LMFDB - Embedded newform 804.2.y.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	804.49
Dual form			804.2.y.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{3} +(-0.185691 - 1.29151i) q^{5} +(-3.04666 - 0.290921i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{3} +(-0.185691 - 1.29151i) q^{5} +(-3.04666 - 0.290921i) q^{7} +(0.415415 + 0.909632i) q^{9} +(0.984578 + 0.394165i) q^{11} +(-3.94453 - 3.76110i) q^{13} +(0.542029 - 1.18688i) q^{15} +(2.13643 - 6.17282i) q^{17} +(4.77112 - 0.455586i) q^{19} +(-2.40573 - 1.89189i) q^{21} +(0.276717 - 5.80900i) q^{23} +(3.16395 - 0.929019i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(-2.17185 + 3.76175i) q^{29} +(3.99906 - 3.81309i) q^{31} +(0.615178 + 0.863896i) q^{33} +(0.190011 + 3.98882i) q^{35} +(-4.12673 - 7.14771i) q^{37} +(-1.28495 - 5.29662i) q^{39} +(-7.07470 + 1.36354i) q^{41} +(-0.627646 - 0.724342i) q^{43} +(1.09766 - 0.705423i) q^{45} +(-5.79658 + 2.98835i) q^{47} +(2.32402 + 0.447919i) q^{49} +(5.13456 - 4.03786i) q^{51} +(-4.13821 + 4.77575i) q^{53} +(0.326241 - 1.34478i) q^{55} +(4.26003 + 2.19620i) q^{57} +(9.27800 + 2.72427i) q^{59} +(1.51948 - 0.608306i) q^{61} +(-1.00100 - 2.89220i) q^{63} +(-4.12504 + 5.79280i) q^{65} +(-6.77501 - 4.59340i) q^{67} +(3.37337 - 4.73724i) q^{69} +(4.38663 + 12.6743i) q^{71} +(11.3932 - 4.56114i) q^{73} +(3.16395 + 0.929019i) q^{75} +(-2.88501 - 1.48732i) q^{77} +(1.15448 - 4.75883i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(2.64377 - 2.07909i) q^{83} +(-8.36897 - 1.61299i) q^{85} +(-3.86083 + 1.99040i) q^{87} +(-9.00151 + 5.78492i) q^{89} +(10.9235 + 12.6064i) q^{91} +(5.42574 - 1.04573i) q^{93} +(-1.47435 - 6.07734i) q^{95} +(8.48076 + 14.6891i) q^{97} +(0.0504629 + 1.05935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{23}{33}\right)$	$1$

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
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$		0			0
$5$	−0.185691	−	1.29151i	−0.0830435	−	0.577581i	−0.988278	−	0.152667i	$-0.951214\pi$
$5$	−0.185691	−	1.29151i	−0.0830435	−	0.577581i	0.905234	−	0.424913i	$-0.139695\pi$
$6$		0			0
$7$	−3.04666	−	0.290921i	−1.15153	−	0.109958i	−0.498222	−	0.867049i	$-0.666014\pi$
$7$	−3.04666	−	0.290921i	−1.15153	−	0.109958i	−0.653309	+	0.757092i	$0.726620\pi$
$8$		0			0
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$		0			0
$11$	0.984578	+	0.394165i	0.296861	+	0.118845i	0.515312	−	0.857003i	$-0.327676\pi$
$11$	0.984578	+	0.394165i	0.296861	+	0.118845i	−0.218451	+	0.975848i	$0.570100\pi$
$12$		0			0
$13$	−3.94453	−	3.76110i	−1.09402	−	1.04314i	−0.998863	−	0.0476797i	$-0.984817\pi$
$13$	−3.94453	−	3.76110i	−1.09402	−	1.04314i	−0.0951535	−	0.995463i	$-0.530334\pi$
$14$		0			0
$15$	0.542029	−	1.18688i	0.139951	−	0.306451i
$16$		0			0
$17$	2.13643	−	6.17282i	0.518161	−	1.49713i	−0.317702	−	0.948191i	$-0.602911\pi$
$17$	2.13643	−	6.17282i	0.518161	−	1.49713i	0.835863	−	0.548938i	$-0.184968\pi$
$18$		0			0
$19$	4.77112	−	0.455586i	1.09457	−	0.104519i	0.467883	−	0.883790i	$-0.345017\pi$
$19$	4.77112	−	0.455586i	1.09457	−	0.104519i	0.626686	+	0.779272i	$0.284411\pi$
$20$		0			0
$21$	−2.40573	−	1.89189i	−0.524974	−	0.412844i
$22$		0			0
$23$	0.276717	−	5.80900i	0.0576994	−	1.21126i	−0.765473	−	0.643468i	$-0.777495\pi$
$23$	0.276717	−	5.80900i	0.0576994	−	1.21126i	0.823172	−	0.567792i	$-0.192202\pi$
$24$		0			0
$25$	3.16395	−	0.929019i	0.632790	−	0.185804i
$26$		0			0
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$		0			0
$29$	−2.17185	+	3.76175i	−0.403302	+	0.698540i	−0.994122	−	0.108264i	$-0.965471\pi$
$29$	−2.17185	+	3.76175i	−0.403302	+	0.698540i	0.590820	+	0.806803i	$0.298804\pi$
$30$		0			0
$31$	3.99906	−	3.81309i	0.718252	−	0.684852i	−0.240001	−	0.970773i	$-0.577148\pi$
$31$	3.99906	−	3.81309i	0.718252	−	0.684852i	0.958253	+	0.285921i	$0.0922993\pi$
$32$		0			0
$33$	0.615178	+	0.863896i	0.107089	+	0.150385i
$34$		0			0
$35$	0.190011	+	3.98882i	0.0321177	+	0.674233i
$36$		0			0
$37$	−4.12673	−	7.14771i	−0.678431	−	1.17508i	−0.975453	−	0.220206i	$-0.929327\pi$
$37$	−4.12673	−	7.14771i	−0.678431	−	1.17508i	0.297022	−	0.954871i	$-0.404006\pi$
$38$		0			0
$39$	−1.28495	−	5.29662i	−0.205756	−	0.848137i
$40$		0			0
$41$	−7.07470	+	1.36354i	−1.10488	+	0.212949i	−0.708900	−	0.705309i	$-0.750808\pi$
$41$	−7.07470	+	1.36354i	−1.10488	+	0.212949i	−0.395983	+	0.918258i	$0.629596\pi$
$42$		0			0
$43$	−0.627646	−	0.724342i	−0.0957151	−	0.110461i	0.705871	−	0.708340i	$-0.250556\pi$
$43$	−0.627646	−	0.724342i	−0.0957151	−	0.110461i	−0.801586	+	0.597879i	$0.796010\pi$
$44$		0			0
$45$	1.09766	−	0.705423i	0.163629	−	0.105158i
$46$		0			0
$47$	−5.79658	+	2.98835i	−0.845519	+	0.435895i	−0.825836	−	0.563911i	$-0.809296\pi$
$47$	−5.79658	+	2.98835i	−0.845519	+	0.435895i	−0.0196832	+	0.999806i	$0.506266\pi$
$48$		0			0
$49$	2.32402	+	0.447919i	0.332003	+	0.0639884i
$50$		0			0
$51$	5.13456	−	4.03786i	0.718982	−	0.565414i
$52$		0			0
$53$	−4.13821	+	4.77575i	−0.568427	+	0.656000i	−0.965076	−	0.261971i	$-0.915628\pi$
$53$	−4.13821	+	4.77575i	−0.568427	+	0.656000i	0.396649	+	0.917970i	$0.370173\pi$
$54$		0			0
$55$	0.326241	−	1.34478i	0.0439904	−	0.181331i
$56$		0			0
$57$	4.26003	+	2.19620i	0.564255	+	0.290893i
$58$		0			0
$59$	9.27800	+	2.72427i	1.20789	+	0.354669i	0.822866	−	0.568236i	$-0.192374\pi$
$59$	9.27800	+	2.72427i	1.20789	+	0.354669i	0.385027	+	0.922905i	$0.374192\pi$
$60$		0			0
$61$	1.51948	−	0.608306i	0.194549	−	0.0778857i	−0.272342	−	0.962200i	$-0.587798\pi$
$61$	1.51948	−	0.608306i	0.194549	−	0.0778857i	0.466891	+	0.884315i	$0.345374\pi$
$62$		0			0
$63$	−1.00100	−	2.89220i	−0.126114	−	0.364382i
$64$		0			0
$65$	−4.12504	+	5.79280i	−0.511648	+	0.718509i
$66$		0			0
$67$	−6.77501	−	4.59340i	−0.827699	−	0.561173i
$67$	−6.77501	−	4.59340i	−0.827699	−	0.561173i
$68$		0			0
$69$	3.37337	−	4.73724i	0.406106	−	0.570296i
$70$		0			0
$71$	4.38663	+	12.6743i	0.520597	+	1.50417i	0.832485	+	0.554048i	$0.186918\pi$
$71$	4.38663	+	12.6743i	0.520597	+	1.50417i	−0.311888	+	0.950119i	$0.600961\pi$
$72$		0			0
$73$	11.3932	−	4.56114i	1.33347	−	0.533841i	0.408111	−	0.912933i	$-0.366188\pi$
$73$	11.3932	−	4.56114i	1.33347	−	0.533841i	0.925359	+	0.379092i	$0.123764\pi$
$74$		0			0
$75$	3.16395	+	0.929019i	0.365341	+	0.107274i
$76$		0			0
$77$	−2.88501	−	1.48732i	−0.328777	−	0.169496i
$78$		0			0
$79$	1.15448	−	4.75883i	0.129889	−	0.535410i	−0.869267	−	0.494342i	$-0.835409\pi$
$79$	1.15448	−	4.75883i	0.129889	−	0.535410i	0.999156	−	0.0410675i	$-0.0130759\pi$
$80$		0			0
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$		0			0
$83$	2.64377	−	2.07909i	0.290192	−	0.228209i	−0.462441	−	0.886650i	$-0.653026\pi$
$83$	2.64377	−	2.07909i	0.290192	−	0.228209i	0.752632	+	0.658441i	$0.228784\pi$
$84$		0			0
$85$	−8.36897	−	1.61299i	−0.907743	−	0.174953i
$86$		0			0
$87$	−3.86083	+	1.99040i	−0.413924	+	0.213393i
$88$		0			0
$89$	−9.00151	+	5.78492i	−0.954158	+	0.613200i	−0.922376	−	0.386294i	$-0.873755\pi$
$89$	−9.00151	+	5.78492i	−0.954158	+	0.613200i	−0.0317829	+	0.999495i	$0.510119\pi$
$90$		0			0
$91$	10.9235	+	12.6064i	1.14509	+	1.32151i
$92$		0			0
$93$	5.42574	−	1.04573i	0.562623	−	0.108437i
$94$		0			0
$95$	−1.47435	−	6.07734i	−0.151265	−	0.623522i
$96$		0			0
$97$	8.48076	+	14.6891i	0.861091	+	1.49145i	0.870877	+	0.491501i	$0.163552\pi$
$97$	8.48076	+	14.6891i	0.861091	+	1.49145i	−0.00978577	+	0.999952i	$0.503115\pi$
$98$		0			0
$99$	0.0504629	+	1.05935i	0.00507171	+	0.106468i
$100$		0			0
$101$	−3.43908	−	4.82951i	−0.342201	−	0.480554i	0.607232	−	0.794525i	$-0.292280\pi$
$101$	−3.43908	−	4.82951i	−0.342201	−	0.480554i	−0.949433	+	0.313971i	$0.898341\pi$
$102$		0			0
$103$	−5.12501	+	4.88669i	−0.504982	+	0.481500i	−0.899213	−	0.437512i	$-0.855860\pi$
$103$	−5.12501	+	4.88669i	−0.504982	+	0.481500i	0.394230	+	0.919012i	$0.371011\pi$
$104$		0			0
$105$	−1.99667	+	3.45833i	−0.194855	+	0.337499i
$106$		0			0
$107$	1.09424	−	7.61059i	0.105784	−	0.735744i	−0.866030	−	0.499993i	$-0.833336\pi$
$107$	1.09424	−	7.61059i	0.105784	−	0.735744i	0.971814	−	0.235751i	$-0.0757549\pi$
$108$		0			0
$109$	19.1723	−	5.62949i	1.83637	−	0.539207i	0.836411	−	0.548102i	$-0.184649\pi$
$109$	19.1723	−	5.62949i	1.83637	−	0.539207i	0.999960	+	0.00889465i	$0.00283129\pi$
$110$		0			0
$111$	0.392716	−	8.24412i	0.0372749	−	0.782497i
$112$		0			0
$113$	−9.36654	−	7.36593i	−0.881130	−	0.692928i	0.0713757	−	0.997450i	$-0.477261\pi$
$113$	−9.36654	−	7.36593i	−0.881130	−	0.692928i	−0.952506	+	0.304521i	$0.901503\pi$
$114$		0			0
$115$	−7.55376	+	0.721297i	−0.704392	+	0.0672613i
$116$		0			0
$117$	1.78260	−	5.15049i	0.164802	−	0.476163i
$118$		0			0
$119$	−8.30480	+	18.1850i	−0.761300	+	1.66701i
$120$		0			0
$121$	−7.14705	−	6.81470i	−0.649732	−	0.619518i
$122$		0			0
$123$	−6.68880	−	2.67779i	−0.603109	−	0.241448i
$124$		0			0
$125$	−4.49750	−	9.84815i	−0.402269	−	0.880846i
$126$		0			0
$127$	5.00711	+	0.478121i	0.444309	+	0.0424264i	0.314813	−	0.949154i	$-0.398058\pi$
$127$	5.00711	+	0.478121i	0.444309	+	0.0424264i	0.129496	+	0.991580i	$0.458664\pi$
$128$		0			0
$129$	−0.136400	−	0.948686i	−0.0120094	−	0.0835272i
$130$		0			0
$131$	10.8623	+	6.98078i	0.949045	+	0.609914i	0.920946	−	0.389691i	$-0.127418\pi$
$131$	10.8623	+	6.98078i	0.949045	+	0.609914i	0.0280991	+	0.999605i	$0.491055\pi$
$132$		0			0
$133$	−14.6685			−1.27192
$134$		0			0
$135$	1.30479			0.112298
$136$		0			0
$137$	−3.89126	−	2.50076i	−0.332453	−	0.213654i	0.363755	−	0.931495i	$-0.381495\pi$
$137$	−3.89126	−	2.50076i	−0.332453	−	0.213654i	−0.696208	+	0.717840i	$0.745131\pi$
$138$		0			0
$139$	0.110306	+	0.767197i	0.00935606	+	0.0650728i	0.993965	−	0.109702i	$-0.0349895\pi$
$139$	0.110306	+	0.767197i	0.00935606	+	0.0650728i	−0.984609	+	0.174774i	$0.944080\pi$
$140$		0			0
$141$	−6.49202	−	0.619913i	−0.546727	−	0.0522061i
$142$		0			0
$143$	−2.40120	−	5.25790i	−0.200799	−	0.439687i
$144$		0			0
$145$	5.26163	+	2.10644i	0.436954	+	0.174930i
$146$		0			0
$147$	1.71293	+	1.63328i	0.141280	+	0.134710i
$148$		0			0
$149$	−9.31225	+	20.3910i	−0.762890	+	1.67050i	−0.0211785	+	0.999776i	$0.506742\pi$
$149$	−9.31225	+	20.3910i	−0.762890	+	1.67050i	−0.741711	+	0.670719i	$0.765985\pi$
$150$		0			0
$151$	4.46963	−	12.9141i	0.363733	−	1.05094i	−0.603569	−	0.797311i	$-0.706255\pi$
$151$	4.46963	−	12.9141i	0.363733	−	1.05094i	0.967302	−	0.253627i	$-0.0816235\pi$
$152$		0			0
$153$	6.50250	−	0.620914i	0.525696	−	0.0501979i
$154$		0			0
$155$	−5.66724	−	4.45676i	−0.455203	−	0.357976i
$156$		0			0
$157$	−0.587951	+	12.3426i	−0.0469236	+	0.985048i	0.845535	+	0.533919i	$0.179281\pi$
$157$	−0.587951	+	12.3426i	−0.0469236	+	0.985048i	−0.892459	+	0.451129i	$0.851022\pi$
$158$		0			0
$159$	−6.06325	+	1.78033i	−0.480847	+	0.141189i
$160$		0			0
$161$	−2.53302	+	17.6176i	−0.199630	+	1.38846i
$162$		0			0
$163$	4.44442	−	7.69795i	0.348113	−	0.602950i	−0.637801	−	0.770201i	$-0.720156\pi$
$163$	4.44442	−	7.69795i	0.348113	−	0.602950i	0.985914	+	0.167251i	$0.0534891\pi$
$164$		0			0
$165$	1.00150	−	0.954925i	0.0779664	−	0.0743408i
$166$		0			0
$167$	13.2162	+	18.5595i	1.02270	+	1.43618i	0.895904	+	0.444247i	$0.146529\pi$
$167$	13.2162	+	18.5595i	1.02270	+	1.43618i	0.126792	+	0.991929i	$0.459532\pi$
$168$		0			0
$169$	0.794867	+	16.6863i	0.0611436	+	1.28356i
$170$		0			0
$171$	2.39641	+	4.15070i	0.183258	+	0.317412i
$172$		0			0
$173$	2.21470	+	9.12913i	0.168381	+	0.694075i	0.991925	+	0.126823i	$0.0404781\pi$
$173$	2.21470	+	9.12913i	0.168381	+	0.694075i	−0.823545	+	0.567252i	$0.808007\pi$
$174$		0			0
$175$	−9.90976	+	1.90995i	−0.749108	+	0.144379i
$176$		0			0
$177$	6.33230	+	7.30786i	0.475965	+	0.549293i
$178$		0			0
$179$	2.85401	−	1.83416i	0.213319	−	0.137092i	−0.429618	−	0.903011i	$-0.641352\pi$
$179$	2.85401	−	1.83416i	0.213319	−	0.137092i	0.642937	+	0.765919i	$0.277716\pi$
$180$		0			0
$181$	−10.5129	+	5.41980i	−0.781421	+	0.402850i	−0.802292	−	0.596932i	$-0.796386\pi$
$181$	−10.5129	+	5.41980i	−0.781421	+	0.402850i	0.0208713	+	0.999782i	$0.493356\pi$
$182$		0			0
$183$	1.60714	+	0.309751i	0.118803	+	0.0228974i
$184$		0			0
$185$	−8.46504	+	6.65698i	−0.622362	+	0.489431i
$186$		0			0
$187$	4.53660	−	5.23551i	0.331749	−	0.382859i
$188$		0			0
$189$	0.721545	−	2.97425i	0.0524847	−	0.216345i
$190$		0			0
$191$	9.37388	+	4.83257i	0.678270	+	0.349673i	0.762696	−	0.646757i	$-0.223875\pi$
$191$	9.37388	+	4.83257i	0.678270	+	0.349673i	−0.0844256	+	0.996430i	$0.526906\pi$
$192$		0			0
$193$	−9.07219	−	2.66384i	−0.653031	−	0.191747i	−0.0615974	−	0.998101i	$-0.519619\pi$
$193$	−9.07219	−	2.66384i	−0.653031	−	0.191747i	−0.591433	+	0.806354i	$0.701438\pi$
$194$		0			0
$195$	−6.60203	+	2.64305i	−0.472781	+	0.189273i
$196$		0			0
$197$	1.65633	+	4.78564i	0.118008	+	0.340963i	0.988500	−	0.151220i	$-0.0483203\pi$
$197$	1.65633	+	4.78564i	0.118008	+	0.340963i	−0.870492	+	0.492183i	$0.836199\pi$
$198$		0			0
$199$	−6.63710	+	9.32050i	−0.470492	+	0.660713i	−0.979825	−	0.199856i	$-0.935953\pi$
$199$	−6.63710	+	9.32050i	−0.470492	+	0.660713i	0.509334	+	0.860569i	$0.329892\pi$
$200$		0			0
$201$	−3.21612	−	7.52706i	−0.226848	−	0.530918i
$202$		0			0
$203$	7.71126	−	10.8290i	0.541225	−	0.760043i
$204$		0			0
$205$	3.07473	+	8.88385i	0.214748	+	0.620475i
$206$		0			0
$207$	5.39900	−	2.16144i	0.375257	−	0.150230i
$208$		0			0
$209$	4.87711	+	1.43205i	0.337357	+	0.0990569i
$210$		0			0
$211$	3.74709	+	1.93176i	0.257960	+	0.132988i	0.582357	−	0.812933i	$-0.302131\pi$
$211$	3.74709	+	1.93176i	0.257960	+	0.132988i	−0.324396	+	0.945921i	$0.605161\pi$
$212$		0			0
$213$	−3.16199	+	13.0339i	−0.216656	+	0.893069i
$214$		0			0
$215$	−0.818946	+	0.945114i	−0.0558517	+	0.0644563i
$216$		0			0
$217$	−13.2931	+	10.4538i	−0.902394	+	0.709651i
$218$		0			0
$219$	12.0505	+	2.32254i	0.814296	+	0.156943i
$220$		0			0
$221$	−31.6438	+	16.3135i	−2.12860	+	1.09737i
$222$		0			0
$223$	23.6136	−	15.1755i	1.58128	−	1.01623i	0.605944	−	0.795507i	$-0.292796\pi$
$223$	23.6136	−	15.1755i	1.58128	−	1.01623i	0.975337	−	0.220720i	$-0.0708408\pi$
$224$		0			0
$225$	2.15942	+	2.49210i	0.143961	+	0.166140i
$226$		0			0
$227$	16.9600	−	3.26877i	1.12567	−	0.216956i	0.407760	−	0.913089i	$-0.366310\pi$
$227$	16.9600	−	3.26877i	1.12567	−	0.216956i	0.717913	+	0.696133i	$0.245098\pi$
$228$		0			0
$229$	−1.19600	−	4.92998i	−0.0790339	−	0.325782i	0.918546	−	0.395315i	$-0.129364\pi$
$229$	−1.19600	−	4.92998i	−0.0790339	−	0.325782i	−0.997580	+	0.0695323i	$0.977849\pi$
$230$		0			0
$231$	−1.62291	−	2.81097i	−0.106780	−	0.184948i
$232$		0			0
$233$	−1.09204	−	22.9248i	−0.0715420	−	1.50185i	−0.694442	−	0.719549i	$-0.744349\pi$
$233$	−1.09204	−	22.9248i	−0.0715420	−	1.50185i	0.622900	−	0.782302i	$-0.285955\pi$
$234$		0			0
$235$	4.93585	+	6.93143i	0.321979	+	0.452157i
$236$		0			0
$237$	3.54402	−	3.37922i	0.230209	−	0.219504i
$238$		0			0
$239$	7.77547	−	13.4675i	0.502953	−	0.871141i	−0.497041	−	0.867727i	$-0.665580\pi$
$239$	7.77547	−	13.4675i	0.502953	−	0.871141i	0.999994	−	0.00341360i	$-0.00108659\pi$
$240$		0			0
$241$	2.92629	−	20.3528i	0.188499	−	1.31104i	−0.647397	−	0.762153i	$-0.724142\pi$
$241$	2.92629	−	20.3528i	0.188499	−	1.31104i	0.835896	−	0.548887i	$-0.184948\pi$
$242$		0			0
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$		0			0
$245$	0.146941	−	3.08467i	0.00938772	−	0.197073i
$246$		0			0
$247$	−20.5333	−	16.1476i	−1.30650	−	1.02745i
$248$		0			0
$249$	3.34812	−	0.319707i	0.212179	−	0.0202606i
$250$		0			0
$251$	−5.70236	+	16.4759i	−0.359930	+	1.03995i	0.609119	+	0.793079i	$0.291523\pi$
$251$	−5.70236	+	16.4759i	−0.359930	+	1.03995i	−0.969049	+	0.246870i	$0.920598\pi$
$252$		0			0
$253$	2.56216	−	5.61034i	0.161081	−	0.352719i
$254$		0			0
$255$	−6.16838	−	5.88154i	−0.386279	−	0.368316i
$256$		0			0
$257$	14.7907	+	5.92130i	0.922618	+	0.369360i	0.783840	−	0.620963i	$-0.213258\pi$
$257$	14.7907	+	5.92130i	0.922618	+	0.369360i	0.138778	+	0.990324i	$0.455683\pi$
$258$		0			0
$259$	10.4934	+	22.9772i	0.652025	+	1.42774i
$260$		0			0
$261$	−4.32403	−	0.412894i	−0.267651	−	0.0255575i
$262$		0			0
$263$	−0.0636452	−	0.442662i	−0.00392453	−	0.0272957i	0.987765	−	0.155949i	$-0.0498436\pi$
$263$	−0.0636452	−	0.442662i	−0.00392453	−	0.0272957i	−0.991690	+	0.128653i	$0.958935\pi$
$264$		0			0
$265$	6.93636	+	4.45773i	0.426097	+	0.273836i
$266$		0			0
$267$	−10.7001			−0.654837
$268$		0			0
$269$	−2.62592			−0.160105			−0.0800527	−	0.996791i	$-0.525509\pi$
$269$	−2.62592			−0.160105			−0.0800527	+	0.996791i	$0.525509\pi$
$270$		0			0
$271$	5.69524	+	3.66011i	0.345961	+	0.222336i	0.702069	−	0.712109i	$-0.252260\pi$
$271$	5.69524	+	3.66011i	0.345961	+	0.222336i	−0.356108	+	0.934445i	$0.615896\pi$
$272$		0			0
$273$	2.37390	+	16.5108i	0.143675	+	0.999281i
$274$		0			0
$275$	3.48134	+	0.332428i	0.209933	+	0.0200462i
$276$		0			0
$277$	8.38146	+	18.3528i	0.503593	+	1.10271i	0.975285	+	0.220951i	$0.0709162\pi$
$277$	8.38146	+	18.3528i	0.503593	+	1.10271i	−0.471692	+	0.881763i	$0.656357\pi$
$278$		0			0
$279$	5.12978	+	2.05365i	0.307112	+	0.122949i
$280$		0			0
$281$	−13.6766	−	13.0406i	−0.815877	−	0.777937i	0.162073	−	0.986779i	$-0.448182\pi$
$281$	−13.6766	−	13.0406i	−0.815877	−	0.777937i	−0.977949	+	0.208842i	$0.933031\pi$
$282$		0			0
$283$	−0.00337552	+	0.00739136i	−0.000200654	+	0.000439371i	−0.909732	−	0.415195i	$-0.863713\pi$
$283$	−0.00337552	+	0.00739136i	−0.000200654	+	0.000439371i	0.909532	+	0.415635i	$0.136441\pi$
$284$		0			0
$285$	2.04536	−	5.90968i	0.121157	−	0.350059i
$286$		0			0
$287$	21.9509	−	2.09606i	1.29572	−	0.123726i
$288$		0			0
$289$	−20.1765	−	15.8669i	−1.18685	−	0.933350i
$290$		0			0
$291$	−0.807062	+	16.9423i	−0.0473108	+	0.993176i
$292$		0			0
$293$	9.75251	−	2.86359i	0.569748	−	0.167293i	0.0158450	−	0.999874i	$-0.494956\pi$
$293$	9.75251	−	2.86359i	0.569748	−	0.167293i	0.553903	+	0.832581i	$0.313138\pi$
$294$		0			0
$295$	1.79557	−	12.4885i	0.104542	−	0.727108i
$296$		0			0
$297$	−0.530273	+	0.918461i	−0.0307696	+	0.0532945i
$298$		0			0
$299$	−22.9398	+	21.8730i	−1.32664	+	1.26495i
$300$		0			0
$301$	1.70150	+	2.38942i	0.0980728	+	0.137724i
$302$		0			0
$303$	−0.282107	−	5.92215i	−0.0162066	−	0.340218i
$304$		0			0
$305$	−1.06779	−	1.84946i	−0.0611413	−	0.105900i
$306$		0			0
$307$	4.50171	+	18.5563i	0.256926	+	1.05906i	0.943334	+	0.331846i	$0.107671\pi$
$307$	4.50171	+	18.5563i	0.256926	+	1.05906i	−0.686408	+	0.727217i	$0.740813\pi$
$308$		0			0
$309$	−6.95338	+	1.34015i	−0.395564	+	0.0762387i
$310$		0			0
$311$	−15.0998	−	17.4261i	−0.856229	−	0.988141i	0.143770	−	0.989611i	$-0.454077\pi$
$311$	−15.0998	−	17.4261i	−0.856229	−	0.988141i	−0.999999	+	0.00147020i	$0.999532\pi$
$312$		0			0
$313$	−15.3111	+	9.83986i	−0.865436	+	0.556182i	−0.896353	−	0.443340i	$-0.853793\pi$
$313$	−15.3111	+	9.83986i	−0.865436	+	0.556182i	0.0309177	+	0.999522i	$0.490157\pi$
$314$		0			0
$315$	−3.54942	+	1.82985i	−0.199987	+	0.103101i
$316$		0			0
$317$	6.20718	+	1.19634i	0.348630	+	0.0671930i	0.360560	−	0.932736i	$-0.382585\pi$
$317$	6.20718	+	1.19634i	0.348630	+	0.0671930i	−0.0119302	+	0.999929i	$0.503798\pi$
$318$		0			0
$319$	−3.62111	+	2.84767i	−0.202743	+	0.159439i
$320$		0			0
$321$	5.03513	−	5.81085i	0.281033	−	0.324330i
$322$		0			0
$323$	7.38092	−	30.4246i	0.410686	−	1.69287i
$324$		0			0
$325$	−15.9744	−	8.23539i	−0.886102	−	0.456817i
$326$		0			0
$327$	19.1723	+	5.62949i	1.06023	+	0.311312i
$328$		0			0
$329$	18.5296	−	7.41814i	1.02157	−	0.408975i
$330$		0			0
$331$	−4.46916	−	12.9128i	−0.245647	−	0.709751i	−0.998660	−	0.0517457i	$-0.983521\pi$
$331$	−4.46916	−	12.9128i	−0.245647	−	0.709751i	0.753013	−	0.658006i	$-0.228600\pi$
$332$		0			0
$333$	4.78748	−	6.72308i	0.262352	−	0.368422i
$334$		0			0
$335$	−4.67436	+	9.60294i	−0.255387	+	0.524664i
$336$		0			0
$337$	−7.35578	+	10.3297i	−0.400695	+	0.562697i	−0.964793	−	0.263011i	$-0.915285\pi$
$337$	−7.35578	+	10.3297i	−0.400695	+	0.562697i	0.564098	+	0.825708i	$0.309224\pi$
$338$		0			0
$339$	−3.89731	−	11.2605i	−0.211673	−	0.611589i
$340$		0			0
$341$	5.44037	−	2.17800i	0.294613	−	0.117945i
$342$		0			0
$343$	13.6056	+	3.99497i	0.734635	+	0.215708i
$344$		0			0
$345$	−6.74459	−	3.47708i	−0.363117	−	0.187200i
$346$		0			0
$347$	−7.81134	+	32.1988i	−0.419335	+	1.72852i	0.234710	+	0.972066i	$0.424586\pi$
$347$	−7.81134	+	32.1988i	−0.419335	+	1.72852i	−0.654044	+	0.756456i	$0.726929\pi$
$348$		0			0
$349$	23.1808	−	26.7521i	1.24084	−	1.43201i	0.378558	−	0.925578i	$-0.376420\pi$
$349$	23.1808	−	26.7521i	1.24084	−	1.43201i	0.862282	−	0.506428i	$-0.169034\pi$
$350$		0			0
$351$	4.28419	−	3.36912i	0.228673	−	0.179830i
$352$		0			0
$353$	−14.2309	−	2.74278i	−0.757433	−	0.145983i	−0.204107	−	0.978948i	$-0.565429\pi$
$353$	−14.2309	−	2.74278i	−0.757433	−	0.145983i	−0.553325	+	0.832965i	$0.686641\pi$
$354$		0			0
$355$	15.5545	−	8.01888i	0.825545	−	0.425598i
$356$		0			0
$357$	−16.8180	+	10.8083i	−0.890102	+	0.572034i
$358$		0			0
$359$	−9.62553	−	11.1085i	−0.508016	−	0.586282i	0.442573	−	0.896732i	$-0.354066\pi$
$359$	−9.62553	−	11.1085i	−0.508016	−	0.586282i	−0.950590	+	0.310450i	$0.899520\pi$
$360$		0			0
$361$	3.89936	−	0.751540i	0.205229	−	0.0395547i
$362$		0			0
$363$	−2.32818	−	9.59687i	−0.122198	−	0.503705i
$364$		0			0
$365$	−8.00636	−	13.8674i	−0.419072	−	0.725854i
$366$		0			0
$367$	0.321226	+	6.74335i	0.0167678	+	0.352000i	0.991623	+	0.129163i	$0.0412289\pi$
$367$	0.321226	+	6.74335i	0.0167678	+	0.352000i	−0.974856	+	0.222838i	$0.928468\pi$
$368$		0			0
$369$	−4.17925	−	5.86894i	−0.217563	−	0.305525i
$370$		0			0
$371$	13.9971	−	13.3462i	0.726694	−	0.692901i
$372$		0			0
$373$	15.8550	−	27.4616i	0.820939	−	1.42191i	−0.0840451	−	0.996462i	$-0.526784\pi$
$373$	15.8550	−	27.4616i	0.820939	−	1.42191i	0.904984	−	0.425446i	$-0.139883\pi$
$374$		0			0
$375$	1.54078	−	10.7163i	0.0795653	−	0.553389i
$376$		0			0
$377$	22.7153	−	6.66980i	1.16990	−	0.343512i
$378$		0			0
$379$	−0.640955	+	13.4553i	−0.0329236	+	0.691152i	0.920722	+	0.390220i	$0.127601\pi$
$379$	−0.640955	+	13.4553i	−0.0329236	+	0.691152i	−0.953645	+	0.300933i	$0.902702\pi$
$380$		0			0
$381$	3.95375	+	3.10927i	0.202557	+	0.159293i
$382$		0			0
$383$	−14.5142	+	1.38594i	−0.741642	+	0.0708182i	−0.459036	−	0.888418i	$-0.651805\pi$
$383$	−14.5142	+	1.38594i	−0.741642	+	0.0708182i	−0.282606	+	0.959236i	$0.591199\pi$
$384$		0			0
$385$	−1.38517	+	4.00220i	−0.0705950	+	0.203971i
$386$		0			0
$387$	0.398151	−	0.871829i	0.0202392	−	0.0443176i
$388$		0			0
$389$	6.56011	+	6.25505i	0.332611	+	0.317144i	0.837918	−	0.545796i	$-0.183773\pi$
$389$	6.56011	+	6.25505i	0.332611	+	0.317144i	−0.505308	+	0.862939i	$0.668621\pi$
$390$		0			0
$391$	−35.2667	−	14.1187i	−1.78351	−	0.714012i
$392$		0			0
$393$	5.36386	+	11.7452i	0.270571	+	0.592468i
$394$		0			0
$395$	−6.36045	−	0.607349i	−0.320029	−	0.0305590i
$396$		0			0
$397$	−0.640344	−	4.45369i	−0.0321379	−	0.223524i	0.967423	−	0.253167i	$-0.0814722\pi$
$397$	−0.640344	−	4.45369i	−0.0321379	−	0.223524i	−0.999561	+	0.0296426i	$0.990563\pi$
$398$		0			0
$399$	−12.3400	−	7.93041i	−0.617770	−	0.397017i
$400$		0			0
$401$	16.4253			0.820240			0.410120	−	0.912032i	$-0.365487\pi$
$401$	16.4253			0.820240			0.410120	+	0.912032i	$0.365487\pi$
$402$		0			0
$403$	−30.1159			−1.50018
$404$		0			0
$405$	1.09766	+	0.705423i	0.0545431	+	0.0350527i
$406$		0			0
$407$	−1.24571	−	8.66410i	−0.0617475	−	0.429463i
$408$		0			0
$409$	−1.19914	−	0.114504i	−0.0592938	−	0.00566187i	0.0653670	−	0.997861i	$-0.479178\pi$
$409$	−1.19914	−	0.114504i	−0.0592938	−	0.00566187i	−0.124661	+	0.992199i	$0.539784\pi$
$410$		0			0
$411$	−1.92152	−	4.20755i	−0.0947818	−	0.207543i
$412$		0			0
$413$	−27.4744	−	10.9991i	−1.35193	−	0.541230i
$414$		0			0
$415$	−3.17608	−	3.02839i	−0.155908	−	0.148658i
$416$		0			0
$417$	−0.321983	+	0.705043i	−0.0157676	+	0.0345261i
$418$		0			0
$419$	−9.09381	+	26.2748i	−0.444262	+	1.28361i	0.471493	+	0.881870i	$0.343715\pi$
$419$	−9.09381	+	26.2748i	−0.444262	+	1.28361i	−0.915754	+	0.401739i	$0.868406\pi$
$420$		0			0
$421$	−1.68223	+	0.160633i	−0.0819868	+	0.00782879i	−0.135969	−	0.990713i	$-0.543415\pi$
$421$	−1.68223	+	0.160633i	−0.0819868	+	0.00782879i	0.0539820	+	0.998542i	$0.482809\pi$
$422$		0			0
$423$	−5.12628	−	4.03135i	−0.249248	−	0.196011i
$424$		0			0
$425$	1.02490	−	21.5153i	0.0497149	−	1.04364i
$426$		0			0
$427$	−4.80630	+	1.41126i	−0.232593	+	0.0682955i
$428$		0			0
$429$	0.822615	−	5.72141i	0.0397162	−	0.276232i
$430$		0			0
$431$	18.9775	−	32.8699i	0.914112	−	1.58329i	0.105915	−	0.994375i	$-0.466223\pi$
$431$	18.9775	−	32.8699i	0.914112	−	1.58329i	0.808197	−	0.588913i	$-0.200444\pi$
$432$		0			0
$433$	25.7032	−	24.5079i	1.23522	−	1.17778i	0.257858	−	0.966183i	$-0.416983\pi$
$433$	25.7032	−	24.5079i	1.23522	−	1.17778i	0.977358	−	0.211593i	$-0.0678651\pi$
$434$		0			0
$435$	3.28754	+	4.61670i	0.157625	+	0.221354i
$436$		0			0
$437$	−1.32625	−	27.8415i	−0.0634433	−	1.33184i
$438$		0			0
$439$	−14.9223	−	25.8462i	−0.712203	−	1.23357i	−0.964029	−	0.265799i	$-0.914364\pi$
$439$	−14.9223	−	25.8462i	−0.712203	−	1.23357i	0.251826	−	0.967773i	$-0.418969\pi$
$440$		0			0
$441$	0.557993	+	2.30008i	0.0265711	+	0.109528i
$442$		0			0
$443$	18.0807	−	3.48476i	0.859039	−	0.165566i	0.259334	−	0.965788i	$-0.416497\pi$
$443$	18.0807	−	3.48476i	0.859039	−	0.165566i	0.599704	+	0.800222i	$0.295285\pi$
$444$		0			0
$445$	9.14278	+	10.5513i	0.433409	+	0.500181i
$446$		0			0
$447$	−18.8582	+	12.1194i	−0.891961	+	0.573228i
$448$		0			0
$449$	19.6445	−	10.1275i	0.927083	−	0.477945i	0.0725637	−	0.997364i	$-0.476882\pi$
$449$	19.6445	−	10.1275i	0.927083	−	0.477945i	0.854520	+	0.519419i	$0.173852\pi$
$450$		0			0
$451$	−7.50305	−	1.44609i	−0.353305	−	0.0680939i
$452$		0			0
$453$	10.7420	−	8.44760i	0.504703	−	0.396903i
$454$		0			0
$455$	14.2528	−	16.4487i	0.668184	−	0.771125i
$456$		0			0
$457$	4.57192	−	18.8457i	0.213865	−	0.881565i	−0.759167	−	0.650896i	$-0.774393\pi$
$457$	4.57192	−	18.8457i	0.213865	−	0.881565i	0.973032	−	0.230669i	$-0.0740915\pi$
$458$		0			0
$459$	5.80594	+	2.99317i	0.270998	+	0.139709i
$460$		0			0
$461$	16.4381	+	4.82667i	0.765600	+	0.224801i	0.641140	−	0.767424i	$-0.278462\pi$
$461$	16.4381	+	4.82667i	0.765600	+	0.224801i	0.124460	+	0.992225i	$0.460280\pi$
$462$		0			0
$463$	−11.8779	+	4.75520i	−0.552014	+	0.220993i	−0.630864	−	0.775893i	$-0.717299\pi$
$463$	−11.8779	+	4.75520i	−0.552014	+	0.220993i	0.0788500	+	0.996886i	$0.474875\pi$
$464$		0			0
$465$	−2.35807	−	6.81321i	−0.109353	−	0.315955i
$466$		0			0
$467$	−11.5982	+	16.2874i	−0.536701	+	0.753691i	−0.990515	−	0.137406i	$-0.956124\pi$
$467$	−11.5982	+	16.2874i	−0.536701	+	0.753691i	0.453814	+	0.891096i	$0.350063\pi$
$468$		0			0
$469$	19.3049	+	15.9655i	0.891415	+	0.737219i
$470$		0			0
$471$	−7.16754	+	10.0654i	−0.330263	+	0.463789i
$472$		0			0
$473$	−0.332456	−	0.960567i	−0.0152863	−	0.0441669i
$474$		0			0
$475$	14.6723	−	5.87391i	0.673213	−	0.269514i
$476$		0			0
$477$	−6.06325	−	1.78033i	−0.277617	−	0.0815158i
$478$		0			0
$479$	9.20836	+	4.74724i	0.420741	+	0.216907i	0.655577	−	0.755128i	$-0.272425\pi$
$479$	9.20836	+	4.74724i	0.420741	+	0.216907i	−0.234837	+	0.972035i	$0.575456\pi$
$480$		0			0
$481$	−10.6053	+	43.7154i	−0.483558	+	1.99325i
$482$		0			0
$483$	−11.6557	+	13.4514i	−0.530352	+	0.612059i
$484$		0			0
$485$	17.3963	−	13.6806i	0.789926	−	0.621205i
$486$		0			0
$487$	30.7872	+	5.93375i	1.39510	+	0.268884i	0.830748	−	0.556648i	$-0.187913\pi$
$487$	30.7872	+	5.93375i	1.39510	+	0.268884i	0.564355	+	0.825532i	$0.309125\pi$
$488$		0			0
$489$	7.90071	−	4.07310i	0.357282	−	0.184192i
$490$		0			0
$491$	30.8142	−	19.8031i	1.39063	−	0.893700i	0.390982	−	0.920399i	$-0.372136\pi$
$491$	30.8142	−	19.8031i	1.39063	−	0.893700i	0.999644	+	0.0266980i	$0.00849925\pi$
$492$		0			0
$493$	18.5806	+	21.4432i	0.836828	+	0.965751i
$494$		0			0
$495$	1.35878	−	0.261884i	0.0610728	−	0.0117708i
$496$		0			0
$497$	−9.67735	−	39.8906i	−0.434089	−	1.78934i
$498$		0			0
$499$	−9.30790	−	16.1218i	−0.416679	−	0.721709i	0.578924	−	0.815381i	$-0.303473\pi$
$499$	−9.30790	−	16.1218i	−0.416679	−	0.721709i	−0.995603	+	0.0936723i	$0.970139\pi$
$500$		0			0
$501$	1.08412	+	22.7584i	0.0484348	+	1.01677i
$502$		0			0
$503$	0.156334	+	0.219541i	0.00697061	+	0.00978885i	0.818047	−	0.575152i	$-0.195057\pi$
$503$	0.156334	+	0.219541i	0.00697061	+	0.00978885i	−0.811076	+	0.584941i	$0.801118\pi$
$504$		0			0
$505$	−5.59875	+	5.33840i	−0.249141	+	0.237556i
$506$		0			0
$507$	−8.35261	+	14.4671i	−0.370952	+	0.642509i
$508$		0			0
$509$	5.39789	−	37.5431i	0.239257	−	1.66407i	−0.416528	−	0.909123i	$-0.636753\pi$
$509$	5.39789	−	37.5431i	0.239257	−	1.66407i	0.655785	−	0.754947i	$-0.272338\pi$
$510$		0			0
$511$	−36.0381	+	10.5817i	−1.59423	+	0.468109i
$512$		0			0
$513$	−0.228052	+	4.78739i	−0.0100687	+	0.211368i
$514$		0			0
$515$	7.26287	+	5.71159i	0.320040	+	0.251683i
$516$		0			0
$517$	−6.88509	+	0.657447i	−0.302806	+	0.0289145i
$518$		0			0
$519$	−3.07245	+	8.87727i	−0.134866	+	0.389669i
$520$		0			0
$521$	−6.82404	+	14.9426i	−0.298967	+	0.654646i	−0.998182	−	0.0602649i	$-0.980805\pi$
$521$	−6.82404	+	14.9426i	−0.298967	+	0.654646i	0.699216	+	0.714911i	$0.253533\pi$
$522$		0			0
$523$	−2.10333	−	2.00552i	−0.0919722	−	0.0876953i	0.642698	−	0.766119i	$-0.277815\pi$
$523$	−2.10333	−	2.00552i	−0.0919722	−	0.0876953i	−0.734671	+	0.678424i	$0.762663\pi$
$524$		0			0
$525$	−9.36922	−	3.75087i	−0.408906	−	0.163701i
$526$		0			0
$527$	−14.9938	−	32.8319i	−0.653141	−	1.43018i
$528$		0			0
$529$	−10.7720	−	1.02861i	−0.468350	−	0.0447220i
$530$		0			0
$531$	1.37614	+	9.57127i	0.0597194	+	0.415358i
$532$		0			0
$533$	33.0348	+	21.2302i	1.43090	+	0.919580i
$534$		0			0
$535$	−10.0323			−0.433736
$536$		0			0
$537$	3.39257			0.146400
$538$		0			0
$539$	2.11163	+	1.35706i	0.0909543	+	0.0584528i
$540$		0			0
$541$	3.89992	+	27.1245i	0.167671	+	1.16618i	0.883682	+	0.468087i	$0.155057\pi$
$541$	3.89992	+	27.1245i	0.167671	+	1.16618i	−0.716012	+	0.698088i	$0.754034\pi$
$542$		0			0
$543$	−11.7742	−	1.12430i	−0.505280	−	0.0482484i
$544$		0			0
$545$	−10.8307	−	23.7158i	−0.463935	−	1.01587i
$546$		0			0
$547$	5.96982	+	2.38995i	0.255251	+	0.102187i	0.495759	−	0.868460i	$-0.334890\pi$
$547$	5.96982	+	2.38995i	0.255251	+	0.102187i	−0.240508	+	0.970647i	$0.577314\pi$
$548$		0			0
$549$	1.18455	+	1.12946i	0.0505553	+	0.0482044i
$550$		0			0
$551$	−8.64834	+	18.9372i	−0.368432	+	0.806753i
$552$		0			0
$553$	−4.90175	+	14.1627i	−0.208444	+	0.602258i
$554$		0			0
$555$	−10.7203	+	1.02366i	−0.455051	+	0.0434521i
$556$		0			0
$557$	11.7794	+	9.26346i	0.499111	+	0.392505i	0.835734	−	0.549134i	$-0.185042\pi$
$557$	11.7794	+	9.26346i	0.499111	+	0.392505i	−0.336623	+	0.941639i	$0.609285\pi$
$558$		0			0
$559$	−0.248556	+	5.21783i	−0.0105128	+	0.220691i
$560$		0			0
$561$	6.64696	−	1.95172i	0.280635	−	0.0824019i
$562$		0			0
$563$	1.26298	−	8.78420i	0.0532281	−	0.370210i	−0.945745	−	0.324909i	$-0.894666\pi$
$563$	1.26298	−	8.78420i	0.0532281	−	0.370210i	0.998973	−	0.0453007i	$-0.0144246\pi$
$564$		0			0
$565$	−7.77388	+	13.4648i	−0.327050	+	0.566467i
$566$		0			0
$567$	2.21500	−	2.11200i	0.0930214	−	0.0886957i
$568$		0			0
$569$	−1.72117	−	2.41705i	−0.0721554	−	0.101328i	0.776921	−	0.629598i	$-0.216780\pi$
$569$	−1.72117	−	2.41705i	−0.0721554	−	0.101328i	−0.849077	+	0.528270i	$0.822841\pi$
$570$		0			0
$571$	−0.242074	−	5.08177i	−0.0101305	−	0.212665i	−0.998257	−	0.0590212i	$-0.981202\pi$
$571$	−0.242074	−	5.08177i	−0.0101305	−	0.212665i	0.988126	−	0.153644i	$-0.0491010\pi$
$572$		0			0
$573$	5.27313	+	9.13332i	0.220288	+	0.381550i
$574$		0			0
$575$	−4.52116	−	18.6365i	−0.188545	−	0.777194i
$576$		0			0
$577$	15.1618	−	2.92220i	0.631195	−	0.121653i	0.136388	−	0.990656i	$-0.456451\pi$
$577$	15.1618	−	2.92220i	0.631195	−	0.121653i	0.494807	+	0.869003i	$0.335239\pi$
$578$		0			0
$579$	−6.19184	−	7.14576i	−0.257324	−	0.296968i
$580$		0			0
$581$	−8.65954	+	5.56515i	−0.359258	+	0.230881i
$582$		0			0
$583$	−5.95683	+	3.07096i	−0.246707	+	0.127186i
$584$		0			0
$585$	−6.98292	−	1.34585i	−0.288708	−	0.0556439i
$586$		0			0
$587$	−0.228789	+	0.179922i	−0.00944315	+	0.00742617i	−0.622869	−	0.782326i	$-0.714033\pi$
$587$	−0.228789	+	0.179922i	−0.00944315	+	0.00742617i	0.613426	+	0.789752i	$0.289791\pi$
$588$		0			0
$589$	17.3428	−	20.0146i	0.714597	−	0.824689i
$590$		0			0
$591$	−1.19392	+	4.92141i	−0.0491114	+	0.202440i
$592$		0			0
$593$	−23.0094	−	11.8622i	−0.944882	−	0.487121i	−0.0843045	−	0.996440i	$-0.526867\pi$
$593$	−23.0094	−	11.8622i	−0.944882	−	0.487121i	−0.860578	+	0.509319i	$0.829897\pi$
$594$		0			0
$595$	25.0282	+	7.34894i	1.02606	+	0.301277i
$596$		0			0
$597$	−10.6225	+	4.25262i	−0.434751	+	0.174048i
$598$		0			0
$599$	9.87282	+	28.5256i	0.403393	+	1.16553i	0.945614	+	0.325291i	$0.105462\pi$
$599$	9.87282	+	28.5256i	0.403393	+	1.16553i	−0.542222	+	0.840236i	$0.682417\pi$
$600$		0			0
$601$	−12.8117	+	17.9915i	−0.522598	+	0.733887i	−0.988545	−	0.150926i	$-0.951774\pi$
$601$	−12.8117	+	17.9915i	−0.522598	+	0.733887i	0.465947	+	0.884813i	$0.345714\pi$
$602$		0			0
$603$	1.36386	−	8.07093i	0.0555407	−	0.328674i
$604$		0			0
$605$	−7.47410	+	10.4959i	−0.303865	+	0.426719i
$606$		0			0
$607$	−7.58746	−	21.9225i	−0.307965	−	0.889808i	−0.987702	−	0.156351i	$-0.950027\pi$
$607$	−7.58746	−	21.9225i	−0.307965	−	0.889808i	0.679736	−	0.733457i	$-0.262094\pi$
$608$		0			0
$609$	12.3417	−	4.94087i	0.500111	−	0.200214i
$610$		0			0
$611$	34.1043	+	10.0139i	1.37971	+	0.405120i
$612$		0			0
$613$	26.5829	+	13.7045i	1.07367	+	0.553518i	0.902044	−	0.431643i	$-0.142066\pi$
$613$	26.5829	+	13.7045i	1.07367	+	0.553518i	0.171631	+	0.985161i	$0.445096\pi$
$614$		0			0
$615$	−2.21634	+	9.13589i	−0.0893716	+	0.368395i
$616$		0			0
$617$	−5.27677	+	6.08972i	−0.212435	+	0.245163i	−0.851959	−	0.523608i	$-0.824586\pi$
$617$	−5.27677	+	6.08972i	−0.212435	+	0.245163i	0.639525	+	0.768771i	$0.279131\pi$
$618$		0			0
$619$	−37.5819	+	29.5547i	−1.51054	+	1.18790i	−0.583978	+	0.811770i	$0.698505\pi$
$619$	−37.5819	+	29.5547i	−1.51054	+	1.18790i	−0.926565	+	0.376135i	$0.877253\pi$
$620$		0			0
$621$	5.71049	+	1.10061i	0.229154	+	0.0441658i
$622$		0			0
$623$	29.1075	−	15.0060i	1.16617	−	0.601202i
$624$		0			0
$625$	1.98642	−	1.27660i	0.0794569	−	0.0510639i
$626$		0			0
$627$	3.32866	+	3.84148i	0.132934	+	0.153414i
$628$		0			0
$629$	−52.9380	+	10.2030i	−2.11078	+	0.406819i
$630$		0			0
$631$	4.25286	+	17.5305i	0.169304	+	0.697880i	0.991657	+	0.128903i	$0.0411455\pi$
$631$	4.25286	+	17.5305i	0.169304	+	0.697880i	−0.822353	+	0.568977i	$0.807339\pi$
$632$		0			0
$633$	2.10787	+	3.65093i	0.0837801	+	0.145111i
$634$		0			0
$635$	−0.312277	−	6.55551i	−0.0123923	−	0.260147i
$636$		0			0
$637$	−7.48252	−	10.5077i	−0.296468	−	0.416331i
$638$		0			0
$639$	−9.70671	+	9.25533i	−0.383991	+	0.366135i
$640$		0			0
$641$	14.8009	−	25.6360i	0.584602	−	1.01256i	−0.410323	−	0.911940i	$-0.634584\pi$
$641$	14.8009	−	25.6360i	0.584602	−	1.01256i	0.994925	−	0.100620i	$-0.0320825\pi$
$642$		0			0
$643$	−5.16816	+	35.9453i	−0.203812	+	1.41754i	0.589027	+	0.808114i	$0.299511\pi$
$643$	−5.16816	+	35.9453i	−0.203812	+	1.41754i	−0.792839	+	0.609431i	$0.791398\pi$
$644$		0			0
$645$	−1.19991	+	0.352325i	−0.0472464	+	0.0138728i
$646$		0			0
$647$	−1.54243	+	32.3795i	−0.0606391	+	1.27297i	0.739500	+	0.673157i	$0.235062\pi$
$647$	−1.54243	+	32.3795i	−0.0606391	+	1.27297i	−0.800139	+	0.599814i	$0.795241\pi$
$648$		0			0
$649$	8.06110	+	6.33932i	0.316426	+	0.248840i
$650$		0			0
$651$	−16.8346	+	1.60751i	−0.659801	+	0.0630033i
$652$		0			0
$653$	−4.43059	+	12.8014i	−0.173383	+	0.500956i	−0.997892	−	0.0648917i	$-0.979330\pi$
$653$	−4.43059	+	12.8014i	−0.173383	+	0.500956i	0.824510	+	0.565848i	$0.191451\pi$
$654$		0			0
$655$	6.99871	−	15.3250i	0.273462	−	0.598799i
$656$		0			0
$657$	8.88185	+	8.46883i	0.346514	+	0.330400i
$658$		0			0
$659$	−7.03598	−	2.81678i	−0.274083	−	0.109726i	0.230549	−	0.973061i	$-0.425948\pi$
$659$	−7.03598	−	2.81678i	−0.274083	−	0.109726i	−0.504632	+	0.863334i	$0.668372\pi$
$660$		0			0
$661$	10.4131	+	22.8016i	0.405024	+	0.886879i	0.996736	+	0.0807296i	$0.0257250\pi$
$661$	10.4131	+	22.8016i	0.405024	+	0.886879i	−0.591712	+	0.806150i	$0.701548\pi$
$662$		0			0
$663$	−35.4403	−	3.38413i	−1.37639	−	0.131429i
$664$		0			0
$665$	2.72381	+	18.9445i	0.105625	+	0.734638i
$666$		0			0
$667$	21.2510	+	13.6572i	0.822843	+	0.528809i
$668$		0			0
$669$	28.0695			1.08523
$670$		0			0
$671$	1.73582			0.0670104
$672$		0			0
$673$	−24.3365	−	15.6401i	−0.938102	−	0.602881i	−0.0202458	−	0.999795i	$-0.506445\pi$
$673$	−24.3365	−	15.6401i	−0.938102	−	0.602881i	−0.917856	+	0.396914i	$0.870081\pi$
$674$		0			0
$675$	0.469286	+	3.26396i	0.0180628	+	0.125630i
$676$		0			0
$677$	−7.83614	−	0.748260i	−0.301167	−	0.0287580i	−0.0566214	−	0.998396i	$-0.518033\pi$
$677$	−7.83614	−	0.748260i	−0.301167	−	0.0287580i	−0.244546	+	0.969638i	$0.578639\pi$
$678$		0			0
$679$	−21.5647	−	47.2200i	−0.827576	−	1.81214i
$680$		0			0
$681$	16.0349	+	6.41939i	0.614457	+	0.245992i
$682$		0			0
$683$	30.8794	+	29.4434i	1.18157	+	1.12662i	0.989393	+	0.145261i	$0.0464020\pi$
$683$	30.8794	+	29.4434i	1.18157	+	1.12662i	0.192173	+	0.981361i	$0.438446\pi$
$684$		0			0
$685$	−2.50718	+	5.48997i	−0.0957946	+	0.209761i
$686$		0			0
$687$	1.65921	−	4.79397i	0.0633028	−	0.182901i
$688$		0			0
$689$	34.2854	−	3.27386i	1.30617	−	0.124724i
$690$		0			0
$691$	−11.4977	−	9.04187i	−0.437392	−	0.343969i	0.375056	−	0.927002i	$-0.377623\pi$
$691$	−11.4977	−	9.04187i	−0.437392	−	0.343969i	−0.812448	+	0.583033i	$0.801866\pi$
$692$		0			0
$693$	0.154443	−	3.24215i	0.00586679	−	0.123159i
$694$		0			0
$695$	0.970359	−	0.284923i	0.0368078	−	0.0108078i
$696$		0			0
$697$	−6.69776	+	46.5840i	−0.253696	+	1.76449i
$698$		0			0
$699$	11.4754	−	19.8759i	0.434039	−	0.751777i
$700$		0			0
$701$	−21.2248	+	20.2378i	−0.801649	+	0.764371i	−0.975406	−	0.220418i	$-0.929258\pi$
$701$	−21.2248	+	20.2378i	−0.801649	+	0.764371i	0.173757	+	0.984789i	$0.444409\pi$
$702$		0			0
$703$	−22.9455	−	32.2225i	−0.865407	−	1.21529i
$704$		0			0
$705$	0.404887	+	8.49962i	0.0152489	+	0.320114i
$706$		0			0
$707$	9.07271	+	15.7144i	0.341214	+	0.591000i
$708$		0			0
$709$	−9.80329	−	40.4097i	−0.368170	−	1.51762i	−0.791231	−	0.611518i	$-0.790559\pi$
$709$	−9.80329	−	40.4097i	−0.368170	−	1.51762i	0.423060	−	0.906102i	$-0.360956\pi$
$710$		0			0
$711$	4.80837	−	0.926737i	0.180328	−	0.0347554i
$712$		0			0
$713$	−21.0437	−	24.2857i	−0.788091	−	0.909506i
$714$		0			0
$715$	−6.34474	+	4.07752i	−0.237280	+	0.152491i
$716$		0			0
$717$	13.8222	−	7.12585i	0.516201	−	0.266120i
$718$		0			0
$719$	23.6610	+	4.56029i	0.882408	+	0.170070i	0.610275	−	0.792189i	$-0.291059\pi$
$719$	23.6610	+	4.56029i	0.882408	+	0.170070i	0.272133	+	0.962260i	$0.412271\pi$
$720$		0			0
$721$	17.0358	−	13.3971i	0.634447	−	0.498935i
$722$		0			0
$723$	13.4653	−	15.5398i	0.500781	−	0.577932i
$724$		0			0
$725$	−3.37688	+	13.9197i	−0.125414	+	0.516964i
$726$		0			0
$727$	−6.18567	−	3.18894i	−0.229414	−	0.118271i	0.339688	−	0.940538i	$-0.389679\pi$
$727$	−6.18567	−	3.18894i	−0.229414	−	0.118271i	−0.569102	+	0.822267i	$0.692709\pi$
$728$		0			0
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$		0			0
$731$	−5.81216	+	2.32684i	−0.214970	+	0.0860612i
$732$		0			0
$733$	−13.7995	−	39.8711i	−0.509697	−	1.47267i	−0.847162	−	0.531335i	$-0.821691\pi$
$733$	−13.7995	−	39.8711i	−0.509697	−	1.47267i	0.337465	−	0.941338i	$-0.390431\pi$
$734$		0			0
$735$	1.79132	−	2.51555i	0.0660737	−	0.0927875i
$736$		0			0
$737$	−4.85996	−	7.19303i	−0.179019	−	0.264959i
$738$		0			0
$739$	−8.78428	+	12.3358i	−0.323135	+	0.453780i	−0.943907	−	0.330212i	$-0.892880\pi$
$739$	−8.78428	+	12.3358i	−0.323135	+	0.453780i	0.620772	+	0.783991i	$0.286819\pi$
$740$		0			0
$741$	−8.54369	−	24.6854i	−0.313860	−	0.906840i
$742$		0			0
$743$	−25.2499	+	10.1085i	−0.926330	+	0.370846i	−0.785269	−	0.619155i	$-0.787475\pi$
$743$	−25.2499	+	10.1085i	−0.926330	+	0.370846i	−0.141060	+	0.990001i	$0.545051\pi$
$744$		0			0
$745$	28.0644	+	8.24044i	1.02820	+	0.301906i
$746$		0			0
$747$	2.98947	+	1.54118i	0.109379	+	0.0563887i
$748$		0			0
$749$	−5.54786	+	22.8686i	−0.202714	+	0.835599i
$750$		0			0
$751$	−23.6215	+	27.2607i	−0.861961	+	0.994756i	0.138029	+	0.990428i	$0.455923\pi$
$751$	−23.6215	+	27.2607i	−0.861961	+	0.994756i	−0.999991	+	0.00432806i	$0.998622\pi$
$752$		0			0
$753$	−13.7047	+	10.7775i	−0.499426	+	0.392753i
$754$		0			0
$755$	−17.5087	−	3.37452i	−0.637207	−	0.122812i
$756$		0			0
$757$	5.17044	−	2.66555i	0.187923	−	0.0968810i	−0.361697	−	0.932296i	$-0.617803\pi$
$757$	5.17044	−	2.66555i	0.187923	−	0.0968810i	0.549620	+	0.835415i	$0.314772\pi$
$758$		0			0
$759$	5.18860	−	3.33451i	0.188334	−	0.121035i
$760$		0			0
$761$	19.2920	+	22.2641i	0.699334	+	0.807074i	0.988662	−	0.150155i	$-0.0479774\pi$
$761$	19.2920	+	22.2641i	0.699334	+	0.807074i	−0.289328	+	0.957230i	$0.593432\pi$
$762$		0			0
$763$	−60.0492	+	11.5735i	−2.17393	+	0.418990i
$764$		0			0
$765$	−2.00937	−	8.28274i	−0.0726490	−	0.299463i
$766$		0			0
$767$	−26.3511	−	45.6415i	−0.951484	−	1.64802i
$768$		0			0
$769$	−1.53280	−	32.1774i	−0.0552741	−	1.16035i	−0.840739	−	0.541441i	$-0.817879\pi$
$769$	−1.53280	−	32.1774i	−0.0552741	−	1.16035i	0.785465	−	0.618906i	$-0.212424\pi$
$770$		0			0
$771$	9.24142	+	12.9778i	0.332822	+	0.467383i
$772$		0			0
$773$	1.97879	−	1.88677i	0.0711720	−	0.0678623i	−0.653658	−	0.756790i	$-0.726767\pi$
$773$	1.97879	−	1.88677i	0.0711720	−	0.0678623i	0.724830	+	0.688927i	$0.241918\pi$
$774$		0			0
$775$	9.11038	−	15.7796i	0.327255	−	0.566822i
$776$		0			0
$777$	−3.59486	+	25.0028i	−0.128965	+	0.896971i
$778$		0			0
$779$	−33.1330	+	9.72873i	−1.18711	+	0.348568i
$780$		0			0
$781$	−0.676807	+	14.2079i	−0.0242181	+	0.508400i
$782$		0			0
$783$	−3.41438	−	2.68509i	−0.122020	−	0.0959574i
$784$		0			0
$785$	16.0498	−	1.53257i	0.572841	−	0.0546997i
$786$		0			0
$787$	−1.46177	+	4.22350i	−0.0521064	+	0.150552i	−0.968051	−	0.250753i	$-0.919322\pi$
$787$	−1.46177	+	4.22350i	−0.0521064	+	0.150552i	0.915945	+	0.401304i	$0.131443\pi$
$788$		0			0
$789$	0.185779	−	0.406800i	0.00661392	−	0.0144825i
$790$		0			0
$791$	26.3938	+	25.1664i	0.938455	+	0.894815i
$792$		0			0
$793$	−8.28152	−	3.31542i	−0.294086	−	0.117734i
$794$		0			0
$795$	3.42521	+	7.50016i	0.121480	+	0.266003i
$796$		0			0
$797$	51.3895	+	4.90711i	1.82031	+	0.173819i	0.948658	−	0.316304i	$-0.102442\pi$
$797$	51.3895	+	4.90711i	1.82031	+	0.173819i	0.871653	+	0.490123i	$0.163048\pi$
$798$		0			0
$799$	6.06251	+	42.1657i	0.214476	+	1.49171i
$800$		0			0
$801$	−9.00151	−	5.78492i	−0.318053	−	0.204400i
$802$		0			0
$803$	13.0153			0.459300
$804$		0			0
$805$	23.2236			0.818525
$806$		0			0
$807$	−2.20907	−	1.41968i	−0.0777628	−	0.0499751i
$808$		0			0
$809$	6.42961	+	44.7189i	0.226053	+	1.57223i	0.714497	+	0.699639i	$0.246656\pi$
$809$	6.42961	+	44.7189i	0.226053	+	1.57223i	−0.488444	+	0.872595i	$0.662435\pi$
$810$		0			0
$811$	15.9154	+	1.51974i	0.558867	+	0.0533653i	0.370668	−	0.928766i	$-0.379129\pi$
$811$	15.9154	+	1.51974i	0.558867	+	0.0533653i	0.188199	+	0.982131i	$0.439735\pi$
$812$		0			0
$813$	2.81233	+	6.15815i	0.0986329	+	0.215976i
$814$		0			0
$815$	−10.7673	−	4.31056i	−0.377161	−	0.150992i
$816$		0			0
$817$	−3.32457	−	3.16997i	−0.116312	−	0.110903i
$818$		0			0
$819$	−6.92938	+	15.1732i	−0.242132	+	0.530195i
$820$		0			0
$821$	0.386280	−	1.11608i	0.0134813	−	0.0389516i	−0.938059	−	0.346474i	$-0.887379\pi$
$821$	0.386280	−	1.11608i	0.0134813	−	0.0389516i	0.951541	+	0.307523i	$0.0995000\pi$
$822$		0			0
$823$	4.31606	−	0.412134i	0.150449	−	0.0143661i	−0.0195600	−	0.999809i	$-0.506227\pi$
$823$	4.31606	−	0.412134i	0.150449	−	0.0143661i	0.170009	+	0.985443i	$0.445620\pi$
$824$		0			0
$825$	2.74897	+	2.16181i	0.0957067	+	0.0752646i
$826$		0			0
$827$	−0.787166	+	16.5247i	−0.0273725	+	0.574619i	0.942969	+	0.332880i	$0.108021\pi$
$827$	−0.787166	+	16.5247i	−0.0273725	+	0.574619i	−0.970342	+	0.241738i	$0.922282\pi$
$828$		0			0
$829$	44.0360	−	12.9301i	1.52943	−	0.449082i	0.594557	−	0.804054i	$-0.297328\pi$
$829$	44.0360	−	12.9301i	1.52943	−	0.449082i	0.934877	+	0.354971i	$0.115509\pi$
$830$		0			0
$831$	−2.87136	+	19.9707i	−0.0996064	+	0.692777i
$832$		0			0
$833$	7.73005	−	13.3888i	0.267830	−	0.463896i
$834$		0			0
$835$	21.5156	−	20.5151i	0.744579	−	0.709955i
$836$		0			0
$837$	3.20516	+	4.50101i	0.110786	+	0.155578i
$838$		0			0
$839$	−0.442635	−	9.29205i	−0.0152815	−	0.320797i	−0.993546	−	0.113434i	$-0.963815\pi$
$839$	−0.442635	−	9.29205i	−0.0152815	−	0.320797i	0.978264	−	0.207363i	$-0.0664881\pi$
$840$		0			0
$841$	5.06616	+	8.77484i	0.174695	+	0.302581i
$842$		0			0
$843$	−4.45520	−	18.3646i	−0.153445	−	0.632509i
$844$		0			0
$845$	21.4029	−	4.12507i	0.736283	−	0.141907i
$846$		0			0
$847$	19.7921	+	22.8413i	0.680065	+	0.784837i
$848$		0			0
$849$	−0.00683574	+	0.00439306i	−0.000234602	+	0.000150770i
$850$		0			0
$851$	−42.6630	+	21.9943i	−1.46247	+	0.753955i
$852$		0			0
$853$	−4.08246	−	0.786830i	−0.139781	−	0.0269406i	0.118881	−	0.992909i	$-0.462069\pi$
$853$	−4.08246	−	0.786830i	−0.139781	−	0.0269406i	−0.258662	+	0.965968i	$0.583281\pi$
$854$		0			0
$855$	4.91568	−	3.86573i	0.168113	−	0.132205i
$856$		0			0
$857$	−26.3135	+	30.3674i	−0.898851	+	1.03733i	0.100251	+	0.994962i	$0.468035\pi$
$857$	−26.3135	+	30.3674i	−0.898851	+	1.03733i	−0.999102	+	0.0423671i	$0.986510\pi$
$858$		0			0
$859$	1.27902	−	5.27220i	0.0436397	−	0.179885i	−0.945821	−	0.324690i	$-0.894740\pi$
$859$	1.27902	−	5.27220i	0.0436397	−	0.179885i	0.989460	+	0.144804i	$0.0462553\pi$
$860$		0			0
$861$	19.5995	+	10.1042i	0.667949	+	0.344352i
$862$		0			0
$863$	−22.9364	−	6.73473i	−0.780763	−	0.229253i	−0.133022	−	0.991113i	$-0.542468\pi$
$863$	−22.9364	−	6.73473i	−0.780763	−	0.229253i	−0.647741	+	0.761860i	$0.724286\pi$
$864$		0			0
$865$	11.3791	−	4.55551i	0.386901	−	0.154892i
$866$		0			0
$867$	−8.39520	−	24.2563i	−0.285116	−	0.823789i
$868$		0			0
$869$	3.01244	−	4.23038i	0.102190	−	0.143506i
$870$		0			0
$871$	9.44799	+	43.6003i	0.320133	+	1.47734i
$872$		0			0
$873$	−9.83865	+	13.8165i	−0.332988	+	0.467616i
$874$		0			0
$875$	10.8373	+	31.3124i	0.366369	+	1.05855i
$876$		0			0
$877$	−0.185503	+	0.0742641i	−0.00626398	+	0.00250772i	−0.374792	−	0.927109i	$-0.622286\pi$
$877$	−0.185503	+	0.0742641i	−0.00626398	+	0.00250772i	0.368528	+	0.929617i	$0.379862\pi$
$878$		0			0
$879$	9.75251	+	2.86359i	0.328944	+	0.0965866i
$880$		0			0
$881$	−10.0506	−	5.18144i	−0.338613	−	0.174567i	0.280530	−	0.959845i	$-0.409490\pi$
$881$	−10.0506	−	5.18144i	−0.338613	−	0.174567i	−0.619143	+	0.785278i	$0.712520\pi$
$882$		0			0
$883$	−10.0798	+	41.5494i	−0.339212	+	1.39825i	0.505407	+	0.862881i	$0.331342\pi$
$883$	−10.0798	+	41.5494i	−0.339212	+	1.39825i	−0.844619	+	0.535368i	$0.820173\pi$
$884$		0			0
$885$	8.26232	−	9.53523i	0.277735	−	0.320523i
$886$		0			0
$887$	−18.6826	+	14.6922i	−0.627300	+	0.493314i	−0.880466	−	0.474108i	$-0.842770\pi$
$887$	−18.6826	+	14.6922i	−0.627300	+	0.493314i	0.253166	+	0.967423i	$0.418528\pi$
$888$		0			0
$889$	−15.1159	−	2.91335i	−0.506970	−	0.0977105i
$890$		0			0
$891$	−0.942652	+	0.485971i	−0.0315800	+	0.0162806i
$892$		0			0
$893$	−26.2947	+	16.8986i	−0.879920	+	0.565490i
$894$		0			0
$895$	−2.89880	−	3.34540i	−0.0968963	−	0.111824i
$896$		0			0
$897$	−31.1236	+	5.99858i	−1.03919	+	0.200287i
$898$		0			0
$899$	5.65856	+	23.3249i	0.188724	+	0.777930i
$900$		0			0
$901$	20.6388	+	35.7475i	0.687579	+	1.19092i
$902$		0			0
$903$	0.139574	+	2.93001i	0.00464472	+	0.0975046i
$904$		0			0
$905$	8.95188	+	12.5712i	0.297570	+	0.417879i
$906$		0			0
$907$	−6.34346	+	6.04848i	−0.210631	+	0.200836i	−0.788049	−	0.615612i	$-0.788909\pi$
$907$	−6.34346	+	6.04848i	−0.210631	+	0.200836i	0.577418	+	0.816449i	$0.304060\pi$
$908$		0			0
$909$	2.96443	−	5.13455i	0.0983240	−	0.170302i
$910$		0			0
$911$	6.97940	−	48.5428i	0.231238	−	1.60830i	−0.461523	−	0.887128i	$-0.652697\pi$
$911$	6.97940	−	48.5428i	0.231238	−	1.60830i	0.692761	−	0.721167i	$-0.256394\pi$
$912$		0			0
$913$	3.42250	−	1.00494i	0.113268	−	0.0332586i
$914$		0			0
$915$	0.101615	−	2.13315i	0.00335928	−	0.0705199i
$916$		0			0
$917$	−31.0630	−	24.4282i	−1.02579	−	0.806690i
$918$		0			0
$919$	4.12291	−	0.393690i	0.136002	−	0.0129866i	−0.0268329	−	0.999640i	$-0.508542\pi$
$919$	4.12291	−	0.393690i	0.136002	−	0.0129866i	0.162835	+	0.986653i	$0.447936\pi$
$920$		0			0
$921$	−6.24521	+	18.0443i	−0.205787	+	0.594581i
$922$		0			0
$923$	30.3663	−	66.4929i	0.999518	−	2.18864i
$924$		0			0
$925$	−19.6971	−	18.7812i	−0.647638	−	0.617522i
$926$		0			0
$927$	−6.57409	−	2.63187i	−0.215922	−	0.0864420i
$928$		0			0
$929$	−14.8082	−	32.4254i	−0.485841	−	1.06384i	−0.980816	−	0.194937i	$-0.937550\pi$
$929$	−14.8082	−	32.4254i	−0.485841	−	1.06384i	0.494974	−	0.868908i	$-0.335177\pi$
$930$		0			0
$931$	11.2923	+	1.07828i	0.370089	+	0.0353392i
$932$		0			0
$933$	−3.28149	−	22.8233i	−0.107431	−	0.747201i
$934$		0			0
$935$	−7.60412	−	4.88687i	−0.248681	−	0.159818i
$936$		0			0
$937$	33.4286			1.09207			0.546033	−	0.837764i	$-0.316137\pi$
$937$	33.4286			1.09207			0.546033	+	0.837764i	$0.316137\pi$
$938$		0			0
$939$	−18.2004			−0.593947
$940$		0			0
$941$	−36.2357	−	23.2873i	−1.18125	−	0.759144i	−0.205635	−	0.978629i	$-0.565926\pi$
$941$	−36.2357	−	23.2873i	−1.18125	−	0.759144i	−0.975616	+	0.219485i	$0.929562\pi$
$942$		0			0
$943$	5.96310	+	41.4742i	0.194185	+	1.35059i
$944$		0			0
$945$	−3.97526	−	0.379591i	−0.129315	−	0.0123481i
$946$		0			0
$947$	−8.99265	−	19.6912i	−0.292222	−	0.639877i	0.705399	−	0.708810i	$-0.250768\pi$
$947$	−8.99265	−	19.6912i	−0.292222	−	0.639877i	−0.997621	+	0.0689333i	$0.978040\pi$
$948$		0			0
$949$	−62.0956	−	24.8593i	−2.01571	−	0.806968i
$950$		0			0
$951$	4.57503	+	4.36228i	0.148355	+	0.141457i
$952$		0			0
$953$	15.7027	−	34.3841i	0.508660	−	1.11381i	−0.464897	−	0.885365i	$-0.653909\pi$
$953$	15.7027	−	34.3841i	0.508660	−	1.11381i	0.973557	−	0.228445i	$-0.0733642\pi$
$954$		0			0
$955$	4.50067	−	13.0038i	0.145638	−	0.420794i
$956$		0			0
$957$	−4.58583	+	0.437894i	−0.148239	+	0.0141551i
$958$		0			0
$959$	11.1278	+	8.75103i	0.359337	+	0.282586i
$960$		0			0
$961$	−0.0222606	+	0.467307i	−0.000718083	+	0.0150744i
$962$		0			0
$963$	7.37740	−	2.16620i	0.237733	−	0.0698048i
$964$		0			0
$965$	−1.75574	+	12.2115i	−0.0565194	+	0.393101i
$966$		0			0
$967$	−3.78019	+	6.54749i	−0.121563	+	0.210553i	−0.920384	−	0.391015i	$-0.872124\pi$
$967$	−3.78019	+	6.54749i	−0.121563	+	0.210553i	0.798821	+	0.601568i	$0.205457\pi$
$968$		0			0
$969$	22.6580	−	21.6044i	0.727880	−	0.694032i
$970$		0			0
$971$	11.7357	+	16.4805i	0.376617	+	0.528884i	0.958766	−	0.284198i	$-0.0917273\pi$
$971$	11.7357	+	16.4805i	0.376617	+	0.528884i	−0.582149	+	0.813082i	$0.697788\pi$
$972$		0			0
$973$	−0.112872	−	2.36948i	−0.00361852	−	0.0759621i
$974$		0			0
$975$	−8.98616	−	15.5645i	−0.287787	−	0.498462i
$976$		0			0
$977$	0.647224	+	2.66789i	0.0207065	+	0.0853534i	0.981227	−	0.192855i	$-0.0617746\pi$
$977$	0.647224	+	2.66789i	0.0207065	+	0.0853534i	−0.960521	+	0.278208i	$0.910259\pi$
$978$		0			0
$979$	−11.1429	+	2.14762i	−0.356129	+	0.0686382i
$980$		0			0
$981$	13.0852	+	15.1011i	0.417779	+	0.482143i
$982$		0			0
$983$	17.1928	−	11.0491i	0.548365	−	0.352413i	−0.236938	−	0.971525i	$-0.576144\pi$
$983$	17.1928	−	11.0491i	0.548365	−	0.352413i	0.785303	+	0.619112i	$0.212507\pi$
$984$		0			0
$985$	5.87313	−	3.02781i	0.187134	−	0.0964741i
$986$		0			0
$987$	19.5987	+	3.77733i	0.623832	+	0.120234i
$988$		0			0
$989$	−4.38138	+	3.44556i	−0.139320	+	0.109562i
$990$		0			0
$991$	12.2722	−	14.1629i	0.389839	−	0.449898i	−0.526576	−	0.850128i	$-0.676524\pi$
$991$	12.2722	−	14.1629i	0.389839	−	0.449898i	0.916415	+	0.400230i	$0.131070\pi$
$992$		0			0
$993$	3.22149	−	13.2791i	0.102231	−	0.421401i
$994$		0			0
$995$	13.2700	+	6.84114i	0.420686	+	0.216879i
$996$		0			0
$997$	−11.2687	−	3.30880i	−0.356884	−	0.104791i	0.0983753	−	0.995149i	$-0.468635\pi$
$997$	−11.2687	−	3.30880i	−0.356884	−	0.104791i	−0.455260	+	0.890359i	$0.650454\pi$
$998$		0			0
$999$	7.66226	−	3.06750i	0.242423	−	0.0970515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.49.1	✓	100
67.26	even	33	inner	804.2.y.a.361.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.49.1	✓	100	1.1	even	1	trivial
804.2.y.a.361.1	yes	100	67.26	even	33	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{3} +(-0.185691 - 1.29151i) q^{5} +(-3.04666 - 0.290921i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{3} +(-0.185691 - 1.29151i) q^{5} +(-3.04666 - 0.290921i) q^{7} +(0.415415 + 0.909632i) q^{9} +(0.984578 + 0.394165i) q^{11} +(-3.94453 - 3.76110i) q^{13} +(0.542029 - 1.18688i) q^{15} +(2.13643 - 6.17282i) q^{17} +(4.77112 - 0.455586i) q^{19} +(-2.40573 - 1.89189i) q^{21} +(0.276717 - 5.80900i) q^{23} +(3.16395 - 0.929019i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(-2.17185 + 3.76175i) q^{29} +(3.99906 - 3.81309i) q^{31} +(0.615178 + 0.863896i) q^{33} +(0.190011 + 3.98882i) q^{35} +(-4.12673 - 7.14771i) q^{37} +(-1.28495 - 5.29662i) q^{39} +(-7.07470 + 1.36354i) q^{41} +(-0.627646 - 0.724342i) q^{43} +(1.09766 - 0.705423i) q^{45} +(-5.79658 + 2.98835i) q^{47} +(2.32402 + 0.447919i) q^{49} +(5.13456 - 4.03786i) q^{51} +(-4.13821 + 4.77575i) q^{53} +(0.326241 - 1.34478i) q^{55} +(4.26003 + 2.19620i) q^{57} +(9.27800 + 2.72427i) q^{59} +(1.51948 - 0.608306i) q^{61} +(-1.00100 - 2.89220i) q^{63} +(-4.12504 + 5.79280i) q^{65} +(-6.77501 - 4.59340i) q^{67} +(3.37337 - 4.73724i) q^{69} +(4.38663 + 12.6743i) q^{71} +(11.3932 - 4.56114i) q^{73} +(3.16395 + 0.929019i) q^{75} +(-2.88501 - 1.48732i) q^{77} +(1.15448 - 4.75883i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(2.64377 - 2.07909i) q^{83} +(-8.36897 - 1.61299i) q^{85} +(-3.86083 + 1.99040i) q^{87} +(-9.00151 + 5.78492i) q^{89} +(10.9235 + 12.6064i) q^{91} +(5.42574 - 1.04573i) q^{93} +(-1.47435 - 6.07734i) q^{95} +(8.48076 + 14.6891i) q^{97} +(0.0504629 + 1.05935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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