LMFDB - Embedded newform 804.2.i.d.565.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.i (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 11x^{6} + 4x^{5} + 91x^{4} - 6x^{3} + 129x^{2} + 36x + 144 $ x^8 - x^7 + 11x^6 + 4x^5 + 91x^4 - 6x^3 + 129x^2 + 36x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			565.3
Root			$0.641129 - 1.11047i$ of defining polynomial
Character	$\chi$	$=$	804.565
Dual form			804.2.i.d.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.28226 q^{5} +(0.641129 + 1.11047i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.28226 q^{5} +(0.641129 + 1.11047i) q^{7} +1.00000 q^{9} +(1.00000 + 1.73205i) q^{11} +(-2.31904 + 4.01669i) q^{13} -1.28226 q^{15} +(2.81904 - 4.88271i) q^{17} +(1.17791 - 2.04020i) q^{19} +(-0.641129 - 1.11047i) q^{21} +(-3.89699 + 6.74978i) q^{23} -3.35582 q^{25} -1.00000 q^{27} +(3.25586 + 5.63932i) q^{29} +(4.11473 + 7.12692i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(0.822092 + 1.42391i) q^{35} +(5.71603 - 9.90045i) q^{37} +(2.31904 - 4.01669i) q^{39} +(3.07795 + 5.33117i) q^{41} -0.591390 q^{43} +1.28226 q^{45} +(3.07795 + 5.33117i) q^{47} +(2.67791 - 4.63827i) q^{49} +(-2.81904 + 4.88271i) q^{51} +9.63807 q^{53} +(1.28226 + 2.22094i) q^{55} +(-1.17791 + 2.04020i) q^{57} -8.14979 q^{59} +(-6.67619 + 11.5635i) q^{61} +(0.641129 + 1.11047i) q^{63} +(-2.97360 + 5.15043i) q^{65} +(-6.86021 + 4.46514i) q^{67} +(3.89699 - 6.74978i) q^{69} +(7.46150 + 12.9237i) q^{71} +(1.86021 - 3.22198i) q^{73} +3.35582 q^{75} +(-1.28226 + 2.22094i) q^{77} +(1.75452 + 3.03892i) q^{79} +1.00000 q^{81} +(1.81904 - 3.15066i) q^{83} +(3.61473 - 6.26090i) q^{85} +(-3.25586 - 5.63932i) q^{87} +7.07624 q^{89} -5.94720 q^{91} +(-4.11473 - 7.12692i) q^{93} +(1.51038 - 2.61606i) q^{95} +(7.03812 - 12.1904i) q^{97} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9	$ 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9} + 8 q^{11} - 2 q^{15} + 4 q^{17} - 5 q^{19} - q^{21} + q^{23} + 2 q^{25} - 8 q^{27} - 2 q^{29} + 9 q^{31} - 8 q^{33} + 21 q^{35} - 5 q^{37} + 11 q^{41} + 6 q^{43} + 2 q^{45} + 11 q^{47} + 7 q^{49} - 4 q^{51} + 40 q^{53} + 2 q^{55} + 5 q^{57} + 28 q^{59} + 20 q^{61} + q^{63} - 4 q^{65} - 33 q^{67} - q^{69} + 11 q^{71} - 7 q^{73} - 2 q^{75} - 2 q^{77} + 12 q^{79} + 8 q^{81} - 4 q^{83} + 5 q^{85} + 2 q^{87} - 16 q^{89} - 8 q^{91} - 9 q^{93} - 18 q^{95} + 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9 + 8 * q^11 - 2 * q^15 + 4 * q^17 - 5 * q^19 - q^21 + q^23 + 2 * q^25 - 8 * q^27 - 2 * q^29 + 9 * q^31 - 8 * q^33 + 21 * q^35 - 5 * q^37 + 11 * q^41 + 6 * q^43 + 2 * q^45 + 11 * q^47 + 7 * q^49 - 4 * q^51 + 40 * q^53 + 2 * q^55 + 5 * q^57 + 28 * q^59 + 20 * q^61 + q^63 - 4 * q^65 - 33 * q^67 - q^69 + 11 * q^71 - 7 * q^73 - 2 * q^75 - 2 * q^77 + 12 * q^79 + 8 * q^81 - 4 * q^83 + 5 * q^85 + 2 * q^87 - 16 * q^89 - 8 * q^91 - 9 * q^93 - 18 * q^95 + 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.28226			0.573443			0.286722	−	0.958014i	$-0.407435\pi$
$5$	1.28226			0.573443			0.286722	+	0.958014i	$0.407435\pi$
$6$		0			0
$7$	0.641129	+	1.11047i	0.242324	+	0.419717i	0.961376	−	0.275239i	$-0.0887570\pi$
$7$	0.641129	+	1.11047i	0.242324	+	0.419717i	−0.719052	+	0.694956i	$0.755424\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	−2.31904	+	4.01669i	−0.643185	+	1.11403i	0.341533	+	0.939870i	$0.389054\pi$
$13$	−2.31904	+	4.01669i	−0.643185	+	1.11403i	−0.984718	+	0.174159i	$0.944279\pi$
$14$		0			0
$15$	−1.28226			−0.331078
$16$		0			0
$17$	2.81904	−	4.88271i	0.683717	−	1.18423i	−0.290121	−	0.956990i	$-0.593696\pi$
$17$	2.81904	−	4.88271i	0.683717	−	1.18423i	0.973838	−	0.227242i	$-0.0729710\pi$
$18$		0			0
$19$	1.17791	−	2.04020i	0.270231	−	0.468053i	−0.698690	−	0.715424i	$-0.746233\pi$
$19$	1.17791	−	2.04020i	0.270231	−	0.468053i	0.968921	+	0.247371i	$0.0795667\pi$
$20$		0			0
$21$	−0.641129	−	1.11047i	−0.139906	−	0.242324i
$22$		0			0
$23$	−3.89699	+	6.74978i	−0.812578	+	1.40743i	0.0984754	+	0.995139i	$0.468603\pi$
$23$	−3.89699	+	6.74978i	−0.812578	+	1.40743i	−0.911054	+	0.412288i	$0.864730\pi$
$24$		0			0
$25$	−3.35582			−0.671163
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.25586	+	5.63932i	0.604598	+	1.04719i	0.992115	+	0.125332i	$0.0399996\pi$
$29$	3.25586	+	5.63932i	0.604598	+	1.04719i	−0.387517	+	0.921863i	$0.626667\pi$
$30$		0			0
$31$	4.11473	+	7.12692i	0.739028	+	1.28003i	0.952934	+	0.303179i	$0.0980480\pi$
$31$	4.11473	+	7.12692i	0.739028	+	1.28003i	−0.213906	+	0.976854i	$0.568619\pi$
$32$		0			0
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$	0.822092	+	1.42391i	0.138959	+	0.240684i
$36$		0			0
$37$	5.71603	−	9.90045i	0.939709	−	1.62762i	0.173695	−	0.984800i	$-0.444429\pi$
$37$	5.71603	−	9.90045i	0.939709	−	1.62762i	0.766014	−	0.642824i	$-0.222237\pi$
$38$		0			0
$39$	2.31904	−	4.01669i	0.371343	−	0.643185i
$40$		0			0
$41$	3.07795	+	5.33117i	0.480695	+	0.832589i	0.999755	−	0.0221494i	$-0.00705094\pi$
$41$	3.07795	+	5.33117i	0.480695	+	0.832589i	−0.519059	+	0.854738i	$0.673718\pi$
$42$		0			0
$43$	−0.591390			−0.0901861			−0.0450930	−	0.998983i	$-0.514358\pi$
$43$	−0.591390			−0.0901861			−0.0450930	+	0.998983i	$0.514358\pi$
$44$		0			0
$45$	1.28226			0.191148
$46$		0			0
$47$	3.07795	+	5.33117i	0.448966	+	0.777631i	0.998319	−	0.0579590i	$-0.0184593\pi$
$47$	3.07795	+	5.33117i	0.448966	+	0.777631i	−0.549353	+	0.835590i	$0.685126\pi$
$48$		0			0
$49$	2.67791	−	4.63827i	0.382558	−	0.662610i
$50$		0			0
$51$	−2.81904	+	4.88271i	−0.394744	+	0.683717i
$52$		0			0
$53$	9.63807			1.32389			0.661946	−	0.749552i	$-0.269731\pi$
$53$	9.63807			1.32389			0.661946	+	0.749552i	$0.269731\pi$
$54$		0			0
$55$	1.28226	+	2.22094i	0.172900	+	0.299471i
$56$		0			0
$57$	−1.17791	+	2.04020i	−0.156018	+	0.270231i
$58$		0			0
$59$	−8.14979			−1.06101			−0.530506	−	0.847681i	$-0.677998\pi$
$59$	−8.14979			−1.06101			−0.530506	+	0.847681i	$0.677998\pi$
$60$		0			0
$61$	−6.67619	+	11.5635i	−0.854799	+	1.48055i	0.0220331	+	0.999757i	$0.492986\pi$
$61$	−6.67619	+	11.5635i	−0.854799	+	1.48055i	−0.876832	+	0.480797i	$0.840347\pi$
$62$		0			0
$63$	0.641129	+	1.11047i	0.0807746	+	0.139906i
$64$		0			0
$65$	−2.97360	+	5.15043i	−0.368830	+	0.638832i
$66$		0			0
$67$	−6.86021	+	4.46514i	−0.838108	+	0.545504i
$67$	−6.86021	+	4.46514i	−0.838108	+	0.545504i
$68$		0			0
$69$	3.89699	−	6.74978i	0.469142	−	0.812578i
$70$		0			0
$71$	7.46150	+	12.9237i	0.885518	+	1.53376i	0.845119	+	0.534578i	$0.179529\pi$
$71$	7.46150	+	12.9237i	0.885518	+	1.53376i	0.0403984	+	0.999184i	$0.487137\pi$
$72$		0			0
$73$	1.86021	−	3.22198i	0.217721	−	0.377104i	−0.736390	−	0.676558i	$-0.763471\pi$
$73$	1.86021	−	3.22198i	0.217721	−	0.377104i	0.954111	+	0.299453i	$0.0968043\pi$
$74$		0			0
$75$	3.35582			0.387496
$76$		0			0
$77$	−1.28226	+	2.22094i	−0.146127	+	0.253099i
$78$		0			0
$79$	1.75452	+	3.03892i	0.197399	+	0.341905i	0.947684	−	0.319209i	$-0.103417\pi$
$79$	1.75452	+	3.03892i	0.197399	+	0.341905i	−0.750285	+	0.661114i	$0.770084\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	1.81904	−	3.15066i	0.199665	−	0.345830i	−0.748755	−	0.662847i	$-0.769348\pi$
$83$	1.81904	−	3.15066i	0.199665	−	0.345830i	0.948420	+	0.317017i	$0.102681\pi$
$84$		0			0
$85$	3.61473	−	6.26090i	0.392073	−	0.679090i
$86$		0			0
$87$	−3.25586	−	5.63932i	−0.349065	−	0.604598i
$88$		0			0
$89$	7.07624			0.750079			0.375040	−	0.927009i	$-0.377629\pi$
$89$	7.07624			0.750079			0.375040	+	0.927009i	$0.377629\pi$
$90$		0			0
$91$	−5.94720			−0.623436
$92$		0			0
$93$	−4.11473	−	7.12692i	−0.426678	−	0.739028i
$94$		0			0
$95$	1.51038	−	2.61606i	0.154962	−	0.268402i
$96$		0			0
$97$	7.03812	−	12.1904i	0.714613	−	1.23775i	−0.248496	−	0.968633i	$-0.579936\pi$
$97$	7.03812	−	12.1904i	0.714613	−	1.23775i	0.963109	−	0.269112i	$-0.0867303\pi$
$98$		0			0
$99$	1.00000	+	1.73205i	0.100504	+	0.174078i
$100$		0			0
$101$	−6.45711	−	11.1840i	−0.642506	−	1.11285i	−0.984871	−	0.173287i	$-0.944561\pi$
$101$	−6.45711	−	11.1840i	−0.642506	−	1.11285i	0.342365	−	0.939567i	$-0.388772\pi$
$102$		0			0
$103$	−4.46017	−	7.72523i	−0.439473	−	0.761190i	0.558176	−	0.829723i	$-0.311502\pi$
$103$	−4.46017	−	7.72523i	−0.439473	−	0.761190i	−0.997649	+	0.0685330i	$0.978168\pi$
$104$		0			0
$105$	−0.822092	−	1.42391i	−0.0802280	−	0.138959i
$106$		0			0
$107$	1.84677			0.178534			0.0892671	−	0.996008i	$-0.471548\pi$
$107$	1.84677			0.178534			0.0892671	+	0.996008i	$0.471548\pi$
$108$		0			0
$109$	−8.69087			−0.832434			−0.416217	−	0.909265i	$-0.636644\pi$
$109$	−8.69087			−0.832434			−0.416217	+	0.909265i	$0.636644\pi$
$110$		0			0
$111$	−5.71603	+	9.90045i	−0.542541	+	0.939709i
$112$		0			0
$113$	4.71469	+	8.16608i	0.443520	+	0.768200i	0.997948	−	0.0640322i	$-0.0203960\pi$
$113$	4.71469	+	8.16608i	0.443520	+	0.768200i	−0.554427	+	0.832232i	$0.687063\pi$
$114$		0			0
$115$	−4.99694	+	8.65496i	−0.465967	+	0.807079i
$116$		0			0
$117$	−2.31904	+	4.01669i	−0.214395	+	0.371343i
$118$		0			0
$119$	7.22946			0.662724
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−3.07795	−	5.33117i	−0.277530	−	0.480695i
$124$		0			0
$125$	−10.7143			−0.958317
$126$		0			0
$127$	−7.50134	−	12.9927i	−0.665636	−	1.15292i	−0.979112	−	0.203320i	$-0.934827\pi$
$127$	−7.50134	−	12.9927i	−0.665636	−	1.15292i	0.313476	−	0.949596i	$-0.398506\pi$
$128$		0			0
$129$	0.591390			0.0520689
$130$		0			0
$131$	21.8345			1.90769			0.953847	−	0.300294i	$-0.0970848\pi$
$131$	21.8345			1.90769			0.953847	+	0.300294i	$0.0970848\pi$
$132$		0			0
$133$	3.02076			0.261933
$134$		0			0
$135$	−1.28226			−0.110359
$136$		0			0
$137$	−11.9966			−1.02494			−0.512468	−	0.858706i	$-0.671269\pi$
$137$	−11.9966			−1.02494			−0.512468	+	0.858706i	$0.671269\pi$
$138$		0			0
$139$	−14.6408			−1.24181			−0.620906	−	0.783885i	$-0.713235\pi$
$139$	−14.6408			−1.24181			−0.620906	+	0.783885i	$0.713235\pi$
$140$		0			0
$141$	−3.07795	−	5.33117i	−0.259210	−	0.448966i
$142$		0			0
$143$	−9.27615			−0.775710
$144$		0			0
$145$	4.17485	+	7.23106i	0.346703	+	0.600506i
$146$		0			0
$147$	−2.67791	+	4.63827i	−0.220870	+	0.382558i
$148$		0			0
$149$	−16.0943			−1.31850			−0.659249	−	0.751925i	$-0.729126\pi$
$149$	−16.0943			−1.31850			−0.659249	+	0.751925i	$0.729126\pi$
$150$		0			0
$151$	8.59824	−	14.8926i	0.699715	−	1.21194i	−0.268851	−	0.963182i	$-0.586644\pi$
$151$	8.59824	−	14.8926i	0.699715	−	1.21194i	0.968565	−	0.248760i	$-0.0800229\pi$
$152$		0			0
$153$	2.81904	−	4.88271i	0.227906	−	0.394744i
$154$		0			0
$155$	5.27615	+	9.13855i	0.423790	+	0.734026i
$156$		0			0
$157$	6.07624	−	10.5243i	0.484936	−	0.839934i	−0.514914	−	0.857242i	$-0.672176\pi$
$157$	6.07624	−	10.5243i	0.484936	−	0.839934i	0.999850	+	0.0173075i	$0.00550942\pi$
$158$		0			0
$159$	−9.63807			−0.764349
$160$		0			0
$161$	−9.99389			−0.787629
$162$		0			0
$163$	−8.29703	−	14.3709i	−0.649874	−	1.12561i	−0.983153	−	0.182786i	$-0.941488\pi$
$163$	−8.29703	−	14.3709i	−0.649874	−	1.12561i	0.333279	−	0.942828i	$-0.391845\pi$
$164$		0			0
$165$	−1.28226	−	2.22094i	−0.0998236	−	0.172900i
$166$		0			0
$167$	−1.02774	−	1.78009i	−0.0795287	−	0.137748i	0.823518	−	0.567290i	$-0.192008\pi$
$167$	−1.02774	−	1.78009i	−0.0795287	−	0.137748i	−0.903047	+	0.429542i	$0.858675\pi$
$168$		0			0
$169$	−4.25586	−	7.37137i	−0.327374	−	0.567028i
$170$		0			0
$171$	1.17791	−	2.04020i	0.0900768	−	0.156018i
$172$		0			0
$173$	3.35887	−	5.81774i	0.255370	−	0.442314i	−0.709626	−	0.704579i	$-0.751136\pi$
$173$	3.35887	−	5.81774i	0.255370	−	0.442314i	0.964996	+	0.262265i	$0.0844693\pi$
$174$		0			0
$175$	−2.15151	−	3.72652i	−0.162639	−	0.281699i
$176$		0			0
$177$	8.14979			0.612576
$178$		0			0
$179$	−7.94720			−0.594002			−0.297001	−	0.954877i	$-0.595986\pi$
$179$	−7.94720			−0.594002			−0.297001	+	0.954877i	$0.595986\pi$
$180$		0			0
$181$	−12.3173	−	21.3342i	−0.915539	−	1.58576i	−0.806110	−	0.591766i	$-0.798431\pi$
$181$	−12.3173	−	21.3342i	−0.915539	−	1.58576i	−0.109429	−	0.993995i	$-0.534902\pi$
$182$		0			0
$183$	6.67619	−	11.5635i	0.493518	−	0.854799i
$184$		0			0
$185$	7.32942	−	12.6949i	0.538869	−	0.933349i
$186$		0			0
$187$	11.2761			0.824593
$188$		0			0
$189$	−0.641129	−	1.11047i	−0.0466353	−	0.0807746i
$190$		0			0
$191$	10.6628	−	18.4684i	0.771530	−	1.33633i	−0.165195	−	0.986261i	$-0.552825\pi$
$191$	10.6628	−	18.4684i	0.771530	−	1.33633i	0.936724	−	0.350068i	$-0.113841\pi$
$192$		0			0
$193$	2.02955			0.146090			0.0730452	−	0.997329i	$-0.476728\pi$
$193$	2.02955			0.146090			0.0730452	+	0.997329i	$0.476728\pi$
$194$		0			0
$195$	2.97360	−	5.15043i	0.212944	−	0.368830i
$196$		0			0
$197$	11.7363	+	20.3279i	0.836178	+	1.44830i	0.893068	+	0.449922i	$0.148548\pi$
$197$	11.7363	+	20.3279i	0.836178	+	1.44830i	−0.0568905	+	0.998380i	$0.518119\pi$
$198$		0			0
$199$	−4.77920	+	8.27782i	−0.338789	+	0.586799i	−0.984205	−	0.177032i	$-0.943350\pi$
$199$	−4.77920	+	8.27782i	−0.338789	+	0.586799i	0.645417	+	0.763831i	$0.276684\pi$
$200$		0			0
$201$	6.86021	−	4.46514i	0.483882	−	0.314947i
$202$		0			0
$203$	−4.17485	+	7.23106i	−0.293017	+	0.507521i
$204$		0			0
$205$	3.94673	+	6.83593i	0.275651	+	0.477442i
$206$		0			0
$207$	−3.89699	+	6.74978i	−0.270859	+	0.469142i
$208$		0			0
$209$	4.71163			0.325910
$210$		0			0
$211$	−10.6792	+	18.4970i	−0.735190	+	1.27339i	0.219450	+	0.975624i	$0.429574\pi$
$211$	−10.6792	+	18.4970i	−0.735190	+	1.27339i	−0.954640	+	0.297762i	$0.903760\pi$
$212$		0			0
$213$	−7.46150	−	12.9237i	−0.511254	−	0.885518i
$214$		0			0
$215$	−0.758314			−0.0517166
$216$		0			0
$217$	−5.27615	+	9.13855i	−0.358168	+	0.620365i
$218$		0			0
$219$	−1.86021	+	3.22198i	−0.125701	+	0.217721i
$220$		0			0
$221$	13.0749	+	22.6464i	0.879513	+	1.52336i
$222$		0			0
$223$	−16.9939			−1.13799			−0.568997	−	0.822339i	$-0.692669\pi$
$223$	−16.9939			−1.13799			−0.568997	+	0.822339i	$0.692669\pi$
$224$		0			0
$225$	−3.35582			−0.223721
$226$		0			0
$227$	−4.33200	−	7.50324i	−0.287525	−	0.498007i	0.685694	−	0.727890i	$-0.259499\pi$
$227$	−4.33200	−	7.50324i	−0.287525	−	0.498007i	−0.973218	+	0.229883i	$0.926166\pi$
$228$		0			0
$229$	−10.1130	+	17.5163i	−0.668287	+	1.15751i	0.310096	+	0.950705i	$0.399639\pi$
$229$	−10.1130	+	17.5163i	−0.668287	+	1.15751i	−0.978383	+	0.206801i	$0.933695\pi$
$230$		0			0
$231$	1.28226	−	2.22094i	0.0843664	−	0.146127i
$232$		0			0
$233$	−1.41043	−	2.44293i	−0.0924001	−	0.160042i	0.816120	−	0.577882i	$-0.196121\pi$
$233$	−1.41043	−	2.44293i	−0.0924001	−	0.160042i	−0.908521	+	0.417840i	$0.862787\pi$
$234$		0			0
$235$	3.94673	+	6.83593i	0.257456	+	0.445927i
$236$		0			0
$237$	−1.75452	−	3.03892i	−0.113968	−	0.197399i
$238$		0			0
$239$	−6.46017	−	11.1893i	−0.417873	−	0.723778i	0.577852	−	0.816142i	$-0.303891\pi$
$239$	−6.46017	−	11.1893i	−0.417873	−	0.723778i	−0.995725	+	0.0923637i	$0.970558\pi$
$240$		0			0
$241$	11.7732			0.758379			0.379190	−	0.925319i	$-0.376203\pi$
$241$	11.7732			0.758379			0.379190	+	0.925319i	$0.376203\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	3.43377	−	5.94746i	0.219375	−	0.379969i
$246$		0			0
$247$	5.46322	+	9.46258i	0.347616	+	0.602089i
$248$		0			0
$249$	−1.81904	+	3.15066i	−0.115277	+	0.199665i
$250$		0			0
$251$	−4.38661	+	7.59783i	−0.276880	+	0.479571i	−0.970608	−	0.240667i	$-0.922634\pi$
$251$	−4.38661	+	7.59783i	−0.276880	+	0.479571i	0.693728	+	0.720238i	$0.255967\pi$
$252$		0			0
$253$	−15.5880			−0.980006
$254$		0			0
$255$	−3.61473	+	6.26090i	−0.226363	+	0.392073i
$256$		0			0
$257$	−11.8895	−	20.5933i	−0.741649	−	1.28457i	−0.951744	−	0.306893i	$-0.900711\pi$
$257$	−11.8895	−	20.5933i	−0.741649	−	1.28457i	0.210095	−	0.977681i	$-0.432623\pi$
$258$		0			0
$259$	14.6588			0.910856
$260$		0			0
$261$	3.25586	+	5.63932i	0.201533	+	0.349065i
$262$		0			0
$263$	−10.8675			−0.670121			−0.335060	−	0.942197i	$-0.608757\pi$
$263$	−10.8675			−0.670121			−0.335060	+	0.942197i	$0.608757\pi$
$264$		0			0
$265$	12.3585			0.759176
$266$		0			0
$267$	−7.07624			−0.433059
$268$		0			0
$269$	29.2172			1.78141			0.890703	−	0.454585i	$-0.150213\pi$
$269$	29.2172			1.78141			0.890703	+	0.454585i	$0.150213\pi$
$270$		0			0
$271$	24.1706			1.46826			0.734128	−	0.679011i	$-0.237591\pi$
$271$	24.1706			1.46826			0.734128	+	0.679011i	$0.237591\pi$
$272$		0			0
$273$	5.94720			0.359941
$274$		0			0
$275$	−3.35582	−	5.81244i	−0.202363	−	0.350503i
$276$		0			0
$277$	−5.92644			−0.356085			−0.178043	−	0.984023i	$-0.556977\pi$
$277$	−5.92644			−0.356085			−0.178043	+	0.984023i	$0.556977\pi$
$278$		0			0
$279$	4.11473	+	7.12692i	0.246343	+	0.426678i
$280$		0			0
$281$	2.66141	−	4.60971i	0.158767	−	0.274992i	−0.775658	−	0.631154i	$-0.782582\pi$
$281$	2.66141	−	4.60971i	0.158767	−	0.274992i	0.934424	+	0.356162i	$0.115915\pi$
$282$		0			0
$283$	20.8614			1.24008			0.620041	−	0.784569i	$-0.287116\pi$
$283$	20.8614			1.24008			0.620041	+	0.784569i	$0.287116\pi$
$284$		0			0
$285$	−1.51038	+	2.61606i	−0.0894673	+	0.154962i
$286$		0			0
$287$	−3.94673	+	6.83593i	−0.232968	+	0.403512i
$288$		0			0
$289$	−7.39393	−	12.8067i	−0.434937	−	0.753333i
$290$		0			0
$291$	−7.03812	+	12.1904i	−0.412582	+	0.714613i
$292$		0			0
$293$	1.42594			0.0833042			0.0416521	−	0.999132i	$-0.486738\pi$
$293$	1.42594			0.0833042			0.0416521	+	0.999132i	$0.486738\pi$
$294$		0			0
$295$	−10.4501			−0.608430
$296$		0			0
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$		0			0
$299$	−18.0745	−	31.3060i	−1.04528	−	1.81047i
$300$		0			0
$301$	−0.379157	−	0.656719i	−0.0218542	−	0.0378527i
$302$		0			0
$303$	6.45711	+	11.1840i	0.370951	+	0.642506i
$304$		0			0
$305$	−8.56060	+	14.8274i	−0.490178	+	0.849014i
$306$		0			0
$307$	−5.85715	+	10.1449i	−0.334285	+	0.578999i	−0.983347	−	0.181736i	$-0.941828\pi$
$307$	−5.85715	+	10.1449i	−0.334285	+	0.578999i	0.649062	+	0.760736i	$0.275162\pi$
$308$		0			0
$309$	4.46017	+	7.72523i	0.253730	+	0.439473i
$310$		0			0
$311$	20.7231			1.17510			0.587550	−	0.809188i	$-0.300093\pi$
$311$	20.7231			1.17510			0.587550	+	0.809188i	$0.300093\pi$
$312$		0			0
$313$	14.0520			0.794268			0.397134	−	0.917761i	$-0.370005\pi$
$313$	14.0520			0.794268			0.397134	+	0.917761i	$0.370005\pi$
$314$		0			0
$315$	0.822092	+	1.42391i	0.0463197	+	0.0802280i
$316$		0			0
$317$	−13.7130	+	23.7516i	−0.770197	+	1.33402i	0.167258	+	0.985913i	$0.446509\pi$
$317$	−13.7130	+	23.7516i	−0.770197	+	1.33402i	−0.937455	+	0.348107i	$0.886824\pi$
$318$		0			0
$319$	−6.51172	+	11.2786i	−0.364586	+	0.631482i
$320$		0			0
$321$	−1.84677			−0.103077
$322$		0			0
$323$	−6.64113	−	11.5028i	−0.369522	−	0.640031i
$324$		0			0
$325$	7.78226	−	13.4793i	0.431682	−	0.747695i
$326$		0			0
$327$	8.69087			0.480606
$328$		0			0
$329$	−3.94673	+	6.83593i	−0.217590	+	0.376877i
$330$		0			0
$331$	−6.75147	−	11.6939i	−0.371094	−	0.642754i	0.618640	−	0.785675i	$-0.287684\pi$
$331$	−6.75147	−	11.6939i	−0.371094	−	0.642754i	−0.989734	+	0.142921i	$0.954351\pi$
$332$		0			0
$333$	5.71603	−	9.90045i	0.313236	−	0.542541i
$334$		0			0
$335$	−8.79656	+	5.72547i	−0.480607	+	0.312816i
$336$		0			0
$337$	8.36878	−	14.4951i	0.455876	−	0.789601i	−0.542862	−	0.839822i	$-0.682659\pi$
$337$	8.36878	−	14.4951i	0.455876	−	0.789601i	0.998738	+	0.0502212i	$0.0159926\pi$
$338$		0			0
$339$	−4.71469	−	8.16608i	−0.256067	−	0.443520i
$340$		0			0
$341$	−8.22946	+	14.2538i	−0.445650	+	0.771889i
$342$		0			0
$343$	15.8433			0.855460
$344$		0			0
$345$	4.99694	−	8.65496i	0.269026	−	0.465967i
$346$		0			0
$347$	−4.74376	−	8.21644i	−0.254658	−	0.441081i	0.710144	−	0.704056i	$-0.248630\pi$
$347$	−4.74376	−	8.21644i	−0.254658	−	0.441081i	−0.964803	+	0.262975i	$0.915296\pi$
$348$		0			0
$349$	8.48217			0.454040			0.227020	−	0.973890i	$-0.427102\pi$
$349$	8.48217			0.454040			0.227020	+	0.973890i	$0.427102\pi$
$350$		0			0
$351$	2.31904	−	4.01669i	0.123781	−	0.214395i
$352$		0			0
$353$	−4.92167	+	8.52458i	−0.261954	+	0.453718i	−0.966761	−	0.255681i	$-0.917700\pi$
$353$	−4.92167	+	8.52458i	−0.261954	+	0.453718i	0.704807	+	0.709399i	$0.251034\pi$
$354$		0			0
$355$	9.56757	+	16.5715i	0.507794	+	0.879525i
$356$		0			0
$357$	−7.22946			−0.382624
$358$		0			0
$359$	29.7324			1.56922			0.784608	−	0.619992i	$-0.212864\pi$
$359$	29.7324			1.56922			0.784608	+	0.619992i	$0.212864\pi$
$360$		0			0
$361$	6.72507	+	11.6482i	0.353951	+	0.613061i
$362$		0			0
$363$	−3.50000	+	6.06218i	−0.183702	+	0.318182i
$364$		0			0
$365$	2.38527	−	4.13141i	0.124851	−	0.216248i
$366$		0			0
$367$	3.95160	+	6.84437i	0.206272	+	0.357273i	0.950537	−	0.310611i	$-0.100534\pi$
$367$	3.95160	+	6.84437i	0.206272	+	0.357273i	−0.744265	+	0.667884i	$0.767200\pi$
$368$		0			0
$369$	3.07795	+	5.33117i	0.160232	+	0.277530i
$370$		0			0
$371$	6.17925	+	10.7028i	0.320810	+	0.555660i
$372$		0			0
$373$	−11.5260	−	19.9637i	−0.596795	−	1.03368i	−0.993291	−	0.115642i	$-0.963107\pi$
$373$	−11.5260	−	19.9637i	−0.596795	−	1.03368i	0.396496	−	0.918036i	$-0.370226\pi$
$374$		0			0
$375$	10.7143			0.553285
$376$		0			0
$377$	−30.2018			−1.55547
$378$		0			0
$379$	−2.80732	+	4.86241i	−0.144202	+	0.249765i	−0.929075	−	0.369891i	$-0.879395\pi$
$379$	−2.80732	+	4.86241i	−0.144202	+	0.249765i	0.784873	+	0.619657i	$0.212728\pi$
$380$		0			0
$381$	7.50134	+	12.9927i	0.384305	+	0.665636i
$382$		0			0
$383$	9.92473	−	17.1901i	0.507130	−	0.878375i	−0.492836	−	0.870122i	$-0.664040\pi$
$383$	9.92473	−	17.1901i	0.507130	−	0.878375i	0.999966	−	0.00825243i	$-0.00262686\pi$
$384$		0			0
$385$	−1.64418	+	2.84781i	−0.0837954	+	0.145138i
$386$		0			0
$387$	−0.591390			−0.0300620
$388$		0			0
$389$	8.92033	−	15.4505i	0.452279	−	0.783370i	−0.546248	−	0.837623i	$-0.683945\pi$
$389$	8.92033	−	15.4505i	0.452279	−	0.783370i	0.998527	+	0.0542535i	$0.0172779\pi$
$390$		0			0
$391$	21.9715	+	38.0558i	1.11115	+	1.92456i
$392$		0			0
$393$	−21.8345			−1.10141
$394$		0			0
$395$	2.24975	+	3.89668i	0.113197	+	0.196063i
$396$		0			0
$397$	−12.9966			−0.652279			−0.326139	−	0.945322i	$-0.605748\pi$
$397$	−12.9966			−0.652279			−0.326139	+	0.945322i	$0.605748\pi$
$398$		0			0
$399$	−3.02076			−0.151227
$400$		0			0
$401$	−10.2053			−0.509627			−0.254813	−	0.966990i	$-0.582014\pi$
$401$	−10.2053			−0.509627			−0.254813	+	0.966990i	$0.582014\pi$
$402$		0			0
$403$	−38.1688			−1.90133
$404$		0			0
$405$	1.28226			0.0637159
$406$		0			0
$407$	22.8641			1.13333
$408$		0			0
$409$	14.8966	+	25.8017i	0.736590	+	1.27581i	0.954022	+	0.299736i	$0.0968986\pi$
$409$	14.8966	+	25.8017i	0.736590	+	1.27581i	−0.217432	+	0.976075i	$0.569768\pi$
$410$		0			0
$411$	11.9966			0.591747
$412$		0			0
$413$	−5.22507	−	9.05008i	−0.257109	−	0.445325i
$414$		0			0
$415$	2.33247	−	4.03996i	0.114497	−	0.198314i
$416$		0			0
$417$	14.6408			0.716961
$418$		0			0
$419$	−0.535440	+	0.927409i	−0.0261579	+	0.0453069i	−0.878808	−	0.477175i	$-0.841661\pi$
$419$	−0.535440	+	0.927409i	−0.0261579	+	0.0453069i	0.852650	+	0.522482i	$0.174994\pi$
$420$		0			0
$421$	1.80254	−	3.12210i	0.0878506	−	0.152162i	−0.818752	−	0.574148i	$-0.805334\pi$
$421$	1.80254	−	3.12210i	0.0878506	−	0.152162i	0.906602	+	0.421986i	$0.138667\pi$
$422$		0			0
$423$	3.07795	+	5.33117i	0.149655	+	0.259210i
$424$		0			0
$425$	−9.46017	+	16.3855i	−0.458885	+	0.794813i
$426$		0			0
$427$	−17.1212			−0.828553
$428$		0			0
$429$	9.27615			0.447857
$430$		0			0
$431$	−11.4030	−	19.7505i	−0.549262	−	0.951350i	−0.998325	−	0.0578497i	$-0.981576\pi$
$431$	−11.4030	−	19.7505i	−0.549262	−	0.951350i	0.449063	−	0.893500i	$-0.351758\pi$
$432$		0			0
$433$	−11.5905	−	20.0754i	−0.557006	−	0.964762i	−0.997744	−	0.0671266i	$-0.978617\pi$
$433$	−11.5905	−	20.0754i	−0.557006	−	0.964762i	0.440739	−	0.897635i	$-0.354716\pi$
$434$		0			0
$435$	−4.17485	−	7.23106i	−0.200169	−	0.346703i
$436$		0			0
$437$	9.18059	+	15.9012i	0.439167	+	0.760660i
$438$		0			0
$439$	−2.98704	+	5.17370i	−0.142564	+	0.246927i	−0.928461	−	0.371429i	$-0.878868\pi$
$439$	−2.98704	+	5.17370i	−0.142564	+	0.246927i	0.785898	+	0.618357i	$0.212201\pi$
$440$		0			0
$441$	2.67791	−	4.63827i	0.127519	−	0.220870i
$442$		0			0
$443$	−6.07929	−	10.5296i	−0.288836	−	0.500278i	0.684696	−	0.728829i	$-0.259935\pi$
$443$	−6.07929	−	10.5296i	−0.288836	−	0.500278i	−0.973532	+	0.228550i	$0.926602\pi$
$444$		0			0
$445$	9.07356			0.430128
$446$		0			0
$447$	16.0943			0.761235
$448$		0			0
$449$	3.97313	+	6.88166i	0.187503	+	0.324765i	0.944417	−	0.328749i	$-0.106627\pi$
$449$	3.97313	+	6.88166i	0.187503	+	0.324765i	−0.756914	+	0.653515i	$0.773294\pi$
$450$		0			0
$451$	−6.15590	+	10.6623i	−0.289870	+	0.502070i
$452$		0			0
$453$	−8.59824	+	14.8926i	−0.403980	+	0.699715i
$454$		0			0
$455$	−7.62585			−0.357505
$456$		0			0
$457$	16.7528	+	29.0167i	0.783663	+	1.35734i	0.929794	+	0.368079i	$0.119984\pi$
$457$	16.7528	+	29.0167i	0.783663	+	1.35734i	−0.146131	+	0.989265i	$0.546682\pi$
$458$		0			0
$459$	−2.81904	+	4.88271i	−0.131581	+	0.227906i
$460$		0			0
$461$	10.4052			0.484617			0.242309	−	0.970199i	$-0.422095\pi$
$461$	10.4052			0.484617			0.242309	+	0.970199i	$0.422095\pi$
$462$		0			0
$463$	13.3250	−	23.0796i	0.619266	−	1.07260i	−0.370354	−	0.928891i	$-0.620763\pi$
$463$	13.3250	−	23.0796i	0.619266	−	1.07260i	0.989620	−	0.143710i	$-0.0459032\pi$
$464$		0			0
$465$	−5.27615	−	9.13855i	−0.244675	−	0.423790i
$466$		0			0
$467$	6.12645	−	10.6113i	0.283498	−	0.491034i	−0.688746	−	0.725003i	$-0.741838\pi$
$467$	6.12645	−	10.6113i	0.283498	−	0.491034i	0.972244	+	0.233970i	$0.0751716\pi$
$468$		0			0
$469$	−9.35668	−	4.75531i	−0.432051	−	0.219580i
$470$		0			0
$471$	−6.07624	+	10.5243i	−0.279978	+	0.484936i
$472$		0			0
$473$	−0.591390	−	1.02432i	−0.0271921	−	0.0470981i
$474$		0			0
$475$	−3.95284	+	6.84652i	−0.181369	+	0.314140i
$476$		0			0
$477$	9.63807			0.441297
$478$		0			0
$479$	−3.73363	+	6.46684i	−0.170594	+	0.295478i	−0.938628	−	0.344932i	$-0.887902\pi$
$479$	−3.73363	+	6.46684i	−0.170594	+	0.295478i	0.768034	+	0.640409i	$0.221235\pi$
$480$		0			0
$481$	26.5113	+	45.9190i	1.20881	+	2.09373i
$482$		0			0
$483$	9.99389			0.454738
$484$		0			0
$485$	9.02468	−	15.6312i	0.409790	−	0.709776i
$486$		0			0
$487$	6.03850	−	10.4590i	0.273630	−	0.473942i	−0.696158	−	0.717888i	$-0.745109\pi$
$487$	6.03850	−	10.4590i	0.273630	−	0.473942i	0.969789	+	0.243947i	$0.0784422\pi$
$488$		0			0
$489$	8.29703	+	14.3709i	0.375205	+	0.649874i
$490$		0			0
$491$	−37.0200			−1.67069			−0.835345	−	0.549726i	$-0.814732\pi$
$491$	−37.0200			−1.67069			−0.835345	+	0.549726i	$0.814732\pi$
$492$		0			0
$493$	36.7136			1.65350
$494$		0			0
$495$	1.28226	+	2.22094i	0.0576332	+	0.0998236i
$496$		0			0
$497$	−9.56757	+	16.5715i	−0.429164	+	0.743334i
$498$		0			0
$499$	−11.0234	+	19.0932i	−0.493477	+	0.854727i	−0.999972	−	0.00751586i	$-0.997608\pi$
$499$	−11.0234	+	19.0932i	−0.493477	+	0.854727i	0.506495	+	0.862243i	$0.330941\pi$
$500$		0			0
$501$	1.02774	+	1.78009i	0.0459159	+	0.0795287i
$502$		0			0
$503$	2.32942	+	4.03467i	0.103864	+	0.179897i	0.913273	−	0.407347i	$-0.133546\pi$
$503$	2.32942	+	4.03467i	0.103864	+	0.179897i	−0.809410	+	0.587244i	$0.800213\pi$
$504$		0			0
$505$	−8.27968	−	14.3408i	−0.368441	−	0.638158i
$506$		0			0
$507$	4.25586	+	7.37137i	0.189009	+	0.327374i
$508$		0			0
$509$	15.3377			0.679833			0.339916	−	0.940456i	$-0.389601\pi$
$509$	15.3377			0.679833			0.339916	+	0.940456i	$0.389601\pi$
$510$		0			0
$511$	4.77054			0.211036
$512$		0			0
$513$	−1.17791	+	2.04020i	−0.0520059	+	0.0900768i
$514$		0			0
$515$	−5.71908	−	9.90574i	−0.252013	−	0.436499i
$516$		0			0
$517$	−6.15590	+	10.6623i	−0.270736	+	0.468929i
$518$		0			0
$519$	−3.35887	+	5.81774i	−0.147438	+	0.255370i
$520$		0			0
$521$	7.43205			0.325604			0.162802	−	0.986659i	$-0.447947\pi$
$521$	7.43205			0.325604			0.162802	+	0.986659i	$0.447947\pi$
$522$		0			0
$523$	5.77064	−	9.99503i	0.252332	−	0.437052i	−0.711835	−	0.702347i	$-0.752136\pi$
$523$	5.77064	−	9.99503i	0.252332	−	0.437052i	0.964168	+	0.265294i	$0.0854691\pi$
$524$		0			0
$525$	2.15151	+	3.72652i	0.0938996	+	0.162639i
$526$		0			0
$527$	46.3983			2.02114
$528$		0			0
$529$	−18.8730	−	32.6891i	−0.820567	−	1.42126i
$530$		0			0
$531$	−8.14979			−0.353671
$532$		0			0
$533$	−28.5515			−1.23670
$534$		0			0
$535$	2.36804			0.102379
$536$		0			0
$537$	7.94720			0.342947
$538$		0			0
$539$	10.7116			0.461383
$540$		0			0
$541$	−37.5611			−1.61488			−0.807439	−	0.589952i	$-0.799147\pi$
$541$	−37.5611			−1.61488			−0.807439	+	0.589952i	$0.799147\pi$
$542$		0			0
$543$	12.3173	+	21.3342i	0.528587	+	0.915539i
$544$		0			0
$545$	−11.1439			−0.477354
$546$		0			0
$547$	−10.3420	−	17.9129i	−0.442192	−	0.765899i	0.555660	−	0.831410i	$-0.312466\pi$
$547$	−10.3420	−	17.9129i	−0.442192	−	0.765899i	−0.997852	+	0.0655107i	$0.979132\pi$
$548$		0			0
$549$	−6.67619	+	11.5635i	−0.284933	+	0.493518i
$550$		0			0
$551$	15.3404			0.653523
$552$		0			0
$553$	−2.24975	+	3.89668i	−0.0956690	+	0.165704i
$554$		0			0
$555$	−7.32942	+	12.6949i	−0.311116	+	0.538869i
$556$		0			0
$557$	−13.9908	−	24.2328i	−0.592811	−	1.02678i	−0.993852	−	0.110718i	$-0.964685\pi$
$557$	−13.9908	−	24.2328i	−0.592811	−	1.02678i	0.401041	−	0.916060i	$-0.368648\pi$
$558$		0			0
$559$	1.37145	−	2.37543i	0.0580063	−	0.100470i
$560$		0			0
$561$	−11.2761			−0.476079
$562$		0			0
$563$	13.5792			0.572294			0.286147	−	0.958186i	$-0.407625\pi$
$563$	13.5792			0.572294			0.286147	+	0.958186i	$0.407625\pi$
$564$		0			0
$565$	6.04544	+	10.4710i	0.254334	+	0.440519i
$566$		0			0
$567$	0.641129	+	1.11047i	0.0269249	+	0.0466353i
$568$		0			0
$569$	4.76137	+	8.24693i	0.199607	+	0.345729i	0.948401	−	0.317073i	$-0.102700\pi$
$569$	4.76137	+	8.24693i	0.199607	+	0.345729i	−0.748794	+	0.662803i	$0.769367\pi$
$570$		0			0
$571$	9.16361	+	15.8718i	0.383485	+	0.664216i	0.991558	−	0.129666i	$-0.0413904\pi$
$571$	9.16361	+	15.8718i	0.383485	+	0.664216i	−0.608073	+	0.793881i	$0.708057\pi$
$572$		0			0
$573$	−10.6628	+	18.4684i	−0.445443	+	0.771530i
$574$		0			0
$575$	13.0776	−	22.6510i	0.545373	−	0.944613i
$576$		0			0
$577$	10.9862	+	19.0286i	0.457361	+	0.792172i	0.998821	−	0.0485545i	$-0.0154614\pi$
$577$	10.9862	+	19.0286i	0.457361	+	0.792172i	−0.541460	+	0.840727i	$0.682128\pi$
$578$		0			0
$579$	−2.02955			−0.0843453
$580$		0			0
$581$	4.66495			0.193535
$582$		0			0
$583$	9.63807	+	16.6936i	0.399168	+	0.691380i
$584$		0			0
$585$	−2.97360	+	5.15043i	−0.122943	+	0.212944i
$586$		0			0
$587$	1.23118	−	2.13247i	0.0508162	−	0.0880163i	−0.839498	−	0.543362i	$-0.817151\pi$
$587$	1.23118	−	2.13247i	0.0508162	−	0.0880163i	0.890315	+	0.455346i	$0.150484\pi$
$588$		0			0
$589$	19.3871			0.798831
$590$		0			0
$591$	−11.7363	−	20.3279i	−0.482767	−	0.836178i
$592$		0			0
$593$	6.41129	−	11.1047i	0.263280	−	0.456014i	−0.703832	−	0.710367i	$-0.748529\pi$
$593$	6.41129	−	11.1047i	0.263280	−	0.456014i	0.967112	+	0.254352i	$0.0818623\pi$
$594$		0			0
$595$	9.27003			0.380034
$596$		0			0
$597$	4.77920	−	8.27782i	0.195600	−	0.338789i
$598$		0			0
$599$	−12.1796	−	21.0957i	−0.497646	−	0.861948i	0.502350	−	0.864664i	$-0.332469\pi$
$599$	−12.1796	−	21.0957i	−0.497646	−	0.861948i	−0.999996	+	0.00271607i	$0.999135\pi$
$600$		0			0
$601$	3.85276	−	6.67317i	0.157157	−	0.272204i	−0.776685	−	0.629889i	$-0.783100\pi$
$601$	3.85276	−	6.67317i	0.157157	−	0.272204i	0.933842	+	0.357685i	$0.116434\pi$
$602$		0			0
$603$	−6.86021	+	4.46514i	−0.279369	+	0.181835i
$604$		0			0
$605$	4.48790	−	7.77327i	0.182459	−	0.316029i
$606$		0			0
$607$	−3.95577	−	6.85160i	−0.160560	−	0.278098i	0.774510	−	0.632562i	$-0.217997\pi$
$607$	−3.95577	−	6.85160i	−0.160560	−	0.278098i	−0.935070	+	0.354464i	$0.884663\pi$
$608$		0			0
$609$	4.17485	−	7.23106i	0.169174	−	0.293017i
$610$		0			0
$611$	−28.5515			−1.15507
$612$		0			0
$613$	9.42081	−	16.3173i	0.380503	−	0.659050i	−0.610631	−	0.791915i	$-0.709084\pi$
$613$	9.42081	−	16.3173i	0.380503	−	0.659050i	0.991134	+	0.132865i	$0.0424176\pi$
$614$		0			0
$615$	−3.94673	−	6.83593i	−0.159147	−	0.275651i
$616$		0			0
$617$	−8.56987			−0.345010			−0.172505	−	0.985009i	$-0.555186\pi$
$617$	−8.56987			−0.345010			−0.172505	+	0.985009i	$0.555186\pi$
$618$		0			0
$619$	11.2147	−	19.4244i	0.450756	−	0.780733i	−0.547677	−	0.836690i	$-0.684488\pi$
$619$	11.2147	−	19.4244i	0.450756	−	0.780733i	0.998433	+	0.0559571i	$0.0178210\pi$
$620$		0			0
$621$	3.89699	−	6.74978i	0.156381	−	0.270859i
$622$		0			0
$623$	4.53678	+	7.85793i	0.181762	+	0.314821i
$624$		0			0
$625$	3.04057			0.121623
$626$		0			0
$627$	−4.71163			−0.188164
$628$		0			0
$629$	−32.2274	−	55.8194i	−1.28499	−	2.22567i
$630$		0			0
$631$	−15.4527	+	26.7649i	−0.615163	+	1.06549i	0.375193	+	0.926947i	$0.377576\pi$
$631$	−15.4527	+	26.7649i	−0.615163	+	1.06549i	−0.990356	+	0.138547i	$0.955757\pi$
$632$		0			0
$633$	10.6792	−	18.4970i	0.424462	−	0.735190i
$634$		0			0
$635$	−9.61865	−	16.6600i	−0.381704	−	0.661132i
$636$		0			0
$637$	12.4203	+	21.5126i	0.492111	+	0.852362i
$638$		0			0
$639$	7.46150	+	12.9237i	0.295173	+	0.511254i
$640$		0			0
$641$	20.4537	+	35.4268i	0.807872	+	1.39927i	0.914335	+	0.404958i	$0.132714\pi$
$641$	20.4537	+	35.4268i	0.807872	+	1.39927i	−0.106464	+	0.994317i	$0.533953\pi$
$642$		0			0
$643$	1.68208			0.0663347			0.0331673	−	0.999450i	$-0.489441\pi$
$643$	1.68208			0.0663347			0.0331673	+	0.999450i	$0.489441\pi$
$644$		0			0
$645$	0.758314			0.0298586
$646$		0			0
$647$	−2.64161	+	4.57539i	−0.103852	+	0.179877i	−0.913269	−	0.407358i	$-0.866450\pi$
$647$	−2.64161	+	4.57539i	−0.103852	+	0.179877i	0.809416	+	0.587235i	$0.199784\pi$
$648$		0			0
$649$	−8.14979	−	14.1159i	−0.319907	−	0.554096i
$650$		0			0
$651$	5.27615	−	9.13855i	0.206788	−	0.358168i
$652$		0			0
$653$	−18.3303	+	31.7490i	−0.717319	+	1.24243i	0.244739	+	0.969589i	$0.421298\pi$
$653$	−18.3303	+	31.7490i	−0.717319	+	1.24243i	−0.962058	+	0.272844i	$0.912036\pi$
$654$		0			0
$655$	27.9975			1.09395
$656$		0			0
$657$	1.86021	−	3.22198i	0.0725737	−	0.125701i
$658$		0			0
$659$	−21.9485	−	38.0160i	−0.854994	−	1.48089i	−0.876651	−	0.481127i	$-0.840227\pi$
$659$	−21.9485	−	38.0160i	−0.854994	−	1.48089i	0.0216568	−	0.999765i	$-0.493106\pi$
$660$		0			0
$661$	5.32136			0.206977			0.103488	−	0.994631i	$-0.467000\pi$
$661$	5.32136			0.206977			0.103488	+	0.994631i	$0.467000\pi$
$662$		0			0
$663$	−13.0749	−	22.6464i	−0.507787	−	0.879513i
$664$		0			0
$665$	3.87340			0.150204
$666$		0			0
$667$	−50.7522			−1.96513
$668$		0			0
$669$	16.9939			0.657022
$670$		0			0
$671$	−26.7048			−1.03093
$672$		0			0
$673$	−33.9223			−1.30761			−0.653803	−	0.756664i	$-0.726828\pi$
$673$	−33.9223			−1.30761			−0.653803	+	0.756664i	$0.726828\pi$
$674$		0			0
$675$	3.35582			0.129165
$676$		0			0
$677$	−1.99523	−	3.45583i	−0.0766828	−	0.132819i	0.825134	−	0.564937i	$-0.191100\pi$
$677$	−1.99523	−	3.45583i	−0.0766828	−	0.132819i	−0.901817	+	0.432119i	$0.857766\pi$
$678$		0			0
$679$	18.0494			0.692671
$680$		0			0
$681$	4.33200	+	7.50324i	0.166002	+	0.287525i
$682$		0			0
$683$	15.8702	−	27.4880i	0.607257	−	1.05180i	−0.384434	−	0.923153i	$-0.625603\pi$
$683$	15.8702	−	27.4880i	0.607257	−	1.05180i	0.991690	−	0.128647i	$-0.0410634\pi$
$684$		0			0
$685$	−15.3827			−0.587742
$686$		0			0
$687$	10.1130	−	17.5163i	0.385836	−	0.668287i
$688$		0			0
$689$	−22.3510	+	38.7131i	−0.851507	+	1.47485i
$690$		0			0
$691$	8.63769	+	14.9609i	0.328593	+	0.569140i	0.982233	−	0.187666i	$-0.0600921\pi$
$691$	8.63769	+	14.9609i	0.328593	+	0.569140i	−0.653640	+	0.756806i	$0.726759\pi$
$692$		0			0
$693$	−1.28226	+	2.22094i	−0.0487089	+	0.0843664i
$694$		0			0
$695$	−18.7732			−0.712109
$696$		0			0
$697$	34.7074			1.31464
$698$		0			0
$699$	1.41043	+	2.44293i	0.0533472	+	0.0924001i
$700$		0			0
$701$	5.07977	+	8.79842i	0.191860	+	0.332312i	0.945867	−	0.324555i	$-0.105215\pi$
$701$	5.07977	+	8.79842i	0.191860	+	0.332312i	−0.754007	+	0.656867i	$0.771881\pi$
$702$		0			0
$703$	−13.4659	−	23.3236i	−0.507876	−	0.879667i
$704$		0			0
$705$	−3.94673	−	6.83593i	−0.148642	−	0.257456i
$706$		0			0
$707$	8.27968	−	14.3408i	0.311389	−	0.539342i
$708$		0			0
$709$	−20.1229	+	34.8539i	−0.755732	+	1.30897i	0.189277	+	0.981924i	$0.439385\pi$
$709$	−20.1229	+	34.8539i	−0.755732	+	1.30897i	−0.945010	+	0.327043i	$0.893948\pi$
$710$		0			0
$711$	1.75452	+	3.03892i	0.0657997	+	0.113968i
$712$		0			0
$713$	−64.1402			−2.40207
$714$		0			0
$715$	−11.8944			−0.444826
$716$		0			0
$717$	6.46017	+	11.1893i	0.241259	+	0.417873i
$718$		0			0
$719$	3.13696	−	5.43337i	0.116989	−	0.202631i	−0.801584	−	0.597882i	$-0.796009\pi$
$719$	3.13696	−	5.43337i	0.116989	−	0.202631i	0.918573	+	0.395251i	$0.129343\pi$
$720$		0			0
$721$	5.71908	−	9.90574i	0.212990	−	0.368909i
$722$		0			0
$723$	−11.7732			−0.437851
$724$		0			0
$725$	−10.9261	−	18.9245i	−0.405784	−	0.702838i
$726$		0			0
$727$	0.378420	−	0.655443i	0.0140348	−	0.0243090i	−0.858923	−	0.512105i	$-0.828866\pi$
$727$	0.378420	−	0.655443i	0.0140348	−	0.0243090i	0.872958	+	0.487796i	$0.162199\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.66715	+	2.88759i	−0.0616617	+	0.106801i
$732$		0			0
$733$	−18.8878	−	32.7147i	−0.697638	−	1.20834i	−0.969283	−	0.245946i	$-0.920901\pi$
$733$	−18.8878	−	32.7147i	−0.697638	−	1.20834i	0.271646	−	0.962397i	$-0.412432\pi$
$734$		0			0
$735$	−3.43377	+	5.94746i	−0.126656	+	0.219375i
$736$		0			0
$737$	−14.5941	−	7.41709i	−0.537579	−	0.273212i
$738$		0			0
$739$	18.9589	−	32.8378i	0.697415	−	1.20796i	−0.271944	−	0.962313i	$-0.587667\pi$
$739$	18.9589	−	32.8378i	0.697415	−	1.20796i	0.969360	−	0.245646i	$-0.0790000\pi$
$740$		0			0
$741$	−5.46322	−	9.46258i	−0.200696	−	0.347616i
$742$		0			0
$743$	8.51000	−	14.7398i	0.312202	−	0.540749i	−0.666637	−	0.745383i	$-0.732267\pi$
$743$	8.51000	−	14.7398i	0.312202	−	0.540749i	0.978839	+	0.204633i	$0.0656002\pi$
$744$		0			0
$745$	−20.6371			−0.756084
$746$		0			0
$747$	1.81904	−	3.15066i	0.0665551	−	0.115277i
$748$		0			0
$749$	1.18402	+	2.05078i	0.0432631	+	0.0749339i
$750$		0			0
$751$	37.0191			1.35084			0.675422	−	0.737431i	$-0.263961\pi$
$751$	37.0191			1.35084			0.675422	+	0.737431i	$0.263961\pi$
$752$		0			0
$753$	4.38661	−	7.59783i	0.159857	−	0.276880i
$754$		0			0
$755$	11.0252	−	19.0961i	0.401247	−	0.694979i
$756$		0			0
$757$	12.5159	+	21.6782i	0.454898	+	0.787906i	0.998682	−	0.0513188i	$-0.0163425\pi$
$757$	12.5159	+	21.6782i	0.454898	+	0.787906i	−0.543785	+	0.839225i	$0.683009\pi$
$758$		0			0
$759$	15.5880			0.565807
$760$		0			0
$761$	8.19723			0.297149			0.148575	−	0.988901i	$-0.452531\pi$
$761$	8.19723			0.297149			0.148575	+	0.988901i	$0.452531\pi$
$762$		0			0
$763$	−5.57197	−	9.65093i	−0.201719	−	0.349387i
$764$		0			0
$765$	3.61473	−	6.26090i	0.130691	−	0.226363i
$766$		0			0
$767$	18.8997	−	32.7352i	0.682427	−	1.18200i
$768$		0			0
$769$	9.62635	+	16.6733i	0.347135	+	0.601256i	0.985739	−	0.168280i	$-0.0538212\pi$
$769$	9.62635	+	16.6733i	0.347135	+	0.601256i	−0.638604	+	0.769535i	$0.720488\pi$
$770$		0			0
$771$	11.8895	+	20.5933i	0.428191	+	0.741649i
$772$		0			0
$773$	18.2744	+	31.6522i	0.657286	+	1.13845i	0.981316	+	0.192405i	$0.0616288\pi$
$773$	18.2744	+	31.6522i	0.657286	+	1.13845i	−0.324030	+	0.946047i	$0.605038\pi$
$774$		0			0
$775$	−13.8083	−	23.9166i	−0.496008	−	0.859111i
$776$		0			0
$777$	−14.6588			−0.525883
$778$		0			0
$779$	14.5022			0.519594
$780$		0			0
$781$	−14.9230	+	25.8474i	−0.533987	+	0.924893i
$782$		0			0
$783$	−3.25586	−	5.63932i	−0.116355	−	0.201533i
$784$		0			0
$785$	7.79130	−	13.4949i	0.278083	−	0.481655i
$786$		0			0
$787$	1.50990	−	2.61523i	0.0538223	−	0.0932229i	−0.837859	−	0.545887i	$-0.816193\pi$
$787$	1.50990	−	2.61523i	0.0538223	−	0.0932229i	0.891681	+	0.452664i	$0.149526\pi$
$788$		0			0
$789$	10.8675			0.386895
$790$		0			0
$791$	−6.04544	+	10.4710i	−0.214951	+	0.372306i
$792$		0			0
$793$	−30.9647	−	53.6324i	−1.09959	−	1.90454i
$794$		0			0
$795$	−12.3585			−0.438311
$796$		0			0
$797$	−6.92081	−	11.9872i	−0.245148	−	0.424608i	0.717026	−	0.697047i	$-0.245503\pi$
$797$	−6.92081	−	11.9872i	−0.245148	−	0.424608i	−0.962173	+	0.272439i	$0.912170\pi$
$798$		0			0
$799$	34.7074			1.22786
$800$		0			0
$801$	7.07624			0.250026
$802$		0			0
$803$	7.44084			0.262582
$804$		0			0
$805$	−12.8147			−0.451660
$806$		0			0
$807$	−29.2172			−1.02850
$808$		0			0
$809$	−37.5906			−1.32162			−0.660808	−	0.750555i	$-0.729786\pi$
$809$	−37.5906			−1.32162			−0.660808	+	0.750555i	$0.729786\pi$
$810$		0			0
$811$	−18.1368	−	31.4139i	−0.636870	−	1.10309i	−0.986116	−	0.166060i	$-0.946895\pi$
$811$	−18.1368	−	31.4139i	−0.636870	−	1.10309i	0.349245	−	0.937031i	$-0.386438\pi$
$812$		0			0
$813$	−24.1706			−0.847698
$814$		0			0
$815$	−10.6389	−	18.4272i	−0.372666	−	0.645476i
$816$		0			0
$817$	−0.696602	+	1.20655i	−0.0243710	+	0.0422119i
$818$		0			0
$819$	−5.94720			−0.207812
$820$		0			0
$821$	0.771014	−	1.33544i	0.0269086	−	0.0466070i	−0.852258	−	0.523122i	$-0.824767\pi$
$821$	0.771014	−	1.33544i	0.0269086	−	0.0466070i	0.879166	+	0.476515i	$0.158100\pi$
$822$		0			0
$823$	−16.0346	+	27.7727i	−0.558931	+	0.968096i	0.438656	+	0.898655i	$0.355455\pi$
$823$	−16.0346	+	27.7727i	−0.558931	+	0.968096i	−0.997586	+	0.0694408i	$0.977879\pi$
$824$		0			0
$825$	3.35582	+	5.81244i	0.116834	+	0.202363i
$826$		0			0
$827$	−1.07480	+	1.86160i	−0.0373744	+	0.0647343i	−0.884108	−	0.467283i	$-0.845233\pi$
$827$	−1.07480	+	1.86160i	−0.0373744	+	0.0647343i	0.846733	+	0.532018i	$0.178566\pi$
$828$		0			0
$829$	41.1307			1.42853			0.714264	−	0.699876i	$-0.246762\pi$
$829$	41.1307			1.42853			0.714264	+	0.699876i	$0.246762\pi$
$830$		0			0
$831$	5.92644			0.205586
$832$		0			0
$833$	−15.0982	−	26.1509i	−0.523123	−	0.906076i
$834$		0			0
$835$	−1.31782	−	2.28254i	−0.0456052	−	0.0789904i
$836$		0			0
$837$	−4.11473	−	7.12692i	−0.142226	−	0.246343i
$838$		0			0
$839$	−2.94415	−	5.09942i	−0.101643	−	0.176051i	0.810719	−	0.585436i	$-0.199077\pi$
$839$	−2.94415	−	5.09942i	−0.101643	−	0.176051i	−0.912362	+	0.409385i	$0.865743\pi$
$840$		0			0
$841$	−6.70125	+	11.6069i	−0.231078	+	0.400238i
$842$		0			0
$843$	−2.66141	+	4.60971i	−0.0916640	+	0.158767i
$844$		0			0
$845$	−5.45711	−	9.45199i	−0.187730	−	0.325158i
$846$		0			0
$847$	8.97580			0.308412
$848$		0			0
$849$	−20.8614			−0.715962
$850$		0			0
$851$	44.5506	+	77.1639i	1.52717	+	2.64514i
$852$		0			0
$853$	−15.0315	+	26.0354i	−0.514670	+	0.891434i	0.485185	+	0.874411i	$0.338752\pi$
$853$	−15.0315	+	26.0354i	−0.514670	+	0.891434i	−0.999855	+	0.0170228i	$0.994581\pi$
$854$		0			0
$855$	1.51038	−	2.61606i	0.0516539	−	0.0894673i
$856$		0			0
$857$	16.6694			0.569414			0.284707	−	0.958615i	$-0.408104\pi$
$857$	16.6694			0.569414			0.284707	+	0.958615i	$0.408104\pi$
$858$		0			0
$859$	−12.9792	−	22.4807i	−0.442845	−	0.767030i	0.555054	−	0.831814i	$-0.312697\pi$
$859$	−12.9792	−	22.4807i	−0.442845	−	0.767030i	−0.997899	+	0.0647841i	$0.979364\pi$
$860$		0			0
$861$	3.94673	−	6.83593i	0.134504	−	0.232968i
$862$		0			0
$863$	12.4000			0.422102			0.211051	−	0.977475i	$-0.432311\pi$
$863$	12.4000			0.422102			0.211051	+	0.977475i	$0.432311\pi$
$864$		0			0
$865$	4.30694	−	7.45984i	0.146440	−	0.253642i
$866$		0			0
$867$	7.39393	+	12.8067i	0.251111	+	0.434937i
$868$		0			0
$869$	−3.50904	+	6.07784i	−0.119036	+	0.206177i
$870$		0			0
$871$	−2.02602	−	37.9102i	−0.0686491	−	1.28454i
$872$		0			0
$873$	7.03812	−	12.1904i	0.238204	−	0.412582i
$874$		0			0
$875$	−6.86925	−	11.8979i	−0.232223	−	0.402222i
$876$		0			0
$877$	−15.9091	+	27.5553i	−0.537212	+	0.930478i	0.461841	+	0.886963i	$0.347189\pi$
$877$	−15.9091	+	27.5553i	−0.537212	+	0.930478i	−0.999053	+	0.0435153i	$0.986144\pi$
$878$		0			0
$879$	−1.42594			−0.0480957
$880$		0			0
$881$	−1.61960	+	2.80523i	−0.0545658	+	0.0945107i	−0.892018	−	0.452000i	$-0.850711\pi$
$881$	−1.61960	+	2.80523i	−0.0545658	+	0.0945107i	0.837452	+	0.546510i	$0.184044\pi$
$882$		0			0
$883$	−6.69536	−	11.5967i	−0.225317	−	0.390260i	0.731098	−	0.682273i	$-0.239008\pi$
$883$	−6.69536	−	11.5967i	−0.225317	−	0.390260i	−0.956414	+	0.292013i	$0.905675\pi$
$884$		0			0
$885$	10.4501			0.351277
$886$		0			0
$887$	16.3822	−	28.3748i	0.550061	−	0.952733i	−0.448209	−	0.893929i	$-0.647938\pi$
$887$	16.3822	−	28.3748i	0.550061	−	0.952733i	0.998270	−	0.0588044i	$-0.0187288\pi$
$888$		0			0
$889$	9.61865	−	16.6600i	0.322599	−	0.558758i
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	14.5022			0.485297
$894$		0			0
$895$	−10.1904			−0.340626
$896$		0			0
$897$	18.0745	+	31.3060i	0.603491	+	1.04528i
$898$		0			0
$899$	−26.7940	+	46.4085i	−0.893629	+	1.54781i
$900$		0			0
$901$	27.1701	−	47.0600i	0.905167	−	1.56779i
$902$		0			0
$903$	0.379157	+	0.656719i	0.0126176	+	0.0218542i
$904$		0			0
$905$	−15.7940	−	27.3560i	−0.525010	−	0.909343i
$906$		0			0
$907$	8.27528	+	14.3332i	0.274776	+	0.475926i	0.970079	−	0.242791i	$-0.0780629\pi$
$907$	8.27528	+	14.3332i	0.274776	+	0.475926i	−0.695302	+	0.718717i	$0.744730\pi$
$908$		0			0
$909$	−6.45711	−	11.1840i	−0.214169	−	0.370951i
$910$		0			0
$911$	9.85632			0.326554			0.163277	−	0.986580i	$-0.447794\pi$
$911$	9.85632			0.326554			0.163277	+	0.986580i	$0.447794\pi$
$912$		0			0
$913$	7.27615			0.240805
$914$		0			0
$915$	8.56060	−	14.8274i	0.283005	−	0.490178i
$916$		0			0
$917$	13.9988	+	24.2466i	0.462280	+	0.800692i
$918$		0			0
$919$	18.6571	−	32.3151i	0.615442	−	1.06598i	−0.374865	−	0.927079i	$-0.622311\pi$
$919$	18.6571	−	32.3151i	0.615442	−	1.06598i	0.990307	−	0.138897i	$-0.0443556\pi$
$920$		0			0
$921$	5.85715	−	10.1449i	0.193000	−	0.334285i
$922$		0			0
$923$	−69.2140			−2.27821
$924$		0			0
$925$	−19.1819	+	33.2241i	−0.630698	+	1.09240i
$926$		0			0
$927$	−4.46017	−	7.72523i	−0.146491	−	0.253730i
$928$		0			0
$929$	24.8111			0.814026			0.407013	−	0.913422i	$-0.366570\pi$
$929$	24.8111			0.814026			0.407013	+	0.913422i	$0.366570\pi$
$930$		0			0
$931$	−6.30866	−	10.9269i	−0.206758	−	0.358115i
$932$		0			0
$933$	−20.7231			−0.678444
$934$		0			0
$935$	14.4589			0.472857
$936$		0			0
$937$	−10.4963			−0.342900			−0.171450	−	0.985193i	$-0.554845\pi$
$937$	−10.4963			−0.342900			−0.171450	+	0.985193i	$0.554845\pi$
$938$		0			0
$939$	−14.0520			−0.458571
$940$		0			0
$941$	43.7527			1.42630			0.713148	−	0.701014i	$-0.247269\pi$
$941$	43.7527			1.42630			0.713148	+	0.701014i	$0.247269\pi$
$942$		0			0
$943$	−47.9790			−1.56241
$944$		0			0
$945$	−0.822092	−	1.42391i	−0.0267427	−	0.0463197i
$946$		0			0
$947$	−7.37390			−0.239620			−0.119810	−	0.992797i	$-0.538228\pi$
$947$	−7.37390			−0.239620			−0.119810	+	0.992797i	$0.538228\pi$
$948$		0			0
$949$	8.62779	+	14.9438i	0.280070	+	0.485095i
$950$		0			0
$951$	13.7130	−	23.7516i	0.444673	−	0.770197i
$952$		0			0
$953$	−13.2857			−0.430366			−0.215183	−	0.976574i	$-0.569035\pi$
$953$	−13.2857			−0.430366			−0.215183	+	0.976574i	$0.569035\pi$
$954$		0			0
$955$	13.6724	−	23.6813i	0.442428	−	0.766308i
$956$		0			0
$957$	6.51172	−	11.2786i	0.210494	−	0.364586i
$958$		0			0
$959$	−7.69134	−	13.3218i	−0.248366	−	0.430183i
$960$		0			0
$961$	−18.3620	+	31.8040i	−0.592323	+	1.02593i
$962$		0			0
$963$	1.84677			0.0595114
$964$		0			0
$965$	2.60241			0.0837745
$966$		0			0
$967$	8.44549	+	14.6280i	0.271589	+	0.470405i	0.969269	−	0.246004i	$-0.0791177\pi$
$967$	8.44549	+	14.6280i	0.271589	+	0.470405i	−0.697680	+	0.716409i	$0.745784\pi$
$968$		0			0
$969$	6.64113	+	11.5028i	0.213344	+	0.369522i
$970$		0			0
$971$	20.9174	+	36.2300i	0.671270	+	1.16267i	0.977544	+	0.210731i	$0.0675844\pi$
$971$	20.9174	+	36.2300i	0.671270	+	1.16267i	−0.306274	+	0.951944i	$0.599082\pi$
$972$		0			0
$973$	−9.38661	−	16.2581i	−0.300921	−	0.521210i
$974$		0			0
$975$	−7.78226	+	13.4793i	−0.249232	+	0.431682i
$976$		0			0
$977$	−12.1339	+	21.0165i	−0.388198	+	0.672379i	−0.992207	−	0.124599i	$-0.960236\pi$
$977$	−12.1339	+	21.0165i	−0.388198	+	0.672379i	0.604009	+	0.796977i	$0.293569\pi$
$978$		0			0
$979$	7.07624	+	12.2564i	0.226157	+	0.391716i
$980$		0			0
$981$	−8.69087			−0.277478
$982$		0			0
$983$	32.2502			1.02862			0.514311	−	0.857604i	$-0.328048\pi$
$983$	32.2502			1.02862			0.514311	+	0.857604i	$0.328048\pi$
$984$		0			0
$985$	15.0490	+	26.0656i	0.479500	+	0.830519i
$986$		0			0
$987$	3.94673	−	6.83593i	0.125626	−	0.217590i
$988$		0			0
$989$	2.30464	−	3.99175i	0.0732832	−	0.126930i
$990$		0			0
$991$	−22.4457			−0.713013			−0.356506	−	0.934293i	$-0.616032\pi$
$991$	−22.4457			−0.713013			−0.356506	+	0.934293i	$0.616032\pi$
$992$		0			0
$993$	6.75147	+	11.6939i	0.214251	+	0.371094i
$994$		0			0
$995$	−6.12817	+	10.6143i	−0.194276	+	0.336496i
$996$		0			0
$997$	−37.3169			−1.18184			−0.590919	−	0.806731i	$-0.701235\pi$
$997$	−37.3169			−1.18184			−0.590919	+	0.806731i	$0.701235\pi$
$998$		0			0
$999$	−5.71603	+	9.90045i	−0.180847	+	0.313236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.d.565.3	yes	8
3.2	odd	2		2412.2.l.e.1369.2		8
67.37	even	3	inner	804.2.i.d.37.3	✓	8
201.104	odd	6		2412.2.l.e.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.d.37.3	✓	8	67.37	even	3	inner
804.2.i.d.565.3	yes	8	1.1	even	1	trivial
2412.2.l.e.37.2		8	201.104	odd	6
2412.2.l.e.1369.2		8	3.2	odd	2

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.28226 q^{5} +(0.641129 + 1.11047i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.28226 q^{5} +(0.641129 + 1.11047i) q^{7} +1.00000 q^{9} +(1.00000 + 1.73205i) q^{11} +(-2.31904 + 4.01669i) q^{13} -1.28226 q^{15} +(2.81904 - 4.88271i) q^{17} +(1.17791 - 2.04020i) q^{19} +(-0.641129 - 1.11047i) q^{21} +(-3.89699 + 6.74978i) q^{23} -3.35582 q^{25} -1.00000 q^{27} +(3.25586 + 5.63932i) q^{29} +(4.11473 + 7.12692i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(0.822092 + 1.42391i) q^{35} +(5.71603 - 9.90045i) q^{37} +(2.31904 - 4.01669i) q^{39} +(3.07795 + 5.33117i) q^{41} -0.591390 q^{43} +1.28226 q^{45} +(3.07795 + 5.33117i) q^{47} +(2.67791 - 4.63827i) q^{49} +(-2.81904 + 4.88271i) q^{51} +9.63807 q^{53} +(1.28226 + 2.22094i) q^{55} +(-1.17791 + 2.04020i) q^{57} -8.14979 q^{59} +(-6.67619 + 11.5635i) q^{61} +(0.641129 + 1.11047i) q^{63} +(-2.97360 + 5.15043i) q^{65} +(-6.86021 + 4.46514i) q^{67} +(3.89699 - 6.74978i) q^{69} +(7.46150 + 12.9237i) q^{71} +(1.86021 - 3.22198i) q^{73} +3.35582 q^{75} +(-1.28226 + 2.22094i) q^{77} +(1.75452 + 3.03892i) q^{79} +1.00000 q^{81} +(1.81904 - 3.15066i) q^{83} +(3.61473 - 6.26090i) q^{85} +(-3.25586 - 5.63932i) q^{87} +7.07624 q^{89} -5.94720 q^{91} +(-4.11473 - 7.12692i) q^{93} +(1.51038 - 2.61606i) q^{95} +(7.03812 - 12.1904i) q^{97} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9	\( 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9} + 8 q^{11} - 2 q^{15} + 4 q^{17} - 5 q^{19} - q^{21} + q^{23} + 2 q^{25} - 8 q^{27} - 2 q^{29} + 9 q^{31} - 8 q^{33} + 21 q^{35} - 5 q^{37} + 11 q^{41} + 6 q^{43} + 2 q^{45} + 11 q^{47} + 7 q^{49} - 4 q^{51} + 40 q^{53} + 2 q^{55} + 5 q^{57} + 28 q^{59} + 20 q^{61} + q^{63} - 4 q^{65} - 33 q^{67} - q^{69} + 11 q^{71} - 7 q^{73} - 2 q^{75} - 2 q^{77} + 12 q^{79} + 8 q^{81} - 4 q^{83} + 5 q^{85} + 2 q^{87} - 16 q^{89} - 8 q^{91} - 9 q^{93} - 18 q^{95} + 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9 + 8 * q^11 - 2 * q^15 + 4 * q^17 - 5 * q^19 - q^21 + q^23 + 2 * q^25 - 8 * q^27 - 2 * q^29 + 9 * q^31 - 8 * q^33 + 21 * q^35 - 5 * q^37 + 11 * q^41 + 6 * q^43 + 2 * q^45 + 11 * q^47 + 7 * q^49 - 4 * q^51 + 40 * q^53 + 2 * q^55 + 5 * q^57 + 28 * q^59 + 20 * q^61 + q^63 - 4 * q^65 - 33 * q^67 - q^69 + 11 * q^71 - 7 * q^73 - 2 * q^75 - 2 * q^77 + 12 * q^79 + 8 * q^81 - 4 * q^83 + 5 * q^85 + 2 * q^87 - 16 * q^89 - 8 * q^91 - 9 * q^93 - 18 * q^95 + 20 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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