LMFDB - Embedded newform 804.2.q.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	804.25
Dual form			804.2.q.a.193.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{3} +(3.26560 - 2.09868i) q^{5} +(0.572019 + 3.97848i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{3} +(3.26560 - 2.09868i) q^{5} +(0.572019 + 3.97848i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-2.40139 + 1.54328i) q^{11} +(-2.03931 + 4.46546i) q^{13} +(-0.552442 + 3.84232i) q^{15} +(1.18346 + 0.347496i) q^{17} +(-0.964189 + 6.70608i) q^{19} +(-3.38133 - 2.17305i) q^{21} +(4.75490 - 5.48745i) q^{23} +(4.18265 - 9.15872i) q^{25} +(0.841254 + 0.540641i) q^{27} -3.33219 q^{29} +(0.100956 + 0.221064i) q^{31} +(0.406243 - 2.82548i) q^{33} +(10.2175 + 11.7917i) q^{35} +6.92010 q^{37} +(-2.03931 - 4.46546i) q^{39} +(-2.55334 - 0.749727i) q^{41} +(-2.45691 - 0.721414i) q^{43} +(-2.54206 - 2.93369i) q^{45} +(-7.03517 + 8.11902i) q^{47} +(-8.78465 + 2.57941i) q^{49} +(-1.03762 + 0.666839i) q^{51} +(7.83449 - 2.30041i) q^{53} +(-4.60314 + 10.0795i) q^{55} +(-4.43671 - 5.12023i) q^{57} +(1.91400 + 4.19107i) q^{59} +(10.5278 + 6.76581i) q^{61} +(3.85658 - 1.13239i) q^{63} +(2.71198 + 18.8623i) q^{65} +(3.55850 - 7.37137i) q^{67} +(1.03334 + 7.18703i) q^{69} +(12.5202 - 3.67626i) q^{71} +(-4.29165 - 2.75807i) q^{73} +(4.18265 + 9.15872i) q^{75} +(-7.51355 - 8.67110i) q^{77} +(-1.47497 + 3.22973i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(2.45764 - 1.57943i) q^{83} +(4.59400 - 1.34892i) q^{85} +(2.18212 - 2.51830i) q^{87} +(-6.07715 - 7.01340i) q^{89} +(-18.9323 - 5.55901i) q^{91} +(-0.233181 - 0.0684682i) q^{93} +(10.9252 + 23.9229i) q^{95} -16.7003 q^{97} +(1.86932 + 2.15732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$	$1$

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
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$		0			0
$5$	3.26560	−	2.09868i	1.46042	−	0.938556i	0.461751	−	0.887009i	$-0.347221\pi$
$5$	3.26560	−	2.09868i	1.46042	−	0.938556i	0.998671	−	0.0515466i	$-0.0164151\pi$
$6$		0			0
$7$	0.572019	+	3.97848i	0.216203	+	1.50372i	0.751879	+	0.659301i	$0.229148\pi$
$7$	0.572019	+	3.97848i	0.216203	+	1.50372i	−0.535676	+	0.844423i	$0.679943\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	−2.40139	+	1.54328i	−0.724046	+	0.465316i	−0.850042	−	0.526714i	$-0.823424\pi$
$11$	−2.40139	+	1.54328i	−0.724046	+	0.465316i	0.125996	+	0.992031i	$0.459787\pi$
$12$		0			0
$13$	−2.03931	+	4.46546i	−0.565602	+	1.23850i	0.383504	+	0.923539i	$0.374717\pi$
$13$	−2.03931	+	4.46546i	−0.565602	+	1.23850i	−0.949106	+	0.314957i	$0.898010\pi$
$14$		0			0
$15$	−0.552442	+	3.84232i	−0.142640	+	0.992082i
$16$		0			0
$17$	1.18346	+	0.347496i	0.287032	+	0.0842801i	0.422079	−	0.906559i	$-0.361300\pi$
$17$	1.18346	+	0.347496i	0.287032	+	0.0842801i	−0.135047	+	0.990839i	$0.543119\pi$
$18$		0			0
$19$	−0.964189	+	6.70608i	−0.221200	+	1.53848i	0.512309	+	0.858801i	$0.328790\pi$
$19$	−0.964189	+	6.70608i	−0.221200	+	1.53848i	−0.733509	+	0.679679i	$0.762119\pi$
$20$		0			0
$21$	−3.38133	−	2.17305i	−0.737866	−	0.474198i
$22$		0			0
$23$	4.75490	−	5.48745i	0.991466	−	1.14421i	0.00191943	−	0.999998i	$-0.499389\pi$
$23$	4.75490	−	5.48745i	0.991466	−	1.14421i	0.989546	−	0.144214i	$-0.0460655\pi$
$24$		0			0
$25$	4.18265	−	9.15872i	0.836529	−	1.83174i
$26$		0			0
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$		0			0
$29$	−3.33219			−0.618772			−0.309386	−	0.950937i	$-0.600124\pi$
$29$	−3.33219			−0.618772			−0.309386	+	0.950937i	$0.600124\pi$
$30$		0			0
$31$	0.100956	+	0.221064i	0.0181323	+	0.0397042i	0.918481	−	0.395464i	$-0.129416\pi$
$31$	0.100956	+	0.221064i	0.0181323	+	0.0397042i	−0.900349	+	0.435168i	$0.856689\pi$
$32$		0			0
$33$	0.406243	−	2.82548i	0.0707179	−	0.491853i
$34$		0			0
$35$	10.2175	+	11.7917i	1.72708	+	1.99315i
$36$		0			0
$37$	6.92010			1.13766			0.568829	−	0.822456i	$-0.307397\pi$
$37$	6.92010			1.13766			0.568829	+	0.822456i	$0.307397\pi$
$38$		0			0
$39$	−2.03931	−	4.46546i	−0.326551	−	0.715046i
$40$		0			0
$41$	−2.55334	−	0.749727i	−0.398764	−	0.117088i	0.0762006	−	0.997093i	$-0.475721\pi$
$41$	−2.55334	−	0.749727i	−0.398764	−	0.117088i	−0.474965	+	0.880005i	$0.657539\pi$
$42$		0			0
$43$	−2.45691	−	0.721414i	−0.374675	−	0.110015i	0.0889727	−	0.996034i	$-0.471642\pi$
$43$	−2.45691	−	0.721414i	−0.374675	−	0.110015i	−0.463648	+	0.886019i	$0.653460\pi$
$44$		0			0
$45$	−2.54206	−	2.93369i	−0.378948	−	0.437329i
$46$		0			0
$47$	−7.03517	+	8.11902i	−1.02619	+	1.18428i	−0.0434897	+	0.999054i	$0.513848\pi$
$47$	−7.03517	+	8.11902i	−1.02619	+	1.18428i	−0.982696	+	0.185227i	$0.940698\pi$
$48$		0			0
$49$	−8.78465	+	2.57941i	−1.25495	+	0.368486i
$50$		0			0
$51$	−1.03762	+	0.666839i	−0.145296	+	0.0933762i
$52$		0			0
$53$	7.83449	−	2.30041i	1.07615	−	0.315986i	0.304812	−	0.952412i	$-0.401406\pi$
$53$	7.83449	−	2.30041i	1.07615	−	0.315986i	0.771337	+	0.636426i	$0.219588\pi$
$54$		0			0
$55$	−4.60314	+	10.0795i	−0.620688	+	1.35912i
$56$		0			0
$57$	−4.43671	−	5.12023i	−0.587656	−	0.678192i
$58$		0			0
$59$	1.91400	+	4.19107i	0.249181	+	0.545631i	0.992348	−	0.123476i	$-0.0394041\pi$
$59$	1.91400	+	4.19107i	0.249181	+	0.545631i	−0.743166	+	0.669107i	$0.766677\pi$
$60$		0			0
$61$	10.5278	+	6.76581i	1.34795	+	0.866274i	0.997525	−	0.0703174i	$-0.0224012\pi$
$61$	10.5278	+	6.76581i	1.34795	+	0.866274i	0.350424	+	0.936591i	$0.386038\pi$
$62$		0			0
$63$	3.85658	−	1.13239i	0.485883	−	0.142668i
$64$		0			0
$65$	2.71198	+	18.8623i	0.336380	+	2.33958i
$66$		0			0
$67$	3.55850	−	7.37137i	0.434740	−	0.900556i
$67$	3.55850	−	7.37137i	0.434740	−	0.900556i
$68$		0			0
$69$	1.03334	+	7.18703i	0.124399	+	0.865217i
$70$		0			0
$71$	12.5202	−	3.67626i	1.48588	−	0.436292i	0.564653	−	0.825329i	$-0.309010\pi$
$71$	12.5202	−	3.67626i	1.48588	−	0.436292i	0.921222	+	0.389036i	$0.127192\pi$
$72$		0			0
$73$	−4.29165	−	2.75807i	−0.502299	−	0.322808i	0.264836	−	0.964293i	$-0.414682\pi$
$73$	−4.29165	−	2.75807i	−0.502299	−	0.322808i	−0.767135	+	0.641485i	$0.778319\pi$
$74$		0			0
$75$	4.18265	+	9.15872i	0.482970	+	1.05756i
$76$		0			0
$77$	−7.51355	−	8.67110i	−0.856248	−	0.988163i
$78$		0			0
$79$	−1.47497	+	3.22973i	−0.165947	+	0.363373i	−0.974276	−	0.225358i	$-0.927645\pi$
$79$	−1.47497	+	3.22973i	−0.165947	+	0.363373i	0.808329	+	0.588731i	$0.200372\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	2.45764	−	1.57943i	0.269761	−	0.173365i	−0.398766	−	0.917053i	$-0.630561\pi$
$83$	2.45764	−	1.57943i	0.269761	−	0.173365i	0.668527	+	0.743688i	$0.266925\pi$
$84$		0			0
$85$	4.59400	−	1.34892i	0.498289	−	0.146311i
$86$		0			0
$87$	2.18212	−	2.51830i	0.233948	−	0.269990i
$88$		0			0
$89$	−6.07715	−	7.01340i	−0.644176	−	0.743419i	0.335931	−	0.941887i	$-0.390949\pi$
$89$	−6.07715	−	7.01340i	−0.644176	−	0.743419i	−0.980107	+	0.198467i	$0.936404\pi$
$90$		0			0
$91$	−18.9323	−	5.55901i	−1.98464	−	0.582743i
$92$		0			0
$93$	−0.233181	−	0.0684682i	−0.0241798	−	0.00709982i
$94$		0			0
$95$	10.9252	+	23.9229i	1.12090	+	2.45444i
$96$		0			0
$97$	−16.7003			−1.69566			−0.847829	−	0.530270i	$-0.822091\pi$
$97$	−16.7003			−1.69566			−0.847829	+	0.530270i	$0.822091\pi$
$98$		0			0
$99$	1.86932	+	2.15732i	0.187874	+	0.216818i
$100$		0			0
$101$	−1.53055	+	10.6452i	−0.152296	+	1.05924i	0.760064	+	0.649849i	$0.225168\pi$
$101$	−1.53055	+	10.6452i	−0.152296	+	1.05924i	−0.912359	+	0.409390i	$0.865741\pi$
$102$		0			0
$103$	−2.86975	−	6.28387i	−0.282765	−	0.619168i	0.713947	−	0.700200i	$-0.246906\pi$
$103$	−2.86975	−	6.28387i	−0.282765	−	0.619168i	−0.996712	+	0.0810318i	$0.974178\pi$
$104$		0			0
$105$	−15.6026			−1.52266
$106$		0			0
$107$	−4.85437	−	3.11971i	−0.469289	−	0.301594i	0.284540	−	0.958664i	$-0.408159\pi$
$107$	−4.85437	−	3.11971i	−0.469289	−	0.301594i	−0.753829	+	0.657070i	$0.771796\pi$
$108$		0			0
$109$	5.83171	−	12.7697i	0.558576	−	1.22311i	−0.394084	−	0.919074i	$-0.628938\pi$
$109$	5.83171	−	12.7697i	0.558576	−	1.22311i	0.952660	−	0.304037i	$-0.0983347\pi$
$110$		0			0
$111$	−4.53170	+	5.22987i	−0.430130	+	0.496397i
$112$		0			0
$113$	10.8812	+	6.99294i	1.02362	+	0.657841i	0.940883	−	0.338731i	$-0.109998\pi$
$113$	10.8812	+	6.99294i	1.02362	+	0.657841i	0.0827369	+	0.996571i	$0.473634\pi$
$114$		0			0
$115$	4.01125	−	27.8988i	0.374051	−	2.60158i
$116$		0			0
$117$	4.71023	+	1.38305i	0.435461	+	0.127863i
$118$		0			0
$119$	−0.705542	+	4.90715i	−0.0646769	+	0.449838i
$120$		0			0
$121$	−1.18460	+	2.59392i	−0.107691	+	0.235811i
$122$		0			0
$123$	2.23869	−	1.43872i	0.201856	−	0.129725i
$124$		0			0
$125$	−2.80011	−	19.4752i	−0.250449	−	1.74191i
$126$		0			0
$127$	−1.22946	−	8.55110i	−0.109097	−	0.758788i	−0.968773	−	0.247948i	$-0.920244\pi$
$127$	−1.22946	−	8.55110i	−0.109097	−	0.758788i	0.859676	−	0.510840i	$-0.170665\pi$
$128$		0			0
$129$	2.15414	−	1.38438i	0.189662	−	0.121888i
$130$		0			0
$131$	9.46356	−	10.9215i	0.826835	−	0.954219i	−0.172692	−	0.984976i	$-0.555246\pi$
$131$	9.46356	−	10.9215i	0.826835	−	0.954219i	0.999527	+	0.0307572i	$0.00979187\pi$
$132$		0			0
$133$	−27.2315			−2.36127
$134$		0			0
$135$	3.88183			0.334095
$136$		0			0
$137$	5.92934	−	6.84283i	0.506578	−	0.584622i	−0.443641	−	0.896204i	$-0.646314\pi$
$137$	5.92934	−	6.84283i	0.506578	−	0.584622i	0.950219	+	0.311582i	$0.100859\pi$
$138$		0			0
$139$	13.4179	−	8.62318i	1.13809	−	0.731409i	0.170860	−	0.985295i	$-0.445345\pi$
$139$	13.4179	−	8.62318i	1.13809	−	0.731409i	0.967234	+	0.253887i	$0.0817090\pi$
$140$		0			0
$141$	−1.52889	−	10.6337i	−0.128756	−	0.895515i
$142$		0			0
$143$	−1.99428	−	13.8705i	−0.166770	−	1.15991i
$144$		0			0
$145$	−10.8816	+	6.99318i	−0.903668	+	0.580752i
$146$		0			0
$147$	3.80334	−	8.32814i	0.313694	−	0.686894i
$148$		0			0
$149$	−0.822957	+	5.72379i	−0.0674193	+	0.468911i	0.927944	+	0.372720i	$0.121575\pi$
$149$	−0.822957	+	5.72379i	−0.0674193	+	0.468911i	−0.995363	+	0.0961908i	$0.969334\pi$
$150$		0			0
$151$	3.05395	+	0.896720i	0.248527	+	0.0729740i	0.403623	−	0.914925i	$-0.367751\pi$
$151$	3.05395	+	0.896720i	0.248527	+	0.0729740i	−0.155096	+	0.987899i	$0.549569\pi$
$152$		0			0
$153$	0.175535	−	1.22087i	0.0141911	−	0.0987014i
$154$		0			0
$155$	0.793624	+	0.510031i	0.0637454	+	0.0409667i
$156$		0			0
$157$	0.0804488	−	0.0928429i	0.00642052	−	0.00740967i	−0.752530	−	0.658558i	$-0.771167\pi$
$157$	0.0804488	−	0.0928429i	0.00642052	−	0.00740967i	0.758951	+	0.651148i	$0.225712\pi$
$158$		0			0
$159$	−3.39196	+	7.42736i	−0.269000	+	0.589028i
$160$		0			0
$161$	24.5516	+	15.7784i	1.93494	+	1.24351i
$162$		0			0
$163$	−14.4925			−1.13514			−0.567568	−	0.823326i	$-0.692116\pi$
$163$	−14.4925			−1.13514			−0.567568	+	0.823326i	$0.692116\pi$
$164$		0			0
$165$	−4.60314	−	10.0795i	−0.358354	−	0.784686i
$166$		0			0
$167$	1.54355	−	10.7356i	0.119443	−	0.830748i	−0.838728	−	0.544551i	$-0.816700\pi$
$167$	1.54355	−	10.7356i	0.119443	−	0.830748i	0.958171	−	0.286196i	$-0.0923909\pi$
$168$		0			0
$169$	−7.26837	−	8.38815i	−0.559105	−	0.645242i
$170$		0			0
$171$	6.77504			0.518100
$172$		0			0
$173$	−1.55438	−	3.40361i	−0.118177	−	0.258772i	0.841294	−	0.540577i	$-0.181794\pi$
$173$	−1.55438	−	3.40361i	−0.118177	−	0.258772i	−0.959472	+	0.281805i	$0.909067\pi$
$174$		0			0
$175$	38.8303	+	11.4016i	2.93530	+	0.861881i
$176$		0			0
$177$	−4.42081	−	1.29807i	−0.332288	−	0.0975686i
$178$		0			0
$179$	−6.74305	−	7.78189i	−0.503999	−	0.581646i	0.445553	−	0.895256i	$-0.353007\pi$
$179$	−6.74305	−	7.78189i	−0.503999	−	0.581646i	−0.949552	+	0.313610i	$0.898462\pi$
$180$		0			0
$181$	14.7672	−	17.0423i	1.09764	−	1.26675i	0.136514	−	0.990638i	$-0.456410\pi$
$181$	14.7672	−	17.0423i	1.09764	−	1.26675i	0.961127	−	0.276107i	$-0.0890444\pi$
$182$		0			0
$183$	−12.0075	+	3.52572i	−0.887621	+	0.260629i
$184$		0			0
$185$	22.5983	−	14.5231i	1.66146	−	1.06776i
$186$		0			0
$187$	−3.37824	+	0.991940i	−0.247041	+	0.0725378i
$188$		0			0
$189$	−1.66972	+	3.65617i	−0.121454	+	0.265947i
$190$		0			0
$191$	−13.8442	−	15.9771i	−1.00173	−	1.15606i	−0.987732	−	0.156159i	$-0.950089\pi$
$191$	−13.8442	−	15.9771i	−1.00173	−	1.15606i	−0.0140001	−	0.999902i	$-0.504457\pi$
$192$		0			0
$193$	−7.75518	−	16.9815i	−0.558230	−	1.22235i	−0.952831	−	0.303501i	$-0.901844\pi$
$193$	−7.75518	−	16.9815i	−0.558230	−	1.22235i	0.394601	−	0.918853i	$-0.370883\pi$
$194$		0			0
$195$	−16.0311	−	10.3026i	−1.14801	−	0.737783i
$196$		0			0
$197$	10.2519	−	3.01023i	0.730417	−	0.214470i	0.104682	−	0.994506i	$-0.466617\pi$
$197$	10.2519	−	3.01023i	0.730417	−	0.214470i	0.625735	+	0.780036i	$0.284799\pi$
$198$		0			0
$199$	1.84476	+	12.8306i	0.130771	+	0.909534i	0.944552	+	0.328362i	$0.106497\pi$
$199$	1.84476	+	12.8306i	0.130771	+	0.909534i	−0.813781	+	0.581172i	$0.802594\pi$
$200$		0			0
$201$	3.24058	+	7.51656i	0.228573	+	0.530177i
$202$		0			0
$203$	−1.90608	−	13.2571i	−0.133780	−	0.930463i
$204$		0			0
$205$	−9.91162	+	2.91031i	−0.692257	+	0.203265i
$206$		0			0
$207$	−6.10829	−	3.92556i	−0.424556	−	0.272845i
$208$		0			0
$209$	−8.03396	−	17.5919i	−0.555721	−	1.21686i
$210$		0			0
$211$	15.5776	+	17.9776i	1.07241	+	1.23763i	0.970057	+	0.242877i	$0.0780913\pi$
$211$	15.5776	+	17.9776i	1.07241	+	1.23763i	0.102352	+	0.994748i	$0.467363\pi$
$212$		0			0
$213$	−5.42066	+	11.8696i	−0.371417	+	0.813290i
$214$		0			0
$215$	−9.53731	+	2.80041i	−0.650439	+	0.190986i
$216$		0			0
$217$	−0.821748	+	0.528106i	−0.0557839	+	0.0358501i
$218$		0			0
$219$	4.89484	−	1.43726i	0.330763	−	0.0971207i
$220$		0			0
$221$	−3.96517	+	4.57605i	−0.266726	+	0.307818i
$222$		0			0
$223$	−5.41180	−	6.24555i	−0.362401	−	0.418233i	0.545042	−	0.838409i	$-0.316514\pi$
$223$	−5.41180	−	6.24555i	−0.362401	−	0.418233i	−0.907443	+	0.420176i	$0.861968\pi$
$224$		0			0
$225$	−9.66075	−	2.83665i	−0.644050	−	0.189110i
$226$		0			0
$227$	16.4969	+	4.84391i	1.09493	+	0.321502i	0.778838	−	0.627225i	$-0.215809\pi$
$227$	16.4969	+	4.84391i	1.09493	+	0.321502i	0.316097	+	0.948727i	$0.397628\pi$
$228$		0			0
$229$	11.4543	+	25.0814i	0.756921	+	1.65743i	0.753513	+	0.657433i	$0.228358\pi$
$229$	11.4543	+	25.0814i	0.756921	+	1.65743i	0.00340797	+	0.999994i	$0.498915\pi$
$230$		0			0
$231$	11.4735			0.754901
$232$		0			0
$233$	4.40464	+	5.08323i	0.288558	+	0.333013i	0.881458	−	0.472263i	$-0.156563\pi$
$233$	4.40464	+	5.08323i	0.288558	+	0.333013i	−0.592900	+	0.805276i	$0.702017\pi$
$234$		0			0
$235$	−5.93489	+	41.2780i	−0.387149	+	2.69268i
$236$		0			0
$237$	−1.47497	−	3.22973i	−0.0958096	−	0.209794i
$238$		0			0
$239$	−16.4076			−1.06132			−0.530659	−	0.847585i	$-0.678056\pi$
$239$	−16.4076			−1.06132			−0.530659	+	0.847585i	$0.678056\pi$
$240$		0			0
$241$	−6.79764	−	4.36858i	−0.437874	−	0.281405i	0.303074	−	0.952967i	$-0.401987\pi$
$241$	−6.79764	−	4.36858i	−0.437874	−	0.281405i	−0.740948	+	0.671562i	$0.765624\pi$
$242$		0			0
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$		0			0
$245$	−23.2738	+	26.8594i	−1.48691	+	1.71599i
$246$		0			0
$247$	−27.9795	−	17.9813i	−1.78029	−	1.14412i
$248$		0			0
$249$	−0.415759	+	2.89167i	−0.0263477	+	0.183252i
$250$		0			0
$251$	−19.7463	−	5.79804i	−1.24638	−	0.365969i	−0.408969	−	0.912548i	$-0.634111\pi$
$251$	−19.7463	−	5.79804i	−1.24638	−	0.365969i	−0.837407	+	0.546579i	$0.815930\pi$
$252$		0			0
$253$	−2.94971	+	20.5157i	−0.185446	+	1.28981i
$254$		0			0
$255$	−1.98898	+	4.35526i	−0.124555	+	0.272737i
$256$		0			0
$257$	−5.36704	+	3.44918i	−0.334787	+	0.215154i	−0.697223	−	0.716854i	$-0.745581\pi$
$257$	−5.36704	+	3.44918i	−0.334787	+	0.215154i	0.362437	+	0.932008i	$0.381945\pi$
$258$		0			0
$259$	3.95843	+	27.5315i	0.245965	+	1.71072i
$260$		0			0
$261$	0.474220	+	3.29827i	0.0293535	+	0.204158i
$262$		0			0
$263$	−23.4436	+	15.0663i	−1.44560	+	0.929028i	−0.446177	+	0.894945i	$0.647215\pi$
$263$	−23.4436	+	15.0663i	−1.44560	+	0.929028i	−0.999419	+	0.0340838i	$0.989149\pi$
$264$		0			0
$265$	20.7565	−	23.9543i	1.27506	−	1.47150i
$266$		0			0
$267$	9.28006			0.567930
$268$		0			0
$269$	−14.5779			−0.888832			−0.444416	−	0.895821i	$-0.646589\pi$
$269$	−14.5779			−0.888832			−0.444416	+	0.895821i	$0.646589\pi$
$270$		0			0
$271$	−9.41903	+	10.8701i	−0.572165	+	0.660314i	−0.965902	−	0.258910i	$-0.916637\pi$
$271$	−9.41903	+	10.8701i	−0.572165	+	0.660314i	0.393736	+	0.919223i	$0.371182\pi$
$272$		0			0
$273$	16.5992	−	10.6677i	1.00463	−	0.645637i
$274$		0			0
$275$	4.09030	+	28.4487i	0.246654	+	1.71552i
$276$		0			0
$277$	−2.45373	−	17.0660i	−0.147430	−	1.02540i	−0.920406	−	0.390964i	$-0.872142\pi$
$277$	−2.45373	−	17.0660i	−0.147430	−	1.02540i	0.772976	−	0.634436i	$-0.218767\pi$
$278$		0			0
$279$	0.204446	−	0.131389i	0.0122399	−	0.00786608i
$280$		0			0
$281$	2.83781	−	6.21393i	0.169289	−	0.370692i	−0.805904	−	0.592046i	$-0.798320\pi$
$281$	2.83781	−	6.21393i	0.169289	−	0.370692i	0.975194	+	0.221354i	$0.0710476\pi$
$282$		0			0
$283$	1.72051	−	11.9664i	0.102274	−	0.711331i	−0.872578	−	0.488476i	$-0.837553\pi$
$283$	1.72051	−	11.9664i	0.102274	−	0.711331i	0.974852	−	0.222855i	$-0.0715378\pi$
$284$		0			0
$285$	−25.2342	−	7.40944i	−1.49475	−	0.438897i
$286$		0			0
$287$	1.52222	−	10.5873i	0.0898537	−	0.624946i
$288$		0			0
$289$	−13.0215	−	8.36840i	−0.765970	−	0.492259i
$290$		0			0
$291$	10.9364	−	12.6212i	0.641101	−	0.739870i
$292$		0			0
$293$	7.95074	−	17.4097i	0.464487	−	1.01709i	−0.521954	−	0.852973i	$-0.674797\pi$
$293$	7.95074	−	17.4097i	0.464487	−	1.01709i	0.986442	−	0.164112i	$-0.0524759\pi$
$294$		0			0
$295$	15.0461	+	9.66952i	0.876016	+	0.562981i
$296$		0			0
$297$	−2.85454			−0.165637
$298$		0			0
$299$	14.8073	+	32.4234i	0.856327	+	1.87510i
$300$		0			0
$301$	1.46473	−	10.1874i	0.0844257	−	0.587194i
$302$		0			0
$303$	−7.04282	−	8.12785i	−0.404600	−	0.466933i
$304$		0			0
$305$	48.5789			2.78162
$306$		0			0
$307$	−1.34953	−	2.95505i	−0.0770215	−	0.168654i	0.867204	−	0.497953i	$-0.165915\pi$
$307$	−1.34953	−	2.95505i	−0.0770215	−	0.168654i	−0.944226	+	0.329299i	$0.893187\pi$
$308$		0			0
$309$	6.62832	+	1.94625i	0.377072	+	0.110718i
$310$		0			0
$311$	−14.9114	−	4.37837i	−0.845546	−	0.248275i	−0.169864	−	0.985468i	$-0.554333\pi$
$311$	−14.9114	−	4.37837i	−0.845546	−	0.248275i	−0.675683	+	0.737193i	$0.736151\pi$
$312$		0			0
$313$	6.30613	+	7.27766i	0.356444	+	0.411358i	0.905445	−	0.424464i	$-0.139537\pi$
$313$	6.30613	+	7.27766i	0.356444	+	0.411358i	−0.549001	+	0.835821i	$0.684992\pi$
$314$		0			0
$315$	10.2175	−	11.7917i	0.575692	−	0.664384i
$316$		0			0
$317$	23.9623	−	7.03598i	1.34586	−	0.395180i	0.472103	−	0.881543i	$-0.343495\pi$
$317$	23.9623	−	7.03598i	1.34586	−	0.395180i	0.873757	+	0.486363i	$0.161677\pi$
$318$		0			0
$319$	8.00189	−	5.14250i	0.448020	−	0.287925i
$320$		0			0
$321$	5.53666	−	1.62571i	0.309026	−	0.0907382i
$322$		0			0
$323$	−3.47141	+	7.60134i	−0.193155	+	0.422950i
$324$		0			0
$325$	32.3682	+	37.3549i	1.79546	+	2.07208i
$326$		0			0
$327$	5.83171	+	12.7697i	0.322494	+	0.706164i
$328$		0			0
$329$	−36.3256	−	23.3451i	−2.00270	−	1.28705i
$330$		0			0
$331$	26.1704	−	7.68432i	1.43846	−	0.422369i	0.532749	−	0.846273i	$-0.321159\pi$
$331$	26.1704	−	7.68432i	1.43846	−	0.422369i	0.905707	+	0.423905i	$0.139341\pi$
$332$		0			0
$333$	−0.984833	−	6.84967i	−0.0539685	−	0.375359i
$334$		0			0
$335$	−3.84945	−	31.5401i	−0.210318	−	1.72322i
$336$		0			0
$337$	2.25062	+	15.6534i	0.122599	+	0.852696i	0.954593	+	0.297912i	$0.0962901\pi$
$337$	2.25062	+	15.6534i	0.122599	+	0.852696i	−0.831994	+	0.554784i	$0.812801\pi$
$338$		0			0
$339$	−12.4106	+	3.64408i	−0.674052	+	0.197919i
$340$		0			0
$341$	−0.583599	−	0.375056i	−0.0316036	−	0.0203104i
$342$		0			0
$343$	−3.59909	−	7.88090i	−0.194333	−	0.425529i
$344$		0			0
$345$	18.4577	+	21.3013i	0.993730	+	1.14683i
$346$		0			0
$347$	−8.81862	+	19.3101i	−0.473409	+	1.03662i	0.510815	+	0.859691i	$0.329344\pi$
$347$	−8.81862	+	19.3101i	−0.473409	+	1.03662i	−0.984224	+	0.176929i	$0.943384\pi$
$348$		0			0
$349$	4.60412	−	1.35189i	0.246453	−	0.0723651i	−0.156173	−	0.987730i	$-0.549916\pi$
$349$	4.60412	−	1.35189i	0.246453	−	0.0723651i	0.402626	+	0.915365i	$0.368098\pi$
$350$		0			0
$351$	−4.12978	+	2.65405i	−0.220432	+	0.141663i
$352$		0			0
$353$	−28.0475	+	8.23548i	−1.49282	+	0.438330i	−0.923439	−	0.383746i	$-0.874634\pi$
$353$	−28.0475	+	8.23548i	−1.49282	+	0.438330i	−0.569377	+	0.822077i	$0.692816\pi$
$354$		0			0
$355$	33.1707	−	38.2811i	1.76052	−	2.03175i
$356$		0			0
$357$	−3.24655	−	3.74671i	−0.171825	−	0.198297i
$358$		0			0
$359$	10.6079	+	3.11476i	0.559864	+	0.164391i	0.549408	−	0.835555i	$-0.314853\pi$
$359$	10.6079	+	3.11476i	0.559864	+	0.164391i	0.0104561	+	0.999945i	$0.496672\pi$
$360$		0			0
$361$	−25.8115	−	7.57893i	−1.35850	−	0.398891i
$362$		0			0
$363$	−1.18460	−	2.59392i	−0.0621755	−	0.136145i
$364$		0			0
$365$	−19.8031			−1.03654
$366$		0			0
$367$	11.4872	+	13.2569i	0.599624	+	0.692003i	0.971705	−	0.236197i	$-0.0759010\pi$
$367$	11.4872	+	13.2569i	0.599624	+	0.692003i	−0.372081	+	0.928200i	$0.621356\pi$
$368$		0			0
$369$	−0.378718	+	2.63404i	−0.0197153	+	0.137123i
$370$		0			0
$371$	13.6336	+	29.8535i	0.707822	+	1.54991i
$372$		0			0
$373$	−16.4107			−0.849713			−0.424857	−	0.905261i	$-0.639675\pi$
$373$	−16.4107			−0.849713			−0.424857	+	0.905261i	$0.639675\pi$
$374$		0			0
$375$	16.5520	+	10.6373i	0.854743	+	0.549310i
$376$		0			0
$377$	6.79536	−	14.8798i	0.349979	−	0.766347i
$378$		0			0
$379$	18.3251	−	21.1483i	0.941297	−	1.08631i	−0.0548392	−	0.998495i	$-0.517465\pi$
$379$	18.3251	−	21.1483i	0.941297	−	1.08631i	0.996136	−	0.0878197i	$-0.0279899\pi$
$380$		0			0
$381$	7.26762	+	4.67062i	0.372331	+	0.239283i
$382$		0			0
$383$	1.39118	−	9.67588i	0.0710861	−	0.494414i	−0.922911	−	0.385012i	$-0.874197\pi$
$383$	1.39118	−	9.67588i	0.0710861	−	0.494414i	0.993998	−	0.109402i	$-0.0348937\pi$
$384$		0			0
$385$	−42.7341	−	12.5479i	−2.17793	−	0.639498i
$386$		0			0
$387$	−0.364416	+	2.53457i	−0.0185243	+	0.128839i
$388$		0			0
$389$	4.40173	−	9.63845i	0.223177	−	0.488689i	−0.764611	−	0.644492i	$-0.777069\pi$
$389$	4.40173	−	9.63845i	0.223177	−	0.488689i	0.987788	+	0.155803i	$0.0497964\pi$
$390$		0			0
$391$	7.53411	−	4.84188i	0.381016	−	0.244864i
$392$		0			0
$393$	2.05663	+	14.3042i	0.103743	+	0.721550i
$394$		0			0
$395$	1.96150	+	13.6425i	0.0986936	+	0.686429i
$396$		0			0
$397$	7.78273	−	5.00165i	0.390604	−	0.251026i	−0.330568	−	0.943782i	$-0.607240\pi$
$397$	7.78273	−	5.00165i	0.390604	−	0.251026i	0.721172	+	0.692756i	$0.243604\pi$
$398$		0			0
$399$	17.8329	−	20.5802i	0.892760	−	1.03030i
$400$		0			0
$401$	38.6068			1.92793			0.963966	−	0.266027i	$-0.0857110\pi$
$401$	38.6068			1.92793			0.963966	+	0.266027i	$0.0857110\pi$
$402$		0			0
$403$	−1.19303			−0.0594292
$404$		0			0
$405$	−2.54206	+	2.93369i	−0.126316	+	0.145776i
$406$		0			0
$407$	−16.6179	+	10.6797i	−0.823717	+	0.529371i
$408$		0			0
$409$	−2.31700	−	16.1151i	−0.114568	−	0.796838i	−0.963379	−	0.268142i	$-0.913590\pi$
$409$	−2.31700	−	16.1151i	−0.114568	−	0.796838i	0.848811	−	0.528696i	$-0.177319\pi$
$410$		0			0
$411$	1.28857	+	8.96220i	0.0635604	+	0.442072i
$412$		0			0
$413$	−15.5793	+	10.0122i	−0.766605	+	0.492667i
$414$		0			0
$415$	4.71097	−	10.3156i	0.231253	−	0.506372i
$416$		0			0
$417$	−2.26991	+	15.7876i	−0.111158	+	0.773121i
$418$		0			0
$419$	−15.0679	−	4.42432i	−0.736113	−	0.216142i	−0.107876	−	0.994164i	$-0.534405\pi$
$419$	−15.0679	−	4.42432i	−0.736113	−	0.216142i	−0.628237	+	0.778022i	$0.716223\pi$
$420$		0			0
$421$	−2.59136	+	18.0233i	−0.126295	+	0.878402i	0.823897	+	0.566739i	$0.191795\pi$
$421$	−2.59136	+	18.0233i	−0.126295	+	0.878402i	−0.950193	+	0.311663i	$0.899114\pi$
$422$		0			0
$423$	9.03759	+	5.80811i	0.439423	+	0.282400i
$424$		0			0
$425$	8.13262	−	9.38554i	0.394490	−	0.455266i
$426$		0			0
$427$	−20.8955	+	45.7549i	−1.01121	+	2.21423i
$428$		0			0
$429$	11.7886	+	7.57609i	0.569160	+	0.365777i
$430$		0			0
$431$	27.9434			1.34599			0.672993	−	0.739649i	$-0.265009\pi$
$431$	27.9434			1.34599			0.672993	+	0.739649i	$0.265009\pi$
$432$		0			0
$433$	12.0141	+	26.3073i	0.577363	+	1.26425i	0.942784	+	0.333405i	$0.108198\pi$
$433$	12.0141	+	26.3073i	0.577363	+	1.26425i	−0.365421	+	0.930842i	$0.619075\pi$
$434$		0			0
$435$	1.84084	−	12.8033i	0.0882616	−	0.613873i
$436$		0			0
$437$	32.2147	+	37.1777i	1.54104	+	1.77845i
$438$		0			0
$439$	−29.8423			−1.42429			−0.712147	−	0.702030i	$-0.752277\pi$
$439$	−29.8423			−1.42429			−0.712147	+	0.702030i	$0.752277\pi$
$440$		0			0
$441$	3.80334	+	8.32814i	0.181111	+	0.396578i
$442$		0			0
$443$	−13.4904	−	3.96114i	−0.640948	−	0.188199i	−0.0549208	−	0.998491i	$-0.517491\pi$
$443$	−13.4904	−	3.96114i	−0.640948	−	0.188199i	−0.586027	+	0.810291i	$0.699309\pi$
$444$		0			0
$445$	−34.5644	−	10.1490i	−1.63851	−	0.481110i
$446$		0			0
$447$	−3.78683	−	4.37024i	−0.179111	−	0.206705i
$448$		0			0
$449$	2.97405	−	3.43223i	0.140354	−	0.161977i	−0.681221	−	0.732078i	$-0.738551\pi$
$449$	2.97405	−	3.43223i	0.140354	−	0.161977i	0.821575	+	0.570101i	$0.193096\pi$
$450$		0			0
$451$	7.28860	−	2.14013i	0.343207	−	0.100775i
$452$		0			0
$453$	−2.67761	+	1.72079i	−0.125805	+	0.0808499i
$454$		0			0
$455$	−73.4918	+	21.5791i	−3.44535	+	1.01165i
$456$		0			0
$457$	3.05445	−	6.68831i	0.142881	−	0.312866i	−0.824639	−	0.565659i	$-0.808622\pi$
$457$	3.05445	−	6.68831i	0.142881	−	0.312866i	0.967520	+	0.252793i	$0.0813492\pi$
$458$		0			0
$459$	0.807721	+	0.932160i	0.0377012	+	0.0435095i
$460$		0			0
$461$	−11.8280	−	25.8997i	−0.550886	−	1.20627i	−0.956367	−	0.292168i	$-0.905623\pi$
$461$	−11.8280	−	25.8997i	−0.550886	−	1.20627i	0.405482	−	0.914103i	$-0.367104\pi$
$462$		0			0
$463$	−23.7759	−	15.2798i	−1.10496	−	0.710113i	−0.144769	−	0.989465i	$-0.546244\pi$
$463$	−23.7759	−	15.2798i	−1.10496	−	0.710113i	−0.960189	+	0.279352i	$0.909880\pi$
$464$		0			0
$465$	−0.905169	+	0.265782i	−0.0419762	+	0.0123253i
$466$		0			0
$467$	3.06667	+	21.3292i	0.141909	+	0.986996i	0.928979	+	0.370133i	$0.120688\pi$
$467$	3.06667	+	21.3292i	0.141909	+	0.986996i	−0.787070	+	0.616863i	$0.788403\pi$
$468$		0			0
$469$	31.3624	+	9.94087i	1.44818	+	0.459027i
$470$		0			0
$471$	0.0174832	+	0.121598i	0.000805584	+	0.00560296i
$472$		0			0
$473$	7.01334	−	2.05930i	0.322474	−	0.0946869i
$474$		0			0
$475$	57.3862	+	36.8799i	2.63306	+	1.69217i
$476$		0			0
$477$	−3.39196	−	7.42736i	−0.155307	−	0.340075i
$478$		0			0
$479$	−14.0074	−	16.1654i	−0.640013	−	0.738615i	0.339364	−	0.940655i	$-0.389788\pi$
$479$	−14.0074	−	16.1654i	−0.640013	−	0.738615i	−0.979377	+	0.202041i	$0.935243\pi$
$480$		0			0
$481$	−14.1122	+	30.9014i	−0.643462	+	1.40898i
$482$		0			0
$483$	−28.0024	+	8.22224i	−1.27415	+	0.374125i
$484$		0			0
$485$	−54.5365	+	35.0485i	−2.47638	+	1.59147i
$486$		0			0
$487$	−3.31122	+	0.972262i	−0.150046	+	0.0440574i	−0.355893	−	0.934527i	$-0.615823\pi$
$487$	−3.31122	+	0.972262i	−0.150046	+	0.0440574i	0.205847	+	0.978584i	$0.434005\pi$
$488$		0			0
$489$	9.49054	−	10.9527i	0.429177	−	0.495297i
$490$		0			0
$491$	15.0838	+	17.4077i	0.680724	+	0.785598i	0.986014	−	0.166662i	$-0.0532988\pi$
$491$	15.0838	+	17.4077i	0.680724	+	0.785598i	−0.305290	+	0.952260i	$0.598753\pi$
$492$		0			0
$493$	−3.94352	−	1.15792i	−0.177607	−	0.0521502i
$494$		0			0
$495$	10.6320	+	3.12183i	0.477872	+	0.140316i
$496$		0			0
$497$	21.7877	+	47.7085i	0.977314	+	2.14002i
$498$		0			0
$499$	14.6737			0.656883			0.328442	−	0.944524i	$-0.393477\pi$
$499$	14.6737			0.656883			0.328442	+	0.944524i	$0.393477\pi$
$500$		0			0
$501$	7.10263	+	8.19688i	0.317322	+	0.366209i
$502$		0			0
$503$	3.44518	−	23.9618i	0.153613	−	1.06840i	−0.756485	−	0.654011i	$-0.773085\pi$
$503$	3.44518	−	23.9618i	0.153613	−	1.06840i	0.910099	−	0.414392i	$-0.136006\pi$
$504$		0			0
$505$	17.3427	+	37.9752i	0.771740	+	1.68987i
$506$		0			0
$507$	11.0991			0.492929
$508$		0			0
$509$	22.0683	+	14.1825i	0.978162	+	0.628627i	0.928967	−	0.370163i	$-0.120698\pi$
$509$	22.0683	+	14.1825i	0.978162	+	0.628627i	0.0491952	+	0.998789i	$0.484334\pi$
$510$		0			0
$511$	8.51804	−	18.6519i	0.376816	−	0.825112i
$512$		0			0
$513$	−4.43671	+	5.12023i	−0.195885	+	0.226064i
$514$		0			0
$515$	−22.5592	−	14.4979i	−0.994079	−	0.638856i
$516$		0			0
$517$	4.36427	−	30.3542i	0.191940	−	1.33498i
$518$		0			0
$519$	3.59018	+	1.05417i	0.157591	+	0.0462730i
$520$		0			0
$521$	0.997854	−	6.94022i	0.0437168	−	0.304057i	−0.956218	−	0.292655i	$-0.905461\pi$
$521$	0.997854	−	6.94022i	0.0437168	−	0.304057i	0.999935	−	0.0114022i	$-0.00362950\pi$
$522$		0			0
$523$	−9.46062	+	20.7159i	−0.413684	+	0.905842i	0.582013	+	0.813179i	$0.302265\pi$
$523$	−9.46062	+	20.7159i	−0.413684	+	0.905842i	−0.995698	+	0.0926628i	$0.970462\pi$
$524$		0			0
$525$	−34.0452	+	21.8795i	−1.48586	+	0.954901i
$526$		0			0
$527$	0.0426593	+	0.296702i	0.00185827	+	0.0129246i
$528$		0			0
$529$	−4.22977	−	29.4187i	−0.183903	−	1.27907i
$530$		0			0
$531$	3.87602	−	2.49097i	0.168205	−	0.108099i
$532$		0			0
$533$	8.55492	−	9.87290i	0.370555	−	0.427643i
$534$		0			0
$535$	−22.3997			−0.968424
$536$		0			0
$537$	10.2969			0.444345
$538$		0			0
$539$	17.1146	−	19.7513i	0.737179	−	0.850750i
$540$		0			0
$541$	−20.9733	+	13.4787i	−0.901712	+	0.579495i	−0.907298	−	0.420489i	$-0.861858\pi$
$541$	−20.9733	+	13.4787i	−0.901712	+	0.579495i	0.00558537	+	0.999984i	$0.498222\pi$
$542$		0			0
$543$	3.20923	+	22.3207i	0.137721	+	0.957872i
$544$		0			0
$545$	−7.75533	−	53.9395i	−0.332202	−	2.31051i
$546$		0			0
$547$	10.8073	−	6.94544i	0.462087	−	0.296965i	−0.288808	−	0.957387i	$-0.593259\pi$
$547$	10.8073	−	6.94544i	0.462087	−	0.296965i	0.750895	+	0.660422i	$0.229622\pi$
$548$		0			0
$549$	5.19868	−	11.3835i	0.221874	−	0.485837i
$550$		0			0
$551$	3.21286	−	22.3459i	0.136872	−	0.951969i
$552$		0			0
$553$	−13.6931	−	4.02067i	−0.582292	−	0.170976i
$554$		0			0
$555$	−3.82296	+	26.5892i	−0.162275	+	1.12865i
$556$		0			0
$557$	−2.14490	−	1.37844i	−0.0908822	−	0.0584065i	0.494410	−	0.869229i	$-0.335384\pi$
$557$	−2.14490	−	1.37844i	−0.0908822	−	0.0584065i	−0.585293	+	0.810822i	$0.699020\pi$
$558$		0			0
$559$	8.23184	−	9.50005i	0.348170	−	0.401809i
$560$		0			0
$561$	1.46262	−	3.20268i	0.0617517	−	0.135217i
$562$		0			0
$563$	1.97158	+	1.26706i	0.0830922	+	0.0534001i	0.581527	−	0.813527i	$-0.302455\pi$
$563$	1.97158	+	1.26706i	0.0830922	+	0.0534001i	−0.498435	+	0.866927i	$0.666092\pi$
$564$		0			0
$565$	50.2097			2.11234
$566$		0			0
$567$	−1.66972	−	3.65617i	−0.0701215	−	0.153545i
$568$		0			0
$569$	−0.142489	+	0.991032i	−0.00597344	+	0.0415462i	−0.992590	−	0.121510i	$-0.961226\pi$
$569$	−0.142489	+	0.991032i	−0.00597344	+	0.0415462i	0.986617	+	0.163057i	$0.0521353\pi$
$570$		0			0
$571$	−6.00068	−	6.92515i	−0.251121	−	0.289809i	0.616167	−	0.787615i	$-0.288684\pi$
$571$	−6.00068	−	6.92515i	−0.251121	−	0.289809i	−0.867288	+	0.497806i	$0.834139\pi$
$572$		0			0
$573$	21.1407			0.883165
$574$		0			0
$575$	−30.3699	−	66.5009i	−1.26651	−	2.77328i
$576$		0			0
$577$	34.5096	+	10.1329i	1.43665	+	0.421839i	0.905104	−	0.425189i	$-0.139792\pi$
$577$	34.5096	+	10.1329i	1.43665	+	0.421839i	0.531548	+	0.847028i	$0.321611\pi$
$578$		0			0
$579$	17.9123	+	5.25953i	0.744410	+	0.218579i
$580$		0			0
$581$	7.68955	+	8.87422i	0.319016	+	0.368165i
$582$		0			0
$583$	−15.2635	+	17.6150i	−0.632149	+	0.729539i
$584$		0			0
$585$	18.2843	−	5.36876i	0.755963	−	0.221971i
$586$		0			0
$587$	−26.9863	+	17.3430i	−1.11384	+	0.715824i	−0.962127	−	0.272600i	$-0.912116\pi$
$587$	−26.9863	+	17.3430i	−1.11384	+	0.715824i	−0.151716	+	0.988424i	$0.548480\pi$
$588$		0			0
$589$	−1.57981	+	0.463875i	−0.0650950	+	0.0191136i
$590$		0			0
$591$	−4.43858	+	9.71914i	−0.182579	+	0.399792i
$592$		0			0
$593$	−3.86088	−	4.45569i	−0.158547	−	0.182973i	0.670918	−	0.741532i	$-0.265900\pi$
$593$	−3.86088	−	4.45569i	−0.158547	−	0.182973i	−0.829465	+	0.558558i	$0.811355\pi$
$594$		0			0
$595$	7.99450	+	17.5055i	0.327743	+	0.717656i
$596$		0			0
$597$	−10.9048	−	7.00806i	−0.446302	−	0.286821i
$598$		0			0
$599$	17.6060	−	5.16959i	0.719361	−	0.211224i	0.0984923	−	0.995138i	$-0.468598\pi$
$599$	17.6060	−	5.16959i	0.719361	−	0.211224i	0.620869	+	0.783914i	$0.286780\pi$
$600$		0			0
$601$	6.22844	+	43.3198i	0.254063	+	1.76705i	0.573271	+	0.819366i	$0.305674\pi$
$601$	6.22844	+	43.3198i	0.254063	+	1.76705i	−0.319208	+	0.947685i	$0.603417\pi$
$602$		0			0
$603$	−7.80277	−	2.47323i	−0.317753	−	0.100718i
$604$		0			0
$605$	1.57535	+	10.9568i	0.0640471	+	0.445457i
$606$		0			0
$607$	−21.1529	+	6.21105i	−0.858570	+	0.252099i	−0.681247	−	0.732054i	$-0.738562\pi$
$607$	−21.1529	+	6.21105i	−0.858570	+	0.252099i	−0.177323	+	0.984153i	$0.556744\pi$
$608$		0			0
$609$	11.2672	+	7.24101i	0.456571	+	0.293420i
$610$		0			0
$611$	−21.9083	−	47.9725i	−0.886315	−	1.94076i
$612$		0			0
$613$	−10.8211	−	12.4882i	−0.437059	−	0.504393i	0.493899	−	0.869519i	$-0.335571\pi$
$613$	−10.8211	−	12.4882i	−0.437059	−	0.504393i	−0.930958	+	0.365126i	$0.881026\pi$
$614$		0			0
$615$	4.29126	−	9.39655i	0.173040	−	0.378905i
$616$		0			0
$617$	41.7400	−	12.2560i	1.68039	−	0.493407i	0.704141	−	0.710060i	$-0.251332\pi$
$617$	41.7400	−	12.2560i	1.68039	−	0.493407i	0.976249	+	0.216653i	$0.0695139\pi$
$618$		0			0
$619$	−14.2544	+	9.16076i	−0.572934	+	0.368202i	−0.794797	−	0.606876i	$-0.792423\pi$
$619$	−14.2544	+	9.16076i	−0.572934	+	0.368202i	0.221863	+	0.975078i	$0.428786\pi$
$620$		0			0
$621$	6.96682	−	2.04564i	0.279569	−	0.0820888i
$622$		0			0
$623$	24.4264	−	28.1896i	0.978624	−	1.12939i
$624$		0			0
$625$	−17.0484	−	19.6749i	−0.681937	−	0.786997i
$626$		0			0
$627$	18.5562	+	5.44860i	0.741064	+	0.217596i
$628$		0			0
$629$	8.18968	+	2.40471i	0.326544	+	0.0958819i
$630$		0			0
$631$	11.9183	+	26.0975i	0.474461	+	1.03892i	0.983950	+	0.178447i	$0.0571072\pi$
$631$	11.9183	+	26.0975i	0.474461	+	1.03892i	−0.509489	+	0.860477i	$0.670166\pi$
$632$		0			0
$633$	−23.7877			−0.945477
$634$		0			0
$635$	−21.9609	−	25.3443i	−0.871493	−	1.00576i
$636$		0			0
$637$	6.39636	−	44.4877i	0.253433	−	1.76267i
$638$		0			0
$639$	−5.42066	−	11.8696i	−0.214438	−	0.469553i
$640$		0			0
$641$	25.3570			1.00154			0.500771	−	0.865580i	$-0.333050\pi$
$641$	25.3570			1.00154			0.500771	+	0.865580i	$0.333050\pi$
$642$		0			0
$643$	11.0986	+	7.13266i	0.437687	+	0.281284i	0.740871	−	0.671648i	$-0.234413\pi$
$643$	11.0986	+	7.13266i	0.437687	+	0.281284i	−0.303183	+	0.952932i	$0.598049\pi$
$644$		0			0
$645$	4.12920	−	9.04169i	0.162587	−	0.356016i
$646$		0			0
$647$	13.9380	−	16.0853i	0.547958	−	0.632377i	−0.412448	−	0.910981i	$-0.635326\pi$
$647$	13.9380	−	16.0853i	0.547958	−	0.632377i	0.960406	+	0.278604i	$0.0898718\pi$
$648$		0			0
$649$	−11.0643	−	7.11057i	−0.434310	−	0.279114i
$650$		0			0
$651$	0.139015	−	0.966872i	0.00544843	−	0.0378947i
$652$		0			0
$653$	−16.1863	−	4.75272i	−0.633418	−	0.185988i	−0.0507665	−	0.998711i	$-0.516166\pi$
$653$	−16.1863	−	4.75272i	−0.633418	−	0.185988i	−0.582651	+	0.812722i	$0.697985\pi$
$654$		0			0
$655$	7.98348	−	55.5263i	0.311940	−	2.16959i
$656$		0			0
$657$	−2.11924	+	4.64048i	−0.0826793	+	0.181042i
$658$		0			0
$659$	−13.4380	+	8.63605i	−0.523468	+	0.336413i	−0.775543	−	0.631295i	$-0.782524\pi$
$659$	−13.4380	+	8.63605i	−0.523468	+	0.336413i	0.252074	+	0.967708i	$0.418887\pi$
$660$		0			0
$661$	1.49668	+	10.4096i	0.0582140	+	0.404887i	0.998005	+	0.0631373i	$0.0201106\pi$
$661$	1.49668	+	10.4096i	0.0582140	+	0.404887i	−0.939791	+	0.341750i	$0.888980\pi$
$662$		0			0
$663$	−0.861714	−	5.99335i	−0.0334662	−	0.232762i
$664$		0			0
$665$	−88.9274	+	57.1502i	−3.44846	+	2.21619i
$666$		0			0
$667$	−15.8442	+	18.2852i	−0.613491	+	0.708007i
$668$		0			0
$669$	8.26404			0.319506
$670$		0			0
$671$	−35.7229			−1.37907
$672$		0			0
$673$	13.9413	−	16.0891i	0.537398	−	0.620190i	−0.420502	−	0.907291i	$-0.638146\pi$
$673$	13.9413	−	16.0891i	0.537398	−	0.620190i	0.957900	+	0.287101i	$0.0926916\pi$
$674$		0			0
$675$	8.47024	−	5.44349i	0.326020	−	0.209520i
$676$		0			0
$677$	0.578717	+	4.02506i	0.0222419	+	0.154696i	0.997916	−	0.0645318i	$-0.0205554\pi$
$677$	0.578717	+	4.02506i	0.0222419	+	0.154696i	−0.975674	+	0.219228i	$0.929646\pi$
$678$		0			0
$679$	−9.55289	−	66.4418i	−0.366606	−	2.54980i
$680$		0			0
$681$	−14.4639	+	9.29540i	−0.554259	+	0.356201i
$682$		0			0
$683$	−10.8576	+	23.7748i	−0.415454	+	0.909717i	0.580013	+	0.814607i	$0.303047\pi$
$683$	−10.8576	+	23.7748i	−0.415454	+	0.909717i	−0.995467	+	0.0951097i	$0.969680\pi$
$684$		0			0
$685$	5.00201	−	34.7897i	0.191117	−	1.32925i
$686$		0			0
$687$	−26.4562	−	7.76825i	−1.00937	−	0.296377i
$688$		0			0
$689$	−5.70452	+	39.6758i	−0.217325	+	1.51153i
$690$		0			0
$691$	14.0127	+	9.00543i	0.533069	+	0.342583i	0.779323	−	0.626623i	$-0.215563\pi$
$691$	14.0127	+	9.00543i	0.533069	+	0.342583i	−0.246254	+	0.969205i	$0.579200\pi$
$692$		0			0
$693$	−7.51355	+	8.67110i	−0.285416	+	0.329388i
$694$		0			0
$695$	25.7204	−	56.3198i	0.975629	−	2.13633i
$696$		0			0
$697$	−2.76125	−	1.77455i	−0.104590	−	0.0672158i
$698$		0			0
$699$	−6.72607			−0.254404
$700$		0			0
$701$	13.6815	+	29.9583i	0.516743	+	1.13151i	0.970658	+	0.240464i	$0.0772997\pi$
$701$	13.6815	+	29.9583i	0.516743	+	1.13151i	−0.453915	+	0.891045i	$0.649973\pi$
$702$		0			0
$703$	−6.67229	+	46.4068i	−0.251650	+	1.75026i
$704$		0			0
$705$	−27.3093	−	31.5167i	−1.02853	−	1.18699i
$706$		0			0
$707$	−43.2273			−1.62573
$708$		0			0
$709$	13.5491	+	29.6684i	0.508847	+	1.11422i	0.973492	+	0.228723i	$0.0734549\pi$
$709$	13.5491	+	29.6684i	0.508847	+	1.11422i	−0.464644	+	0.885497i	$0.653818\pi$
$710$		0			0
$711$	3.40677	+	1.00032i	0.127764	+	0.0375148i
$712$		0			0
$713$	1.69311	+	0.497143i	0.0634076	+	0.0186182i
$714$		0			0
$715$	−35.6223	−	41.1103i	−1.33220	−	1.53744i
$716$		0			0
$717$	10.7447	−	12.4000i	0.401267	−	0.463087i
$718$		0			0
$719$	−25.0890	+	7.36679i	−0.935661	+	0.274735i	−0.713805	−	0.700345i	$-0.753030\pi$
$719$	−25.0890	+	7.36679i	−0.935661	+	0.274735i	−0.221856	+	0.975079i	$0.571211\pi$
$720$		0			0
$721$	23.3587	−	15.0117i	0.869923	−	0.559066i
$722$		0			0
$723$	7.75305	−	2.27650i	0.288339	−	0.0846640i
$724$		0			0
$725$	−13.9374	+	30.5186i	−0.517621	+	1.13343i
$726$		0			0
$727$	−1.88250	−	2.17252i	−0.0698179	−	0.0805742i	0.719766	−	0.694217i	$-0.244249\pi$
$727$	−1.88250	−	2.17252i	−0.0698179	−	0.0805742i	−0.789584	+	0.613643i	$0.789704\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−2.65697	−	1.70753i	−0.0982716	−	0.0631553i
$732$		0			0
$733$	6.19826	−	1.81997i	0.228938	−	0.0672223i	−0.165251	−	0.986251i	$-0.552844\pi$
$733$	6.19826	−	1.81997i	0.228938	−	0.0672223i	0.394189	+	0.919029i	$0.371025\pi$
$734$		0			0
$735$	−5.05789	−	35.1784i	−0.186563	−	1.29757i
$736$		0			0
$737$	2.83073	+	23.1933i	0.104271	+	0.854336i
$738$		0			0
$739$	−1.09698	−	7.62965i	−0.0403530	−	0.280661i	0.959647	−	0.281208i	$-0.0907351\pi$
$739$	−1.09698	−	7.62965i	−0.0403530	−	0.280661i	−1.00000		0.000546671i	$0.999826\pi$
$740$		0			0
$741$	31.9120	−	9.37021i	1.17232	−	0.344223i
$742$		0			0
$743$	−30.1502	−	19.3763i	−1.10610	−	0.710849i	−0.145662	−	0.989334i	$-0.546531\pi$
$743$	−30.1502	−	19.3763i	−1.10610	−	0.710849i	−0.960440	+	0.278485i	$0.910168\pi$
$744$		0			0
$745$	9.32493	+	20.4187i	0.341639	+	0.748085i
$746$		0			0
$747$	−1.91311	−	2.20785i	−0.0699972	−	0.0807811i
$748$		0			0
$749$	9.63492	−	21.0975i	0.352052	−	0.770887i
$750$		0			0
$751$	37.1529	−	10.9091i	1.35573	−	0.398078i	0.478473	−	0.878102i	$-0.341190\pi$
$751$	37.1529	−	10.9091i	1.35573	−	0.398078i	0.877255	+	0.480025i	$0.159372\pi$
$752$		0			0
$753$	17.3129	−	11.1264i	0.630919	−	0.405467i
$754$		0			0
$755$	11.8549	−	3.48091i	0.431444	−	0.126683i
$756$		0			0
$757$	−0.944943	+	1.09052i	−0.0343445	+	0.0396357i	−0.772662	−	0.634818i	$-0.781075\pi$
$757$	−0.944943	+	1.09052i	−0.0343445	+	0.0396357i	0.738317	+	0.674453i	$0.235621\pi$
$758$		0			0
$759$	−13.5731	−	15.6641i	−0.492671	−	0.568572i
$760$		0			0
$761$	49.3883	+	14.5017i	1.79033	+	0.525687i	0.996585	−	0.0825693i	$-0.0263126\pi$
$761$	49.3883	+	14.5017i	1.79033	+	0.525687i	0.793741	+	0.608256i	$0.208131\pi$
$762$		0			0
$763$	54.1397	+	15.8968i	1.95999	+	0.575504i
$764$		0			0
$765$	−1.98898	−	4.35526i	−0.0719118	−	0.157465i
$766$		0			0
$767$	−22.6183			−0.816700
$768$		0			0
$769$	−12.4086	−	14.3202i	−0.447464	−	0.516401i	0.486543	−	0.873657i	$-0.338258\pi$
$769$	−12.4086	−	14.3202i	−0.447464	−	0.516401i	−0.934007	+	0.357256i	$0.883712\pi$
$770$		0			0
$771$	0.907941	−	6.31487i	0.0326987	−	0.227425i
$772$		0			0
$773$	−12.6693	−	27.7419i	−0.455684	−	0.997808i	−0.988450	−	0.151546i	$-0.951575\pi$
$773$	−12.6693	−	27.7419i	−0.455684	−	0.997808i	0.532766	−	0.846262i	$-0.321152\pi$
$774$		0			0
$775$	2.44692			0.0878961
$776$		0			0
$777$	−23.3991	−	15.0377i	−0.839439	−	0.539475i
$778$		0			0
$779$	7.48963	−	16.4000i	0.268344	−	0.587591i
$780$		0			0
$781$	−24.3924	+	28.1503i	−0.872829	+	1.00730i
$782$		0			0
$783$	−2.80322	−	1.80152i	−0.100179	−	0.0643810i
$784$		0			0
$785$	0.0678668	−	0.472024i	0.00242227	−	0.0168473i
$786$		0			0
$787$	12.6645	+	3.71864i	0.451442	+	0.132555i	0.499547	−	0.866287i	$-0.333500\pi$
$787$	12.6645	+	3.71864i	0.451442	+	0.132555i	−0.0481047	+	0.998842i	$0.515318\pi$
$788$		0			0
$789$	3.96596	−	27.5838i	0.141192	−	0.982011i
$790$		0			0
$791$	−21.5970	+	47.2909i	−0.767901	+	1.68147i
$792$		0			0
$793$	−51.6819	+	33.2140i	−1.83528	+	1.17946i
$794$		0			0
$795$	4.51082	+	31.3734i	0.159982	+	1.11270i
$796$		0			0
$797$	−3.49390	−	24.3006i	−0.123760	−	0.860771i	−0.953236	−	0.302228i	$-0.902270\pi$
$797$	−3.49390	−	24.3006i	−0.123760	−	0.860771i	0.829476	−	0.558543i	$-0.188639\pi$
$798$		0			0
$799$	−11.1472	+	7.16386i	−0.394359	+	0.253439i
$800$		0			0
$801$	−6.07715	+	7.01340i	−0.214725	+	0.247806i
$802$		0			0
$803$	14.5624			0.513896
$804$		0			0
$805$	113.289			3.99293
$806$		0			0
$807$	9.54651	−	11.0173i	0.336053	−	0.387826i
$808$		0			0
$809$	−2.74714	+	1.76548i	−0.0965845	+	0.0620711i	−0.588042	−	0.808831i	$-0.700101\pi$
$809$	−2.74714	+	1.76548i	−0.0965845	+	0.0620711i	0.491457	+	0.870902i	$0.336464\pi$
$810$		0			0
$811$	2.59845	+	18.0726i	0.0912438	+	0.634614i	0.983205	+	0.182503i	$0.0584199\pi$
$811$	2.59845	+	18.0726i	0.0912438	+	0.634614i	−0.891962	+	0.452111i	$0.850671\pi$
$812$		0			0
$813$	−2.04695	−	14.2369i	−0.0717897	−	0.499308i
$814$		0			0
$815$	−47.3266	+	30.4149i	−1.65778	+	1.06539i
$816$		0			0
$817$	7.20678	−	15.7807i	0.252133	−	0.552095i
$818$		0			0
$819$	−2.80809	+	19.5307i	−0.0981226	+	0.682458i
$820$		0			0
$821$	23.1605	+	6.80055i	0.808308	+	0.237341i	0.659674	−	0.751552i	$-0.270694\pi$
$821$	23.1605	+	6.80055i	0.808308	+	0.237341i	0.148634	+	0.988892i	$0.452512\pi$
$822$		0			0
$823$	5.60885	−	39.0104i	0.195512	−	1.35982i	−0.621598	−	0.783336i	$-0.713516\pi$
$823$	5.60885	−	39.0104i	0.195512	−	1.35982i	0.817111	−	0.576481i	$-0.195575\pi$
$824$		0			0
$825$	−24.1786	−	15.5387i	−0.841792	−	0.540987i
$826$		0			0
$827$	18.6925	−	21.5722i	0.650000	−	0.750140i	−0.331109	−	0.943592i	$-0.607423\pi$
$827$	18.6925	−	21.5722i	0.650000	−	0.750140i	0.981110	+	0.193452i	$0.0619684\pi$
$828$		0			0
$829$	−19.1270	+	41.8824i	−0.664309	+	1.45463i	0.214142	+	0.976802i	$0.431304\pi$
$829$	−19.1270	+	41.8824i	−0.664309	+	1.45463i	−0.878451	+	0.477832i	$0.841423\pi$
$830$		0			0
$831$	14.5045	+	9.32148i	0.503156	+	0.323359i
$832$		0			0
$833$	−11.2926			−0.391266
$834$		0			0
$835$	−17.4900	−	38.2977i	−0.605265	−	1.32535i
$836$		0			0
$837$	−0.0345861	+	0.240552i	−0.00119547	+	0.00831468i
$838$		0			0
$839$	−31.4260	−	36.2675i	−1.08495	−	1.25209i	−0.965820	−	0.259215i	$-0.916536\pi$
$839$	−31.4260	−	36.2675i	−1.08495	−	1.25209i	−0.119126	−	0.992879i	$-0.538009\pi$
$840$		0			0
$841$	−17.8965			−0.617121
$842$		0			0
$843$	2.83781	+	6.21393i	0.0977393	+	0.214019i
$844$		0			0
$845$	−41.3396	−	12.1384i	−1.42213	−	0.417574i
$846$		0			0
$847$	−10.9975	−	3.22915i	−0.377877	−	0.110955i
$848$		0			0
$849$	7.91694	+	9.13663i	0.271709	+	0.313568i
$850$		0			0
$851$	32.9044	−	37.9737i	1.12795	−	1.30172i
$852$		0			0
$853$	−54.3296	+	15.9526i	−1.86021	+	0.546207i	−0.860912	+	0.508754i	$0.830106\pi$
$853$	−54.3296	+	15.9526i	−1.86021	+	0.546207i	−0.999298	+	0.0374531i	$0.988076\pi$
$854$		0			0
$855$	22.1246	−	14.2186i	0.756645	−	0.486266i
$856$		0			0
$857$	31.8974	−	9.36591i	1.08959	−	0.319933i	0.312883	−	0.949792i	$-0.398705\pi$
$857$	31.8974	−	9.36591i	1.08959	−	0.319933i	0.776710	+	0.629858i	$0.216887\pi$
$858$		0			0
$859$	4.55623	−	9.97675i	0.155457	−	0.340402i	−0.815839	−	0.578280i	$-0.803724\pi$
$859$	4.55623	−	9.97675i	0.155457	−	0.340402i	0.971295	+	0.237877i	$0.0764516\pi$
$860$		0			0
$861$	7.00447	+	8.08359i	0.238712	+	0.275488i
$862$		0			0
$863$	18.0244	+	39.4680i	0.613558	+	1.34350i	0.920113	+	0.391652i	$0.128096\pi$
$863$	18.0244	+	39.4680i	0.613558	+	1.34350i	−0.306555	+	0.951853i	$0.599176\pi$
$864$		0			0
$865$	−12.2191	−	7.85271i	−0.415460	−	0.267000i
$866$		0			0
$867$	14.8517	−	4.36084i	0.504389	−	0.148102i
$868$		0			0
$869$	−1.44240	−	10.0321i	−0.0489302	−	0.340317i
$870$		0			0
$871$	25.6597	+	30.9228i	0.869445	+	1.04778i
$872$		0			0
$873$	2.37670	+	16.5303i	0.0804391	+	0.559466i
$874$		0			0
$875$	75.8798	−	22.2803i	2.56521	−	0.753212i
$876$		0			0
$877$	−9.20892	−	5.91821i	−0.310963	−	0.199844i	0.375845	−	0.926682i	$-0.377352\pi$
$877$	−9.20892	−	5.91821i	−0.310963	−	0.199844i	−0.686808	+	0.726839i	$0.740989\pi$
$878$		0			0
$879$	7.95074	+	17.4097i	0.268172	+	0.587215i
$880$		0			0
$881$	24.2272	+	27.9596i	0.816234	+	0.941984i	0.999153	−	0.0411442i	$-0.0131003\pi$
$881$	24.2272	+	27.9596i	0.816234	+	0.941984i	−0.182920	+	0.983128i	$0.558555\pi$
$882$		0			0
$883$	−23.6803	+	51.8526i	−0.796906	+	1.74498i	−0.141176	+	0.989985i	$0.545088\pi$
$883$	−23.6803	+	51.8526i	−0.796906	+	1.74498i	−0.655730	+	0.754996i	$0.727639\pi$
$884$		0			0
$885$	−17.1608	+	5.03887i	−0.576854	+	0.169380i
$886$		0			0
$887$	29.9006	−	19.2159i	1.00396	−	0.645208i	0.0681392	−	0.997676i	$-0.478294\pi$
$887$	29.9006	−	19.2159i	1.00396	−	0.645208i	0.935824	+	0.352468i	$0.114657\pi$
$888$		0			0
$889$	33.3171	−	9.78279i	1.11742	−	0.328104i
$890$		0			0
$891$	1.86932	−	2.15732i	0.0626247	−	0.0722728i
$892$		0			0
$893$	−47.6636	−	55.0067i	−1.59500	−	1.84073i
$894$		0			0
$895$	−38.3518	−	11.2611i	−1.28196	−	0.376417i
$896$		0			0
$897$	−34.2007	−	10.0422i	−1.14193	−	0.335300i
$898$		0			0
$899$	−0.336406	−	0.736626i	−0.0112198	−	0.0245679i
$900$		0			0
$901$	10.0712			0.335520
$902$		0			0
$903$	6.73995	+	7.77832i	0.224292	+	0.258846i
$904$		0			0
$905$	12.4577	−	86.6451i	0.414107	−	2.88018i
$906$		0			0
$907$	4.38828	+	9.60898i	0.145710	+	0.319061i	0.968389	−	0.249446i	$-0.0802485\pi$
$907$	4.38828	+	9.60898i	0.145710	+	0.319061i	−0.822678	+	0.568507i	$0.807521\pi$
$908$		0			0
$909$	10.7547			0.356710
$910$		0			0
$911$	16.3912	+	10.5340i	0.543064	+	0.349006i	0.783236	−	0.621724i	$-0.213568\pi$
$911$	16.3912	+	10.5340i	0.543064	+	0.349006i	−0.240172	+	0.970730i	$0.577204\pi$
$912$		0			0
$913$	−3.46426	+	7.58566i	−0.114650	+	0.251049i
$914$		0			0
$915$	−31.8124	+	36.7135i	−1.05169	+	1.21371i
$916$		0			0
$917$	48.8644	+	31.4033i	1.61365	+	1.03703i
$918$		0			0
$919$	1.33396	−	9.27790i	0.0440033	−	0.306050i	−0.955920	−	0.293629i	$-0.905137\pi$
$919$	1.33396	−	9.27790i	0.0440033	−	0.306050i	0.999923	−	0.0124210i	$-0.00395381\pi$
$920$		0			0
$921$	3.11703	+	0.915242i	0.102710	+	0.0301583i
$922$		0			0
$923$	−9.11634	+	63.4055i	−0.300068	+	2.08702i
$924$		0			0
$925$	28.9443	−	63.3793i	0.951684	−	2.08390i
$926$		0			0
$927$	−5.81150	+	3.73482i	−0.190875	+	0.122668i
$928$		0			0
$929$	2.48848	+	17.3078i	0.0816444	+	0.567849i	0.989049	+	0.147590i	$0.0471516\pi$
$929$	2.48848	+	17.3078i	0.0816444	+	0.567849i	−0.907404	+	0.420259i	$0.861939\pi$
$930$		0			0
$931$	−8.82764	−	61.3976i	−0.289314	−	2.01222i
$932$		0			0
$933$	13.0738	−	8.40204i	0.428018	−	0.275070i
$934$		0			0
$935$	−8.95022	+	10.3291i	−0.292703	+	0.337798i
$936$		0			0
$937$	−27.5893			−0.901304			−0.450652	−	0.892700i	$-0.648809\pi$
$937$	−27.5893			−0.901304			−0.450652	+	0.892700i	$0.648809\pi$
$938$		0			0
$939$	−9.62973			−0.314254
$940$		0			0
$941$	−3.07707	+	3.55113i	−0.100310	+	0.115763i	−0.803685	−	0.595056i	$-0.797130\pi$
$941$	−3.07707	+	3.55113i	−0.100310	+	0.115763i	0.703375	+	0.710819i	$0.251675\pi$
$942$		0			0
$943$	−16.2550	+	10.4464i	−0.529334	+	0.340183i
$944$		0			0
$945$	2.22048	+	15.4438i	0.0722322	+	0.502386i
$946$		0			0
$947$	−3.14064	−	21.8436i	−0.102057	−	0.709822i	−0.975033	−	0.222059i	$-0.928722\pi$
$947$	−3.14064	−	21.8436i	−0.102057	−	0.709822i	0.872976	−	0.487763i	$-0.162187\pi$
$948$		0			0
$949$	21.0681	−	13.5396i	0.683898	−	0.439515i
$950$		0			0
$951$	−10.3746	+	22.7171i	−0.336418	+	0.736653i
$952$		0			0
$953$	−2.11412	+	14.7040i	−0.0684830	+	0.476310i	0.926502	+	0.376289i	$0.122800\pi$
$953$	−2.11412	+	14.7040i	−0.0684830	+	0.476310i	−0.994985	+	0.100021i	$0.968109\pi$
$954$		0			0
$955$	−78.7404	−	23.1203i	−2.54798	−	0.748154i
$956$		0			0
$957$	−1.35368	+	9.41505i	−0.0437582	+	0.304345i
$958$		0			0
$959$	30.6157	+	19.6755i	0.988634	+	0.635356i
$960$		0			0
$961$	20.2620	−	23.3836i	0.653613	−	0.754310i
$962$		0			0
$963$	−2.39711	+	5.24894i	−0.0772458	+	0.169145i
$964$		0			0
$965$	−60.9640	−	39.1792i	−1.96250	−	1.26122i
$966$		0			0
$967$	−1.32352			−0.0425614			−0.0212807	−	0.999774i	$-0.506774\pi$
$967$	−1.32352			−0.0425614			−0.0212807	+	0.999774i	$0.506774\pi$
$968$		0			0
$969$	−3.47141	−	7.60134i	−0.111518	−	0.244190i
$970$		0			0
$971$	5.31372	−	36.9577i	0.170525	−	1.18603i	−0.707252	−	0.706961i	$-0.750065\pi$
$971$	5.31372	−	36.9577i	0.170525	−	1.18603i	0.877777	−	0.479069i	$-0.159025\pi$
$972$		0			0
$973$	41.9825	+	48.4503i	1.34590	+	1.55325i
$974$		0			0
$975$	−49.4276			−1.58295
$976$		0			0
$977$	−21.8121	−	47.7618i	−0.697831	−	1.52804i	−0.842582	−	0.538568i	$-0.818965\pi$
$977$	−21.8121	−	47.7618i	−0.697831	−	1.52804i	0.144751	−	0.989468i	$-0.453762\pi$
$978$		0			0
$979$	25.4172	+	7.46318i	0.812339	+	0.238524i
$980$		0			0
$981$	−13.4696	−	3.95504i	−0.430052	−	0.126275i
$982$		0			0
$983$	4.81579	+	5.55772i	0.153600	+	0.177264i	0.827334	−	0.561710i	$-0.189856\pi$
$983$	4.81579	+	5.55772i	0.153600	+	0.177264i	−0.673734	+	0.738974i	$0.735311\pi$
$984$		0			0
$985$	27.1611	−	31.3456i	0.865425	−	0.998753i
$986$		0			0
$987$	41.4312	−	12.1653i	1.31877	−	0.387226i
$988$		0			0
$989$	−15.6411	+	10.0519i	−0.497358	+	0.319632i
$990$		0			0
$991$	−5.86337	+	1.72164i	−0.186256	+	0.0546897i	−0.373530	−	0.927618i	$-0.621853\pi$
$991$	−5.86337	+	1.72164i	−0.186256	+	0.0546897i	0.187274	+	0.982308i	$0.440035\pi$
$992$		0			0
$993$	−11.3305	+	24.8104i	−0.359564	+	0.787335i
$994$		0			0
$995$	32.9514	+	38.0280i	1.04463	+	1.20557i
$996$		0			0
$997$	7.70031	+	16.8613i	0.243871	+	0.534004i	0.991499	−	0.130114i	$-0.0415344\pi$
$997$	7.70031	+	16.8613i	0.243871	+	0.534004i	−0.747628	+	0.664118i	$0.768807\pi$
$998$		0			0
$999$	5.82156	+	3.74129i	0.184186	+	0.118369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.25.6	✓	60
67.59	even	11	inner	804.2.q.a.193.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.25.6	✓	60	1.1	even	1	trivial
804.2.q.a.193.6	yes	60	67.59	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{3} +(3.26560 - 2.09868i) q^{5} +(0.572019 + 3.97848i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{3} +(3.26560 - 2.09868i) q^{5} +(0.572019 + 3.97848i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-2.40139 + 1.54328i) q^{11} +(-2.03931 + 4.46546i) q^{13} +(-0.552442 + 3.84232i) q^{15} +(1.18346 + 0.347496i) q^{17} +(-0.964189 + 6.70608i) q^{19} +(-3.38133 - 2.17305i) q^{21} +(4.75490 - 5.48745i) q^{23} +(4.18265 - 9.15872i) q^{25} +(0.841254 + 0.540641i) q^{27} -3.33219 q^{29} +(0.100956 + 0.221064i) q^{31} +(0.406243 - 2.82548i) q^{33} +(10.2175 + 11.7917i) q^{35} +6.92010 q^{37} +(-2.03931 - 4.46546i) q^{39} +(-2.55334 - 0.749727i) q^{41} +(-2.45691 - 0.721414i) q^{43} +(-2.54206 - 2.93369i) q^{45} +(-7.03517 + 8.11902i) q^{47} +(-8.78465 + 2.57941i) q^{49} +(-1.03762 + 0.666839i) q^{51} +(7.83449 - 2.30041i) q^{53} +(-4.60314 + 10.0795i) q^{55} +(-4.43671 - 5.12023i) q^{57} +(1.91400 + 4.19107i) q^{59} +(10.5278 + 6.76581i) q^{61} +(3.85658 - 1.13239i) q^{63} +(2.71198 + 18.8623i) q^{65} +(3.55850 - 7.37137i) q^{67} +(1.03334 + 7.18703i) q^{69} +(12.5202 - 3.67626i) q^{71} +(-4.29165 - 2.75807i) q^{73} +(4.18265 + 9.15872i) q^{75} +(-7.51355 - 8.67110i) q^{77} +(-1.47497 + 3.22973i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(2.45764 - 1.57943i) q^{83} +(4.59400 - 1.34892i) q^{85} +(2.18212 - 2.51830i) q^{87} +(-6.07715 - 7.01340i) q^{89} +(-18.9323 - 5.55901i) q^{91} +(-0.233181 - 0.0684682i) q^{93} +(10.9252 + 23.9229i) q^{95} -16.7003 q^{97} +(1.86932 + 2.15732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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