LMFDB - Embedded newform 351.2.t.c.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(64,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("351.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.t (of order $6$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.8
Root			$-0.651881 + 1.60470i$ of defining polynomial
Character	$\chi$	$=$	351.64
Dual form			351.2.t.c.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41717 - 0.818205i) q^{2} +(0.338918 - 0.587023i) q^{4} +(0.950358 + 0.548689i) q^{5} +(2.77942 - 1.60470i) q^{7} +2.16360i q^{8} +1.79576 q^{10} +(-1.52289 + 0.879239i) q^{11} +(1.37514 - 3.33302i) q^{13} +(2.62594 - 4.54826i) q^{14} +(2.44810 + 4.24024i) q^{16} -1.47360 q^{17} +3.61452i q^{19} +(0.644186 - 0.371921i) q^{20} +(-1.43879 + 2.49207i) q^{22} +(2.34599 - 4.06337i) q^{23} +(-1.89788 - 3.28722i) q^{25} +(-0.778285 - 5.84860i) q^{26} -2.17544i q^{28} +(-0.959085 - 1.66118i) q^{29} +(-5.68224 - 3.28064i) q^{31} +(3.19130 + 1.84250i) q^{32} +(-2.08834 + 1.20570i) q^{34} +3.52192 q^{35} +11.6237i q^{37} +(2.95742 + 5.12239i) q^{38} +(-1.18715 + 2.05620i) q^{40} +(-4.68013 - 2.70208i) q^{41} +(0.889142 + 1.54004i) q^{43} +1.19196i q^{44} -7.67798i q^{46} +(-8.90053 + 5.13872i) q^{47} +(1.65010 - 2.85806i) q^{49} +(-5.37925 - 3.10571i) q^{50} +(-1.49050 - 1.93685i) q^{52} -11.7738 q^{53} -1.92972 q^{55} +(3.47193 + 6.01355i) q^{56} +(-2.71838 - 1.56946i) q^{58} +(4.78585 + 2.76311i) q^{59} +(-0.985148 - 1.70633i) q^{61} -10.7370 q^{62} -3.76225 q^{64} +(3.13566 - 2.41304i) q^{65} +(7.15434 + 4.13056i) q^{67} +(-0.499428 + 0.865034i) q^{68} +(4.99117 - 2.88165i) q^{70} -5.84860i q^{71} +1.24694i q^{73} +(9.51060 + 16.4728i) q^{74} +(2.12180 + 1.22502i) q^{76} +(-2.82182 + 4.88754i) q^{77} +(-0.242912 - 0.420735i) q^{79} +5.37300i q^{80} -8.84340 q^{82} +(13.4351 - 7.75677i) q^{83} +(-1.40044 - 0.808546i) q^{85} +(2.52014 + 1.45500i) q^{86} +(-1.90232 - 3.29492i) q^{88} +13.4245i q^{89} +(-1.52640 - 11.4705i) q^{91} +(-1.59019 - 2.75429i) q^{92} +(-8.40905 + 14.5649i) q^{94} +(-1.98325 + 3.43508i) q^{95} +(5.15756 - 2.97772i) q^{97} -5.40048i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) $ 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.41717	−	0.818205i	1.00209	−	0.578558i	0.0932254	−	0.995645i	$-0.470282\pi$
$2$	1.41717	−	0.818205i	1.00209	−	0.578558i	0.908867	+	0.417087i	$0.136949\pi$
$3$		0			0
$3$		0			0
$4$	0.338918	−	0.587023i	0.169459	−	0.293511i
$5$	0.950358	+	0.548689i	0.425013	+	0.245381i	0.697220	−	0.716857i	$-0.254420\pi$
$5$	0.950358	+	0.548689i	0.425013	+	0.245381i	−0.272207	+	0.962239i	$0.587754\pi$
$6$		0			0
$7$	2.77942	−	1.60470i	1.05052	−	0.606518i	0.127725	−	0.991810i	$-0.459232\pi$
$7$	2.77942	−	1.60470i	1.05052	−	0.606518i	0.922795	+	0.385291i	$0.125899\pi$
$8$			2.16360i			0.764949i
$9$		0			0
$10$	1.79576			0.567869
$11$	−1.52289	+	0.879239i	−0.459168	+	0.265101i	−0.711694	−	0.702489i	$-0.752072\pi$
$11$	−1.52289	+	0.879239i	−0.459168	+	0.265101i	0.252527	+	0.967590i	$0.418738\pi$
$12$		0			0
$13$	1.37514	−	3.33302i	0.381394	−	0.924412i
$13$	1.37514	−	3.33302i	0.381394	−	0.924412i
$14$	2.62594	−	4.54826i	0.701812	−	1.21557i
$15$		0			0
$16$	2.44810	+	4.24024i	0.612026	+	1.06006i
$17$	−1.47360			−0.357399			−0.178700	−	0.983904i	$-0.557189\pi$
$17$	−1.47360			−0.357399			−0.178700	+	0.983904i	$0.557189\pi$
$18$		0			0
$19$			3.61452i			0.829227i	0.909998	+	0.414614i	$0.136083\pi$
$19$			3.61452i			0.829227i	−0.909998	+	0.414614i	$0.863917\pi$
$20$	0.644186	−	0.371921i	0.144044	−	0.0831641i
$21$		0			0
$22$	−1.43879	+	2.49207i	−0.306752	+	0.531310i
$23$	2.34599	−	4.06337i	0.489172	−	0.847270i	−0.510751	−	0.859729i	$-0.670632\pi$
$23$	2.34599	−	4.06337i	0.489172	−	0.847270i	0.999922	+	0.0124586i	$0.00396580\pi$
$24$		0			0
$25$	−1.89788	−	3.28722i	−0.379576	−	0.657445i
$26$	−0.778285	−	5.84860i	−0.152634	−	1.14700i
$27$		0			0
$28$		−	2.17544i		−	0.411120i
$29$	−0.959085	−	1.66118i	−0.178098	−	0.308474i	0.763131	−	0.646244i	$-0.223661\pi$
$29$	−0.959085	−	1.66118i	−0.178098	−	0.308474i	−0.941229	+	0.337769i	$0.890328\pi$
$30$		0			0
$31$	−5.68224	−	3.28064i	−1.02056	−	0.589221i	−0.106294	−	0.994335i	$-0.533899\pi$
$31$	−5.68224	−	3.28064i	−1.02056	−	0.589221i	−0.914266	+	0.405114i	$0.867232\pi$
$32$	3.19130	+	1.84250i	0.564148	+	0.325711i
$33$		0			0
$34$	−2.08834	+	1.20570i	−0.358147	+	0.206776i
$35$	3.52192			0.595313
$36$		0			0
$37$			11.6237i			1.91093i	0.295103	+	0.955465i	$0.404646\pi$
$37$			11.6237i			1.91093i	−0.295103	+	0.955465i	$0.595354\pi$
$38$	2.95742	+	5.12239i	0.479756	+	0.830962i
$39$		0			0
$40$	−1.18715	+	2.05620i	−0.187704	+	0.325113i
$41$	−4.68013	−	2.70208i	−0.730914	−	0.421993i	0.0878426	−	0.996134i	$-0.472003\pi$
$41$	−4.68013	−	2.70208i	−0.730914	−	0.421993i	−0.818756	+	0.574141i	$0.805336\pi$
$42$		0			0
$43$	0.889142	+	1.54004i	0.135593	+	0.234854i	0.925824	−	0.377955i	$-0.123373\pi$
$43$	0.889142	+	1.54004i	0.135593	+	0.234854i	−0.790231	+	0.612809i	$0.790039\pi$
$44$			1.19196i			0.179695i
$45$		0			0
$46$		−	7.67798i		−	1.13206i
$47$	−8.90053	+	5.13872i	−1.29828	+	0.749559i	−0.980106	−	0.198475i	$-0.936401\pi$
$47$	−8.90053	+	5.13872i	−1.29828	+	0.749559i	−0.318169	+	0.948034i	$0.603068\pi$
$48$		0			0
$49$	1.65010	−	2.85806i	0.235729	−	0.408294i
$50$	−5.37925	−	3.10571i	−0.760740	−	0.439214i
$51$		0			0
$52$	−1.49050	−	1.93685i	−0.206695	−	0.268593i
$53$	−11.7738			−1.61726			−0.808628	−	0.588320i	$-0.799789\pi$
$53$	−11.7738			−1.61726			−0.808628	+	0.588320i	$0.799789\pi$
$54$		0			0
$55$	−1.92972			−0.260203
$56$	3.47193	+	6.01355i	0.463956	+	0.803595i
$57$		0			0
$58$	−2.71838	−	1.56946i	−0.356940	−	0.206080i
$59$	4.78585	+	2.76311i	0.623064	+	0.359726i	0.778061	−	0.628189i	$-0.216203\pi$
$59$	4.78585	+	2.76311i	0.623064	+	0.359726i	−0.154997	+	0.987915i	$0.549537\pi$
$60$		0			0
$61$	−0.985148	−	1.70633i	−0.126135	−	0.218473i	0.796041	−	0.605243i	$-0.206924\pi$
$61$	−0.985148	−	1.70633i	−0.126135	−	0.218473i	−0.922176	+	0.386770i	$0.873591\pi$
$62$	−10.7370			−1.36359
$63$		0			0
$64$	−3.76225			−0.470282
$65$	3.13566	−	2.41304i	0.388931	−	0.299300i
$66$		0			0
$67$	7.15434	+	4.13056i	0.874042	+	0.504628i	0.868689	−	0.495357i	$-0.164963\pi$
$67$	7.15434	+	4.13056i	0.874042	+	0.504628i	0.00535270	+	0.999986i	$0.498296\pi$
$68$	−0.499428	+	0.865034i	−0.0605645	+	0.104901i
$69$		0			0
$70$	4.99117	−	2.88165i	0.596558	−	0.344423i
$71$		−	5.84860i		−	0.694101i	−0.937846	−	0.347051i	$-0.887183\pi$
$71$		−	5.84860i		−	0.694101i	0.937846	−	0.347051i	$-0.112817\pi$
$72$		0			0
$73$			1.24694i			0.145943i	0.997334	+	0.0729714i	$0.0232482\pi$
$73$			1.24694i			0.145943i	−0.997334	+	0.0729714i	$0.976752\pi$
$74$	9.51060	+	16.4728i	1.10558	+	1.91493i
$75$		0			0
$76$	2.12180	+	1.22502i	0.243388	+	0.140520i
$77$	−2.82182	+	4.88754i	−0.321577	+	0.556987i
$78$		0			0
$79$	−0.242912	−	0.420735i	−0.0273297	−	0.0473364i	0.852037	−	0.523481i	$-0.175367\pi$
$79$	−0.242912	−	0.420735i	−0.0273297	−	0.0473364i	−0.879367	+	0.476145i	$0.842034\pi$
$80$			5.37300i			0.600719i
$81$		0			0
$82$	−8.84340			−0.976590
$83$	13.4351	−	7.75677i	1.47470	−	0.851417i	0.475103	−	0.879930i	$-0.342411\pi$
$83$	13.4351	−	7.75677i	1.47470	−	0.851417i	0.999593	+	0.0285134i	$0.00907732\pi$
$84$		0			0
$85$	−1.40044	−	0.808546i	−0.151899	−	0.0876991i
$86$	2.52014	+	1.45500i	0.271753	+	0.156897i
$87$		0			0
$88$	−1.90232	−	3.29492i	−0.202788	−	0.351240i
$89$			13.4245i			1.42300i	0.702688	+	0.711498i	$0.251983\pi$
$89$			13.4245i			1.42300i	−0.702688	+	0.711498i	$0.748017\pi$
$90$		0			0
$91$	−1.52640	−	11.4705i	−0.160011	−	1.20244i
$92$	−1.59019	−	2.75429i	−0.165789	−	0.287155i
$93$		0			0
$94$	−8.40905	+	14.5649i	−0.867327	+	1.50225i
$95$	−1.98325	+	3.43508i	−0.203477	+	0.352432i
$96$		0			0
$97$	5.15756	−	2.97772i	0.523671	−	0.302342i	−0.214764	−	0.976666i	$-0.568898\pi$
$97$	5.15756	−	2.97772i	0.523671	−	0.302342i	0.738435	+	0.674324i	$0.235565\pi$
$98$		−	5.40048i		−	0.545531i
$99$		0			0
$100$	−2.57290			−0.257290
$101$	−7.94290	−	13.7575i	−0.790348	−	1.36892i	−0.925752	−	0.378132i	$-0.876567\pi$
$101$	−7.94290	−	13.7575i	−0.790348	−	1.36892i	0.135404	−	0.990790i	$-0.456767\pi$
$102$		0			0
$103$	3.12594	−	5.41429i	0.308008	−	0.533486i	−0.669918	−	0.742435i	$-0.733671\pi$
$103$	3.12594	−	5.41429i	0.308008	−	0.533486i	0.977927	+	0.208949i	$0.0670043\pi$
$104$	7.21132	+	2.97525i	0.707128	+	0.291747i
$105$		0			0
$106$	−16.6855	+	9.63338i	−1.62064	+	0.935676i
$107$	10.6339			1.02802			0.514010	−	0.857784i	$-0.328160\pi$
$107$	10.6339			1.02802			0.514010	+	0.857784i	$0.328160\pi$
$108$		0			0
$109$		−	16.0203i		−	1.53447i	−0.641368	−	0.767234i	$-0.721633\pi$
$109$		−	16.0203i		−	1.53447i	0.641368	−	0.767234i	$-0.278367\pi$
$110$	−2.73474	+	1.57890i	−0.260747	+	0.150542i
$111$		0			0
$112$	13.6086	+	7.85693i	1.28589	+	0.742410i
$113$	−1.48868	+	2.57847i	−0.140043	+	0.242562i	−0.927513	−	0.373792i	$-0.878057\pi$
$113$	−1.48868	+	2.57847i	−0.140043	+	0.242562i	0.787470	+	0.616354i	$0.211391\pi$
$114$		0			0
$115$	4.45905	−	2.57443i	0.415809	−	0.240067i
$116$	−1.30020			−0.120721
$117$		0			0
$118$	9.04316			0.832490
$119$	−4.09574	+	2.36467i	−0.375455	+	0.216769i
$120$		0			0
$121$	−3.95388	+	6.84832i	−0.359443	+	0.622574i
$122$	−2.79225	−	1.61211i	−0.252798	−	0.145953i
$123$		0			0
$124$	−3.85162	+	2.22374i	−0.345886	+	0.199697i
$125$		−	9.65228i		−	0.863326i
$126$		0			0
$127$	6.12947			0.543903			0.271951	−	0.962311i	$-0.412331\pi$
$127$	6.12947			0.543903			0.271951	+	0.962311i	$0.412331\pi$
$128$	−11.7144	+	6.76329i	−1.03541	+	0.597796i
$129$		0			0
$130$	2.46942	−	5.98530i	0.216582	−	0.524945i
$131$	4.21264	−	7.29650i	0.368060	−	0.637498i	−0.621202	−	0.783650i	$-0.713356\pi$
$131$	4.21264	−	7.29650i	0.368060	−	0.637498i	0.989262	+	0.146152i	$0.0466889\pi$
$132$		0			0
$133$	5.80020	+	10.0462i	0.502941	+	0.871120i
$134$	13.5186			1.16783
$135$		0			0
$136$		−	3.18828i		−	0.273392i
$137$	6.70647	−	3.87198i	0.572973	−	0.330806i	−0.185363	−	0.982670i	$-0.559346\pi$
$137$	6.70647	−	3.87198i	0.572973	−	0.330806i	0.758336	+	0.651864i	$0.226013\pi$
$138$		0			0
$139$	−6.29796	+	10.9084i	−0.534186	+	0.925237i	0.465016	+	0.885302i	$0.346049\pi$
$139$	−6.29796	+	10.9084i	−0.534186	+	0.925237i	−0.999202	+	0.0399353i	$0.987285\pi$
$140$	1.19364	−	2.06745i	0.100881	−	0.174731i
$141$		0			0
$142$	−4.78535	−	8.28847i	−0.401578	−	0.695553i
$143$	0.836341	+	6.28488i	0.0699384	+	0.525568i
$144$		0			0
$145$		−	2.10496i		−	0.174807i
$146$	1.02025	+	1.76712i	0.0844364	+	0.146248i
$147$		0			0
$148$	6.82340	+	3.93949i	0.560880	+	0.323824i
$149$	−6.76751	−	3.90722i	−0.554416	−	0.320092i	0.196485	−	0.980507i	$-0.437047\pi$
$149$	−6.76751	−	3.90722i	−0.554416	−	0.320092i	−0.750901	+	0.660415i	$0.770381\pi$
$150$		0			0
$151$	−15.3081	+	8.83816i	−1.24576	+	0.719239i	−0.970261	−	0.242062i	$-0.922176\pi$
$151$	−15.3081	+	8.83816i	−1.24576	+	0.719239i	−0.275498	+	0.961302i	$0.588843\pi$
$152$	−7.82038			−0.634317
$153$		0			0
$154$			9.23532i			0.744203i
$155$	−3.60011	−	6.23557i	−0.289168	−	0.500853i
$156$		0			0
$157$	8.89974	−	15.4148i	0.710277	−	1.23024i	−0.254477	−	0.967079i	$-0.581903\pi$
$157$	8.89974	−	15.4148i	0.710277	−	1.23024i	0.964753	−	0.263156i	$-0.0847635\pi$
$158$	−0.688495	−	0.397503i	−0.0547737	−	0.0316236i
$159$		0			0
$160$	2.02192	+	3.50207i	0.159847	+	0.276863i
$161$		−	15.0584i		−	1.18677i
$162$		0			0
$163$			16.7251i			1.31001i	0.755624	+	0.655006i	$0.227334\pi$
$163$			16.7251i			1.31001i	−0.755624	+	0.655006i	$0.772666\pi$
$164$	−3.17236	+	1.83156i	−0.247720	+	0.143021i
$165$		0			0
$166$	12.6933	−	21.9854i	0.985188	−	1.70640i
$167$	4.62006	+	2.66739i	0.357511	+	0.206409i	0.667988	−	0.744172i	$-0.267156\pi$
$167$	4.62006	+	2.66739i	0.357511	+	0.206409i	−0.310477	+	0.950581i	$0.600489\pi$
$168$		0			0
$169$	−9.21800	−	9.16670i	−0.709077	−	0.705131i
$170$	−2.64622			−0.202956
$171$		0			0
$172$	1.20538			0.0919097
$173$	−6.15330	−	10.6578i	−0.467827	−	0.810299i	0.531498	−	0.847060i	$-0.321629\pi$
$173$	−6.15330	−	10.6578i	−0.467827	−	0.810299i	−0.999324	+	0.0367604i	$0.988296\pi$
$174$		0			0
$175$	−10.5500	−	6.09104i	−0.797505	−	0.460440i
$176$	−7.45637	−	4.30494i	−0.562045	−	0.324497i
$177$		0			0
$178$	10.9840	+	19.0249i	0.823286	+	1.42597i
$179$	18.8439			1.40846			0.704228	−	0.709974i	$-0.251293\pi$
$179$	18.8439			1.40846			0.704228	+	0.709974i	$0.251293\pi$
$180$		0			0
$181$	10.8768			0.808469			0.404235	−	0.914655i	$-0.367538\pi$
$181$	10.8768			0.808469			0.404235	+	0.914655i	$0.367538\pi$
$182$	−11.5484	−	15.0068i	−0.856025	−	1.11238i
$183$		0			0
$184$	8.79151	+	5.07578i	0.648119	+	0.374191i
$185$	−6.37782	+	11.0467i	−0.468907	+	0.812170i
$186$		0			0
$187$	2.24412	−	1.29564i	0.164106	−	0.0947468i
$188$			6.96641i			0.508078i
$189$		0			0
$190$			6.49081i			0.470893i
$191$	9.29853	+	16.1055i	0.672818	+	1.16536i	0.977101	+	0.212774i	$0.0682498\pi$
$191$	9.29853	+	16.1055i	0.672818	+	1.16536i	−0.304283	+	0.952582i	$0.598417\pi$
$192$		0			0
$193$	−11.2214	−	6.47868i	−0.807735	−	0.466346i	0.0384339	−	0.999261i	$-0.487763\pi$
$193$	−11.2214	−	6.47868i	−0.807735	−	0.466346i	−0.846169	+	0.532915i	$0.821096\pi$
$194$	4.87277	−	8.43989i	0.349845	−	0.605949i
$195$		0			0
$196$	−1.11850	−	1.93729i	−0.0798927	−	0.138378i
$197$			14.0963i			1.00432i	0.864774	+	0.502162i	$0.167462\pi$
$197$			14.0963i			1.00432i	−0.864774	+	0.502162i	$0.832538\pi$
$198$		0			0
$199$	16.6913			1.18321			0.591607	−	0.806226i	$-0.298494\pi$
$199$	16.6913			1.18321			0.591607	+	0.806226i	$0.298494\pi$
$200$	7.11225	−	4.10626i	0.502912	−	0.290356i
$201$		0			0
$202$	−22.5129	−	12.9978i	−1.58400	−	0.914524i
$203$	−5.33139	−	3.07808i	−0.374191	−	0.216039i
$204$		0			0
$205$	−2.96520	−	5.13588i	−0.207098	−	0.358705i
$206$		−	10.2306i		−	0.712802i
$207$		0			0
$208$	17.4993	−	2.32866i	1.21336	−	0.161464i
$209$	−3.17802	−	5.50450i	−0.219829	−	0.380754i
$210$		0			0
$211$	−2.74067	+	4.74698i	−0.188675	+	0.326795i	−0.944809	−	0.327622i	$-0.893753\pi$
$211$	−2.74067	+	4.74698i	−0.188675	+	0.326795i	0.756133	+	0.654417i	$0.227086\pi$
$212$	−3.99035	+	6.91149i	−0.274058	+	0.474683i
$213$		0			0
$214$	15.0701	−	8.70072i	1.03017	−	0.594769i
$215$			1.95145i			0.133088i
$216$		0			0
$217$	−21.0578			−1.42949
$218$	−13.1079	−	22.7035i	−0.887778	−	1.53768i
$219$		0			0
$220$	−0.654015	+	1.13279i	−0.0440937	+	0.0763725i
$221$	−2.02640	+	4.91152i	−0.136310	+	0.330385i
$222$		0			0
$223$	7.94603	−	4.58764i	0.532105	−	0.307211i	−0.209768	−	0.977751i	$-0.567271\pi$
$223$	7.94603	−	4.58764i	0.532105	−	0.307211i	0.741873	+	0.670540i	$0.233938\pi$
$224$	11.8266			0.790198
$225$		0			0
$226$			4.87217i			0.324092i
$227$	2.98340	−	1.72247i	0.198015	−	0.114324i	−0.397714	−	0.917509i	$-0.630196\pi$
$227$	2.98340	−	1.72247i	0.198015	−	0.114324i	0.595729	+	0.803185i	$0.296863\pi$
$228$		0			0
$229$	10.8095	+	6.24088i	0.714313	+	0.412409i	0.812656	−	0.582744i	$-0.198021\pi$
$229$	10.8095	+	6.24088i	0.714313	+	0.412409i	−0.0983427	+	0.995153i	$0.531354\pi$
$230$	4.21283	−	7.29683i	0.277786	−	0.481139i
$231$		0			0
$232$	3.59414	−	2.07508i	0.235967	−	0.136236i
$233$	5.08821			0.333340			0.166670	−	0.986013i	$-0.446699\pi$
$233$	5.08821			0.333340			0.166670	+	0.986013i	$0.446699\pi$
$234$		0			0
$235$	−11.2782			−0.735711
$236$	3.24402	−	1.87293i	0.211167	−	0.121918i
$237$		0			0
$238$	−3.86957	+	6.70230i	−0.250827	+	0.434446i
$239$	1.31463	+	0.759003i	0.0850365	+	0.0490958i	0.541915	−	0.840433i	$-0.317699\pi$
$239$	1.31463	+	0.759003i	0.0850365	+	0.0490958i	−0.456879	+	0.889529i	$0.651033\pi$
$240$		0			0
$241$	16.5435	−	9.55141i	1.06566	−	0.615260i	0.138669	−	0.990339i	$-0.455718\pi$
$241$	16.5435	−	9.55141i	1.06566	−	0.615260i	0.926993	+	0.375079i	$0.122384\pi$
$242$			12.9403i			0.831836i
$243$		0			0
$244$	−1.33554			−0.0854990
$245$	3.13637	−	1.81079i	0.200376	−	0.115687i
$246$		0			0
$247$	12.0472	+	4.97045i	0.766548	+	0.316262i
$248$	7.09801	−	12.2941i	0.450724	−	0.780677i
$249$		0			0
$250$	−7.89754	−	13.6789i	−0.499484	−	0.865132i
$251$	7.96535			0.502768			0.251384	−	0.967887i	$-0.419114\pi$
$251$	7.96535			0.502768			0.251384	+	0.967887i	$0.419114\pi$
$252$		0			0
$253$			8.25073i			0.518719i
$254$	8.68651	−	5.01516i	0.545040	−	0.314679i
$255$		0			0
$256$	−7.30526	+	12.6531i	−0.456579	+	0.790818i
$257$	−10.5328	+	18.2433i	−0.657017	+	1.13799i	0.324367	+	0.945931i	$0.394849\pi$
$257$	−10.5328	+	18.2433i	−0.657017	+	1.13799i	−0.981384	+	0.192056i	$0.938484\pi$
$258$		0			0
$259$	18.6526	+	32.3072i	1.15901	+	2.00747i
$260$	−0.353775	−	2.65852i	−0.0219402	−	0.164875i
$261$		0			0
$262$		−	13.7872i		−	0.851776i
$263$	12.0525	+	20.8755i	0.743187	+	1.28724i	0.951037	+	0.309077i	$0.100020\pi$
$263$	12.0525	+	20.8755i	0.743187	+	1.28724i	−0.207850	+	0.978161i	$0.566647\pi$
$264$		0			0
$265$	−11.1893	−	6.46016i	−0.687355	−	0.396844i
$266$	16.4398	+	9.49151i	1.00799	+	0.581962i
$267$		0			0
$268$	4.84947	−	2.79984i	0.296228	−	0.171027i
$269$	21.7780			1.32783			0.663913	−	0.747809i	$-0.268894\pi$
$269$	21.7780			1.32783			0.663913	+	0.747809i	$0.268894\pi$
$270$		0			0
$271$			5.09950i			0.309773i	0.987932	+	0.154886i	$0.0495012\pi$
$271$			5.09950i			0.309773i	−0.987932	+	0.154886i	$0.950499\pi$
$272$	−3.60752	−	6.24840i	−0.218738	−	0.378865i
$273$		0			0
$274$	6.33615	−	10.9745i	0.382781	−	0.662996i
$275$	5.78051	+	3.33738i	0.348578	+	0.201252i
$276$		0			0
$277$	−6.13878	−	10.6327i	−0.368844	−	0.638856i	0.620541	−	0.784174i	$-0.286913\pi$
$277$	−6.13878	−	10.6327i	−0.368844	−	0.638856i	−0.989385	+	0.145318i	$0.953580\pi$
$278$			20.6121i			1.23623i
$279$		0			0
$280$			7.62003i			0.455384i
$281$	6.33254	−	3.65609i	0.377768	−	0.218104i	−0.299079	−	0.954228i	$-0.596679\pi$
$281$	6.33254	−	3.65609i	0.377768	−	0.218104i	0.676847	+	0.736124i	$0.263346\pi$
$282$		0			0
$283$	−6.39883	+	11.0831i	−0.380371	+	0.658822i	−0.991115	−	0.133006i	$-0.957537\pi$
$283$	−6.39883	+	11.0831i	−0.380371	+	0.658822i	0.610744	+	0.791828i	$0.290870\pi$
$284$	−3.43326	−	1.98219i	−0.203727	−	0.117622i
$285$		0			0
$286$	6.32756	+	8.22246i	0.374156	+	0.486204i
$287$	−17.3440			−1.02379
$288$		0			0
$289$	−14.8285			−0.872266
$290$	−1.72229	−	2.98309i	−0.101136	−	0.175173i
$291$		0			0
$292$	0.731980	+	0.422609i	0.0428359	+	0.0247313i
$293$	5.69346	+	3.28712i	0.332616	+	0.192036i	0.657002	−	0.753889i	$-0.271824\pi$
$293$	5.69346	+	3.28712i	0.332616	+	0.192036i	−0.324386	+	0.945925i	$0.605158\pi$
$294$		0			0
$295$	3.03218	+	5.25188i	0.176540	+	0.305777i
$296$	−25.1492			−1.46176
$297$		0			0
$298$	−12.7876			−0.740768
$299$	−10.3172	−	13.4069i	−0.596660	−	0.775340i
$300$		0			0
$301$	4.94259	+	2.85361i	0.284886	+	0.164479i
$302$	−14.4628	+	25.0504i	−0.832243	+	1.44149i
$303$		0			0
$304$	−15.3264	+	8.84872i	−0.879031	+	0.507509i
$305$		−	2.16216i		−	0.123805i
$306$		0			0
$307$		−	24.3307i		−	1.38863i	−0.719672	−	0.694315i	$-0.755708\pi$
$307$		−	24.3307i		−	1.38863i	0.719672	−	0.694315i	$-0.244292\pi$
$308$	1.91273	+	3.31295i	0.108988	+	0.188773i
$309$		0			0
$310$	−10.2039	−	5.89125i	−0.579545	−	0.334601i
$311$	5.58336	−	9.67066i	0.316603	−	0.548373i	−0.663174	−	0.748465i	$-0.730791\pi$
$311$	5.58336	−	9.67066i	0.316603	−	0.548373i	0.979777	+	0.200093i	$0.0641244\pi$
$312$		0			0
$313$	−8.90138	−	15.4176i	−0.503136	−	0.871456i	−0.999993	−	0.00362437i	$-0.998846\pi$
$313$	−8.90138	−	15.4176i	−0.503136	−	0.871456i	0.496858	−	0.867832i	$-0.334487\pi$
$314$		−	29.1272i		−	1.64374i
$315$		0			0
$316$	−0.329308			−0.0185250
$317$	−26.7276	+	15.4312i	−1.50117	+	0.866700i	−0.501170	+	0.865349i	$0.667097\pi$
$317$	−26.7276	+	15.4312i	−1.50117	+	0.866700i	−0.999999	+	0.00135144i	$0.999570\pi$
$318$		0			0
$319$	2.92116	+	1.68653i	0.163553	+	0.0944276i
$320$	−3.57549	−	2.06431i	−0.199876	−	0.115398i
$321$		0			0
$322$	−12.3208	−	21.3403i	−0.686613	−	1.18925i
$323$		−	5.32634i		−	0.296365i
$324$		0			0
$325$	−13.5662	+	1.80528i	−0.752518	+	0.100139i
$326$	13.6846	+	23.7024i	0.757918	+	1.31275i
$327$		0			0
$328$	5.84622	−	10.1259i	0.322803	−	0.559112i
$329$	−16.4922	+	28.5653i	−0.909243	+	1.57486i
$330$		0			0
$331$	−15.0730	+	8.70242i	−0.828489	+	0.478328i	−0.853335	−	0.521363i	$-0.825424\pi$
$331$	−15.0730	+	8.70242i	−0.828489	+	0.478328i	0.0248461	+	0.999691i	$0.492090\pi$
$332$		−	10.5156i		−	0.577120i
$333$		0			0
$334$	8.72989			0.477678
$335$	4.53279	+	7.85102i	0.247653	+	0.428947i
$336$		0			0
$337$	−4.37915	+	7.58491i	−0.238548	+	0.413176i	−0.960298	−	0.278977i	$-0.910005\pi$
$337$	−4.37915	+	7.58491i	−0.238548	+	0.413176i	0.721750	+	0.692154i	$0.243338\pi$
$338$	−20.5637	−	5.44859i	−1.11852	−	0.296364i
$339$		0			0
$340$	−0.949270	+	0.548061i	−0.0514814	+	0.0297228i
$341$	11.5379			0.624811
$342$		0			0
$343$			11.8741i			0.641141i
$344$	−3.33203	+	1.92375i	−0.179651	+	0.103722i
$345$		0			0
$346$	−17.4406	−	10.0693i	−0.937611	−	0.541330i
$347$	−3.63878	+	6.30255i	−0.195340	+	0.338339i	−0.947012	−	0.321198i	$-0.895914\pi$
$347$	−3.63878	+	6.30255i	−0.195340	+	0.338339i	0.751672	+	0.659537i	$0.229248\pi$
$348$		0			0
$349$	10.8475	−	6.26279i	0.580652	−	0.335240i	−0.180740	−	0.983531i	$-0.557849\pi$
$349$	10.8475	−	6.26279i	0.580652	−	0.335240i	0.761392	+	0.648291i	$0.224516\pi$
$350$	−19.9349			−1.06556
$351$		0			0
$352$	−6.47999			−0.345385
$353$	1.42107	−	0.820458i	0.0756361	−	0.0436686i	−0.461705	−	0.887034i	$-0.652762\pi$
$353$	1.42107	−	0.820458i	0.0756361	−	0.0436686i	0.537341	+	0.843365i	$0.319429\pi$
$354$		0			0
$355$	3.20906	−	5.55826i	0.170319	−	0.295002i
$356$	7.88050	+	4.54981i	0.417666	+	0.241139i
$357$		0			0
$358$	26.7050	−	15.4181i	1.41140	−	0.814874i
$359$			7.00788i			0.369862i	0.982752	+	0.184931i	$0.0592061\pi$
$359$			7.00788i			0.369862i	−0.982752	+	0.184931i	$0.940794\pi$
$360$		0			0
$361$	5.93526			0.312382
$362$	15.4144	−	8.89948i	0.810160	−	0.467746i
$363$		0			0
$364$	−7.25078	−	2.99153i	−0.380044	−	0.156799i
$365$	−0.684180	+	1.18504i	−0.0358116	+	0.0620276i
$366$		0			0
$367$	0.596340	+	1.03289i	0.0311287	+	0.0539165i	0.881170	−	0.472799i	$-0.156756\pi$
$367$	0.596340	+	1.03289i	0.0311287	+	0.0539165i	−0.850041	+	0.526716i	$0.823423\pi$
$368$	22.9729			1.19754
$369$		0			0
$370$			20.8735i			1.08516i
$371$	−32.7243	+	18.8934i	−1.69896	+	0.980895i
$372$		0			0
$373$	−8.65200	+	14.9857i	−0.447984	+	0.775931i	−0.998255	−	0.0590555i	$-0.981191\pi$
$373$	−8.65200	+	14.9857i	−0.447984	+	0.775931i	0.550271	+	0.834986i	$0.314524\pi$
$374$	2.12020	−	3.67230i	0.109633	−	0.189890i
$375$		0			0
$376$	−11.1181	−	19.2572i	−0.573375	−	0.993114i
$377$	−6.85563	+	0.912292i	−0.353083	+	0.0469854i
$378$		0			0
$379$			1.54294i			0.0792554i	0.999215	+	0.0396277i	$0.0126172\pi$
$379$			1.54294i			0.0792554i	−0.999215	+	0.0396277i	$0.987383\pi$
$380$	1.34431	+	2.32842i	0.0689619	+	0.119446i
$381$		0			0
$382$	26.3552	+	15.2162i	1.34845	+	0.778529i
$383$	−20.4912	−	11.8306i	−1.04705	−	0.604515i	−0.125229	−	0.992128i	$-0.539967\pi$
$383$	−20.4912	−	11.8306i	−1.04705	−	0.604515i	−0.921822	+	0.387612i	$0.873300\pi$
$384$		0			0
$385$	−5.36348	+	3.09661i	−0.273348	+	0.157818i
$386$	−21.2036			−1.07923
$387$		0			0
$388$		−	4.03681i		−	0.204938i
$389$	−2.58336	−	4.47450i	−0.130981	−	0.226866i	0.793074	−	0.609126i	$-0.208479\pi$
$389$	−2.58336	−	4.47450i	−0.130981	−	0.226866i	−0.924055	+	0.382259i	$0.875146\pi$
$390$		0			0
$391$	−3.45703	+	5.98776i	−0.174830	+	0.302814i
$392$	6.18371	+	3.57016i	0.312324	+	0.180321i
$393$		0			0
$394$	11.5337	+	19.9769i	0.581059	+	1.00642i
$395$		−	0.533132i		−	0.0268248i
$396$		0			0
$397$			14.0455i			0.704926i	0.935826	+	0.352463i	$0.114656\pi$
$397$			14.0455i			0.704926i	−0.935826	+	0.352463i	$0.885344\pi$
$398$	23.6544	−	13.6569i	1.18569	−	0.684558i
$399$		0			0
$400$	9.29242	−	16.0949i	0.464621	−	0.804747i
$401$	−12.9801	−	7.49409i	−0.648198	−	0.374237i	0.139568	−	0.990213i	$-0.455429\pi$
$401$	−12.9801	−	7.49409i	−0.648198	−	0.374237i	−0.787765	+	0.615976i	$0.788762\pi$
$402$		0			0
$403$	−18.7483	+	14.4277i	−0.933919	+	0.718694i
$404$	−10.7680			−0.535726
$405$		0			0
$406$	−10.0740			−0.499964
$407$	−10.2200	−	17.7016i	−0.506589	−	0.877438i
$408$		0			0
$409$	0.411886	+	0.237803i	0.0203665	+	0.0117586i	0.510149	−	0.860086i	$-0.329590\pi$
$409$	0.411886	+	0.237803i	0.0203665	+	0.0117586i	−0.489782	+	0.871845i	$0.662924\pi$
$410$	−8.40439	−	4.85228i	−0.415063	−	0.239637i
$411$		0			0
$412$	−2.11887	−	3.67000i	−0.104389	−	0.180808i
$413$	17.7358			0.872722
$414$		0			0
$415$	17.0242			0.835687
$416$	10.5296	−	8.10298i	0.516254	−	0.397281i
$417$		0			0
$418$	−9.00762	−	5.20055i	−0.440577	−	0.254367i
$419$	6.45908	−	11.1875i	0.315547	−	0.546543i	−0.664007	−	0.747726i	$-0.731145\pi$
$419$	6.45908	−	11.1875i	0.315547	−	0.546543i	0.979554	+	0.201184i	$0.0644788\pi$
$420$		0			0
$421$	−27.3802	+	15.8080i	−1.33443	+	0.770433i	−0.985975	−	0.166893i	$-0.946626\pi$
$421$	−27.3802	+	15.8080i	−1.33443	+	0.770433i	−0.348454	+	0.937326i	$0.613293\pi$
$422$			8.96971i			0.436639i
$423$		0			0
$424$		−	25.4738i		−	1.23712i
$425$	2.79671	+	4.84404i	0.135660	+	0.234970i
$426$		0			0
$427$	−5.47627	−	3.16173i	−0.265016	−	0.153007i
$428$	3.60402	−	6.24235i	0.174207	−	0.301735i
$429$		0			0
$430$	1.59669	+	2.76554i	0.0769991	+	0.133366i
$431$		−	12.5560i		−	0.604799i	−0.953181	−	0.302400i	$-0.902212\pi$
$431$		−	12.5560i		−	0.604799i	0.953181	−	0.302400i	$-0.0977877\pi$
$432$		0			0
$433$	−27.9766			−1.34447			−0.672235	−	0.740338i	$-0.734665\pi$
$433$	−27.9766			−1.34447			−0.672235	+	0.740338i	$0.734665\pi$
$434$	−29.8425	+	17.2296i	−1.43248	+	0.827045i
$435$		0			0
$436$	−9.40428	−	5.42957i	−0.450384	−	0.260029i
$437$	14.6871	+	8.47960i	0.702580	+	0.405635i
$438$		0			0
$439$	5.76780	+	9.99012i	0.275282	+	0.476802i	0.970206	−	0.242281i	$-0.0778955\pi$
$439$	5.76780	+	9.99012i	0.275282	+	0.476802i	−0.694924	+	0.719083i	$0.744562\pi$
$440$		−	4.17514i		−	0.199042i
$441$		0			0
$442$	1.14688	+	8.61847i	0.0545514	+	0.409939i
$443$	13.1323	+	22.7457i	0.623932	+	1.08068i	0.988746	+	0.149602i	$0.0477992\pi$
$443$	13.1323	+	22.7457i	0.623932	+	1.08068i	−0.364814	+	0.931080i	$0.618868\pi$
$444$		0			0
$445$	−7.36589	+	12.7581i	−0.349177	+	0.604792i
$446$	7.50726	−	13.0030i	0.355479	−	0.615708i
$447$		0			0
$448$	−10.4569	+	6.03728i	−0.494041	+	0.285235i
$449$			29.9575i			1.41378i	0.707323	+	0.706891i	$0.249903\pi$
$449$			29.9575i			1.41378i	−0.707323	+	0.706891i	$0.750097\pi$
$450$		0			0
$451$	9.50308			0.447483
$452$	1.00908	+	1.74778i	0.0474631	+	0.0822085i
$453$		0			0
$454$	2.81866	−	4.88206i	0.132286	−	0.229127i
$455$	4.84312	−	11.7386i	0.227049	−	0.550315i
$456$		0			0
$457$	−9.92475	+	5.73006i	−0.464260	+	0.268041i	−0.713834	−	0.700315i	$-0.753043\pi$
$457$	−9.92475	+	5.73006i	−0.464260	+	0.268041i	0.249574	+	0.968356i	$0.419710\pi$
$458$	20.4253			0.954410
$459$		0			0
$460$		−	3.49008i		−	0.162726i
$461$	24.6926	−	14.2563i	1.15005	−	0.663981i	0.201149	−	0.979561i	$-0.435532\pi$
$461$	24.6926	−	14.2563i	1.15005	−	0.663981i	0.948899	+	0.315580i	$0.102199\pi$
$462$		0			0
$463$	−1.46868	−	0.847942i	−0.0682553	−	0.0394072i	0.465484	−	0.885056i	$-0.345880\pi$
$463$	−1.46868	−	0.847942i	−0.0682553	−	0.0394072i	−0.533739	+	0.845649i	$0.679214\pi$
$464$	4.69588	−	8.13351i	0.218001	−	0.377589i
$465$		0			0
$466$	7.21086	−	4.16319i	0.334037	−	0.192856i
$467$	−14.1217			−0.653476			−0.326738	−	0.945115i	$-0.605949\pi$
$467$	−14.1217			−0.653476			−0.326738	+	0.945115i	$0.605949\pi$
$468$		0			0
$469$	26.5132			1.22427
$470$	−15.9832	+	9.22791i	−0.737251	+	0.425652i
$471$		0			0
$472$	−5.97827	+	10.3547i	−0.275172	+	0.476612i
$473$	−2.70813	−	1.56354i	−0.124520	−	0.0718915i
$474$		0			0
$475$	11.8817	−	6.85992i	0.545171	−	0.314755i
$476$			3.20572i			0.146934i
$477$		0			0
$478$	2.48408			0.113619
$479$	24.0438	−	13.8817i	1.09859	−	0.634272i	0.162740	−	0.986669i	$-0.447967\pi$
$479$	24.0438	−	13.8817i	1.09859	−	0.634272i	0.935850	+	0.352397i	$0.114633\pi$
$480$		0			0
$481$	38.7421	+	15.9842i	1.76649	+	0.728818i
$482$	15.6300	−	27.0720i	0.711927	−	1.23309i
$483$		0			0
$484$	2.68008	+	4.64203i	0.121822	+	0.211001i
$485$	6.53537			0.296756
$486$		0			0
$487$		−	27.5898i		−	1.25021i	−0.780539	−	0.625107i	$-0.785055\pi$
$487$		−	27.5898i		−	1.25021i	0.780539	−	0.625107i	$-0.214945\pi$
$488$	3.69181	−	2.13147i	0.167121	−	0.0964871i
$489$		0			0
$490$	2.96319	−	5.13239i	0.133863	−	0.231858i
$491$	20.3683	−	35.2790i	0.919210	−	1.59212i	0.118591	−	0.992943i	$-0.462162\pi$
$491$	20.3683	−	35.2790i	0.919210	−	1.59212i	0.800618	−	0.599175i	$-0.204504\pi$
$492$		0			0
$493$	1.41330	+	2.44791i	0.0636520	+	0.110249i
$494$	21.1399	−	2.81312i	0.951128	−	0.126568i
$495$		0			0
$496$		−	32.1254i		−	1.44248i
$497$	−9.38523	−	16.2557i	−0.420985	−	0.729168i
$498$		0			0
$499$	13.5293	+	7.81113i	0.605654	+	0.349674i	0.771262	−	0.636517i	$-0.219626\pi$
$499$	13.5293	+	7.81113i	0.605654	+	0.349674i	−0.165609	+	0.986192i	$0.552959\pi$
$500$	−5.66611	−	3.27133i	−0.253396	−	0.146298i
$501$		0			0
$502$	11.2883	−	6.51729i	0.503820	−	0.290881i
$503$	−30.2181			−1.34736			−0.673679	−	0.739024i	$-0.735287\pi$
$503$	−30.2181			−1.34736			−0.673679	+	0.739024i	$0.735287\pi$
$504$		0			0
$505$		−	17.4327i		−	0.775746i
$506$	6.75078	+	11.6927i	0.300109	+	0.519804i
$507$		0			0
$508$	2.07739	−	3.59814i	0.0921691	−	0.159642i
$509$	13.0660	+	7.54366i	0.579140	+	0.334367i	0.760792	−	0.648996i	$-0.224811\pi$
$509$	13.0660	+	7.54366i	0.579140	+	0.334367i	−0.181651	+	0.983363i	$0.558144\pi$
$510$		0			0
$511$	2.00095	+	3.46575i	0.0885170	+	0.153316i
$512$		−	3.14438i		−	0.138963i
$513$		0			0
$514$			34.4719i			1.52049i
$515$	5.94152	−	3.43034i	0.261815	−	0.151159i
$516$		0			0
$517$	9.03633	−	15.6514i	0.397417	−	0.688347i
$518$	52.8678	+	30.5232i	2.32288	+	1.34111i
$519$		0			0
$520$	5.22085	+	6.78433i	0.228949	+	0.297512i
$521$	−26.8690			−1.17715			−0.588576	−	0.808442i	$-0.700311\pi$
$521$	−26.8690			−1.17715			−0.588576	+	0.808442i	$0.700311\pi$
$522$		0			0
$523$	24.9855			1.09254			0.546270	−	0.837609i	$-0.316047\pi$
$523$	24.9855			1.09254			0.546270	+	0.837609i	$0.316047\pi$
$524$	−2.85547	−	4.94583i	−0.124742	−	0.216059i
$525$		0			0
$526$	34.1608	+	19.7228i	1.48948	+	0.859954i
$527$	8.37333	+	4.83434i	0.364748	+	0.210587i
$528$		0			0
$529$	0.492707	+	0.853394i	0.0214221	+	0.0371041i
$530$	−21.1429			−0.918390
$531$		0			0
$532$	7.86317			0.340911
$533$	−15.4419	+	11.8832i	−0.668862	+	0.514720i
$534$		0			0
$535$	10.1060	+	5.83471i	0.436921	+	0.252257i
$536$	−8.93689	+	15.4792i	−0.386015	+	0.668598i
$537$		0			0
$538$	30.8631	−	17.8188i	1.33060	−	0.768225i
$539$			5.80334i			0.249967i
$540$		0			0
$541$		−	33.1735i		−	1.42624i	−0.701042	−	0.713120i	$-0.747281\pi$
$541$		−	33.1735i		−	1.42624i	0.701042	−	0.713120i	$-0.252719\pi$
$542$	4.17244	+	7.22687i	0.179222	+	0.310421i
$543$		0			0
$544$	−4.70269	−	2.71510i	−0.201626	−	0.116409i
$545$	8.79017	−	15.2250i	0.376530	−	0.652168i
$546$		0			0
$547$	−9.36201	−	16.2155i	−0.400291	−	0.693324i	0.593470	−	0.804856i	$-0.297758\pi$
$547$	−9.36201	−	16.2155i	−0.400291	−	0.693324i	−0.993761	+	0.111532i	$0.964424\pi$
$548$		−	5.24913i		−	0.224232i
$549$		0			0
$550$	10.9226			0.465743
$551$	6.00438	−	3.46663i	0.255795	−	0.147683i
$552$		0			0
$553$	−1.35030	−	0.779599i	−0.0574208	−	0.0331519i
$554$	−17.3994	−	10.0456i	−0.739230	−	0.426795i
$555$		0			0
$556$	4.26898	+	7.39409i	0.181045	+	0.313579i
$557$		−	27.4258i		−	1.16207i	−0.813879	−	0.581035i	$-0.802648\pi$
$557$		−	27.4258i		−	1.16207i	0.813879	−	0.581035i	$-0.197352\pi$
$558$		0			0
$559$	6.35567	−	0.845762i	0.268816	−	0.0357719i
$560$	8.62203	+	14.9338i	0.364347	+	0.631068i
$561$		0			0
$562$	5.98286	−	10.3626i	0.252372	−	0.437121i
$563$	−9.85731	+	17.0734i	−0.415436	+	0.719556i	−0.995474	−	0.0950331i	$-0.969704\pi$
$563$	−9.85731	+	17.0734i	−0.415436	+	0.719556i	0.580038	+	0.814589i	$0.303038\pi$
$564$		0			0
$565$	−2.82955	+	1.63364i	−0.119040	+	0.0687279i
$566$			20.9422i			0.880267i
$567$		0			0
$568$	12.6540			0.530952
$569$	9.70872	+	16.8160i	0.407011	+	0.704963i	0.994553	−	0.104230i	$-0.0332379\pi$
$569$	9.70872	+	16.8160i	0.407011	+	0.704963i	−0.587543	+	0.809193i	$0.699905\pi$
$570$		0			0
$571$	−4.99536	+	8.65223i	−0.209050	+	0.362084i	−0.951415	−	0.307910i	$-0.900370\pi$
$571$	−4.99536	+	8.65223i	−0.209050	+	0.362084i	0.742366	+	0.669995i	$0.233704\pi$
$572$	3.97282	+	1.63911i	0.166112	+	0.0685344i
$573$		0			0
$574$	−24.5795	+	14.1910i	−1.02593	+	0.592320i
$575$	−17.8096			−0.742711
$576$		0			0
$577$			17.2976i			0.720107i	0.932932	+	0.360054i	$0.117242\pi$
$577$			17.2976i			0.720107i	−0.932932	+	0.360054i	$0.882758\pi$
$578$	−21.0146	+	12.1328i	−0.874090	+	0.504656i
$579$		0			0
$580$	−1.23566	−	0.713408i	−0.0513079	−	0.0296227i
$581$	24.8945	−	43.1186i	1.03280	−	1.78886i
$582$		0			0
$583$	17.9302	−	10.3520i	0.742591	−	0.428735i
$584$	−2.69787			−0.111639
$585$		0			0
$586$	10.7582			0.444415
$587$	19.0473	−	10.9970i	0.786166	−	0.453893i	−0.0524453	−	0.998624i	$-0.516702\pi$
$587$	19.0473	−	10.9970i	0.786166	−	0.453893i	0.838611	+	0.544731i	$0.183368\pi$
$588$		0			0
$589$	11.8579	−	20.5386i	0.488598	−	0.846277i
$590$	8.59423	+	4.96188i	0.353819	+	0.204277i
$591$		0			0
$592$	−49.2875	+	28.4561i	−2.02570	+	1.16954i
$593$		−	29.8711i		−	1.22666i	−0.789826	−	0.613330i	$-0.789829\pi$
$593$		−	29.8711i		−	1.22666i	0.789826	−	0.613330i	$-0.210171\pi$
$594$		0			0
$595$	−5.18988			−0.212765
$596$	−4.58726	+	2.64845i	−0.187901	+	0.108485i
$597$		0			0
$598$	−25.5908	−	10.5583i	−1.04649	−	0.431760i
$599$	−0.00682877	+	0.0118278i	−0.000279016	+	0.000483270i	−0.866165	−	0.499758i	$-0.833422\pi$
$599$	−0.00682877	+	0.0118278i	−0.000279016	+	0.000483270i	0.865886	+	0.500242i	$0.166755\pi$
$600$		0			0
$601$	−3.25799	−	5.64301i	−0.132896	−	0.230183i	0.791896	−	0.610657i	$-0.209094\pi$
$601$	−3.25799	−	5.64301i	−0.132896	−	0.230183i	−0.924792	+	0.380473i	$0.875761\pi$
$602$	9.33934			0.380643
$603$		0			0
$604$			11.9816i			0.487526i
$605$	−7.51520	+	4.33890i	−0.305536	+	0.176401i
$606$		0			0
$607$	17.7921	−	30.8168i	0.722158	−	1.25081i	−0.237975	−	0.971271i	$-0.576484\pi$
$607$	17.7921	−	30.8168i	0.722158	−	1.25081i	0.960133	−	0.279543i	$-0.0901831\pi$
$608$	−6.65975	+	11.5350i	−0.270088	+	0.467807i
$609$		0			0
$610$	−1.76909	−	3.06415i	−0.0716284	−	0.124064i
$611$	4.88801	+	36.7320i	0.197748	+	1.48602i
$612$		0			0
$613$		−	2.03420i		−	0.0821607i	−0.999156	−	0.0410803i	$-0.986920\pi$
$613$		−	2.03420i		−	0.0821607i	0.999156	−	0.0410803i	$-0.0130800\pi$
$614$	−19.9075	−	34.4809i	−0.803403	−	1.39153i
$615$		0			0
$616$	−10.5747	−	6.10530i	−0.426067	−	0.245990i
$617$	−2.65725	−	1.53417i	−0.106977	−	0.0617632i	0.445557	−	0.895254i	$-0.353006\pi$
$617$	−2.65725	−	1.53417i	−0.106977	−	0.0617632i	−0.552534	+	0.833490i	$0.686339\pi$
$618$		0			0
$619$	−3.43093	+	1.98085i	−0.137901	+	0.0796169i	−0.567363	−	0.823468i	$-0.692036\pi$
$619$	−3.43093	+	1.98085i	−0.137901	+	0.0796169i	0.429463	+	0.903085i	$0.358703\pi$
$620$	−4.88056			−0.196008
$621$		0			0
$622$		−	18.2733i		−	0.732693i
$623$	21.5423	+	37.3123i	0.863074	+	1.49489i
$624$		0			0
$625$	−4.19330	+	7.26301i	−0.167732	+	0.290520i
$626$	−25.2296	−	14.5663i	−1.00838	−	0.582186i
$627$		0			0
$628$	−6.03256	−	10.4487i	−0.240725	−	0.416948i
$629$		−	17.1287i		−	0.682966i
$630$		0			0
$631$			8.56943i			0.341144i	0.985345	+	0.170572i	$0.0545615\pi$
$631$			8.56943i			0.341144i	−0.985345	+	0.170572i	$0.945438\pi$
$632$	0.910304	−	0.525564i	0.0362099	−	0.0209058i
$633$		0			0
$634$	−25.2517	+	43.7372i	−1.00287	+	1.73703i
$635$	5.82519	+	3.36317i	0.231166	+	0.133464i
$636$		0			0
$637$	−7.25685	−	9.43004i	−0.287527	−	0.373632i
$638$	5.51971			0.218527
$639$		0			0
$640$	−14.8438			−0.586752
$641$	−5.45756	−	9.45277i	−0.215561	−	0.373362i	0.737885	−	0.674926i	$-0.235825\pi$
$641$	−5.45756	−	9.45277i	−0.215561	−	0.373362i	−0.953446	+	0.301564i	$0.902491\pi$
$642$		0			0
$643$	−25.3834	−	14.6551i	−1.00102	−	0.577941i	−0.0924728	−	0.995715i	$-0.529477\pi$
$643$	−25.3834	−	14.6551i	−1.00102	−	0.577941i	−0.908551	+	0.417774i	$0.862810\pi$
$644$	−8.83961	−	5.10355i	−0.348329	−	0.201108i
$645$		0			0
$646$	−4.35803	−	7.54834i	−0.171465	−	0.296985i
$647$	5.27064			0.207210			0.103605	−	0.994619i	$-0.466962\pi$
$647$	5.27064			0.207210			0.103605	+	0.994619i	$0.466962\pi$
$648$		0			0
$649$	−9.71773			−0.381454
$650$	−17.7486	+	13.6583i	−0.696156	+	0.535724i
$651$		0			0
$652$	9.81802	+	5.66843i	0.384503	+	0.221993i
$653$	10.5317	−	18.2414i	0.412137	−	0.713842i	−0.582986	−	0.812482i	$-0.698116\pi$
$653$	10.5317	−	18.2414i	0.412137	−	0.713842i	0.995123	+	0.0986399i	$0.0314492\pi$
$654$		0			0
$655$	8.00702	−	4.62286i	0.312860	−	0.180630i
$656$		−	26.4599i		−	1.03308i
$657$		0			0
$658$			53.9759i			2.10420i
$659$	4.60414	+	7.97460i	0.179352	+	0.310646i	0.941659	−	0.336569i	$-0.109267\pi$
$659$	4.60414	+	7.97460i	0.179352	+	0.310646i	−0.762307	+	0.647216i	$0.775933\pi$
$660$		0			0
$661$	−8.39767	−	4.84840i	−0.326632	−	0.188581i	0.327713	−	0.944777i	$-0.393722\pi$
$661$	−8.39767	−	4.84840i	−0.326632	−	0.188581i	−0.654345	+	0.756196i	$0.727055\pi$
$662$	−14.2407	+	24.6657i	−0.553481	+	0.958658i
$663$		0			0
$664$	16.7826	+	29.0683i	0.651290	+	1.12807i
$665$			12.7300i			0.493650i
$666$		0			0
$667$	−9.00000			−0.348481
$668$	3.13164	−	1.80805i	0.121167	−	0.0699557i
$669$		0			0
$670$	12.8475	+	7.41750i	0.496342	+	0.286563i
$671$	3.00054	+	1.73236i	0.115835	+	0.0668771i
$672$		0			0
$673$	13.8136	+	23.9259i	0.532475	+	0.922275i	0.999281	+	0.0379146i	$0.0120715\pi$
$673$	13.8136	+	23.9259i	0.532475	+	0.922275i	−0.466805	+	0.884360i	$0.654595\pi$
$674$			14.3322i			0.552054i
$675$		0			0
$676$	−8.50521	+	2.30442i	−0.327123	+	0.0886314i
$677$	−11.4941	−	19.9084i	−0.441755	−	0.765141i	0.556065	−	0.831139i	$-0.312310\pi$
$677$	−11.4941	−	19.9084i	−0.441755	−	0.765141i	−0.997820	+	0.0659973i	$0.978977\pi$
$678$		0			0
$679$	9.55668	−	16.5527i	0.366752	−	0.635232i
$680$	1.74937	−	3.03000i	0.0670854	−	0.116195i
$681$		0			0
$682$	16.3512	−	9.44035i	0.626118	−	0.361490i
$683$		−	19.2616i		−	0.737023i	−0.929623	−	0.368512i	$-0.879867\pi$
$683$		−	19.2616i		−	0.737023i	0.929623	−	0.368512i	$-0.120133\pi$
$684$		0			0
$685$	8.49806			0.324694
$686$	9.71544	+	16.8276i	0.370937	+	0.642482i
$687$		0			0
$688$	−4.35343	+	7.54036i	−0.165973	+	0.287473i
$689$	−16.1906	+	39.2423i	−0.616812	+	1.49501i
$690$		0			0
$691$	−0.829355	+	0.478828i	−0.0315502	+	0.0182155i	−0.515692	−	0.856774i	$-0.672465\pi$
$691$	−0.829355	+	0.478828i	−0.0315502	+	0.0182155i	0.484142	+	0.874989i	$0.339132\pi$
$692$	−8.34185			−0.317109
$693$		0			0
$694$			11.9091i			0.452062i
$695$	−11.9706	+	6.91125i	−0.454072	+	0.262159i
$696$		0			0
$697$	6.89662	+	3.98177i	0.261228	+	0.150820i
$698$	10.2485	−	17.7509i	0.387911	−	0.671882i
$699$		0			0
$700$	−7.15116	+	4.12872i	−0.270288	+	0.156051i
$701$	5.78079			0.218337			0.109169	−	0.994023i	$-0.465181\pi$
$701$	5.78079			0.218337			0.109169	+	0.994023i	$0.465181\pi$
$702$		0			0
$703$	−42.0142			−1.58460
$704$	5.72949	−	3.30792i	0.215938	−	0.124672i
$705$		0			0
$706$	1.34260	−	2.32546i	0.0505296	−	0.0875198i
$707$	−44.1532	−	25.4919i	−1.66055	−	0.958721i
$708$		0			0
$709$	4.84652	−	2.79814i	0.182015	−	0.105086i	−0.406224	−	0.913773i	$-0.633155\pi$
$709$	4.84652	−	2.79814i	0.182015	−	0.105086i	0.588239	+	0.808687i	$0.299821\pi$
$710$		−	10.5027i		−	0.394159i
$711$		0			0
$712$	−29.0453			−1.08852
$713$	−26.6609	+	15.3927i	−0.998459	+	0.576461i
$714$		0			0
$715$	−2.65362	+	6.43178i	−0.0992399	+	0.240535i
$716$	6.38652	−	11.0618i	0.238675	−	0.413398i
$717$		0			0
$718$	5.73388	+	9.93137i	0.213987	+	0.370636i
$719$	−17.4320			−0.650102			−0.325051	−	0.945696i	$-0.605382\pi$
$719$	−17.4320			−0.650102			−0.325051	+	0.945696i	$0.605382\pi$
$720$		0			0
$721$		−	20.0647i		−	0.747250i
$722$	8.41129	−	4.85626i	0.313036	−	0.180731i
$723$		0			0
$724$	3.68635	−	6.38495i	0.137002	−	0.237295i
$725$	−3.64046	+	6.30546i	−0.135203	+	0.234179i
$726$		0			0
$727$	−12.0213	−	20.8215i	−0.445845	−	0.772225i	0.552266	−	0.833668i	$-0.313763\pi$
$727$	−12.0213	−	20.8215i	−0.445845	−	0.772225i	−0.998111	+	0.0614425i	$0.980430\pi$
$728$	24.8176	−	3.30253i	0.919803	−	0.122400i
$729$		0			0
$730$			2.23920i			0.0828764i
$731$	−1.31024	−	2.26940i	−0.0484608	−	0.0839367i
$732$		0			0
$733$	−11.8926	−	6.86619i	−0.439263	−	0.253608i	0.264022	−	0.964517i	$-0.414951\pi$
$733$	−11.8926	−	6.86619i	−0.439263	−	0.253608i	−0.703285	+	0.710908i	$0.748284\pi$
$734$	1.69023	+	0.975856i	0.0623876	+	0.0360195i
$735$		0			0
$736$	14.9735	−	8.64495i	0.551930	−	0.318657i
$737$	−14.5270			−0.535109
$738$		0			0
$739$		−	13.1229i		−	0.482732i	−0.970434	−	0.241366i	$-0.922405\pi$
$739$		−	13.1229i		−	0.482732i	0.970434	−	0.241366i	$-0.0775954\pi$
$740$	4.32311	+	7.48785i	0.158921	+	0.275259i
$741$		0			0
$742$	−30.9173	+	53.5503i	−1.13501	+	1.96589i
$743$	30.7672	+	17.7634i	1.12874	+	0.651677i	0.943617	−	0.331039i	$-0.107399\pi$
$743$	30.7672	+	17.7634i	1.12874	+	0.651677i	0.185120	+	0.982716i	$0.440732\pi$
$744$		0			0
$745$	−4.28770	−	7.42652i	−0.157089	−	0.272087i
$746$			28.3164i			1.03674i
$747$		0			0
$748$		−	1.75646i		−	0.0642227i
$749$	29.5561	−	17.0642i	1.07996	−	0.623512i
$750$		0			0
$751$	−11.7119	+	20.2856i	−0.427374	+	0.740233i	−0.996639	−	0.0819210i	$-0.973894\pi$
$751$	−11.7119	+	20.2856i	−0.427374	+	0.740233i	0.569265	+	0.822154i	$0.307228\pi$
$752$	−43.5788	−	25.1603i	−1.58916	−	0.917500i
$753$		0			0
$754$	−8.96916	+	6.90218i	−0.326638	+	0.251363i
$755$	−19.3976			−0.705951
$756$		0			0
$757$	18.7868			0.682817			0.341409	−	0.939915i	$-0.389096\pi$
$757$	18.7868			0.682817			0.341409	+	0.939915i	$0.389096\pi$
$758$	1.26244	+	2.18661i	0.0458538	+	0.0794212i
$759$		0			0
$760$	−7.43216	−	4.29096i	−0.269593	−	0.155649i
$761$	−14.6714	−	8.47054i	−0.531838	−	0.307057i	0.209927	−	0.977717i	$-0.432677\pi$
$761$	−14.6714	−	8.47054i	−0.531838	−	0.307057i	−0.741765	+	0.670660i	$0.766011\pi$
$762$		0			0
$763$	−25.7077	−	44.5271i	−0.930682	−	1.61199i
$764$	12.6057			0.456060
$765$		0			0
$766$	−38.7194			−1.39899
$767$	15.7907	−	12.1517i	0.570168	−	0.438771i
$768$		0			0
$769$	−33.2707	−	19.2088i	−1.19977	−	0.692688i	−0.239267	−	0.970954i	$-0.576907\pi$
$769$	−33.2707	−	19.2088i	−1.19977	−	0.692688i	−0.960504	+	0.278266i	$0.910240\pi$
$770$	−5.06732	+	8.77685i	−0.182613	+	0.316296i
$771$		0			0
$772$	−7.60627	+	4.39148i	−0.273756	+	0.158053i
$773$			21.1236i			0.759761i	0.925036	+	0.379881i	$0.124035\pi$
$773$			21.1236i			0.759761i	−0.925036	+	0.379881i	$0.875965\pi$
$774$		0			0
$775$			24.9051i			0.894617i
$776$	6.44261	+	11.1589i	0.231276	+	0.400582i
$777$		0			0
$778$	−7.32212	−	4.22743i	−0.262511	−	0.151561i
$779$	9.76670	−	16.9164i	0.349928	−	0.606094i
$780$		0			0
$781$	5.14232	+	8.90676i	0.184007	+	0.318709i
$782$			11.3142i			0.404597i
$783$		0			0
$784$	16.1585			0.577089
$785$	16.9159	−	9.76638i	0.603753	−	0.348577i
$786$		0			0
$787$	−2.57534	−	1.48688i	−0.0918011	−	0.0530014i	0.453397	−	0.891309i	$-0.350212\pi$
$787$	−2.57534	−	1.48688i	−0.0918011	−	0.0530014i	−0.545198	+	0.838307i	$0.683545\pi$
$788$	8.27487	+	4.77750i	0.294780	+	0.170191i
$789$		0			0
$790$	−0.436211	−	0.755540i	−0.0155197	−	0.0268809i
$791$			9.55551i			0.339755i
$792$		0			0
$793$	−7.04193	+	0.937084i	−0.250066	+	0.0332768i
$794$	11.4921	+	19.9049i	0.407840	+	0.706400i
$795$		0			0
$796$	5.65697	−	9.79816i	0.200506	−	0.347287i
$797$	−14.8513	+	25.7233i	−0.526061	+	0.911165i	0.473478	+	0.880806i	$0.342998\pi$
$797$	−14.8513	+	25.7233i	−0.526061	+	0.911165i	−0.999539	+	0.0303591i	$0.990335\pi$
$798$		0			0
$799$	13.1158	−	7.57240i	0.464003	−	0.267892i
$800$		−	13.9874i		−	0.494528i
$801$		0			0
$802$	−24.5268			−0.866071
$803$	−1.09635	−	1.89894i	−0.0386895	−	0.0670122i
$804$		0			0
$805$	8.26237	−	14.3108i	0.291210	−	0.504391i
$806$	−14.7648	+	35.7864i	−0.520067	+	1.26052i
$807$		0			0
$808$	29.7658	−	17.1853i	1.04716	−	0.604576i
$809$	−1.78891			−0.0628946			−0.0314473	−	0.999505i	$-0.510012\pi$
$809$	−1.78891			−0.0628946			−0.0314473	+	0.999505i	$0.510012\pi$
$810$		0			0
$811$			17.3429i			0.608991i	0.952514	+	0.304496i	$0.0984879\pi$
$811$			17.3429i			0.608991i	−0.952514	+	0.304496i	$0.901512\pi$
$812$	−3.61381	+	2.08643i	−0.126820	+	0.0732194i
$813$		0			0
$814$	−28.9671	−	16.7242i	−1.01530	−	0.586182i
$815$	−9.17689	+	15.8948i	−0.321452	+	0.556772i
$816$		0			0
$817$	−5.56650	+	3.21382i	−0.194747	+	0.112437i
$818$	0.778285			0.0272121
$819$		0			0
$820$	−4.01983			−0.140379
$821$	−30.1046	+	17.3809i	−1.05066	+	0.606598i	−0.922834	−	0.385198i	$-0.874133\pi$
$821$	−30.1046	+	17.3809i	−1.05066	+	0.606598i	−0.127825	+	0.991797i	$0.540800\pi$
$822$		0			0
$823$	10.0169	−	17.3498i	0.349167	−	0.604776i	−0.636934	−	0.770918i	$-0.719798\pi$
$823$	10.0169	−	17.3498i	0.349167	−	0.604776i	0.986102	+	0.166142i	$0.0531311\pi$
$824$	11.7144	+	6.76329i	0.408089	+	0.235610i
$825$		0			0
$826$	25.1347	−	14.5115i	0.874548	−	0.504920i
$827$		−	11.7034i		−	0.406966i	−0.979078	−	0.203483i	$-0.934774\pi$
$827$		−	11.7034i		−	0.406966i	0.979078	−	0.203483i	$-0.0652262\pi$
$828$		0			0
$829$	25.2016			0.875287			0.437644	−	0.899149i	$-0.355813\pi$
$829$	25.2016			0.875287			0.437644	+	0.899149i	$0.355813\pi$
$830$	24.1263	−	13.9293i	0.837435	−	0.483493i
$831$		0			0
$832$	−5.17361	+	12.5397i	−0.179363	+	0.434734i
$833$	−2.43158	+	4.21163i	−0.0842494	+	0.145924i
$834$		0			0
$835$	2.92714	+	5.06995i	0.101298	+	0.175453i
$836$	−4.30836			−0.149008
$837$		0			0
$838$		−	21.1394i		−	0.730248i
$839$	10.9918	−	6.34609i	0.379478	−	0.219091i	−0.298113	−	0.954530i	$-0.596357\pi$
$839$	10.9918	−	6.34609i	0.379478	−	0.219091i	0.677591	+	0.735439i	$0.263024\pi$
$840$		0			0
$841$	12.6603	−	21.9283i	0.436562	−	0.756148i
$842$	−25.8683	+	44.8052i	−0.891480	+	1.54409i
$843$		0			0
$844$	1.85772	+	3.21767i	0.0639454	+	0.110757i
$845$	−3.73072	−	13.7695i	−0.128341	−	0.473684i
$846$		0			0
$847$			25.3791i			0.872036i
$848$	−28.8235	−	49.9238i	−0.989803	−	1.71439i
$849$		0			0
$850$	7.92683	+	4.57656i	0.271888	+	0.156975i
$851$	47.2315	+	27.2691i	1.61908	+	0.934773i
$852$		0			0
$853$	−5.60579	+	3.23650i	−0.191939	+	0.110816i	−0.592890	−	0.805284i	$-0.702013\pi$
$853$	−5.60579	+	3.23650i	−0.191939	+	0.110816i	0.400951	+	0.916099i	$0.368680\pi$
$854$	−10.3478			−0.354093
$855$		0			0
$856$			23.0076i			0.786382i
$857$	13.2153	+	22.8895i	0.451425	+	0.781890i	0.998475	−	0.0552094i	$-0.0175826\pi$
$857$	13.2153	+	22.8895i	0.451425	+	0.781890i	−0.547050	+	0.837100i	$0.684249\pi$
$858$		0			0
$859$	1.49096	−	2.58242i	0.0508710	−	0.0881112i	−0.839469	−	0.543408i	$-0.817134\pi$
$859$	1.49096	−	2.58242i	0.0508710	−	0.0881112i	0.890340	+	0.455297i	$0.150467\pi$
$860$	1.14555	+	0.661381i	0.0390628	+	0.0225529i
$861$		0			0
$862$	−10.2733	−	17.7940i	−0.349911	−	0.606064i
$863$		−	3.40827i		−	0.116019i	−0.998316	−	0.0580095i	$-0.981525\pi$
$863$		−	3.40827i		−	0.116019i	0.998316	−	0.0580095i	$-0.0184754\pi$
$864$		0			0
$865$		−	13.5050i		−	0.459184i
$866$	−39.6476	+	22.8906i	−1.34728	+	0.777853i
$867$		0			0
$868$	−7.13684	+	12.3614i	−0.242240	+	0.419572i
$869$	0.739854	+	0.427155i	0.0250978	+	0.0144902i
$870$		0			0
$871$	23.6054	−	18.1655i	0.799839	−	0.615513i
$872$	34.6616			1.17379
$873$		0			0
$874$	27.7522			0.938732
$875$	−15.4890	−	26.8277i	−0.523623	−	0.906942i
$876$		0			0
$877$	13.8761	+	8.01136i	0.468562	+	0.270524i	0.715638	−	0.698472i	$-0.246136\pi$
$877$	13.8761	+	8.01136i	0.468562	+	0.270524i	−0.247076	+	0.968996i	$0.579470\pi$
$878$	16.3479	+	9.43847i	0.551715	+	0.318533i
$879$		0			0
$880$	−4.72415	−	8.18246i	−0.159251	−	0.275831i
$881$	26.8852			0.905787			0.452894	−	0.891565i	$-0.350392\pi$
$881$	26.8852			0.905787			0.452894	+	0.891565i	$0.350392\pi$
$882$		0			0
$883$	−16.3368			−0.549778			−0.274889	−	0.961476i	$-0.588641\pi$
$883$	−16.3368			−0.549778			−0.274889	+	0.961476i	$0.588641\pi$
$884$	2.19639	+	2.85414i	0.0738726	+	0.0959951i
$885$		0			0
$886$	37.2213	+	21.4897i	1.25047	+	0.721962i
$887$	12.4100	−	21.4947i	0.416686	−	0.721721i	−0.578918	−	0.815386i	$-0.696525\pi$
$887$	12.4100	−	21.4947i	0.416686	−	0.721721i	0.995604	+	0.0936651i	$0.0298583\pi$
$888$		0			0
$889$	17.0363	−	9.83594i	0.571381	−	0.329887i
$890$			24.1072i			0.808076i
$891$		0			0
$892$		−	6.21933i		−	0.208239i
$893$	−18.5740	−	32.1711i	−0.621555	−	1.07656i
$894$		0			0
$895$	17.9084	+	10.3394i	0.598612	+	0.345609i
$896$	−21.7061	+	37.5960i	−0.725149	+	1.25599i
$897$		0			0
$898$	24.5114	+	42.4549i	0.817955	+	1.41674i
$899$			12.5857i			0.419756i
$900$		0			0
$901$	17.3498			0.578006
$902$	13.4675	−	7.77546i	0.448419	−	0.258895i
$903$		0			0
$904$	−5.57878	−	3.22091i	−0.185547	−	0.107126i
$905$	10.3369	+	5.96800i	0.343610	+	0.198383i
$906$		0			0
$907$	14.4337	+	25.0000i	0.479265	+	0.830111i	0.999717	−	0.0237800i	$-0.00757011\pi$
$907$	14.4337	+	25.0000i	0.479265	+	0.830111i	−0.520453	+	0.853891i	$0.674237\pi$
$908$		−	2.33510i		−	0.0774930i
$909$		0			0
$910$	−2.74106	−	20.5983i	−0.0908651	−	0.682827i
$911$	6.64094	+	11.5024i	0.220024	+	0.381093i	0.954815	−	0.297201i	$-0.0960530\pi$
$911$	6.64094	+	11.5024i	0.220024	+	0.381093i	−0.734791	+	0.678294i	$0.762720\pi$
$912$		0			0
$913$	−13.6401	+	23.6254i	−0.451422	+	0.781886i
$914$	−9.37672	+	16.2410i	−0.310154	+	0.537203i
$915$		0			0
$916$	7.32708	−	4.23029i	0.242093	−	0.139773i
$917$		−	27.0400i		−	0.892940i
$918$		0			0
$919$	−3.98083			−0.131316			−0.0656578	−	0.997842i	$-0.520915\pi$
$919$	−3.98083			−0.131316			−0.0656578	+	0.997842i	$0.520915\pi$
$920$	5.57005	+	9.64761i	0.183639	+	0.318072i
$921$		0			0
$922$	23.3291	−	40.4072i	0.768303	−	1.33074i
$923$	−19.4935	−	8.04262i	−0.641636	−	0.264726i
$924$		0			0
$925$	38.2098	−	22.0605i	1.25633	−	0.725344i
$926$	−2.77516			−0.0911975
$927$		0			0
$928$		−	7.06846i		−	0.232033i
$929$	6.37258	−	3.67921i	0.209077	−	0.120711i	−0.391805	−	0.920048i	$-0.628149\pi$
$929$	6.37258	−	3.67921i	0.209077	−	0.120711i	0.600883	+	0.799337i	$0.294816\pi$
$930$		0			0
$931$	10.3305	+	5.96432i	0.338569	+	0.195473i
$932$	1.72448	−	2.98689i	0.0564873	−	0.0978389i
$933$		0			0
$934$	−20.0129	+	11.5545i	−0.654843	+	0.378074i
$935$	2.84362			0.0929964
$936$		0			0
$937$	8.02666			0.262220			0.131110	−	0.991368i	$-0.458146\pi$
$937$	8.02666			0.262220			0.131110	+	0.991368i	$0.458146\pi$
$938$	37.5738	−	21.6932i	1.22683	−	0.708309i
$939$		0			0
$940$	−3.82240	+	6.62058i	−0.124673	+	0.215940i
$941$	12.3516	+	7.13120i	0.402650	+	0.232470i	0.687627	−	0.726064i	$-0.258652\pi$
$941$	12.3516	+	7.13120i	0.402650	+	0.232470i	−0.284977	+	0.958534i	$0.591986\pi$
$942$		0			0
$943$	−21.9590	+	12.6781i	−0.715085	+	0.412854i
$944$			27.0575i			0.880648i
$945$		0			0
$946$	−5.11717			−0.166374
$947$	−7.11939	+	4.11038i	−0.231349	+	0.133569i	−0.611194	−	0.791481i	$-0.709311\pi$
$947$	−7.11939	+	4.11038i	−0.231349	+	0.133569i	0.379845	+	0.925050i	$0.375977\pi$
$948$		0			0
$949$	4.15606	+	1.71471i	0.134911	+	0.0556617i
$950$	11.2256	−	19.4434i	0.364208	−	0.630826i
$951$		0			0
$952$	−5.11621	−	8.86154i	−0.165817	−	0.287204i
$953$	34.3915			1.11405			0.557025	−	0.830496i	$-0.311943\pi$
$953$	34.3915			1.11405			0.557025	+	0.830496i	$0.311943\pi$
$954$		0			0
$955$			20.4080i			0.660388i
$956$	0.891104	−	0.514479i	0.0288204	−	0.0166394i
$957$		0			0
$958$	22.7162	−	39.3455i	0.733926	−	1.27120i
$959$	12.4267	−	21.5237i	0.401280	−	0.695037i
$960$		0			0
$961$	6.02525	+	10.4360i	0.194363	+	0.336647i
$962$	67.9826	−	9.04658i	2.19185	−	0.291673i
$963$		0			0
$964$		−	12.9486i		−	0.417045i
$965$	−7.10957	−	12.3141i	−0.228865	−	0.396406i
$966$		0			0
$967$	−43.1384	−	24.9059i	−1.38724	−	0.800921i	−0.394233	−	0.919010i	$-0.628990\pi$
$967$	−43.1384	−	24.9059i	−1.38724	−	0.800921i	−0.993003	+	0.118089i	$0.962323\pi$
$968$	−14.8170	−	8.55462i	−0.476238	−	0.274956i
$969$		0			0
$970$	9.26175	−	5.34727i	0.297377	−	0.171691i
$971$	−49.8192			−1.59878			−0.799388	−	0.600815i	$-0.794843\pi$
$971$	−49.8192			−1.59878			−0.799388	+	0.600815i	$0.794843\pi$
$972$		0			0
$973$			40.4253i			1.29597i
$974$	−22.5741	−	39.0995i	−0.723322	−	1.25283i
$975$		0			0
$976$	4.82349	−	8.35454i	0.154396	−	0.267422i
$977$	−37.7814	−	21.8131i	−1.20873	−	0.697863i	−0.246252	−	0.969206i	$-0.579199\pi$
$977$	−37.7814	−	21.8131i	−1.20873	−	0.697863i	−0.962483	+	0.271343i	$0.912532\pi$
$978$		0			0
$979$	−11.8034	−	20.4440i	−0.377237	−	0.653394i
$980$		−	2.45483i		−	0.0784167i
$981$		0			0
$982$		−	66.6618i		−	2.12726i
$983$	−49.7372	+	28.7158i	−1.58637	+	0.915891i	−0.592472	+	0.805591i	$0.701848\pi$
$983$	−49.7372	+	28.7158i	−1.58637	+	0.915891i	−0.993898	+	0.110300i	$0.964819\pi$
$984$		0			0
$985$	−7.73451	+	13.3966i	−0.246442	+	0.426850i
$986$	4.00579	+	2.31274i	0.127570	+	0.0736528i
$987$		0			0
$988$	7.00079	−	5.38743i	0.222725	−	0.171397i
$989$	8.34366			0.265313
$990$		0			0
$991$	7.92798			0.251841			0.125920	−	0.992040i	$-0.459812\pi$
$991$	7.92798			0.251841			0.125920	+	0.992040i	$0.459812\pi$
$992$	−12.0892	−	20.9391i	−0.383831	−	0.664816i
$993$		0			0
$994$	−26.6010	−	15.3581i	−0.843732	−	0.487129i
$995$	15.8627	+	9.15833i	0.502881	+	0.290339i
$996$		0			0
$997$	23.0997	+	40.0098i	0.731573	+	1.26712i	0.956210	+	0.292680i	$0.0945470\pi$
$997$	23.0997	+	40.0098i	0.731573	+	1.26712i	−0.224637	+	0.974443i	$0.572120\pi$
$998$	25.5644			0.809228
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.t.c.64.8		20
3.2	odd	2		117.2.t.c.103.3	yes	20
9.2	odd	6		117.2.t.c.25.8	yes	20
9.4	even	3		1053.2.b.i.649.8		10
9.5	odd	6		1053.2.b.j.649.3		10
9.7	even	3	inner	351.2.t.c.181.3		20
13.12	even	2	inner	351.2.t.c.64.3		20
39.38	odd	2		117.2.t.c.103.8	yes	20
117.25	even	6	inner	351.2.t.c.181.8		20
117.38	odd	6		117.2.t.c.25.3	✓	20
117.77	odd	6		1053.2.b.j.649.8		10
117.103	even	6		1053.2.b.i.649.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.3	✓	20	117.38	odd	6
117.2.t.c.25.8	yes	20	9.2	odd	6
117.2.t.c.103.3	yes	20	3.2	odd	2
117.2.t.c.103.8	yes	20	39.38	odd	2
351.2.t.c.64.3		20	13.12	even	2	inner
351.2.t.c.64.8		20	1.1	even	1	trivial
351.2.t.c.181.3		20	9.7	even	3	inner
351.2.t.c.181.8		20	117.25	even	6	inner
1053.2.b.i.649.3		10	117.103	even	6
1053.2.b.i.649.8		10	9.4	even	3
1053.2.b.j.649.3		10	9.5	odd	6
1053.2.b.j.649.8		10	117.77	odd	6

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41717 - 0.818205i) q^{2} +(0.338918 - 0.587023i) q^{4} +(0.950358 + 0.548689i) q^{5} +(2.77942 - 1.60470i) q^{7} +2.16360i q^{8} +1.79576 q^{10} +(-1.52289 + 0.879239i) q^{11} +(1.37514 - 3.33302i) q^{13} +(2.62594 - 4.54826i) q^{14} +(2.44810 + 4.24024i) q^{16} -1.47360 q^{17} +3.61452i q^{19} +(0.644186 - 0.371921i) q^{20} +(-1.43879 + 2.49207i) q^{22} +(2.34599 - 4.06337i) q^{23} +(-1.89788 - 3.28722i) q^{25} +(-0.778285 - 5.84860i) q^{26} -2.17544i q^{28} +(-0.959085 - 1.66118i) q^{29} +(-5.68224 - 3.28064i) q^{31} +(3.19130 + 1.84250i) q^{32} +(-2.08834 + 1.20570i) q^{34} +3.52192 q^{35} +11.6237i q^{37} +(2.95742 + 5.12239i) q^{38} +(-1.18715 + 2.05620i) q^{40} +(-4.68013 - 2.70208i) q^{41} +(0.889142 + 1.54004i) q^{43} +1.19196i q^{44} -7.67798i q^{46} +(-8.90053 + 5.13872i) q^{47} +(1.65010 - 2.85806i) q^{49} +(-5.37925 - 3.10571i) q^{50} +(-1.49050 - 1.93685i) q^{52} -11.7738 q^{53} -1.92972 q^{55} +(3.47193 + 6.01355i) q^{56} +(-2.71838 - 1.56946i) q^{58} +(4.78585 + 2.76311i) q^{59} +(-0.985148 - 1.70633i) q^{61} -10.7370 q^{62} -3.76225 q^{64} +(3.13566 - 2.41304i) q^{65} +(7.15434 + 4.13056i) q^{67} +(-0.499428 + 0.865034i) q^{68} +(4.99117 - 2.88165i) q^{70} -5.84860i q^{71} +1.24694i q^{73} +(9.51060 + 16.4728i) q^{74} +(2.12180 + 1.22502i) q^{76} +(-2.82182 + 4.88754i) q^{77} +(-0.242912 - 0.420735i) q^{79} +5.37300i q^{80} -8.84340 q^{82} +(13.4351 - 7.75677i) q^{83} +(-1.40044 - 0.808546i) q^{85} +(2.52014 + 1.45500i) q^{86} +(-1.90232 - 3.29492i) q^{88} +13.4245i q^{89} +(-1.52640 - 11.4705i) q^{91} +(-1.59019 - 2.75429i) q^{92} +(-8.40905 + 14.5649i) q^{94} +(-1.98325 + 3.43508i) q^{95} +(5.15756 - 2.97772i) q^{97} -5.40048i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

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