LMFDB - Embedded newform 804.2.s.b.5.1

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			5.1
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.1

$q$-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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

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	0.326320	−	0.945259i	$-0.394191\pi$
$5$	2.48625	−	0.730028i	1.11188	−	0.326478i	0.785564	+	0.618781i	$0.212373\pi$
$6$		0			0
$7$	3.64531	+	3.15868i	1.37780	+	1.19387i	0.958179	+	0.286170i	$0.0923821\pi$
$7$	3.64531	+	3.15868i	1.37780	+	1.19387i	0.419620	+	0.907700i	$0.362163\pi$
$8$		0			0
$9$	2.96228	+	0.474256i	0.987425	+	0.158085i
$10$		0			0
$11$	−6.01277	+	1.76551i	−1.81292	+	0.532320i	−0.998827	−	0.0484186i	$-0.984582\pi$
$11$	−6.01277	+	1.76551i	−1.81292	+	0.532320i	−0.814090	+	0.580739i	$0.802764\pi$
$12$		0			0
$13$	2.22147	+	3.45668i	0.616126	+	0.958711i	0.999385	+	0.0350697i	$0.0111653\pi$
$13$	2.22147	+	3.45668i	0.616126	+	0.958711i	−0.383259	+	0.923641i	$0.625198\pi$
$14$		0			0
$15$	−4.39301	+	0.919007i	−1.13427	+	0.237287i
$16$		0			0
$17$	0.235591	+	0.0338728i	0.0571391	+	0.00821537i	0.170825	−	0.985301i	$-0.445357\pi$
$17$	0.235591	+	0.0338728i	0.0571391	+	0.00821537i	−0.113686	+	0.993517i	$0.536266\pi$
$18$		0			0
$19$	−0.749547	−	0.865023i	−0.171958	−	0.198450i	0.663229	−	0.748417i	$-0.269186\pi$
$19$	−0.749547	−	0.865023i	−0.171958	−	0.198450i	−0.835186	+	0.549967i	$0.814640\pi$
$20$		0			0
$21$	−5.86018	−	5.95441i	−1.27880	−	1.29936i
$22$		0			0
$23$	1.84028	−	0.840429i	0.383725	−	0.175242i	−0.214207	−	0.976788i	$-0.568717\pi$
$23$	1.84028	−	0.840429i	0.383725	−	0.175242i	0.597932	+	0.801547i	$0.295989\pi$
$24$		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	$-0.991028\pi$
$29$		−	0.303522i		−	0.0563626i	0.999603	−	0.0281813i	$-0.00897157\pi$
$30$		0			0
$31$	−4.77999	+	7.43781i	−0.858511	+	1.33587i	0.0821840	+	0.996617i	$0.473810\pi$
$31$	−4.77999	+	7.43781i	−0.858511	+	1.33587i	−0.940695	+	0.339253i	$0.889826\pi$
$32$		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	−0.874327	−	0.485338i	$-0.838697\pi$
$41$	0.648759	−	4.51222i	0.101319	−	0.704690i	0.975646	−	0.219352i	$-0.0703944\pi$
$42$		0			0
$43$	3.70767	+	0.533082i	0.565414	+	0.0812942i	0.419093	−	0.907943i	$-0.362348\pi$
$43$	3.70767	+	0.533082i	0.565414	+	0.0812942i	0.146320	+	0.989237i	$0.453257\pi$
$44$		0			0
$45$	7.71117	−	0.983427i	1.14951	−	0.146601i
$46$		0			0
$47$	4.93924	−	2.25568i	0.720463	−	0.329024i	−0.0212204	−	0.999775i	$-0.506755\pi$
$47$	4.93924	−	2.25568i	0.720463	−	0.329024i	0.741683	+	0.670751i	$0.234028\pi$
$48$		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	0.920624	+	0.390451i	$0.127681\pi$
$53$	1.07232	+	7.45815i	0.147294	+	1.02446i	−0.773329	+	0.634004i	$0.781410\pi$
$54$		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	0.365368	+	0.930863i	$0.380943\pi$
$59$	−4.86335	+	7.56752i	−0.633155	+	0.985208i	−0.998522	+	0.0543445i	$0.982693\pi$
$60$		0			0
$61$	0.272313	−	0.927412i	0.0348661	−	0.118743i	−0.940221	−	0.340564i	$-0.889382\pi$
$61$	0.272313	−	0.927412i	0.0348661	−	0.118743i	0.975087	+	0.221821i	$0.0712001\pi$
$62$		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	0.915742	−	0.401767i	$-0.131604\pi$
$71$	16.0736	−	2.31103i	1.90758	−	0.274269i	0.991839	+	0.127498i	$0.0406947\pi$
$72$		0			0
$73$	13.2311	+	3.88499i	1.54858	+	0.454704i	0.940676	−	0.339307i	$-0.110193\pi$
$73$	13.2311	+	3.88499i	1.54858	+	0.454704i	0.607903	+	0.794011i	$0.292011\pi$
$74$		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	0.768442	−	0.639919i	$-0.221032\pi$
$79$	−1.18099	−	1.83765i	−0.132871	−	0.206752i	−0.901313	+	0.433168i	$0.857396\pi$
$80$		0			0
$81$	8.55016	+	2.80976i	0.950018	+	0.312195i
$82$		0			0
$83$	−1.09530	−	3.73026i	−0.120225	−	0.409449i	0.877285	−	0.479969i	$-0.159352\pi$
$83$	−1.09530	−	3.73026i	−0.120225	−	0.409449i	−0.997510	+	0.0705203i	$0.977534\pi$
$84$		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	0.863307	−	0.504679i	$-0.168389\pi$
$89$	9.87966	+	4.51189i	1.04724	+	0.478259i	0.183935	+	0.982938i	$0.441116\pi$
$90$		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	$-0.954735\pi$
$97$		−	2.79168i		−	0.283452i	0.989906	−	0.141726i	$-0.0452652\pi$
$98$		0			0
$99$	−18.6488	+	2.37833i	−1.87427	+	0.239031i
$100$		0			0
$101$	−12.0577	−	13.9154i	−1.19979	−	1.38463i	−0.902973	−	0.429698i	$-0.858620\pi$
$101$	−12.0577	−	13.9154i	−1.19979	−	1.38463i	−0.296818	−	0.954934i	$-0.595926\pi$
$102$		0			0
$103$	−10.4201	−	6.69660i	−1.02672	−	0.659836i	−0.0850555	−	0.996376i	$-0.527107\pi$
$103$	−10.4201	−	6.69660i	−1.02672	−	0.659836i	−0.941669	+	0.336540i	$0.890743\pi$
$104$		0			0
$105$	−18.9167	−	10.5260i	−1.84608	−	1.02724i
$106$		0			0
$107$	0.143467	−	0.488605i	0.0138695	−	0.0472352i	−0.952268	−	0.305265i	$-0.901255\pi$
$107$	0.143467	−	0.488605i	0.0138695	−	0.0472352i	0.966137	+	0.258030i	$0.0830732\pi$
$108$		0			0
$109$	−8.72485	−	13.5761i	−0.835689	−	1.30036i	−0.951675	−	0.307107i	$-0.900639\pi$
$109$	−8.72485	−	13.5761i	−0.835689	−	1.30036i	0.115986	−	0.993251i	$-0.462997\pi$
$110$		0			0
$111$	3.80607	+	0.302746i	0.361257	+	0.0287354i
$112$		0			0
$113$	−6.52185	−	1.91499i	−0.613524	−	0.180147i	−0.0398163	−	0.999207i	$-0.512677\pi$
$113$	−6.52185	−	1.91499i	−0.613524	−	0.180147i	−0.573708	+	0.819060i	$0.694495\pi$
$114$		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	−0.907832	−	0.419334i	$-0.862264\pi$
$127$	−4.09720	+	4.72842i	−0.363568	+	0.419580i	0.544264	+	0.838914i	$0.316809\pi$
$128$		0			0
$129$	−6.32843	−	1.42962i	−0.557187	−	0.125871i
$130$		0			0
$131$	8.98874	−	4.10502i	0.785350	−	0.358657i	0.0179603	−	0.999839i	$-0.494283\pi$
$131$	8.98874	−	4.10502i	0.785350	−	0.358657i	0.767389	+	0.641182i	$0.221555\pi$
$132$		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	−0.825407	−	0.564539i	$-0.809054\pi$
$137$	−8.32825	−	18.2363i	−0.711530	−	1.55803i	0.113876	−	0.993495i	$-0.463673\pi$
$138$		0			0
$139$	−1.43656	−	4.89247i	−0.121847	−	0.414974i	0.875867	−	0.482553i	$-0.160291\pi$
$139$	−1.43656	−	4.89247i	−0.121847	−	0.414974i	−0.997714	+	0.0675796i	$0.978472\pi$
$140$		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	−0.0721340	−	0.997395i	$-0.522981\pi$
$149$	11.0450	−	9.57056i	0.904843	−	0.784051i	0.976977	+	0.213344i	$0.0684355\pi$
$150$		0			0
$151$	−1.67622	+	11.6584i	−0.136409	+	0.948743i	0.800541	+	0.599278i	$0.204546\pi$
$151$	−1.67622	+	11.6584i	−0.136409	+	0.948743i	−0.936949	+	0.349465i	$0.886363\pi$
$152$		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	0.982576	−	0.185863i	$-0.0595079\pi$
$157$	2.48920	+	5.45059i	0.198660	+	0.435005i	−0.783916	+	0.620867i	$0.786781\pi$
$158$		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	−0.993112	−	0.117171i	$-0.962617\pi$
$167$	−13.1615	+	11.4045i	−1.01847	+	0.882507i	−0.0253561	+	0.999678i	$0.508072\pi$
$168$		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	−0.618361	−	0.785894i	$-0.712203\pi$
$173$	4.64811	−	7.23260i	0.353389	−	0.549885i	0.971751	+	0.236009i	$0.0758396\pi$
$174$		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	0.607826	+	0.794070i	$0.292042\pi$
$179$	−5.22231	+	11.4353i	−0.390334	+	0.854712i	−0.998160	+	0.0606413i	$0.980685\pi$
$180$		0			0
$181$	7.27604	+	15.9323i	0.540824	+	1.18424i	0.960937	+	0.276767i	$0.0892631\pi$
$181$	7.27604	+	15.9323i	0.540824	+	1.18424i	−0.420113	+	0.907472i	$0.638010\pi$
$182$		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	−0.760331	−	0.649536i	$-0.774963\pi$
$191$	3.15748	−	6.91391i	0.228467	−	0.500273i	0.988797	+	0.149264i	$0.0476903\pi$
$192$		0			0
$193$	−1.55588	−	0.999901i	−0.111994	−	0.0719744i	0.483445	−	0.875375i	$-0.339385\pi$
$193$	−1.55588	−	0.999901i	−0.111994	−	0.0719744i	−0.595439	+	0.803401i	$0.703022\pi$
$194$		0			0
$195$	−12.9357	−	13.1437i	−0.926342	−	0.941238i
$196$		0			0
$197$	1.04976	+	7.30122i	0.0747921	+	0.520190i	0.992434	+	0.122781i	$0.0391814\pi$
$197$	1.04976	+	7.30122i	0.0747921	+	0.520190i	−0.917642	+	0.397409i	$0.869909\pi$
$198$		0			0
$199$	11.1805	−	12.9029i	0.792562	−	0.914665i	−0.205387	−	0.978681i	$-0.565845\pi$
$199$	11.1805	−	12.9029i	0.792562	−	0.914665i	0.997949	+	0.0640159i	$0.0203909\pi$
$200$		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	−0.595697	−	0.803209i	$-0.703124\pi$
$211$	5.83106	−	12.7682i	0.401427	−	0.879002i	0.997124	−	0.0757924i	$-0.0241486\pi$
$212$		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	−0.270037	−	0.962850i	$-0.587036\pi$
$223$	9.47470	−	20.7467i	0.634473	−	1.38930i	0.904510	−	0.426452i	$-0.140237\pi$
$224$		0			0
$225$	4.71181	−	2.06162i	0.314120	−	0.137441i
$226$		0			0
$227$	8.02748	+	1.15418i	0.532802	+	0.0766054i	0.403465	−	0.914995i	$-0.367806\pi$
$227$	8.02748	+	1.15418i	0.532802	+	0.0766054i	0.129338	+	0.991601i	$0.458715\pi$
$228$		0			0
$229$	−5.96495	+	9.28164i	−0.394175	+	0.613348i	−0.980451	−	0.196763i	$-0.936957\pi$
$229$	−5.96495	+	9.28164i	−0.394175	+	0.613348i	0.586276	+	0.810111i	$0.300593\pi$
$230$		0			0
$231$	45.7484	+	25.4563i	3.01003	+	1.67490i
$232$		0			0
$233$	−6.11597	+	13.3921i	−0.400671	+	0.877346i	0.596531	+	0.802590i	$0.296545\pi$
$233$	−6.11597	+	13.3921i	−0.400671	+	0.877346i	−0.997202	+	0.0747565i	$0.976182\pi$
$234$		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	0.624793	−	0.780791i	$-0.285183\pi$
$241$	11.3059	+	3.31970i	0.728275	+	0.213841i	0.103482	+	0.994631i	$0.467002\pi$
$242$		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	−0.979698	−	0.200481i	$-0.935749\pi$
$251$	0.266123	−	1.85092i	0.0167975	−	0.116829i	0.996495	+	0.0836521i	$0.0266585\pi$
$252$		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	0.966845	+	0.255365i	$0.0821955\pi$
$257$	4.67380	+	15.9175i	0.291544	+	0.992907i	−0.675301	+	0.737542i	$0.735986\pi$
$258$		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	0.998367	+	0.0571226i	$0.0181926\pi$
$263$	3.07107	+	10.4591i	0.189370	+	0.644935i	−0.808997	+	0.587813i	$0.799989\pi$
$264$		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	$0.126032\pi$
$269$			12.6511i			0.771353i	−0.922634	+	0.385676i	$0.873968\pi$
$270$		0			0
$271$	16.8404	−	7.69077i	1.02298	−	0.467181i	0.167973	−	0.985792i	$-0.446278\pi$
$271$	16.8404	−	7.69077i	1.02298	−	0.467181i	0.855011	+	0.518610i	$0.173550\pi$
$272$		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	−0.832768	−	0.553622i	$-0.813245\pi$
$277$	−2.76721	+	3.19353i	−0.166265	+	0.191880i	0.666503	+	0.745503i	$0.267791\pi$
$278$		0			0
$279$	−17.6871	+	19.7659i	−1.05890	+	1.18335i
$280$		0			0
$281$	1.13085	−	0.726751i	0.0674606	−	0.0433543i	−0.506476	−	0.862254i	$-0.669052\pi$
$281$	1.13085	−	0.726751i	0.0674606	−	0.0433543i	0.573936	+	0.818900i	$0.305416\pi$
$282$		0			0
$283$	−11.0999	−	12.8100i	−0.659821	−	0.761474i	0.322927	−	0.946424i	$-0.395333\pi$
$283$	−11.0999	−	12.8100i	−0.659821	−	0.761474i	−0.982748	+	0.184950i	$0.940788\pi$
$284$		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	−0.979338	−	0.202229i	$-0.935182\pi$
$293$	−12.9485	−	20.1483i	−0.756460	−	1.17708i	0.222878	−	0.974846i	$-0.428455\pi$
$294$		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	−0.0692060	−	0.997602i	$-0.522047\pi$
$307$	−17.6161	−	11.3212i	−1.00541	−	0.646135i	−0.936200	+	0.351467i	$0.885683\pi$
$308$		0			0
$309$	17.0716	+	12.9934i	0.971172	+	0.739170i
$310$		0			0
$311$	3.81967	−	26.5664i	0.216593	−	1.50644i	−0.533892	−	0.845553i	$-0.679271\pi$
$311$	3.81967	−	26.5664i	0.216593	−	1.50644i	0.750485	−	0.660887i	$-0.229820\pi$
$312$		0			0
$313$	−7.13321	−	3.25763i	−0.403193	−	0.184132i	0.203488	−	0.979077i	$-0.434772\pi$
$313$	−7.13321	−	3.25763i	−0.403193	−	0.184132i	−0.606681	+	0.794945i	$0.707499\pi$
$314$		0			0
$315$	31.2160	+	20.7722i	1.75882	+	1.17038i
$316$		0			0
$317$	−27.3537	+	3.93286i	−1.53633	+	0.220892i	−0.857918	−	0.513786i	$-0.828243\pi$
$317$	−27.3537	+	3.93286i	−1.53633	+	0.220892i	−0.678416	+	0.734678i	$0.737333\pi$
$318$		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	−0.290474	−	0.956883i	$-0.593813\pi$
$331$	−5.45068	+	0.783689i	−0.299596	+	0.0430755i	−0.00912255	+	0.999958i	$0.502904\pi$
$332$		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	0.876875	−	0.480719i	$-0.159624\pi$
$337$	9.65316	+	8.36451i	0.525841	+	0.455644i	−0.351033	+	0.936363i	$0.614170\pi$
$338$		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	−0.505923	−	0.862579i	$-0.668848\pi$
$347$	1.27673	−	0.820506i	0.0685386	−	0.0440471i	0.574461	+	0.818532i	$0.305212\pi$
$348$		0			0
$349$	−1.05529	−	7.33972i	−0.0564885	−	0.392886i	−0.998377	−	0.0569591i	$-0.981860\pi$
$349$	−1.05529	−	7.33972i	−0.0564885	−	0.392886i	0.941888	−	0.335927i	$-0.109050\pi$
$350$		0			0
$351$	−6.98059	−	20.1774i	−0.372596	−	1.07699i
$352$		0			0
$353$	−3.05627	−	21.2568i	−0.162669	−	1.13139i	−0.893577	−	0.448910i	$-0.851812\pi$
$353$	−3.05627	−	21.2568i	−0.162669	−	1.13139i	0.730908	−	0.682476i	$-0.239097\pi$
$354$		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	−0.164359	−	0.986401i	$-0.552556\pi$
$359$	−11.3677	−	1.63442i	−0.599962	−	0.0862615i	−0.435603	+	0.900139i	$0.643465\pi$
$360$		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	−0.112097	−	0.993697i	$-0.535757\pi$
$367$	−17.9406	−	8.19319i	−0.936491	−	0.427681i	−0.824394	+	0.566016i	$0.808484\pi$
$368$		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	$0.0379908\pi$
$373$			4.59919i			0.238137i	−0.992886	+	0.119069i	$0.962009\pi$
$374$		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	0.219452	−	0.975623i	$-0.429573\pi$
$379$	21.4242	−	9.78412i	1.10049	−	0.502576i	0.881037	+	0.473047i	$0.156846\pi$
$380$		0			0
$381$	7.72361	−	7.60138i	0.395693	−	0.389430i
$382$		0			0
$383$	−21.9247	−	25.3025i	−1.12030	−	1.29290i	−0.951638	−	0.307223i	$-0.900600\pi$
$383$	−21.9247	−	25.3025i	−1.12030	−	1.29290i	−0.168663	−	0.985674i	$-0.553945\pi$
$384$		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	0.594564	−	0.804049i	$-0.297325\pi$
$389$	−7.57002	−	11.7792i	−0.383815	−	0.597228i	−0.978379	+	0.206820i	$0.933688\pi$
$390$		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	0.139060	−	0.990284i	$-0.455592\pi$
$397$	15.7692	−	4.63025i	0.791433	−	0.232386i	0.652373	+	0.757898i	$0.273774\pi$
$398$		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	0.726265	−	0.687415i	$-0.241254\pi$
$409$	3.01750	+	2.61468i	0.149206	+	0.129288i	−0.577059	+	0.816702i	$0.695800\pi$
$410$		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	0.0388176	−	0.999246i	$-0.487641\pi$
$419$	−4.20561	−	0.604675i	−0.205457	−	0.0295403i	−0.244275	+	0.969706i	$0.578550\pi$
$420$		0			0
$421$	−3.22520	−	3.72208i	−0.157187	−	0.181403i	0.671694	−	0.740829i	$-0.265567\pi$
$421$	−3.22520	−	3.72208i	−0.157187	−	0.181403i	−0.828880	+	0.559426i	$0.811022\pi$
$422$		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	$0.344446\pi$
$431$			36.6610i			1.76590i	−0.469468	+	0.882949i	$0.655554\pi$
$432$		0			0
$433$	−3.85517	+	5.99876i	−0.185268	+	0.288282i	−0.921447	−	0.388505i	$-0.872992\pi$
$433$	−3.85517	+	5.99876i	−0.185268	+	0.288282i	0.736179	+	0.676787i	$0.236628\pi$
$434$		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	−0.0861059	−	0.996286i	$-0.527442\pi$
$443$	5.83435	−	40.5788i	0.277198	−	1.92796i	0.363304	−	0.931671i	$-0.381649\pi$
$444$		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	−0.719989	−	0.693985i	$-0.755853\pi$
$449$	−14.1335	+	6.45457i	−0.667003	+	0.304610i	0.0529862	+	0.998595i	$0.483126\pi$
$450$		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	−0.826516	−	0.562913i	$-0.809680\pi$
$457$	−14.0626	+	9.03746i	−0.657819	+	0.422755i	0.168697	+	0.985668i	$0.446044\pi$
$458$		0			0
$459$	−1.14810	−	0.459801i	−0.0535889	−	0.0214617i
$460$		0			0
$461$	−6.54290	+	10.1810i	−0.304733	+	0.474175i	−0.959520	−	0.281639i	$-0.909122\pi$
$461$	−6.54290	+	10.1810i	−0.304733	+	0.474175i	0.654787	+	0.755813i	$0.272758\pi$
$462$		0			0
$463$	2.13123	−	7.25830i	0.0990466	−	0.337322i	−0.895030	−	0.446007i	$-0.852846\pi$
$463$	2.13123	−	7.25830i	0.0990466	−	0.337322i	0.994076	+	0.108685i	$0.0346639\pi$
$464$		0			0
$465$	14.1631	−	37.0672i	0.656799	−	1.71895i
$466$		0			0
$467$	−7.55982	−	6.55062i	−0.349827	−	0.303127i	0.462167	−	0.886793i	$-0.347072\pi$
$467$	−7.55982	−	6.55062i	−0.349827	−	0.303127i	−0.811994	+	0.583666i	$0.801618\pi$
$468$		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	0.831633	−	0.555325i	$-0.187406\pi$
$479$	20.9351	+	9.56076i	0.956551	+	0.436842i	0.124917	+	0.992167i	$0.460133\pi$
$480$		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	0.466892	−	0.884314i	$-0.345374\pi$
$487$	25.6875	−	3.69331i	1.16401	−	0.167360i	0.697120	+	0.716955i	$0.254465\pi$
$488$		0			0
$489$	−25.4240	−	2.02230i	−1.14971	−	0.0914514i
$490$		0			0
$491$	27.6162	+	12.6119i	1.24630	+	0.569166i	0.925775	−	0.378074i	$-0.123414\pi$
$491$	27.6162	+	12.6119i	1.24630	+	0.569166i	0.320525	+	0.947240i	$0.396141\pi$
$492$		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	$-0.859303\pi$
$499$		−	19.1108i		−	0.855517i	0.903893	−	0.427758i	$-0.140697\pi$
$500$		0			0
$501$	24.2909	−	17.8834i	1.08524	−	0.798972i
$502$		0			0
$503$	24.0623	+	27.7693i	1.07288	+	1.23817i	0.969903	+	0.243491i	$0.0782925\pi$
$503$	24.0623	+	27.7693i	1.07288	+	1.23817i	0.102981	+	0.994683i	$0.467162\pi$
$504$		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	−0.945453	−	0.325757i	$-0.894381\pi$
$509$	0.587268	−	2.00005i	0.0260302	−	0.0886507i	0.971484	+	0.237106i	$0.0761990\pi$
$510$		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	0.843904	−	0.536494i	$-0.180251\pi$
$521$	4.40009	+	5.07797i	0.192771	+	0.222470i	−0.651133	+	0.758964i	$0.725706\pi$
$522$		0			0
$523$	34.4842	−	22.1616i	1.50789	−	0.969061i	0.514105	−	0.857727i	$-0.328124\pi$
$523$	34.4842	−	22.1616i	1.50789	−	0.969061i	0.993783	−	0.111333i	$-0.0355121\pi$
$524$		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	0.973283	+	0.229609i	$0.0737447\pi$
$541$	6.48103	+	22.0724i	0.278641	+	0.948965i	−0.694642	+	0.719356i	$0.744437\pi$
$542$		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	−0.675548	−	0.737316i	$-0.736093\pi$
$547$	−11.8312	−	40.2932i	−0.505864	−	1.72281i	0.169684	−	0.985499i	$-0.445725\pi$
$548$		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	−0.987080	−	0.160227i	$-0.948777\pi$
$557$	−1.65371	+	5.63203i	−0.0700701	+	0.238637i	0.917010	+	0.398864i	$0.130595\pi$
$558$		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	0.680473	−	0.732773i	$-0.261774\pi$
$563$	20.3288	+	5.96908i	0.856757	+	0.251567i	0.176284	+	0.984339i	$0.443592\pi$
$564$		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	−0.756830	−	0.653611i	$-0.773253\pi$
$569$	−5.19009	+	4.49724i	−0.217580	+	0.188534i	0.539250	+	0.842145i	$0.318708\pi$
$570$		0			0
$571$	−8.43609	+	18.4725i	−0.353040	+	0.773049i	0.646906	+	0.762570i	$0.276063\pi$
$571$	−8.43609	+	18.4725i	−0.353040	+	0.773049i	−0.999945	+	0.0104787i	$0.996664\pi$
$572$		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	0.836106	−	0.548568i	$-0.184827\pi$
$577$	35.6420	+	5.12454i	1.48379	+	0.213337i	0.647688	+	0.761906i	$0.275736\pi$
$578$		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	−0.215262	−	0.976556i	$-0.569061\pi$
$587$	3.18875	−	0.936301i	0.131614	−	0.0386453i	0.346876	+	0.937911i	$0.387242\pi$
$588$		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	−0.818922	−	0.573905i	$-0.805428\pi$
$593$	3.67919	−	8.05629i	0.151086	−	0.330832i	0.970008	+	0.243072i	$0.0781552\pi$
$594$		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	0.973157	+	0.230141i	$0.0739186\pi$
$599$	2.55166	+	17.7472i	0.104258	+	0.725129i	−0.868900	+	0.494988i	$0.835172\pi$
$600$		0			0
$601$	4.28571	−	4.94597i	0.174818	−	0.201750i	−0.661578	−	0.749876i	$-0.730113\pi$
$601$	4.28571	−	4.94597i	0.174818	−	0.201750i	0.836396	+	0.548126i	$0.184658\pi$
$602$		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	−0.963741	−	0.266838i	$-0.914021\pi$
$607$	−2.81396	−	19.5715i	−0.114215	−	0.794384i	0.849526	−	0.527546i	$-0.176888\pi$
$608$		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	−0.693410	−	0.720544i	$-0.743892\pi$
$613$	7.55708	−	16.5477i	0.305228	−	0.668355i	0.998637	+	0.0521884i	$0.0166196\pi$
$614$		0			0
$615$	1.29676	+	20.4184i	0.0522903	+	0.823350i
$616$		0			0
$617$	−4.53596	+	0.652173i	−0.182611	+	0.0262555i	−0.233014	−	0.972473i	$-0.574859\pi$
$617$	−4.53596	+	0.652173i	−0.182611	+	0.0262555i	0.0504026	+	0.998729i	$0.483950\pi$
$618$		0			0
$619$	11.7426	−	3.44793i	0.471973	−	0.138584i	−0.0370918	−	0.999312i	$-0.511809\pi$
$619$	11.7426	−	3.44793i	0.471973	−	0.138584i	0.509065	+	0.860728i	$0.329991\pi$
$620$		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	−0.807497	−	0.589872i	$-0.799178\pi$
$631$	1.62062	−	2.52174i	0.0645160	−	0.100389i	0.872013	+	0.489483i	$0.162815\pi$
$632$		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	0.118221	−	0.992987i	$-0.462281\pi$
$643$	−8.09347	−	2.37646i	−0.319175	−	0.0937183i	−0.437396	+	0.899269i	$0.644099\pi$
$644$		0			0
$645$	−16.7777	+	1.06554i	−0.660622	+	0.0419555i
$646$		0			0
$647$	−12.7390	−	27.8944i	−0.500820	−	1.09664i	−0.976202	−	0.216864i	$-0.930417\pi$
$647$	−12.7390	−	27.8944i	−0.500820	−	1.09664i	0.475382	−	0.879780i	$-0.342310\pi$
$648$		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	0.493559	+	0.869712i	$0.335696\pi$
$653$	−5.75048	+	39.9955i	−0.225034	+	1.56514i	−0.718593	+	0.695431i	$0.755213\pi$
$654$		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	0.879385	−	0.476110i	$-0.157954\pi$
$659$	−3.02418	−	10.2994i	−0.117805	−	0.401208i	−0.997191	+	0.0749021i	$0.976136\pi$
$660$		0			0
$661$	−0.415841	−	0.360328i	−0.0161743	−	0.0140151i	0.646736	−	0.762714i	$-0.276134\pi$
$661$	−0.415841	−	0.360328i	−0.0161743	−	0.0140151i	−0.662910	+	0.748699i	$0.730679\pi$
$662$		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	−0.773560	−	0.633724i	$-0.781526\pi$
$673$	−20.7848	+	9.49212i	−0.801197	+	0.365894i	−0.0276375	+	0.999618i	$0.508798\pi$
$674$		0			0
$675$	−8.41853	+	2.91248i	−0.324029	+	0.112101i
$676$		0			0
$677$	−14.3718	+	16.5859i	−0.552352	+	0.637449i	−0.961430	−	0.275051i	$-0.911305\pi$
$677$	−14.3718	+	16.5859i	−0.552352	+	0.637449i	0.409077	+	0.912500i	$0.365851\pi$
$678$		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	−0.999557	−	0.0297686i	$-0.990523\pi$
$683$	−36.2668	+	23.3072i	−1.38771	+	0.891827i	−0.388152	+	0.921595i	$0.626887\pi$
$684$		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	−0.0887557	−	0.996053i	$-0.528289\pi$
$691$	−18.4515	−	5.41786i	−0.701929	−	0.206105i	−0.613173	+	0.789948i	$0.710107\pi$
$692$		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	0.730994	−	0.682384i	$-0.239057\pi$
$701$	10.9597	+	7.04335i	0.413941	+	0.266023i	−0.317053	+	0.948408i	$0.602693\pi$
$702$		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	0.0732489	−	0.997314i	$-0.476663\pi$
$709$	−21.3951	−	13.7498i	−0.803511	−	0.516385i	−0.876760	+	0.480929i	$0.840300\pi$
$710$		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	0.865317	−	0.501225i	$-0.167117\pi$
$719$	49.2521	−	7.08138i	1.83679	−	0.264091i	0.971477	+	0.237134i	$0.0762082\pi$
$720$		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	−0.211376	−	0.977405i	$-0.567795\pi$
$727$	−29.3484	−	13.4030i	−1.08847	−	0.497088i	−0.877095	+	0.480317i	$0.840522\pi$
$728$		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	−0.0132482	−	0.999912i	$-0.504217\pi$
$733$	6.92412	−	0.995538i	0.255748	−	0.0367710i	0.268996	+	0.963141i	$0.413308\pi$
$734$		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	0.911458	−	0.411393i	$-0.134958\pi$
$739$	17.2341	+	14.9334i	0.633966	+	0.549335i	−0.277492	+	0.960728i	$0.589503\pi$
$740$		0			0
$741$	−2.90751	+	7.60942i	−0.106810	+	0.279539i
$742$		0			0
$743$	−8.39865	+	28.6032i	−0.308117	+	1.04935i	0.649274	+	0.760554i	$0.275073\pi$
$743$	−8.39865	+	28.6032i	−0.308117	+	1.04935i	−0.957391	+	0.288795i	$0.906745\pi$
$744$		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	0.922459	+	0.386095i	$0.126176\pi$
$751$	4.00492	+	27.8548i	0.146142	+	1.01644i	−0.776318	+	0.630342i	$0.782915\pi$
$752$		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	0.0980883	−	0.995178i	$-0.468727\pi$
$757$	25.1592	−	11.4898i	0.914428	−	0.417605i	0.816339	+	0.577573i	$0.196000\pi$
$758$		0			0
$759$	17.6835	−	13.0189i	0.641869	−	0.472556i
$760$		0			0
$761$	37.7010	+	5.42058i	1.36666	+	0.196496i	0.786290	−	0.617857i	$-0.211999\pi$
$761$	37.7010	+	5.42058i	1.36666	+	0.196496i	0.580370	+	0.814353i	$0.302908\pi$
$762$		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	−0.0753250	−	0.997159i	$-0.523999\pi$
$769$	−24.3548	−	11.1224i	−0.878255	−	0.401086i	−0.802930	+	0.596073i	$0.796727\pi$
$770$		0			0
$771$	−5.88369	−	28.1250i	−0.211896	−	1.01290i
$772$		0			0
$773$	−0.211784	+	0.329542i	−0.00761734	+	0.0118528i	−0.845041	−	0.534701i	$-0.820424\pi$
$773$	−0.211784	+	0.329542i	−0.00761734	+	0.0118528i	0.837424	+	0.546554i	$0.184061\pi$
$774$		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	0.509737	−	0.860330i	$-0.329743\pi$
$787$	21.2209	+	3.05111i	0.756444	+	0.108760i	0.246706	+	0.969090i	$0.420652\pi$
$788$		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	0.416146	−	0.909298i	$-0.363380\pi$
$797$	−11.9890	−	10.3885i	−0.424672	−	0.367980i	−0.840818	+	0.541317i	$0.817926\pi$
$798$		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	−0.622329	−	0.782756i	$-0.713813\pi$
$809$	−20.5550	+	6.03549i	−0.722676	+	0.212197i	−0.100347	+	0.994953i	$0.531995\pi$
$810$		0			0
$811$	−3.30713	−	2.86565i	−0.116129	−	0.100626i	0.594861	−	0.803829i	$-0.297207\pi$
$811$	−3.30713	−	2.86565i	−0.116129	−	0.100626i	−0.710990	+	0.703202i	$0.751753\pi$
$812$		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	−0.174433	−	0.984669i	$-0.555809\pi$
$821$	−17.7424	−	2.55097i	−0.619213	−	0.0890294i	−0.444780	+	0.895640i	$0.646718\pi$
$822$		0			0
$823$	−3.69498	−	4.26423i	−0.128799	−	0.148642i	0.687687	−	0.726007i	$-0.258626\pi$
$823$	−3.69498	−	4.26423i	−0.128799	−	0.148642i	−0.816486	+	0.577366i	$0.804081\pi$
$824$		0			0
$825$	13.2623	−	13.0524i	0.461733	−	0.454425i
$826$		0			0
$827$	3.69725	−	1.68848i	0.128566	−	0.0587142i	−0.350093	−	0.936715i	$-0.613850\pi$
$827$	3.69725	−	1.68848i	0.128566	−	0.0587142i	0.478659	+	0.878001i	$0.341123\pi$
$828$		0			0
$829$	28.3806	−	18.2391i	0.985699	−	0.633470i	0.0547040	−	0.998503i	$-0.482578\pi$
$829$	28.3806	−	18.2391i	0.985699	−	0.633470i	0.930995	+	0.365032i	$0.118942\pi$
$830$		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	0.693572	−	0.720387i	$-0.256036\pi$
$839$	17.4758	+	7.98095i	0.603333	+	0.275533i	−0.0902390	+	0.995920i	$0.528763\pi$
$840$		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	−0.861181	−	0.508298i	$-0.830275\pi$
$853$	−5.20127	−	36.1756i	−0.178088	−	1.23863i	0.683093	−	0.730331i	$-0.260634\pi$
$854$		0			0
$855$	−6.63057	−	5.93322i	−0.226761	−	0.202912i
$856$		0			0
$857$	−2.91881	−	20.3008i	−0.0997047	−	0.693461i	−0.976958	−	0.213433i	$-0.931536\pi$
$857$	−2.91881	−	20.3008i	−0.0997047	−	0.693461i	0.877253	−	0.480028i	$-0.159374\pi$
$858$		0			0
$859$	33.1077	−	21.2770i	1.12962	−	0.725963i	0.164139	−	0.986437i	$-0.447515\pi$
$859$	33.1077	−	21.2770i	1.12962	−	0.725963i	0.965481	+	0.260474i	$0.0838790\pi$
$860$		0			0
$861$	−30.6695	+	22.5794i	−1.04521	+	0.769505i
$862$		0			0
$863$	−4.68744	+	7.29380i	−0.159562	+	0.248284i	−0.911825	−	0.410580i	$-0.865326\pi$
$863$	−4.68744	+	7.29380i	−0.159562	+	0.248284i	0.752262	+	0.658864i	$0.228963\pi$
$864$		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	−0.0333637	−	0.999443i	$-0.510622\pi$
$877$	−17.8210	−	5.23270i	−0.601771	−	0.176696i	−0.568407	+	0.822747i	$0.692440\pi$
$878$		0			0
$879$	19.5897	+	36.5663i	0.660745	+	1.23335i
$880$		0			0
$881$	−10.7768	−	4.92162i	−0.363081	−	0.165814i	0.225517	−	0.974239i	$-0.427593\pi$
$881$	−10.7768	−	4.92162i	−0.363081	−	0.165814i	−0.588598	+	0.808426i	$0.700320\pi$
$882$		0			0
$883$	8.75570	+	13.6241i	0.294653	+	0.458488i	0.956743	−	0.290936i	$-0.0939667\pi$
$883$	8.75570	+	13.6241i	0.294653	+	0.458488i	−0.662090	+	0.749424i	$0.730330\pi$
$884$		0			0
$885$	14.4101	−	37.7137i	0.484391	−	1.26773i
$886$		0			0
$887$	3.61930	+	12.3262i	0.121524	+	0.413873i	0.997674	−	0.0681656i	$-0.0217146\pi$
$887$	3.61930	+	12.3262i	0.121524	+	0.413873i	−0.876150	+	0.482039i	$0.839896\pi$
$888$		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	0.874918	−	0.484271i	$-0.160915\pi$
$907$	24.0288	+	15.4424i	0.797864	+	0.512756i	−0.0770544	+	0.997027i	$0.524552\pi$
$908$		0			0
$909$	−29.1189	−	46.9397i	−0.965814	−	1.55689i
$910$		0			0
$911$	4.01668	−	13.6796i	0.133079	−	0.453224i	−0.865809	−	0.500374i	$-0.833196\pi$
$911$	4.01668	−	13.6796i	0.133079	−	0.453224i	0.998888	+	0.0471501i	$0.0150139\pi$
$912$		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	−0.489389	+	0.872066i	$0.662780\pi$
$919$	−43.1148	+	37.3592i	−1.42223	+	1.23237i	−0.932837	+	0.360299i	$0.882675\pi$
$920$		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	−0.651236	−	0.758875i	$-0.725749\pi$
$929$	5.87019	−	6.77456i	0.192595	−	0.222266i	0.843831	+	0.536609i	$0.180295\pi$
$930$		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	$0.226116\pi$
$937$			39.9228i			1.30422i	−0.758124	+	0.652110i	$0.773884\pi$
$938$		0			0
$939$	11.8688	+	6.60427i	0.387323	+	0.215522i
$940$		0			0
$941$	11.5091	+	25.2015i	0.375187	+	0.821545i	0.999195	+	0.0401265i	$0.0127761\pi$
$941$	11.5091	+	25.2015i	0.375187	+	0.821545i	−0.624008	+	0.781418i	$0.714497\pi$
$942$		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	0.556484	−	0.830859i	$-0.312150\pi$
$947$	−5.74607	−	4.97900i	−0.186722	−	0.161796i	−0.743206	+	0.669063i	$0.766696\pi$
$948$		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	−0.715793	−	0.698313i	$-0.753935\pi$
$953$	−3.90378	+	3.38265i	−0.126456	+	0.109575i	0.589337	+	0.807887i	$0.299389\pi$
$954$		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	−0.854247	−	0.519868i	$-0.825981\pi$
$971$	−14.3727	+	12.4540i	−0.461242	+	0.399668i	0.393005	+	0.919537i	$0.371436\pi$
$972$		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	−0.390521	−	0.920594i	$-0.627705\pi$
$977$	19.0389	−	29.6252i	0.609109	−	0.947793i	0.999630	−	0.0271986i	$-0.00865865\pi$
$978$		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	0.642510	+	0.766277i	$0.277893\pi$
$983$	−11.2042	+	24.5338i	−0.357358	+	0.782506i	−0.999868	+	0.0162284i	$0.994834\pi$
$984$		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	−0.706380	−	0.707833i	$-0.749673\pi$
$991$	−37.2954	+	5.36227i	−1.18473	+	0.170338i	−0.478347	+	0.878171i	$0.658764\pi$
$992$		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	0.457858	−	0.889025i	$-0.348617\pi$
$997$	−5.07184	−	3.25947i	−0.160627	−	0.103228i	−0.618485	+	0.785797i	$0.712253\pi$
$998$		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.5.1	✓	200
3.2	odd	2	inner	804.2.s.b.5.7	yes	200
67.27	odd	22	inner	804.2.s.b.161.7	yes	200
201.161	even	22	inner	804.2.s.b.161.1	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.1	✓	200	1.1	even	1	trivial
804.2.s.b.5.7	yes	200	3.2	odd	2	inner
804.2.s.b.161.1	yes	200	201.161	even	22	inner
804.2.s.b.161.7	yes	200	67.27	odd	22	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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