LMFDB - Embedded newform 804.2.y.b.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			361.4
Character	$\chi$	$=$	804.361
Dual form			804.2.y.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{3} +(-0.102535 + 0.713146i) q^{5} +(-0.326230 + 0.0311512i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.102535 + 0.713146i) q^{5} +(-0.326230 + 0.0311512i) q^{7} +(0.415415 - 0.909632i) q^{9} +(4.09323 - 1.63868i) q^{11} +(-0.881004 + 0.840036i) q^{13} +(-0.299298 - 0.655371i) q^{15} +(-0.980712 - 2.83358i) q^{17} +(3.20978 + 0.306497i) q^{19} +(0.257600 - 0.202579i) q^{21} +(0.354214 + 7.43587i) q^{23} +(4.29940 + 1.26242i) q^{25} +(0.142315 + 0.989821i) q^{27} +(1.75788 + 3.04474i) q^{29} +(-2.44441 - 2.33074i) q^{31} +(-2.55750 + 3.59151i) q^{33} +(0.0112346 - 0.235843i) q^{35} +(-5.46054 + 9.45793i) q^{37} +(0.286990 - 1.18299i) q^{39} +(5.88757 + 1.13474i) q^{41} +(6.70231 - 7.73488i) q^{43} +(0.606106 + 0.389520i) q^{45} +(11.8033 + 6.08502i) q^{47} +(-6.76805 + 1.30443i) q^{49} +(2.35698 + 1.85355i) q^{51} +(8.32662 + 9.60943i) q^{53} +(0.748920 + 3.08709i) q^{55} +(-2.86594 + 1.47750i) q^{57} +(-1.66367 + 0.488497i) q^{59} +(-10.1583 - 4.06679i) q^{61} +(-0.107185 + 0.309690i) q^{63} +(-0.508734 - 0.714418i) q^{65} +(8.16762 + 0.538524i) q^{67} +(-4.31812 - 6.06395i) q^{69} +(3.65591 - 10.5631i) q^{71} +(-7.63635 - 3.05713i) q^{73} +(-4.29940 + 1.26242i) q^{75} +(-1.28429 + 0.662096i) q^{77} +(1.42762 + 5.88472i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(8.92980 + 7.02247i) q^{83} +(2.12131 - 0.408850i) q^{85} +(-3.12493 - 1.61101i) q^{87} +(-4.70017 - 3.02062i) q^{89} +(0.261242 - 0.301489i) q^{91} +(3.31646 + 0.639194i) q^{93} +(-0.547691 + 2.25761i) q^{95} +(-4.06749 + 7.04510i) q^{97} +(0.209791 - 4.40406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{10}{33}\right)$	$1$

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
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$		0			0
$5$	−0.102535	+	0.713146i	−0.0458550	+	0.318928i	0.953964	+	0.299920i	$0.0969600\pi$
$5$	−0.102535	+	0.713146i	−0.0458550	+	0.318928i	−0.999819	+	0.0190084i	$0.993949\pi$
$6$		0			0
$7$	−0.326230	+	0.0311512i	−0.123303	+	0.0117740i	−0.156525	−	0.987674i	$-0.550029\pi$
$7$	−0.326230	+	0.0311512i	−0.123303	+	0.0117740i	0.0332219	+	0.999448i	$0.489423\pi$
$8$		0			0
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$		0			0
$11$	4.09323	−	1.63868i	1.23415	−	0.494081i	0.339401	−	0.940642i	$-0.389776\pi$
$11$	4.09323	−	1.63868i	1.23415	−	0.494081i	0.894753	+	0.446561i	$0.147351\pi$
$12$		0			0
$13$	−0.881004	+	0.840036i	−0.244347	+	0.232984i	−0.802349	−	0.596855i	$-0.796417\pi$
$13$	−0.881004	+	0.840036i	−0.244347	+	0.232984i	0.558002	+	0.829840i	$0.311568\pi$
$14$		0			0
$15$	−0.299298	−	0.655371i	−0.0772784	−	0.169216i
$16$		0			0
$17$	−0.980712	−	2.83358i	−0.237858	−	0.687244i	−0.999241	−	0.0389430i	$-0.987601\pi$
$17$	−0.980712	−	2.83358i	−0.237858	−	0.687244i	0.761384	−	0.648301i	$-0.224520\pi$
$18$		0			0
$19$	3.20978	+	0.306497i	0.736374	+	0.0703152i	0.456502	−	0.889722i	$-0.349102\pi$
$19$	3.20978	+	0.306497i	0.736374	+	0.0703152i	0.279871	+	0.960037i	$0.409708\pi$
$20$		0			0
$21$	0.257600	−	0.202579i	0.0562130	−	0.0442064i
$22$		0			0
$23$	0.354214	+	7.43587i	0.0738588	+	1.55049i	0.666798	+	0.745239i	$0.267665\pi$
$23$	0.354214	+	7.43587i	0.0738588	+	1.55049i	−0.592939	+	0.805247i	$0.702032\pi$
$24$		0			0
$25$	4.29940	+	1.26242i	0.859880	+	0.252484i
$26$		0			0
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$		0			0
$29$	1.75788	+	3.04474i	0.326430	+	0.565393i	0.981801	−	0.189914i	$-0.0608209\pi$
$29$	1.75788	+	3.04474i	0.326430	+	0.565393i	−0.655371	+	0.755307i	$0.727488\pi$
$30$		0			0
$31$	−2.44441	−	2.33074i	−0.439028	−	0.418613i	0.438057	−	0.898947i	$-0.355667\pi$
$31$	−2.44441	−	2.33074i	−0.439028	−	0.418613i	−0.877085	+	0.480335i	$0.840515\pi$
$32$		0			0
$33$	−2.55750	+	3.59151i	−0.445204	+	0.625202i
$34$		0			0
$35$	0.0112346	−	0.235843i	0.00189900	−	0.0398648i
$36$		0			0
$37$	−5.46054	+	9.45793i	−0.897707	+	1.55487i	−0.0672896	+	0.997733i	$0.521435\pi$
$37$	−5.46054	+	9.45793i	−0.897707	+	1.55487i	−0.830418	+	0.557141i	$0.811898\pi$
$38$		0			0
$39$	0.286990	−	1.18299i	0.0459552	−	0.189430i
$40$		0			0
$41$	5.88757	+	1.13474i	0.919483	+	0.177216i	0.626968	−	0.779045i	$-0.284296\pi$
$41$	5.88757	+	1.13474i	0.919483	+	0.177216i	0.292515	+	0.956261i	$0.405508\pi$
$42$		0			0
$43$	6.70231	−	7.73488i	1.02209	−	1.17956i	0.0384810	−	0.999259i	$-0.487748\pi$
$43$	6.70231	−	7.73488i	1.02209	−	1.17956i	0.983612	−	0.180299i	$-0.0577064\pi$
$44$		0			0
$45$	0.606106	+	0.389520i	0.0903529	+	0.0580663i
$46$		0			0
$47$	11.8033	+	6.08502i	1.72169	+	0.887592i	0.974935	+	0.222491i	$0.0714188\pi$
$47$	11.8033	+	6.08502i	1.72169	+	0.887592i	0.746754	+	0.665101i	$0.231611\pi$
$48$		0			0
$49$	−6.76805	+	1.30443i	−0.966864	+	0.186348i
$50$		0			0
$51$	2.35698	+	1.85355i	0.330043	+	0.259549i
$52$		0			0
$53$	8.32662	+	9.60943i	1.14375	+	1.31996i	0.940094	+	0.340914i	$0.110737\pi$
$53$	8.32662	+	9.60943i	1.14375	+	1.31996i	0.203655	+	0.979043i	$0.434718\pi$
$54$		0			0
$55$	0.748920	+	3.08709i	0.100984	+	0.416263i
$56$		0			0
$57$	−2.86594	+	1.47750i	−0.379603	+	0.195699i
$58$		0			0
$59$	−1.66367	+	0.488497i	−0.216591	+	0.0635970i	−0.388228	−	0.921563i	$-0.626913\pi$
$59$	−1.66367	+	0.488497i	−0.216591	+	0.0635970i	0.171637	+	0.985160i	$0.445095\pi$
$60$		0			0
$61$	−10.1583	−	4.06679i	−1.30064	−	0.520699i	−0.385083	−	0.922882i	$-0.625827\pi$
$61$	−10.1583	−	4.06679i	−1.30064	−	0.520699i	−0.915559	+	0.402183i	$0.868251\pi$
$62$		0			0
$63$	−0.107185	+	0.309690i	−0.0135040	+	0.0390172i
$64$		0			0
$65$	−0.508734	−	0.714418i	−0.0631007	−	0.0886126i
$66$		0			0
$67$	8.16762	+	0.538524i	0.997833	+	0.0657912i
$67$	8.16762	+	0.538524i	0.997833	+	0.0657912i
$68$		0			0
$69$	−4.31812	−	6.06395i	−0.519840	−	0.730014i
$70$		0			0
$71$	3.65591	−	10.5631i	0.433876	−	1.25360i	−0.490272	−	0.871570i	$-0.663103\pi$
$71$	3.65591	−	10.5631i	0.433876	−	1.25360i	0.924148	−	0.382034i	$-0.124776\pi$
$72$		0			0
$73$	−7.63635	−	3.05713i	−0.893767	−	0.357810i	−0.121114	−	0.992639i	$-0.538647\pi$
$73$	−7.63635	−	3.05713i	−0.893767	−	0.357810i	−0.772653	+	0.634828i	$0.781071\pi$
$74$		0			0
$75$	−4.29940	+	1.26242i	−0.496452	+	0.145771i
$76$		0			0
$77$	−1.28429	+	0.662096i	−0.146358	+	0.0754528i
$78$		0			0
$79$	1.42762	+	5.88472i	0.160619	+	0.662082i	0.994000	+	0.109382i	$0.0348873\pi$
$79$	1.42762	+	5.88472i	0.160619	+	0.662082i	−0.833380	+	0.552700i	$0.813598\pi$
$80$		0			0
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$		0			0
$83$	8.92980	+	7.02247i	0.980172	+	0.770816i	0.973389	−	0.229161i	$-0.0735982\pi$
$83$	8.92980	+	7.02247i	0.980172	+	0.770816i	0.00678382	+	0.999977i	$0.497841\pi$
$84$		0			0
$85$	2.12131	−	0.408850i	0.230089	−	0.0443460i
$86$		0			0
$87$	−3.12493	−	1.61101i	−0.335028	−	0.172719i
$88$		0			0
$89$	−4.70017	−	3.02062i	−0.498217	−	0.320185i	0.267285	−	0.963617i	$-0.413873\pi$
$89$	−4.70017	−	3.02062i	−0.498217	−	0.320185i	−0.765503	+	0.643433i	$0.777510\pi$
$90$		0			0
$91$	0.261242	−	0.301489i	0.0273856	−	0.0316047i
$92$		0			0
$93$	3.31646	+	0.639194i	0.343900	+	0.0662814i
$94$		0			0
$95$	−0.547691	+	2.25761i	−0.0561919	+	0.231626i
$96$		0			0
$97$	−4.06749	+	7.04510i	−0.412991	+	0.715322i	−0.995215	−	0.0977066i	$-0.968849\pi$
$97$	−4.06749	+	7.04510i	−0.412991	+	0.715322i	0.582224	+	0.813028i	$0.302183\pi$
$98$		0			0
$99$	0.209791	−	4.40406i	0.0210848	−	0.442625i
$100$		0			0
$101$	9.03046	−	12.6815i	0.898564	−	1.26186i	−0.0659492	−	0.997823i	$-0.521008\pi$
$101$	9.03046	−	12.6815i	0.898564	−	1.26186i	0.964513	−	0.264034i	$-0.0850531\pi$
$102$		0			0
$103$	8.17439	+	7.79426i	0.805447	+	0.767992i	0.976096	−	0.217340i	$-0.0697381\pi$
$103$	8.17439	+	7.79426i	0.805447	+	0.767992i	−0.170649	+	0.985332i	$0.554587\pi$
$104$		0			0
$105$	0.118055	+	0.204478i	0.0115210	+	0.0199550i
$106$		0			0
$107$	−1.69109	−	11.7618i	−0.163484	−	1.13705i	−0.892004	−	0.452028i	$-0.850701\pi$
$107$	−1.69109	−	11.7618i	−0.163484	−	1.13705i	0.728520	−	0.685025i	$-0.240209\pi$
$108$		0			0
$109$	−2.76804	−	0.812771i	−0.265130	−	0.0778493i	0.146465	−	0.989216i	$-0.453210\pi$
$109$	−2.76804	−	0.812771i	−0.265130	−	0.0778493i	−0.411596	+	0.911366i	$0.635028\pi$
$110$		0			0
$111$	−0.519646	−	10.9087i	−0.0493226	−	1.03541i
$112$		0			0
$113$	0.447901	−	0.352234i	0.0421350	−	0.0331353i	−0.596869	−	0.802338i	$-0.703589\pi$
$113$	0.447901	−	0.352234i	0.0421350	−	0.0331353i	0.639004	+	0.769203i	$0.279347\pi$
$114$		0			0
$115$	−5.33918	−	0.509830i	−0.497881	−	0.0475419i
$116$		0			0
$117$	0.398141	+	1.15035i	0.0368082	+	0.106350i
$118$		0			0
$119$	0.408207	+	0.893848i	0.0374203	+	0.0819390i
$120$		0			0
$121$	6.10817	−	5.82412i	0.555288	−	0.529466i
$122$		0			0
$123$	−5.56642	+	2.22846i	−0.501907	+	0.200933i
$124$		0			0
$125$	−2.83762	+	6.21351i	−0.253804	+	0.555753i
$126$		0			0
$127$	−13.2333	+	1.26363i	−1.17427	+	0.112129i	−0.663897	−	0.747824i	$-0.731098\pi$
$127$	−13.2333	+	1.26363i	−1.17427	+	0.112129i	−0.510372	+	0.859954i	$0.670492\pi$
$128$		0			0
$129$	−1.45655	+	10.1305i	−0.128242	+	0.891944i
$130$		0			0
$131$	−6.50313	+	4.17931i	−0.568181	+	0.365148i	−0.792971	−	0.609259i	$-0.791467\pi$
$131$	−6.50313	+	4.17931i	−0.568181	+	0.365148i	0.224790	+	0.974407i	$0.427830\pi$
$132$		0			0
$133$	−1.05667			−0.0916252
$134$		0			0
$135$	−0.720479			−0.0620090
$136$		0			0
$137$	−4.53851	+	2.91672i	−0.387751	+	0.249192i	−0.719963	−	0.694012i	$-0.755841\pi$
$137$	−4.53851	+	2.91672i	−0.387751	+	0.249192i	0.332212	+	0.943205i	$0.392205\pi$
$138$		0			0
$139$	2.98636	−	20.7706i	0.253300	−	1.76174i	−0.324807	−	0.945780i	$-0.605299\pi$
$139$	2.98636	−	20.7706i	0.253300	−	1.76174i	0.578107	−	0.815961i	$-0.303792\pi$
$140$		0			0
$141$	−13.2194	+	1.26230i	−1.11327	+	0.106305i
$142$		0			0
$143$	−2.22960	+	4.88214i	−0.186449	+	0.408265i
$144$		0			0
$145$	−2.35158	+	0.941433i	−0.195288	+	0.0781817i
$146$		0			0
$147$	4.98841	−	4.75644i	0.411437	−	0.392305i
$148$		0			0
$149$	−0.436746	−	0.956341i	−0.0357796	−	0.0783465i	0.890898	−	0.454203i	$-0.150076\pi$
$149$	−0.436746	−	0.956341i	−0.0357796	−	0.0783465i	−0.926678	+	0.375856i	$0.877349\pi$
$150$		0			0
$151$	−1.85695	−	5.36530i	−0.151116	−	0.436622i	0.843880	−	0.536532i	$-0.180266\pi$
$151$	−1.85695	−	5.36530i	−0.151116	−	0.436622i	−0.994996	+	0.0999099i	$0.968145\pi$
$152$		0			0
$153$	−2.98492	−	0.285025i	−0.241316	−	0.0230429i
$154$		0			0
$155$	1.91279	−	1.50424i	0.153639	−	0.120823i
$156$		0			0
$157$	−0.530665	−	11.1400i	−0.0423517	−	0.889072i	−0.915672	−	0.401926i	$-0.868341\pi$
$157$	−0.530665	−	11.1400i	−0.0423517	−	0.889072i	0.873321	−	0.487146i	$-0.161962\pi$
$158$		0			0
$159$	−12.2001	−	3.58226i	−0.967527	−	0.284092i
$160$		0			0
$161$	−0.347191	−	2.41477i	−0.0273625	−	0.190310i
$162$		0			0
$163$	−8.61344	−	14.9189i	−0.674656	−	1.16854i	−0.976569	−	0.215204i	$-0.930958\pi$
$163$	−8.61344	−	14.9189i	−0.674656	−	1.16854i	0.301913	−	0.953336i	$-0.402375\pi$
$164$		0			0
$165$	−2.29904	−	2.19213i	−0.178980	−	0.170657i
$166$		0			0
$167$	8.60075	−	12.0781i	0.665546	−	0.934629i	−0.334423	−	0.942423i	$-0.608542\pi$
$167$	8.60075	−	12.0781i	0.665546	−	0.934629i	0.999970	+	0.00779409i	$0.00248096\pi$
$168$		0			0
$169$	−0.548057	+	11.5051i	−0.0421582	+	0.885010i
$170$		0			0
$171$	1.61219	−	2.79239i	0.123287	−	0.213540i
$172$		0			0
$173$	4.95662	−	20.4314i	0.376844	−	1.55337i	−0.395680	−	0.918389i	$-0.629491\pi$
$173$	4.95662	−	20.4314i	0.376844	−	1.55337i	0.772524	−	0.634985i	$-0.218994\pi$
$174$		0			0
$175$	−1.44192	−	0.277907i	−0.108999	−	0.0210078i
$176$		0			0
$177$	1.13547	−	1.31040i	0.0853469	−	0.0984955i
$178$		0			0
$179$	15.8197	+	10.1667i	1.18242	+	0.759897i	0.975830	−	0.218530i	$-0.0701260\pi$
$179$	15.8197	+	10.1667i	1.18242	+	0.759897i	0.206593	+	0.978427i	$0.433762\pi$
$180$		0			0
$181$	−17.8806	−	9.21808i	−1.32905	−	0.685175i	−0.360215	−	0.932869i	$-0.617297\pi$
$181$	−17.8806	−	9.21808i	−1.32905	−	0.685175i	−0.968838	+	0.247695i	$0.920327\pi$
$182$		0			0
$183$	10.7444	−	2.07082i	0.794250	−	0.153079i
$184$		0			0
$185$	−6.18499	−	4.86393i	−0.454729	−	0.357603i
$186$		0			0
$187$	−8.65761	−	9.99142i	−0.633107	−	0.730645i
$188$		0			0
$189$	−0.0772614	−	0.318476i	−0.00561994	−	0.0231657i
$190$		0			0
$191$	−13.0624	+	6.73415i	−0.945164	+	0.487266i	−0.860673	−	0.509158i	$-0.829957\pi$
$191$	−13.0624	+	6.73415i	−0.945164	+	0.487266i	−0.0844910	+	0.996424i	$0.526926\pi$
$192$		0			0
$193$	−14.1152	+	4.14459i	−1.01603	+	0.298334i	−0.747020	−	0.664802i	$-0.768516\pi$
$193$	−14.1152	+	4.14459i	−1.01603	+	0.298334i	−0.269014	+	0.963136i	$0.586698\pi$
$194$		0			0
$195$	0.814218	+	0.325964i	0.0583074	+	0.0233427i
$196$		0			0
$197$	−0.697317	+	2.01477i	−0.0496818	+	0.143546i	−0.967112	−	0.254350i	$-0.918138\pi$
$197$	−0.697317	+	2.01477i	−0.0496818	+	0.143546i	0.917430	+	0.397896i	$0.130260\pi$
$198$		0			0
$199$	9.79353	+	13.7531i	0.694245	+	0.974930i	0.999741	+	0.0227373i	$0.00723813\pi$
$199$	9.79353	+	13.7531i	0.694245	+	0.974930i	−0.305497	+	0.952193i	$0.598822\pi$
$200$		0			0
$201$	−7.16219	+	3.96271i	−0.505182	+	0.279508i
$202$		0			0
$203$	−0.668320	−	0.938524i	−0.0469069	−	0.0658715i
$204$		0			0
$205$	−1.41291	+	4.08234i	−0.0986821	+	0.285123i
$206$		0			0
$207$	6.91105	+	2.76677i	0.480351	+	0.192304i
$208$		0			0
$209$	13.6406	−	4.00524i	0.943540	−	0.277048i
$210$		0			0
$211$	−4.18975	+	2.15997i	−0.288434	+	0.148698i	−0.596372	−	0.802708i	$-0.703392\pi$
$211$	−4.18975	+	2.15997i	−0.288434	+	0.148698i	0.307937	+	0.951407i	$0.400361\pi$
$212$		0			0
$213$	2.63527	+	10.8627i	0.180566	+	0.744303i
$214$		0			0
$215$	4.82888	+	5.57282i	0.329327	+	0.380063i
$216$		0			0
$217$	0.870043	+	0.684210i	0.0590624	+	0.0464472i
$218$		0			0
$219$	8.07692	−	1.55670i	0.545787	−	0.105192i
$220$		0			0
$221$	3.24432	+	1.67256i	0.218237	+	0.112509i
$222$		0			0
$223$	5.91305	+	3.80009i	0.395967	+	0.254473i	0.723439	−	0.690388i	$-0.242560\pi$
$223$	5.91305	+	3.80009i	0.395967	+	0.254473i	−0.327472	+	0.944861i	$0.606197\pi$
$224$		0			0
$225$	2.93437	−	3.38645i	0.195625	−	0.225763i
$226$		0			0
$227$	−20.5706	−	3.96467i	−1.36532	−	0.263144i	−0.546628	−	0.837375i	$-0.684089\pi$
$227$	−20.5706	−	3.96467i	−1.36532	−	0.263144i	−0.818693	+	0.574231i	$0.805301\pi$
$228$		0			0
$229$	4.47979	−	18.4660i	0.296033	−	1.22026i	−0.608394	−	0.793635i	$-0.708186\pi$
$229$	4.47979	−	18.4660i	0.296033	−	1.22026i	0.904427	−	0.426629i	$-0.140299\pi$
$230$		0			0
$231$	0.722454	−	1.25133i	0.0475340	−	0.0823313i
$232$		0			0
$233$	−0.508972	+	10.6846i	−0.0333439	+	0.699974i	0.918873	+	0.394553i	$0.129100\pi$
$233$	−0.508972	+	10.6846i	−0.0333439	+	0.699974i	−0.952217	+	0.305422i	$0.901203\pi$
$234$		0			0
$235$	−5.54976	+	7.79355i	−0.362026	+	0.508395i
$236$		0			0
$237$	−4.38251	−	4.17871i	−0.284674	−	0.271436i
$238$		0			0
$239$	−2.49419	−	4.32006i	−0.161335	−	0.279441i	0.774012	−	0.633170i	$-0.218247\pi$
$239$	−2.49419	−	4.32006i	−0.161335	−	0.279441i	−0.935348	+	0.353729i	$0.884913\pi$
$240$		0			0
$241$	−1.29812	−	9.02859i	−0.0836189	−	0.581583i	−0.987953	−	0.154756i	$-0.950541\pi$
$241$	−1.29812	−	9.02859i	−0.0836189	−	0.581583i	0.904334	−	0.426826i	$-0.140368\pi$
$242$		0			0
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$		0			0
$245$	−0.236291	−	4.96035i	−0.0150961	−	0.316905i
$246$		0			0
$247$	−3.08530	+	2.42630i	−0.196313	+	0.154382i
$248$		0			0
$249$	−11.3089	−	1.07986i	−0.716670	−	0.0684336i
$250$		0			0
$251$	−0.0240368	−	0.0694498i	−0.00151719	−	0.00438364i	0.944240	−	0.329259i	$-0.106799\pi$
$251$	−0.0240368	−	0.0694498i	−0.00151719	−	0.00438364i	−0.945757	+	0.324875i	$0.894678\pi$
$252$		0			0
$253$	13.6349	+	29.8563i	0.857219	+	1.87705i
$254$		0			0
$255$	−1.56352	+	1.49081i	−0.0979115	+	0.0933584i
$256$		0			0
$257$	−7.98959	+	3.19855i	−0.498377	+	0.199520i	−0.607212	−	0.794540i	$-0.707712\pi$
$257$	−7.98959	+	3.19855i	−0.498377	+	0.199520i	0.108835	+	0.994060i	$0.465288\pi$
$258$		0			0
$259$	1.48677	−	3.25556i	0.0923831	−	0.202291i
$260$		0			0
$261$	3.49984	−	0.334194i	0.216635	−	0.0206861i
$262$		0			0
$263$	−1.80131	+	12.5284i	−0.111074	+	0.772533i	0.855805	+	0.517298i	$0.173062\pi$
$263$	−1.80131	+	12.5284i	−0.111074	+	0.772533i	−0.966879	+	0.255235i	$0.917847\pi$
$264$		0			0
$265$	−7.70669	+	4.95279i	−0.473418	+	0.304248i
$266$		0			0
$267$	5.58711			0.341925
$268$		0			0
$269$	9.23820			0.563263			0.281632	−	0.959523i	$-0.409124\pi$
$269$	9.23820			0.563263			0.281632	+	0.959523i	$0.409124\pi$
$270$		0			0
$271$	15.0226	−	9.65444i	0.912558	−	0.586466i	0.00206876	−	0.999998i	$-0.499341\pi$
$271$	15.0226	−	9.65444i	0.912558	−	0.586466i	0.910489	+	0.413532i	$0.135705\pi$
$272$		0			0
$273$	−0.0567733	+	0.394867i	−0.00343608	+	0.0238984i
$274$		0			0
$275$	19.6671	−	1.87798i	1.18597	−	0.113247i
$276$		0			0
$277$	4.11164	−	9.00323i	0.247044	−	0.540952i	−0.744967	−	0.667101i	$-0.767535\pi$
$277$	4.11164	−	9.00323i	0.247044	−	0.540952i	0.992011	+	0.126150i	$0.0402620\pi$
$278$		0			0
$279$	−3.13555	+	1.25529i	−0.187721	+	0.0751521i
$280$		0			0
$281$	−13.0235	+	12.4179i	−0.776916	+	0.740788i	−0.970710	−	0.240254i	$-0.922769\pi$
$281$	−13.0235	+	12.4179i	−0.776916	+	0.740788i	0.193794	+	0.981042i	$0.437921\pi$
$282$		0			0
$283$	−13.3427	−	29.2165i	−0.793143	−	1.73674i	−0.667427	−	0.744675i	$-0.732604\pi$
$283$	−13.3427	−	29.2165i	−0.793143	−	1.73674i	−0.125716	−	0.992066i	$-0.540123\pi$
$284$		0			0
$285$	−0.759811	−	2.19533i	−0.0450073	−	0.130040i
$286$		0			0
$287$	−1.95605	−	0.186780i	−0.115462	−	0.0110253i
$288$		0			0
$289$	6.29552	−	4.95085i	0.370324	−	0.291226i
$290$		0			0
$291$	−0.387078	−	8.12577i	−0.0226909	−	0.476341i
$292$		0			0
$293$	−14.9318	−	4.38436i	−0.872323	−	0.256137i	−0.185220	−	0.982697i	$-0.559300\pi$
$293$	−14.9318	−	4.38436i	−0.872323	−	0.256137i	−0.687103	+	0.726560i	$0.741118\pi$
$294$		0			0
$295$	−0.177786	−	1.23653i	−0.0103511	−	0.0719934i
$296$		0			0
$297$	2.20453	+	3.81836i	0.127920	+	0.221564i
$298$		0			0
$299$	−6.55846	−	6.25348i	−0.379286	−	0.361648i
$300$		0			0
$301$	−1.94554	+	2.73213i	−0.112139	+	0.157478i
$302$		0			0
$303$	−0.740766	+	15.5506i	−0.0425559	+	0.893358i
$304$		0			0
$305$	3.94180	−	6.82739i	0.225707	−	0.390935i
$306$		0			0
$307$	−2.20538	+	9.09068i	−0.125867	+	0.518833i	0.873614	+	0.486620i	$0.161770\pi$
$307$	−2.20538	+	9.09068i	−0.125867	+	0.518833i	−0.999481	+	0.0322124i	$0.989745\pi$
$308$		0			0
$309$	−11.0906	−	2.13754i	−0.630924	−	0.121601i
$310$		0			0
$311$	−4.70566	+	5.43062i	−0.266834	+	0.307942i	−0.873316	−	0.487155i	$-0.838035\pi$
$311$	−4.70566	+	5.43062i	−0.266834	+	0.307942i	0.606482	+	0.795097i	$0.292580\pi$
$312$		0			0
$313$	24.3218	+	15.6307i	1.37475	+	0.883497i	0.999064	−	0.0432511i	$-0.0137715\pi$
$313$	24.3218	+	15.6307i	1.37475	+	0.883497i	0.375684	+	0.926748i	$0.377408\pi$
$314$		0			0
$315$	−0.209864	−	0.108192i	−0.0118245	−	0.00609595i
$316$		0			0
$317$	21.2653	−	4.09855i	1.19438	−	0.230198i	0.446962	−	0.894553i	$-0.352506\pi$
$317$	21.2653	−	4.09855i	1.19438	−	0.230198i	0.747417	+	0.664355i	$0.231294\pi$
$318$		0			0
$319$	12.1848	+	9.58220i	0.682215	+	0.536500i
$320$		0			0
$321$	7.78152	+	8.98036i	0.434322	+	0.501235i
$322$		0			0
$323$	−2.27938	−	9.39575i	−0.126828	−	0.522794i
$324$		0			0
$325$	−4.84827	+	2.49946i	−0.268934	+	0.138645i
$326$		0			0
$327$	2.76804	−	0.812771i	0.153073	−	0.0449463i
$328$		0			0
$329$	−4.04014	−	1.61743i	−0.222740	−	0.0891718i
$330$		0			0
$331$	0.123791	−	0.357670i	0.00680416	−	0.0196593i	−0.941548	−	0.336880i	$-0.890628\pi$
$331$	0.123791	−	0.357670i	0.00680416	−	0.0196593i	0.948352	+	0.317221i	$0.102750\pi$
$332$		0			0
$333$	6.33485	+	8.89605i	0.347148	+	0.487501i
$334$		0			0
$335$	−1.22151	+	5.76948i	−0.0667383	+	0.315221i
$336$		0			0
$337$	16.6813	+	23.4255i	0.908686	+	1.27607i	0.960747	+	0.277427i	$0.0894816\pi$
$337$	16.6813	+	23.4255i	0.908686	+	1.27607i	−0.0520609	+	0.998644i	$0.516579\pi$
$338$		0			0
$339$	−0.186367	+	0.538471i	−0.0101221	+	0.0292458i
$340$		0			0
$341$	−13.8248	−	5.53463i	−0.748657	−	0.299717i
$342$		0			0
$343$	4.36838	−	1.28267i	0.235870	−	0.0692577i
$344$		0			0
$345$	4.76724	−	2.45768i	0.256659	−	0.132317i
$346$		0			0
$347$	2.87474	+	11.8498i	0.154324	+	0.636132i	0.995449	+	0.0952917i	$0.0303784\pi$
$347$	2.87474	+	11.8498i	0.154324	+	0.636132i	−0.841125	+	0.540840i	$0.818106\pi$
$348$		0			0
$349$	3.97303	+	4.58512i	0.212672	+	0.245436i	0.852055	−	0.523452i	$-0.175356\pi$
$349$	3.97303	+	4.58512i	0.212672	+	0.245436i	−0.639384	+	0.768888i	$0.720810\pi$
$350$		0			0
$351$	−0.956866	−	0.752488i	−0.0510737	−	0.0401648i
$352$		0			0
$353$	−11.6555	+	2.24641i	−0.620359	+	0.119564i	−0.489740	−	0.871868i	$-0.662908\pi$
$353$	−11.6555	+	2.24641i	−0.620359	+	0.119564i	−0.130618	+	0.991433i	$0.541696\pi$
$354$		0			0
$355$	7.15814	+	3.69028i	0.379914	+	0.195860i
$356$		0			0
$357$	−0.826656	−	0.531260i	−0.0437513	−	0.0281173i
$358$		0			0
$359$	−6.74346	+	7.78237i	−0.355906	+	0.410738i	−0.905264	−	0.424850i	$-0.860327\pi$
$359$	−6.74346	+	7.78237i	−0.355906	+	0.410738i	0.549358	+	0.835587i	$0.314872\pi$
$360$		0			0
$361$	−8.44791	−	1.62820i	−0.444627	−	0.0856948i
$362$		0			0
$363$	−1.98976	+	8.20189i	−0.104435	+	0.430487i
$364$		0			0
$365$	2.96317	−	5.13237i	0.155100	−	0.268640i
$366$		0			0
$367$	1.26681	−	26.5936i	0.0661270	−	1.38818i	−0.685253	−	0.728306i	$-0.740308\pi$
$367$	1.26681	−	26.5936i	0.0661270	−	1.38818i	0.751379	−	0.659870i	$-0.229389\pi$
$368$		0			0
$369$	3.47797	−	4.88413i	0.181056	−	0.254258i
$370$		0			0
$371$	−3.01574	−	2.87550i	−0.156569	−	0.149288i
$372$		0			0
$373$	6.46594	+	11.1993i	0.334794	+	0.579879i	0.983445	−	0.181206i	$-0.0580001\pi$
$373$	6.46594	+	11.1993i	0.334794	+	0.579879i	−0.648652	+	0.761085i	$0.724667\pi$
$374$		0			0
$375$	−0.972124	−	6.76127i	−0.0502003	−	0.349150i
$376$		0			0
$377$	−4.10639	−	1.20574i	−0.211490	−	0.0620990i
$378$		0			0
$379$	1.30520	+	27.3994i	0.0670434	+	1.40742i	0.742416	+	0.669939i	$0.233680\pi$
$379$	1.30520	+	27.3994i	0.0670434	+	1.40742i	−0.675373	+	0.737476i	$0.736017\pi$
$380$		0			0
$381$	10.4494	−	8.21752i	0.535340	−	0.420996i
$382$		0			0
$383$	5.12063	+	0.488961i	0.261652	+	0.0249847i	0.225058	−	0.974345i	$-0.427743\pi$
$383$	5.12063	+	0.488961i	0.261652	+	0.0249847i	0.0365944	+	0.999330i	$0.488349\pi$
$384$		0			0
$385$	−0.340487	−	0.983771i	−0.0173528	−	0.0501376i
$386$		0			0
$387$	−4.25165	−	9.30982i	−0.216124	−	0.473245i
$388$		0			0
$389$	−4.17526	+	3.98111i	−0.211694	+	0.201850i	−0.788506	−	0.615027i	$-0.789145\pi$
$389$	−4.17526	+	3.98111i	−0.211694	+	0.201850i	0.576812	+	0.816877i	$0.304297\pi$
$390$		0			0
$391$	20.7228	−	8.29614i	1.04800	−	0.419554i
$392$		0			0
$393$	3.21128	−	7.03171i	0.161987	−	0.354703i
$394$		0			0
$395$	−4.34304	+	0.414710i	−0.218522	+	0.0208663i
$396$		0			0
$397$	−0.517530	+	3.59950i	−0.0259741	+	0.180654i	−0.998678	−	0.0513941i	$-0.983634\pi$
$397$	−0.517530	+	3.59950i	−0.0259741	+	0.180654i	0.972704	+	0.232048i	$0.0745426\pi$
$398$		0			0
$399$	0.888930	−	0.571281i	0.0445022	−	0.0285998i
$400$		0			0
$401$	36.3052			1.81300			0.906498	−	0.422210i	$-0.138745\pi$
$401$	36.3052			1.81300			0.906498	+	0.422210i	$0.138745\pi$
$402$		0			0
$403$	4.11143			0.204805
$404$		0			0
$405$	0.606106	−	0.389520i	0.0301176	−	0.0193554i
$406$		0			0
$407$	−6.85270	+	47.6616i	−0.339676	+	2.36250i
$408$		0			0
$409$	3.36626	−	0.321438i	0.166451	−	0.0158941i	−0.0114979	−	0.999934i	$-0.503660\pi$
$409$	3.36626	−	0.321438i	0.166451	−	0.0158941i	0.177949	+	0.984040i	$0.443054\pi$
$410$		0			0
$411$	2.24114	−	4.90740i	0.110547	−	0.242064i
$412$		0			0
$413$	0.527521	−	0.211188i	0.0259576	−	0.0103919i
$414$		0			0
$415$	−5.92366	+	5.64820i	−0.290781	+	0.277259i
$416$		0			0
$417$	8.71716	+	19.0879i	0.426881	+	0.934739i
$418$		0			0
$419$	−5.33102	−	15.4030i	−0.260437	−	0.752484i	−0.997091	−	0.0762147i	$-0.975717\pi$
$419$	−5.33102	−	15.4030i	−0.260437	−	0.752484i	0.736654	−	0.676270i	$-0.236405\pi$
$420$		0			0
$421$	−20.3523	−	1.94340i	−0.991908	−	0.0947157i	−0.413535	−	0.910488i	$-0.635706\pi$
$421$	−20.3523	−	1.94340i	−0.991908	−	0.0947157i	−0.578373	+	0.815772i	$0.696312\pi$
$422$		0			0
$423$	10.4384	−	8.20885i	0.507532	−	0.399128i
$424$		0			0
$425$	−0.639310	−	13.4208i	−0.0310111	−	0.651003i
$426$		0			0
$427$	3.44064	+	1.01026i	0.166504	+	0.0488900i
$428$		0			0
$429$	−0.763827	−	5.31253i	−0.0368779	−	0.256492i
$430$		0			0
$431$	−9.92354	−	17.1881i	−0.478000	−	0.827920i	0.521682	−	0.853140i	$-0.325305\pi$
$431$	−9.92354	−	17.1881i	−0.478000	−	0.827920i	−0.999682	+	0.0252199i	$0.991971\pi$
$432$		0			0
$433$	7.06311	+	6.73466i	0.339431	+	0.323647i	0.840553	−	0.541730i	$-0.182230\pi$
$433$	7.06311	+	6.73466i	0.339431	+	0.323647i	−0.501121	+	0.865377i	$0.667079\pi$
$434$		0			0
$435$	1.46930	−	2.06335i	0.0704477	−	0.0989299i
$436$		0			0
$437$	−1.14212	+	23.9761i	−0.0546350	+	1.14693i
$438$		0			0
$439$	−14.3951	+	24.9331i	−0.687041	+	1.18999i	0.285749	+	0.958304i	$0.407758\pi$
$439$	−14.3951	+	24.9331i	−0.687041	+	1.18999i	−0.972791	+	0.231686i	$0.925576\pi$
$440$		0			0
$441$	−1.62499	+	6.69831i	−0.0773806	+	0.318967i
$442$		0			0
$443$	−13.9515	−	2.68894i	−0.662857	−	0.127755i	−0.153283	−	0.988182i	$-0.548985\pi$
$443$	−13.9515	−	2.68894i	−0.662857	−	0.127755i	−0.509574	+	0.860427i	$0.670197\pi$
$444$		0			0
$445$	2.63607	−	3.04219i	0.124962	−	0.144214i
$446$		0			0
$447$	0.884451	+	0.568402i	0.0418331	+	0.0268845i
$448$		0			0
$449$	−3.75622	−	1.93646i	−0.177267	−	0.0913874i	0.367309	−	0.930099i	$-0.380279\pi$
$449$	−3.75622	−	1.93646i	−0.177267	−	0.0913874i	−0.544576	+	0.838712i	$0.683309\pi$
$450$		0			0
$451$	25.9586	−	5.00311i	1.22234	−	0.235587i
$452$		0			0
$453$	4.46286	+	3.50963i	0.209684	+	0.164897i
$454$		0			0
$455$	0.188219	+	0.217217i	0.00882386	+	0.0101833i
$456$		0			0
$457$	−2.55181	−	10.5187i	−0.119368	−	0.492043i	−0.999839	−	0.0179426i	$-0.994288\pi$
$457$	−2.55181	−	10.5187i	−0.119368	−	0.492043i	0.880471	−	0.474101i	$-0.157227\pi$
$458$		0			0
$459$	2.66517	−	1.37399i	0.124399	−	0.0641324i
$460$		0			0
$461$	22.2974	−	6.54711i	1.03849	−	0.304929i	0.282334	−	0.959316i	$-0.408891\pi$
$461$	22.2974	−	6.54711i	1.03849	−	0.304929i	0.756160	+	0.654387i	$0.227073\pi$
$462$		0			0
$463$	4.26021	+	1.70553i	0.197989	+	0.0792628i	0.468538	−	0.883443i	$-0.344781\pi$
$463$	4.26021	+	1.70553i	0.197989	+	0.0792628i	−0.270549	+	0.962706i	$0.587205\pi$
$464$		0			0
$465$	−0.795891	+	2.29958i	−0.0369086	+	0.106640i
$466$		0			0
$467$	−0.810893	−	1.13874i	−0.0375237	−	0.0526946i	0.795388	−	0.606101i	$-0.207267\pi$
$467$	−0.810893	−	1.13874i	−0.0375237	−	0.0526946i	−0.832912	+	0.553406i	$0.813328\pi$
$468$		0			0
$469$	−2.68130	+	0.0787483i	−0.123811	+	0.00363626i
$470$		0			0
$471$	6.46918	+	9.08470i	0.298084	+	0.418601i
$472$		0			0
$473$	14.7591	−	42.6436i	0.678623	−	1.96075i
$474$		0			0
$475$	13.4132	+	5.36983i	0.615440	+	0.246385i
$476$		0			0
$477$	12.2001	−	3.58226i	0.558602	−	0.164020i
$478$		0			0
$479$	−0.432889	+	0.223170i	−0.0197792	+	0.0101969i	−0.468088	−	0.883682i	$-0.655057\pi$
$479$	−0.432889	+	0.223170i	−0.0197792	+	0.0101969i	0.448309	+	0.893879i	$0.352027\pi$
$480$		0			0
$481$	−3.13424	−	12.9195i	−0.142909	−	0.589080i
$482$		0			0
$483$	1.59760	+	1.84373i	0.0726932	+	0.0838925i
$484$		0			0
$485$	−4.60713	−	3.62308i	−0.209199	−	0.164516i
$486$		0			0
$487$	−34.8452	+	6.71586i	−1.57899	+	0.304325i	−0.902022	−	0.431690i	$-0.857917\pi$
$487$	−34.8452	+	6.71586i	−1.57899	+	0.304325i	−0.676965	+	0.736015i	$0.736705\pi$
$488$		0			0
$489$	15.3119	+	7.89381i	0.692426	+	0.356970i
$490$		0			0
$491$	−9.57543	−	6.15376i	−0.432133	−	0.277715i	0.306438	−	0.951891i	$-0.400863\pi$
$491$	−9.57543	−	6.15376i	−0.432133	−	0.277715i	−0.738571	+	0.674175i	$0.764499\pi$
$492$		0			0
$493$	6.90354	−	7.96710i	0.310920	−	0.358820i
$494$		0			0
$495$	3.11923	+	0.601182i	0.140199	+	0.0270211i
$496$		0			0
$497$	−0.863615	+	3.55987i	−0.0387384	+	0.159682i
$498$		0			0
$499$	6.59221	−	11.4180i	0.295108	−	0.511142i	−0.679902	−	0.733303i	$-0.737978\pi$
$499$	6.59221	−	11.4180i	0.295108	−	0.511142i	0.975010	+	0.222161i	$0.0713111\pi$
$500$		0			0
$501$	−0.705517	+	14.8106i	−0.0315202	+	0.661690i
$502$		0			0
$503$	−22.3679	+	31.4113i	−0.997336	+	1.40056i	−0.0825670	+	0.996586i	$0.526312\pi$
$503$	−22.3679	+	31.4113i	−0.997336	+	1.40056i	−0.914769	+	0.403977i	$0.867628\pi$
$504$		0			0
$505$	8.11782	+	7.74033i	0.361238	+	0.344440i
$506$		0			0
$507$	−5.75909	−	9.97503i	−0.255770	−	0.443007i
$508$		0			0
$509$	−0.140873	−	0.979793i	−0.00624409	−	0.0434286i	0.986461	−	0.163995i	$-0.0524381\pi$
$509$	−0.140873	−	0.979793i	−0.00624409	−	0.0434286i	−0.992705	+	0.120566i	$0.961529\pi$
$510$		0			0
$511$	2.58644	+	0.759447i	0.114417	+	0.0335959i
$512$		0			0
$513$	0.153422	+	3.22073i	0.00677375	+	0.142199i
$514$		0			0
$515$	−6.39661	+	5.03035i	−0.281868	+	0.221664i
$516$		0			0
$517$	58.2850	+	5.56554i	2.56337	+	0.244772i
$518$		0			0
$519$	6.87630	+	19.8678i	0.301836	+	0.872099i
$520$		0			0
$521$	−11.6293	−	25.4647i	−0.509490	−	1.11563i	−0.973267	−	0.229675i	$-0.926234\pi$
$521$	−11.6293	−	25.4647i	−0.509490	−	1.11563i	0.463778	−	0.885952i	$-0.346494\pi$
$522$		0			0
$523$	−10.7369	+	10.2376i	−0.469492	+	0.447660i	−0.887516	−	0.460776i	$-0.847571\pi$
$523$	−10.7369	+	10.2376i	−0.469492	+	0.447660i	0.418024	+	0.908436i	$0.362723\pi$
$524$		0			0
$525$	1.36327	−	0.545770i	0.0594979	−	0.0238194i
$526$		0			0
$527$	−4.20707	+	9.21220i	−0.183263	+	0.401290i
$528$		0			0
$529$	−32.2709	+	3.08149i	−1.40308	+	0.133978i
$530$		0			0
$531$	−0.246760	+	1.71626i	−0.0107085	+	0.0744792i
$532$		0			0
$533$	−6.14019	+	3.94606i	−0.265961	+	0.170923i
$534$		0			0
$535$	8.56125			0.370135
$536$		0			0
$537$	−18.8050			−0.811494
$538$		0			0
$539$	−25.5656	+	16.4300i	−1.10119	+	0.707691i
$540$		0			0
$541$	−2.55693	+	17.7839i	−0.109931	+	0.764588i	0.858050	+	0.513566i	$0.171676\pi$
$541$	−2.55693	+	17.7839i	−0.109931	+	0.764588i	−0.967981	+	0.251022i	$0.919233\pi$
$542$		0			0
$543$	20.0258	−	1.91223i	0.859388	−	0.0820616i
$544$		0			0
$545$	0.863445	−	1.89068i	0.0369859	−	0.0809879i
$546$		0			0
$547$	23.7616	−	9.51269i	1.01597	−	0.406733i	0.196899	−	0.980424i	$-0.436913\pi$
$547$	23.7616	−	9.51269i	1.01597	−	0.406733i	0.819072	+	0.573691i	$0.194489\pi$
$548$		0			0
$549$	−7.91921	+	7.55095i	−0.337983	+	0.322267i
$550$		0			0
$551$	4.70920	+	10.3117i	0.200619	+	0.439294i
$552$		0			0
$553$	−0.649047	−	1.87530i	−0.0276003	−	0.0797458i
$554$		0			0
$555$	7.83278	+	0.747940i	0.332483	+	0.0317483i
$556$		0			0
$557$	9.59997	−	7.54950i	0.406764	−	0.319883i	−0.393727	−	0.919227i	$-0.628815\pi$
$557$	9.59997	−	7.54950i	0.406764	−	0.319883i	0.800491	+	0.599345i	$0.204572\pi$
$558$		0			0
$559$	0.592812	+	12.4446i	0.0250733	+	0.526352i
$560$		0			0
$561$	12.6850	+	3.72466i	0.535562	+	0.157255i
$562$		0			0
$563$	1.91712	+	13.3339i	0.0807971	+	0.561956i	0.989502	+	0.144518i	$0.0461630\pi$
$563$	1.91712	+	13.3339i	0.0807971	+	0.561956i	−0.908705	+	0.417439i	$0.862928\pi$
$564$		0			0
$565$	0.205268	+	0.355535i	0.00863570	+	0.0149575i
$566$		0			0
$567$	0.237178	+	0.226148i	0.00996052	+	0.00949734i
$568$		0			0
$569$	−11.9236	+	16.7444i	−0.499865	+	0.701961i	−0.985015	−	0.172469i	$-0.944825\pi$
$569$	−11.9236	+	16.7444i	−0.499865	+	0.701961i	0.485150	+	0.874431i	$0.338765\pi$
$570$		0			0
$571$	2.22592	−	46.7279i	0.0931519	−	1.95550i	−0.157731	−	0.987482i	$-0.550418\pi$
$571$	2.22592	−	46.7279i	0.0931519	−	1.95550i	0.250883	−	0.968018i	$-0.419279\pi$
$572$		0			0
$573$	7.34806	−	12.7272i	0.306969	−	0.531687i
$574$		0			0
$575$	−7.86427	+	32.4170i	−0.327963	+	1.35188i
$576$		0			0
$577$	−21.4079	−	4.12603i	−0.891222	−	0.171769i	−0.276970	−	0.960879i	$-0.589330\pi$
$577$	−21.4079	−	4.12603i	−0.891222	−	0.171769i	−0.614252	+	0.789110i	$0.710542\pi$
$578$		0			0
$579$	9.63372	−	11.1179i	0.400364	−	0.462044i
$580$		0			0
$581$	−3.13192	−	2.01277i	−0.129934	−	0.0835036i
$582$		0			0
$583$	49.8296	+	25.6889i	2.06373	+	1.06393i
$584$		0			0
$585$	−0.861193	+	0.165981i	−0.0356059	+	0.00686248i
$586$		0			0
$587$	−14.9760	−	11.7773i	−0.618126	−	0.486100i	0.259310	−	0.965794i	$-0.416505\pi$
$587$	−14.9760	−	11.7773i	−0.618126	−	0.486100i	−0.877435	+	0.479695i	$0.840747\pi$
$588$		0			0
$589$	−7.13164	−	8.23035i	−0.293854	−	0.339126i
$590$		0			0
$591$	−0.502644	−	2.07193i	−0.0206760	−	0.0852277i
$592$		0			0
$593$	5.43848	−	2.80373i	0.223332	−	0.115135i	−0.342930	−	0.939361i	$-0.611419\pi$
$593$	5.43848	−	2.80373i	0.223332	−	0.115135i	0.566262	+	0.824225i	$0.308389\pi$
$594$		0			0
$595$	−0.679300	+	0.199460i	−0.0278486	+	0.00817708i
$596$		0			0
$597$	−15.6743	−	6.27505i	−0.641507	−	0.256821i
$598$		0			0
$599$	−1.13253	+	3.27224i	−0.0462741	+	0.133700i	−0.965770	−	0.259398i	$-0.916476\pi$
$599$	−1.13253	+	3.27224i	−0.0462741	+	0.133700i	0.919496	+	0.393099i	$0.128597\pi$
$600$		0			0
$601$	18.6343	+	26.1683i	0.760111	+	1.06743i	0.995429	+	0.0955080i	$0.0304476\pi$
$601$	18.6343	+	26.1683i	0.760111	+	1.06743i	−0.235318	+	0.971919i	$0.575613\pi$
$602$		0			0
$603$	3.88281	−	7.20582i	0.158120	−	0.293444i
$604$		0			0
$605$	3.52715	+	4.95319i	0.143399	+	0.201376i
$606$		0			0
$607$	7.75463	−	22.4055i	0.314751	−	0.909413i	−0.671038	−	0.741423i	$-0.734151\pi$
$607$	7.75463	−	22.4055i	0.314751	−	0.909413i	0.985789	−	0.167990i	$-0.0537276\pi$
$608$		0			0
$609$	1.06963	+	0.428216i	0.0433436	+	0.0173522i
$610$		0			0
$611$	−15.5104	+	4.55426i	−0.627484	+	0.184246i
$612$		0			0
$613$	−36.4903	+	18.8120i	−1.47383	+	0.759811i	−0.993123	−	0.117072i	$-0.962649\pi$
$613$	−36.4903	+	18.8120i	−1.47383	+	0.759811i	−0.480704	+	0.876883i	$0.659619\pi$
$614$		0			0
$615$	−1.01846	−	4.19816i	−0.0410684	−	0.169286i
$616$		0			0
$617$	−32.3021	−	37.2787i	−1.30044	−	1.50078i	−0.740052	−	0.672549i	$-0.765199\pi$
$617$	−32.3021	−	37.2787i	−1.30044	−	1.50078i	−0.560383	−	0.828234i	$-0.689346\pi$
$618$		0			0
$619$	−18.5309	−	14.5728i	−0.744818	−	0.585731i	0.171972	−	0.985102i	$-0.444986\pi$
$619$	−18.5309	−	14.5728i	−0.744818	−	0.585731i	−0.916790	+	0.399370i	$0.869229\pi$
$620$		0			0
$621$	−7.30977	+	1.40884i	−0.293331	+	0.0565349i
$622$		0			0
$623$	1.62743	+	0.839000i	0.0652017	+	0.0336138i
$624$		0			0
$625$	14.7077	+	9.45208i	0.588309	+	0.378083i
$626$		0			0
$627$	−9.30981	+	10.7441i	−0.371798	+	0.429078i
$628$		0			0
$629$	32.1550	+	6.19738i	1.28211	+	0.247106i
$630$		0			0
$631$	−1.14959	+	4.73867i	−0.0457644	+	0.188644i	−0.990106	−	0.140324i	$-0.955186\pi$
$631$	−1.14959	+	4.73867i	−0.0457644	+	0.188644i	0.944341	+	0.328968i	$0.106701\pi$
$632$		0			0
$633$	2.35688	−	4.08223i	0.0936774	−	0.162254i
$634$		0			0
$635$	0.455726	−	9.56687i	0.0180849	−	0.379649i
$636$		0			0
$637$	4.86691	−	6.83461i	0.192834	−	0.270797i
$638$		0			0
$639$	−8.08977	−	7.71358i	−0.320026	−	0.305145i
$640$		0			0
$641$	−19.6087	−	33.9633i	−0.774497	−	1.34147i	−0.935077	−	0.354446i	$-0.884670\pi$
$641$	−19.6087	−	33.9633i	−0.774497	−	1.34147i	0.160579	−	0.987023i	$-0.448664\pi$
$642$		0			0
$643$	1.73435	+	12.0626i	0.0683959	+	0.475704i	0.995017	+	0.0997070i	$0.0317906\pi$
$643$	1.73435	+	12.0626i	0.0683959	+	0.475704i	−0.926621	+	0.375997i	$0.877300\pi$
$644$		0			0
$645$	−7.07520	−	2.07747i	−0.278586	−	0.0818002i
$646$		0			0
$647$	−2.23817	−	46.9849i	−0.0879914	−	1.84717i	−0.424430	−	0.905461i	$-0.639525\pi$
$647$	−2.23817	−	46.9849i	−0.0879914	−	1.84717i	0.336438	−	0.941706i	$-0.390778\pi$
$648$		0			0
$649$	−6.00929	+	4.72576i	−0.235885	+	0.185502i
$650$		0			0
$651$	−1.10184	−	0.105213i	−0.0431845	−	0.00412362i
$652$		0			0
$653$	4.94030	+	14.2741i	0.193329	+	0.558587i	0.999450	−	0.0331637i	$-0.0105583\pi$
$653$	4.94030	+	14.2741i	0.193329	+	0.558587i	−0.806121	+	0.591750i	$0.798437\pi$
$654$		0			0
$655$	−2.31366	−	5.06620i	−0.0904021	−	0.197953i
$656$		0			0
$657$	−5.95312	+	5.67629i	−0.232253	+	0.221453i
$658$		0			0
$659$	38.9959	−	15.6116i	1.51906	−	0.608141i	0.545816	−	0.837905i	$-0.316220\pi$
$659$	38.9959	−	15.6116i	1.51906	−	0.608141i	0.973246	+	0.229764i	$0.0737953\pi$
$660$		0			0
$661$	0.585684	−	1.28247i	0.0227804	−	0.0498822i	−0.897900	−	0.440200i	$-0.854908\pi$
$661$	0.585684	−	1.28247i	0.0227804	−	0.0498822i	0.920680	+	0.390318i	$0.127635\pi$
$662$		0			0
$663$	−3.63355	+	0.346962i	−0.141116	+	0.0134749i
$664$		0			0
$665$	0.108346	−	0.753562i	0.00420147	−	0.0292219i
$666$		0			0
$667$	−22.0176	+	14.1499i	−0.852525	+	0.547885i
$668$		0			0
$669$	−7.02886			−0.271751
$670$		0			0
$671$	−48.2446			−1.86246
$672$		0			0
$673$	36.5880	−	23.5137i	1.41036	−	0.906386i	0.410379	−	0.911915i	$-0.365396\pi$
$673$	36.5880	−	23.5137i	1.41036	−	0.906386i	0.999985	+	0.00552956i	$0.00176012\pi$
$674$		0			0
$675$	−0.637700	+	4.43530i	−0.0245451	+	0.170715i
$676$		0			0
$677$	−47.9745	+	4.58101i	−1.84381	+	0.176063i	−0.957768	−	0.287541i	$-0.907162\pi$
$677$	−47.9745	+	4.58101i	−1.84381	+	0.176063i	−0.886043	+	0.463604i	$0.846556\pi$
$678$		0			0
$679$	1.10747	−	2.42503i	0.0425010	−	0.0930641i
$680$		0			0
$681$	19.4486	−	7.78604i	0.745272	−	0.298362i
$682$		0			0
$683$	−10.1209	+	9.65023i	−0.387264	+	0.369256i	−0.858554	−	0.512722i	$-0.828637\pi$
$683$	−10.1209	+	9.65023i	−0.387264	+	0.369256i	0.471290	+	0.881978i	$0.343789\pi$
$684$		0			0
$685$	−1.61469	−	3.53568i	−0.0616942	−	0.135091i
$686$		0			0
$687$	6.21481	+	17.9565i	0.237110	+	0.685083i
$688$		0			0
$689$	−15.4081	−	1.47129i	−0.587000	−	0.0560517i
$690$		0			0
$691$	−26.0624	+	20.4957i	−0.991459	+	0.779692i	−0.975459	−	0.220180i	$-0.929336\pi$
$691$	−26.0624	+	20.4957i	−0.991459	+	0.779692i	−0.0160001	+	0.999872i	$0.505093\pi$
$692$		0			0
$693$	0.0687515	+	1.44327i	0.00261165	+	0.0548254i
$694$		0			0
$695$	14.5063	+	4.25943i	0.550254	+	0.161569i
$696$		0			0
$697$	−2.55864	−	17.7957i	−0.0969155	−	0.674062i
$698$		0			0
$699$	−5.34838	−	9.26367i	−0.202294	−	0.350384i
$700$		0			0
$701$	−33.4536	−	31.8979i	−1.26352	−	1.20477i	−0.968426	−	0.249301i	$-0.919799\pi$
$701$	−33.4536	−	31.8979i	−1.26352	−	1.20477i	−0.295098	−	0.955467i	$-0.595352\pi$
$702$		0			0
$703$	−20.4259	+	28.6842i	−0.770379	+	1.08185i
$704$		0			0
$705$	0.455245	−	9.55677i	0.0171455	−	0.359929i
$706$		0			0
$707$	−2.55096	+	4.41839i	−0.0959388	+	0.166171i
$708$		0			0
$709$	7.48908	−	30.8704i	0.281258	−	1.15936i	−0.639363	−	0.768905i	$-0.720802\pi$
$709$	7.48908	−	30.8704i	0.281258	−	1.15936i	0.920621	−	0.390457i	$-0.127683\pi$
$710$		0			0
$711$	5.94598	+	1.14599i	0.222992	+	0.0429781i
$712$		0			0
$713$	16.4652	−	19.0019i	0.616627	−	0.711625i
$714$		0			0
$715$	−3.25307	−	2.09062i	−0.121658	−	0.0781848i
$716$		0			0
$717$	4.43384	+	2.28580i	0.165585	+	0.0853649i
$718$		0			0
$719$	6.39074	−	1.23171i	0.238334	−	0.0459352i	−0.0686853	−	0.997638i	$-0.521880\pi$
$719$	6.39074	−	1.23171i	0.238334	−	0.0459352i	0.307020	+	0.951703i	$0.400668\pi$
$720$		0			0
$721$	−2.90953	−	2.28808i	−0.108357	−	0.0852126i
$722$		0			0
$723$	5.97327	+	6.89352i	0.222148	+	0.256373i
$724$		0			0
$725$	3.71410	+	15.3097i	0.137938	+	0.568589i
$726$		0			0
$727$	−14.0701	+	7.25365i	−0.521832	+	0.269023i	−0.698955	−	0.715166i	$-0.746351\pi$
$727$	−14.0701	+	7.25365i	−0.521832	+	0.269023i	0.177123	+	0.984189i	$0.443321\pi$
$728$		0			0
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$		0			0
$731$	−28.4904	−	11.4059i	−1.05376	−	0.421861i
$732$		0			0
$733$	−3.53861	+	10.2241i	−0.130702	+	0.377638i	−0.991296	−	0.131654i	$-0.957971\pi$
$733$	−3.53861	+	10.2241i	−0.130702	+	0.377638i	0.860594	+	0.509291i	$0.170092\pi$
$734$		0			0
$735$	2.88055	+	4.04517i	0.106251	+	0.149208i
$736$		0			0
$737$	34.3144	−	11.1798i	1.26399	−	0.411814i
$738$		0			0
$739$	−3.94211	−	5.53591i	−0.145013	−	0.203642i	0.735681	−	0.677328i	$-0.236862\pi$
$739$	−3.94211	−	5.53591i	−0.145013	−	0.203642i	−0.880694	+	0.473687i	$0.842923\pi$
$740$		0			0
$741$	1.28376	−	3.70917i	0.0471600	−	0.136260i
$742$		0			0
$743$	23.7916	+	9.52474i	0.872831	+	0.349429i	0.764452	−	0.644681i	$-0.223010\pi$
$743$	23.7916	+	9.52474i	0.872831	+	0.349429i	0.108379	+	0.994110i	$0.465434\pi$
$744$		0			0
$745$	0.726792	−	0.213405i	0.0266276	−	0.00781857i
$746$		0			0
$747$	10.0974	−	5.20559i	0.369446	−	0.190463i
$748$		0			0
$749$	0.918076	+	3.78436i	0.0335458	+	0.138278i
$750$		0			0
$751$	−15.4947	−	17.8819i	−0.565410	−	0.652518i	0.398993	−	0.916954i	$-0.369360\pi$
$751$	−15.4947	−	17.8819i	−0.565410	−	0.652518i	−0.964403	+	0.264436i	$0.914814\pi$
$752$		0			0
$753$	0.0577685	+	0.0454296i	0.00210520	+	0.00165555i
$754$		0			0
$755$	4.01664	−	0.774144i	0.146181	−	0.0281740i
$756$		0			0
$757$	41.8843	+	21.5929i	1.52231	+	0.784806i	0.997781	−	0.0665856i	$-0.0212106\pi$
$757$	41.8843	+	21.5929i	1.52231	+	0.784806i	0.524531	+	0.851392i	$0.324241\pi$
$758$		0			0
$759$	−27.6119	−	17.7451i	−1.00225	−	0.644107i
$760$		0			0
$761$	−24.3639	+	28.1174i	−0.883189	+	1.01925i	0.116471	+	0.993194i	$0.462842\pi$
$761$	−24.3639	+	28.1174i	−0.883189	+	1.01925i	−0.999660	+	0.0260608i	$0.991704\pi$
$762$		0			0
$763$	0.928337	+	0.178922i	0.0336081	+	0.00647742i
$764$		0			0
$765$	0.509323	−	2.09946i	0.0184146	−	0.0759060i
$766$		0			0
$767$	1.05534	−	1.82791i	0.0381063	−	0.0660020i
$768$		0			0
$769$	0.159039	−	3.33863i	0.00573508	−	0.120394i	−0.994184	−	0.107693i	$-0.965654\pi$
$769$	0.159039	−	3.33863i	0.00573508	−	0.120394i	0.999919	−	0.0127017i	$-0.00404317\pi$
$770$		0			0
$771$	4.99201	−	7.01029i	0.179783	−	0.252469i
$772$		0			0
$773$	22.0127	+	20.9891i	0.791743	+	0.754926i	0.973566	−	0.228406i	$-0.0733512\pi$
$773$	22.0127	+	20.9891i	0.791743	+	0.754926i	−0.181823	+	0.983331i	$0.558200\pi$
$774$		0			0
$775$	−7.56712	−	13.1066i	−0.271819	−	0.470804i
$776$		0			0
$777$	0.509343	+	3.54256i	0.0182726	+	0.127089i
$778$		0			0
$779$	18.5500	+	5.44677i	0.664622	+	0.195151i
$780$		0			0
$781$	−2.34501	−	49.2278i	−0.0839111	−	1.76151i
$782$		0			0
$783$	−2.76357	+	2.17330i	−0.0987621	+	0.0776673i
$784$		0			0
$785$	7.99888	+	0.763801i	0.285492	+	0.0272612i
$786$		0			0
$787$	−14.4488	−	41.7470i	−0.515043	−	1.48812i	−0.840104	−	0.542426i	$-0.817506\pi$
$787$	−14.4488	−	41.7470i	−0.515043	−	1.48812i	0.325061	−	0.945693i	$-0.394615\pi$
$788$		0			0
$789$	−5.25800	−	11.5134i	−0.187190	−	0.409888i
$790$		0			0
$791$	−0.135146	+	0.128862i	−0.00480525	+	0.00458180i
$792$		0			0
$793$	12.3658	−	4.95052i	0.439122	−	0.175798i
$794$		0			0
$795$	3.80560	−	8.33311i	0.134971	−	0.295545i
$796$		0			0
$797$	19.2601	−	1.83912i	0.682229	−	0.0651450i	0.251814	−	0.967776i	$-0.418973\pi$
$797$	19.2601	−	1.83912i	0.682229	−	0.0651450i	0.430416	+	0.902631i	$0.358367\pi$
$798$		0			0
$799$	5.66677	−	39.4133i	0.200476	−	1.39434i
$800$		0			0
$801$	−4.70017	+	3.02062i	−0.166072	+	0.106728i
$802$		0			0
$803$	−36.2670			−1.27983
$804$		0			0
$805$	1.75768			0.0619501
$806$		0			0
$807$	−7.77167	+	4.99455i	−0.273576	+	0.175816i
$808$		0			0
$809$	0.0211360	−	0.147004i	0.000743101	−	0.00516838i	−0.989447	−	0.144899i	$-0.953714\pi$
$809$	0.0211360	−	0.147004i	0.000743101	−	0.00516838i	0.990190	+	0.139730i	$0.0446235\pi$
$810$		0			0
$811$	−15.5075	+	1.48079i	−0.544543	+	0.0519975i	−0.363703	−	0.931515i	$-0.618488\pi$
$811$	−15.5075	+	1.48079i	−0.544543	+	0.0519975i	−0.180840	+	0.983513i	$0.557882\pi$
$812$		0			0
$813$	−7.41823	+	16.2437i	−0.260169	+	0.569690i
$814$		0			0
$815$	11.5225	−	4.61293i	0.403617	−	0.161584i
$816$		0			0
$817$	23.8836	−	22.7730i	0.835583	−	0.796727i
$818$		0			0
$819$	−0.165720	−	0.362877i	−0.00579074	−	0.0126800i
$820$		0			0
$821$	−8.72612	−	25.2125i	−0.304544	−	0.879921i	−0.988610	−	0.150501i	$-0.951911\pi$
$821$	−8.72612	−	25.2125i	−0.304544	−	0.879921i	0.684066	−	0.729420i	$-0.260210\pi$
$822$		0			0
$823$	−29.9074	−	2.85581i	−1.04250	−	0.0995472i	−0.440270	−	0.897866i	$-0.645117\pi$
$823$	−29.9074	−	2.85581i	−1.04250	−	0.0995472i	−0.602235	+	0.798319i	$0.705723\pi$
$824$		0			0
$825$	−15.5297	+	12.2127i	−0.540676	+	0.425192i
$826$		0			0
$827$	−0.951840	−	19.9816i	−0.0330987	−	0.694827i	−0.953053	−	0.302803i	$-0.902078\pi$
$827$	−0.951840	−	19.9816i	−0.0330987	−	0.694827i	0.919955	−	0.392025i	$-0.128225\pi$
$828$		0			0
$829$	−39.3576	−	11.5564i	−1.36695	−	0.401371i	−0.485739	−	0.874104i	$-0.661450\pi$
$829$	−39.3576	−	11.5564i	−1.36695	−	0.401371i	−0.881206	+	0.472732i	$0.843268\pi$
$830$		0			0
$831$	1.40858	+	9.79692i	0.0488632	+	0.339851i
$832$		0			0
$833$	10.3337	+	17.8985i	0.358042	+	0.620147i
$834$		0			0
$835$	7.73154	+	7.37201i	0.267561	+	0.255119i
$836$		0			0
$837$	1.95914	−	2.75122i	0.0677177	−	0.0950962i
$838$		0			0
$839$	−0.589511	+	12.3754i	−0.0203522	+	0.427245i	0.965581	+	0.260104i	$0.0837567\pi$
$839$	−0.589511	+	12.3754i	−0.0203522	+	0.427245i	−0.985933	+	0.167141i	$0.946546\pi$
$840$		0			0
$841$	8.31972	−	14.4102i	0.286887	−	0.496903i
$842$		0			0
$843$	4.24245	−	17.4876i	0.146118	−	0.602305i
$844$		0			0
$845$	−8.14864	−	1.57052i	−0.280322	−	0.0540276i
$846$		0			0
$847$	−1.81124	+	2.09028i	−0.0622349	+	0.0718229i
$848$		0			0
$849$	27.0203	+	17.3649i	0.927333	+	0.595961i
$850$		0			0
$851$	−72.2622	−	37.2537i	−2.47712	−	1.27704i
$852$		0			0
$853$	−42.8945	+	8.26724i	−1.46868	+	0.283065i	−0.859977	−	0.510333i	$-0.829522\pi$
$853$	−42.8945	+	8.26724i	−1.46868	+	0.283065i	−0.608704	+	0.793398i	$0.708310\pi$
$854$		0			0
$855$	1.82608	+	1.43604i	0.0624505	+	0.0491117i
$856$		0			0
$857$	−36.3995	−	42.0072i	−1.24338	−	1.43494i	−0.859166	−	0.511697i	$-0.829017\pi$
$857$	−36.3995	−	42.0072i	−1.24338	−	1.43494i	−0.384217	−	0.923243i	$-0.625528\pi$
$858$		0			0
$859$	−6.24423	−	25.7391i	−0.213050	−	0.878206i	−0.973478	−	0.228782i	$-0.926526\pi$
$859$	−6.24423	−	25.7391i	−0.213050	−	0.878206i	0.760427	−	0.649423i	$-0.224990\pi$
$860$		0			0
$861$	1.74651	−	0.900390i	0.0595210	−	0.0306852i
$862$		0			0
$863$	−46.7849	+	13.7373i	−1.59258	+	0.467623i	−0.953468	−	0.301494i	$-0.902515\pi$
$863$	−46.7849	+	13.7373i	−1.59258	+	0.467623i	−0.639108	+	0.769117i	$0.720696\pi$
$864$		0			0
$865$	14.0624	+	5.62972i	0.478135	+	0.191416i
$866$		0			0
$867$	−2.61949	+	7.56853i	−0.0889627	+	0.257041i
$868$		0			0
$869$	15.4867	+	21.7481i	0.525352	+	0.737753i
$870$		0			0
$871$	−7.64809	+	6.38665i	−0.259146	+	0.216403i
$872$		0			0
$873$	4.71875	+	6.62656i	0.159706	+	0.224275i
$874$		0			0
$875$	0.732157	−	2.11543i	0.0247514	−	0.0715145i
$876$		0			0
$877$	−22.4831	−	9.00086i	−0.759199	−	0.303937i	−0.0404262	−	0.999183i	$-0.512872\pi$
$877$	−22.4831	−	9.00086i	−0.759199	−	0.303937i	−0.718773	+	0.695245i	$0.755296\pi$
$878$		0			0
$879$	14.9318	−	4.38436i	0.503636	−	0.147881i
$880$		0			0
$881$	32.5674	−	16.7897i	1.09722	−	0.565658i	0.188086	−	0.982153i	$-0.439772\pi$
$881$	32.5674	−	16.7897i	1.09722	−	0.565658i	0.909138	+	0.416494i	$0.136741\pi$
$882$		0			0
$883$	4.25061	+	17.5213i	0.143045	+	0.589638i	0.997535	+	0.0701706i	$0.0223544\pi$
$883$	4.25061	+	17.5213i	0.143045	+	0.589638i	−0.854490	+	0.519467i	$0.826130\pi$
$884$		0			0
$885$	0.818080	+	0.944114i	0.0274995	+	0.0317361i
$886$		0			0
$887$	2.06743	+	1.62584i	0.0694174	+	0.0545905i	0.652265	−	0.757991i	$-0.273819\pi$
$887$	2.06743	+	1.62584i	0.0694174	+	0.0545905i	−0.582847	+	0.812582i	$0.698061\pi$
$888$		0			0
$889$	4.27775	−	0.824468i	0.143471	−	0.0276518i
$890$		0			0
$891$	−3.91893	−	2.02035i	−0.131289	−	0.0676842i
$892$		0			0
$893$	36.0209	+	23.1492i	1.20539	+	0.774660i
$894$		0			0
$895$	−8.87244	+	10.2393i	−0.296573	+	0.342263i
$896$		0			0
$897$	8.89822	+	1.71499i	0.297103	+	0.0572619i
$898$		0			0
$899$	2.79951	−	11.5397i	0.0933688	−	0.384871i
$900$		0			0
$901$	19.0631	−	33.0182i	0.635084	−	1.10000i
$902$		0			0
$903$	0.159592	−	3.35026i	0.00531090	−	0.111490i
$904$		0			0
$905$	8.40722	−	11.8063i	0.279465	−	0.392454i
$906$		0			0
$907$	39.1892	+	37.3668i	1.30126	+	1.24074i	0.952865	+	0.303395i	$0.0981202\pi$
$907$	39.1892	+	37.3668i	1.30126	+	1.24074i	0.348391	+	0.937349i	$0.386728\pi$
$908$		0			0
$909$	−7.78411	−	13.4825i	−0.258183	−	0.447186i
$910$		0			0
$911$	1.17965	+	8.20463i	0.0390835	+	0.271831i	0.999987	−	0.00505110i	$-0.00160782\pi$
$911$	1.17965	+	8.20463i	0.0390835	+	0.271831i	−0.960904	+	0.276882i	$0.910699\pi$
$912$		0			0
$913$	48.0593	+	14.1115i	1.59053	+	0.467022i
$914$		0			0
$915$	0.375116	+	7.87466i	0.0124010	+	0.260328i
$916$		0			0
$917$	1.99132	−	1.56599i	0.0657593	−	0.0517137i
$918$		0			0
$919$	−14.8593	−	1.41889i	−0.490163	−	0.0468049i	−0.152951	−	0.988234i	$-0.548878\pi$
$919$	−14.8593	−	1.41889i	−0.490163	−	0.0468049i	−0.337212	+	0.941429i	$0.609484\pi$
$920$		0			0
$921$	−3.05951	−	8.83988i	−0.100814	−	0.291284i
$922$		0			0
$923$	5.65247	+	12.3772i	0.186053	+	0.407400i
$924$		0			0
$925$	−35.4169	+	33.7700i	−1.16450	+	1.11035i
$926$		0			0
$927$	10.4857	−	4.19783i	0.344395	−	0.137875i
$928$		0			0
$929$	0.571598	−	1.25162i	0.0187535	−	0.0410645i	−0.900023	−	0.435841i	$-0.856451\pi$
$929$	0.571598	−	1.25162i	0.0187535	−	0.0410645i	0.918777	+	0.394777i	$0.129178\pi$
$930$		0			0
$931$	−22.1237	+	2.11256i	−0.725076	+	0.0692364i
$932$		0			0
$933$	1.02264	−	7.11261i	0.0334797	−	0.232856i
$934$		0			0
$935$	8.01305	−	5.14967i	0.262055	−	0.168412i
$936$		0			0
$937$	−14.6426			−0.478352			−0.239176	−	0.970976i	$-0.576877\pi$
$937$	−14.6426			−0.478352			−0.239176	+	0.970976i	$0.576877\pi$
$938$		0			0
$939$	−28.9113			−0.943486
$940$		0			0
$941$	38.1707	−	24.5308i	1.24433	−	0.799683i	0.258271	−	0.966073i	$-0.416847\pi$
$941$	38.1707	−	24.5308i	1.24433	−	0.799683i	0.986060	+	0.166390i	$0.0532110\pi$
$942$		0			0
$943$	−6.35229	+	44.1811i	−0.206859	+	1.43874i
$944$		0			0
$945$	0.235042	−	0.0224438i	0.00764591	−	0.000730096i
$946$		0			0
$947$	13.4793	−	29.5156i	0.438019	−	0.959128i	−0.553939	−	0.832557i	$-0.686876\pi$
$947$	13.4793	−	29.5156i	0.438019	−	0.959128i	0.991958	−	0.126570i	$-0.0403969\pi$
$948$		0			0
$949$	9.29576	−	3.72146i	0.301753	−	0.120804i
$950$		0			0
$951$	−15.6737	+	14.9448i	−0.508254	+	0.484619i
$952$		0			0
$953$	0.0113566	+	0.0248674i	0.000367875	+	0.000805534i	0.909816	−	0.415012i	$-0.136223\pi$
$953$	0.0113566	+	0.0248674i	0.000367875	+	0.000805534i	−0.909448	+	0.415818i	$0.863495\pi$
$954$		0			0
$955$	−3.46307	−	10.0059i	−0.112062	−	0.323783i
$956$		0			0
$957$	−15.4310	−	1.47348i	−0.498813	−	0.0476309i
$958$		0			0
$959$	1.38974	−	1.09290i	0.0448769	−	0.0352916i
$960$		0			0
$961$	−0.932251	−	19.5704i	−0.0300726	−	0.631302i
$962$		0			0
$963$	−11.4014	−	3.34775i	−0.367404	−	0.107880i
$964$		0			0
$965$	−1.50840	−	10.4912i	−0.0485571	−	0.337722i
$966$		0			0
$967$	0.741865	+	1.28495i	0.0238568	+	0.0413211i	0.877707	−	0.479197i	$-0.159072\pi$
$967$	0.741865	+	1.28495i	0.0238568	+	0.0413211i	−0.853851	+	0.520518i	$0.825739\pi$
$968$		0			0
$969$	6.99727	+	6.67188i	0.224785	+	0.214332i
$970$		0			0
$971$	0.227778	−	0.319870i	0.00730975	−	0.0102651i	−0.810905	−	0.585178i	$-0.801025\pi$
$971$	0.227778	−	0.319870i	0.00730975	−	0.0102651i	0.818215	+	0.574913i	$0.194964\pi$
$972$		0			0
$973$	−0.327212	+	6.86903i	−0.0104899	+	0.220211i
$974$		0			0
$975$	2.72732	−	4.72385i	0.0873440	−	0.151284i
$976$		0			0
$977$	−2.77637	+	11.4443i	−0.0888238	+	0.366137i	−0.998825	−	0.0484696i	$-0.984566\pi$
$977$	−2.77637	+	11.4443i	−0.0888238	+	0.366137i	0.910001	+	0.414606i	$0.136081\pi$
$978$		0			0
$979$	−24.1887	−	4.66199i	−0.773075	−	0.148998i
$980$		0			0
$981$	−1.88921	+	2.18026i	−0.0603178	+	0.0696105i
$982$		0			0
$983$	28.4669	+	18.2946i	0.907954	+	0.583507i	0.909139	−	0.416492i	$-0.136741\pi$
$983$	28.4669	+	18.2946i	0.907954	+	0.583507i	−0.00118472	+	0.999999i	$0.500377\pi$
$984$		0			0
$985$	−1.36532	−	0.703873i	−0.0435028	−	0.0224272i
$986$		0			0
$987$	4.27323	−	0.823598i	0.136019	−	0.0262154i
$988$		0			0
$989$	59.8896	+	47.0977i	1.90438	+	1.49762i
$990$		0			0
$991$	25.7248	+	29.6880i	0.817174	+	0.943069i	0.999191	−	0.0402266i	$-0.0128080\pi$
$991$	25.7248	+	29.6880i	0.817174	+	0.943069i	−0.182017	+	0.983295i	$0.558263\pi$
$992$		0			0
$993$	0.0892315	+	0.367817i	0.00283168	+	0.0116723i
$994$		0			0
$995$	−10.8121	+	5.57404i	−0.342768	+	0.176709i
$996$		0			0
$997$	−49.7669	+	14.6129i	−1.57613	+	0.462795i	−0.948779	−	0.315939i	$-0.897680\pi$
$997$	−49.7669	+	14.6129i	−1.57613	+	0.462795i	−0.627354	+	0.778734i	$0.715862\pi$
$998$		0			0
$999$	−10.1388	−	4.05896i	−0.320777	−	0.128420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.361.4	yes	120
67.49	even	33	inner	804.2.y.b.49.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.49.4	✓	120	67.49	even	33	inner
804.2.y.b.361.4	yes	120	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.102535 + 0.713146i) q^{5} +(-0.326230 + 0.0311512i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.102535 + 0.713146i) q^{5} +(-0.326230 + 0.0311512i) q^{7} +(0.415415 - 0.909632i) q^{9} +(4.09323 - 1.63868i) q^{11} +(-0.881004 + 0.840036i) q^{13} +(-0.299298 - 0.655371i) q^{15} +(-0.980712 - 2.83358i) q^{17} +(3.20978 + 0.306497i) q^{19} +(0.257600 - 0.202579i) q^{21} +(0.354214 + 7.43587i) q^{23} +(4.29940 + 1.26242i) q^{25} +(0.142315 + 0.989821i) q^{27} +(1.75788 + 3.04474i) q^{29} +(-2.44441 - 2.33074i) q^{31} +(-2.55750 + 3.59151i) q^{33} +(0.0112346 - 0.235843i) q^{35} +(-5.46054 + 9.45793i) q^{37} +(0.286990 - 1.18299i) q^{39} +(5.88757 + 1.13474i) q^{41} +(6.70231 - 7.73488i) q^{43} +(0.606106 + 0.389520i) q^{45} +(11.8033 + 6.08502i) q^{47} +(-6.76805 + 1.30443i) q^{49} +(2.35698 + 1.85355i) q^{51} +(8.32662 + 9.60943i) q^{53} +(0.748920 + 3.08709i) q^{55} +(-2.86594 + 1.47750i) q^{57} +(-1.66367 + 0.488497i) q^{59} +(-10.1583 - 4.06679i) q^{61} +(-0.107185 + 0.309690i) q^{63} +(-0.508734 - 0.714418i) q^{65} +(8.16762 + 0.538524i) q^{67} +(-4.31812 - 6.06395i) q^{69} +(3.65591 - 10.5631i) q^{71} +(-7.63635 - 3.05713i) q^{73} +(-4.29940 + 1.26242i) q^{75} +(-1.28429 + 0.662096i) q^{77} +(1.42762 + 5.88472i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(8.92980 + 7.02247i) q^{83} +(2.12131 - 0.408850i) q^{85} +(-3.12493 - 1.61101i) q^{87} +(-4.70017 - 3.02062i) q^{89} +(0.261242 - 0.301489i) q^{91} +(3.31646 + 0.639194i) q^{93} +(-0.547691 + 2.25761i) q^{95} +(-4.06749 + 7.04510i) q^{97} +(0.209791 - 4.40406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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