LMFDB - Embedded newform 804.2.q.a.241.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, 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:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			241.6
Character	$\chi$	$=$	804.241
Dual form			804.2.q.a.397.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{3} +(4.02046 + 1.18051i) q^{5} +(-1.53030 - 1.76606i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{3} +(4.02046 + 1.18051i) q^{5} +(-1.53030 - 1.76606i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-1.37457 - 0.403609i) q^{11} +(4.29158 + 2.75803i) q^{13} +(2.74399 - 3.16674i) q^{15} +(-1.11272 - 7.73916i) q^{17} +(3.10875 - 3.58769i) q^{19} +(-2.24217 + 0.658361i) q^{21} +(-2.10949 + 4.61914i) q^{23} +(10.5642 + 6.78921i) q^{25} +(-0.959493 + 0.281733i) q^{27} +5.38081 q^{29} +(-3.73643 + 2.40126i) q^{31} +(-0.938151 + 1.08268i) q^{33} +(-4.06765 - 8.90690i) q^{35} -2.96472 q^{37} +(4.29158 - 2.75803i) q^{39} +(0.524636 + 3.64892i) q^{41} +(-0.665817 - 4.63086i) q^{43} +(-1.74067 - 3.81153i) q^{45} +(-3.74261 + 8.19517i) q^{47} +(0.219055 - 1.52356i) q^{49} +(-7.50203 - 2.20280i) q^{51} +(-0.218855 + 1.52217i) q^{53} +(-5.04992 - 3.24539i) q^{55} +(-1.97205 - 4.31819i) q^{57} +(5.76654 - 3.70593i) q^{59} +(4.47734 - 1.31467i) q^{61} +(-0.332566 + 2.31304i) q^{63} +(13.9982 + 16.1548i) q^{65} +(7.44904 - 3.39291i) q^{67} +(3.32540 + 3.83772i) q^{69} +(-1.65795 + 11.5313i) q^{71} +(-9.89995 + 2.90689i) q^{73} +(10.5642 - 6.78921i) q^{75} +(1.39070 + 3.04521i) q^{77} +(-9.47130 - 6.08683i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(6.19011 + 1.81758i) q^{83} +(4.66253 - 32.4286i) q^{85} +(2.23527 - 4.89455i) q^{87} +(-5.87066 - 12.8549i) q^{89} +(-1.69655 - 11.7998i) q^{91} +(0.632092 + 4.39630i) q^{93} +(16.7339 - 10.7542i) q^{95} +6.06108 q^{97} +(0.595122 + 1.30314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

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
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$		0			0
$5$	4.02046	+	1.18051i	1.79800	+	0.527942i	0.997453	−	0.0713227i	$-0.0227220\pi$
$5$	4.02046	+	1.18051i	1.79800	+	0.527942i	0.800551	+	0.599264i	$0.204540\pi$
$6$		0			0
$7$	−1.53030	−	1.76606i	−0.578398	−	0.667507i	0.388861	−	0.921296i	$-0.372869\pi$
$7$	−1.53030	−	1.76606i	−0.578398	−	0.667507i	−0.967260	+	0.253789i	$0.918323\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	−1.37457	−	0.403609i	−0.414447	−	0.121693i	0.0678598	−	0.997695i	$-0.478383\pi$
$11$	−1.37457	−	0.403609i	−0.414447	−	0.121693i	−0.482307	+	0.876002i	$0.660201\pi$
$12$		0			0
$13$	4.29158	+	2.75803i	1.19027	+	0.764940i	0.977246	−	0.212107i	$-0.0680327\pi$
$13$	4.29158	+	2.75803i	1.19027	+	0.764940i	0.213023	+	0.977047i	$0.431669\pi$
$14$		0			0
$15$	2.74399	−	3.16674i	0.708496	−	0.817648i
$16$		0			0
$17$	−1.11272	−	7.73916i	−0.269875	−	1.87702i	−0.449489	−	0.893286i	$-0.648394\pi$
$17$	−1.11272	−	7.73916i	−0.269875	−	1.87702i	0.179614	−	0.983737i	$-0.442515\pi$
$18$		0			0
$19$	3.10875	−	3.58769i	0.713196	−	0.823072i	−0.277276	−	0.960790i	$-0.589432\pi$
$19$	3.10875	−	3.58769i	0.713196	−	0.823072i	0.990471	+	0.137719i	$0.0439770\pi$
$20$		0			0
$21$	−2.24217	+	0.658361i	−0.489282	+	0.143666i
$22$		0			0
$23$	−2.10949	+	4.61914i	−0.439859	+	0.963156i	0.551765	+	0.833999i	$0.313954\pi$
$23$	−2.10949	+	4.61914i	−0.439859	+	0.963156i	−0.991624	+	0.129157i	$0.958773\pi$
$24$		0			0
$25$	10.5642	+	6.78921i	2.11284	+	1.35784i
$26$		0			0
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$		0			0
$29$	5.38081			0.999191			0.499595	−	0.866259i	$-0.333482\pi$
$29$	5.38081			0.999191			0.499595	+	0.866259i	$0.333482\pi$
$30$		0			0
$31$	−3.73643	+	2.40126i	−0.671083	+	0.431279i	−0.831316	−	0.555800i	$-0.812412\pi$
$31$	−3.73643	+	2.40126i	−0.671083	+	0.431279i	0.160233	+	0.987079i	$0.448776\pi$
$32$		0			0
$33$	−0.938151	+	1.08268i	−0.163311	+	0.188471i
$34$		0			0
$35$	−4.06765	−	8.90690i	−0.687558	−	1.50554i
$36$		0			0
$37$	−2.96472			−0.487396			−0.243698	−	0.969851i	$-0.578361\pi$
$37$	−2.96472			−0.487396			−0.243698	+	0.969851i	$0.578361\pi$
$38$		0			0
$39$	4.29158	−	2.75803i	0.687202	−	0.441638i
$40$		0			0
$41$	0.524636	+	3.64892i	0.0819343	+	0.569866i	0.988891	+	0.148642i	$0.0474902\pi$
$41$	0.524636	+	3.64892i	0.0819343	+	0.569866i	−0.906957	+	0.421224i	$0.861601\pi$
$42$		0			0
$43$	−0.665817	−	4.63086i	−0.101536	−	0.706199i	−0.975466	−	0.220148i	$-0.929346\pi$
$43$	−0.665817	−	4.63086i	−0.101536	−	0.706199i	0.873930	−	0.486051i	$-0.161563\pi$
$44$		0			0
$45$	−1.74067	−	3.81153i	−0.259484	−	0.568190i
$46$		0			0
$47$	−3.74261	+	8.19517i	−0.545916	+	1.19539i	0.412748	+	0.910845i	$0.364569\pi$
$47$	−3.74261	+	8.19517i	−0.545916	+	1.19539i	−0.958663	+	0.284543i	$0.908158\pi$
$48$		0			0
$49$	0.219055	−	1.52356i	0.0312936	−	0.217651i
$50$		0			0
$51$	−7.50203	−	2.20280i	−1.05049	−	0.308453i
$52$		0			0
$53$	−0.218855	+	1.52217i	−0.0300620	+	0.209086i	−0.999316	−	0.0369759i	$-0.988228\pi$
$53$	−0.218855	+	1.52217i	−0.0300620	+	0.209086i	0.969254	+	0.246062i	$0.0791366\pi$
$54$		0			0
$55$	−5.04992	−	3.24539i	−0.680932	−	0.437608i
$56$		0			0
$57$	−1.97205	−	4.31819i	−0.261205	−	0.571959i
$58$		0			0
$59$	5.76654	−	3.70593i	0.750740	−	0.482471i	−0.108467	−	0.994100i	$-0.534594\pi$
$59$	5.76654	−	3.70593i	0.750740	−	0.482471i	0.859206	+	0.511629i	$0.170958\pi$
$60$		0			0
$61$	4.47734	−	1.31467i	0.573265	−	0.168326i	0.0177648	−	0.999842i	$-0.494345\pi$
$61$	4.47734	−	1.31467i	0.573265	−	0.168326i	0.555500	+	0.831516i	$0.312527\pi$
$62$		0			0
$63$	−0.332566	+	2.31304i	−0.0418993	+	0.291416i
$64$		0			0
$65$	13.9982	+	16.1548i	1.73627	+	2.00376i
$66$		0			0
$67$	7.44904	−	3.39291i	0.910045	−	0.414510i
$67$	7.44904	−	3.39291i	0.910045	−	0.414510i
$68$		0			0
$69$	3.32540	+	3.83772i	0.400331	+	0.462007i
$70$		0			0
$71$	−1.65795	+	11.5313i	−0.196762	+	1.36851i	0.616841	+	0.787088i	$0.288412\pi$
$71$	−1.65795	+	11.5313i	−0.196762	+	1.36851i	−0.813603	+	0.581421i	$0.802497\pi$
$72$		0			0
$73$	−9.89995	+	2.90689i	−1.15870	+	0.340225i	−0.803928	−	0.594727i	$-0.797260\pi$
$73$	−9.89995	+	2.90689i	−1.15870	+	0.340225i	−0.354773	+	0.934952i	$0.615442\pi$
$74$		0			0
$75$	10.5642	−	6.78921i	1.21985	−	0.783951i
$76$		0			0
$77$	1.39070	+	3.04521i	0.158485	+	0.347033i
$78$		0			0
$79$	−9.47130	−	6.08683i	−1.06560	−	0.684822i	−0.114416	−	0.993433i	$-0.536500\pi$
$79$	−9.47130	−	6.08683i	−1.06560	−	0.684822i	−0.951188	+	0.308611i	$0.900136\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	6.19011	+	1.81758i	0.679453	+	0.199505i	0.603208	−	0.797584i	$-0.293889\pi$
$83$	6.19011	+	1.81758i	0.679453	+	0.199505i	0.0762449	+	0.997089i	$0.475707\pi$
$84$		0			0
$85$	4.66253	−	32.4286i	0.505722	−	3.51737i
$86$		0			0
$87$	2.23527	−	4.89455i	0.239646	−	0.524751i
$88$		0			0
$89$	−5.87066	−	12.8549i	−0.622288	−	1.36262i	−0.913843	−	0.406067i	$-0.866900\pi$
$89$	−5.87066	−	12.8549i	−0.622288	−	1.36262i	0.291555	−	0.956554i	$-0.405827\pi$
$90$		0			0
$91$	−1.69655	−	11.7998i	−0.177847	−	1.23695i
$92$		0			0
$93$	0.632092	+	4.39630i	0.0655449	+	0.455875i
$94$		0			0
$95$	16.7339	−	10.7542i	1.71686	−	1.10336i
$96$		0			0
$97$	6.06108			0.615409			0.307705	−	0.951482i	$-0.400439\pi$
$97$	6.06108			0.615409			0.307705	+	0.951482i	$0.400439\pi$
$98$		0			0
$99$	0.595122	+	1.30314i	0.0598120	+	0.130970i
$100$		0			0
$101$	−7.82493	+	9.03046i	−0.778610	+	0.898564i	−0.997008	−	0.0772958i	$-0.975371\pi$
$101$	−7.82493	+	9.03046i	−0.778610	+	0.898564i	0.218398	+	0.975860i	$0.429917\pi$
$102$		0			0
$103$	−7.60600	+	4.88808i	−0.749442	+	0.481637i	−0.858765	−	0.512369i	$-0.828768\pi$
$103$	−7.60600	+	4.88808i	−0.749442	+	0.481637i	0.109324	+	0.994006i	$0.465132\pi$
$104$		0			0
$105$	−9.79177			−0.955578
$106$		0			0
$107$	9.83908	−	2.88901i	0.951180	−	0.279292i	0.230902	−	0.972977i	$-0.425832\pi$
$107$	9.83908	−	2.88901i	0.951180	−	0.279292i	0.720278	+	0.693685i	$0.244014\pi$
$108$		0			0
$109$	−11.9257	−	7.66421i	−1.14228	−	0.734098i	−0.174192	−	0.984712i	$-0.555731\pi$
$109$	−11.9257	−	7.66421i	−1.14228	−	0.734098i	−0.968087	+	0.250613i	$0.919368\pi$
$110$		0			0
$111$	−1.23159	+	2.69680i	−0.116897	+	0.255969i
$112$		0			0
$113$	−4.40556	+	1.29359i	−0.414440	+	0.121691i	−0.482304	−	0.876004i	$-0.660200\pi$
$113$	−4.40556	+	1.29359i	−0.414440	+	0.121691i	0.0678639	+	0.997695i	$0.478382\pi$
$114$		0			0
$115$	−13.9341	+	16.0808i	−1.29936	+	1.49954i
$116$		0			0
$117$	−0.726006	−	5.04948i	−0.0671193	−	0.466825i
$118$		0			0
$119$	−11.9650	+	13.8084i	−1.09683	+	1.26581i
$120$		0			0
$121$	−7.52726	−	4.83747i	−0.684296	−	0.439770i
$122$		0			0
$123$	3.53712	+	1.03859i	0.318931	+	0.0936466i
$124$		0			0
$125$	20.7383	+	23.9333i	1.85489	+	2.14066i
$126$		0			0
$127$	7.40886	+	8.55029i	0.657430	+	0.758715i	0.982355	−	0.187025i	$-0.0598845\pi$
$127$	7.40886	+	8.55029i	0.657430	+	0.758715i	−0.324925	+	0.945740i	$0.605339\pi$
$128$		0			0
$129$	−4.48897	−	1.31808i	−0.395232	−	0.116050i
$130$		0			0
$131$	−4.55512	+	9.97432i	−0.397982	+	0.871460i	0.599488	+	0.800383i	$0.295371\pi$
$131$	−4.55512	+	9.97432i	−0.397982	+	0.871460i	−0.997471	+	0.0710766i	$0.977357\pi$
$132$		0			0
$133$	−11.0934			−0.961917
$134$		0			0
$135$	−4.19019			−0.360634
$136$		0			0
$137$	−6.83155	+	14.9590i	−0.583659	+	1.27803i	0.355540	+	0.934661i	$0.384297\pi$
$137$	−6.83155	+	14.9590i	−0.583659	+	1.27803i	−0.939199	+	0.343374i	$0.888430\pi$
$138$		0			0
$139$	12.8699	+	3.77894i	1.09161	+	0.320526i	0.777514	−	0.628865i	$-0.216480\pi$
$139$	12.8699	+	3.77894i	1.09161	+	0.320526i	0.314097	+	0.949391i	$0.398298\pi$
$140$		0			0
$141$	5.89985	+	6.80879i	0.496857	+	0.573404i
$142$		0			0
$143$	−4.78589	−	5.52322i	−0.400216	−	0.461874i
$144$		0			0
$145$	21.6333	+	6.35211i	1.79655	+	0.527514i
$146$		0			0
$147$	−1.29488	−	0.832169i	−0.106800	−	0.0686361i
$148$		0			0
$149$	−8.11775	+	9.36838i	−0.665032	+	0.767488i	−0.983590	−	0.180415i	$-0.942256\pi$
$149$	−8.11775	+	9.36838i	−0.665032	+	0.767488i	0.318559	+	0.947903i	$0.396801\pi$
$150$		0			0
$151$	0.161896	+	1.12601i	0.0131749	+	0.0916336i	0.995348	−	0.0963455i	$-0.0307154\pi$
$151$	0.161896	+	1.12601i	0.0131749	+	0.0916336i	−0.982173	+	0.187979i	$0.939806\pi$
$152$		0			0
$153$	−5.12019	+	5.90901i	−0.413943	+	0.477716i
$154$		0			0
$155$	−17.8569	+	5.24326i	−1.43430	+	0.421149i
$156$		0			0
$157$	1.77787	−	3.89299i	0.141890	−	0.310695i	−0.825324	−	0.564660i	$-0.809007\pi$
$157$	1.77787	−	3.89299i	0.141890	−	0.310695i	0.967213	+	0.253965i	$0.0817347\pi$
$158$		0			0
$159$	1.29370	+	0.831409i	0.102597	+	0.0659350i
$160$		0			0
$161$	11.3858	−	3.34317i	0.897327	−	0.263479i
$162$		0			0
$163$	−8.61121			−0.674482			−0.337241	−	0.941418i	$-0.609494\pi$
$163$	−8.61121			−0.674482			−0.337241	+	0.941418i	$0.609494\pi$
$164$		0			0
$165$	−5.04992	+	3.24539i	−0.393136	+	0.252653i
$166$		0			0
$167$	−9.58917	+	11.0665i	−0.742032	+	0.856351i	−0.993771	−	0.111444i	$-0.964452\pi$
$167$	−9.58917	+	11.0665i	−0.742032	+	0.856351i	0.251738	+	0.967795i	$0.418998\pi$
$168$		0			0
$169$	5.41052	+	11.8474i	0.416194	+	0.911337i
$170$		0			0
$171$	−4.74719			−0.363027
$172$		0			0
$173$	−8.35512	+	5.36951i	−0.635228	+	0.408236i	−0.818242	−	0.574874i	$-0.805051\pi$
$173$	−8.35512	+	5.36951i	−0.635228	+	0.408236i	0.183014	+	0.983110i	$0.441415\pi$
$174$		0			0
$175$	−4.17626	−	29.0465i	−0.315696	−	2.19571i
$176$		0			0
$177$	−0.975526	−	6.78493i	−0.0733250	−	0.509986i
$178$		0			0
$179$	−4.67905	−	10.2457i	−0.349729	−	0.765799i	−0.999982	−	0.00608131i	$-0.998064\pi$
$179$	−4.67905	−	10.2457i	−0.349729	−	0.765799i	0.650253	−	0.759718i	$-0.274663\pi$
$180$		0			0
$181$	−4.87740	+	10.6800i	−0.362535	+	0.793840i	0.637198	+	0.770700i	$0.280093\pi$
$181$	−4.87740	+	10.6800i	−0.362535	+	0.793840i	−0.999732	+	0.0231396i	$0.992634\pi$
$182$		0			0
$183$	0.664093	−	4.61887i	0.0490911	−	0.341436i
$184$		0			0
$185$	−11.9195	−	3.49989i	−0.876341	−	0.257317i
$186$		0			0
$187$	−1.59408	+	11.0871i	−0.116571	+	0.810769i
$188$		0			0
$189$	1.96587	+	1.26339i	0.142996	+	0.0918978i
$190$		0			0
$191$	−5.72098	−	12.5272i	−0.413956	−	0.906437i	−0.995663	−	0.0930381i	$-0.970342\pi$
$191$	−5.72098	−	12.5272i	−0.413956	−	0.906437i	0.581707	−	0.813399i	$-0.302385\pi$
$192$		0			0
$193$	−20.3666	+	13.0888i	−1.46602	+	0.942155i	−0.467721	+	0.883876i	$0.654925\pi$
$193$	−20.3666	+	13.0888i	−1.46602	+	0.942155i	−0.998300	+	0.0582782i	$0.981439\pi$
$194$		0			0
$195$	20.5100	−	6.02228i	1.46875	−	0.431265i
$196$		0			0
$197$	−2.66178	+	18.5131i	−0.189644	+	1.31900i	0.643287	+	0.765625i	$0.277570\pi$
$197$	−2.66178	+	18.5131i	−0.189644	+	1.31900i	−0.832931	+	0.553377i	$0.813339\pi$
$198$		0			0
$199$	8.53764	+	9.85296i	0.605217	+	0.698458i	0.972830	−	0.231521i	$-0.0743702\pi$
$199$	8.53764	+	9.85296i	0.605217	+	0.698458i	−0.367613	+	0.929979i	$0.619825\pi$
$200$		0			0
$201$	0.00813786	−	8.18535i	0.000574001	−	0.577350i
$202$		0			0
$203$	−8.23424	−	9.50282i	−0.577930	−	0.666967i
$204$		0			0
$205$	−2.19832	+	15.2897i	−0.153538	+	1.06788i
$206$		0			0
$207$	4.87233	−	1.43065i	0.338650	−	0.0994367i
$208$		0			0
$209$	−5.72120	+	3.67679i	−0.395744	+	0.254329i
$210$		0			0
$211$	−6.56983	−	14.3859i	−0.452286	−	0.990368i	−0.989178	−	0.146718i	$-0.953129\pi$
$211$	−6.56983	−	14.3859i	−0.452286	−	0.990368i	0.536892	−	0.843651i	$-0.319598\pi$
$212$		0			0
$213$	9.80047	+	6.29838i	0.671517	+	0.431558i
$214$		0			0
$215$	2.78990	−	19.4042i	0.190270	−	1.32335i
$216$		0			0
$217$	9.95862	+	2.92411i	0.676035	+	0.198502i
$218$		0			0
$219$	−1.46839	+	10.2129i	−0.0992246	+	0.690122i
$220$		0			0
$221$	16.5695	−	36.2821i	1.11459	−	2.44060i
$222$		0			0
$223$	−0.466043	−	1.02049i	−0.0312085	−	0.0683371i	0.893386	−	0.449290i	$-0.148323\pi$
$223$	−0.466043	−	1.02049i	−0.0312085	−	0.0683371i	−0.924594	+	0.380953i	$0.875596\pi$
$224$		0			0
$225$	−1.78715	−	12.4299i	−0.119143	−	0.828659i
$226$		0			0
$227$	2.49524	+	17.3548i	0.165615	+	1.15188i	0.887818	+	0.460195i	$0.152221\pi$
$227$	2.49524	+	17.3548i	0.165615	+	1.15188i	−0.722203	+	0.691681i	$0.756870\pi$
$228$		0			0
$229$	−2.46725	+	1.58561i	−0.163041	+	0.104780i	−0.619617	−	0.784905i	$-0.712712\pi$
$229$	−2.46725	+	1.58561i	−0.163041	+	0.104780i	0.456576	+	0.889684i	$0.349076\pi$
$230$		0			0
$231$	3.34773			0.220265
$232$		0			0
$233$	−6.08027	−	13.3139i	−0.398332	−	0.872225i	−0.997437	−	0.0715546i	$-0.977204\pi$
$233$	−6.08027	−	13.3139i	−0.398332	−	0.872225i	0.599105	−	0.800671i	$-0.295523\pi$
$234$		0			0
$235$	−24.7215	+	28.5302i	−1.61265	+	1.86110i
$236$		0			0
$237$	−9.47130	+	6.08683i	−0.615227	+	0.395382i
$238$		0			0
$239$	18.9309			1.22454			0.612269	−	0.790649i	$-0.290257\pi$
$239$	18.9309			1.22454			0.612269	+	0.790649i	$0.290257\pi$
$240$		0			0
$241$	5.69790	−	1.67305i	0.367034	−	0.107771i	−0.0930144	−	0.995665i	$-0.529650\pi$
$241$	5.69790	−	1.67305i	0.367034	−	0.107771i	0.460048	+	0.887894i	$0.347832\pi$
$242$		0			0
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$		0			0
$245$	2.67928	−	5.86682i	0.171173	−	0.374817i
$246$		0			0
$247$	23.2364	−	6.82282i	1.47850	−	0.434125i
$248$		0			0
$249$	4.22480	−	4.87567i	0.267736	−	0.308983i
$250$		0			0
$251$	2.38731	+	16.6041i	0.150686	+	1.04804i	0.915074	+	0.403286i	$0.132132\pi$
$251$	2.38731	+	16.6041i	0.150686	+	1.04804i	−0.764388	+	0.644756i	$0.776959\pi$
$252$		0			0
$253$	4.76396	−	5.49790i	0.299507	−	0.345650i
$254$		0			0
$255$	−27.5612	−	17.7125i	−1.72595	−	1.10920i
$256$		0			0
$257$	−9.06668	−	2.66222i	−0.565564	−	0.166065i	−0.0135629	−	0.999908i	$-0.504317\pi$
$257$	−9.06668	−	2.66222i	−0.565564	−	0.166065i	−0.552001	+	0.833844i	$0.686136\pi$
$258$		0			0
$259$	4.53690	+	5.23586i	0.281909	+	0.325341i
$260$		0			0
$261$	−3.52368	−	4.06654i	−0.218110	−	0.251713i
$262$		0			0
$263$	−14.9508	−	4.38995i	−0.921906	−	0.270696i	−0.213861	−	0.976864i	$-0.568604\pi$
$263$	−14.9508	−	4.38995i	−0.921906	−	0.270696i	−0.708044	+	0.706168i	$0.750422\pi$
$264$		0			0
$265$	−2.67684	+	5.86145i	−0.164437	+	0.360066i
$266$		0			0
$267$	−14.1320			−0.864866
$268$		0			0
$269$	21.2268			1.29422			0.647111	−	0.762396i	$-0.275977\pi$
$269$	21.2268			1.29422			0.647111	+	0.762396i	$0.275977\pi$
$270$		0			0
$271$	9.74871	−	21.3467i	0.592192	−	1.29672i	−0.341916	−	0.939730i	$-0.611076\pi$
$271$	9.74871	−	21.3467i	0.592192	−	1.29672i	0.934108	−	0.356990i	$-0.116197\pi$
$272$		0			0
$273$	−11.4382	−	3.35857i	−0.692273	−	0.203270i
$274$		0			0
$275$	−11.7810	−	13.5960i	−0.710423	−	0.819872i
$276$		0			0
$277$	5.58934	+	6.45044i	0.335831	+	0.387569i	0.898398	−	0.439182i	$-0.144732\pi$
$277$	5.58934	+	6.45044i	0.335831	+	0.387569i	−0.562567	+	0.826751i	$0.690186\pi$
$278$		0			0
$279$	4.26159	+	1.25132i	0.255135	+	0.0749144i
$280$		0			0
$281$	5.52119	+	3.54825i	0.329366	+	0.211671i	0.694864	−	0.719141i	$-0.255465\pi$
$281$	5.52119	+	3.54825i	0.329366	+	0.211671i	−0.365497	+	0.930812i	$0.619101\pi$
$282$		0			0
$283$	20.0700	−	23.1620i	1.19304	−	1.37684i	0.284687	−	0.958620i	$-0.408110\pi$
$283$	20.0700	−	23.1620i	1.19304	−	1.37684i	0.908348	−	0.418216i	$-0.137344\pi$
$284$		0			0
$285$	−2.83087	−	19.6892i	−0.167687	−	1.16629i
$286$		0			0
$287$	5.64136	−	6.51047i	0.332999	−	0.384301i
$288$		0			0
$289$	−42.3451	+	12.4336i	−2.49089	+	0.731391i
$290$		0			0
$291$	2.51786	−	5.51335i	0.147600	−	0.323198i
$292$		0			0
$293$	14.6962	+	9.44467i	0.858561	+	0.551763i	0.894234	−	0.447600i	$-0.147721\pi$
$293$	14.6962	+	9.44467i	0.858561	+	0.551763i	−0.0356733	+	0.999364i	$0.511358\pi$
$294$		0			0
$295$	27.5590	−	8.09207i	1.60455	−	0.471138i
$296$		0			0
$297$	1.43260			0.0831277
$298$		0			0
$299$	−21.7927	+	14.0053i	−1.26031	+	0.809950i
$300$		0			0
$301$	−7.15947	+	8.26247i	−0.412665	+	0.476241i
$302$		0			0
$303$	4.96380	+	10.8692i	0.285163	+	0.624419i
$304$		0			0
$305$	19.5530			1.11960
$306$		0			0
$307$	7.09090	−	4.55704i	0.404699	−	0.260084i	−0.322419	−	0.946597i	$-0.604496\pi$
$307$	7.09090	−	4.55704i	0.404699	−	0.260084i	0.727118	+	0.686513i	$0.240860\pi$
$308$		0			0
$309$	1.28671	+	8.94924i	0.0731982	+	0.509105i
$310$		0			0
$311$	3.06426	+	21.3124i	0.173758	+	1.20851i	0.870856	+	0.491538i	$0.163565\pi$
$311$	3.06426	+	21.3124i	0.173758	+	1.20851i	−0.697098	+	0.716976i	$0.745526\pi$
$312$		0			0
$313$	−7.47412	−	16.3660i	−0.422462	−	0.925064i	−0.994490	−	0.104829i	$-0.966570\pi$
$313$	−7.47412	−	16.3660i	−0.422462	−	0.925064i	0.572028	−	0.820234i	$-0.306157\pi$
$314$		0			0
$315$	−4.06765	+	8.90690i	−0.229186	+	0.501847i
$316$		0			0
$317$	1.10449	−	7.68188i	0.0620342	−	0.431457i	−0.935010	−	0.354622i	$-0.884609\pi$
$317$	1.10449	−	7.68188i	0.0620342	−	0.431457i	0.997044	−	0.0768350i	$-0.0244815\pi$
$318$		0			0
$319$	−7.39628	−	2.17174i	−0.414112	−	0.121594i
$320$		0			0
$321$	1.45936	−	10.1501i	0.0814536	−	0.566522i
$322$		0			0
$323$	−31.2249	−	20.0670i	−1.73740	−	1.11656i
$324$		0			0
$325$	26.6123	+	58.2729i	1.47619	+	3.23240i
$326$		0			0
$327$	−11.9257	+	7.66421i	−0.659495	+	0.423832i
$328$		0			0
$329$	20.2005	−	5.93139i	1.11369	−	0.327008i
$330$		0			0
$331$	4.98649	−	34.6818i	0.274082	−	1.90628i	−0.129921	−	0.991524i	$-0.541472\pi$
$331$	4.98649	−	34.6818i	0.274082	−	1.90628i	0.404003	−	0.914758i	$-0.367619\pi$
$332$		0			0
$333$	1.94148	+	2.24058i	0.106392	+	0.122783i
$334$		0			0
$335$	33.9539	−	4.84739i	1.85510	−	0.264841i
$336$		0			0
$337$	−2.77626	−	3.20397i	−0.151232	−	0.174531i	0.675078	−	0.737746i	$-0.264110\pi$
$337$	−2.77626	−	3.20397i	−0.151232	−	0.174531i	−0.826311	+	0.563215i	$0.809564\pi$
$338$		0			0
$339$	−0.653445	+	4.54481i	−0.0354903	+	0.246840i
$340$		0			0
$341$	6.10514	−	1.79263i	0.330612	−	0.0970765i
$342$		0			0
$343$	−16.7870	+	10.7883i	−0.906412	+	0.582515i
$344$		0			0
$345$	8.83916	+	19.3551i	0.475885	+	1.04204i
$346$		0			0
$347$	−11.2615	−	7.23736i	−0.604552	−	0.388522i	0.202259	−	0.979332i	$-0.435172\pi$
$347$	−11.2615	−	7.23736i	−0.604552	−	0.388522i	−0.806810	+	0.590810i	$0.798808\pi$
$348$		0			0
$349$	3.21571	−	22.3658i	0.172133	−	1.19721i	−0.702233	−	0.711947i	$-0.747814\pi$
$349$	3.21571	−	22.3658i	0.172133	−	1.19721i	0.874366	−	0.485266i	$-0.161277\pi$
$350$		0			0
$351$	−4.89477	−	1.43723i	−0.261263	−	0.0767138i
$352$		0			0
$353$	−4.56359	+	31.7405i	−0.242895	+	1.68937i	0.394547	+	0.918876i	$0.370902\pi$
$353$	−4.56359	+	31.7405i	−0.242895	+	1.68937i	−0.637442	+	0.770498i	$0.720008\pi$
$354$		0			0
$355$	−20.2785	+	44.4038i	−1.07627	+	2.35671i
$356$		0			0
$357$	7.59008	+	16.6200i	0.401710	+	0.879622i
$358$		0			0
$359$	−1.65151	−	11.4865i	−0.0871635	−	0.606235i	−0.985848	−	0.167640i	$-0.946385\pi$
$359$	−1.65151	−	11.4865i	−0.0871635	−	0.606235i	0.898685	−	0.438595i	$-0.144524\pi$
$360$		0			0
$361$	−0.503197	−	3.49981i	−0.0264840	−	0.184201i
$362$		0			0
$363$	−7.52726	+	4.83747i	−0.395078	+	0.253902i
$364$		0			0
$365$	−43.2340			−2.26297
$366$		0			0
$367$	−9.75748	−	21.3659i	−0.509336	−	1.11529i	−0.973321	−	0.229448i	$-0.926308\pi$
$367$	−9.75748	−	21.3659i	−0.509336	−	1.11529i	0.463985	−	0.885843i	$-0.346419\pi$
$368$		0			0
$369$	2.41411	−	2.78603i	0.125673	−	0.145035i
$370$		0			0
$371$	3.02315	−	1.94286i	0.156954	−	0.100868i
$372$		0			0
$373$	19.9771			1.03438			0.517188	−	0.855872i	$-0.326979\pi$
$373$	19.9771			1.03438			0.517188	+	0.855872i	$0.326979\pi$
$374$		0			0
$375$	30.3855	−	8.92198i	1.56910	−	0.460729i
$376$		0			0
$377$	23.0921	+	14.8404i	1.18931	+	0.764321i
$378$		0			0
$379$	0.316602	−	0.693263i	0.0162628	−	0.0356105i	−0.901326	−	0.433141i	$-0.857405\pi$
$379$	0.316602	−	0.693263i	0.0162628	−	0.0356105i	0.917589	+	0.397530i	$0.130133\pi$
$380$		0			0
$381$	10.8554	−	3.18742i	0.556137	−	0.163297i
$382$		0			0
$383$	−4.67331	+	5.39329i	−0.238795	+	0.275584i	−0.862479	−	0.506092i	$-0.831090\pi$
$383$	−4.67331	+	5.39329i	−0.238795	+	0.275584i	0.623684	+	0.781676i	$0.285635\pi$
$384$		0			0
$385$	1.99634	+	13.8849i	0.101743	+	0.707639i
$386$		0			0
$387$	−3.06375	+	3.53576i	−0.155739	+	0.179733i
$388$		0			0
$389$	12.2993	+	7.90427i	0.623599	+	0.400763i	0.813935	−	0.580956i	$-0.197321\pi$
$389$	12.2993	+	7.90427i	0.623599	+	0.400763i	−0.190336	+	0.981719i	$0.560958\pi$
$390$		0			0
$391$	38.0955	+	11.1859i	1.92657	+	0.565693i
$392$		0			0
$393$	7.18069	+	8.28696i	0.362218	+	0.418022i
$394$		0			0
$395$	−30.8934	−	35.6529i	−1.55441	−	1.79389i
$396$		0			0
$397$	−24.1824	−	7.10060i	−1.21368	−	0.356369i	−0.388612	−	0.921401i	$-0.627045\pi$
$397$	−24.1824	−	7.10060i	−1.21368	−	0.356369i	−0.825068	+	0.565033i	$0.808864\pi$
$398$		0			0
$399$	−4.60835	+	10.0909i	−0.230706	+	0.505176i
$400$		0			0
$401$	4.25905			0.212687			0.106343	−	0.994329i	$-0.466086\pi$
$401$	4.25905			0.212687			0.106343	+	0.994329i	$0.466086\pi$
$402$		0			0
$403$	−22.6579			−1.12867
$404$		0			0
$405$	−1.74067	+	3.81153i	−0.0864945	+	0.189397i
$406$		0			0
$407$	4.07520	+	1.19659i	0.202000	+	0.0593126i
$408$		0			0
$409$	16.0195	+	18.4875i	0.792116	+	0.914150i	0.997921	−	0.0644427i	$-0.0205270\pi$
$409$	16.0195	+	18.4875i	0.792116	+	0.914150i	−0.205806	+	0.978593i	$0.565982\pi$
$410$		0			0
$411$	10.7693	+	12.4284i	0.531209	+	0.613048i
$412$		0			0
$413$	−15.3694	−	4.51287i	−0.756279	−	0.222064i
$414$		0			0
$415$	22.7414	+	14.6150i	1.11633	+	0.717423i
$416$		0			0
$417$	8.78380	−	10.1370i	0.430145	−	0.496413i
$418$		0			0
$419$	0.126511	+	0.879904i	0.00618047	+	0.0429861i	0.992678	−	0.120788i	$-0.0385422\pi$
$419$	0.126511	+	0.879904i	0.00618047	+	0.0429861i	−0.986498	+	0.163774i	$0.947633\pi$
$420$		0			0
$421$	9.58323	−	11.0596i	0.467058	−	0.539014i	−0.472533	−	0.881313i	$-0.656660\pi$
$421$	9.58323	−	11.0596i	0.467058	−	0.539014i	0.939591	+	0.342299i	$0.111206\pi$
$422$		0			0
$423$	8.64439	−	2.53822i	0.420304	−	0.123413i
$424$		0			0
$425$	40.7878	−	89.3127i	1.97850	−	4.33230i
$426$		0			0
$427$	−9.17345	−	5.89542i	−0.443934	−	0.285299i
$428$		0			0
$429$	−7.01223	+	2.05898i	−0.338553	+	0.0994083i
$430$		0			0
$431$	21.1322			1.01790			0.508950	−	0.860796i	$-0.330034\pi$
$431$	21.1322			1.01790			0.508950	+	0.860796i	$0.330034\pi$
$432$		0			0
$433$	22.8733	−	14.6998i	1.09922	−	0.706426i	0.140302	−	0.990109i	$-0.455193\pi$
$433$	22.8733	−	14.6998i	1.09922	−	0.706426i	0.958918	+	0.283683i	$0.0915562\pi$
$434$		0			0
$435$	14.7649	−	17.0396i	0.707922	−	0.816986i
$436$		0			0
$437$	10.0141	+	21.9279i	0.479041	+	1.04895i
$438$		0			0
$439$	1.67117			0.0797604			0.0398802	−	0.999204i	$-0.487302\pi$
$439$	1.67117			0.0797604			0.0398802	+	0.999204i	$0.487302\pi$
$440$		0			0
$441$	−1.29488	+	0.832169i	−0.0616610	+	0.0396271i
$442$		0			0
$443$	1.73818	+	12.0893i	0.0825834	+	0.574380i	0.988534	+	0.150997i	$0.0482484\pi$
$443$	1.73818	+	12.0893i	0.0825834	+	0.574380i	−0.905951	+	0.423383i	$0.860843\pi$
$444$		0			0
$445$	−8.42730	−	58.6132i	−0.399492	−	2.77853i
$446$		0			0
$447$	5.14954	+	11.2759i	0.243565	+	0.533333i
$448$		0			0
$449$	15.0527	−	32.9607i	0.710379	−	1.55551i	−0.116536	−	0.993187i	$-0.537179\pi$
$449$	15.0527	−	32.9607i	0.710379	−	1.55551i	0.826915	−	0.562327i	$-0.190094\pi$
$450$		0			0
$451$	0.751591	−	5.22743i	0.0353911	−	0.246150i
$452$		0			0
$453$	1.09151	+	0.320497i	0.0512837	+	0.0150582i
$454$		0			0
$455$	7.10888	−	49.4434i	0.333270	−	2.31794i
$456$		0			0
$457$	−29.6858	−	19.0779i	−1.38864	−	0.892427i	−0.389059	−	0.921213i	$-0.627200\pi$
$457$	−29.6858	−	19.0779i	−1.38864	−	0.892427i	−0.999586	+	0.0287856i	$0.990836\pi$
$458$		0			0
$459$	3.24802	+	7.11218i	0.151605	+	0.331968i
$460$		0			0
$461$	10.7103	−	6.88308i	0.498828	−	0.320577i	−0.266919	−	0.963719i	$-0.586006\pi$
$461$	10.7103	−	6.88308i	0.498828	−	0.320577i	0.765747	+	0.643142i	$0.222369\pi$
$462$		0			0
$463$	−7.30028	+	2.14355i	−0.339273	+	0.0996194i	−0.446931	−	0.894569i	$-0.647483\pi$
$463$	−7.30028	+	2.14355i	−0.339273	+	0.0996194i	0.107658	+	0.994188i	$0.465665\pi$
$464$		0			0
$465$	−2.64859	+	18.4213i	−0.122825	+	0.854269i
$466$		0			0
$467$	5.57343	+	6.43209i	0.257908	+	0.297641i	0.869906	−	0.493218i	$-0.164179\pi$
$467$	5.57343	+	6.43209i	0.257908	+	0.297641i	−0.611998	+	0.790859i	$0.709634\pi$
$468$		0			0
$469$	−17.3913	−	7.96326i	−0.803057	−	0.367709i
$470$		0			0
$471$	−2.80264	−	3.23442i	−0.129139	−	0.149034i
$472$		0			0
$473$	−0.953847	+	6.63415i	−0.0438579	+	0.305039i
$474$		0			0
$475$	57.1990	−	16.7952i	2.62447	−	0.770615i
$476$		0			0
$477$	1.29370	−	0.831409i	0.0592343	−	0.0380676i
$478$		0			0
$479$	−11.7173	−	25.6574i	−0.535378	−	1.17231i	−0.963282	−	0.268490i	$-0.913475\pi$
$479$	−11.7173	−	25.6574i	−0.535378	−	1.17231i	0.427904	−	0.903824i	$-0.359252\pi$
$480$		0			0
$481$	−12.7233	−	8.17678i	−0.580133	−	0.372829i
$482$		0			0
$483$	1.68878	−	11.7457i	0.0768420	−	0.534448i
$484$		0			0
$485$	24.3683	+	7.15519i	1.10651	+	0.324900i
$486$		0			0
$487$	−3.63846	+	25.3061i	−0.164875	+	1.14673i	0.724409	+	0.689371i	$0.242113\pi$
$487$	−3.63846	+	25.3061i	−0.164875	+	1.14673i	−0.889283	+	0.457357i	$0.848796\pi$
$488$		0			0
$489$	−3.57723	+	7.83303i	−0.161768	+	0.354222i
$490$		0			0
$491$	7.04081	+	15.4172i	0.317747	+	0.695770i	0.999354	−	0.0359493i	$-0.0114455\pi$
$491$	7.04081	+	15.4172i	0.317747	+	0.695770i	−0.681606	+	0.731719i	$0.738718\pi$
$492$		0			0
$493$	−5.98735	−	41.6429i	−0.269657	−	1.87550i
$494$		0			0
$495$	0.854295	+	5.94176i	0.0383977	+	0.267062i
$496$		0			0
$497$	22.9020	−	14.7182i	1.02730	−	0.660203i
$498$		0			0
$499$	23.5221			1.05299			0.526497	−	0.850177i	$-0.323505\pi$
$499$	23.5221			1.05299			0.526497	+	0.850177i	$0.323505\pi$
$500$		0			0
$501$	6.08295	+	13.3198i	0.271766	+	0.595085i
$502$		0			0
$503$	−14.9864	+	17.2953i	−0.668212	+	0.771158i	−0.984096	−	0.177640i	$-0.943154\pi$
$503$	−14.9864	+	17.2953i	−0.668212	+	0.771158i	0.315883	+	0.948798i	$0.397699\pi$
$504$		0			0
$505$	−42.1204	+	27.0691i	−1.87433	+	1.20456i
$506$		0			0
$507$	13.0244			0.578433
$508$		0			0
$509$	−31.0340	+	9.11240i	−1.37556	+	0.403900i	−0.884221	−	0.467069i	$-0.845310\pi$
$509$	−31.0340	+	9.11240i	−1.37556	+	0.403900i	−0.491337	+	0.870969i	$0.663492\pi$
$510$		0			0
$511$	20.2836	+	13.0355i	0.897294	+	0.576656i
$512$		0			0
$513$	−1.97205	+	4.31819i	−0.0870683	+	0.190653i
$514$		0			0
$515$	−36.3501	+	10.6733i	−1.60178	+	0.470324i
$516$		0			0
$517$	8.45211	−	9.75426i	0.371723	−	0.428992i
$518$		0			0
$519$	1.41344	+	9.83066i	0.0620429	+	0.431518i
$520$		0			0
$521$	−4.40046	+	5.07841i	−0.192788	+	0.222489i	−0.843911	−	0.536483i	$-0.819753\pi$
$521$	−4.40046	+	5.07841i	−0.192788	+	0.222489i	0.651123	+	0.758972i	$0.274298\pi$
$522$		0			0
$523$	14.2729	+	9.17263i	0.624110	+	0.401091i	0.814125	−	0.580690i	$-0.197217\pi$
$523$	14.2729	+	9.17263i	0.624110	+	0.401091i	−0.190015	+	0.981781i	$0.560854\pi$
$524$		0			0
$525$	−28.1565	−	8.26751i	−1.22885	−	0.360824i
$526$		0			0
$527$	22.7414	+	26.2449i	0.990629	+	1.14325i
$528$		0			0
$529$	−1.82467	−	2.10579i	−0.0793337	−	0.0915559i
$530$		0			0
$531$	−6.57704	−	1.93119i	−0.285419	−	0.0838066i
$532$		0			0
$533$	−7.81232	+	17.1066i	−0.338389	+	0.740969i
$534$		0			0
$535$	42.9681			1.85768
$536$		0			0
$537$	−11.2636			−0.486059
$538$		0			0
$539$	−0.916028	+	2.00582i	−0.0394561	+	0.0863969i
$540$		0			0
$541$	−20.4748	−	6.01196i	−0.880282	−	0.258474i	−0.189799	−	0.981823i	$-0.560784\pi$
$541$	−20.4748	−	6.01196i	−0.880282	−	0.258474i	−0.690483	+	0.723349i	$0.742602\pi$
$542$		0			0
$543$	7.68875	+	8.87329i	0.329956	+	0.380789i
$544$		0			0
$545$	−38.8993	−	44.8922i	−1.66626	−	1.92297i
$546$		0			0
$547$	−16.6098	−	4.87709i	−0.710185	−	0.208529i	−0.0933634	−	0.995632i	$-0.529762\pi$
$547$	−16.6098	−	4.87709i	−0.710185	−	0.208529i	−0.616822	+	0.787103i	$0.711580\pi$
$548$		0			0
$549$	−3.92559	−	2.52283i	−0.167540	−	0.107672i
$550$		0			0
$551$	16.7276	−	19.3046i	0.712618	−	0.822405i
$552$		0			0
$553$	3.74421	+	26.0415i	0.159220	+	1.10740i
$554$		0			0
$555$	−8.13516	+	9.38847i	−0.345318	+	0.398519i
$556$		0			0
$557$	9.42932	−	2.76870i	0.399533	−	0.117314i	−0.0757922	−	0.997124i	$-0.524149\pi$
$557$	9.42932	−	2.76870i	0.399533	−	0.117314i	0.475325	+	0.879810i	$0.342330\pi$
$558$		0			0
$559$	9.91464	−	21.7100i	0.419345	−	0.918237i
$560$		0			0
$561$	9.42297	+	6.05578i	0.397838	+	0.255675i
$562$		0			0
$563$	27.6572	−	8.12088i	1.16561	−	0.342254i	0.359000	−	0.933337i	$-0.383118\pi$
$563$	27.6572	−	8.12088i	1.16561	−	0.342254i	0.806610	+	0.591083i	$0.201300\pi$
$564$		0			0
$565$	−19.2395			−0.809410
$566$		0			0
$567$	1.96587	−	1.26339i	0.0825586	−	0.0530572i
$568$		0			0
$569$	25.4643	−	29.3874i	1.06752	−	1.23198i	0.0959101	−	0.995390i	$-0.469424\pi$
$569$	25.4643	−	29.3874i	1.06752	−	1.23198i	0.971609	−	0.236593i	$-0.0760307\pi$
$570$		0			0
$571$	15.0224	+	32.8944i	0.628666	+	1.37659i	0.909045	+	0.416698i	$0.136813\pi$
$571$	15.0224	+	32.8944i	0.628666	+	1.37659i	−0.280379	+	0.959889i	$0.590460\pi$
$572$		0			0
$573$	−13.7717			−0.575322
$574$		0			0
$575$	−53.6454	+	34.4758i	−2.23717	+	1.43774i
$576$		0			0
$577$	−2.56314	−	17.8270i	−0.106705	−	0.742148i	−0.970985	−	0.239138i	$-0.923135\pi$
$577$	−2.56314	−	17.8270i	−0.106705	−	0.742148i	0.864281	−	0.503010i	$-0.167774\pi$
$578$		0			0
$579$	3.44542	+	23.9634i	0.143187	+	0.995886i
$580$		0			0
$581$	−6.26276	−	13.7135i	−0.259823	−	0.568934i
$582$		0			0
$583$	0.915191	−	2.00399i	0.0379033	−	0.0829967i
$584$		0			0
$585$	3.04211	−	21.1583i	0.125776	−	0.874788i
$586$		0			0
$587$	−24.4683	−	7.18454i	−1.00992	−	0.296538i	−0.265396	−	0.964139i	$-0.585503\pi$
$587$	−24.4683	−	7.18454i	−1.00992	−	0.296538i	−0.744519	+	0.667601i	$0.767321\pi$
$588$		0			0
$589$	−3.00066	+	20.8701i	−0.123640	+	0.859935i
$590$		0			0
$591$	15.7343	+	10.1119i	0.647225	+	0.415946i
$592$		0			0
$593$	−8.88530	−	19.4561i	−0.364875	−	0.798966i	−0.999655	−	0.0262723i	$-0.991636\pi$
$593$	−8.88530	−	19.4561i	−0.364875	−	0.798966i	0.634779	−	0.772693i	$-0.281091\pi$
$594$		0			0
$595$	−64.4058	+	41.3911i	−2.64038	+	1.69687i
$596$		0			0
$597$	12.5092	−	3.67304i	0.511969	−	0.150328i
$598$		0			0
$599$	1.87796	−	13.0615i	0.0767314	−	0.533678i	−0.914810	−	0.403885i	$-0.867660\pi$
$599$	1.87796	−	13.0615i	0.0767314	−	0.533678i	0.991541	−	0.129793i	$-0.0414313\pi$
$600$		0			0
$601$	16.5009	+	19.0431i	0.673087	+	0.776784i	0.984856	−	0.173374i	$-0.0554668\pi$
$601$	16.5009	+	19.0431i	0.673087	+	0.776784i	−0.311769	+	0.950158i	$0.600921\pi$
$602$		0			0
$603$	−7.44227	−	3.40772i	−0.303073	−	0.138773i
$604$		0			0
$605$	−24.5523	−	28.3349i	−0.998194	−	1.15198i
$606$		0			0
$607$	1.17089	−	8.14371i	0.0475249	−	0.330543i	−0.952164	−	0.305588i	$-0.901147\pi$
$607$	1.17089	−	8.14371i	0.0475249	−	0.330543i	0.999689	−	0.0249544i	$-0.00794406\pi$
$608$		0			0
$609$	−12.0647	+	3.54251i	−0.488886	+	0.143550i
$610$		0			0
$611$	−38.6642	+	24.8480i	−1.56419	+	1.00524i
$612$		0			0
$613$	−1.05561	−	2.31146i	−0.0426356	−	0.0933588i	0.887116	−	0.461547i	$-0.152705\pi$
$613$	−1.05561	−	2.31146i	−0.0426356	−	0.0933588i	−0.929751	+	0.368188i	$0.879978\pi$
$614$		0			0
$615$	12.9948	+	8.35123i	0.524000	+	0.336754i
$616$		0			0
$617$	2.23028	−	15.5120i	0.0897879	−	0.624488i	−0.894388	−	0.447292i	$-0.852388\pi$
$617$	2.23028	−	15.5120i	0.0897879	−	0.624488i	0.984176	−	0.177196i	$-0.0567026\pi$
$618$		0			0
$619$	29.7875	+	8.74640i	1.19726	+	0.351547i	0.818805	−	0.574072i	$-0.194637\pi$
$619$	29.7875	+	8.74640i	1.19726	+	0.351547i	0.378456	+	0.925619i	$0.376455\pi$
$620$		0			0
$621$	0.722679	−	5.02634i	0.0290001	−	0.201700i
$622$		0			0
$623$	−13.7187	+	30.0398i	−0.549629	+	1.20352i
$624$		0			0
$625$	29.0407	+	63.5902i	1.16163	+	2.54361i
$626$		0			0
$627$	0.967856	+	6.73158i	0.0386524	+	0.268834i
$628$		0			0
$629$	3.29891	+	22.9444i	0.131536	+	0.914854i
$630$		0			0
$631$	25.7888	−	16.5734i	1.02663	−	0.659778i	0.0849880	−	0.996382i	$-0.472915\pi$
$631$	25.7888	−	16.5734i	1.02663	−	0.659778i	0.941646	+	0.336604i	$0.109278\pi$
$632$		0			0
$633$	−15.8151			−0.628594
$634$		0			0
$635$	19.6933	+	43.1223i	0.781505	+	1.71126i
$636$		0			0
$637$	5.14211	−	5.93432i	0.203738	−	0.235126i
$638$		0			0
$639$	9.80047	−	6.29838i	0.387701	−	0.249160i
$640$		0			0
$641$	−25.0365			−0.988881			−0.494441	−	0.869211i	$-0.664627\pi$
$641$	−25.0365			−0.988881			−0.494441	+	0.869211i	$0.664627\pi$
$642$		0			0
$643$	−18.7155	+	5.49537i	−0.738068	+	0.216716i	−0.629095	−	0.777329i	$-0.716574\pi$
$643$	−18.7155	+	5.49537i	−0.738068	+	0.216716i	−0.108973	+	0.994045i	$0.534756\pi$
$644$		0			0
$645$	−16.4917	−	10.5986i	−0.649360	−	0.417318i
$646$		0			0
$647$	10.1264	−	22.1737i	0.398109	−	0.871737i	−0.599349	−	0.800488i	$-0.704574\pi$
$647$	10.1264	−	22.1737i	0.398109	−	0.871737i	0.997458	−	0.0712499i	$-0.0226988\pi$
$648$		0			0
$649$	−9.42224	+	2.76662i	−0.369855	+	0.108599i
$650$		0			0
$651$	6.79683	−	7.84396i	0.266389	−	0.307429i
$652$		0			0
$653$	−1.02680	−	7.14154i	−0.0401817	−	0.279470i	0.959818	−	0.280625i	$-0.0905416\pi$
$653$	−1.02680	−	7.14154i	−0.0401817	−	0.279470i	−0.999999	+	0.00115455i	$0.999632\pi$
$654$		0			0
$655$	−30.0885	+	34.7240i	−1.17565	+	1.35678i
$656$		0			0
$657$	8.67996	+	5.57827i	0.338638	+	0.217629i
$658$		0			0
$659$	−13.9341	−	4.09143i	−0.542797	−	0.159380i	−0.00117118	−	0.999999i	$-0.500373\pi$
$659$	−13.9341	−	4.09143i	−0.542797	−	0.159380i	−0.541626	+	0.840620i	$0.682191\pi$
$660$		0			0
$661$	−27.0136	−	31.1754i	−1.05071	−	1.21258i	−0.976540	−	0.215337i	$-0.930915\pi$
$661$	−27.0136	−	31.1754i	−1.05071	−	1.21258i	−0.0741694	−	0.997246i	$-0.523631\pi$
$662$		0			0
$663$	−26.1202	−	30.1443i	−1.01442	−	1.17071i
$664$		0			0
$665$	−44.6005	−	13.0959i	−1.72953	−	0.507836i
$666$		0			0
$667$	−11.3507	+	24.8547i	−0.439503	+	0.962377i
$668$		0			0
$669$	−1.12187			−0.0433741
$670$		0			0
$671$	−6.68502			−0.258072
$672$		0			0
$673$	5.00844	−	10.9669i	0.193061	−	0.422745i	−0.788202	−	0.615416i	$-0.788988\pi$
$673$	5.00844	−	10.9669i	0.193061	−	0.422745i	0.981263	+	0.192672i	$0.0617152\pi$
$674$		0			0
$675$	−12.0490	−	3.53792i	−0.463768	−	0.136174i
$676$		0			0
$677$	11.9878	+	13.8347i	0.460729	+	0.531709i	0.937810	−	0.347150i	$-0.112851\pi$
$677$	11.9878	+	13.8347i	0.460729	+	0.531709i	−0.477081	+	0.878859i	$0.658305\pi$
$678$		0			0
$679$	−9.27526	−	10.7042i	−0.355952	−	0.410790i
$680$		0			0
$681$	16.8230	+	4.93968i	0.644659	+	0.189289i
$682$		0			0
$683$	−14.9527	−	9.60952i	−0.572149	−	0.367698i	0.222346	−	0.974968i	$-0.428628\pi$
$683$	−14.9527	−	9.60952i	−0.572149	−	0.367698i	−0.794496	+	0.607270i	$0.792265\pi$
$684$		0			0
$685$	−45.1253	+	52.0774i	−1.72415	+	1.98977i
$686$		0			0
$687$	0.417385	+	2.90297i	0.0159242	+	0.110755i
$688$		0			0
$689$	−5.13742	+	5.92889i	−0.195720	+	0.225873i
$690$		0			0
$691$	−30.5555	+	8.97192i	−1.16239	+	0.341308i	−0.805360	−	0.592786i	$-0.798028\pi$
$691$	−30.5555	+	8.97192i	−1.16239	+	0.341308i	−0.357028	+	0.934094i	$0.616210\pi$
$692$		0			0
$693$	1.39070	−	3.04521i	0.0528283	−	0.115678i
$694$		0			0
$695$	47.2818	+	30.3862i	1.79350	+	1.15261i
$696$		0			0
$697$	27.6558	−	8.12048i	1.04754	−	0.307585i
$698$		0			0
$699$	−14.6366			−0.553608
$700$		0			0
$701$	36.9322	−	23.7349i	1.39491	−	0.896455i	0.395156	−	0.918614i	$-0.370690\pi$
$701$	36.9322	−	23.7349i	1.39491	−	0.896455i	0.999754	+	0.0221594i	$0.00705413\pi$
$702$		0			0
$703$	−9.21656	+	10.6365i	−0.347609	+	0.401162i
$704$		0			0
$705$	15.6823	+	34.3393i	0.590628	+	1.29329i
$706$		0			0
$707$	27.9228			1.05014
$708$		0			0
$709$	−5.21680	+	3.35264i	−0.195921	+	0.125911i	−0.634923	−	0.772575i	$-0.718968\pi$
$709$	−5.21680	+	3.35264i	−0.195921	+	0.125911i	0.439002	+	0.898486i	$0.355332\pi$
$710$		0			0
$711$	1.60226	+	11.1440i	0.0600894	+	0.417931i
$712$		0			0
$713$	−3.20978	−	22.3245i	−0.120207	−	0.836060i
$714$		0			0
$715$	−12.7213	−	27.8557i	−0.475748	−	1.04174i
$716$		0			0
$717$	7.86418	−	17.2202i	0.293693	−	0.643099i
$718$		0			0
$719$	6.48682	−	45.1168i	0.241917	−	1.68257i	−0.400562	−	0.916270i	$-0.631185\pi$
$719$	6.48682	−	45.1168i	0.241917	−	1.68257i	0.642480	−	0.766303i	$-0.277906\pi$
$720$		0			0
$721$	20.2721	+	5.95242i	0.754972	+	0.221680i
$722$		0			0
$723$	0.845129	−	5.87800i	0.0314307	−	0.218605i
$724$		0			0
$725$	56.8440	+	36.5314i	2.11113	+	1.35674i
$726$		0			0
$727$	8.86076	+	19.4024i	0.328627	+	0.719594i	0.999764	−	0.0217404i	$-0.00692073\pi$
$727$	8.86076	+	19.4024i	0.328627	+	0.719594i	−0.671136	+	0.741334i	$0.734193\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	−35.0981	+	10.3057i	−1.29815	+	0.381171i
$732$		0			0
$733$	6.38073	−	44.3790i	0.235678	−	1.63917i	−0.437160	−	0.899384i	$-0.644016\pi$
$733$	6.38073	−	44.3790i	0.235678	−	1.63917i	0.672837	−	0.739790i	$-0.265075\pi$
$734$		0			0
$735$	−4.22363	−	4.87433i	−0.155791	−	0.179792i
$736$		0			0
$737$	−11.6086	+	1.65729i	−0.427608	+	0.0610470i
$738$		0			0
$739$	21.1573	+	24.4169i	0.778285	+	0.898189i	0.996984	−	0.0776036i	$-0.0247269\pi$
$739$	21.1573	+	24.4169i	0.778285	+	0.898189i	−0.218699	+	0.975792i	$0.570181\pi$
$740$		0			0
$741$	3.44649	−	23.9709i	0.126610	−	0.880591i
$742$		0			0
$743$	−10.2972	+	3.02352i	−0.377766	+	0.110922i	−0.465103	−	0.885257i	$-0.653983\pi$
$743$	−10.2972	+	3.02352i	−0.377766	+	0.110922i	0.0873368	+	0.996179i	$0.472164\pi$
$744$		0			0
$745$	−43.6966	+	28.0821i	−1.60092	+	1.02885i
$746$		0			0
$747$	−2.68003	−	5.86844i	−0.0980570	−	0.214715i
$748$		0			0
$749$	−20.1589	−	12.9553i	−0.736590	−	0.473378i
$750$		0			0
$751$	4.38189	−	30.4767i	0.159897	−	1.11211i	−0.738922	−	0.673791i	$-0.764665\pi$
$751$	4.38189	−	30.4767i	0.159897	−	1.11211i	0.898819	−	0.438319i	$-0.144426\pi$
$752$		0			0
$753$	16.0954	+	4.72603i	0.586548	+	0.172226i
$754$		0			0
$755$	−0.678376	+	4.71821i	−0.0246886	+	0.171713i
$756$		0			0
$757$	16.6814	−	36.5273i	0.606297	−	1.32761i	−0.318781	−	0.947829i	$-0.603273\pi$
$757$	16.6814	−	36.5273i	0.606297	−	1.32761i	0.925078	−	0.379777i	$-0.123999\pi$
$758$		0			0
$759$	−3.02205	−	6.61736i	−0.109693	−	0.240195i
$760$		0			0
$761$	−3.49794	−	24.3287i	−0.126800	−	0.881915i	−0.949573	−	0.313545i	$-0.898483\pi$
$761$	−3.49794	−	24.3287i	−0.126800	−	0.881915i	0.822773	−	0.568370i	$-0.192426\pi$
$762$		0			0
$763$	4.71450	+	32.7901i	0.170676	+	1.18708i
$764$		0			0
$765$	−27.5612	+	17.7125i	−0.996477	+	0.640397i
$766$		0			0
$767$	34.9686			1.26264
$768$		0			0
$769$	11.2007	+	24.5261i	0.403908	+	0.884435i	0.996859	+	0.0791964i	$0.0252354\pi$
$769$	11.2007	+	24.5261i	0.403908	+	0.884435i	−0.592951	+	0.805238i	$0.702037\pi$
$770$		0			0
$771$	−6.18807	+	7.14142i	−0.222858	+	0.257192i
$772$		0			0
$773$	−38.2507	+	24.5822i	−1.37578	+	0.884162i	−0.999110	−	0.0421842i	$-0.986568\pi$
$773$	−38.2507	+	24.5822i	−1.37578	+	0.884162i	−0.376673	+	0.926346i	$0.622932\pi$
$774$		0			0
$775$	−55.7751			−2.00350
$776$		0			0
$777$	6.64740	−	1.95185i	0.238474	−	0.0700224i
$778$		0			0
$779$	14.7221	+	9.46135i	0.527476	+	0.338988i
$780$		0			0
$781$	6.93308	−	15.1813i	0.248085	−	0.543231i
$782$		0			0
$783$	−5.16285	+	1.51595i	−0.184505	+	0.0541756i
$784$		0			0
$785$	11.7436	−	13.5528i	0.419147	−	0.483721i
$786$		0			0
$787$	−0.755777	−	5.25655i	−0.0269405	−	0.187376i	0.971907	−	0.235364i	$-0.0756281\pi$
$787$	−0.755777	−	5.25655i	−0.0269405	−	0.187376i	−0.998848	+	0.0479881i	$0.984719\pi$
$788$		0			0
$789$	−10.2040	+	11.7761i	−0.363273	+	0.419239i
$790$		0			0
$791$	9.02637	+	5.80089i	0.320941	+	0.206256i
$792$		0			0
$793$	22.8408	+	6.70665i	0.811099	+	0.238160i
$794$		0			0
$795$	4.21977	+	4.86987i	0.149660	+	0.172717i
$796$		0			0
$797$	−19.7466	−	22.7888i	−0.699462	−	0.807222i	0.289218	−	0.957263i	$-0.406605\pi$
$797$	−19.7466	−	22.7888i	−0.699462	−	0.807222i	−0.988680	+	0.150041i	$0.952059\pi$
$798$		0			0
$799$	67.5883	+	19.8457i	2.39110	+	0.702091i
$800$		0			0
$801$	−5.87066	+	12.8549i	−0.207429	+	0.454207i
$802$		0			0
$803$	14.7814			0.521624
$804$		0			0
$805$	49.7228			1.75250
$806$		0			0
$807$	8.81794	−	19.3086i	0.310406	−	0.679695i
$808$		0			0
$809$	−9.19176	−	2.69894i	−0.323165	−	0.0948899i	0.116126	−	0.993234i	$-0.462952\pi$
$809$	−9.19176	−	2.69894i	−0.323165	−	0.0948899i	−0.439291	+	0.898345i	$0.644770\pi$
$810$		0			0
$811$	22.4509	+	25.9097i	0.788357	+	0.909813i	0.997683	−	0.0680331i	$-0.0216723\pi$
$811$	22.4509	+	25.9097i	0.788357	+	0.909813i	−0.209326	+	0.977846i	$0.567127\pi$
$812$		0			0
$813$	−15.3679	−	17.7355i	−0.538975	−	0.622011i
$814$		0			0
$815$	−34.6210	−	10.1656i	−1.21272	−	0.356087i
$816$		0			0
$817$	−18.6839	−	12.0074i	−0.653668	−	0.420087i
$818$		0			0
$819$	−7.80668	+	9.00938i	−0.272787	+	0.314813i
$820$		0			0
$821$	−1.00274	−	6.97420i	−0.0349958	−	0.243401i	0.964813	−	0.262936i	$-0.0846907\pi$
$821$	−1.00274	−	6.97420i	−0.0349958	−	0.243401i	−0.999809	+	0.0195343i	$0.993782\pi$
$822$		0			0
$823$	17.7959	−	20.5376i	0.620328	−	0.715896i	−0.355441	−	0.934699i	$-0.615669\pi$
$823$	17.7959	−	20.5376i	0.620328	−	0.715896i	0.975769	+	0.218802i	$0.0702149\pi$
$824$		0			0
$825$	−17.2614	+	5.06841i	−0.600965	+	0.176459i
$826$		0			0
$827$	−16.3634	+	35.8308i	−0.569011	+	1.24596i	0.378311	+	0.925678i	$0.376505\pi$
$827$	−16.3634	+	35.8308i	−0.569011	+	1.24596i	−0.947322	+	0.320282i	$0.896222\pi$
$828$		0			0
$829$	25.1511	+	16.1637i	0.873535	+	0.561387i	0.898832	−	0.438293i	$-0.144417\pi$
$829$	25.1511	+	16.1637i	0.873535	+	0.561387i	−0.0252968	+	0.999680i	$0.508053\pi$
$830$		0			0
$831$	8.18942	−	2.40463i	0.284088	−	0.0834157i
$832$		0			0
$833$	−12.0348			−0.416982
$834$		0			0
$835$	−51.6170	+	33.1723i	−1.78628	+	1.14797i
$836$		0			0
$837$	2.90857	−	3.35667i	0.100535	−	0.116023i
$838$		0			0
$839$	−19.8039	−	43.3645i	−0.683707	−	1.49711i	−0.858667	−	0.512534i	$-0.828707\pi$
$839$	−19.8039	−	43.3645i	−0.683707	−	1.49711i	0.174960	−	0.984576i	$-0.444020\pi$
$840$		0			0
$841$	−0.0469292			−0.00161825
$842$		0			0
$843$	5.52119	−	3.54825i	0.190160	−	0.122208i
$844$		0			0
$845$	7.76678	+	54.0191i	0.267185	+	1.85831i
$846$		0			0
$847$	2.97569	+	20.6963i	0.102246	+	0.711135i
$848$		0			0
$849$	−12.7315	−	27.8781i	−0.436944	−	0.956774i
$850$		0			0
$851$	6.25404	−	13.6944i	0.214386	−	0.469439i
$852$		0			0
$853$	−7.43888	+	51.7385i	−0.254702	+	1.77149i	0.314462	+	0.949270i	$0.398176\pi$
$853$	−7.43888	+	51.7385i	−0.254702	+	1.77149i	−0.569164	+	0.822224i	$0.692733\pi$
$854$		0			0
$855$	−19.0859	−	5.60412i	−0.652723	−	0.191657i
$856$		0			0
$857$	1.59778	−	11.1128i	0.0545791	−	0.379606i	−0.944164	−	0.329477i	$-0.893128\pi$
$857$	1.59778	−	11.1128i	0.0545791	−	0.379606i	0.998743	−	0.0501291i	$-0.0159633\pi$
$858$		0			0
$859$	−33.8339	−	21.7437i	−1.15440	−	0.741887i	−0.183888	−	0.982947i	$-0.558868\pi$
$859$	−33.8339	−	21.7437i	−1.15440	−	0.741887i	−0.970510	+	0.241060i	$0.922505\pi$
$860$		0			0
$861$	−3.57863	−	7.83611i	−0.121959	−	0.267054i
$862$		0			0
$863$	7.40062	−	4.75609i	0.251920	−	0.161899i	−0.408586	−	0.912720i	$-0.633978\pi$
$863$	7.40062	−	4.75609i	0.251920	−	0.161899i	0.660506	+	0.750821i	$0.270342\pi$
$864$		0			0
$865$	−39.9302	+	11.7246i	−1.35767	+	0.398647i
$866$		0			0
$867$	−6.28075	+	43.6836i	−0.213306	+	1.48357i
$868$		0			0
$869$	10.5622	+	12.1895i	0.358299	+	0.413499i
$870$		0			0
$871$	41.3259	+	5.98371i	1.40027	+	0.202750i
$872$		0			0
$873$	−3.96916	−	4.58066i	−0.134336	−	0.155032i
$874$		0			0
$875$	10.5318	−	73.2501i	0.356039	−	2.47631i
$876$		0			0
$877$	50.9973	−	14.9742i	1.72206	−	0.505642i	0.736711	−	0.676207i	$-0.236378\pi$
$877$	50.9973	−	14.9742i	1.72206	−	0.505642i	0.985346	+	0.170566i	$0.0545595\pi$
$878$		0			0
$879$	14.6962	−	9.44467i	0.495690	−	0.318561i
$880$		0			0
$881$	9.34173	+	20.4555i	0.314731	+	0.689165i	0.999205	−	0.0398728i	$-0.0126953\pi$
$881$	9.34173	+	20.4555i	0.314731	+	0.689165i	−0.684474	+	0.729037i	$0.739968\pi$
$882$		0			0
$883$	−6.37473	−	4.09679i	−0.214527	−	0.137868i	0.428965	−	0.903321i	$-0.358878\pi$
$883$	−6.37473	−	4.09679i	−0.214527	−	0.137868i	−0.643491	+	0.765453i	$0.722515\pi$
$884$		0			0
$885$	4.08764	−	28.4302i	0.137404	−	0.955669i
$886$		0			0
$887$	−12.0064	−	3.52538i	−0.403134	−	0.118371i	0.0738787	−	0.997267i	$-0.476462\pi$
$887$	−12.0064	−	3.52538i	−0.403134	−	0.118371i	−0.477013	+	0.878896i	$0.658280\pi$
$888$		0			0
$889$	3.76253	−	26.1690i	0.126191	−	0.877679i
$890$		0			0
$891$	0.595122	−	1.30314i	0.0199373	−	0.0436567i
$892$		0			0
$893$	17.7669	+	38.9040i	0.594546	+	1.30187i
$894$		0			0
$895$	−6.71676	−	46.7161i	−0.224517	−	1.56155i
$896$		0			0
$897$	3.68668	+	25.6414i	0.123095	+	0.856142i
$898$		0			0
$899$	−20.1050	+	12.9207i	−0.670540	+	0.430930i
$900$		0			0
$901$	12.0238			0.400572
$902$		0			0
$903$	4.54165	+	9.94483i	0.151137	+	0.330943i
$904$		0			0
$905$	−32.2173	+	37.1808i	−1.07094	+	1.23593i
$906$		0			0
$907$	8.54531	−	5.49174i	0.283743	−	0.182350i	−0.391026	−	0.920380i	$-0.627880\pi$
$907$	8.54531	−	5.49174i	0.283743	−	0.182350i	0.674769	+	0.738029i	$0.264243\pi$
$908$		0			0
$909$	11.9490			0.396323
$910$		0			0
$911$	43.2885	−	12.7106i	1.43421	−	0.421122i	0.529923	−	0.848046i	$-0.322221\pi$
$911$	43.2885	−	12.7106i	1.43421	−	0.421122i	0.904288	+	0.426923i	$0.140403\pi$
$912$		0			0
$913$	−7.77513	−	4.99677i	−0.257319	−	0.165369i
$914$		0			0
$915$	8.12259	−	17.7860i	0.268525	−	0.587987i
$916$		0			0
$917$	24.5859	−	7.21907i	0.811898	−	0.238395i
$918$		0			0
$919$	0.582924	−	0.672730i	0.0192289	−	0.0221913i	−0.746054	−	0.665886i	$-0.768054\pi$
$919$	0.582924	−	0.672730i	0.0192289	−	0.0221913i	0.765283	+	0.643694i	$0.222599\pi$
$920$		0			0
$921$	−1.19957	−	8.34317i	−0.0395271	−	0.274917i
$922$		0			0
$923$	−38.9188	+	44.9147i	−1.28103	+	1.47838i
$924$		0			0
$925$	−31.3199	−	20.1281i	−1.02979	−	0.661807i
$926$		0			0
$927$	8.67504	+	2.54722i	0.284926	+	0.0836617i
$928$		0			0
$929$	15.5616	+	17.9591i	0.510561	+	0.589218i	0.951242	−	0.308445i	$-0.0998086\pi$
$929$	15.5616	+	17.9591i	0.510561	+	0.589218i	−0.440682	+	0.897664i	$0.645263\pi$
$930$		0			0
$931$	−4.78507	−	5.52226i	−0.156824	−	0.180985i
$932$		0			0
$933$	20.6594	+	6.06614i	0.676357	+	0.198596i
$934$		0			0
$935$	−19.4974	+	42.6934i	−0.637634	+	1.39622i
$936$		0			0
$937$	14.7886			0.483122			0.241561	−	0.970386i	$-0.422341\pi$
$937$	14.7886			0.483122			0.241561	+	0.970386i	$0.422341\pi$
$938$		0			0
$939$	−17.9919			−0.587145
$940$		0			0
$941$	−3.21652	+	7.04320i	−0.104856	+	0.229602i	−0.954786	−	0.297293i	$-0.903916\pi$
$941$	−3.21652	+	7.04320i	−0.104856	+	0.229602i	0.849931	+	0.526894i	$0.176644\pi$
$942$		0			0
$943$	−17.9616	−	5.27399i	−0.584909	−	0.171745i
$944$		0			0
$945$	6.41224	+	7.40012i	0.208590	+	0.240726i
$946$		0			0
$947$	31.2623	+	36.0787i	1.01589	+	1.17240i	0.984943	+	0.172878i	$0.0553066\pi$
$947$	31.2623	+	36.0787i	1.01589	+	1.17240i	0.0309460	+	0.999521i	$0.490148\pi$
$948$		0			0
$949$	−50.5037	−	14.8292i	−1.63942	−	0.481377i
$950$		0			0
$951$	−6.52886	−	4.19585i	−0.211713	−	0.136060i
$952$		0			0
$953$	21.4654	−	24.7724i	0.695334	−	0.802458i	−0.292780	−	0.956180i	$-0.594580\pi$
$953$	21.4654	−	24.7724i	0.695334	−	0.802458i	0.988114	+	0.153722i	$0.0491259\pi$
$954$		0			0
$955$	−8.21245	−	57.1188i	−0.265749	−	1.84832i
$956$		0			0
$957$	−5.04801	+	5.82571i	−0.163179	+	0.188319i
$958$		0			0
$959$	36.8728	−	10.8268i	1.19068	−	0.349617i
$960$		0			0
$961$	−4.68299	+	10.2543i	−0.151064	+	0.330784i
$962$		0			0
$963$	−8.62660	−	5.54398i	−0.277988	−	0.178652i
$964$		0			0
$965$	−97.3347	+	28.5800i	−3.13332	+	0.920024i
$966$		0			0
$967$	−11.7186			−0.376845			−0.188423	−	0.982088i	$-0.560337\pi$
$967$	−11.7186			−0.376845			−0.188423	+	0.982088i	$0.560337\pi$
$968$		0			0
$969$	−31.2249	+	20.0670i	−1.00309	+	0.644645i
$970$		0			0
$971$	−28.0774	+	32.4031i	−0.901047	+	1.03986i	0.0979547	+	0.995191i	$0.468770\pi$
$971$	−28.0774	+	32.4031i	−0.901047	+	1.03986i	−0.999002	+	0.0446727i	$0.985775\pi$
$972$		0			0
$973$	−13.0210	−	28.5119i	−0.417433	−	0.914050i
$974$		0			0
$975$	64.0620			2.05163
$976$		0			0
$977$	5.37668	−	3.45538i	0.172015	−	0.110548i	−0.451800	−	0.892119i	$-0.649218\pi$
$977$	5.37668	−	3.45538i	0.172015	−	0.110548i	0.623816	+	0.781572i	$0.285582\pi$
$978$		0			0
$979$	2.88123	+	20.0394i	0.0920846	+	0.640463i
$980$		0			0
$981$	2.01748	+	14.0319i	0.0644131	+	0.448003i
$982$		0			0
$983$	5.67773	+	12.4325i	0.181091	+	0.396535i	0.978307	−	0.207160i	$-0.0664220\pi$
$983$	5.67773	+	12.4325i	0.181091	+	0.396535i	−0.797216	+	0.603694i	$0.793695\pi$
$984$		0			0
$985$	−32.5565	+	71.2888i	−1.03734	+	2.27145i
$986$		0			0
$987$	2.99619	−	20.8390i	0.0953698	−	0.663312i
$988$		0			0
$989$	22.7951	+	6.69324i	0.724842	+	0.212833i
$990$		0			0
$991$	−7.33066	+	50.9859i	−0.232866	+	1.61962i	0.452737	+	0.891644i	$0.350447\pi$
$991$	−7.33066	+	50.9859i	−0.232866	+	1.61962i	−0.685604	+	0.727975i	$0.740462\pi$
$992$		0			0
$993$	−29.4762	−	18.9432i	−0.935398	−	0.601144i
$994$		0			0
$995$	22.6937	+	49.6922i	0.719438	+	1.57535i
$996$		0			0
$997$	−21.4049	+	13.7561i	−0.677900	+	0.435660i	−0.833766	−	0.552119i	$-0.813820\pi$
$997$	−21.4049	+	13.7561i	−0.677900	+	0.435660i	0.155866	+	0.987778i	$0.450183\pi$
$998$		0			0
$999$	2.84462	−	0.835257i	0.0899999	−	0.0264264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.241.6	✓	60
67.62	even	11	inner	804.2.q.a.397.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.241.6	✓	60	1.1	even	1	trivial
804.2.q.a.397.6	yes	60	67.62	even	11	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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{3} +(4.02046 + 1.18051i) q^{5} +(-1.53030 - 1.76606i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{3} +(4.02046 + 1.18051i) q^{5} +(-1.53030 - 1.76606i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-1.37457 - 0.403609i) q^{11} +(4.29158 + 2.75803i) q^{13} +(2.74399 - 3.16674i) q^{15} +(-1.11272 - 7.73916i) q^{17} +(3.10875 - 3.58769i) q^{19} +(-2.24217 + 0.658361i) q^{21} +(-2.10949 + 4.61914i) q^{23} +(10.5642 + 6.78921i) q^{25} +(-0.959493 + 0.281733i) q^{27} +5.38081 q^{29} +(-3.73643 + 2.40126i) q^{31} +(-0.938151 + 1.08268i) q^{33} +(-4.06765 - 8.90690i) q^{35} -2.96472 q^{37} +(4.29158 - 2.75803i) q^{39} +(0.524636 + 3.64892i) q^{41} +(-0.665817 - 4.63086i) q^{43} +(-1.74067 - 3.81153i) q^{45} +(-3.74261 + 8.19517i) q^{47} +(0.219055 - 1.52356i) q^{49} +(-7.50203 - 2.20280i) q^{51} +(-0.218855 + 1.52217i) q^{53} +(-5.04992 - 3.24539i) q^{55} +(-1.97205 - 4.31819i) q^{57} +(5.76654 - 3.70593i) q^{59} +(4.47734 - 1.31467i) q^{61} +(-0.332566 + 2.31304i) q^{63} +(13.9982 + 16.1548i) q^{65} +(7.44904 - 3.39291i) q^{67} +(3.32540 + 3.83772i) q^{69} +(-1.65795 + 11.5313i) q^{71} +(-9.89995 + 2.90689i) q^{73} +(10.5642 - 6.78921i) q^{75} +(1.39070 + 3.04521i) q^{77} +(-9.47130 - 6.08683i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(6.19011 + 1.81758i) q^{83} +(4.66253 - 32.4286i) q^{85} +(2.23527 - 4.89455i) q^{87} +(-5.87066 - 12.8549i) q^{89} +(-1.69655 - 11.7998i) q^{91} +(0.632092 + 4.39630i) q^{93} +(16.7339 - 10.7542i) q^{95} +6.06108 q^{97} +(0.595122 + 1.30314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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