LMFDB - Embedded newform 804.2.s.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			161.1
Character	$\chi$	$=$	804.161
Dual form			804.2.s.b.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72660 + 0.137338i) q^{3} +(2.48625 + 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(2.96228 - 0.474256i) q^{9} +O(q^{10})$	\(q+(-1.72660 + 0.137338i) q^{3} +(2.48625 + 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(2.96228 - 0.474256i) q^{9} +(-6.01277 - 1.76551i) q^{11} +(2.22147 - 3.45668i) q^{13} +(-4.39301 - 0.919007i) q^{15} +(0.235591 - 0.0338728i) q^{17} +(-0.749547 + 0.865023i) q^{19} +(-5.86018 + 5.95441i) q^{21} +(1.84028 + 0.840429i) q^{23} +(1.44221 + 0.926855i) q^{25} +(-5.04952 + 1.22568i) q^{27} +0.303522i q^{29} +(-4.77999 - 7.43781i) q^{31} +(10.6241 + 2.22254i) q^{33} +(11.3691 - 5.19208i) q^{35} -2.20438 q^{37} +(-3.36086 + 6.27339i) q^{39} +(0.648759 + 4.51222i) q^{41} +(3.70767 - 0.533082i) q^{43} +(7.71117 + 0.983427i) q^{45} +(4.93924 + 2.25568i) q^{47} +(2.31483 - 16.1000i) q^{49} +(-0.402118 + 0.0908404i) q^{51} +(1.07232 - 7.45815i) q^{53} +(-13.6603 - 8.77897i) q^{55} +(1.17537 - 1.59649i) q^{57} +(-4.86335 - 7.56752i) q^{59} +(0.272313 + 0.927412i) q^{61} +(9.30040 - 11.0857i) q^{63} +(8.04661 - 6.97242i) q^{65} +(6.65218 + 4.76954i) q^{67} +(-3.29285 - 1.19834i) q^{69} +(16.0736 + 2.31103i) q^{71} +(13.2311 - 3.88499i) q^{73} +(-2.61742 - 1.40223i) q^{75} +(-27.4951 + 12.5566i) q^{77} +(-1.18099 + 1.83765i) q^{79} +(8.55016 - 2.80976i) q^{81} +(-1.09530 + 3.73026i) q^{83} +(0.610465 + 0.0877716i) q^{85} +(-0.0416852 - 0.524060i) q^{87} +(9.87966 - 4.51189i) q^{89} +(-2.82059 - 19.6176i) q^{91} +(9.27461 + 12.1856i) q^{93} +(-2.49505 + 1.60347i) q^{95} +2.79168i q^{97} +(-18.6488 - 2.37833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72660	+	0.137338i	−0.996851	+	0.0792923i
$3$	−1.72660	+	0.137338i	−0.996851	+	0.0792923i
$4$		0			0
$5$	2.48625	+	0.730028i	1.11188	+	0.326478i	0.785564	−	0.618781i	$-0.212373\pi$
$5$	2.48625	+	0.730028i	1.11188	+	0.326478i	0.326320	+	0.945259i	$0.394191\pi$
$6$		0			0
$7$	3.64531	−	3.15868i	1.37780	−	1.19387i	0.419620	−	0.907700i	$-0.362163\pi$
$7$	3.64531	−	3.15868i	1.37780	−	1.19387i	0.958179	−	0.286170i	$-0.0923821\pi$
$8$		0			0
$9$	2.96228	−	0.474256i	0.987425	−	0.158085i
$10$		0			0
$11$	−6.01277	−	1.76551i	−1.81292	−	0.532320i	−0.814090	−	0.580739i	$-0.802764\pi$
$11$	−6.01277	−	1.76551i	−1.81292	−	0.532320i	−0.998827	+	0.0484186i	$0.984582\pi$
$12$		0			0
$13$	2.22147	−	3.45668i	0.616126	−	0.958711i	−0.383259	−	0.923641i	$-0.625198\pi$
$13$	2.22147	−	3.45668i	0.616126	−	0.958711i	0.999385	−	0.0350697i	$-0.0111653\pi$
$14$		0			0
$15$	−4.39301	−	0.919007i	−1.13427	−	0.237287i
$16$		0			0
$17$	0.235591	−	0.0338728i	0.0571391	−	0.00821537i	−0.113686	−	0.993517i	$-0.536266\pi$
$17$	0.235591	−	0.0338728i	0.0571391	−	0.00821537i	0.170825	+	0.985301i	$0.445357\pi$
$18$		0			0
$19$	−0.749547	+	0.865023i	−0.171958	+	0.198450i	−0.835186	−	0.549967i	$-0.814640\pi$
$19$	−0.749547	+	0.865023i	−0.171958	+	0.198450i	0.663229	+	0.748417i	$0.269186\pi$
$20$		0			0
$21$	−5.86018	+	5.95441i	−1.27880	+	1.29936i
$22$		0			0
$23$	1.84028	+	0.840429i	0.383725	+	0.175242i	0.597932	−	0.801547i	$-0.295989\pi$
$23$	1.84028	+	0.840429i	0.383725	+	0.175242i	−0.214207	+	0.976788i	$0.568717\pi$
$24$		0			0
$25$	1.44221	+	0.926855i	0.288443	+	0.185371i
$26$		0			0
$27$	−5.04952	+	1.22568i	−0.971781	+	0.235883i
$28$		0			0
$29$			0.303522i			0.0563626i	0.999603	+	0.0281813i	$0.00897157\pi$
$29$			0.303522i			0.0563626i	−0.999603	+	0.0281813i	$0.991028\pi$
$30$		0			0
$31$	−4.77999	−	7.43781i	−0.858511	−	1.33587i	−0.940695	−	0.339253i	$-0.889826\pi$
$31$	−4.77999	−	7.43781i	−0.858511	−	1.33587i	0.0821840	−	0.996617i	$-0.473810\pi$
$32$		0			0
$33$	10.6241	+	2.22254i	1.84942	+	0.386894i
$34$		0			0
$35$	11.3691	−	5.19208i	1.92172	−	0.877622i
$36$		0			0
$37$	−2.20438			−0.362398			−0.181199	−	0.983446i	$-0.557998\pi$
$37$	−2.20438			−0.362398			−0.181199	+	0.983446i	$0.557998\pi$
$38$		0			0
$39$	−3.36086	+	6.27339i	−0.538168	+	1.00455i
$40$		0			0
$41$	0.648759	+	4.51222i	0.101319	+	0.704690i	0.975646	+	0.219352i	$0.0703944\pi$
$41$	0.648759	+	4.51222i	0.101319	+	0.704690i	−0.874327	+	0.485338i	$0.838697\pi$
$42$		0			0
$43$	3.70767	−	0.533082i	0.565414	−	0.0812942i	0.146320	−	0.989237i	$-0.453257\pi$
$43$	3.70767	−	0.533082i	0.565414	−	0.0812942i	0.419093	+	0.907943i	$0.362348\pi$
$44$		0			0
$45$	7.71117	+	0.983427i	1.14951	+	0.146601i
$46$		0			0
$47$	4.93924	+	2.25568i	0.720463	+	0.329024i	0.741683	−	0.670751i	$-0.234028\pi$
$47$	4.93924	+	2.25568i	0.720463	+	0.329024i	−0.0212204	+	0.999775i	$0.506755\pi$
$48$		0			0
$49$	2.31483	−	16.1000i	0.330691	−	2.30000i
$50$		0			0
$51$	−0.402118	+	0.0908404i	−0.0563078	+	0.0127202i
$52$		0			0
$53$	1.07232	−	7.45815i	0.147294	−	1.02446i	−0.773329	−	0.634004i	$-0.781410\pi$
$53$	1.07232	−	7.45815i	0.147294	−	1.02446i	0.920624	−	0.390451i	$-0.127681\pi$
$54$		0			0
$55$	−13.6603	−	8.77897i	−1.84196	−	1.18376i
$56$		0			0
$57$	1.17537	−	1.59649i	0.155681	−	0.211460i
$58$		0			0
$59$	−4.86335	−	7.56752i	−0.633155	−	0.985208i	−0.998522	−	0.0543445i	$-0.982693\pi$
$59$	−4.86335	−	7.56752i	−0.633155	−	0.985208i	0.365368	−	0.930863i	$-0.380943\pi$
$60$		0			0
$61$	0.272313	+	0.927412i	0.0348661	+	0.118743i	0.975087	−	0.221821i	$-0.0712001\pi$
$61$	0.272313	+	0.927412i	0.0348661	+	0.118743i	−0.940221	+	0.340564i	$0.889382\pi$
$62$		0			0
$63$	9.30040	−	11.0857i	1.17174	−	1.39667i
$64$		0			0
$65$	8.04661	−	6.97242i	0.998059	−	0.864823i
$66$		0			0
$67$	6.65218	+	4.76954i	0.812693	+	0.582692i
$67$	6.65218	+	4.76954i	0.812693	+	0.582692i
$68$		0			0
$69$	−3.29285	−	1.19834i	−0.396413	−	0.144263i
$70$		0			0
$71$	16.0736	+	2.31103i	1.90758	+	0.274269i	0.991839	−	0.127498i	$-0.0406947\pi$
$71$	16.0736	+	2.31103i	1.90758	+	0.274269i	0.915742	+	0.401767i	$0.131604\pi$
$72$		0			0
$73$	13.2311	−	3.88499i	1.54858	−	0.454704i	0.607903	−	0.794011i	$-0.292011\pi$
$73$	13.2311	−	3.88499i	1.54858	−	0.454704i	0.940676	+	0.339307i	$0.110193\pi$
$74$		0			0
$75$	−2.61742	−	1.40223i	−0.302233	−	0.161916i
$76$		0			0
$77$	−27.4951	+	12.5566i	−3.13336	+	1.43096i
$78$		0			0
$79$	−1.18099	+	1.83765i	−0.132871	+	0.206752i	−0.901313	−	0.433168i	$-0.857396\pi$
$79$	−1.18099	+	1.83765i	−0.132871	+	0.206752i	0.768442	+	0.639919i	$0.221032\pi$
$80$		0			0
$81$	8.55016	−	2.80976i	0.950018	−	0.312195i
$82$		0			0
$83$	−1.09530	+	3.73026i	−0.120225	+	0.409449i	−0.997510	−	0.0705203i	$-0.977534\pi$
$83$	−1.09530	+	3.73026i	−0.120225	+	0.409449i	0.877285	+	0.479969i	$0.159352\pi$
$84$		0			0
$85$	0.610465	+	0.0877716i	0.0662142	+	0.00952016i
$86$		0			0
$87$	−0.0416852	−	0.524060i	−0.00446912	−	0.0561851i
$88$		0			0
$89$	9.87966	−	4.51189i	1.04724	−	0.478259i	0.183935	−	0.982938i	$-0.441116\pi$
$89$	9.87966	−	4.51189i	1.04724	−	0.478259i	0.863307	+	0.504679i	$0.168389\pi$
$90$		0			0
$91$	−2.82059	−	19.6176i	−0.295678	−	2.05648i
$92$		0			0
$93$	9.27461	+	12.1856i	0.961732	+	1.26359i
$94$		0			0
$95$	−2.49505	+	1.60347i	−0.255987	+	0.164513i
$96$		0			0
$97$			2.79168i			0.283452i	0.989906	+	0.141726i	$0.0452652\pi$
$97$			2.79168i			0.283452i	−0.989906	+	0.141726i	$0.954735\pi$
$98$		0			0
$99$	−18.6488	−	2.37833i	−1.87427	−	0.239031i
$100$		0			0
$101$	−12.0577	+	13.9154i	−1.19979	+	1.38463i	−0.296818	+	0.954934i	$0.595926\pi$
$101$	−12.0577	+	13.9154i	−1.19979	+	1.38463i	−0.902973	+	0.429698i	$0.858620\pi$
$102$		0			0
$103$	−10.4201	+	6.69660i	−1.02672	+	0.659836i	−0.941669	−	0.336540i	$-0.890743\pi$
$103$	−10.4201	+	6.69660i	−1.02672	+	0.659836i	−0.0850555	+	0.996376i	$0.527107\pi$
$104$		0			0
$105$	−18.9167	+	10.5260i	−1.84608	+	1.02724i
$106$		0			0
$107$	0.143467	+	0.488605i	0.0138695	+	0.0472352i	0.966137	−	0.258030i	$-0.0830732\pi$
$107$	0.143467	+	0.488605i	0.0138695	+	0.0472352i	−0.952268	+	0.305265i	$0.901255\pi$
$108$		0			0
$109$	−8.72485	+	13.5761i	−0.835689	+	1.30036i	0.115986	+	0.993251i	$0.462997\pi$
$109$	−8.72485	+	13.5761i	−0.835689	+	1.30036i	−0.951675	+	0.307107i	$0.900639\pi$
$110$		0			0
$111$	3.80607	−	0.302746i	0.361257	−	0.0287354i
$112$		0			0
$113$	−6.52185	+	1.91499i	−0.613524	+	0.180147i	−0.573708	−	0.819060i	$-0.694495\pi$
$113$	−6.52185	+	1.91499i	−0.613524	+	0.180147i	−0.0398163	+	0.999207i	$0.512677\pi$
$114$		0			0
$115$	3.96186	+	3.43297i	0.369445	+	0.320126i
$116$		0			0
$117$	4.94127	−	11.2932i	0.456820	−	1.04406i
$118$		0			0
$119$	0.751808	−	0.867633i	0.0689182	−	0.0795358i
$120$		0			0
$121$	23.7825	+	15.2841i	2.16205	+	1.38946i
$122$		0			0
$123$	−1.73985	−	7.70169i	−0.156877	−	0.694438i
$124$		0			0
$125$	−5.57533	−	6.43428i	−0.498673	−	0.575499i
$126$		0			0
$127$	−4.09720	−	4.72842i	−0.363568	−	0.419580i	0.544264	−	0.838914i	$-0.316809\pi$
$127$	−4.09720	−	4.72842i	−0.363568	−	0.419580i	−0.907832	+	0.419334i	$0.862264\pi$
$128$		0			0
$129$	−6.32843	+	1.42962i	−0.557187	+	0.125871i
$130$		0			0
$131$	8.98874	+	4.10502i	0.785350	+	0.358657i	0.767389	−	0.641182i	$-0.221555\pi$
$131$	8.98874	+	4.10502i	0.785350	+	0.358657i	0.0179603	+	0.999839i	$0.494283\pi$
$132$		0			0
$133$			5.52086i			0.478720i
$134$		0			0
$135$	−13.4491	−	0.638942i	−1.15752	−	0.0549914i
$136$		0			0
$137$	−8.32825	+	18.2363i	−0.711530	+	1.55803i	0.113876	+	0.993495i	$0.463673\pi$
$137$	−8.32825	+	18.2363i	−0.711530	+	1.55803i	−0.825407	+	0.564539i	$0.809054\pi$
$138$		0			0
$139$	−1.43656	+	4.89247i	−0.121847	+	0.414974i	−0.997714	−	0.0675796i	$-0.978472\pi$
$139$	−1.43656	+	4.89247i	−0.121847	+	0.414974i	0.875867	+	0.482553i	$0.160291\pi$
$140$		0			0
$141$	−8.83787	−	3.21630i	−0.744283	−	0.270861i
$142$		0			0
$143$	−19.4600	+	16.8622i	−1.62733	+	1.41009i
$144$		0			0
$145$	−0.221579	+	0.754630i	−0.0184012	+	0.0626686i
$146$		0			0
$147$	−1.78563	+	28.1162i	−0.147277	+	2.31898i
$148$		0			0
$149$	11.0450	+	9.57056i	0.904843	+	0.784051i	0.976977	−	0.213344i	$-0.0684355\pi$
$149$	11.0450	+	9.57056i	0.904843	+	0.784051i	−0.0721340	+	0.997395i	$0.522981\pi$
$150$		0			0
$151$	−1.67622	−	11.6584i	−0.136409	−	0.948743i	−0.936949	−	0.349465i	$-0.886363\pi$
$151$	−1.67622	−	11.6584i	−0.136409	−	0.948743i	0.800541	−	0.599278i	$-0.204546\pi$
$152$		0			0
$153$	0.681820	−	0.212071i	0.0551219	−	0.0171449i
$154$		0			0
$155$	−6.45442	−	21.9818i	−0.518432	−	1.76562i
$156$		0			0
$157$	2.48920	−	5.45059i	0.198660	−	0.435005i	−0.783916	−	0.620867i	$-0.786781\pi$
$157$	2.48920	−	5.45059i	0.198660	−	0.435005i	0.982576	+	0.185863i	$0.0595079\pi$
$158$		0			0
$159$	−0.827174	+	13.0245i	−0.0655992	+	1.03291i
$160$		0			0
$161$	9.36305	−	2.74924i	0.737912	−	0.216671i
$162$		0			0
$163$	14.7249			1.15334			0.576672	−	0.816976i	$-0.304351\pi$
$163$	14.7249			1.15334			0.576672	+	0.816976i	$0.304351\pi$
$164$		0			0
$165$	24.7916	+	13.2817i	1.93002	+	1.03398i
$166$		0			0
$167$	−13.1615	−	11.4045i	−1.01847	−	0.882507i	−0.0253561	−	0.999678i	$-0.508072\pi$
$167$	−13.1615	−	11.4045i	−1.01847	−	0.882507i	−0.993112	+	0.117171i	$0.962617\pi$
$168$		0			0
$169$	−1.61330	−	3.53263i	−0.124100	−	0.271741i
$170$		0			0
$171$	−1.81012	+	2.91792i	−0.138424	+	0.223139i
$172$		0			0
$173$	4.64811	+	7.23260i	0.353389	+	0.549885i	0.971751	−	0.236009i	$-0.0758396\pi$
$173$	4.64811	+	7.23260i	0.353389	+	0.549885i	−0.618361	+	0.785894i	$0.712203\pi$
$174$		0			0
$175$	8.18497	−	1.17682i	0.618725	−	0.0889593i
$176$		0			0
$177$	9.43636	+	12.3981i	0.709281	+	0.931901i
$178$		0			0
$179$	−5.22231	−	11.4353i	−0.390334	−	0.854712i	−0.998160	−	0.0606413i	$-0.980685\pi$
$179$	−5.22231	−	11.4353i	−0.390334	−	0.854712i	0.607826	−	0.794070i	$-0.292042\pi$
$180$		0			0
$181$	7.27604	−	15.9323i	0.540824	−	1.18424i	−0.420113	−	0.907472i	$-0.638010\pi$
$181$	7.27604	−	15.9323i	0.540824	−	1.18424i	0.960937	−	0.276767i	$-0.0892631\pi$
$182$		0			0
$183$	−0.597544	−	1.56387i	−0.0441717	−	0.115604i
$184$		0			0
$185$	−5.48063	−	1.60926i	−0.402944	−	0.118315i
$186$		0			0
$187$	−1.47635	−	0.212268i	−0.107962	−	0.0155226i
$188$		0			0
$189$	−14.5356	+	20.4178i	−1.05731	+	1.48518i
$190$		0			0
$191$	3.15748	+	6.91391i	0.228467	+	0.500273i	0.988797	−	0.149264i	$-0.0476903\pi$
$191$	3.15748	+	6.91391i	0.228467	+	0.500273i	−0.760331	+	0.649536i	$0.774963\pi$
$192$		0			0
$193$	−1.55588	+	0.999901i	−0.111994	+	0.0719744i	−0.595439	−	0.803401i	$-0.703022\pi$
$193$	−1.55588	+	0.999901i	−0.111994	+	0.0719744i	0.483445	+	0.875375i	$0.339385\pi$
$194$		0			0
$195$	−12.9357	+	13.1437i	−0.926342	+	0.941238i
$196$		0			0
$197$	1.04976	−	7.30122i	0.0747921	−	0.520190i	−0.917642	−	0.397409i	$-0.869909\pi$
$197$	1.04976	−	7.30122i	0.0747921	−	0.520190i	0.992434	−	0.122781i	$-0.0391814\pi$
$198$		0			0
$199$	11.1805	+	12.9029i	0.792562	+	0.914665i	0.997949	−	0.0640159i	$-0.0203909\pi$
$199$	11.1805	+	12.9029i	0.792562	+	0.914665i	−0.205387	+	0.978681i	$0.565845\pi$
$200$		0			0
$201$	−12.1407	−	7.32147i	−0.856337	−	0.516417i
$202$		0			0
$203$	0.958729	+	1.10643i	0.0672896	+	0.0776563i
$204$		0			0
$205$	−1.68107	+	11.6921i	−0.117411	+	0.816612i
$206$		0			0
$207$	5.85000	+	1.61682i	0.406603	+	0.112377i
$208$		0			0
$209$	6.03406	−	3.87785i	0.417384	−	0.268237i
$210$		0			0
$211$	5.83106	+	12.7682i	0.401427	+	0.879002i	0.997124	+	0.0757924i	$0.0241486\pi$
$211$	5.83106	+	12.7682i	0.401427	+	0.879002i	−0.595697	+	0.803209i	$0.703124\pi$
$212$		0			0
$213$	−28.0700	−	1.78270i	−1.92332	−	0.122149i
$214$		0			0
$215$	9.60734	+	1.38133i	0.655215	+	0.0942057i
$216$		0			0
$217$	−40.9182	−	12.0147i	−2.77771	−	0.815609i
$218$		0			0
$219$	−22.3112	+	8.52495i	−1.50765	+	0.576063i
$220$		0			0
$221$	0.406271	−	0.889609i	0.0273287	−	0.0598416i
$222$		0			0
$223$	9.47470	+	20.7467i	0.634473	+	1.38930i	0.904510	+	0.426452i	$0.140237\pi$
$223$	9.47470	+	20.7467i	0.634473	+	1.38930i	−0.270037	+	0.962850i	$0.587036\pi$
$224$		0			0
$225$	4.71181	+	2.06162i	0.314120	+	0.137441i
$226$		0			0
$227$	8.02748	−	1.15418i	0.532802	−	0.0766054i	0.129338	−	0.991601i	$-0.458715\pi$
$227$	8.02748	−	1.15418i	0.532802	−	0.0766054i	0.403465	+	0.914995i	$0.367806\pi$
$228$		0			0
$229$	−5.96495	−	9.28164i	−0.394175	−	0.613348i	0.586276	−	0.810111i	$-0.300593\pi$
$229$	−5.96495	−	9.28164i	−0.394175	−	0.613348i	−0.980451	+	0.196763i	$0.936957\pi$
$230$		0			0
$231$	45.7484	−	25.4563i	3.01003	−	1.67490i
$232$		0			0
$233$	−6.11597	−	13.3921i	−0.400671	−	0.877346i	−0.997202	−	0.0747565i	$-0.976182\pi$
$233$	−6.11597	−	13.3921i	−0.400671	−	0.877346i	0.596531	−	0.802590i	$-0.296545\pi$
$234$		0			0
$235$	10.6335	+	9.21395i	0.693651	+	0.601052i
$236$		0			0
$237$	1.78671	−	3.33507i	0.116059	−	0.216636i
$238$		0			0
$239$	−22.8427			−1.47757			−0.738784	−	0.673942i	$-0.764600\pi$
$239$	−22.8427			−1.47757			−0.738784	+	0.673942i	$0.764600\pi$
$240$		0			0
$241$	11.3059	−	3.31970i	0.728275	−	0.213841i	0.103482	−	0.994631i	$-0.467002\pi$
$241$	11.3059	−	3.31970i	0.728275	−	0.213841i	0.624793	+	0.780791i	$0.285183\pi$
$242$		0			0
$243$	−14.3768	+	6.02558i	−0.922272	+	0.386541i
$244$		0			0
$245$	17.5087	−	38.3387i	1.11859	−	2.44937i
$246$		0			0
$247$	1.32501	+	4.51257i	0.0843084	+	0.287128i
$248$		0			0
$249$	1.37884	−	6.59108i	0.0873804	−	0.417693i
$250$		0			0
$251$	0.266123	+	1.85092i	0.0167975	+	0.116829i	0.996495	−	0.0836521i	$-0.0266585\pi$
$251$	0.266123	+	1.85092i	0.0167975	+	0.116829i	−0.979698	+	0.200481i	$0.935749\pi$
$252$		0			0
$253$	−9.58140	−	8.30233i	−0.602378	−	0.521963i
$254$		0			0
$255$	−1.06608	−	0.0677059i	−0.0667606	−	0.00423991i
$256$		0			0
$257$	4.67380	−	15.9175i	0.291544	−	0.992907i	−0.675301	−	0.737542i	$-0.735986\pi$
$257$	4.67380	−	15.9175i	0.291544	−	0.992907i	0.966845	−	0.255365i	$-0.0821955\pi$
$258$		0			0
$259$	−8.03565	+	6.96293i	−0.499311	+	0.432655i
$260$		0			0
$261$	0.143947	+	0.899115i	0.00891010	+	0.0556538i
$262$		0			0
$263$	3.07107	−	10.4591i	0.189370	−	0.644935i	−0.808997	−	0.587813i	$-0.799989\pi$
$263$	3.07107	−	10.4591i	0.189370	−	0.644935i	0.998367	−	0.0571226i	$-0.0181926\pi$
$264$		0			0
$265$	8.11071	−	17.7600i	0.498237	−	1.09099i
$266$		0			0
$267$	−16.4385	+	9.14707i	−1.00602	+	0.559792i
$268$		0			0
$269$		−	12.6511i		−	0.771353i	−0.922634	−	0.385676i	$-0.873968\pi$
$269$		−	12.6511i		−	0.771353i	0.922634	−	0.385676i	$-0.126032\pi$
$270$		0			0
$271$	16.8404	+	7.69077i	1.02298	+	0.467181i	0.855011	−	0.518610i	$-0.173550\pi$
$271$	16.8404	+	7.69077i	1.02298	+	0.467181i	0.167973	+	0.985792i	$0.446278\pi$
$272$		0			0
$273$	7.56427	+	33.4843i	0.457810	+	2.02656i
$274$		0			0
$275$	−7.03533	−	8.11920i	−0.424246	−	0.489606i
$276$		0			0
$277$	−2.76721	−	3.19353i	−0.166265	−	0.191880i	0.666503	−	0.745503i	$-0.267791\pi$
$277$	−2.76721	−	3.19353i	−0.166265	−	0.191880i	−0.832768	+	0.553622i	$0.813245\pi$
$278$		0			0
$279$	−17.6871	−	19.7659i	−1.05890	−	1.18335i
$280$		0			0
$281$	1.13085	+	0.726751i	0.0674606	+	0.0433543i	0.573936	−	0.818900i	$-0.305416\pi$
$281$	1.13085	+	0.726751i	0.0674606	+	0.0433543i	−0.506476	+	0.862254i	$0.669052\pi$
$282$		0			0
$283$	−11.0999	+	12.8100i	−0.659821	+	0.761474i	−0.982748	−	0.184950i	$-0.940788\pi$
$283$	−11.0999	+	12.8100i	−0.659821	+	0.761474i	0.322927	+	0.946424i	$0.395333\pi$
$284$		0			0
$285$	4.08773	−	3.11122i	0.242136	−	0.184293i
$286$		0			0
$287$	16.6176	+	14.3992i	0.980906	+	0.849960i
$288$		0			0
$289$	−16.2570	+	4.77349i	−0.956296	+	0.280794i
$290$		0			0
$291$	−0.383405	−	4.82010i	−0.0224756	−	0.282559i
$292$		0			0
$293$	−12.9485	+	20.1483i	−0.756460	+	1.17708i	0.222878	+	0.974846i	$0.428455\pi$
$293$	−12.9485	+	20.1483i	−0.756460	+	1.17708i	−0.979338	+	0.202229i	$0.935182\pi$
$294$		0			0
$295$	−6.56699	−	22.3651i	−0.382345	−	1.30215i
$296$		0			0
$297$	32.5256	+	1.54522i	1.88732	+	0.0896630i
$298$		0			0
$299$	6.99323	−	4.49428i	0.404429	−	0.259911i
$300$		0			0
$301$	11.8318	−	13.6546i	0.681972	−	0.787037i
$302$		0			0
$303$	18.9078	−	25.6823i	1.08622	−	1.47541i
$304$		0			0
$305$			2.50457i			0.143411i
$306$		0			0
$307$	−17.6161	+	11.3212i	−1.00541	+	0.646135i	−0.936200	−	0.351467i	$-0.885683\pi$
$307$	−17.6161	+	11.3212i	−1.00541	+	0.646135i	−0.0692060	+	0.997602i	$0.522047\pi$
$308$		0			0
$309$	17.0716	−	12.9934i	0.971172	−	0.739170i
$310$		0			0
$311$	3.81967	+	26.5664i	0.216593	+	1.50644i	0.750485	+	0.660887i	$0.229820\pi$
$311$	3.81967	+	26.5664i	0.216593	+	1.50644i	−0.533892	+	0.845553i	$0.679271\pi$
$312$		0			0
$313$	−7.13321	+	3.25763i	−0.403193	+	0.184132i	−0.606681	−	0.794945i	$-0.707499\pi$
$313$	−7.13321	+	3.25763i	−0.403193	+	0.184132i	0.203488	+	0.979077i	$0.434772\pi$
$314$		0			0
$315$	31.2160	−	20.7722i	1.75882	−	1.17038i
$316$		0			0
$317$	−27.3537	−	3.93286i	−1.53633	−	0.220892i	−0.678416	−	0.734678i	$-0.737333\pi$
$317$	−27.3537	−	3.93286i	−1.53633	−	0.220892i	−0.857918	+	0.513786i	$0.828243\pi$
$318$		0			0
$319$	0.535870	−	1.82501i	0.0300030	−	0.102181i
$320$		0			0
$321$	−0.314815	−	0.823920i	−0.0175712	−	0.0459868i
$322$		0			0
$323$	−0.147286	+	0.229181i	−0.00819519	+	0.0127520i
$324$		0			0
$325$	6.40768	−	2.92629i	0.355434	−	0.162321i
$326$		0			0
$327$	13.1998	−	24.6388i	0.729949	−	1.36253i
$328$		0			0
$329$	25.1301	−	7.37885i	1.38546	−	0.406809i
$330$		0			0
$331$	−5.45068	−	0.783689i	−0.299596	−	0.0430755i	−0.00912255	−	0.999958i	$-0.502904\pi$
$331$	−5.45068	−	0.783689i	−0.299596	−	0.0430755i	−0.290474	+	0.956883i	$0.593813\pi$
$332$		0			0
$333$	−6.52998	+	1.04544i	−0.357841	+	0.0572898i
$334$		0			0
$335$	13.0571	+	16.7145i	0.713384	+	0.913212i
$336$		0			0
$337$	9.65316	−	8.36451i	0.525841	−	0.455644i	−0.351033	−	0.936363i	$-0.614170\pi$
$337$	9.65316	−	8.36451i	0.525841	−	0.455644i	0.876875	+	0.480719i	$0.159624\pi$
$338$		0			0
$339$	10.9976	−	4.20211i	0.597308	−	0.228227i
$340$		0			0
$341$	15.6094	+	53.1609i	0.845299	+	2.87882i
$342$		0			0
$343$	−24.1623	−	37.5973i	−1.30464	−	2.03006i
$344$		0			0
$345$	−7.31202	−	5.38324i	−0.393666	−	0.289824i
$346$		0			0
$347$	1.27673	+	0.820506i	0.0685386	+	0.0440471i	0.574461	−	0.818532i	$-0.305212\pi$
$347$	1.27673	+	0.820506i	0.0685386	+	0.0440471i	−0.505923	+	0.862579i	$0.668848\pi$
$348$		0			0
$349$	−1.05529	+	7.33972i	−0.0564885	+	0.392886i	0.941888	+	0.335927i	$0.109050\pi$
$349$	−1.05529	+	7.33972i	−0.0564885	+	0.392886i	−0.998377	+	0.0569591i	$0.981860\pi$
$350$		0			0
$351$	−6.98059	+	20.1774i	−0.372596	+	1.07699i
$352$		0			0
$353$	−3.05627	+	21.2568i	−0.162669	+	1.13139i	0.730908	+	0.682476i	$0.239097\pi$
$353$	−3.05627	+	21.2568i	−0.162669	+	1.13139i	−0.893577	+	0.448910i	$0.851812\pi$
$354$		0			0
$355$	38.2757	+	17.4799i	2.03146	+	0.927739i
$356$		0			0
$357$	−1.17891	+	1.60131i	−0.0623946	+	0.0847501i
$358$		0			0
$359$	−11.3677	+	1.63442i	−0.599962	+	0.0862615i	−0.435603	−	0.900139i	$-0.643465\pi$
$359$	−11.3677	+	1.63442i	−0.599962	+	0.0862615i	−0.164359	+	0.986401i	$0.552556\pi$
$360$		0			0
$361$	2.51754	+	17.5099i	0.132502	+	0.921571i
$362$		0			0
$363$	−43.1620	−	23.1232i	−2.26542	−	1.21366i
$364$		0			0
$365$	35.7318			1.87029
$366$		0			0
$367$	−17.9406	+	8.19319i	−0.936491	+	0.427681i	−0.824394	−	0.566016i	$-0.808484\pi$
$367$	−17.9406	+	8.19319i	−0.936491	+	0.427681i	−0.112097	+	0.993697i	$0.535757\pi$
$368$		0			0
$369$	4.06175	+	13.0588i	0.211446	+	0.679812i
$370$		0			0
$371$	−19.6490	−	30.5744i	−1.02012	−	1.58734i
$372$		0			0
$373$		−	4.59919i		−	0.238137i	−0.992886	−	0.119069i	$-0.962009\pi$
$373$		−	4.59919i		−	0.238137i	0.992886	−	0.119069i	$-0.0379908\pi$
$374$		0			0
$375$	10.5100	+	10.3437i	0.542736	+	0.534146i
$376$		0			0
$377$	1.04918	+	0.674266i	0.0540354	+	0.0347264i
$378$		0			0
$379$	21.4242	+	9.78412i	1.10049	+	0.502576i	0.881037	−	0.473047i	$-0.156846\pi$
$379$	21.4242	+	9.78412i	1.10049	+	0.502576i	0.219452	+	0.975623i	$0.429573\pi$
$380$		0			0
$381$	7.72361	+	7.60138i	0.395693	+	0.389430i
$382$		0			0
$383$	−21.9247	+	25.3025i	−1.12030	+	1.29290i	−0.168663	+	0.985674i	$0.553945\pi$
$383$	−21.9247	+	25.3025i	−1.12030	+	1.29290i	−0.951638	+	0.307223i	$0.900600\pi$
$384$		0			0
$385$	−77.5262	+	11.1466i	−3.95110	+	0.568083i
$386$		0			0
$387$	10.7303	−	3.33752i	0.545452	−	0.169656i
$388$		0			0
$389$	−7.57002	+	11.7792i	−0.383815	+	0.597228i	−0.978379	−	0.206820i	$-0.933688\pi$
$389$	−7.57002	+	11.7792i	−0.383815	+	0.597228i	0.594564	+	0.804049i	$0.297325\pi$
$390$		0			0
$391$	0.462021	+	0.135662i	0.0233654	+	0.00686071i
$392$		0			0
$393$	−16.0837	−	5.85321i	−0.811316	−	0.295256i
$394$		0			0
$395$	−4.27776	+	3.70670i	−0.215237	+	0.186504i
$396$		0			0
$397$	15.7692	+	4.63025i	0.791433	+	0.232386i	0.652373	−	0.757898i	$-0.273774\pi$
$397$	15.7692	+	4.63025i	0.791433	+	0.232386i	0.139060	+	0.990284i	$0.455592\pi$
$398$		0			0
$399$	−0.758226	−	9.53231i	−0.0379588	−	0.477212i
$400$		0			0
$401$	23.8879			1.19290			0.596452	−	0.802648i	$-0.296576\pi$
$401$	23.8879			1.19290			0.596452	+	0.802648i	$0.296576\pi$
$402$		0			0
$403$	−36.3287			−1.80966
$404$		0			0
$405$	23.3090	−	0.743888i	1.15823	−	0.0369641i
$406$		0			0
$407$	13.2544	+	3.89185i	0.656997	+	0.192912i
$408$		0			0
$409$	3.01750	−	2.61468i	0.149206	−	0.129288i	−0.577059	−	0.816702i	$-0.695800\pi$
$409$	3.01750	−	2.61468i	0.149206	−	0.129288i	0.726265	+	0.687415i	$0.241254\pi$
$410$		0			0
$411$	11.8750	−	32.6306i	0.585750	−	1.60955i
$412$		0			0
$413$	−41.6318	−	12.2242i	−2.04857	−	0.601514i
$414$		0			0
$415$	−5.44639	+	8.47474i	−0.267353	+	0.416009i
$416$		0			0
$417$	1.80843	−	8.64462i	0.0885594	−	0.423329i
$418$		0			0
$419$	−4.20561	+	0.604675i	−0.205457	+	0.0295403i	−0.244275	−	0.969706i	$-0.578550\pi$
$419$	−4.20561	+	0.604675i	−0.205457	+	0.0295403i	0.0388176	+	0.999246i	$0.487641\pi$
$420$		0			0
$421$	−3.22520	+	3.72208i	−0.157187	+	0.181403i	−0.828880	−	0.559426i	$-0.811022\pi$
$421$	−3.22520	+	3.72208i	−0.157187	+	0.181403i	0.671694	+	0.740829i	$0.265567\pi$
$422$		0			0
$423$	15.7012	+	4.33947i	0.763417	+	0.210992i
$424$		0			0
$425$	0.371168	+	0.169507i	0.0180043	+	0.00822228i
$426$		0			0
$427$	3.92206	+	2.52056i	0.189802	+	0.121978i
$428$		0			0
$429$	31.2837	−	31.7868i	1.51039	−	1.53468i
$430$		0			0
$431$		−	36.6610i		−	1.76590i	−0.469468	−	0.882949i	$-0.655554\pi$
$431$		−	36.6610i		−	1.76590i	0.469468	−	0.882949i	$-0.344446\pi$
$432$		0			0
$433$	−3.85517	−	5.99876i	−0.185268	−	0.288282i	0.736179	−	0.676787i	$-0.236628\pi$
$433$	−3.85517	−	5.99876i	−0.185268	−	0.288282i	−0.921447	+	0.388505i	$0.872992\pi$
$434$		0			0
$435$	0.278939	−	1.33337i	0.0133741	−	0.0639304i
$436$		0			0
$437$	−2.10637	+	0.961947i	−0.100761	+	0.0460161i
$438$		0			0
$439$	16.9963			0.811187			0.405593	−	0.914054i	$-0.367065\pi$
$439$	16.9963			0.811187			0.405593	+	0.914054i	$0.367065\pi$
$440$		0			0
$441$	−0.778357	−	48.7905i	−0.0370646	−	2.32336i
$442$		0			0
$443$	5.83435	+	40.5788i	0.277198	+	1.92796i	0.363304	+	0.931671i	$0.381649\pi$
$443$	5.83435	+	40.5788i	0.277198	+	1.92796i	−0.0861059	+	0.996286i	$0.527442\pi$
$444$		0			0
$445$	27.8571	−	4.00524i	1.32055	−	0.189867i
$446$		0			0
$447$	−20.3847	−	15.0076i	−0.964163	−	0.709835i
$448$		0			0
$449$	−14.1335	−	6.45457i	−0.667003	−	0.304610i	0.0529862	−	0.998595i	$-0.483126\pi$
$449$	−14.1335	−	6.45457i	−0.667003	−	0.304610i	−0.719989	+	0.693985i	$0.755853\pi$
$450$		0			0
$451$	4.06552	−	28.2763i	0.191438	−	1.33148i
$452$		0			0
$453$	4.49529	+	19.8991i	0.211207	+	0.934940i
$454$		0			0
$455$	7.30873	−	50.8333i	0.342639	−	2.38310i
$456$		0			0
$457$	−14.0626	−	9.03746i	−0.657819	−	0.422755i	0.168697	−	0.985668i	$-0.446044\pi$
$457$	−14.0626	−	9.03746i	−0.657819	−	0.422755i	−0.826516	+	0.562913i	$0.809680\pi$
$458$		0			0
$459$	−1.14810	+	0.459801i	−0.0535889	+	0.0214617i
$460$		0			0
$461$	−6.54290	−	10.1810i	−0.304733	−	0.474175i	0.654787	−	0.755813i	$-0.272758\pi$
$461$	−6.54290	−	10.1810i	−0.304733	−	0.474175i	−0.959520	+	0.281639i	$0.909122\pi$
$462$		0			0
$463$	2.13123	+	7.25830i	0.0990466	+	0.337322i	0.994076	−	0.108685i	$-0.0346639\pi$
$463$	2.13123	+	7.25830i	0.0990466	+	0.337322i	−0.895030	+	0.446007i	$0.852846\pi$
$464$		0			0
$465$	14.1631	+	37.0672i	0.656799	+	1.71895i
$466$		0			0
$467$	−7.55982	+	6.55062i	−0.349827	+	0.303127i	−0.811994	−	0.583666i	$-0.801618\pi$
$467$	−7.55982	+	6.55062i	−0.349827	+	0.303127i	0.462167	+	0.886793i	$0.347072\pi$
$468$		0			0
$469$	39.3147	−	3.62566i	1.81539	−	0.167417i
$470$		0			0
$471$	−3.54927	+	9.75284i	−0.163542	+	0.449387i
$472$		0			0
$473$	−23.2345	−	3.34061i	−1.06832	−	0.153602i
$474$		0			0
$475$	−1.88276	+	0.552828i	−0.0863869	+	0.0253655i
$476$		0			0
$477$	−0.360565	−	22.6016i	−0.0165091	−	1.03486i
$478$		0			0
$479$	20.9351	−	9.56076i	0.956551	−	0.436842i	0.124917	−	0.992167i	$-0.460133\pi$
$479$	20.9351	−	9.56076i	0.956551	−	0.436842i	0.831633	+	0.555325i	$0.187406\pi$
$480$		0			0
$481$	−4.89697	+	7.61983i	−0.223283	+	0.347434i
$482$		0			0
$483$	−15.7886	+	6.03274i	−0.718408	+	0.274499i
$484$		0			0
$485$	−2.03800	+	6.94080i	−0.0925409	+	0.315166i
$486$		0			0
$487$	25.6875	+	3.69331i	1.16401	+	0.167360i	0.697120	−	0.716955i	$-0.254465\pi$
$487$	25.6875	+	3.69331i	1.16401	+	0.167360i	0.466892	+	0.884314i	$0.345374\pi$
$488$		0			0
$489$	−25.4240	+	2.02230i	−1.14971	+	0.0914514i
$490$		0			0
$491$	27.6162	−	12.6119i	1.24630	−	0.569166i	0.320525	−	0.947240i	$-0.396141\pi$
$491$	27.6162	−	12.6119i	1.24630	−	0.569166i	0.925775	+	0.378074i	$0.123414\pi$
$492$		0			0
$493$	0.0102811	+	0.0715069i	0.000463039	+	0.00322051i
$494$		0			0
$495$	−44.6292	−	19.5272i	−2.00593	−	0.877684i
$496$		0			0
$497$	65.8930	−	42.3468i	2.95570	−	1.89952i
$498$		0			0
$499$			19.1108i			0.855517i	0.903893	+	0.427758i	$0.140697\pi$
$499$			19.1108i			0.855517i	−0.903893	+	0.427758i	$0.859303\pi$
$500$		0			0
$501$	24.2909	+	17.8834i	1.08524	+	0.798972i
$502$		0			0
$503$	24.0623	−	27.7693i	1.07288	−	1.23817i	0.102981	−	0.994683i	$-0.467162\pi$
$503$	24.0623	−	27.7693i	1.07288	−	1.23817i	0.969903	−	0.243491i	$-0.0782925\pi$
$504$		0			0
$505$	−40.1372	+	25.7946i	−1.78608	+	1.14784i
$506$		0			0
$507$	3.27068	+	5.87787i	0.145256	+	0.261045i
$508$		0			0
$509$	0.587268	+	2.00005i	0.0260302	+	0.0886507i	0.971484	−	0.237106i	$-0.0761990\pi$
$509$	0.587268	+	2.00005i	0.0260302	+	0.0886507i	−0.945453	+	0.325757i	$0.894381\pi$
$510$		0			0
$511$	35.9599	−	55.9547i	1.59077	−	2.47529i
$512$		0			0
$513$	2.72461	−	5.28667i	0.120295	−	0.233412i
$514$		0			0
$515$	−30.7957	+	9.04243i	−1.35702	+	0.398457i
$516$		0			0
$517$	−25.7161	−	22.2831i	−1.13099	−	0.980011i
$518$		0			0
$519$	−9.01873	−	11.8494i	−0.395878	−	0.520132i
$520$		0			0
$521$	4.40009	−	5.07797i	0.192771	−	0.222470i	−0.651133	−	0.758964i	$-0.725706\pi$
$521$	4.40009	−	5.07797i	0.192771	−	0.222470i	0.843904	+	0.536494i	$0.180251\pi$
$522$		0			0
$523$	34.4842	+	22.1616i	1.50789	+	0.969061i	0.993783	+	0.111333i	$0.0355121\pi$
$523$	34.4842	+	22.1616i	1.50789	+	0.969061i	0.514105	+	0.857727i	$0.328124\pi$
$524$		0			0
$525$	−13.9705	+	3.15600i	−0.609723	+	0.137739i
$526$		0			0
$527$	−1.37806	−	1.59037i	−0.0600293	−	0.0692775i
$528$		0			0
$529$	−12.3815	−	14.2890i	−0.538325	−	0.621260i
$530$		0			0
$531$	−17.9955	−	20.1106i	−0.780940	−	0.872727i
$532$		0			0
$533$	17.0385	+	7.78122i	0.738019	+	0.337042i
$534$		0			0
$535$			1.31953i			0.0570482i
$536$		0			0
$537$	10.5873	+	19.0269i	0.456877	+	0.821070i
$538$		0			0
$539$	−42.3433	+	92.7188i	−1.82385	+	3.99368i
$540$		0			0
$541$	6.48103	−	22.0724i	0.278641	−	0.948965i	−0.694642	−	0.719356i	$-0.744437\pi$
$541$	6.48103	−	22.0724i	0.278641	−	0.948965i	0.973283	−	0.229609i	$-0.0737447\pi$
$542$		0			0
$543$	−10.3747	+	28.5080i	−0.445220	+	1.22339i
$544$		0			0
$545$	−31.6031	+	27.3842i	−1.35373	+	1.17301i
$546$		0			0
$547$	−11.8312	+	40.2932i	−0.505864	+	1.72281i	0.169684	+	0.985499i	$0.445725\pi$
$547$	−11.8312	+	40.2932i	−0.505864	+	1.72281i	−0.675548	+	0.737316i	$0.736093\pi$
$548$		0			0
$549$	1.24650	+	2.61810i	0.0531992	+	0.111738i
$550$		0			0
$551$	−0.262553	−	0.227504i	−0.0111852	−	0.00969199i
$552$		0			0
$553$	1.49949	+	10.4292i	0.0637647	+	0.443493i
$554$		0			0
$555$	9.68385	+	2.02584i	0.411057	+	0.0859921i
$556$		0			0
$557$	−1.65371	−	5.63203i	−0.0700701	−	0.238637i	0.917010	−	0.398864i	$-0.130595\pi$
$557$	−1.65371	−	5.63203i	−0.0700701	−	0.238637i	−0.987080	+	0.160227i	$0.948777\pi$
$558$		0			0
$559$	6.39379	−	14.0004i	0.270428	−	0.592156i
$560$		0			0
$561$	2.57822	+	0.163741i	0.108853	+	0.00691314i
$562$		0			0
$563$	20.3288	−	5.96908i	0.856757	−	0.251567i	0.176284	−	0.984339i	$-0.443592\pi$
$563$	20.3288	−	5.96908i	0.856757	−	0.251567i	0.680473	+	0.732773i	$0.261774\pi$
$564$		0			0
$565$	−17.6129			−0.740981
$566$		0			0
$567$	22.2929	−	37.2497i	0.936214	−	1.56434i
$568$		0			0
$569$	−5.19009	−	4.49724i	−0.217580	−	0.188534i	0.539250	−	0.842145i	$-0.318708\pi$
$569$	−5.19009	−	4.49724i	−0.217580	−	0.188534i	−0.756830	+	0.653611i	$0.773253\pi$
$570$		0			0
$571$	−8.43609	−	18.4725i	−0.353040	−	0.773049i	−0.999945	−	0.0104787i	$-0.996664\pi$
$571$	−8.43609	−	18.4725i	−0.353040	−	0.773049i	0.646906	−	0.762570i	$-0.276063\pi$
$572$		0			0
$573$	−6.40123	−	11.5039i	−0.267415	−	0.480582i
$574$		0			0
$575$	1.87513	+	2.91775i	0.0781982	+	0.121679i
$576$		0			0
$577$	35.6420	−	5.12454i	1.48379	−	0.213337i	0.647688	−	0.761906i	$-0.275736\pi$
$577$	35.6420	−	5.12454i	1.48379	−	0.213337i	0.836106	+	0.548568i	$0.184827\pi$
$578$		0			0
$579$	2.54905	−	1.94011i	0.105935	−	0.0806281i
$580$		0			0
$581$	7.78998	+	17.0577i	0.323183	+	0.707672i
$582$		0			0
$583$	−19.6150	+	42.9509i	−0.812371	+	1.77884i
$584$		0			0
$585$	20.5296	−	24.4704i	0.848793	−	1.01173i
$586$		0			0
$587$	3.18875	+	0.936301i	0.131614	+	0.0386453i	0.346876	−	0.937911i	$-0.387242\pi$
$587$	3.18875	+	0.936301i	0.131614	+	0.0386453i	−0.215262	+	0.976556i	$0.569061\pi$
$588$		0			0
$589$	10.0167	+	1.44018i	0.412731	+	0.0593418i
$590$		0			0
$591$	−0.809770	+	12.7504i	−0.0333095	+	0.524483i
$592$		0			0
$593$	3.67919	+	8.05629i	0.151086	+	0.330832i	0.970008	−	0.243072i	$-0.0781552\pi$
$593$	3.67919	+	8.05629i	0.151086	+	0.330832i	−0.818922	+	0.573905i	$0.805428\pi$
$594$		0			0
$595$	2.50258	−	1.60831i	0.102596	−	0.0659342i
$596$		0			0
$597$	−21.0762	−	20.7427i	−0.862592	−	0.848941i
$598$		0			0
$599$	2.55166	−	17.7472i	0.104258	−	0.725129i	−0.868900	−	0.494988i	$-0.835172\pi$
$599$	2.55166	−	17.7472i	0.104258	−	0.725129i	0.973157	−	0.230141i	$-0.0739186\pi$
$600$		0			0
$601$	4.28571	+	4.94597i	0.174818	+	0.201750i	0.836396	−	0.548126i	$-0.184658\pi$
$601$	4.28571	+	4.94597i	0.174818	+	0.201750i	−0.661578	+	0.749876i	$0.730113\pi$
$602$		0			0
$603$	21.9676	+	10.9739i	0.894589	+	0.446890i
$604$		0			0
$605$	47.9714	+	55.3620i	1.95032	+	2.25079i
$606$		0			0
$607$	−2.81396	+	19.5715i	−0.114215	+	0.794384i	0.849526	+	0.527546i	$0.176888\pi$
$607$	−2.81396	+	19.5715i	−0.114215	+	0.794384i	−0.963741	+	0.266838i	$0.914021\pi$
$608$		0			0
$609$	−1.80729	−	1.77869i	−0.0732353	−	0.0720762i
$610$		0			0
$611$	18.7696	−	12.0625i	0.759335	−	0.487995i
$612$		0			0
$613$	7.55708	+	16.5477i	0.305228	+	0.668355i	0.998637	−	0.0521884i	$-0.0166196\pi$
$613$	7.55708	+	16.5477i	0.305228	+	0.668355i	−0.693410	+	0.720544i	$0.743892\pi$
$614$		0			0
$615$	1.29676	−	20.4184i	0.0522903	−	0.823350i
$616$		0			0
$617$	−4.53596	−	0.652173i	−0.182611	−	0.0262555i	0.0504026	−	0.998729i	$-0.483950\pi$
$617$	−4.53596	−	0.652173i	−0.182611	−	0.0262555i	−0.233014	+	0.972473i	$0.574859\pi$
$618$		0			0
$619$	11.7426	+	3.44793i	0.471973	+	0.138584i	0.509065	−	0.860728i	$-0.329991\pi$
$619$	11.7426	+	3.44793i	0.471973	+	0.138584i	−0.0370918	+	0.999312i	$0.511809\pi$
$620$		0			0
$621$	−10.3227	−	1.98816i	−0.414234	−	0.0797822i
$622$		0			0
$623$	21.7628	−	47.6540i	0.871910	−	1.90922i
$624$		0			0
$625$	−12.7253	−	27.8646i	−0.509013	−	1.11458i
$626$		0			0
$627$	−9.88581	+	7.52420i	−0.394801	+	0.300487i
$628$		0			0
$629$	−0.519331	+	0.0746685i	−0.0207071	+	0.00297723i
$630$		0			0
$631$	1.62062	+	2.52174i	0.0645160	+	0.100389i	0.872013	−	0.489483i	$-0.162815\pi$
$631$	1.62062	+	2.52174i	0.0645160	+	0.100389i	−0.807497	+	0.589872i	$0.799178\pi$
$632$		0			0
$633$	−11.8215	−	21.2448i	−0.469861	−	0.844404i
$634$		0			0
$635$	−6.73477	−	14.7471i	−0.267261	−	0.585221i
$636$		0			0
$637$	−50.5103	−	43.7674i	−2.00129	−	1.73413i
$638$		0			0
$639$	48.7104	−	0.777078i	1.92695	−	0.0307407i
$640$		0			0
$641$	−40.6694			−1.60634			−0.803172	−	0.595747i	$-0.796856\pi$
$641$	−40.6694			−1.60634			−0.803172	+	0.595747i	$0.796856\pi$
$642$		0			0
$643$	−8.09347	+	2.37646i	−0.319175	+	0.0937183i	−0.437396	−	0.899269i	$-0.644099\pi$
$643$	−8.09347	+	2.37646i	−0.319175	+	0.0937183i	0.118221	+	0.992987i	$0.462281\pi$
$644$		0			0
$645$	−16.7777	−	1.06554i	−0.660622	−	0.0419555i
$646$		0			0
$647$	−12.7390	+	27.8944i	−0.500820	+	1.09664i	0.475382	+	0.879780i	$0.342310\pi$
$647$	−12.7390	+	27.8944i	−0.500820	+	1.09664i	−0.976202	+	0.216864i	$0.930417\pi$
$648$		0			0
$649$	15.8817	+	54.0880i	0.623410	+	2.12314i
$650$		0			0
$651$	72.2994	+	15.1249i	2.83364	+	0.592790i
$652$		0			0
$653$	−5.75048	−	39.9955i	−0.225034	−	1.56514i	−0.718593	−	0.695431i	$-0.755213\pi$
$653$	−5.75048	−	39.9955i	−0.225034	−	1.56514i	0.493559	−	0.869712i	$-0.335696\pi$
$654$		0			0
$655$	19.3514	+	16.7681i	0.756123	+	0.655185i
$656$		0			0
$657$	37.3516	−	17.7833i	1.45722	−	0.693794i
$658$		0			0
$659$	−3.02418	+	10.2994i	−0.117805	+	0.401208i	−0.997191	−	0.0749021i	$-0.976136\pi$
$659$	−3.02418	+	10.2994i	−0.117805	+	0.401208i	0.879385	+	0.476110i	$0.157954\pi$
$660$		0			0
$661$	−0.415841	+	0.360328i	−0.0161743	+	0.0140151i	−0.662910	−	0.748699i	$-0.730679\pi$
$661$	−0.415841	+	0.360328i	−0.0161743	+	0.0140151i	0.646736	+	0.762714i	$0.276134\pi$
$662$		0			0
$663$	−0.579289	+	1.59179i	−0.0224977	+	0.0618201i
$664$		0			0
$665$	−4.03038	+	13.7262i	−0.156292	+	0.532280i
$666$		0			0
$667$	−0.255088	+	0.558566i	−0.00987707	+	0.0216278i
$668$		0			0
$669$	−19.2083	−	34.5200i	−0.742636	−	1.33462i
$670$		0			0
$671$		−	6.05708i		−	0.233831i
$672$		0			0
$673$	−20.7848	−	9.49212i	−0.801197	−	0.365894i	−0.0276375	−	0.999618i	$-0.508798\pi$
$673$	−20.7848	−	9.49212i	−0.801197	−	0.365894i	−0.773560	+	0.633724i	$0.781526\pi$
$674$		0			0
$675$	−8.41853	−	2.91248i	−0.324029	−	0.112101i
$676$		0			0
$677$	−14.3718	−	16.5859i	−0.552352	−	0.637449i	0.409077	−	0.912500i	$-0.365851\pi$
$677$	−14.3718	−	16.5859i	−0.552352	−	0.637449i	−0.961430	+	0.275051i	$0.911305\pi$
$678$		0			0
$679$	8.81802	+	10.1765i	0.338405	+	0.390540i
$680$		0			0
$681$	−13.7017	+	3.09528i	−0.525051	+	0.118611i
$682$		0			0
$683$	−36.2668	−	23.3072i	−1.38771	−	0.891827i	−0.388152	−	0.921595i	$-0.626887\pi$
$683$	−36.2668	−	23.3072i	−1.38771	−	0.891827i	−0.999557	+	0.0297686i	$0.990523\pi$
$684$		0			0
$685$	−34.0191	+	39.2601i	−1.29980	+	1.50005i
$686$		0			0
$687$	11.5738	+	15.2064i	0.441567	+	0.580162i
$688$		0			0
$689$	−23.3983	−	20.2747i	−0.891404	−	0.772406i
$690$		0			0
$691$	−18.4515	+	5.41786i	−0.701929	+	0.206105i	−0.613173	−	0.789948i	$-0.710107\pi$
$691$	−18.4515	+	5.41786i	−0.701929	+	0.206105i	−0.0887557	+	0.996053i	$0.528289\pi$
$692$		0			0
$693$	−75.4930	+	50.2358i	−2.86774	+	1.90830i
$694$		0			0
$695$	−7.14328	+	11.1152i	−0.270960	+	0.421622i
$696$		0			0
$697$	0.305683	+	1.04106i	0.0115786	+	0.0394330i
$698$		0			0
$699$	12.3991	+	22.2828i	0.468976	+	0.842814i
$700$		0			0
$701$	10.9597	−	7.04335i	0.413941	−	0.266023i	−0.317053	−	0.948408i	$-0.602693\pi$
$701$	10.9597	−	7.04335i	0.413941	−	0.266023i	0.730994	+	0.682384i	$0.239057\pi$
$702$		0			0
$703$	1.65229	−	1.90684i	0.0623171	−	0.0719178i
$704$		0			0
$705$	−19.6252	−	14.4484i	−0.739126	−	0.544158i
$706$		0			0
$707$			88.8125i			3.34014i
$708$		0			0
$709$	−21.3951	+	13.7498i	−0.803511	+	0.516385i	−0.876760	−	0.480929i	$-0.840300\pi$
$709$	−21.3951	+	13.7498i	−0.803511	+	0.516385i	0.0732489	+	0.997314i	$0.476663\pi$
$710$		0			0
$711$	−2.62689	+	6.00371i	−0.0985160	+	0.225157i
$712$		0			0
$713$	−2.54558	−	17.7049i	−0.0953328	−	0.663054i
$714$		0			0
$715$	−60.6922	+	27.7172i	−2.26976	+	1.03656i
$716$		0			0
$717$	39.4401	−	3.13717i	1.47292	−	0.117160i
$718$		0			0
$719$	49.2521	+	7.08138i	1.83679	+	0.264091i	0.971477	−	0.237134i	$-0.0762082\pi$
$719$	49.2521	+	7.08138i	1.83679	+	0.264091i	0.865317	+	0.501225i	$0.167117\pi$
$720$		0			0
$721$	−16.8322	+	57.3250i	−0.626862	+	2.13490i
$722$		0			0
$723$	−19.0648	+	7.28452i	−0.709026	+	0.270914i
$724$		0			0
$725$	−0.281321	+	0.437744i	−0.0104480	+	0.0162574i
$726$		0			0
$727$	−29.3484	+	13.4030i	−1.08847	+	0.497088i	−0.877095	−	0.480317i	$-0.840522\pi$
$727$	−29.3484	+	13.4030i	−1.08847	+	0.497088i	−0.211376	+	0.977405i	$0.567795\pi$
$728$		0			0
$729$	23.9954	−	12.3782i	0.888719	−	0.458453i
$730$		0			0
$731$	0.855434	−	0.251178i	0.0316394	−	0.00929016i
$732$		0			0
$733$	6.92412	+	0.995538i	0.255748	+	0.0367710i	0.268996	−	0.963141i	$-0.413308\pi$
$733$	6.92412	+	0.995538i	0.255748	+	0.0367710i	−0.0132482	+	0.999912i	$0.504217\pi$
$734$		0			0
$735$	−24.9651	+	68.6002i	−0.920852	+	2.53036i
$736$		0			0
$737$	−31.5773	−	40.4226i	−1.16317	−	1.48899i
$738$		0			0
$739$	17.2341	−	14.9334i	0.633966	−	0.549335i	−0.277492	−	0.960728i	$-0.589503\pi$
$739$	17.2341	−	14.9334i	0.633966	−	0.549335i	0.911458	+	0.411393i	$0.134958\pi$
$740$		0			0
$741$	−2.90751	−	7.60942i	−0.106810	−	0.279539i
$742$		0			0
$743$	−8.39865	−	28.6032i	−0.308117	−	1.04935i	−0.957391	−	0.288795i	$-0.906745\pi$
$743$	−8.39865	−	28.6032i	−0.308117	−	1.04935i	0.649274	−	0.760554i	$-0.275073\pi$
$744$		0			0
$745$	20.4739	+	31.8580i	0.750104	+	1.16719i
$746$		0			0
$747$	−1.47549	+	11.5695i	−0.0539854	+	0.423306i
$748$		0			0
$749$	2.06633	+	1.32795i	0.0755021	+	0.0485223i
$750$		0			0
$751$	4.00492	−	27.8548i	0.146142	−	1.01644i	−0.776318	−	0.630342i	$-0.782915\pi$
$751$	4.00492	−	27.8548i	0.146142	−	1.01644i	0.922459	−	0.386095i	$-0.126176\pi$
$752$		0			0
$753$	−0.713690	−	3.15925i	−0.0260083	−	0.115130i
$754$		0			0
$755$	4.34343	−	30.2092i	0.158074	−	1.09943i
$756$		0			0
$757$	25.1592	+	11.4898i	0.914428	+	0.417605i	0.816339	−	0.577573i	$-0.196000\pi$
$757$	25.1592	+	11.4898i	0.914428	+	0.417605i	0.0980883	+	0.995178i	$0.468727\pi$
$758$		0			0
$759$	17.6835	+	13.0189i	0.641869	+	0.472556i
$760$		0			0
$761$	37.7010	−	5.42058i	1.36666	−	0.196496i	0.580370	−	0.814353i	$-0.302908\pi$
$761$	37.7010	−	5.42058i	1.36666	−	0.196496i	0.786290	+	0.617857i	$0.211999\pi$
$762$		0			0
$763$	11.0779	+	77.0483i	0.401046	+	2.78934i
$764$		0			0
$765$	1.84999	−	0.0295130i	0.0668866	−	0.00106704i
$766$		0			0
$767$	−36.9623			−1.33463
$768$		0			0
$769$	−24.3548	+	11.1224i	−0.878255	+	0.401086i	−0.802930	−	0.596073i	$-0.796727\pi$
$769$	−24.3548	+	11.1224i	−0.878255	+	0.401086i	−0.0753250	+	0.997159i	$0.523999\pi$
$770$		0			0
$771$	−5.88369	+	28.1250i	−0.211896	+	1.01290i
$772$		0			0
$773$	−0.211784	−	0.329542i	−0.00761734	−	0.0118528i	0.837424	−	0.546554i	$-0.184061\pi$
$773$	−0.211784	−	0.329542i	−0.00761734	−	0.0118528i	−0.845041	+	0.534701i	$0.820424\pi$
$774$		0			0
$775$		−	15.1573i		−	0.544465i
$776$		0			0
$777$	12.9181	−	13.1258i	0.463433	−	0.470885i
$778$		0			0
$779$	−4.38945	−	2.82093i	−0.157268	−	0.101070i
$780$		0			0
$781$	−92.5664	−	42.2737i	−3.31229	−	1.51267i
$782$		0			0
$783$	−0.372022	−	1.53264i	−0.0132950	−	0.0547721i
$784$		0			0
$785$	10.1679	−	11.7343i	0.362906	−	0.418816i
$786$		0			0
$787$	21.2209	−	3.05111i	0.756444	−	0.108760i	0.246706	−	0.969090i	$-0.420652\pi$
$787$	21.2209	−	3.05111i	0.756444	−	0.108760i	0.509737	+	0.860330i	$0.329743\pi$
$788$		0			0
$789$	−3.86606	+	18.4804i	−0.137635	+	0.657920i
$790$		0			0
$791$	−17.7253	+	27.5812i	−0.630241	+	0.980674i
$792$		0			0
$793$	3.81070	+	1.11892i	0.135322	+	0.0397341i
$794$		0			0
$795$	−11.5648	+	31.7782i	−0.410161	+	1.12706i
$796$		0			0
$797$	−11.9890	+	10.3885i	−0.424672	+	0.367980i	−0.840818	−	0.541317i	$-0.817926\pi$
$797$	−11.9890	+	10.3885i	−0.424672	+	0.367980i	0.416146	+	0.909298i	$0.363380\pi$
$798$		0			0
$799$	1.24005	+	0.364110i	0.0438697	+	0.0128813i
$800$		0			0
$801$	27.1265	−	18.0510i	0.958468	−	0.637799i
$802$		0			0
$803$	−86.4143			−3.04949
$804$		0			0
$805$	25.2859			0.891210
$806$		0			0
$807$	1.73748	+	21.8434i	0.0611624	+	0.768924i
$808$		0			0
$809$	−20.5550	−	6.03549i	−0.722676	−	0.212197i	−0.100347	−	0.994953i	$-0.531995\pi$
$809$	−20.5550	−	6.03549i	−0.722676	−	0.212197i	−0.622329	+	0.782756i	$0.713813\pi$
$810$		0			0
$811$	−3.30713	+	2.86565i	−0.116129	+	0.100626i	−0.710990	−	0.703202i	$-0.751753\pi$
$811$	−3.30713	+	2.86565i	−0.116129	+	0.100626i	0.594861	+	0.803829i	$0.297207\pi$
$812$		0			0
$813$	−30.1329	−	10.9660i	−1.05681	−	0.384595i
$814$		0			0
$815$	36.6098	+	10.7496i	1.28238	+	0.376542i
$816$		0			0
$817$	−2.31794	+	3.60679i	−0.0810945	+	0.126186i
$818$		0			0
$819$	−17.6591	−	56.7751i	−0.617060	−	1.98388i
$820$		0			0
$821$	−17.7424	+	2.55097i	−0.619213	+	0.0890294i	−0.444780	−	0.895640i	$-0.646718\pi$
$821$	−17.7424	+	2.55097i	−0.619213	+	0.0890294i	−0.174433	+	0.984669i	$0.555809\pi$
$822$		0			0
$823$	−3.69498	+	4.26423i	−0.128799	+	0.148642i	−0.816486	−	0.577366i	$-0.804081\pi$
$823$	−3.69498	+	4.26423i	−0.128799	+	0.148642i	0.687687	+	0.726007i	$0.258626\pi$
$824$		0			0
$825$	13.2623	+	13.0524i	0.461733	+	0.454425i
$826$		0			0
$827$	3.69725	+	1.68848i	0.128566	+	0.0587142i	0.478659	−	0.878001i	$-0.341123\pi$
$827$	3.69725	+	1.68848i	0.128566	+	0.0587142i	−0.350093	+	0.936715i	$0.613850\pi$
$828$		0			0
$829$	28.3806	+	18.2391i	0.985699	+	0.633470i	0.930995	−	0.365032i	$-0.118942\pi$
$829$	28.3806	+	18.2391i	0.985699	+	0.633470i	0.0547040	+	0.998503i	$0.482578\pi$
$830$		0			0
$831$	5.21644	+	5.13389i	0.180956	+	0.178093i
$832$		0			0
$833$		−	3.87143i		−	0.134137i
$834$		0			0
$835$	−24.3971	−	37.9627i	−0.844298	−	1.31375i
$836$		0			0
$837$	33.2531	+	31.6986i	1.14939	+	1.09567i
$838$		0			0
$839$	17.4758	−	7.98095i	0.603333	−	0.275533i	−0.0902390	−	0.995920i	$-0.528763\pi$
$839$	17.4758	−	7.98095i	0.603333	−	0.275533i	0.693572	+	0.720387i	$0.256036\pi$
$840$		0			0
$841$	28.9079			0.996823
$842$		0			0
$843$	−2.05233	−	1.09950i	−0.0706859	−	0.0378687i
$844$		0			0
$845$	−1.43214	−	9.96075i	−0.0492671	−	0.342660i
$846$		0			0
$847$	134.972	−	19.4061i	4.63771	−	0.666802i
$848$		0			0
$849$	17.4058	−	23.6421i	0.597364	−	0.811395i
$850$		0			0
$851$	−4.05668	−	1.85262i	−0.139061	−	0.0635071i
$852$		0			0
$853$	−5.20127	+	36.1756i	−0.178088	+	1.23863i	0.683093	+	0.730331i	$0.260634\pi$
$853$	−5.20127	+	36.1756i	−0.178088	+	1.23863i	−0.861181	+	0.508298i	$0.830275\pi$
$854$		0			0
$855$	−6.63057	+	5.93322i	−0.226761	+	0.202912i
$856$		0			0
$857$	−2.91881	+	20.3008i	−0.0997047	+	0.693461i	0.877253	+	0.480028i	$0.159374\pi$
$857$	−2.91881	+	20.3008i	−0.0997047	+	0.693461i	−0.976958	+	0.213433i	$0.931536\pi$
$858$		0			0
$859$	33.1077	+	21.2770i	1.12962	+	0.725963i	0.965481	−	0.260474i	$-0.0838790\pi$
$859$	33.1077	+	21.2770i	1.12962	+	0.725963i	0.164139	+	0.986437i	$0.447515\pi$
$860$		0			0
$861$	−30.6695	−	22.5794i	−1.04521	−	0.769505i
$862$		0			0
$863$	−4.68744	−	7.29380i	−0.159562	−	0.248284i	0.752262	−	0.658864i	$-0.228963\pi$
$863$	−4.68744	−	7.29380i	−0.159562	−	0.248284i	−0.911825	+	0.410580i	$0.865326\pi$
$864$		0			0
$865$	6.27635	+	21.3753i	0.213402	+	0.726782i
$866$		0			0
$867$	27.4138	−	10.4746i	0.931020	−	0.355737i
$868$		0			0
$869$	10.3454	−	8.96431i	0.350943	−	0.304093i
$870$		0			0
$871$	31.2644	−	12.3991i	1.05935	−	0.420126i
$872$		0			0
$873$	1.32397	+	8.26972i	0.0448096	+	0.279888i
$874$		0			0
$875$	−40.6477	−	5.84425i	−1.37414	−	0.197572i
$876$		0			0
$877$	−17.8210	+	5.23270i	−0.601771	+	0.176696i	−0.568407	−	0.822747i	$-0.692440\pi$
$877$	−17.8210	+	5.23270i	−0.601771	+	0.176696i	−0.0333637	+	0.999443i	$0.510622\pi$
$878$		0			0
$879$	19.5897	−	36.5663i	0.660745	−	1.23335i
$880$		0			0
$881$	−10.7768	+	4.92162i	−0.363081	+	0.165814i	−0.588598	−	0.808426i	$-0.700320\pi$
$881$	−10.7768	+	4.92162i	−0.363081	+	0.165814i	0.225517	+	0.974239i	$0.427593\pi$
$882$		0			0
$883$	8.75570	−	13.6241i	0.294653	−	0.458488i	−0.662090	−	0.749424i	$-0.730330\pi$
$883$	8.75570	−	13.6241i	0.294653	−	0.458488i	0.956743	+	0.290936i	$0.0939667\pi$
$884$		0			0
$885$	14.4101	+	37.7137i	0.484391	+	1.26773i
$886$		0			0
$887$	3.61930	−	12.3262i	0.121524	−	0.413873i	−0.876150	−	0.482039i	$-0.839896\pi$
$887$	3.61930	−	12.3262i	0.121524	−	0.413873i	0.997674	+	0.0681656i	$0.0217146\pi$
$888$		0			0
$889$	−29.8712	−	4.29482i	−1.00185	−	0.144044i
$890$		0			0
$891$	−56.3708	+	1.79903i	−1.88849	+	0.0602697i
$892$		0			0
$893$	−5.65341	+	2.58183i	−0.189184	+	0.0863975i
$894$		0			0
$895$	−4.63589	−	32.2433i	−0.154961	−	1.07778i
$896$		0			0
$897$	−11.4573	+	8.72025i	−0.382547	+	0.291161i
$898$		0			0
$899$	2.25754	−	1.45083i	0.0752931	−	0.0483879i
$900$		0			0
$901$		−	1.79339i		−	0.0597466i
$902$		0			0
$903$	−18.5534	+	25.2009i	−0.617418	+	0.838634i
$904$		0			0
$905$	29.7211	−	34.2999i	0.987962	−	1.14017i
$906$		0			0
$907$	24.0288	−	15.4424i	0.797864	−	0.512756i	−0.0770544	−	0.997027i	$-0.524552\pi$
$907$	24.0288	−	15.4424i	0.797864	−	0.512756i	0.874918	+	0.484271i	$0.160915\pi$
$908$		0			0
$909$	−29.1189	+	46.9397i	−0.965814	+	1.55689i
$910$		0			0
$911$	4.01668	+	13.6796i	0.133079	+	0.453224i	0.998888	−	0.0471501i	$-0.0150139\pi$
$911$	4.01668	+	13.6796i	0.133079	+	0.453224i	−0.865809	+	0.500374i	$0.833196\pi$
$912$		0			0
$913$	13.1716	−	20.4954i	0.435916	−	0.678299i
$914$		0			0
$915$	−0.343974	−	4.32439i	−0.0113714	−	0.142960i
$916$		0			0
$917$	45.7332	−	13.4285i	1.51024	−	0.443448i
$918$		0			0
$919$	−43.1148	−	37.3592i	−1.42223	−	1.23237i	−0.932837	−	0.360299i	$-0.882675\pi$
$919$	−43.1148	−	37.3592i	−1.42223	−	1.23237i	−0.489389	−	0.872066i	$-0.662780\pi$
$920$		0			0
$921$	28.8611	−	21.9665i	0.951007	−	0.723822i
$922$		0			0
$923$	43.6955	−	50.4273i	1.43825	−	1.65983i
$924$		0			0
$925$	−3.17919	−	2.04314i	−0.104531	−	0.0671780i
$926$		0			0
$927$	−27.6914	+	24.7790i	−0.909504	+	0.813849i
$928$		0			0
$929$	5.87019	+	6.77456i	0.192595	+	0.222266i	0.843831	−	0.536609i	$-0.180295\pi$
$929$	5.87019	+	6.77456i	0.192595	+	0.222266i	−0.651236	+	0.758875i	$0.725749\pi$
$930$		0			0
$931$	12.1918	+	14.0701i	0.399571	+	0.461129i
$932$		0			0
$933$	−10.2436	−	45.3448i	−0.335361	−	1.48452i
$934$		0			0
$935$	−3.51562	−	1.60553i	−0.114973	−	0.0525064i
$936$		0			0
$937$		−	39.9228i		−	1.30422i	−0.758124	−	0.652110i	$-0.773884\pi$
$937$		−	39.9228i		−	1.30422i	0.758124	−	0.652110i	$-0.226116\pi$
$938$		0			0
$939$	11.8688	−	6.60427i	0.387323	−	0.215522i
$940$		0			0
$941$	11.5091	−	25.2015i	0.375187	−	0.821545i	−0.624008	−	0.781418i	$-0.714497\pi$
$941$	11.5091	−	25.2015i	0.375187	−	0.821545i	0.999195	−	0.0401265i	$-0.0127761\pi$
$942$		0			0
$943$	−2.59830	+	8.84899i	−0.0846123	+	0.288163i
$944$		0			0
$945$	−51.0446	+	40.1524i	−1.66048	+	1.30616i
$946$		0			0
$947$	−5.74607	+	4.97900i	−0.186722	+	0.161796i	−0.743206	−	0.669063i	$-0.766696\pi$
$947$	−5.74607	+	4.97900i	−0.186722	+	0.161796i	0.556484	+	0.830859i	$0.312150\pi$
$948$		0			0
$949$	15.9633	−	54.3660i	0.518190	−	1.76479i
$950$		0			0
$951$	47.7689	+	3.03376i	1.54901	+	0.0983765i
$952$		0			0
$953$	−3.90378	−	3.38265i	−0.126456	−	0.109575i	0.589337	−	0.807887i	$-0.299389\pi$
$953$	−3.90378	−	3.38265i	−0.126456	−	0.109575i	−0.715793	+	0.698313i	$0.753935\pi$
$954$		0			0
$955$	2.80292	+	19.4947i	0.0907003	+	0.630834i
$956$		0			0
$957$	−0.674588	+	3.22464i	−0.0218063	+	0.104238i
$958$		0			0
$959$	27.2437	+	92.7834i	0.879744	+	2.99613i
$960$		0			0
$961$	−19.5948	+	42.9067i	−0.632091	+	1.38409i
$962$		0			0
$963$	0.656714	+	1.37934i	0.0211623	+	0.0444487i
$964$		0			0
$965$	−4.59825	+	1.35017i	−0.148023	+	0.0434634i
$966$		0			0
$967$	−20.7656			−0.667777			−0.333888	−	0.942613i	$-0.608361\pi$
$967$	−20.7656			−0.667777			−0.333888	+	0.942613i	$0.608361\pi$
$968$		0			0
$969$	0.222827	−	0.415931i	0.00715825	−	0.0133616i
$970$		0			0
$971$	−14.3727	−	12.4540i	−0.461242	−	0.399668i	0.393005	−	0.919537i	$-0.371436\pi$
$971$	−14.3727	−	12.4540i	−0.461242	−	0.399668i	−0.854247	+	0.519868i	$0.825981\pi$
$972$		0			0
$973$	10.2170	+	22.3722i	0.327543	+	0.717220i
$974$		0			0
$975$	−10.6616	+	5.93255i	−0.341444	+	0.189994i
$976$		0			0
$977$	19.0389	+	29.6252i	0.609109	+	0.947793i	0.999630	+	0.0271986i	$0.00865865\pi$
$977$	19.0389	+	29.6252i	0.609109	+	0.947793i	−0.390521	+	0.920594i	$0.627705\pi$
$978$		0			0
$979$	−67.3699	+	9.68632i	−2.15315	+	0.309576i
$980$		0			0
$981$	−19.4069	+	44.3541i	−0.619613	+	1.41612i
$982$		0			0
$983$	−11.2042	−	24.5338i	−0.357358	−	0.782506i	−0.999868	−	0.0162284i	$-0.994834\pi$
$983$	−11.2042	−	24.5338i	−0.357358	−	0.782506i	0.642510	−	0.766277i	$-0.277893\pi$
$984$		0			0
$985$	7.94005	−	17.3863i	0.252991	−	0.553973i
$986$		0			0
$987$	−42.3761	+	16.1916i	−1.34885	+	0.515385i
$988$		0			0
$989$	7.27117	+	2.13501i	0.231210	+	0.0678893i
$990$		0			0
$991$	−37.2954	−	5.36227i	−1.18473	−	0.170338i	−0.478347	−	0.878171i	$-0.658764\pi$
$991$	−37.2954	−	5.36227i	−1.18473	−	0.170338i	−0.706380	+	0.707833i	$0.749673\pi$
$992$		0			0
$993$	9.51876	+	0.604528i	0.302069	+	0.0191841i
$994$		0			0
$995$	18.3779	+	40.2419i	0.582618	+	1.27575i
$996$		0			0
$997$	−5.07184	+	3.25947i	−0.160627	+	0.103228i	−0.618485	−	0.785797i	$-0.712253\pi$
$997$	−5.07184	+	3.25947i	−0.160627	+	0.103228i	0.457858	+	0.889025i	$0.348617\pi$
$998$		0			0
$999$	11.1311	−	2.70187i	0.352171	−	0.0854834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.161.1	yes	200
3.2	odd	2	inner	804.2.s.b.161.7	yes	200
67.5	odd	22	inner	804.2.s.b.5.7	yes	200
201.5	even	22	inner	804.2.s.b.5.1	✓	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.1	✓	200	201.5	even	22	inner
804.2.s.b.5.7	yes	200	67.5	odd	22	inner
804.2.s.b.161.1	yes	200	1.1	even	1	trivial
804.2.s.b.161.7	yes	200	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72660 + 0.137338i) q^{3} +(2.48625 + 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(2.96228 - 0.474256i) q^{9} +O(q^{10})\)	\(q+(-1.72660 + 0.137338i) q^{3} +(2.48625 + 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(2.96228 - 0.474256i) q^{9} +(-6.01277 - 1.76551i) q^{11} +(2.22147 - 3.45668i) q^{13} +(-4.39301 - 0.919007i) q^{15} +(0.235591 - 0.0338728i) q^{17} +(-0.749547 + 0.865023i) q^{19} +(-5.86018 + 5.95441i) q^{21} +(1.84028 + 0.840429i) q^{23} +(1.44221 + 0.926855i) q^{25} +(-5.04952 + 1.22568i) q^{27} +0.303522i q^{29} +(-4.77999 - 7.43781i) q^{31} +(10.6241 + 2.22254i) q^{33} +(11.3691 - 5.19208i) q^{35} -2.20438 q^{37} +(-3.36086 + 6.27339i) q^{39} +(0.648759 + 4.51222i) q^{41} +(3.70767 - 0.533082i) q^{43} +(7.71117 + 0.983427i) q^{45} +(4.93924 + 2.25568i) q^{47} +(2.31483 - 16.1000i) q^{49} +(-0.402118 + 0.0908404i) q^{51} +(1.07232 - 7.45815i) q^{53} +(-13.6603 - 8.77897i) q^{55} +(1.17537 - 1.59649i) q^{57} +(-4.86335 - 7.56752i) q^{59} +(0.272313 + 0.927412i) q^{61} +(9.30040 - 11.0857i) q^{63} +(8.04661 - 6.97242i) q^{65} +(6.65218 + 4.76954i) q^{67} +(-3.29285 - 1.19834i) q^{69} +(16.0736 + 2.31103i) q^{71} +(13.2311 - 3.88499i) q^{73} +(-2.61742 - 1.40223i) q^{75} +(-27.4951 + 12.5566i) q^{77} +(-1.18099 + 1.83765i) q^{79} +(8.55016 - 2.80976i) q^{81} +(-1.09530 + 3.73026i) q^{83} +(0.610465 + 0.0877716i) q^{85} +(-0.0416852 - 0.524060i) q^{87} +(9.87966 - 4.51189i) q^{89} +(-2.82059 - 19.6176i) q^{91} +(9.27461 + 12.1856i) q^{93} +(-2.49505 + 1.60347i) q^{95} +2.79168i q^{97} +(-18.6488 - 2.37833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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