LMFDB - Embedded newform 143.4.g.a.21.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.16
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20788 + 1.20788i) q^{2} -9.63914 q^{3} +5.08205i q^{4} +(9.61526 + 9.61526i) q^{5} +(11.6429 - 11.6429i) q^{6} +(19.2678 + 19.2678i) q^{7} +(-15.8016 - 15.8016i) q^{8} +65.9130 q^{9} +O(q^{10})$	\(q+(-1.20788 + 1.20788i) q^{2} -9.63914 q^{3} +5.08205i q^{4} +(9.61526 + 9.61526i) q^{5} +(11.6429 - 11.6429i) q^{6} +(19.2678 + 19.2678i) q^{7} +(-15.8016 - 15.8016i) q^{8} +65.9130 q^{9} -23.2282 q^{10} +(9.61744 + 35.1924i) q^{11} -48.9866i q^{12} +(-1.08613 + 46.8596i) q^{13} -46.5465 q^{14} +(-92.6828 - 92.6828i) q^{15} -2.48360 q^{16} +60.6166 q^{17} +(-79.6151 + 79.6151i) q^{18} +(-53.4086 + 53.4086i) q^{19} +(-48.8652 + 48.8652i) q^{20} +(-185.725 - 185.725i) q^{21} +(-54.1249 - 30.8915i) q^{22} -80.9060i q^{23} +(152.313 + 152.313i) q^{24} +59.9065i q^{25} +(-55.2889 - 57.9127i) q^{26} -375.088 q^{27} +(-97.9200 + 97.9200i) q^{28} +173.617i q^{29} +223.900 q^{30} +(-16.8509 - 16.8509i) q^{31} +(129.412 - 129.412i) q^{32} +(-92.7039 - 339.224i) q^{33} +(-73.2176 + 73.2176i) q^{34} +370.530i q^{35} +334.973i q^{36} +(201.011 - 201.011i) q^{37} -129.022i q^{38} +(10.4694 - 451.686i) q^{39} -303.872i q^{40} +(137.687 - 137.687i) q^{41} +448.668 q^{42} -29.5948 q^{43} +(-178.849 + 48.8763i) q^{44} +(633.771 + 633.771i) q^{45} +(97.7248 + 97.7248i) q^{46} +(171.627 - 171.627i) q^{47} +23.9398 q^{48} +399.499i q^{49} +(-72.3598 - 72.3598i) q^{50} -584.292 q^{51} +(-238.143 - 5.51978i) q^{52} -136.664 q^{53} +(453.062 - 453.062i) q^{54} +(-245.910 + 430.858i) q^{55} -608.923i q^{56} +(514.813 - 514.813i) q^{57} +(-209.708 - 209.708i) q^{58} +(-467.578 + 467.578i) q^{59} +(471.019 - 471.019i) q^{60} -190.383i q^{61} +40.7078 q^{62} +(1270.00 + 1270.00i) q^{63} +292.760i q^{64} +(-461.011 + 440.124i) q^{65} +(521.718 + 297.767i) q^{66} +(-675.645 - 675.645i) q^{67} +308.056i q^{68} +779.864i q^{69} +(-447.557 - 447.557i) q^{70} +(306.512 + 306.512i) q^{71} +(-1041.53 - 1041.53i) q^{72} +(193.622 + 193.622i) q^{73} +485.594i q^{74} -577.447i q^{75} +(-271.425 - 271.425i) q^{76} +(-492.774 + 863.388i) q^{77} +(532.937 + 558.229i) q^{78} -34.4956i q^{79} +(-23.8805 - 23.8805i) q^{80} +1835.88 q^{81} +332.619i q^{82} +(529.788 - 529.788i) q^{83} +(943.865 - 943.865i) q^{84} +(582.844 + 582.844i) q^{85} +(35.7469 - 35.7469i) q^{86} -1673.52i q^{87} +(404.124 - 708.065i) q^{88} +(30.0630 - 30.0630i) q^{89} -1531.04 q^{90} +(-923.810 + 881.955i) q^{91} +411.168 q^{92} +(162.428 + 162.428i) q^{93} +414.609i q^{94} -1027.08 q^{95} +(-1247.42 + 1247.42i) q^{96} +(-1316.47 - 1316.47i) q^{97} +(-482.547 - 482.547i) q^{98} +(633.915 + 2319.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.20788	+	1.20788i	−0.427050	+	0.427050i	−0.887622	−	0.460572i	$-0.847644\pi$
$2$	−1.20788	+	1.20788i	−0.427050	+	0.427050i	0.460572	+	0.887622i	$0.347644\pi$
$3$	−9.63914			−1.85505			−0.927527	−	0.373757i	$-0.878069\pi$
$3$	−9.63914			−1.85505			−0.927527	+	0.373757i	$0.878069\pi$
$4$			5.08205i			0.635256i
$5$	9.61526	+	9.61526i	0.860015	+	0.860015i	0.991339	−	0.131324i	$-0.0419230\pi$
$5$	9.61526	+	9.61526i	0.860015	+	0.860015i	−0.131324	+	0.991339i	$0.541923\pi$
$6$	11.6429	−	11.6429i	0.792201	−	0.792201i
$7$	19.2678	+	19.2678i	1.04037	+	1.04037i	0.999150	+	0.0412148i	$0.0131228\pi$
$7$	19.2678	+	19.2678i	1.04037	+	1.04037i	0.0412148	+	0.999150i	$0.486877\pi$
$8$	−15.8016	−	15.8016i	−0.698337	−	0.698337i
$9$	65.9130			2.44122
$10$	−23.2282			−0.734539
$11$	9.61744	+	35.1924i	0.263615	+	0.964628i
$11$	9.61744	+	35.1924i	0.263615	+	0.964628i
$12$		−	48.9866i		−	1.17843i
$13$	−1.08613	+	46.8596i	−0.0231722	+	0.999731i
$13$	−1.08613	+	46.8596i	−0.0231722	+	0.999731i
$14$	−46.5465			−0.888576
$15$	−92.6828	−	92.6828i	−1.59537	−	1.59537i
$16$	−2.48360			−0.0388063
$17$	60.6166			0.864805			0.432402	−	0.901681i	$-0.357666\pi$
$17$	60.6166			0.864805			0.432402	+	0.901681i	$0.357666\pi$
$18$	−79.6151	+	79.6151i	−1.04253	+	1.04253i
$19$	−53.4086	+	53.4086i	−0.644883	+	0.644883i	−0.951752	−	0.306869i	$-0.900719\pi$
$19$	−53.4086	+	53.4086i	−0.644883	+	0.644883i	0.306869	+	0.951752i	$0.400719\pi$
$20$	−48.8652	+	48.8652i	−0.546330	+	0.546330i
$21$	−185.725	−	185.725i	−1.92993	−	1.92993i
$22$	−54.1249	−	30.8915i	−0.524522	−	0.299368i
$23$		−	80.9060i		−	0.733481i	−0.930323	−	0.366740i	$-0.880474\pi$
$23$		−	80.9060i		−	0.733481i	0.930323	−	0.366740i	$-0.119526\pi$
$24$	152.313	+	152.313i	1.29545	+	1.29545i
$25$			59.9065i			0.479252i
$26$	−55.2889	−	57.9127i	−0.417040	−	0.436831i
$27$	−375.088			−2.67355
$28$	−97.9200	+	97.9200i	−0.660898	+	0.660898i
$29$			173.617i			1.11172i	0.831277	+	0.555859i	$0.187611\pi$
$29$			173.617i			1.11172i	−0.831277	+	0.555859i	$0.812389\pi$
$30$	223.900			1.36261
$31$	−16.8509	−	16.8509i	−0.0976295	−	0.0976295i	0.656605	−	0.754235i	$-0.271992\pi$
$31$	−16.8509	−	16.8509i	−0.0976295	−	0.0976295i	−0.754235	+	0.656605i	$0.771992\pi$
$32$	129.412	−	129.412i	0.714909	−	0.714909i
$33$	−92.7039	−	339.224i	−0.489021	−	1.78944i
$34$	−73.2176	+	73.2176i	−0.369315	+	0.369315i
$35$			370.530i			1.78946i
$36$			334.973i			1.55080i
$37$	201.011	−	201.011i	0.893134	−	0.893134i	−0.101683	−	0.994817i	$-0.532423\pi$
$37$	201.011	−	201.011i	0.893134	−	0.893134i	0.994817	+	0.101683i	$0.0324228\pi$
$38$		−	129.022i		−	0.550795i
$39$	10.4694	−	451.686i	0.0429857	−	1.85456i
$40$		−	303.872i		−	1.20116i
$41$	137.687	−	137.687i	0.524466	−	0.524466i	−0.394451	−	0.918917i	$-0.629065\pi$
$41$	137.687	−	137.687i	0.524466	−	0.524466i	0.918917	+	0.394451i	$0.129065\pi$
$42$	448.668			1.64836
$43$	−29.5948			−0.104957			−0.0524786	−	0.998622i	$-0.516712\pi$
$43$	−29.5948			−0.104957			−0.0524786	+	0.998622i	$0.516712\pi$
$44$	−178.849	+	48.8763i	−0.612786	+	0.167463i
$45$	633.771	+	633.771i	2.09949	+	2.09949i
$46$	97.7248	+	97.7248i	0.313233	+	0.313233i
$47$	171.627	−	171.627i	0.532645	−	0.532645i	−0.388714	−	0.921359i	$-0.627080\pi$
$47$	171.627	−	171.627i	0.532645	−	0.532645i	0.921359	+	0.388714i	$0.127080\pi$
$48$	23.9398			0.0719877
$49$			399.499i			1.16472i
$50$	−72.3598	−	72.3598i	−0.204665	−	0.204665i
$51$	−584.292			−1.60426
$52$	−238.143	−	5.51978i	−0.635085	−	0.0147203i
$53$	−136.664			−0.354194			−0.177097	−	0.984193i	$-0.556671\pi$
$53$	−136.664			−0.354194			−0.177097	+	0.984193i	$0.556671\pi$
$54$	453.062	−	453.062i	1.14174	−	1.14174i
$55$	−245.910	+	430.858i	−0.602881	+	1.05631i
$56$		−	608.923i		−	1.45305i
$57$	514.813	−	514.813i	1.19629	−	1.19629i
$58$	−209.708	−	209.708i	−0.474760	−	0.474760i
$59$	−467.578	+	467.578i	−1.03175	+	1.03175i	−0.0322747	+	0.999479i	$0.510275\pi$
$59$	−467.578	+	467.578i	−1.03175	+	1.03175i	−0.999479	+	0.0322747i	$0.989725\pi$
$60$	471.019	−	471.019i	1.01347	−	1.01347i
$61$		−	190.383i		−	0.399608i	−0.979836	−	0.199804i	$-0.935970\pi$
$61$		−	190.383i		−	0.399608i	0.979836	−	0.199804i	$-0.0640305\pi$
$62$	40.7078			0.0833854
$63$	1270.00	+	1270.00i	2.53976	+	2.53976i
$64$			292.760i			0.571798i
$65$	−461.011	+	440.124i	−0.879713	+	0.839856i
$66$	521.718	+	297.767i	0.973016	+	0.555343i
$67$	−675.645	−	675.645i	−1.23199	−	1.23199i	−0.963199	−	0.268789i	$-0.913377\pi$
$67$	−675.645	−	675.645i	−1.23199	−	1.23199i	−0.268789	−	0.963199i	$-0.586623\pi$
$68$			308.056i			0.549372i
$69$			779.864i			1.36065i
$70$	−447.557	−	447.557i	−0.764189	−	0.764189i
$71$	306.512	+	306.512i	0.512342	+	0.512342i	0.915243	−	0.402901i	$-0.131998\pi$
$71$	306.512	+	306.512i	0.512342	+	0.512342i	−0.402901	+	0.915243i	$0.631998\pi$
$72$	−1041.53	−	1041.53i	−1.70480	−	1.70480i
$73$	193.622	+	193.622i	0.310435	+	0.310435i	0.845078	−	0.534643i	$-0.179554\pi$
$73$	193.622	+	193.622i	0.310435	+	0.310435i	−0.534643	+	0.845078i	$0.679554\pi$
$74$			485.594i			0.762826i
$75$		−	577.447i		−	0.889037i
$76$	−271.425	−	271.425i	−0.409666	−	0.409666i
$77$	−492.774	+	863.388i	−0.729309	+	1.27782i
$78$	532.937	+	558.229i	0.773631	+	0.810346i
$79$		−	34.4956i		−	0.0491273i	−0.999698	−	0.0245637i	$-0.992180\pi$
$79$		−	34.4956i		−	0.0491273i	0.999698	−	0.0245637i	$-0.00781965\pi$
$80$	−23.8805	−	23.8805i	−0.0333740	−	0.0333740i
$81$	1835.88			2.51835
$82$			332.619i			0.447947i
$83$	529.788	−	529.788i	0.700623	−	0.700623i	−0.263921	−	0.964544i	$-0.585016\pi$
$83$	529.788	−	529.788i	0.700623	−	0.700623i	0.964544	+	0.263921i	$0.0850158\pi$
$84$	943.865	−	943.865i	1.22600	−	1.22600i
$85$	582.844	+	582.844i	0.743745	+	0.743745i
$86$	35.7469	−	35.7469i	0.0448220	−	0.0448220i
$87$		−	1673.52i		−	2.06230i
$88$	404.124	−	708.065i	0.489543	−	0.857727i
$89$	30.0630	−	30.0630i	0.0358053	−	0.0358053i	−0.688977	−	0.724783i	$-0.741940\pi$
$89$	30.0630	−	30.0630i	0.0358053	−	0.0358053i	0.724783	+	0.688977i	$0.241940\pi$
$90$	−1531.04			−1.79317
$91$	−923.810	+	881.955i	−1.06419	+	1.01598i
$92$	411.168			0.465948
$93$	162.428	+	162.428i	0.181108	+	0.181108i
$94$			414.609i			0.454932i
$95$	−1027.08			−1.10922
$96$	−1247.42	+	1247.42i	−1.32619	+	1.32619i
$97$	−1316.47	−	1316.47i	−1.37801	−	1.37801i	−0.847969	−	0.530045i	$-0.822175\pi$
$97$	−1316.47	−	1316.47i	−1.37801	−	1.37801i	−0.530045	−	0.847969i	$-0.677825\pi$
$98$	−482.547	−	482.547i	−0.497394	−	0.497394i
$99$	633.915	+	2319.64i	0.643544	+	2.35487i
$100$	−304.447			−0.304447
$101$	1678.51			1.65364			0.826820	−	0.562466i	$-0.190147\pi$
$101$	1678.51			1.65364			0.826820	+	0.562466i	$0.190147\pi$
$102$	705.755	−	705.755i	0.685099	−	0.685099i
$103$			462.109i			0.442067i	0.975266	+	0.221034i	$0.0709431\pi$
$103$			462.109i			0.442067i	−0.975266	+	0.221034i	$0.929057\pi$
$104$	757.617	−	723.292i	0.714331	−	0.681967i
$105$		−	3571.59i		−	3.31954i
$106$	165.074	−	165.074i	0.151259	−	0.151259i
$107$		−	188.533i		−	0.170338i	−0.996367	−	0.0851689i	$-0.972857\pi$
$107$		−	188.533i		−	0.170338i	0.996367	−	0.0851689i	$-0.0271430\pi$
$108$		−	1906.22i		−	1.69839i
$109$	472.188	−	472.188i	0.414930	−	0.414930i	−0.468522	−	0.883452i	$-0.655213\pi$
$109$	472.188	−	472.188i	0.414930	−	0.414930i	0.883452	+	0.468522i	$0.155213\pi$
$110$	−223.396	−	817.455i	−0.193636	−	0.708557i
$111$	−1937.57	+	1937.57i	−1.65681	+	1.65681i
$112$	−47.8536	−	47.8536i	−0.0403727	−	0.0403727i
$113$	952.049			0.792577			0.396289	−	0.918126i	$-0.370298\pi$
$113$	952.049			0.792577			0.396289	+	0.918126i	$0.370298\pi$
$114$			1243.67i			1.02175i
$115$	777.932	−	777.932i	0.630805	−	0.630805i
$116$	−882.329			−0.706226
$117$	−71.5903	+	3088.66i	−0.0565686	+	2.44057i
$118$		−	1129.56i		−	0.881222i
$119$	1167.95	+	1167.95i	0.899712	+	0.899712i
$120$			2929.07i			2.22822i
$121$	−1146.01	+	676.922i	−0.861014	+	0.508581i
$122$	229.960	+	229.960i	0.170653	+	0.170653i
$123$	−1327.19	+	1327.19i	−0.972913	+	0.972913i
$124$	85.6372	−	85.6372i	0.0620197	−	0.0620197i
$125$	625.891	−	625.891i	0.447851	−	0.447851i
$126$	−3068.02			−2.16921
$127$	−985.441			−0.688534			−0.344267	−	0.938872i	$-0.611872\pi$
$127$	−985.441			−0.688534			−0.344267	+	0.938872i	$0.611872\pi$
$128$	681.679	+	681.679i	0.470722	+	0.470722i
$129$	285.268			0.194701
$130$	25.2289	−	1088.46i	0.0170209	−	0.734342i
$131$		−	10.8330i		−	0.00722508i	−0.999993	−	0.00361254i	$-0.998850\pi$
$131$		−	10.8330i		−	0.00722508i	0.999993	−	0.00361254i	$-0.00114991\pi$
$132$	1723.96	−	471.126i	1.13675	−	0.310653i
$133$	−2058.14			−1.34183
$134$	1632.20			1.05224
$135$	−3606.57	−	3606.57i	−2.29929	−	2.29929i
$136$	−957.836	−	957.836i	−0.603925	−	0.603925i
$137$	605.551	−	605.551i	0.377633	−	0.377633i	−0.492615	−	0.870248i	$-0.663959\pi$
$137$	605.551	−	605.551i	0.377633	−	0.377633i	0.870248	+	0.492615i	$0.163959\pi$
$138$	−941.983	−	941.983i	−0.581065	−	0.581065i
$139$			3123.89i			1.90622i	0.302621	+	0.953111i	$0.402139\pi$
$139$			3123.89i			1.90622i	−0.302621	+	0.953111i	$0.597861\pi$
$140$	−1883.05			−1.13676
$141$	−1654.33	+	1654.33i	−0.988085	+	0.988085i
$142$	−740.460			−0.437592
$143$	−1659.55	+	412.446i	−0.970477	+	0.241192i
$144$	−163.702			−0.0947348
$145$	−1669.37	+	1669.37i	−0.956094	+	0.956094i
$146$	−467.744			−0.265142
$147$		−	3850.82i		−	2.16062i
$148$	1021.55	+	1021.55i	0.567369	+	0.567369i
$149$	387.566	−	387.566i	0.213091	−	0.213091i	−0.592488	−	0.805579i	$-0.701854\pi$
$149$	387.566	−	387.566i	0.213091	−	0.213091i	0.805579	+	0.592488i	$0.201854\pi$
$150$	697.487	+	697.487i	0.379664	+	0.379664i
$151$	−1583.77	−	1583.77i	−0.853546	−	0.853546i	0.137022	−	0.990568i	$-0.456247\pi$
$151$	−1583.77	−	1583.77i	−0.853546	−	0.853546i	−0.990568	+	0.137022i	$0.956247\pi$
$152$	1687.88			0.900691
$153$	3995.42			2.11118
$154$	−447.658	−	1638.08i	−0.234242	−	0.857146i
$155$		−	324.052i		−	0.167926i
$156$	2295.49	+	53.2059i	1.17812	+	0.0273070i
$157$	1544.24			0.784992			0.392496	−	0.919754i	$-0.371612\pi$
$157$	1544.24			0.784992			0.392496	+	0.919754i	$0.371612\pi$
$158$	41.6666	+	41.6666i	0.0209798	+	0.0209798i
$159$	1317.33			0.657049
$160$	2488.67			1.22966
$161$	1558.88	−	1558.88i	0.763088	−	0.763088i
$162$	−2217.52	+	2217.52i	−1.07546	+	1.07546i
$163$	116.025	−	116.025i	0.0557534	−	0.0557534i	−0.678680	−	0.734434i	$-0.737448\pi$
$163$	116.025	−	116.025i	0.0557534	−	0.0557534i	0.734434	+	0.678680i	$0.237448\pi$
$164$	699.733	+	699.733i	0.333170	+	0.333170i
$165$	2370.36	−	4153.10i	1.11838	−	1.95951i
$166$			1279.84i			0.598403i
$167$	576.122	+	576.122i	0.266956	+	0.266956i	0.827873	−	0.560916i	$-0.189551\pi$
$167$	576.122	+	576.122i	0.266956	+	0.266956i	−0.560916	+	0.827873i	$0.689551\pi$
$168$			5869.50i			2.69549i
$169$	−2194.64	−	101.791i	−0.998926	−	0.0463320i
$170$	−1408.01			−0.635233
$171$	−3520.32	+	3520.32i	−1.57430	+	1.57430i
$172$		−	150.402i		−	0.0666747i
$173$	3595.60			1.58016			0.790082	−	0.613002i	$-0.210038\pi$
$173$	3595.60			1.58016			0.790082	+	0.613002i	$0.210038\pi$
$174$	2021.41	+	2021.41i	0.880705	+	0.880705i
$175$	−1154.27	+	1154.27i	−0.498597	+	0.498597i
$176$	−23.8859	−	87.4039i	−0.0102299	−	0.0374336i
$177$	4507.05	−	4507.05i	1.91396	−	1.91396i
$178$			72.6250i			0.0305813i
$179$		−	1244.09i		−	0.519482i	−0.965678	−	0.259741i	$-0.916363\pi$
$179$		−	1244.09i		−	0.519482i	0.965678	−	0.259741i	$-0.0836372\pi$
$180$	−3220.85	+	3220.85i	−1.33371	+	1.33371i
$181$		−	610.499i		−	0.250707i	−0.992112	−	0.125354i	$-0.959993\pi$
$181$		−	610.499i		−	0.250707i	0.992112	−	0.125354i	$-0.0400066\pi$
$182$	50.5557	−	2181.15i	0.0205903	−	0.888338i
$183$			1835.13i			0.741293i
$184$	−1278.44	+	1278.44i	−0.512217	+	0.512217i
$185$	3865.54			1.53622
$186$	−392.388			−0.154684
$187$	582.976	+	2133.24i	0.227976	+	0.834215i
$188$	872.215	+	872.215i	0.338366	+	0.338366i
$189$	−7227.14	−	7227.14i	−2.78146	−	2.78146i
$190$	1240.58	−	1240.58i	0.473692	−	0.473692i
$191$	3895.25			1.47566			0.737829	−	0.674988i	$-0.235851\pi$
$191$	3895.25			1.47566			0.737829	+	0.674988i	$0.235851\pi$
$192$		−	2821.96i		−	1.06072i
$193$	1368.89	+	1368.89i	0.510544	+	0.510544i	0.914693	−	0.404149i	$-0.132432\pi$
$193$	1368.89	+	1368.89i	0.510544	+	0.510544i	−0.404149	+	0.914693i	$0.632432\pi$
$194$	3180.28			1.17696
$195$	4443.75	−	4242.41i	1.63191	−	1.55798i
$196$	−2030.27			−0.739895
$197$	−2026.24	+	2026.24i	−0.732811	+	0.732811i	−0.971176	−	0.238365i	$-0.923389\pi$
$197$	−2026.24	+	2026.24i	−0.732811	+	0.732811i	0.238365	+	0.971176i	$0.423389\pi$
$198$	−3567.54	−	2036.15i	−1.28047	−	0.730823i
$199$		−	1811.92i		−	0.645444i	−0.946494	−	0.322722i	$-0.895402\pi$
$199$		−	1811.92i		−	0.645444i	0.946494	−	0.322722i	$-0.104598\pi$
$200$	946.615	−	946.615i	0.334679	−	0.334679i
$201$	6512.64	+	6512.64i	2.28540	+	2.28540i
$202$	−2027.44	+	2027.44i	−0.706188	+	0.706188i
$203$	−3345.22	+	3345.22i	−1.15659	+	1.15659i
$204$		−	2969.40i		−	1.01912i
$205$	2647.80			0.902098
$206$	−558.172	−	558.172i	−0.188785	−	0.188785i
$207$		−	5332.76i		−	1.79059i
$208$	2.69752	−	116.381i	0.000899229	−	0.0387959i
$209$	−2393.23	−	1365.92i	−0.792073	−	0.452071i
$210$	4314.06	+	4314.06i	1.41761	+	1.41761i
$211$		−	3739.12i		−	1.21996i	−0.792416	−	0.609981i	$-0.791177\pi$
$211$		−	3739.12i		−	1.21996i	0.792416	−	0.609981i	$-0.208823\pi$
$212$		−	694.535i		−	0.225004i
$213$	−2954.51	−	2954.51i	−0.950422	−	0.950422i
$214$	227.725	+	227.725i	0.0727428	+	0.0727428i
$215$	−284.561	−	284.561i	−0.0902647	−	0.0902647i
$216$	5926.98	+	5926.98i	1.86704	+	1.86704i
$217$		−	649.361i		−	0.203141i
$218$			1140.69i			0.354392i
$219$	−1866.35	−	1866.35i	−0.575873	−	0.575873i
$220$	−2189.64	−	1249.73i	−0.671026	−	0.382984i
$221$	−65.8377	+	2840.47i	−0.0200395	+	0.864572i
$222$		−	4680.71i		−	1.41508i
$223$	262.813	+	262.813i	0.0789204	+	0.0789204i	0.745465	−	0.666545i	$-0.232227\pi$
$223$	262.813	+	262.813i	0.0789204	+	0.0789204i	−0.666545	+	0.745465i	$0.732227\pi$
$224$	4986.99			1.48753
$225$			3948.62i			1.16996i
$226$	−1149.96	+	1149.96i	−0.338470	+	0.338470i
$227$	−336.415	+	336.415i	−0.0983641	+	0.0983641i	−0.754576	−	0.656212i	$-0.772158\pi$
$227$	−336.415	+	336.415i	−0.0983641	+	0.0983641i	0.656212	+	0.754576i	$0.272158\pi$
$228$	2616.30	+	2616.30i	0.759952	+	0.759952i
$229$	−2908.67	+	2908.67i	−0.839346	+	0.839346i	−0.988773	−	0.149427i	$-0.952257\pi$
$229$	−2908.67	+	2908.67i	−0.839346	+	0.839346i	0.149427	+	0.988773i	$0.452257\pi$
$230$			1879.30i			0.538771i
$231$	4749.92	−	8322.32i	1.35291	−	2.37043i
$232$	2743.42	−	2743.42i	0.776354	−	0.776354i
$233$	−4720.74			−1.32732			−0.663661	−	0.748033i	$-0.730998\pi$
$233$	−4720.74			−1.32732			−0.663661	+	0.748033i	$0.730998\pi$
$234$	−3644.26	−	3817.20i	−1.01809	−	1.06640i
$235$	3300.47			0.916165
$236$	−2376.25	−	2376.25i	−0.655428	−	0.655428i
$237$			332.508i			0.0911339i
$238$	−2821.49			−0.768445
$239$	−2842.62	+	2842.62i	−0.769348	+	0.769348i	−0.977992	−	0.208644i	$-0.933095\pi$
$239$	−2842.62	+	2842.62i	−0.769348	+	0.769348i	0.208644	+	0.977992i	$0.433095\pi$
$240$	230.187	+	230.187i	0.0619105	+	0.0619105i
$241$	3842.20	+	3842.20i	1.02696	+	1.02696i	0.999626	+	0.0273358i	$0.00870234\pi$
$241$	3842.20	+	3842.20i	1.02696	+	1.02696i	0.0273358	+	0.999626i	$0.491298\pi$
$242$	566.602	−	2201.88i	0.150506	−	0.584886i
$243$	−7568.89			−1.99813
$244$	967.536			0.253853
$245$	−3841.28	+	3841.28i	−1.00168	+	1.00168i
$246$		−	3206.16i		−	0.830966i
$247$	−2444.70	−	2560.71i	−0.629766	−	0.659653i
$248$			532.541i			0.136357i
$249$	−5106.70	+	5106.70i	−1.29969	+	1.29969i
$250$			1512.00i			0.382510i
$251$			5775.65i			1.45241i	0.687476	+	0.726207i	$0.258719\pi$
$251$			5775.65i			1.45241i	−0.687476	+	0.726207i	$0.741281\pi$
$252$	−6454.21	+	6454.21i	−1.61340	+	1.61340i
$253$	2847.28	−	778.109i	0.707536	−	0.193357i
$254$	1190.30	−	1190.30i	0.294038	−	0.294038i
$255$	−5618.12	−	5618.12i	−1.37969	−	1.37969i
$256$	−3988.86			−0.973842
$257$			6739.31i			1.63575i	0.575399	+	0.817873i	$0.304847\pi$
$257$			6739.31i			1.63575i	−0.575399	+	0.817873i	$0.695153\pi$
$258$	−344.570	+	344.570i	−0.0831472	+	0.0831472i
$259$	7746.08			1.85837
$260$	−2236.73	−	2342.88i	−0.533523	−	0.558843i
$261$			11443.6i			2.71395i
$262$	13.0850	+	13.0850i	0.00308547	+	0.00308547i
$263$		−	4193.45i		−	0.983191i	−0.870824	−	0.491595i	$-0.836414\pi$
$263$		−	4193.45i		−	0.983191i	0.870824	−	0.491595i	$-0.163586\pi$
$264$	−3895.41	+	6825.14i	−0.908128	+	1.59113i
$265$	−1314.06	−	1314.06i	−0.304612	−	0.304612i
$266$	2485.98	−	2485.98i	0.573028	−	0.573028i
$267$	−289.781	+	289.781i	−0.0664207	+	0.0664207i
$268$	3433.66	−	3433.66i	0.782628	−	0.782628i
$269$	1804.83			0.409080			0.204540	−	0.978858i	$-0.434430\pi$
$269$	1804.83			0.409080			0.204540	+	0.978858i	$0.434430\pi$
$270$	8712.61			1.96383
$271$	−928.069	−	928.069i	−0.208030	−	0.208030i	0.595400	−	0.803430i	$-0.296994\pi$
$271$	−928.069	−	928.069i	−0.208030	−	0.208030i	−0.803430	+	0.595400i	$0.796994\pi$
$272$	−150.547			−0.0335599
$273$	8904.73	−	8501.29i	1.97414	−	1.88469i
$274$			1462.87i			0.322537i
$275$	−2108.25	+	576.147i	−0.462299	+	0.126338i
$276$	−3963.31			−0.864359
$277$	−2737.25			−0.593737			−0.296869	−	0.954918i	$-0.595942\pi$
$277$	−2737.25			−0.593737			−0.296869	+	0.954918i	$0.595942\pi$
$278$	−3773.29	−	3773.29i	−0.814053	−	0.814053i
$279$	−1110.70	−	1110.70i	−0.238335	−	0.238335i
$280$	5854.96	−	5854.96i	1.24964	−	1.24964i
$281$	2169.79	+	2169.79i	0.460636	+	0.460636i	0.898864	−	0.438228i	$-0.144394\pi$
$281$	2169.79	+	2169.79i	0.460636	+	0.460636i	−0.438228	+	0.898864i	$0.644394\pi$
$282$		−	3996.47i		−	0.843924i
$283$	6182.76			1.29868			0.649340	−	0.760498i	$-0.275045\pi$
$283$	6182.76			1.29868			0.649340	+	0.760498i	$0.275045\pi$
$284$	−1557.71	+	1557.71i	−0.325468	+	0.325468i
$285$	9900.12			2.05766
$286$	1506.35	−	2502.72i	0.311442	−	0.517444i
$287$	5305.87			1.09127
$288$	8529.96	−	8529.96i	1.74525	−	1.74525i
$289$	−1238.63			−0.252113
$290$		−	4032.80i		−	0.816601i
$291$	12689.7	+	12689.7i	2.55629	+	2.55629i
$292$	−983.995	+	983.995i	−0.197205	+	0.197205i
$293$	−5995.05	−	5995.05i	−1.19534	−	1.19534i	−0.975547	−	0.219793i	$-0.929462\pi$
$293$	−5995.05	−	5995.05i	−1.19534	−	1.19534i	−0.219793	−	0.975547i	$-0.570538\pi$
$294$	4651.34	+	4651.34i	0.922692	+	0.922692i
$295$	−8991.77			−1.77465
$296$	−6352.56			−1.24742
$297$	−3607.39	−	13200.3i	−0.704788	−	2.57898i
$298$			936.266i			0.182001i
$299$	3791.22	+	87.8747i	0.733284	+	0.0169964i
$300$	2934.61			0.564766
$301$	−570.227	−	570.227i	−0.109194	−	0.109194i
$302$	3826.01			0.729015
$303$	−16179.4			−3.06759
$304$	132.646	−	132.646i	0.0250255	−	0.0250255i
$305$	1830.58	−	1830.58i	0.343668	−	0.343668i
$306$	−4825.99	+	4825.99i	−0.901581	+	0.901581i
$307$	4148.81	+	4148.81i	0.771288	+	0.771288i	0.978332	−	0.207044i	$-0.0663843\pi$
$307$	4148.81	+	4148.81i	0.771288	+	0.771288i	−0.207044	+	0.978332i	$0.566384\pi$
$308$	−4387.78	−	2504.30i	−0.811744	−	0.463298i
$309$		−	4454.33i		−	0.820058i
$310$	391.416	+	391.416i	0.0717127	+	0.0717127i
$311$		−	8079.39i		−	1.47312i	−0.676373	−	0.736560i	$-0.736449\pi$
$311$		−	8079.39i		−	1.47312i	0.676373	−	0.736560i	$-0.263551\pi$
$312$	−7302.77	+	6971.91i	−1.32512	+	1.26509i
$313$	−9668.03			−1.74591			−0.872954	−	0.487802i	$-0.837799\pi$
$313$	−9668.03			−1.74591			−0.872954	+	0.487802i	$0.837799\pi$
$314$	−1865.26	+	1865.26i	−0.335231	+	0.335231i
$315$			24422.8i			4.36847i
$316$	175.308			0.0312084
$317$	−2452.47	−	2452.47i	−0.434525	−	0.434525i	0.455639	−	0.890164i	$-0.349411\pi$
$317$	−2452.47	−	2452.47i	−0.434525	−	0.434525i	−0.890164	+	0.455639i	$0.849411\pi$
$318$	−1591.17	+	1591.17i	−0.280593	+	0.280593i
$319$	−6109.99	+	1669.75i	−1.07239	+	0.293066i
$320$	−2814.97	+	2814.97i	−0.491755	+	0.491755i
$321$			1817.29i			0.315986i
$322$			3765.89i			0.651754i
$323$	−3237.45	+	3237.45i	−0.557698	+	0.557698i
$324$			9330.01i			1.59980i
$325$	−2807.19	−	65.0664i	−0.479123	−	0.0111053i
$326$			280.290i			0.0476190i
$327$	−4551.49	+	4551.49i	−0.769718	+	0.769718i
$328$	−4351.34			−0.732508
$329$	6613.74			1.10829
$330$	2153.34	+	7879.57i	0.359205	+	1.31441i
$331$	−800.961	−	800.961i	−0.133005	−	0.133005i	0.637470	−	0.770475i	$-0.279981\pi$
$331$	−800.961	−	800.961i	−0.133005	−	0.133005i	−0.770475	+	0.637470i	$0.779981\pi$
$332$	2692.41	+	2692.41i	0.445075	+	0.445075i
$333$	13249.2	−	13249.2i	2.18034	−	2.18034i
$334$	−1391.77			−0.228008
$335$		−	12993.0i		−	2.11906i
$336$	461.268	+	461.268i	0.0748935	+	0.0748935i
$337$	−4404.76			−0.711996			−0.355998	−	0.934487i	$-0.615859\pi$
$337$	−4404.76			−0.711996			−0.355998	+	0.934487i	$0.615859\pi$
$338$	2773.82	−	2527.91i	0.446378	−	0.406806i
$339$	−9176.93			−1.47027
$340$	−2962.04	+	2962.04i	−0.472468	+	0.472468i
$341$	430.962	−	755.087i	0.0684395	−	0.119913i
$342$		−	8504.26i		−	1.34461i
$343$	−1088.61	+	1088.61i	−0.171368	+	0.171368i
$344$	467.643	+	467.643i	0.0732954	+	0.0732954i
$345$	−7498.60	+	7498.60i	−1.17018	+	1.17018i
$346$	−4343.05	+	4343.05i	−0.674809	+	0.674809i
$347$		−	4820.58i		−	0.745770i	−0.927878	−	0.372885i	$-0.878369\pi$
$347$		−	4820.58i		−	0.745770i	0.927878	−	0.372885i	$-0.121631\pi$
$348$	8504.89			1.31009
$349$	−5110.33	−	5110.33i	−0.783811	−	0.783811i	0.196661	−	0.980472i	$-0.436990\pi$
$349$	−5110.33	−	5110.33i	−0.783811	−	0.783811i	−0.980472	+	0.196661i	$0.936990\pi$
$350$		−	2788.43i		−	0.425852i
$351$	407.396	−	17576.5i	0.0619521	−	2.67283i
$352$	5798.95	+	3309.71i	0.878082	+	0.501160i
$353$	387.242	+	387.242i	0.0583876	+	0.0583876i	0.735698	−	0.677310i	$-0.236854\pi$
$353$	387.242	+	387.242i	0.0583876	+	0.0583876i	−0.677310	+	0.735698i	$0.736854\pi$
$354$			10888.0i			1.63471i
$355$			5894.39i			0.881244i
$356$	152.782	+	152.782i	0.0227455	+	0.0227455i
$357$	−11258.0	−	11258.0i	−1.66901	−	1.66901i
$358$	1502.71	+	1502.71i	0.221845	+	0.221845i
$359$	1950.02	+	1950.02i	0.286680	+	0.286680i	0.835766	−	0.549086i	$-0.185024\pi$
$359$	1950.02	+	1950.02i	0.286680	+	0.286680i	−0.549086	+	0.835766i	$0.685024\pi$
$360$		−	20029.1i		−	2.93230i
$361$			1154.04i			0.168252i
$362$	737.410	+	737.410i	0.107065	+	0.107065i
$363$	11046.5	−	6524.94i	1.59723	−	0.943446i
$364$	−4482.14	−	4694.85i	−0.645406	−	0.676035i
$365$			3723.45i			0.533957i
$366$	−2216.62	−	2216.62i	−0.316570	−	0.316570i
$367$	9443.65			1.34320			0.671600	−	0.740914i	$-0.265607\pi$
$367$	9443.65			1.34320			0.671600	+	0.740914i	$0.265607\pi$
$368$			200.938i			0.0284637i
$369$	9075.38	−	9075.38i	1.28034	−	1.28034i
$370$	−4669.11	+	4669.11i	−0.656042	+	0.656042i
$371$	−2633.23	−	2633.23i	−0.368491	−	0.368491i
$372$	−825.469	+	825.469i	−0.115050	+	0.115050i
$373$			12390.0i			1.71993i	0.510357	+	0.859963i	$0.329513\pi$
$373$			12390.0i			1.71993i	−0.510357	+	0.859963i	$0.670487\pi$
$374$	−3280.87	−	1872.54i	−0.453609	−	0.258894i
$375$	−6033.06	+	6033.06i	−0.830788	+	0.830788i
$376$	−5423.93			−0.743931
$377$	−8135.61	−	188.571i	−1.11142	−	0.0257610i
$378$	17459.0			2.37565
$379$	3758.26	+	3758.26i	0.509364	+	0.509364i	0.914331	−	0.404967i	$-0.132717\pi$
$379$	3758.26	+	3758.26i	0.509364	+	0.509364i	−0.404967	+	0.914331i	$0.632717\pi$
$380$		−	5219.65i		−	0.704637i
$381$	9498.81			1.27727
$382$	−4705.00	+	4705.00i	−0.630180	+	0.630180i
$383$	5435.37	+	5435.37i	0.725156	+	0.725156i	0.969651	−	0.244495i	$-0.0786222\pi$
$383$	5435.37	+	5435.37i	0.725156	+	0.725156i	−0.244495	+	0.969651i	$0.578622\pi$
$384$	−6570.80	−	6570.80i	−0.873215	−	0.873215i
$385$	−13039.9	+	3563.56i	−1.72616	+	0.471729i
$386$	−3306.91			−0.436056
$387$	−1950.68			−0.256224
$388$	6690.37	−	6690.37i	0.875392	−	0.875392i
$389$		−	3543.85i		−	0.461903i	−0.972965	−	0.230951i	$-0.925816\pi$
$389$		−	3543.85i		−	0.461903i	0.972965	−	0.230951i	$-0.0741839\pi$
$390$	−243.185	+	10491.8i	−0.0315747	+	1.36224i
$391$		−	4904.24i		−	0.634318i
$392$	6312.70	−	6312.70i	0.813366	−	0.813366i
$393$			104.421i			0.0134029i
$394$		−	4894.92i		−	0.625894i
$395$	331.684	−	331.684i	0.0422503	−	0.0422503i
$396$	−11788.5	+	3221.59i	−1.49595	+	0.408815i
$397$	2449.82	−	2449.82i	0.309706	−	0.309706i	−0.535090	−	0.844795i	$-0.679722\pi$
$397$	2449.82	−	2449.82i	0.309706	−	0.309706i	0.844795	+	0.535090i	$0.179722\pi$
$398$	2188.58	+	2188.58i	0.275637	+	0.275637i
$399$	19838.7			2.48916
$400$		−	148.784i		−	0.0185980i
$401$	7534.08	−	7534.08i	0.938239	−	0.938239i	−0.0599616	−	0.998201i	$-0.519098\pi$
$401$	7534.08	−	7534.08i	0.938239	−	0.938239i	0.998201	+	0.0599616i	$0.0190978\pi$
$402$	−15733.0			−1.95196
$403$	807.929	−	771.325i	0.0998656	−	0.0953410i
$404$			8530.25i			1.05049i
$405$	17652.4	+	17652.4i	2.16582	+	2.16582i
$406$		−	8081.25i		−	0.987847i
$407$	9007.25	+	5140.84i	1.09699	+	0.626098i
$408$	9232.72	+	9232.72i	1.12031	+	1.12031i
$409$	−11089.4	+	11089.4i	−1.34067	+	1.34067i	−0.445281	+	0.895391i	$0.646896\pi$
$409$	−11089.4	+	11089.4i	−1.34067	+	1.34067i	−0.895391	+	0.445281i	$0.853104\pi$
$410$	−3198.22	+	3198.22i	−0.385241	+	0.385241i
$411$	−5836.99	+	5836.99i	−0.700529	+	0.700529i
$412$	−2348.46			−0.280826
$413$	−18018.4			−2.14680
$414$	6441.34	+	6441.34i	0.764672	+	0.764672i
$415$	10188.1			1.20509
$416$	5923.65	+	6204.77i	0.698151	+	0.731283i
$417$		−	30111.6i		−	3.53614i
$418$	4540.61	−	1240.87i	0.531312	−	0.145198i
$419$	−575.332			−0.0670807			−0.0335404	−	0.999437i	$-0.510678\pi$
$419$	−575.332			−0.0670807			−0.0335404	+	0.999437i	$0.510678\pi$
$420$	18151.0			2.10876
$421$	−578.747	−	578.747i	−0.0669985	−	0.0669985i	0.672814	−	0.739812i	$-0.265086\pi$
$421$	−578.747	−	578.747i	−0.0669985	−	0.0669985i	−0.739812	+	0.672814i	$0.765086\pi$
$422$	4516.41	+	4516.41i	0.520985	+	0.520985i
$423$	11312.4	−	11312.4i	1.30031	−	1.30031i
$424$	2159.51	+	2159.51i	0.247347	+	0.247347i
$425$			3631.32i			0.414459i
$426$	7137.40			0.811756
$427$	3668.27	−	3668.27i	0.415738	−	0.415738i
$428$	958.133			0.108208
$429$	15996.6	−	3975.62i	1.80029	−	0.447424i
$430$	687.432			0.0770952
$431$	−249.071	+	249.071i	−0.0278360	+	0.0278360i	−0.720888	−	0.693052i	$-0.756266\pi$
$431$	−249.071	+	249.071i	−0.0278360	+	0.0278360i	0.693052	+	0.720888i	$0.256266\pi$
$432$	931.570			0.103750
$433$			5248.59i			0.582519i	0.956644	+	0.291260i	$0.0940744\pi$
$433$			5248.59i			0.582519i	−0.956644	+	0.291260i	$0.905926\pi$
$434$	784.351	+	784.351i	0.0867513	+	0.0867513i
$435$	16091.3	−	16091.3i	1.77361	−	1.77361i
$436$	2399.68	+	2399.68i	0.263587	+	0.263587i
$437$	4321.08	+	4321.08i	0.473009	+	0.473009i
$438$	4508.65			0.491853
$439$	11515.9			1.25199			0.625994	−	0.779828i	$-0.284693\pi$
$439$	11515.9			1.25199			0.625994	+	0.779828i	$0.284693\pi$
$440$	10694.0	−	2922.47i	1.15867	−	0.316644i
$441$			26332.2i			2.84334i
$442$	−3351.42	−	3510.47i	−0.360658	−	0.377774i
$443$	−6835.66			−0.733120			−0.366560	−	0.930394i	$-0.619465\pi$
$443$	−6835.66			−0.733120			−0.366560	+	0.930394i	$0.619465\pi$
$444$	−9846.82	−	9846.82i	−1.05250	−	1.05250i
$445$	578.127			0.0615861
$446$	−634.894			−0.0674060
$447$	−3735.80	+	3735.80i	−0.395296	+	0.395296i
$448$	−5640.86	+	5640.86i	−0.594879	+	0.594879i
$449$	5223.62	−	5223.62i	0.549037	−	0.549037i	−0.377125	−	0.926162i	$-0.623087\pi$
$449$	5223.62	−	5223.62i	0.549037	−	0.549037i	0.926162	+	0.377125i	$0.123087\pi$
$450$	−4769.46	−	4769.46i	−0.499632	−	0.499632i
$451$	6169.74	+	3521.34i	0.644172	+	0.367658i
$452$			4838.36i			0.503490i
$453$	15266.2	+	15266.2i	1.58337	+	1.58337i
$454$		−	812.698i		−	0.0840128i
$455$	−17362.9	−	402.445i	−1.78898	−	0.0414658i
$456$	−16269.7			−1.67083
$457$	7059.71	−	7059.71i	0.722624	−	0.722624i	−0.246515	−	0.969139i	$-0.579285\pi$
$457$	7059.71	−	7059.71i	0.722624	−	0.722624i	0.969139	+	0.246515i	$0.0792854\pi$
$458$		−	7026.65i		−	0.716886i
$459$	−22736.6			−2.31210
$460$	3953.49	+	3953.49i	0.400722	+	0.400722i
$461$	−12506.1	+	12506.1i	−1.26348	+	1.26348i	−0.314090	+	0.949393i	$0.601699\pi$
$461$	−12506.1	+	12506.1i	−1.26348	+	1.26348i	−0.949393	+	0.314090i	$0.898301\pi$
$462$	4315.04	+	15789.7i	0.434532	+	1.59005i
$463$	7824.61	−	7824.61i	0.785401	−	0.785401i	−0.195336	−	0.980736i	$-0.562580\pi$
$463$	7824.61	−	7824.61i	0.785401	−	0.785401i	0.980736	+	0.195336i	$0.0625797\pi$
$464$		−	431.195i		−	0.0431417i
$465$			3123.58i			0.311511i
$466$	5702.10	−	5702.10i	0.566834	−	0.566834i
$467$			5201.12i			0.515373i	0.966229	+	0.257686i	$0.0829601\pi$
$467$			5201.12i			0.515373i	−0.966229	+	0.257686i	$0.917040\pi$
$468$	−15696.7	−	363.826i	−1.55039	−	0.0359356i
$469$		−	26036.4i		−	2.56343i
$470$	−3986.57	+	3986.57i	−0.391249	+	0.391249i
$471$	−14885.1			−1.45620
$472$	14776.9			1.44102
$473$	−284.626	−	1041.51i	−0.0276683	−	0.101245i
$474$	−401.630	−	401.630i	−0.0389187	−	0.0389187i
$475$	−3199.52	−	3199.52i	−0.309061	−	0.309061i
$476$	−5935.58	+	5935.58i	−0.571548	+	0.571548i
$477$	−9007.97			−0.864668
$478$		−	6867.10i		−	0.657100i
$479$	−3821.37	−	3821.37i	−0.364515	−	0.364515i	0.500957	−	0.865472i	$-0.332982\pi$
$479$	−3821.37	−	3821.37i	−0.364515	−	0.364515i	−0.865472	+	0.500957i	$0.832982\pi$
$480$	−23988.6			−2.28109
$481$	9200.95	+	9637.60i	0.872198	+	0.913590i
$482$	−9281.84			−0.877129
$483$	−15026.3	+	15026.3i	−1.41557	+	1.41557i
$484$	−3440.15	−	5824.08i	−0.323079	−	0.546964i
$485$		−	25316.4i		−	2.37023i
$486$	9142.31	−	9142.31i	0.853300	−	0.853300i
$487$	−4139.07	−	4139.07i	−0.385131	−	0.385131i	0.487815	−	0.872947i	$-0.337794\pi$
$487$	−4139.07	−	4139.07i	−0.385131	−	0.385131i	−0.872947	+	0.487815i	$0.837794\pi$
$488$	−3008.35	+	3008.35i	−0.279061	+	0.279061i
$489$	−1118.39	+	1118.39i	−0.103426	+	0.103426i
$490$		−	9279.62i		−	0.855532i
$491$	−9946.24			−0.914191			−0.457095	−	0.889418i	$-0.651110\pi$
$491$	−9946.24			−0.914191			−0.457095	+	0.889418i	$0.651110\pi$
$492$	−6744.82	−	6744.82i	−0.618049	−	0.618049i
$493$			10524.1i			0.961419i
$494$	6045.94	+	140.136i	0.550647	+	0.0127632i
$495$	−16208.7	+	28399.2i	−1.47177	+	2.57868i
$496$	41.8510	+	41.8510i	0.00378864	+	0.00378864i
$497$			11811.6i			1.06605i
$498$		−	12336.6i		−	1.11007i
$499$	−9254.47	−	9254.47i	−0.830235	−	0.830235i	0.157314	−	0.987549i	$-0.449717\pi$
$499$	−9254.47	−	9254.47i	−0.830235	−	0.830235i	−0.987549	+	0.157314i	$0.949717\pi$
$500$	3180.81	+	3180.81i	0.284500	+	0.284500i
$501$	−5553.33	−	5553.33i	−0.495218	−	0.495218i
$502$	−6976.30	−	6976.30i	−0.620254	−	0.620254i
$503$			11904.5i			1.05526i	0.849475	+	0.527629i	$0.176919\pi$
$503$			11904.5i			1.05526i	−0.849475	+	0.527629i	$0.823081\pi$
$504$		−	40136.0i		−	3.54722i
$505$	16139.3	+	16139.3i	1.42216	+	1.42216i
$506$	−2499.31	+	4379.03i	−0.219580	+	0.384727i
$507$	21154.5	+	981.182i	1.85306	+	0.0859484i
$508$		−	5008.06i		−	0.437395i
$509$	5014.47	+	5014.47i	0.436665	+	0.436665i	0.890888	−	0.454223i	$-0.150083\pi$
$509$	5014.47	+	5014.47i	0.436665	+	0.436665i	−0.454223	+	0.890888i	$0.650083\pi$
$510$	13572.0			1.17839
$511$			7461.35i			0.645930i
$512$	−635.367	+	635.367i	−0.0548428	+	0.0548428i
$513$	20032.9	−	20032.9i	1.72412	−	1.72412i
$514$	−8140.28	−	8140.28i	−0.698546	−	0.698546i
$515$	−4443.30	+	4443.30i	−0.380184	+	0.380184i
$516$			1449.75i			0.123685i
$517$	7690.56	+	4389.34i	0.654217	+	0.373391i
$518$	−9356.34	+	9356.34i	−0.793618	+	0.793618i
$519$	−34658.5			−2.93129
$520$	14239.3	+	330.046i	1.20084	+	0.0278336i
$521$	4837.05			0.406747			0.203374	−	0.979101i	$-0.434809\pi$
$521$	4837.05			0.406747			0.203374	+	0.979101i	$0.434809\pi$
$522$	−13822.5	−	13822.5i	−1.15899	−	1.15899i
$523$		−	6038.14i		−	0.504836i	−0.967618	−	0.252418i	$-0.918774\pi$
$523$		−	6038.14i		−	0.504836i	0.967618	−	0.252418i	$-0.0812258\pi$
$524$	55.0539			0.00458978
$525$	11126.1	−	11126.1i	0.924923	−	0.924923i
$526$	5065.19	+	5065.19i	0.419872	+	0.419872i
$527$	−1021.45	−	1021.45i	−0.0844304	−	0.0844304i
$528$	230.240	+	842.499i	0.0189771	+	0.0694414i
$529$	5621.22			0.462006
$530$	3174.46			0.260170
$531$	−30819.5	+	30819.5i	−2.51874	+	2.51874i
$532$		−	10459.5i		−	0.852404i
$533$	6302.42	+	6601.51i	0.512172	+	0.536479i
$534$		−	700.042i		−	0.0567300i
$535$	1812.79	−	1812.79i	0.146493	−	0.146493i
$536$			21352.5i			1.72068i
$537$			11991.9i			0.963668i
$538$	−2180.02	+	2180.02i	−0.174698	+	0.174698i
$539$	−14059.3	+	3842.16i	−1.12352	+	0.307038i
$540$	18328.8	−	18328.8i	1.46064	−	1.46064i
$541$	−1181.55	−	1181.55i	−0.0938981	−	0.0938981i	0.658597	−	0.752495i	$-0.271150\pi$
$541$	−1181.55	−	1181.55i	−0.0938981	−	0.0938981i	−0.752495	+	0.658597i	$0.771150\pi$
$542$	2241.99			0.177679
$543$			5884.69i			0.465076i
$544$	7844.53	−	7844.53i	0.618256	−	0.618256i
$545$	9080.42			0.713693
$546$	−487.313	+	21024.4i	−0.0381961	+	1.64791i
$547$		−	251.248i		−	0.0196391i	−0.999952	−	0.00981954i	$-0.996874\pi$
$547$		−	251.248i		−	0.0196391i	0.999952	−	0.00981954i	$-0.00312571\pi$
$548$	3077.44	+	3077.44i	0.239894	+	0.239894i
$549$		−	12548.7i		−	0.975531i
$550$	1850.60	−	3242.43i	0.143472	−	0.251378i
$551$	−9272.63	−	9272.63i	−0.716928	−	0.716928i
$552$	12323.1	−	12323.1i	0.950189	−	0.950189i
$553$	664.656	−	664.656i	0.0511104	−	0.0511104i
$554$	3306.27	−	3306.27i	0.253556	−	0.253556i
$555$	−37260.5			−2.84976
$556$	−15875.8			−1.21094
$557$	−4382.53	−	4382.53i	−0.333382	−	0.333382i	0.520487	−	0.853869i	$-0.325750\pi$
$557$	−4382.53	−	4382.53i	−0.333382	−	0.333382i	−0.853869	+	0.520487i	$0.825750\pi$
$558$	2683.18			0.203562
$559$	32.1438	−	1386.80i	0.00243209	−	0.104929i
$560$		−	920.250i		−	0.0694423i
$561$	−5619.39	−	20562.6i	−0.422907	−	1.54751i
$562$	−5241.69			−0.393429
$563$	22575.9			1.68998			0.844992	−	0.534779i	$-0.179605\pi$
$563$	22575.9			1.68998			0.844992	+	0.534779i	$0.179605\pi$
$564$	−8407.40	−	8407.40i	−0.627687	−	0.627687i
$565$	9154.20	+	9154.20i	0.681628	+	0.681628i
$566$	−7468.03	+	7468.03i	−0.554602	+	0.554602i
$567$	35373.4	+	35373.4i	2.62000	+	2.62000i
$568$		−	9686.74i		−	0.715575i
$569$	−3434.41			−0.253037			−0.126519	−	0.991964i	$-0.540380\pi$
$569$	−3434.41			−0.253037			−0.126519	+	0.991964i	$0.540380\pi$
$570$	−11958.2	+	11958.2i	−0.878724	+	0.878724i
$571$	7184.66			0.526565			0.263283	−	0.964719i	$-0.415195\pi$
$571$	7184.66			0.526565			0.263283	+	0.964719i	$0.415195\pi$
$572$	−2096.07	−	8433.90i	−0.153219	−	0.616502i
$573$	−37546.9			−2.73742
$574$	−6408.85	+	6408.85i	−0.466029	+	0.466029i
$575$	4846.79			0.351522
$576$			19296.7i			1.39589i
$577$	16129.0	+	16129.0i	1.16371	+	1.16371i	0.983658	+	0.180049i	$0.0576256\pi$
$577$	16129.0	+	16129.0i	1.16371	+	1.16371i	0.180049	+	0.983658i	$0.442374\pi$
$578$	1496.12	−	1496.12i	0.107665	−	0.107665i
$579$	−13194.9	−	13194.9i	−0.947086	−	0.947086i
$580$	−8483.82	−	8483.82i	−0.607365	−	0.607365i
$581$	20415.7			1.45781
$582$	−30655.2			−2.18333
$583$	−1314.36	−	4809.55i	−0.0933711	−	0.341666i
$584$		−	6119.05i		−	0.433576i
$585$	−30386.6	+	29009.9i	−2.14757	+	2.05028i
$586$	14482.6			1.02094
$587$	−8213.68	−	8213.68i	−0.577538	−	0.577538i	0.356686	−	0.934224i	$-0.383906\pi$
$587$	−8213.68	−	8213.68i	−0.577538	−	0.577538i	−0.934224	+	0.356686i	$0.883906\pi$
$588$	19570.1			1.37254
$589$	1799.97			0.125919
$590$	10861.0	−	10861.0i	0.757864	−	0.757864i
$591$	19531.2	−	19531.2i	1.35940	−	1.35940i
$592$	−499.231	+	499.231i	−0.0346592	+	0.0346592i
$593$	−5453.88	−	5453.88i	−0.377680	−	0.377680i	0.492585	−	0.870264i	$-0.336052\pi$
$593$	−5453.88	−	5453.88i	−0.377680	−	0.377680i	−0.870264	+	0.492585i	$0.836052\pi$
$594$	20301.6	+	11587.0i	1.40233	+	0.800373i
$595$			22460.3i			1.54753i
$596$	1969.63	+	1969.63i	0.135368	+	0.135368i
$597$			17465.3i			1.19733i
$598$	−4685.48	+	4473.20i	−0.320407	+	0.305891i
$599$	20024.7			1.36592			0.682960	−	0.730455i	$-0.260692\pi$
$599$	20024.7			1.36592			0.682960	+	0.730455i	$0.260692\pi$
$600$	−9124.56	+	9124.56i	−0.620847	+	0.620847i
$601$		−	11263.3i		−	0.764462i	−0.924067	−	0.382231i	$-0.875156\pi$
$601$		−	11263.3i		−	0.764462i	0.924067	−	0.382231i	$-0.124844\pi$
$602$	1377.53			0.0932625
$603$	−44533.8	−	44533.8i	−3.00756	−	3.00756i
$604$	8048.80	−	8048.80i	0.542221	−	0.542221i
$605$	−17528.0	−	4510.40i	−1.17787	−	0.303097i
$606$	19542.7	−	19542.7i	1.31002	−	1.31002i
$607$			13.9094i			0.000930093i	1.00000		0.000465047i	$0.000148029\pi$
$607$			13.9094i			0.000930093i	−1.00000		0.000465047i	$0.999852\pi$
$608$			13823.5i			0.922065i
$609$	32245.0	−	32245.0i	2.14554	−	2.14554i
$610$			4422.25i			0.293527i
$611$	7855.94	+	8228.76i	0.520159	+	0.544844i
$612$			20304.9i			1.34114i
$613$	1257.68	−	1257.68i	0.0828664	−	0.0828664i	−0.664459	−	0.747325i	$-0.731338\pi$
$613$	1257.68	−	1257.68i	0.0828664	−	0.0828664i	0.747325	+	0.664459i	$0.231338\pi$
$614$	−10022.5			−0.658757
$615$	−25522.5			−1.67344
$616$	21429.5	−	5856.29i	1.40165	−	0.383046i
$617$	−2008.21	−	2008.21i	−0.131033	−	0.131033i	0.638548	−	0.769582i	$-0.279535\pi$
$617$	−2008.21	−	2008.21i	−0.131033	−	0.131033i	−0.769582	+	0.638548i	$0.779535\pi$
$618$	5380.30	+	5380.30i	0.350206	+	0.350206i
$619$	−5379.80	+	5379.80i	−0.349325	+	0.349325i	−0.859858	−	0.510533i	$-0.829448\pi$
$619$	−5379.80	+	5379.80i	−0.349325	+	0.349325i	0.510533	+	0.859858i	$0.329448\pi$
$620$	1646.85			0.106676
$621$			30346.9i			1.96100i
$622$	9758.94	+	9758.94i	0.629096	+	0.629096i
$623$	1158.50			0.0745011
$624$	−26.0018	+	1121.81i	−0.00166812	+	0.0719684i
$625$	19524.5			1.24957
$626$	11677.8	−	11677.8i	0.745591	−	0.745591i
$627$	23068.7	+	13166.3i	1.46934	+	0.838616i
$628$			7847.90i			0.498671i
$629$	12184.6	−	12184.6i	0.772386	−	0.772386i
$630$	−29499.8	−	29499.8i	−1.86556	−	1.86556i
$631$	1269.04	−	1269.04i	0.0800631	−	0.0800631i	−0.665941	−	0.746004i	$-0.731970\pi$
$631$	1269.04	−	1269.04i	0.0800631	−	0.0800631i	0.746004	+	0.665941i	$0.231970\pi$
$632$	−545.084	+	545.084i	−0.0343074	+	0.0343074i
$633$			36041.9i			2.26309i
$634$	5924.58			0.371128
$635$	−9475.27	−	9475.27i	−0.592149	−	0.592149i
$636$			6694.72i			0.417395i
$637$	−18720.3	−	433.909i	−1.16441	−	0.0269892i
$638$	5363.28	−	9397.00i	0.332812	−	0.583120i
$639$	20203.1	+	20203.1i	1.25074	+	1.25074i
$640$			13109.0i			0.809657i
$641$		−	10318.2i		−	0.635797i	−0.948125	−	0.317898i	$-0.897023\pi$
$641$		−	10318.2i		−	0.635797i	0.948125	−	0.317898i	$-0.102977\pi$
$642$	−2195.07	−	2195.07i	−0.134942	−	0.134942i
$643$	12527.6	+	12527.6i	0.768335	+	0.768335i	0.977813	−	0.209478i	$-0.0671764\pi$
$643$	12527.6	+	12527.6i	0.768335	+	0.768335i	−0.209478	+	0.977813i	$0.567176\pi$
$644$	7922.32	+	7922.32i	0.484756	+	0.484756i
$645$	2742.93	+	2742.93i	0.167446	+	0.167446i
$646$		−	7820.90i		−	0.476330i
$647$		−	11019.5i		−	0.669585i	−0.942292	−	0.334793i	$-0.891334\pi$
$647$		−	11019.5i		−	0.669585i	0.942292	−	0.334793i	$-0.108666\pi$
$648$	−29009.7	−	29009.7i	−1.75866	−	1.75866i
$649$	−20952.1	−	11958.3i	−1.26724	−	0.723272i
$650$	3469.34	−	3312.16i	0.209352	−	0.199867i
$651$			6259.29i			0.376837i
$652$	589.647	+	589.647i	0.0354177	+	0.0354177i
$653$	−13016.3			−0.780042			−0.390021	−	0.920806i	$-0.627532\pi$
$653$	−13016.3			−0.780042			−0.390021	+	0.920806i	$0.627532\pi$
$654$		−	10995.3i		−	0.657417i
$655$	104.162	−	104.162i	0.00621368	−	0.00621368i
$656$	−341.960	+	341.960i	−0.0203526	+	0.0203526i
$657$	12762.2	+	12762.2i	0.757840	+	0.757840i
$658$	−7988.61	+	7988.61i	−0.473296	+	0.473296i
$659$			11073.0i			0.654542i	0.944931	+	0.327271i	$0.106129\pi$
$659$			11073.0i			0.654542i	−0.944931	+	0.327271i	$0.893871\pi$
$660$	21106.3	+	12046.3i	1.24479	+	0.710456i
$661$	−1550.67	+	1550.67i	−0.0912469	+	0.0912469i	−0.751257	−	0.660010i	$-0.770552\pi$
$661$	−1550.67	+	1550.67i	−0.0912469	+	0.0912469i	0.660010	+	0.751257i	$0.270552\pi$
$662$	1934.93			0.113600
$663$	634.619	−	27379.7i	0.0371743	−	1.60383i
$664$	−16742.9			−0.978542
$665$	−19789.5	−	19789.5i	−1.15399	−	1.15399i
$666$			32007.0i			1.86223i
$667$	14046.6			0.815424
$668$	−2927.88	+	2927.88i	−0.169586	+	0.169586i
$669$	−2533.29	−	2533.29i	−0.146402	−	0.146402i
$670$	15694.0	+	15694.0i	0.904944	+	0.904944i
$671$	6700.04	−	1831.00i	0.385473	−	0.105343i
$672$	−48070.3			−2.75945
$673$	2808.72			0.160874			0.0804369	−	0.996760i	$-0.474368\pi$
$673$	2808.72			0.160874			0.0804369	+	0.996760i	$0.474368\pi$
$674$	5320.43	−	5320.43i	0.304058	−	0.304058i
$675$		−	22470.2i		−	1.28130i
$676$	517.309	−	11153.3i	0.0294327	−	0.634574i
$677$		−	10581.3i		−	0.600700i	−0.953829	−	0.300350i	$-0.902896\pi$
$677$		−	10581.3i		−	0.600700i	0.953829	−	0.300350i	$-0.0971035\pi$
$678$	11084.6	−	11084.6i	0.627881	−	0.627881i
$679$		−	50731.1i		−	2.86728i
$680$		−	18419.7i		−	1.03877i
$681$	3242.75	−	3242.75i	0.182471	−	0.182471i
$682$	391.505	+	1432.61i	0.0219817	+	0.0804359i
$683$	−748.578	+	748.578i	−0.0419379	+	0.0419379i	−0.727765	−	0.685827i	$-0.759441\pi$
$683$	−748.578	+	748.578i	−0.0419379	+	0.0419379i	0.685827	+	0.727765i	$0.259441\pi$
$684$	−17890.5	−	17890.5i	−1.00009	−	1.00009i
$685$	11645.1			0.649540
$686$		−	2629.81i		−	0.146365i
$687$	28037.1	−	28037.1i	1.55703	−	1.55703i
$688$	73.5016			0.00407300
$689$	148.436	−	6404.04i	0.00820748	−	0.354099i
$690$		−	18114.8i		−	0.999448i
$691$	21035.1	+	21035.1i	1.15805	+	1.15805i	0.984894	+	0.173158i	$0.0553970\pi$
$691$	21035.1	+	21035.1i	1.15805	+	1.15805i	0.173158	+	0.984894i	$0.444603\pi$
$692$			18273.0i			1.00381i
$693$	−32480.2	+	56908.6i	−1.78041	+	3.11945i
$694$	5822.68	+	5822.68i	0.318481	+	0.318481i
$695$	−30037.0	+	30037.0i	−1.63938	+	1.63938i
$696$	−26444.2	+	26444.2i	−1.44018	+	1.44018i
$697$	8346.12	−	8346.12i	0.453561	−	0.453561i
$698$	12345.3			0.669453
$699$	45503.9			2.46225
$700$	−5866.04	−	5866.04i	−0.316737	−	0.316737i
$701$	14099.7			0.759682			0.379841	−	0.925052i	$-0.375979\pi$
$701$	14099.7			0.759682			0.379841	+	0.925052i	$0.375979\pi$
$702$	20738.2	+	21722.4i	1.11498	+	1.16789i
$703$			21471.4i			1.15193i
$704$	−10302.9	+	2815.61i	−0.551572	+	0.150735i
$705$	−31813.7			−1.69954
$706$	−935.484			−0.0498689
$707$	32341.2	+	32341.2i	1.72039	+	1.72039i
$708$	22905.0	+	22905.0i	1.21585	+	1.21585i
$709$	−19886.0	+	19886.0i	−1.05336	+	1.05336i	−0.0548693	+	0.998494i	$0.517474\pi$
$709$	−19886.0	+	19886.0i	−1.05336	+	1.05336i	−0.998494	+	0.0548693i	$0.982526\pi$
$710$	−7119.72	−	7119.72i	−0.376336	−	0.376336i
$711$		−	2273.71i		−	0.119931i
$712$	−950.084			−0.0500083
$713$	−1363.34	+	1363.34i	−0.0716094	+	0.0716094i
$714$	27196.7			1.42551
$715$	−19922.7	−	11991.2i	−1.04205	−	0.627196i
$716$	6322.50			0.330004
$717$	27400.5	−	27400.5i	1.42718	−	1.42718i
$718$	−4710.78			−0.244854
$719$			27965.9i			1.45056i	0.688454	+	0.725280i	$0.258290\pi$
$719$			27965.9i			1.45056i	−0.688454	+	0.725280i	$0.741710\pi$
$720$	−1574.04	−	1574.04i	−0.0814734	−	0.0814734i
$721$	−8903.83	+	8903.83i	−0.459911	+	0.459911i
$722$	−1393.95	−	1393.95i	−0.0718522	−	0.0718522i
$723$	−37035.5	−	37035.5i	−1.90507	−	1.90507i
$724$	3102.59			0.159263
$725$	−10400.8			−0.532793
$726$	−5461.56	+	21224.3i	−0.279197	+	1.08500i
$727$			9626.30i			0.491086i	0.969386	+	0.245543i	$0.0789663\pi$
$727$			9626.30i			0.491086i	−0.969386	+	0.245543i	$0.921034\pi$
$728$	28533.9	+	661.372i	1.45266	+	0.0336704i
$729$	23388.9			1.18828
$730$	−4497.48	−	4497.48i	−0.228026	−	0.228026i
$731$	−1793.93			−0.0907674
$732$	−9326.22			−0.470911
$733$	−7134.56	+	7134.56i	−0.359510	+	0.359510i	−0.863632	−	0.504122i	$-0.831816\pi$
$733$	−7134.56	+	7134.56i	−0.359510	+	0.359510i	0.504122	+	0.863632i	$0.331816\pi$
$734$	−11406.8	+	11406.8i	−0.573614	+	0.573614i
$735$	37026.7	−	37026.7i	1.85816	−	1.85816i
$736$	−10470.2	−	10470.2i	−0.524372	−	0.524372i
$737$	17279.6	−	30275.6i	0.863639	−	1.51318i
$738$			21923.9i			1.09354i
$739$	6244.87	+	6244.87i	0.310854	+	0.310854i	0.845240	−	0.534386i	$-0.179457\pi$
$739$	6244.87	+	6244.87i	0.310854	+	0.310854i	−0.534386	+	0.845240i	$0.679457\pi$
$740$			19644.9i			0.975891i
$741$	23564.8	+	24683.1i	1.16825	+	1.22369i
$742$	6361.25			0.314729
$743$	−21084.1	+	21084.1i	−1.04105	+	1.04105i	−0.0419304	+	0.999121i	$0.513351\pi$
$743$	−21084.1	+	21084.1i	−1.04105	+	1.04105i	−0.999121	+	0.0419304i	$0.986649\pi$
$744$		−	5133.24i		−	0.252949i
$745$	7453.09			0.366524
$746$	−14965.7	−	14965.7i	−0.734495	−	0.734495i
$747$	34919.9	−	34919.9i	1.71038	−	1.71038i
$748$	−10841.2	+	2962.71i	−0.529940	+	0.144823i
$749$	3632.62	−	3632.62i	0.177214	−	0.177214i
$750$		−	14574.4i		−	0.709577i
$751$		−	19560.3i		−	0.950422i	−0.879872	−	0.475211i	$-0.842372\pi$
$751$		−	19560.3i		−	0.950422i	0.879872	−	0.475211i	$-0.157628\pi$
$752$	−426.252	+	426.252i	−0.0206700	+	0.0206700i
$753$		−	55672.3i		−	2.69431i
$754$	10054.6	−	9599.08i	0.485633	−	0.463631i
$755$		−	30456.8i		−	1.46813i
$756$	36728.7	−	36728.7i	1.76694	−	1.76694i
$757$	−26249.4			−1.26031			−0.630153	−	0.776471i	$-0.717008\pi$
$757$	−26249.4			−1.26031			−0.630153	+	0.776471i	$0.717008\pi$
$758$	−9079.07			−0.435048
$759$	−27445.3	+	7500.30i	−1.31252	+	0.358687i
$760$	16229.4	+	16229.4i	0.774607	+	0.774607i
$761$	2339.67	+	2339.67i	0.111449	+	0.111449i	0.760632	−	0.649183i	$-0.224889\pi$
$761$	2339.67	+	2339.67i	0.111449	+	0.111449i	−0.649183	+	0.760632i	$0.724889\pi$
$762$	−11473.4	+	11473.4i	−0.545457	+	0.545457i
$763$	18196.1			0.863358
$764$			19795.9i			0.937421i
$765$	38417.0	+	38417.0i	1.81565	+	1.81565i
$766$	−13130.6			−0.619356
$767$	−21402.7	−	22418.4i	−1.00757	−	1.05538i
$768$	38449.2			1.80653
$769$	280.265	−	280.265i	0.0131425	−	0.0131425i	−0.700505	−	0.713648i	$-0.747042\pi$
$769$	280.265	−	280.265i	0.0131425	−	0.0131425i	0.713648	+	0.700505i	$0.247042\pi$
$770$	11446.2	−	20054.9i	0.535706	−	0.938610i
$771$		−	64961.1i		−	3.03439i
$772$	−6956.77	+	6956.77i	−0.324326	+	0.324326i
$773$	−13203.6	−	13203.6i	−0.614362	−	0.614362i	0.329717	−	0.944080i	$-0.393047\pi$
$773$	−13203.6	−	13203.6i	−0.614362	−	0.614362i	−0.944080	+	0.329717i	$0.893047\pi$
$774$	2356.19	−	2356.19i	0.109420	−	0.109420i
$775$	1009.48	−	1009.48i	0.0467891	−	0.0467891i
$776$			41604.6i			1.92464i
$777$	−74665.5			−3.44738
$778$	4280.55	+	4280.55i	0.197256	+	0.197256i
$779$			14707.4i			0.676439i
$780$	21560.1	+	22583.3i	0.989714	+	1.03668i
$781$	−7839.03	+	13734.8i	−0.359158	+	0.629281i
$782$	5923.74	+	5923.74i	0.270886	+	0.270886i
$783$		−	65121.6i		−	2.97223i
$784$		−	992.196i		−	0.0451984i
$785$	14848.3	+	14848.3i	0.675105	+	0.675105i
$786$	−126.128	−	126.128i	−0.00572372	−	0.00572372i
$787$	24580.8	+	24580.8i	1.11336	+	1.11336i	0.992694	+	0.120663i	$0.0385020\pi$
$787$	24580.8	+	24580.8i	1.11336	+	1.11336i	0.120663	+	0.992694i	$0.461498\pi$
$788$	−10297.5	−	10297.5i	−0.465523	−	0.465523i
$789$			40421.2i			1.82387i
$790$			801.270i			0.0360860i
$791$	18343.9	+	18343.9i	0.824570	+	0.824570i
$792$	26637.0	−	46670.7i	1.19508	−	2.09390i
$793$	8921.27	+	206.781i	0.399500	+	0.00925980i
$794$			5918.19i			0.264520i
$795$	12666.4	+	12666.4i	0.565072	+	0.565072i
$796$	9208.24			0.410022
$797$		−	28248.4i		−	1.25547i	−0.778427	−	0.627736i	$-0.783982\pi$
$797$		−	28248.4i		−	1.25547i	0.778427	−	0.627736i	$-0.216018\pi$
$798$	−23962.7	+	23962.7i	−1.06300	+	1.06300i
$799$	10403.4	−	10403.4i	0.460634	−	0.460634i
$800$	7752.63	+	7752.63i	0.342621	+	0.342621i
$801$	1981.54	−	1981.54i	0.0874087	−	0.0874087i
$802$			18200.5i			0.801351i
$803$	−4951.87	+	8676.16i	−0.217619	+	0.381289i
$804$	−33097.6	+	33097.6i	−1.45182	+	1.45182i
$805$	29978.1			1.31253
$806$	−44.2141	+	1907.55i	−0.00193223	+	0.0833630i
$807$	−17397.0			−0.758865
$808$	−26523.0	−	26523.0i	−1.15480	−	1.15480i
$809$		−	33885.6i		−	1.47263i	−0.676641	−	0.736313i	$-0.736565\pi$
$809$		−	33885.6i		−	1.47263i	0.676641	−	0.736313i	$-0.263435\pi$
$810$	−42644.1			−1.84983
$811$	−23913.2	+	23913.2i	−1.03539	+	1.03539i	−0.0360442	+	0.999350i	$0.511476\pi$
$811$	−23913.2	+	23913.2i	−1.03539	+	1.03539i	−0.999350	+	0.0360442i	$0.988524\pi$
$812$	−17000.6	−	17000.6i	−0.734733	−	0.734733i
$813$	8945.79	+	8945.79i	0.385907	+	0.385907i
$814$	−17089.2	+	4670.17i	−0.735843	+	0.201093i
$815$	2231.23			0.0958976
$816$	1451.15			0.0622553
$817$	1580.61	−	1580.61i	0.0676851	−	0.0676851i
$818$		−	26789.3i		−	1.14507i
$819$	−60891.1	+	58132.3i	−2.59793	+	2.48023i
$820$			13456.2i			0.573063i
$821$	16345.9	−	16345.9i	0.694855	−	0.694855i	−0.268441	−	0.963296i	$-0.586509\pi$
$821$	16345.9	−	16345.9i	0.694855	−	0.694855i	0.963296	+	0.268441i	$0.0865085\pi$
$822$		−	14100.8i		−	0.598323i
$823$		−	7543.83i		−	0.319516i	−0.987156	−	0.159758i	$-0.948929\pi$
$823$		−	7543.83i		−	0.319516i	0.987156	−	0.159758i	$-0.0510713\pi$
$824$	7302.04	−	7302.04i	0.308712	−	0.308712i
$825$	20321.7	−	5553.56i	0.857590	−	0.234364i
$826$	21764.1	−	21764.1i	0.916792	−	0.916792i
$827$	−8930.55	−	8930.55i	−0.375509	−	0.375509i	0.493970	−	0.869479i	$-0.335545\pi$
$827$	−8930.55	−	8930.55i	−0.375509	−	0.375509i	−0.869479	+	0.493970i	$0.835545\pi$
$828$	27101.3			1.13748
$829$		−	16925.7i		−	0.709112i	−0.935035	−	0.354556i	$-0.884632\pi$
$829$		−	16925.7i		−	0.709112i	0.935035	−	0.354556i	$-0.115368\pi$
$830$	−12306.0	+	12306.0i	−0.514635	+	0.514635i
$831$	26384.7			1.10141
$832$	−13718.6	−	317.977i	−0.571644	−	0.0132498i
$833$			24216.2i			1.00725i
$834$	36371.2	+	36371.2i	1.51011	+	1.51011i
$835$			11079.1i			0.459173i
$836$	6941.68	−	12162.5i	0.287181	−	0.503169i
$837$	6320.58	+	6320.58i	0.261017	+	0.261017i
$838$	694.933	−	694.933i	0.0286468	−	0.0286468i
$839$	20710.9	−	20710.9i	0.852231	−	0.852231i	−0.138177	−	0.990408i	$-0.544124\pi$
$839$	20710.9	−	20710.9i	0.852231	−	0.852231i	0.990408	+	0.138177i	$0.0441243\pi$
$840$	−56436.7	+	56436.7i	−2.31816	+	2.31816i
$841$	−5753.79			−0.235917
$842$	1398.11			0.0572235
$843$	−20914.9	−	20914.9i	−0.854504	−	0.854504i
$844$	19002.4			0.774988
$845$	−20123.3	−	22080.8i	−0.819245	−	0.898938i
$846$			27328.1i			1.11059i
$847$	−35123.9	−	9038.30i	−1.42488	−	0.366659i
$848$	339.420			0.0137450
$849$	−59596.5			−2.40912
$850$	−4386.21	−	4386.21i	−0.176995	−	0.176995i
$851$	−16263.0	−	16263.0i	−0.655097	−	0.655097i
$852$	15015.0	−	15015.0i	0.603761	−	0.603761i
$853$	−14040.5	−	14040.5i	−0.563586	−	0.563586i	0.366739	−	0.930324i	$-0.380474\pi$
$853$	−14040.5	−	14040.5i	−0.563586	−	0.563586i	−0.930324	+	0.366739i	$0.880474\pi$
$854$			8861.66i			0.355082i
$855$	−67697.6			−2.70785
$856$	−2979.11	+	2979.11i	−0.118953	+	0.118953i
$857$	−15195.7			−0.605691			−0.302845	−	0.953040i	$-0.597937\pi$
$857$	−15195.7			−0.605691			−0.302845	+	0.953040i	$0.597937\pi$
$858$	−14519.9	+	24124.1i	−0.577741	+	0.959886i
$859$	−9765.29			−0.387878			−0.193939	−	0.981014i	$-0.562126\pi$
$859$	−9765.29			−0.387878			−0.193939	+	0.981014i	$0.562126\pi$
$860$	1446.15	−	1446.15i	0.0573412	−	0.0573412i
$861$	−51144.0			−2.02437
$862$		−	601.695i		−	0.0237747i
$863$	255.416	+	255.416i	0.0100747	+	0.0100747i	0.712126	−	0.702051i	$-0.247732\pi$
$863$	255.416	+	255.416i	0.0100747	+	0.0100747i	−0.702051	+	0.712126i	$0.747732\pi$
$864$	−48541.0	+	48541.0i	−1.91134	+	1.91134i
$865$	34572.6	+	34572.6i	1.35896	+	1.35896i
$866$	−6339.66	−	6339.66i	−0.248765	−	0.248765i
$867$	11939.3			0.467683
$868$	3300.09			0.129046
$869$	1213.98	−	331.760i	0.0473896	−	0.0129507i
$870$			38872.7i			1.51484i
$871$	32394.3	−	30926.6i	1.26021	−	1.20311i
$872$	−14922.6			−0.579522
$873$	−86772.6	−	86772.6i	−3.36404	−	3.36404i
$874$	−10438.7			−0.403998
$875$	24119.1			0.931858
$876$	9484.87	−	9484.87i	0.365827	−	0.365827i
$877$	−27232.7	+	27232.7i	−1.04856	+	1.04856i	−0.0497963	+	0.998759i	$0.515857\pi$
$877$	−27232.7	+	27232.7i	−1.04856	+	1.04856i	−0.998759	+	0.0497963i	$0.984143\pi$
$878$	−13909.8	+	13909.8i	−0.534662	+	0.534662i
$879$	57787.1	+	57787.1i	2.21742	+	2.21742i
$880$	610.742	−	1070.08i	0.0233956	−	0.0409914i
$881$			2615.85i			0.100034i	0.998748	+	0.0500172i	$0.0159276\pi$
$881$			2615.85i			0.100034i	−0.998748	+	0.0500172i	$0.984072\pi$
$882$	−31806.1	−	31806.1i	−1.21425	−	1.21425i
$883$		−	26500.9i		−	1.01000i	−0.863120	−	0.504998i	$-0.831493\pi$
$883$		−	26500.9i		−	1.01000i	0.863120	−	0.504998i	$-0.168507\pi$
$884$	−14435.4	−	334.590i	−0.549225	−	0.0127302i
$885$	86672.9			3.29207
$886$	8256.66	−	8256.66i	0.313079	−	0.313079i
$887$			3481.73i			0.131798i	0.997826	+	0.0658992i	$0.0209916\pi$
$887$			3481.73i			0.131798i	−0.997826	+	0.0658992i	$0.979008\pi$
$888$	61233.2			2.31402
$889$	−18987.3	−	18987.3i	−0.716326	−	0.716326i
$890$	−698.308	+	698.308i	−0.0263004	+	0.0263004i
$891$	17656.4	+	64608.9i	0.663875	+	2.42927i
$892$	−1335.63	+	1335.63i	−0.0501347	+	0.0501347i
$893$			18332.7i			0.686987i
$894$		−	9024.80i		−	0.337622i
$895$	11962.2	−	11962.2i	0.446763	−	0.446763i
$896$			26268.9i			0.979446i
$897$	−36544.1	−	847.036i	−1.36028	−	0.0315292i
$898$			12619.0i			0.468933i
$899$	2925.60	−	2925.60i	0.108537	−	0.108537i
$900$	−20067.1			−0.743224
$901$	−8284.13			−0.306309
$902$	−11705.7	+	3198.95i	−0.432102	+	0.118086i
$903$	5496.50	+	5496.50i	0.202560	+	0.202560i
$904$	−15043.9	−	15043.9i	−0.553486	−	0.553486i
$905$	5870.11	−	5870.11i	0.215612	−	0.215612i
$906$	−36879.5			−1.35236
$907$			2064.54i			0.0755810i	0.999286	+	0.0377905i	$0.0120319\pi$
$907$			2064.54i			0.0755810i	−0.999286	+	0.0377905i	$0.987968\pi$
$908$	−1709.68	−	1709.68i	−0.0624864	−	0.0624864i
$909$	110635.			4.03691
$910$	21458.4	−	20486.2i	0.781692	−	0.746276i
$911$	−6151.41			−0.223716			−0.111858	−	0.993724i	$-0.535680\pi$
$911$	−6151.41			−0.223716			−0.111858	+	0.993724i	$0.535680\pi$
$912$	−1278.59	+	1278.59i	−0.0464237	+	0.0464237i
$913$	23739.7	+	13549.3i	0.860536	+	0.491146i
$914$			17054.6i			0.617194i
$915$	−17645.2	+	17645.2i	−0.637523	+	0.637523i
$916$	−14782.0	−	14782.0i	−0.533200	−	0.533200i
$917$	208.729	−	208.729i	0.00751672	−	0.00751672i
$918$	27463.1	−	27463.1i	0.987381	−	0.987381i
$919$		−	14684.7i		−	0.527100i	−0.964646	−	0.263550i	$-0.915107\pi$
$919$		−	14684.7i		−	0.527100i	0.964646	−	0.263550i	$-0.0848934\pi$
$920$	−24585.1			−0.881028
$921$	−39991.0	−	39991.0i	−1.43078	−	1.43078i
$922$		−	30211.7i		−	1.07914i
$923$	−14695.9	+	14030.1i	−0.524077	+	0.500333i
$924$	42294.4	+	24139.3i	1.50583	+	0.859443i
$925$	12041.8	+	12041.8i	0.428036	+	0.428036i
$926$			18902.4i			0.670811i
$927$			30459.0i			1.07919i
$928$	22468.2	+	22468.2i	0.794777	+	0.794777i
$929$	−29643.3	−	29643.3i	−1.04690	−	1.04690i	−0.998845	−	0.0480501i	$-0.984699\pi$
$929$	−29643.3	−	29643.3i	−1.04690	−	1.04690i	−0.0480501	−	0.998845i	$-0.515301\pi$
$930$	−3772.92	−	3772.92i	−0.133031	−	0.133031i
$931$	−21336.7	−	21336.7i	−0.751107	−	0.751107i
$932$		−	23991.0i		−	0.843190i
$933$			77878.4i			2.73272i
$934$	−6282.33	−	6282.33i	−0.220090	−	0.220090i
$935$	−14906.2	+	26117.1i	−0.521375	+	0.913500i
$936$	49936.8	−	47674.3i	1.74384	−	1.66483i
$937$			7676.08i			0.267627i	0.991007	+	0.133814i	$0.0427223\pi$
$937$			7676.08i			0.267627i	−0.991007	+	0.133814i	$0.957278\pi$
$938$	31448.9	+	31448.9i	1.09472	+	1.09472i
$939$	93191.5			3.23875
$940$			16773.1i			0.581999i
$941$	2837.37	−	2837.37i	0.0982951	−	0.0982951i	−0.656249	−	0.754544i	$-0.727858\pi$
$941$	2837.37	−	2837.37i	0.0982951	−	0.0982951i	0.754544	+	0.656249i	$0.227858\pi$
$942$	17979.5	−	17979.5i	0.621872	−	0.621872i
$943$	−11139.7	−	11139.7i	−0.384686	−	0.384686i
$944$	1161.28	−	1161.28i	0.0400385	−	0.0400385i
$945$		−	138982.i		−	4.78420i
$946$	1601.81	+	914.226i	0.0550523	+	0.0314208i
$947$	−14786.3	+	14786.3i	−0.507382	+	0.507382i	−0.913722	−	0.406340i	$-0.866805\pi$
$947$	−14786.3	+	14786.3i	−0.507382	+	0.507382i	0.406340	+	0.913722i	$0.366805\pi$
$948$	−1689.82			−0.0578933
$949$	−9283.34	+	8862.74i	−0.317545	+	0.303158i
$950$	7729.28			0.263969
$951$	23639.7	+	23639.7i	0.806067	+	0.806067i
$952$		−	36910.8i		−	1.25660i
$953$	6394.21			0.217344			0.108672	−	0.994078i	$-0.465340\pi$
$953$	6394.21			0.217344			0.108672	+	0.994078i	$0.465340\pi$
$954$	10880.5	−	10880.5i	0.369257	−	0.369257i
$955$	37453.9	+	37453.9i	1.26909	+	1.26909i
$956$	−14446.4	−	14446.4i	−0.488733	−	0.488733i
$957$	58895.1	−	16095.0i	1.98935	−	0.543653i
$958$	9231.52			0.311333
$959$	23335.3			0.785752
$960$	27133.9	−	27133.9i	0.912231	−	0.912231i
$961$		−	29223.1i		−	0.980937i
$962$	−22754.7	−	527.419i	−0.762621	−	0.0176764i
$963$		−	12426.8i		−	0.415833i
$964$	−19526.2	+	19526.2i	−0.652384	+	0.652384i
$965$			26324.5i			0.878150i
$966$		−	36299.9i		−	1.20904i
$967$	−23404.8	+	23404.8i	−0.778332	+	0.778332i	−0.979547	−	0.201215i	$-0.935511\pi$
$967$	−23404.8	+	23404.8i	−0.778332	+	0.778332i	0.201215	+	0.979547i	$0.435511\pi$
$968$	28805.1	+	7412.31i	0.956439	+	0.246117i
$969$	31206.2	−	31206.2i	1.03456	−	1.03456i
$970$	30579.2	+	30579.2i	1.01221	+	1.01221i
$971$	−9886.68			−0.326754			−0.163377	−	0.986564i	$-0.552239\pi$
$971$	−9886.68			−0.326754			−0.163377	+	0.986564i	$0.552239\pi$
$972$		−	38465.5i		−	1.26932i
$973$	−60190.6	+	60190.6i	−1.98317	+	1.98317i
$974$	9999.00			0.328941
$975$	27058.9	+	627.184i	0.888799	+	0.0206010i
$976$			472.836i			0.0155073i
$977$	−7059.11	−	7059.11i	−0.231158	−	0.231158i	0.582018	−	0.813176i	$-0.302263\pi$
$977$	−7059.11	−	7059.11i	−0.231158	−	0.231158i	−0.813176	+	0.582018i	$0.802263\pi$
$978$		−	2701.75i		−	0.0883359i
$979$	1347.12	+	768.859i	0.0439776	+	0.0250999i
$980$	−19521.6	−	19521.6i	−0.636321	−	0.636321i
$981$	31123.4	−	31123.4i	1.01294	−	1.01294i
$982$	12013.9	−	12013.9i	0.390405	−	0.390405i
$983$	−20661.3	+	20661.3i	−0.670391	+	0.670391i	−0.957806	−	0.287415i	$-0.907204\pi$
$983$	−20661.3	+	20661.3i	−0.670391	+	0.670391i	0.287415	+	0.957806i	$0.407204\pi$
$984$	41943.2			1.35884
$985$	−38965.7			−1.26046
$986$	−12711.8	−	12711.8i	−0.410574	−	0.410574i
$987$	−63750.8			−2.05594
$988$	13013.7	−	12424.1i	0.419049	−	0.400063i
$989$			2394.39i			0.0769841i
$990$	−14724.7	−	53880.9i	−0.472708	−	1.72975i
$991$	−48281.8			−1.54765			−0.773826	−	0.633399i	$-0.781659\pi$
$991$	−48281.8			−1.54765			−0.773826	+	0.633399i	$0.781659\pi$
$992$	−4361.43			−0.139592
$993$	7720.58	+	7720.58i	0.246732	+	0.246732i
$994$	−14267.1	−	14267.1i	−0.455255	−	0.455255i
$995$	17422.0	−	17422.0i	0.555091	−	0.555091i
$996$	−25952.5	−	25952.5i	−0.825638	−	0.825638i
$997$			4868.65i			0.154656i	0.997006	+	0.0773278i	$0.0246388\pi$
$997$			4868.65i			0.154656i	−0.997006	+	0.0773278i	$0.975361\pi$
$998$	22356.6			0.709104
$999$	−75396.7	+	75396.7i	−2.38783	+	2.38783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.16	✓	80
11.10	odd	2	inner	143.4.g.a.21.25	yes	80
13.5	odd	4	inner	143.4.g.a.109.25	yes	80
143.109	even	4	inner	143.4.g.a.109.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.16	✓	80	1.1	even	1	trivial
143.4.g.a.21.25	yes	80	11.10	odd	2	inner
143.4.g.a.109.16	yes	80	143.109	even	4	inner
143.4.g.a.109.25	yes	80	13.5	odd	4	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20788 + 1.20788i) q^{2} -9.63914 q^{3} +5.08205i q^{4} +(9.61526 + 9.61526i) q^{5} +(11.6429 - 11.6429i) q^{6} +(19.2678 + 19.2678i) q^{7} +(-15.8016 - 15.8016i) q^{8} +65.9130 q^{9} +O(q^{10})\)	\(q+(-1.20788 + 1.20788i) q^{2} -9.63914 q^{3} +5.08205i q^{4} +(9.61526 + 9.61526i) q^{5} +(11.6429 - 11.6429i) q^{6} +(19.2678 + 19.2678i) q^{7} +(-15.8016 - 15.8016i) q^{8} +65.9130 q^{9} -23.2282 q^{10} +(9.61744 + 35.1924i) q^{11} -48.9866i q^{12} +(-1.08613 + 46.8596i) q^{13} -46.5465 q^{14} +(-92.6828 - 92.6828i) q^{15} -2.48360 q^{16} +60.6166 q^{17} +(-79.6151 + 79.6151i) q^{18} +(-53.4086 + 53.4086i) q^{19} +(-48.8652 + 48.8652i) q^{20} +(-185.725 - 185.725i) q^{21} +(-54.1249 - 30.8915i) q^{22} -80.9060i q^{23} +(152.313 + 152.313i) q^{24} +59.9065i q^{25} +(-55.2889 - 57.9127i) q^{26} -375.088 q^{27} +(-97.9200 + 97.9200i) q^{28} +173.617i q^{29} +223.900 q^{30} +(-16.8509 - 16.8509i) q^{31} +(129.412 - 129.412i) q^{32} +(-92.7039 - 339.224i) q^{33} +(-73.2176 + 73.2176i) q^{34} +370.530i q^{35} +334.973i q^{36} +(201.011 - 201.011i) q^{37} -129.022i q^{38} +(10.4694 - 451.686i) q^{39} -303.872i q^{40} +(137.687 - 137.687i) q^{41} +448.668 q^{42} -29.5948 q^{43} +(-178.849 + 48.8763i) q^{44} +(633.771 + 633.771i) q^{45} +(97.7248 + 97.7248i) q^{46} +(171.627 - 171.627i) q^{47} +23.9398 q^{48} +399.499i q^{49} +(-72.3598 - 72.3598i) q^{50} -584.292 q^{51} +(-238.143 - 5.51978i) q^{52} -136.664 q^{53} +(453.062 - 453.062i) q^{54} +(-245.910 + 430.858i) q^{55} -608.923i q^{56} +(514.813 - 514.813i) q^{57} +(-209.708 - 209.708i) q^{58} +(-467.578 + 467.578i) q^{59} +(471.019 - 471.019i) q^{60} -190.383i q^{61} +40.7078 q^{62} +(1270.00 + 1270.00i) q^{63} +292.760i q^{64} +(-461.011 + 440.124i) q^{65} +(521.718 + 297.767i) q^{66} +(-675.645 - 675.645i) q^{67} +308.056i q^{68} +779.864i q^{69} +(-447.557 - 447.557i) q^{70} +(306.512 + 306.512i) q^{71} +(-1041.53 - 1041.53i) q^{72} +(193.622 + 193.622i) q^{73} +485.594i q^{74} -577.447i q^{75} +(-271.425 - 271.425i) q^{76} +(-492.774 + 863.388i) q^{77} +(532.937 + 558.229i) q^{78} -34.4956i q^{79} +(-23.8805 - 23.8805i) q^{80} +1835.88 q^{81} +332.619i q^{82} +(529.788 - 529.788i) q^{83} +(943.865 - 943.865i) q^{84} +(582.844 + 582.844i) q^{85} +(35.7469 - 35.7469i) q^{86} -1673.52i q^{87} +(404.124 - 708.065i) q^{88} +(30.0630 - 30.0630i) q^{89} -1531.04 q^{90} +(-923.810 + 881.955i) q^{91} +411.168 q^{92} +(162.428 + 162.428i) q^{93} +414.609i q^{94} -1027.08 q^{95} +(-1247.42 + 1247.42i) q^{96} +(-1316.47 - 1316.47i) q^{97} +(-482.547 - 482.547i) q^{98} +(633.915 + 2319.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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