LMFDB - Embedded newform 804.2.q.b.397.6

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			397.6
Character	$\chi$	$=$	804.397
Dual form			804.2.q.b.241.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(1.80159 - 0.528994i) q^{5} +(2.39007 - 2.75829i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(1.80159 - 0.528994i) q^{5} +(2.39007 - 2.75829i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(2.98671 - 0.876979i) q^{11} +(0.127238 - 0.0817712i) q^{13} +(-1.22960 - 1.41903i) q^{15} +(-0.323618 + 2.25081i) q^{17} +(-1.17218 - 1.35276i) q^{19} +(-3.50190 - 1.02825i) q^{21} +(0.274352 + 0.600747i) q^{23} +(-1.24038 + 0.797147i) q^{25} +(0.959493 + 0.281733i) q^{27} +2.20772 q^{29} +(1.43445 + 0.921865i) q^{31} +(-2.03845 - 2.35250i) q^{33} +(2.84681 - 6.23364i) q^{35} -3.35268 q^{37} +(-0.127238 - 0.0817712i) q^{39} +(1.30141 - 9.05150i) q^{41} +(-0.0505065 + 0.351281i) q^{43} +(-0.780002 + 1.70797i) q^{45} +(-0.965628 - 2.11443i) q^{47} +(-0.899518 - 6.25629i) q^{49} +(2.18184 - 0.640647i) q^{51} +(0.154553 + 1.07494i) q^{53} +(4.91691 - 3.15991i) q^{55} +(-0.743578 + 1.62821i) q^{57} +(9.65283 + 6.20349i) q^{59} +(-11.7220 - 3.44189i) q^{61} +(0.519413 + 3.61259i) q^{63} +(0.185975 - 0.214626i) q^{65} +(5.35460 - 6.19098i) q^{67} +(0.432489 - 0.499119i) q^{69} +(-0.518837 - 3.60859i) q^{71} +(-0.182327 - 0.0535362i) q^{73} +(1.24038 + 0.797147i) q^{75} +(4.71950 - 10.3343i) q^{77} +(-7.44167 + 4.78247i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(6.58998 - 1.93499i) q^{83} +(0.607639 + 4.22622i) q^{85} +(-0.917121 - 2.00822i) q^{87} +(-1.09285 + 2.39302i) q^{89} +(0.0785604 - 0.546400i) q^{91} +(0.242666 - 1.68778i) q^{93} +(-2.82738 - 1.81705i) q^{95} -6.01452 q^{97} +(-1.29311 + 2.83151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	1.80159	−	0.528994i	0.805694	−	0.236573i	0.147149	−	0.989114i	$-0.452990\pi$
$5$	1.80159	−	0.528994i	0.805694	−	0.236573i	0.658545	+	0.752541i	$0.271172\pi$
$6$		0			0
$7$	2.39007	−	2.75829i	0.903363	−	1.04254i	−0.0955270	−	0.995427i	$-0.530454\pi$
$7$	2.39007	−	2.75829i	0.903363	−	1.04254i	0.998890	−	0.0471093i	$-0.0150009\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	2.98671	−	0.876979i	0.900528	−	0.264419i	0.201479	−	0.979493i	$-0.435425\pi$
$11$	2.98671	−	0.876979i	0.900528	−	0.264419i	0.699049	+	0.715074i	$0.253607\pi$
$12$		0			0
$13$	0.127238	−	0.0817712i	0.0352896	−	0.0226792i	−0.522877	−	0.852408i	$-0.675141\pi$
$13$	0.127238	−	0.0817712i	0.0352896	−	0.0226792i	0.558167	+	0.829729i	$0.311505\pi$
$14$		0			0
$15$	−1.22960	−	1.41903i	−0.317480	−	0.366392i
$16$		0			0
$17$	−0.323618	+	2.25081i	−0.0784888	+	0.545902i	0.912199	+	0.409748i	$0.134383\pi$
$17$	−0.323618	+	2.25081i	−0.0784888	+	0.545902i	−0.990688	+	0.136154i	$0.956526\pi$
$18$		0			0
$19$	−1.17218	−	1.35276i	−0.268916	−	0.310345i	0.605190	−	0.796081i	$-0.293097\pi$
$19$	−1.17218	−	1.35276i	−0.268916	−	0.310345i	−0.874106	+	0.485736i	$0.838552\pi$
$20$		0			0
$21$	−3.50190	−	1.02825i	−0.764178	−	0.224383i
$22$		0			0
$23$	0.274352	+	0.600747i	0.0572063	+	0.125264i	0.936076	−	0.351797i	$-0.114429\pi$
$23$	0.274352	+	0.600747i	0.0572063	+	0.125264i	−0.878870	+	0.477061i	$0.841702\pi$
$24$		0			0
$25$	−1.24038	+	0.797147i	−0.248077	+	0.159429i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	2.20772			0.409964			0.204982	−	0.978766i	$-0.434286\pi$
$29$	2.20772			0.409964			0.204982	+	0.978766i	$0.434286\pi$
$30$		0			0
$31$	1.43445	+	0.921865i	0.257635	+	0.165572i	0.663082	−	0.748547i	$-0.269248\pi$
$31$	1.43445	+	0.921865i	0.257635	+	0.165572i	−0.405448	+	0.914118i	$0.632884\pi$
$32$		0			0
$33$	−2.03845	−	2.35250i	−0.354849	−	0.409518i
$34$		0			0
$35$	2.84681	−	6.23364i	0.481198	−	1.05368i
$36$		0			0
$37$	−3.35268			−0.551177			−0.275589	−	0.961276i	$-0.588873\pi$
$37$	−3.35268			−0.551177			−0.275589	+	0.961276i	$0.588873\pi$
$38$		0			0
$39$	−0.127238	−	0.0817712i	−0.0203744	−	0.0130939i
$40$		0			0
$41$	1.30141	−	9.05150i	0.203246	−	1.41361i	−0.591324	−	0.806434i	$-0.701394\pi$
$41$	1.30141	−	9.05150i	0.203246	−	1.41361i	0.794570	−	0.607173i	$-0.207697\pi$
$42$		0			0
$43$	−0.0505065	+	0.351281i	−0.00770217	+	0.0535698i	−0.993310	−	0.115478i	$-0.963160\pi$
$43$	−0.0505065	+	0.351281i	−0.00770217	+	0.0535698i	0.985608	+	0.169048i	$0.0540692\pi$
$44$		0			0
$45$	−0.780002	+	1.70797i	−0.116276	+	0.254609i
$46$		0			0
$47$	−0.965628	−	2.11443i	−0.140851	−	0.308421i	0.826039	−	0.563613i	$-0.190589\pi$
$47$	−0.965628	−	2.11443i	−0.140851	−	0.308421i	−0.966891	+	0.255191i	$0.917862\pi$
$48$		0			0
$49$	−0.899518	−	6.25629i	−0.128503	−	0.893755i
$50$		0			0
$51$	2.18184	−	0.640647i	0.305519	−	0.0897086i
$52$		0			0
$53$	0.154553	+	1.07494i	0.0212295	+	0.147654i	0.997679	−	0.0680913i	$-0.0216909\pi$
$53$	0.154553	+	1.07494i	0.0212295	+	0.147654i	−0.976450	+	0.215746i	$0.930782\pi$
$54$		0			0
$55$	4.91691	−	3.15991i	0.662996	−	0.426082i
$56$		0			0
$57$	−0.743578	+	1.62821i	−0.0984893	+	0.215661i
$58$		0			0
$59$	9.65283	+	6.20349i	1.25669	+	0.807626i	0.987828	−	0.155552i	$-0.0497157\pi$
$59$	9.65283	+	6.20349i	1.25669	+	0.807626i	0.268863	+	0.963178i	$0.413352\pi$
$60$		0			0
$61$	−11.7220	−	3.44189i	−1.50085	−	0.440689i	−0.574863	−	0.818250i	$-0.694945\pi$
$61$	−11.7220	−	3.44189i	−1.50085	−	0.440689i	−0.925985	+	0.377561i	$0.876763\pi$
$62$		0			0
$63$	0.519413	+	3.61259i	0.0654398	+	0.455144i
$64$		0			0
$65$	0.185975	−	0.214626i	0.0230673	−	0.0266211i
$66$		0			0
$67$	5.35460	−	6.19098i	0.654168	−	0.756349i
$67$	5.35460	−	6.19098i	0.654168	−	0.756349i
$68$		0			0
$69$	0.432489	−	0.499119i	0.0520655	−	0.0600868i
$70$		0			0
$71$	−0.518837	−	3.60859i	−0.0615746	−	0.428261i	−0.997170	−	0.0751856i	$-0.976045\pi$
$71$	−0.518837	−	3.60859i	−0.0615746	−	0.428261i	0.935595	−	0.353075i	$-0.114864\pi$
$72$		0			0
$73$	−0.182327	−	0.0535362i	−0.0213398	−	0.00626593i	0.271045	−	0.962567i	$-0.412631\pi$
$73$	−0.182327	−	0.0535362i	−0.0213398	−	0.00626593i	−0.292385	+	0.956301i	$0.594449\pi$
$74$		0			0
$75$	1.24038	+	0.797147i	0.143227	+	0.0920466i
$76$		0			0
$77$	4.71950	−	10.3343i	0.537837	−	1.17770i
$78$		0			0
$79$	−7.44167	+	4.78247i	−0.837254	+	0.538070i	−0.887575	−	0.460663i	$-0.847612\pi$
$79$	−7.44167	+	4.78247i	−0.837254	+	0.538070i	0.0503216	+	0.998733i	$0.483975\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	6.58998	−	1.93499i	0.723344	−	0.212393i	0.100721	−	0.994915i	$-0.467885\pi$
$83$	6.58998	−	1.93499i	0.723344	−	0.212393i	0.622623	+	0.782522i	$0.286067\pi$
$84$		0			0
$85$	0.607639	+	4.22622i	0.0659077	+	0.458398i
$86$		0			0
$87$	−0.917121	−	2.00822i	−0.0983257	−	0.215303i
$88$		0			0
$89$	−1.09285	+	2.39302i	−0.115842	+	0.253659i	−0.958668	−	0.284528i	$-0.908163\pi$
$89$	−1.09285	+	2.39302i	−0.115842	+	0.253659i	0.842826	+	0.538187i	$0.180891\pi$
$90$		0			0
$91$	0.0785604	−	0.546400i	0.00823537	−	0.0572782i
$92$		0			0
$93$	0.242666	−	1.68778i	0.0251633	−	0.175014i
$94$		0			0
$95$	−2.82738	−	1.81705i	−0.290083	−	0.186425i
$96$		0			0
$97$	−6.01452			−0.610682			−0.305341	−	0.952243i	$-0.598770\pi$
$97$	−6.01452			−0.610682			−0.305341	+	0.952243i	$0.598770\pi$
$98$		0			0
$99$	−1.29311	+	2.83151i	−0.129962	+	0.284577i
$100$		0			0
$101$	−3.97370	−	4.58590i	−0.395398	−	0.456314i	0.522788	−	0.852463i	$-0.324892\pi$
$101$	−3.97370	−	4.58590i	−0.395398	−	0.456314i	−0.918186	+	0.396149i	$0.870346\pi$
$102$		0			0
$103$	10.5857	+	6.80299i	1.04304	+	0.670319i	0.945736	−	0.324937i	$-0.105343\pi$
$103$	10.5857	+	6.80299i	1.04304	+	0.670319i	0.0973002	+	0.995255i	$0.468979\pi$
$104$		0			0
$105$	−6.85292			−0.668777
$106$		0			0
$107$	5.55867	+	1.63217i	0.537377	+	0.157788i	0.539149	−	0.842210i	$-0.318746\pi$
$107$	5.55867	+	1.63217i	0.537377	+	0.157788i	−0.00177233	+	0.999998i	$0.500564\pi$
$108$		0			0
$109$	−11.6445	+	7.48349i	−1.11534	+	0.716788i	−0.962451	−	0.271454i	$-0.912495\pi$
$109$	−11.6445	+	7.48349i	−1.11534	+	0.716788i	−0.152893	+	0.988243i	$0.548859\pi$
$110$		0			0
$111$	1.39275	+	3.04971i	0.132194	+	0.289465i
$112$		0			0
$113$	7.26981	+	2.13461i	0.683886	+	0.200807i	0.605178	−	0.796090i	$-0.293102\pi$
$113$	7.26981	+	2.13461i	0.683886	+	0.200807i	0.0787088	+	0.996898i	$0.474920\pi$
$114$		0			0
$115$	0.812061	+	0.937168i	0.0757250	+	0.0873914i
$116$		0			0
$117$	−0.0215249	+	0.149709i	−0.00198998	+	0.0138406i
$118$		0			0
$119$	5.43492	+	6.27223i	0.498218	+	0.574975i
$120$		0			0
$121$	−1.10242	+	0.708479i	−0.100220	+	0.0644072i
$122$		0			0
$123$	−8.77416	+	2.57633i	−0.791140	+	0.232300i
$124$		0			0
$125$	−7.96096	+	9.18743i	−0.712050	+	0.821749i
$126$		0			0
$127$	2.19274	−	2.53056i	0.194574	−	0.224550i	−0.650076	−	0.759869i	$-0.725263\pi$
$127$	2.19274	−	2.53056i	0.194574	−	0.224550i	0.844650	+	0.535319i	$0.179808\pi$
$128$		0			0
$129$	0.340517	−	0.0999849i	0.0299809	−	0.00880318i
$130$		0			0
$131$	4.90417	+	10.7386i	0.428479	+	0.938238i	0.993571	+	0.113210i	$0.0361134\pi$
$131$	4.90417	+	10.7386i	0.428479	+	0.938238i	−0.565092	+	0.825028i	$0.691159\pi$
$132$		0			0
$133$	−6.53291			−0.566475
$134$		0			0
$135$	1.87765			0.161602
$136$		0			0
$137$	0.467114	+	1.02284i	0.0399082	+	0.0873869i	0.928536	−	0.371242i	$-0.121068\pi$
$137$	0.467114	+	1.02284i	0.0399082	+	0.0873869i	−0.888628	+	0.458629i	$0.848341\pi$
$138$		0			0
$139$	−20.1089	+	5.90451i	−1.70562	+	0.500814i	−0.981919	−	0.189302i	$-0.939377\pi$
$139$	−20.1089	+	5.90451i	−1.70562	+	0.500814i	−0.723698	+	0.690117i	$0.757559\pi$
$140$		0			0
$141$	−1.52222	+	1.75673i	−0.128194	+	0.147944i
$142$		0			0
$143$	0.308313	−	0.355812i	0.0257824	−	0.0297545i
$144$		0			0
$145$	3.97741	−	1.16787i	0.330306	−	0.0969865i
$146$		0			0
$147$	−5.31724	+	3.41719i	−0.438559	+	0.281845i
$148$		0			0
$149$	8.84336	+	10.2058i	0.724476	+	0.836090i	0.991838	−	0.127506i	$-0.0406972\pi$
$149$	8.84336	+	10.2058i	0.724476	+	0.836090i	−0.267361	+	0.963596i	$0.586152\pi$
$150$		0			0
$151$	−0.0477575	+	0.332161i	−0.00388645	+	0.0270309i	−0.991672	−	0.128786i	$-0.958892\pi$
$151$	−0.0477575	+	0.332161i	−0.00388645	+	0.0270309i	0.987786	+	0.155817i	$0.0498010\pi$
$152$		0			0
$153$	−1.48912	−	1.71854i	−0.120389	−	0.138936i
$154$		0			0
$155$	3.07195	+	0.902005i	0.246745	+	0.0724508i
$156$		0			0
$157$	7.65072	+	16.7527i	0.610594	+	1.33701i	0.922167	+	0.386792i	$0.126417\pi$
$157$	7.65072	+	16.7527i	0.610594	+	1.33701i	−0.311573	+	0.950222i	$0.600856\pi$
$158$		0			0
$159$	0.913595	−	0.587132i	0.0724528	−	0.0465626i
$160$		0			0
$161$	2.31276	+	0.679087i	0.182271	+	0.0535195i
$162$		0			0
$163$	−4.98076			−0.390123			−0.195062	−	0.980791i	$-0.562491\pi$
$163$	−4.98076			−0.390123			−0.195062	+	0.980791i	$0.562491\pi$
$164$		0			0
$165$	−4.91691	−	3.15991i	−0.382781	−	0.245998i
$166$		0			0
$167$	0.481617	+	0.555816i	0.0372687	+	0.0430103i	0.774078	−	0.633090i	$-0.218214\pi$
$167$	0.481617	+	0.555816i	0.0372687	+	0.0430103i	−0.736809	+	0.676101i	$0.763668\pi$
$168$		0			0
$169$	−5.39089	+	11.8044i	−0.414684	+	0.908031i
$170$		0			0
$171$	1.78996			0.136882
$172$		0			0
$173$	20.6953	+	13.3001i	1.57344	+	1.01119i	0.978208	+	0.207629i	$0.0665748\pi$
$173$	20.6953	+	13.3001i	1.57344	+	1.01119i	0.595228	+	0.803557i	$0.297062\pi$
$174$		0			0
$175$	−0.765847	+	5.32658i	−0.0578926	+	0.402652i
$176$		0			0
$177$	1.63297	−	11.3575i	0.122741	−	0.853685i
$178$		0			0
$179$	−4.72850	+	10.3540i	−0.353424	+	0.773892i	0.646515	+	0.762901i	$0.276226\pi$
$179$	−4.72850	+	10.3540i	−0.353424	+	0.773892i	−0.999940	+	0.0109905i	$0.996502\pi$
$180$		0			0
$181$	−4.23803	−	9.28000i	−0.315010	−	0.689777i	0.684209	−	0.729286i	$-0.260148\pi$
$181$	−4.23803	−	9.28000i	−0.315010	−	0.689777i	−0.999219	+	0.0395095i	$0.987420\pi$
$182$		0			0
$183$	1.73864	+	12.0925i	0.128524	+	0.893904i
$184$		0			0
$185$	−6.04015	+	1.77355i	−0.444081	+	0.130394i
$186$		0			0
$187$	1.00736	+	7.00633i	0.0736654	+	0.512354i
$188$		0			0
$189$	3.07036	−	1.97320i	0.223336	−	0.143529i
$190$		0			0
$191$	4.15038	−	9.08807i	0.300311	−	0.657590i	−0.697974	−	0.716123i	$-0.745915\pi$
$191$	4.15038	−	9.08807i	0.300311	−	0.657590i	0.998285	+	0.0585330i	$0.0186423\pi$
$192$		0			0
$193$	−1.59199	−	1.02311i	−0.114594	−	0.0736449i	0.482089	−	0.876122i	$-0.339878\pi$
$193$	−1.59199	−	1.02311i	−0.114594	−	0.0736449i	−0.596682	+	0.802478i	$0.703515\pi$
$194$		0			0
$195$	−0.272488	−	0.0800096i	−0.0195132	−	0.00572960i
$196$		0			0
$197$	2.39553	+	16.6613i	0.170674	+	1.18707i	0.877464	+	0.479643i	$0.159234\pi$
$197$	2.39553	+	16.6613i	0.170674	+	1.18707i	−0.706790	+	0.707424i	$0.749857\pi$
$198$		0			0
$199$	9.79527	−	11.3043i	0.694368	−	0.801344i	−0.293612	−	0.955925i	$-0.594857\pi$
$199$	9.79527	−	11.3043i	0.694368	−	0.801344i	0.987980	+	0.154581i	$0.0494027\pi$
$200$		0			0
$201$	−7.85590	−	2.29888i	−0.554112	−	0.162151i
$202$		0			0
$203$	5.27662	−	6.08954i	0.370346	−	0.427402i
$204$		0			0
$205$	−2.44359	−	16.9955i	−0.170667	−	1.18702i
$206$		0			0
$207$	−0.633677	−	0.186064i	−0.0440436	−	0.0129324i
$208$		0			0
$209$	−4.68730	−	3.01235i	−0.324228	−	0.208368i
$210$		0			0
$211$	0.861860	−	1.88721i	0.0593329	−	0.129921i	−0.877643	−	0.479315i	$-0.840885\pi$
$211$	0.861860	−	1.88721i	0.0593329	−	0.129921i	0.936976	+	0.349394i	$0.113613\pi$
$212$		0			0
$213$	−3.06696	+	1.97101i	−0.210144	+	0.135052i
$214$		0			0
$215$	0.0948334	+	0.659581i	0.00646758	+	0.0449830i
$216$		0			0
$217$	5.97121	−	1.75331i	0.405352	−	0.119022i
$218$		0			0
$219$	0.0270433	+	0.188091i	0.00182742	+	0.0127100i
$220$		0			0
$221$	0.142875	+	0.312852i	0.00961080	+	0.0210447i
$222$		0			0
$223$	−6.89712	+	15.1026i	−0.461865	+	1.01134i	0.525193	+	0.850983i	$0.323993\pi$
$223$	−6.89712	+	15.1026i	−0.461865	+	1.01134i	−0.987058	+	0.160361i	$0.948734\pi$
$224$		0			0
$225$	0.209836	−	1.45944i	0.0139891	−	0.0972960i
$226$		0			0
$227$	1.09176	−	7.59336i	0.0724627	−	0.503989i	−0.920976	−	0.389620i	$-0.872606\pi$
$227$	1.09176	−	7.59336i	0.0724627	−	0.503989i	0.993438	−	0.114369i	$-0.0364846\pi$
$228$		0			0
$229$	−1.91219	−	1.22889i	−0.126361	−	0.0812072i	0.475934	−	0.879481i	$-0.342110\pi$
$229$	−1.91219	−	1.22889i	−0.126361	−	0.0812072i	−0.602294	+	0.798274i	$0.705747\pi$
$230$		0			0
$231$	−11.3609			−0.747495
$232$		0			0
$233$	−2.14010	+	4.68616i	−0.140202	+	0.307000i	−0.966688	−	0.255957i	$-0.917609\pi$
$233$	−2.14010	+	4.68616i	−0.140202	+	0.307000i	0.826486	+	0.562958i	$0.190337\pi$
$234$		0			0
$235$	−2.85818	−	3.29852i	−0.186447	−	0.215172i
$236$		0			0
$237$	7.44167	+	4.78247i	0.483389	+	0.310655i
$238$		0			0
$239$	−12.0387			−0.778720			−0.389360	−	0.921086i	$-0.627304\pi$
$239$	−12.0387			−0.778720			−0.389360	+	0.921086i	$0.627304\pi$
$240$		0			0
$241$	−8.06231	−	2.36731i	−0.519339	−	0.152492i	0.0115498	−	0.999933i	$-0.496324\pi$
$241$	−8.06231	−	2.36731i	−0.519339	−	0.152492i	−0.530888	+	0.847442i	$0.678142\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−4.93010	−	10.7954i	−0.314972	−	0.689693i
$246$		0			0
$247$	−0.259763	−	0.0762733i	−0.0165283	−	0.00485315i
$248$		0			0
$249$	−4.49771	−	5.19063i	−0.285031	−	0.328943i
$250$		0			0
$251$	0.427529	−	2.97353i	0.0269854	−	0.187688i	−0.971870	−	0.235518i	$-0.924321\pi$
$251$	0.427529	−	2.97353i	0.0269854	−	0.187688i	0.998855	+	0.0478300i	$0.0152306\pi$
$252$		0			0
$253$	1.34625	+	1.55366i	0.0846382	+	0.0976777i
$254$		0			0
$255$	3.59189	−	2.30836i	0.224933	−	0.144555i
$256$		0			0
$257$	−17.6046	+	5.16917i	−1.09814	+	0.322444i	−0.780115	−	0.625637i	$-0.784839\pi$
$257$	−17.6046	+	5.16917i	−1.09814	+	0.322444i	−0.318030	+	0.948081i	$0.603021\pi$
$258$		0			0
$259$	−8.01315	+	9.24767i	−0.497913	+	0.574622i
$260$		0			0
$261$	−1.44575	+	1.66849i	−0.0894897	+	0.103277i
$262$		0			0
$263$	8.01178	−	2.35247i	0.494028	−	0.145060i	−0.0252226	−	0.999682i	$-0.508029\pi$
$263$	8.01178	−	2.35247i	0.494028	−	0.145060i	0.519250	+	0.854622i	$0.326211\pi$
$264$		0			0
$265$	0.847076	+	1.85484i	0.0520355	+	0.113942i
$266$		0			0
$267$	2.63075			0.160999
$268$		0			0
$269$	18.0917			1.10307			0.551534	−	0.834152i	$-0.314043\pi$
$269$	18.0917			1.10307			0.551534	+	0.834152i	$0.314043\pi$
$270$		0			0
$271$	−9.80415	−	21.4681i	−0.595559	−	1.30409i	−0.932024	−	0.362397i	$-0.881958\pi$
$271$	−9.80415	−	21.4681i	−0.595559	−	1.30409i	0.336464	−	0.941696i	$-0.390769\pi$
$272$		0			0
$273$	−0.529658	+	0.155522i	−0.0320563	+	0.00941259i
$274$		0			0
$275$	−3.00559	+	3.46864i	−0.181244	+	0.209167i
$276$		0			0
$277$	−1.81945	+	2.09975i	−0.109320	+	0.126162i	−0.807772	−	0.589495i	$-0.799327\pi$
$277$	−1.81945	+	2.09975i	−0.109320	+	0.126162i	0.698452	+	0.715657i	$0.253872\pi$
$278$		0			0
$279$	−1.63606	+	0.480392i	−0.0979486	+	0.0287603i
$280$		0			0
$281$	−7.82491	+	5.02876i	−0.466795	+	0.299991i	−0.752814	−	0.658233i	$-0.771304\pi$
$281$	−7.82491	+	5.02876i	−0.466795	+	0.299991i	0.286019	+	0.958224i	$0.407668\pi$
$282$		0			0
$283$	16.2079	+	18.7050i	0.963462	+	1.11189i	0.993669	+	0.112351i	$0.0358381\pi$
$283$	16.2079	+	18.7050i	0.963462	+	1.11189i	−0.0302065	+	0.999544i	$0.509616\pi$
$284$		0			0
$285$	−0.478308	+	3.32671i	−0.0283325	+	0.197057i
$286$		0			0
$287$	−21.8562	−	25.2234i	−1.29013	−	1.48889i
$288$		0			0
$289$	11.3500	+	3.33265i	0.667645	+	0.196038i
$290$		0			0
$291$	2.49852	+	5.47100i	0.146466	+	0.320716i
$292$		0			0
$293$	−19.6734	+	12.6433i	−1.14933	+	0.738630i	−0.969506	−	0.245069i	$-0.921189\pi$
$293$	−19.6734	+	12.6433i	−1.14933	+	0.738630i	−0.179824	+	0.983699i	$0.557553\pi$
$294$		0			0
$295$	20.6720	+	6.06985i	1.20357	+	0.353400i
$296$		0			0
$297$	3.11281			0.180623
$298$		0			0
$299$	0.0840319	+	0.0540040i	0.00485969	+	0.00312313i
$300$		0			0
$301$	0.848220	+	0.978898i	0.0488906	+	0.0564228i
$302$		0			0
$303$	−2.52074	+	5.51966i	−0.144813	+	0.317096i
$304$		0			0
$305$	−22.9389			−1.31348
$306$		0			0
$307$	16.5533	+	10.6382i	0.944749	+	0.607153i	0.919738	−	0.392534i	$-0.128401\pi$
$307$	16.5533	+	10.6382i	0.944749	+	0.607153i	0.0250114	+	0.999687i	$0.492038\pi$
$308$		0			0
$309$	1.79078	−	12.4551i	0.101874	−	0.708547i
$310$		0			0
$311$	3.65481	−	25.4198i	0.207245	−	1.44142i	−0.574848	−	0.818260i	$-0.694939\pi$
$311$	3.65481	−	25.4198i	0.207245	−	1.44142i	0.782093	−	0.623162i	$-0.214152\pi$
$312$		0			0
$313$	10.2070	−	22.3501i	0.576931	−	1.26330i	−0.366093	−	0.930578i	$-0.619305\pi$
$313$	10.2070	−	22.3501i	0.576931	−	1.26330i	0.943024	−	0.332725i	$-0.107968\pi$
$314$		0			0
$315$	2.84681	+	6.23364i	0.160399	+	0.351226i
$316$		0			0
$317$	−1.42831	−	9.93412i	−0.0802219	−	0.557956i	−0.989805	−	0.142432i	$-0.954508\pi$
$317$	−1.42831	−	9.93412i	−0.0802219	−	0.557956i	0.909583	−	0.415523i	$-0.136401\pi$
$318$		0			0
$319$	6.59384	−	1.93613i	0.369184	−	0.108402i
$320$		0			0
$321$	−0.824478	−	5.73437i	−0.0460179	−	0.320061i
$322$		0			0
$323$	3.42415	−	2.20057i	0.190525	−	0.122443i
$324$		0			0
$325$	−0.0926409	+	0.202855i	−0.00513879	+	0.0112524i
$326$		0			0
$327$	11.6445	+	7.48349i	0.643944	+	0.413838i
$328$		0			0
$329$	−8.14014	−	2.39016i	−0.448780	−	0.131774i
$330$		0			0
$331$	4.16695	+	28.9818i	0.229036	+	1.59298i	0.702182	+	0.711998i	$0.252209\pi$
$331$	4.16695	+	28.9818i	0.229036	+	1.59298i	−0.473145	+	0.880984i	$0.656882\pi$
$332$		0			0
$333$	2.19554	−	2.53379i	0.120315	−	0.138851i
$334$		0			0
$335$	6.37178	−	13.9861i	0.348128	−	0.764145i
$336$		0			0
$337$	8.99004	−	10.3751i	0.489718	−	0.565165i	−0.456072	−	0.889943i	$-0.650744\pi$
$337$	8.99004	−	10.3751i	0.489718	−	0.565165i	0.945790	+	0.324778i	$0.105289\pi$
$338$		0			0
$339$	−1.07828	−	7.49960i	−0.0585641	−	0.407322i
$340$		0			0
$341$	5.09275	+	1.49537i	0.275788	+	0.0809786i
$342$		0			0
$343$	2.08594	+	1.34055i	0.112630	+	0.0723829i
$344$		0			0
$345$	0.515136	−	1.12799i	0.0277340	−	0.0607289i
$346$		0			0
$347$	7.30508	−	4.69469i	0.392157	−	0.252024i	−0.329672	−	0.944096i	$-0.606938\pi$
$347$	7.30508	−	4.69469i	0.392157	−	0.252024i	0.721829	+	0.692071i	$0.243302\pi$
$348$		0			0
$349$	−2.16651	−	15.0684i	−0.115971	−	0.806595i	−0.961920	−	0.273331i	$-0.911874\pi$
$349$	−2.16651	−	15.0684i	−0.115971	−	0.806595i	0.845949	−	0.533264i	$-0.179035\pi$
$350$		0			0
$351$	0.145122	−	0.0426116i	0.00774604	−	0.00227444i
$352$		0			0
$353$	3.35632	+	23.3437i	0.178639	+	1.24246i	0.859917	+	0.510434i	$0.170515\pi$
$353$	3.35632	+	23.3437i	0.178639	+	1.24246i	−0.681278	+	0.732025i	$0.738576\pi$
$354$		0			0
$355$	−2.84365	−	6.22673i	−0.150925	−	0.330480i
$356$		0			0
$357$	3.44768	−	7.54936i	0.182470	−	0.399554i
$358$		0			0
$359$	2.72336	−	18.9414i	0.143733	−	0.999688i	−0.782476	−	0.622680i	$-0.786044\pi$
$359$	2.72336	−	18.9414i	0.143733	−	0.999688i	0.926210	−	0.377008i	$-0.123047\pi$
$360$		0			0
$361$	2.24801	−	15.6353i	0.118316	−	0.822908i
$362$		0			0
$363$	1.10242	+	0.708479i	0.0578618	+	0.0371855i
$364$		0			0
$365$	−0.356799			−0.0186757
$366$		0			0
$367$	2.71899	−	5.95376i	0.141930	−	0.310784i	−0.825296	−	0.564700i	$-0.808992\pi$
$367$	2.71899	−	5.95376i	0.141930	−	0.310784i	0.967226	+	0.253917i	$0.0817190\pi$
$368$		0			0
$369$	5.98843	+	6.91101i	0.311745	+	0.359773i
$370$		0			0
$371$	3.33439	+	2.14288i	0.173113	+	0.111253i
$372$		0			0
$373$	−10.5721			−0.547403			−0.273702	−	0.961815i	$-0.588248\pi$
$373$	−10.5721			−0.547403			−0.273702	+	0.961815i	$0.588248\pi$
$374$		0			0
$375$	11.6643	+	3.42494i	0.602341	+	0.176863i
$376$		0			0
$377$	0.280907	−	0.180528i	0.0144675	−	0.00929767i
$378$		0			0
$379$	7.02781	+	15.3888i	0.360994	+	0.790467i	0.999778	+	0.0210808i	$0.00671071\pi$
$379$	7.02781	+	15.3888i	0.360994	+	0.790467i	−0.638783	+	0.769387i	$0.720562\pi$
$380$		0			0
$381$	−3.21277	−	0.943355i	−0.164595	−	0.0483295i
$382$		0			0
$383$	−5.59587	−	6.45798i	−0.285936	−	0.329987i	0.594551	−	0.804058i	$-0.297330\pi$
$383$	−5.59587	−	6.45798i	−0.285936	−	0.329987i	−0.880487	+	0.474070i	$0.842784\pi$
$384$		0			0
$385$	3.03583	−	21.1147i	0.154720	−	1.07610i
$386$		0			0
$387$	−0.232405	−	0.268210i	−0.0118138	−	0.0136339i
$388$		0			0
$389$	−3.34597	+	2.15032i	−0.169647	+	0.109026i	−0.622709	−	0.782453i	$-0.713968\pi$
$389$	−3.34597	+	2.15032i	−0.169647	+	0.109026i	0.453062	+	0.891479i	$0.350332\pi$
$390$		0			0
$391$	−1.44095	+	0.423102i	−0.0728721	+	0.0213972i
$392$		0			0
$393$	7.73093	−	8.92197i	0.389974	−	0.450054i
$394$		0			0
$395$	−10.8769	+	12.5526i	−0.547278	+	0.631592i
$396$		0			0
$397$	27.2849	−	8.01157i	1.36939	−	0.402089i	0.487327	−	0.873220i	$-0.337972\pi$
$397$	27.2849	−	8.01157i	1.36939	−	0.402089i	0.882064	+	0.471130i	$0.156154\pi$
$398$		0			0
$399$	2.71387	+	5.94254i	0.135863	+	0.297499i
$400$		0			0
$401$	−26.2138			−1.30906			−0.654528	−	0.756038i	$-0.727133\pi$
$401$	−26.2138			−1.30906			−0.654528	+	0.756038i	$0.727133\pi$
$402$		0			0
$403$	0.257899			0.0128469
$404$		0			0
$405$	−0.780002	−	1.70797i	−0.0387586	−	0.0848695i
$406$		0			0
$407$	−10.0135	+	2.94023i	−0.496351	+	0.145742i
$408$		0			0
$409$	−0.667743	+	0.770616i	−0.0330178	+	0.0381045i	−0.772018	−	0.635600i	$-0.780753\pi$
$409$	−0.667743	+	0.770616i	−0.0330178	+	0.0381045i	0.739001	+	0.673705i	$0.235298\pi$
$410$		0			0
$411$	0.736359	−	0.849804i	0.0363219	−	0.0419177i
$412$		0			0
$413$	40.1820	−	11.7985i	1.97723	−	0.580566i
$414$		0			0
$415$	10.8488	−	6.97212i	0.532548	−	0.342248i
$416$		0			0
$417$	13.7245	+	15.8389i	0.672091	+	0.775634i
$418$		0			0
$419$	0.160215	−	1.11432i	0.00782700	−	0.0544380i	−0.985534	−	0.169480i	$-0.945791\pi$
$419$	0.160215	−	1.11432i	0.00782700	−	0.0544380i	0.993361	+	0.115042i	$0.0367003\pi$
$420$		0			0
$421$	−3.58169	−	4.13349i	−0.174561	−	0.201454i	0.661727	−	0.749745i	$-0.269824\pi$
$421$	−3.58169	−	4.13349i	−0.174561	−	0.201454i	−0.836287	+	0.548291i	$0.815279\pi$
$422$		0			0
$423$	2.23033	+	0.654885i	0.108442	+	0.0318416i
$424$		0			0
$425$	−1.39282	−	3.04984i	−0.0675615	−	0.147939i
$426$		0			0
$427$	−37.5102	+	24.1063i	−1.81524	+	1.16659i
$428$		0			0
$429$	−0.451736	−	0.132642i	−0.0218100	−	0.00640400i
$430$		0			0
$431$	−14.6894			−0.707562			−0.353781	−	0.935328i	$-0.615104\pi$
$431$	−14.6894			−0.707562			−0.353781	+	0.935328i	$0.615104\pi$
$432$		0			0
$433$	−1.71109	−	1.09965i	−0.0822298	−	0.0528459i	0.498880	−	0.866671i	$-0.333745\pi$
$433$	−1.71109	−	1.09965i	−0.0822298	−	0.0528459i	−0.581110	+	0.813825i	$0.697381\pi$
$434$		0			0
$435$	−2.71461	−	3.13282i	−0.130155	−	0.150207i
$436$		0			0
$437$	0.491080	−	1.07532i	0.0234915	−	0.0514393i
$438$		0			0
$439$	9.82775			0.469053			0.234526	−	0.972110i	$-0.424646\pi$
$439$	9.82775			0.469053			0.234526	+	0.972110i	$0.424646\pi$
$440$		0			0
$441$	5.31724	+	3.41719i	0.253202	+	0.162723i
$442$		0			0
$443$	−0.124244	+	0.864136i	−0.00590301	+	0.0410563i	−0.992560	−	0.121756i	$-0.961147\pi$
$443$	−0.124244	+	0.864136i	−0.00590301	+	0.0410563i	0.986657	+	0.162812i	$0.0520565\pi$
$444$		0			0
$445$	−0.702981	+	4.88934i	−0.0333245	+	0.231777i
$446$		0			0
$447$	5.60984	−	12.2838i	0.265336	−	0.581006i
$448$		0			0
$449$	11.2869	+	24.7148i	0.532660	+	1.16636i	0.964420	+	0.264375i	$0.0851655\pi$
$449$	11.2869	+	24.7148i	0.532660	+	1.16636i	−0.431760	+	0.901989i	$0.642107\pi$
$450$		0			0
$451$	−4.05104	−	28.1756i	−0.190756	−	1.32674i
$452$		0			0
$453$	0.321983	−	0.0945428i	0.0151281	−	0.00444201i
$454$		0			0
$455$	−0.147509	−	1.02594i	−0.00691531	−	0.0480970i
$456$		0			0
$457$	0.560778	−	0.360390i	0.0262321	−	0.0168583i	−0.527459	−	0.849580i	$-0.676855\pi$
$457$	0.560778	−	0.360390i	0.0262321	−	0.0168583i	0.553691	+	0.832722i	$0.313219\pi$
$458$		0			0
$459$	−0.944635	+	2.06846i	−0.0440918	+	0.0965476i
$460$		0			0
$461$	−13.9996	−	8.99697i	−0.652024	−	0.419031i	0.172381	−	0.985030i	$-0.444854\pi$
$461$	−13.9996	−	8.99697i	−0.652024	−	0.419031i	−0.824405	+	0.566000i	$0.808490\pi$
$462$		0			0
$463$	−20.4270	−	5.99792i	−0.949325	−	0.278747i	−0.229819	−	0.973233i	$-0.573813\pi$
$463$	−20.4270	−	5.99792i	−0.949325	−	0.278747i	−0.719506	+	0.694486i	$0.755632\pi$
$464$		0			0
$465$	−0.455640	−	3.16905i	−0.0211298	−	0.146961i
$466$		0			0
$467$	−10.5463	+	12.1711i	−0.488024	+	0.563210i	−0.945337	−	0.326096i	$-0.894267\pi$
$467$	−10.5463	+	12.1711i	−0.488024	+	0.563210i	0.457312	+	0.889306i	$0.348812\pi$
$468$		0			0
$469$	−4.27866	−	29.5664i	−0.197570	−	1.36525i
$470$		0			0
$471$	12.0606	−	13.9187i	0.555723	−	0.641339i
$472$		0			0
$473$	0.157217	+	1.09347i	0.00722885	+	0.0502777i
$474$		0			0
$475$	2.53230	+	0.743551i	0.116190	+	0.0341165i
$476$		0			0
$477$	−0.913595	−	0.587132i	−0.0418306	−	0.0268829i
$478$		0			0
$479$	16.8867	−	36.9767i	0.771573	−	1.68951i	0.0484141	−	0.998827i	$-0.484583\pi$
$479$	16.8867	−	36.9767i	0.771573	−	1.68951i	0.723159	−	0.690682i	$-0.242689\pi$
$480$		0			0
$481$	−0.426590	+	0.274153i	−0.0194508	+	0.0125003i
$482$		0			0
$483$	−0.343035	−	2.38586i	−0.0156086	−	0.108560i
$484$		0			0
$485$	−10.8357	+	3.18164i	−0.492023	+	0.144471i
$486$		0			0
$487$	−0.476441	−	3.31372i	−0.0215896	−	0.150159i	0.976175	−	0.216984i	$-0.0696220\pi$
$487$	−0.476441	−	3.31372i	−0.0215896	−	0.150159i	−0.997765	+	0.0668254i	$0.978713\pi$
$488$		0			0
$489$	2.06908	+	4.53066i	0.0935672	+	0.204883i
$490$		0			0
$491$	−3.63248	+	7.95402i	−0.163931	+	0.358960i	−0.973715	−	0.227769i	$-0.926857\pi$
$491$	−3.63248	+	7.95402i	−0.163931	+	0.358960i	0.809784	+	0.586728i	$0.199584\pi$
$492$		0			0
$493$	−0.714458	+	4.96916i	−0.0321776	+	0.223800i
$494$		0			0
$495$	−0.831794	+	5.78525i	−0.0373864	+	0.260028i
$496$		0			0
$497$	−11.1936	−	7.19369i	−0.502101	−	0.322681i
$498$		0			0
$499$	−28.2167			−1.26315			−0.631575	−	0.775314i	$-0.717591\pi$
$499$	−28.2167			−1.26315			−0.631575	+	0.775314i	$0.717591\pi$
$500$		0			0
$501$	0.305517	−	0.668989i	0.0136495	−	0.0298882i
$502$		0			0
$503$	−18.0907	−	20.8778i	−0.806625	−	0.930895i	0.192100	−	0.981375i	$-0.438470\pi$
$503$	−18.0907	−	20.8778i	−0.806625	−	0.930895i	−0.998725	+	0.0504802i	$0.983925\pi$
$504$		0			0
$505$	−9.58488	−	6.15983i	−0.426522	−	0.274109i
$506$		0			0
$507$	12.9771			0.576334
$508$		0			0
$509$	36.5184	+	10.7228i	1.61865	+	0.475278i	0.960655	−	0.277745i	$-0.0895870\pi$
$509$	36.5184	+	10.7228i	1.61865	+	0.475278i	0.657994	+	0.753023i	$0.271405\pi$
$510$		0			0
$511$	−0.583444	+	0.374957i	−0.0258100	+	0.0165871i
$512$		0			0
$513$	−0.743578	−	1.62821i	−0.0328298	−	0.0718871i
$514$		0			0
$515$	22.6697	+	6.65643i	0.998948	+	0.293318i
$516$		0			0
$517$	−4.73837	−	5.46837i	−0.208393	−	0.240498i
$518$		0			0
$519$	3.50103	−	24.3502i	0.153678	−	1.06885i
$520$		0			0
$521$	14.4210	+	16.6428i	0.631797	+	0.729133i	0.977902	−	0.209063i	$-0.0670413\pi$
$521$	14.4210	+	16.6428i	0.631797	+	0.729133i	−0.346105	+	0.938196i	$0.612496\pi$
$522$		0			0
$523$	26.2701	−	16.8828i	1.14871	−	0.738232i	0.179329	−	0.983789i	$-0.442607\pi$
$523$	26.2701	−	16.8828i	1.14871	−	0.738232i	0.969382	+	0.245557i	$0.0789709\pi$
$524$		0			0
$525$	5.16337	−	1.51610i	0.225348	−	0.0661682i
$526$		0			0
$527$	−2.53916	+	2.93034i	−0.110607	+	0.127648i
$528$		0			0
$529$	14.7762	−	17.0526i	0.642442	−	0.741418i
$530$		0			0
$531$	−11.0095	+	3.23269i	−0.477774	+	0.140287i
$532$		0			0
$533$	−0.574563	−	1.25812i	−0.0248871	−	0.0544951i
$534$		0			0
$535$	10.8778			0.470290
$536$		0			0
$537$	11.3826			0.491195
$538$		0			0
$539$	−8.17323	−	17.8969i	−0.352046	−	0.770873i
$540$		0			0
$541$	32.3709	−	9.50495i	1.39173	−	0.408650i	0.501896	−	0.864928i	$-0.332636\pi$
$541$	32.3709	−	9.50495i	1.39173	−	0.408650i	0.889837	+	0.456279i	$0.150818\pi$
$542$		0			0
$543$	−6.68084	+	7.71010i	−0.286702	+	0.330872i
$544$		0			0
$545$	−17.0199	+	19.6421i	−0.729054	+	0.841373i
$546$		0			0
$547$	4.46969	−	1.31242i	0.191110	−	0.0561151i	−0.184777	−	0.982781i	$-0.559156\pi$
$547$	4.46969	−	1.31242i	0.191110	−	0.0561151i	0.375887	+	0.926665i	$0.377338\pi$
$548$		0			0
$549$	10.2775	−	6.60494i	0.438632	−	0.281892i
$550$		0			0
$551$	−2.58784	−	2.98653i	−0.110246	−	0.127230i
$552$		0			0
$553$	−4.59469	+	31.9568i	−0.195386	+	1.35894i
$554$		0			0
$555$	4.12244	+	4.75755i	0.174988	+	0.201947i
$556$		0			0
$557$	11.4980	+	3.37613i	0.487188	+	0.143051i	0.516096	−	0.856531i	$-0.327385\pi$
$557$	11.4980	+	3.37613i	0.487188	+	0.143051i	−0.0289082	+	0.999582i	$0.509203\pi$
$558$		0			0
$559$	0.0222983	+	0.0488264i	0.000943116	+	0.00206514i
$560$		0			0
$561$	5.95471	−	3.82686i	0.251408	−	0.161570i
$562$		0			0
$563$	−12.2202	−	3.58817i	−0.515020	−	0.151224i	0.0138865	−	0.999904i	$-0.495580\pi$
$563$	−12.2202	−	3.58817i	−0.515020	−	0.151224i	−0.528907	+	0.848680i	$0.677398\pi$
$564$		0			0
$565$	14.2264			0.598509
$566$		0			0
$567$	−3.07036	−	1.97320i	−0.128943	−	0.0828666i
$568$		0			0
$569$	−6.38741	−	7.37146i	−0.267774	−	0.309028i	0.605899	−	0.795542i	$-0.292814\pi$
$569$	−6.38741	−	7.37146i	−0.267774	−	0.309028i	−0.873673	+	0.486514i	$0.838268\pi$
$570$		0			0
$571$	−13.6240	+	29.8325i	−0.570149	+	1.24845i	0.376570	+	0.926388i	$0.377104\pi$
$571$	−13.6240	+	29.8325i	−0.570149	+	1.24845i	−0.946718	+	0.322063i	$0.895624\pi$
$572$		0			0
$573$	−9.99093			−0.417377
$574$		0			0
$575$	−0.819186	−	0.526459i	−0.0341624	−	0.0219548i
$576$		0			0
$577$	3.11666	−	21.6768i	0.129748	−	0.902418i	−0.816124	−	0.577877i	$-0.803881\pi$
$577$	3.11666	−	21.6768i	0.129748	−	0.902418i	0.945872	−	0.324541i	$-0.105210\pi$
$578$		0			0
$579$	−0.269316	+	1.87314i	−0.0111924	+	0.0778448i
$580$		0			0
$581$	10.4133	−	22.8019i	0.432015	−	0.945981i
$582$		0			0
$583$	1.40430	+	3.07500i	0.0581603	+	0.127353i
$584$		0			0
$585$	0.0404162	+	0.281101i	0.00167100	+	0.0116221i
$586$		0			0
$587$	−40.1456	+	11.7878i	−1.65699	+	0.486535i	−0.970599	−	0.240702i	$-0.922622\pi$
$587$	−40.1456	+	11.7878i	−1.65699	+	0.486535i	−0.686387	+	0.727237i	$0.740804\pi$
$588$		0			0
$589$	−0.434363	−	3.02106i	−0.0178976	−	0.124481i
$590$		0			0
$591$	14.1605	−	9.10039i	0.582485	−	0.374340i
$592$		0			0
$593$	−10.3443	+	22.6509i	−0.424790	+	0.930160i	0.569354	+	0.822093i	$0.307194\pi$
$593$	−10.3443	+	22.6509i	−0.424790	+	0.930160i	−0.994144	+	0.108067i	$0.965534\pi$
$594$		0			0
$595$	13.1095	+	8.42494i	0.537435	+	0.345389i
$596$		0			0
$597$	−14.3519	−	4.21410i	−0.587384	−	0.172472i
$598$		0			0
$599$	−0.761522	−	5.29650i	−0.0311150	−	0.216409i	0.968332	−	0.249667i	$-0.0803210\pi$
$599$	−0.761522	−	5.29650i	−0.0311150	−	0.216409i	−0.999447	+	0.0332573i	$0.989412\pi$
$600$		0			0
$601$	−10.7870	+	12.4488i	−0.440010	+	0.507799i	−0.931828	−	0.362899i	$-0.881787\pi$
$601$	−10.7870	+	12.4488i	−0.440010	+	0.507799i	0.491818	+	0.870698i	$0.336332\pi$
$602$		0			0
$603$	1.17232	+	8.10097i	0.0477405	+	0.329897i
$604$		0			0
$605$	−1.61132	+	1.85956i	−0.0655093	+	0.0756018i
$606$		0			0
$607$	−5.69852	−	39.6341i	−0.231296	−	1.60870i	−0.692510	−	0.721408i	$-0.743495\pi$
$607$	−5.69852	−	39.6341i	−0.231296	−	1.60870i	0.461215	−	0.887289i	$-0.347414\pi$
$608$		0			0
$609$	−7.73123	−	2.27009i	−0.313285	−	0.0919888i
$610$		0			0
$611$	−0.295764	−	0.190076i	−0.0119653	−	0.00768966i
$612$		0			0
$613$	−15.8609	+	34.7306i	−0.640617	+	1.40276i	0.258915	+	0.965900i	$0.416635\pi$
$613$	−15.8609	+	34.7306i	−0.640617	+	1.40276i	−0.899532	+	0.436856i	$0.856092\pi$
$614$		0			0
$615$	−14.4446	+	9.28296i	−0.582461	+	0.374325i
$616$		0			0
$617$	4.04520	+	28.1350i	0.162854	+	1.13267i	0.893221	+	0.449618i	$0.148440\pi$
$617$	4.04520	+	28.1350i	0.162854	+	1.13267i	−0.730367	+	0.683055i	$0.760651\pi$
$618$		0			0
$619$	37.3405	−	10.9642i	1.50084	−	0.440687i	0.574860	−	0.818252i	$-0.305057\pi$
$619$	37.3405	−	10.9642i	1.50084	−	0.440687i	0.925983	+	0.377564i	$0.123238\pi$
$620$		0			0
$621$	0.0939888	+	0.653706i	0.00377164	+	0.0262323i
$622$		0			0
$623$	3.98863	+	8.73389i	0.159801	+	0.349916i
$624$		0			0
$625$	−6.41973	+	14.0572i	−0.256789	+	0.562289i
$626$		0			0
$627$	−0.792951	+	5.51509i	−0.0316674	+	0.220252i
$628$		0			0
$629$	1.08499	−	7.54625i	0.0432613	−	0.300889i
$630$		0			0
$631$	−19.8377	−	12.7489i	−0.789726	−	0.507526i	0.0825222	−	0.996589i	$-0.473702\pi$
$631$	−19.8377	−	12.7489i	−0.789726	−	0.507526i	−0.872248	+	0.489063i	$0.837339\pi$
$632$		0			0
$633$	−2.07470			−0.0824617
$634$		0			0
$635$	2.61176	−	5.71896i	0.103645	−	0.226950i
$636$		0			0
$637$	−0.626037	−	0.722485i	−0.0248045	−	0.0286259i
$638$		0			0
$639$	3.06696	+	1.97101i	0.121327	+	0.0779721i
$640$		0			0
$641$	9.27567			0.366367			0.183183	−	0.983079i	$-0.441360\pi$
$641$	9.27567			0.366367			0.183183	+	0.983079i	$0.441360\pi$
$642$		0			0
$643$	−14.4824	−	4.25242i	−0.571131	−	0.167699i	−0.0165997	−	0.999862i	$-0.505284\pi$
$643$	−14.4824	−	4.25242i	−0.571131	−	0.167699i	−0.554531	+	0.832163i	$0.687102\pi$
$644$		0			0
$645$	0.560580	−	0.360263i	0.0220728	−	0.0141853i
$646$		0			0
$647$	−18.8893	−	41.3618i	−0.742614	−	1.62610i	−0.779206	−	0.626768i	$-0.784377\pi$
$647$	−18.8893	−	41.3618i	−0.742614	−	1.62610i	0.0365914	−	0.999330i	$-0.488350\pi$
$648$		0			0
$649$	34.2706	+	10.0627i	1.34524	+	0.394997i
$650$		0			0
$651$	−4.07539	−	4.70325i	−0.159727	−	0.184335i
$652$		0			0
$653$	−5.89912	+	41.0293i	−0.230850	+	1.60560i	0.463591	+	0.886050i	$0.346561\pi$
$653$	−5.89912	+	41.0293i	−0.230850	+	1.60560i	−0.694441	+	0.719550i	$0.744348\pi$
$654$		0			0
$655$	14.5160	+	16.7523i	0.567185	+	0.654567i
$656$		0			0
$657$	0.159859	−	0.102735i	0.00623669	−	0.00400808i
$658$		0			0
$659$	−40.2471	+	11.8176i	−1.56781	+	0.460349i	−0.946362	−	0.323109i	$-0.895272\pi$
$659$	−40.2471	+	11.8176i	−1.56781	+	0.460349i	−0.621444	+	0.783459i	$0.713454\pi$
$660$		0			0
$661$	−26.5427	+	30.6319i	−1.03239	+	1.19144i	−0.0511443	+	0.998691i	$0.516287\pi$
$661$	−26.5427	+	30.6319i	−1.03239	+	1.19144i	−0.981247	+	0.192752i	$0.938259\pi$
$662$		0			0
$663$	0.225228	−	0.259927i	0.00874713	−	0.0100947i
$664$		0			0
$665$	−11.7696	+	3.45587i	−0.456406	+	0.134013i
$666$		0			0
$667$	0.605693	+	1.32628i	0.0234525	+	0.0513539i
$668$		0			0
$669$	16.6030			0.641907
$670$		0			0
$671$	−38.0287			−1.46808
$672$		0			0
$673$	12.4346	+	27.2280i	0.479319	+	1.04956i	0.982650	+	0.185468i	$0.0593801\pi$
$673$	12.4346	+	27.2280i	0.479319	+	1.04956i	−0.503332	+	0.864093i	$0.667893\pi$
$674$		0			0
$675$	−1.41472	+	0.415400i	−0.0544527	+	0.0159888i
$676$		0			0
$677$	−11.1167	+	12.8294i	−0.427250	+	0.493072i	−0.928032	−	0.372501i	$-0.878500\pi$
$677$	−11.1167	+	12.8294i	−0.427250	+	0.493072i	0.500782	+	0.865573i	$0.333046\pi$
$678$		0			0
$679$	−14.3751	+	16.5898i	−0.551667	+	0.636658i
$680$		0			0
$681$	−7.36070	+	2.16130i	−0.282062	+	0.0828210i
$682$		0			0
$683$	−29.1879	+	18.7579i	−1.11684	+	0.717753i	−0.962774	−	0.270307i	$-0.912875\pi$
$683$	−29.1879	+	18.7579i	−1.11684	+	0.717753i	−0.154071	+	0.988060i	$0.549238\pi$
$684$		0			0
$685$	1.38262	+	1.59563i	0.0528272	+	0.0609659i
$686$		0			0
$687$	−0.323485	+	2.24988i	−0.0123417	+	0.0858384i
$688$		0			0
$689$	0.107564	+	0.124136i	0.00409786	+	0.00472919i
$690$		0			0
$691$	−5.52113	−	1.62115i	−0.210033	−	0.0616714i	0.175023	−	0.984564i	$-0.444000\pi$
$691$	−5.52113	−	1.62115i	−0.210033	−	0.0616714i	−0.385057	+	0.922893i	$0.625818\pi$
$692$		0			0
$693$	4.71950	+	10.3343i	0.179279	+	0.392567i
$694$		0			0
$695$	−33.1045	+	21.2750i	−1.25573	+	0.807007i
$696$		0			0
$697$	19.9521	+	5.85845i	0.755738	+	0.221905i
$698$		0			0
$699$	5.15171			0.194856
$700$		0			0
$701$	−28.8091	−	18.5145i	−1.08810	−	0.699282i	−0.131689	−	0.991291i	$-0.542040\pi$
$701$	−28.8091	−	18.5145i	−1.08810	−	0.699282i	−0.956416	+	0.292009i	$0.905676\pi$
$702$		0			0
$703$	3.92994	+	4.53539i	0.148220	+	0.171055i
$704$		0			0
$705$	−1.81311	+	3.97015i	−0.0682856	+	0.149525i
$706$		0			0
$707$	−22.1467			−0.832912
$708$		0			0
$709$	−18.8465	−	12.1119i	−0.707796	−	0.454873i	0.136576	−	0.990630i	$-0.456390\pi$
$709$	−18.8465	−	12.1119i	−0.707796	−	0.454873i	−0.844372	+	0.535757i	$0.820026\pi$
$710$		0			0
$711$	1.25891	−	8.75589i	0.0472127	−	0.328372i
$712$		0			0
$713$	−0.160263	+	1.11466i	−0.00600191	+	0.0417442i
$714$		0			0
$715$	0.367231	−	0.804123i	0.0137336	−	0.0300725i
$716$		0			0
$717$	5.00106	+	10.9508i	0.186768	+	0.408965i
$718$		0			0
$719$	1.86702	+	12.9854i	0.0696280	+	0.484273i	0.994562	+	0.104146i	$0.0332108\pi$
$719$	1.86702	+	12.9854i	0.0696280	+	0.484273i	−0.924934	+	0.380128i	$0.875880\pi$
$720$		0			0
$721$	44.0651	−	12.9387i	1.64107	−	0.481862i
$722$		0			0
$723$	1.19582	+	8.31715i	0.0444732	+	0.309318i
$724$		0			0
$725$	−2.73843	+	1.75988i	−0.101703	+	0.0653603i
$726$		0			0
$727$	−5.99097	+	13.1184i	−0.222193	+	0.486534i	−0.987596	−	0.157017i	$-0.949812\pi$
$727$	−5.99097	+	13.1184i	−0.222193	+	0.486534i	0.765403	+	0.643551i	$0.222540\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−0.774321	−	0.227361i	−0.0286393	−	0.00840926i
$732$		0			0
$733$	4.96003	+	34.4977i	0.183203	+	1.27420i	0.849129	+	0.528186i	$0.177128\pi$
$733$	4.96003	+	34.4977i	0.183203	+	1.27420i	−0.665926	+	0.746018i	$0.731963\pi$
$734$		0			0
$735$	−7.77181	+	8.96915i	−0.286668	+	0.330832i
$736$		0			0
$737$	10.5633	−	23.1866i	0.389104	−	0.854088i
$738$		0			0
$739$	27.7273	−	31.9990i	1.01996	−	1.17710i	0.0358875	−	0.999356i	$-0.488574\pi$
$739$	27.7273	−	31.9990i	1.01996	−	1.17710i	0.984077	−	0.177745i	$-0.0568803\pi$
$740$		0			0
$741$	0.0385288	+	0.267974i	0.00141539	+	0.00984426i
$742$		0			0
$743$	32.2711	+	9.47566i	1.18391	+	0.347628i	0.813681	−	0.581311i	$-0.197460\pi$
$743$	32.2711	+	9.47566i	1.18391	+	0.347628i	0.370232	+	0.928939i	$0.379278\pi$
$744$		0			0
$745$	21.3309	+	13.7085i	0.781503	+	0.502242i
$746$		0			0
$747$	−2.85315	+	6.24753i	−0.104391	+	0.228585i
$748$		0			0
$749$	17.7876	−	11.4314i	0.649946	−	0.417695i
$750$		0			0
$751$	−3.31150	−	23.0320i	−0.120838	−	0.840448i	−0.956610	−	0.291371i	$-0.905888\pi$
$751$	−3.31150	−	23.0320i	−0.120838	−	0.840448i	0.835772	−	0.549077i	$-0.185021\pi$
$752$		0			0
$753$	−2.88242	+	0.846355i	−0.105041	+	0.0308429i
$754$		0			0
$755$	0.0896717	+	0.623680i	0.00326349	+	0.0226980i
$756$		0			0
$757$	−3.48582	−	7.63289i	−0.126694	−	0.277422i	0.835646	−	0.549268i	$-0.185093\pi$
$757$	−3.48582	−	7.63289i	−0.126694	−	0.277422i	−0.962341	+	0.271846i	$0.912366\pi$
$758$		0			0
$759$	0.854004	−	1.87001i	0.0309984	−	0.0678770i
$760$		0			0
$761$	3.62796	−	25.2330i	0.131514	−	0.914697i	−0.812069	−	0.583561i	$-0.801659\pi$
$761$	3.62796	−	25.2330i	0.131514	−	0.914697i	0.943583	−	0.331136i	$-0.107432\pi$
$762$		0			0
$763$	−7.18965	+	50.0051i	−0.260283	+	1.81031i
$764$		0			0
$765$	−3.59189	−	2.30836i	−0.129865	−	0.0834591i
$766$		0			0
$767$	1.73548			0.0626644
$768$		0			0
$769$	−5.58070	+	12.2200i	−0.201245	+	0.440666i	−0.983167	−	0.182712i	$-0.941513\pi$
$769$	−5.58070	+	12.2200i	−0.201245	+	0.440666i	0.781921	+	0.623377i	$0.214240\pi$
$770$		0			0
$771$	12.0153	+	13.8663i	0.432719	+	0.499384i
$772$		0			0
$773$	21.8186	+	14.0219i	0.784759	+	0.504334i	0.870610	−	0.491974i	$-0.163724\pi$
$773$	21.8186	+	14.0219i	0.784759	+	0.504334i	−0.0858507	+	0.996308i	$0.527361\pi$
$774$		0			0
$775$	−2.51413			−0.0903102
$776$		0			0
$777$	11.7408	+	3.44740i	0.421198	+	0.123675i
$778$		0			0
$779$	−13.7700	+	8.84946i	−0.493363	+	0.317065i
$780$		0			0
$781$	−4.71427	−	10.3228i	−0.168690	−	0.369379i
$782$		0			0
$783$	2.11829	+	0.621987i	0.0757017	+	0.0222280i
$784$		0			0
$785$	22.6455	+	26.1343i	0.808254	+	0.932775i
$786$		0			0
$787$	−4.55422	+	31.6753i	−0.162340	+	1.12910i	0.731866	+	0.681448i	$0.238650\pi$
$787$	−4.55422	+	31.6753i	−0.162340	+	1.12910i	−0.894207	+	0.447654i	$0.852260\pi$
$788$		0			0
$789$	−5.46810	−	6.31052i	−0.194669	−	0.224660i
$790$		0			0
$791$	23.2633	−	14.9504i	0.827146	−	0.531575i
$792$		0			0
$793$	−1.77294	+	0.520581i	−0.0629588	+	0.0184864i
$794$		0			0
$795$	1.33533	−	1.54106i	0.0473594	−	0.0546556i
$796$		0			0
$797$	35.0418	−	40.4404i	1.24124	−	1.43247i	0.379449	−	0.925213i	$-0.376113\pi$
$797$	35.0418	−	40.4404i	1.24124	−	1.43247i	0.861794	−	0.507259i	$-0.169341\pi$
$798$		0			0
$799$	5.07168	−	1.48918i	0.179423	−	0.0526834i
$800$		0			0
$801$	−1.09285	−	2.39302i	−0.0386141	−	0.0845530i
$802$		0			0
$803$	−0.591510			−0.0208739
$804$		0			0
$805$	4.52587			0.159516
$806$		0			0
$807$	−7.51555	−	16.4568i	−0.264560	−	0.579305i
$808$		0			0
$809$	−20.9722	+	6.15799i	−0.737343	+	0.216503i	−0.628777	−	0.777586i	$-0.716444\pi$
$809$	−20.9722	+	6.15799i	−0.737343	+	0.216503i	−0.108566	+	0.994089i	$0.534626\pi$
$810$		0			0
$811$	7.95474	−	9.18026i	0.279329	−	0.322363i	−0.598697	−	0.800975i	$-0.704315\pi$
$811$	7.95474	−	9.18026i	0.279329	−	0.322363i	0.878026	+	0.478613i	$0.158860\pi$
$812$		0			0
$813$	−15.4553	+	17.8363i	−0.542040	+	0.625547i
$814$		0			0
$815$	−8.97328	+	2.63479i	−0.314320	+	0.0922927i
$816$		0			0
$817$	0.534402	−	0.343440i	0.0186964	−	0.0120154i
$818$		0			0
$819$	0.361495	+	0.417188i	0.0126317	+	0.0145777i
$820$		0			0
$821$	1.19503	−	8.31164i	0.0417069	−	0.290078i	−0.958284	−	0.285818i	$-0.907735\pi$
$821$	1.19503	−	8.31164i	0.0417069	−	0.290078i	0.999991	−	0.00426037i	$-0.00135612\pi$
$822$		0			0
$823$	−15.0362	−	17.3527i	−0.524130	−	0.604879i	0.430530	−	0.902576i	$-0.358327\pi$
$823$	−15.0362	−	17.3527i	−0.524130	−	0.604879i	−0.954660	+	0.297698i	$0.903781\pi$
$824$		0			0
$825$	4.40376	+	1.29306i	0.153319	+	0.0450185i
$826$		0			0
$827$	−15.3920	−	33.7038i	−0.535233	−	1.17200i	−0.963344	−	0.268270i	$-0.913548\pi$
$827$	−15.3920	−	33.7038i	−0.535233	−	1.17200i	0.428111	−	0.903726i	$-0.359179\pi$
$828$		0			0
$829$	3.62442	−	2.32928i	0.125881	−	0.0808991i	−0.476185	−	0.879345i	$-0.657981\pi$
$829$	3.62442	−	2.32928i	0.125881	−	0.0808991i	0.602066	+	0.798446i	$0.294344\pi$
$830$		0			0
$831$	2.66583	+	0.782758i	0.0924766	+	0.0271536i
$832$		0			0
$833$	14.3728			0.497988
$834$		0			0
$835$	1.16170	+	0.746578i	0.0402022	+	0.0258364i
$836$		0			0
$837$	1.11662	+	1.28865i	0.0385962	+	0.0445424i
$838$		0			0
$839$	−12.2414	+	26.8049i	−0.422619	+	0.925407i	0.571848	+	0.820360i	$0.306227\pi$
$839$	−12.2414	+	26.8049i	−0.422619	+	0.925407i	−0.994467	+	0.105048i	$0.966500\pi$
$840$		0			0
$841$	−24.1260			−0.831930
$842$		0			0
$843$	7.82491	+	5.02876i	0.269504	+	0.173200i
$844$		0			0
$845$	−3.46771	+	24.1184i	−0.119293	+	0.829699i
$846$		0			0
$847$	−0.680661	+	4.73410i	−0.0233878	+	0.162666i
$848$		0			0
$849$	10.2816	−	22.5136i	0.352864	−	0.772664i
$850$		0			0
$851$	−0.919815	−	2.01411i	−0.0315308	−	0.0690429i
$852$		0			0
$853$	2.71917	+	18.9122i	0.0931026	+	0.647543i	0.981922	+	0.189285i	$0.0606172\pi$
$853$	2.71917	+	18.9122i	0.0931026	+	0.647543i	−0.888819	+	0.458258i	$0.848474\pi$
$854$		0			0
$855$	3.22478	−	0.946880i	0.110285	−	0.0323826i
$856$		0			0
$857$	0.822835	+	5.72294i	0.0281075	+	0.195492i	0.999037	−	0.0438732i	$-0.0139698\pi$
$857$	0.822835	+	5.72294i	0.0281075	+	0.195492i	−0.970930	+	0.239365i	$0.923061\pi$
$858$		0			0
$859$	1.17985	−	0.758246i	0.0402561	−	0.0258710i	−0.520358	−	0.853948i	$-0.674201\pi$
$859$	1.17985	−	0.758246i	0.0402561	−	0.0258710i	0.560614	+	0.828077i	$0.310565\pi$
$860$		0			0
$861$	−13.8646	+	30.3593i	−0.472505	+	1.03464i
$862$		0			0
$863$	10.7561	+	6.91254i	0.366142	+	0.235305i	0.710755	−	0.703439i	$-0.248353\pi$
$863$	10.7561	+	6.91254i	0.366142	+	0.235305i	−0.344613	+	0.938745i	$0.611990\pi$
$864$		0			0
$865$	44.3201	+	13.0136i	1.50693	+	0.442474i
$866$		0			0
$867$	−1.68346	−	11.7087i	−0.0571733	−	0.397649i
$868$		0			0
$869$	−18.0320	+	20.8101i	−0.611695	+	0.705933i
$870$		0			0
$871$	0.175066	−	1.22558i	0.00593190	−	0.0415273i
$872$		0			0
$873$	3.93867	−	4.54547i	0.133304	−	0.153841i
$874$		0			0
$875$	6.31435	+	43.9173i	0.213464	+	1.48467i
$876$		0			0
$877$	−24.0465	−	7.06069i	−0.811993	−	0.238423i	−0.150728	−	0.988575i	$-0.548162\pi$
$877$	−24.0465	−	7.06069i	−0.811993	−	0.238423i	−0.661265	+	0.750153i	$0.729980\pi$
$878$		0			0
$879$	19.6734	+	12.6433i	0.663566	+	0.426448i
$880$		0			0
$881$	13.6079	−	29.7971i	0.458461	−	1.00389i	−0.529375	−	0.848388i	$-0.677573\pi$
$881$	13.6079	−	29.7971i	0.458461	−	1.00389i	0.987836	−	0.155501i	$-0.0496993\pi$
$882$		0			0
$883$	−23.5445	+	15.1312i	−0.792337	+	0.509204i	−0.873107	−	0.487529i	$-0.837898\pi$
$883$	−23.5445	+	15.1312i	−0.792337	+	0.509204i	0.0807698	+	0.996733i	$0.474262\pi$
$884$		0			0
$885$	−3.06614	−	21.3254i	−0.103067	−	0.716847i
$886$		0			0
$887$	31.8191	−	9.34292i	1.06838	−	0.313705i	0.300159	−	0.953889i	$-0.402960\pi$
$887$	31.8191	−	9.34292i	1.06838	−	0.313705i	0.768221	+	0.640185i	$0.221142\pi$
$888$		0			0
$889$	−1.73920	−	12.0964i	−0.0583310	−	0.405701i
$890$		0			0
$891$	−1.29311	−	2.83151i	−0.0433207	−	0.0948591i
$892$		0			0
$893$	−1.72844	+	3.78475i	−0.0578400	+	0.126652i
$894$		0			0
$895$	−3.04162	+	21.1549i	−0.101670	+	0.707131i
$896$		0			0
$897$	0.0142157	−	0.0988722i	0.000474647	−	0.00330125i
$898$		0			0
$899$	3.16687	+	2.03522i	0.105621	+	0.0678784i
$900$		0			0
$901$	−2.46950			−0.0822709
$902$		0			0
$903$	0.538074	−	1.17822i	0.0179060	−	0.0392086i
$904$		0			0
$905$	−12.5442	−	14.4768i	−0.416985	−	0.481226i
$906$		0			0
$907$	9.61457	+	6.17891i	0.319246	+	0.205167i	0.690442	−	0.723387i	$-0.257416\pi$
$907$	9.61457	+	6.17891i	0.319246	+	0.205167i	−0.371196	+	0.928555i	$0.621052\pi$
$908$		0			0
$909$	6.06801			0.201263
$910$		0			0
$911$	10.0896	+	2.96257i	0.334283	+	0.0981542i	0.444566	−	0.895746i	$-0.353358\pi$
$911$	10.0896	+	2.96257i	0.334283	+	0.0981542i	−0.110284	+	0.993900i	$0.535176\pi$
$912$		0			0
$913$	17.9854	−	11.5585i	0.595231	−	0.382532i
$914$		0			0
$915$	9.52918	+	20.8660i	0.315025	+	0.689808i
$916$		0			0
$917$	41.3416	+	12.1390i	1.36522	+	0.400865i
$918$		0			0
$919$	−35.1516	−	40.5671i	−1.15954	−	1.33818i	−0.931159	−	0.364613i	$-0.881201\pi$
$919$	−35.1516	−	40.5671i	−1.15954	−	1.33818i	−0.228384	−	0.973571i	$-0.573344\pi$
$920$		0			0
$921$	2.80033	−	19.4767i	0.0922739	−	0.641779i
$922$		0			0
$923$	−0.361094	−	0.416725i	−0.0118856	−	0.0137167i
$924$		0			0
$925$	4.15861	−	2.67258i	0.136734	−	0.0878739i
$926$		0			0
$927$	−12.0735	+	3.54510i	−0.396545	+	0.116436i
$928$		0			0
$929$	−27.8552	+	32.1466i	−0.913899	+	1.05470i	0.0844021	+	0.996432i	$0.473102\pi$
$929$	−27.8552	+	32.1466i	−0.913899	+	1.05470i	−0.998301	+	0.0582641i	$0.981443\pi$
$930$		0			0
$931$	−7.40888	+	8.55031i	−0.242816	+	0.280225i
$932$		0			0
$933$	−24.6409	+	7.23522i	−0.806706	+	0.236870i
$934$		0			0
$935$	5.52115	+	12.0896i	0.180561	+	0.395373i
$936$		0			0
$937$	−19.4677			−0.635982			−0.317991	−	0.948094i	$-0.603008\pi$
$937$	−19.4677			−0.635982			−0.317991	+	0.948094i	$0.603008\pi$
$938$		0			0
$939$	−24.5705			−0.801828
$940$		0			0
$941$	−12.7189	−	27.8506i	−0.414626	−	0.907903i	−0.995576	−	0.0939640i	$-0.970046\pi$
$941$	−12.7189	−	27.8506i	−0.414626	−	0.907903i	0.580950	−	0.813939i	$-0.302681\pi$
$942$		0			0
$943$	5.79471	−	1.70148i	0.188702	−	0.0554078i
$944$		0			0
$945$	4.48771	−	5.17909i	0.145985	−	0.168476i
$946$		0			0
$947$	−9.46207	+	10.9198i	−0.307476	+	0.354846i	−0.888366	−	0.459136i	$-0.848159\pi$
$947$	−9.46207	+	10.9198i	−0.307476	+	0.354846i	0.580890	+	0.813982i	$0.302705\pi$
$948$		0			0
$949$	−0.0275768	+	0.00809727i	−0.000895179	+	0.000262848i
$950$		0			0
$951$	−8.44305	+	5.42602i	−0.273785	+	0.175951i
$952$		0			0
$953$	−9.05837	−	10.4539i	−0.293430	−	0.338636i	0.589824	−	0.807532i	$-0.299197\pi$
$953$	−9.05837	−	10.4539i	−0.293430	−	0.338636i	−0.883253	+	0.468896i	$0.844652\pi$
$954$		0			0
$955$	2.66974	−	18.5685i	0.0863909	−	0.600862i
$956$		0			0
$957$	−4.50034	−	5.19367i	−0.145475	−	0.167888i
$958$		0			0
$959$	3.93772	+	1.15622i	0.127156	+	0.0373362i
$960$		0			0
$961$	−11.6701	−	25.5539i	−0.376453	−	0.824318i
$962$		0			0
$963$	−4.87367	+	3.13212i	−0.157052	+	0.100931i
$964$		0			0
$965$	−3.40932	−	1.00107i	−0.109750	−	0.0322255i
$966$		0			0
$967$	−48.0577			−1.54543			−0.772716	−	0.634752i	$-0.781102\pi$
$967$	−48.0577			−1.54543			−0.772716	+	0.634752i	$0.781102\pi$
$968$		0			0
$969$	−3.42415	−	2.20057i	−0.110000	−	0.0706925i
$970$		0			0
$971$	28.9869	+	33.4527i	0.930233	+	1.07355i	0.997124	+	0.0757863i	$0.0241467\pi$
$971$	28.9869	+	33.4527i	0.930233	+	1.07355i	−0.0668906	+	0.997760i	$0.521308\pi$
$972$		0			0
$973$	−31.7754	+	69.5785i	−1.01867	+	2.23058i
$974$		0			0
$975$	0.223008			0.00714198
$976$		0			0
$977$	41.4151	+	26.6159i	1.32499	+	0.851518i	0.995693	−	0.0927096i	$-0.0295528\pi$
$977$	41.4151	+	26.6159i	1.32499	+	0.851518i	0.329294	+	0.944227i	$0.393189\pi$
$978$		0			0
$979$	−1.16542	+	8.10566i	−0.0372469	+	0.259058i
$980$		0			0
$981$	1.96991	−	13.7010i	0.0628943	−	0.437439i
$982$		0			0
$983$	10.4075	−	22.7893i	0.331948	−	0.726865i	−0.667901	−	0.744250i	$-0.732807\pi$
$983$	10.4075	−	22.7893i	0.331948	−	0.726865i	0.999849	+	0.0173852i	$0.00553416\pi$
$984$		0			0
$985$	13.1295	+	28.7495i	0.418340	+	0.916036i
$986$		0			0
$987$	1.20737	+	8.39744i	0.0384310	+	0.267293i
$988$		0			0
$989$	−0.224887	+	0.0660329i	−0.00715100	+	0.00209972i
$990$		0			0
$991$	−7.01593	−	48.7969i	−0.222868	−	1.55008i	−0.727110	−	0.686521i	$-0.759137\pi$
$991$	−7.01593	−	48.7969i	−0.222868	−	1.55008i	0.504242	−	0.863562i	$-0.331772\pi$
$992$		0			0
$993$	24.6317	−	15.8299i	0.781664	−	0.502345i
$994$		0			0
$995$	11.6671	−	25.5474i	0.369872	−	0.809907i
$996$		0			0
$997$	−12.1571	−	7.81290i	−0.385019	−	0.247437i	0.333785	−	0.942649i	$-0.391674\pi$
$997$	−12.1571	−	7.81290i	−0.385019	−	0.247437i	−0.718805	+	0.695212i	$0.755310\pi$
$998$		0			0
$999$	−3.21687	−	0.944560i	−0.101777	−	0.0298845i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.241.6	✓	60	67.40	even	11	inner
804.2.q.b.397.6	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(1.80159 - 0.528994i) q^{5} +(2.39007 - 2.75829i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(1.80159 - 0.528994i) q^{5} +(2.39007 - 2.75829i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(2.98671 - 0.876979i) q^{11} +(0.127238 - 0.0817712i) q^{13} +(-1.22960 - 1.41903i) q^{15} +(-0.323618 + 2.25081i) q^{17} +(-1.17218 - 1.35276i) q^{19} +(-3.50190 - 1.02825i) q^{21} +(0.274352 + 0.600747i) q^{23} +(-1.24038 + 0.797147i) q^{25} +(0.959493 + 0.281733i) q^{27} +2.20772 q^{29} +(1.43445 + 0.921865i) q^{31} +(-2.03845 - 2.35250i) q^{33} +(2.84681 - 6.23364i) q^{35} -3.35268 q^{37} +(-0.127238 - 0.0817712i) q^{39} +(1.30141 - 9.05150i) q^{41} +(-0.0505065 + 0.351281i) q^{43} +(-0.780002 + 1.70797i) q^{45} +(-0.965628 - 2.11443i) q^{47} +(-0.899518 - 6.25629i) q^{49} +(2.18184 - 0.640647i) q^{51} +(0.154553 + 1.07494i) q^{53} +(4.91691 - 3.15991i) q^{55} +(-0.743578 + 1.62821i) q^{57} +(9.65283 + 6.20349i) q^{59} +(-11.7220 - 3.44189i) q^{61} +(0.519413 + 3.61259i) q^{63} +(0.185975 - 0.214626i) q^{65} +(5.35460 - 6.19098i) q^{67} +(0.432489 - 0.499119i) q^{69} +(-0.518837 - 3.60859i) q^{71} +(-0.182327 - 0.0535362i) q^{73} +(1.24038 + 0.797147i) q^{75} +(4.71950 - 10.3343i) q^{77} +(-7.44167 + 4.78247i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(6.58998 - 1.93499i) q^{83} +(0.607639 + 4.22622i) q^{85} +(-0.917121 - 2.00822i) q^{87} +(-1.09285 + 2.39302i) q^{89} +(0.0785604 - 0.546400i) q^{91} +(0.242666 - 1.68778i) q^{93} +(-2.82738 - 1.81705i) q^{95} -6.01452 q^{97} +(-1.29311 + 2.83151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more