LMFDB - Embedded newform 804.2.s.b.161.7

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			161.7
Character	$\chi$	$=$	804.161
Dual form			804.2.s.b.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02689 - 1.39481i) q^{3} +(-2.48625 - 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(-0.891005 + 2.86463i) q^{9} +O(q^{10})$	\(q+(-1.02689 - 1.39481i) q^{3} +(-2.48625 - 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(-0.891005 + 2.86463i) q^{9} +(6.01277 + 1.76551i) q^{11} +(2.22147 - 3.45668i) q^{13} +(1.53484 + 4.21751i) q^{15} +(-0.235591 + 0.0338728i) q^{17} +(-0.749547 + 0.865023i) q^{19} +(-8.14910 - 1.84092i) q^{21} +(-1.84028 - 0.840429i) q^{23} +(1.44221 + 0.926855i) q^{25} +(4.91059 - 1.69887i) q^{27} -0.303522i q^{29} +(-4.77999 - 7.43781i) q^{31} +(-3.71188 - 10.1997i) q^{33} +(-11.3691 + 5.19208i) q^{35} -2.20438 q^{37} +(-7.10262 + 0.451082i) q^{39} +(-0.648759 - 4.51222i) q^{41} +(3.70767 - 0.533082i) q^{43} +(4.30652 - 6.47172i) q^{45} +(-4.93924 - 2.25568i) q^{47} +(2.31483 - 16.1000i) q^{49} +(0.289171 + 0.293821i) q^{51} +(-1.07232 + 7.45815i) q^{53} +(-13.6603 - 8.77897i) q^{55} +(1.97625 + 0.157196i) q^{57} +(4.86335 + 7.56752i) q^{59} +(0.272313 + 0.927412i) q^{61} +(5.80047 + 13.2569i) q^{63} +(-8.04661 + 6.97242i) q^{65} +(6.65218 + 4.76954i) q^{67} +(0.717522 + 3.42988i) q^{69} +(-16.0736 - 2.31103i) q^{71} +(13.2311 - 3.88499i) q^{73} +(-0.188203 - 2.96340i) q^{75} +(27.4951 - 12.5566i) q^{77} +(-1.18099 + 1.83765i) q^{79} +(-7.41222 - 5.10480i) q^{81} +(1.09530 - 3.73026i) q^{83} +(0.610465 + 0.0877716i) q^{85} +(-0.423356 + 0.311683i) q^{87} +(-9.87966 + 4.51189i) q^{89} +(-2.82059 - 19.6176i) q^{91} +(-5.46584 + 14.3050i) q^{93} +(2.49505 - 1.60347i) q^{95} +2.79168i q^{97} +(-10.4149 + 15.6513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.02689	−	1.39481i	−0.592874	−	0.805295i
$3$	−1.02689	−	1.39481i	−0.592874	−	0.805295i
$4$		0			0
$5$	−2.48625	−	0.730028i	−1.11188	−	0.326478i	−0.326320	−	0.945259i	$-0.605809\pi$
$5$	−2.48625	−	0.730028i	−1.11188	−	0.326478i	−0.785564	+	0.618781i	$0.787627\pi$
$6$		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
$9$	−0.891005	+	2.86463i	−0.297002	+	0.954877i
$10$		0			0
$11$	6.01277	+	1.76551i	1.81292	+	0.532320i	0.998827	−	0.0484186i	$-0.0154181\pi$
$11$	6.01277	+	1.76551i	1.81292	+	0.532320i	0.814090	+	0.580739i	$0.197236\pi$
$12$		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
$15$	1.53484	+	4.21751i	0.396295	+	1.08896i
$16$		0			0
$17$	−0.235591	+	0.0338728i	−0.0571391	+	0.00821537i	−0.170825	−	0.985301i	$-0.554643\pi$
$17$	−0.235591	+	0.0338728i	−0.0571391	+	0.00821537i	0.113686	+	0.993517i	$0.463734\pi$
$18$		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
$21$	−8.14910	−	1.84092i	−1.77828	−	0.401721i
$22$		0			0
$23$	−1.84028	−	0.840429i	−0.383725	−	0.175242i	0.214207	−	0.976788i	$-0.431283\pi$
$23$	−1.84028	−	0.840429i	−0.383725	−	0.175242i	−0.597932	+	0.801547i	$0.704011\pi$
$24$		0			0
$25$	1.44221	+	0.926855i	0.288443	+	0.185371i
$26$		0			0
$27$	4.91059	−	1.69887i	0.945043	−	0.326947i
$28$		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	−0.940695	−	0.339253i	$-0.889826\pi$
$31$	−4.77999	−	7.43781i	−0.858511	−	1.33587i	0.0821840	−	0.996617i	$-0.473810\pi$
$32$		0			0
$33$	−3.71188	−	10.1997i	−0.646155	−	1.77553i
$34$		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
$39$	−7.10262	+	0.451082i	−1.13733	+	0.0722309i
$40$		0			0
$41$	−0.648759	−	4.51222i	−0.101319	−	0.704690i	−0.975646	−	0.219352i	$-0.929606\pi$
$41$	−0.648759	−	4.51222i	−0.101319	−	0.704690i	0.874327	−	0.485338i	$-0.161303\pi$
$42$		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
$45$	4.30652	−	6.47172i	0.641978	−	0.964747i
$46$		0			0
$47$	−4.93924	−	2.25568i	−0.720463	−	0.329024i	0.0212204	−	0.999775i	$-0.493245\pi$
$47$	−4.93924	−	2.25568i	−0.720463	−	0.329024i	−0.741683	+	0.670751i	$0.765972\pi$
$48$		0			0
$49$	2.31483	−	16.1000i	0.330691	−	2.30000i
$50$		0			0
$51$	0.289171	+	0.293821i	0.0404921	+	0.0411432i
$52$		0			0
$53$	−1.07232	+	7.45815i	−0.147294	+	1.02446i	0.773329	+	0.634004i	$0.218590\pi$
$53$	−1.07232	+	7.45815i	−0.147294	+	1.02446i	−0.920624	+	0.390451i	$0.872319\pi$
$54$		0			0
$55$	−13.6603	−	8.77897i	−1.84196	−	1.18376i
$56$		0			0
$57$	1.97625	+	0.157196i	0.261760	+	0.0208211i
$58$		0			0
$59$	4.86335	+	7.56752i	0.633155	+	0.985208i	0.998522	+	0.0543445i	$0.0173069\pi$
$59$	4.86335	+	7.56752i	0.633155	+	0.985208i	−0.365368	+	0.930863i	$0.619057\pi$
$60$		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
$63$	5.80047	+	13.2569i	0.730790	+	1.67021i
$64$		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
$69$	0.717522	+	3.42988i	0.0863795	+	0.412908i
$70$		0			0
$71$	−16.0736	−	2.31103i	−1.90758	−	0.274269i	−0.915742	−	0.401767i	$-0.868396\pi$
$71$	−16.0736	−	2.31103i	−1.90758	−	0.274269i	−0.991839	+	0.127498i	$0.959305\pi$
$72$		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
$75$	−0.188203	−	2.96340i	−0.0217318	−	0.342183i
$76$		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
$81$	−7.41222	−	5.10480i	−0.823580	−	0.567200i
$82$		0			0
$83$	1.09530	−	3.73026i	0.120225	−	0.409449i	−0.877285	−	0.479969i	$-0.840648\pi$
$83$	1.09530	−	3.73026i	0.120225	−	0.409449i	0.997510	+	0.0705203i	$0.0224660\pi$
$84$		0			0
$85$	0.610465	+	0.0877716i	0.0662142	+	0.00952016i
$86$		0			0
$87$	−0.423356	+	0.311683i	−0.0453885	+	0.0334159i
$88$		0			0
$89$	−9.87966	+	4.51189i	−1.04724	+	0.478259i	−0.863307	−	0.504679i	$-0.831611\pi$
$89$	−9.87966	+	4.51189i	−1.04724	+	0.478259i	−0.183935	+	0.982938i	$0.558884\pi$
$90$		0			0
$91$	−2.82059	−	19.6176i	−0.295678	−	2.05648i
$92$		0			0
$93$	−5.46584	+	14.3050i	−0.566781	+	1.48336i
$94$		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
$99$	−10.4149	+	15.6513i	−1.04674	+	1.57301i
$100$		0			0
$101$	12.0577	−	13.9154i	1.19979	−	1.38463i	0.296818	−	0.954934i	$-0.404074\pi$
$101$	12.0577	−	13.9154i	1.19979	−	1.38463i	0.902973	−	0.429698i	$-0.141380\pi$
$102$		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	0.952268	−	0.305265i	$-0.0987450\pi$
$107$	−0.143467	−	0.488605i	−0.0138695	−	0.0472352i	−0.966137	+	0.258030i	$0.916927\pi$
$108$		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
$111$	2.26365	+	3.07470i	0.214856	+	0.291837i
$112$		0			0
$113$	6.52185	−	1.91499i	0.613524	−	0.180147i	0.0398163	−	0.999207i	$-0.487323\pi$
$113$	6.52185	−	1.91499i	0.613524	−	0.180147i	0.573708	+	0.819060i	$0.305505\pi$
$114$		0			0
$115$	3.96186	+	3.43297i	0.369445	+	0.320126i
$116$		0			0
$117$	7.92277	+	9.44362i	0.732460	+	0.873063i
$118$		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
$123$	−5.62750	+	5.53844i	−0.507414	+	0.499384i
$124$		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
$129$	−4.55090	−	4.62408i	−0.400685	−	0.407128i
$130$		0			0
$131$	−8.98874	−	4.10502i	−0.785350	−	0.358657i	−0.0179603	−	0.999839i	$-0.505717\pi$
$131$	−8.98874	−	4.10502i	−0.785350	−	0.358657i	−0.767389	+	0.641182i	$0.778445\pi$
$132$		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	$-0.536327\pi$
$137$	8.32825	−	18.2363i	0.711530	−	1.55803i	0.825407	−	0.564539i	$-0.190946\pi$
$138$		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
$141$	1.92580	+	9.20564i	0.162182	+	0.775255i
$142$		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
$147$	−24.8336	+	13.3041i	−2.04824	+	1.09731i
$148$		0			0
$149$	−11.0450	−	9.57056i	−0.904843	−	0.784051i	0.0721340	−	0.997395i	$-0.477019\pi$
$149$	−11.0450	−	9.57056i	−0.904843	−	0.784051i	−0.976977	+	0.213344i	$0.931565\pi$
$150$		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
$153$	0.112879	−	0.705061i	0.00912575	−	0.0570008i
$154$		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
$159$	11.5039	−	6.16299i	0.912316	−	0.488757i
$160$		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
$165$	1.78262	+	28.0686i	0.138776	+	2.18514i
$166$		0			0
$167$	13.1615	+	11.4045i	1.01847	+	0.882507i	0.993112	−	0.117171i	$-0.0373826\pi$
$167$	13.1615	+	11.4045i	1.01847	+	0.882507i	0.0253561	+	0.999678i	$0.491928\pi$
$168$		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	$-0.287797\pi$
$173$	−4.64811	−	7.23260i	−0.353389	−	0.549885i	−0.971751	+	0.236009i	$0.924160\pi$
$174$		0			0
$175$	8.18497	−	1.17682i	0.618725	−	0.0889593i
$176$		0			0
$177$	5.56116	−	14.5545i	0.418003	−	1.09398i
$178$		0			0
$179$	5.22231	+	11.4353i	0.390334	+	0.854712i	0.998160	+	0.0606413i	$0.0193146\pi$
$179$	5.22231	+	11.4353i	0.390334	+	0.854712i	−0.607826	+	0.794070i	$0.707958\pi$
$180$		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
$183$	1.01393	−	1.33217i	0.0749520	−	0.0984771i
$184$		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
$189$	12.5344	−	21.7039i	0.911746	−	1.57873i
$190$		0			0
$191$	−3.15748	−	6.91391i	−0.228467	−	0.500273i	0.760331	−	0.649536i	$-0.225037\pi$
$191$	−3.15748	−	6.91391i	−0.228467	−	0.500273i	−0.988797	+	0.149264i	$0.952310\pi$
$192$		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
$195$	17.9882	+	4.06361i	1.28816	+	0.291001i
$196$		0			0
$197$	−1.04976	+	7.30122i	−0.0747921	+	0.520190i	0.917642	+	0.397409i	$0.130091\pi$
$197$	−1.04976	+	7.30122i	−0.0747921	+	0.520190i	−0.992434	+	0.122781i	$0.960819\pi$
$198$		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
$201$	−0.178426	−	14.1763i	−0.0125852	−	0.999921i
$202$		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
$207$	4.04722	−	4.52290i	0.281301	−	0.314364i
$208$		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
$213$	13.2823	+	24.7928i	0.910087	+	1.69877i
$214$		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
$219$	−19.0056	−	14.4654i	−1.28428	−	0.977482i
$220$		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
$225$	−3.94012	+	3.30558i	−0.262675	+	0.220372i
$226$		0			0
$227$	−8.02748	+	1.15418i	−0.532802	+	0.0766054i	−0.403465	−	0.914995i	$-0.632194\pi$
$227$	−8.02748	+	1.15418i	−0.532802	+	0.0766054i	−0.129338	+	0.991601i	$0.541285\pi$
$228$		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	$0.0238180\pi$
$233$	6.11597	+	13.3921i	0.400671	+	0.877346i	−0.596531	+	0.802590i	$0.703455\pi$
$234$		0			0
$235$	10.6335	+	9.21395i	0.693651	+	0.601052i
$236$		0			0
$237$	3.77591	−	0.239805i	0.245272	−	0.0155770i
$238$		0			0
$239$	22.8427			1.47757			0.738784	−	0.673942i	$-0.235400\pi$
$239$	22.8427			1.47757			0.738784	+	0.673942i	$0.235400\pi$
$240$		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
$243$	0.491277	+	15.5807i	0.0315154	+	0.999503i
$244$		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
$249$	−6.32776	+	2.30281i	−0.401006	+	0.145935i
$250$		0			0
$251$	−0.266123	−	1.85092i	−0.0167975	−	0.116829i	0.979698	−	0.200481i	$-0.0642506\pi$
$251$	−0.266123	−	1.85092i	−0.0167975	−	0.116829i	−0.996495	+	0.0836521i	$0.973342\pi$
$252$		0			0
$253$	−9.58140	−	8.30233i	−0.602378	−	0.521963i
$254$		0			0
$255$	−0.504454	−	0.941615i	−0.0315901	−	0.0589662i
$256$		0			0
$257$	−4.67380	+	15.9175i	−0.291544	+	0.992907i	0.675301	+	0.737542i	$0.264014\pi$
$257$	−4.67380	+	15.9175i	−0.291544	+	0.992907i	−0.966845	+	0.255365i	$0.917805\pi$
$258$		0			0
$259$	−8.03565	+	6.96293i	−0.499311	+	0.432655i
$260$		0			0
$261$	0.869478	+	0.270439i	0.0538193	+	0.0167398i
$262$		0			0
$263$	−3.07107	+	10.4591i	−0.189370	+	0.644935i	0.808997	+	0.587813i	$0.200011\pi$
$263$	−3.07107	+	10.4591i	−0.189370	+	0.644935i	−0.998367	+	0.0571226i	$0.981807\pi$
$264$		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	0.855011	−	0.518610i	$-0.173550\pi$
$271$	16.8404	+	7.69077i	1.02298	+	0.467181i	0.167973	+	0.985792i	$0.446278\pi$
$272$		0			0
$273$	−24.4665	+	24.0793i	−1.48078	+	1.45734i
$274$		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
$279$	25.5656	−	7.06578i	1.53057	−	0.423017i
$280$		0			0
$281$	−1.13085	−	0.726751i	−0.0674606	−	0.0433543i	0.506476	−	0.862254i	$-0.330948\pi$
$281$	−1.13085	−	0.726751i	−0.0674606	−	0.0433543i	−0.573936	+	0.818900i	$0.694584\pi$
$282$		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
$285$	−4.79868	−	1.83354i	−0.284249	−	0.108610i
$286$		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
$291$	3.89387	−	2.86674i	0.228263	−	0.168051i
$292$		0			0
$293$	12.9485	−	20.1483i	0.756460	−	1.17708i	−0.222878	−	0.974846i	$-0.571545\pi$
$293$	12.9485	−	20.1483i	0.756460	−	1.17708i	0.979338	−	0.202229i	$-0.0648185\pi$
$294$		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
$303$	−31.7913	−	2.52877i	−1.82636	−	0.145274i
$304$		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
$309$	20.0408	+	7.65745i	1.14008	+	0.435617i
$310$		0			0
$311$	−3.81967	−	26.5664i	−0.216593	−	1.50644i	−0.750485	−	0.660887i	$-0.770180\pi$
$311$	−3.81967	−	26.5664i	−0.216593	−	1.50644i	0.533892	−	0.845553i	$-0.320729\pi$
$312$		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
$315$	−4.74350	−	37.1944i	−0.267266	−	2.09567i
$316$		0			0
$317$	27.3537	+	3.93286i	1.53633	+	0.220892i	0.857918	−	0.513786i	$-0.171757\pi$
$317$	27.3537	+	3.93286i	1.53633	+	0.220892i	0.678416	+	0.734678i	$0.262667\pi$
$318$		0			0
$319$	0.535870	−	1.82501i	0.0300030	−	0.102181i
$320$		0			0
$321$	−0.534188	+	0.701852i	−0.0298154	+	0.0391736i
$322$		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
$327$	27.8956	−	1.77163i	1.54263	−	0.0979712i
$328$		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
$333$	1.96411	−	6.31473i	0.107633	−	0.346045i
$334$		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
$339$	−9.36825	−	7.13028i	−0.508814	−	0.387264i
$340$		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
$345$	0.719968	−	9.05133i	0.0387618	−	0.487307i
$346$		0			0
$347$	−1.27673	−	0.820506i	−0.0685386	−	0.0440471i	0.505923	−	0.862579i	$-0.331152\pi$
$347$	−1.27673	−	0.820506i	−0.0685386	−	0.0440471i	−0.574461	+	0.818532i	$0.694788\pi$
$348$		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
$351$	5.03629	−	20.7483i	0.268817	−	1.10746i
$352$		0			0
$353$	3.05627	−	21.2568i	0.162669	−	1.13139i	−0.730908	−	0.682476i	$-0.760903\pi$
$353$	3.05627	−	21.2568i	0.162669	−	1.13139i	0.893577	−	0.448910i	$-0.148188\pi$
$354$		0			0
$355$	38.2757	+	17.4799i	2.03146	+	0.927739i
$356$		0			0
$357$	1.98221	+	0.157670i	0.104910	+	0.00834480i
$358$		0			0
$359$	11.3677	−	1.63442i	0.599962	−	0.0862615i	0.164359	−	0.986401i	$-0.447444\pi$
$359$	11.3677	−	1.63442i	0.599962	−	0.0862615i	0.435603	+	0.900139i	$0.356535\pi$
$360$		0			0
$361$	2.51754	+	17.5099i	0.132502	+	0.921571i
$362$		0			0
$363$	−3.10352	−	48.8672i	−0.162892	−	2.56487i
$364$		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
$369$	13.5039	+	2.16195i	0.702984	+	0.112547i
$370$		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
$375$	3.24937	−	14.3838i	0.167797	−	0.742777i
$376$		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
$381$	−2.38790	+	10.5704i	−0.122336	+	0.541537i
$382$		0			0
$383$	21.9247	−	25.3025i	1.12030	−	1.29290i	0.168663	−	0.985674i	$-0.446055\pi$
$383$	21.9247	−	25.3025i	1.12030	−	1.29290i	0.951638	−	0.307223i	$-0.0993996\pi$
$384$		0			0
$385$	−77.5262	+	11.1466i	−3.95110	+	0.568083i
$386$		0			0
$387$	−1.77646	+	11.0961i	−0.0903028	+	0.564045i
$388$		0			0
$389$	7.57002	−	11.7792i	0.383815	−	0.597228i	−0.594564	−	0.804049i	$-0.702675\pi$
$389$	7.57002	−	11.7792i	0.383815	−	0.597228i	0.978379	+	0.206820i	$0.0663116\pi$
$390$		0			0
$391$	0.462021	+	0.135662i	0.0233654	+	0.00686071i
$392$		0			0
$393$	3.50469	+	16.7530i	0.176788	+	0.845077i
$394$		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
$399$	7.70057	−	5.66930i	0.385511	−	0.283820i
$400$		0			0
$401$	−23.8879			−1.19290			−0.596452	−	0.802648i	$-0.703424\pi$
$401$	−23.8879			−1.19290			−0.596452	+	0.802648i	$0.703424\pi$
$402$		0			0
$403$	−36.3287			−1.80966
$404$		0			0
$405$	14.7020	+	18.1029i	0.730547	+	0.899541i
$406$		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
$411$	−33.9884	+	7.11030i	−1.67653	+	0.350725i
$412$		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
$417$	8.29926	−	3.02028i	0.406417	−	0.147904i
$418$		0			0
$419$	4.20561	−	0.604675i	0.205457	−	0.0295403i	−0.0388176	−	0.999246i	$-0.512359\pi$
$419$	4.20561	−	0.604675i	0.205457	−	0.0295403i	0.244275	+	0.969706i	$0.421450\pi$
$420$		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
$423$	10.8626	−	12.1393i	0.528156	−	0.590232i
$424$		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
$429$	−43.5028	−	9.82749i	−2.10034	−	0.474475i
$430$		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	0.736179	−	0.676787i	$-0.236628\pi$
$433$	−3.85517	−	5.99876i	−0.185268	−	0.288282i	−0.921447	+	0.388505i	$0.872992\pi$
$434$		0			0
$435$	1.28010	−	0.465858i	0.0613763	−	0.0223362i
$436$		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
$441$	44.0581	+	20.9763i	2.09800	+	0.998873i
$442$		0			0
$443$	−5.83435	−	40.5788i	−0.277198	−	1.92796i	−0.363304	−	0.931671i	$-0.618351\pi$
$443$	−5.83435	−	40.5788i	−0.277198	−	1.92796i	0.0861059	−	0.996286i	$-0.472558\pi$
$444$		0			0
$445$	27.8571	−	4.00524i	1.32055	−	0.189867i
$446$		0			0
$447$	−2.00715	+	25.2336i	−0.0949351	+	1.19351i
$448$		0			0
$449$	14.1335	+	6.45457i	0.667003	+	0.304610i	0.719989	−	0.693985i	$-0.244147\pi$
$449$	14.1335	+	6.45457i	0.667003	+	0.304610i	−0.0529862	+	0.998595i	$0.516874\pi$
$450$		0			0
$451$	4.06552	−	28.2763i	0.191438	−	1.33148i
$452$		0			0
$453$	−14.5399	+	14.3098i	−0.683146	+	0.672334i
$454$		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
$459$	−1.09934	+	0.566573i	−0.0513129	+	0.0264454i
$460$		0			0
$461$	6.54290	+	10.1810i	0.304733	+	0.474175i	0.959520	−	0.281639i	$-0.0908780\pi$
$461$	6.54290	+	10.1810i	0.304733	+	0.474175i	−0.654787	+	0.755813i	$0.727242\pi$
$462$		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
$465$	24.0325	−	31.5755i	1.11448	−	1.46428i
$466$		0			0
$467$	7.55982	−	6.55062i	0.349827	−	0.303127i	−0.462167	−	0.886793i	$-0.652928\pi$
$467$	7.55982	−	6.55062i	0.349827	−	0.303127i	0.811994	+	0.583666i	$0.198382\pi$
$468$		0			0
$469$	39.3147	−	3.62566i	1.81539	−	0.167417i
$470$		0			0
$471$	−10.1587	+	2.12517i	−0.468088	+	0.0979228i
$472$		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
$477$	−20.4094	−	9.71704i	−0.934482	−	0.444913i
$478$		0			0
$479$	−20.9351	+	9.56076i	−0.956551	+	0.436842i	−0.831633	−	0.555325i	$-0.812594\pi$
$479$	−20.9351	+	9.56076i	−0.956551	+	0.436842i	−0.124917	+	0.992167i	$0.539867\pi$
$480$		0			0
$481$	−4.89697	+	7.61983i	−0.223283	+	0.347434i
$482$		0			0
$483$	13.4495	+	10.2365i	0.611972	+	0.465779i
$484$		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
$489$	−15.1208	−	20.5385i	−0.683788	−	0.928783i
$490$		0			0
$491$	−27.6162	+	12.6119i	−1.24630	+	0.569166i	−0.925775	−	0.378074i	$-0.876586\pi$
$491$	−27.6162	+	12.6119i	−1.24630	+	0.569166i	−0.320525	+	0.947240i	$0.603859\pi$
$492$		0			0
$493$	0.0102811	+	0.0715069i	0.000463039	+	0.00322051i
$494$		0			0
$495$	37.3200	−	31.3098i	1.67741	−	1.40727i
$496$		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
$501$	2.39177	−	30.0690i	0.106856	−	1.34338i
$502$		0			0
$503$	−24.0623	+	27.7693i	−1.07288	+	1.23817i	−0.102981	+	0.994683i	$0.532838\pi$
$503$	−24.0623	+	27.7693i	−1.07288	+	1.23817i	−0.969903	+	0.243491i	$0.921708\pi$
$504$		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	$-0.105619\pi$
$509$	−0.587268	−	2.00005i	−0.0260302	−	0.0886507i	−0.971484	+	0.237106i	$0.923801\pi$
$510$		0			0
$511$	35.9599	−	55.9547i	1.59077	−	2.47529i
$512$		0			0
$513$	−2.21115	+	5.52115i	−0.0976248	+	0.243765i
$514$		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
$519$	−5.31504	+	13.9103i	−0.233304	+	0.610595i
$520$		0			0
$521$	−4.40009	+	5.07797i	−0.192771	+	0.222470i	−0.843904	−	0.536494i	$-0.819749\pi$
$521$	−4.40009	+	5.07797i	−0.192771	+	0.222470i	0.651133	+	0.758964i	$0.274294\pi$
$522$		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
$525$	−10.0465	−	10.2080i	−0.438464	−	0.445515i
$526$		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
$531$	−26.0114	+	7.18901i	−1.12880	+	0.311976i
$532$		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
$543$	−29.6943	+	6.21197i	−1.27430	+	0.266581i
$544$		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
$549$	−2.89933	−	0.0462530i	−0.123740	−	0.00197403i
$550$		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
$555$	−3.38338	−	9.29698i	−0.143616	−	0.394635i
$556$		0			0
$557$	1.65371	+	5.63203i	0.0700701	+	0.238637i	0.987080	−	0.160227i	$-0.0512227\pi$
$557$	1.65371	+	5.63203i	0.0700701	+	0.238637i	−0.917010	+	0.398864i	$0.869405\pi$
$558$		0			0
$559$	6.39379	−	14.0004i	0.270428	−	0.592156i
$560$		0			0
$561$	1.21998	+	2.27721i	0.0515074	+	0.0961440i
$562$		0			0
$563$	−20.3288	+	5.96908i	−0.856757	+	0.251567i	−0.680473	−	0.732773i	$-0.738226\pi$
$563$	−20.3288	+	5.96908i	−0.856757	+	0.251567i	−0.176284	+	0.984339i	$0.556408\pi$
$564$		0			0
$565$	−17.6129			−0.740981
$566$		0			0
$567$	−43.1443	+	4.80425i	−1.81189	+	0.201760i
$568$		0			0
$569$	5.19009	+	4.49724i	0.217580	+	0.188534i	0.756830	−	0.653611i	$-0.226747\pi$
$569$	5.19009	+	4.49724i	0.217580	+	0.188534i	−0.539250	+	0.842145i	$0.681292\pi$
$570$		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
$579$	2.99238	+	1.14337i	0.124359	+	0.0475168i
$580$		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
$585$	−12.8039	−	29.2630i	−0.529374	−	1.20988i
$586$		0			0
$587$	−3.18875	−	0.936301i	−0.131614	−	0.0386453i	0.215262	−	0.976556i	$-0.430939\pi$
$587$	−3.18875	−	0.936301i	−0.131614	−	0.0386453i	−0.346876	+	0.937911i	$0.612758\pi$
$588$		0			0
$589$	10.0167	+	1.44018i	0.412731	+	0.0593418i
$590$		0			0
$591$	11.2618	−	6.03332i	0.463249	−	0.248177i
$592$		0			0
$593$	−3.67919	−	8.05629i	−0.151086	−	0.330832i	0.818922	−	0.573905i	$-0.194572\pi$
$593$	−3.67919	−	8.05629i	−0.151086	−	0.330832i	−0.970008	+	0.243072i	$0.921845\pi$
$594$		0			0
$595$	2.50258	−	1.60831i	0.102596	−	0.0659342i
$596$		0			0
$597$	6.51611	−	28.8445i	0.266687	−	1.18053i
$598$		0			0
$599$	−2.55166	+	17.7472i	−0.104258	+	0.725129i	0.868900	+	0.494988i	$0.164828\pi$
$599$	−2.55166	+	17.7472i	−0.104258	+	0.725129i	−0.973157	+	0.230141i	$0.926081\pi$
$600$		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
$603$	−19.5901	+	14.8064i	−0.797770	+	0.602962i
$604$		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
$609$	−0.558759	+	2.47343i	−0.0226421	+	0.100228i
$610$		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
$615$	18.0346	−	9.66169i	0.727224	−	0.389597i
$616$		0			0
$617$	4.53596	+	0.652173i	0.182611	+	0.0262555i	0.233014	−	0.972473i	$-0.425141\pi$
$617$	4.53596	+	0.652173i	0.182611	+	0.0262555i	−0.0504026	+	0.998729i	$0.516050\pi$
$618$		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
$621$	−10.4646	−	1.00060i	−0.419932	−	0.0401527i
$622$		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
$627$	11.6052	+	4.43426i	0.463466	+	0.177087i
$628$		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
$639$	20.9419	−	43.9857i	0.828447	−	1.74005i
$640$		0			0
$641$	40.6694			1.60634			0.803172	−	0.595747i	$-0.203144\pi$
$641$	40.6694			1.60634			0.803172	+	0.595747i	$0.203144\pi$
$642$		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
$645$	7.93896	+	14.8189i	0.312596	+	0.583494i
$646$		0			0
$647$	12.7390	−	27.8944i	0.500820	−	1.09664i	−0.475382	−	0.879780i	$-0.657690\pi$
$647$	12.7390	−	27.8944i	0.500820	−	1.09664i	0.976202	−	0.216864i	$-0.0695827\pi$
$648$		0			0
$649$	15.8817	+	54.0880i	0.623410	+	2.12314i
$650$		0			0
$651$	25.2602	+	69.4110i	0.990025	+	2.72043i
$652$		0			0
$653$	5.75048	+	39.9955i	0.225034	+	1.56514i	0.718593	+	0.695431i	$0.244787\pi$
$653$	5.75048	+	39.9955i	0.225034	+	1.56514i	−0.493559	+	0.869712i	$0.664304\pi$
$654$		0			0
$655$	19.3514	+	16.7681i	0.756123	+	0.655185i
$656$		0			0
$657$	−0.659876	+	41.3637i	−0.0257442	+	1.61375i
$658$		0			0
$659$	3.02418	−	10.2994i	0.117805	−	0.401208i	−0.879385	−	0.476110i	$-0.842046\pi$
$659$	3.02418	−	10.2994i	0.117805	−	0.401208i	0.997191	+	0.0749021i	$0.0238644\pi$
$660$		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
$663$	1.65803	−	0.346857i	0.0643927	−	0.0134708i
$664$		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
$675$	8.65672	+	2.10127i	0.333197	+	0.0808778i
$676$		0			0
$677$	14.3718	+	16.5859i	0.552352	+	0.637449i	0.961430	−	0.275051i	$-0.0886948\pi$
$677$	14.3718	+	16.5859i	0.552352	+	0.637449i	−0.409077	+	0.912500i	$0.634149\pi$
$678$		0			0
$679$	8.81802	+	10.1765i	0.338405	+	0.390540i
$680$		0			0
$681$	9.85318	+	10.0116i	0.377575	+	0.383646i
$682$		0			0
$683$	36.2668	+	23.3072i	1.38771	+	0.891827i	0.999557	−	0.0297686i	$-0.00947704\pi$
$683$	36.2668	+	23.3072i	1.38771	+	0.891827i	0.388152	+	0.921595i	$0.373113\pi$
$684$		0			0
$685$	−34.0191	+	39.2601i	−1.29980	+	1.50005i
$686$		0			0
$687$	−6.82082	+	17.8512i	−0.260230	+	0.681065i
$688$		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
$693$	11.4717	+	89.9513i	0.435775	+	3.41697i
$694$		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	$-0.760943\pi$
$701$	−10.9597	+	7.04335i	−0.413941	+	0.266023i	0.317053	+	0.948408i	$0.397307\pi$
$702$		0			0
$703$	1.65229	−	1.90684i	0.0623171	−	0.0719178i
$704$		0			0
$705$	1.93236	−	24.2934i	0.0727771	−	0.914942i
$706$		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
$711$	−4.21192	−	5.02044i	−0.157959	−	0.188281i
$712$		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
$717$	−23.4568	−	31.8612i	−0.876012	−	1.18988i
$718$		0			0
$719$	−49.2521	−	7.08138i	−1.83679	−	0.264091i	−0.865317	−	0.501225i	$-0.832883\pi$
$719$	−49.2521	−	7.08138i	−1.83679	−	0.264091i	−0.971477	+	0.237134i	$0.923792\pi$
$720$		0			0
$721$	−16.8322	+	57.3250i	−0.626862	+	2.13490i
$722$		0			0
$723$	−16.2402	−	12.3606i	−0.603980	−	0.459696i
$724$		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
$729$	21.2277	−	16.6849i	0.786211	−	0.617958i
$730$		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
$735$	71.4548	−	14.9482i	2.63565	−	0.551372i
$736$		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
$741$	4.93356	−	6.48204i	0.181239	−	0.238124i
$742$		0			0
$743$	8.39865	+	28.6032i	0.308117	+	1.04935i	0.957391	+	0.288795i	$0.0932545\pi$
$743$	8.39865	+	28.6032i	0.308117	+	1.04935i	−0.649274	+	0.760554i	$0.724927\pi$
$744$		0			0
$745$	20.4739	+	31.8580i	0.750104	+	1.16719i
$746$		0			0
$747$	9.70989	+	6.46132i	0.355266	+	0.236407i
$748$		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
$753$	−2.30841	+	2.27188i	−0.0841233	+	0.0827920i
$754$		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
$759$	−1.74118	+	21.8898i	−0.0632008	+	0.794550i
$760$		0			0
$761$	−37.7010	+	5.42058i	−1.36666	+	0.196496i	−0.786290	−	0.617857i	$-0.788001\pi$
$761$	−37.7010	+	5.42058i	−1.36666	+	0.196496i	−0.580370	+	0.814353i	$0.697092\pi$
$762$		0			0
$763$	11.0779	+	77.0483i	0.401046	+	2.78934i
$764$		0			0
$765$	−0.795360	+	1.67055i	−0.0287563	+	0.0603989i
$766$		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
$771$	27.0014	−	9.82641i	0.972432	−	0.353889i
$772$		0			0
$773$	0.211784	+	0.329542i	0.00761734	+	0.0118528i	0.845041	−	0.534701i	$-0.179576\pi$
$773$	0.211784	+	0.329542i	0.00761734	+	0.0118528i	−0.837424	+	0.546554i	$0.815939\pi$
$774$		0			0
$775$		−	15.1573i		−	0.544465i
$776$		0			0
$777$	17.9637	+	4.05808i	0.644444	+	0.145583i
$778$		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
$783$	−0.515644	−	1.49047i	−0.0184276	−	0.0532650i
$784$		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
$789$	17.7421	−	6.45675i	0.631636	−	0.229866i
$790$		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
$795$	−33.1006	+	6.92457i	−1.17396	+	0.245589i
$796$		0			0
$797$	11.9890	−	10.3885i	0.424672	−	0.367980i	−0.416146	−	0.909298i	$-0.636620\pi$
$797$	11.9890	−	10.3885i	0.424672	−	0.367980i	0.840818	+	0.541317i	$0.182074\pi$
$798$		0			0
$799$	1.24005	+	0.364110i	0.0438697	+	0.0128813i
$800$		0			0
$801$	−4.12208	−	32.3217i	−0.145646	−	1.14203i
$802$		0			0
$803$	86.4143			3.04949
$804$		0			0
$805$	25.2859			0.891210
$806$		0			0
$807$	17.6459	−	12.9913i	0.621167	−	0.457315i
$808$		0			0
$809$	20.5550	+	6.03549i	0.722676	+	0.212197i	0.622329	−	0.782756i	$-0.286187\pi$
$809$	20.5550	+	6.03549i	0.722676	+	0.212197i	0.100347	+	0.994953i	$0.468005\pi$
$810$		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
$813$	−6.56605	−	31.3868i	−0.230281	−	1.10078i
$814$		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
$819$	58.7104	+	9.39945i	2.05151	+	0.328443i
$820$		0			0
$821$	17.7424	−	2.55097i	0.619213	−	0.0890294i	0.174433	−	0.984669i	$-0.444191\pi$
$821$	17.7424	−	2.55097i	0.619213	−	0.0890294i	0.444780	+	0.895640i	$0.353282\pi$
$822$		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
$825$	4.10028	−	18.1505i	0.142753	−	0.631918i
$826$		0			0
$827$	−3.69725	−	1.68848i	−0.128566	−	0.0587142i	0.350093	−	0.936715i	$-0.386150\pi$
$827$	−3.69725	−	1.68848i	−0.128566	−	0.0587142i	−0.478659	+	0.878001i	$0.658877\pi$
$828$		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
$831$	−1.61276	+	7.13912i	−0.0559461	+	0.247653i
$832$		0			0
$833$			3.87143i			0.134137i
$834$		0			0
$835$	−24.3971	−	37.9627i	−0.844298	−	1.31375i
$836$		0			0
$837$	−36.1084	−	28.4034i	−1.24809	−	0.981766i
$838$		0			0
$839$	−17.4758	+	7.98095i	−0.603333	+	0.275533i	−0.693572	−	0.720387i	$-0.743964\pi$
$839$	−17.4758	+	7.98095i	−0.603333	+	0.275533i	0.0902390	+	0.995920i	$0.471237\pi$
$840$		0			0
$841$	28.9079			0.996823
$842$		0			0
$843$	0.147571	+	2.32361i	0.00508260	+	0.0800294i
$844$		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
$849$	29.2659	+	2.32789i	1.00440	+	0.0798929i
$850$		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
$855$	2.37025	+	8.57610i	0.0810609	+	0.293296i
$856$		0			0
$857$	2.91881	−	20.3008i	0.0997047	−	0.693461i	−0.877253	−	0.480028i	$-0.840626\pi$
$857$	2.91881	−	20.3008i	0.0997047	−	0.693461i	0.976958	−	0.213433i	$-0.0684645\pi$
$858$		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
$861$	−3.01983	+	37.9648i	−0.102915	+	1.29384i
$862$		0			0
$863$	4.68744	+	7.29380i	0.159562	+	0.248284i	0.911825	−	0.410580i	$-0.134674\pi$
$863$	4.68744	+	7.29380i	0.159562	+	0.248284i	−0.752262	+	0.658864i	$0.771037\pi$
$864$		0			0
$865$	6.27635	+	21.3753i	0.213402	+	0.726782i
$866$		0			0
$867$	23.3523	+	17.7737i	0.793084	+	0.603625i
$868$		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
$873$	−7.99713	−	2.48740i	−0.270662	−	0.0841857i
$874$		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
$879$	−41.3997	+	2.62926i	−1.39638	+	0.0886829i
$880$		0			0
$881$	10.7768	−	4.92162i	0.363081	−	0.165814i	−0.225517	−	0.974239i	$-0.572407\pi$
$881$	10.7768	−	4.92162i	0.363081	−	0.165814i	0.588598	+	0.808426i	$0.299680\pi$
$882$		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
$885$	−24.4516	+	32.1262i	−0.821931	+	1.07991i
$886$		0			0
$887$	−3.61930	+	12.3262i	−0.121524	+	0.413873i	−0.997674	−	0.0681656i	$-0.978285\pi$
$887$	−3.61930	+	12.3262i	−0.121524	+	0.413873i	0.876150	+	0.482039i	$0.160104\pi$
$888$		0			0
$889$	−29.8712	−	4.29482i	−1.00185	−	0.144044i
$890$		0			0
$891$	−35.5554	−	43.7803i	−1.19115	−	1.46669i
$892$		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
$897$	13.4499	+	5.13913i	0.449080	+	0.171591i
$898$		0			0
$899$	−2.25754	+	1.45083i	−0.0752931	+	0.0483879i
$900$		0			0
$901$		−	1.79339i		−	0.0597466i
$902$		0			0
$903$	−31.1955	−	2.48138i	−1.03812	−	0.0825750i
$904$		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	0.865809	−	0.500374i	$-0.166804\pi$
$911$	−4.01668	−	13.6796i	−0.133079	−	0.453224i	−0.998888	+	0.0471501i	$0.984986\pi$
$912$		0			0
$913$	13.1716	−	20.4954i	0.435916	−	0.678299i
$914$		0			0
$915$	−3.49341	+	2.57191i	−0.115488	+	0.0850248i
$916$		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
$921$	33.8808	+	12.9456i	1.11641	+	0.426572i
$922$		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
$927$	−9.89892	−	35.8165i	−0.325123	−	1.17637i
$928$		0			0
$929$	−5.87019	−	6.77456i	−0.192595	−	0.222266i	0.651236	−	0.758875i	$-0.274251\pi$
$929$	−5.87019	−	6.77456i	−0.192595	−	0.222266i	−0.843831	+	0.536609i	$0.819705\pi$
$930$		0			0
$931$	12.1918	+	14.0701i	0.399571	+	0.461129i
$932$		0			0
$933$	−33.1327	+	32.6084i	−1.08472	+	1.06755i
$934$		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	$0.285503\pi$
$941$	−11.5091	+	25.2015i	−0.375187	+	0.821545i	−0.999195	+	0.0401265i	$0.987224\pi$
$942$		0			0
$943$	−2.59830	+	8.84899i	−0.0846123	+	0.288163i
$944$		0			0
$945$	−47.0081	+	44.8107i	−1.52918	+	1.45769i
$946$		0			0
$947$	5.74607	−	4.97900i	0.186722	−	0.161796i	−0.556484	−	0.830859i	$-0.687850\pi$
$947$	5.74607	−	4.97900i	0.186722	−	0.161796i	0.743206	+	0.669063i	$0.233304\pi$
$948$		0			0
$949$	15.9633	−	54.3660i	0.518190	−	1.76479i
$950$		0			0
$951$	−22.6035	−	42.1918i	−0.732970	−	1.36816i
$952$		0			0
$953$	3.90378	+	3.38265i	0.126456	+	0.109575i	0.715793	−	0.698313i	$-0.246065\pi$
$953$	3.90378	+	3.38265i	0.126456	+	0.109575i	−0.589337	+	0.807887i	$0.700611\pi$
$954$		0			0
$955$	2.80292	+	19.4947i	0.0907003	+	0.630834i
$956$		0			0
$957$	−3.09582	+	1.12664i	−0.100074	+	0.0364190i
$958$		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
$963$	1.52750	+	0.0243683i	0.0492231	+	0.000785258i
$964$		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
$969$	−0.470910	+	0.0299071i	−0.0151278	+	0.000960754i
$970$		0			0
$971$	14.3727	+	12.4540i	0.461242	+	0.399668i	0.854247	−	0.519868i	$-0.174019\pi$
$971$	14.3727	+	12.4540i	0.461242	+	0.399668i	−0.393005	+	0.919537i	$0.628564\pi$
$972$		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	$-0.991341\pi$
$977$	−19.0389	−	29.6252i	−0.609109	−	0.947793i	0.390521	−	0.920594i	$-0.372295\pi$
$978$		0			0
$979$	−67.3699	+	9.68632i	−2.15315	+	0.309576i
$980$		0			0
$981$	−31.1167	−	37.0899i	−0.993481	−	1.18419i
$982$		0			0
$983$	11.2042	+	24.5338i	0.357358	+	0.782506i	0.999868	+	0.0162284i	$0.00516588\pi$
$983$	11.2042	+	24.5338i	0.357358	+	0.782506i	−0.642510	+	0.766277i	$0.722107\pi$
$984$		0			0
$985$	7.94005	−	17.3863i	0.252991	−	0.553973i
$986$		0			0
$987$	36.0978	+	27.4745i	1.14901	+	0.874522i
$988$		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
$993$	4.50413	+	8.40744i	0.142934	+	0.266802i
$994$		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
$999$	−10.8248	+	3.74495i	−0.342481	+	0.118485i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-1.02689 - 1.39481i) q^{3} +(-2.48625 - 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(-0.891005 + 2.86463i) q^{9} +O(q^{10})\)	\(q+(-1.02689 - 1.39481i) q^{3} +(-2.48625 - 0.730028i) q^{5} +(3.64531 - 3.15868i) q^{7} +(-0.891005 + 2.86463i) q^{9} +(6.01277 + 1.76551i) q^{11} +(2.22147 - 3.45668i) q^{13} +(1.53484 + 4.21751i) q^{15} +(-0.235591 + 0.0338728i) q^{17} +(-0.749547 + 0.865023i) q^{19} +(-8.14910 - 1.84092i) q^{21} +(-1.84028 - 0.840429i) q^{23} +(1.44221 + 0.926855i) q^{25} +(4.91059 - 1.69887i) q^{27} -0.303522i q^{29} +(-4.77999 - 7.43781i) q^{31} +(-3.71188 - 10.1997i) q^{33} +(-11.3691 + 5.19208i) q^{35} -2.20438 q^{37} +(-7.10262 + 0.451082i) q^{39} +(-0.648759 - 4.51222i) q^{41} +(3.70767 - 0.533082i) q^{43} +(4.30652 - 6.47172i) q^{45} +(-4.93924 - 2.25568i) q^{47} +(2.31483 - 16.1000i) q^{49} +(0.289171 + 0.293821i) q^{51} +(-1.07232 + 7.45815i) q^{53} +(-13.6603 - 8.77897i) q^{55} +(1.97625 + 0.157196i) q^{57} +(4.86335 + 7.56752i) q^{59} +(0.272313 + 0.927412i) q^{61} +(5.80047 + 13.2569i) q^{63} +(-8.04661 + 6.97242i) q^{65} +(6.65218 + 4.76954i) q^{67} +(0.717522 + 3.42988i) q^{69} +(-16.0736 - 2.31103i) q^{71} +(13.2311 - 3.88499i) q^{73} +(-0.188203 - 2.96340i) q^{75} +(27.4951 - 12.5566i) q^{77} +(-1.18099 + 1.83765i) q^{79} +(-7.41222 - 5.10480i) q^{81} +(1.09530 - 3.73026i) q^{83} +(0.610465 + 0.0877716i) q^{85} +(-0.423356 + 0.311683i) q^{87} +(-9.87966 + 4.51189i) q^{89} +(-2.82059 - 19.6176i) q^{91} +(-5.46584 + 14.3050i) q^{93} +(2.49505 - 1.60347i) q^{95} +2.79168i q^{97} +(-10.4149 + 15.6513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 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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