LMFDB - Embedded newform 804.2.q.b.193.2

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			193.2
Character	$\chi$	$=$	804.193
Dual form			804.2.q.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-1.48760 - 0.956023i) q^{5} +(-0.105071 + 0.730785i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-1.48760 - 0.956023i) q^{5} +(-0.105071 + 0.730785i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.50272 - 1.60840i) q^{11} +(-2.69174 - 5.89410i) q^{13} +(-0.251658 - 1.75032i) q^{15} +(-3.71302 + 1.09024i) q^{17} +(-0.939824 - 6.53662i) q^{19} +(-0.621097 + 0.399155i) q^{21} +(4.18984 + 4.83534i) q^{23} +(-0.778098 - 1.70380i) q^{25} +(-0.841254 + 0.540641i) q^{27} +7.01799 q^{29} +(2.16207 - 4.73427i) q^{31} +(-0.423385 - 2.94471i) q^{33} +(0.854951 - 0.986666i) q^{35} -4.77012 q^{37} +(2.69174 - 5.89410i) q^{39} +(-5.36252 + 1.57458i) q^{41} +(-4.08414 + 1.19921i) q^{43} +(1.15800 - 1.33640i) q^{45} +(-3.54575 - 4.09201i) q^{47} +(6.19344 + 1.81856i) q^{49} +(-3.25546 - 2.09216i) q^{51} +(-12.4504 - 3.65577i) q^{53} +(2.18538 + 4.78532i) q^{55} +(4.32459 - 4.99085i) q^{57} +(-0.638345 + 1.39778i) q^{59} +(-4.33100 + 2.78336i) q^{61} +(-0.708393 - 0.208003i) q^{63} +(-1.63065 + 11.3414i) q^{65} +(2.02680 - 7.93045i) q^{67} +(-0.910540 + 6.33294i) q^{69} +(9.87363 + 2.89916i) q^{71} +(13.8272 - 8.88621i) q^{73} +(0.778098 - 1.70380i) q^{75} +(1.43836 - 1.65995i) q^{77} +(-0.387067 - 0.847559i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-8.20888 - 5.27553i) q^{83} +(6.56580 + 1.92789i) q^{85} +(4.59581 + 5.30384i) q^{87} +(-2.24252 + 2.58801i) q^{89} +(4.59014 - 1.34779i) q^{91} +(4.99377 - 1.46630i) q^{93} +(-4.85108 + 10.6224i) q^{95} -5.05052 q^{97} +(1.94820 - 2.24835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$	$1$

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
$5$	−1.48760	−	0.956023i	−0.665276	−	0.427547i	0.163944	−	0.986470i	$-0.447578\pi$
$5$	−1.48760	−	0.956023i	−0.665276	−	0.427547i	−0.829220	+	0.558923i	$0.811215\pi$
$6$		0			0
$7$	−0.105071	+	0.730785i	−0.0397131	+	0.276211i	−0.999996	−	0.00281747i	$-0.999103\pi$
$7$	−0.105071	+	0.730785i	−0.0397131	+	0.276211i	0.960283	+	0.279028i	$0.0900123\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−2.50272	−	1.60840i	−0.754598	−	0.484951i	0.105917	−	0.994375i	$-0.466222\pi$
$11$	−2.50272	−	1.60840i	−0.754598	−	0.484951i	−0.860516	+	0.509424i	$0.829858\pi$
$12$		0			0
$13$	−2.69174	−	5.89410i	−0.746555	−	1.63473i	−0.772460	−	0.635064i	$-0.780974\pi$
$13$	−2.69174	−	5.89410i	−0.746555	−	1.63473i	0.0259045	−	0.999664i	$-0.491753\pi$
$14$		0			0
$15$	−0.251658	−	1.75032i	−0.0649777	−	0.451930i
$16$		0			0
$17$	−3.71302	+	1.09024i	−0.900540	+	0.264423i	−0.699054	−	0.715069i	$-0.746395\pi$
$17$	−3.71302	+	1.09024i	−0.900540	+	0.264423i	−0.201486	+	0.979491i	$0.564577\pi$
$18$		0			0
$19$	−0.939824	−	6.53662i	−0.215610	−	1.49960i	−0.753982	−	0.656895i	$-0.771869\pi$
$19$	−0.939824	−	6.53662i	−0.215610	−	1.49960i	0.538371	−	0.842708i	$-0.319040\pi$
$20$		0			0
$21$	−0.621097	+	0.399155i	−0.135534	+	0.0871027i
$22$		0			0
$23$	4.18984	+	4.83534i	0.873643	+	1.00824i	0.999868	+	0.0162358i	$0.00516824\pi$
$23$	4.18984	+	4.83534i	0.873643	+	1.00824i	−0.126226	+	0.992002i	$0.540286\pi$
$24$		0			0
$25$	−0.778098	−	1.70380i	−0.155620	−	0.340759i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	7.01799			1.30321			0.651604	−	0.758559i	$-0.274096\pi$
$29$	7.01799			1.30321			0.651604	+	0.758559i	$0.274096\pi$
$30$		0			0
$31$	2.16207	−	4.73427i	0.388319	−	0.850299i	−0.610004	−	0.792399i	$-0.708832\pi$
$31$	2.16207	−	4.73427i	0.388319	−	0.850299i	0.998322	−	0.0579007i	$-0.0184407\pi$
$32$		0			0
$33$	−0.423385	−	2.94471i	−0.0737019	−	0.512608i
$34$		0			0
$35$	0.854951	−	0.986666i	0.144513	−	0.166777i
$36$		0			0
$37$	−4.77012			−0.784203			−0.392101	−	0.919922i	$-0.628252\pi$
$37$	−4.77012			−0.784203			−0.392101	+	0.919922i	$0.628252\pi$
$38$		0			0
$39$	2.69174	−	5.89410i	0.431024	−	0.943811i
$40$		0			0
$41$	−5.36252	+	1.57458i	−0.837484	+	0.245908i	−0.672229	−	0.740343i	$-0.734663\pi$
$41$	−5.36252	+	1.57458i	−0.837484	+	0.245908i	−0.165255	+	0.986251i	$0.552845\pi$
$42$		0			0
$43$	−4.08414	+	1.19921i	−0.622826	+	0.182878i	−0.577894	−	0.816112i	$-0.696125\pi$
$43$	−4.08414	+	1.19921i	−0.622826	+	0.182878i	−0.0449320	+	0.998990i	$0.514307\pi$
$44$		0			0
$45$	1.15800	−	1.33640i	0.172624	−	0.199219i
$46$		0			0
$47$	−3.54575	−	4.09201i	−0.517200	−	0.596881i	0.435727	−	0.900079i	$-0.356491\pi$
$47$	−3.54575	−	4.09201i	−0.517200	−	0.596881i	−0.952928	+	0.303198i	$0.901946\pi$
$48$		0			0
$49$	6.19344	+	1.81856i	0.884778	+	0.259794i
$50$		0			0
$51$	−3.25546	−	2.09216i	−0.455856	−	0.292961i
$52$		0			0
$53$	−12.4504	−	3.65577i	−1.71019	−	0.502158i	−0.727299	−	0.686321i	$-0.759225\pi$
$53$	−12.4504	−	3.65577i	−1.71019	−	0.502158i	−0.982896	+	0.184163i	$0.941043\pi$
$54$		0			0
$55$	2.18538	+	4.78532i	0.294677	+	0.645252i
$56$		0			0
$57$	4.32459	−	4.99085i	0.572806	−	0.661054i
$58$		0			0
$59$	−0.638345	+	1.39778i	−0.0831054	+	0.181975i	−0.946623	−	0.322344i	$-0.895529\pi$
$59$	−0.638345	+	1.39778i	−0.0831054	+	0.181975i	0.863517	+	0.504319i	$0.168257\pi$
$60$		0			0
$61$	−4.33100	+	2.78336i	−0.554528	+	0.356373i	−0.787697	−	0.616063i	$-0.788727\pi$
$61$	−4.33100	+	2.78336i	−0.554528	+	0.356373i	0.233169	+	0.972436i	$0.425090\pi$
$62$		0			0
$63$	−0.708393	−	0.208003i	−0.0892491	−	0.0262059i
$64$		0			0
$65$	−1.63065	+	11.3414i	−0.202258	+	1.40673i
$66$		0			0
$67$	2.02680	−	7.93045i	0.247614	−	0.968859i
$67$	2.02680	−	7.93045i	0.247614	−	0.968859i
$68$		0			0
$69$	−0.910540	+	6.33294i	−0.109616	+	0.762397i
$70$		0			0
$71$	9.87363	+	2.89916i	1.17178	+	0.344067i	0.809002	−	0.587806i	$-0.200008\pi$
$71$	9.87363	+	2.89916i	1.17178	+	0.344067i	0.362783	+	0.931874i	$0.381827\pi$
$72$		0			0
$73$	13.8272	−	8.88621i	1.61835	−	1.04005i	0.661308	−	0.750114i	$-0.270002\pi$
$73$	13.8272	−	8.88621i	1.61835	−	1.04005i	0.957045	−	0.289938i	$-0.0936348\pi$
$74$		0			0
$75$	0.778098	−	1.70380i	0.0898470	−	0.196737i
$76$		0			0
$77$	1.43836	−	1.65995i	0.163916	−	0.189169i
$78$		0			0
$79$	−0.387067	−	0.847559i	−0.0435485	−	0.0953578i	0.886607	−	0.462523i	$-0.153056\pi$
$79$	−0.387067	−	0.847559i	−0.0435485	−	0.0953578i	−0.930156	+	0.367165i	$0.880328\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−8.20888	−	5.27553i	−0.901042	−	0.579064i	0.00605745	−	0.999982i	$-0.498072\pi$
$83$	−8.20888	−	5.27553i	−0.901042	−	0.579064i	−0.907099	+	0.420917i	$0.861708\pi$
$84$		0			0
$85$	6.56580	+	1.92789i	0.712161	+	0.209109i
$86$		0			0
$87$	4.59581	+	5.30384i	0.492722	+	0.568632i
$88$		0			0
$89$	−2.24252	+	2.58801i	−0.237707	+	0.274328i	−0.862051	−	0.506821i	$-0.830821\pi$
$89$	−2.24252	+	2.58801i	−0.237707	+	0.274328i	0.624345	+	0.781149i	$0.285366\pi$
$90$		0			0
$91$	4.59014	−	1.34779i	0.481177	−	0.141286i
$92$		0			0
$93$	4.99377	−	1.46630i	0.517830	−	0.152049i
$94$		0			0
$95$	−4.85108	+	10.6224i	−0.497710	+	1.08983i
$96$		0			0
$97$	−5.05052			−0.512802			−0.256401	−	0.966570i	$-0.582537\pi$
$97$	−5.05052			−0.512802			−0.256401	+	0.966570i	$0.582537\pi$
$98$		0			0
$99$	1.94820	−	2.24835i	0.195802	−	0.225967i
$100$		0			0
$101$	0.494284	+	3.43782i	0.0491831	+	0.342076i	0.999524	+	0.0308641i	$0.00982589\pi$
$101$	0.494284	+	3.43782i	0.0491831	+	0.342076i	−0.950340	+	0.311212i	$0.899265\pi$
$102$		0			0
$103$	−3.76865	+	8.25219i	−0.371336	+	0.813112i	0.628053	+	0.778170i	$0.283852\pi$
$103$	−3.76865	+	8.25219i	−0.371336	+	0.813112i	−0.999389	+	0.0349420i	$0.988875\pi$
$104$		0			0
$105$	1.30555			0.127408
$106$		0			0
$107$	13.3015	−	8.54836i	1.28591	−	0.826401i	0.294301	−	0.955713i	$-0.404913\pi$
$107$	13.3015	−	8.54836i	1.28591	−	0.826401i	0.991604	+	0.129312i	$0.0412768\pi$
$108$		0			0
$109$	6.13972	+	13.4441i	0.588079	+	1.28771i	0.936596	+	0.350410i	$0.113958\pi$
$109$	6.13972	+	13.4441i	0.588079	+	1.28771i	−0.348518	+	0.937302i	$0.613315\pi$
$110$		0			0
$111$	−3.12376	−	3.60502i	−0.296495	−	0.342173i
$112$		0			0
$113$	−9.11915	+	5.86052i	−0.857857	+	0.551311i	−0.894016	−	0.448035i	$-0.852124\pi$
$113$	−9.11915	+	5.86052i	−0.857857	+	0.551311i	0.0361590	+	0.999346i	$0.488488\pi$
$114$		0			0
$115$	−1.61012	−	11.1986i	−0.150145	−	1.04428i
$116$		0			0
$117$	6.21718	−	1.82553i	0.574778	−	0.168770i
$118$		0			0
$119$	−0.406601	−	2.82797i	−0.0372731	−	0.259240i
$120$		0			0
$121$	−0.892911	−	1.95520i	−0.0811738	−	0.177746i
$122$		0			0
$123$	−4.70169	−	3.02159i	−0.423937	−	0.272448i
$124$		0			0
$125$	−1.72966	+	12.0300i	−0.154705	+	1.07600i
$126$		0			0
$127$	−2.08379	+	14.4930i	−0.184906	+	1.28605i	0.660053	+	0.751219i	$0.270534\pi$
$127$	−2.08379	+	14.4930i	−0.184906	+	1.28605i	−0.844959	+	0.534831i	$0.820375\pi$
$128$		0			0
$129$	−3.58085	−	2.30127i	−0.315276	−	0.202616i
$130$		0			0
$131$	−9.65506	−	11.1425i	−0.843566	−	0.973527i	0.156333	−	0.987704i	$-0.450033\pi$
$131$	−9.65506	−	11.1425i	−0.843566	−	0.973527i	−0.999900	+	0.0141770i	$0.995487\pi$
$132$		0			0
$133$	4.87561			0.422769
$134$		0			0
$135$	1.76832			0.152192
$136$		0			0
$137$	11.2791	+	13.0168i	0.963637	+	1.11210i	0.993646	+	0.112547i	$0.0359008\pi$
$137$	11.2791	+	13.0168i	0.963637	+	1.11210i	−0.0300096	+	0.999550i	$0.509554\pi$
$138$		0			0
$139$	−16.7655	−	10.7746i	−1.42203	−	0.913886i	−0.999973	−	0.00731819i	$-0.997671\pi$
$139$	−16.7655	−	10.7746i	−1.42203	−	0.913886i	−0.422061	−	0.906568i	$-0.638693\pi$
$140$		0			0
$141$	0.770564	−	5.35939i	0.0648932	−	0.451342i
$142$		0			0
$143$	−2.74339	+	19.0807i	−0.229413	+	1.59561i
$144$		0			0
$145$	−10.4400	−	6.70936i	−0.866992	−	0.557182i
$146$		0			0
$147$	2.68147	+	5.87160i	0.221164	+	0.484281i
$148$		0			0
$149$	1.44779	+	10.0696i	0.118607	+	0.824932i	0.959092	+	0.283096i	$0.0913614\pi$
$149$	1.44779	+	10.0696i	0.118607	+	0.824932i	−0.840484	+	0.541836i	$0.817729\pi$
$150$		0			0
$151$	−2.00719	+	0.589364i	−0.163343	+	0.0479618i	−0.362381	−	0.932030i	$-0.618036\pi$
$151$	−2.00719	+	0.589364i	−0.163343	+	0.0479618i	0.199039	+	0.979992i	$0.436218\pi$
$152$		0			0
$153$	−0.550727	−	3.83039i	−0.0445236	−	0.309669i
$154$		0			0
$155$	−7.74236	+	4.97571i	−0.621882	+	0.399659i
$156$		0			0
$157$	−0.271501	−	0.313329i	−0.0216681	−	0.0250064i	0.744812	−	0.667274i	$-0.232539\pi$
$157$	−0.271501	−	0.313329i	−0.0216681	−	0.0250064i	−0.766480	+	0.642268i	$0.777994\pi$
$158$		0			0
$159$	−5.39044	−	11.8034i	−0.427489	−	0.936071i
$160$		0			0
$161$	−3.97382	+	2.55382i	−0.313181	+	0.201269i
$162$		0			0
$163$	21.5970			1.69160			0.845802	−	0.533497i	$-0.179122\pi$
$163$	21.5970			1.69160			0.845802	+	0.533497i	$0.179122\pi$
$164$		0			0
$165$	−2.18538	+	4.78532i	−0.170132	+	0.372536i
$166$		0			0
$167$	−2.92030	−	20.3111i	−0.225980	−	1.57172i	−0.714794	−	0.699335i	$-0.753480\pi$
$167$	−2.92030	−	20.3111i	−0.225980	−	1.57172i	0.488814	−	0.872388i	$-0.337430\pi$
$168$		0			0
$169$	−18.9817	+	21.9060i	−1.46013	+	1.68508i
$170$		0			0
$171$	6.60384			0.505008
$172$		0			0
$173$	−8.68144	+	19.0097i	−0.660038	+	1.44528i	0.222449	+	0.974944i	$0.428595\pi$
$173$	−8.68144	+	19.0097i	−0.660038	+	1.44528i	−0.882487	+	0.470337i	$0.844132\pi$
$174$		0			0
$175$	1.32686	−	0.389602i	0.100301	−	0.0294512i
$176$		0			0
$177$	−1.47440	+	0.432923i	−0.110823	+	0.0325404i
$178$		0			0
$179$	11.4291	−	13.1899i	0.854252	−	0.985859i	−0.145742	−	0.989323i	$-0.546557\pi$
$179$	11.4291	−	13.1899i	0.854252	−	0.985859i	0.999994	+	0.00346358i	$0.00110250\pi$
$180$		0			0
$181$	9.84190	+	11.3582i	0.731543	+	0.844246i	0.992644	−	0.121066i	$-0.0386312\pi$
$181$	9.84190	+	11.3582i	0.731543	+	0.844246i	−0.261102	+	0.965311i	$0.584086\pi$
$182$		0			0
$183$	−4.93973	−	1.45044i	−0.365155	−	0.107219i
$184$		0			0
$185$	7.09604	+	4.56035i	0.521711	+	0.335283i
$186$		0			0
$187$	11.0462	+	3.24346i	0.807778	+	0.237185i
$188$		0			0
$189$	−0.306701	−	0.671581i	−0.0223092	−	0.0488503i
$190$		0			0
$191$	2.71479	−	3.13303i	0.196435	−	0.226698i	−0.648984	−	0.760802i	$-0.724806\pi$
$191$	2.71479	−	3.13303i	0.196435	−	0.226698i	0.845419	+	0.534104i	$0.179351\pi$
$192$		0			0
$193$	9.97110	−	21.8337i	0.717736	−	1.57162i	−0.0993153	−	0.995056i	$-0.531665\pi$
$193$	9.97110	−	21.8337i	0.717736	−	1.57162i	0.817051	−	0.576566i	$-0.195607\pi$
$194$		0			0
$195$	−9.63914	+	6.19470i	−0.690273	+	0.443611i
$196$		0			0
$197$	15.7553	+	4.62617i	1.12252	+	0.329601i	0.789763	−	0.613412i	$-0.210204\pi$
$197$	15.7553	+	4.62617i	1.12252	+	0.329601i	0.332755	+	0.943013i	$0.392022\pi$
$198$		0			0
$199$	1.51142	−	10.5121i	0.107141	−	0.745185i	−0.863447	−	0.504440i	$-0.831699\pi$
$199$	1.51142	−	10.5121i	0.107141	−	0.745185i	0.970588	−	0.240745i	$-0.0773918\pi$
$200$		0			0
$201$	7.32071	−	3.66158i	0.516363	−	0.258268i
$202$		0			0
$203$	−0.737387	+	5.12864i	−0.0517544	+	0.359960i
$204$		0			0
$205$	9.48262	+	2.78435i	0.662295	+	0.194467i
$206$		0			0
$207$	−5.38240	+	3.45906i	−0.374102	+	0.240421i
$208$		0			0
$209$	−8.16138	+	17.8709i	−0.564535	+	1.23616i
$210$		0			0
$211$	−2.59792	+	2.99816i	−0.178848	+	0.206402i	−0.838094	−	0.545526i	$-0.816330\pi$
$211$	−2.59792	+	2.99816i	−0.178848	+	0.206402i	0.659246	+	0.751927i	$0.270876\pi$
$212$		0			0
$213$	4.27482	+	9.36054i	0.292906	+	0.641374i
$214$		0			0
$215$	7.22205	+	2.12059i	0.492540	+	0.144623i
$216$		0			0
$217$	3.23256	+	2.07744i	0.219440	+	0.141026i
$218$		0			0
$219$	15.7707	+	4.63068i	1.06568	+	0.312912i
$220$		0			0
$221$	16.4205	+	18.9503i	1.10456	+	1.27473i
$222$		0			0
$223$	−0.404679	+	0.467024i	−0.0270993	+	0.0312743i	−0.769137	−	0.639083i	$-0.779314\pi$
$223$	−0.404679	+	0.467024i	−0.0270993	+	0.0312743i	0.742038	+	0.670358i	$0.233859\pi$
$224$		0			0
$225$	1.79719	−	0.527702i	0.119813	−	0.0351802i
$226$		0			0
$227$	−6.26085	+	1.83835i	−0.415547	+	0.122016i	−0.482821	−	0.875719i	$-0.660388\pi$
$227$	−6.26085	+	1.83835i	−0.415547	+	0.122016i	0.0672741	+	0.997735i	$0.478570\pi$
$228$		0			0
$229$	0.264402	−	0.578959i	0.0174721	−	0.0382587i	−0.900695	−	0.434452i	$-0.856942\pi$
$229$	0.264402	−	0.578959i	0.0174721	−	0.0382587i	0.918167	+	0.396194i	$0.129669\pi$
$230$		0			0
$231$	2.19643			0.144515
$232$		0			0
$233$	−6.32624	+	7.30087i	−0.414446	+	0.478296i	−0.924137	−	0.382062i	$-0.875214\pi$
$233$	−6.32624	+	7.30087i	−0.414446	+	0.478296i	0.509691	+	0.860357i	$0.329760\pi$
$234$		0			0
$235$	1.36260	+	9.47710i	0.0888863	+	0.618218i
$236$		0			0
$237$	0.387067	−	0.847559i	0.0251427	−	0.0550549i
$238$		0			0
$239$	0.455619			0.0294716			0.0147358	−	0.999891i	$-0.495309\pi$
$239$	0.455619			0.0294716			0.0147358	+	0.999891i	$0.495309\pi$
$240$		0			0
$241$	13.6846	−	8.79457i	0.881503	−	0.566508i	−0.0197478	−	0.999805i	$-0.506286\pi$
$241$	13.6846	−	8.79457i	0.881503	−	0.566508i	0.901251	+	0.433297i	$0.142650\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−7.47479	−	8.62637i	−0.477547	−	0.551119i
$246$		0			0
$247$	−35.9977	+	23.1343i	−2.29048	+	1.47200i
$248$		0			0
$249$	−1.38870	−	9.65859i	−0.0880050	−	0.612088i
$250$		0			0
$251$	5.45796	−	1.60260i	0.344503	−	0.101155i	−0.104904	−	0.994482i	$-0.533453\pi$
$251$	5.45796	−	1.60260i	0.344503	−	0.101155i	0.449407	+	0.893327i	$0.351635\pi$
$252$		0			0
$253$	−2.70885	−	18.8404i	−0.170304	−	1.18449i
$254$		0			0
$255$	2.84268	+	6.22460i	0.178015	+	0.389799i
$256$		0			0
$257$	0.483698	+	0.310854i	0.0301723	+	0.0193905i	0.555640	−	0.831423i	$-0.312473\pi$
$257$	0.483698	+	0.310854i	0.0301723	+	0.0193905i	−0.525468	+	0.850814i	$0.676110\pi$
$258$		0			0
$259$	0.501201	−	3.48593i	0.0311431	−	0.216605i
$260$		0			0
$261$	−0.998764	+	6.94656i	−0.0618219	+	0.429981i
$262$		0			0
$263$	−13.5317	−	8.69627i	−0.834398	−	0.536235i	0.0522745	−	0.998633i	$-0.483353\pi$
$263$	−13.5317	−	8.69627i	−0.834398	−	0.536235i	−0.886673	+	0.462398i	$0.846989\pi$
$264$		0			0
$265$	15.0262	+	17.3412i	0.923055	+	1.06526i
$266$		0			0
$267$	−3.42442			−0.209571
$268$		0			0
$269$	3.87866			0.236486			0.118243	−	0.992985i	$-0.462274\pi$
$269$	3.87866			0.236486			0.118243	+	0.992985i	$0.462274\pi$
$270$		0			0
$271$	4.95964	+	5.72373i	0.301277	+	0.347692i	0.886121	−	0.463453i	$-0.153390\pi$
$271$	4.95964	+	5.72373i	0.301277	+	0.347692i	−0.584844	+	0.811145i	$0.698844\pi$
$272$		0			0
$273$	4.02449	+	2.58638i	0.243573	+	0.156535i
$274$		0			0
$275$	−0.793026	+	5.51562i	−0.0478213	+	0.332604i
$276$		0			0
$277$	3.39594	−	23.6193i	0.204042	−	1.41915i	−0.588090	−	0.808796i	$-0.700120\pi$
$277$	3.39594	−	23.6193i	0.204042	−	1.41915i	0.792132	−	0.610350i	$-0.208971\pi$
$278$		0			0
$279$	4.37838	+	2.81382i	0.262127	+	0.168459i
$280$		0			0
$281$	−5.09748	−	11.1619i	−0.304090	−	0.665864i	0.694469	−	0.719522i	$-0.255639\pi$
$281$	−5.09748	−	11.1619i	−0.304090	−	0.665864i	−0.998559	+	0.0536581i	$0.982912\pi$
$282$		0			0
$283$	1.71507	+	11.9286i	0.101950	+	0.709081i	0.975122	+	0.221668i	$0.0711501\pi$
$283$	1.71507	+	11.9286i	0.101950	+	0.709081i	−0.873172	+	0.487413i	$0.837941\pi$
$284$		0			0
$285$	−11.2046	+	3.28998i	−0.663705	+	0.194881i
$286$		0			0
$287$	−0.587232	−	4.08429i	−0.0346632	−	0.241088i
$288$		0			0
$289$	−1.70339	+	1.09471i	−0.100200	+	0.0643944i
$290$		0			0
$291$	−3.30739	−	3.81693i	−0.193882	−	0.223752i
$292$		0			0
$293$	−6.39464	−	14.0023i	−0.373579	−	0.818023i	−0.999279	−	0.0379600i	$-0.987914\pi$
$293$	−6.39464	−	14.0023i	−0.373579	−	0.818023i	0.625700	−	0.780063i	$-0.284813\pi$
$294$		0			0
$295$	2.28591	−	1.46907i	0.133091	−	0.0855324i
$296$		0			0
$297$	2.97499			0.172626
$298$		0			0
$299$	17.2220	−	37.7108i	0.995971	−	2.18087i
$300$		0			0
$301$	−0.447241	−	3.11063i	−0.0257786	−	0.179294i
$302$		0			0
$303$	−2.27445	+	2.62485i	−0.130664	+	0.150794i
$304$		0			0
$305$	9.10376			0.521280
$306$		0			0
$307$	9.96207	−	21.8139i	0.568565	−	1.24498i	−0.378993	−	0.925400i	$-0.623729\pi$
$307$	9.96207	−	21.8139i	0.568565	−	1.24498i	0.947558	−	0.319584i	$-0.103543\pi$
$308$		0			0
$309$	−8.70453	+	2.55588i	−0.495183	+	0.145399i
$310$		0			0
$311$	23.5974	−	6.92883i	1.33809	−	0.392898i	0.467100	−	0.884204i	$-0.345299\pi$
$311$	23.5974	−	6.92883i	1.33809	−	0.392898i	0.870987	+	0.491307i	$0.163481\pi$
$312$		0			0
$313$	−11.1285	+	12.8430i	−0.629022	+	0.725930i	−0.977394	−	0.211426i	$-0.932189\pi$
$313$	−11.1285	+	12.8430i	−0.629022	+	0.725930i	0.348372	+	0.937356i	$0.386735\pi$
$314$		0			0
$315$	0.854951	+	0.986666i	0.0481710	+	0.0555923i
$316$		0			0
$317$	−2.20012	−	0.646013i	−0.123571	−	0.0362837i	0.219362	−	0.975643i	$-0.429602\pi$
$317$	−2.20012	−	0.646013i	−0.123571	−	0.0362837i	−0.342933	+	0.939360i	$0.611420\pi$
$318$		0			0
$319$	−17.5641	−	11.2877i	−0.983398	−	0.631992i
$320$		0			0
$321$	15.1711	+	4.45462i	0.846766	+	0.248633i
$322$		0			0
$323$	10.6161	+	23.2460i	0.590695	+	1.29344i
$324$		0			0
$325$	−7.94790	+	9.17236i	−0.440870	+	0.508791i
$326$		0			0
$327$	−6.13972	+	13.4441i	−0.339527	+	0.743461i
$328$		0			0
$329$	3.36293	−	2.16123i	0.185404	−	0.119152i
$330$		0			0
$331$	8.57734	+	2.51853i	0.471453	+	0.138431i	0.508824	−	0.860870i	$-0.330080\pi$
$331$	8.57734	+	2.51853i	0.471453	+	0.138431i	−0.0373712	+	0.999301i	$0.511898\pi$
$332$		0			0
$333$	0.678859	−	4.72157i	0.0372012	−	0.258740i
$334$		0			0
$335$	−10.5968	+	9.85968i	−0.578964	+	0.538692i
$336$		0			0
$337$	2.27861	−	15.8481i	0.124124	−	0.863302i	−0.828682	−	0.559720i	$-0.810909\pi$
$337$	2.27861	−	15.8481i	0.124124	−	0.863302i	0.952806	−	0.303581i	$-0.0981824\pi$
$338$		0			0
$339$	−10.4009	−	3.05397i	−0.564897	−	0.165869i
$340$		0			0
$341$	−13.0256	+	8.37107i	−0.705378	+	0.453319i
$342$		0			0
$343$	−4.12663	+	9.03606i	−0.222817	+	0.487901i
$344$		0			0
$345$	7.40896	−	8.55040i	0.398885	−	0.460338i
$346$		0			0
$347$	−11.5827	−	25.3626i	−0.621792	−	1.36154i	−0.914208	−	0.405244i	$-0.867186\pi$
$347$	−11.5827	−	25.3626i	−0.621792	−	1.36154i	0.292416	−	0.956291i	$-0.405541\pi$
$348$		0			0
$349$	13.5873	+	3.98958i	0.727310	+	0.213558i	0.624369	−	0.781130i	$-0.285356\pi$
$349$	13.5873	+	3.98958i	0.727310	+	0.213558i	0.102942	+	0.994687i	$0.467174\pi$
$350$		0			0
$351$	5.45103	+	3.50316i	0.290954	+	0.186985i
$352$		0			0
$353$	−22.6461	−	6.64949i	−1.20533	−	0.353917i	−0.383441	−	0.923565i	$-0.625261\pi$
$353$	−22.6461	−	6.64949i	−1.20533	−	0.353917i	−0.821889	+	0.569648i	$0.807079\pi$
$354$		0			0
$355$	−11.9164	−	13.7522i	−0.632455	−	0.729892i
$356$		0			0
$357$	1.87097	−	2.15922i	0.0990224	−	0.114278i
$358$		0			0
$359$	7.11892	−	2.09030i	0.375722	−	0.110322i	−0.0884186	−	0.996083i	$-0.528181\pi$
$359$	7.11892	−	2.09030i	0.375722	−	0.110322i	0.464141	+	0.885761i	$0.346363\pi$
$360$		0			0
$361$	−23.6137	+	6.93362i	−1.24283	+	0.364927i
$362$		0			0
$363$	0.892911	−	1.95520i	0.0468657	−	0.102622i
$364$		0			0
$365$	−29.0648			−1.52132
$366$		0			0
$367$	17.5729	−	20.2803i	0.917300	−	1.05862i	−0.0807827	−	0.996732i	$-0.525742\pi$
$367$	17.5729	−	20.2803i	0.917300	−	1.05862i	0.998083	−	0.0618893i	$-0.0197126\pi$
$368$		0			0
$369$	−0.795384	−	5.53202i	−0.0414061	−	0.287985i
$370$		0			0
$371$	3.97976	−	8.71445i	0.206619	−	0.452432i
$372$		0			0
$373$	−18.4066			−0.953057			−0.476529	−	0.879159i	$-0.658105\pi$
$373$	−18.4066			−0.953057			−0.476529	+	0.879159i	$0.658105\pi$
$374$		0			0
$375$	−10.2244	+	6.57081i	−0.527984	+	0.339315i
$376$		0			0
$377$	−18.8906	−	41.3647i	−0.972917	−	2.13039i
$378$		0			0
$379$	0.297421	+	0.343242i	0.0152775	+	0.0176312i	0.763337	−	0.646001i	$-0.223560\pi$
$379$	0.297421	+	0.343242i	0.0152775	+	0.0176312i	−0.748059	+	0.663632i	$0.769014\pi$
$380$		0			0
$381$	−12.3177	+	7.91611i	−0.631055	+	0.405554i
$382$		0			0
$383$	1.85580	+	12.9074i	0.0948271	+	0.659537i	0.980687	+	0.195584i	$0.0626603\pi$
$383$	1.85580	+	12.9074i	0.0948271	+	0.659537i	−0.885860	+	0.463953i	$0.846431\pi$
$384$		0			0
$385$	−3.72666	+	1.09424i	−0.189928	+	0.0557679i
$386$		0			0
$387$	−0.605772	−	4.21324i	−0.0307931	−	0.214171i
$388$		0			0
$389$	−8.19821	−	17.9516i	−0.415666	−	0.910181i	−0.995439	−	0.0954030i	$-0.969586\pi$
$389$	−8.19821	−	17.9516i	−0.415666	−	0.910181i	0.579773	−	0.814778i	$-0.303141\pi$
$390$		0			0
$391$	−20.8287	−	13.3858i	−1.05335	−	0.676948i
$392$		0			0
$393$	2.09824	−	14.5936i	0.105842	−	0.736150i
$394$		0			0
$395$	−0.234485	+	1.63088i	−0.0117982	+	0.0820583i
$396$		0			0
$397$	10.7991	+	6.94018i	0.541993	+	0.348318i	0.782818	−	0.622251i	$-0.213782\pi$
$397$	10.7991	+	6.94018i	0.541993	+	0.348318i	−0.240825	+	0.970569i	$0.577418\pi$
$398$		0			0
$399$	3.19284	+	3.68474i	0.159842	+	0.184468i
$400$		0			0
$401$	9.40988			0.469907			0.234953	−	0.972007i	$-0.424506\pi$
$401$	9.40988			0.469907			0.234953	+	0.972007i	$0.424506\pi$
$402$		0			0
$403$	−33.7239			−1.67991
$404$		0			0
$405$	1.15800	+	1.33640i	0.0575415	+	0.0664064i
$406$		0			0
$407$	11.9383	+	7.67226i	0.591758	+	0.380300i
$408$		0			0
$409$	1.90931	−	13.2795i	0.0944093	−	0.656631i	−0.886581	−	0.462574i	$-0.846926\pi$
$409$	1.90931	−	13.2795i	0.0944093	−	0.656631i	0.980990	−	0.194057i	$-0.0621648\pi$
$410$		0			0
$411$	−2.45118	+	17.0483i	−0.120908	+	0.840932i
$412$		0			0
$413$	−0.954405	−	0.613359i	−0.0469632	−	0.0301814i
$414$		0			0
$415$	7.16801	+	15.6958i	0.351864	+	0.770475i
$416$		0			0
$417$	−2.83622	−	19.7264i	−0.138891	−	0.966005i
$418$		0			0
$419$	18.4016	−	5.40321i	0.898979	−	0.263964i	0.200584	−	0.979677i	$-0.435716\pi$
$419$	18.4016	−	5.40321i	0.898979	−	0.263964i	0.698395	+	0.715713i	$0.253898\pi$
$420$		0			0
$421$	−2.85477	−	19.8554i	−0.139133	−	0.967692i	−0.933071	−	0.359693i	$-0.882881\pi$
$421$	−2.85477	−	19.8554i	−0.139133	−	0.967692i	0.793938	−	0.607999i	$-0.208028\pi$
$422$		0			0
$423$	4.55497	−	2.92730i	0.221470	−	0.142330i
$424$		0			0
$425$	4.74665	+	5.47792i	0.230246	+	0.265718i
$426$		0			0
$427$	−1.57898	−	3.45748i	−0.0764121	−	0.167319i
$428$		0			0
$429$	−16.2167	+	10.4219i	−0.782952	+	0.503173i
$430$		0			0
$431$	17.5968			0.847608			0.423804	−	0.905754i	$-0.360695\pi$
$431$	17.5968			0.847608			0.423804	+	0.905754i	$0.360695\pi$
$432$		0			0
$433$	−15.7576	+	34.5043i	−0.757261	+	1.65817i	−0.00440120	+	0.999990i	$0.501401\pi$
$433$	−15.7576	+	34.5043i	−0.757261	+	1.65817i	−0.752860	+	0.658181i	$0.771326\pi$
$434$		0			0
$435$	−1.76613	−	12.2837i	−0.0846794	−	0.588958i
$436$		0			0
$437$	27.6690	−	31.9318i	1.32359	−	1.52750i
$438$		0			0
$439$	27.2447			1.30032			0.650160	−	0.759798i	$-0.274702\pi$
$439$	27.2447			1.30032			0.650160	+	0.759798i	$0.274702\pi$
$440$		0			0
$441$	−2.68147	+	5.87160i	−0.127689	+	0.279600i
$442$		0			0
$443$	3.97896	−	1.16833i	0.189046	−	0.0555090i	−0.185839	−	0.982580i	$-0.559500\pi$
$443$	3.97896	−	1.16833i	0.189046	−	0.0555090i	0.374885	+	0.927071i	$0.377682\pi$
$444$		0			0
$445$	5.81017	−	1.70602i	0.275428	−	0.0808731i
$446$		0			0
$447$	−6.66198	+	7.68833i	−0.315101	+	0.363646i
$448$		0			0
$449$	−14.7109	−	16.9773i	−0.694249	−	0.801206i	0.293715	−	0.955893i	$-0.405108\pi$
$449$	−14.7109	−	16.9773i	−0.694249	−	0.801206i	−0.987963	+	0.154687i	$0.950563\pi$
$450$		0			0
$451$	15.9534	+	4.68435i	0.751217	+	0.220577i
$452$		0			0
$453$	−1.75984	−	1.13098i	−0.0826846	−	0.0531381i
$454$		0			0
$455$	−8.11681	−	2.38331i	−0.380522	−	0.111731i
$456$		0			0
$457$	−5.99493	−	13.1271i	−0.280431	−	0.614058i	0.716034	−	0.698065i	$-0.245955\pi$
$457$	−5.99493	−	13.1271i	−0.280431	−	0.614058i	−0.996465	+	0.0840069i	$0.973228\pi$
$458$		0			0
$459$	2.53416	−	2.92458i	0.118285	−	0.136508i
$460$		0			0
$461$	14.6836	−	32.1525i	0.683882	−	1.49749i	−0.174596	−	0.984640i	$-0.555862\pi$
$461$	14.6836	−	32.1525i	0.683882	−	1.49749i	0.858477	−	0.512852i	$-0.171411\pi$
$462$		0			0
$463$	16.6526	−	10.7020i	0.773913	−	0.497364i	−0.0930952	−	0.995657i	$-0.529676\pi$
$463$	16.6526	−	10.7020i	0.773913	−	0.497364i	0.867009	+	0.498293i	$0.166040\pi$
$464$		0			0
$465$	−8.83056	−	2.59289i	−0.409508	−	0.120242i
$466$		0			0
$467$	3.92532	−	27.3012i	0.181642	−	1.26335i	−0.671237	−	0.741243i	$-0.734237\pi$
$467$	3.92532	−	27.3012i	0.181642	−	1.26335i	0.852880	−	0.522108i	$-0.174854\pi$
$468$		0			0
$469$	5.58249	+	2.31442i	0.257776	+	0.106870i
$470$		0			0
$471$	0.0590028	−	0.410373i	0.00271871	−	0.0189090i
$472$		0			0
$473$	12.1503	+	3.56764i	0.558670	+	0.164040i
$474$		0			0
$475$	−10.4058	+	6.68740i	−0.477450	+	0.306839i
$476$		0			0
$477$	5.39044	−	11.8034i	0.246811	−	0.540441i
$478$		0			0
$479$	−23.3361	+	26.9313i	−1.06625	+	1.23052i	−0.0942520	+	0.995548i	$0.530046\pi$
$479$	−23.3361	+	26.9313i	−1.06625	+	1.23052i	−0.972002	+	0.234974i	$0.924500\pi$
$480$		0			0
$481$	12.8399	+	28.1155i	0.585451	+	1.28196i
$482$		0			0
$483$	−4.53235	−	1.33082i	−0.206229	−	0.0605543i
$484$		0			0
$485$	7.51316	+	4.82841i	0.341155	+	0.219247i
$486$		0			0
$487$	−9.21644	−	2.70619i	−0.417637	−	0.122629i	0.0661612	−	0.997809i	$-0.478925\pi$
$487$	−9.21644	−	2.70619i	−0.417637	−	0.122629i	−0.483798	+	0.875180i	$0.660743\pi$
$488$		0			0
$489$	14.1430	+	16.3219i	0.639568	+	0.738101i
$490$		0			0
$491$	−13.3516	+	15.4086i	−0.602551	+	0.695381i	−0.972296	−	0.233752i	$-0.924900\pi$
$491$	−13.3516	+	15.4086i	−0.602551	+	0.695381i	0.369745	+	0.929133i	$0.379445\pi$
$492$		0			0
$493$	−26.0580	+	7.65131i	−1.17359	+	0.344598i
$494$		0			0
$495$	−5.04762	+	1.48212i	−0.226874	+	0.0666161i
$496$		0			0
$497$	−3.15609	+	6.91088i	−0.141570	+	0.309995i
$498$		0			0
$499$	−27.0208			−1.20962			−0.604808	−	0.796371i	$-0.706750\pi$
$499$	−27.0208			−1.20962			−0.604808	+	0.796371i	$0.706750\pi$
$500$		0			0
$501$	13.4377	−	15.5080i	0.600354	−	0.692846i
$502$		0			0
$503$	−2.74180	−	19.0696i	−0.122251	−	0.850272i	−0.954997	−	0.296617i	$-0.904142\pi$
$503$	−2.74180	−	19.0696i	−0.122251	−	0.850272i	0.832746	−	0.553655i	$-0.186767\pi$
$504$		0			0
$505$	2.55134	−	5.58666i	0.113533	−	0.248603i
$506$		0			0
$507$	−28.9859			−1.28731
$508$		0			0
$509$	23.9309	−	15.3795i	1.06072	−	0.681682i	0.110693	−	0.993855i	$-0.464693\pi$
$509$	23.9309	−	15.3795i	1.06072	−	0.681682i	0.950026	+	0.312172i	$0.101057\pi$
$510$		0			0
$511$	5.04107	+	11.0384i	0.223004	+	0.488310i
$512$		0			0
$513$	4.32459	+	4.99085i	0.190935	+	0.220351i
$514$		0			0
$515$	13.4955	−	8.67305i	0.594684	−	0.382180i
$516$		0			0
$517$	2.29242	+	15.9441i	0.100821	+	0.701222i
$518$		0			0
$519$	−20.0517	+	5.88771i	−0.880173	+	0.258442i
$520$		0			0
$521$	−2.42440	−	16.8621i	−0.106215	−	0.738740i	−0.971428	−	0.237336i	$-0.923726\pi$
$521$	−2.42440	−	16.8621i	−0.106215	−	0.738740i	0.865213	−	0.501405i	$-0.167183\pi$
$522$		0			0
$523$	4.13778	+	9.06048i	0.180933	+	0.396187i	0.978267	−	0.207351i	$-0.0664843\pi$
$523$	4.13778	+	9.06048i	0.180933	+	0.396187i	−0.797334	+	0.603538i	$0.793757\pi$
$524$		0			0
$525$	1.16335	+	0.747641i	0.0507729	+	0.0326297i
$526$		0			0
$527$	−2.86631	+	19.9356i	−0.124858	+	0.868409i
$528$		0			0
$529$	−2.55245	+	17.7527i	−0.110976	+	0.771857i
$530$		0			0
$531$	−1.29271	−	0.830772i	−0.0560987	−	0.0360524i
$532$		0			0
$533$	23.7152	+	27.3688i	1.02722	+	1.18548i
$534$		0			0
$535$	−27.9598			−1.20881
$536$		0			0
$537$	17.4527			0.753141
$538$		0			0
$539$	−12.5755	−	14.5129i	−0.541664	−	0.625114i
$540$		0			0
$541$	29.5525	+	18.9922i	1.27056	+	0.816539i	0.989693	−	0.143207i	$-0.0457415\pi$
$541$	29.5525	+	18.9922i	1.27056	+	0.816539i	0.280867	+	0.959747i	$0.409378\pi$
$542$		0			0
$543$	−2.13885	+	14.8760i	−0.0917868	+	0.638392i
$544$		0			0
$545$	3.71943	−	25.8692i	0.159323	−	1.10811i
$546$		0			0
$547$	−7.96729	−	5.12027i	−0.340657	−	0.218927i	0.359115	−	0.933293i	$-0.383079\pi$
$547$	−7.96729	−	5.12027i	−0.340657	−	0.218927i	−0.699772	+	0.714366i	$0.746715\pi$
$548$		0			0
$549$	−2.13867	−	4.68303i	−0.0912762	−	0.199867i
$550$		0			0
$551$	−6.59567	−	45.8739i	−0.280985	−	1.95429i
$552$		0			0
$553$	0.660053	−	0.193809i	0.0280683	−	0.00824160i
$554$		0			0
$555$	1.20044	+	8.34922i	0.0509557	+	0.354405i
$556$		0			0
$557$	−17.9883	+	11.5604i	−0.762190	+	0.489830i	−0.863080	−	0.505068i	$-0.831467\pi$
$557$	−17.9883	+	11.5604i	−0.762190	+	0.489830i	0.100890	+	0.994898i	$0.467831\pi$
$558$		0			0
$559$	18.0617	+	20.8444i	0.763930	+	0.881623i
$560$		0			0
$561$	4.78248	+	10.4722i	0.201917	+	0.442136i
$562$		0			0
$563$	20.0815	−	12.9056i	0.846336	−	0.543907i	−0.0440943	−	0.999027i	$-0.514040\pi$
$563$	20.0815	−	12.9056i	0.846336	−	0.543907i	0.890430	+	0.455121i	$0.150404\pi$
$564$		0			0
$565$	19.1685			0.806423
$566$		0			0
$567$	0.306701	−	0.671581i	0.0128802	−	0.0282037i
$568$		0			0
$569$	−5.79090	−	40.2766i	−0.242767	−	1.68848i	−0.638108	−	0.769947i	$-0.720283\pi$
$569$	−5.79090	−	40.2766i	−0.242767	−	1.68848i	0.395341	−	0.918535i	$-0.370627\pi$
$570$		0			0
$571$	7.67734	−	8.86012i	0.321287	−	0.370784i	−0.572014	−	0.820244i	$-0.693838\pi$
$571$	7.67734	−	8.86012i	0.321287	−	0.370784i	0.893301	+	0.449459i	$0.148383\pi$
$572$		0			0
$573$	4.14559			0.173185
$574$		0			0
$575$	4.97832	−	10.9010i	0.207610	−	0.454603i
$576$		0			0
$577$	−1.18383	+	0.347605i	−0.0492836	+	0.0144710i	−0.306281	−	0.951941i	$-0.599085\pi$
$577$	−1.18383	+	0.347605i	−0.0492836	+	0.0144710i	0.256998	+	0.966412i	$0.417267\pi$
$578$		0			0
$579$	23.0305	−	6.76235i	0.957113	−	0.281034i
$580$		0			0
$581$	4.71779	−	5.44462i	0.195727	−	0.225881i
$582$		0			0
$583$	25.2799	+	29.1746i	1.04699	+	1.20829i
$584$		0			0
$585$	−10.9939	−	3.22811i	−0.454543	−	0.133466i
$586$		0			0
$587$	26.7629	+	17.1995i	1.10462	+	0.709898i	0.960115	−	0.279605i	$-0.0902035\pi$
$587$	26.7629	+	17.1995i	1.10462	+	0.709898i	0.144508	+	0.989504i	$0.453840\pi$
$588$		0			0
$589$	−32.9780	−	9.68323i	−1.35884	−	0.398990i
$590$		0			0
$591$	6.82130	+	14.9366i	0.280591	+	0.614408i
$592$		0			0
$593$	−27.6105	+	31.8642i	−1.13383	+	1.30851i	−0.188615	+	0.982051i	$0.560400\pi$
$593$	−27.6105	+	31.8642i	−1.13383	+	1.30851i	−0.945212	+	0.326456i	$0.894146\pi$
$594$		0			0
$595$	−2.09875	+	4.59562i	−0.0860403	+	0.188402i
$596$		0			0
$597$	8.93430	−	5.74173i	0.365657	−	0.234993i
$598$		0			0
$599$	13.3021	+	3.90585i	0.543509	+	0.159589i	0.541951	−	0.840410i	$-0.317686\pi$
$599$	13.3021	+	3.90585i	0.543509	+	0.159589i	0.00155825	+	0.999999i	$0.499504\pi$
$600$		0			0
$601$	5.81709	−	40.4588i	0.237284	−	1.65035i	−0.428016	−	0.903771i	$-0.640787\pi$
$601$	5.81709	−	40.4588i	0.237284	−	1.65035i	0.665300	−	0.746576i	$-0.268304\pi$
$602$		0			0
$603$	7.56129	+	3.13480i	0.307919	+	0.127659i
$604$		0			0
$605$	−0.540924	+	3.76221i	−0.0219917	+	0.152955i
$606$		0			0
$607$	−5.54600	−	1.62845i	−0.225105	−	0.0660969i	0.167235	−	0.985917i	$-0.446516\pi$
$607$	−5.54600	−	1.62845i	−0.225105	−	0.0660969i	−0.392340	+	0.919820i	$0.628334\pi$
$608$		0			0
$609$	−4.35885	+	2.80126i	−0.176630	+	0.113513i
$610$		0			0
$611$	−14.5745	+	31.9136i	−0.589619	+	1.29109i
$612$		0			0
$613$	−8.69243	+	10.0316i	−0.351084	+	0.405172i	−0.903633	−	0.428308i	$-0.859110\pi$
$613$	−8.69243	+	10.0316i	−0.351084	+	0.405172i	0.552549	+	0.833481i	$0.313655\pi$
$614$		0			0
$615$	4.10553	+	8.98985i	0.165551	+	0.362506i
$616$		0			0
$617$	−25.0756	−	7.36286i	−1.00951	−	0.296418i	−0.265155	−	0.964206i	$-0.585423\pi$
$617$	−25.0756	−	7.36286i	−1.00951	−	0.296418i	−0.744351	+	0.667788i	$0.767241\pi$
$618$		0			0
$619$	−8.70956	−	5.59730i	−0.350067	−	0.224974i	0.353776	−	0.935330i	$-0.384898\pi$
$619$	−8.70956	−	5.59730i	−0.350067	−	0.224974i	−0.703843	+	0.710356i	$0.748534\pi$
$620$		0			0
$621$	−6.13890	−	1.80254i	−0.246346	−	0.0723336i
$622$		0			0
$623$	−1.65565	−	1.91072i	−0.0663323	−	0.0765515i
$624$		0			0
$625$	7.94106	−	9.16447i	0.317642	−	0.366579i
$626$		0			0
$627$	−18.8505	+	5.53501i	−0.752817	+	0.221047i
$628$		0			0
$629$	17.7116	−	5.20059i	0.706207	−	0.207361i
$630$		0			0
$631$	−3.64340	+	7.97794i	−0.145042	+	0.317597i	−0.968184	−	0.250237i	$-0.919491\pi$
$631$	−3.64340	+	7.97794i	−0.145042	+	0.317597i	0.823143	+	0.567834i	$0.192219\pi$
$632$		0			0
$633$	−3.96713			−0.157679
$634$		0			0
$635$	16.9555	−	19.5677i	0.672860	−	0.776522i
$636$		0			0
$637$	−5.95240	−	41.3999i	−0.235843	−	1.64032i
$638$		0			0
$639$	−4.27482	+	9.36054i	−0.169109	+	0.370297i
$640$		0			0
$641$	6.64792			0.262577			0.131288	−	0.991344i	$-0.458089\pi$
$641$	6.64792			0.262577			0.131288	+	0.991344i	$0.458089\pi$
$642$		0			0
$643$	−25.7116	+	16.5239i	−1.01397	+	0.651638i	−0.938417	−	0.345504i	$-0.887708\pi$
$643$	−25.7116	+	16.5239i	−1.01397	+	0.651638i	−0.0755507	+	0.997142i	$0.524071\pi$
$644$		0			0
$645$	3.12681	+	6.84675i	0.123118	+	0.269591i
$646$		0			0
$647$	−16.0529	−	18.5260i	−0.631105	−	0.728334i	0.346671	−	0.937987i	$-0.387312\pi$
$647$	−16.0529	−	18.5260i	−0.631105	−	0.728334i	−0.977776	+	0.209653i	$0.932767\pi$
$648$		0			0
$649$	3.84579	−	2.47154i	0.150960	−	0.0970163i
$650$		0			0
$651$	0.546852	+	3.80344i	0.0214328	+	0.149068i
$652$		0			0
$653$	−38.5310	+	11.3137i	−1.50784	+	0.442741i	−0.928183	−	0.372123i	$-0.878630\pi$
$653$	−38.5310	+	11.3137i	−1.50784	+	0.442741i	−0.579652	+	0.814864i	$0.696812\pi$
$654$		0			0
$655$	3.71036	+	25.8061i	0.144976	+	1.00833i
$656$		0			0
$657$	6.82795	+	14.9511i	0.266384	+	0.583299i
$658$		0			0
$659$	33.0413	+	21.2343i	1.28710	+	0.827172i	0.991746	−	0.128215i	$-0.0409246\pi$
$659$	33.0413	+	21.2343i	1.28710	+	0.827172i	0.295358	+	0.955387i	$0.404561\pi$
$660$		0			0
$661$	3.38514	−	23.5441i	0.131667	−	0.915761i	−0.811716	−	0.584053i	$-0.801466\pi$
$661$	3.38514	−	23.5441i	0.131667	−	0.915761i	0.943382	−	0.331708i	$-0.107625\pi$
$662$		0			0
$663$	−3.56852	+	24.8196i	−0.138590	+	0.963912i
$664$		0			0
$665$	−7.25296	−	4.66120i	−0.281258	−	0.180753i
$666$		0			0
$667$	29.4043	+	33.9343i	1.13854	+	1.31394i
$668$		0			0
$669$	−0.617962			−0.0238918
$670$		0			0
$671$	15.3160			0.591269
$672$		0			0
$673$	−6.09943	−	7.03912i	−0.235116	−	0.271338i	0.625915	−	0.779892i	$-0.284726\pi$
$673$	−6.09943	−	7.03912i	−0.235116	−	0.271338i	−0.861030	+	0.508553i	$0.830180\pi$
$674$		0			0
$675$	1.57572	+	1.01265i	0.0606495	+	0.0389770i
$676$		0			0
$677$	−1.87703	+	13.0550i	−0.0721402	+	0.501746i	0.921431	+	0.388541i	$0.127021\pi$
$677$	−1.87703	+	13.0550i	−0.0721402	+	0.501746i	−0.993572	+	0.113205i	$0.963888\pi$
$678$		0			0
$679$	0.530663	−	3.69084i	0.0203650	−	0.141641i
$680$		0			0
$681$	−5.48932	−	3.52777i	−0.210351	−	0.135184i
$682$		0			0
$683$	−12.2310	−	26.7821i	−0.468006	−	1.02479i	−0.985589	−	0.169157i	$-0.945896\pi$
$683$	−12.2310	−	26.7821i	−0.468006	−	1.02479i	0.517583	−	0.855633i	$-0.326832\pi$
$684$		0			0
$685$	−4.33446	−	30.1468i	−0.165611	−	1.15185i
$686$		0			0
$687$	0.610694	−	0.179316i	0.0232994	−	0.00684133i
$688$		0			0
$689$	11.9658	+	83.2243i	0.455862	+	3.17059i
$690$		0			0
$691$	−1.38214	+	0.888247i	−0.0525791	+	0.0337905i	−0.566666	−	0.823947i	$-0.691767\pi$
$691$	−1.38214	+	0.888247i	−0.0525791	+	0.0337905i	0.514087	+	0.857738i	$0.328131\pi$
$692$		0			0
$693$	1.43836	+	1.65995i	0.0546387	+	0.0630564i
$694$		0			0
$695$	14.6397	+	32.0565i	0.555316	+	1.21597i
$696$		0			0
$697$	18.1945	−	11.6929i	0.689165	−	0.442899i
$698$		0			0
$699$	−9.66043			−0.365391
$700$		0			0
$701$	−0.423947	+	0.928314i	−0.0160123	+	0.0350619i	−0.917469	−	0.397807i	$-0.869771\pi$
$701$	−0.423947	+	0.928314i	−0.0160123	+	0.0350619i	0.901457	+	0.432869i	$0.142499\pi$
$702$		0			0
$703$	4.48307	+	31.1805i	0.169082	+	1.17599i
$704$		0			0
$705$	−6.27000	+	7.23596i	−0.236142	+	0.272522i
$706$		0			0
$707$	−2.56424			−0.0964383
$708$		0			0
$709$	−4.78205	+	10.4712i	−0.179594	+	0.393255i	−0.977923	−	0.208966i	$-0.932990\pi$
$709$	−4.78205	+	10.4712i	−0.179594	+	0.393255i	0.798329	+	0.602221i	$0.205718\pi$
$710$		0			0
$711$	0.894018	−	0.262507i	0.0335283	−	0.00984479i
$712$		0			0
$713$	31.9505	−	9.38151i	1.19656	−	0.351340i
$714$		0			0
$715$	22.3226	−	25.7617i	0.834819	−	0.963433i
$716$		0			0
$717$	0.298367	+	0.344334i	0.0111427	+	0.0128594i
$718$		0			0
$719$	31.7813	+	9.33183i	1.18524	+	0.348018i	0.814193	−	0.580595i	$-0.197180\pi$
$719$	31.7813	+	9.33183i	1.18524	+	0.348018i	0.371049	+	0.928613i	$0.378998\pi$
$720$		0			0
$721$	−5.63460	−	3.62113i	−0.209843	−	0.134858i
$722$		0			0
$723$	15.6080	+	4.58292i	0.580468	+	0.170441i
$724$		0			0
$725$	−5.46068	−	11.9572i	−0.202805	−	0.444080i
$726$		0			0
$727$	−18.3702	+	21.2004i	−0.681314	+	0.786279i	−0.986102	−	0.166142i	$-0.946869\pi$
$727$	−18.3702	+	21.2004i	−0.681314	+	0.786279i	0.304788	+	0.952420i	$0.401415\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	13.8571	−	8.90541i	0.512523	−	0.329379i
$732$		0			0
$733$	−30.9901	−	9.09950i	−1.14464	−	0.336098i	−0.346196	−	0.938162i	$-0.612527\pi$
$733$	−30.9901	−	9.09950i	−1.14464	−	0.336098i	−0.798448	+	0.602064i	$0.794345\pi$
$734$		0			0
$735$	1.62443	−	11.2981i	0.0599179	−	0.416738i
$736$		0			0
$737$	−17.8279	+	16.5878i	−0.656698	+	0.611019i
$738$		0			0
$739$	2.05505	−	14.2932i	0.0755961	−	0.525783i	−0.916474	−	0.400095i	$-0.868977\pi$
$739$	2.05505	−	14.2932i	0.0755961	−	0.525783i	0.992070	−	0.125688i	$-0.0401137\pi$
$740$		0			0
$741$	−41.0572	−	12.0555i	−1.50827	−	0.442869i
$742$		0			0
$743$	−4.77432	+	3.06827i	−0.175153	+	0.112564i	−0.625280	−	0.780401i	$-0.715015\pi$
$743$	−4.77432	+	3.06827i	−0.175153	+	0.112564i	0.450127	+	0.892965i	$0.351379\pi$
$744$		0			0
$745$	7.47302	−	16.3636i	0.273790	−	0.599517i
$746$		0			0
$747$	6.39007	−	7.37454i	0.233801	−	0.269820i
$748$		0			0
$749$	4.84941	+	10.6187i	0.177193	+	0.388000i
$750$		0			0
$751$	−13.0432	−	3.82983i	−0.475953	−	0.139752i	0.0349531	−	0.999389i	$-0.488872\pi$
$751$	−13.0432	−	3.82983i	−0.475953	−	0.139752i	−0.510906	+	0.859637i	$0.670690\pi$
$752$		0			0
$753$	4.78537	+	3.07537i	0.174389	+	0.112073i
$754$		0			0
$755$	3.54934	+	1.04218i	0.129174	+	0.0379289i
$756$		0			0
$757$	24.8713	+	28.7030i	0.903962	+	1.04323i	0.998860	+	0.0477407i	$0.0152021\pi$
$757$	24.8713	+	28.7030i	0.903962	+	1.04323i	−0.0948978	+	0.995487i	$0.530252\pi$
$758$		0			0
$759$	12.4647	−	14.3851i	0.452441	−	0.522145i
$760$		0			0
$761$	−8.41179	+	2.46993i	−0.304927	+	0.0895347i	−0.430617	−	0.902535i	$-0.641704\pi$
$761$	−8.41179	+	2.46993i	−0.304927	+	0.0895347i	0.125689	+	0.992070i	$0.459886\pi$
$762$		0			0
$763$	−10.4699	+	3.07423i	−0.379034	+	0.111294i
$764$		0			0
$765$	−2.84268	+	6.22460i	−0.102777	+	0.225051i
$766$		0			0
$767$	9.95691			0.359523
$768$		0			0
$769$	−17.9079	+	20.6668i	−0.645776	+	0.745265i	−0.980385	−	0.197092i	$-0.936850\pi$
$769$	−17.9079	+	20.6668i	−0.645776	+	0.745265i	0.334609	+	0.942357i	$0.391396\pi$
$770$		0			0
$771$	0.0818272	+	0.569121i	0.00294694	+	0.0204964i
$772$		0			0
$773$	3.97491	−	8.70384i	0.142968	−	0.313055i	−0.824580	−	0.565746i	$-0.808588\pi$
$773$	3.97491	−	8.70384i	0.142968	−	0.313055i	0.967547	+	0.252691i	$0.0813155\pi$
$774$		0			0
$775$	−9.74852			−0.350177
$776$		0			0
$777$	2.96271	−	1.90402i	0.106287	−	0.0683062i
$778$		0			0
$779$	15.3322	+	33.5729i	0.549334	+	1.20287i
$780$		0			0
$781$	−20.0479	−	23.1365i	−0.717371	−	0.827891i
$782$		0			0
$783$	−5.90391	+	3.79421i	−0.210988	+	0.135594i
$784$		0			0
$785$	0.104336	+	0.725670i	0.00372390	+	0.0259003i
$786$		0			0
$787$	46.3818	−	13.6189i	1.65333	−	0.485462i	0.683646	−	0.729814i	$-0.260393\pi$
$787$	46.3818	−	13.6189i	1.65333	−	0.485462i	0.969687	+	0.244351i	$0.0785750\pi$
$788$		0			0
$789$	−2.28915	−	15.9214i	−0.0814959	−	0.566817i
$790$		0			0
$791$	−3.32462	−	7.27990i	−0.118210	−	0.258844i
$792$		0			0
$793$	28.0634	+	18.0352i	0.996559	+	0.640450i
$794$		0			0
$795$	−3.26551	+	22.7121i	−0.115816	+	0.805517i
$796$		0			0
$797$	−4.50301	+	31.3191i	−0.159505	+	1.10938i	0.740044	+	0.672559i	$0.234805\pi$
$797$	−4.50301	+	31.3191i	−0.159505	+	1.10938i	−0.899548	+	0.436821i	$0.856104\pi$
$798$		0			0
$799$	17.6267	+	11.3280i	0.623589	+	0.400756i
$800$		0			0
$801$	−2.24252	−	2.58801i	−0.0792355	−	0.0914427i
$802$		0			0
$803$	−48.8982			−1.72558
$804$		0			0
$805$	8.35297			0.294404
$806$		0			0
$807$	2.53998	+	2.93129i	0.0894115	+	0.103186i
$808$		0			0
$809$	16.6525	+	10.7019i	0.585472	+	0.376260i	0.799589	−	0.600548i	$-0.205051\pi$
$809$	16.6525	+	10.7019i	0.585472	+	0.376260i	−0.214117	+	0.976808i	$0.568687\pi$
$810$		0			0
$811$	−0.900281	+	6.26159i	−0.0316131	+	0.219874i	−0.999504	−	0.0314972i	$-0.989972\pi$
$811$	−0.900281	+	6.26159i	−0.0316131	+	0.219874i	0.967891	+	0.251371i	$0.0808816\pi$
$812$		0			0
$813$	−1.07783	+	7.49650i	−0.0378013	+	0.262914i
$814$		0			0
$815$	−32.1277	−	20.6472i	−1.12538	−	0.723240i
$816$		0			0
$817$	11.6772	+	25.5694i	0.408532	+	0.894561i
$818$		0			0
$819$	0.680823	+	4.73523i	0.0237899	+	0.165462i
$820$		0			0
$821$	42.2491	−	12.4055i	1.47450	−	0.432953i	0.556943	−	0.830550i	$-0.311974\pi$
$821$	42.2491	−	12.4055i	1.47450	−	0.432953i	0.917560	+	0.397597i	$0.130156\pi$
$822$		0			0
$823$	5.61265	+	39.0368i	0.195645	+	1.36074i	0.816741	+	0.577004i	$0.195778\pi$
$823$	5.61265	+	39.0368i	0.195645	+	1.36074i	−0.621097	+	0.783734i	$0.713313\pi$
$824$		0			0
$825$	−4.68775	+	3.01263i	−0.163206	+	0.104886i
$826$		0			0
$827$	19.1927	+	22.1496i	0.667397	+	0.770217i	0.983967	−	0.178352i	$-0.0570766\pi$
$827$	19.1927	+	22.1496i	0.667397	+	0.770217i	−0.316570	+	0.948569i	$0.602531\pi$
$828$		0			0
$829$	−11.6149	−	25.4330i	−0.403400	−	0.883324i	−0.996914	−	0.0784998i	$-0.974987\pi$
$829$	−11.6149	−	25.4330i	−0.403400	−	0.883324i	0.593514	−	0.804824i	$-0.297740\pi$
$830$		0			0
$831$	20.0741	−	12.9009i	0.696364	−	0.447526i
$832$		0			0
$833$	−24.9791			−0.865474
$834$		0			0
$835$	−15.0737	+	33.0068i	−0.521646	+	1.14225i
$836$		0			0
$837$	0.740691	+	5.15162i	0.0256020	+	0.178066i
$838$		0			0
$839$	−15.2438	+	17.5923i	−0.526274	+	0.607352i	−0.955191	−	0.295992i	$-0.904350\pi$
$839$	−15.2438	+	17.5923i	−0.526274	+	0.607352i	0.428917	+	0.903344i	$0.358895\pi$
$840$		0			0
$841$	20.2522			0.698351
$842$		0			0
$843$	5.09748	−	11.1619i	0.175566	−	0.384437i
$844$		0			0
$845$	49.1799	−	14.4405i	1.69184	−	0.496769i
$846$		0			0
$847$	1.52265	−	0.447091i	0.0523189	−	0.0153622i
$848$		0			0
$849$	−7.89189	+	9.10772i	−0.270849	+	0.312576i
$850$		0			0
$851$	−19.9861	−	23.0651i	−0.685113	−	0.790663i
$852$		0			0
$853$	−5.87696	−	1.72563i	−0.201223	−	0.0590844i	0.179568	−	0.983746i	$-0.442530\pi$
$853$	−5.87696	−	1.72563i	−0.201223	−	0.0590844i	−0.380791	+	0.924661i	$0.624348\pi$
$854$		0			0
$855$	−9.82388	−	6.31342i	−0.335969	−	0.215914i
$856$		0			0
$857$	−5.51345	−	1.61890i	−0.188336	−	0.0553004i	0.186204	−	0.982511i	$-0.440381\pi$
$857$	−5.51345	−	1.61890i	−0.188336	−	0.0553004i	−0.374540	+	0.927211i	$0.622199\pi$
$858$		0			0
$859$	0.229692	+	0.502956i	0.00783700	+	0.0171606i	0.913510	−	0.406816i	$-0.133361\pi$
$859$	0.229692	+	0.502956i	0.00783700	+	0.0171606i	−0.905673	+	0.423977i	$0.860634\pi$
$860$		0			0
$861$	2.70214	−	3.11844i	0.0920888	−	0.106276i
$862$		0			0
$863$	−11.8101	+	25.8605i	−0.402020	+	0.880302i	0.595041	+	0.803695i	$0.297136\pi$
$863$	−11.8101	+	25.8605i	−0.402020	+	0.880302i	−0.997061	+	0.0766066i	$0.975591\pi$
$864$		0			0
$865$	31.0883	−	19.9792i	1.05703	−	0.679313i
$866$		0			0
$867$	−1.94281	−	0.570460i	−0.0659813	−	0.0193738i
$868$		0			0
$869$	−0.394493	+	2.74376i	−0.0133823	+	0.0930757i
$870$		0			0
$871$	−52.1985	+	9.40056i	−1.76868	+	0.318526i
$872$		0			0
$873$	0.718764	−	4.99911i	0.0243265	−	0.169194i
$874$		0			0
$875$	−8.60963	−	2.52801i	−0.291058	−	0.0854625i
$876$		0			0
$877$	−36.2048	+	23.2674i	−1.22255	+	0.785684i	−0.982714	−	0.185130i	$-0.940730\pi$
$877$	−36.2048	+	23.2674i	−1.22255	+	0.785684i	−0.239834	+	0.970814i	$0.577093\pi$
$878$		0			0
$879$	6.39464	−	14.0023i	0.215686	−	0.472286i
$880$		0			0
$881$	−8.67632	+	10.0130i	−0.292313	+	0.337347i	−0.882843	−	0.469669i	$-0.844373\pi$
$881$	−8.67632	+	10.0130i	−0.292313	+	0.337347i	0.590530	+	0.807016i	$0.298919\pi$
$882$		0			0
$883$	13.5128	+	29.5889i	0.454742	+	0.995747i	0.988655	+	0.150207i	$0.0479940\pi$
$883$	13.5128	+	29.5889i	0.454742	+	0.995747i	−0.533912	+	0.845540i	$0.679279\pi$
$884$		0			0
$885$	2.60720	+	0.765543i	0.0876401	+	0.0257335i
$886$		0			0
$887$	15.3172	+	9.84378i	0.514302	+	0.330522i	0.771914	−	0.635727i	$-0.219299\pi$
$887$	15.3172	+	9.84378i	0.514302	+	0.330522i	−0.257612	+	0.966248i	$0.582936\pi$
$888$		0			0
$889$	−10.3723	−	3.04560i	−0.347877	−	0.102146i
$890$		0			0
$891$	1.94820	+	2.24835i	0.0652673	+	0.0753224i
$892$		0			0
$893$	−23.4155	+	27.0230i	−0.783571	+	0.904289i
$894$		0			0
$895$	−29.6118	+	8.69481i	−0.989814	+	0.290635i
$896$		0			0
$897$	39.7779	−	11.6799i	1.32815	−	0.389979i
$898$		0			0
$899$	15.1734	−	33.2250i	0.506060	−	1.10812i
$900$		0			0
$901$	50.2143			1.67288
$902$		0			0
$903$	2.05798	−	2.37503i	0.0684852	−	0.0790362i
$904$		0			0
$905$	−3.78216	−	26.3055i	−0.125723	−	0.874425i
$906$		0			0
$907$	−11.9418	+	26.1489i	−0.396522	+	0.868261i	0.601090	+	0.799182i	$0.294733\pi$
$907$	−11.9418	+	26.1489i	−0.396522	+	0.868261i	−0.997611	+	0.0690794i	$0.977994\pi$
$908$		0			0
$909$	−3.47318			−0.115198
$910$		0			0
$911$	−5.67021	+	3.64402i	−0.187863	+	0.120732i	−0.631191	−	0.775627i	$-0.717434\pi$
$911$	−5.67021	+	3.64402i	−0.187863	+	0.120732i	0.443329	+	0.896359i	$0.353797\pi$
$912$		0			0
$913$	12.0594	+	26.4063i	0.399107	+	0.873922i
$914$		0			0
$915$	5.96170	+	6.88017i	0.197088	+	0.227451i
$916$		0			0
$917$	9.15726	−	5.88501i	0.302399	−	0.194340i
$918$		0			0
$919$	−1.14763	−	7.98191i	−0.0378567	−	0.263299i	0.962099	−	0.272700i	$-0.0879166\pi$
$919$	−1.14763	−	7.98191i	−0.0378567	−	0.263299i	−0.999956	+	0.00940092i	$0.997008\pi$
$920$		0			0
$921$	23.0096	−	6.75623i	0.758192	−	0.222625i
$922$		0			0
$923$	−9.48936	−	65.9999i	−0.312346	−	2.17241i
$924$		0			0
$925$	3.71162	+	8.12731i	0.122037	+	0.267224i
$926$		0			0
$927$	−7.63186	−	4.90470i	−0.250663	−	0.161091i
$928$		0			0
$929$	3.11483	−	21.6641i	0.102194	−	0.710777i	−0.872724	−	0.488214i	$-0.837649\pi$
$929$	3.11483	−	21.6641i	0.102194	−	0.710777i	0.974918	−	0.222563i	$-0.0714423\pi$
$930$		0			0
$931$	6.06648	−	42.1933i	0.198821	−	1.38283i
$932$		0			0
$933$	20.6895	+	13.2963i	0.677343	+	0.435302i
$934$		0			0
$935$	−13.3315	−	15.3854i	−0.435987	−	0.503156i
$936$		0			0
$937$	51.6289			1.68664			0.843321	−	0.537409i	$-0.180597\pi$
$937$	51.6289			1.68664			0.843321	+	0.537409i	$0.180597\pi$
$938$		0			0
$939$	−16.9937			−0.554570
$940$		0			0
$941$	−15.7832	−	18.2148i	−0.514517	−	0.593784i	0.437733	−	0.899105i	$-0.355782\pi$
$941$	−15.7832	−	18.2148i	−0.514517	−	0.593784i	−0.952249	+	0.305321i	$0.901236\pi$
$942$		0			0
$943$	−30.0817	−	19.3323i	−0.979595	−	0.629548i
$944$		0			0
$945$	−0.185799	+	1.29226i	−0.00604403	+	0.0420371i
$946$		0			0
$947$	−2.97324	+	20.6794i	−0.0966174	+	0.671989i	0.882741	+	0.469859i	$0.155695\pi$
$947$	−2.97324	+	20.6794i	−0.0966174	+	0.671989i	−0.979359	+	0.202130i	$0.935214\pi$
$948$		0			0
$949$	−89.5955	−	57.5795i	−2.90839	−	1.86911i
$950$		0			0
$951$	−0.952546	−	2.08579i	−0.0308884	−	0.0676362i
$952$		0			0
$953$	0.0402204	+	0.279739i	0.00130287	+	0.00906163i	0.990463	−	0.137783i	$-0.0439975\pi$
$953$	0.0402204	+	0.279739i	0.00130287	+	0.00906163i	−0.989160	+	0.146844i	$0.953088\pi$
$954$		0			0
$955$	−7.03377	+	2.06530i	−0.227607	+	0.0668316i
$956$		0			0
$957$	−2.97131	−	20.6659i	−0.0960489	−	0.668034i
$958$		0			0
$959$	−10.6975	+	6.87490i	−0.345442	+	0.222002i
$960$		0			0
$961$	2.56194	+	2.95664i	0.0826433	+	0.0953755i
$962$		0			0
$963$	6.56835	+	14.3827i	0.211662	+	0.463475i
$964$		0			0
$965$	−35.7065	+	22.9472i	−1.14943	+	0.738696i
$966$		0			0
$967$	25.4842			0.819516			0.409758	−	0.912194i	$-0.365613\pi$
$967$	25.4842			0.819516			0.409758	+	0.912194i	$0.365613\pi$
$968$		0			0
$969$	−10.6161	+	23.2460i	−0.341038	+	0.746768i
$970$		0			0
$971$	1.81973	+	12.6565i	0.0583980	+	0.406167i	0.997963	+	0.0637963i	$0.0203208\pi$
$971$	1.81973	+	12.6565i	0.0583980	+	0.406167i	−0.939565	+	0.342371i	$0.888770\pi$
$972$		0			0
$973$	9.63545	−	11.1199i	0.308898	−	0.356488i
$974$		0			0
$975$	−12.1368			−0.388688
$976$		0			0
$977$	−4.60272	+	10.0785i	−0.147254	+	0.322441i	−0.968858	−	0.247618i	$-0.920352\pi$
$977$	−4.60272	+	10.0785i	−0.147254	+	0.322441i	0.821604	+	0.570059i	$0.193080\pi$
$978$		0			0
$979$	9.77495	−	2.87018i	0.312409	−	0.0917314i
$980$		0			0
$981$	−14.1810	+	4.16393i	−0.452766	+	0.132944i
$982$		0			0
$983$	26.5856	−	30.6814i	0.847949	−	0.978585i	−0.152003	−	0.988380i	$-0.548572\pi$
$983$	26.5856	−	30.6814i	0.847949	−	0.978585i	0.999952	+	0.00979506i	$0.00311791\pi$
$984$		0			0
$985$	−19.0149	−	21.9443i	−0.605864	−	0.699204i
$986$		0			0
$987$	3.83560	+	1.12623i	0.122088	+	0.0358484i
$988$		0			0
$989$	−22.9105	−	14.7237i	−0.728512	−	0.468186i
$990$		0			0
$991$	44.8040	+	13.1556i	1.42325	+	0.417903i	0.900601	−	0.434647i	$-0.143127\pi$
$991$	44.8040	+	13.1556i	1.42325	+	0.417903i	0.522645	+	0.852550i	$0.324945\pi$
$992$		0			0
$993$	3.71358	+	8.13161i	0.117847	+	0.258049i
$994$		0			0
$995$	−12.2982	+	14.1929i	−0.389880	+	0.449945i
$996$		0			0
$997$	−5.09920	+	11.1657i	−0.161493	+	0.353621i	−0.973029	−	0.230682i	$-0.925904\pi$
$997$	−5.09920	+	11.1657i	−0.161493	+	0.353621i	0.811536	+	0.584302i	$0.198632\pi$
$998$		0			0
$999$	4.01288	−	2.57892i	0.126962	−	0.0815935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.193.2	yes	60
67.25	even	11	inner	804.2.q.b.25.2	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.2	✓	60	67.25	even	11	inner
804.2.q.b.193.2	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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-1.48760 - 0.956023i) q^{5} +(-0.105071 + 0.730785i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-1.48760 - 0.956023i) q^{5} +(-0.105071 + 0.730785i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.50272 - 1.60840i) q^{11} +(-2.69174 - 5.89410i) q^{13} +(-0.251658 - 1.75032i) q^{15} +(-3.71302 + 1.09024i) q^{17} +(-0.939824 - 6.53662i) q^{19} +(-0.621097 + 0.399155i) q^{21} +(4.18984 + 4.83534i) q^{23} +(-0.778098 - 1.70380i) q^{25} +(-0.841254 + 0.540641i) q^{27} +7.01799 q^{29} +(2.16207 - 4.73427i) q^{31} +(-0.423385 - 2.94471i) q^{33} +(0.854951 - 0.986666i) q^{35} -4.77012 q^{37} +(2.69174 - 5.89410i) q^{39} +(-5.36252 + 1.57458i) q^{41} +(-4.08414 + 1.19921i) q^{43} +(1.15800 - 1.33640i) q^{45} +(-3.54575 - 4.09201i) q^{47} +(6.19344 + 1.81856i) q^{49} +(-3.25546 - 2.09216i) q^{51} +(-12.4504 - 3.65577i) q^{53} +(2.18538 + 4.78532i) q^{55} +(4.32459 - 4.99085i) q^{57} +(-0.638345 + 1.39778i) q^{59} +(-4.33100 + 2.78336i) q^{61} +(-0.708393 - 0.208003i) q^{63} +(-1.63065 + 11.3414i) q^{65} +(2.02680 - 7.93045i) q^{67} +(-0.910540 + 6.33294i) q^{69} +(9.87363 + 2.89916i) q^{71} +(13.8272 - 8.88621i) q^{73} +(0.778098 - 1.70380i) q^{75} +(1.43836 - 1.65995i) q^{77} +(-0.387067 - 0.847559i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-8.20888 - 5.27553i) q^{83} +(6.56580 + 1.92789i) q^{85} +(4.59581 + 5.30384i) q^{87} +(-2.24252 + 2.58801i) q^{89} +(4.59014 - 1.34779i) q^{91} +(4.99377 - 1.46630i) q^{93} +(-4.85108 + 10.6224i) q^{95} -5.05052 q^{97} +(1.94820 - 2.24835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 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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