LMFDB - Embedded newform 804.2.q.b.397.5

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			397.5
Character	$\chi$	$=$	804.397
Dual form			804.2.q.b.241.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(1.77448 - 0.521035i) q^{5} +(-3.02047 + 3.48581i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(1.77448 - 0.521035i) q^{5} +(-3.02047 + 3.48581i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(3.93894 - 1.15658i) q^{11} +(-0.415421 + 0.266975i) q^{13} +(-1.21110 - 1.39768i) q^{15} +(0.225401 - 1.56770i) q^{17} +(4.53068 + 5.22868i) q^{19} +(4.42555 + 1.29946i) q^{21} +(2.63191 + 5.76307i) q^{23} +(-1.32896 + 0.854071i) q^{25} +(0.959493 + 0.281733i) q^{27} +1.63223 q^{29} +(-2.78213 - 1.78796i) q^{31} +(-2.68836 - 3.10253i) q^{33} +(-3.54354 + 7.75928i) q^{35} +11.4300 q^{37} +(0.415421 + 0.266975i) q^{39} +(0.221415 - 1.53997i) q^{41} +(0.132442 - 0.921155i) q^{43} +(-0.768266 + 1.68227i) q^{45} +(2.43938 + 5.34151i) q^{47} +(-2.03142 - 14.1288i) q^{49} +(-1.51966 + 0.446213i) q^{51} +(-1.20219 - 8.36144i) q^{53} +(6.38696 - 4.10465i) q^{55} +(2.87406 - 6.29332i) q^{57} +(9.70533 + 6.23724i) q^{59} +(8.90205 + 2.61388i) q^{61} +(-0.656411 - 4.56544i) q^{63} +(-0.598053 + 0.690190i) q^{65} +(-6.25848 - 5.27554i) q^{67} +(4.14894 - 4.78813i) q^{69} +(0.873940 + 6.07838i) q^{71} +(-8.77361 - 2.57616i) q^{73} +(1.32896 + 0.854071i) q^{75} +(-7.86585 + 17.2238i) q^{77} +(2.48884 - 1.59948i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-12.3072 + 3.61371i) q^{83} +(-0.416855 - 2.89929i) q^{85} +(-0.678052 - 1.48473i) q^{87} +(-1.56063 + 3.41731i) q^{89} +(0.324143 - 2.25447i) q^{91} +(-0.470652 + 3.27346i) q^{93} +(10.7639 + 6.91755i) q^{95} +8.12305 q^{97} +(-1.70538 + 3.73425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$1$

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
$5$	1.77448	−	0.521035i	0.793572	−	0.233014i	0.140272	−	0.990113i	$-0.455202\pi$
$5$	1.77448	−	0.521035i	0.793572	−	0.233014i	0.653300	+	0.757099i	$0.273384\pi$
$6$		0			0
$7$	−3.02047	+	3.48581i	−1.14163	+	1.31751i	−0.200413	+	0.979711i	$0.564228\pi$
$7$	−3.02047	+	3.48581i	−1.14163	+	1.31751i	−0.941218	+	0.337801i	$0.890317\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	3.93894	−	1.15658i	1.18764	−	0.348721i	0.372522	−	0.928023i	$-0.378493\pi$
$11$	3.93894	−	1.15658i	1.18764	−	0.348721i	0.815113	+	0.579302i	$0.196675\pi$
$12$		0			0
$13$	−0.415421	+	0.266975i	−0.115217	+	0.0740454i	−0.596980	−	0.802256i	$-0.703633\pi$
$13$	−0.415421	+	0.266975i	−0.115217	+	0.0740454i	0.481763	+	0.876301i	$0.339997\pi$
$14$		0			0
$15$	−1.21110	−	1.39768i	−0.312704	−	0.360879i
$16$		0			0
$17$	0.225401	−	1.56770i	0.0546677	−	0.380222i	−0.944059	−	0.329776i	$-0.893027\pi$
$17$	0.225401	−	1.56770i	0.0546677	−	0.380222i	0.998727	−	0.0504459i	$-0.0160642\pi$
$18$		0			0
$19$	4.53068	+	5.22868i	1.03941	+	1.19954i	0.979522	+	0.201336i	$0.0645283\pi$
$19$	4.53068	+	5.22868i	1.03941	+	1.19954i	0.0598862	+	0.998205i	$0.480926\pi$
$20$		0			0
$21$	4.42555	+	1.29946i	0.965735	+	0.283565i
$22$		0			0
$23$	2.63191	+	5.76307i	0.548790	+	1.20168i	0.957344	+	0.288949i	$0.0933059\pi$
$23$	2.63191	+	5.76307i	0.548790	+	1.20168i	−0.408554	+	0.912734i	$0.633967\pi$
$24$		0			0
$25$	−1.32896	+	0.854071i	−0.265792	+	0.170814i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	1.63223			0.303097			0.151549	−	0.988450i	$-0.451574\pi$
$29$	1.63223			0.303097			0.151549	+	0.988450i	$0.451574\pi$
$30$		0			0
$31$	−2.78213	−	1.78796i	−0.499685	−	0.321128i	0.266405	−	0.963861i	$-0.414164\pi$
$31$	−2.78213	−	1.78796i	−0.499685	−	0.321128i	−0.766090	+	0.642733i	$0.777800\pi$
$32$		0			0
$33$	−2.68836	−	3.10253i	−0.467983	−	0.540081i
$34$		0			0
$35$	−3.54354	+	7.75928i	−0.598968	+	1.31156i
$36$		0			0
$37$	11.4300			1.87908			0.939540	−	0.342440i	$-0.111253\pi$
$37$	11.4300			1.87908			0.939540	+	0.342440i	$0.111253\pi$
$38$		0			0
$39$	0.415421	+	0.266975i	0.0665205	+	0.0427502i
$40$		0			0
$41$	0.221415	−	1.53997i	0.0345792	−	0.240503i	−0.965200	−	0.261512i	$-0.915779\pi$
$41$	0.221415	−	1.53997i	0.0345792	−	0.240503i	0.999779	+	0.0210090i	$0.00668786\pi$
$42$		0			0
$43$	0.132442	−	0.921155i	0.0201972	−	0.140475i	−0.977228	−	0.212194i	$-0.931939\pi$
$43$	0.132442	−	0.921155i	0.0201972	−	0.140475i	0.997425	+	0.0717187i	$0.0228484\pi$
$44$		0			0
$45$	−0.768266	+	1.68227i	−0.114526	+	0.250778i
$46$		0			0
$47$	2.43938	+	5.34151i	0.355821	+	0.779139i	0.999899	+	0.0141796i	$0.00451366\pi$
$47$	2.43938	+	5.34151i	0.355821	+	0.779139i	−0.644079	+	0.764959i	$0.722759\pi$
$48$		0			0
$49$	−2.03142	−	14.1288i	−0.290203	−	2.01840i
$50$		0			0
$51$	−1.51966	+	0.446213i	−0.212795	+	0.0624823i
$52$		0			0
$53$	−1.20219	−	8.36144i	−0.165134	−	1.14853i	−0.888771	−	0.458351i	$-0.848440\pi$
$53$	−1.20219	−	8.36144i	−0.165134	−	1.14853i	0.723637	−	0.690181i	$-0.242469\pi$
$54$		0			0
$55$	6.38696	−	4.10465i	0.861218	−	0.553471i
$56$		0			0
$57$	2.87406	−	6.29332i	0.380679	−	0.833571i
$58$		0			0
$59$	9.70533	+	6.23724i	1.26353	+	0.812019i	0.988763	−	0.149493i	$-0.0477641\pi$
$59$	9.70533	+	6.23724i	1.26353	+	0.812019i	0.274763	+	0.961512i	$0.411400\pi$
$60$		0			0
$61$	8.90205	+	2.61388i	1.13979	+	0.334673i	0.796549	−	0.604574i	$-0.206657\pi$
$61$	8.90205	+	2.61388i	1.13979	+	0.334673i	0.343242	+	0.939247i	$0.388475\pi$
$62$		0			0
$63$	−0.656411	−	4.56544i	−0.0827000	−	0.575191i
$64$		0			0
$65$	−0.598053	+	0.690190i	−0.0741794	+	0.0856076i
$66$		0			0
$67$	−6.25848	−	5.27554i	−0.764596	−	0.644510i
$67$	−6.25848	−	5.27554i	−0.764596	−	0.644510i
$68$		0			0
$69$	4.14894	−	4.78813i	0.499474	−	0.576423i
$70$		0			0
$71$	0.873940	+	6.07838i	0.103718	+	0.721371i	0.973625	+	0.228156i	$0.0732696\pi$
$71$	0.873940	+	6.07838i	0.103718	+	0.721371i	−0.869907	+	0.493216i	$0.835821\pi$
$72$		0			0
$73$	−8.77361	−	2.57616i	−1.02687	−	0.301517i	−0.275435	−	0.961320i	$-0.588822\pi$
$73$	−8.77361	−	2.57616i	−1.02687	−	0.301517i	−0.751439	+	0.659803i	$0.770640\pi$
$74$		0			0
$75$	1.32896	+	0.854071i	0.153455	+	0.0986196i
$76$		0			0
$77$	−7.86585	+	17.2238i	−0.896397	+	1.96284i
$78$		0			0
$79$	2.48884	−	1.59948i	0.280017	−	0.179956i	−0.393092	−	0.919499i	$-0.628595\pi$
$79$	2.48884	−	1.59948i	0.280017	−	0.179956i	0.673109	+	0.739543i	$0.264958\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−12.3072	+	3.61371i	−1.35089	+	0.396656i	−0.875541	−	0.483143i	$-0.839495\pi$
$83$	−12.3072	+	3.61371i	−1.35089	+	0.396656i	−0.475345	+	0.879799i	$0.657677\pi$
$84$		0			0
$85$	−0.416855	−	2.89929i	−0.0452143	−	0.314472i
$86$		0			0
$87$	−0.678052	−	1.48473i	−0.0726948	−	0.159179i
$88$		0			0
$89$	−1.56063	+	3.41731i	−0.165427	+	0.362234i	−0.974132	−	0.225980i	$-0.927442\pi$
$89$	−1.56063	+	3.41731i	−0.165427	+	0.362234i	0.808705	+	0.588214i	$0.200169\pi$
$90$		0			0
$91$	0.324143	−	2.25447i	0.0339795	−	0.236332i
$92$		0			0
$93$	−0.470652	+	3.27346i	−0.0488044	+	0.339442i
$94$		0			0
$95$	10.7639	+	6.91755i	1.10436	+	0.709726i
$96$		0			0
$97$	8.12305			0.824771			0.412386	−	0.911009i	$-0.364696\pi$
$97$	8.12305			0.824771			0.412386	+	0.911009i	$0.364696\pi$
$98$		0			0
$99$	−1.70538	+	3.73425i	−0.171397	+	0.375306i
$100$		0			0
$101$	6.39442	+	7.37956i	0.636269	+	0.734293i	0.978710	−	0.205246i	$-0.0657993\pi$
$101$	6.39442	+	7.37956i	0.636269	+	0.734293i	−0.342442	+	0.939539i	$0.611254\pi$
$102$		0			0
$103$	−2.16340	−	1.39033i	−0.213166	−	0.136994i	0.429701	−	0.902971i	$-0.358619\pi$
$103$	−2.16340	−	1.39033i	−0.213166	−	0.136994i	−0.642867	+	0.765978i	$0.722255\pi$
$104$		0			0
$105$	8.53013			0.832455
$106$		0			0
$107$	9.41534	+	2.76459i	0.910216	+	0.267263i	0.703132	−	0.711060i	$-0.251784\pi$
$107$	9.41534	+	2.76459i	0.910216	+	0.267263i	0.207084	+	0.978323i	$0.433603\pi$
$108$		0			0
$109$	−0.366325	+	0.235423i	−0.0350876	+	0.0225494i	−0.558067	−	0.829796i	$-0.688457\pi$
$109$	−0.366325	+	0.235423i	−0.0350876	+	0.0225494i	0.522979	+	0.852345i	$0.324820\pi$
$110$		0			0
$111$	−4.74819	−	10.3971i	−0.450678	−	0.986848i
$112$		0			0
$113$	−17.6966	−	5.19619i	−1.66476	−	0.488816i	−0.692242	−	0.721665i	$-0.743377\pi$
$113$	−17.6966	−	5.19619i	−1.66476	−	0.488816i	−0.972513	+	0.232849i	$0.925195\pi$
$114$		0			0
$115$	7.67303	+	8.85515i	0.715514	+	0.825747i
$116$		0			0
$117$	0.0702767	−	0.488785i	0.00649708	−	0.0451882i
$118$		0			0
$119$	4.78387	+	5.52089i	0.438537	+	0.506099i
$120$		0			0
$121$	4.92380	−	3.16433i	0.447618	−	0.287667i
$122$		0			0
$123$	−1.49279	+	0.438322i	−0.134600	+	0.0395222i
$124$		0			0
$125$	−7.96870	+	9.19636i	−0.712742	+	0.822548i
$126$		0			0
$127$	−7.87392	+	9.08699i	−0.698697	+	0.806340i	−0.988576	−	0.150724i	$-0.951840\pi$
$127$	−7.87392	+	9.08699i	−0.698697	+	0.806340i	0.289879	+	0.957063i	$0.406385\pi$
$128$		0			0
$129$	−0.892931	+	0.262188i	−0.0786182	+	0.0230844i
$130$		0			0
$131$	−6.13035	−	13.4236i	−0.535611	−	1.17283i	−0.963184	−	0.268844i	$-0.913358\pi$
$131$	−6.13035	−	13.4236i	−0.535611	−	1.17283i	0.427572	−	0.903981i	$-0.359369\pi$
$132$		0			0
$133$	−31.9110			−2.76703
$134$		0			0
$135$	1.84940			0.159171
$136$		0			0
$137$	−6.23726	−	13.6577i	−0.532885	−	1.16686i	−0.964327	−	0.264714i	$-0.914722\pi$
$137$	−6.23726	−	13.6577i	−0.532885	−	1.16686i	0.431442	−	0.902141i	$-0.358005\pi$
$138$		0			0
$139$	4.84302	−	1.42204i	0.410780	−	0.120616i	−0.0698123	−	0.997560i	$-0.522240\pi$
$139$	4.84302	−	1.42204i	0.410780	−	0.120616i	0.480592	+	0.876944i	$0.340422\pi$
$140$		0			0
$141$	3.84545	−	4.43788i	0.323845	−	0.373737i
$142$		0			0
$143$	−1.32754	+	1.53206i	−0.111015	+	0.128118i
$144$		0			0
$145$	2.89636	−	0.850448i	0.240530	−	0.0706259i
$146$		0			0
$147$	−12.0081	+	7.71717i	−0.990415	+	0.636501i
$148$		0			0
$149$	2.46350	+	2.84303i	0.201818	+	0.232910i	0.847632	−	0.530584i	$-0.178027\pi$
$149$	2.46350	+	2.84303i	0.201818	+	0.232910i	−0.645814	+	0.763495i	$0.723482\pi$
$150$		0			0
$151$	1.67536	−	11.6524i	0.136339	−	0.948259i	−0.800708	−	0.599055i	$-0.795543\pi$
$151$	1.67536	−	11.6524i	0.136339	−	0.948259i	0.937047	−	0.349204i	$-0.113548\pi$
$152$		0			0
$153$	1.03718	+	1.19697i	0.0838510	+	0.0967692i
$154$		0			0
$155$	−5.86842	−	1.72312i	−0.471363	−	0.138405i
$156$		0			0
$157$	−7.34411	−	16.0813i	−0.586123	−	1.28343i	−0.937757	−	0.347293i	$-0.887101\pi$
$157$	−7.34411	−	16.0813i	−0.586123	−	1.28343i	0.351633	−	0.936138i	$-0.385626\pi$
$158$		0			0
$159$	−7.10642	+	4.56702i	−0.563576	+	0.362188i
$160$		0			0
$161$	−28.0386	−	8.23287i	−2.20975	−	0.648841i
$162$		0			0
$163$	−19.4711			−1.52510			−0.762548	−	0.646932i	$-0.776052\pi$
$163$	−19.4711			−1.52510			−0.762548	+	0.646932i	$0.776052\pi$
$164$		0			0
$165$	−6.38696	−	4.10465i	−0.497224	−	0.319547i
$166$		0			0
$167$	−2.18599	−	2.52277i	−0.169157	−	0.195217i	0.664841	−	0.746985i	$-0.268499\pi$
$167$	−2.18599	−	2.52277i	−0.169157	−	0.195217i	−0.833998	+	0.551767i	$0.813954\pi$
$168$		0			0
$169$	−5.29910	+	11.6034i	−0.407623	+	0.892569i
$170$		0			0
$171$	−6.91853			−0.529074
$172$		0			0
$173$	7.50499	+	4.82316i	0.570594	+	0.366698i	0.793898	−	0.608050i	$-0.208048\pi$
$173$	7.50499	+	4.82316i	0.570594	+	0.366698i	−0.223305	+	0.974749i	$0.571684\pi$
$174$		0			0
$175$	1.03696	−	7.21220i	0.0783866	−	0.545191i
$176$		0			0
$177$	1.64185	−	11.4193i	0.123409	−	0.858329i
$178$		0			0
$179$	8.46433	−	18.5343i	0.632653	−	1.38532i	−0.273295	−	0.961930i	$-0.588114\pi$
$179$	8.46433	−	18.5343i	0.632653	−	1.38532i	0.905949	−	0.423388i	$-0.139159\pi$
$180$		0			0
$181$	−4.97945	−	10.9035i	−0.370120	−	0.810449i	−0.999445	−	0.0333072i	$-0.989396\pi$
$181$	−4.97945	−	10.9035i	−0.370120	−	0.810449i	0.629325	−	0.777142i	$-0.283331\pi$
$182$		0			0
$183$	−1.32038	−	9.18344i	−0.0976052	−	0.678859i
$184$		0			0
$185$	20.2823	−	5.95543i	1.49119	−	0.437852i
$186$		0			0
$187$	−0.925322	−	6.43576i	−0.0676663	−	0.470629i
$188$		0			0
$189$	−3.88019	+	2.49364i	−0.282242	+	0.181386i
$190$		0			0
$191$	−0.748511	+	1.63901i	−0.0541604	+	0.118595i	−0.934777	−	0.355234i	$-0.884401\pi$
$191$	−0.748511	+	1.63901i	−0.0541604	+	0.118595i	0.880617	+	0.473829i	$0.157128\pi$
$192$		0			0
$193$	−3.47383	−	2.23249i	−0.250052	−	0.160698i	0.409611	−	0.912260i	$-0.365664\pi$
$193$	−3.47383	−	2.23249i	−0.250052	−	0.160698i	−0.659663	+	0.751562i	$0.729301\pi$
$194$		0			0
$195$	0.876259	+	0.257293i	0.0627502	+	0.0184251i
$196$		0			0
$197$	3.22256	+	22.4134i	0.229598	+	1.59689i	0.699806	+	0.714333i	$0.253270\pi$
$197$	3.22256	+	22.4134i	0.229598	+	1.59689i	−0.470208	+	0.882556i	$0.655821\pi$
$198$		0			0
$199$	−6.09750	+	7.03689i	−0.432240	+	0.498832i	−0.929527	−	0.368755i	$-0.879784\pi$
$199$	−6.09750	+	7.03689i	−0.432240	+	0.498832i	0.497287	+	0.867586i	$0.334330\pi$
$200$		0			0
$201$	−2.19894	+	7.88446i	−0.155101	+	0.556127i
$202$		0			0
$203$	−4.93010	+	5.68964i	−0.346025	+	0.399334i
$204$		0			0
$205$	−0.409483	−	2.84802i	−0.0285996	−	0.198914i
$206$		0			0
$207$	−6.07897	−	1.78495i	−0.422518	−	0.124062i
$208$		0			0
$209$	23.8934	+	15.3554i	1.65274	+	1.06215i
$210$		0			0
$211$	3.50792	−	7.68126i	0.241495	−	0.528800i	−0.749611	−	0.661879i	$-0.769759\pi$
$211$	3.50792	−	7.68126i	0.241495	−	0.528800i	0.991105	+	0.133079i	$0.0424864\pi$
$212$		0			0
$213$	5.16604	−	3.32002i	0.353972	−	0.227484i
$214$		0			0
$215$	−0.244938	−	1.70358i	−0.0167046	−	0.116183i
$216$		0			0
$217$	14.6358	−	4.29747i	0.993545	−	0.291731i
$218$		0			0
$219$	1.30133	+	9.05094i	0.0879356	+	0.611606i
$220$		0			0
$221$	0.324899	+	0.711430i	0.0218551	+	0.0478559i
$222$		0			0
$223$	−5.08626	+	11.1374i	−0.340601	+	0.745813i	−0.999982	−	0.00599632i	$-0.998091\pi$
$223$	−5.08626	+	11.1374i	−0.340601	+	0.745813i	0.659381	+	0.751809i	$0.270819\pi$
$224$		0			0
$225$	0.224820	−	1.56366i	0.0149880	−	0.104244i
$226$		0			0
$227$	−3.88689	+	27.0339i	−0.257982	+	1.79430i	0.289178	+	0.957275i	$0.406618\pi$
$227$	−3.88689	+	27.0339i	−0.257982	+	1.79430i	−0.547160	+	0.837028i	$0.684291\pi$
$228$		0			0
$229$	−9.84033	−	6.32399i	−0.650267	−	0.417901i	0.173497	−	0.984834i	$-0.444493\pi$
$229$	−9.84033	−	6.32399i	−0.650267	−	0.417901i	−0.823764	+	0.566933i	$0.808130\pi$
$230$		0			0
$231$	18.9349			1.24583
$232$		0			0
$233$	9.28928	−	20.3407i	0.608561	−	1.33256i	−0.314993	−	0.949094i	$-0.602002\pi$
$233$	9.28928	−	20.3407i	0.608561	−	1.33256i	0.923554	−	0.383469i	$-0.125271\pi$
$234$		0			0
$235$	7.11175	+	8.20740i	0.463920	+	0.535392i
$236$		0			0
$237$	−2.48884	−	1.59948i	−0.161668	−	0.103898i
$238$		0			0
$239$	−15.6819			−1.01438			−0.507189	−	0.861835i	$-0.669315\pi$
$239$	−15.6819			−1.01438			−0.507189	+	0.861835i	$0.669315\pi$
$240$		0			0
$241$	17.5003	+	5.13854i	1.12729	+	0.331003i	0.791643	−	0.610985i	$-0.209226\pi$
$241$	17.5003	+	5.13854i	1.12729	+	0.331003i	0.335649	+	0.941987i	$0.391044\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−10.9663	−	24.0129i	−0.700613	−	1.53413i
$246$		0			0
$247$	−3.27806	−	0.962526i	−0.208578	−	0.0612440i
$248$		0			0
$249$	8.39973	+	9.69380i	0.532311	+	0.614320i
$250$		0			0
$251$	3.56712	−	24.8099i	0.225155	−	1.56599i	−0.492954	−	0.870055i	$-0.664083\pi$
$251$	3.56712	−	24.8099i	0.225155	−	1.56599i	0.718109	−	0.695930i	$-0.245008\pi$
$252$		0			0
$253$	17.0324	+	19.6564i	1.07082	+	1.23579i
$254$		0			0
$255$	−2.46412	+	1.58359i	−0.154309	+	0.0991685i
$256$		0			0
$257$	12.5970	−	3.69881i	0.785778	−	0.230725i	0.135858	−	0.990728i	$-0.456621\pi$
$257$	12.5970	−	3.69881i	0.785778	−	0.230725i	0.649919	+	0.760003i	$0.274803\pi$
$258$		0			0
$259$	−34.5240	+	39.8428i	−2.14522	+	2.47571i
$260$		0			0
$261$	−1.06888	+	1.23356i	−0.0661622	+	0.0763552i
$262$		0			0
$263$	−14.5251	+	4.26494i	−0.895654	+	0.262988i	−0.696991	−	0.717080i	$-0.745478\pi$
$263$	−14.5251	+	4.26494i	−0.895654	+	0.262988i	−0.198663	+	0.980068i	$0.563660\pi$
$264$		0			0
$265$	−6.48987	−	14.2108i	−0.398670	−	0.872965i
$266$		0			0
$267$	3.75680			0.229913
$268$		0			0
$269$	−10.9118			−0.665302			−0.332651	−	0.943050i	$-0.607943\pi$
$269$	−10.9118			−0.665302			−0.332651	+	0.943050i	$0.607943\pi$
$270$		0			0
$271$	6.62936	+	14.5163i	0.402705	+	0.881801i	0.996989	+	0.0775458i	$0.0247084\pi$
$271$	6.62936	+	14.5163i	0.402705	+	0.881801i	−0.594284	+	0.804256i	$0.702564\pi$
$272$		0			0
$273$	−2.18539	+	0.641688i	−0.132266	+	0.0388367i
$274$		0			0
$275$	−4.24690	+	4.90118i	−0.256097	+	0.295552i
$276$		0			0
$277$	14.4193	−	16.6407i	0.866369	−	0.999843i	−0.133592	−	0.991036i	$-0.542651\pi$
$277$	14.4193	−	16.6407i	0.866369	−	0.999843i	0.999961	−	0.00880696i	$-0.00280338\pi$
$278$		0			0
$279$	3.17316	−	0.931724i	0.189972	−	0.0557808i
$280$		0			0
$281$	−14.7827	+	9.50024i	−0.881859	+	0.566737i	−0.901359	−	0.433073i	$-0.857429\pi$
$281$	−14.7827	+	9.50024i	−0.881859	+	0.566737i	0.0194993	+	0.999810i	$0.493793\pi$
$282$		0			0
$283$	−7.70210	−	8.88869i	−0.457842	−	0.528378i	0.479148	−	0.877734i	$-0.340946\pi$
$283$	−7.70210	−	8.88869i	−0.457842	−	0.528378i	−0.936990	+	0.349356i	$0.886400\pi$
$284$		0			0
$285$	1.82093	−	12.6649i	0.107863	−	0.750202i
$286$		0			0
$287$	4.69928	+	5.42325i	0.277390	+	0.320125i
$288$		0			0
$289$	13.9045	+	4.08273i	0.817913	+	0.240161i
$290$		0			0
$291$	−3.37444	−	7.38899i	−0.197813	−	0.433150i
$292$		0			0
$293$	19.5937	−	12.5921i	1.14468	−	0.735639i	0.176104	−	0.984372i	$-0.443650\pi$
$293$	19.5937	−	12.5921i	1.14468	−	0.735639i	0.968572	+	0.248733i	$0.0800140\pi$
$294$		0			0
$295$	20.4717	+	6.01105i	1.19191	+	0.349977i
$296$		0			0
$297$	4.10523			0.238210
$298$		0			0
$299$	−2.63194	−	1.69145i	−0.152209	−	0.0978189i
$300$		0			0
$301$	2.81093	+	3.24399i	0.162020	+	0.186981i
$302$		0			0
$303$	4.05634	−	8.88215i	0.233031	−	0.510266i
$304$		0			0
$305$	17.1585			0.982490
$306$		0			0
$307$	−15.0816	−	9.69236i	−0.860753	−	0.553172i	0.0341585	−	0.999416i	$-0.489125\pi$
$307$	−15.0816	−	9.69236i	−0.860753	−	0.553172i	−0.894911	+	0.446244i	$0.852761\pi$
$308$		0			0
$309$	−0.365983	+	2.54547i	−0.0208200	+	0.144807i
$310$		0			0
$311$	0.00768065	−	0.0534201i	0.000435530	−	0.00302918i	−0.989603	−	0.143829i	$-0.954058\pi$
$311$	0.00768065	−	0.0534201i	0.000435530	−	0.00302918i	0.990038	+	0.140800i	$0.0449675\pi$
$312$		0			0
$313$	3.64685	−	7.98548i	0.206132	−	0.451366i	−0.778125	−	0.628109i	$-0.783829\pi$
$313$	3.64685	−	7.98548i	0.206132	−	0.451366i	0.984257	+	0.176743i	$0.0565563\pi$
$314$		0			0
$315$	−3.54354	−	7.75928i	−0.199656	−	0.437186i
$316$		0			0
$317$	1.38885	+	9.65969i	0.0780058	+	0.542542i	0.990926	+	0.134405i	$0.0429123\pi$
$317$	1.38885	+	9.65969i	0.0780058	+	0.542542i	−0.912921	+	0.408137i	$0.866179\pi$
$318$		0			0
$319$	6.42925	−	1.88780i	0.359969	−	0.105696i
$320$		0			0
$321$	−1.39651	−	9.71295i	−0.0779457	−	0.542124i
$322$		0			0
$323$	9.21820	−	5.92418i	0.512914	−	0.329630i
$324$		0			0
$325$	0.324062	−	0.709597i	0.0179757	−	0.0393614i
$326$		0			0
$327$	0.366325	+	0.235423i	0.0202578	+	0.0130189i
$328$		0			0
$329$	−25.9876	−	7.63064i	−1.43274	−	0.420691i
$330$		0			0
$331$	−3.54626	−	24.6648i	−0.194920	−	1.35570i	−0.818756	−	0.574142i	$-0.805336\pi$
$331$	−3.54626	−	24.6648i	−0.194920	−	1.35570i	0.623836	−	0.781555i	$-0.285573\pi$
$332$		0			0
$333$	−7.48506	+	8.63821i	−0.410179	+	0.473371i
$334$		0			0
$335$	−13.8543	−	6.10047i	−0.756942	−	0.333304i
$336$		0			0
$337$	−6.81542	+	7.86541i	−0.371259	+	0.428456i	−0.910381	−	0.413772i	$-0.864211\pi$
$337$	−6.81542	+	7.86541i	−0.371259	+	0.428456i	0.539121	+	0.842228i	$0.318757\pi$
$338$		0			0
$339$	2.62481	+	18.2560i	0.142560	+	0.991528i
$340$		0			0
$341$	−13.0266	−	3.82494i	−0.705427	−	0.207132i
$342$		0			0
$343$	28.2249	+	18.1391i	1.52400	+	0.979417i
$344$		0			0
$345$	4.86743	−	10.6582i	0.262054	−	0.573818i
$346$		0			0
$347$	−12.2066	+	7.84470i	−0.655284	+	0.421125i	−0.825594	−	0.564265i	$-0.809160\pi$
$347$	−12.2066	+	7.84470i	−0.655284	+	0.421125i	0.170310	+	0.985391i	$0.445523\pi$
$348$		0			0
$349$	−2.48399	−	17.2766i	−0.132965	−	0.924793i	−0.941660	−	0.336565i	$-0.890735\pi$
$349$	−2.48399	−	17.2766i	−0.132965	−	0.924793i	0.808695	−	0.588228i	$-0.200174\pi$
$350$		0			0
$351$	−0.473809	+	0.139123i	−0.0252900	+	0.00742582i
$352$		0			0
$353$	0.962906	+	6.69716i	0.0512503	+	0.356454i	0.999269	+	0.0382381i	$0.0121745\pi$
$353$	0.962906	+	6.69716i	0.0512503	+	0.356454i	−0.948018	+	0.318216i	$0.896916\pi$
$354$		0			0
$355$	4.71784	+	10.3306i	0.250397	+	0.548293i
$356$		0			0
$357$	3.03468	−	6.64502i	0.160612	−	0.351692i
$358$		0			0
$359$	1.81395	−	12.6163i	0.0957366	−	0.665862i	−0.884282	−	0.466954i	$-0.845351\pi$
$359$	1.81395	−	12.6163i	0.0957366	−	0.665862i	0.980018	−	0.198908i	$-0.0637396\pi$
$360$		0			0
$361$	−4.10808	+	28.5723i	−0.216215	+	1.50381i
$362$		0			0
$363$	−4.92380	−	3.16433i	−0.258432	−	0.166084i
$364$		0			0
$365$	−16.9109			−0.885156
$366$		0			0
$367$	2.26465	−	4.95888i	0.118214	−	0.258852i	−0.841271	−	0.540614i	$-0.818192\pi$
$367$	2.26465	−	4.95888i	0.118214	−	0.258852i	0.959484	+	0.281763i	$0.0909191\pi$
$368$		0			0
$369$	1.01884	+	1.17580i	0.0530386	+	0.0612098i
$370$		0			0
$371$	32.7776	+	21.0649i	1.70173	+	1.09363i
$372$		0			0
$373$	1.09455			0.0566735			0.0283367	−	0.999598i	$-0.490979\pi$
$373$	1.09455			0.0566735			0.0283367	+	0.999598i	$0.490979\pi$
$374$		0			0
$375$	11.6756	+	3.42827i	0.602927	+	0.177035i
$376$		0			0
$377$	−0.678062	+	0.435764i	−0.0349219	+	0.0224430i
$378$		0			0
$379$	−9.66924	−	21.1727i	−0.496675	−	1.08757i	−0.977536	−	0.210770i	$-0.932403\pi$
$379$	−9.66924	−	21.1727i	−0.496675	−	1.08757i	0.480860	−	0.876797i	$-0.340324\pi$
$380$		0			0
$381$	11.5368	+	3.38750i	0.591046	+	0.173547i
$382$		0			0
$383$	7.50660	+	8.66307i	0.383569	+	0.442662i	0.914398	−	0.404817i	$-0.132665\pi$
$383$	7.50660	+	8.66307i	0.383569	+	0.442662i	−0.530829	+	0.847479i	$0.678119\pi$
$384$		0			0
$385$	−4.98360	+	34.6617i	−0.253988	+	1.76652i
$386$		0			0
$387$	0.609432	+	0.703322i	0.0309791	+	0.0357518i
$388$		0			0
$389$	15.8095	−	10.1602i	0.801576	−	0.515141i	−0.0745540	−	0.997217i	$-0.523753\pi$
$389$	15.8095	−	10.1602i	0.801576	−	0.515141i	0.876130	+	0.482076i	$0.160117\pi$
$390$		0			0
$391$	9.62798	−	2.82703i	0.486908	−	0.142969i
$392$		0			0
$393$	−9.66390	+	11.1527i	−0.487479	+	0.562581i
$394$		0			0
$395$	3.58302	−	4.13503i	0.180281	−	0.208056i
$396$		0			0
$397$	18.7418	−	5.50310i	0.940626	−	0.276193i	0.224747	−	0.974417i	$-0.427844\pi$
$397$	18.7418	−	5.50310i	0.940626	−	0.276193i	0.715879	+	0.698225i	$0.246026\pi$
$398$		0			0
$399$	13.2563	+	29.0272i	0.663645	+	1.45318i
$400$		0			0
$401$	8.91856			0.445372			0.222686	−	0.974890i	$-0.428518\pi$
$401$	8.91856			0.445372			0.222686	+	0.974890i	$0.428518\pi$
$402$		0			0
$403$	1.63309			0.0813502
$404$		0			0
$405$	−0.768266	−	1.68227i	−0.0381755	−	0.0835926i
$406$		0			0
$407$	45.0221	−	13.2197i	2.23166	−	0.655275i
$408$		0			0
$409$	5.63197	−	6.49964i	0.278483	−	0.321387i	−0.599227	−	0.800579i	$-0.704525\pi$
$409$	5.63197	−	6.49964i	0.278483	−	0.321387i	0.877710	+	0.479193i	$0.159071\pi$
$410$		0			0
$411$	−9.83242	+	11.3472i	−0.484998	+	0.559717i
$412$		0			0
$413$	−51.0565	+	14.9915i	−2.51233	+	0.737685i
$414$		0			0
$415$	−19.9560	+	12.8249i	−0.979600	+	0.629551i
$416$		0			0
$417$	−3.30540	−	3.81463i	−0.161866	−	0.186803i
$418$		0			0
$419$	5.38137	−	37.4282i	0.262897	−	1.82849i	−0.247899	−	0.968786i	$-0.579740\pi$
$419$	5.38137	−	37.4282i	0.262897	−	1.82849i	0.510796	−	0.859702i	$-0.329351\pi$
$420$		0			0
$421$	−14.8157	−	17.0982i	−0.722074	−	0.833317i	0.269481	−	0.963006i	$-0.413148\pi$
$421$	−14.8157	−	17.0982i	−0.722074	−	0.833317i	−0.991555	+	0.129688i	$0.958602\pi$
$422$		0			0
$423$	−5.63430	−	1.65438i	−0.273949	−	0.0804387i
$424$		0			0
$425$	1.03937	+	2.27591i	0.0504171	+	0.110398i
$426$		0			0
$427$	−35.9999	+	23.1357i	−1.74216	+	1.11962i
$428$		0			0
$429$	1.94509	+	0.571131i	0.0939100	+	0.0275745i
$430$		0			0
$431$	34.3651			1.65531			0.827653	−	0.561240i	$-0.189675\pi$
$431$	34.3651			1.65531			0.827653	+	0.561240i	$0.189675\pi$
$432$		0			0
$433$	24.4773	+	15.7306i	1.17630	+	0.755964i	0.974703	−	0.223503i	$-0.0717494\pi$
$433$	24.4773	+	15.7306i	1.17630	+	0.755964i	0.201600	+	0.979468i	$0.435386\pi$
$434$		0			0
$435$	−1.97679	−	2.28133i	−0.0947796	−	0.109382i
$436$		0			0
$437$	−18.2089	+	39.8720i	−0.871051	+	1.90734i
$438$		0			0
$439$	33.7667			1.61159			0.805797	−	0.592191i	$-0.201737\pi$
$439$	33.7667			1.61159			0.805797	+	0.592191i	$0.201737\pi$
$440$		0			0
$441$	12.0081	+	7.71717i	0.571817	+	0.367484i
$442$		0			0
$443$	2.29650	−	15.9725i	0.109110	−	0.758877i	−0.859651	−	0.510882i	$-0.829319\pi$
$443$	2.29650	−	15.9725i	0.109110	−	0.758877i	0.968761	−	0.247996i	$-0.0797719\pi$
$444$		0			0
$445$	−0.988777	+	6.87710i	−0.0468725	+	0.326006i
$446$		0			0
$447$	1.56274	−	3.42192i	0.0739150	−	0.161851i
$448$		0			0
$449$	7.83955	+	17.1662i	0.369971	+	0.810124i	0.999452	+	0.0331077i	$0.0105404\pi$
$449$	7.83955	+	17.1662i	0.369971	+	0.810124i	−0.629481	+	0.777016i	$0.716732\pi$
$450$		0			0
$451$	−0.908959	−	6.32195i	−0.0428012	−	0.297689i
$452$		0			0
$453$	−11.2954	+	3.31662i	−0.530702	+	0.155828i
$454$		0			0
$455$	−0.599469	−	4.16940i	−0.0281035	−	0.195464i
$456$		0			0
$457$	−1.44648	+	0.929595i	−0.0676634	+	0.0434846i	−0.574035	−	0.818831i	$-0.694623\pi$
$457$	−1.44648	+	0.929595i	−0.0676634	+	0.0434846i	0.506372	+	0.862315i	$0.330986\pi$
$458$		0			0
$459$	0.657941	−	1.44069i	0.0307101	−	0.0672457i
$460$		0			0
$461$	18.2495	+	11.7282i	0.849963	+	0.546238i	0.891563	−	0.452896i	$-0.149609\pi$
$461$	18.2495	+	11.7282i	0.849963	+	0.546238i	−0.0416002	+	0.999134i	$0.513246\pi$
$462$		0			0
$463$	−11.6258	−	3.41366i	−0.540299	−	0.158646i	0.000185625	−	1.00000i	$-0.499941\pi$
$463$	−11.6258	−	3.41366i	−0.540299	−	0.158646i	−0.540485	+	0.841354i	$0.681759\pi$
$464$		0			0
$465$	0.870422	+	6.05392i	0.0403649	+	0.280744i
$466$		0			0
$467$	−0.0328409	+	0.0379004i	−0.00151969	+	0.00175382i	−0.756509	−	0.653983i	$-0.773097\pi$
$467$	−0.0328409	+	0.0379004i	−0.00151969	+	0.00175382i	0.754989	+	0.655737i	$0.227642\pi$
$468$		0			0
$469$	37.2931	−	5.88126i	1.72204	−	0.271571i
$470$		0			0
$471$	−11.5773	+	13.3609i	−0.533452	+	0.615636i
$472$		0			0
$473$	−0.543706	−	3.78156i	−0.0249996	−	0.173876i
$474$		0			0
$475$	−10.4867	−	3.07919i	−0.481165	−	0.141283i
$476$		0			0
$477$	7.10642	+	4.56702i	0.325381	+	0.209110i
$478$		0			0
$479$	10.8701	−	23.8022i	0.496667	−	1.08755i	−0.480872	−	0.876791i	$-0.659680\pi$
$479$	10.8701	−	23.8022i	0.496667	−	1.08755i	0.977538	−	0.210757i	$-0.0675930\pi$
$480$		0			0
$481$	−4.74826	+	3.05152i	−0.216502	+	0.139137i
$482$		0			0
$483$	4.15876	+	28.9248i	0.189230	+	1.31613i
$484$		0			0
$485$	14.4142	−	4.23239i	0.654516	−	0.192183i
$486$		0			0
$487$	0.575244	+	4.00091i	0.0260668	+	0.181298i	0.998695	−	0.0510676i	$-0.0162624\pi$
$487$	0.575244	+	4.00091i	0.0260668	+	0.181298i	−0.972628	+	0.232366i	$0.925353\pi$
$488$		0			0
$489$	8.08859	+	17.7115i	0.365779	+	0.800944i
$490$		0			0
$491$	16.2832	−	35.6553i	0.734852	−	1.60910i	−0.0569906	−	0.998375i	$-0.518151\pi$
$491$	16.2832	−	35.6553i	0.734852	−	1.60910i	0.791842	−	0.610726i	$-0.209122\pi$
$492$		0			0
$493$	0.367906	−	2.55884i	0.0165696	−	0.115244i
$494$		0			0
$495$	−1.08048	+	7.51492i	−0.0485641	+	0.337770i
$496$		0			0
$497$	−23.8278	−	15.3132i	−1.06882	−	0.686891i
$498$		0			0
$499$	−3.36150			−0.150481			−0.0752406	−	0.997165i	$-0.523972\pi$
$499$	−3.36150			−0.150481			−0.0752406	+	0.997165i	$0.523972\pi$
$500$		0			0
$501$	−1.38670	+	3.03644i	−0.0619530	+	0.135658i
$502$		0			0
$503$	23.3166	+	26.9088i	1.03963	+	1.19980i	0.979465	+	0.201614i	$0.0646186\pi$
$503$	23.3166	+	26.9088i	1.03963	+	1.19980i	0.0601692	+	0.998188i	$0.480836\pi$
$504$		0			0
$505$	15.1918	+	9.76317i	0.676026	+	0.434455i
$506$		0			0
$507$	12.7562			0.566521
$508$		0			0
$509$	−24.8060	−	7.28369i	−1.09950	−	0.322844i	−0.318849	−	0.947805i	$-0.603296\pi$
$509$	−24.8060	−	7.28369i	−1.09950	−	0.322844i	−0.780655	+	0.624962i	$0.785115\pi$
$510$		0			0
$511$	35.4805	−	22.8019i	1.56956	−	1.00870i
$512$		0			0
$513$	2.87406	+	6.29332i	0.126893	+	0.277857i
$514$		0			0
$515$	−4.56333	−	1.33992i	−0.201084	−	0.0590437i
$516$		0			0
$517$	15.7865	+	18.2185i	0.694288	+	0.801251i
$518$		0			0
$519$	1.26962	−	8.83039i	0.0557301	−	0.387611i
$520$		0			0
$521$	−2.95775	−	3.41343i	−0.129581	−	0.149545i	0.687251	−	0.726420i	$-0.258817\pi$
$521$	−2.95775	−	3.41343i	−0.129581	−	0.149545i	−0.816832	+	0.576875i	$0.804272\pi$
$522$		0			0
$523$	−6.32057	+	4.06198i	−0.276379	+	0.177618i	−0.671486	−	0.741017i	$-0.734344\pi$
$523$	−6.32057	+	4.06198i	−0.276379	+	0.177618i	0.395107	+	0.918635i	$0.370707\pi$
$524$		0			0
$525$	−6.99121	+	2.05281i	−0.305122	+	0.0895918i
$526$		0			0
$527$	−3.43008	+	3.95852i	−0.149417	+	0.172436i
$528$		0			0
$529$	−11.2243	+	12.9535i	−0.488011	+	0.563195i
$530$		0			0
$531$	−11.0694	+	3.25028i	−0.480372	+	0.141050i
$532$		0			0
$533$	0.319154	+	0.698849i	0.0138241	+	0.0302705i
$534$		0			0
$535$	18.1478			0.784598
$536$		0			0
$537$	−20.3756			−0.879272
$538$		0			0
$539$	−24.3427	−	53.3031i	−1.04852	−	2.29593i
$540$		0			0
$541$	14.0683	−	4.13082i	0.604842	−	0.177598i	0.0350487	−	0.999386i	$-0.488841\pi$
$541$	14.0683	−	4.13082i	0.604842	−	0.177598i	0.569793	+	0.821788i	$0.307023\pi$
$542$		0			0
$543$	−7.84961	+	9.05894i	−0.336859	+	0.388756i
$544$		0			0
$545$	−0.527374	+	0.608622i	−0.0225902	+	0.0260705i
$546$		0			0
$547$	25.5091	−	7.49015i	1.09069	−	0.320256i	0.313543	−	0.949574i	$-0.398484\pi$
$547$	25.5091	−	7.49015i	1.09069	−	0.320256i	0.777148	+	0.629318i	$0.216666\pi$
$548$		0			0
$549$	−7.80504	+	5.01600i	−0.333111	+	0.214078i
$550$		0			0
$551$	7.39510	+	8.53440i	0.315042	+	0.363578i
$552$		0			0
$553$	−1.94199	+	13.5068i	−0.0825818	+	0.574369i
$554$		0			0
$555$	−13.8428	−	15.9755i	−0.587595	−	0.678121i
$556$		0			0
$557$	1.08920	+	0.319819i	0.0461510	+	0.0135512i	0.304727	−	0.952440i	$-0.401435\pi$
$557$	1.08920	+	0.319819i	0.0461510	+	0.0135512i	−0.258576	+	0.965991i	$0.583253\pi$
$558$		0			0
$559$	0.190906	+	0.418026i	0.00807446	+	0.0176806i
$560$		0			0
$561$	−5.46978	+	3.51521i	−0.230934	+	0.148412i
$562$		0			0
$563$	33.8986	+	9.95352i	1.42865	+	0.419491i	0.902423	−	0.430850i	$-0.141786\pi$
$563$	33.8986	+	9.95352i	1.42865	+	0.419491i	0.526231	+	0.850341i	$0.323605\pi$
$564$		0			0
$565$	−34.1097			−1.43500
$566$		0			0
$567$	3.88019	+	2.49364i	0.162953	+	0.104723i
$568$		0			0
$569$	−23.3991	−	27.0040i	−0.980941	−	1.13207i	−0.991234	−	0.132119i	$-0.957822\pi$
$569$	−23.3991	−	27.0040i	−0.980941	−	1.13207i	0.0102926	−	0.999947i	$-0.496724\pi$
$570$		0			0
$571$	−16.5013	+	36.1328i	−0.690557	+	1.51211i	0.160499	+	0.987036i	$0.448690\pi$
$571$	−16.5013	+	36.1328i	−0.690557	+	1.51211i	−0.851057	+	0.525074i	$0.824038\pi$
$572$		0			0
$573$	1.80184			0.0752729
$574$		0			0
$575$	−8.41977	−	5.41106i	−0.351129	−	0.225657i
$576$		0			0
$577$	1.00560	−	6.99407i	0.0418635	−	0.291167i	−0.958125	−	0.286351i	$-0.907558\pi$
$577$	1.00560	−	6.99407i	0.0418635	−	0.291167i	0.999988	−	0.00481642i	$-0.00153312\pi$
$578$		0			0
$579$	−0.587667	+	4.08732i	−0.0244226	+	0.169863i
$580$		0			0
$581$	24.5767	−	53.8155i	1.01961	−	2.23264i
$582$		0			0
$583$	−14.4060	−	31.5448i	−0.596636	−	1.30645i
$584$		0			0
$585$	−0.129969	−	0.903957i	−0.00537357	−	0.0373740i
$586$		0			0
$587$	32.1613	−	9.44342i	1.32744	−	0.389772i	0.460268	−	0.887780i	$-0.347753\pi$
$587$	32.1613	−	9.44342i	1.32744	−	0.389772i	0.867172	+	0.498008i	$0.165935\pi$
$588$		0			0
$589$	−3.25622	−	22.6475i	−0.134170	−	0.933175i
$590$		0			0
$591$	19.0493	−	12.2422i	0.783581	−	0.503577i
$592$		0			0
$593$	−8.81490	+	19.3019i	−0.361985	+	0.792636i	0.637764	+	0.770232i	$0.279859\pi$
$593$	−8.81490	+	19.3019i	−0.361985	+	0.792636i	−0.999749	+	0.0224043i	$0.992868\pi$
$594$		0			0
$595$	11.3655	+	7.30414i	0.465939	+	0.299441i
$596$		0			0
$597$	8.93397	+	2.62325i	0.365643	+	0.107362i
$598$		0			0
$599$	−4.89689	−	34.0586i	−0.200081	−	1.39160i	−0.804037	−	0.594579i	$-0.797319\pi$
$599$	−4.89689	−	34.0586i	−0.200081	−	1.39160i	0.603956	−	0.797018i	$-0.293590\pi$
$600$		0			0
$601$	−24.8307	+	28.6562i	−1.01287	+	1.16891i	−0.0272976	+	0.999627i	$0.508690\pi$
$601$	−24.8307	+	28.6562i	−1.01287	+	1.16891i	−0.985568	+	0.169282i	$0.945855\pi$
$602$		0			0
$603$	8.08543	−	1.27510i	0.329264	−	0.0519261i
$604$		0			0
$605$	7.08846	−	8.18052i	0.288187	−	0.332585i
$606$		0			0
$607$	−3.35391	−	23.3270i	−0.136131	−	0.946813i	−0.937337	−	0.348424i	$-0.886717\pi$
$607$	−3.35391	−	23.3270i	−0.136131	−	0.946813i	0.801206	−	0.598389i	$-0.204192\pi$
$608$		0			0
$609$	7.22351	+	2.12102i	0.292712	+	0.0859479i
$610$		0			0
$611$	−2.43942	−	1.56772i	−0.0986883	−	0.0634231i
$612$		0			0
$613$	−1.42453	+	3.11929i	−0.0575363	+	0.125987i	−0.936216	−	0.351424i	$-0.885697\pi$
$613$	−1.42453	+	3.11929i	−0.0575363	+	0.125987i	0.878680	+	0.477411i	$0.158425\pi$
$614$		0			0
$615$	−2.42054	+	1.55559i	−0.0976057	+	0.0627274i
$616$		0			0
$617$	−6.05846	−	42.1375i	−0.243904	−	1.69639i	−0.632158	−	0.774839i	$-0.717831\pi$
$617$	−6.05846	−	42.1375i	−0.243904	−	1.69639i	0.388254	−	0.921552i	$-0.373078\pi$
$618$		0			0
$619$	−41.1031	+	12.0690i	−1.65207	+	0.485093i	−0.969370	−	0.245603i	$-0.921014\pi$
$619$	−41.1031	+	12.0690i	−1.65207	+	0.485093i	−0.682703	+	0.730696i	$0.739196\pi$
$620$		0			0
$621$	0.901651	+	6.27112i	0.0361820	+	0.251651i
$622$		0			0
$623$	−7.19824	−	15.7620i	−0.288391	−	0.631489i
$624$		0			0
$625$	−6.06744	+	13.2858i	−0.242698	+	0.531434i
$626$		0			0
$627$	4.04205	−	28.1131i	0.161424	−	1.12273i
$628$		0			0
$629$	2.57633	−	17.9188i	0.102725	−	0.714468i
$630$		0			0
$631$	−28.4121	−	18.2593i	−1.13107	−	0.726892i	−0.165284	−	0.986246i	$-0.552854\pi$
$631$	−28.4121	−	18.2593i	−1.13107	−	0.726892i	−0.965782	+	0.259354i	$0.916490\pi$
$632$		0			0
$633$	−8.44437			−0.335633
$634$		0			0
$635$	−9.23749	+	20.2273i	−0.366579	+	0.802695i
$636$		0			0
$637$	4.61593	+	5.32707i	0.182890	+	0.211066i
$638$		0			0
$639$	−5.16604	−	3.32002i	−0.204366	−	0.131338i
$640$		0			0
$641$	5.58754			0.220695			0.110347	−	0.993893i	$-0.464804\pi$
$641$	5.58754			0.220695			0.110347	+	0.993893i	$0.464804\pi$
$642$		0			0
$643$	−39.4820	−	11.5929i	−1.55702	−	0.457181i	−0.613828	−	0.789440i	$-0.710371\pi$
$643$	−39.4820	−	11.5929i	−1.55702	−	0.457181i	−0.943188	+	0.332258i	$0.892189\pi$
$644$		0			0
$645$	−1.44788	+	0.930496i	−0.0570102	+	0.0366382i
$646$		0			0
$647$	16.0446	+	35.1328i	0.630779	+	1.38121i	0.907414	+	0.420238i	$0.138053\pi$
$647$	16.0446	+	35.1328i	0.630779	+	1.38121i	−0.276635	+	0.960975i	$0.589219\pi$
$648$		0			0
$649$	45.4426	+	13.3431i	1.78378	+	0.523764i
$650$		0			0
$651$	−9.98906	−	11.5280i	−0.391502	−	0.451818i
$652$		0			0
$653$	0.138287	−	0.961807i	0.00541159	−	0.0376384i	−0.986937	−	0.161108i	$-0.948493\pi$
$653$	0.138287	−	0.961807i	0.00541159	−	0.0376384i	0.992348	+	0.123470i	$0.0394022\pi$
$654$		0			0
$655$	−17.8724	−	20.6258i	−0.698331	−	0.805917i
$656$		0			0
$657$	7.69243	−	4.94362i	0.300110	−	0.192869i
$658$		0			0
$659$	−33.8671	+	9.94428i	−1.31928	+	0.387374i	−0.864231	−	0.503095i	$-0.832195\pi$
$659$	−33.8671	+	9.94428i	−1.31928	+	0.387374i	−0.455044	+	0.890469i	$0.650377\pi$
$660$		0			0
$661$	−15.9115	+	18.3628i	−0.618885	+	0.714232i	−0.975495	−	0.220022i	$-0.929387\pi$
$661$	−15.9115	+	18.3628i	−0.618885	+	0.714232i	0.356610	+	0.934253i	$0.383933\pi$
$662$		0			0
$663$	0.512171	−	0.591077i	0.0198911	−	0.0229555i
$664$		0			0
$665$	−56.6254	+	16.6267i	−2.19584	+	0.644757i
$666$		0			0
$667$	4.29587	+	9.40665i	0.166337	+	0.364227i
$668$		0			0
$669$	12.2438			0.473373
$670$		0			0
$671$	38.0878			1.47036
$672$		0			0
$673$	−17.5316	−	38.3890i	−0.675795	−	1.47979i	−0.867038	−	0.498243i	$-0.833979\pi$
$673$	−17.5316	−	38.3890i	−0.675795	−	1.47979i	0.191242	−	0.981543i	$-0.438748\pi$
$674$		0			0
$675$	−1.51575	+	0.445064i	−0.0583411	+	0.0171305i
$676$		0			0
$677$	−14.8448	+	17.1319i	−0.570533	+	0.658431i	−0.965542	−	0.260247i	$-0.916196\pi$
$677$	−14.8448	+	17.1319i	−0.570533	+	0.658431i	0.395009	+	0.918677i	$0.370742\pi$
$678$		0			0
$679$	−24.5354	+	28.3154i	−0.941584	+	1.08665i
$680$		0			0
$681$	26.2056	−	7.69465i	1.00420	−	0.294860i
$682$		0			0
$683$	−31.5462	+	20.2735i	−1.20708	+	0.775744i	−0.980168	−	0.198171i	$-0.936500\pi$
$683$	−31.5462	+	20.2735i	−1.20708	+	0.775744i	−0.226914	+	0.973915i	$0.572864\pi$
$684$		0			0
$685$	−18.1840	−	20.9855i	−0.694776	−	0.801814i
$686$		0			0
$687$	−1.66469	+	11.5782i	−0.0635118	+	0.441734i
$688$		0			0
$689$	2.73171	+	3.15256i	0.104070	+	0.120103i
$690$		0			0
$691$	16.5198	+	4.85066i	0.628445	+	0.184528i	0.580419	−	0.814318i	$-0.302889\pi$
$691$	16.5198	+	4.85066i	0.628445	+	0.184528i	0.0480258	+	0.998846i	$0.484707\pi$
$692$		0			0
$693$	−7.86585	−	17.2238i	−0.298799	−	0.654278i
$694$		0			0
$695$	7.85292	−	5.04676i	0.297878	−	0.191435i
$696$		0			0
$697$	−2.36430	−	0.694222i	−0.0895544	−	0.0262955i
$698$		0			0
$699$	−22.3614			−0.845788
$700$		0			0
$701$	29.1690	+	18.7458i	1.10170	+	0.708019i	0.959469	−	0.281815i	$-0.0909365\pi$
$701$	29.1690	+	18.7458i	1.10170	+	0.708019i	0.142230	+	0.989834i	$0.454573\pi$
$702$		0			0
$703$	51.7856	+	59.7638i	1.95313	+	2.25403i
$704$		0			0
$705$	4.51139	−	9.87856i	0.169909	−	0.372048i
$706$		0			0
$707$	−45.0379			−1.69382
$708$		0			0
$709$	15.7435	+	10.1177i	0.591259	+	0.379979i	0.801788	−	0.597608i	$-0.203882\pi$
$709$	15.7435	+	10.1177i	0.591259	+	0.379979i	−0.210529	+	0.977588i	$0.567519\pi$
$710$		0			0
$711$	−0.421038	+	2.92838i	−0.0157901	+	0.109823i
$712$		0			0
$713$	2.98187	−	20.7393i	0.111672	−	0.776695i
$714$		0			0
$715$	−1.55744	+	3.41031i	−0.0582449	+	0.127539i
$716$		0			0
$717$	6.51450	+	14.2648i	0.243288	+	0.532727i
$718$		0			0
$719$	0.115861	+	0.805828i	0.00432087	+	0.0300523i	0.991868	−	0.127272i	$-0.0406222\pi$
$719$	0.115861	+	0.805828i	0.00432087	+	0.0300523i	−0.987547	+	0.157325i	$0.949713\pi$
$720$		0			0
$721$	11.3809	−	3.34175i	0.423848	−	0.124453i
$722$		0			0
$723$	−2.59569	−	18.0534i	−0.0965348	−	0.671414i
$724$		0			0
$725$	−2.16917	+	1.39404i	−0.0805608	+	0.0517733i
$726$		0			0
$727$	9.69537	−	21.2299i	0.359581	−	0.787373i	−0.640234	−	0.768180i	$-0.721163\pi$
$727$	9.69537	−	21.2299i	0.359581	−	0.787373i	0.999816	−	0.0191937i	$-0.00610993\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−1.41424	−	0.415258i	−0.0523075	−	0.0153589i
$732$		0			0
$733$	7.05196	+	49.0475i	0.260470	+	1.81161i	0.529315	+	0.848425i	$0.322449\pi$
$733$	7.05196	+	49.0475i	0.260470	+	1.81161i	−0.268845	+	0.963184i	$0.586642\pi$
$734$		0			0
$735$	−17.2873	+	19.9506i	−0.637653	+	0.735890i
$736$		0			0
$737$	−30.7534	−	13.5416i	−1.13282	−	0.498813i
$738$		0			0
$739$	−5.93306	+	6.84712i	−0.218251	+	0.251875i	−0.854308	−	0.519767i	$-0.826019\pi$
$739$	−5.93306	+	6.84712i	−0.218251	+	0.251875i	0.636057	+	0.771642i	$0.280564\pi$
$740$		0			0
$741$	0.486212	+	3.38168i	0.0178614	+	0.124229i
$742$		0			0
$743$	−5.38620	−	1.58153i	−0.197600	−	0.0580207i	0.181435	−	0.983403i	$-0.441926\pi$
$743$	−5.38620	−	1.58153i	−0.197600	−	0.0580207i	−0.379035	+	0.925382i	$0.623744\pi$
$744$		0			0
$745$	5.85276	+	3.76134i	0.214429	+	0.137805i
$746$		0			0
$747$	5.32842	−	11.6676i	0.194957	−	0.426896i
$748$		0			0
$749$	−38.0756	+	24.4697i	−1.39125	+	0.894104i
$750$		0			0
$751$	−2.55729	−	17.7864i	−0.0933169	−	0.649033i	−0.981771	−	0.190068i	$-0.939129\pi$
$751$	−2.55729	−	17.7864i	−0.0933169	−	0.649033i	0.888454	−	0.458966i	$-0.151780\pi$
$752$		0			0
$753$	−24.0497	+	7.06163i	−0.876420	+	0.257340i
$754$		0			0
$755$	−3.09841	−	21.5499i	−0.112763	−	0.784281i
$756$		0			0
$757$	1.19822	+	2.62374i	0.0435501	+	0.0953614i	0.930157	−	0.367163i	$-0.119671\pi$
$757$	1.19822	+	2.62374i	0.0435501	+	0.0953614i	−0.886606	+	0.462525i	$0.846944\pi$
$758$		0			0
$759$	10.8046	−	23.6587i	0.392182	−	0.858758i
$760$		0			0
$761$	−3.84810	+	26.7641i	−0.139493	+	0.970198i	0.793054	+	0.609151i	$0.208490\pi$
$761$	−3.84810	+	26.7641i	−0.139493	+	0.970198i	−0.932548	+	0.361047i	$0.882419\pi$
$762$		0			0
$763$	0.285835	−	1.98803i	0.0103479	−	0.0719714i
$764$		0			0
$765$	2.46412	+	1.58359i	0.0890904	+	0.0572549i
$766$		0			0
$767$	−5.69698			−0.205706
$768$		0			0
$769$	4.59671	−	10.0654i	0.165762	−	0.362967i	−0.808463	−	0.588547i	$-0.799700\pi$
$769$	4.59671	−	10.0654i	0.165762	−	0.362967i	0.974225	+	0.225580i	$0.0724276\pi$
$770$		0			0
$771$	−8.59752	−	9.92207i	−0.309632	−	0.357335i
$772$		0			0
$773$	12.4522	+	8.00256i	0.447876	+	0.287832i	0.745072	−	0.666984i	$-0.232415\pi$
$773$	12.4522	+	8.00256i	0.447876	+	0.287832i	−0.297196	+	0.954816i	$0.596052\pi$
$774$		0			0
$775$	5.22438			0.187665
$776$		0			0
$777$	50.5841	+	14.8528i	1.81469	+	0.532842i
$778$		0			0
$779$	9.05518	−	5.81941i	0.324436	−	0.208502i
$780$		0			0
$781$	10.4725	+	22.9316i	0.374736	+	0.820558i
$782$		0			0
$783$	1.56611	+	0.459852i	0.0559683	+	0.0164338i
$784$		0			0
$785$	−21.4109	−	24.7095i	−0.764189	−	0.881921i
$786$		0			0
$787$	0.647058	−	4.50039i	0.0230651	−	0.160422i	−0.975034	−	0.222058i	$-0.928723\pi$
$787$	0.647058	−	4.50039i	0.0230651	−	0.160422i	0.998099	+	0.0616360i	$0.0196318\pi$
$788$		0			0
$789$	9.91346	+	11.4407i	0.352929	+	0.407301i
$790$		0			0
$791$	71.5650	−	45.9920i	2.54456	−	1.63529i
$792$		0			0
$793$	−4.39594	+	1.29076i	−0.156104	+	0.0458364i
$794$		0			0
$795$	−10.2306	+	11.8068i	−0.362843	+	0.418744i
$796$		0			0
$797$	−15.5834	+	17.9842i	−0.551993	+	0.637034i	−0.961346	−	0.275342i	$-0.911209\pi$
$797$	−15.5834	+	17.9842i	−0.551993	+	0.637034i	0.409353	+	0.912376i	$0.365754\pi$
$798$		0			0
$799$	8.92370	−	2.62023i	0.315698	−	0.0926972i
$800$		0			0
$801$	−1.56063	−	3.41731i	−0.0551422	−	0.120745i
$802$		0			0
$803$	−37.5383			−1.32470
$804$		0			0
$805$	−54.0435			−1.90478
$806$		0			0
$807$	4.53291	+	9.92569i	0.159566	+	0.349401i
$808$		0			0
$809$	−3.53058	+	1.03667i	−0.124129	+	0.0364475i	−0.343207	−	0.939260i	$-0.611513\pi$
$809$	−3.53058	+	1.03667i	−0.124129	+	0.0364475i	0.219078	+	0.975707i	$0.429695\pi$
$810$		0			0
$811$	21.2806	−	24.5592i	0.747264	−	0.862389i	−0.247036	−	0.969006i	$-0.579457\pi$
$811$	21.2806	−	24.5592i	0.747264	−	0.862389i	0.994300	+	0.106617i	$0.0340020\pi$
$812$		0			0
$813$	10.4505	−	12.0606i	0.366516	−	0.422982i
$814$		0			0
$815$	−34.5511	+	10.1451i	−1.21027	+	0.355368i
$816$		0			0
$817$	5.41648	−	3.48096i	0.189499	−	0.121783i
$818$		0			0
$819$	1.49154	+	1.72133i	0.0521187	+	0.0601482i
$820$		0			0
$821$	−0.125132	+	0.870315i	−0.00436715	+	0.0303742i	−0.991889	−	0.127111i	$-0.959430\pi$
$821$	−0.125132	+	0.870315i	−0.00436715	+	0.0303742i	0.987521	+	0.157485i	$0.0503387\pi$
$822$		0			0
$823$	−31.9427	−	36.8639i	−1.11345	−	1.28499i	−0.954665	−	0.297682i	$-0.903787\pi$
$823$	−31.9427	−	36.8639i	−1.11345	−	1.28499i	−0.158789	−	0.987313i	$-0.550759\pi$
$824$		0			0
$825$	6.22249	+	1.82709i	0.216639	+	0.0636111i
$826$		0			0
$827$	−5.27182	−	11.5437i	−0.183319	−	0.401413i	0.795554	−	0.605883i	$-0.207180\pi$
$827$	−5.27182	−	11.5437i	−0.183319	−	0.401413i	−0.978873	+	0.204470i	$0.934453\pi$
$828$		0			0
$829$	−11.4307	+	7.34607i	−0.397005	+	0.255140i	−0.723877	−	0.689929i	$-0.757642\pi$
$829$	−11.4307	+	7.34607i	−0.397005	+	0.255140i	0.326872	+	0.945069i	$0.394005\pi$
$830$		0			0
$831$	−21.1269	−	6.20342i	−0.732884	−	0.215194i
$832$		0			0
$833$	−22.6076			−0.783307
$834$		0			0
$835$	−5.19345	−	3.33763i	−0.179727	−	0.115503i
$836$		0			0
$837$	−2.16570	−	2.49935i	−0.0748577	−	0.0863903i
$838$		0			0
$839$	−13.5772	+	29.7299i	−0.468736	+	1.02639i	0.516672	+	0.856183i	$0.327171\pi$
$839$	−13.5772	+	29.7299i	−0.468736	+	1.02639i	−0.985409	+	0.170206i	$0.945557\pi$
$840$		0			0
$841$	−26.3358			−0.908132
$842$		0			0
$843$	14.7827	+	9.50024i	0.509142	+	0.327206i
$844$		0			0
$845$	−3.35737	+	23.3510i	−0.115497	+	0.803300i
$846$		0			0
$847$	−3.84193	+	26.7212i	−0.132010	+	0.918151i
$848$		0			0
$849$	−4.88587	+	10.6986i	−0.167683	+	0.367174i
$850$		0			0
$851$	30.0827	+	65.8719i	1.03122	+	2.25806i
$852$		0			0
$853$	−6.70948	−	46.6655i	−0.229728	−	1.59780i	−0.699252	−	0.714876i	$-0.746483\pi$
$853$	−6.70948	−	46.6655i	−0.229728	−	1.59780i	0.469523	−	0.882920i	$-0.344426\pi$
$854$		0			0
$855$	−12.2768	+	3.60480i	−0.419858	+	0.123281i
$856$		0			0
$857$	−4.46826	−	31.0774i	−0.152633	−	1.06158i	−0.911784	−	0.410670i	$-0.865295\pi$
$857$	−4.46826	−	31.0774i	−0.152633	−	1.06158i	0.759151	−	0.650915i	$-0.225614\pi$
$858$		0			0
$859$	−28.7134	+	18.4530i	−0.979689	+	0.629608i	−0.929379	−	0.369126i	$-0.879657\pi$
$859$	−28.7134	+	18.4530i	−0.979689	+	0.629608i	−0.0503092	+	0.998734i	$0.516021\pi$
$860$		0			0
$861$	2.98102	−	6.52751i	0.101593	−	0.222457i
$862$		0			0
$863$	1.20213	+	0.772564i	0.0409211	+	0.0262984i	0.560941	−	0.827855i	$-0.310439\pi$
$863$	1.20213	+	0.772564i	0.0409211	+	0.0262984i	−0.520020	+	0.854154i	$0.674076\pi$
$864$		0			0
$865$	15.8305	+	4.64826i	0.538253	+	0.158045i
$866$		0			0
$867$	−2.06236	−	14.3440i	−0.0700414	−	0.487148i
$868$		0			0
$869$	7.95348	−	9.17881i	0.269803	−	0.311370i
$870$		0			0
$871$	4.00834	+	0.520713i	0.135817	+	0.0176437i
$872$		0			0
$873$	−5.31947	+	6.13899i	−0.180037	+	0.207773i
$874$		0			0
$875$	−7.98756	−	55.5547i	−0.270029	−	1.87809i
$876$		0			0
$877$	38.7793	+	11.3866i	1.30949	+	0.384500i	0.860687	−	0.509134i	$-0.170034\pi$
$877$	38.7793	+	11.3866i	1.30949	+	0.384500i	0.448798	+	0.893633i	$0.351852\pi$
$878$		0			0
$879$	−19.5937	−	12.5921i	−0.660879	−	0.424721i
$880$		0			0
$881$	2.87336	−	6.29179i	0.0968061	−	0.211976i	−0.855033	−	0.518573i	$-0.826463\pi$
$881$	2.87336	−	6.29179i	0.0968061	−	0.211976i	0.951839	+	0.306598i	$0.0991906\pi$
$882$		0			0
$883$	24.5436	−	15.7732i	0.825957	−	0.530810i	−0.0580339	−	0.998315i	$-0.518483\pi$
$883$	24.5436	−	15.7732i	0.825957	−	0.530810i	0.883991	+	0.467504i	$0.154847\pi$
$884$		0			0
$885$	−3.03643	−	21.1188i	−0.102068	−	0.709902i
$886$		0			0
$887$	−20.9515	+	6.15192i	−0.703483	+	0.206561i	−0.613861	−	0.789415i	$-0.710384\pi$
$887$	−20.9515	+	6.15192i	−0.703483	+	0.206561i	−0.0896226	+	0.995976i	$0.528566\pi$
$888$		0			0
$889$	−7.89256	−	54.8940i	−0.264708	−	1.84108i
$890$		0			0
$891$	−1.70538	−	3.73425i	−0.0571322	−	0.125102i
$892$		0			0
$893$	−16.8770	+	36.9554i	−0.564766	+	1.23667i
$894$		0			0
$895$	5.36278	−	37.2990i	0.179258	−	1.24677i
$896$		0			0
$897$	−0.445246	+	3.09675i	−0.0148663	+	0.103398i
$898$		0			0
$899$	−4.54107	−	2.91837i	−0.151453	−	0.0973330i
$900$		0			0
$901$	−13.3792			−0.445725
$902$		0			0
$903$	1.78313	−	3.90452i	0.0593390	−	0.129934i
$904$		0			0
$905$	−14.5170	−	16.7536i	−0.482563	−	0.556907i
$906$		0			0
$907$	−9.49431	−	6.10163i	−0.315254	−	0.202601i	0.373439	−	0.927655i	$-0.378179\pi$
$907$	−9.49431	−	6.10163i	−0.315254	−	0.202601i	−0.688692	+	0.725054i	$0.741815\pi$
$908$		0			0
$909$	−9.76455			−0.323870
$910$		0			0
$911$	−32.2891	−	9.48093i	−1.06978	−	0.314117i	−0.300999	−	0.953624i	$-0.597320\pi$
$911$	−32.2891	−	9.48093i	−1.06978	−	0.314117i	−0.768785	+	0.639507i	$0.779138\pi$
$912$		0			0
$913$	−44.2977	+	28.4684i	−1.46604	+	0.942166i
$914$		0			0
$915$	−7.12788	−	15.6079i	−0.235640	−	0.515981i
$916$		0			0
$917$	65.3087	+	19.1764i	2.15668	+	0.633259i
$918$		0			0
$919$	−15.1262	−	17.4566i	−0.498968	−	0.575840i	0.449272	−	0.893395i	$-0.351684\pi$
$919$	−15.1262	−	17.4566i	−0.498968	−	0.575840i	−0.948240	+	0.317555i	$0.897138\pi$
$920$		0			0
$921$	−2.55136	+	17.7451i	−0.0840700	+	0.584720i
$922$		0			0
$923$	−1.98583	−	2.29177i	−0.0653643	−	0.0754344i
$924$		0			0
$925$	−15.1900	+	9.76202i	−0.499444	+	0.320973i
$926$		0			0
$927$	2.46747	−	0.724515i	0.0810424	−	0.0237962i
$928$		0			0
$929$	21.4413	−	24.7446i	0.703467	−	0.811844i	−0.285749	−	0.958304i	$-0.592243\pi$
$929$	21.4413	−	24.7446i	0.703467	−	0.811844i	0.989217	+	0.146460i	$0.0467880\pi$
$930$		0			0
$931$	64.6714	−	74.6348i	2.11952	−	2.44606i
$932$		0			0
$933$	−0.0517833	+	0.0152050i	−0.00169531	+	0.000497788i
$934$		0			0
$935$	−4.99522	−	10.9380i	−0.163361	−	0.357711i
$936$		0			0
$937$	−21.6247			−0.706448			−0.353224	−	0.935539i	$-0.614915\pi$
$937$	−21.6247			−0.706448			−0.353224	+	0.935539i	$0.614915\pi$
$938$		0			0
$939$	−8.77880			−0.286485
$940$		0			0
$941$	8.52130	+	18.6590i	0.277786	+	0.608267i	0.996176	−	0.0873741i	$-0.0278475\pi$
$941$	8.52130	+	18.6590i	0.277786	+	0.608267i	−0.718389	+	0.695641i	$0.755120\pi$
$942$		0			0
$943$	9.45772	−	2.77704i	0.307986	−	0.0904328i
$944$		0			0
$945$	−5.58604	+	6.44664i	−0.181714	+	0.209709i
$946$		0			0
$947$	−17.8289	+	20.5757i	−0.579362	+	0.668619i	−0.967467	−	0.252996i	$-0.918584\pi$
$947$	−17.8289	+	20.5757i	−0.579362	+	0.668619i	0.388106	+	0.921615i	$0.373130\pi$
$948$		0			0
$949$	4.33251	−	1.27214i	0.140639	−	0.0412954i
$950$		0			0
$951$	8.20981	−	5.27612i	0.266221	−	0.171090i
$952$		0			0
$953$	27.4964	+	31.7325i	0.890696	+	1.02792i	0.999427	+	0.0338464i	$0.0107757\pi$
$953$	27.4964	+	31.7325i	0.890696	+	1.02792i	−0.108731	+	0.994071i	$0.534679\pi$
$954$		0			0
$955$	−0.474237	+	3.29839i	−0.0153460	+	0.106734i
$956$		0			0
$957$	−4.38801	−	5.06403i	−0.141844	−	0.163697i
$958$		0			0
$959$	66.4476	+	19.5108i	2.14570	+	0.630035i
$960$		0			0
$961$	−8.33445	−	18.2499i	−0.268853	−	0.588707i
$962$		0			0
$963$	−8.25508	+	5.30522i	−0.266016	+	0.170958i
$964$		0			0
$965$	−7.32745	−	2.15153i	−0.235879	−	0.0692603i
$966$		0			0
$967$	4.39852			0.141447			0.0707234	−	0.997496i	$-0.477469\pi$
$967$	4.39852			0.141447			0.0707234	+	0.997496i	$0.477469\pi$
$968$		0			0
$969$	−9.21820	−	5.92418i	−0.296131	−	0.190312i
$970$		0			0
$971$	1.84078	+	2.12437i	0.0590733	+	0.0681743i	0.784517	−	0.620107i	$-0.212911\pi$
$971$	1.84078	+	2.12437i	0.0590733	+	0.0681743i	−0.725444	+	0.688281i	$0.758365\pi$
$972$		0			0
$973$	−9.67125	+	21.1771i	−0.310046	+	0.678906i
$974$		0			0
$975$	−0.780093			−0.0249830
$976$		0			0
$977$	43.9891	+	28.2701i	1.40734	+	0.904440i	0.999961	−	0.00882098i	$-0.00280784\pi$
$977$	43.9891	+	28.2701i	1.40734	+	0.904440i	0.407375	+	0.913261i	$0.366444\pi$
$978$		0			0
$979$	−2.19486	+	15.2656i	−0.0701480	+	0.487890i
$980$		0			0
$981$	0.0619712	−	0.431019i	0.00197859	−	0.0137614i
$982$		0			0
$983$	7.54234	−	16.5154i	0.240563	−	0.526760i	−0.750386	−	0.661000i	$-0.770132\pi$
$983$	7.54234	−	16.5154i	0.240563	−	0.526760i	0.990949	+	0.134240i	$0.0428594\pi$
$984$		0			0
$985$	17.3965	+	38.0931i	0.554300	+	1.21375i
$986$		0			0
$987$	3.85455	+	26.8090i	0.122692	+	0.853340i
$988$		0			0
$989$	5.65726	−	1.66112i	0.179890	−	0.0528206i
$990$		0			0
$991$	2.95134	+	20.5270i	0.0937524	+	0.652062i	0.981462	+	0.191658i	$0.0613865\pi$
$991$	2.95134	+	20.5270i	0.0937524	+	0.652062i	−0.887709	+	0.460404i	$0.847704\pi$
$992$		0			0
$993$	−20.9627	+	13.4719i	−0.665231	+	0.427518i
$994$		0			0
$995$	−7.15343	+	15.6638i	−0.226779	+	0.496577i
$996$		0			0
$997$	−35.0270	−	22.5105i	−1.10932	−	0.712913i	−0.148171	−	0.988962i	$-0.547339\pi$
$997$	−35.0270	−	22.5105i	−1.10932	−	0.712913i	−0.961144	+	0.276048i	$0.910975\pi$
$998$		0			0
$999$	10.9670	+	3.22020i	0.346981	+	0.101883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.397.5	yes	60
67.40	even	11	inner	804.2.q.b.241.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.241.5	✓	60	67.40	even	11	inner
804.2.q.b.397.5	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(1.77448 - 0.521035i) q^{5} +(-3.02047 + 3.48581i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(1.77448 - 0.521035i) q^{5} +(-3.02047 + 3.48581i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(3.93894 - 1.15658i) q^{11} +(-0.415421 + 0.266975i) q^{13} +(-1.21110 - 1.39768i) q^{15} +(0.225401 - 1.56770i) q^{17} +(4.53068 + 5.22868i) q^{19} +(4.42555 + 1.29946i) q^{21} +(2.63191 + 5.76307i) q^{23} +(-1.32896 + 0.854071i) q^{25} +(0.959493 + 0.281733i) q^{27} +1.63223 q^{29} +(-2.78213 - 1.78796i) q^{31} +(-2.68836 - 3.10253i) q^{33} +(-3.54354 + 7.75928i) q^{35} +11.4300 q^{37} +(0.415421 + 0.266975i) q^{39} +(0.221415 - 1.53997i) q^{41} +(0.132442 - 0.921155i) q^{43} +(-0.768266 + 1.68227i) q^{45} +(2.43938 + 5.34151i) q^{47} +(-2.03142 - 14.1288i) q^{49} +(-1.51966 + 0.446213i) q^{51} +(-1.20219 - 8.36144i) q^{53} +(6.38696 - 4.10465i) q^{55} +(2.87406 - 6.29332i) q^{57} +(9.70533 + 6.23724i) q^{59} +(8.90205 + 2.61388i) q^{61} +(-0.656411 - 4.56544i) q^{63} +(-0.598053 + 0.690190i) q^{65} +(-6.25848 - 5.27554i) q^{67} +(4.14894 - 4.78813i) q^{69} +(0.873940 + 6.07838i) q^{71} +(-8.77361 - 2.57616i) q^{73} +(1.32896 + 0.854071i) q^{75} +(-7.86585 + 17.2238i) q^{77} +(2.48884 - 1.59948i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-12.3072 + 3.61371i) q^{83} +(-0.416855 - 2.89929i) q^{85} +(-0.678052 - 1.48473i) q^{87} +(-1.56063 + 3.41731i) q^{89} +(0.324143 - 2.25447i) q^{91} +(-0.470652 + 3.27346i) q^{93} +(10.7639 + 6.91755i) q^{95} +8.12305 q^{97} +(-1.70538 + 3.73425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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