LMFDB - Embedded newform 1161.2.f.d.388.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1161,2,Mod(388,1161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1161, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1161.388");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1161 = 3^{3} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1161.f (of order $3$, degree $2$, 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:	$9.27063167467$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 387)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			388.19
Character	$\chi$	$=$	1161.388
Dual form			1161.2.f.d.775.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04491 + 1.80984i) q^{2} +(-1.18368 + 2.05019i) q^{4} +(0.136674 - 0.236726i) q^{5} +(1.21012 + 2.09599i) q^{7} -0.767710 q^{8} +O(q^{10})$	\(q+(1.04491 + 1.80984i) q^{2} +(-1.18368 + 2.05019i) q^{4} +(0.136674 - 0.236726i) q^{5} +(1.21012 + 2.09599i) q^{7} -0.767710 q^{8} +0.571248 q^{10} +(-0.799468 - 1.38472i) q^{11} +(-1.73339 + 3.00232i) q^{13} +(-2.52893 + 4.38024i) q^{14} +(1.56517 + 2.71095i) q^{16} +3.58535 q^{17} +0.324858 q^{19} +(0.323556 + 0.560415i) q^{20} +(1.67075 - 2.89382i) q^{22} +(-2.17572 + 3.76846i) q^{23} +(2.46264 + 4.26542i) q^{25} -7.24495 q^{26} -5.72956 q^{28} +(-2.99685 - 5.19069i) q^{29} +(0.950453 - 1.64623i) q^{31} +(-4.03863 + 6.99512i) q^{32} +(3.74637 + 6.48891i) q^{34} +0.661566 q^{35} +2.23031 q^{37} +(0.339448 + 0.587942i) q^{38} +(-0.104926 + 0.181737i) q^{40} +(-5.20786 + 9.02028i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.78525 q^{44} -9.09374 q^{46} +(4.35738 + 7.54720i) q^{47} +(0.571231 - 0.989401i) q^{49} +(-5.14648 + 8.91397i) q^{50} +(-4.10355 - 7.10756i) q^{52} -4.52956 q^{53} -0.437066 q^{55} +(-0.929019 - 1.60911i) q^{56} +(6.26287 - 10.8476i) q^{58} +(4.95329 - 8.57935i) q^{59} +(-5.50849 - 9.54098i) q^{61} +3.97256 q^{62} -10.6194 q^{64} +(0.473818 + 0.820677i) q^{65} +(2.86882 - 4.96894i) q^{67} +(-4.24390 + 7.35065i) q^{68} +(0.691278 + 1.19733i) q^{70} -6.74222 q^{71} +0.832499 q^{73} +(2.33048 + 4.03650i) q^{74} +(-0.384528 + 0.666022i) q^{76} +(1.93490 - 3.35135i) q^{77} +(4.00799 + 6.94204i) q^{79} +0.855671 q^{80} -21.7670 q^{82} +(-3.40533 - 5.89820i) q^{83} +(0.490024 - 0.848746i) q^{85} +(-1.04491 + 1.80984i) q^{86} +(0.613759 + 1.06306i) q^{88} +9.69164 q^{89} -8.39042 q^{91} +(-5.15071 - 8.92129i) q^{92} +(-9.10615 + 15.7723i) q^{94} +(0.0443997 - 0.0769025i) q^{95} +(-0.848918 - 1.47037i) q^{97} +2.38754 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) $ 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8	$ 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) $ 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8 - 4 * q^10 - 10 * q^11 + q^13 - 10 * q^14 - 22 * q^16 + 40 * q^17 + 16 * q^19 - 30 * q^20 - 15 * q^22 - 19 * q^23 - 19 * q^25 + 50 * q^26 - 6 * q^28 - 25 * q^29 + 11 * q^31 - 36 * q^32 - 9 * q^34 + 18 * q^37 - 28 * q^38 - 12 * q^40 - 12 * q^41 + 20 * q^43 + 10 * q^44 + 8 * q^46 - 38 * q^47 - 37 * q^49 - 36 * q^50 + 8 * q^52 + 138 * q^53 - 18 * q^55 - 30 * q^56 + 27 * q^58 - 31 * q^59 - 19 * q^61 + 64 * q^62 + 22 * q^64 - 47 * q^65 - 9 * q^67 - 68 * q^68 + 6 * q^70 + 42 * q^71 - 4 * q^73 + 16 * q^74 - 37 * q^76 - 85 * q^77 + 4 * q^79 + 122 * q^80 + 2 * q^82 - 19 * q^83 + 6 * q^85 + 6 * q^86 - 60 * q^88 + 108 * q^89 - 6 * q^91 - 85 * q^92 + 19 * q^94 + 11 * q^95 - 2 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times$.

$n$	$433$	$947$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.04491	+	1.80984i	0.738864	+	1.27975i	0.953007	+	0.302947i	$0.0979706\pi$
$2$	1.04491	+	1.80984i	0.738864	+	1.27975i	−0.214144	+	0.976802i	$0.568696\pi$
$3$		0			0
$3$		0			0
$4$	−1.18368	+	2.05019i	−0.591839	+	1.02510i
$5$	0.136674	−	0.236726i	0.0611224	−	0.105867i	−0.833845	−	0.551999i	$-0.813865\pi$
$5$	0.136674	−	0.236726i	0.0611224	−	0.105867i	0.894967	+	0.446132i	$0.147199\pi$
$6$		0			0
$7$	1.21012	+	2.09599i	0.457381	+	0.792208i	0.998822	−	0.0485314i	$-0.0154541\pi$
$7$	1.21012	+	2.09599i	0.457381	+	0.792208i	−0.541440	+	0.840739i	$0.682121\pi$
$8$	−0.767710			−0.271426
$9$		0			0
$10$	0.571248			0.180645
$11$	−0.799468	−	1.38472i	−0.241049	−	0.417508i	0.719965	−	0.694011i	$-0.244158\pi$
$11$	−0.799468	−	1.38472i	−0.241049	−	0.417508i	−0.961013	+	0.276502i	$0.910825\pi$
$12$		0			0
$13$	−1.73339	+	3.00232i	−0.480756	+	0.832693i	−0.999756	−	0.0220806i	$-0.992971\pi$
$13$	−1.73339	+	3.00232i	−0.480756	+	0.832693i	0.519000	+	0.854774i	$0.326304\pi$
$14$	−2.52893	+	4.38024i	−0.675885	+	1.17067i
$15$		0			0
$16$	1.56517	+	2.71095i	0.391292	+	0.677738i
$17$	3.58535			0.869575			0.434788	−	0.900533i	$-0.356823\pi$
$17$	3.58535			0.869575			0.434788	+	0.900533i	$0.356823\pi$
$18$		0			0
$19$	0.324858			0.0745276			0.0372638	−	0.999305i	$-0.488136\pi$
$19$	0.324858			0.0745276			0.0372638	+	0.999305i	$0.488136\pi$
$20$	0.323556	+	0.560415i	0.0723493	+	0.125313i
$21$		0			0
$22$	1.67075	−	2.89382i	0.356204	−	0.616964i
$23$	−2.17572	+	3.76846i	−0.453669	+	0.785778i	−0.998611	−	0.0526959i	$-0.983219\pi$
$23$	−2.17572	+	3.76846i	−0.453669	+	0.785778i	0.544941	+	0.838474i	$0.316552\pi$
$24$		0			0
$25$	2.46264	+	4.26542i	0.492528	+	0.853084i
$26$	−7.24495			−1.42085
$27$		0			0
$28$	−5.72956			−1.08278
$29$	−2.99685	−	5.19069i	−0.556500	−	0.963887i	−0.997785	−	0.0665197i	$-0.978810\pi$
$29$	−2.99685	−	5.19069i	−0.556500	−	0.963887i	0.441285	−	0.897367i	$-0.354523\pi$
$30$		0			0
$31$	0.950453	−	1.64623i	0.170706	−	0.295672i	−0.767961	−	0.640497i	$-0.778728\pi$
$31$	0.950453	−	1.64623i	0.170706	−	0.295672i	0.938667	+	0.344825i	$0.112062\pi$
$32$	−4.03863	+	6.99512i	−0.713936	+	1.23657i
$33$		0			0
$34$	3.74637	+	6.48891i	0.642498	+	1.11284i
$35$	0.661566			0.111825
$36$		0			0
$37$	2.23031			0.366661			0.183330	−	0.983051i	$-0.441312\pi$
$37$	2.23031			0.366661			0.183330	+	0.983051i	$0.441312\pi$
$38$	0.339448	+	0.587942i	0.0550658	+	0.0953767i
$39$		0			0
$40$	−0.104926	+	0.181737i	−0.0165902	+	0.0287351i
$41$	−5.20786	+	9.02028i	−0.813331	+	1.40873i	0.0971886	+	0.995266i	$0.469015\pi$
$41$	−5.20786	+	9.02028i	−0.813331	+	1.40873i	−0.910520	+	0.413465i	$0.864318\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i
$44$	3.78525			0.570648
$45$		0			0
$46$	−9.09374			−1.34080
$47$	4.35738	+	7.54720i	0.635589	+	1.10087i	0.986390	+	0.164422i	$0.0525760\pi$
$47$	4.35738	+	7.54720i	0.635589	+	1.10087i	−0.350801	+	0.936450i	$0.614091\pi$
$48$		0			0
$49$	0.571231	−	0.989401i	0.0816044	−	0.141343i
$50$	−5.14648	+	8.91397i	−0.727822	+	1.26063i
$51$		0			0
$52$	−4.10355	−	7.10756i	−0.569060	−	0.985641i
$53$	−4.52956			−0.622182			−0.311091	−	0.950380i	$-0.600694\pi$
$53$	−4.52956			−0.622182			−0.311091	+	0.950380i	$0.600694\pi$
$54$		0			0
$55$	−0.437066			−0.0589339
$56$	−0.929019	−	1.60911i	−0.124145	−	0.215026i
$57$		0			0
$58$	6.26287	−	10.8476i	0.822356	−	1.42436i
$59$	4.95329	−	8.57935i	0.644864	−	1.11694i	−0.339469	−	0.940617i	$-0.610247\pi$
$59$	4.95329	−	8.57935i	0.644864	−	1.11694i	0.984333	−	0.176320i	$-0.0564192\pi$
$60$		0			0
$61$	−5.50849	−	9.54098i	−0.705289	−	1.22160i	−0.966587	−	0.256339i	$-0.917484\pi$
$61$	−5.50849	−	9.54098i	−0.705289	−	1.22160i	0.261298	−	0.965258i	$-0.415850\pi$
$62$	3.97256			0.504515
$63$		0			0
$64$	−10.6194			−1.32742
$65$	0.473818	+	0.820677i	0.0587699	+	0.101792i
$66$		0			0
$67$	2.86882	−	4.96894i	0.350482	−	0.607053i	−0.635852	−	0.771811i	$-0.719351\pi$
$67$	2.86882	−	4.96894i	0.350482	−	0.607053i	0.986334	+	0.164758i	$0.0526844\pi$
$68$	−4.24390	+	7.35065i	−0.514649	+	0.891398i
$69$		0			0
$70$	0.691278	+	1.19733i	0.0826235	+	0.143108i
$71$	−6.74222			−0.800155			−0.400077	−	0.916481i	$-0.631017\pi$
$71$	−6.74222			−0.800155			−0.400077	+	0.916481i	$0.631017\pi$
$72$		0			0
$73$	0.832499			0.0974367			0.0487183	−	0.998813i	$-0.484486\pi$
$73$	0.832499			0.0974367			0.0487183	+	0.998813i	$0.484486\pi$
$74$	2.33048	+	4.03650i	0.270912	+	0.469234i
$75$		0			0
$76$	−0.384528	+	0.666022i	−0.0441084	+	0.0763979i
$77$	1.93490	−	3.35135i	0.220502	−	0.381921i
$78$		0			0
$79$	4.00799	+	6.94204i	0.450934	+	0.781040i	0.998444	−	0.0557587i	$-0.0177578\pi$
$79$	4.00799	+	6.94204i	0.450934	+	0.781040i	−0.547511	+	0.836799i	$0.684424\pi$
$80$	0.855671			0.0956669
$81$		0			0
$82$	−21.7670			−2.40376
$83$	−3.40533	−	5.89820i	−0.373783	−	0.647412i	0.616361	−	0.787464i	$-0.288606\pi$
$83$	−3.40533	−	5.89820i	−0.373783	−	0.647412i	−0.990144	+	0.140052i	$0.955273\pi$
$84$		0			0
$85$	0.490024	−	0.848746i	0.0531505	−	0.0920595i
$86$	−1.04491	+	1.80984i	−0.112676	+	0.195160i
$87$		0			0
$88$	0.613759	+	1.06306i	0.0654269	+	0.113323i
$89$	9.69164			1.02731			0.513656	−	0.857996i	$-0.328291\pi$
$89$	9.69164			1.02731			0.513656	+	0.857996i	$0.328291\pi$
$90$		0			0
$91$	−8.39042			−0.879555
$92$	−5.15071	−	8.92129i	−0.536998	−	0.930109i
$93$		0			0
$94$	−9.10615	+	15.7723i	−0.939227	+	1.62679i
$95$	0.0443997	−	0.0769025i	0.00455531	−	0.00789003i
$96$		0			0
$97$	−0.848918	−	1.47037i	−0.0861946	−	0.149293i	0.819705	−	0.572786i	$-0.194137\pi$
$97$	−0.848918	−	1.47037i	−0.0861946	−	0.149293i	−0.905900	+	0.423492i	$0.860804\pi$
$98$	2.38754			0.241178
$99$		0			0
$100$	−11.6599			−1.16599
$101$	−5.50615	−	9.53694i	−0.547883	−	0.948961i	−0.998419	−	0.0562029i	$-0.982101\pi$
$101$	−5.50615	−	9.53694i	−0.547883	−	0.948961i	0.450537	−	0.892758i	$-0.351233\pi$
$102$		0			0
$103$	−2.34516	+	4.06193i	−0.231075	+	0.400234i	−0.958125	−	0.286351i	$-0.907558\pi$
$103$	−2.34516	+	4.06193i	−0.231075	+	0.400234i	0.727050	+	0.686585i	$0.240891\pi$
$104$	1.33074	−	2.30491i	0.130490	−	0.226015i
$105$		0			0
$106$	−4.73298	−	8.19777i	−0.459708	−	0.796238i
$107$	18.1464			1.75427			0.877137	−	0.480239i	$-0.159450\pi$
$107$	18.1464			1.75427			0.877137	+	0.480239i	$0.159450\pi$
$108$		0			0
$109$	−2.03854			−0.195257			−0.0976285	−	0.995223i	$-0.531126\pi$
$109$	−2.03854			−0.195257			−0.0976285	+	0.995223i	$0.531126\pi$
$110$	−0.456695	−	0.791018i	−0.0435441	−	0.0754206i
$111$		0			0
$112$	−3.78807	+	6.56114i	−0.357939	+	0.619969i
$113$	−0.438162	+	0.758919i	−0.0412188	+	0.0713931i	−0.885899	−	0.463879i	$-0.846457\pi$
$113$	−0.438162	+	0.758919i	−0.0412188	+	0.0713931i	0.844680	+	0.535272i	$0.179791\pi$
$114$		0			0
$115$	0.594729	+	1.03010i	0.0554587	+	0.0960574i
$116$	14.1892			1.31743
$117$		0			0
$118$	20.7030			1.90587
$119$	4.33870	+	7.51484i	0.397728	+	0.688884i
$120$		0			0
$121$	4.22170	−	7.31220i	0.383791	−	0.664746i
$122$	11.5118	−	19.9389i	1.04223	−	1.80519i
$123$		0			0
$124$	2.25006	+	3.89722i	0.202062	+	0.349981i
$125$	2.71305			0.242663
$126$		0			0
$127$	3.12225			0.277055			0.138527	−	0.990359i	$-0.455763\pi$
$127$	3.12225			0.277055			0.138527	+	0.990359i	$0.455763\pi$
$128$	−3.01904	−	5.22913i	−0.266848	−	0.462194i
$129$		0			0
$130$	−0.990196	+	1.71507i	−0.0868459	+	0.150422i
$131$	−0.763641	+	1.32266i	−0.0667196	+	0.115562i	−0.897455	−	0.441105i	$-0.854587\pi$
$131$	−0.763641	+	1.32266i	−0.0667196	+	0.115562i	0.830736	+	0.556667i	$0.187920\pi$
$132$		0			0
$133$	0.393117	+	0.680898i	0.0340876	+	0.0590414i
$134$	11.9907			1.03583
$135$		0			0
$136$	−2.75251			−0.236026
$137$	−2.15844	−	3.73854i	−0.184408	−	0.319405i	0.758969	−	0.651127i	$-0.225704\pi$
$137$	−2.15844	−	3.73854i	−0.184408	−	0.319405i	−0.943377	+	0.331722i	$0.892370\pi$
$138$		0			0
$139$	9.30729	−	16.1207i	0.789434	−	1.36734i	−0.136880	−	0.990588i	$-0.543707\pi$
$139$	9.30729	−	16.1207i	0.789434	−	1.36734i	0.926314	−	0.376753i	$-0.122959\pi$
$140$	−0.783081	+	1.35634i	−0.0661824	+	0.114631i
$141$		0			0
$142$	−7.04502	−	12.2023i	−0.591205	−	1.02400i
$143$	5.54316			0.463542
$144$		0			0
$145$	−1.63836			−0.136059
$146$	0.869888	+	1.50669i	0.0719924	+	0.124695i
$147$		0			0
$148$	−2.63997	+	4.57256i	−0.217004	+	0.375862i
$149$	2.55883	−	4.43203i	0.209628	−	0.363086i	−0.741969	−	0.670434i	$-0.766108\pi$
$149$	2.55883	−	4.43203i	0.209628	−	0.363086i	0.951597	+	0.307348i	$0.0994414\pi$
$150$		0			0
$151$	−6.44831	−	11.1688i	−0.524756	−	0.908904i	−0.999584	−	0.0288259i	$-0.990823\pi$
$151$	−6.44831	−	11.1688i	−0.524756	−	0.908904i	0.474828	−	0.880078i	$-0.342510\pi$
$152$	−0.249397			−0.0202288
$153$		0			0
$154$	8.08719			0.651685
$155$	−0.259804	−	0.449994i	−0.0208680	−	0.0361444i
$156$		0			0
$157$	5.65985	−	9.80315i	0.451705	−	0.782377i	−0.546787	−	0.837272i	$-0.684149\pi$
$157$	5.65985	−	9.80315i	0.451705	−	0.782377i	0.998492	+	0.0548952i	$0.0174825\pi$
$158$	−8.37598	+	14.5076i	−0.666357	+	1.15416i
$159$		0			0
$160$	1.10395	+	1.91210i	0.0872750	+	0.151165i
$161$	−10.5315			−0.830000
$162$		0			0
$163$	9.46663			0.741484			0.370742	−	0.928736i	$-0.379103\pi$
$163$	9.46663			0.741484			0.370742	+	0.928736i	$0.379103\pi$
$164$	−12.3289	−	21.3542i	−0.962723	−	1.66748i
$165$		0			0
$166$	7.11653	−	12.3262i	0.552350	−	0.956698i
$167$	0.882435	−	1.52842i	0.0682849	−	0.118273i	−0.829862	−	0.557969i	$-0.811581\pi$
$167$	0.882435	−	1.52842i	0.0682849	−	0.118273i	0.898146	+	0.439696i	$0.144914\pi$
$168$		0			0
$169$	0.490722	+	0.849956i	0.0377479	+	0.0653812i
$170$	2.04813			0.157084
$171$		0			0
$172$	−2.36736			−0.180509
$173$	10.5360	+	18.2490i	0.801041	+	1.38744i	0.918932	+	0.394416i	$0.129053\pi$
$173$	10.5360	+	18.2490i	0.801041	+	1.38744i	−0.117891	+	0.993027i	$0.537613\pi$
$174$		0			0
$175$	−5.96017	+	10.3233i	−0.450546	+	0.780369i
$176$	2.50260	−	4.33464i	0.188641	−	0.326735i
$177$		0			0
$178$	10.1269	+	17.5403i	0.759043	+	1.31470i
$179$	−7.77067			−0.580807			−0.290403	−	0.956904i	$-0.593790\pi$
$179$	−7.77067			−0.580807			−0.290403	+	0.956904i	$0.593790\pi$
$180$		0			0
$181$	21.4202			1.59215			0.796074	−	0.605199i	$-0.206907\pi$
$181$	21.4202			1.59215			0.796074	+	0.605199i	$0.206907\pi$
$182$	−8.76724	−	15.1853i	−0.649871	−	1.12561i
$183$		0			0
$184$	1.67032	−	2.89308i	0.123138	−	0.213281i
$185$	0.304825	−	0.527973i	0.0224112	−	0.0388174i
$186$		0			0
$187$	−2.86637	−	4.96470i	−0.209610	−	0.363055i
$188$	−20.6309			−1.50467
$189$		0			0
$190$	0.185575			0.0134630
$191$	−8.60539	−	14.9050i	−0.622664	−	1.07849i	−0.988988	−	0.147998i	$-0.952717\pi$
$191$	−8.60539	−	14.9050i	−0.622664	−	1.07849i	0.366324	−	0.930487i	$-0.380616\pi$
$192$		0			0
$193$	2.47681	−	4.28996i	0.178285	−	0.308798i	−0.763008	−	0.646389i	$-0.776279\pi$
$193$	2.47681	−	4.28996i	0.178285	−	0.308798i	0.941293	+	0.337590i	$0.109612\pi$
$194$	1.77409	−	3.07281i	0.127372	−	0.220615i
$195$		0			0
$196$	1.35231	+	2.34227i	0.0965934	+	0.167305i
$197$	−0.691719			−0.0492830			−0.0246415	−	0.999696i	$-0.507844\pi$
$197$	−0.691719			−0.0492830			−0.0246415	+	0.999696i	$0.507844\pi$
$198$		0			0
$199$	13.5430			0.960036			0.480018	−	0.877259i	$-0.340630\pi$
$199$	13.5430			0.960036			0.480018	+	0.877259i	$0.340630\pi$
$200$	−1.89059	−	3.27460i	−0.133685	−	0.231549i
$201$		0			0
$202$	11.5069	−	19.9305i	0.809621	−	1.40231i
$203$	7.25307	−	12.5627i	0.509066	−	0.881728i
$204$		0			0
$205$	1.42356	+	2.46567i	0.0994256	+	0.172210i
$206$	−9.80192			−0.682932
$207$		0			0
$208$	−10.8522			−0.752464
$209$	−0.259714	−	0.449838i	−0.0179648	−	0.0311159i
$210$		0			0
$211$	−9.50220	+	16.4583i	−0.654159	+	1.13304i	0.327945	+	0.944697i	$0.393644\pi$
$211$	−9.50220	+	16.4583i	−0.654159	+	1.13304i	−0.982104	+	0.188339i	$0.939690\pi$
$212$	5.36154	−	9.28646i	0.368232	−	0.637796i
$213$		0			0
$214$	18.9613	+	32.8420i	1.29617	+	2.24503i
$215$	0.273348			0.0186422
$216$		0			0
$217$	4.60064			0.312312
$218$	−2.13010	−	3.68943i	−0.144268	−	0.249880i
$219$		0			0
$220$	0.517345	−	0.896068i	0.0348794	−	0.0604129i
$221$	−6.21481	+	10.7644i	−0.418053	+	0.724089i
$222$		0			0
$223$	−2.19760	−	3.80635i	−0.147162	−	0.254892i	0.783016	−	0.622002i	$-0.213681\pi$
$223$	−2.19760	−	3.80635i	−0.147162	−	0.254892i	−0.930177	+	0.367110i	$0.880347\pi$
$224$	−19.5489			−1.30616
$225$		0			0
$226$	−1.83136			−0.121820
$227$	14.1508	+	24.5099i	0.939223	+	1.62678i	0.766925	+	0.641737i	$0.221786\pi$
$227$	14.1508	+	24.5099i	0.939223	+	1.62678i	0.172298	+	0.985045i	$0.444881\pi$
$228$		0			0
$229$	13.1976	−	22.8589i	0.872120	−	1.51056i	0.0123204	−	0.999924i	$-0.496078\pi$
$229$	13.1976	−	22.8589i	0.872120	−	1.51056i	0.859799	−	0.510632i	$-0.170588\pi$
$230$	−1.24288	+	2.15273i	−0.0819529	+	0.141947i
$231$		0			0
$232$	2.30071	+	3.98494i	0.151049	+	0.261624i
$233$	28.1007			1.84094			0.920470	−	0.390814i	$-0.127806\pi$
$233$	28.1007			1.84094			0.920470	+	0.390814i	$0.127806\pi$
$234$		0			0
$235$	2.38216			0.155395
$236$	11.7262	+	20.3104i	0.763311	+	1.32209i
$237$		0			0
$238$	−9.06710	+	15.7047i	−0.587733	+	1.01798i
$239$	−2.79192	+	4.83574i	−0.180594	+	0.312798i	−0.942083	−	0.335380i	$-0.891135\pi$
$239$	−2.79192	+	4.83574i	−0.180594	+	0.312798i	0.761489	+	0.648178i	$0.224469\pi$
$240$		0			0
$241$	−3.59718	−	6.23050i	−0.231715	−	0.401342i	0.726598	−	0.687063i	$-0.241100\pi$
$241$	−3.59718	−	6.23050i	−0.231715	−	0.401342i	−0.958313	+	0.285721i	$0.907767\pi$
$242$	17.6452			1.13428
$243$		0			0
$244$	26.0811			1.66967
$245$	−0.156145	−	0.270451i	−0.00997572	−	0.0172785i
$246$		0			0
$247$	−0.563106	+	0.975329i	−0.0358296	+	0.0620587i
$248$	−0.729672	+	1.26383i	−0.0463342	+	0.0802532i
$249$		0			0
$250$	2.83490	+	4.91019i	0.179295	+	0.310548i
$251$	−5.34271			−0.337229			−0.168614	−	0.985682i	$-0.553929\pi$
$251$	−5.34271			−0.337229			−0.168614	+	0.985682i	$0.553929\pi$
$252$		0			0
$253$	6.95768			0.437425
$254$	3.26247	+	5.65077i	0.204706	+	0.354561i
$255$		0			0
$256$	−4.31012	+	7.46535i	−0.269383	+	0.466585i
$257$	−8.34743	+	14.4582i	−0.520698	+	0.901876i	0.479012	+	0.877808i	$0.340995\pi$
$257$	−8.34743	+	14.4582i	−0.520698	+	0.901876i	−0.999710	+	0.0240677i	$0.992338\pi$
$258$		0			0
$259$	2.69894	+	4.67470i	0.167704	+	0.290472i
$260$	−2.24339			−0.139129
$261$		0			0
$262$	−3.19175			−0.197187
$263$	−8.74573	−	15.1480i	−0.539285	−	0.934069i	−0.998943	−	0.0459725i	$-0.985361\pi$
$263$	−8.74573	−	15.1480i	−0.539285	−	0.934069i	0.459658	−	0.888096i	$-0.347972\pi$
$264$		0			0
$265$	−0.619072	+	1.07226i	−0.0380293	+	0.0658687i
$266$	−0.821544	+	1.42296i	−0.0503721	+	0.0872471i
$267$		0			0
$268$	6.79152	+	11.7633i	0.414858	+	0.718555i
$269$	−32.3234			−1.97079			−0.985395	−	0.170286i	$-0.945531\pi$
$269$	−32.3234			−1.97079			−0.985395	+	0.170286i	$0.945531\pi$
$270$		0			0
$271$	3.81719			0.231878			0.115939	−	0.993256i	$-0.463012\pi$
$271$	3.81719			0.231878			0.115939	+	0.993256i	$0.463012\pi$
$272$	5.61168	+	9.71971i	0.340258	+	0.589344i
$273$		0			0
$274$	4.51077	−	7.81288i	0.272505	−	0.471993i
$275$	3.93760	−	6.82013i	0.237446	−	0.411269i
$276$		0			0
$277$	−14.2015	−	24.5976i	−0.853283	−	1.47793i	−0.878229	−	0.478241i	$-0.841275\pi$
$277$	−14.2015	−	24.5976i	−0.853283	−	1.47793i	0.0249458	−	0.999689i	$-0.492059\pi$
$278$	38.9012			2.33314
$279$		0			0
$280$	−0.507891			−0.0303523
$281$	−3.36279	−	5.82452i	−0.200607	−	0.347461i	0.748117	−	0.663567i	$-0.230958\pi$
$281$	−3.36279	−	5.82452i	−0.200607	−	0.347461i	−0.948724	+	0.316105i	$0.897625\pi$
$282$		0			0
$283$	−15.3979	+	26.6700i	−0.915312	+	1.58537i	−0.108868	+	0.994056i	$0.534722\pi$
$283$	−15.3979	+	26.6700i	−0.915312	+	1.58537i	−0.806444	+	0.591310i	$0.798611\pi$
$284$	7.98062	−	13.8228i	0.473563	−	0.820235i
$285$		0			0
$286$	5.79211	+	10.0322i	0.342494	+	0.593218i
$287$	−25.2085			−1.48801
$288$		0			0
$289$	−4.14526			−0.243839
$290$	−1.71194	−	2.96517i	−0.100529	−	0.174121i
$291$		0			0
$292$	−0.985411	+	1.70678i	−0.0576668	+	0.0998819i
$293$	−2.23699	+	3.87458i	−0.130686	+	0.226355i	−0.923941	−	0.382534i	$-0.875051\pi$
$293$	−2.23699	+	3.87458i	−0.130686	+	0.226355i	0.793255	+	0.608889i	$0.208385\pi$
$294$		0			0
$295$	−1.35397	−	2.34515i	−0.0788313	−	0.136540i
$296$	−1.71223			−0.0995214
$297$		0			0
$298$	10.6950			0.619546
$299$	−7.54275	−	13.0644i	−0.436208	−	0.755535i
$300$		0			0
$301$	−1.21012	+	2.09599i	−0.0697500	+	0.120811i
$302$	13.4758	−	23.3408i	0.775447	−	1.34311i
$303$		0			0
$304$	0.508458	+	0.880675i	0.0291621	+	0.0505102i
$305$	−3.01147			−0.172436
$306$		0			0
$307$	15.8569			0.904999			0.452500	−	0.891765i	$-0.350532\pi$
$307$	15.8569			0.904999			0.452500	+	0.891765i	$0.350532\pi$
$308$	4.58060	+	7.93383i	0.261004	+	0.452072i
$309$		0			0
$310$	0.542945	−	0.940408i	0.0308372	−	0.0534116i
$311$	4.27370	−	7.40227i	0.242339	−	0.419744i	−0.719041	−	0.694968i	$-0.755419\pi$
$311$	4.27370	−	7.40227i	0.242339	−	0.419744i	0.961380	+	0.275224i	$0.0887519\pi$
$312$		0			0
$313$	−11.4403	−	19.8152i	−0.646644	−	1.12002i	−0.983919	−	0.178614i	$-0.942839\pi$
$313$	−11.4403	−	19.8152i	−0.646644	−	1.12002i	0.337275	−	0.941406i	$-0.390495\pi$
$314$	23.6562			1.33500
$315$		0			0
$316$	−18.9767			−1.06752
$317$	−13.6986	−	23.7267i	−0.769391	−	1.33262i	−0.937894	−	0.346923i	$-0.887227\pi$
$317$	−13.6986	−	23.7267i	−0.769391	−	1.33262i	0.168503	−	0.985701i	$-0.446107\pi$
$318$		0			0
$319$	−4.79176	+	8.29958i	−0.268287	+	0.464687i
$320$	−1.45139	+	2.51388i	−0.0811353	+	0.140530i
$321$		0			0
$322$	−11.0045	−	19.0603i	−0.613257	−	1.06219i
$323$	1.16473			0.0648074
$324$		0			0
$325$	−17.0749			−0.947143
$326$	9.89179	+	17.1331i	0.547855	+	0.948913i
$327$		0			0
$328$	3.99813	−	6.92496i	0.220760	−	0.382367i
$329$	−10.5459	+	18.2660i	−0.581413	+	1.00704i
$330$		0			0
$331$	11.5499	+	20.0051i	0.634841	+	1.09958i	0.986549	+	0.163467i	$0.0522678\pi$
$331$	11.5499	+	20.0051i	0.634841	+	1.09958i	−0.351707	+	0.936110i	$0.614399\pi$
$332$	16.1233			0.884878
$333$		0			0
$334$	3.68826			0.201813
$335$	−0.784186	−	1.35825i	−0.0428447	−	0.0742091i
$336$		0			0
$337$	−11.0031	+	19.0580i	−0.599378	+	1.03815i	0.393535	+	0.919310i	$0.371252\pi$
$337$	−11.0031	+	19.0580i	−0.599378	+	1.03815i	−0.992913	+	0.118843i	$0.962081\pi$
$338$	−1.02552	+	1.77626i	−0.0557810	+	0.0966156i
$339$		0			0
$340$	1.16006	+	2.00928i	0.0629131	+	0.108969i
$341$	−3.03943			−0.164594
$342$		0			0
$343$	19.7067			1.06406
$344$	−0.383855	−	0.664856i	−0.0206961	−	0.0358466i
$345$		0			0
$346$	−22.0185	+	38.1371i	−1.18372	+	2.05026i
$347$	2.70165	−	4.67940i	0.145032	−	0.251203i	−0.784353	−	0.620315i	$-0.787005\pi$
$347$	2.70165	−	4.67940i	0.145032	−	0.251203i	0.929385	+	0.369112i	$0.120338\pi$
$348$		0			0
$349$	−2.35604	−	4.08078i	−0.126116	−	0.218439i	0.796053	−	0.605227i	$-0.206918\pi$
$349$	−2.35604	−	4.08078i	−0.126116	−	0.218439i	−0.922169	+	0.386788i	$0.873584\pi$
$350$	−24.9114			−1.33157
$351$		0			0
$352$	12.9150			0.688373
$353$	−12.5130	−	21.6732i	−0.666001	−	1.15355i	−0.979013	−	0.203799i	$-0.934671\pi$
$353$	−12.5130	−	21.6732i	−0.666001	−	1.15355i	0.313012	−	0.949749i	$-0.398662\pi$
$354$		0			0
$355$	−0.921486	+	1.59606i	−0.0489074	+	0.0847101i
$356$	−11.4718	+	19.8697i	−0.608003	+	1.05309i
$357$		0			0
$358$	−8.11966	−	14.0637i	−0.429137	−	0.743287i
$359$	−11.4471			−0.604156			−0.302078	−	0.953283i	$-0.597680\pi$
$359$	−11.4471			−0.604156			−0.302078	+	0.953283i	$0.597680\pi$
$360$		0			0
$361$	−18.8945			−0.994446
$362$	22.3822	+	38.7670i	1.17638	+	2.03755i
$363$		0			0
$364$	9.93156	−	17.2020i	0.520555	−	0.901628i
$365$	0.113781	−	0.197074i	0.00595557	−	0.0103153i
$366$		0			0
$367$	8.16377	+	14.1401i	0.426146	+	0.738106i	0.996527	−	0.0832745i	$-0.0265378\pi$
$367$	8.16377	+	14.1401i	0.426146	+	0.738106i	−0.570381	+	0.821380i	$0.693204\pi$
$368$	−13.6215			−0.710069
$369$		0			0
$370$	1.27406			0.0662353
$371$	−5.48130	−	9.49388i	−0.284575	−	0.492898i
$372$		0			0
$373$	−8.14914	+	14.1147i	−0.421946	+	0.730833i	−0.996130	−	0.0878940i	$-0.971986\pi$
$373$	−8.14914	+	14.1147i	−0.421946	+	0.730833i	0.574183	+	0.818727i	$0.305320\pi$
$374$	5.99021	−	10.3753i	0.309746	−	0.536496i
$375$		0			0
$376$	−3.34520	−	5.79406i	−0.172516	−	0.298806i
$377$	20.7788			1.07016
$378$		0			0
$379$	34.9308			1.79427			0.897136	−	0.441754i	$-0.145644\pi$
$379$	34.9308			1.79427			0.897136	+	0.441754i	$0.145644\pi$
$380$	0.105110	+	0.182056i	0.00539202	+	0.00933926i
$381$		0			0
$382$	17.9837	−	31.1487i	0.920128	−	1.59371i
$383$	−13.7964	+	23.8960i	−0.704962	+	1.22103i	0.261744	+	0.965137i	$0.415703\pi$
$383$	−13.7964	+	23.8960i	−0.704962	+	1.22103i	−0.966705	+	0.255892i	$0.917631\pi$
$384$		0			0
$385$	−0.528901	−	0.916083i	−0.0269553	−	0.0466879i
$386$	10.3522			0.526913
$387$		0			0
$388$	4.01938			0.204053
$389$	−7.06235	−	12.2324i	−0.358075	−	0.620205i	0.629564	−	0.776949i	$-0.283234\pi$
$389$	−7.06235	−	12.2324i	−0.358075	−	0.620205i	−0.987639	+	0.156744i	$0.949900\pi$
$390$		0			0
$391$	−7.80072	+	13.5112i	−0.394500	+	0.683293i
$392$	−0.438540	+	0.759573i	−0.0221496	+	0.0383642i
$393$		0			0
$394$	−0.722785	−	1.25190i	−0.0364134	−	0.0630698i
$395$	2.19115			0.110249
$396$		0			0
$397$	29.4385			1.47748			0.738738	−	0.673993i	$-0.235422\pi$
$397$	29.4385			1.47748			0.738738	+	0.673993i	$0.235422\pi$
$398$	14.1512	+	24.5106i	0.709336	+	1.22861i
$399$		0			0
$400$	−7.70889	+	13.3522i	−0.385445	+	0.667610i
$401$	−8.52898	+	14.7726i	−0.425917	+	0.737710i	−0.996506	−	0.0835263i	$-0.973382\pi$
$401$	−8.52898	+	14.7726i	−0.425917	+	0.737710i	0.570589	+	0.821236i	$0.306715\pi$
$402$		0			0
$403$	3.29501	+	5.70713i	0.164136	+	0.284292i
$404$	26.0701			1.29703
$405$		0			0
$406$	30.3153			1.50452
$407$	−1.78306	−	3.08835i	−0.0883831	−	0.153084i
$408$		0			0
$409$	18.7113	−	32.4089i	0.925215	−	1.60252i	0.133999	−	0.990981i	$-0.457218\pi$
$409$	18.7113	−	32.4089i	0.925215	−	1.60252i	0.791216	−	0.611537i	$-0.209449\pi$
$410$	−2.97498	+	5.15282i	−0.146924	+	0.254480i
$411$		0			0
$412$	−5.55182	−	9.61604i	−0.273519	−	0.473748i
$413$	23.9763			1.17979
$414$		0			0
$415$	−1.86168			−0.0913862
$416$	−14.0010	−	24.2505i	−0.686458	−	1.18898i
$417$		0			0
$418$	0.542756	−	0.940081i	0.0265471	−	0.0459808i
$419$	17.0673	−	29.5615i	0.833794	−	1.44417i	−0.0612141	−	0.998125i	$-0.519497\pi$
$419$	17.0673	−	29.5615i	0.833794	−	1.44417i	0.895008	−	0.446049i	$-0.147169\pi$
$420$		0			0
$421$	−11.2844	−	19.5451i	−0.549966	−	0.952569i	−0.998276	−	0.0586909i	$-0.981307\pi$
$421$	−11.2844	−	19.5451i	−0.549966	−	0.952569i	0.448310	−	0.893878i	$-0.352026\pi$
$422$	−39.7158			−1.93334
$423$		0			0
$424$	3.47738			0.168877
$425$	8.82943	+	15.2930i	0.428290	+	0.741820i
$426$		0			0
$427$	13.3318	−	23.0914i	0.645172	−	1.11747i
$428$	−21.4795	+	37.2035i	−1.03825	+	1.79830i
$429$		0			0
$430$	0.285624	+	0.494716i	0.0137740	+	0.0238573i
$431$	2.17813			0.104917			0.0524583	−	0.998623i	$-0.483294\pi$
$431$	2.17813			0.104917			0.0524583	+	0.998623i	$0.483294\pi$
$432$		0			0
$433$	−29.5089			−1.41811			−0.709054	−	0.705154i	$-0.750878\pi$
$433$	−29.5089			−1.41811			−0.709054	+	0.705154i	$0.750878\pi$
$434$	4.80726	+	8.32642i	0.230756	+	0.399681i
$435$		0			0
$436$	2.41298	−	4.17940i	0.115561	−	0.200157i
$437$	−0.706802	+	1.22422i	−0.0338109	+	0.0585622i
$438$		0			0
$439$	−5.32696	−	9.22656i	−0.254242	−	0.440360i	0.710448	−	0.703750i	$-0.248493\pi$
$439$	−5.32696	−	9.22656i	−0.254242	−	0.440360i	−0.964689	+	0.263391i	$0.915159\pi$
$440$	0.335539			0.0159962
$441$		0			0
$442$	−25.9757			−1.23554
$443$	7.10985	+	12.3146i	0.337799	+	0.585085i	0.984018	−	0.178067i	$-0.0569843\pi$
$443$	7.10985	+	12.3146i	0.337799	+	0.585085i	−0.646219	+	0.763152i	$0.723651\pi$
$444$		0			0
$445$	1.32459	−	2.29427i	0.0627918	−	0.108759i
$446$	4.59259	−	7.95459i	0.217465	−	0.376661i
$447$		0			0
$448$	−12.8507	−	22.2581i	−0.607138	−	1.05159i
$449$	11.9133			0.562221			0.281111	−	0.959675i	$-0.409297\pi$
$449$	11.9133			0.562221			0.281111	+	0.959675i	$0.409297\pi$
$450$		0			0
$451$	16.6541			0.784210
$452$	−1.03729	−	1.79663i	−0.0487898	−	0.0845065i
$453$		0			0
$454$	−29.5727	+	51.2214i	−1.38792	+	2.40394i
$455$	−1.14675	+	1.98623i	−0.0537605	+	0.0931160i
$456$		0			0
$457$	−7.68042	−	13.3029i	−0.359275	−	0.622283i	0.628565	−	0.777757i	$-0.283643\pi$
$457$	−7.68042	−	13.3029i	−0.359275	−	0.622283i	−0.987840	+	0.155474i	$0.950309\pi$
$458$	55.1611			2.57751
$459$		0			0
$460$	−2.81587			−0.131291
$461$	−7.88703	−	13.6607i	−0.367336	−	0.636244i	0.621812	−	0.783166i	$-0.286397\pi$
$461$	−7.88703	−	13.6607i	−0.367336	−	0.636244i	−0.989148	+	0.146922i	$0.953063\pi$
$462$		0			0
$463$	2.36131	−	4.08992i	0.109740	−	0.190075i	−0.805925	−	0.592017i	$-0.798332\pi$
$463$	2.36131	−	4.08992i	0.109740	−	0.190075i	0.915665	+	0.401943i	$0.131665\pi$
$464$	9.38114	−	16.2486i	0.435508	−	0.754322i
$465$		0			0
$466$	29.3628	+	50.8578i	1.36020	+	2.35594i
$467$	24.0572			1.11324			0.556618	−	0.830768i	$-0.312099\pi$
$467$	24.0572			1.11324			0.556618	+	0.830768i	$0.312099\pi$
$468$		0			0
$469$	13.8864			0.641216
$470$	2.48915	+	4.31133i	0.114816	+	0.198867i
$471$		0			0
$472$	−3.80269	+	6.58645i	−0.175033	+	0.303166i
$473$	0.799468	−	1.38472i	0.0367596	−	0.0636694i
$474$		0			0
$475$	0.800010	+	1.38566i	0.0367070	+	0.0635783i
$476$	−20.5425			−0.941563
$477$		0			0
$478$	−11.6692			−0.533738
$479$	−12.1281	−	21.0065i	−0.554148	−	0.959812i	−0.997969	−	0.0636966i	$-0.979711\pi$
$479$	−12.1281	−	21.0065i	−0.554148	−	0.959812i	0.443822	−	0.896115i	$-0.353622\pi$
$480$		0			0
$481$	−3.86600	+	6.69611i	−0.176274	+	0.305316i
$482$	7.51746	−	13.0206i	0.342411	−	0.593073i
$483$		0			0
$484$	9.99427	+	17.3106i	0.454285	+	0.786845i
$485$	−0.464100			−0.0210737
$486$		0			0
$487$	−32.1708			−1.45780			−0.728899	−	0.684621i	$-0.759968\pi$
$487$	−32.1708			−1.45780			−0.728899	+	0.684621i	$0.759968\pi$
$488$	4.22892	+	7.32470i	0.191434	+	0.331574i
$489$		0			0
$490$	0.326315	−	0.565194i	0.0147414	−	0.0255329i
$491$	3.59674	−	6.22973i	0.162319	−	0.281144i	−0.773381	−	0.633941i	$-0.781436\pi$
$491$	3.59674	−	6.22973i	0.162319	−	0.281144i	0.935700	+	0.352797i	$0.114769\pi$
$492$		0			0
$493$	−10.7447	−	18.6104i	−0.483919	−	0.838172i
$494$	−2.35358			−0.105893
$495$		0			0
$496$	5.95048			0.267184
$497$	−8.15888	−	14.1316i	−0.365976	−	0.633889i
$498$		0			0
$499$	−20.0166	+	34.6698i	−0.896066	+	1.55203i	−0.0635872	+	0.997976i	$0.520254\pi$
$499$	−20.0166	+	34.6698i	−0.896066	+	1.55203i	−0.832479	+	0.554056i	$0.813079\pi$
$500$	−3.21138	+	5.56228i	−0.143617	+	0.248753i
$501$		0			0
$502$	−5.58266	−	9.66945i	−0.249166	−	0.431569i
$503$	31.2924			1.39526			0.697630	−	0.716458i	$-0.254238\pi$
$503$	31.2924			1.39526			0.697630	+	0.716458i	$0.254238\pi$
$504$		0			0
$505$	−3.01019			−0.133952
$506$	7.27015	+	12.5923i	0.323198	+	0.559795i
$507$		0			0
$508$	−3.69574	+	6.40121i	−0.163972	+	0.284008i
$509$	−21.4060	+	37.0762i	−0.948803	+	1.64338i	−0.200852	+	0.979621i	$0.564371\pi$
$509$	−21.4060	+	37.0762i	−0.948803	+	1.64338i	−0.747951	+	0.663754i	$0.768962\pi$
$510$		0			0
$511$	1.00742	+	1.74491i	0.0445657	+	0.0771901i
$512$	−30.0909			−1.32984
$513$		0			0
$514$	−34.8893			−1.53890
$515$	0.641043	+	1.11032i	0.0282477	+	0.0489265i
$516$		0			0
$517$	6.96717	−	12.0675i	0.306416	−	0.530728i
$518$	−5.64030	+	9.76929i	−0.247821	+	0.429238i
$519$		0			0
$520$	−0.363755	−	0.630042i	−0.0159517	−	0.0276292i
$521$	2.79772			0.122570			0.0612851	−	0.998120i	$-0.480480\pi$
$521$	2.79772			0.122570			0.0612851	+	0.998120i	$0.480480\pi$
$522$		0			0
$523$	−7.44564			−0.325575			−0.162788	−	0.986661i	$-0.552049\pi$
$523$	−7.44564			−0.325575			−0.162788	+	0.986661i	$0.552049\pi$
$524$	−1.80781	−	3.13122i	−0.0789745	−	0.136788i
$525$		0			0
$526$	18.2770	−	31.6567i	0.796916	−	1.38030i
$527$	3.40771	−	5.90232i	0.148442	−	0.257109i
$528$		0			0
$529$	2.03247	+	3.52034i	0.0883683	+	0.153058i
$530$	−2.58750			−0.112394
$531$		0			0
$532$	−1.86130			−0.0806974
$533$	−18.0545	−	31.2713i	−0.782027	−	1.35451i
$534$		0			0
$535$	2.48013	−	4.29572i	0.107226	−	0.185720i
$536$	−2.20242	+	3.81471i	−0.0951301	+	0.164770i
$537$		0			0
$538$	−33.7750	−	58.5001i	−1.45614	−	2.52212i
$539$	−1.82672			−0.0786825
$540$		0			0
$541$	−36.9090			−1.58684			−0.793421	−	0.608673i	$-0.791702\pi$
$541$	−36.9090			−1.58684			−0.793421	+	0.608673i	$0.791702\pi$
$542$	3.98862	+	6.90850i	0.171326	+	0.296745i
$543$		0			0
$544$	−14.4799	+	25.0799i	−0.620821	+	1.07529i
$545$	−0.278616	+	0.482576i	−0.0119346	+	0.0206713i
$546$		0			0
$547$	−19.8177	−	34.3252i	−0.847343	−	1.46764i	−0.883571	−	0.468298i	$-0.844867\pi$
$547$	−19.8177	−	34.3252i	−0.847343	−	1.46764i	0.0362277	−	0.999344i	$-0.488466\pi$
$548$	10.2196			0.436560
$549$		0			0
$550$	16.4578			0.701762
$551$	−0.973551	−	1.68624i	−0.0414747	−	0.0718362i
$552$		0			0
$553$	−9.70027	+	16.8014i	−0.412497	+	0.714466i
$554$	29.6785	−	51.4047i	1.26092	−	2.18398i
$555$		0			0
$556$	22.0337	+	38.1635i	0.934436	+	1.61849i
$557$	−24.8972			−1.05493			−0.527464	−	0.849578i	$-0.676857\pi$
$557$	−24.8972			−1.05493			−0.527464	+	0.849578i	$0.676857\pi$
$558$		0			0
$559$	−3.46678			−0.146629
$560$	1.03546	+	1.79347i	0.0437563	+	0.0757881i
$561$		0			0
$562$	7.02762	−	12.1722i	0.296442	−	0.513453i
$563$	6.80608	−	11.7885i	0.286842	−	0.496825i	−0.686212	−	0.727401i	$-0.740728\pi$
$563$	6.80608	−	11.7885i	0.286842	−	0.496825i	0.973054	+	0.230576i	$0.0740612\pi$
$564$		0			0
$565$	0.119771	+	0.207449i	0.00503879	+	0.00872744i
$566$	−64.3579			−2.70516
$567$		0			0
$568$	5.17607			0.217183
$569$	5.30680	+	9.19165i	0.222473	+	0.385334i	0.955558	−	0.294802i	$-0.0952539\pi$
$569$	5.30680	+	9.19165i	0.222473	+	0.385334i	−0.733086	+	0.680136i	$0.761921\pi$
$570$		0			0
$571$	−17.4674	+	30.2545i	−0.730990	+	1.26611i	0.225471	+	0.974250i	$0.427608\pi$
$571$	−17.4674	+	30.2545i	−0.730990	+	1.26611i	−0.956461	+	0.291861i	$0.905725\pi$
$572$	−6.56131	+	11.3645i	−0.274342	+	0.475175i
$573$		0			0
$574$	−26.3406	−	45.6233i	−1.09944	−	1.90428i
$575$	−21.4321			−0.893780
$576$		0			0
$577$	−17.0364			−0.709236			−0.354618	−	0.935011i	$-0.615389\pi$
$577$	−17.0364			−0.709236			−0.354618	+	0.935011i	$0.615389\pi$
$578$	−4.33143	−	7.50226i	−0.180164	−	0.312053i
$579$		0			0
$580$	1.93929	−	3.35896i	0.0805248	−	0.139473i
$581$	8.24169	−	14.2750i	0.341923	−	0.592228i
$582$		0			0
$583$	3.62124	+	6.27216i	0.149976	+	0.259766i
$584$	−0.639118			−0.0264469
$585$		0			0
$586$	−9.34981			−0.386237
$587$	−0.824967	−	1.42888i	−0.0340500	−	0.0589764i	0.848498	−	0.529198i	$-0.177507\pi$
$587$	−0.824967	−	1.42888i	−0.0340500	−	0.0589764i	−0.882548	+	0.470222i	$0.844174\pi$
$588$		0			0
$589$	0.308763	−	0.534793i	0.0127223	−	0.0220358i
$590$	2.82956	−	4.90094i	0.116491	−	0.201769i
$591$		0			0
$592$	3.49081	+	6.04626i	0.143472	+	0.248500i
$593$	2.89587			0.118919			0.0594596	−	0.998231i	$-0.481062\pi$
$593$	2.89587			0.118919			0.0594596	+	0.998231i	$0.481062\pi$
$594$		0			0
$595$	2.37195			0.0972403
$596$	6.05767	+	10.4922i	0.248132	+	0.429777i
$597$		0			0
$598$	15.7630	−	27.3023i	0.644597	−	1.11647i
$599$	4.20198	−	7.27804i	0.171688	−	0.297373i	−0.767322	−	0.641262i	$-0.778411\pi$
$599$	4.20198	−	7.27804i	0.171688	−	0.297373i	0.939010	+	0.343889i	$0.111744\pi$
$600$		0			0
$601$	−15.2704	−	26.4491i	−0.622892	−	1.07888i	−0.988945	−	0.148286i	$-0.952624\pi$
$601$	−15.2704	−	26.4491i	−0.622892	−	1.07888i	0.366053	−	0.930594i	$-0.380709\pi$
$602$	−5.05786			−0.206143
$603$		0			0
$604$	30.5309			1.24229
$605$	−1.15399	−	1.99877i	−0.0469165	−	0.0812618i
$606$		0			0
$607$	18.6263	−	32.2616i	0.756017	−	1.30946i	−0.188850	−	0.982006i	$-0.560476\pi$
$607$	18.6263	−	32.2616i	0.756017	−	1.30946i	0.944867	−	0.327454i	$-0.106191\pi$
$608$	−1.31198	+	2.27242i	−0.0532080	+	0.0921589i
$609$		0			0
$610$	−3.14671	−	5.45027i	−0.127407	−	0.220675i
$611$	−30.2121			−1.22225
$612$		0			0
$613$	−15.5040			−0.626199			−0.313099	−	0.949720i	$-0.601367\pi$
$613$	−15.5040			−0.626199			−0.313099	+	0.949720i	$0.601367\pi$
$614$	16.5690	+	28.6984i	0.668671	+	1.15817i
$615$		0			0
$616$	−1.48544	+	2.57286i	−0.0598501	+	0.103663i
$617$	−18.6789	+	32.3528i	−0.751985	+	1.30248i	0.194874	+	0.980828i	$0.437570\pi$
$617$	−18.6789	+	32.3528i	−0.751985	+	1.30248i	−0.946859	+	0.321648i	$0.895763\pi$
$618$		0			0
$619$	20.4282	+	35.3827i	0.821079	+	1.42215i	0.904879	+	0.425668i	$0.139961\pi$
$619$	20.4282	+	35.3827i	0.821079	+	1.42215i	−0.0838006	+	0.996483i	$0.526706\pi$
$620$	1.23010			0.0494020
$621$		0			0
$622$	17.8626			0.716223
$623$	11.7280	+	20.3135i	0.469873	+	0.813845i
$624$		0			0
$625$	−11.9424	+	20.6848i	−0.477696	+	0.827394i
$626$	23.9082	−	41.4102i	0.955564	−	1.65509i
$627$		0			0
$628$	13.3989	+	23.2076i	0.534674	+	0.926082i
$629$	7.99645			0.318839
$630$		0			0
$631$	−22.1435			−0.881520			−0.440760	−	0.897625i	$-0.645291\pi$
$631$	−22.1435			−0.881520			−0.440760	+	0.897625i	$0.645291\pi$
$632$	−3.07697	−	5.32947i	−0.122395	−	0.211995i
$633$		0			0
$634$	28.6277	−	49.5846i	1.13695	−	1.96926i
$635$	0.426730	−	0.739118i	0.0169343	−	0.0293310i
$636$		0			0
$637$	1.98033	+	3.43004i	0.0784636	+	0.135903i
$638$	−20.0279			−0.792911
$639$		0			0
$640$	−1.65049			−0.0652415
$641$	5.25836	+	9.10774i	0.207693	+	0.359734i	0.950987	−	0.309230i	$-0.100071\pi$
$641$	5.25836	+	9.10774i	0.207693	+	0.359734i	−0.743295	+	0.668964i	$0.766738\pi$
$642$		0			0
$643$	3.31908	−	5.74882i	0.130892	−	0.226711i	−0.793129	−	0.609054i	$-0.791549\pi$
$643$	3.31908	−	5.74882i	0.130892	−	0.226711i	0.924021	+	0.382343i	$0.124883\pi$
$644$	12.4659	−	21.5916i	0.491226	−	0.850829i
$645$		0			0
$646$	1.21704	+	2.10798i	0.0478838	+	0.0829372i
$647$	41.0456			1.61367			0.806834	−	0.590779i	$-0.201179\pi$
$647$	41.0456			1.61367			0.806834	+	0.590779i	$0.201179\pi$
$648$		0			0
$649$	−15.8400			−0.621774
$650$	−17.8417	−	30.9027i	−0.699809	−	1.21211i
$651$		0			0
$652$	−11.2054	+	19.4084i	−0.438839	+	0.760092i
$653$	−13.0373	+	22.5812i	−0.510188	+	0.883671i	0.489742	+	0.871867i	$0.337091\pi$
$653$	−13.0373	+	22.5812i	−0.510188	+	0.883671i	−0.999930	+	0.0118041i	$0.996243\pi$
$654$		0			0
$655$	0.208740	+	0.361547i	0.00815613	+	0.0141268i
$656$	−32.6047			−1.27300
$657$		0			0
$658$	−44.0780			−1.71834
$659$	0.483468	+	0.837391i	0.0188332	+	0.0326201i	0.875288	−	0.483601i	$-0.160672\pi$
$659$	0.483468	+	0.837391i	0.0188332	+	0.0326201i	−0.856455	+	0.516221i	$0.827338\pi$
$660$		0			0
$661$	9.02772	−	15.6365i	0.351138	−	0.608188i	−0.635311	−	0.772256i	$-0.719128\pi$
$661$	9.02772	−	15.6365i	0.351138	−	0.608188i	0.986449	+	0.164068i	$0.0524616\pi$
$662$	−24.1373	+	41.8070i	−0.938122	+	1.62488i
$663$		0			0
$664$	2.61430	+	4.52811i	0.101455	+	0.175725i
$665$	0.214915			0.00833406
$666$		0			0
$667$	26.0812			1.00987
$668$	2.08904	+	3.61832i	0.0808273	+	0.139997i
$669$		0			0
$670$	1.63881	−	2.83850i	0.0633127	−	0.109661i
$671$	−8.80771	+	15.2554i	−0.340018	+	0.588928i
$672$		0			0
$673$	5.43861	+	9.41994i	0.209643	+	0.363112i	0.951602	−	0.307333i	$-0.0994365\pi$
$673$	5.43861	+	9.41994i	0.209643	+	0.363112i	−0.741959	+	0.670445i	$0.766103\pi$
$674$	−45.9891			−1.77143
$675$		0			0
$676$	−2.32343			−0.0893626
$677$	−6.68319	−	11.5756i	−0.256856	−	0.444888i	0.708542	−	0.705669i	$-0.249353\pi$
$677$	−6.68319	−	11.5756i	−0.256856	−	0.444888i	−0.965398	+	0.260781i	$0.916020\pi$
$678$		0			0
$679$	2.05458	−	3.55864i	0.0788476	−	0.136568i
$680$	−0.376196	+	0.651591i	−0.0144265	+	0.0249874i
$681$		0			0
$682$	−3.17593	−	5.50087i	−0.121613	−	0.210639i
$683$	19.4039			0.742471			0.371236	−	0.928539i	$-0.378934\pi$
$683$	19.4039			0.742471			0.371236	+	0.928539i	$0.378934\pi$
$684$		0			0
$685$	−1.18001			−0.0450860
$686$	20.5917	+	35.6659i	0.786196	+	1.36173i
$687$		0			0
$688$	−1.56517	+	2.71095i	−0.0596715	+	0.103354i
$689$	7.85149	−	13.5992i	0.299118	−	0.518087i
$690$		0			0
$691$	12.4326	+	21.5339i	0.472959	+	0.819189i	0.999521	−	0.0309479i	$-0.00985261\pi$
$691$	12.4326	+	21.5339i	0.472959	+	0.819189i	−0.526562	+	0.850137i	$0.676519\pi$
$692$	−49.8851			−1.89635
$693$		0			0
$694$	11.2919			0.428637
$695$	−2.54413	−	4.40656i	−0.0965043	−	0.167150i
$696$		0			0
$697$	−18.6720	+	32.3409i	−0.707253	+	1.22500i
$698$	4.92370	−	8.52810i	0.186365	−	0.322793i
$699$		0			0
$700$	−14.1098	−	24.4390i	−0.533302	−	0.923706i
$701$	−33.5387			−1.26674			−0.633369	−	0.773850i	$-0.718328\pi$
$701$	−33.5387			−1.26674			−0.633369	+	0.773850i	$0.718328\pi$
$702$		0			0
$703$	0.724536			0.0273264
$704$	8.48985	+	14.7048i	0.319973	+	0.554210i
$705$		0			0
$706$	26.1500	−	45.2931i	0.984168	−	1.70463i
$707$	13.3262	−	23.0816i	0.501183	−	0.868074i
$708$		0			0
$709$	−3.61137	−	6.25507i	−0.135628	−	0.234914i	0.790209	−	0.612837i	$-0.209972\pi$
$709$	−3.61137	−	6.25507i	−0.135628	−	0.234914i	−0.925837	+	0.377923i	$0.876638\pi$
$710$	−3.85148			−0.144544
$711$		0			0
$712$	−7.44037			−0.278840
$713$	4.13584	+	7.16349i	0.154889	+	0.268275i
$714$		0			0
$715$	0.757605	−	1.31221i	0.0283328	−	0.0490739i
$716$	9.19797	−	15.9314i	0.343744	−	0.595383i
$717$		0			0
$718$	−11.9612	−	20.7174i	−0.446389	−	0.773168i
$719$	17.6476			0.658144			0.329072	−	0.944305i	$-0.393264\pi$
$719$	17.6476			0.658144			0.329072	+	0.944305i	$0.393264\pi$
$720$		0			0
$721$	−11.3517			−0.422758
$722$	−19.7430	−	34.1959i	−0.734760	−	1.27264i
$723$		0			0
$724$	−25.3546	+	43.9154i	−0.942295	+	1.63210i
$725$	14.7603	−	25.5656i	0.548184	−	0.949483i
$726$		0			0
$727$	−3.51589	−	6.08970i	−0.130397	−	0.225855i	0.793433	−	0.608658i	$-0.208292\pi$
$727$	−3.51589	−	6.08970i	−0.130397	−	0.225855i	−0.923830	+	0.382804i	$0.874959\pi$
$728$	6.44141			0.238734
$729$		0			0
$730$	0.475564			0.0176014
$731$	1.79268	+	3.10500i	0.0663045	+	0.114843i
$732$		0			0
$733$	−20.0560	+	34.7379i	−0.740784	+	1.28307i	0.211355	+	0.977409i	$0.432212\pi$
$733$	−20.0560	+	34.7379i	−0.740784	+	1.28307i	−0.952139	+	0.305666i	$0.901121\pi$
$734$	−17.0608	+	29.5502i	−0.629727	+	1.09072i
$735$		0			0
$736$	−17.5739	−	30.4389i	−0.647782	−	1.12199i
$737$	−9.17412			−0.337933
$738$		0			0
$739$	−48.1715			−1.77202			−0.886008	−	0.463670i	$-0.846532\pi$
$739$	−48.1715			−1.77202			−0.886008	+	0.463670i	$0.846532\pi$
$740$	0.721630	+	1.24990i	0.0265277	+	0.0459473i
$741$		0			0
$742$	11.4549	−	19.8405i	0.420524	−	0.728369i
$743$	16.6656	−	28.8656i	0.611400	−	1.05898i	−0.379604	−	0.925149i	$-0.623940\pi$
$743$	16.6656	−	28.8656i	0.611400	−	1.05898i	0.991005	−	0.133827i	$-0.0427268\pi$
$744$		0			0
$745$	−0.699452	−	1.21149i	−0.0256259	−	0.0443854i
$746$	−34.0605			−1.24704
$747$		0			0
$748$	13.5714			0.496221
$749$	21.9592	+	38.0345i	0.802373	+	1.38975i
$750$		0			0
$751$	19.6490	−	34.0332i	0.717004	−	1.24189i	−0.245177	−	0.969478i	$-0.578846\pi$
$751$	19.6490	−	34.0332i	0.717004	−	1.24189i	0.962182	−	0.272409i	$-0.0878204\pi$
$752$	−13.6401	+	23.6253i	−0.497402	+	0.861525i
$753$		0			0
$754$	21.7120	+	37.6063i	0.790704	+	1.36954i
$755$	−3.52526			−0.128298
$756$		0			0
$757$	23.7890			0.864627			0.432313	−	0.901723i	$-0.357697\pi$
$757$	23.7890			0.864627			0.432313	+	0.901723i	$0.357697\pi$
$758$	36.4995	+	63.2190i	1.32572	+	2.29622i
$759$		0			0
$760$	−0.0340861	+	0.0590388i	−0.00123643	+	0.00214156i
$761$	−12.2868	+	21.2813i	−0.445395	+	0.771448i	−0.998080	−	0.0619432i	$-0.980270\pi$
$761$	−12.2868	+	21.2813i	−0.445395	+	0.771448i	0.552684	+	0.833391i	$0.313604\pi$
$762$		0			0
$763$	−2.46688	−	4.27275i	−0.0893069	−	0.154684i
$764$	40.7440			1.47407
$765$		0			0
$766$	−57.6639			−2.08348
$767$	17.1720	+	29.7427i	0.620044	+	1.07395i
$768$		0			0
$769$	12.0908	−	20.9418i	0.436005	−	0.755182i	−0.561372	−	0.827563i	$-0.689726\pi$
$769$	12.0908	−	20.9418i	0.436005	−	0.755182i	0.997377	+	0.0723810i	$0.0230597\pi$
$770$	1.10531	−	1.91445i	0.0398326	−	0.0689920i
$771$		0			0
$772$	5.86350	+	10.1559i	0.211032	+	0.365518i
$773$	−7.66684			−0.275757			−0.137878	−	0.990449i	$-0.544028\pi$
$773$	−7.66684			−0.275757			−0.137878	+	0.990449i	$0.544028\pi$
$774$		0			0
$775$	9.36250			0.336311
$776$	0.651722	+	1.12882i	0.0233955	+	0.0405221i
$777$		0			0
$778$	14.7591	−	25.5634i	0.529138	−	0.916494i
$779$	−1.69182	+	2.93031i	−0.0606157	+	0.104989i
$780$		0			0
$781$	5.39019	+	9.33608i	0.192876	+	0.334071i
$782$	−32.6043			−1.16593
$783$		0			0
$784$	3.57629			0.127725
$785$	−1.54711	−	2.67967i	−0.0552187	−	0.0956415i
$786$		0			0
$787$	7.00049	−	12.1252i	0.249540	−	0.432217i	−0.713858	−	0.700291i	$-0.753054\pi$
$787$	7.00049	−	12.1252i	0.249540	−	0.432217i	0.963398	+	0.268074i	$0.0863871\pi$
$788$	0.818773	−	1.41816i	0.0291676	−	0.0505197i
$789$		0			0
$790$	2.28956	+	3.96563i	0.0814587	+	0.141091i
$791$	−2.12091			−0.0754109
$792$		0			0
$793$	38.1934			1.35629
$794$	30.7606	+	53.2789i	1.09165	+	1.89080i
$795$		0			0
$796$	−16.0305	+	27.7657i	−0.568187	+	0.984129i
$797$	−3.56346	+	6.17210i	−0.126224	+	0.218627i	−0.922211	−	0.386687i	$-0.873619\pi$
$797$	−3.56346	+	6.17210i	−0.126224	+	0.218627i	0.795987	+	0.605314i	$0.206953\pi$
$798$		0			0
$799$	15.6227	+	27.0594i	0.552692	+	0.957291i
$800$	−39.7828			−1.40653
$801$		0			0
$802$	−35.6481			−1.25878
$803$	−0.665556	−	1.15278i	−0.0234870	−	0.0406806i
$804$		0			0
$805$	−1.43938	+	2.49309i	−0.0507316	+	0.0878697i
$806$	−6.88599	+	11.9269i	−0.242549	+	0.420106i
$807$		0			0
$808$	4.22713	+	7.32160i	0.148710	+	0.257573i
$809$	−28.5298			−1.00306			−0.501528	−	0.865141i	$-0.667229\pi$
$809$	−28.5298			−1.00306			−0.501528	+	0.865141i	$0.667229\pi$
$810$		0			0
$811$	21.0869			0.740463			0.370231	−	0.928940i	$-0.379278\pi$
$811$	21.0869			0.740463			0.370231	+	0.928940i	$0.379278\pi$
$812$	17.1706	+	29.7404i	0.602570	+	1.04368i
$813$		0			0
$814$	3.72628	−	6.45411i	0.130606	−	0.226216i
$815$	1.29384	−	2.24100i	0.0453213	−	0.0784988i
$816$		0			0
$817$	0.162429	+	0.281336i	0.00568268	+	0.00984269i
$818$	78.2066			2.73443
$819$		0			0
$820$	−6.74014			−0.235376
$821$	3.38052	+	5.85524i	0.117981	+	0.204349i	0.918968	−	0.394333i	$-0.129024\pi$
$821$	3.38052	+	5.85524i	0.117981	+	0.204349i	−0.800986	+	0.598683i	$0.795691\pi$
$822$		0			0
$823$	−25.7399	+	44.5828i	−0.897237	+	1.55406i	−0.0662248	+	0.997805i	$0.521095\pi$
$823$	−25.7399	+	44.5828i	−0.897237	+	1.55406i	−0.831012	+	0.556255i	$0.812238\pi$
$824$	1.80040	−	3.11838i	0.0627199	−	0.108634i
$825$		0			0
$826$	25.0531	+	43.3932i	0.871708	+	1.50984i
$827$	32.7541			1.13897			0.569486	−	0.822001i	$-0.307142\pi$
$827$	32.7541			1.13897			0.569486	+	0.822001i	$0.307142\pi$
$828$		0			0
$829$	−31.7417			−1.10243			−0.551217	−	0.834362i	$-0.685836\pi$
$829$	−31.7417			−1.10243			−0.551217	+	0.834362i	$0.685836\pi$
$830$	−1.94529	−	3.36934i	−0.0675219	−	0.116951i
$831$		0			0
$832$	18.4075	−	31.8827i	0.638166	−	1.10534i
$833$	2.04806	−	3.54735i	0.0709612	−	0.122908i
$834$		0			0
$835$	−0.241212	−	0.417791i	−0.00834748	−	0.0144583i
$836$	1.22967			0.0425291
$837$		0			0
$838$	71.3354			2.46424
$839$	14.5744	+	25.2436i	0.503164	+	0.871506i	0.999993	+	0.00365762i	$0.00116426\pi$
$839$	14.5744	+	25.2436i	0.503164	+	0.871506i	−0.496829	+	0.867848i	$0.665502\pi$
$840$		0			0
$841$	−3.46217	+	5.99666i	−0.119385	+	0.206781i
$842$	23.5823	−	40.8457i	0.812700	−	1.40764i
$843$		0			0
$844$	−22.4951	−	38.9627i	−0.774313	−	1.34115i
$845$	0.268276			0.00922896
$846$		0			0
$847$	20.4350			0.702156
$848$	−7.08952	−	12.2794i	−0.243455	−	0.421677i
$849$		0			0
$850$	−18.4519	+	31.9597i	−0.632896	+	1.09621i
$851$	−4.85254	+	8.40484i	−0.166343	+	0.288114i
$852$		0			0
$853$	27.0832	+	46.9095i	0.927312	+	1.60615i	0.787800	+	0.615931i	$0.211220\pi$
$853$	27.0832	+	46.9095i	0.927312	+	1.60615i	0.139511	+	0.990220i	$0.455447\pi$
$854$	55.7223			1.90678
$855$		0			0
$856$	−13.9311			−0.476156
$857$	−0.862497	−	1.49389i	−0.0294623	−	0.0510302i	0.850918	−	0.525298i	$-0.176046\pi$
$857$	−0.862497	−	1.49389i	−0.0294623	−	0.0510302i	−0.880381	+	0.474268i	$0.842713\pi$
$858$		0			0
$859$	−7.64074	+	13.2341i	−0.260699	+	0.451543i	−0.966428	−	0.256939i	$-0.917286\pi$
$859$	−7.64074	+	13.2341i	−0.260699	+	0.451543i	0.705729	+	0.708482i	$0.250620\pi$
$860$	−0.323556	+	0.560415i	−0.0110332	+	0.0191100i
$861$		0			0
$862$	2.27595	+	3.94206i	0.0775191	+	0.134267i
$863$	−31.2885			−1.06507			−0.532537	−	0.846407i	$-0.678761\pi$
$863$	−31.2885			−1.06507			−0.532537	+	0.846407i	$0.678761\pi$
$864$		0			0
$865$	5.76001			0.195846
$866$	−30.8342	−	53.4064i	−1.04779	−	1.81482i
$867$		0			0
$868$	−5.44568	+	9.43219i	−0.184838	+	0.320149i
$869$	6.40851	−	11.0999i	0.217394	−	0.376537i
$870$		0			0
$871$	9.94557	+	17.2262i	0.336993	+	0.583688i
$872$	1.56501			0.0529979
$873$		0			0
$874$	−2.95418			−0.0999266
$875$	3.28311	+	5.68652i	0.110990	+	0.192239i
$876$		0			0
$877$	−5.27153	+	9.13056i	−0.178007	+	0.308317i	−0.941198	−	0.337856i	$-0.890298\pi$
$877$	−5.27153	+	9.13056i	−0.178007	+	0.308317i	0.763191	+	0.646173i	$0.223632\pi$
$878$	11.1324	−	19.2819i	0.375700	−	0.650731i
$879$		0			0
$880$	−0.684081	−	1.18486i	−0.0230604	−	0.0399417i
$881$	42.4065			1.42871			0.714356	−	0.699783i	$-0.246720\pi$
$881$	42.4065			1.42871			0.714356	+	0.699783i	$0.246720\pi$
$882$		0			0
$883$	−40.6960			−1.36953			−0.684765	−	0.728764i	$-0.740095\pi$
$883$	−40.6960			−1.36953			−0.684765	+	0.728764i	$0.740095\pi$
$884$	−14.7127	−	25.4831i	−0.494841	−	0.857089i
$885$		0			0
$886$	−14.8583	+	25.7354i	−0.499175	+	0.864596i
$887$	−12.2660	+	21.2454i	−0.411853	+	0.713351i	−0.995092	−	0.0989498i	$-0.968452\pi$
$887$	−12.2660	+	21.2454i	−0.411853	+	0.713351i	0.583239	+	0.812300i	$0.301785\pi$
$888$		0			0
$889$	3.77829	+	6.54419i	0.126720	+	0.219485i
$890$	5.53633			0.185578
$891$		0			0
$892$	10.4050			0.348385
$893$	1.41553	+	2.45177i	0.0473690	+	0.0820454i
$894$		0			0
$895$	−1.06205	+	1.83952i	−0.0355003	+	0.0614884i
$896$	7.30678	−	12.6557i	0.244102	−	0.422798i
$897$		0			0
$898$	12.4483	+	21.5611i	0.415405	+	0.719502i
$899$	−11.3934			−0.379993
$900$		0			0
$901$	−16.2400			−0.541034
$902$	17.4020	+	30.1412i	0.579424	+	1.00359i
$903$		0			0
$904$	0.336381	−	0.582630i	0.0111879	−	0.0193780i
$905$	2.92758	−	5.07071i	0.0973160	−	0.168556i
$906$		0			0
$907$	15.0814	+	26.1218i	0.500770	+	0.867359i	1.00000		0.000888993i	$0.000282975\pi$
$907$	15.0814	+	26.1218i	0.500770	+	0.867359i	−0.499230	+	0.866470i	$0.666384\pi$
$908$	−67.0001			−2.22348
$909$		0			0
$910$	−4.79301			−0.158887
$911$	−3.73340	−	6.46644i	−0.123693	−	0.214243i	0.797528	−	0.603282i	$-0.206140\pi$
$911$	−3.73340	−	6.46644i	−0.123693	−	0.214243i	−0.921221	+	0.389039i	$0.872807\pi$
$912$		0			0
$913$	−5.44490	+	9.43084i	−0.180200	+	0.312115i
$914$	16.0507	−	27.8007i	0.530911	−	0.919564i
$915$		0			0
$916$	31.2433	+	54.1151i	1.03231	+	1.78801i
$917$	−3.69638			−0.122065
$918$		0			0
$919$	28.7562			0.948579			0.474289	−	0.880369i	$-0.342705\pi$
$919$	28.7562			0.948579			0.474289	+	0.880369i	$0.342705\pi$
$920$	−0.456579	−	0.790818i	−0.0150530	−	0.0260725i
$921$		0			0
$922$	16.4825	−	28.5485i	0.542822	−	0.940195i
$923$	11.6869	−	20.2423i	0.384679	−	0.666283i
$924$		0			0
$925$	5.49246	+	9.51321i	0.180591	+	0.312792i
$926$	9.86945			0.324330
$927$		0			0
$928$	48.4126			1.58922
$929$	17.7359	+	30.7195i	0.581896	+	1.00787i	0.995255	+	0.0973047i	$0.0310221\pi$
$929$	17.7359	+	30.7195i	0.581896	+	1.00787i	−0.413359	+	0.910568i	$0.635645\pi$
$930$		0			0
$931$	0.185569	−	0.321415i	0.00608179	−	0.0105340i
$932$	−33.2622	+	57.6118i	−1.08954	+	1.88714i
$933$		0			0
$934$	25.1377	+	43.5397i	0.822530	+	1.42466i
$935$	−1.56703			−0.0512475
$936$		0			0
$937$	−37.7639			−1.23369			−0.616847	−	0.787083i	$-0.711590\pi$
$937$	−37.7639			−1.23369			−0.616847	+	0.787083i	$0.711590\pi$
$938$	14.5101	+	25.1322i	0.473771	+	0.820596i
$939$		0			0
$940$	−2.81971	+	4.88388i	−0.0919688	+	0.159295i
$941$	9.21120	−	15.9543i	0.300277	−	0.520094i	−0.675922	−	0.736973i	$-0.736254\pi$
$941$	9.21120	−	15.9543i	0.300277	−	0.520094i	0.976199	+	0.216879i	$0.0695877\pi$
$942$		0			0
$943$	−22.6617	−	39.2512i	−0.737967	−	1.27820i
$944$	31.0109			1.00932
$945$		0			0
$946$	3.34149			0.108641
$947$	−8.26337	−	14.3126i	−0.268523	−	0.465096i	0.699957	−	0.714185i	$-0.253202\pi$
$947$	−8.26337	−	14.3126i	−0.268523	−	0.465096i	−0.968481	+	0.249089i	$0.919869\pi$
$948$		0			0
$949$	−1.44305	+	2.49943i	−0.0468432	+	0.0811349i
$950$	−1.67188	+	2.89578i	−0.0542429	+	0.0939514i
$951$		0			0
$952$	−3.33086	−	5.76922i	−0.107954	−	0.186981i
$953$	25.4326			0.823842			0.411921	−	0.911219i	$-0.364858\pi$
$953$	25.4326			0.823842			0.411921	+	0.911219i	$0.364858\pi$
$954$		0			0
$955$	−4.70453			−0.152235
$956$	−6.60947	−	11.4479i	−0.213765	−	0.370253i
$957$		0			0
$958$	25.3456	−	43.8999i	0.818879	−	1.41834i
$959$	5.22394	−	9.04814i	0.168690	−	0.292180i
$960$		0			0
$961$	13.6933	+	23.7175i	0.441719	+	0.765079i
$962$	−16.1585			−0.520971
$963$		0			0
$964$	17.0316			0.548551
$965$	−0.677031	−	1.17265i	−0.0217944	−	0.0377490i
$966$		0			0
$967$	7.07071	−	12.2468i	0.227379	−	0.393832i	−0.729652	−	0.683819i	$-0.760318\pi$
$967$	7.07071	−	12.2468i	0.227379	−	0.393832i	0.957030	+	0.289987i	$0.0936511\pi$
$968$	−3.24104	+	5.61365i	−0.104171	+	0.180430i
$969$		0			0
$970$	−0.484943	−	0.839946i	−0.0155706	−	0.0269690i
$971$	27.1607			0.871627			0.435814	−	0.900037i	$-0.356461\pi$
$971$	27.1607			0.871627			0.435814	+	0.900037i	$0.356461\pi$
$972$		0			0
$973$	45.0517			1.44429
$974$	−33.6156	−	58.2240i	−1.07711	−	1.86562i
$975$		0			0
$976$	17.2434	−	29.8665i	0.551948	−	0.956002i
$977$	−3.63720	+	6.29981i	−0.116364	+	0.201549i	−0.918324	−	0.395829i	$-0.870457\pi$
$977$	−3.63720	+	6.29981i	−0.116364	+	0.201549i	0.801960	+	0.597378i	$0.203791\pi$
$978$		0			0
$979$	−7.74816	−	13.4202i	−0.247632	−	0.428911i
$980$	0.739301			0.0236161
$981$		0			0
$982$	15.0331			0.479725
$983$	19.8887	+	34.4483i	0.634351	+	1.09873i	0.986652	+	0.162842i	$0.0520661\pi$
$983$	19.8887	+	34.4483i	0.634351	+	1.09873i	−0.352301	+	0.935887i	$0.614601\pi$
$984$		0			0
$985$	−0.0945400	+	0.163748i	−0.00301229	+	0.00521745i
$986$	22.4546	−	38.8925i	0.715100	−	1.23859i
$987$		0			0
$988$	−1.33307	−	2.30895i	−0.0424107	−	0.0734575i
$989$	−4.35144			−0.138368
$990$		0			0
$991$	−7.74113			−0.245905			−0.122953	−	0.992413i	$-0.539236\pi$
$991$	−7.74113			−0.245905			−0.122953	+	0.992413i	$0.539236\pi$
$992$	7.67706	+	13.2971i	0.243747	+	0.422182i
$993$		0			0
$994$	17.0506	−	29.5325i	0.540812	−	0.936715i
$995$	1.85097	−	3.20598i	0.0586797	−	0.101636i
$996$		0			0
$997$	2.18933	+	3.79204i	0.0693369	+	0.120095i	0.898610	−	0.438749i	$-0.144578\pi$
$997$	2.18933	+	3.79204i	0.0693369	+	0.120095i	−0.829273	+	0.558844i	$0.811245\pi$
$998$	−83.6623			−2.64828
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.d.388.19		40
3.2	odd	2		387.2.f.d.130.2	✓	40
9.2	odd	6		387.2.f.d.259.2	yes	40
9.4	even	3		3483.2.a.u.1.2		20
9.5	odd	6		3483.2.a.t.1.19		20
9.7	even	3	inner	1161.2.f.d.775.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.d.130.2	✓	40	3.2	odd	2
387.2.f.d.259.2	yes	40	9.2	odd	6
1161.2.f.d.388.19		40	1.1	even	1	trivial
1161.2.f.d.775.19		40	9.7	even	3	inner
3483.2.a.t.1.19		20	9.5	odd	6
3483.2.a.u.1.2		20	9.4	even	3

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:	\( N \)	\(=\)	\( 1161 = 3^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1161.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.04491 + 1.80984i) q^{2} +(-1.18368 + 2.05019i) q^{4} +(0.136674 - 0.236726i) q^{5} +(1.21012 + 2.09599i) q^{7} -0.767710 q^{8} +O(q^{10})\)	\(q+(1.04491 + 1.80984i) q^{2} +(-1.18368 + 2.05019i) q^{4} +(0.136674 - 0.236726i) q^{5} +(1.21012 + 2.09599i) q^{7} -0.767710 q^{8} +0.571248 q^{10} +(-0.799468 - 1.38472i) q^{11} +(-1.73339 + 3.00232i) q^{13} +(-2.52893 + 4.38024i) q^{14} +(1.56517 + 2.71095i) q^{16} +3.58535 q^{17} +0.324858 q^{19} +(0.323556 + 0.560415i) q^{20} +(1.67075 - 2.89382i) q^{22} +(-2.17572 + 3.76846i) q^{23} +(2.46264 + 4.26542i) q^{25} -7.24495 q^{26} -5.72956 q^{28} +(-2.99685 - 5.19069i) q^{29} +(0.950453 - 1.64623i) q^{31} +(-4.03863 + 6.99512i) q^{32} +(3.74637 + 6.48891i) q^{34} +0.661566 q^{35} +2.23031 q^{37} +(0.339448 + 0.587942i) q^{38} +(-0.104926 + 0.181737i) q^{40} +(-5.20786 + 9.02028i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.78525 q^{44} -9.09374 q^{46} +(4.35738 + 7.54720i) q^{47} +(0.571231 - 0.989401i) q^{49} +(-5.14648 + 8.91397i) q^{50} +(-4.10355 - 7.10756i) q^{52} -4.52956 q^{53} -0.437066 q^{55} +(-0.929019 - 1.60911i) q^{56} +(6.26287 - 10.8476i) q^{58} +(4.95329 - 8.57935i) q^{59} +(-5.50849 - 9.54098i) q^{61} +3.97256 q^{62} -10.6194 q^{64} +(0.473818 + 0.820677i) q^{65} +(2.86882 - 4.96894i) q^{67} +(-4.24390 + 7.35065i) q^{68} +(0.691278 + 1.19733i) q^{70} -6.74222 q^{71} +0.832499 q^{73} +(2.33048 + 4.03650i) q^{74} +(-0.384528 + 0.666022i) q^{76} +(1.93490 - 3.35135i) q^{77} +(4.00799 + 6.94204i) q^{79} +0.855671 q^{80} -21.7670 q^{82} +(-3.40533 - 5.89820i) q^{83} +(0.490024 - 0.848746i) q^{85} +(-1.04491 + 1.80984i) q^{86} +(0.613759 + 1.06306i) q^{88} +9.69164 q^{89} -8.39042 q^{91} +(-5.15071 - 8.92129i) q^{92} +(-9.10615 + 15.7723i) q^{94} +(0.0443997 - 0.0769025i) q^{95} +(-0.848918 - 1.47037i) q^{97} +2.38754 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) \) 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8	\( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) \) 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8 - 4 * q^10 - 10 * q^11 + q^13 - 10 * q^14 - 22 * q^16 + 40 * q^17 + 16 * q^19 - 30 * q^20 - 15 * q^22 - 19 * q^23 - 19 * q^25 + 50 * q^26 - 6 * q^28 - 25 * q^29 + 11 * q^31 - 36 * q^32 - 9 * q^34 + 18 * q^37 - 28 * q^38 - 12 * q^40 - 12 * q^41 + 20 * q^43 + 10 * q^44 + 8 * q^46 - 38 * q^47 - 37 * q^49 - 36 * q^50 + 8 * q^52 + 138 * q^53 - 18 * q^55 - 30 * q^56 + 27 * q^58 - 31 * q^59 - 19 * q^61 + 64 * q^62 + 22 * q^64 - 47 * q^65 - 9 * q^67 - 68 * q^68 + 6 * q^70 + 42 * q^71 - 4 * q^73 + 16 * q^74 - 37 * q^76 - 85 * q^77 + 4 * q^79 + 122 * q^80 + 2 * q^82 - 19 * q^83 + 6 * q^85 + 6 * q^86 - 60 * q^88 + 108 * q^89 - 6 * q^91 - 85 * q^92 + 19 * q^94 + 11 * q^95 - 2 * q^97 + 10 * q^98

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