LMFDB - Embedded newform 945.2.t.c.341.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(341,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("945.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.t (of order $6$, degree $2$, not 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.8
Character	$\chi$	$=$	945.341
Dual form			945.2.t.c.521.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.103991i q^{2} +1.98919 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.107447 + 2.64357i) q^{7} -0.414839i q^{8} +O(q^{10})$	\(q-0.103991i q^{2} +1.98919 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.107447 + 2.64357i) q^{7} -0.414839i q^{8} +(0.0900587 - 0.0519954i) q^{10} +(-2.53457 - 1.46334i) q^{11} +(-2.40454 - 1.38826i) q^{13} +(0.274907 + 0.0111734i) q^{14} +3.93523 q^{16} +(3.62041 + 6.27073i) q^{17} +(6.40301 + 3.69678i) q^{19} +(0.994593 + 1.72269i) q^{20} +(-0.152173 + 0.263572i) q^{22} +(0.159465 - 0.0920672i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.144366 + 0.250050i) q^{26} +(-0.213731 + 5.25855i) q^{28} +(1.84819 - 1.06705i) q^{29} -2.83342i q^{31} -1.23891i q^{32} +(0.652098 - 0.376489i) q^{34} +(-2.34312 + 1.22873i) q^{35} +(-1.26588 + 2.19256i) q^{37} +(0.384431 - 0.665854i) q^{38} +(0.359261 - 0.207419i) q^{40} +(-3.74637 + 6.48890i) q^{41} +(0.223536 + 0.387176i) q^{43} +(-5.04173 - 2.91085i) q^{44} +(-0.00957414 - 0.0165829i) q^{46} -0.588831 q^{47} +(-6.97691 - 0.568084i) q^{49} +(0.0900587 + 0.0519954i) q^{50} +(-4.78308 - 2.76151i) q^{52} +(-6.46888 + 3.73481i) q^{53} -2.92667i q^{55} +(1.09665 + 0.0445730i) q^{56} +(-0.110964 - 0.192195i) q^{58} +8.14263 q^{59} -12.6412i q^{61} -0.294649 q^{62} +7.74163 q^{64} -2.77652i q^{65} +3.10342 q^{67} +(7.20166 + 12.4736i) q^{68} +(0.127777 + 0.243663i) q^{70} +5.62459i q^{71} +(11.3988 - 6.58111i) q^{73} +(0.228006 + 0.131640i) q^{74} +(12.7368 + 7.35359i) q^{76} +(4.14076 - 6.54308i) q^{77} -9.11435 q^{79} +(1.96762 + 3.40801i) q^{80} +(0.674785 + 0.389587i) q^{82} +(4.90339 + 8.49292i) q^{83} +(-3.62041 + 6.27073i) q^{85} +(0.0402627 - 0.0232457i) q^{86} +(-0.607048 + 1.05144i) q^{88} +(7.98030 - 13.8223i) q^{89} +(3.92832 - 6.20740i) q^{91} +(0.317206 - 0.183139i) q^{92} +0.0612330i q^{94} +7.39356i q^{95} +(-1.69927 + 0.981074i) q^{97} +(-0.0590755 + 0.725534i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 16 q^{5} + q^{7}+O(q^{10}) $ 32 * q - 32 * q^4 + 16 * q^5 + q^7	$ 32 q - 32 q^{4} + 16 q^{5} + q^{7} - 3 q^{11} + 6 q^{13} + 15 q^{14} + 32 q^{16} + 3 q^{17} - 16 q^{20} - 21 q^{22} + 9 q^{23} - 16 q^{25} - 12 q^{26} - 31 q^{28} - 18 q^{29} - 30 q^{34} - q^{35} - q^{37} + 30 q^{38} - 6 q^{41} - 19 q^{43} - 21 q^{44} + 6 q^{46} + 30 q^{47} + 5 q^{49} + 21 q^{52} + 24 q^{53} - 30 q^{56} - 30 q^{59} + 76 q^{64} - 50 q^{67} + 3 q^{68} + 9 q^{70} + 12 q^{73} - 60 q^{74} + 54 q^{76} + 27 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} + 42 q^{83} - 3 q^{85} - 51 q^{86} + 42 q^{88} - 30 q^{89} - 57 q^{91} - 6 q^{92} - 42 q^{97} - 6 q^{98}+O(q^{100}) $ 32 * q - 32 * q^4 + 16 * q^5 + q^7 - 3 * q^11 + 6 * q^13 + 15 * q^14 + 32 * q^16 + 3 * q^17 - 16 * q^20 - 21 * q^22 + 9 * q^23 - 16 * q^25 - 12 * q^26 - 31 * q^28 - 18 * q^29 - 30 * q^34 - q^35 - q^37 + 30 * q^38 - 6 * q^41 - 19 * q^43 - 21 * q^44 + 6 * q^46 + 30 * q^47 + 5 * q^49 + 21 * q^52 + 24 * q^53 - 30 * q^56 - 30 * q^59 + 76 * q^64 - 50 * q^67 + 3 * q^68 + 9 * q^70 + 12 * q^73 - 60 * q^74 + 54 * q^76 + 27 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 + 42 * q^83 - 3 * q^85 - 51 * q^86 + 42 * q^88 - 30 * q^89 - 57 * q^91 - 6 * q^92 - 42 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		−	0.103991i		−	0.0735326i	−0.999324	−	0.0367663i	$-0.988294\pi$
$2$		−	0.103991i		−	0.0735326i	0.999324	−	0.0367663i	$-0.0117057\pi$
$3$		0			0
$3$		0			0
$4$	1.98919			0.994593
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.107447	+	2.64357i	−0.0406110	+	0.999175i
$7$	−0.107447	+	2.64357i	−0.0406110	+	0.999175i
$8$		−	0.414839i		−	0.146668i
$9$		0			0
$10$	0.0900587	−	0.0519954i	0.0284790	−	0.0164424i
$11$	−2.53457	−	1.46334i	−0.764202	−	0.441212i	0.0666004	−	0.997780i	$-0.478785\pi$
$11$	−2.53457	−	1.46334i	−0.764202	−	0.441212i	−0.830802	+	0.556567i	$0.812118\pi$
$12$		0			0
$13$	−2.40454	−	1.38826i	−0.666899	−	0.385034i	0.128001	−	0.991774i	$-0.459144\pi$
$13$	−2.40454	−	1.38826i	−0.666899	−	0.385034i	−0.794901	+	0.606740i	$0.792477\pi$
$14$	0.274907	+	0.0111734i	0.0734719	+	0.00298623i
$15$		0			0
$16$	3.93523			0.983808
$17$	3.62041	+	6.27073i	0.878078	+	1.52088i	0.853448	+	0.521179i	$0.174507\pi$
$17$	3.62041	+	6.27073i	0.878078	+	1.52088i	0.0246300	+	0.999697i	$0.492159\pi$
$18$		0			0
$19$	6.40301	+	3.69678i	1.46895	+	0.848100i	0.999394	−	0.0348020i	$-0.0110800\pi$
$19$	6.40301	+	3.69678i	1.46895	+	0.848100i	0.469558	+	0.882902i	$0.344413\pi$
$20$	0.994593	+	1.72269i	0.222398	+	0.385204i
$21$		0			0
$22$	−0.152173	+	0.263572i	−0.0324435	+	0.0561938i
$23$	0.159465	−	0.0920672i	0.0332508	−	0.0191973i	−0.483282	−	0.875464i	$-0.660556\pi$
$23$	0.159465	−	0.0920672i	0.0332508	−	0.0191973i	0.516533	+	0.856267i	$0.327222\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.144366	+	0.250050i	−0.0283126	+	0.0490388i
$27$		0			0
$28$	−0.213731	+	5.25855i	−0.0403914	+	0.993772i
$29$	1.84819	−	1.06705i	0.343201	−	0.198147i	−0.318486	−	0.947928i	$-0.603174\pi$
$29$	1.84819	−	1.06705i	0.343201	−	0.198147i	0.661686	+	0.749781i	$0.269841\pi$
$30$		0			0
$31$		−	2.83342i		−	0.508897i	−0.967086	−	0.254448i	$-0.918106\pi$
$31$		−	2.83342i		−	0.508897i	0.967086	−	0.254448i	$-0.0818939\pi$
$32$		−	1.23891i		−	0.219010i
$33$		0			0
$34$	0.652098	−	0.376489i	0.111834	−	0.0645673i
$35$	−2.34312	+	1.22873i	−0.396060	+	0.207694i
$36$		0			0
$37$	−1.26588	+	2.19256i	−0.208109	+	0.360455i	−0.951119	−	0.308825i	$-0.900064\pi$
$37$	−1.26588	+	2.19256i	−0.208109	+	0.360455i	0.743010	+	0.669281i	$0.233398\pi$
$38$	0.384431	−	0.665854i	0.0623630	−	0.108016i
$39$		0			0
$40$	0.359261	−	0.207419i	0.0568041	−	0.0327959i
$41$	−3.74637	+	6.48890i	−0.585084	+	1.01340i	0.409781	+	0.912184i	$0.365605\pi$
$41$	−3.74637	+	6.48890i	−0.585084	+	1.01340i	−0.994865	+	0.101211i	$0.967728\pi$
$42$		0			0
$43$	0.223536	+	0.387176i	0.0340889	+	0.0590438i	0.882567	−	0.470188i	$-0.155814\pi$
$43$	0.223536	+	0.387176i	0.0340889	+	0.0590438i	−0.848478	+	0.529231i	$0.822480\pi$
$44$	−5.04173	−	2.91085i	−0.760070	−	0.438827i
$45$		0			0
$46$	−0.00957414	−	0.0165829i	−0.00141163	−	0.00244501i
$47$	−0.588831			−0.0858899			−0.0429449	−	0.999077i	$-0.513674\pi$
$47$	−0.588831			−0.0858899			−0.0429449	+	0.999077i	$0.513674\pi$
$48$		0			0
$49$	−6.97691	−	0.568084i	−0.996701	−	0.0811549i
$50$	0.0900587	+	0.0519954i	0.0127362	+	0.00735326i
$51$		0			0
$52$	−4.78308	−	2.76151i	−0.663293	−	0.382953i
$53$	−6.46888	+	3.73481i	−0.888570	+	0.513016i	−0.873474	−	0.486870i	$-0.838138\pi$
$53$	−6.46888	+	3.73481i	−0.888570	+	0.513016i	−0.0150952	+	0.999886i	$0.504805\pi$
$54$		0			0
$55$		−	2.92667i		−	0.394632i
$56$	1.09665	+	0.0445730i	0.146547	+	0.00595631i
$57$		0			0
$58$	−0.110964	−	0.192195i	−0.0145703	−	0.0252364i
$59$	8.14263			1.06008			0.530040	−	0.847973i	$-0.322177\pi$
$59$	8.14263			1.06008			0.530040	+	0.847973i	$0.322177\pi$
$60$		0			0
$61$		−	12.6412i		−	1.61854i	−0.587434	−	0.809272i	$-0.699862\pi$
$61$		−	12.6412i		−	1.61854i	0.587434	−	0.809272i	$-0.300138\pi$
$62$	−0.294649			−0.0374205
$63$		0			0
$64$	7.74163			0.967704
$65$		−	2.77652i		−	0.344385i
$66$		0			0
$67$	3.10342			0.379143			0.189572	−	0.981867i	$-0.439290\pi$
$67$	3.10342			0.379143			0.189572	+	0.981867i	$0.439290\pi$
$68$	7.20166	+	12.4736i	0.873330	+	1.51265i
$69$		0			0
$70$	0.127777	+	0.243663i	0.0152723	+	0.0291233i
$71$			5.62459i			0.667516i	0.942659	+	0.333758i	$0.108317\pi$
$71$			5.62459i			0.667516i	−0.942659	+	0.333758i	$0.891683\pi$
$72$		0			0
$73$	11.3988	−	6.58111i	1.33413	−	0.770261i	0.348201	−	0.937420i	$-0.386793\pi$
$73$	11.3988	−	6.58111i	1.33413	−	0.770261i	0.985930	+	0.167159i	$0.0534594\pi$
$74$	0.228006	+	0.131640i	0.0265052	+	0.0153028i
$75$		0			0
$76$	12.7368	+	7.35359i	1.46101	+	0.843514i
$77$	4.14076	−	6.54308i	0.471883	−	0.745654i
$78$		0			0
$79$	−9.11435			−1.02544			−0.512722	−	0.858555i	$-0.671363\pi$
$79$	−9.11435			−1.02544			−0.512722	+	0.858555i	$0.671363\pi$
$80$	1.96762	+	3.40801i	0.219986	+	0.381027i
$81$		0			0
$82$	0.674785	+	0.389587i	0.0745176	+	0.0430227i
$83$	4.90339	+	8.49292i	0.538217	+	0.932219i	0.999000	+	0.0447065i	$0.0142353\pi$
$83$	4.90339	+	8.49292i	0.538217	+	0.932219i	−0.460783	+	0.887513i	$0.652431\pi$
$84$		0			0
$85$	−3.62041	+	6.27073i	−0.392688	+	0.680156i
$86$	0.0402627	−	0.0232457i	0.00434164	−	0.00250665i
$87$		0			0
$88$	−0.607048	+	1.05144i	−0.0647115	+	0.112084i
$89$	7.98030	−	13.8223i	0.845910	−	1.46516i	−0.0389185	−	0.999242i	$-0.512391\pi$
$89$	7.98030	−	13.8223i	0.845910	−	1.46516i	0.884829	−	0.465917i	$-0.154275\pi$
$90$		0			0
$91$	3.92832	−	6.20740i	0.411800	−	0.650712i
$92$	0.317206	−	0.183139i	0.0330710	−	0.0190935i
$93$		0			0
$94$			0.0612330i			0.00631571i
$95$			7.39356i			0.758564i
$96$		0			0
$97$	−1.69927	+	0.981074i	−0.172535	+	0.0996130i	−0.583781	−	0.811912i	$-0.698427\pi$
$97$	−1.69927	+	0.981074i	−0.172535	+	0.0996130i	0.411246	+	0.911525i	$0.365094\pi$
$98$	−0.0590755	+	0.725534i	−0.00596753	+	0.0732900i
$99$		0			0
$100$	−0.994593	+	1.72269i	−0.0994593	+	0.172269i
$101$	2.85272	−	4.94105i	0.283856	−	0.491653i	−0.688475	−	0.725260i	$-0.741720\pi$
$101$	2.85272	−	4.94105i	0.283856	−	0.491653i	0.972331	+	0.233607i	$0.0750529\pi$
$102$		0			0
$103$	−10.4398	+	6.02741i	−1.02866	+	0.593899i	−0.916601	−	0.399803i	$-0.869079\pi$
$103$	−10.4398	+	6.02741i	−1.02866	+	0.593899i	−0.112061	+	0.993701i	$0.535745\pi$
$104$	−0.575904	+	0.997496i	−0.0564721	+	0.0978125i
$105$		0			0
$106$	0.388386	+	0.672704i	0.0377234	+	0.0653388i
$107$	−2.07619	−	1.19869i	−0.200713	−	0.115882i	0.396275	−	0.918132i	$-0.370303\pi$
$107$	−2.07619	−	1.19869i	−0.200713	−	0.115882i	−0.596988	+	0.802250i	$0.703636\pi$
$108$		0			0
$109$	−5.16660	−	8.94882i	−0.494871	−	0.857141i	0.505112	−	0.863054i	$-0.331451\pi$
$109$	−5.16660	−	8.94882i	−0.494871	−	0.857141i	−0.999983	+	0.00591270i	$0.998118\pi$
$110$	−0.304347			−0.0290183
$111$		0			0
$112$	−0.422827	+	10.4031i	−0.0399534	+	0.982997i
$113$	−7.32912	−	4.23147i	−0.689466	−	0.398063i	0.113946	−	0.993487i	$-0.463651\pi$
$113$	−7.32912	−	4.23147i	−0.689466	−	0.398063i	−0.803412	+	0.595424i	$0.796984\pi$
$114$		0			0
$115$	0.159465	+	0.0920672i	0.0148702	+	0.00858531i
$116$	3.67640	−	2.12257i	0.341345	−	0.197076i
$117$		0			0
$118$		−	0.846759i		−	0.0779505i
$119$	−16.9661	+	8.89703i	−1.55528	+	0.815589i
$120$		0			0
$121$	−1.21730	−	2.10842i	−0.110664	−	0.191675i
$122$	−1.31457			−0.119016
$123$		0			0
$124$		−	5.63620i		−	0.506145i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.15631			0.546284			0.273142	−	0.961974i	$-0.411937\pi$
$127$	6.15631			0.546284			0.273142	+	0.961974i	$0.411937\pi$
$128$		−	3.28287i		−	0.290167i
$129$		0			0
$130$	−0.288733			−0.0253235
$131$	−10.4097	−	18.0301i	−0.909498	−	1.57530i	−0.814764	−	0.579793i	$-0.803133\pi$
$131$	−10.4097	−	18.0301i	−0.909498	−	1.57530i	−0.0947339	−	0.995503i	$-0.530200\pi$
$132$		0			0
$133$	−10.4607	+	16.5296i	−0.907056	+	1.43330i
$134$		−	0.322727i		−	0.0278794i
$135$		0			0
$136$	2.60134	−	1.50188i	0.223063	−	0.128786i
$137$	−4.83774	−	2.79307i	−0.413316	−	0.238628i	0.278897	−	0.960321i	$-0.410031\pi$
$137$	−4.83774	−	2.79307i	−0.413316	−	0.238628i	−0.692214	+	0.721693i	$0.743364\pi$
$138$		0			0
$139$	12.4855	+	7.20849i	1.05900	+	0.611416i	0.925157	−	0.379586i	$-0.123933\pi$
$139$	12.4855	+	7.20849i	1.05900	+	0.611416i	0.133847	+	0.991002i	$0.457267\pi$
$140$	−4.66090	+	2.44418i	−0.393918	+	0.206571i
$141$		0			0
$142$	0.584906			0.0490842
$143$	4.06298	+	7.03730i	0.339764	+	0.588488i
$144$		0			0
$145$	1.84819	+	1.06705i	0.153484	+	0.0886140i
$146$	−0.684375	−	1.18537i	−0.0566393	−	0.0981021i
$147$		0			0
$148$	−2.51807	+	4.36142i	−0.206984	+	0.358506i
$149$	1.34036	−	0.773860i	0.109807	−	0.0633971i	−0.444091	−	0.895982i	$-0.646473\pi$
$149$	1.34036	−	0.773860i	0.109807	−	0.0633971i	0.553898	+	0.832585i	$0.313140\pi$
$150$		0			0
$151$	7.65406	−	13.2572i	0.622878	−	1.07886i	−0.366069	−	0.930588i	$-0.619297\pi$
$151$	7.65406	−	13.2572i	0.622878	−	1.07886i	0.988947	−	0.148269i	$-0.0473701\pi$
$152$	1.53357	−	2.65622i	0.124389	−	0.215448i
$153$		0			0
$154$	−0.680420	−	0.430601i	−0.0548298	−	0.0346988i
$155$	2.45381	−	1.41671i	0.197095	−	0.113793i
$156$		0			0
$157$			4.42545i			0.353189i	0.984284	+	0.176595i	$0.0565082\pi$
$157$			4.42545i			0.353189i	−0.984284	+	0.176595i	$0.943492\pi$
$158$			0.947808i			0.0754036i
$159$		0			0
$160$	1.07292	−	0.619453i	0.0848220	−	0.0489720i
$161$	0.226252	+	0.431449i	0.0178312	+	0.0340029i
$162$		0			0
$163$	−2.67530	+	4.63375i	−0.209546	+	0.362944i	−0.951571	−	0.307428i	$-0.900532\pi$
$163$	−2.67530	+	4.63375i	−0.209546	+	0.362944i	0.742026	+	0.670371i	$0.233865\pi$
$164$	−7.45222	+	12.9076i	−0.581920	+	1.00792i
$165$		0			0
$166$	0.883186	−	0.509907i	0.0685485	−	0.0395765i
$167$	10.2622	−	17.7747i	0.794116	−	1.37545i	−0.129284	−	0.991608i	$-0.541268\pi$
$167$	10.2622	−	17.7747i	0.794116	−	1.37545i	0.923399	−	0.383841i	$-0.125399\pi$
$168$		0			0
$169$	−2.64546	−	4.58207i	−0.203497	−	0.352467i
$170$	0.652098	+	0.376489i	0.0500136	+	0.0288754i
$171$		0			0
$172$	0.444655	+	0.770165i	0.0339046	+	0.0587245i
$173$	21.3176			1.62074			0.810372	−	0.585915i	$-0.199265\pi$
$173$	21.3176			1.62074			0.810372	+	0.585915i	$0.199265\pi$
$174$		0			0
$175$	−2.23567	−	1.41484i	−0.169001	−	0.106952i
$176$	−9.97413	−	5.75857i	−0.751828	−	0.434068i
$177$		0			0
$178$	−1.43739	−	0.829878i	−0.107737	−	0.0622020i
$179$	2.03822	−	1.17677i	0.152344	−	0.0879556i	−0.421890	−	0.906647i	$-0.638633\pi$
$179$	2.03822	−	1.17677i	0.152344	−	0.0879556i	0.574234	+	0.818691i	$0.305300\pi$
$180$		0			0
$181$			1.64325i			0.122142i	0.998133	+	0.0610711i	$0.0194516\pi$
$181$			1.64325i			0.122142i	−0.998133	+	0.0610711i	$0.980548\pi$
$182$	−0.645513	−	0.408509i	−0.0478486	−	0.0302807i
$183$		0			0
$184$	−0.0381930	−	0.0661522i	−0.00281563	−	0.00487681i
$185$	−2.53176			−0.186138
$186$		0			0
$187$		−	21.1915i		−	1.54967i
$188$	−1.17130			−0.0854255
$189$		0			0
$190$	0.768862			0.0557791
$191$		−	13.5068i		−	0.977319i	−0.872475	−	0.488659i	$-0.837486\pi$
$191$		−	13.5068i		−	0.977319i	0.872475	−	0.488659i	$-0.162514\pi$
$192$		0			0
$193$	−15.7119			−1.13097			−0.565485	−	0.824759i	$-0.691311\pi$
$193$	−15.7119			−1.13097			−0.565485	+	0.824759i	$0.691311\pi$
$194$	0.102023	+	0.176708i	0.00732480	+	0.0126869i
$195$		0			0
$196$	−13.8784	−	1.13003i	−0.991312	−	0.0807161i
$197$		−	24.6295i		−	1.75478i	−0.479781	−	0.877388i	$-0.659284\pi$
$197$		−	24.6295i		−	1.75478i	0.479781	−	0.877388i	$-0.340716\pi$
$198$		0			0
$199$	−14.4687	+	8.35349i	−1.02566	+	0.592163i	−0.915737	−	0.401778i	$-0.868392\pi$
$199$	−14.4687	+	8.35349i	−1.02566	+	0.592163i	−0.109919	+	0.993941i	$0.535059\pi$
$200$	0.359261	+	0.207419i	0.0254036	+	0.0146668i
$201$		0			0
$202$	−0.513824	−	0.296656i	−0.0361525	−	0.0208727i
$203$	2.62225	+	5.00047i	0.184046	+	0.350964i
$204$		0			0
$205$	−7.49273			−0.523315
$206$	0.626795	+	1.08564i	0.0436709	+	0.0756402i
$207$		0			0
$208$	−9.46242	−	5.46313i	−0.656101	−	0.378800i
$209$	−10.8193	−	18.7395i	−0.748384	−	1.29624i
$210$		0			0
$211$	−3.73218	+	6.46432i	−0.256934	+	0.445022i	−0.965419	−	0.260703i	$-0.916046\pi$
$211$	−3.73218	+	6.46432i	−0.256934	+	0.445022i	0.708485	+	0.705726i	$0.249379\pi$
$212$	−12.8678	+	7.42923i	−0.883765	+	0.510242i
$213$		0			0
$214$	−0.124653	+	0.215905i	−0.00852109	+	0.0147590i
$215$	−0.223536	+	0.387176i	−0.0152450	+	0.0264052i
$216$		0			0
$217$	7.49034	+	0.304441i	0.508477	+	0.0206668i
$218$	−0.930594	+	0.537279i	−0.0630278	+	0.0363891i
$219$		0			0
$220$		−	5.82169i		−	0.392498i
$221$		−	20.1043i		−	1.35236i
$222$		0			0
$223$	−9.35222	+	5.39951i	−0.626271	+	0.361578i	−0.779306	−	0.626643i	$-0.784428\pi$
$223$	−9.35222	+	5.39951i	−0.626271	+	0.361578i	0.153036	+	0.988221i	$0.451095\pi$
$224$	3.27513	+	0.133116i	0.218829	+	0.00889419i
$225$		0			0
$226$	−0.440034	+	0.762161i	−0.0292706	+	0.0506982i
$227$	−6.02014	+	10.4272i	−0.399571	+	0.692077i	−0.993673	−	0.112313i	$-0.964174\pi$
$227$	−6.02014	+	10.4272i	−0.399571	+	0.692077i	0.594102	+	0.804390i	$0.297507\pi$
$228$		0			0
$229$	−10.4214	+	6.01682i	−0.688668	+	0.397603i	−0.803113	−	0.595827i	$-0.796824\pi$
$229$	−10.4214	+	6.01682i	−0.688668	+	0.397603i	0.114445	+	0.993430i	$0.463491\pi$
$230$	0.00957414	−	0.0165829i	0.000631300	−	0.00109344i
$231$		0			0
$232$	−0.442655	−	0.766701i	−0.0290617	−	0.0503364i
$233$	−20.9187	−	12.0774i	−1.37043	−	0.791218i	−0.379448	−	0.925213i	$-0.623886\pi$
$233$	−20.9187	−	12.0774i	−1.37043	−	0.791218i	−0.990982	+	0.133995i	$0.957220\pi$
$234$		0			0
$235$	−0.294416	−	0.509943i	−0.0192056	−	0.0332650i
$236$	16.1972			1.05435
$237$		0			0
$238$	0.925209	+	1.76432i	0.0599724	+	0.114364i
$239$	13.7317	+	7.92802i	0.888232	+	0.512821i	0.873364	−	0.487069i	$-0.161934\pi$
$239$	13.7317	+	7.92802i	0.888232	+	0.512821i	0.0148680	+	0.999889i	$0.495267\pi$
$240$		0			0
$241$	4.43827	+	2.56244i	0.285894	+	0.165061i	0.636089	−	0.771616i	$-0.280551\pi$
$241$	4.43827	+	2.56244i	0.285894	+	0.165061i	−0.350194	+	0.936677i	$0.613885\pi$
$242$	−0.219257	+	0.126588i	−0.0140943	+	0.00813737i
$243$		0			0
$244$		−	25.1458i		−	1.60979i
$245$	−2.99648	−	6.32622i	−0.191438	−	0.404168i
$246$		0			0
$247$	−10.2642	−	17.7781i	−0.653095	−	1.13119i
$248$	−1.17541			−0.0746387
$249$		0			0
$250$			0.103991i			0.00657695i
$251$	21.3411			1.34704			0.673519	−	0.739170i	$-0.264782\pi$
$251$	21.3411			1.34704			0.673519	+	0.739170i	$0.264782\pi$
$252$		0			0
$253$	−0.538901			−0.0338804
$254$		−	0.640200i		−	0.0401697i
$255$		0			0
$256$	15.1419			0.946367
$257$	−5.32111	−	9.21643i	−0.331922	−	0.574905i	0.650967	−	0.759106i	$-0.274364\pi$
$257$	−5.32111	−	9.21643i	−0.331922	−	0.574905i	−0.982889	+	0.184201i	$0.941030\pi$
$258$		0			0
$259$	−5.66018	−	3.58202i	−0.351706	−	0.222576i
$260$		−	5.52302i		−	0.342523i
$261$		0			0
$262$	−1.87496	+	1.08251i	−0.115836	+	0.0668777i
$263$	9.21740	+	5.32167i	0.568369	+	0.328148i	0.756498	−	0.653996i	$-0.226909\pi$
$263$	9.21740	+	5.32167i	0.568369	+	0.328148i	−0.188128	+	0.982144i	$0.560242\pi$
$264$		0			0
$265$	−6.46888	−	3.73481i	−0.397380	−	0.229428i
$266$	1.71893	+	1.08781i	0.105394	+	0.0666982i
$267$		0			0
$268$	6.17328			0.377093
$269$	−3.88366	−	6.72670i	−0.236791	−	0.410134i	0.723001	−	0.690847i	$-0.242762\pi$
$269$	−3.88366	−	6.72670i	−0.236791	−	0.410134i	−0.959792	+	0.280713i	$0.909429\pi$
$270$		0			0
$271$	−6.45273	−	3.72548i	−0.391975	−	0.226307i	0.291040	−	0.956711i	$-0.405999\pi$
$271$	−6.45273	−	3.72548i	−0.391975	−	0.226307i	−0.683016	+	0.730404i	$0.739332\pi$
$272$	14.2471	+	24.6768i	0.863860	+	1.49625i
$273$		0			0
$274$	−0.290454	+	0.503081i	−0.0175469	+	0.0303922i
$275$	2.53457	−	1.46334i	0.152840	−	0.0882424i
$276$		0			0
$277$	8.48617	−	14.6985i	0.509884	−	0.883146i	−0.490050	−	0.871694i	$-0.663022\pi$
$277$	8.48617	−	14.6985i	0.509884	−	0.883146i	0.999934	−	0.0114513i	$-0.00364514\pi$
$278$	0.749617	−	1.29837i	0.0449590	−	0.0778713i
$279$		0			0
$280$	0.509726	+	0.972017i	0.0304619	+	0.0580891i
$281$	−21.1443	+	12.2077i	−1.26136	+	0.728249i	−0.973338	−	0.229374i	$-0.926332\pi$
$281$	−21.1443	+	12.2077i	−1.26136	+	0.728249i	−0.288026	+	0.957623i	$0.592999\pi$
$282$		0			0
$283$			27.5665i			1.63866i	0.573323	+	0.819329i	$0.305654\pi$
$283$			27.5665i			1.63866i	−0.573323	+	0.819329i	$0.694346\pi$
$284$			11.1884i			0.663907i
$285$		0			0
$286$	0.731814	−	0.422513i	0.0432731	−	0.0249837i
$287$	−16.7513	−	10.6010i	−0.988798	−	0.625756i
$288$		0			0
$289$	−17.7147	+	30.6828i	−1.04204	+	1.80487i
$290$	0.110964	−	0.192195i	0.00651602	−	0.0112861i
$291$		0			0
$292$	22.6744	−	13.0911i	1.32692	−	0.766096i
$293$	−9.60393	+	16.6345i	−0.561068	+	0.971798i	0.436336	+	0.899784i	$0.356276\pi$
$293$	−9.60393	+	16.6345i	−0.561068	+	0.971798i	−0.997404	+	0.0720141i	$0.977057\pi$
$294$		0			0
$295$	4.07132	+	7.05173i	0.237041	+	0.410567i
$296$	0.909560	+	0.525135i	0.0528671	+	0.0305228i
$297$		0			0
$298$	−0.0804743	−	0.139386i	−0.00466175	−	0.00807439i
$299$	−0.511253			−0.0295665
$300$		0			0
$301$	−1.04754	+	0.549332i	−0.0603794	+	0.0316630i
$302$	−1.37863	−	0.795951i	−0.0793311	−	0.0458018i
$303$		0			0
$304$	25.1973	+	14.5477i	1.44517	+	0.834367i
$305$	10.9476	−	6.32062i	0.626860	−	0.361918i
$306$		0			0
$307$		−	27.5679i		−	1.57339i	−0.617345	−	0.786693i	$-0.711792\pi$
$307$		−	27.5679i		−	1.57339i	0.617345	−	0.786693i	$-0.288208\pi$
$308$	8.23674	−	13.0154i	0.469332	−	0.741622i
$309$		0			0
$310$	−0.147325	−	0.255174i	−0.00836748	−	0.0144929i
$311$	−13.5987			−0.771112			−0.385556	−	0.922684i	$-0.625990\pi$
$311$	−13.5987			−0.771112			−0.385556	+	0.922684i	$0.625990\pi$
$312$		0			0
$313$		−	13.2687i		−	0.749993i	−0.927026	−	0.374997i	$-0.877644\pi$
$313$		−	13.2687i		−	0.749993i	0.927026	−	0.374997i	$-0.122356\pi$
$314$	0.460206			0.0259709
$315$		0			0
$316$	−18.1301			−1.01990
$317$		−	25.2418i		−	1.41772i	−0.705349	−	0.708861i	$-0.749210\pi$
$317$		−	25.2418i		−	1.41772i	0.705349	−	0.708861i	$-0.250790\pi$
$318$		0			0
$319$	−6.24583			−0.349699
$320$	3.87082	+	6.70445i	0.216385	+	0.374790i
$321$		0			0
$322$	0.0448667	−	0.0235281i	0.00250032	−	0.00131117i
$323$			53.5354i			2.97879i
$324$		0			0
$325$	2.40454	−	1.38826i	0.133380	−	0.0770069i
$326$	0.481868	+	0.278207i	0.0266882	+	0.0154084i
$327$		0			0
$328$	2.69184	+	1.55414i	0.148632	+	0.0858129i
$329$	0.0632679	−	1.55662i	0.00348807	−	0.0858190i
$330$		0			0
$331$	−8.35946			−0.459478			−0.229739	−	0.973252i	$-0.573787\pi$
$331$	−8.35946			−0.459478			−0.229739	+	0.973252i	$0.573787\pi$
$332$	9.75376	+	16.8940i	0.535307	+	0.927179i
$333$		0			0
$334$	−1.84841	−	1.06718i	−0.101140	−	0.0583934i
$335$	1.55171	+	2.68764i	0.0847790	+	0.146842i
$336$		0			0
$337$	−6.46876	+	11.2042i	−0.352376	+	0.610333i	−0.986665	−	0.162763i	$-0.947959\pi$
$337$	−6.46876	+	11.2042i	−0.352376	+	0.610333i	0.634289	+	0.773096i	$0.281293\pi$
$338$	−0.476493	+	0.275103i	−0.0259178	+	0.0149637i
$339$		0			0
$340$	−7.20166	+	12.4736i	−0.390565	+	0.676478i
$341$	−4.14624	+	7.18150i	−0.224532	+	0.388900i
$342$		0			0
$343$	2.25141	−	18.3829i	0.121565	−	0.992583i
$344$	0.160615	−	0.0927314i	0.00865981	−	0.00499974i
$345$		0			0
$346$		−	2.21683i		−	0.119178i
$347$			23.8842i			1.28217i	0.767469	+	0.641086i	$0.221516\pi$
$347$			23.8842i			1.28217i	−0.767469	+	0.641086i	$0.778484\pi$
$348$		0			0
$349$	19.0470	−	10.9968i	1.01956	−	0.588644i	0.105585	−	0.994410i	$-0.466329\pi$
$349$	19.0470	−	10.9968i	1.01956	−	0.588644i	0.913977	+	0.405766i	$0.132995\pi$
$350$	−0.147130	+	0.232490i	−0.00786442	+	0.0124271i
$351$		0			0
$352$	−1.81293	+	3.14009i	−0.0966297	+	0.167368i
$353$	−4.39642	+	7.61483i	−0.233998	+	0.405296i	−0.958981	−	0.283470i	$-0.908514\pi$
$353$	−4.39642	+	7.61483i	−0.233998	+	0.405296i	0.724983	+	0.688767i	$0.241848\pi$
$354$		0			0
$355$	−4.87104	+	2.81230i	−0.258528	+	0.149261i
$356$	15.8743	−	27.4951i	0.841336	−	1.45724i
$357$		0			0
$358$	−0.122373	−	0.211956i	−0.00646760	−	0.0112022i
$359$	0.261276	+	0.150848i	0.0137896	+	0.00796143i	0.506879	−	0.862017i	$-0.330799\pi$
$359$	0.261276	+	0.150848i	0.0137896	+	0.00796143i	−0.493089	+	0.869979i	$0.664132\pi$
$360$		0			0
$361$	17.8324	+	30.8866i	0.938547	+	1.62561i
$362$	0.170883			0.00898143
$363$		0			0
$364$	7.81417	−	12.3477i	0.409574	−	0.647194i
$365$	11.3988	+	6.58111i	0.596641	+	0.344471i
$366$		0			0
$367$	22.8249	+	13.1780i	1.19145	+	0.687884i	0.958635	−	0.284637i	$-0.0918732\pi$
$367$	22.8249	+	13.1780i	1.19145	+	0.687884i	0.232814	+	0.972521i	$0.425207\pi$
$368$	0.627532	−	0.362306i	0.0327124	−	0.0188865i
$369$		0			0
$370$			0.263279i			0.0136872i
$371$	−9.17817	−	17.5022i	−0.476507	−	0.908671i
$372$		0			0
$373$	−18.3837	−	31.8415i	−0.951872	−	1.64869i	−0.741370	−	0.671096i	$-0.765824\pi$
$373$	−18.3837	−	31.8415i	−0.951872	−	1.64869i	−0.210501	−	0.977594i	$-0.567510\pi$
$374$	−2.20372			−0.113952
$375$		0			0
$376$			0.244270i			0.0125973i
$377$	−5.92540			−0.305174
$378$		0			0
$379$	35.0467			1.80023			0.900114	−	0.435654i	$-0.143483\pi$
$379$	35.0467			1.80023			0.900114	+	0.435654i	$0.143483\pi$
$380$			14.7072i			0.754462i
$381$		0			0
$382$	−1.40458			−0.0718648
$383$	−9.15609	−	15.8588i	−0.467855	−	0.810348i	0.531471	−	0.847077i	$-0.321640\pi$
$383$	−9.15609	−	15.8588i	−0.467855	−	0.810348i	−0.999325	+	0.0367289i	$0.988306\pi$
$384$		0			0
$385$	7.73686	+	0.314461i	0.394307	+	0.0160264i
$386$			1.63390i			0.0831632i
$387$		0			0
$388$	−3.38016	+	1.95154i	−0.171602	+	0.0990744i
$389$	20.6139	+	11.9014i	1.04516	+	0.603426i	0.921292	−	0.388872i	$-0.127135\pi$
$389$	20.6139	+	11.9014i	1.04516	+	0.603426i	0.123872	+	0.992298i	$0.460469\pi$
$390$		0			0
$391$	1.15466	+	0.666641i	0.0583935	+	0.0337135i
$392$	−0.235663	+	2.89429i	−0.0119028	+	0.146184i
$393$		0			0
$394$	−2.56124			−0.129033
$395$	−4.55718	−	7.89326i	−0.229296	−	0.397153i
$396$		0			0
$397$	4.81881	+	2.78214i	0.241849	+	0.139632i	0.616026	−	0.787726i	$-0.288741\pi$
$397$	4.81881	+	2.78214i	0.241849	+	0.139632i	−0.374177	+	0.927357i	$0.622075\pi$
$398$	0.868686	+	1.50461i	0.0435433	+	0.0754192i
$399$		0			0
$400$	−1.96762	+	3.40801i	−0.0983808	+	0.170401i
$401$	7.30769	−	4.21910i	0.364929	−	0.210692i	−0.306312	−	0.951931i	$-0.599095\pi$
$401$	7.30769	−	4.21910i	0.364929	−	0.210692i	0.671241	+	0.741240i	$0.265762\pi$
$402$		0			0
$403$	−3.93353	+	6.81307i	−0.195943	+	0.339383i
$404$	5.67459	−	9.82867i	0.282321	−	0.488995i
$405$		0			0
$406$	0.520003	−	0.272690i	0.0258073	−	0.0135334i
$407$	6.41691	−	3.70481i	0.318075	−	0.183640i
$408$		0			0
$409$			3.83286i			0.189523i	0.995500	+	0.0947614i	$0.0302088\pi$
$409$			3.83286i			0.189523i	−0.995500	+	0.0947614i	$0.969791\pi$
$410$			0.779175i			0.0384807i
$411$		0			0
$412$	−20.7667	+	11.9896i	−1.02310	+	0.590687i
$413$	−0.874897	+	21.5256i	−0.0430509	+	1.05921i
$414$		0			0
$415$	−4.90339	+	8.49292i	−0.240698	+	0.416901i
$416$	−1.71992	+	2.97900i	−0.0843262	+	0.146057i
$417$		0			0
$418$	−1.94874	+	1.12510i	−0.0953158	+	0.0550306i
$419$	−8.65942	+	14.9985i	−0.423040	+	0.732727i	−0.996235	−	0.0866920i	$-0.972370\pi$
$419$	−8.65942	+	14.9985i	−0.423040	+	0.732727i	0.573195	+	0.819419i	$0.305704\pi$
$420$		0			0
$421$	−10.8236	−	18.7470i	−0.527510	−	0.913673i	−0.999486	−	0.0320622i	$-0.989793\pi$
$421$	−10.8236	−	18.7470i	−0.527510	−	0.913673i	0.471976	−	0.881611i	$-0.343541\pi$
$422$	0.672230	+	0.388112i	0.0327236	+	0.0188930i
$423$		0			0
$424$	1.54934	+	2.68354i	0.0752428	+	0.130324i
$425$	−7.24081			−0.351231
$426$		0			0
$427$	33.4180	+	1.35826i	1.61721	+	0.0657307i
$428$	−4.12993	−	2.38442i	−0.199628	−	0.115255i
$429$		0			0
$430$	0.0402627	+	0.0232457i	0.00194164	+	0.00112101i
$431$	26.5015	−	15.3007i	1.27653	−	0.737008i	0.300325	−	0.953837i	$-0.402905\pi$
$431$	26.5015	−	15.3007i	1.27653	−	0.737008i	0.976210	+	0.216829i	$0.0695715\pi$
$432$		0			0
$433$			33.9236i			1.63027i	0.579274	+	0.815133i	$0.303336\pi$
$433$			33.9236i			1.63027i	−0.579274	+	0.815133i	$0.696664\pi$
$434$	0.0316590	−	0.778926i	0.00151968	−	0.0373896i
$435$		0			0
$436$	−10.2773	−	17.8009i	−0.492195	−	0.852507i
$437$	1.36141			0.0651250
$438$		0			0
$439$			0.196382i			0.00937278i	0.999989	+	0.00468639i	$0.00149173\pi$
$439$			0.196382i			0.00937278i	−0.999989	+	0.00468639i	$0.998508\pi$
$440$	−1.21410			−0.0578798
$441$		0			0
$442$	−2.09066			−0.0994426
$443$		−	6.82671i		−	0.324347i	−0.986762	−	0.162173i	$-0.948150\pi$
$443$		−	6.82671i		−	0.324347i	0.986762	−	0.162173i	$-0.0518504\pi$
$444$		0			0
$445$	15.9606			0.756605
$446$	0.561499	+	0.972544i	0.0265877	+	0.0460513i
$447$		0			0
$448$	−0.831811	+	20.4655i	−0.0392994	+	0.966905i
$449$		−	1.56290i		−	0.0737579i	−0.999320	−	0.0368789i	$-0.988258\pi$
$449$		−	1.56290i		−	0.0737579i	0.999320	−	0.0368789i	$-0.0117416\pi$
$450$		0			0
$451$	18.9909	−	10.9644i	0.894245	−	0.516292i
$452$	−14.5790	−	8.41718i	−0.685738	−	0.395911i
$453$		0			0
$454$	1.08433	+	0.626039i	0.0508902	+	0.0293815i
$455$	7.33993	+	0.298328i	0.344101	+	0.0139858i
$456$		0			0
$457$	5.59317			0.261637			0.130819	−	0.991406i	$-0.458239\pi$
$457$	5.59317			0.261637			0.130819	+	0.991406i	$0.458239\pi$
$458$	0.625694	+	1.08373i	0.0292368	+	0.0506396i
$459$		0			0
$460$	0.317206	+	0.183139i	0.0147898	+	0.00853889i
$461$	3.97429	+	6.88368i	0.185101	+	0.320605i	0.943611	−	0.331057i	$-0.107405\pi$
$461$	3.97429	+	6.88368i	0.185101	+	0.320605i	−0.758509	+	0.651662i	$0.774072\pi$
$462$		0			0
$463$	5.54581	−	9.60562i	0.257735	−	0.446411i	−0.707899	−	0.706313i	$-0.750357\pi$
$463$	5.54581	−	9.60562i	0.257735	−	0.446411i	0.965635	+	0.259902i	$0.0836904\pi$
$464$	7.27306	−	4.19911i	0.337644	−	0.194939i
$465$		0			0
$466$	−1.25594	+	2.17535i	−0.0581803	+	0.100771i
$467$	−6.26534	+	10.8519i	−0.289925	+	0.502165i	−0.973792	−	0.227442i	$-0.926964\pi$
$467$	−6.26534	+	10.8519i	−0.289925	+	0.502165i	0.683866	+	0.729607i	$0.260297\pi$
$468$		0			0
$469$	−0.333452	+	8.20411i	−0.0153974	+	0.378830i
$470$	−0.0530294	+	0.0306165i	−0.00244606	+	0.00141223i
$471$		0			0
$472$		−	3.37788i		−	0.155479i
$473$		−	1.30843i		−	0.0601618i
$474$		0			0
$475$	−6.40301	+	3.69678i	−0.293790	+	0.169620i
$476$	−33.7487	+	17.6978i	−1.54687	+	0.811179i
$477$		0			0
$478$	0.824441	−	1.42797i	0.0377090	−	0.0653140i
$479$	−9.12862	+	15.8112i	−0.417098	+	0.722434i	−0.995646	−	0.0932138i	$-0.970286\pi$
$479$	−9.12862	+	15.8112i	−0.417098	+	0.722434i	0.578549	+	0.815648i	$0.303619\pi$
$480$		0			0
$481$	6.08771	−	3.51474i	0.277575	−	0.160258i
$482$	0.266470	−	0.461540i	0.0121374	−	0.0210226i
$483$		0			0
$484$	−2.42143	−	4.19405i	−0.110065	−	0.190638i
$485$	−1.69927	−	0.981074i	−0.0771599	−	0.0445483i
$486$		0			0
$487$	−8.81372	−	15.2658i	−0.399388	−	0.691760i	0.594263	−	0.804271i	$-0.297444\pi$
$487$	−8.81372	−	15.2658i	−0.399388	−	0.691760i	−0.993650	+	0.112511i	$0.964111\pi$
$488$	−5.24407			−0.237388
$489$		0			0
$490$	−0.657869	+	0.311606i	−0.0297195	+	0.0140769i
$491$	22.4180	+	12.9430i	1.01171	+	0.584111i	0.911692	−	0.410875i	$-0.134777\pi$
$491$	22.4180	+	12.9430i	1.01171	+	0.584111i	0.100018	+	0.994986i	$0.468110\pi$
$492$		0			0
$493$	13.3824	+	7.72634i	0.602714	+	0.347977i
$494$	−1.84876	+	1.06738i	−0.0831796	+	0.0480238i
$495$		0			0
$496$		−	11.1502i		−	0.500657i
$497$	−14.8690	−	0.604343i	−0.666966	−	0.0271085i
$498$		0			0
$499$	−8.01638	−	13.8848i	−0.358863	−	0.621568i	0.628908	−	0.777479i	$-0.283502\pi$
$499$	−8.01638	−	13.8848i	−0.358863	−	0.621568i	−0.987771	+	0.155911i	$0.950169\pi$
$500$	−1.98919			−0.0889591
$501$		0			0
$502$		−	2.21928i		−	0.0990512i
$503$	−4.02737			−0.179572			−0.0897858	−	0.995961i	$-0.528618\pi$
$503$	−4.02737			−0.179572			−0.0897858	+	0.995961i	$0.528618\pi$
$504$		0			0
$505$	5.70544			0.253889
$506$			0.0560407i			0.00249131i
$507$		0			0
$508$	12.2460			0.543330
$509$	12.3484	+	21.3880i	0.547331	+	0.948006i	0.998456	+	0.0555448i	$0.0176896\pi$
$509$	12.3484	+	21.3880i	0.547331	+	0.948006i	−0.451125	+	0.892461i	$0.648977\pi$
$510$		0			0
$511$	16.1729	+	30.8407i	0.715445	+	1.36431i
$512$		−	8.14035i		−	0.359756i
$513$		0			0
$514$	−0.958424	+	0.553346i	−0.0422743	+	0.0244071i
$515$	−10.4398	−	6.02741i	−0.460032	−	0.265600i
$516$		0			0
$517$	1.49244	+	0.861658i	0.0656372	+	0.0378957i
$518$	−0.372497	+	0.588607i	−0.0163666	+	0.0258619i
$519$		0			0
$520$	−1.15181			−0.0505102
$521$	−12.5314	−	21.7049i	−0.549009	−	0.950911i	−0.998343	−	0.0575471i	$-0.981672\pi$
$521$	−12.5314	−	21.7049i	−0.549009	−	0.950911i	0.449334	−	0.893364i	$-0.351661\pi$
$522$		0			0
$523$	15.9386	+	9.20215i	0.696946	+	0.402382i	0.806209	−	0.591631i	$-0.201516\pi$
$523$	15.9386	+	9.20215i	0.696946	+	0.402382i	−0.109263	+	0.994013i	$0.534849\pi$
$524$	−20.7068	−	35.8652i	−0.904580	−	1.56678i
$525$		0			0
$526$	0.553405	−	0.958525i	0.0241296	−	0.0417937i
$527$	17.7676	−	10.2581i	0.773969	−	0.446851i
$528$		0			0
$529$	−11.4830	+	19.8892i	−0.499263	+	0.864749i
$530$	−0.388386	+	0.672704i	−0.0168704	+	0.0292204i
$531$		0			0
$532$	−20.8082	+	32.8804i	−0.902151	+	1.42555i
$533$	18.0166	−	10.4019i	0.780384	−	0.450555i
$534$		0			0
$535$		−	2.39738i		−	0.103648i
$536$		−	1.28742i		−	0.0556080i
$537$		0			0
$538$	−0.699514	+	0.403865i	−0.0301582	+	0.0174118i
$539$	16.8522	+	11.6494i	0.725875	+	0.501776i
$540$		0			0
$541$	−16.3146	+	28.2578i	−0.701420	+	1.21490i	0.266548	+	0.963822i	$0.414117\pi$
$541$	−16.3146	+	28.2578i	−0.701420	+	1.21490i	−0.967968	+	0.251074i	$0.919216\pi$
$542$	−0.387416	+	0.671024i	−0.0166409	+	0.0288230i
$543$		0			0
$544$	7.76884	−	4.48534i	0.333086	−	0.192307i
$545$	5.16660	−	8.94882i	0.221313	−	0.383325i
$546$		0			0
$547$	6.87713	+	11.9115i	0.294045	+	0.509300i	0.974762	−	0.223246i	$-0.0716652\pi$
$547$	6.87713	+	11.9115i	0.294045	+	0.509300i	−0.680718	+	0.732546i	$0.738332\pi$
$548$	−9.62317	−	5.55594i	−0.411081	−	0.237338i
$549$		0			0
$550$	−0.152173	−	0.263572i	−0.00648870	−	0.0112388i
$551$	15.7787			0.672194
$552$		0			0
$553$	0.979305	−	24.0944i	0.0416443	−	1.02460i
$554$	−1.52851	−	0.882483i	−0.0649400	−	0.0374931i
$555$		0			0
$556$	24.8359	+	14.3390i	1.05328	+	0.608110i
$557$	−18.3957	+	10.6208i	−0.779451	+	0.450016i	−0.836236	−	0.548370i	$-0.815248\pi$
$557$	−18.3957	+	10.6208i	−0.779451	+	0.450016i	0.0567848	+	0.998386i	$0.481915\pi$
$558$		0			0
$559$		−	1.24131i		−	0.0525017i
$560$	−9.22073	+	4.83535i	−0.389647	+	0.204331i
$561$		0			0
$562$	1.26949	+	2.19881i	0.0535500	+	0.0927514i
$563$	−7.48251			−0.315350			−0.157675	−	0.987491i	$-0.550400\pi$
$563$	−7.48251			−0.315350			−0.157675	+	0.987491i	$0.550400\pi$
$564$		0			0
$565$		−	8.46294i		−	0.356039i
$566$	2.86666			0.120495
$567$		0			0
$568$	2.33330			0.0979030
$569$			9.27735i			0.388927i	0.980910	+	0.194463i	$0.0622966\pi$
$569$			9.27735i			0.388927i	−0.980910	+	0.194463i	$0.937703\pi$
$570$		0			0
$571$	0.874760			0.0366076			0.0183038	−	0.999832i	$-0.494173\pi$
$571$	0.874760			0.0366076			0.0183038	+	0.999832i	$0.494173\pi$
$572$	8.08203	+	13.9985i	0.337927	+	0.585306i
$573$		0			0
$574$	−1.10240	+	1.74198i	−0.0460135	+	0.0727089i
$575$			0.184134i			0.00767893i
$576$		0			0
$577$	−11.3961	+	6.57956i	−0.474427	+	0.273911i	−0.718091	−	0.695949i	$-0.754984\pi$
$577$	−11.3961	+	6.57956i	−0.474427	+	0.273911i	0.243664	+	0.969860i	$0.421651\pi$
$578$	3.19072	+	1.84216i	0.132717	+	0.0766240i
$579$		0			0
$580$	3.67640	+	2.12257i	0.152654	+	0.0881349i
$581$	−22.9785	+	12.0499i	−0.953308	+	0.499915i
$582$		0			0
$583$	21.8611			0.905395
$584$	−2.73010	−	4.72867i	−0.112972	−	0.195674i
$585$		0			0
$586$	1.72983	+	0.998721i	0.0714588	+	0.0412568i
$587$	9.18223	+	15.9041i	0.378991	+	0.656432i	0.990916	−	0.134484i	$-0.0429378\pi$
$587$	9.18223	+	15.9041i	0.378991	+	0.656432i	−0.611925	+	0.790916i	$0.709604\pi$
$588$		0			0
$589$	10.4745	−	18.1424i	0.431595	−	0.747545i
$590$	0.733315	−	0.423379i	0.0301901	−	0.0174303i
$591$		0			0
$592$	−4.98152	+	8.62825i	−0.204739	+	0.354619i
$593$	14.5682	−	25.2329i	0.598245	−	1.03619i	−0.394836	−	0.918752i	$-0.629198\pi$
$593$	14.5682	−	25.2329i	0.598245	−	1.03619i	0.993080	−	0.117438i	$-0.0374682\pi$
$594$		0			0
$595$	−16.1881	−	10.2446i	−0.663647	−	0.419986i
$596$	2.66624	−	1.53935i	0.109213	−	0.0630543i
$597$		0			0
$598$			0.0531656i			0.00217410i
$599$		−	9.77430i		−	0.399367i	−0.979860	−	0.199683i	$-0.936009\pi$
$599$		−	9.77430i		−	0.399367i	0.979860	−	0.199683i	$-0.0639914\pi$
$600$		0			0
$601$	−12.0062	+	6.93177i	−0.489742	+	0.282753i	−0.724467	−	0.689309i	$-0.757914\pi$
$601$	−12.0062	+	6.93177i	−0.489742	+	0.282753i	0.234725	+	0.972062i	$0.424581\pi$
$602$	0.0571255	+	0.108935i	0.00232826	+	0.00443986i
$603$		0			0
$604$	15.2253	−	26.3711i	0.619510	−	1.07302i
$605$	1.21730	−	2.10842i	0.0494902	−	0.0857196i
$606$		0			0
$607$	3.88964	−	2.24568i	0.157876	−	0.0911495i	−0.418981	−	0.907995i	$-0.637613\pi$
$607$	3.88964	−	2.24568i	0.157876	−	0.0911495i	0.576856	+	0.816846i	$0.304279\pi$
$608$	4.57996	−	7.93273i	0.185742	−	0.321714i
$609$		0			0
$610$	−0.657286	−	1.13845i	−0.0266127	−	0.0460946i
$611$	1.41587	+	0.817452i	0.0572799	+	0.0330706i
$612$		0			0
$613$	−10.2897	−	17.8222i	−0.415596	−	0.719834i	0.579895	−	0.814692i	$-0.303094\pi$
$613$	−10.2897	−	17.8222i	−0.415596	−	0.719834i	−0.995491	+	0.0948577i	$0.969760\pi$
$614$	−2.86681			−0.115695
$615$		0			0
$616$	−2.71432	−	1.71775i	−0.109363	−	0.0692100i
$617$	−8.84986	−	5.10947i	−0.356282	−	0.205700i	0.311167	−	0.950355i	$-0.399280\pi$
$617$	−8.84986	−	5.10947i	−0.356282	−	0.205700i	−0.667449	+	0.744656i	$0.732614\pi$
$618$		0			0
$619$	−12.3888	−	7.15270i	−0.497949	−	0.287491i	0.229917	−	0.973210i	$-0.426155\pi$
$619$	−12.3888	−	7.15270i	−0.497949	−	0.287491i	−0.727866	+	0.685719i	$0.759488\pi$
$620$	4.88109	−	2.81810i	0.196029	−	0.113178i
$621$		0			0
$622$			1.41414i			0.0567019i
$623$	35.6827	+	22.5816i	1.42960	+	0.904714i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.37983			−0.0551490
$627$		0			0
$628$			8.80304i			0.351280i
$629$	−18.3320			−0.730943
$630$		0			0
$631$	1.77064			0.0704882			0.0352441	−	0.999379i	$-0.488779\pi$
$631$	1.77064			0.0704882			0.0352441	+	0.999379i	$0.488779\pi$
$632$			3.78098i			0.150399i
$633$		0			0
$634$	−2.62492			−0.104249
$635$	3.07816	+	5.33152i	0.122153	+	0.211575i
$636$		0			0
$637$	15.9876	+	11.0518i	0.633452	+	0.437887i
$638$			0.649509i			0.0257143i
$639$		0			0
$640$	2.84305	−	1.64143i	0.112381	−	0.0648834i
$641$	29.2397	+	16.8815i	1.15490	+	0.666781i	0.950076	−	0.312018i	$-0.101005\pi$
$641$	29.2397	+	16.8815i	1.15490	+	0.666781i	0.204822	+	0.978799i	$0.434338\pi$
$642$		0			0
$643$	19.3941	+	11.1972i	0.764827	+	0.441573i	0.831026	−	0.556233i	$-0.187754\pi$
$643$	19.3941	+	11.1972i	0.764827	+	0.441573i	−0.0661992	+	0.997806i	$0.521087\pi$
$644$	0.450057	+	0.858232i	0.0177347	+	0.0338191i
$645$		0			0
$646$	5.56719			0.219038
$647$	24.0354	+	41.6305i	0.944928	+	1.63666i	0.755896	+	0.654692i	$0.227202\pi$
$647$	24.0354	+	41.6305i	0.944928	+	1.63666i	0.189032	+	0.981971i	$0.439465\pi$
$648$		0			0
$649$	−20.6381	−	11.9154i	−0.810116	−	0.467720i
$650$	−0.144366	−	0.250050i	−0.00566252	−	0.00980777i
$651$		0			0
$652$	−5.32167	+	9.21740i	−0.208413	+	0.360981i
$653$	11.7614	−	6.79044i	0.460259	−	0.265731i	−0.251894	−	0.967755i	$-0.581053\pi$
$653$	11.7614	−	6.79044i	0.460259	−	0.265731i	0.712153	+	0.702024i	$0.247720\pi$
$654$		0			0
$655$	10.4097	−	18.0301i	0.406740	−	0.704494i
$656$	−14.7428	+	25.5353i	−0.575610	+	0.996986i
$657$		0			0
$658$	−0.161874	−	0.00657928i	−0.00631050	−	0.000256487i
$659$	−31.8718	+	18.4012i	−1.24155	+	0.716810i	−0.969410	−	0.245448i	$-0.921065\pi$
$659$	−31.8718	+	18.4012i	−1.24155	+	0.716810i	−0.272141	+	0.962257i	$0.587732\pi$
$660$		0			0
$661$		−	39.8075i		−	1.54833i	−0.632984	−	0.774165i	$-0.718170\pi$
$661$		−	39.8075i		−	1.54833i	0.632984	−	0.774165i	$-0.281830\pi$
$662$			0.869307i			0.0337866i
$663$		0			0
$664$	3.52319	−	2.03412i	0.136726	−	0.0789390i
$665$	−19.5454	−	0.794412i	−0.757938	−	0.0308060i
$666$		0			0
$667$	0.196481	−	0.340316i	0.00760779	−	0.0131771i
$668$	20.4135	−	35.3572i	0.789822	−	1.36801i
$669$		0			0
$670$	0.279490	−	0.161364i	0.0107976	−	0.00623402i
$671$	−18.4984	+	32.0401i	−0.714122	+	1.23690i
$672$		0			0
$673$	−14.9975	−	25.9765i	−0.578112	−	1.00132i	−0.995696	−	0.0926811i	$-0.970456\pi$
$673$	−14.9975	−	25.9765i	−0.578112	−	1.00132i	0.417584	−	0.908638i	$-0.362877\pi$
$674$	1.16514	+	0.672691i	0.0448793	+	0.0259111i
$675$		0			0
$676$	−5.26231	−	9.11459i	−0.202397	−	0.350561i
$677$	10.5107			0.403958			0.201979	−	0.979390i	$-0.435263\pi$
$677$	10.5107			0.403958			0.201979	+	0.979390i	$0.435263\pi$
$678$		0			0
$679$	−2.41096	−	4.59755i	−0.0925240	−	0.176438i
$680$	2.60134	+	1.50188i	0.0997568	+	0.0575946i
$681$		0			0
$682$	0.746810	+	0.431171i	0.0285968	+	0.0165104i
$683$	−13.9019	+	8.02627i	−0.531942	+	0.307117i	−0.741807	−	0.670614i	$-0.766031\pi$
$683$	−13.9019	+	8.02627i	−0.531942	+	0.307117i	0.209865	+	0.977730i	$0.432698\pi$
$684$		0			0
$685$		−	5.58614i		−	0.213436i
$686$	−1.91165	−	0.234126i	−0.0729872	−	0.00893899i
$687$		0			0
$688$	0.879667	+	1.52363i	0.0335370	+	0.0580877i
$689$	20.7396			0.790115
$690$		0			0
$691$			12.2307i			0.465278i	0.972563	+	0.232639i	$0.0747361\pi$
$691$			12.2307i			0.465278i	−0.972563	+	0.232639i	$0.925264\pi$
$692$	42.4046			1.61198
$693$		0			0
$694$	2.48374			0.0942814
$695$			14.4170i			0.546867i
$696$		0			0
$697$	−54.2535			−2.05500
$698$	−1.14356	−	1.98071i	−0.0432845	−	0.0749710i
$699$		0			0
$700$	−4.44717	−	2.81437i	−0.168087	−	0.106373i
$701$			43.2427i			1.63325i	0.577166	+	0.816627i	$0.304158\pi$
$701$			43.2427i			1.63325i	−0.577166	+	0.816627i	$0.695842\pi$
$702$		0			0
$703$	−16.2109	+	9.35935i	−0.611404	+	0.352994i
$704$	−19.6217	−	11.3286i	−0.739521	−	0.426963i
$705$		0			0
$706$	0.791872	+	0.457187i	0.0298025	+	0.0172065i
$707$	12.7555	+	8.07226i	0.479720	+	0.303588i
$708$		0			0
$709$	5.70294			0.214178			0.107089	−	0.994249i	$-0.465847\pi$
$709$	5.70294			0.214178			0.107089	+	0.994249i	$0.465847\pi$
$710$	0.292453	+	0.506543i	0.0109756	+	0.0190102i
$711$		0			0
$712$	−5.73402	−	3.31054i	−0.214891	−	0.124068i
$713$	−0.260865	−	0.451831i	−0.00976946	−	0.0169212i
$714$		0			0
$715$	−4.06298	+	7.03730i	−0.151947	+	0.263180i
$716$	4.05439	−	2.34080i	0.151520	−	0.0874800i
$717$		0			0
$718$	0.0156868	−	0.0271703i	0.000585425	−	0.00101398i
$719$	24.4397	−	42.3309i	0.911448	−	1.57867i	0.0994282	−	0.995045i	$-0.468299\pi$
$719$	24.4397	−	42.3309i	0.911448	−	1.57867i	0.812020	−	0.583630i	$-0.198368\pi$
$720$		0			0
$721$	−14.8122	−	28.2459i	−0.551634	−	1.05193i
$722$	3.21192	−	1.85440i	0.119535	−	0.0690138i
$723$		0			0
$724$			3.26874i			0.121482i
$725$			2.13411i			0.0792588i
$726$		0			0
$727$	−10.9887	+	6.34435i	−0.407550	+	0.235299i	−0.689736	−	0.724060i	$-0.742274\pi$
$727$	−10.9887	+	6.34435i	−0.407550	+	0.235299i	0.282187	+	0.959360i	$0.408940\pi$
$728$	−2.57507	−	1.62962i	−0.0954384	−	0.0603977i
$729$		0			0
$730$	0.684375	−	1.18537i	0.0253298	−	0.0438726i
$731$	−1.61858	+	2.80347i	−0.0598655	+	0.103690i
$732$		0			0
$733$	30.0914	−	17.3733i	1.11145	−	0.641698i	0.172248	−	0.985054i	$-0.444897\pi$
$733$	30.0914	−	17.3733i	1.11145	−	0.641698i	0.939205	+	0.343356i	$0.111564\pi$
$734$	1.37039	−	2.37358i	0.0505819	−	0.0876104i
$735$		0			0
$736$	−0.114062	−	0.197562i	−0.00420440	−	0.00728223i
$737$	−7.86584	−	4.54135i	−0.289742	−	0.167283i
$738$		0			0
$739$	6.28839	+	10.8918i	0.231322	+	0.400662i	0.958197	−	0.286108i	$-0.0923615\pi$
$739$	6.28839	+	10.8918i	0.231322	+	0.400662i	−0.726875	+	0.686770i	$0.759028\pi$
$740$	−5.03613			−0.185132
$741$		0			0
$742$	−1.82007	+	0.954445i	−0.0668169	+	0.0350388i
$743$	−29.1685	−	16.8405i	−1.07009	−	0.617817i	−0.141884	−	0.989883i	$-0.545316\pi$
$743$	−29.1685	−	16.8405i	−1.07009	−	0.617817i	−0.928206	+	0.372067i	$0.878649\pi$
$744$		0			0
$745$	1.34036	+	0.773860i	0.0491072	+	0.0283520i
$746$	−3.31122	+	1.91173i	−0.121232	+	0.0699936i
$747$		0			0
$748$		−	42.1538i		−	1.54130i
$749$	3.39190	−	5.35976i	0.123937	−	0.195841i
$750$		0			0
$751$	26.8558	+	46.5156i	0.979981	+	1.69738i	0.662409	+	0.749143i	$0.269534\pi$
$751$	26.8558	+	46.5156i	0.979981	+	1.69738i	0.317572	+	0.948234i	$0.397132\pi$
$752$	−2.31719			−0.0844992
$753$		0			0
$754$			0.616187i			0.0224402i
$755$	15.3081			0.557119
$756$		0			0
$757$	16.9208			0.614998			0.307499	−	0.951548i	$-0.400508\pi$
$757$	16.9208			0.614998			0.307499	+	0.951548i	$0.400508\pi$
$758$		−	3.64453i		−	0.132375i
$759$		0			0
$760$	3.06713			0.111257
$761$	8.16387	+	14.1402i	0.295940	+	0.512583i	0.975203	−	0.221312i	$-0.0710338\pi$
$761$	8.16387	+	14.1402i	0.295940	+	0.512583i	−0.679263	+	0.733895i	$0.737700\pi$
$762$		0			0
$763$	24.2119	−	12.6967i	0.876531	−	0.459653i
$764$		−	26.8676i		−	0.972034i
$765$		0			0
$766$	−1.64917	+	0.952149i	−0.0595870	+	0.0344026i
$767$	−19.5793	−	11.3041i	−0.706967	−	0.408168i
$768$		0			0
$769$	38.6374	+	22.3073i	1.39330	+	0.804423i	0.993679	−	0.112256i	$-0.0358078\pi$
$769$	38.6374	+	22.3073i	1.39330	+	0.804423i	0.399623	+	0.916680i	$0.369141\pi$
$770$	0.0327010	−	0.804562i	0.00117846	−	0.0289944i
$771$		0			0
$772$	−31.2540			−1.12485
$773$	−6.98070	−	12.0909i	−0.251078	−	0.434881i	0.712745	−	0.701424i	$-0.247452\pi$
$773$	−6.98070	−	12.0909i	−0.251078	−	0.434881i	−0.963823	+	0.266543i	$0.914119\pi$
$774$		0			0
$775$	2.45381	+	1.41671i	0.0881435	+	0.0508897i
$776$	0.406987	+	0.704923i	0.0146100	+	0.0253053i
$777$		0			0
$778$	1.23764	−	2.14365i	0.0443715	−	0.0768536i
$779$	−47.9761	+	27.6990i	−1.71892	+	0.992419i
$780$		0			0
$781$	8.23067	−	14.2559i	0.294516	−	0.510117i
$782$	0.0693245	−	0.120074i	0.00247904	−	0.00429382i
$783$		0			0
$784$	−27.4558	−	2.23554i	−0.980563	−	0.0798409i
$785$	−3.83255	+	2.21273i	−0.136790	+	0.0789755i
$786$		0			0
$787$			13.1825i			0.469906i	0.972007	+	0.234953i	$0.0754935\pi$
$787$			13.1825i			0.469906i	−0.972007	+	0.234953i	$0.924506\pi$
$788$		−	48.9926i		−	1.74529i
$789$		0			0
$790$	−0.820826	+	0.473904i	−0.0292037	+	0.0168608i
$791$	11.9737	−	18.9204i	0.425735	−	0.672731i
$792$		0			0
$793$	−17.5493	+	30.3964i	−0.623196	+	1.07941i
$794$	0.289317	−	0.501112i	0.0102675	−	0.0177838i
$795$		0			0
$796$	−28.7809	+	16.6166i	−1.02011	+	0.588961i
$797$	−14.1612	+	24.5280i	−0.501617	+	0.868825i	0.498382	+	0.866958i	$0.333928\pi$
$797$	−14.1612	+	24.5280i	−0.501617	+	0.868825i	−0.999998	+	0.00186773i	$0.999405\pi$
$798$		0			0
$799$	−2.13181	−	3.69240i	−0.0754180	−	0.130628i
$800$	1.07292	+	0.619453i	0.0379336	+	0.0219010i
$801$		0			0
$802$	−0.438747	−	0.759932i	−0.0154927	−	0.0268341i
$803$	−38.5215			−1.35939
$804$		0			0
$805$	−0.260520	+	0.411664i	−0.00918212	+	0.0145093i
$806$	0.708496	+	0.409050i	0.0249557	+	0.0144082i
$807$		0			0
$808$	−2.04974	−	1.18342i	−0.0721096	−	0.0416325i
$809$	16.5879	−	9.57704i	0.583200	−	0.336711i	−0.179204	−	0.983812i	$-0.557352\pi$
$809$	16.5879	−	9.57704i	0.583200	−	0.336711i	0.762404	+	0.647101i	$0.224019\pi$
$810$		0			0
$811$		−	14.6454i		−	0.514269i	−0.966376	−	0.257134i	$-0.917222\pi$
$811$		−	14.6454i		−	0.514269i	0.966376	−	0.257134i	$-0.0827783\pi$
$812$	5.21614	+	9.94687i	0.183051	+	0.349067i
$813$		0			0
$814$	−0.385266	−	0.667300i	−0.0135036	−	0.0233889i
$815$	−5.35060			−0.187423
$816$		0			0
$817$			3.30546i			0.115643i
$818$	0.398582			0.0139361
$819$		0			0
$820$	−14.9044			−0.520485
$821$			4.73593i			0.165285i	0.996579	+	0.0826426i	$0.0263360\pi$
$821$			4.73593i			0.165285i	−0.996579	+	0.0826426i	$0.973664\pi$
$822$		0			0
$823$	−2.76948			−0.0965379			−0.0482690	−	0.998834i	$-0.515370\pi$
$823$	−2.76948			−0.0965379			−0.0482690	+	0.998834i	$0.515370\pi$
$824$	2.50040	+	4.33083i	0.0871057	+	0.150871i
$825$		0			0
$826$	2.23846	+	0.0909813i	0.0778862	+	0.00316564i
$827$		−	5.25434i		−	0.182711i	−0.995818	−	0.0913556i	$-0.970880\pi$
$827$		−	5.25434i		−	0.182711i	0.995818	−	0.0913556i	$-0.0291200\pi$
$828$		0			0
$829$	−15.3816	+	8.88058i	−0.534226	+	0.308435i	−0.742736	−	0.669585i	$-0.766472\pi$
$829$	−15.3816	+	8.88058i	−0.534226	+	0.308435i	0.208510	+	0.978020i	$0.433139\pi$
$830$	0.883186	+	0.509907i	0.0306558	+	0.0176991i
$831$		0			0
$832$	−18.6151	−	10.7474i	−0.645361	−	0.372599i
$833$	−21.6970	−	45.8070i	−0.751755	−	1.58712i
$834$		0			0
$835$	20.5245			0.710279
$836$	−21.5215	−	37.2764i	−0.744338	−	1.28923i
$837$		0			0
$838$	1.55971	+	0.900499i	0.0538793	+	0.0311072i
$839$	8.51777	+	14.7532i	0.294066	+	0.509338i	0.974767	−	0.223224i	$-0.0716581\pi$
$839$	8.51777	+	14.7532i	0.294066	+	0.509338i	−0.680701	+	0.732561i	$0.738325\pi$
$840$		0			0
$841$	−12.2228	+	21.1705i	−0.421476	+	0.730017i
$842$	−1.94952	+	1.12555i	−0.0671848	+	0.0387891i
$843$		0			0
$844$	−7.42399	+	12.8587i	−0.255544	+	0.442616i
$845$	2.64546	−	4.58207i	0.0910066	−	0.157628i
$846$		0			0
$847$	5.70456	−	2.99147i	0.196011	−	0.102788i
$848$	−25.4566	+	14.6974i	−0.874182	+	0.504709i
$849$		0			0
$850$			0.752978i			0.0258269i
$851$			0.466183i			0.0159806i
$852$		0			0
$853$	−2.55801	+	1.47687i	−0.0875847	+	0.0505670i	−0.543153	−	0.839634i	$-0.682770\pi$
$853$	−2.55801	+	1.47687i	−0.0875847	+	0.0505670i	0.455568	+	0.890201i	$0.349436\pi$
$854$	0.141246	−	3.47516i	0.00483335	−	0.118918i
$855$		0			0
$856$	−0.497263	+	0.861285i	−0.0169961	+	0.0294381i
$857$	19.1804	−	33.2214i	0.655190	−	1.13482i	−0.326656	−	0.945143i	$-0.605922\pi$
$857$	19.1804	−	33.2214i	0.655190	−	1.13482i	0.981846	−	0.189680i	$-0.0607449\pi$
$858$		0			0
$859$	−9.09692	+	5.25211i	−0.310383	+	0.179200i	−0.647098	−	0.762407i	$-0.724017\pi$
$859$	−9.09692	+	5.25211i	−0.310383	+	0.179200i	0.336715	+	0.941607i	$0.390684\pi$
$860$	−0.444655	+	0.770165i	−0.0151626	+	0.0262624i
$861$		0			0
$862$	−1.59113	−	2.75592i	−0.0541941	−	0.0938669i
$863$	39.3048	+	22.6927i	1.33795	+	0.772467i	0.986504	−	0.163740i	$-0.0523558\pi$
$863$	39.3048	+	22.6927i	1.33795	+	0.772467i	0.351449	+	0.936207i	$0.385689\pi$
$864$		0			0
$865$	10.6588	+	18.4616i	0.362410	+	0.627712i
$866$	3.52775			0.119878
$867$		0			0
$868$	14.8997	+	0.605590i	0.505728	+	0.0205550i
$869$	23.1010	+	13.3374i	0.783647	+	0.452439i
$870$		0			0
$871$	−7.46230	−	4.30836i	−0.252850	−	0.145983i
$872$	−3.71231	+	2.14331i	−0.125715	+	0.0725815i
$873$		0			0
$874$		−	0.141574i		−	0.00478881i
$875$	0.107447	−	2.64357i	0.00363235	−	0.0893689i
$876$		0			0
$877$	−16.7656	−	29.0388i	−0.566134	−	0.980572i	−0.996943	−	0.0781294i	$-0.975105\pi$
$877$	−16.7656	−	29.0388i	−0.566134	−	0.980572i	0.430810	−	0.902443i	$-0.358228\pi$
$878$	0.0204219			0.000689205
$879$		0			0
$880$		−	11.5171i		−	0.388242i
$881$	−55.1097			−1.85669			−0.928347	−	0.371714i	$-0.878770\pi$
$881$	−55.1097			−1.85669			−0.928347	+	0.371714i	$0.878770\pi$
$882$		0			0
$883$	3.42725			0.115336			0.0576680	−	0.998336i	$-0.481634\pi$
$883$	3.42725			0.115336			0.0576680	+	0.998336i	$0.481634\pi$
$884$		−	39.9912i		−	1.34505i
$885$		0			0
$886$	−0.709915			−0.0238501
$887$	−19.6195	−	33.9819i	−0.658757	−	1.14100i	−0.980938	−	0.194322i	$-0.937749\pi$
$887$	−19.6195	−	33.9819i	−0.658757	−	1.14100i	0.322181	−	0.946678i	$-0.395584\pi$
$888$		0			0
$889$	−0.661474	+	16.2746i	−0.0221851	+	0.545834i
$890$		−	1.65976i		−	0.0556351i
$891$		0			0
$892$	−18.6033	+	10.7406i	−0.622885	+	0.359623i
$893$	−3.77030	−	2.17678i	−0.126168	−	0.0728432i
$894$		0			0
$895$	2.03822	+	1.17677i	0.0681301	+	0.0393349i
$896$	8.67849	+	0.352733i	0.289928	+	0.0117840i
$897$		0			0
$898$	−0.162527			−0.00542361
$899$	−3.02341	−	5.23670i	−0.100836	−	0.174654i
$900$		0			0
$901$	−46.8400	−	27.0431i	−1.56047	−	0.900936i
$902$	−1.14019	−	1.97487i	−0.0379643	−	0.0657561i
$903$		0			0
$904$	−1.75538	+	3.04040i	−0.0583830	+	0.101122i
$905$	−1.42310	+	0.821627i	−0.0473054	+	0.0273118i
$906$		0			0
$907$	5.59186	−	9.68539i	0.185675	−	0.321598i	−0.758129	−	0.652105i	$-0.773886\pi$
$907$	5.59186	−	9.68539i	0.185675	−	0.321598i	0.943804	+	0.330507i	$0.107220\pi$
$908$	−11.9752	+	20.7416i	−0.397410	+	0.688335i
$909$		0			0
$910$	0.0310233	−	0.763285i	0.00102841	−	0.0253027i
$911$	4.71312	−	2.72112i	0.156153	−	0.0901548i	−0.419888	−	0.907576i	$-0.637930\pi$
$911$	4.71312	−	2.72112i	0.156153	−	0.0901548i	0.576040	+	0.817421i	$0.304597\pi$
$912$		0			0
$913$		−	28.7012i		−	0.949872i
$914$		−	0.581638i		−	0.0192389i
$915$		0			0
$916$	−20.7302	+	11.9686i	−0.684945	+	0.395453i
$917$	48.7823	−	25.5814i	1.61093	−	0.844773i
$918$		0			0
$919$	−1.39443	+	2.41523i	−0.0459981	+	0.0796710i	−0.888108	−	0.459635i	$-0.847980\pi$
$919$	−1.39443	+	2.41523i	−0.0459981	+	0.0796710i	0.842110	+	0.539306i	$0.181313\pi$
$920$	0.0381930	−	0.0661522i	0.00125919	−	0.00218097i
$921$		0			0
$922$	0.715839	−	0.413290i	0.0235749	−	0.0136110i
$923$	7.80841	−	13.5246i	0.257017	−	0.445166i
$924$		0			0
$925$	−1.26588	−	2.19256i	−0.0416218	−	0.0720911i
$926$	−0.998896	−	0.576713i	−0.0328257	−	0.0189520i
$927$		0			0
$928$	−1.32198	−	2.28973i	−0.0433961	−	0.0751642i
$929$	12.3464			0.405073			0.202536	−	0.979275i	$-0.435082\pi$
$929$	12.3464			0.405073			0.202536	+	0.979275i	$0.435082\pi$
$930$		0			0
$931$	−42.5732	−	29.4296i	−1.39528	−	0.964515i
$932$	−41.6112	−	24.0242i	−1.36302	−	0.786940i
$933$		0			0
$934$	1.12850	+	0.651537i	0.0369255	+	0.0213189i
$935$	18.3524	−	10.5957i	0.600186	−	0.346518i
$936$		0			0
$937$			12.0267i			0.392894i	0.980514	+	0.196447i	$0.0629403\pi$
$937$			12.0267i			0.392894i	−0.980514	+	0.196447i	$0.937060\pi$
$938$	0.853152	+	0.0346759i	0.0278564	+	0.00113221i
$939$		0			0
$940$	−0.585648	−	1.01437i	−0.0191017	−	0.0330851i
$941$	13.6425			0.444734			0.222367	−	0.974963i	$-0.428622\pi$
$941$	13.6425			0.444734			0.222367	+	0.974963i	$0.428622\pi$
$942$		0			0
$943$			1.37967i			0.0449282i
$944$	32.0432			1.04292
$945$		0			0
$946$	−0.136065			−0.00442385
$947$			6.31702i			0.205276i	0.994719	+	0.102638i	$0.0327282\pi$
$947$			6.31702i			0.205276i	−0.994719	+	0.102638i	$0.967272\pi$
$948$		0			0
$949$	−36.5452			−1.18631
$950$	0.384431	+	0.665854i	0.0124726	+	0.0216032i
$951$		0			0
$952$	3.69083	+	7.03819i	0.119620	+	0.228109i
$953$		−	41.8480i		−	1.35559i	−0.735251	−	0.677795i	$-0.762936\pi$
$953$		−	41.8480i		−	1.35559i	0.735251	−	0.677795i	$-0.237064\pi$
$954$		0			0
$955$	11.6972	−	6.75341i	0.378514	−	0.218535i
$956$	27.3150	+	15.7703i	0.883429	+	0.510048i
$957$		0			0
$958$	1.64422	+	0.949293i	0.0531224	+	0.0306703i
$959$	7.90347	−	12.4888i	0.255217	−	0.403284i
$960$		0			0
$961$	22.9717			0.741024
$962$	−0.365500	−	0.633065i	−0.0117842	−	0.0204108i
$963$		0			0
$964$	8.82855	+	5.09717i	0.284349	+	0.164169i
$965$	−7.85597	−	13.6069i	−0.252893	−	0.438023i
$966$		0			0
$967$	5.58321	−	9.67040i	0.179544	−	0.310979i	−0.762180	−	0.647365i	$-0.775871\pi$
$967$	5.58321	−	9.67040i	0.179544	−	0.310979i	0.941724	+	0.336385i	$0.109204\pi$
$968$	−0.874655	+	0.504982i	−0.0281125	+	0.0162307i
$969$		0			0
$970$	−0.102023	+	0.176708i	−0.00327575	+	0.00567377i
$971$	−2.71987	+	4.71095i	−0.0872847	+	0.151182i	−0.906362	−	0.422501i	$-0.861152\pi$
$971$	−2.71987	+	4.71095i	−0.0872847	+	0.151182i	0.819078	+	0.573682i	$0.194486\pi$
$972$		0			0
$973$	−20.3977	+	32.2317i	−0.653919	+	1.03330i
$974$	−1.58750	+	0.916545i	−0.0508669	+	0.0293680i
$975$		0			0
$976$		−	49.7462i		−	1.59234i
$977$		−	24.4137i		−	0.781064i	−0.920589	−	0.390532i	$-0.872291\pi$
$977$		−	24.4137i		−	0.781064i	0.920589	−	0.390532i	$-0.127709\pi$
$978$		0			0
$979$	−40.4533	+	23.3557i	−1.29289	+	0.746452i
$980$	−5.96056	−	12.5840i	−0.190403	−	0.401982i
$981$		0			0
$982$	1.34596	−	2.33126i	0.0429512	−	0.0743936i
$983$	−2.29228	+	3.97034i	−0.0731124	+	0.126634i	−0.900264	−	0.435345i	$-0.856627\pi$
$983$	−2.29228	+	3.97034i	−0.0731124	+	0.126634i	0.827151	+	0.561979i	$0.189960\pi$
$984$		0			0
$985$	21.3297	−	12.3147i	0.679622	−	0.392380i
$986$	0.803468	−	1.39165i	0.0255876	−	0.0443191i
$987$		0			0
$988$	−20.4174	−	35.3640i	−0.649564	−	1.12508i
$989$	0.0712924	+	0.0411607i	0.00226697	+	0.00130883i
$990$		0			0
$991$	23.9244	+	41.4382i	0.759983	+	1.31633i	0.942859	+	0.333193i	$0.108126\pi$
$991$	23.9244	+	41.4382i	0.759983	+	1.31633i	−0.182876	+	0.983136i	$0.558541\pi$
$992$	−3.51034			−0.111453
$993$		0			0
$994$	−0.0628461	+	1.54624i	−0.00199336	+	0.0490437i
$995$	−14.4687	−	8.35349i	−0.458687	−	0.264823i
$996$		0			0
$997$	−41.1381	−	23.7511i	−1.30286	−	0.752204i	−0.321963	−	0.946752i	$-0.604343\pi$
$997$	−41.1381	−	23.7511i	−1.30286	−	0.752204i	−0.980893	+	0.194548i	$0.937676\pi$
$998$	−1.44389	+	0.833630i	−0.0457055	+	0.0263881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.t.c.341.8		32
3.2	odd	2		315.2.t.c.131.9	yes	32
7.3	odd	6		945.2.be.c.206.9		32
9.2	odd	6		945.2.be.c.656.9		32
9.7	even	3		315.2.be.c.236.8	yes	32
21.17	even	6		315.2.be.c.311.8	yes	32
63.38	even	6	inner	945.2.t.c.521.9		32
63.52	odd	6		315.2.t.c.101.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.8	✓	32	63.52	odd	6
315.2.t.c.131.9	yes	32	3.2	odd	2
315.2.be.c.236.8	yes	32	9.7	even	3
315.2.be.c.311.8	yes	32	21.17	even	6
945.2.t.c.341.8		32	1.1	even	1	trivial
945.2.t.c.521.9		32	63.38	even	6	inner
945.2.be.c.206.9		32	7.3	odd	6
945.2.be.c.656.9		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.103991i q^{2} +1.98919 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.107447 + 2.64357i) q^{7} -0.414839i q^{8} +O(q^{10})\)	\(q-0.103991i q^{2} +1.98919 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.107447 + 2.64357i) q^{7} -0.414839i q^{8} +(0.0900587 - 0.0519954i) q^{10} +(-2.53457 - 1.46334i) q^{11} +(-2.40454 - 1.38826i) q^{13} +(0.274907 + 0.0111734i) q^{14} +3.93523 q^{16} +(3.62041 + 6.27073i) q^{17} +(6.40301 + 3.69678i) q^{19} +(0.994593 + 1.72269i) q^{20} +(-0.152173 + 0.263572i) q^{22} +(0.159465 - 0.0920672i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.144366 + 0.250050i) q^{26} +(-0.213731 + 5.25855i) q^{28} +(1.84819 - 1.06705i) q^{29} -2.83342i q^{31} -1.23891i q^{32} +(0.652098 - 0.376489i) q^{34} +(-2.34312 + 1.22873i) q^{35} +(-1.26588 + 2.19256i) q^{37} +(0.384431 - 0.665854i) q^{38} +(0.359261 - 0.207419i) q^{40} +(-3.74637 + 6.48890i) q^{41} +(0.223536 + 0.387176i) q^{43} +(-5.04173 - 2.91085i) q^{44} +(-0.00957414 - 0.0165829i) q^{46} -0.588831 q^{47} +(-6.97691 - 0.568084i) q^{49} +(0.0900587 + 0.0519954i) q^{50} +(-4.78308 - 2.76151i) q^{52} +(-6.46888 + 3.73481i) q^{53} -2.92667i q^{55} +(1.09665 + 0.0445730i) q^{56} +(-0.110964 - 0.192195i) q^{58} +8.14263 q^{59} -12.6412i q^{61} -0.294649 q^{62} +7.74163 q^{64} -2.77652i q^{65} +3.10342 q^{67} +(7.20166 + 12.4736i) q^{68} +(0.127777 + 0.243663i) q^{70} +5.62459i q^{71} +(11.3988 - 6.58111i) q^{73} +(0.228006 + 0.131640i) q^{74} +(12.7368 + 7.35359i) q^{76} +(4.14076 - 6.54308i) q^{77} -9.11435 q^{79} +(1.96762 + 3.40801i) q^{80} +(0.674785 + 0.389587i) q^{82} +(4.90339 + 8.49292i) q^{83} +(-3.62041 + 6.27073i) q^{85} +(0.0402627 - 0.0232457i) q^{86} +(-0.607048 + 1.05144i) q^{88} +(7.98030 - 13.8223i) q^{89} +(3.92832 - 6.20740i) q^{91} +(0.317206 - 0.183139i) q^{92} +0.0612330i q^{94} +7.39356i q^{95} +(-1.69927 + 0.981074i) q^{97} +(-0.0590755 + 0.725534i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 16 q^{5} + q^{7}+O(q^{10}) \) 32 * q - 32 * q^4 + 16 * q^5 + q^7	\( 32 q - 32 q^{4} + 16 q^{5} + q^{7} - 3 q^{11} + 6 q^{13} + 15 q^{14} + 32 q^{16} + 3 q^{17} - 16 q^{20} - 21 q^{22} + 9 q^{23} - 16 q^{25} - 12 q^{26} - 31 q^{28} - 18 q^{29} - 30 q^{34} - q^{35} - q^{37} + 30 q^{38} - 6 q^{41} - 19 q^{43} - 21 q^{44} + 6 q^{46} + 30 q^{47} + 5 q^{49} + 21 q^{52} + 24 q^{53} - 30 q^{56} - 30 q^{59} + 76 q^{64} - 50 q^{67} + 3 q^{68} + 9 q^{70} + 12 q^{73} - 60 q^{74} + 54 q^{76} + 27 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} + 42 q^{83} - 3 q^{85} - 51 q^{86} + 42 q^{88} - 30 q^{89} - 57 q^{91} - 6 q^{92} - 42 q^{97} - 6 q^{98}+O(q^{100}) \) 32 * q - 32 * q^4 + 16 * q^5 + q^7 - 3 * q^11 + 6 * q^13 + 15 * q^14 + 32 * q^16 + 3 * q^17 - 16 * q^20 - 21 * q^22 + 9 * q^23 - 16 * q^25 - 12 * q^26 - 31 * q^28 - 18 * q^29 - 30 * q^34 - q^35 - q^37 + 30 * q^38 - 6 * q^41 - 19 * q^43 - 21 * q^44 + 6 * q^46 + 30 * q^47 + 5 * q^49 + 21 * q^52 + 24 * q^53 - 30 * q^56 - 30 * q^59 + 76 * q^64 - 50 * q^67 + 3 * q^68 + 9 * q^70 + 12 * q^73 - 60 * q^74 + 54 * q^76 + 27 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 + 42 * q^83 - 3 * q^85 - 51 * q^86 + 42 * q^88 - 30 * q^89 - 57 * q^91 - 6 * q^92 - 42 * q^97 - 6 * q^98

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