3748i	−0.931390	+	0.781529i	0.0446767	+	0.999001i	$0.485774\pi$
$440$		0			0
$441$	−4.72329	−	4.22238i	−0.224919	−	0.201065i
$442$		0			0
$443$	1.03294	+	5.85811i	0.0490766	+	0.278327i	0.999464	−	0.0327422i	$-0.0104240\pi$
$443$	1.03294	+	5.85811i	0.0490766	+	0.278327i	−0.950387	+	0.311069i	$0.899313\pi$
$444$		0			0
$445$	−33.1445	+	12.0636i	−1.57120	+	0.571871i
$446$		0			0
$447$	2.63366	−	3.04064i	0.124568	−	0.143817i
$448$		0			0
$449$	19.4650	−	33.7144i	0.918610	−	1.59108i	0.117082	−	0.993122i	$-0.462646\pi$
$449$	19.4650	−	33.7144i	0.918610	−	1.59108i	0.801528	−	0.597957i	$-0.204021\pi$
$450$		0			0
$451$	18.1978	+	31.5195i	0.856900	+	1.48419i
$452$		0			0
$453$	−7.36960	−	9.06748i	−0.346254	−	0.426028i
$454$		0			0
$455$	31.4300	+	26.3729i	1.47346	+	1.23638i
$456$		0			0
$457$	7.23258	+	2.63244i	0.338326	+	0.123141i	0.505596	−	0.862771i	$-0.331273\pi$
$457$	7.23258	+	2.63244i	0.338326	+	0.123141i	−0.167270	+	0.985911i	$0.553495\pi$
$458$		0			0
$459$	28.4272	+	18.2448i	1.32687	+	0.851592i
$460$		0			0
$461$	4.17959	+	1.52124i	0.194663	+	0.0708514i	0.437512	−	0.899213i	$-0.355860\pi$
$461$	4.17959	+	1.52124i	0.194663	+	0.0708514i	−0.242849	+	0.970064i	$0.578082\pi$
$462$		0			0
$463$	19.9133	+	16.7092i	0.925448	+	0.776543i	0.974995	−	0.222229i	$-0.0713332\pi$
$463$	19.9133	+	16.7092i	0.925448	+	0.776543i	−0.0495466	+	0.998772i	$0.515778\pi$
$464$		0			0
$465$	−7.27571	+	19.0557i	−0.337403	+	0.883686i
$466$		0			0
$467$	11.2157	+	19.4262i	0.519002	+	0.898938i	0.999756	+	0.0220824i	$0.00702962\pi$
$467$	11.2157	+	19.4262i	0.519002	+	0.898938i	−0.480754	+	0.876855i	$0.659637\pi$
$468$		0			0
$469$	9.74545	−	16.8796i	0.450003	−	0.779428i
$470$		0			0
$471$	−7.31568	−	21.1235i	−0.337089	−	0.973318i
$472$		0			0
$473$	33.2108	−	12.0878i	1.52704	−	0.555796i
$474$		0			0
$475$	−4.00389	−	22.7072i	−0.183711	−	1.04188i
$476$		0			0
$477$	−8.92002	+	14.3893i	−0.408420	+	0.658841i
$478$		0			0
$479$	−15.6143	+	13.1019i	−0.713434	+	0.598642i	−0.925560	−	0.378600i	$-0.876406\pi$
$479$	−15.6143	+	13.1019i	−0.713434	+	0.598642i	0.212126	+	0.977242i	$0.431961\pi$
$480$		0			0
$481$	2.79779	−	15.8670i	0.127568	−	0.723474i
$482$		0			0
$483$	2.75270	−	1.53229i	0.125252	−	0.0697216i
$484$		0			0
$485$	−43.7409			−1.98617
$486$		0			0
$487$	−13.3179			−0.603490			−0.301745	−	0.953389i	$-0.597569\pi$
$487$	−13.3179			−0.603490			−0.301745	+	0.953389i	$0.597569\pi$
$488$		0			0
$489$	35.9579	−	20.0159i	1.62607	−	0.905152i
$490$		0			0
$491$	5.05923	−	28.6923i	0.228320	−	1.29487i	−0.627917	−	0.778281i	$-0.716092\pi$
$491$	5.05923	−	28.6923i	0.228320	−	1.29487i	0.856236	−	0.516584i	$-0.172797\pi$
$492$		0			0
$493$	−17.0050	+	14.2689i	−0.765866	+	0.642638i
$494$		0			0
$495$	22.0217	−	35.5242i	0.989802	−	1.59670i
$496$		0			0
$497$	−0.417200	−	2.36606i	−0.0187140	−	0.106132i
$498$		0			0
$499$	38.4852	−	14.0075i	1.72283	−	0.627060i	0.724754	−	0.689007i	$-0.241953\pi$
$499$	38.4852	−	14.0075i	1.72283	−	0.627060i	0.998079	+	0.0619471i	$0.0197310\pi$
$500$		0			0
$501$	1.02121	+	2.94867i	0.0456243	+	0.131737i
$502$		0			0
$503$	−13.3076	+	23.0494i	−0.593355	+	1.02772i	0.400422	+	0.916331i	$0.368864\pi$
$503$	−13.3076	+	23.0494i	−0.593355	+	1.02772i	−0.993777	+	0.111390i	$0.964470\pi$
$504$		0			0
$505$	12.1918	+	21.1168i	0.542529	+	0.939687i
$506$		0			0
$507$	0.416591	−	1.09109i	0.0185015	−	0.0484568i
$508$		0			0
$509$	−34.3233	−	28.8007i	−1.52135	−	1.27657i	−0.836635	−	0.547760i	$-0.815481\pi$
$509$	−34.3233	−	28.8007i	−1.52135	−	1.27657i	−0.684719	−	0.728807i	$-0.740075\pi$
$510$		0			0
$511$	4.24100	+	1.54360i	0.187611	+	0.0682848i
$512$		0			0
$513$	−10.6579	+	5.50271i	−0.470558	+	0.242951i
$514$		0			0
$515$	−60.5669	−	22.0445i	−2.66890	−	0.971399i
$516$		0			0
$517$	−4.02017	−	3.37332i	−0.176807	−	0.148358i
$518$		0			0
$519$	−16.7832	−	20.6499i	−0.736700	−	0.906429i
$520$		0			0
$521$	4.51846	+	7.82620i	0.197957	+	0.342872i	0.947866	−	0.318669i	$-0.103236\pi$
$521$	4.51846	+	7.82620i	0.197957	+	0.342872i	−0.749909	+	0.661541i	$0.769903\pi$
$522$		0			0
$523$	20.5530	−	35.5988i	0.898719	−	1.55663i	0.0695850	−	0.997576i	$-0.477832\pi$
$523$	20.5530	−	35.5988i	0.898719	−	1.55663i	0.829134	−	0.559050i	$-0.188834\pi$
$524$		0			0
$525$	−34.1915	+	39.4752i	−1.49224	+	1.72284i
$526$		0			0
$527$	−18.5813	+	6.76303i	−0.809414	+	0.294602i
$528$		0			0
$529$	−3.93086	−	22.2930i	−0.170907	−	0.969261i
$530$		0			0
$531$	−13.2987	−	11.8884i	−0.577116	−	0.515911i
$532$		0			0
$533$	27.2003	−	22.8238i	1.17818	−	0.988607i
$534$		0			0
$535$	9.06669	−	51.4197i	0.391987	−	2.22307i
$536$		0			0
$537$	−0.181780	+	11.6035i	−0.00784440	+	0.500729i
$538$		0			0
$539$	−7.59960			−0.327338
$540$		0			0
$541$	14.3485			0.616891			0.308446	−	0.951242i	$-0.400191\pi$
$541$	14.3485			0.616891			0.308446	+	0.951242i	$0.400191\pi$
$542$		0			0
$543$	−8.36920	−	5.00837i	−0.359157	−	0.214930i
$544$		0			0
$545$	6.38338	−	36.2019i	0.273434	−	1.55072i
$546$		0			0
$547$	−0.390619	+	0.327768i	−0.0167017	+	0.0140144i	−0.651100	−	0.758992i	$-0.725692\pi$
$547$	−0.390619	+	0.327768i	−0.0167017	+	0.0140144i	0.634399	+	0.773006i	$0.281248\pi$
$548$		0			0
$549$	−2.50644	−	17.3828i	−0.106972	−	0.741880i
$550$		0			0
$551$	−1.36880	−	7.76285i	−0.0583129	−	0.330709i
$552$		0			0
$553$	30.9539	−	11.2663i	1.31629	−	0.479092i
$554$		0			0
$555$	30.2188	+	5.81787i	1.28272	+	0.246955i
$556$		0			0
$557$	16.2043	−	28.0666i	0.686596	−	1.18922i	−0.286336	−	0.958129i	$-0.592437\pi$
$557$	16.2043	−	28.0666i	0.686596	−	1.18922i	0.972932	−	0.231090i	$-0.0742293\pi$
$558$		0			0
$559$	−17.2399	−	29.8604i	−0.729171	−	1.26296i
$560$		0			0
$561$	40.0081	−	6.41004i	1.68914	−	0.270632i
$562$		0			0
$563$	−13.8134	−	11.5908i	−0.582164	−	0.488494i	0.303493	−	0.952834i	$-0.401847\pi$
$563$	−13.8134	−	11.5908i	−0.582164	−	0.488494i	−0.885657	+	0.464340i	$0.846292\pi$
$564$		0			0
$565$	13.4523	+	4.89625i	0.565944	+	0.205987i
$566$		0			0
$567$	24.8969	+	10.8721i	1.04557	+	0.456583i
$568$		0			0
$569$	−12.5275	−	4.55964i	−0.525180	−	0.191150i	0.0658047	−	0.997833i	$-0.479039\pi$
$569$	−12.5275	−	4.55964i	−0.525180	−	0.191150i	−0.590985	+	0.806682i	$0.701261\pi$
$570$		0			0
$571$	−8.04048	−	6.74677i	−0.336484	−	0.282343i	0.458852	−	0.888513i	$-0.348261\pi$
$571$	−8.04048	−	6.74677i	−0.336484	−	0.282343i	−0.795336	+	0.606169i	$0.792705\pi$
$572$		0			0
$573$	−8.32604	+	1.33399i	−0.347825	+	0.0557280i
$574$		0			0
$575$	−3.00944	−	5.21250i	−0.125502	−	0.217376i
$576$		0			0
$577$	−12.6173	+	21.8537i	−0.525264	+	0.909783i	0.474304	+	0.880361i	$0.342700\pi$
$577$	−12.6173	+	21.8537i	−0.525264	+	0.909783i	−0.999567	+	0.0294218i	$0.990633\pi$
$578$		0			0
$579$	−34.3150	−	6.60648i	−1.42608	−	0.274556i
$580$		0			0
$581$	−31.9681	+	11.6355i	−1.32626	+	0.482720i
$582$		0			0
$583$	3.52643	+	19.9994i	0.146050	+	0.828290i
$584$		0			0
$585$	−37.8616	−	15.1398i	−1.56538	−	0.625952i
$586$		0			0
$587$	−28.0835	+	23.5648i	−1.15913	+	0.972625i	−0.999893	−	0.0146152i	$-0.995348\pi$
$587$	−28.0835	+	23.5648i	−1.15913	+	0.972625i	−0.159236	+	0.987240i	$0.550903\pi$
$588$		0			0
$589$	1.21929	−	6.91495i	0.0502400	−	0.284925i
$590$		0			0
$591$	37.7883	+	22.6136i	1.55440	+	0.930200i
$592$		0			0
$593$	−35.3739			−1.45263			−0.726316	−	0.687360i	$-0.758769\pi$
$593$	−35.3739			−1.45263			−0.726316	+	0.687360i	$0.758769\pi$
$594$		0			0
$595$	−75.9698			−3.11446
$596$		0			0
$597$	−0.372560	+	23.7815i	−0.0152479	+	0.973311i
$598$		0			0
$599$	2.79966	−	15.8776i	0.114391	−	0.648743i	−0.872659	−	0.488330i	$-0.837606\pi$
$599$	2.79966	−	15.8776i	0.114391	−	0.648743i	0.987050	−	0.160413i	$-0.0512827\pi$
$600$		0			0
$601$	16.1426	−	13.5452i	0.658470	−	0.552522i	−0.251158	−	0.967946i	$-0.580811\pi$
$601$	16.1426	−	13.5452i	0.658470	−	0.552522i	0.909628	+	0.415424i	$0.136367\pi$
$602$		0			0
$603$	−3.95964	+	18.9619i	−0.161249	+	0.772189i
$604$		0			0
$605$	−1.31093	−	7.43466i	−0.0532969	−	0.302262i
$606$		0			0
$607$	−33.5320	+	12.2046i	−1.36102	+	0.495371i	−0.916370	−	0.400333i	$-0.868894\pi$
$607$	−33.5320	+	12.2046i	−1.36102	+	0.495371i	−0.444651	+	0.895704i	$0.646672\pi$
$608$		0			0
$609$	−11.6890	+	13.4953i	−0.473661	+	0.546857i
$610$		0			0
$611$	−2.55995	+	4.43397i	−0.103565	+	0.179379i
$612$		0			0
$613$	11.8441	+	20.5146i	0.478378	+	0.828576i	0.999693	−	0.0247891i	$-0.00789142\pi$
$613$	11.8441	+	20.5146i	0.478378	+	0.828576i	−0.521314	+	0.853365i	$0.674558\pi$
$614$		0			0
$615$	42.7745	+	52.6294i	1.72484	+	2.12222i
$616$		0			0
$617$	−25.9666	−	21.7886i	−1.04538	−	0.877176i	−0.0527772	−	0.998606i	$-0.516807\pi$
$617$	−25.9666	−	21.7886i	−1.04538	−	0.877176i	−0.992600	+	0.121431i	$0.961252\pi$
$618$		0			0
$619$	21.8773	+	7.96270i	0.879325	+	0.320048i	0.741937	−	0.670469i	$-0.233907\pi$
$619$	21.8773	+	7.96270i	0.879325	+	0.320048i	0.137388	+	0.990517i	$0.456129\pi$
$620$		0			0
$621$	−2.12305	+	2.30133i	−0.0851952	+	0.0923492i
$622$		0			0
$623$	−25.8424	−	9.40587i	−1.03535	−	0.376838i
$624$		0			0
$625$	19.0210	+	15.9605i	0.760841	+	0.638421i
$626$		0			0
$627$	−5.13215	+	13.4415i	−0.204958	+	0.536803i
$628$		0			0
$629$	14.9164	+	25.8360i	0.594758	+	1.03015i
$630$		0			0
$631$	−23.3356	+	40.4185i	−0.928976	+	1.60903i	−0.143939	+	0.989587i	$0.545977\pi$
$631$	−23.3356	+	40.4185i	−0.928976	+	1.60903i	−0.785038	+	0.619448i	$0.787357\pi$
$632$		0			0
$633$	−9.09119	−	26.2501i	−0.361342	−	1.04335i
$634$		0			0
$635$	35.4658	−	12.9085i	1.40742	−	0.512258i
$636$		0			0
$637$	1.28746	+	7.30153i	0.0510109	+	0.289297i
$638$		0			0
$639$	1.12853	+	2.10425i	0.0446438	+	0.0832430i
$640$		0			0
$641$	−22.0646	+	18.5144i	−0.871498	+	0.731273i	−0.964413	−	0.264401i	$-0.914826\pi$
$641$	−22.0646	+	18.5144i	−0.871498	+	0.731273i	0.0929152	+	0.995674i	$0.470381\pi$
$642$		0			0
$643$	−1.35036	+	7.65827i	−0.0532530	+	0.302013i	−0.999788	−	0.0205883i	$-0.993446\pi$
$643$	−1.35036	+	7.65827i	−0.0532530	+	0.302013i	0.946535	+	0.322601i	$0.104557\pi$
$644$		0			0
$645$	57.5426	−	32.0311i	2.26574	−	1.26122i
$646$		0			0
$647$	−17.4729			−0.686931			−0.343466	−	0.939165i	$-0.611601\pi$
$647$	−17.4729			−0.686931			−0.343466	+	0.939165i	$0.611601\pi$
$648$		0			0
$649$	−21.3972			−0.839912
$650$		0			0
$651$	−13.8958	+	7.73510i	−0.544620	+	0.303162i
$652$		0			0
$653$	5.46595	−	30.9990i	0.213899	−	1.21308i	−0.668907	−	0.743346i	$-0.733238\pi$
$653$	5.46595	−	30.9990i	0.213899	−	1.21308i	0.882806	−	0.469737i	$-0.155651\pi$
$654$		0			0
$655$	−3.80645	+	3.19399i	−0.148730	+	0.124799i
$656$		0			0
$657$	−4.48320	−	0.140502i	−0.174906	−	0.00548150i
$658$		0			0
$659$	−3.67232	−	20.8268i	−0.143053	−	0.811295i	−0.968910	−	0.247415i	$-0.920419\pi$
$659$	−3.67232	−	20.8268i	−0.143053	−	0.811295i	0.825856	−	0.563881i	$-0.190692\pi$
$660$		0			0
$661$	−27.2732	+	9.92664i	−1.06081	+	0.386101i	−0.812731	−	0.582640i	$-0.802020\pi$
$661$	−27.2732	+	9.92664i	−1.06081	+	0.386101i	−0.248074	+	0.968741i	$0.579798\pi$
$662$		0			0
$663$	−12.9364	−	37.3530i	−0.502410	−	1.45067i
$664$		0			0
$665$	13.4883	−	23.3625i	0.523055	−	0.905959i
$666$		0			0
$667$	−1.02883	−	1.78199i	−0.0398365	−	0.0689988i
$668$		0			0
$669$	−15.5646	+	40.7649i	−0.601762	+	1.57606i
$670$		0			0
$671$	−16.1382	−	13.5416i	−0.623009	−	0.522767i
$672$		0			0
$673$	35.8436	+	13.0460i	1.38167	+	0.502886i	0.922683	−	0.385558i	$-0.125991\pi$
$673$	35.8436	+	13.0460i	1.38167	+	0.502886i	0.458984	+	0.888444i	$0.348213\pi$
$674$		0			0
$675$	20.0233	−	47.8848i	0.770698	−	1.84309i
$676$		0			0
$677$	2.39245	+	0.870782i	0.0919495	+	0.0334669i	0.387585	−	0.921834i	$-0.373309\pi$
$677$	2.39245	+	0.870782i	0.0919495	+	0.0334669i	−0.295636	+	0.955301i	$0.595531\pi$
$678$		0			0
$679$	−26.1254	−	21.9218i	−1.00260	−	0.841281i
$680$		0			0
$681$	5.54862	+	6.82697i	0.212623	+	0.261610i
$682$		0			0
$683$	1.75272	+	3.03581i	0.0670661	+	0.116162i	0.897609	−	0.440793i	$-0.145303\pi$
$683$	1.75272	+	3.03581i	0.0670661	+	0.116162i	−0.830543	+	0.556955i	$0.811969\pi$
$684$		0			0
$685$	−14.9610	+	25.9133i	−0.571632	+	0.990096i
$686$		0			0
$687$	12.7009	−	14.6636i	0.484570	−	0.559452i
$688$		0			0
$689$	18.6176	−	6.77624i	0.709273	−	0.258154i
$690$		0			0
$691$	0.187196	+	1.06164i	0.00712129	+	0.0403868i	0.988161	−	0.153418i	$-0.0490282\pi$
$691$	0.187196	+	1.06164i	0.00712129	+	0.0403868i	−0.981040	+	0.193805i	$0.937917\pi$
$692$		0			0
$693$	30.9568	−	10.1811i	1.17595	−	0.386746i
$694$		0			0
$695$	23.1114	−	19.3928i	0.876666	−	0.735610i
$696$		0			0
$697$	−11.4167	+	64.7474i	−0.432439	+	2.45248i
$698$		0			0
$699$	0.488682	−	31.1939i	0.0184837	−	1.17986i
$700$		0			0
$701$	3.67210			0.138693			0.0693466	−	0.997593i	$-0.477909\pi$
$701$	3.67210			0.138693			0.0693466	+	0.997593i	$0.477909\pi$
$702$		0			0
$703$	−10.5936			−0.399545
$704$		0			0
$705$	−8.39130	−	5.02160i	−0.316035	−	0.189124i
$706$		0			0
$707$	−3.30133	+	18.7228i	−0.124159	+	0.704143i
$708$		0			0
$709$	7.93092	−	6.65483i	0.297852	−	0.249928i	−0.481598	−	0.876393i	$-0.659943\pi$
$709$	7.93092	−	6.65483i	0.297852	−	0.249928i	0.779450	+	0.626465i	$0.215499\pi$
$710$		0			0
$711$	−25.7254	+	20.2475i	−0.964778	+	0.759340i
$712$		0			0
$713$	−0.318282	−	1.80506i	−0.0119197	−	0.0676002i
$714$		0			0
$715$	−45.9629	+	16.7291i	−1.71892	+	0.625634i
$716$		0			0
$717$	−14.8967	−	2.86798i	−0.556327	−	0.107107i
$718$		0			0
$719$	−9.08709	+	15.7393i	−0.338891	+	0.586977i	−0.984224	−	0.176924i	$-0.943385\pi$
$719$	−9.08709	+	15.7393i	−0.338891	+	0.586977i	0.645333	+	0.763901i	$0.276719\pi$
$720$		0			0
$721$	−25.1270	−	43.5212i	−0.935778	−	1.62081i
$722$		0			0
$723$	10.6741	−	1.71019i	0.396975	−	0.0636026i
$724$		0			0
$725$	26.1293	+	21.9250i	0.970416	+	0.814276i
$726$		0			0
$727$	−0.883705	−	0.321642i	−0.0327748	−	0.0119291i	0.325581	−	0.945514i	$-0.394440\pi$
$727$	−0.883705	−	0.321642i	−0.0327748	−	0.0119291i	−0.358356	+	0.933585i	$0.616662\pi$
$728$		0			0
$729$	−26.8808	−	2.53395i	−0.995586	−	0.0938498i
$730$		0			0
$731$	59.9932	+	21.8358i	2.21893	+	0.807625i
$732$		0			0
$733$	−28.6895	−	24.0733i	−1.05967	−	0.889169i	−0.0655929	−	0.997846i	$-0.520894\pi$
$733$	−28.6895	−	24.0733i	−1.05967	−	0.889169i	−0.994077	+	0.108678i	$0.965338\pi$
$734$		0			0
$735$	−13.9828	+	2.24030i	−0.515764	+	0.0826349i
$736$		0			0
$737$	11.6181	+	20.1231i	0.427957	+	0.741243i
$738$		0			0
$739$	−3.11908	+	5.40240i	−0.114737	+	0.198731i	−0.917675	−	0.397333i	$-0.869936\pi$
$739$	−3.11908	+	5.40240i	−0.114737	+	0.198731i	0.802938	+	0.596063i	$0.203269\pi$
$740$		0			0
$741$	13.7838	+	2.65372i	0.506359	+	0.0974867i
$742$		0			0
$743$	6.18428	−	2.25089i	0.226879	−	0.0825773i	−0.226079	−	0.974109i	$-0.572591\pi$
$743$	6.18428	−	2.25089i	0.226879	−	0.0825773i	0.452958	+	0.891532i	$0.350369\pi$
$744$		0			0
$745$	−1.56136	−	8.85490i	−0.0572037	−	0.324419i
$746$		0			0
$747$	26.5683	−	20.9109i	0.972084	−	0.765091i
$748$		0			0
$749$	31.1855	−	26.1678i	1.13949	−	0.956150i
$750$		0			0
$751$	−2.97417	+	16.8673i	−0.108529	+	0.615498i	0.881223	+	0.472701i	$0.156721\pi$
$751$	−2.97417	+	16.8673i	−0.108529	+	0.615498i	−0.989752	+	0.142797i	$0.954390\pi$
$752$		0			0
$753$	−16.8156	−	10.0630i	−0.612796	−	0.366715i
$754$		0			0
$755$	−26.1177			−0.950521
$756$		0			0
$757$	−25.8202			−0.938450			−0.469225	−	0.883079i	$-0.655467\pi$
$757$	−25.8202			−0.938450			−0.469225	+	0.883079i	$0.655467\pi$
$758$		0			0
$759$	−0.0588311	+	3.75535i	−0.00213544	+	0.136310i
$760$		0			0
$761$	5.24639	−	29.7538i	0.190182	−	1.07857i	−0.728934	−	0.684584i	$-0.759984\pi$
$761$	5.24639	−	29.7538i	0.190182	−	1.07857i	0.919115	−	0.393989i	$-0.128905\pi$
$762$		0			0
$763$	21.9561	−	18.4234i	0.794864	−	0.666970i
$764$		0			0
$765$	71.7230	−	23.5882i	2.59315	−	0.852833i
$766$		0			0
$767$	3.62491	+	20.5579i	0.130888	+	0.742303i
$768$		0			0
$769$	−0.437052	+	0.159074i	−0.0157605	+	0.00573635i	−0.349888	−	0.936791i	$-0.613780\pi$
$769$	−0.437052	+	0.159074i	−0.0157605	+	0.00573635i	0.334128	+	0.942528i	$0.391558\pi$
$770$		0			0
$771$	−3.16178	+	3.65038i	−0.113869	+	0.131465i
$772$		0			0
$773$	−15.6270	+	27.0668i	−0.562066	+	0.973527i	0.435250	+	0.900310i	$0.356660\pi$
$773$	−15.6270	+	27.0668i	−0.562066	+	0.973527i	−0.997316	+	0.0732171i	$0.976673\pi$
$774$		0			0
$775$	15.1918	+	26.3131i	0.545707	+	0.945193i
$776$		0			0
$777$	15.1332	+	18.6198i	0.542901	+	0.667980i
$778$		0			0
$779$	−17.8843	−	15.0067i	−0.640772	−	0.537672i
$780$		0			0
$781$	2.69148	+	0.979620i	0.0963089	+	0.0350536i
$782$		0			0
$783$	6.84532	−	16.3702i	0.244632	−	0.585025i
$784$		0			0
$785$	−46.9537	−	17.0898i	−1.67585	−	0.609960i
$786$		0			0
$787$	14.6668	+	12.3069i	0.522816	+	0.438694i	0.865612	−	0.500715i	$-0.166930\pi$
$787$	14.6668	+	12.3069i	0.522816	+	0.438694i	−0.342796	+	0.939410i	$0.611374\pi$
$788$		0			0
$789$	2.79804	−	7.32830i	0.0996130	−	0.260895i
$790$		0			0
$791$	5.58088	+	9.66637i	0.198433	+	0.343696i
$792$		0			0
$793$	−10.2764	+	17.7993i	−0.364927	+	0.632073i
$794$		0			0
$795$	12.3841	+	35.7582i	0.439219	+	1.26821i
$796$		0			0
$797$	18.6308	−	6.78105i	0.659936	−	0.240197i	0.00972742	−	0.999953i	$-0.496904\pi$
$797$	18.6308	−	6.78105i	0.659936	−	0.240197i	0.650209	+	0.759756i	$0.274681\pi$
$798$		0			0
$799$	−1.64620	−	9.33607i	−0.0582384	−	0.330286i
$800$		0			0
$801$	27.3182	+	0.856144i	0.965243	+	0.0302504i
$802$		0			0
$803$	−4.12163	+	3.45846i	−0.145449	+	0.122046i
$804$		0			0
$805$	1.22282	−	6.93496i	0.0430987	−	0.244425i
$806$		0			0
$807$	32.1375	−	17.8893i	1.13129	−	0.629733i
$808$		0			0
$809$	−3.93819			−0.138459			−0.0692297	−	0.997601i	$-0.522054\pi$
$809$	−3.93819			−0.138459			−0.0692297	+	0.997601i	$0.522054\pi$
$810$		0			0
$811$	45.3354			1.59194			0.795971	−	0.605334i	$-0.206961\pi$
$811$	45.3354			1.59194			0.795971	+	0.605334i	$0.206961\pi$
$812$		0			0
$813$	−45.6501	+	25.4111i	−1.60102	+	0.891206i
$814$		0			0
$815$	15.9734	−	90.5897i	0.559524	−	3.17322i
$816$		0			0
$817$	−17.3667	+	14.5724i	−0.607585	+	0.509824i
$818$		0			0
$819$	−15.0262	−	28.0179i	−0.525057	−	0.979023i
$820$		0			0
$821$	−3.58025	−	20.3046i	−0.124952	−	0.708636i	−0.981337	−	0.192298i	$-0.938406\pi$
$821$	−3.58025	−	20.3046i	−0.124952	−	0.708636i	0.856385	−	0.516338i	$-0.172705\pi$
$822$		0			0
$823$	−5.64627	+	2.05507i	−0.196817	+	0.0716354i	−0.438548	−	0.898708i	$-0.644507\pi$
$823$	−5.64627	+	2.05507i	−0.196817	+	0.0716354i	0.241731	+	0.970343i	$0.422285\pi$
$824$		0			0
$825$	−20.3748	−	58.8308i	−0.709361	−	2.04822i
$826$		0			0
$827$	−14.5606	+	25.2196i	−0.506320	+	0.876973i	0.493653	+	0.869659i	$0.335661\pi$
$827$	−14.5606	+	25.2196i	−0.506320	+	0.876973i	−0.999973	+	0.00731362i	$0.997672\pi$
$828$		0			0
$829$	19.3995	+	33.6010i	0.673774	+	1.16701i	0.976826	+	0.214037i	$0.0686612\pi$
$829$	19.3995	+	33.6010i	0.673774	+	1.16701i	−0.303051	+	0.952974i	$0.598005\pi$
$830$		0			0
$831$	−6.13942	+	16.0797i	−0.212974	+	0.557797i
$832$		0			0
$833$	−10.5164	−	8.82431i	−0.364372	−	0.305744i
$834$		0			0
$835$	6.55436	+	2.38559i	0.226823	+	0.0825568i
$836$		0			0
$837$	10.7173	−	11.6173i	0.370444	−	0.401551i
$838$		0			0
$839$	3.24585	+	1.18139i	0.112059	+	0.0407862i	0.397441	−	0.917628i	$-0.369898\pi$
$839$	3.24585	+	1.18139i	0.112059	+	0.0407862i	−0.285382	+	0.958414i	$0.592120\pi$
$840$		0			0
$841$	−13.2825	−	11.1454i	−0.458019	−	0.384323i
$842$		0			0
$843$	−15.2710	−	18.7893i	−0.525962	−	0.647139i
$844$		0			0
$845$	−1.30527	−	2.26080i	−0.0449027	−	0.0777737i
$846$		0			0
$847$	2.94307	−	5.09755i	0.101125	−	0.175154i
$848$		0			0
$849$	−7.58840	+	8.76106i	−0.260433	+	0.300679i
$850$		0			0
$851$	−2.59856	+	0.945798i	−0.0890774	+	0.0324215i
$852$		0			0
$853$	−1.82989	−	10.3778i	−0.0626543	−	0.355330i	−0.999976	−	0.00686617i	$-0.997814\pi$
$853$	−1.82989	−	10.3778i	−0.0626543	−	0.355330i	0.937322	−	0.348464i	$-0.113297\pi$
$854$		0			0
$855$	−5.48040	+	26.2445i	−0.187426	+	0.897544i
$856$		0			0
$857$	7.83914	−	6.57782i	0.267780	−	0.224694i	−0.499003	−	0.866600i	$-0.666301\pi$
$857$	7.83914	−	6.57782i	0.267780	−	0.224694i	0.766783	+	0.641906i	$0.221856\pi$
$858$		0			0
$859$	1.54366	−	8.75452i	0.0526689	−	0.298700i	−0.947083	−	0.320990i	$-0.895984\pi$
$859$	1.54366	−	8.75452i	0.0526689	−	0.298700i	0.999752	+	0.0222896i	$0.00709558\pi$
$860$		0			0
$861$	−0.828287	+	52.8717i	−0.0282280	+	1.80186i
$862$		0			0
$863$	24.3518			0.828945			0.414472	−	0.910062i	$-0.363966\pi$
$863$	24.3518			0.828945			0.414472	+	0.910062i	$0.363966\pi$
$864$		0			0
$865$	−59.4793			−2.02236
$866$		0			0
$867$	37.5404	+	22.4653i	1.27494	+	0.762961i
$868$		0			0
$869$	−6.81917	+	38.6734i	−0.231324	+	1.31191i
$870$		0			0
$871$	17.3656	−	14.5714i	0.588410	−	0.493735i
$872$		0			0
$873$	31.4715	+	12.5845i	1.06515	+	0.425922i
$874$		0			0
$875$	10.1237	+	57.4143i	0.342243	+	1.94096i
$876$		0			0
$877$	20.4043	−	7.42654i	0.689003	−	0.250777i	0.0262947	−	0.999654i	$-0.491629\pi$
$877$	20.4043	−	7.42654i	0.689003	−	0.250777i	0.662708	+	0.748878i	$0.269407\pi$
$878$		0			0
$879$	−23.7152	−	4.56576i	−0.799894	−	0.153999i
$880$		0			0
$881$	−5.84661	+	10.1266i	−0.196977	+	0.341175i	−0.947547	−	0.319617i	$-0.896446\pi$
$881$	−5.84661	+	10.1266i	−0.196977	+	0.341175i	0.750570	+	0.660791i	$0.229779\pi$
$882$		0			0
$883$	7.11755	+	12.3280i	0.239525	+	0.414869i	0.960578	−	0.278011i	$-0.0896751\pi$
$883$	7.11755	+	12.3280i	0.239525	+	0.414869i	−0.721053	+	0.692880i	$0.756342\pi$
$884$		0			0
$885$	−39.3695	+	6.30772i	−1.32339	+	0.212032i
$886$		0			0
$887$	−9.76192	−	8.19123i	−0.327773	−	0.275034i	0.464019	−	0.885826i	$-0.346407\pi$
$887$	−9.76192	−	8.19123i	−0.327773	−	0.275034i	−0.791792	+	0.610791i	$0.790852\pi$
$888$		0			0
$889$	27.6523	+	10.0646i	0.927427	+	0.337556i
$890$		0			0
$891$	−26.0651	+	19.2238i	−0.873215	+	0.644023i
$892$		0			0
$893$	3.16334	+	1.15136i	0.105857	+	0.0385289i
$894$		0			0
$895$	19.8709	+	16.6737i	0.664212	+	0.557340i
$896$		0			0
$897$	3.61802	−	0.579673i	0.120802	−	0.0193547i
$898$		0			0
$899$	5.19360	+	8.99558i	0.173216	+	0.300019i
$900$		0			0
$901$	−18.3425	+	31.7701i	−0.611077	+	1.05842i
$902$		0			0
$903$	50.4219	+	9.70747i	1.67794	+	0.323044i
$904$		0			0
$905$	−20.4861	+	7.45633i	−0.680981	+	0.247857i
$906$		0			0
$907$	9.05289	+	51.3415i	0.300596	+	1.70477i	0.643542	+	0.765411i	$0.277464\pi$
$907$	9.05289	+	51.3415i	0.300596	+	1.70477i	−0.342946	+	0.939355i	$0.611425\pi$
$908$		0			0
$909$	−2.69654	−	18.7012i	−0.0894385	−	0.620280i
$910$		0			0
$911$	9.76975	−	8.19779i	0.323686	−	0.271605i	−0.466435	−	0.884555i	$-0.654462\pi$
$911$	9.76975	−	8.19779i	0.323686	−	0.271605i	0.790121	+	0.612950i	$0.210017\pi$
$912$		0			0
$913$	7.04261	−	39.9406i	0.233076	−	1.32184i
$914$		0			0
$915$	−33.6853	−	20.1583i	−1.11360	−	0.666412i
$916$		0			0
$917$	−3.87424			−0.127939
$918$		0			0
$919$	13.0259			0.429685			0.214843	−	0.976649i	$-0.431076\pi$
$919$	13.0259			0.429685			0.214843	+	0.976649i	$0.431076\pi$
$920$		0			0
$921$	0.0483628	−	3.08712i	0.00159361	−	0.101724i
$922$		0			0
$923$	0.485230	−	2.75188i	0.0159715	−	0.0905791i
$924$		0			0
$925$	35.1156	−	29.4655i	1.15459	−	0.968819i
$926$		0			0
$927$	37.2354	+	33.2865i	1.22297	+	1.09327i
$928$		0			0
$929$	9.47991	+	53.7632i	0.311026	+	1.76391i	0.593689	+	0.804695i	$0.297671\pi$
$929$	9.47991	+	53.7632i	0.311026	+	1.76391i	−0.282663	+	0.959219i	$0.591218\pi$
$930$		0			0
$931$	4.58086	−	1.66730i	0.150131	−	0.0546434i
$932$		0			0
$933$	9.63440	−	11.1232i	0.315416	−	0.364158i
$934$		0			0
$935$	45.2838	−	78.4338i	1.48094	−	2.56506i
$936$		0			0
$937$	−17.1680	−	29.7359i	−0.560856	−	0.971431i	−0.997422	−	0.0717585i	$-0.977139\pi$
$937$	−17.1680	−	29.7359i	−0.560856	−	0.971431i	0.436566	−	0.899672i	$-0.356194\pi$
$938$		0			0
$939$	−30.9502	−	38.0808i	−1.01002	−	1.24272i
$940$		0			0
$941$	38.3849	+	32.2088i	1.25131	+	1.04998i	0.996552	+	0.0829713i	$0.0264410\pi$
$941$	38.3849	+	32.2088i	1.25131	+	1.04998i	0.254760	+	0.967004i	$0.418003\pi$
$942$		0			0
$943$	−5.72675	−	2.08436i	−0.186488	−	0.0678763i
$944$		0			0
$945$	53.9575	−	27.8584i	1.75524	−	0.906234i
$946$		0			0
$947$	20.8369	+	7.58400i	0.677107	+	0.246447i	0.657605	−	0.753363i	$-0.271570\pi$
$947$	20.8369	+	7.58400i	0.677107	+	0.246447i	0.0195023	+	0.999810i	$0.493792\pi$
$948$		0			0
$949$	4.02106	+	3.37407i	0.130529	+	0.109527i
$950$		0			0
$951$	−12.8900	+	33.7600i	−0.417987	+	1.09474i
$952$		0			0
$953$	8.14929	+	14.1150i	0.263981	+	0.457229i	0.967296	−	0.253649i	$-0.0816309\pi$
$953$	8.14929	+	14.1150i	0.263981	+	0.457229i	−0.703315	+	0.710878i	$0.748298\pi$
$954$		0			0
$955$	−9.42396	+	16.3228i	−0.304952	+	0.528192i
$956$		0			0
$957$	−6.96549	−	20.1123i	−0.225162	−	0.650139i
$958$		0			0
$959$	−21.9229	+	7.97930i	−0.707928	+	0.257665i
$960$		0			0
$961$	−3.77639	−	21.4170i	−0.121819	−	0.690870i
$962$		0			0
$963$	−21.3173	+	34.3879i	−0.686939	+	1.10813i
$964$		0			0
$965$	−59.8359	+	50.2082i	−1.92618	+	1.61626i
$966$		0			0
$967$	3.90007	−	22.1184i	0.125418	−	0.711279i	−0.855641	−	0.517570i	$-0.826837\pi$
$967$	3.90007	−	22.1184i	0.125418	−	0.711279i	0.981059	−	0.193710i	$-0.0620520\pi$
$968$		0			0
$969$	−22.7096	+	12.6413i	−0.729538	+	0.406097i
$970$		0			0
$971$	−43.8482			−1.40715			−0.703577	−	0.710619i	$-0.748415\pi$
$971$	−43.8482			−1.40715			−0.703577	+	0.710619i	$0.748415\pi$
$972$		0			0
$973$	23.5231			0.754114
$974$		0			0
$975$	−53.0716	+	29.5423i	−1.69965	+	0.946110i
$976$		0			0
$977$	2.06020	−	11.6840i	0.0659117	−	0.373804i	−0.933954	−	0.357394i	$-0.883665\pi$
$977$	2.06020	−	11.6840i	0.0659117	−	0.373804i	0.999865	−	0.0164098i	$-0.00522362\pi$
$978$		0			0
$979$	25.1150	−	21.0740i	0.802679	−	0.673527i
$980$		0			0
$981$	−15.0084	+	24.2107i	−0.479180	+	0.772988i
$982$		0			0
$983$	−4.56799	−	25.9064i	−0.145696	−	0.826285i	−0.966805	−	0.255514i	$-0.917755\pi$
$983$	−4.56799	−	25.9064i	−0.145696	−	0.826285i	0.821109	−	0.570771i	$-0.193356\pi$
$984$		0			0
$985$	92.4981	−	33.6666i	2.94723	−	1.07271i
$986$		0			0
$987$	−2.49523	−	7.20478i	−0.0794240	−	0.229331i
$988$		0			0
$989$	−2.95895	+	5.12505i	−0.0940892	+	0.162967i
$990$		0			0
$991$	4.79382	+	8.30315i	0.152281	+	0.263758i	0.932066	−	0.362290i	$-0.118005\pi$
$991$	4.79382	+	8.30315i	0.152281	+	0.263758i	−0.779785	+	0.626048i	$0.784672\pi$
$992$		0			0
$993$	12.4252	−	32.5426i	0.394301	−	1.03271i
$994$		0			0
$995$	40.7255	+	34.1728i	1.29109	+	1.08335i
$996$		0			0
$997$	−17.7110	−	6.44629i	−0.560914	−	0.204156i	0.0459751	−	0.998943i	$-0.485361\pi$
$997$	−17.7110	−	6.44629i	−0.560914	−	0.204156i	−0.606889	+	0.794787i	$0.707583\pi$
$998$		0			0
$999$	−20.0686	−	12.8801i	−0.634941	−	0.407508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.f.193.1		30
4.3	odd	2		216.2.q.b.193.5	yes	30
12.11	even	2		648.2.q.b.145.5		30
27.7	even	9	inner	432.2.u.f.385.1		30
108.7	odd	18		216.2.q.b.169.5	✓	30
108.47	even	18		648.2.q.b.505.5		30
108.67	odd	18		5832.2.a.k.1.2		15
108.95	even	18		5832.2.a.l.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.169.5	✓	30	108.7	odd	18
216.2.q.b.193.5	yes	30	4.3	odd	2
432.2.u.f.193.1		30	1.1	even	1	trivial
432.2.u.f.385.1		30	27.7	even	9	inner
648.2.q.b.145.5		30	12.11	even	2
648.2.q.b.505.5		30	108.47	even	18
5832.2.a.k.1.2		15	108.67	odd	18
5832.2.a.l.1.14		15	108.95	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.51338 + 0.842423i) q^{3} +(-0.672282 + 3.81270i) q^{5} +(-2.31237 + 1.94030i) q^{7} +(1.58065 - 2.54981i) q^{9} +O(q^{10})\)	\(q+(-1.51338 + 0.842423i) q^{3} +(-0.672282 + 3.81270i) q^{5} +(-2.31237 + 1.94030i) q^{7} +(1.58065 - 2.54981i) q^{9} +(-0.624892 - 3.54394i) q^{11} +(-3.29907 + 1.20076i) q^{13} +(-2.19449 - 6.33642i) q^{15} +(3.25033 - 5.62973i) q^{17} +(1.15418 + 1.99910i) q^{19} +(1.86493 - 4.88441i) q^{21} +(0.461596 + 0.387325i) q^{23} +(-9.38628 - 3.41633i) q^{25} +(-0.244098 + 5.19042i) q^{27} +(-3.20886 - 1.16793i) q^{29} +(-2.33017 - 1.95524i) q^{31} +(3.93119 + 4.83690i) q^{33} +(-5.84324 - 10.1208i) q^{35} +(-2.29461 + 3.97438i) q^{37} +(3.98120 - 4.59643i) q^{39} +(-9.50385 + 3.45912i) q^{41} +(1.70541 + 9.67188i) q^{43} +(8.65905 + 7.74073i) q^{45} +(1.11715 - 0.937396i) q^{47} +(0.366713 - 2.07973i) q^{49} +(-0.176369 + 11.2581i) q^{51} -5.64327 q^{53} +13.9321 q^{55} +(-3.43081 - 2.05309i) q^{57} +(1.03250 - 5.85562i) q^{59} +(4.48457 - 3.76300i) q^{61} +(1.29239 + 8.96304i) q^{63} +(-2.36025 - 13.3856i) q^{65} +(-6.06757 + 2.20842i) q^{67} +(-1.02486 - 0.197311i) q^{69} +(-0.397962 + 0.689290i) q^{71} +(-0.747567 - 1.29482i) q^{73} +(17.0830 - 2.73701i) q^{75} +(8.32129 + 6.98239i) q^{77} +(-10.2545 - 3.73232i) q^{79} +(-4.00311 - 8.06071i) q^{81} +(10.5905 + 3.85461i) q^{83} +(19.2794 + 16.1773i) q^{85} +(5.84013 - 0.935696i) q^{87} +(4.55528 + 7.88997i) q^{89} +(5.29881 - 9.17781i) q^{91} +(5.17357 + 0.996041i) q^{93} +(-8.39792 + 3.05659i) q^{95} +(1.96190 + 11.1265i) q^{97} +(-10.0241 - 4.00835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q - 3 * q^7 - 6 * q^9	\( 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) \) 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Introduction

L-functions

Modular forms

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Database

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