LMFDB - Embedded newform 189.4.h.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(37,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.983694 q^{2} -7.03235 q^{4} +(-9.35711 - 16.2070i) q^{5} +(-18.4989 + 0.890133i) q^{7} +14.7872 q^{8} +O(q^{10})$	\(q-0.983694 q^{2} -7.03235 q^{4} +(-9.35711 - 16.2070i) q^{5} +(-18.4989 + 0.890133i) q^{7} +14.7872 q^{8} +(9.20454 + 15.9427i) q^{10} +(11.7479 - 20.3480i) q^{11} +(-23.8730 + 41.3493i) q^{13} +(18.1972 - 0.875618i) q^{14} +41.7126 q^{16} +(47.7799 + 82.7573i) q^{17} +(28.4637 - 49.3006i) q^{19} +(65.8024 + 113.973i) q^{20} +(-11.5564 + 20.0163i) q^{22} +(16.3118 + 28.2528i) q^{23} +(-112.611 + 195.048i) q^{25} +(23.4838 - 40.6751i) q^{26} +(130.090 - 6.25972i) q^{28} +(-81.3794 - 140.953i) q^{29} -40.4543 q^{31} -159.330 q^{32} +(-47.0009 - 81.4079i) q^{34} +(187.522 + 291.482i) q^{35} +(-127.944 + 221.605i) q^{37} +(-27.9996 + 48.4967i) q^{38} +(-138.366 - 239.657i) q^{40} +(35.9678 - 62.2981i) q^{41} +(237.322 + 411.054i) q^{43} +(-82.6156 + 143.094i) q^{44} +(-16.0458 - 27.7921i) q^{46} +264.872 q^{47} +(341.415 - 32.9329i) q^{49} +(110.775 - 191.868i) q^{50} +(167.883 - 290.783i) q^{52} +(-13.1765 - 22.8223i) q^{53} -439.708 q^{55} +(-273.547 + 13.1626i) q^{56} +(80.0525 + 138.655i) q^{58} -39.1340 q^{59} +421.615 q^{61} +39.7947 q^{62} -176.969 q^{64} +893.531 q^{65} -369.434 q^{67} +(-336.005 - 581.978i) q^{68} +(-184.465 - 286.729i) q^{70} -685.628 q^{71} +(113.553 + 196.679i) q^{73} +(125.858 - 217.992i) q^{74} +(-200.167 + 346.699i) q^{76} +(-199.211 + 386.873i) q^{77} -686.729 q^{79} +(-390.310 - 676.037i) q^{80} +(-35.3813 + 61.2823i) q^{82} +(49.0800 + 85.0091i) q^{83} +(894.165 - 1548.74i) q^{85} +(-233.452 - 404.351i) q^{86} +(173.720 - 300.891i) q^{88} +(-529.104 + 916.436i) q^{89} +(404.818 - 786.165i) q^{91} +(-114.710 - 198.684i) q^{92} -260.553 q^{94} -1065.35 q^{95} +(-706.073 - 1222.95i) q^{97} +(-335.848 + 32.3959i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.983694			−0.347788			−0.173894	−	0.984764i	$-0.555635\pi$
$2$	−0.983694			−0.347788			−0.173894	+	0.984764i	$0.555635\pi$
$3$		0			0
$3$		0			0
$4$	−7.03235			−0.879043
$5$	−9.35711	−	16.2070i	−0.836926	−	1.44960i	−0.892453	−	0.451140i	$-0.851017\pi$
$5$	−9.35711	−	16.2070i	−0.836926	−	1.44960i	0.0555274	−	0.998457i	$-0.482316\pi$
$6$		0			0
$7$	−18.4989	+	0.890133i	−0.998844	+	0.0480626i
$7$	−18.4989	+	0.890133i	−0.998844	+	0.0480626i
$8$	14.7872			0.653510
$9$		0			0
$10$	9.20454	+	15.9427i	0.291073	+	0.504153i
$11$	11.7479	−	20.3480i	0.322013	−	0.557742i	−0.658890	−	0.752239i	$-0.728974\pi$
$11$	11.7479	−	20.3480i	0.322013	−	0.557742i	0.980903	+	0.194496i	$0.0623073\pi$
$12$		0			0
$13$	−23.8730	+	41.3493i	−0.509322	+	0.882172i	0.490619	+	0.871374i	$0.336771\pi$
$13$	−23.8730	+	41.3493i	−0.509322	+	0.882172i	−0.999942	+	0.0107981i	$0.996563\pi$
$14$	18.1972	−	0.875618i	0.347387	−	0.0167156i
$15$		0			0
$16$	41.7126			0.651760
$17$	47.7799	+	82.7573i	0.681667	+	1.18068i	0.974472	+	0.224510i	$0.0720780\pi$
$17$	47.7799	+	82.7573i	0.681667	+	1.18068i	−0.292805	+	0.956172i	$0.594589\pi$
$18$		0			0
$19$	28.4637	−	49.3006i	0.343686	−	0.595281i	−0.641428	−	0.767183i	$-0.721658\pi$
$19$	28.4637	−	49.3006i	0.343686	−	0.595281i	0.985114	+	0.171902i	$0.0549912\pi$
$20$	65.8024	+	113.973i	0.735694	+	1.27426i
$21$		0			0
$22$	−11.5564	+	20.0163i	−0.111992	+	0.193976i
$23$	16.3118	+	28.2528i	0.147880	+	0.256136i	0.930444	−	0.366435i	$-0.119422\pi$
$23$	16.3118	+	28.2528i	0.147880	+	0.256136i	−0.782564	+	0.622571i	$0.786088\pi$
$24$		0			0
$25$	−112.611	+	195.048i	−0.900889	+	1.56039i
$26$	23.4838	−	40.6751i	0.177136	−	0.306809i
$27$		0			0
$28$	130.090	−	6.25972i	0.878027	−	0.0422491i
$29$	−81.3794	−	140.953i	−0.521096	−	0.902564i	−0.999699	−	0.0245330i	$-0.992190\pi$
$29$	−81.3794	−	140.953i	−0.521096	−	0.902564i	0.478603	−	0.878031i	$-0.341143\pi$
$30$		0			0
$31$	−40.4543			−0.234381			−0.117190	−	0.993109i	$-0.537389\pi$
$31$	−40.4543			−0.234381			−0.117190	+	0.993109i	$0.537389\pi$
$32$	−159.330			−0.880184
$33$		0			0
$34$	−47.0009	−	81.4079i	−0.237076	−	0.410627i
$35$	187.522	+	291.482i	0.905630	+	1.40770i
$36$		0			0
$37$	−127.944	+	221.605i	−0.568482	+	0.984639i	0.428235	+	0.903667i	$0.359136\pi$
$37$	−127.944	+	221.605i	−0.568482	+	0.984639i	−0.996716	+	0.0809715i	$0.974198\pi$
$38$	−27.9996	+	48.4967i	−0.119530	+	0.207032i
$39$		0			0
$40$	−138.366	−	239.657i	−0.546939	−	0.947326i
$41$	35.9678	−	62.2981i	0.137006	−	0.237301i	−0.789356	−	0.613935i	$-0.789585\pi$
$41$	35.9678	−	62.2981i	0.137006	−	0.237301i	0.926362	+	0.376635i	$0.122919\pi$
$42$		0			0
$43$	237.322	+	411.054i	0.841658	+	1.45779i	0.888492	+	0.458892i	$0.151753\pi$
$43$	237.322	+	411.054i	0.841658	+	1.45779i	−0.0468344	+	0.998903i	$0.514913\pi$
$44$	−82.6156	+	143.094i	−0.283063	+	0.490280i
$45$		0			0
$46$	−16.0458	−	27.7921i	−0.0514310	−	0.0890810i
$47$	264.872			0.822033			0.411017	−	0.911628i	$-0.365174\pi$
$47$	264.872			0.822033			0.411017	+	0.911628i	$0.365174\pi$
$48$		0			0
$49$	341.415	−	32.9329i	0.995380	−	0.0960142i
$50$	110.775	−	191.868i	0.313319	−	0.542684i
$51$		0			0
$52$	167.883	−	290.783i	0.447716	−	0.775467i
$53$	−13.1765	−	22.8223i	−0.0341495	−	0.0591487i	0.848446	−	0.529283i	$-0.177539\pi$
$53$	−13.1765	−	22.8223i	−0.0341495	−	0.0591487i	−0.882595	+	0.470134i	$0.844206\pi$
$54$		0			0
$55$	−439.708			−1.07800
$56$	−273.547	+	13.1626i	−0.652754	+	0.0314094i
$57$		0			0
$58$	80.0525	+	138.655i	0.181231	+	0.313901i
$59$	−39.1340			−0.0863527			−0.0431764	−	0.999067i	$-0.513748\pi$
$59$	−39.1340			−0.0863527			−0.0431764	+	0.999067i	$0.513748\pi$
$60$		0			0
$61$	421.615			0.884955			0.442477	−	0.896780i	$-0.354100\pi$
$61$	421.615			0.884955			0.442477	+	0.896780i	$0.354100\pi$
$62$	39.7947			0.0815150
$63$		0			0
$64$	−176.969			−0.345642
$65$	893.531			1.70506
$66$		0			0
$67$	−369.434			−0.673634			−0.336817	−	0.941570i	$-0.609350\pi$
$67$	−369.434			−0.673634			−0.336817	+	0.941570i	$0.609350\pi$
$68$	−336.005	−	581.978i	−0.599215	−	1.03787i
$69$		0			0
$70$	−184.465	−	286.729i	−0.314968	−	0.489581i
$71$	−685.628			−1.14604			−0.573022	−	0.819540i	$-0.694229\pi$
$71$	−685.628			−1.14604			−0.573022	+	0.819540i	$0.694229\pi$
$72$		0			0
$73$	113.553	+	196.679i	0.182060	+	0.315336i	0.942582	−	0.333976i	$-0.108390\pi$
$73$	113.553	+	196.679i	0.182060	+	0.315336i	−0.760522	+	0.649312i	$0.775057\pi$
$74$	125.858	−	217.992i	0.197711	−	0.342446i
$75$		0			0
$76$	−200.167	+	346.699i	−0.302115	+	0.523278i
$77$	−199.211	+	386.873i	−0.294834	+	0.572575i
$78$		0			0
$79$	−686.729			−0.978013			−0.489006	−	0.872280i	$-0.662641\pi$
$79$	−686.729			−0.978013			−0.489006	+	0.872280i	$0.662641\pi$
$80$	−390.310	−	676.037i	−0.545475	−	0.944790i
$81$		0			0
$82$	−35.3813	+	61.2823i	−0.0476490	+	0.0825304i
$83$	49.0800	+	85.0091i	0.0649064	+	0.112421i	0.896652	−	0.442735i	$-0.145992\pi$
$83$	49.0800	+	85.0091i	0.0649064	+	0.112421i	−0.831746	+	0.555156i	$0.812658\pi$
$84$		0			0
$85$	894.165	−	1548.74i	1.14101	−	1.97629i
$86$	−233.452	−	404.351i	−0.292719	−	0.507004i
$87$		0			0
$88$	173.720	−	300.891i	0.210438	−	0.364490i
$89$	−529.104	+	916.436i	−0.630168	+	1.09148i	0.357349	+	0.933971i	$0.383681\pi$
$89$	−529.104	+	916.436i	−0.630168	+	1.09148i	−0.987517	+	0.157512i	$0.949653\pi$
$90$		0			0
$91$	404.818	−	786.165i	0.466334	−	0.905632i
$92$	−114.710	−	198.684i	−0.129993	−	0.225154i
$93$		0			0
$94$	−260.553			−0.285894
$95$	−1065.35			−1.15056
$96$		0			0
$97$	−706.073	−	1222.95i	−0.739081	−	1.28013i	−0.952910	−	0.303254i	$-0.901927\pi$
$97$	−706.073	−	1222.95i	−0.739081	−	1.28013i	0.213829	−	0.976871i	$-0.431407\pi$
$98$	−335.848	+	32.3959i	−0.346182	+	0.0333926i
$99$		0			0
$100$	791.920	−	1371.65i	0.791920	−	1.37165i
$101$	700.731	−	1213.70i	0.690350	−	1.19572i	−0.281374	−	0.959598i	$-0.590790\pi$
$101$	700.731	−	1213.70i	0.690350	−	1.19572i	0.971723	−	0.236122i	$-0.0758766\pi$
$102$		0			0
$103$	1000.91	+	1733.63i	0.957500	+	1.65844i	0.728539	+	0.685004i	$0.240200\pi$
$103$	1000.91	+	1733.63i	0.957500	+	1.65844i	0.228961	+	0.973436i	$0.426467\pi$
$104$	−353.016	+	611.442i	−0.332847	+	0.576508i
$105$		0			0
$106$	12.9616	+	22.4502i	0.0118768	+	0.0205712i
$107$	−58.5775	+	101.459i	−0.0529243	+	0.0916677i	−0.891274	−	0.453465i	$-0.850188\pi$
$107$	−58.5775	+	101.459i	−0.0529243	+	0.0916677i	0.838350	+	0.545133i	$0.183521\pi$
$108$		0			0
$109$	348.784	+	604.111i	0.306490	+	0.530856i	0.977592	−	0.210509i	$-0.0675121\pi$
$109$	348.784	+	604.111i	0.306490	+	0.530856i	−0.671102	+	0.741365i	$0.734179\pi$
$110$	432.538			0.374917
$111$		0			0
$112$	−771.636	+	37.1298i	−0.651007	+	0.0313253i
$113$	401.566	−	695.532i	0.334302	−	0.579028i	−0.649048	−	0.760747i	$-0.724833\pi$
$113$	401.566	−	695.532i	0.334302	−	0.579028i	0.983351	+	0.181719i	$0.0581661\pi$
$114$		0			0
$115$	305.262	−	528.730i	0.247529	−	0.428733i
$116$	572.288	+	991.232i	0.458066	+	0.793393i
$117$		0			0
$118$	38.4959			0.0300325
$119$	−957.539	−	1488.38i	−0.737626	−	1.14655i
$120$		0			0
$121$	389.471	+	674.584i	0.292616	+	0.506825i
$122$	−414.740			−0.307777
$123$		0			0
$124$	284.489			0.206031
$125$	1875.58			1.34206
$126$		0			0
$127$	−1151.01			−0.804220			−0.402110	−	0.915591i	$-0.631723\pi$
$127$	−1151.01			−0.804220			−0.402110	+	0.915591i	$0.631723\pi$
$128$	1448.73			1.00039
$129$		0			0
$130$	−878.961			−0.593000
$131$	1259.17	+	2180.94i	0.839802	+	1.45458i	0.890060	+	0.455843i	$0.150662\pi$
$131$	1259.17	+	2180.94i	0.839802	+	1.45458i	−0.0502587	+	0.998736i	$0.516005\pi$
$132$		0			0
$133$	−482.662	+	937.342i	−0.314678	+	0.611111i
$134$	363.410			0.234282
$135$		0			0
$136$	706.533	+	1223.75i	0.445476	+	0.771587i
$137$	−1412.19	+	2445.99i	−0.880669	+	1.52536i	−0.0300713	+	0.999548i	$0.509573\pi$
$137$	−1412.19	+	2445.99i	−0.880669	+	1.52536i	−0.850598	+	0.525816i	$0.823760\pi$
$138$		0			0
$139$	−760.305	+	1316.89i	−0.463944	+	0.803575i	−0.999153	−	0.0411450i	$-0.986899\pi$
$139$	−760.305	+	1316.89i	−0.463944	+	0.803575i	0.535209	+	0.844720i	$0.320233\pi$
$140$	−1318.72	−	2049.80i	−0.796088	−	1.23743i
$141$		0			0
$142$	674.448			0.398581
$143$	560.919	+	971.539i	0.328017	+	0.568141i
$144$		0			0
$145$	−1522.95	+	2637.83i	−0.872237	+	1.51076i
$146$	−111.701	−	193.472i	−0.0633182	−	0.109670i
$147$		0			0
$148$	899.744	−	1558.40i	0.499720	−	0.865540i
$149$	−682.896	−	1182.81i	−0.375470	−	0.650333i	0.614927	−	0.788584i	$-0.289185\pi$
$149$	−682.896	−	1182.81i	−0.375470	−	0.650333i	−0.990397	+	0.138251i	$0.955852\pi$
$150$		0			0
$151$	−1283.05	+	2222.31i	−0.691478	+	1.19768i	0.279875	+	0.960036i	$0.409707\pi$
$151$	−1283.05	+	2222.31i	−0.691478	+	1.19768i	−0.971354	+	0.237639i	$0.923626\pi$
$152$	420.900	−	729.020i	0.224602	−	0.389022i
$153$		0			0
$154$	195.963	−	380.565i	0.102540	−	0.199135i
$155$	378.535	+	655.643i	0.196159	+	0.339758i
$156$		0			0
$157$	−1338.35			−0.680329			−0.340164	−	0.940366i	$-0.610483\pi$
$157$	−1338.35			−0.680329			−0.340164	+	0.940366i	$0.610483\pi$
$158$	675.531			0.340142
$159$		0			0
$160$	1490.87	+	2582.27i	0.736649	+	1.27591i
$161$	−326.898	−	508.125i	−0.160020	−	0.248732i
$162$		0			0
$163$	315.058	−	545.696i	0.151394	−	0.262222i	−0.780346	−	0.625348i	$-0.784957\pi$
$163$	315.058	−	545.696i	0.151394	−	0.262222i	0.931740	+	0.363126i	$0.118290\pi$
$164$	−252.938	+	438.102i	−0.120434	+	0.208598i
$165$		0			0
$166$	−48.2797	−	83.6230i	−0.0225737	−	0.0390988i
$167$	−147.049	+	254.696i	−0.0681375	+	0.118018i	−0.898081	−	0.439829i	$-0.855039\pi$
$167$	−147.049	+	254.696i	−0.0681375	+	0.118018i	0.829944	+	0.557847i	$0.188372\pi$
$168$		0			0
$169$	−41.3439	−	71.6098i	−0.0188184	−	0.0325944i
$170$	−879.585	+	1523.49i	−0.396830	+	0.687329i
$171$		0			0
$172$	−1668.93	−	2890.67i	−0.739854	−	1.28146i
$173$	1849.52			0.812809			0.406405	−	0.913693i	$-0.366782\pi$
$173$	1849.52			0.812809			0.406405	+	0.913693i	$0.366782\pi$
$174$		0			0
$175$	1909.56	−	3708.41i	0.824851	−	1.60188i
$176$	490.038	−	848.771i	0.209875	−	0.363514i
$177$		0			0
$178$	520.477	−	901.493i	0.219165	−	0.379605i
$179$	1180.05	+	2043.91i	0.492744	+	0.853457i	0.999965	−	0.00835864i	$-0.00266067\pi$
$179$	1180.05	+	2043.91i	0.492744	+	0.853457i	−0.507221	+	0.861816i	$0.669327\pi$
$180$		0			0
$181$	3236.18			1.32897			0.664485	−	0.747301i	$-0.268651\pi$
$181$	3236.18			1.32897			0.664485	+	0.747301i	$0.268651\pi$
$182$	−398.217	+	773.346i	−0.162186	+	0.314968i
$183$		0			0
$184$	241.206	+	417.781i	0.0966410	+	0.167387i
$185$	4788.74			1.90311
$186$		0			0
$187$	2245.27			0.878022
$188$	−1862.67			−0.722603
$189$		0			0
$190$	1047.98			0.400150
$191$	−1180.13			−0.447075			−0.223538	−	0.974695i	$-0.571761\pi$
$191$	−1180.13			−0.447075			−0.223538	+	0.974695i	$0.571761\pi$
$192$		0			0
$193$	−3255.38			−1.21413			−0.607065	−	0.794652i	$-0.707653\pi$
$193$	−3255.38			−1.21413			−0.607065	+	0.794652i	$0.707653\pi$
$194$	694.560	+	1203.01i	0.257044	+	0.445213i
$195$		0			0
$196$	−2400.95	+	231.595i	−0.874982	+	0.0844006i
$197$	−2361.04			−0.853895			−0.426948	−	0.904276i	$-0.640411\pi$
$197$	−2361.04			−0.853895			−0.426948	+	0.904276i	$0.640411\pi$
$198$		0			0
$199$	859.969	+	1489.51i	0.306340	+	0.530596i	0.977559	−	0.210663i	$-0.0675623\pi$
$199$	859.969	+	1489.51i	0.306340	+	0.530596i	−0.671219	+	0.741259i	$0.734229\pi$
$200$	−1665.21	+	2884.22i	−0.588739	+	1.01973i
$201$		0			0
$202$	−689.305	+	1193.91i	−0.240096	+	0.415858i
$203$	1630.89	+	2535.04i	0.563873	+	0.876476i
$204$		0			0
$205$	−1346.22			−0.458654
$206$	−984.589	−	1705.36i	−0.333008	−	0.576786i
$207$		0			0
$208$	−995.808	+	1724.79i	−0.331956	+	0.574965i
$209$	−668.781	−	1158.36i	−0.221342	−	0.383376i
$210$		0			0
$211$	−1266.79	+	2194.14i	−0.413315	+	0.715882i	−0.995250	−	0.0973529i	$-0.968962\pi$
$211$	−1266.79	+	2194.14i	−0.413315	+	0.715882i	0.581935	+	0.813235i	$0.302296\pi$
$212$	92.6614	+	160.494i	0.0300189	+	0.0519943i
$213$		0			0
$214$	57.6224	−	99.8049i	0.0184065	−	0.0318810i
$215$	4441.30	−	7692.56i	1.40881	−	2.44013i
$216$		0			0
$217$	748.358	−	36.0097i	0.234110	−	0.0112650i
$218$	−343.096	−	594.260i	−0.106594	−	0.184626i
$219$		0			0
$220$	3092.18			0.947611
$221$	−4562.61			−1.38875
$222$		0			0
$223$	−199.300	−	345.198i	−0.0598481	−	0.103660i	0.834549	−	0.550934i	$-0.185728\pi$
$223$	−199.300	−	345.198i	−0.0598481	−	0.103660i	−0.894397	+	0.447274i	$0.852395\pi$
$224$	2947.43	−	141.825i	0.879167	−	0.0423040i
$225$		0			0
$226$	−395.018	+	684.191i	−0.116266	+	0.201379i
$227$	−1388.39	+	2404.76i	−0.405949	+	0.703124i	−0.994431	−	0.105386i	$-0.966392\pi$
$227$	−1388.39	+	2404.76i	−0.405949	+	0.703124i	0.588482	+	0.808510i	$0.299726\pi$
$228$		0			0
$229$	−502.539	−	870.423i	−0.145016	−	0.251175i	0.784363	−	0.620302i	$-0.212990\pi$
$229$	−502.539	−	870.423i	−0.145016	−	0.251175i	−0.929379	+	0.369127i	$0.879657\pi$
$230$	−300.285	+	520.108i	−0.0860878	+	0.149108i
$231$		0			0
$232$	−1203.38	−	2084.31i	−0.340541	−	0.589834i
$233$	1139.41	−	1973.52i	0.320367	−	0.554891i	−0.660197	−	0.751092i	$-0.729527\pi$
$233$	1139.41	−	1973.52i	0.320367	−	0.554891i	0.980564	+	0.196201i	$0.0628606\pi$
$234$		0			0
$235$	−2478.44	−	4292.78i	−0.687981	−	1.19162i
$236$	275.204			0.0759078
$237$		0			0
$238$	941.926	+	1464.12i	0.256538	+	0.398758i
$239$	1125.17	−	1948.86i	0.304525	−	0.527453i	−0.672630	−	0.739979i	$-0.734836\pi$
$239$	1125.17	−	1948.86i	0.304525	−	0.527453i	0.977155	+	0.212526i	$0.0681689\pi$
$240$		0			0
$241$	−598.261	+	1036.22i	−0.159906	+	0.276966i	−0.934835	−	0.355083i	$-0.884453\pi$
$241$	−598.261	+	1036.22i	−0.159906	+	0.276966i	0.774928	+	0.632049i	$0.217786\pi$
$242$	−383.121	−	663.585i	−0.101768	−	0.176268i
$243$		0			0
$244$	−2964.94			−0.777913
$245$	−3728.40	−	5225.16i	−0.972241	−	1.36254i
$246$		0			0
$247$	1359.03	+	2353.91i	0.350094	+	0.606380i
$248$	−598.207			−0.153170
$249$		0			0
$250$	−1845.00			−0.466752
$251$	−1826.87			−0.459407			−0.229704	−	0.973261i	$-0.573776\pi$
$251$	−1826.87			−0.459407			−0.229704	+	0.973261i	$0.573776\pi$
$252$		0			0
$253$	766.520			0.190477
$254$	1132.25			0.279699
$255$		0			0
$256$	−9.35280			−0.00228340
$257$	1186.37	+	2054.85i	0.287952	+	0.498748i	0.973321	−	0.229449i	$-0.0736923\pi$
$257$	1186.37	+	2054.85i	0.287952	+	0.498748i	−0.685369	+	0.728196i	$0.740359\pi$
$258$		0			0
$259$	2169.55	−	4213.33i	0.520500	−	1.01082i
$260$	−6283.62			−1.49882
$261$		0			0
$262$	−1238.64	−	2145.38i	−0.292073	−	0.505886i
$263$	−856.469	+	1483.45i	−0.200807	+	0.347807i	−0.948789	−	0.315912i	$-0.897690\pi$
$263$	−856.469	+	1483.45i	−0.200807	+	0.347807i	0.747982	+	0.663719i	$0.231023\pi$
$264$		0			0
$265$	−246.587	+	427.101i	−0.0571612	+	0.0990062i
$266$	474.792	−	922.058i	0.109441	−	0.212538i
$267$		0			0
$268$	2597.98			0.592154
$269$	−188.806	−	327.021i	−0.0427943	−	0.0741220i	0.843835	−	0.536603i	$-0.180293\pi$
$269$	−188.806	−	327.021i	−0.0427943	−	0.0741220i	−0.886629	+	0.462481i	$0.846959\pi$
$270$		0			0
$271$	871.508	−	1509.50i	0.195352	−	0.338359i	−0.751664	−	0.659546i	$-0.770748\pi$
$271$	871.508	−	1509.50i	0.195352	−	0.338359i	0.947016	+	0.321187i	$0.104082\pi$
$272$	1993.03	+	3452.03i	0.444283	+	0.769521i
$273$		0			0
$274$	1389.17	−	2406.10i	0.306287	−	0.530504i
$275$	2645.90	+	4582.83i	0.580195	+	1.00493i
$276$		0			0
$277$	2582.68	−	4473.33i	0.560210	−	0.970311i	−0.437268	−	0.899331i	$-0.644054\pi$
$277$	2582.68	−	4473.33i	0.560210	−	0.970311i	0.997478	−	0.0709803i	$-0.0226127\pi$
$278$	747.908	−	1295.41i	0.161354	−	0.279474i
$279$		0			0
$280$	2772.93	+	4310.21i	0.591838	+	0.919944i
$281$	−2505.60	−	4339.83i	−0.531927	−	0.921325i	−0.999305	−	0.0372673i	$-0.988135\pi$
$281$	−2505.60	−	4339.83i	−0.531927	−	0.921325i	0.467378	−	0.884057i	$-0.345199\pi$
$282$		0			0
$283$	7359.29			1.54581			0.772906	−	0.634521i	$-0.218803\pi$
$283$	7359.29			1.54581			0.772906	+	0.634521i	$0.218803\pi$
$284$	4821.57			1.00742
$285$		0			0
$286$	−551.772	−	955.698i	−0.114080	−	0.197593i
$287$	−609.910	+	1184.46i	−0.125442	+	0.243611i
$288$		0			0
$289$	−2109.35	+	3653.49i	−0.429340	+	0.743638i
$290$	1498.12	−	2594.82i	0.303354	−	0.525424i
$291$		0			0
$292$	−798.542	−	1383.12i	−0.160038	−	0.277194i
$293$	−2022.15	+	3502.47i	−0.403193	+	0.698350i	−0.994109	−	0.108382i	$-0.965433\pi$
$293$	−2022.15	+	3502.47i	−0.403193	+	0.698350i	0.590917	+	0.806733i	$0.298766\pi$
$294$		0			0
$295$	366.181	+	634.244i	0.0722708	+	0.125177i
$296$	−1891.93	+	3276.93i	−0.371508	+	0.643471i
$297$		0			0
$298$	671.761	+	1163.52i	0.130584	+	0.226178i
$299$	−1557.65			−0.301274
$300$		0			0
$301$	−4756.08	−	7392.78i	−0.910751	−	1.41566i
$302$	1262.13	−	2186.07i	0.240488	−	0.416538i
$303$		0			0
$304$	1187.30	−	2056.46i	0.224001	−	0.387980i
$305$	−3945.10	−	6833.11i	−0.740641	−	1.28283i
$306$		0			0
$307$	116.626			0.0216813			0.0108407	−	0.999941i	$-0.496549\pi$
$307$	116.626			0.0216813			0.0108407	+	0.999941i	$0.496549\pi$
$308$	1400.92	−	2720.62i	0.259172	−	0.503318i
$309$		0			0
$310$	−372.363	−	644.952i	−0.0682220	−	0.118164i
$311$	−9349.76			−1.70475			−0.852373	−	0.522934i	$-0.824837\pi$
$311$	−9349.76			−1.70475			−0.852373	+	0.522934i	$0.824837\pi$
$312$		0			0
$313$	3154.98			0.569744			0.284872	−	0.958566i	$-0.408049\pi$
$313$	3154.98			0.569744			0.284872	+	0.958566i	$0.408049\pi$
$314$	1316.52			0.236610
$315$		0			0
$316$	4829.31			0.859716
$317$	−8372.50			−1.48343			−0.741714	−	0.670717i	$-0.765987\pi$
$317$	−8372.50			−1.48343			−0.741714	+	0.670717i	$0.765987\pi$
$318$		0			0
$319$	−3824.16			−0.671198
$320$	1655.92	+	2868.13i	0.289277	+	0.501042i
$321$		0			0
$322$	321.568	+	499.840i	0.0556530	+	0.0865062i
$323$	5439.98			0.937117
$324$		0			0
$325$	−5376.74	−	9312.78i	−0.917685	−	1.58948i
$326$	−309.921	+	536.798i	−0.0526531	+	0.0911979i
$327$		0			0
$328$	531.865	−	921.216i	0.0895345	−	0.155078i
$329$	−4899.83	+	235.771i	−0.821083	+	0.0395091i
$330$		0			0
$331$	−1780.45			−0.295656			−0.147828	−	0.989013i	$-0.547228\pi$
$331$	−1780.45			−0.295656			−0.147828	+	0.989013i	$0.547228\pi$
$332$	−345.148	−	597.813i	−0.0570555	−	0.0988231i
$333$		0			0
$334$	144.651	−	250.543i	0.0236974	−	0.0410451i
$335$	3456.83	+	5987.41i	0.563782	+	0.976499i
$336$		0			0
$337$	2592.47	−	4490.29i	0.419053	−	0.725821i	−0.576792	−	0.816891i	$-0.695696\pi$
$337$	2592.47	−	4490.29i	0.419053	−	0.725821i	0.995844	+	0.0910707i	$0.0290289\pi$
$338$	40.6698	+	70.4422i	0.00654481	+	0.0113359i
$339$		0			0
$340$	−6288.07	+	10891.3i	−1.00300	+	1.73724i
$341$	−475.255	+	823.166i	−0.0754736	+	0.130724i
$342$		0			0
$343$	−6286.48	+	913.125i	−0.989615	+	0.143744i
$344$	3509.34	+	6078.35i	0.550031	+	0.952682i
$345$		0			0
$346$	−1819.36			−0.282686
$347$	3849.42			0.595526			0.297763	−	0.954640i	$-0.403760\pi$
$347$	3849.42			0.595526			0.297763	+	0.954640i	$0.403760\pi$
$348$		0			0
$349$	1083.53	+	1876.72i	0.166189	+	0.287847i	0.937077	−	0.349123i	$-0.113521\pi$
$349$	1083.53	+	1876.72i	0.166189	+	0.287847i	−0.770888	+	0.636971i	$0.780187\pi$
$350$	−1878.42	+	3647.94i	−0.286874	+	0.557116i
$351$		0			0
$352$	−1871.80	+	3242.06i	−0.283431	+	0.490916i
$353$	2831.82	−	4904.86i	0.426977	−	0.739545i	−0.569626	−	0.821904i	$-0.692912\pi$
$353$	2831.82	−	4904.86i	0.426977	−	0.739545i	0.996603	+	0.0823587i	$0.0262453\pi$
$354$		0			0
$355$	6415.50	+	11112.0i	0.959153	+	1.66130i
$356$	3720.85	−	6444.69i	0.553945	−	0.959461i
$357$		0			0
$358$	−1160.81	−	2010.58i	−0.171371	−	0.296823i
$359$	3691.47	−	6393.81i	0.542697	−	0.939979i	−0.456051	−	0.889954i	$-0.650737\pi$
$359$	3691.47	−	6393.81i	0.542697	−	0.939979i	0.998748	−	0.0500250i	$-0.0159301\pi$
$360$		0			0
$361$	1809.13	+	3133.51i	0.263760	+	0.456846i
$362$	−3183.42			−0.462201
$363$		0			0
$364$	−2846.82	+	5528.59i	−0.409928	+	0.796090i
$365$	2125.05	−	3680.70i	0.304741	−	0.527826i
$366$		0			0
$367$	−5955.70	+	10315.6i	−0.847098	+	1.46722i	0.0366883	+	0.999327i	$0.488319\pi$
$367$	−5955.70	+	10315.6i	−0.847098	+	1.46722i	−0.883786	+	0.467890i	$0.845014\pi$
$368$	680.407	+	1178.50i	0.0963823	+	0.166939i
$369$		0			0
$370$	−4710.65			−0.661879
$371$	264.064	+	410.457i	0.0369529	+	0.0574390i
$372$		0			0
$373$	−3468.84	−	6008.21i	−0.481528	−	0.834031i	0.518247	−	0.855231i	$-0.326585\pi$
$373$	−3468.84	−	6008.21i	−0.481528	−	0.834031i	−0.999775	+	0.0211999i	$0.993251\pi$
$374$	−2208.65			−0.305366
$375$		0			0
$376$	3916.73			0.537207
$377$	7771.09			1.06162
$378$		0			0
$379$	6490.60			0.879683			0.439841	−	0.898075i	$-0.355035\pi$
$379$	6490.60			0.879683			0.439841	+	0.898075i	$0.355035\pi$
$380$	7491.93			1.01139
$381$		0			0
$382$	1160.89			0.155488
$383$	3703.61	+	6414.84i	0.494114	+	0.855830i	0.999977	−	0.00678376i	$-0.00215935\pi$
$383$	3703.61	+	6414.84i	0.494114	+	0.855830i	−0.505863	+	0.862614i	$0.668826\pi$
$384$		0			0
$385$	8134.09	−	391.398i	1.07676	−	0.0518117i
$386$	3202.29			0.422260
$387$		0			0
$388$	4965.35	+	8600.24i	0.649684	+	1.12529i
$389$	−2037.65	+	3529.31i	−0.265586	+	0.460008i	−0.967717	−	0.252039i	$-0.918899\pi$
$389$	−2037.65	+	3529.31i	−0.265586	+	0.460008i	0.702131	+	0.712048i	$0.252232\pi$
$390$		0			0
$391$	−1558.75	+	2699.84i	−0.201610	+	0.349199i
$392$	5048.59	−	486.986i	0.650490	−	0.0627462i
$393$		0			0
$394$	2322.54			0.296975
$395$	6425.80	+	11129.8i	0.818524	+	1.41773i
$396$		0			0
$397$	4255.62	−	7370.95i	0.537994	−	0.931833i	−0.461018	−	0.887391i	$-0.652516\pi$
$397$	4255.62	−	7370.95i	0.537994	−	0.931833i	0.999012	−	0.0444418i	$-0.0141509\pi$
$398$	−845.947	−	1465.22i	−0.106541	−	0.184535i
$399$		0			0
$400$	−4697.31	+	8135.97i	−0.587163	+	1.01700i
$401$	−4158.54	−	7202.80i	−0.517874	−	0.896984i	−0.999784	−	0.0207639i	$-0.993390\pi$
$401$	−4158.54	−	7202.80i	−0.517874	−	0.896984i	0.481910	−	0.876221i	$-0.339943\pi$
$402$		0			0
$403$	965.767	−	1672.76i	0.119375	−	0.206764i
$404$	−4927.78	+	8535.17i	−0.606847	+	1.05109i
$405$		0			0
$406$	−1604.30	−	2493.70i	−0.196109	−	0.304828i
$407$	3006.15	+	5206.81i	0.366117	+	0.634133i
$408$		0			0
$409$	−6180.42			−0.747193			−0.373596	−	0.927591i	$-0.621876\pi$
$409$	−6180.42			−0.747193			−0.373596	+	0.927591i	$0.621876\pi$
$410$	1324.27			0.159515
$411$		0			0
$412$	−7038.74	−	12191.5i	−0.841684	−	1.45784i
$413$	723.934	−	34.8344i	0.0862529	−	0.00415034i
$414$		0			0
$415$	918.495	−	1590.88i	0.108644	−	0.188176i
$416$	3803.70	−	6588.20i	0.448297	−	0.776474i
$417$		0			0
$418$	657.876	+	1139.47i	0.0769803	+	0.133334i
$419$	1187.31	−	2056.48i	0.138434	−	0.239775i	−0.788470	−	0.615073i	$-0.789126\pi$
$419$	1187.31	−	2056.48i	0.138434	−	0.239775i	0.926904	+	0.375298i	$0.122460\pi$
$420$		0			0
$421$	−272.600	−	472.158i	−0.0315576	−	0.0546593i	0.849815	−	0.527081i	$-0.176713\pi$
$421$	−272.600	−	472.158i	−0.0315576	−	0.0546593i	−0.881373	+	0.472421i	$0.843380\pi$
$422$	1246.13	−	2158.37i	0.143746	−	0.248976i
$423$		0			0
$424$	−194.843	−	337.478i	−0.0223170	−	0.0386543i
$425$	−21522.2			−2.45642
$426$		0			0
$427$	−7799.39	+	375.293i	−0.883932	+	0.0425333i
$428$	411.938	−	713.497i	0.0465228	−	0.0805798i
$429$		0			0
$430$	−4368.88	+	7567.12i	−0.489968	+	0.848649i
$431$	−1440.19	−	2494.49i	−0.160955	−	0.278783i	0.774256	−	0.632872i	$-0.218124\pi$
$431$	−1440.19	−	2494.49i	−0.160955	−	0.278783i	−0.935212	+	0.354090i	$0.884791\pi$
$432$		0			0
$433$	12051.3			1.33753			0.668765	−	0.743474i	$-0.266823\pi$
$433$	12051.3			1.33753			0.668765	+	0.743474i	$0.266823\pi$
$434$	−736.156	+	35.4225i	−0.0814208	+	0.00391782i
$435$		0			0
$436$	−2452.77	−	4248.32i	−0.269418	−	0.466645i
$437$	1857.18			0.203297
$438$		0			0
$439$	−11432.1			−1.24288			−0.621440	−	0.783462i	$-0.713452\pi$
$439$	−11432.1			−1.24288			−0.621440	+	0.783462i	$0.713452\pi$
$440$	−6502.06			−0.704485
$441$		0			0
$442$	4488.21			0.482992
$443$	12333.1			1.32271			0.661356	−	0.750073i	$-0.269981\pi$
$443$	12333.1			1.32271			0.661356	+	0.750073i	$0.269981\pi$
$444$		0			0
$445$	19803.6			2.10962
$446$	196.051	+	339.569i	0.0208145	+	0.0360517i
$447$		0			0
$448$	3273.72	−	157.526i	0.345243	−	0.0166125i
$449$	−7715.04			−0.810902			−0.405451	−	0.914117i	$-0.632886\pi$
$449$	−7715.04			−0.810902			−0.405451	+	0.914117i	$0.632886\pi$
$450$		0			0
$451$	−845.096	−	1463.75i	−0.0882351	−	0.152828i
$452$	−2823.95	+	4891.22i	−0.293866	+	0.508991i
$453$		0			0
$454$	1365.75	−	2365.54i	0.141184	−	0.244539i
$455$	−16529.3	+	795.361i	−1.70309	+	0.0819497i
$456$		0			0
$457$	−6538.69			−0.669293			−0.334647	−	0.942344i	$-0.608617\pi$
$457$	−6538.69			−0.669293			−0.334647	+	0.942344i	$0.608617\pi$
$458$	494.345	+	856.230i	0.0504350	+	0.0873559i
$459$		0			0
$460$	−2146.71	+	3718.21i	−0.217589	+	0.376875i
$461$	4562.67	+	7902.77i	0.460965	+	0.798414i	0.999009	−	0.0445022i	$-0.0141702\pi$
$461$	4562.67	+	7902.77i	0.460965	+	0.798414i	−0.538045	+	0.842916i	$0.680837\pi$
$462$		0			0
$463$	−6181.47	+	10706.6i	−0.620469	+	1.07468i	0.368929	+	0.929458i	$0.379725\pi$
$463$	−6181.47	+	10706.6i	−0.620469	+	1.07468i	−0.989398	+	0.145227i	$0.953609\pi$
$464$	−3394.55	−	5879.53i	−0.339629	−	0.588255i
$465$		0			0
$466$	−1120.83	+	1941.34i	−0.111420	+	0.192985i
$467$	6161.47	−	10672.0i	0.610532	−	1.05747i	−0.380618	−	0.924732i	$-0.624289\pi$
$467$	6161.47	−	10672.0i	0.610532	−	1.05747i	0.991151	−	0.132741i	$-0.0423778\pi$
$468$		0			0
$469$	6834.10	−	328.845i	0.672856	−	0.0323766i
$470$	2438.03	+	4222.78i	0.239272	+	0.414431i
$471$		0			0
$472$	−578.683			−0.0564323
$473$	11152.2			1.08410
$474$		0			0
$475$	6410.66	+	11103.6i	0.619245	+	1.07256i
$476$	6733.75	+	10466.8i	0.648405	+	1.00787i
$477$		0			0
$478$	−1106.83	+	1917.08i	−0.105910	+	0.183442i
$479$	2579.54	−	4467.90i	0.246059	−	0.426187i	−0.716370	−	0.697721i	$-0.754198\pi$
$479$	2579.54	−	4467.90i	0.246059	−	0.426187i	0.962429	+	0.271534i	$0.0875310\pi$
$480$		0			0
$481$	−6108.81	−	10580.8i	−0.579081	−	1.00300i
$482$	588.506	−	1019.32i	0.0556135	−	0.0963255i
$483$		0			0
$484$	−2738.90	−	4743.91i	−0.257222	−	0.445521i
$485$	−13213.6	+	22886.6i	−1.23711	+	2.14274i
$486$		0			0
$487$	2035.57	+	3525.71i	0.189405	+	0.328059i	0.945052	−	0.326920i	$-0.106011\pi$
$487$	2035.57	+	3525.71i	0.189405	+	0.328059i	−0.755647	+	0.654979i	$0.772677\pi$
$488$	6234.52			0.578326
$489$		0			0
$490$	3667.61	+	5139.96i	0.338134	+	0.473877i
$491$	−4038.87	+	6995.52i	−0.371225	+	0.642981i	−0.989754	−	0.142781i	$-0.954396\pi$
$491$	−4038.87	+	6995.52i	−0.371225	+	0.642981i	0.618529	+	0.785762i	$0.287729\pi$
$492$		0			0
$493$	7776.61	−	13469.5i	0.710427	−	1.23050i
$494$	−1336.87	−	2315.53i	−0.121758	−	0.210892i
$495$		0			0
$496$	−1687.46			−0.152760
$497$	12683.3	−	610.300i	1.14472	−	0.0550819i
$498$		0			0
$499$	2872.21	+	4974.82i	0.257671	+	0.446300i	0.965618	−	0.259967i	$-0.0837115\pi$
$499$	2872.21	+	4974.82i	0.257671	+	0.446300i	−0.707946	+	0.706266i	$0.750378\pi$
$500$	−13189.7			−1.17973
$501$		0			0
$502$	1797.08			0.159776
$503$	−5458.59			−0.483870			−0.241935	−	0.970292i	$-0.577782\pi$
$503$	−5458.59			−0.483870			−0.241935	+	0.970292i	$0.577782\pi$
$504$		0			0
$505$	−26227.3			−2.31109
$506$	−754.021			−0.0662457
$507$		0			0
$508$	8094.33			0.706944
$509$	−2310.16	−	4001.31i	−0.201171	−	0.348438i	0.747735	−	0.663997i	$-0.231141\pi$
$509$	−2310.16	−	4001.31i	−0.201171	−	0.348438i	−0.948906	+	0.315559i	$0.897808\pi$
$510$		0			0
$511$	−2275.67	−	3537.26i	−0.197005	−	0.306222i
$512$	−11580.6			−0.999600
$513$		0			0
$514$	−1167.02	−	2021.35i	−0.100146	−	0.173459i
$515$	18731.2	−	32443.5i	1.60271	−	2.77598i
$516$		0			0
$517$	3111.70	−	5389.63i	0.264705	−	0.458483i
$518$	−2134.18	+	4144.63i	−0.181024	+	0.351553i
$519$		0			0
$520$	13212.8			1.11427
$521$	10010.3	+	17338.3i	0.841763	+	1.45798i	0.888403	+	0.459064i	$0.151815\pi$
$521$	10010.3	+	17338.3i	0.841763	+	1.45798i	−0.0466408	+	0.998912i	$0.514852\pi$
$522$		0			0
$523$	1592.45	−	2758.20i	0.133141	−	0.230608i	−0.791745	−	0.610852i	$-0.790827\pi$
$523$	1592.45	−	2758.20i	0.133141	−	0.230608i	0.924886	+	0.380245i	$0.124160\pi$
$524$	−8854.90	−	15337.1i	−0.738222	−	1.27864i
$525$		0			0
$526$	842.503	−	1459.26i	0.0698382	−	0.120963i
$527$	−1932.90	−	3347.89i	−0.159770	−	0.276729i
$528$		0			0
$529$	5551.35	−	9615.22i	0.456263	−	0.790271i
$530$	242.566	−	420.137i	0.0198800	−	0.0344332i
$531$		0			0
$532$	3394.25	−	6591.71i	0.276615	−	0.537193i
$533$	1717.32	+	2974.49i	0.139560	+	0.241725i
$534$		0			0
$535$	2192.47			0.177175
$536$	−5462.90			−0.440226
$537$		0			0
$538$	185.727	+	321.688i	0.0148834	+	0.0257788i
$539$	3340.81	−	7334.03i	0.266974	−	0.586083i
$540$		0			0
$541$	4189.85	−	7257.04i	0.332968	−	0.576718i	−0.650124	−	0.759828i	$-0.725283\pi$
$541$	4189.85	−	7257.04i	0.332968	−	0.576718i	0.983092	+	0.183110i	$0.0586165\pi$
$542$	−857.298	+	1484.88i	−0.0679411	+	0.117677i
$543$		0			0
$544$	−7612.80	−	13185.7i	−0.599992	−	1.03922i
$545$	6527.21	−	11305.5i	0.513019	−	0.888574i
$546$		0			0
$547$	5077.36	+	8794.24i	0.396878	+	0.687412i	0.993339	−	0.115230i	$-0.0367604\pi$
$547$	5077.36	+	8794.24i	0.396878	+	0.687412i	−0.596461	+	0.802642i	$0.703427\pi$
$548$	9931.02	−	17201.0i	0.774146	−	1.34086i
$549$		0			0
$550$	−2602.76	−	4508.10i	−0.201785	−	0.349502i
$551$	−9265.44			−0.716372
$552$		0			0
$553$	12703.7	−	611.280i	0.976883	−	0.0470059i
$554$	−2540.57	+	4400.39i	−0.194834	+	0.337463i
$555$		0			0
$556$	5346.73	−	9260.80i	0.407827	−	0.706377i
$557$	−3995.60	−	6920.58i	−0.303948	−	0.526453i	0.673079	−	0.739571i	$-0.264972\pi$
$557$	−3995.60	−	6920.58i	−0.303948	−	0.526453i	−0.977027	+	0.213118i	$0.931638\pi$
$558$		0			0
$559$	−22662.4			−1.71470
$560$	7822.05	+	12158.5i	0.590253	+	0.917481i
$561$		0			0
$562$	2464.74	+	4269.06i	0.184998	+	0.320426i
$563$	−14053.7			−1.05203			−0.526015	−	0.850476i	$-0.676314\pi$
$563$	−14053.7			−1.05203			−0.526015	+	0.850476i	$0.676314\pi$
$564$		0			0
$565$	−15030.0			−1.11914
$566$	−7239.29			−0.537615
$567$		0			0
$568$	−10138.5			−0.748950
$569$	−13247.9			−0.976064			−0.488032	−	0.872826i	$-0.662285\pi$
$569$	−13247.9			−0.976064			−0.488032	+	0.872826i	$0.662285\pi$
$570$		0			0
$571$	−9359.52			−0.685961			−0.342980	−	0.939343i	$-0.611436\pi$
$571$	−9359.52			−0.685961			−0.342980	+	0.939343i	$0.611436\pi$
$572$	−3944.57	−	6832.20i	−0.288341	−	0.499421i
$573$		0			0
$574$	599.965	−	1165.15i	0.0436273	−	0.0847252i
$575$	−7347.55			−0.532894
$576$		0			0
$577$	7432.51	+	12873.5i	0.536256	+	0.928822i	0.999101	+	0.0423832i	$0.0134950\pi$
$577$	7432.51	+	12873.5i	0.536256	+	0.928822i	−0.462846	+	0.886439i	$0.653172\pi$
$578$	2074.95	−	3593.92i	0.149319	−	0.258629i
$579$		0			0
$580$	10709.9	−	18550.1i	0.766734	−	1.32802i
$581$	−983.594	−	1528.88i	−0.0702347	−	0.109172i
$582$		0			0
$583$	−619.185			−0.0439863
$584$	1679.13	+	2908.34i	0.118978	+	0.206075i
$585$		0			0
$586$	1989.18	−	3445.36i	0.140226	−	0.242878i
$587$	−6942.90	−	12025.5i	−0.488184	−	0.845560i	0.511723	−	0.859150i	$-0.329007\pi$
$587$	−6942.90	−	12025.5i	−0.488184	−	0.845560i	−0.999908	+	0.0135902i	$0.995674\pi$
$588$		0			0
$589$	−1151.48	+	1994.42i	−0.0805533	+	0.139522i
$590$	−360.210	−	623.902i	−0.0251349	−	0.0435350i
$591$		0			0
$592$	−5336.87	+	9243.73i	−0.370514	+	0.641748i
$593$	11671.1	−	20214.9i	0.808220	−	1.39988i	−0.105875	−	0.994379i	$-0.533764\pi$
$593$	11671.1	−	20214.9i	0.808220	−	1.39988i	0.914095	−	0.405499i	$-0.132902\pi$
$594$		0			0
$595$	−15162.4	+	29445.8i	−1.04470	+	2.02884i
$596$	4802.36	+	8317.93i	0.330054	+	0.571671i
$597$		0			0
$598$	1532.25			0.104780
$599$	−3719.50			−0.253714			−0.126857	−	0.991921i	$-0.540489\pi$
$599$	−3719.50			−0.253714			−0.126857	+	0.991921i	$0.540489\pi$
$600$		0			0
$601$	−4161.44	−	7207.83i	−0.282444	−	0.489207i	0.689542	−	0.724245i	$-0.257812\pi$
$601$	−4161.44	−	7207.83i	−0.282444	−	0.489207i	−0.971986	+	0.235038i	$0.924478\pi$
$602$	4678.53	+	7272.24i	0.316749	+	0.492349i
$603$		0			0
$604$	9022.86	−	15628.0i	0.607839	−	1.05281i
$605$	7288.65	−	12624.3i	0.489795	−	0.848350i
$606$		0			0
$607$	−9711.68	−	16821.1i	−0.649398	−	1.12479i	−0.983267	−	0.182171i	$-0.941687\pi$
$607$	−9711.68	−	16821.1i	−0.649398	−	1.12479i	0.333868	−	0.942620i	$-0.391646\pi$
$608$	−4535.14	+	7855.09i	−0.302507	+	0.523957i
$609$		0			0
$610$	3880.77	+	6721.69i	0.257586	+	0.446153i
$611$	−6323.30	+	10952.3i	−0.418680	+	0.725175i
$612$		0			0
$613$	6784.18	+	11750.5i	0.446999	+	0.774225i	0.998189	−	0.0601546i	$-0.0191594\pi$
$613$	6784.18	+	11750.5i	0.446999	+	0.774225i	−0.551190	+	0.834380i	$0.685826\pi$
$614$	−114.724			−0.00754052
$615$		0			0
$616$	−2945.78	+	5720.78i	−0.192677	+	0.374183i
$617$	5017.11	−	8689.89i	0.327360	−	0.567004i	−0.654627	−	0.755952i	$-0.727174\pi$
$617$	5017.11	−	8689.89i	0.327360	−	0.567004i	0.981987	+	0.188948i	$0.0605076\pi$
$618$		0			0
$619$	−220.777	+	382.398i	−0.0143357	+	0.0248301i	−0.873104	−	0.487534i	$-0.837897\pi$
$619$	−220.777	+	382.398i	−0.0143357	+	0.0248301i	0.858769	+	0.512364i	$0.171230\pi$
$620$	−2661.99	−	4610.71i	−0.172433	−	0.298662i
$621$		0			0
$622$	9197.30			0.592891
$623$	8972.08	−	17424.0i	0.576980	−	1.12051i
$624$		0			0
$625$	−3473.63	−	6016.50i	−0.222312	−	0.385056i
$626$	−3103.53			−0.198150
$627$		0			0
$628$	9411.71			0.598038
$629$	−24452.6			−1.55006
$630$		0			0
$631$	3901.54			0.246145			0.123073	−	0.992398i	$-0.460725\pi$
$631$	3901.54			0.246145			0.123073	+	0.992398i	$0.460725\pi$
$632$	−10154.8			−0.639141
$633$		0			0
$634$	8235.98			0.515919
$635$	10770.2	+	18654.5i	0.673073	+	1.16580i
$636$		0			0
$637$	−6788.87	+	14903.5i	−0.422268	+	0.926999i
$638$	3761.81			0.233435
$639$		0			0
$640$	−13555.9	−	23479.5i	−0.837256	−	1.45017i
$641$	−13771.2	+	23852.3i	−0.848562	+	1.46975i	0.0339302	+	0.999424i	$0.489198\pi$
$641$	−13771.2	+	23852.3i	−0.848562	+	1.46975i	−0.882492	+	0.470328i	$0.844136\pi$
$642$		0			0
$643$	−11402.8	+	19750.3i	−0.699352	+	1.21131i	0.269340	+	0.963045i	$0.413195\pi$
$643$	−11402.8	+	19750.3i	−0.699352	+	1.21131i	−0.968691	+	0.248268i	$0.920139\pi$
$644$	2298.86	+	3573.31i	0.140664	+	0.218646i
$645$		0			0
$646$	−5351.28			−0.325918
$647$	5936.93	+	10283.1i	0.360750	+	0.624837i	0.988084	−	0.153913i	$-0.0491876\pi$
$647$	5936.93	+	10283.1i	0.360750	+	0.624837i	−0.627335	+	0.778750i	$0.715854\pi$
$648$		0			0
$649$	−459.744	+	796.300i	−0.0278067	+	0.0481626i
$650$	5289.07	+	9160.93i	0.319160	+	0.552802i
$651$		0			0
$652$	−2215.60	+	3837.52i	−0.133082	+	0.230505i
$653$	13827.9	+	23950.5i	0.828676	+	1.43531i	0.899077	+	0.437791i	$0.144239\pi$
$653$	13827.9	+	23950.5i	0.828676	+	1.43531i	−0.0704007	+	0.997519i	$0.522428\pi$
$654$		0			0
$655$	23564.3	−	40814.7i	1.40570	−	2.43475i
$656$	1500.31	−	2598.62i	0.0892948	−	0.154663i
$657$		0			0
$658$	4819.94	−	231.927i	0.285563	−	0.0137408i
$659$	14076.8	+	24381.8i	0.832102	+	1.44124i	0.896368	+	0.443310i	$0.146196\pi$
$659$	14076.8	+	24381.8i	0.832102	+	1.44124i	−0.0642662	+	0.997933i	$0.520471\pi$
$660$		0			0
$661$	−12918.8			−0.760185			−0.380092	−	0.924949i	$-0.624108\pi$
$661$	−12918.8			−0.760185			−0.380092	+	0.924949i	$0.624108\pi$
$662$	1751.42			0.102826
$663$		0			0
$664$	725.758	+	1257.05i	0.0424170	+	0.0734683i
$665$	19707.8	−	948.306i	1.14923	−	0.0552988i
$666$		0			0
$667$	2654.89	−	4598.40i	0.154119	−	0.266942i
$668$	1034.10	−	1791.11i	0.0598958	−	0.103743i
$669$		0			0
$670$	−3400.47	−	5889.78i	−0.196077	−	0.339615i
$671$	4953.11	−	8579.04i	0.284967	−	0.493577i
$672$		0			0
$673$	6143.90	+	10641.5i	0.351902	+	0.609512i	0.986583	−	0.163263i	$-0.0522018\pi$
$673$	6143.90	+	10641.5i	0.351902	+	0.609512i	−0.634681	+	0.772774i	$0.718868\pi$
$674$	−2550.20	+	4417.07i	−0.145742	+	0.252432i
$675$		0			0
$676$	290.745	+	503.585i	0.0165422	+	0.0286519i
$677$	−26060.0			−1.47942			−0.739710	−	0.672926i	$-0.765037\pi$
$677$	−26060.0			−1.47942			−0.739710	+	0.672926i	$0.765037\pi$
$678$		0			0
$679$	14150.1	+	21994.8i	0.799753	+	1.24312i
$680$	13222.2	−	22901.6i	0.745660	−	1.29152i
$681$		0			0
$682$	467.506	−	809.744i	0.0262489	−	0.0454644i
$683$	6109.75	+	10582.4i	0.342289	+	0.592862i	0.984857	−	0.173367i	$-0.0554646\pi$
$683$	6109.75	+	10582.4i	0.342289	+	0.592862i	−0.642569	+	0.766228i	$0.722131\pi$
$684$		0			0
$685$	52856.2			2.94822
$686$	6183.97	−	898.236i	0.344177	−	0.0499924i
$687$		0			0
$688$	9899.34	+	17146.2i	0.548559	+	0.950132i
$689$	1258.25			0.0695725
$690$		0			0
$691$	2678.31			0.147449			0.0737247	−	0.997279i	$-0.476511\pi$
$691$	2678.31			0.147449			0.0737247	+	0.997279i	$0.476511\pi$
$692$	−13006.4			−0.714495
$693$		0			0
$694$	−3786.65			−0.207117
$695$	28457.0			1.55315
$696$		0			0
$697$	6874.16			0.373569
$698$	−1065.86	−	1846.12i	−0.0577985	−	0.100110i
$699$		0			0
$700$	−13428.7	+	26078.8i	−0.725080	+	1.40812i
$701$	6169.00			0.332382			0.166191	−	0.986094i	$-0.446853\pi$
$701$	6169.00			0.332382			0.166191	+	0.986094i	$0.446853\pi$
$702$		0			0
$703$	7283.51	+	12615.4i	0.390758	+	0.676813i
$704$	−2079.02	+	3600.97i	−0.111301	+	0.192779i
$705$		0			0
$706$	−2785.65	+	4824.89i	−0.148498	+	0.257205i
$707$	−11882.4	+	23075.8i	−0.632082	+	1.22752i
$708$		0			0
$709$	−34544.5			−1.82982			−0.914912	−	0.403654i	$-0.867740\pi$
$709$	−34544.5			−1.82982			−0.914912	+	0.403654i	$0.867740\pi$
$710$	−6310.89	−	10930.8i	−0.333582	−	0.577781i
$711$		0			0
$712$	−7823.99	+	13551.5i	−0.411821	+	0.713295i
$713$	−659.882	−	1142.95i	−0.0346603	−	0.0600333i
$714$		0			0
$715$	10497.2	−	18181.6i	0.549051	−	0.950984i
$716$	−8298.52	−	14373.5i	−0.433143	−	0.750226i
$717$		0			0
$718$	−3631.28	+	6289.55i	−0.188744	+	0.326914i
$719$	−6508.90	+	11273.7i	−0.337609	+	0.584756i	−0.983982	−	0.178265i	$-0.942952\pi$
$719$	−6508.90	+	11273.7i	−0.337609	+	0.584756i	0.646373	+	0.763021i	$0.276285\pi$
$720$		0			0
$721$	−20058.8	−	31179.2i	−1.03610	−	1.61050i
$722$	−1779.63	−	3082.42i	−0.0917328	−	0.158886i
$723$		0			0
$724$	−22758.0			−1.16822
$725$	36656.9			1.87780
$726$		0			0
$727$	5297.44	+	9175.44i	0.270249	+	0.468086i	0.968926	−	0.247352i	$-0.0795605\pi$
$727$	5297.44	+	9175.44i	0.270249	+	0.468086i	−0.698676	+	0.715438i	$0.746227\pi$
$728$	5986.13	−	11625.2i	0.304754	−	0.591839i
$729$		0			0
$730$	−2090.40	+	3620.68i	−0.105985	+	0.183572i
$731$	−22678.5	+	39280.3i	−1.14746	+	1.98746i
$732$		0			0
$733$	16030.0	+	27764.8i	0.807753	+	1.39907i	0.914417	+	0.404774i	$0.132650\pi$
$733$	16030.0	+	27764.8i	0.807753	+	1.39907i	−0.106664	+	0.994295i	$0.534017\pi$
$734$	5858.59	−	10147.4i	0.294611	−	0.510281i
$735$		0			0
$736$	−2598.96	−	4501.53i	−0.130162	−	0.225447i
$737$	−4340.09	+	7517.25i	−0.216919	+	0.375714i
$738$		0			0
$739$	11637.3	+	20156.5i	0.579278	+	1.00334i	0.995562	+	0.0941045i	$0.0299988\pi$
$739$	11637.3	+	20156.5i	0.579278	+	1.00334i	−0.416284	+	0.909235i	$0.636668\pi$
$740$	−33676.0			−1.67291
$741$		0			0
$742$	−259.758	−	403.765i	−0.0128518	−	0.0199766i
$743$	5197.48	−	9002.30i	0.256631	−	0.444498i	−0.708706	−	0.705504i	$-0.750721\pi$
$743$	5197.48	−	9002.30i	0.256631	−	0.444498i	0.965337	+	0.261006i	$0.0840541\pi$
$744$		0			0
$745$	−12779.9	+	22135.4i	−0.628481	+	1.08856i
$746$	3412.28	+	5910.25i	0.167470	+	0.290066i
$747$		0			0
$748$	−15789.5			−0.771819
$749$	993.305	−	1929.02i	0.0484574	−	0.0941054i
$750$		0			0
$751$	−10421.9	−	18051.2i	−0.506390	−	0.877094i	−0.999973	−	0.00739463i	$-0.997646\pi$
$751$	−10421.9	−	18051.2i	−0.506390	−	0.877094i	0.493582	−	0.869699i	$-0.335687\pi$
$752$	11048.5			0.535769
$753$		0			0
$754$	−7644.38			−0.369220
$755$	48022.6			2.31486
$756$		0			0
$757$	−2016.92			−0.0968376			−0.0484188	−	0.998827i	$-0.515418\pi$
$757$	−2016.92			−0.0968376			−0.0484188	+	0.998827i	$0.515418\pi$
$758$	−6384.77			−0.305944
$759$		0			0
$760$	−15753.6			−0.751900
$761$	−4382.28	−	7590.33i	−0.208748	−	0.361563i	0.742572	−	0.669766i	$-0.233606\pi$
$761$	−4382.28	−	7590.33i	−0.208748	−	0.361563i	−0.951320	+	0.308203i	$0.900272\pi$
$762$		0			0
$763$	−6989.83	−	10864.9i	−0.331650	−	0.515512i
$764$	8299.10			0.392999
$765$		0			0
$766$	−3643.22	−	6310.24i	−0.171847	−	0.297648i
$767$	934.247	−	1618.16i	0.0439814	−	0.0761780i
$768$		0			0
$769$	−3372.48	+	5841.30i	−0.158146	+	0.273918i	−0.934200	−	0.356749i	$-0.883885\pi$
$769$	−3372.48	+	5841.30i	−0.158146	+	0.273918i	0.776054	+	0.630667i	$0.217218\pi$
$770$	−8001.45	+	385.016i	−0.374484	+	0.0180195i
$771$		0			0
$772$	22892.9			1.06727
$773$	−18762.5	−	32497.5i	−0.873013	−	1.51210i	−0.858865	−	0.512203i	$-0.828830\pi$
$773$	−18762.5	−	32497.5i	−0.873013	−	1.51210i	−0.0141481	−	0.999900i	$-0.504504\pi$
$774$		0			0
$775$	4555.60	−	7890.54i	0.211151	−	0.365724i
$776$	−10440.9	−	18084.1i	−0.482996	−	0.836574i
$777$		0			0
$778$	2004.42	−	3471.76i	0.0923677	−	0.159986i
$779$	−2047.56	−	3546.47i	−0.0941737	−	0.163114i
$780$		0			0
$781$	−8054.72	+	13951.2i	−0.369040	+	0.639197i
$782$	1533.34	−	2655.81i	0.0701176	−	0.121447i
$783$		0			0
$784$	14241.3	−	1373.72i	0.648749	−	0.0625782i
$785$	12523.0	+	21690.6i	0.569384	+	0.986203i
$786$		0			0
$787$	−17321.3			−0.784548			−0.392274	−	0.919848i	$-0.628312\pi$
$787$	−17321.3			−0.784548			−0.392274	+	0.919848i	$0.628312\pi$
$788$	16603.7			0.750611
$789$		0			0
$790$	−6321.02	−	10948.3i	−0.284673	−	0.493068i
$791$	−6809.39	+	13224.0i	−0.306086	+	0.594426i
$792$		0			0
$793$	−10065.2	+	17433.5i	−0.450727	+	0.780682i
$794$	−4186.23	+	7250.76i	−0.187108	+	0.324081i
$795$		0			0
$796$	−6047.60	−	10474.7i	−0.269286	−	0.466417i
$797$	−353.194	+	611.751i	−0.0156973	+	0.0271886i	−0.873767	−	0.486344i	$-0.838330\pi$
$797$	−353.194	+	611.751i	−0.0156973	+	0.0271886i	0.858070	+	0.513533i	$0.171663\pi$
$798$		0			0
$799$	12655.6	+	21920.1i	0.560353	+	0.970560i
$800$	17942.4	−	31077.1i	0.792948	−	1.37343i
$801$		0			0
$802$	4090.73	+	7085.36i	0.180111	+	0.311961i
$803$	5336.05			0.234502
$804$		0			0
$805$	−5176.36	+	10052.6i	−0.226637	+	0.440134i
$806$	−950.020	+	1645.48i	−0.0415174	+	0.0719102i
$807$		0			0
$808$	10361.9	−	17947.3i	0.451150	−	0.781415i
$809$	−21051.5	−	36462.3i	−0.914872	−	1.58460i	−0.807089	−	0.590430i	$-0.798958\pi$
$809$	−21051.5	−	36462.3i	−0.914872	−	1.58460i	−0.107783	−	0.994174i	$-0.534375\pi$
$810$		0			0
$811$	−14795.0			−0.640595			−0.320297	−	0.947317i	$-0.603783\pi$
$811$	−14795.0			−0.640595			−0.320297	+	0.947317i	$0.603783\pi$
$812$	−11469.0	−	17827.2i	−0.495669	−	0.770460i
$813$		0			0
$814$	−2957.14	−	5121.91i	−0.127331	−	0.220544i
$815$	−11792.1			−0.506822
$816$		0			0
$817$	27020.3			1.15706
$818$	6079.64			0.259865
$819$		0			0
$820$	9467.08			0.403177
$821$	−2943.09			−0.125109			−0.0625546	−	0.998042i	$-0.519925\pi$
$821$	−2943.09			−0.125109			−0.0625546	+	0.998042i	$0.519925\pi$
$822$		0			0
$823$	25930.8			1.09829			0.549145	−	0.835727i	$-0.314954\pi$
$823$	25930.8			1.09829			0.549145	+	0.835727i	$0.314954\pi$
$824$	14800.7	+	25635.5i	0.625736	+	1.08381i
$825$		0			0
$826$	−712.130	+	34.2664i	−0.0299978	+	0.00144344i
$827$	8017.84			0.337131			0.168566	−	0.985690i	$-0.446086\pi$
$827$	8017.84			0.337131			0.168566	+	0.985690i	$0.446086\pi$
$828$		0			0
$829$	3326.49	+	5761.64i	0.139365	+	0.241387i	0.927256	−	0.374427i	$-0.122161\pi$
$829$	3326.49	+	5761.64i	0.139365	+	0.241387i	−0.787891	+	0.615814i	$0.788827\pi$
$830$	−903.518	+	1564.94i	−0.0377850	+	0.0654456i
$831$		0			0
$832$	4224.78	−	7317.54i	0.176043	−	0.304916i
$833$	19038.2	+	26681.1i	0.791880	+	1.10978i
$834$		0			0
$835$	5503.80			0.228104
$836$	4703.10	+	8146.01i	0.194569	+	0.337004i
$837$		0			0
$838$	−1167.95	+	2022.95i	−0.0481457	+	0.0833909i
$839$	6231.37	+	10793.0i	0.256413	+	0.444121i	0.965278	−	0.261223i	$-0.0841258\pi$
$839$	6231.37	+	10793.0i	0.256413	+	0.444121i	−0.708865	+	0.705344i	$0.750793\pi$
$840$		0			0
$841$	−1050.71	+	1819.89i	−0.0430815	+	0.0746193i
$842$	268.156	+	464.459i	0.0109754	+	0.0190099i
$843$		0			0
$844$	8908.51	−	15430.0i	0.363322	−	0.629291i
$845$	−773.720	+	1340.12i	−0.0314991	+	0.0545581i
$846$		0			0
$847$	−7805.24	−	12132.4i	−0.316637	−	0.492175i
$848$	−549.625	−	951.978i	−0.0222573	−	0.0385508i
$849$		0			0
$850$	21171.3			0.854316
$851$	−8347.96			−0.336268
$852$		0			0
$853$	−9538.32	−	16520.8i	−0.382867	−	0.663145i	0.608604	−	0.793474i	$-0.291730\pi$
$853$	−9538.32	−	16520.8i	−0.382867	−	0.663145i	−0.991471	+	0.130329i	$0.958397\pi$
$854$	7672.22	−	369.174i	0.307421	−	0.0147926i
$855$		0			0
$856$	−866.200	+	1500.30i	−0.0345866	+	0.0599057i
$857$	19453.0	−	33693.6i	0.775382	−	1.34300i	−0.159198	−	0.987247i	$-0.550891\pi$
$857$	19453.0	−	33693.6i	0.775382	−	1.34300i	0.934580	−	0.355754i	$-0.115776\pi$
$858$		0			0
$859$	−3647.67	−	6317.95i	−0.144886	−	0.250949i	0.784445	−	0.620199i	$-0.212948\pi$
$859$	−3647.67	−	6317.95i	−0.144886	−	0.250949i	−0.929330	+	0.369250i	$0.879615\pi$
$860$	−31232.8	+	54096.7i	−1.23840	+	2.14498i
$861$		0			0
$862$	1416.71	+	2453.81i	0.0559784	+	0.0969574i
$863$	−19742.5	+	34195.0i	−0.778728	+	1.34880i	0.153947	+	0.988079i	$0.450801\pi$
$863$	−19742.5	+	34195.0i	−0.778728	+	1.34880i	−0.932675	+	0.360717i	$0.882532\pi$
$864$		0			0
$865$	−17306.1	−	29975.1i	−0.680261	−	1.17825i
$866$	−11854.8			−0.465178
$867$		0			0
$868$	−5262.71	+	253.233i	−0.205793	+	0.00990239i
$869$	−8067.66	+	13973.6i	−0.314933	+	0.545479i
$870$		0			0
$871$	8819.50	−	15275.8i	0.343097	−	0.594261i
$872$	5157.54	+	8933.13i	0.200294	+	0.346920i
$873$		0			0
$874$	−1826.89			−0.0707043
$875$	−34696.1	+	1669.52i	−1.34051	+	0.0645028i
$876$		0			0
$877$	33.0753	+	57.2881i	0.00127352	+	0.00220579i	0.866661	−	0.498897i	$-0.166261\pi$
$877$	33.0753	+	57.2881i	0.00127352	+	0.00220579i	−0.865388	+	0.501102i	$0.832928\pi$
$878$	11245.7			0.432259
$879$		0			0
$880$	−18341.4			−0.702599
$881$	1739.66			0.0665275			0.0332638	−	0.999447i	$-0.489410\pi$
$881$	1739.66			0.0665275			0.0332638	+	0.999447i	$0.489410\pi$
$882$		0			0
$883$	6720.66			0.256136			0.128068	−	0.991765i	$-0.459122\pi$
$883$	6720.66			0.256136			0.128068	+	0.991765i	$0.459122\pi$
$884$	32085.8			1.22077
$885$		0			0
$886$	−12132.0			−0.460024
$887$	14041.6	+	24320.7i	0.531532	+	0.920641i	0.999323	+	0.0368016i	$0.0117170\pi$
$887$	14041.6	+	24320.7i	0.531532	+	0.920641i	−0.467790	+	0.883840i	$0.654950\pi$
$888$		0			0
$889$	21292.4	−	1024.56i	0.803291	−	0.0386530i
$890$	−19480.6			−0.733700
$891$		0			0
$892$	1401.55	+	2427.55i	0.0526091	+	0.0911216i
$893$	7539.25	−	13058.4i	0.282521	−	0.489341i
$894$		0			0
$895$	22083.7	−	38250.1i	0.824780	−	1.42856i
$896$	−26799.8	+	1289.56i	−0.999238	+	0.0480816i
$897$		0			0
$898$	7589.24			0.282022
$899$	3292.15	+	5702.17i	0.122135	+	0.211544i
$900$		0			0
$901$	1259.14	−	2180.90i	0.0465572	−	0.0806395i
$902$	831.316	+	1439.88i	0.0306871	+	0.0531517i
$903$		0			0
$904$	5938.05	−	10285.0i	0.218470	−	0.378400i
$905$	−30281.3	−	52448.8i	−1.11225	−	1.92647i
$906$		0			0
$907$	−13679.2	+	23693.1i	−0.500785	+	0.867385i	0.499215	+	0.866478i	$0.333622\pi$
$907$	−13679.2	+	23693.1i	−0.500785	+	0.867385i	−1.00000		0.000906587i	$0.999711\pi$
$908$	9763.61	−	16911.1i	0.356847	−	0.618077i
$909$		0			0
$910$	16259.8	−	782.392i	0.592315	−	0.0285011i
$911$	−21330.1	−	36944.8i	−0.775739	−	1.34362i	−0.934378	−	0.356283i	$-0.884044\pi$
$911$	−21330.1	−	36944.8i	−0.775739	−	1.34362i	0.158639	−	0.987337i	$-0.449289\pi$
$912$		0			0
$913$	2306.36			0.0836028
$914$	6432.07			0.232773
$915$		0			0
$916$	3534.03	+	6121.11i	0.127475	+	0.220794i
$917$	−25234.5	−	39224.1i	−0.908742	−	1.41253i
$918$		0			0
$919$	2911.22	−	5042.38i	0.104496	−	0.180993i	−0.809036	−	0.587759i	$-0.800010\pi$
$919$	2911.22	−	5042.38i	0.104496	−	0.180993i	0.913532	+	0.406766i	$0.133344\pi$
$920$	4513.98	−	7818.45i	0.161763	−	0.280181i
$921$		0			0
$922$	−4488.27	−	7773.91i	−0.160318	−	0.277679i
$923$	16368.0	−	28350.2i	0.583705	−	1.01101i
$924$		0			0
$925$	−28815.8	−	49910.4i	−1.02428	−	1.77410i
$926$	6080.68	−	10532.0i	0.215792	−	0.373763i
$927$		0			0
$928$	12966.2	+	22458.1i	0.458660	+	0.794423i
$929$	11851.5			0.418551			0.209276	−	0.977857i	$-0.432889\pi$
$929$	11851.5			0.418551			0.209276	+	0.977857i	$0.432889\pi$
$930$		0			0
$931$	8094.34	−	17769.4i	0.284942	−	0.625529i
$932$	−8012.74	+	13878.5i	−0.281616	+	0.487773i
$933$		0			0
$934$	−6061.00	+	10498.0i	−0.212336	+	0.367777i
$935$	−21009.2	−	36389.0i	−0.734839	−	1.27278i
$936$		0			0
$937$	−55465.1			−1.93379			−0.966897	−	0.255166i	$-0.917870\pi$
$937$	−55465.1			−1.93379			−0.966897	+	0.255166i	$0.917870\pi$
$938$	−6722.66	+	323.483i	−0.234011	+	0.0112602i
$939$		0			0
$940$	17429.2	+	30188.3i	0.604765	+	1.04748i
$941$	18619.5			0.645035			0.322517	−	0.946564i	$-0.395471\pi$
$941$	18619.5			0.645035			0.322517	+	0.946564i	$0.395471\pi$
$942$		0			0
$943$	2346.80			0.0810416
$944$	−1632.38			−0.0562813
$945$		0			0
$946$	−10970.4			−0.377037
$947$	−54045.4			−1.85453			−0.927266	−	0.374404i	$-0.877847\pi$
$947$	−54045.4			−1.85453			−0.927266	+	0.374404i	$0.877847\pi$
$948$		0			0
$949$	−10843.4			−0.370908
$950$	−6306.13	−	10922.5i	−0.215366	−	0.373025i
$951$		0			0
$952$	−14159.4	−	22009.1i	−0.482046	−	0.749284i
$953$	−56381.3			−1.91644			−0.958222	−	0.286026i	$-0.907666\pi$
$953$	−56381.3			−1.91644			−0.958222	+	0.286026i	$0.907666\pi$
$954$		0			0
$955$	11042.6	+	19126.4i	0.374169	+	0.648079i
$956$	−7912.62	+	13705.1i	−0.267691	+	0.463654i
$957$		0			0
$958$	−2537.48	+	4395.04i	−0.0855765	+	0.148223i
$959$	23946.7	−	46505.0i	0.806339	−	1.56593i
$960$		0			0
$961$	−28154.4			−0.945066
$962$	6009.20	+	10408.2i	0.201398	+	0.348831i
$963$		0			0
$964$	4207.18	−	7287.05i	0.140564	−	0.243465i
$965$	30460.9	+	52759.8i	1.01614	+	1.76000i
$966$		0			0
$967$	−15168.1	+	26272.0i	−0.504420	+	0.873682i	0.495567	+	0.868570i	$0.334960\pi$
$967$	−15168.1	+	26272.0i	−0.504420	+	0.873682i	−0.999987	+	0.00511174i	$0.998373\pi$
$968$	5759.20	+	9975.23i	0.191227	+	0.331215i
$969$		0			0
$970$	12998.1	−	22513.5i	0.430253	−	0.745220i
$971$	16590.1	−	28734.9i	0.548302	−	0.949686i	−0.450090	−	0.892983i	$-0.648608\pi$
$971$	16590.1	−	28734.9i	0.548302	−	0.949686i	0.998391	−	0.0567028i	$-0.0180587\pi$
$972$		0			0
$973$	12892.6	−	25037.7i	0.424786	−	0.824944i
$974$	−2002.38	−	3468.22i	−0.0658729	−	0.114095i
$975$		0			0
$976$	17586.7			0.576778
$977$	−55161.8			−1.80633			−0.903165	−	0.429294i	$-0.858762\pi$
$977$	−55161.8			−1.80633			−0.903165	+	0.429294i	$0.858762\pi$
$978$		0			0
$979$	12431.8	+	21532.5i	0.405844	+	0.702943i
$980$	26219.4	+	36745.1i	0.854642	+	1.19773i
$981$		0			0
$982$	3973.01	−	6881.46i	0.129108	−	0.223621i
$983$	−362.248	+	627.432i	−0.0117537	+	0.0203581i	−0.871842	−	0.489786i	$-0.837075\pi$
$983$	−362.248	+	627.432i	−0.0117537	+	0.0203581i	0.860089	+	0.510144i	$0.170408\pi$
$984$		0			0
$985$	22092.5	+	38265.4i	0.714647	+	1.23780i
$986$	−7649.80	+	13249.8i	−0.247078	+	0.427952i
$987$		0			0
$988$	−9557.18	−	16553.5i	−0.307747	−	0.533034i
$989$	−7742.29	+	13410.0i	−0.248929	+	0.431157i
$990$		0			0
$991$	−12504.0	−	21657.6i	−0.400810	−	0.694224i	0.593014	−	0.805192i	$-0.297938\pi$
$991$	−12504.0	−	21657.6i	−0.400810	−	0.694224i	−0.993824	+	0.110969i	$0.964605\pi$
$992$	6445.60			0.206298
$993$		0			0
$994$	−12476.5	+	600.348i	−0.398120	+	0.0191568i
$995$	16093.7	−	27875.0i	0.512767	−	0.888138i
$996$		0			0
$997$	−3751.44	+	6497.68i	−0.119167	+	0.206403i	−0.919438	−	0.393236i	$-0.871356\pi$
$997$	−3751.44	+	6497.68i	−0.119167	+	0.206403i	0.800271	+	0.599639i	$0.204689\pi$
$998$	−2825.38	−	4893.70i	−0.0896151	−	0.155218i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.h.a.37.10		44
3.2	odd	2		63.4.h.a.58.13	yes	44
7.4	even	3		189.4.g.a.172.13		44
9.2	odd	6		63.4.g.a.16.10	yes	44
9.7	even	3		189.4.g.a.100.13		44
21.11	odd	6		63.4.g.a.4.10	✓	44
63.11	odd	6		63.4.h.a.25.13	yes	44
63.25	even	3	inner	189.4.h.a.46.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.10	✓	44	21.11	odd	6
63.4.g.a.16.10	yes	44	9.2	odd	6
63.4.h.a.25.13	yes	44	63.11	odd	6
63.4.h.a.58.13	yes	44	3.2	odd	2
189.4.g.a.100.13		44	9.7	even	3
189.4.g.a.172.13		44	7.4	even	3
189.4.h.a.37.10		44	1.1	even	1	trivial
189.4.h.a.46.10		44	63.25	even	3	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.983694 q^{2} -7.03235 q^{4} +(-9.35711 - 16.2070i) q^{5} +(-18.4989 + 0.890133i) q^{7} +14.7872 q^{8} +O(q^{10})\)	\(q-0.983694 q^{2} -7.03235 q^{4} +(-9.35711 - 16.2070i) q^{5} +(-18.4989 + 0.890133i) q^{7} +14.7872 q^{8} +(9.20454 + 15.9427i) q^{10} +(11.7479 - 20.3480i) q^{11} +(-23.8730 + 41.3493i) q^{13} +(18.1972 - 0.875618i) q^{14} +41.7126 q^{16} +(47.7799 + 82.7573i) q^{17} +(28.4637 - 49.3006i) q^{19} +(65.8024 + 113.973i) q^{20} +(-11.5564 + 20.0163i) q^{22} +(16.3118 + 28.2528i) q^{23} +(-112.611 + 195.048i) q^{25} +(23.4838 - 40.6751i) q^{26} +(130.090 - 6.25972i) q^{28} +(-81.3794 - 140.953i) q^{29} -40.4543 q^{31} -159.330 q^{32} +(-47.0009 - 81.4079i) q^{34} +(187.522 + 291.482i) q^{35} +(-127.944 + 221.605i) q^{37} +(-27.9996 + 48.4967i) q^{38} +(-138.366 - 239.657i) q^{40} +(35.9678 - 62.2981i) q^{41} +(237.322 + 411.054i) q^{43} +(-82.6156 + 143.094i) q^{44} +(-16.0458 - 27.7921i) q^{46} +264.872 q^{47} +(341.415 - 32.9329i) q^{49} +(110.775 - 191.868i) q^{50} +(167.883 - 290.783i) q^{52} +(-13.1765 - 22.8223i) q^{53} -439.708 q^{55} +(-273.547 + 13.1626i) q^{56} +(80.0525 + 138.655i) q^{58} -39.1340 q^{59} +421.615 q^{61} +39.7947 q^{62} -176.969 q^{64} +893.531 q^{65} -369.434 q^{67} +(-336.005 - 581.978i) q^{68} +(-184.465 - 286.729i) q^{70} -685.628 q^{71} +(113.553 + 196.679i) q^{73} +(125.858 - 217.992i) q^{74} +(-200.167 + 346.699i) q^{76} +(-199.211 + 386.873i) q^{77} -686.729 q^{79} +(-390.310 - 676.037i) q^{80} +(-35.3813 + 61.2823i) q^{82} +(49.0800 + 85.0091i) q^{83} +(894.165 - 1548.74i) q^{85} +(-233.452 - 404.351i) q^{86} +(173.720 - 300.891i) q^{88} +(-529.104 + 916.436i) q^{89} +(404.818 - 786.165i) q^{91} +(-114.710 - 198.684i) q^{92} -260.553 q^{94} -1065.35 q^{95} +(-706.073 - 1222.95i) q^{97} +(-335.848 + 32.3959i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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