LMFDB - Embedded newform 804.2.o.d.365.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.9
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.355178 - 1.69524i) q^{3} -3.60368 q^{5} +(3.20029 + 1.84769i) q^{7} +(-2.74770 + 1.20423i) q^{9} +O(q^{10})$	\(q+(-0.355178 - 1.69524i) q^{3} -3.60368 q^{5} +(3.20029 + 1.84769i) q^{7} +(-2.74770 + 1.20423i) q^{9} +(-1.48078 + 2.56478i) q^{11} +(1.95258 - 1.12732i) q^{13} +(1.27995 + 6.10911i) q^{15} +(4.00058 - 2.30974i) q^{17} +(2.85606 + 4.94684i) q^{19} +(1.99560 - 6.08152i) q^{21} +(7.12280 - 4.11235i) q^{23} +7.98648 q^{25} +(3.01738 + 4.23030i) q^{27} +(-4.16985 - 2.40746i) q^{29} +(-6.73963 - 3.89113i) q^{31} +(4.87387 + 1.59932i) q^{33} +(-11.5328 - 6.65846i) q^{35} +(4.09202 + 7.08759i) q^{37} +(-2.60460 - 2.90969i) q^{39} +(0.243870 - 0.422396i) q^{41} -11.0216i q^{43} +(9.90181 - 4.33964i) q^{45} +(7.37585 + 4.25845i) q^{47} +(3.32788 + 5.76406i) q^{49} +(-5.33648 - 5.96159i) q^{51} +10.5924 q^{53} +(5.33624 - 9.24265i) q^{55} +(7.37169 - 6.59873i) q^{57} +11.3999i q^{59} +(-3.97066 + 2.29246i) q^{61} +(-11.0184 - 1.22301i) q^{63} +(-7.03646 + 4.06250i) q^{65} +(2.48761 - 7.79819i) q^{67} +(-9.50129 - 10.6143i) q^{69} +(12.3588 + 7.13533i) q^{71} +(0.629763 + 1.09078i) q^{73} +(-2.83662 - 13.5390i) q^{75} +(-9.47783 + 5.47203i) q^{77} +(3.80258 + 2.19542i) q^{79} +(6.09967 - 6.61770i) q^{81} +(2.80997 - 1.62234i) q^{83} +(-14.4168 + 8.32354i) q^{85} +(-2.60019 + 7.92398i) q^{87} +2.12774i q^{89} +8.33174 q^{91} +(-4.20263 + 12.8074i) q^{93} +(-10.2923 - 17.8268i) q^{95} +(8.97837 - 5.18366i) q^{97} +(0.980148 - 8.83044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.355178	−	1.69524i	−0.205062	−	0.978749i
$3$	−0.355178	−	1.69524i	−0.205062	−	0.978749i
$4$		0			0
$5$	−3.60368			−1.61161			−0.805806	−	0.592179i	$-0.798268\pi$
$5$	−3.60368			−1.61161			−0.805806	+	0.592179i	$0.798268\pi$
$6$		0			0
$7$	3.20029	+	1.84769i	1.20959	+	0.698359i	0.962671	−	0.270676i	$-0.0872470\pi$
$7$	3.20029	+	1.84769i	1.20959	+	0.698359i	0.246923	+	0.969035i	$0.420580\pi$
$8$		0			0
$9$	−2.74770	+	1.20423i	−0.915899	+	0.401409i
$10$		0			0
$11$	−1.48078	+	2.56478i	−0.446471	+	0.773311i	−0.998153	−	0.0607433i	$-0.980653\pi$
$11$	−1.48078	+	2.56478i	−0.446471	+	0.773311i	0.551682	+	0.834055i	$0.313986\pi$
$12$		0			0
$13$	1.95258	−	1.12732i	0.541547	−	0.312663i	−0.204158	−	0.978938i	$-0.565446\pi$
$13$	1.95258	−	1.12732i	0.541547	−	0.312663i	0.745706	+	0.666275i	$0.232112\pi$
$14$		0			0
$15$	1.27995	+	6.10911i	0.330481	+	1.57736i
$16$		0			0
$17$	4.00058	−	2.30974i	0.970283	−	0.560193i	0.0709605	−	0.997479i	$-0.477394\pi$
$17$	4.00058	−	2.30974i	0.970283	−	0.560193i	0.899323	+	0.437286i	$0.144060\pi$
$18$		0			0
$19$	2.85606	+	4.94684i	0.655225	+	1.13488i	0.981837	+	0.189725i	$0.0607596\pi$
$19$	2.85606	+	4.94684i	0.655225	+	1.13488i	−0.326612	+	0.945158i	$0.605907\pi$
$20$		0			0
$21$	1.99560	−	6.08152i	0.435476	−	1.32710i
$22$		0			0
$23$	7.12280	−	4.11235i	1.48521	−	0.857484i	0.485348	−	0.874321i	$-0.338693\pi$
$23$	7.12280	−	4.11235i	1.48521	−	0.857484i	0.999858	+	0.0168370i	$0.00535963\pi$
$24$		0			0
$25$	7.98648			1.59730
$26$		0			0
$27$	3.01738	+	4.23030i	0.580695	+	0.814121i
$28$		0			0
$29$	−4.16985	−	2.40746i	−0.774321	−	0.447054i	0.0600929	−	0.998193i	$-0.480860\pi$
$29$	−4.16985	−	2.40746i	−0.774321	−	0.447054i	−0.834414	+	0.551138i	$0.814194\pi$
$30$		0			0
$31$	−6.73963	−	3.89113i	−1.21047	−	0.698867i	−0.247611	−	0.968860i	$-0.579645\pi$
$31$	−6.73963	−	3.89113i	−1.21047	−	0.698867i	−0.962862	+	0.269993i	$0.912979\pi$
$32$		0			0
$33$	4.87387	+	1.59932i	0.848432	+	0.278406i
$34$		0			0
$35$	−11.5328	−	6.65846i	−1.94940	−	1.12549i
$36$		0			0
$37$	4.09202	+	7.08759i	0.672724	+	1.16519i	0.977129	+	0.212650i	$0.0682093\pi$
$37$	4.09202	+	7.08759i	0.672724	+	1.16519i	−0.304404	+	0.952543i	$0.598457\pi$
$38$		0			0
$39$	−2.60460	−	2.90969i	−0.417069	−	0.465924i
$40$		0			0
$41$	0.243870	−	0.422396i	0.0380862	−	0.0659672i	−0.846354	−	0.532621i	$-0.821207\pi$
$41$	0.243870	−	0.422396i	0.0380862	−	0.0659672i	0.884440	+	0.466654i	$0.154541\pi$
$42$		0			0
$43$		−	11.0216i		−	1.68077i	−0.541986	−	0.840387i	$-0.682328\pi$
$43$		−	11.0216i		−	1.68077i	0.541986	−	0.840387i	$-0.317672\pi$
$44$		0			0
$45$	9.90181	−	4.33964i	1.47607	−	0.646916i
$46$		0			0
$47$	7.37585	+	4.25845i	1.07588	+	0.621159i	0.929782	−	0.368111i	$-0.119995\pi$
$47$	7.37585	+	4.25845i	1.07588	+	0.621159i	0.146097	+	0.989270i	$0.453329\pi$
$48$		0			0
$49$	3.32788	+	5.76406i	0.475412	+	0.823438i
$50$		0			0
$51$	−5.33648	−	5.96159i	−0.747257	−	0.834789i
$52$		0			0
$53$	10.5924			1.45498			0.727492	−	0.686116i	$-0.240686\pi$
$53$	10.5924			1.45498			0.727492	+	0.686116i	$0.240686\pi$
$54$		0			0
$55$	5.33624	−	9.24265i	0.719539	−	1.24628i
$56$		0			0
$57$	7.37169	−	6.59873i	0.976404	−	0.874023i
$58$		0			0
$59$			11.3999i			1.48414i	0.670324	+	0.742068i	$0.266155\pi$
$59$			11.3999i			1.48414i	−0.670324	+	0.742068i	$0.733845\pi$
$60$		0			0
$61$	−3.97066	+	2.29246i	−0.508391	+	0.293520i	−0.732172	−	0.681120i	$-0.761493\pi$
$61$	−3.97066	+	2.29246i	−0.508391	+	0.293520i	0.223781	+	0.974640i	$0.428160\pi$
$62$		0			0
$63$	−11.0184	−	1.22301i	−1.38819	−	0.154085i
$64$		0			0
$65$	−7.03646	+	4.06250i	−0.872765	+	0.503891i
$66$		0			0
$67$	2.48761	−	7.79819i	0.303910	−	0.952701i
$67$	2.48761	−	7.79819i	0.303910	−	0.952701i
$68$		0			0
$69$	−9.50129	−	10.6143i	−1.14382	−	1.27781i
$70$		0			0
$71$	12.3588	+	7.13533i	1.46672	+	0.846808i	0.999307	−	0.0372332i	$-0.0118544\pi$
$71$	12.3588	+	7.13533i	1.46672	+	0.846808i	0.467408	+	0.884041i	$0.345188\pi$
$72$		0			0
$73$	0.629763	+	1.09078i	0.0737082	+	0.127666i	0.900524	−	0.434807i	$-0.143183\pi$
$73$	0.629763	+	1.09078i	0.0737082	+	0.127666i	−0.826816	+	0.562473i	$0.809850\pi$
$74$		0			0
$75$	−2.83662	−	13.5390i	−0.327545	−	1.56335i
$76$		0			0
$77$	−9.47783	+	5.47203i	−1.08010	+	0.623595i
$78$		0			0
$79$	3.80258	+	2.19542i	0.427824	+	0.247004i	0.698419	−	0.715689i	$-0.253887\pi$
$79$	3.80258	+	2.19542i	0.427824	+	0.247004i	−0.270595	+	0.962693i	$0.587220\pi$
$80$		0			0
$81$	6.09967	−	6.61770i	0.677742	−	0.735300i
$82$		0			0
$83$	2.80997	−	1.62234i	0.308434	−	0.178075i	−0.337791	−	0.941221i	$-0.609680\pi$
$83$	2.80997	−	1.62234i	0.308434	−	0.178075i	0.646226	+	0.763146i	$0.276346\pi$
$84$		0			0
$85$	−14.4168	+	8.32354i	−1.56372	+	0.902815i
$86$		0			0
$87$	−2.60019	+	7.92398i	−0.278770	+	0.849540i
$88$		0			0
$89$			2.12774i			0.225540i	0.993621	+	0.112770i	$0.0359723\pi$
$89$			2.12774i			0.225540i	−0.993621	+	0.112770i	$0.964028\pi$
$90$		0			0
$91$	8.33174			0.873404
$92$		0			0
$93$	−4.20263	+	12.8074i	−0.435793	+	1.32806i
$94$		0			0
$95$	−10.2923	−	17.8268i	−1.05597	−	1.82899i
$96$		0			0
$97$	8.97837	−	5.18366i	0.911615	−	0.526321i	0.0306648	−	0.999530i	$-0.490238\pi$
$97$	8.97837	−	5.18366i	0.911615	−	0.526321i	0.880951	+	0.473208i	$0.156904\pi$
$98$		0			0
$99$	0.980148	−	8.83044i	0.0985086	−	0.887493i
$100$		0			0
$101$	−7.04180	+	12.1968i	−0.700685	+	1.21362i	0.267541	+	0.963546i	$0.413789\pi$
$101$	−7.04180	+	12.1968i	−0.700685	+	1.21362i	−0.968226	+	0.250076i	$0.919544\pi$
$102$		0			0
$103$	−3.26301	+	5.65170i	−0.321514	+	0.556878i	−0.980801	−	0.195013i	$-0.937525\pi$
$103$	−3.26301	+	5.65170i	−0.321514	+	0.556878i	0.659287	+	0.751892i	$0.270858\pi$
$104$		0			0
$105$	−7.19151	+	21.9158i	−0.701819	+	2.13877i
$106$		0			0
$107$		−	1.23281i		−	0.119180i	−0.998223	−	0.0595899i	$-0.981021\pi$
$107$		−	1.23281i		−	0.119180i	0.998223	−	0.0595899i	$-0.0189793\pi$
$108$		0			0
$109$			8.87642i			0.850207i	0.905145	+	0.425103i	$0.139762\pi$
$109$			8.87642i			0.850207i	−0.905145	+	0.425103i	$0.860238\pi$
$110$		0			0
$111$	10.5618	−	9.45433i	1.00248	−	0.897365i
$112$		0			0
$113$	0.367153	−	0.635928i	0.0345388	−	0.0598230i	−0.848239	−	0.529613i	$-0.822337\pi$
$113$	0.367153	−	0.635928i	0.0345388	−	0.0598230i	0.882778	+	0.469790i	$0.155670\pi$
$114$		0			0
$115$	−25.6683	+	14.8196i	−2.39358	+	1.38193i
$116$		0			0
$117$	−4.00754	+	5.44888i	−0.370497	+	0.503749i
$118$		0			0
$119$	17.0707			1.56486
$120$		0			0
$121$	1.11459	+	1.93053i	0.101326	+	0.175503i
$122$		0			0
$123$	−0.802681	−	0.263394i	−0.0723753	−	0.0237494i
$124$		0			0
$125$	−10.7623			−0.962610
$126$		0			0
$127$	−5.78672	+	10.0229i	−0.513488	+	0.889388i	0.486389	+	0.873742i	$0.338314\pi$
$127$	−5.78672	+	10.0229i	−0.513488	+	0.889388i	−0.999878	+	0.0156455i	$0.995020\pi$
$128$		0			0
$129$	−18.6842	+	3.91463i	−1.64506	+	0.344664i
$130$		0			0
$131$		−	18.0364i		−	1.57585i	−0.615770	−	0.787926i	$-0.711155\pi$
$131$		−	18.0364i		−	1.57585i	0.615770	−	0.787926i	$-0.288845\pi$
$132$		0			0
$133$			21.1084i			1.83033i
$134$		0			0
$135$	−10.8737	−	15.2446i	−0.935856	−	1.31205i
$136$		0			0
$137$	2.18254			0.186467			0.0932334	−	0.995644i	$-0.470280\pi$
$137$	2.18254			0.186467			0.0932334	+	0.995644i	$0.470280\pi$
$138$		0			0
$139$			1.48230i			0.125727i	0.998022	+	0.0628637i	$0.0200233\pi$
$139$			1.48230i			0.125727i	−0.998022	+	0.0628637i	$0.979977\pi$
$140$		0			0
$141$	4.59937	−	14.0164i	0.387336	−	1.18039i
$142$		0			0
$143$			6.67725i			0.558380i
$144$		0			0
$145$	15.0268	+	8.67571i	1.24791	+	0.720479i
$146$		0			0
$147$	8.58949	−	7.68884i	0.708450	−	0.634165i
$148$		0			0
$149$		−	2.54319i		−	0.208346i	−0.994559	−	0.104173i	$-0.966780\pi$
$149$		−	2.54319i		−	0.208346i	0.994559	−	0.104173i	$-0.0332196\pi$
$150$		0			0
$151$	−4.61380	−	7.99133i	−0.375466	−	0.650326i	0.614931	−	0.788581i	$-0.289184\pi$
$151$	−4.61380	−	7.99133i	−0.375466	−	0.650326i	−0.990397	+	0.138255i	$0.955851\pi$
$152$		0			0
$153$	−8.21093	+	11.1641i	−0.663815	+	0.902561i
$154$		0			0
$155$	24.2874	+	14.0224i	1.95081	+	1.12630i
$156$		0			0
$157$	1.35503	+	2.34698i	0.108143	+	0.187309i	0.915018	−	0.403413i	$-0.132176\pi$
$157$	1.35503	+	2.34698i	0.108143	+	0.187309i	−0.806875	+	0.590722i	$0.798843\pi$
$158$		0			0
$159$	−3.76221	−	17.9568i	−0.298363	−	1.42406i
$160$		0			0
$161$	30.3933			2.39533
$162$		0			0
$163$	6.61168	−	11.4518i	0.517867	−	0.896972i	−0.481918	−	0.876217i	$-0.660060\pi$
$163$	6.61168	−	11.4518i	0.517867	−	0.896972i	0.999785	−	0.0207554i	$-0.00660713\pi$
$164$		0			0
$165$	−17.5639	−	5.76344i	−1.36734	−	0.448683i
$166$		0			0
$167$	−7.97167	−	4.60245i	−0.616867	−	0.356148i	0.158781	−	0.987314i	$-0.449243\pi$
$167$	−7.97167	−	4.60245i	−0.616867	−	0.356148i	−0.775648	+	0.631166i	$0.782577\pi$
$168$		0			0
$169$	−3.95829	+	6.85597i	−0.304484	+	0.527382i
$170$		0			0
$171$	−13.8047	−	10.1531i	−1.05567	−	0.776425i
$172$		0			0
$173$	−11.5022	+	6.64078i	−0.874493	+	0.504889i	−0.868839	−	0.495095i	$-0.835133\pi$
$173$	−11.5022	+	6.64078i	−0.874493	+	0.504889i	−0.00565462	+	0.999984i	$0.501800\pi$
$174$		0			0
$175$	25.5590	+	14.7565i	1.93208	+	1.11549i
$176$		0			0
$177$	19.3255	−	4.04899i	1.45260	−	0.304340i
$178$		0			0
$179$	−16.1945			−1.21043			−0.605217	−	0.796060i	$-0.706914\pi$
$179$	−16.1945			−1.21043			−0.605217	+	0.796060i	$0.706914\pi$
$180$		0			0
$181$	−0.831318	+	1.43989i	−0.0617914	+	0.107026i	−0.895266	−	0.445532i	$-0.853015\pi$
$181$	−0.831318	+	1.43989i	−0.0617914	+	0.107026i	0.833475	+	0.552557i	$0.186348\pi$
$182$		0			0
$183$	5.29658	+	5.91701i	0.391534	+	0.437398i
$184$		0			0
$185$	−14.7463	−	25.5414i	−1.08417	−	1.87784i
$186$		0			0
$187$			13.6808i			1.00044i
$188$		0			0
$189$	1.84022	+	19.1133i	0.133856	+	1.39029i
$190$		0			0
$191$	7.65708	+	13.2625i	0.554047	+	0.959638i	0.997977	+	0.0635761i	$0.0202506\pi$
$191$	7.65708	+	13.2625i	0.554047	+	0.959638i	−0.443930	+	0.896061i	$0.646416\pi$
$192$		0			0
$193$	7.65307			0.550880			0.275440	−	0.961318i	$-0.411176\pi$
$193$	7.65307			0.550880			0.275440	+	0.961318i	$0.411176\pi$
$194$		0			0
$195$	9.38612	+	10.4856i	0.672154	+	0.750889i
$196$		0			0
$197$	−1.55409	+	2.69175i	−0.110724	+	0.191780i	−0.916062	−	0.401036i	$-0.868650\pi$
$197$	−1.55409	+	2.69175i	−0.110724	+	0.191780i	0.805338	+	0.592815i	$0.201984\pi$
$198$		0			0
$199$	0.134799	+	0.233479i	0.00955567	+	0.0165509i	0.870764	−	0.491702i	$-0.163625\pi$
$199$	0.134799	+	0.233479i	0.00955567	+	0.0165509i	−0.861208	+	0.508253i	$0.830292\pi$
$200$		0			0
$201$	−14.1034	−	1.44735i	−0.994775	−	0.102088i
$202$		0			0
$203$	−8.89646	−	15.4091i	−0.624409	−	1.08151i
$204$		0			0
$205$	−0.878830	+	1.52218i	−0.0613802	+	0.106314i
$206$		0			0
$207$	−14.6191	+	19.8770i	−1.01610	+	1.38154i
$208$		0			0
$209$	−16.9168			−1.17016
$210$		0			0
$211$	−13.5489	−	23.4673i	−0.932743	−	1.61556i	−0.778610	−	0.627508i	$-0.784075\pi$
$211$	−13.5489	−	23.4673i	−0.932743	−	1.61556i	−0.154133	−	0.988050i	$-0.549258\pi$
$212$		0			0
$213$	7.70656	−	23.4854i	0.528045	−	1.60919i
$214$		0			0
$215$			39.7182i			2.70876i
$216$		0			0
$217$	−14.3792	−	24.9054i	−0.976121	−	1.69069i
$218$		0			0
$219$	1.62546	−	1.45502i	0.109839	−	0.0983214i
$220$		0			0
$221$	5.20763	−	9.01987i	0.350303	−	0.606742i
$222$		0			0
$223$	−8.51661			−0.570314			−0.285157	−	0.958481i	$-0.592046\pi$
$223$	−8.51661			−0.570314			−0.285157	+	0.958481i	$0.592046\pi$
$224$		0			0
$225$	−21.9444	+	9.61754i	−1.46296	+	0.641169i
$226$		0			0
$227$	−14.5472	−	8.39882i	−0.965530	−	0.557449i	−0.0676595	−	0.997708i	$-0.521553\pi$
$227$	−14.5472	−	8.39882i	−0.965530	−	0.557449i	−0.897871	+	0.440259i	$0.854886\pi$
$228$		0			0
$229$	−4.13981	+	2.39012i	−0.273566	+	0.157944i	−0.630507	−	0.776183i	$-0.717153\pi$
$229$	−4.13981	+	2.39012i	−0.273566	+	0.157944i	0.356941	+	0.934127i	$0.383820\pi$
$230$		0			0
$231$	12.6427	+	14.1237i	0.831831	+	0.929269i
$232$		0			0
$233$	1.05550	−	1.82818i	0.0691480	−	0.119768i	−0.829378	−	0.558687i	$-0.811305\pi$
$233$	1.05550	−	1.82818i	0.0691480	−	0.119768i	0.898527	+	0.438919i	$0.144639\pi$
$234$		0			0
$235$	−26.5802	−	15.3461i	−1.73390	−	1.00107i
$236$		0			0
$237$	2.37118	−	7.22607i	0.154025	−	0.469384i
$238$		0			0
$239$	6.41223	−	11.1063i	0.414773	−	0.718407i	−0.580632	−	0.814166i	$-0.697194\pi$
$239$	6.41223	−	11.1063i	0.414773	−	0.718407i	0.995405	+	0.0957589i	$0.0305278\pi$
$240$		0			0
$241$	5.62450			0.362306			0.181153	−	0.983455i	$-0.442017\pi$
$241$	5.62450			0.362306			0.181153	+	0.983455i	$0.442017\pi$
$242$		0			0
$243$	−13.3851	−	7.98996i	−0.858654	−	0.512556i
$244$		0			0
$245$	−11.9926	−	20.7718i	−0.766180	−	1.32706i
$246$		0			0
$247$	11.1534	+	6.43939i	0.709671	+	0.409729i
$248$		0			0
$249$	−3.74830	−	4.18736i	−0.237539	−	0.265363i
$250$		0			0
$251$	−10.2371	−	17.7313i	−0.646163	−	1.11919i	−0.984032	−	0.177994i	$-0.943039\pi$
$251$	−10.2371	−	17.7313i	−0.646163	−	1.11919i	0.337869	−	0.941193i	$-0.390294\pi$
$252$		0			0
$253$			24.3579i			1.53137i
$254$		0			0
$255$	19.2310	+	21.4836i	1.20429	+	1.34536i
$256$		0			0
$257$	16.3494	+	9.43933i	1.01985	+	0.588809i	0.914060	−	0.405580i	$-0.132930\pi$
$257$	16.3494	+	9.43933i	1.01985	+	0.588809i	0.105788	+	0.994389i	$0.466264\pi$
$258$		0			0
$259$			30.2431i			1.87921i
$260$		0			0
$261$	14.3566	+	1.59353i	0.888651	+	0.0986372i
$262$		0			0
$263$		−	18.8353i		−	1.16144i	−0.814105	−	0.580718i	$-0.802772\pi$
$263$		−	18.8353i		−	1.16144i	0.814105	−	0.580718i	$-0.197228\pi$
$264$		0			0
$265$	−38.1717			−2.34487
$266$		0			0
$267$	3.60704	−	0.755727i	0.220747	−	0.0462498i
$268$		0			0
$269$			22.2511i			1.35667i	0.734752	+	0.678336i	$0.237299\pi$
$269$			22.2511i			1.35667i	−0.734752	+	0.678336i	$0.762701\pi$
$270$		0			0
$271$			10.8294i			0.657838i	0.944358	+	0.328919i	$0.106684\pi$
$271$			10.8294i			0.657838i	−0.944358	+	0.328919i	$0.893316\pi$
$272$		0			0
$273$	−2.95925	−	14.1243i	−0.179102	−	0.854843i
$274$		0			0
$275$	−11.8262	+	20.4836i	−0.713147	+	1.23521i
$276$		0			0
$277$	−5.46809			−0.328546			−0.164273	−	0.986415i	$-0.552528\pi$
$277$	−5.46809			−0.328546			−0.164273	+	0.986415i	$0.552528\pi$
$278$		0			0
$279$	23.2043	+	2.57559i	1.38920	+	0.154197i
$280$		0			0
$281$	−7.71219	−	13.3579i	−0.460071	−	0.796866i	0.538893	−	0.842374i	$-0.318843\pi$
$281$	−7.71219	−	13.3579i	−0.460071	−	0.796866i	−0.998964	+	0.0455083i	$0.985509\pi$
$282$		0			0
$283$	−14.7372			−0.876038			−0.438019	−	0.898966i	$-0.644320\pi$
$283$	−14.7372			−0.876038			−0.438019	+	0.898966i	$0.644320\pi$
$284$		0			0
$285$	−26.5652	+	23.7797i	−1.57358	+	1.40859i
$286$		0			0
$287$	1.56091	−	0.901192i	0.0921376	−	0.0531957i
$288$		0			0
$289$	2.16976	−	3.75813i	0.127633	−	0.221067i
$290$		0			0
$291$	−11.9765	−	13.3794i	−0.702074	−	0.784314i
$292$		0			0
$293$		−	7.13657i		−	0.416923i	−0.978031	−	0.208461i	$-0.933154\pi$
$293$		−	7.13657i		−	0.416923i	0.978031	−	0.208461i	$-0.0668456\pi$
$294$		0			0
$295$		−	41.0814i		−	2.39185i
$296$		0			0
$297$	−15.3179	+	1.47479i	−0.888833	+	0.0855761i
$298$		0			0
$299$	9.27188	−	16.0594i	0.536206	−	0.928737i
$300$		0			0
$301$	20.3644	−	35.2722i	1.17378	−	2.03306i
$302$		0			0
$303$	23.1776	+	7.60554i	1.33152	+	0.436927i
$304$		0			0
$305$	14.3090	−	8.26130i	0.819330	−	0.473040i
$306$		0			0
$307$	0.0773160	+	0.133915i	0.00441266	+	0.00764295i	0.868223	−	0.496174i	$-0.165262\pi$
$307$	0.0773160	+	0.133915i	0.00441266	+	0.00764295i	−0.863811	+	0.503817i	$0.831929\pi$
$308$		0			0
$309$	10.7399	+	3.52423i	0.610974	+	0.200486i
$310$		0			0
$311$	−22.4333			−1.27208			−0.636039	−	0.771657i	$-0.719428\pi$
$311$	−22.4333			−1.27208			−0.636039	+	0.771657i	$0.719428\pi$
$312$		0			0
$313$			6.54773i			0.370100i	0.982729	+	0.185050i	$0.0592447\pi$
$313$			6.54773i			0.370100i	−0.982729	+	0.185050i	$0.940755\pi$
$314$		0			0
$315$	39.7069	+	4.40733i	2.23723	+	0.248325i
$316$		0			0
$317$	13.9285	−	8.04165i	0.782305	−	0.451664i	−0.0549415	−	0.998490i	$-0.517497\pi$
$317$	13.9285	−	8.04165i	0.782305	−	0.451664i	0.837247	+	0.546826i	$0.184164\pi$
$318$		0			0
$319$	12.3492	−	7.12983i	0.691424	−	0.399194i
$320$		0			0
$321$	−2.08991	+	0.437866i	−0.116647	+	0.0244393i
$322$		0			0
$323$	22.8518	+	13.1935i	1.27151	+	0.734105i
$324$		0			0
$325$	15.5942	−	9.00333i	0.865012	−	0.499415i
$326$		0			0
$327$	15.0477	−	3.15271i	0.832139	−	0.174345i
$328$		0			0
$329$	15.7366	+	27.2565i	0.867585	+	1.50270i
$330$		0			0
$331$	21.7622	+	12.5644i	1.19616	+	0.690602i	0.959696	−	0.281039i	$-0.0906790\pi$
$331$	21.7622	+	12.5644i	1.19616	+	0.690602i	0.236461	+	0.971641i	$0.424012\pi$
$332$		0			0
$333$	−19.7787	−	14.5468i	−1.08387	−	0.797161i
$334$		0			0
$335$	−8.96454	+	28.1022i	−0.489785	+	1.53538i
$336$		0			0
$337$	19.8300	−	11.4488i	1.08021	−	0.623659i	0.149256	−	0.988799i	$-0.452312\pi$
$337$	19.8300	−	11.4488i	1.08021	−	0.623659i	0.930953	+	0.365140i	$0.118979\pi$
$338$		0			0
$339$	−1.20846	−	0.396546i	−0.0656344	−	0.0215374i
$340$		0			0
$341$	19.9598	−	11.5238i	1.08088	−	0.624048i
$342$		0			0
$343$		−	1.27207i		−	0.0686853i
$344$		0			0
$345$	34.2396	+	38.2503i	1.84340	+	2.05933i
$346$		0			0
$347$	12.4805	−	21.6168i	0.669986	−	1.16045i	−0.307922	−	0.951412i	$-0.599633\pi$
$347$	12.4805	−	21.6168i	0.669986	−	1.16045i	0.977908	−	0.209038i	$-0.0670332\pi$
$348$		0			0
$349$	20.2064			1.08162			0.540812	−	0.841144i	$-0.318117\pi$
$349$	20.2064			1.08162			0.540812	+	0.841144i	$0.318117\pi$
$350$		0			0
$351$	10.6606	+	4.85843i	0.569019	+	0.259324i
$352$		0			0
$353$	−17.5145	−	30.3359i	−0.932200	−	1.61462i	−0.779552	−	0.626338i	$-0.784553\pi$
$353$	−17.5145	−	30.3359i	−0.932200	−	1.61462i	−0.152648	−	0.988281i	$-0.548780\pi$
$354$		0			0
$355$	−44.5370	−	25.7134i	−2.36378	−	1.36473i
$356$		0			0
$357$	−6.06313	−	28.9389i	−0.320895	−	1.53161i
$358$		0			0
$359$			13.5980i			0.717674i	0.933400	+	0.358837i	$0.116827\pi$
$359$			13.5980i			0.717674i	−0.933400	+	0.358837i	$0.883173\pi$
$360$		0			0
$361$	−6.81416	+	11.8025i	−0.358640	+	0.621183i
$362$		0			0
$363$	2.87684	−	2.57518i	0.150995	−	0.135162i
$364$		0			0
$365$	−2.26946	−	3.93082i	−0.118789	−	0.205749i
$366$		0			0
$367$	4.52728	+	2.61383i	0.236322	+	0.136441i	0.613485	−	0.789706i	$-0.289767\pi$
$367$	4.52728	+	2.61383i	0.236322	+	0.136441i	−0.377163	+	0.926147i	$0.623100\pi$
$368$		0			0
$369$	−0.161421	+	1.45429i	−0.00840326	+	0.0757074i
$370$		0			0
$371$	33.8989	+	19.5715i	1.75994	+	1.01610i
$372$		0			0
$373$	−1.06973	−	0.617607i	−0.0553884	−	0.0319785i	0.472050	−	0.881572i	$-0.343514\pi$
$373$	−1.06973	−	0.617607i	−0.0553884	−	0.0319785i	−0.527438	+	0.849593i	$0.676847\pi$
$374$		0			0
$375$	3.82254	+	18.2447i	0.197395	+	0.942153i
$376$		0			0
$377$	−10.8559			−0.559109
$378$		0			0
$379$	−0.461731	+	0.266580i	−0.0237175	+	0.0136933i	−0.511812	−	0.859098i	$-0.671026\pi$
$379$	−0.461731	+	0.266580i	−0.0237175	+	0.0136933i	0.488094	+	0.872791i	$0.337692\pi$
$380$		0			0
$381$	19.0465	+	6.24998i	0.975784	+	0.320196i
$382$		0			0
$383$	1.76314	+	3.05384i	0.0900920	+	0.156044i	0.907550	−	0.419945i	$-0.137951\pi$
$383$	1.76314	+	3.05384i	0.0900920	+	0.156044i	−0.817458	+	0.575989i	$0.804617\pi$
$384$		0			0
$385$	34.1550	−	19.7194i	1.74070	−	1.00499i
$386$		0			0
$387$	13.2725	+	30.2840i	0.674678	+	1.53942i
$388$		0			0
$389$	6.31060	−	3.64343i	0.319960	−	0.184729i	−0.331415	−	0.943485i	$-0.607526\pi$
$389$	6.31060	−	3.64343i	0.319960	−	0.184729i	0.651375	+	0.758756i	$0.274193\pi$
$390$		0			0
$391$	18.9969	−	32.9036i	0.960714	−	1.66400i
$392$		0			0
$393$	−30.5761	+	6.40615i	−1.54236	+	0.323148i
$394$		0			0
$395$	−13.7033	−	7.91159i	−0.689487	−	0.398075i
$396$		0			0
$397$	14.1142			0.708371			0.354185	−	0.935175i	$-0.384758\pi$
$397$	14.1142			0.708371			0.354185	+	0.935175i	$0.384758\pi$
$398$		0			0
$399$	35.7839	−	7.49725i	1.79143	−	0.375332i
$400$		0			0
$401$	−2.05940			−0.102842			−0.0514208	−	0.998677i	$-0.516375\pi$
$401$	−2.05940			−0.102842			−0.0514208	+	0.998677i	$0.516375\pi$
$402$		0			0
$403$	−17.5462			−0.874038
$404$		0			0
$405$	−21.9812	+	23.8481i	−1.09226	+	1.18502i
$406$		0			0
$407$	−24.2375			−1.20141
$408$		0			0
$409$	−22.0958	−	12.7570i	−1.09257	−	0.630794i	−0.158309	−	0.987390i	$-0.550604\pi$
$409$	−22.0958	−	12.7570i	−1.09257	−	0.630794i	−0.934259	+	0.356595i	$0.883938\pi$
$410$		0			0
$411$	−0.775190	−	3.69993i	−0.0382373	−	0.182504i
$412$		0			0
$413$	−21.0634	+	36.4828i	−1.03646	+	1.79520i
$414$		0			0
$415$	−10.1262	+	5.84638i	−0.497077	+	0.286987i
$416$		0			0
$417$	2.51287	−	0.526482i	0.123056	−	0.0257820i
$418$		0			0
$419$	−13.2976	+	7.67735i	−0.649628	+	0.375063i	−0.788314	−	0.615273i	$-0.789046\pi$
$419$	−13.2976	+	7.67735i	−0.649628	+	0.375063i	0.138686	+	0.990336i	$0.455712\pi$
$420$		0			0
$421$	15.1923	+	26.3139i	0.740428	+	1.28246i	0.952300	+	0.305162i	$0.0987106\pi$
$421$	15.1923	+	26.3139i	0.740428	+	1.28246i	−0.211872	+	0.977297i	$0.567956\pi$
$422$		0			0
$423$	−25.3948	−	2.81873i	−1.23474	−	0.137051i
$424$		0			0
$425$	31.9505	−	18.4467i	1.54983	−	0.894794i
$426$		0			0
$427$	−16.9430			−0.819930
$428$		0			0
$429$	11.3196	−	2.37161i	0.546514	−	0.114503i
$430$		0			0
$431$	−19.8202	−	11.4432i	−0.954707	−	0.551201i	−0.0601674	−	0.998188i	$-0.519163\pi$
$431$	−19.8202	−	11.4432i	−0.954707	−	0.551201i	−0.894540	+	0.446988i	$0.852497\pi$
$432$		0			0
$433$	22.6525	+	13.0784i	1.08861	+	0.628508i	0.933206	−	0.359343i	$-0.116999\pi$
$433$	22.6525	+	13.0784i	1.08861	+	0.628508i	0.155403	+	0.987851i	$0.450332\pi$
$434$		0			0
$435$	9.37025	−	28.5555i	0.449269	−	1.36913i
$436$		0			0
$437$	40.6863	+	23.4902i	1.94629	+	1.12369i
$438$		0			0
$439$	−7.95944	−	13.7861i	−0.379883	−	0.657977i	0.611162	−	0.791506i	$-0.290702\pi$
$439$	−7.95944	−	13.7861i	−0.379883	−	0.657977i	−0.991045	+	0.133529i	$0.957369\pi$
$440$		0			0
$441$	−16.0853	−	11.8304i	−0.765965	−	0.563351i
$442$		0			0
$443$	−7.66008	+	13.2677i	−0.363942	+	0.630365i	−0.988606	−	0.150528i	$-0.951903\pi$
$443$	−7.66008	+	13.2677i	−0.363942	+	0.630365i	0.624664	+	0.780894i	$0.285236\pi$
$444$		0			0
$445$		−	7.66769i		−	0.363483i
$446$		0			0
$447$	−4.31132	+	0.903285i	−0.203918	+	0.0427239i
$448$		0			0
$449$	−6.40241	−	3.69643i	−0.302149	−	0.174446i	0.341259	−	0.939969i	$-0.389147\pi$
$449$	−6.40241	−	3.69643i	−0.302149	−	0.174446i	−0.643408	+	0.765524i	$0.722480\pi$
$450$		0			0
$451$	0.722236	+	1.25095i	0.0340088	+	0.0589049i
$452$		0			0
$453$	−11.9085	+	10.6599i	−0.559512	+	0.500844i
$454$		0			0
$455$	−30.0249			−1.40759
$456$		0			0
$457$	−2.60191	+	4.50665i	−0.121712	+	0.210812i	−0.920443	−	0.390877i	$-0.872172\pi$
$457$	−2.60191	+	4.50665i	−0.121712	+	0.210812i	0.798731	+	0.601689i	$0.205505\pi$
$458$		0			0
$459$	21.8421	+	9.95429i	1.01950	+	0.464627i
$460$		0			0
$461$			33.6857i			1.56890i	0.620192	+	0.784450i	$0.287055\pi$
$461$			33.6857i			1.56890i	−0.620192	+	0.784450i	$0.712945\pi$
$462$		0			0
$463$	−13.4453	+	7.76263i	−0.624854	+	0.360760i	−0.778757	−	0.627326i	$-0.784149\pi$
$463$	−13.4453	+	7.76263i	−0.624854	+	0.360760i	0.153902	+	0.988086i	$0.450816\pi$
$464$		0			0
$465$	15.1449	−	46.1535i	0.702329	−	2.14032i
$466$		0			0
$467$	11.3144	−	6.53235i	0.523567	−	0.302281i	−0.214826	−	0.976652i	$-0.568918\pi$
$467$	11.3144	−	6.53235i	0.523567	−	0.302281i	0.738393	+	0.674371i	$0.235585\pi$
$468$		0			0
$469$	22.3697	−	20.3601i	1.03294	−	0.940143i
$470$		0			0
$471$	3.49742	−	3.13069i	0.161152	−	0.144255i
$472$		0			0
$473$	28.2680	+	16.3205i	1.29976	+	0.750418i
$474$		0			0
$475$	22.8099	+	39.5078i	1.04659	+	1.81274i
$476$		0			0
$477$	−29.1048	+	12.7557i	−1.33262	+	0.584044i
$478$		0			0
$479$	−0.387072	+	0.223476i	−0.0176858	+	0.0102109i	−0.508817	−	0.860875i	$-0.669917\pi$
$479$	−0.387072	+	0.223476i	−0.0176858	+	0.0102109i	0.491131	+	0.871086i	$0.336584\pi$
$480$		0			0
$481$	15.9800	+	9.22604i	0.728624	+	0.420671i
$482$		0			0
$483$	−10.7950	−	51.5240i	−0.491192	−	2.34443i
$484$		0			0
$485$	−32.3551	+	18.6802i	−1.46917	+	0.848226i
$486$		0			0
$487$	−11.0165	+	6.36037i	−0.499204	+	0.288216i	−0.728385	−	0.685168i	$-0.759729\pi$
$487$	−11.0165	+	6.36037i	−0.499204	+	0.288216i	0.229181	+	0.973384i	$0.426395\pi$
$488$		0			0
$489$	−21.7619	−	7.14099i	−0.984105	−	0.322927i
$490$		0			0
$491$			44.0337i			1.98721i	0.112892	+	0.993607i	$0.463989\pi$
$491$			44.0337i			1.98721i	−0.112892	+	0.993607i	$0.536011\pi$
$492$		0			0
$493$	−22.2424			−1.00175
$494$		0			0
$495$	−3.53214	+	31.8220i	−0.158758	+	1.43029i
$496$		0			0
$497$	26.3677	+	45.6702i	1.18275	+	2.04859i
$498$		0			0
$499$	3.43529	−	1.98336i	0.153785	−	0.0887876i	−0.421133	−	0.906999i	$-0.638367\pi$
$499$	3.43529	−	1.98336i	0.153785	−	0.0887876i	0.574918	+	0.818211i	$0.305034\pi$
$500$		0			0
$501$	−4.97090	+	15.1486i	−0.222083	+	0.676790i
$502$		0			0
$503$	8.23418	−	14.2620i	0.367144	−	0.635912i	−0.621974	−	0.783038i	$-0.713669\pi$
$503$	8.23418	−	14.2620i	0.367144	−	0.635912i	0.989118	+	0.147126i	$0.0470023\pi$
$504$		0			0
$505$	25.3764	−	43.9531i	1.12923	−	1.95589i
$506$		0			0
$507$	13.0284	+	4.27518i	0.578613	+	0.189867i
$508$		0			0
$509$		−	9.04756i		−	0.401026i	−0.979691	−	0.200513i	$-0.935739\pi$
$509$		−	9.04756i		−	0.401026i	0.979691	−	0.200513i	$-0.0642609\pi$
$510$		0			0
$511$			4.65442i			0.205899i
$512$		0			0
$513$	−12.3088	+	27.0085i	−0.543447	+	1.19245i
$514$		0			0
$515$	11.7588	−	20.3669i	0.518156	−	0.897472i
$516$		0			0
$517$	−21.8440	+	12.6116i	−0.960698	+	0.554660i
$518$		0			0
$519$	15.3431	+	17.1403i	0.673485	+	0.752376i
$520$		0			0
$521$	−18.9377			−0.829678			−0.414839	−	0.909895i	$-0.636162\pi$
$521$	−18.9377			−0.829678			−0.414839	+	0.909895i	$0.636162\pi$
$522$		0			0
$523$	−11.4271	−	19.7922i	−0.499670	−	0.865454i	0.500330	−	0.865835i	$-0.333212\pi$
$523$	−11.4271	−	19.7922i	−0.499670	−	0.865454i	−1.00000		0.000380701i	$0.999879\pi$
$524$		0			0
$525$	15.9378	−	48.5699i	0.695585	−	2.11977i
$526$		0			0
$527$	−35.9499			−1.56600
$528$		0			0
$529$	22.3228	−	38.6643i	0.970558	−	1.68106i
$530$		0			0
$531$	−13.7280	−	31.3234i	−0.595746	−	1.35932i
$532$		0			0
$533$		−	1.09968i		−	0.0476325i
$534$		0			0
$535$			4.44263i			0.192072i
$536$		0			0
$537$	5.75194	+	27.4536i	0.248214	+	1.18471i
$538$		0			0
$539$	−19.7114			−0.849031
$540$		0			0
$541$		−	42.8342i		−	1.84159i	−0.390051	−	0.920793i	$-0.627543\pi$
$541$		−	42.8342i		−	1.84159i	0.390051	−	0.920793i	$-0.372457\pi$
$542$		0			0
$543$	2.73622	+	0.897870i	0.117423	+	0.0385313i
$544$		0			0
$545$		−	31.9877i		−	1.37020i
$546$		0			0
$547$	27.8728	+	16.0924i	1.19175	+	0.688060i	0.958704	−	0.284405i	$-0.0917959\pi$
$547$	27.8728	+	16.0924i	1.19175	+	0.688060i	0.233051	+	0.972465i	$0.425129\pi$
$548$		0			0
$549$	8.14953	−	11.0806i	0.347814	−	0.472907i
$550$		0			0
$551$		−	27.5034i		−	1.17169i
$552$		0			0
$553$	8.11290	+	14.0520i	0.344996	+	0.597550i
$554$		0			0
$555$	−38.0613	+	34.0703i	−1.61561	+	1.44621i
$556$		0			0
$557$	−13.7497	−	7.93838i	−0.582593	−	0.336360i	0.179570	−	0.983745i	$-0.442529\pi$
$557$	−13.7497	−	7.93838i	−0.582593	−	0.336360i	−0.762163	+	0.647385i	$0.775863\pi$
$558$		0			0
$559$	−12.4249	−	21.5205i	−0.525515	−	0.910219i
$560$		0			0
$561$	23.1923	−	4.85913i	0.979181	−	0.205153i
$562$		0			0
$563$	21.9295			0.924217			0.462108	−	0.886823i	$-0.347093\pi$
$563$	21.9295			0.924217			0.462108	+	0.886823i	$0.347093\pi$
$564$		0			0
$565$	−1.32310	+	2.29168i	−0.0556633	+	0.0964116i
$566$		0			0
$567$	31.7481	−	9.90825i	1.33330	−	0.416108i
$568$		0			0
$569$	−10.0417	−	5.79755i	−0.420968	−	0.243046i	0.274523	−	0.961580i	$-0.411480\pi$
$569$	−10.0417	−	5.79755i	−0.420968	−	0.243046i	−0.695491	+	0.718534i	$0.744813\pi$
$570$		0			0
$571$	18.0411	−	31.2481i	0.754998	−	1.30769i	−0.190378	−	0.981711i	$-0.560971\pi$
$571$	18.0411	−	31.2481i	0.754998	−	1.30769i	0.945376	−	0.325983i	$-0.105695\pi$
$572$		0			0
$573$	19.7635	−	17.6912i	0.825630	−	0.739058i
$574$		0			0
$575$	56.8861	−	32.8432i	2.37231	−	1.36966i
$576$		0			0
$577$	−31.7861	−	18.3517i	−1.32327	−	0.763993i	−0.339025	−	0.940778i	$-0.610097\pi$
$577$	−31.7861	−	18.3517i	−1.32327	−	0.763993i	−0.984250	+	0.176785i	$0.943430\pi$
$578$		0			0
$579$	−2.71821	−	12.9738i	−0.112965	−	0.539173i
$580$		0			0
$581$	11.9903			0.497440
$582$		0			0
$583$	−15.6851	+	27.1673i	−0.649609	+	1.12516i
$584$		0			0
$585$	14.4419	−	19.6360i	0.597098	−	0.811849i
$586$		0			0
$587$	3.02789	+	5.24447i	0.124975	+	0.216462i	0.921723	−	0.387849i	$-0.126782\pi$
$587$	3.02789	+	5.24447i	0.124975	+	0.216462i	−0.796748	+	0.604311i	$0.793448\pi$
$588$		0			0
$589$		−	44.4532i		−	1.83166i
$590$		0			0
$591$	5.11516	+	1.67850i	0.210409	+	0.0690442i
$592$		0			0
$593$	−0.587963	−	1.01838i	−0.0241447	−	0.0418199i	0.853701	−	0.520764i	$-0.174353\pi$
$593$	−0.587963	−	1.01838i	−0.0241447	−	0.0418199i	−0.877845	+	0.478944i	$0.841020\pi$
$594$		0			0
$595$	−61.5171			−2.52196
$596$		0			0
$597$	0.347926	−	0.311445i	0.0142397	−	0.0127466i
$598$		0			0
$599$	6.14540	−	10.6441i	0.251094	−	0.434908i	−0.712733	−	0.701435i	$-0.752543\pi$
$599$	6.14540	−	10.6441i	0.251094	−	0.434908i	0.963827	+	0.266527i	$0.0858763\pi$
$600$		0			0
$601$	−4.36040	−	7.55243i	−0.177864	−	0.308070i	0.763284	−	0.646063i	$-0.223586\pi$
$601$	−4.36040	−	7.55243i	−0.177864	−	0.308070i	−0.941149	+	0.337992i	$0.890252\pi$
$602$		0			0
$603$	2.55560	+	24.4227i	0.104072	+	0.994570i
$604$		0			0
$605$	−4.01663	−	6.95700i	−0.163299	−	0.282842i
$606$		0			0
$607$	−1.97906	+	3.42782i	−0.0803274	+	0.139131i	−0.903391	−	0.428819i	$-0.858930\pi$
$607$	−1.97906	+	3.42782i	−0.0803274	+	0.139131i	0.823063	+	0.567950i	$0.192263\pi$
$608$		0			0
$609$	−22.9624	+	20.5547i	−0.930483	+	0.832917i
$610$		0			0
$611$	19.2026			0.776853
$612$		0			0
$613$	3.85267	+	6.67301i	0.155608	+	0.269520i	0.933280	−	0.359149i	$-0.116933\pi$
$613$	3.85267	+	6.67301i	0.155608	+	0.269520i	−0.777672	+	0.628670i	$0.783600\pi$
$614$		0			0
$615$	2.89260	+	0.949186i	0.116641	+	0.0382749i
$616$		0			0
$617$			28.9608i			1.16592i	0.812502	+	0.582958i	$0.198105\pi$
$617$			28.9608i			1.16592i	−0.812502	+	0.582958i	$0.801895\pi$
$618$		0			0
$619$	−6.14678	−	10.6465i	−0.247060	−	0.427920i	0.715649	−	0.698460i	$-0.246131\pi$
$619$	−6.14678	−	10.6465i	−0.247060	−	0.427920i	−0.962709	+	0.270540i	$0.912798\pi$
$620$		0			0
$621$	38.8887	+	17.7230i	1.56055	+	0.711201i
$622$		0			0
$623$	−3.93140	+	6.80938i	−0.157508	+	0.272812i
$624$		0			0
$625$	−1.14854			−0.0459418
$626$		0			0
$627$	6.00847	+	28.6780i	0.239955	+	1.14529i
$628$		0			0
$629$	32.7409	+	18.9030i	1.30547	+	0.753711i
$630$		0			0
$631$	−2.05504	+	1.18648i	−0.0818097	+	0.0472328i	−0.540347	−	0.841442i	$-0.681707\pi$
$631$	−2.05504	+	1.18648i	−0.0818097	+	0.0472328i	0.458537	+	0.888675i	$0.348374\pi$
$632$		0			0
$633$	−34.9706	+	31.3037i	−1.38996	+	1.24421i
$634$		0			0
$635$	20.8535	−	36.1192i	0.827544	−	1.43335i
$636$		0			0
$637$	12.9959	+	7.50319i	0.514916	+	0.297287i
$638$		0			0
$639$	−42.5507	−	4.72298i	−1.68328	−	0.186838i
$640$		0			0
$641$	−14.2442	+	24.6717i	−0.562613	+	0.974473i	0.434655	+	0.900597i	$0.356870\pi$
$641$	−14.2442	+	24.6717i	−0.562613	+	0.974473i	−0.997267	+	0.0738763i	$0.976463\pi$
$642$		0			0
$643$	−2.32535			−0.0917029			−0.0458514	−	0.998948i	$-0.514600\pi$
$643$	−2.32535			−0.0917029			−0.0458514	+	0.998948i	$0.514600\pi$
$644$		0			0
$645$	67.3320	−	14.1070i	2.65119	−	0.555464i
$646$		0			0
$647$	−19.9762	−	34.5999i	−0.785347	−	1.36026i	−0.928791	−	0.370603i	$-0.879151\pi$
$647$	−19.9762	−	34.5999i	−0.785347	−	1.36026i	0.143444	−	0.989658i	$-0.454182\pi$
$648$		0			0
$649$	−29.2382	−	16.8807i	−1.14770	−	0.662624i
$650$		0			0
$651$	−37.1136	+	33.2220i	−1.45460	+	1.30207i
$652$		0			0
$653$	−4.75318	−	8.23275i	−0.186006	−	0.322172i	0.757909	−	0.652360i	$-0.226221\pi$
$653$	−4.75318	−	8.23275i	−0.186006	−	0.322172i	−0.943915	+	0.330188i	$0.892888\pi$
$654$		0			0
$655$			64.9975i			2.53966i
$656$		0			0
$657$	−3.04395	−	2.23876i	−0.118756	−	0.0873423i
$658$		0			0
$659$	40.1336	+	23.1711i	1.56338	+	0.902620i	0.996911	+	0.0785391i	$0.0250256\pi$
$659$	40.1336	+	23.1711i	1.56338	+	0.902620i	0.566472	+	0.824081i	$0.308308\pi$
$660$		0			0
$661$			29.0198i			1.12874i	0.825523	+	0.564369i	$0.190881\pi$
$661$			29.0198i			1.12874i	−0.825523	+	0.564369i	$0.809119\pi$
$662$		0			0
$663$	−17.1405	−	5.62453i	−0.665682	−	0.218439i
$664$		0			0
$665$		−	76.0678i		−	2.94978i
$666$		0			0
$667$	−39.6013			−1.53337
$668$		0			0
$669$	3.02492	+	14.4377i	0.116950	+	0.558195i
$670$		0			0
$671$		−	13.5785i		−	0.524193i
$672$		0			0
$673$			18.6836i			0.720199i	0.932914	+	0.360100i	$0.117257\pi$
$673$			18.6836i			0.720199i	−0.932914	+	0.360100i	$0.882743\pi$
$674$		0			0
$675$	24.0982	+	33.7852i	0.927542	+	1.30039i
$676$		0			0
$677$	9.74938	−	16.8864i	0.374699	−	0.648998i	−0.615583	−	0.788072i	$-0.711079\pi$
$677$	9.74938	−	16.8864i	0.374699	−	0.648998i	0.990282	+	0.139074i	$0.0444127\pi$
$678$		0			0
$679$	38.3111			1.47025
$680$		0			0
$681$	−9.07119	+	27.6441i	−0.347609	+	1.05932i
$682$		0			0
$683$	−7.63754	−	13.2286i	−0.292242	−	0.506179i	0.682097	−	0.731262i	$-0.261068\pi$
$683$	−7.63754	−	13.2286i	−0.292242	−	0.506179i	−0.974340	+	0.225083i	$0.927735\pi$
$684$		0			0
$685$	−7.86516			−0.300512
$686$		0			0
$687$	5.52221	+	6.16907i	0.210685	+	0.235365i
$688$		0			0
$689$	20.6826	−	11.9411i	0.787943	−	0.454919i
$690$		0			0
$691$	12.1115	−	20.9777i	0.460743	−	0.798030i	−0.538255	−	0.842782i	$-0.680916\pi$
$691$	12.1115	−	20.9777i	0.460743	−	0.798030i	0.998998	+	0.0447519i	$0.0142497\pi$
$692$		0			0
$693$	19.4526	−	26.4489i	0.738944	−	1.00471i
$694$		0			0
$695$		−	5.34174i		−	0.202624i
$696$		0			0
$697$		−	2.25311i		−	0.0853424i
$698$		0			0
$699$	−3.47410	−	1.14000i	−0.131402	−	0.0431187i
$700$		0			0
$701$	−4.11912	+	7.13453i	−0.155577	+	0.269467i	−0.933269	−	0.359178i	$-0.883057\pi$
$701$	−4.11912	+	7.13453i	−0.155577	+	0.269467i	0.777692	+	0.628646i	$0.216390\pi$
$702$		0			0
$703$	−23.3741	+	40.4852i	−0.881572	+	1.52693i
$704$		0			0
$705$	−16.5746	+	50.5105i	−0.624236	+	1.90233i
$706$		0			0
$707$	−45.0715	+	26.0221i	−1.69509	+	0.978660i
$708$		0			0
$709$	13.5151	+	23.4089i	0.507571	+	0.879139i	0.999962	+	0.00876447i	$0.00278985\pi$
$709$	13.5151	+	23.4089i	0.507571	+	0.879139i	−0.492391	+	0.870374i	$0.663877\pi$
$710$		0			0
$711$	−13.0921	−	1.45318i	−0.490993	−	0.0544986i
$712$		0			0
$713$	−64.0067			−2.39707
$714$		0			0
$715$		−	24.0626i		−	0.899892i
$716$		0			0
$717$	−21.1054	−	6.92557i	−0.788195	−	0.258640i
$718$		0			0
$719$	−37.1549	+	21.4514i	−1.38564	+	0.800002i	−0.992821	−	0.119612i	$-0.961835\pi$
$719$	−37.1549	+	21.4514i	−1.38564	+	0.800002i	−0.392823	+	0.919614i	$0.628502\pi$
$720$		0			0
$721$	−20.8851	+	12.0580i	−0.777802	+	0.449064i
$722$		0			0
$723$	−1.99770	−	9.53490i	−0.0742953	−	0.354607i
$724$		0			0
$725$	−33.3024	−	19.2271i	−1.23682	−	0.714078i
$726$		0			0
$727$	21.5056	−	12.4163i	0.797599	−	0.460494i	−0.0450320	−	0.998986i	$-0.514339\pi$
$727$	21.5056	−	12.4163i	0.797599	−	0.460494i	0.842631	+	0.538492i	$0.181006\pi$
$728$		0			0
$729$	−8.79084	+	25.5288i	−0.325587	+	0.945512i
$730$		0			0
$731$	−25.4569	−	44.0927i	−0.941559	−	1.63083i
$732$		0			0
$733$	−41.1568	−	23.7619i	−1.52016	−	0.877665i	−0.999718	−	0.0237679i	$-0.992434\pi$
$733$	−41.1568	−	23.7619i	−1.52016	−	0.877665i	−0.520442	−	0.853897i	$-0.674233\pi$
$734$		0			0
$735$	−30.9538	+	27.7081i	−1.14175	+	1.02203i
$736$		0			0
$737$	16.3171	+	17.9276i	0.601047	+	0.660371i
$738$		0			0
$739$	−6.28091	+	3.62629i	−0.231047	+	0.133395i	−0.611055	−	0.791588i	$-0.709255\pi$
$739$	−6.28091	+	3.62629i	−0.231047	+	0.133395i	0.380008	+	0.924983i	$0.375921\pi$
$740$		0			0
$741$	6.95490	−	21.1948i	0.255495	−	0.778610i
$742$		0			0
$743$	−20.7112	+	11.9576i	−0.759819	+	0.438681i	−0.829231	−	0.558907i	$-0.811221\pi$
$743$	−20.7112	+	11.9576i	−0.759819	+	0.438681i	0.0694121	+	0.997588i	$0.477888\pi$
$744$		0			0
$745$			9.16482i			0.335773i
$746$		0			0
$747$	−5.76728	+	7.84153i	−0.211014	+	0.286907i
$748$		0			0
$749$	2.27784	−	3.94533i	0.0832304	−	0.144159i
$750$		0			0
$751$	26.7088			0.974618			0.487309	−	0.873230i	$-0.337979\pi$
$751$	26.7088			0.974618			0.487309	+	0.873230i	$0.337979\pi$
$752$		0			0
$753$	−26.4228	+	23.6522i	−0.962899	+	0.861934i
$754$		0			0
$755$	16.6266	+	28.7982i	0.605105	+	1.04807i
$756$		0			0
$757$	−38.1680	−	22.0363i	−1.38724	−	0.800924i	−0.394237	−	0.919009i	$-0.628991\pi$
$757$	−38.1680	−	22.0363i	−1.38724	−	0.800924i	−0.993003	+	0.118085i	$0.962324\pi$
$758$		0			0
$759$	41.2926	−	8.65140i	1.49883	−	0.314026i
$760$		0			0
$761$			3.93893i			0.142786i	0.997448	+	0.0713931i	$0.0227445\pi$
$761$			3.93893i			0.142786i	−0.997448	+	0.0713931i	$0.977256\pi$
$762$		0			0
$763$	−16.4008	+	28.4071i	−0.593750	+	1.02841i
$764$		0			0
$765$	29.5895	−	40.2317i	1.06981	−	1.45458i
$766$		0			0
$767$	12.8513	+	22.2591i	0.464034	+	0.803730i
$768$		0			0
$769$	−13.6091	−	7.85722i	−0.490757	−	0.283339i	0.234131	−	0.972205i	$-0.424775\pi$
$769$	−13.6091	−	7.85722i	−0.490757	−	0.283339i	−0.724888	+	0.688866i	$0.758109\pi$
$770$		0			0
$771$	10.1950	−	31.0688i	0.367164	−	1.11892i
$772$		0			0
$773$	5.69280	+	3.28674i	0.204756	+	0.118216i	0.598872	−	0.800845i	$-0.295616\pi$
$773$	5.69280	+	3.28674i	0.204756	+	0.118216i	−0.394116	+	0.919061i	$0.628949\pi$
$774$		0			0
$775$	−53.8259	−	31.0764i	−1.93348	−	1.11630i
$776$		0			0
$777$	51.2694	−	10.7417i	1.83928	−	0.385356i
$778$		0			0
$779$	2.78603			0.0998200
$780$		0			0
$781$	−36.6012	+	21.1317i	−1.30969	+	0.756151i
$782$		0			0
$783$	−2.39773	−	24.9039i	−0.0856879	−	0.889993i
$784$		0			0
$785$	−4.88308	−	8.45774i	−0.174285	−	0.301870i
$786$		0			0
$787$	−16.0667	+	9.27613i	−0.572717	+	0.330658i	−0.758234	−	0.651983i	$-0.773937\pi$
$787$	−16.0667	+	9.27613i	−0.572717	+	0.330658i	0.185517	+	0.982641i	$0.440604\pi$
$788$		0			0
$789$	−31.9304	+	6.68990i	−1.13675	+	0.238167i
$790$		0			0
$791$	2.34999	−	1.35677i	0.0835560	−	0.0482411i
$792$		0			0
$793$	−5.16869	+	8.95243i	−0.183545	+	0.317910i
$794$		0			0
$795$	13.5578	+	64.7104i	0.480845	+	2.29504i
$796$		0			0
$797$	−9.71007	−	5.60611i	−0.343948	−	0.198579i	0.318068	−	0.948068i	$-0.396966\pi$
$797$	−9.71007	−	5.60611i	−0.343948	−	0.198579i	−0.662017	+	0.749489i	$0.730299\pi$
$798$		0			0
$799$	39.3436			1.39188
$800$		0			0
$801$	−2.56228	−	5.84639i	−0.0905338	−	0.206572i
$802$		0			0
$803$	−3.73016			−0.131634
$804$		0			0
$805$	−109.528			−3.86034
$806$		0			0
$807$	37.7210	−	7.90310i	1.32784	−	0.278202i
$808$		0			0
$809$	−5.69575			−0.200252			−0.100126	−	0.994975i	$-0.531925\pi$
$809$	−5.69575			−0.200252			−0.100126	+	0.994975i	$0.531925\pi$
$810$		0			0
$811$	−3.58570	−	2.07020i	−0.125911	−	0.0726947i	0.435722	−	0.900081i	$-0.356493\pi$
$811$	−3.58570	−	2.07020i	−0.125911	−	0.0726947i	−0.561633	+	0.827387i	$0.689827\pi$
$812$		0			0
$813$	18.3584	−	3.84636i	0.643858	−	0.134898i
$814$		0			0
$815$	−23.8264	+	41.2685i	−0.834601	+	1.44557i
$816$		0			0
$817$	54.5220	−	31.4783i	1.90748	−	1.10129i
$818$		0			0
$819$	−22.8931	+	10.0333i	−0.799949	+	0.350592i
$820$		0			0
$821$	20.9010	−	12.0672i	0.729450	−	0.421148i	−0.0887707	−	0.996052i	$-0.528294\pi$
$821$	20.9010	−	12.0672i	0.729450	−	0.421148i	0.818221	+	0.574904i	$0.194961\pi$
$822$		0			0
$823$	20.4375	+	35.3987i	0.712406	+	1.23392i	0.963952	+	0.266077i	$0.0857277\pi$
$823$	20.4375	+	35.3987i	0.712406	+	1.23392i	−0.251546	+	0.967845i	$0.580939\pi$
$824$		0			0
$825$	38.9251	+	12.7730i	1.35520	+	0.444697i
$826$		0			0
$827$	−37.1522	+	21.4499i	−1.29191	+	0.745884i	−0.978993	−	0.203896i	$-0.934640\pi$
$827$	−37.1522	+	21.4499i	−1.29191	+	0.745884i	−0.312917	+	0.949780i	$0.601306\pi$
$828$		0			0
$829$	18.5255			0.643419			0.321709	−	0.946838i	$-0.395743\pi$
$829$	18.5255			0.643419			0.321709	+	0.946838i	$0.395743\pi$
$830$		0			0
$831$	1.94215	+	9.26974i	0.0673723	+	0.321564i
$832$		0			0
$833$	26.6269	+	15.3731i	0.922568	+	0.532645i
$834$		0			0
$835$	28.7273	+	16.5857i	0.994150	+	0.573973i
$836$		0			0
$837$	−3.87540	−	40.2516i	−0.133953	−	1.39130i
$838$		0			0
$839$	−28.7508	−	16.5993i	−0.992586	−	0.573070i	−0.0865399	−	0.996248i	$-0.527581\pi$
$839$	−28.7508	−	16.5993i	−0.992586	−	0.573070i	−0.906046	+	0.423178i	$0.860914\pi$
$840$		0			0
$841$	−2.90826	−	5.03725i	−0.100285	−	0.173698i
$842$		0			0
$843$	−19.9057	+	17.8185i	−0.685588	+	0.613701i
$844$		0			0
$845$	14.2644	−	24.7067i	0.490711	−	0.849936i
$846$		0			0
$847$			8.23766i			0.283049i
$848$		0			0
$849$	5.23435	+	24.9832i	0.179642	+	0.857422i
$850$		0			0
$851$	58.2933	+	33.6556i	1.99827	+	1.15370i
$852$		0			0
$853$	16.2252	+	28.1029i	0.555541	+	0.962225i	0.997861	+	0.0653678i	$0.0208221\pi$
$853$	16.2252	+	28.1029i	0.555541	+	0.962225i	−0.442320	+	0.896857i	$0.645845\pi$
$854$		0			0
$855$	49.7477	+	36.5884i	1.70134	+	1.25130i
$856$		0			0
$857$	−47.9928			−1.63940			−0.819701	−	0.572791i	$-0.805861\pi$
$857$	−47.9928			−1.63940			−0.819701	+	0.572791i	$0.805861\pi$
$858$		0			0
$859$	−3.44272	+	5.96297i	−0.117464	+	0.203454i	−0.918762	−	0.394812i	$-0.870810\pi$
$859$	−3.44272	+	5.96297i	−0.117464	+	0.203454i	0.801298	+	0.598265i	$0.204143\pi$
$860$		0			0
$861$	−2.08214	−	2.32604i	−0.0709592	−	0.0792711i
$862$		0			0
$863$			0.688741i			0.0234450i	0.999931	+	0.0117225i	$0.00373148\pi$
$863$			0.688741i			0.0234450i	−0.999931	+	0.0117225i	$0.996269\pi$
$864$		0			0
$865$	41.4501	−	23.9312i	1.40934	−	0.813686i
$866$		0			0
$867$	−7.14160	−	2.34346i	−0.242541	−	0.0795881i
$868$		0			0
$869$	−11.2616	+	6.50187i	−0.382023	+	0.220561i
$870$		0			0
$871$	−3.93381	−	18.0309i	−0.133292	−	0.610954i
$872$		0			0
$873$	−18.4275	+	25.0551i	−0.623677	+	0.847988i
$874$		0			0
$875$	−34.4424	−	19.8854i	−1.16437	−	0.672248i
$876$		0			0
$877$	2.02107	+	3.50059i	0.0682466	+	0.118207i	0.898130	−	0.439731i	$-0.144926\pi$
$877$	2.02107	+	3.50059i	0.0682466	+	0.118207i	−0.829883	+	0.557938i	$0.811593\pi$
$878$		0			0
$879$	−12.0982	+	2.53475i	−0.408063	+	0.0854951i
$880$		0			0
$881$	−25.1225	+	14.5045i	−0.846399	+	0.488668i	−0.859434	−	0.511247i	$-0.829184\pi$
$881$	−25.1225	+	14.5045i	−0.846399	+	0.488668i	0.0130355	+	0.999915i	$0.495851\pi$
$882$		0			0
$883$	−18.3892	−	10.6170i	−0.618847	−	0.357292i	0.157573	−	0.987507i	$-0.449633\pi$
$883$	−18.3892	−	10.6170i	−0.618847	−	0.357292i	−0.776420	+	0.630216i	$0.782966\pi$
$884$		0			0
$885$	−69.6430	+	14.5912i	−2.34102	+	0.490479i
$886$		0			0
$887$	29.7696	−	17.1875i	0.999566	−	0.577099i	0.0914458	−	0.995810i	$-0.470851\pi$
$887$	29.7696	−	17.1875i	0.999566	−	0.577099i	0.908120	+	0.418711i	$0.137518\pi$
$888$		0			0
$889$	−37.0383	+	21.3841i	−1.24222	+	0.717199i
$890$		0			0
$891$	7.94071	+	25.4437i	0.266024	+	0.852396i
$892$		0			0
$893$			48.6496i			1.62800i
$894$		0			0
$895$	58.3598			1.95075
$896$		0			0
$897$	−30.5177	−	10.0141i	−1.01896	−	0.334363i
$898$		0			0
$899$	18.7355	+	32.4508i	0.624863	+	1.08229i
$900$		0			0
$901$	42.3759	−	24.4658i	1.41175	−	0.815073i
$902$		0			0
$903$	−67.0279	−	21.9947i	−2.23055	−	0.731938i
$904$		0			0
$905$	2.99580	−	5.18888i	0.0995838	−	0.172484i
$906$		0			0
$907$	11.4099	−	19.7625i	0.378858	−	0.656202i	−0.612038	−	0.790828i	$-0.709650\pi$
$907$	11.4099	−	19.7625i	0.378858	−	0.656202i	0.990896	+	0.134627i	$0.0429835\pi$
$908$		0			0
$909$	4.66107	−	41.9929i	0.154598	−	1.39282i
$910$		0			0
$911$		−	33.8372i		−	1.12108i	−0.828129	−	0.560538i	$-0.810594\pi$
$911$		−	33.8372i		−	1.12108i	0.828129	−	0.560538i	$-0.189406\pi$
$912$		0			0
$913$			9.60929i			0.318021i
$914$		0			0
$915$	−19.0871	−	21.3230i	−0.631002	−	0.704916i
$916$		0			0
$917$	33.3257	−	57.7218i	1.10051	−	1.90614i
$918$		0			0
$919$	1.39111	−	0.803156i	0.0458884	−	0.0264937i	−0.476880	−	0.878968i	$-0.658232\pi$
$919$	1.39111	−	0.803156i	0.0458884	−	0.0264937i	0.522769	+	0.852475i	$0.324899\pi$
$920$		0			0
$921$	0.199558	−	0.178633i	0.00657566	−	0.00588616i
$922$		0			0
$923$	32.1752			1.05906
$924$		0			0
$925$	32.6808	+	56.6049i	1.07454	+	1.86116i
$926$		0			0
$927$	2.15983	−	19.4585i	0.0709382	−	0.639103i
$928$		0			0
$929$	33.5542			1.10088			0.550439	−	0.834875i	$-0.314460\pi$
$929$	33.5542			1.10088			0.550439	+	0.834875i	$0.314460\pi$
$930$		0			0
$931$	−19.0093	+	32.9250i	−0.623004	+	1.07907i
$932$		0			0
$933$	7.96783	+	38.0299i	0.260855	+	1.24504i
$934$		0			0
$935$		−	49.3013i		−	1.61232i
$936$		0			0
$937$		−	30.6902i		−	1.00261i	−0.865272	−	0.501303i	$-0.832854\pi$
$937$		−	30.6902i		−	1.00261i	0.865272	−	0.501303i	$-0.167146\pi$
$938$		0			0
$939$	11.1000	−	2.32561i	0.362235	−	0.0758935i
$940$		0			0
$941$	27.0344			0.881296			0.440648	−	0.897680i	$-0.354749\pi$
$941$	27.0344			0.881296			0.440648	+	0.897680i	$0.354749\pi$
$942$		0			0
$943$		−	4.01152i		−	0.130633i
$944$		0			0
$945$	−6.63154	−	68.8782i	−0.215724	−	2.24061i
$946$		0			0
$947$		−	19.3183i		−	0.627760i	−0.949463	−	0.313880i	$-0.898371\pi$
$947$		−	19.3183i		−	0.627760i	0.949463	−	0.313880i	$-0.101629\pi$
$948$		0			0
$949$	2.45932	+	1.41989i	0.0798330	+	0.0460916i
$950$		0			0
$951$	−18.5797	−	20.7560i	−0.602487	−	0.673061i
$952$		0			0
$953$			24.5725i			0.795983i	0.917389	+	0.397991i	$0.130293\pi$
$953$			24.5725i			0.795983i	−0.917389	+	0.397991i	$0.869707\pi$
$954$		0			0
$955$	−27.5936	−	47.7936i	−0.892909	−	1.54656i
$956$		0			0
$957$	−16.4730	−	18.4026i	−0.532496	−	0.594871i
$958$		0			0
$959$	6.98474	+	4.03264i	0.225549	+	0.130221i
$960$		0			0
$961$	14.7817	+	25.6027i	0.476830	+	0.825894i
$962$		0			0
$963$	1.48458	+	3.38738i	0.0478399	+	0.109157i
$964$		0			0
$965$	−27.5792			−0.887806
$966$		0			0
$967$	−22.5787	+	39.1075i	−0.726083	+	1.25761i	0.232444	+	0.972610i	$0.425328\pi$
$967$	−22.5787	+	39.1075i	−0.726083	+	1.25761i	−0.958527	+	0.285003i	$0.908006\pi$
$968$		0			0
$969$	14.2497	−	43.4254i	0.457766	−	1.39502i
$970$		0			0
$971$	−31.2612	−	18.0487i	−1.00322	−	0.579209i	−0.0940204	−	0.995570i	$-0.529972\pi$
$971$	−31.2612	−	18.0487i	−1.00322	−	0.579209i	−0.909199	+	0.416361i	$0.863305\pi$
$972$		0			0
$973$	−2.73883	+	4.74380i	−0.0878029	+	0.152079i
$974$		0			0
$975$	−20.8016	−	23.2382i	−0.666183	−	0.744218i
$976$		0			0
$977$	16.5345	−	9.54621i	0.528986	−	0.305410i	−0.211617	−	0.977353i	$-0.567873\pi$
$977$	16.5345	−	9.54621i	0.528986	−	0.305410i	0.740604	+	0.671942i	$0.234540\pi$
$978$		0			0
$979$	−5.45719	−	3.15071i	−0.174413	−	0.100697i
$980$		0			0
$981$	−10.6892	−	24.3897i	−0.341281	−	0.778703i
$982$		0			0
$983$	37.2412			1.18781			0.593906	−	0.804535i	$-0.297585\pi$
$983$	37.2412			1.18781			0.593906	+	0.804535i	$0.297585\pi$
$984$		0			0
$985$	5.60042	−	9.70021i	0.178444	−	0.309074i
$986$		0			0
$987$	40.6171	−	36.3582i	1.29286	−	1.15729i
$988$		0			0
$989$	−45.3246	−	78.5045i	−1.44124	−	2.49630i
$990$		0			0
$991$			25.4788i			0.809360i	0.914458	+	0.404680i	$0.132617\pi$
$991$			25.4788i			0.809360i	−0.914458	+	0.404680i	$0.867383\pi$
$992$		0			0
$993$	13.5703	−	41.3548i	0.430639	−	1.31235i
$994$		0			0
$995$	−0.485773	−	0.841384i	−0.0154000	−	0.0266737i
$996$		0			0
$997$	−38.6275			−1.22335			−0.611673	−	0.791111i	$-0.709503\pi$
$997$	−38.6275			−1.22335			−0.611673	+	0.791111i	$0.709503\pi$
$998$		0			0
$999$	−17.6354	+	38.6964i	−0.557960	+	1.22430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.9	✓	36
3.2	odd	2	inner	804.2.o.d.365.10	yes	36
67.38	odd	6	inner	804.2.o.d.641.10	yes	36
201.38	even	6	inner	804.2.o.d.641.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.9	✓	36	1.1	even	1	trivial
804.2.o.d.365.10	yes	36	3.2	odd	2	inner
804.2.o.d.641.9	yes	36	201.38	even	6	inner
804.2.o.d.641.10	yes	36	67.38	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.355178 - 1.69524i) q^{3} -3.60368 q^{5} +(3.20029 + 1.84769i) q^{7} +(-2.74770 + 1.20423i) q^{9} +O(q^{10})\)	\(q+(-0.355178 - 1.69524i) q^{3} -3.60368 q^{5} +(3.20029 + 1.84769i) q^{7} +(-2.74770 + 1.20423i) q^{9} +(-1.48078 + 2.56478i) q^{11} +(1.95258 - 1.12732i) q^{13} +(1.27995 + 6.10911i) q^{15} +(4.00058 - 2.30974i) q^{17} +(2.85606 + 4.94684i) q^{19} +(1.99560 - 6.08152i) q^{21} +(7.12280 - 4.11235i) q^{23} +7.98648 q^{25} +(3.01738 + 4.23030i) q^{27} +(-4.16985 - 2.40746i) q^{29} +(-6.73963 - 3.89113i) q^{31} +(4.87387 + 1.59932i) q^{33} +(-11.5328 - 6.65846i) q^{35} +(4.09202 + 7.08759i) q^{37} +(-2.60460 - 2.90969i) q^{39} +(0.243870 - 0.422396i) q^{41} -11.0216i q^{43} +(9.90181 - 4.33964i) q^{45} +(7.37585 + 4.25845i) q^{47} +(3.32788 + 5.76406i) q^{49} +(-5.33648 - 5.96159i) q^{51} +10.5924 q^{53} +(5.33624 - 9.24265i) q^{55} +(7.37169 - 6.59873i) q^{57} +11.3999i q^{59} +(-3.97066 + 2.29246i) q^{61} +(-11.0184 - 1.22301i) q^{63} +(-7.03646 + 4.06250i) q^{65} +(2.48761 - 7.79819i) q^{67} +(-9.50129 - 10.6143i) q^{69} +(12.3588 + 7.13533i) q^{71} +(0.629763 + 1.09078i) q^{73} +(-2.83662 - 13.5390i) q^{75} +(-9.47783 + 5.47203i) q^{77} +(3.80258 + 2.19542i) q^{79} +(6.09967 - 6.61770i) q^{81} +(2.80997 - 1.62234i) q^{83} +(-14.4168 + 8.32354i) q^{85} +(-2.60019 + 7.92398i) q^{87} +2.12774i q^{89} +8.33174 q^{91} +(-4.20263 + 12.8074i) q^{93} +(-10.2923 - 17.8268i) q^{95} +(8.97837 - 5.18366i) q^{97} +(0.980148 - 8.83044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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