LMFDB - Embedded newform 40.4.d.a.21.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,4,Mod(21,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.21"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.7
Root			$-0.428316 + 1.95360i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.4.d.a.21.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52528 - 2.38191i) q^{2} -1.51777i q^{3} +(-3.34703 - 7.26618i) q^{4} -5.00000i q^{5} +(-3.61520 - 2.31503i) q^{6} +5.13620 q^{7} +(-22.4126 - 3.11063i) q^{8} +24.6964 q^{9} +(-11.9096 - 7.62641i) q^{10} +31.3403i q^{11} +(-11.0284 + 5.08003i) q^{12} -4.75340i q^{13} +(7.83414 - 12.2340i) q^{14} -7.58886 q^{15} +(-41.5948 + 48.6403i) q^{16} +108.154 q^{17} +(37.6689 - 58.8246i) q^{18} +89.8913i q^{19} +(-36.3309 + 16.7352i) q^{20} -7.79558i q^{21} +(74.6499 + 47.8028i) q^{22} -68.5157 q^{23} +(-4.72123 + 34.0172i) q^{24} -25.0000 q^{25} +(-11.3222 - 7.25027i) q^{26} -78.4633i q^{27} +(-17.1910 - 37.3205i) q^{28} -16.5719i q^{29} +(-11.5752 + 18.0760i) q^{30} -300.523 q^{31} +(52.4132 + 173.265i) q^{32} +47.5675 q^{33} +(164.966 - 257.614i) q^{34} -25.6810i q^{35} +(-82.6595 - 179.448i) q^{36} -327.879i q^{37} +(214.113 + 137.109i) q^{38} -7.21458 q^{39} +(-15.5532 + 112.063i) q^{40} -73.4968 q^{41} +(-18.5684 - 11.8904i) q^{42} +0.836008i q^{43} +(227.724 - 104.897i) q^{44} -123.482i q^{45} +(-104.506 + 163.198i) q^{46} +228.335 q^{47} +(73.8249 + 63.1314i) q^{48} -316.619 q^{49} +(-38.1320 + 59.5479i) q^{50} -164.153i q^{51} +(-34.5391 + 15.9098i) q^{52} +647.393i q^{53} +(-186.893 - 119.679i) q^{54} +156.702 q^{55} +(-115.115 - 15.9768i) q^{56} +136.434 q^{57} +(-39.4728 - 25.2768i) q^{58} +753.676i q^{59} +(25.4002 + 55.1420i) q^{60} +290.838i q^{61} +(-458.383 + 715.821i) q^{62} +126.845 q^{63} +(492.648 + 139.435i) q^{64} -23.7670 q^{65} +(72.5538 - 113.302i) q^{66} -801.801i q^{67} +(-361.995 - 785.868i) q^{68} +103.991i q^{69} +(-61.1699 - 39.1707i) q^{70} +767.674 q^{71} +(-553.509 - 76.8213i) q^{72} -48.3194 q^{73} +(-780.980 - 500.108i) q^{74} +37.9443i q^{75} +(653.166 - 300.869i) q^{76} +160.970i q^{77} +(-11.0043 + 17.1845i) q^{78} +451.701 q^{79} +(243.201 + 207.974i) q^{80} +547.712 q^{81} +(-112.103 + 175.063i) q^{82} -976.099i q^{83} +(-56.6441 + 26.0920i) q^{84} -540.771i q^{85} +(1.99130 + 1.27515i) q^{86} -25.1524 q^{87} +(97.4881 - 702.417i) q^{88} -1204.25 q^{89} +(-294.123 - 188.345i) q^{90} -24.4144i q^{91} +(229.324 + 497.847i) q^{92} +456.126i q^{93} +(348.275 - 543.873i) q^{94} +449.456 q^{95} +(262.977 - 79.5513i) q^{96} -559.147 q^{97} +(-482.934 + 754.161i) q^{98} +773.992i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.52528	−	2.38191i	0.539269	−	0.842134i
$2$	1.52528	−	2.38191i	0.539269	−	0.842134i
$3$		−	1.51777i		−	0.292095i	−0.989278	−	0.146048i	$-0.953345\pi$
$3$		−	1.51777i		−	0.292095i	0.989278	−	0.146048i	$-0.0466553\pi$
$4$	−3.34703	−	7.26618i	−0.418379	−	0.908273i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$	−3.61520	−	2.31503i	−0.245983	−	0.157518i
$7$	5.13620			0.277328			0.138664	−	0.990339i	$-0.455719\pi$
$7$	5.13620			0.277328			0.138664	+	0.990339i	$0.455719\pi$
$8$	−22.4126	−	3.11063i	−0.990506	−	0.137472i
$9$	24.6964			0.914680
$10$	−11.9096	−	7.62641i	−0.376614	−	0.241168i
$11$			31.3403i			0.859042i	0.903057	+	0.429521i	$0.141318\pi$
$11$			31.3403i			0.859042i	−0.903057	+	0.429521i	$0.858682\pi$
$12$	−11.0284	+	5.08003i	−0.265302	+	0.122207i
$13$		−	4.75340i		−	0.101412i	−0.998714	−	0.0507060i	$-0.983853\pi$
$13$		−	4.75340i		−	0.101412i	0.998714	−	0.0507060i	$-0.0161471\pi$
$14$	7.83414	−	12.2340i	0.149555	−	0.233548i
$15$	−7.58886			−0.130629
$16$	−41.5948	+	48.6403i	−0.649918	+	0.760004i
$17$	108.154			1.54301			0.771507	−	0.636221i	$-0.219503\pi$
$17$	108.154			1.54301			0.771507	+	0.636221i	$0.219503\pi$
$18$	37.6689	−	58.8246i	0.493258	−	0.770283i
$19$			89.8913i			1.08539i	0.839929	+	0.542697i	$0.182597\pi$
$19$			89.8913i			1.08539i	−0.839929	+	0.542697i	$0.817403\pi$
$20$	−36.3309	+	16.7352i	−0.406192	+	0.187105i
$21$		−	7.79558i		−	0.0810064i
$22$	74.6499	+	47.8028i	0.723428	+	0.463254i
$23$	−68.5157			−0.621152			−0.310576	−	0.950548i	$-0.600522\pi$
$23$	−68.5157			−0.621152			−0.310576	+	0.950548i	$0.600522\pi$
$24$	−4.72123	+	34.0172i	−0.0401549	+	0.289322i
$25$	−25.0000			−0.200000
$26$	−11.3222	−	7.25027i	−0.0854025	−	0.0546883i
$27$		−	78.4633i		−	0.559269i
$28$	−17.1910	−	37.3205i	−0.116028	−	0.251890i
$29$		−	16.5719i		−	0.106115i	−0.998591	−	0.0530573i	$-0.983103\pi$
$29$		−	16.5719i		−	0.106115i	0.998591	−	0.0530573i	$-0.0168966\pi$
$30$	−11.5752	+	18.0760i	−0.0704441	+	0.110007i
$31$	−300.523			−1.74115			−0.870574	−	0.492037i	$-0.836252\pi$
$31$	−300.523			−1.74115			−0.870574	+	0.492037i	$0.836252\pi$
$32$	52.4132	+	173.265i	0.289545	+	0.957164i
$33$	47.5675			0.250922
$34$	164.966	−	257.614i	0.832099	−	1.29942i
$35$		−	25.6810i		−	0.124025i
$36$	−82.6595	−	179.448i	−0.382683	−	0.830779i
$37$		−	327.879i		−	1.45684i	−0.685132	−	0.728419i	$-0.740256\pi$
$37$		−	327.879i		−	1.45684i	0.685132	−	0.728419i	$-0.259744\pi$
$38$	214.113	+	137.109i	0.914046	+	0.585318i
$39$	−7.21458			−0.0296220
$40$	−15.5532	+	112.063i	−0.0614792	+	0.442968i
$41$	−73.4968			−0.279958			−0.139979	−	0.990154i	$-0.544703\pi$
$41$	−73.4968			−0.279958			−0.139979	+	0.990154i	$0.544703\pi$
$42$	−18.5684	−	11.8904i	−0.0682182	−	0.0436842i
$43$			0.836008i			0.00296489i	0.999999	+	0.00148244i	$0.000471876\pi$
$43$			0.836008i			0.00296489i	−0.999999	+	0.00148244i	$0.999528\pi$
$44$	227.724	−	104.897i	0.780244	−	0.359405i
$45$		−	123.482i		−	0.409057i
$46$	−104.506	+	163.198i	−0.334968	+	0.523093i
$47$	228.335			0.708639			0.354319	−	0.935124i	$-0.384713\pi$
$47$	228.335			0.708639			0.354319	+	0.935124i	$0.384713\pi$
$48$	73.8249	+	63.1314i	0.221994	+	0.189838i
$49$	−316.619			−0.923089
$50$	−38.1320	+	59.5479i	−0.107854	+	0.168427i
$51$		−	164.153i		−	0.450707i
$52$	−34.5391	+	15.9098i	−0.0921097	+	0.0424286i
$53$			647.393i			1.67785i	0.544244	+	0.838927i	$0.316817\pi$
$53$			647.393i			1.67785i	−0.544244	+	0.838927i	$0.683183\pi$
$54$	−186.893	−	119.679i	−0.470980	−	0.301596i
$55$	156.702			0.384175
$56$	−115.115	−	15.9768i	−0.274695	−	0.0381248i
$57$	136.434			0.317038
$58$	−39.4728	−	25.2768i	−0.0893627	−	0.0572243i
$59$			753.676i			1.66305i	0.555484	+	0.831527i	$0.312533\pi$
$59$			753.676i			1.66305i	−0.555484	+	0.831527i	$0.687467\pi$
$60$	25.4002	+	55.1420i	0.0546524	+	0.118647i
$61$			290.838i			0.610459i	0.952279	+	0.305229i	$0.0987331\pi$
$61$			290.838i			0.610459i	−0.952279	+	0.305229i	$0.901267\pi$
$62$	−458.383	+	715.821i	−0.938946	+	1.46628i
$63$	126.845			0.253667
$64$	492.648	+	139.435i	0.962203	+	0.272333i
$65$	−23.7670			−0.0453528
$66$	72.5538	−	113.302i	0.135314	−	0.211310i
$67$		−	801.801i		−	1.46202i	−0.682364	−	0.731012i	$-0.739048\pi$
$67$		−	801.801i		−	1.46202i	0.682364	−	0.731012i	$-0.260952\pi$
$68$	−361.995	−	785.868i	−0.645565	−	1.40148i
$69$			103.991i			0.181436i
$70$	−61.1699	−	39.1707i	−0.104446	−	0.0668828i
$71$	767.674			1.28318			0.641592	−	0.767046i	$-0.278274\pi$
$71$	767.674			1.28318			0.641592	+	0.767046i	$0.278274\pi$
$72$	−553.509	−	76.8213i	−0.905996	−	0.125743i
$73$	−48.3194			−0.0774707			−0.0387353	−	0.999250i	$-0.512333\pi$
$73$	−48.3194			−0.0774707			−0.0387353	+	0.999250i	$0.512333\pi$
$74$	−780.980	−	500.108i	−1.22685	−	0.785627i
$75$			37.9443i			0.0584191i
$76$	653.166	−	300.869i	0.985833	−	0.454106i
$77$			160.970i			0.238237i
$78$	−11.0043	+	17.1845i	−0.0159742	+	0.0249457i
$79$	451.701			0.643296			0.321648	−	0.946859i	$-0.395763\pi$
$79$	451.701			0.643296			0.321648	+	0.946859i	$0.395763\pi$
$80$	243.201	+	207.974i	0.339884	+	0.290652i
$81$	547.712			0.751320
$82$	−112.103	+	175.063i	−0.150973	+	0.235762i
$83$		−	976.099i		−	1.29085i	−0.763822	−	0.645427i	$-0.776680\pi$
$83$		−	976.099i		−	1.29085i	0.763822	−	0.645427i	$-0.223320\pi$
$84$	−56.6441	+	26.0920i	−0.0735759	+	0.0338914i
$85$		−	540.771i		−	0.690057i
$86$	1.99130	+	1.27515i	0.00249683	+	0.00159887i
$87$	−25.1524			−0.0309956
$88$	97.4881	−	702.417i	0.118094	−	0.850886i
$89$	−1204.25			−1.43428			−0.717139	−	0.696930i	$-0.754549\pi$
$89$	−1204.25			−1.43428			−0.717139	+	0.696930i	$0.754549\pi$
$90$	−294.123	−	188.345i	−0.344481	−	0.220592i
$91$		−	24.4144i		−	0.0281244i
$92$	229.324	+	497.847i	0.259877	+	0.564176i
$93$			456.126i			0.508581i
$94$	348.275	−	543.873i	0.382147	−	0.596769i
$95$	449.456			0.485403
$96$	262.977	−	79.5513i	0.279583	−	0.0845747i
$97$	−559.147			−0.585287			−0.292643	−	0.956222i	$-0.594535\pi$
$97$	−559.147			−0.585287			−0.292643	+	0.956222i	$0.594535\pi$
$98$	−482.934	+	754.161i	−0.497793	+	0.777364i
$99$			773.992i			0.785749i
$100$	83.6758	+	181.655i	0.0836758	+	0.181655i
$101$			542.070i			0.534039i	0.963691	+	0.267020i	$0.0860389\pi$
$101$			542.070i			0.534039i	−0.963691	+	0.267020i	$0.913961\pi$
$102$	−390.999	−	250.380i	−0.379556	−	0.243052i
$103$	−1764.97			−1.68842			−0.844212	−	0.536009i	$-0.819931\pi$
$103$	−1764.97			−1.68842			−0.844212	+	0.536009i	$0.819931\pi$
$104$	−14.7861	+	106.536i	−0.0139413	+	0.100449i
$105$	−38.9779			−0.0362272
$106$	1542.03	+	987.457i	1.41298	+	0.904814i
$107$			442.840i			0.400103i	0.979785	+	0.200051i	$0.0641109\pi$
$107$			442.840i			0.400103i	−0.979785	+	0.200051i	$0.935889\pi$
$108$	−570.129	+	262.619i	−0.507969	+	0.233986i
$109$		−	1547.20i		−	1.35959i	−0.733403	−	0.679795i	$-0.762069\pi$
$109$		−	1547.20i		−	1.35959i	0.733403	−	0.679795i	$-0.237931\pi$
$110$	239.014	−	373.250i	0.207174	−	0.323527i
$111$	−497.646			−0.425536
$112$	−213.639	+	249.826i	−0.180241	+	0.210771i
$113$	788.524			0.656444			0.328222	−	0.944601i	$-0.393551\pi$
$113$	788.524			0.656444			0.328222	+	0.944601i	$0.393551\pi$
$114$	208.101	−	324.975i	0.170969	−	0.266989i
$115$			342.578i			0.277788i
$116$	−120.414	+	55.4667i	−0.0963810	+	0.0443961i
$117$		−	117.392i		−	0.0927596i
$118$	1795.19	+	1149.57i	1.40051	+	0.896833i
$119$	555.501			0.427922
$120$	170.086	+	23.6061i	0.129389	+	0.0179578i
$121$	348.785			0.262047
$122$	692.751	+	443.610i	0.514088	+	0.329201i
$123$			111.551i			0.0817744i
$124$	1005.86	+	2183.66i	0.728460	+	1.58144i
$125$			125.000i			0.0894427i
$126$	193.475	−	302.135i	0.136795	−	0.213621i
$127$	−1543.92			−1.07875			−0.539374	−	0.842066i	$-0.681339\pi$
$127$	−1543.92			−1.07875			−0.539374	+	0.842066i	$0.681339\pi$
$128$	1083.55	−	960.768i	0.748227	−	0.663443i
$129$	1.26887			0.000866029
$130$	−36.2514	+	56.6110i	−0.0244574	+	0.0381932i
$131$		−	1933.26i		−	1.28938i	−0.764442	−	0.644692i	$-0.776986\pi$
$131$		−	1933.26i		−	1.28938i	0.764442	−	0.644692i	$-0.223014\pi$
$132$	−159.210	−	345.634i	−0.104981	−	0.227906i
$133$			461.699i			0.301010i
$134$	−1909.82	−	1222.97i	−1.23122	−	0.788424i
$135$	−392.317			−0.250113
$136$	−2424.02	−	336.428i	−1.52836	−	0.212121i
$137$	478.247			0.298244			0.149122	−	0.988819i	$-0.452355\pi$
$137$	478.247			0.298244			0.149122	+	0.988819i	$0.452355\pi$
$138$	247.698	+	158.616i	0.152793	+	0.0978426i
$139$			2057.45i			1.25547i	0.778427	+	0.627735i	$0.216018\pi$
$139$			2057.45i			1.25547i	−0.778427	+	0.627735i	$0.783982\pi$
$140$	−186.603	+	85.9550i	−0.112649	+	0.0518895i
$141$		−	346.560i		−	0.206990i
$142$	1170.92	−	1828.53i	0.691981	−	1.08061i
$143$	148.973			0.0871172
$144$	−1027.24	+	1201.24i	−0.594467	+	0.695161i
$145$	−82.8595			−0.0474559
$146$	−73.7007	+	115.093i	−0.0417775	+	0.0652407i
$147$			480.556i			0.269630i
$148$	−2382.43	+	1097.42i	−1.32321	+	0.609510i
$149$		−	2838.89i		−	1.56088i	−0.625231	−	0.780440i	$-0.714995\pi$
$149$		−	2838.89i		−	1.56088i	0.625231	−	0.780440i	$-0.285005\pi$
$150$	90.3801	+	57.8758i	0.0491967	+	0.0315036i
$151$	−2187.09			−1.17869			−0.589346	−	0.807881i	$-0.700615\pi$
$151$	−2187.09			−1.17869			−0.589346	+	0.807881i	$0.700615\pi$
$152$	279.619	−	2014.70i	0.149211	−	1.07509i
$153$	2671.02			1.41136
$154$	383.417	+	245.525i	0.200627	+	0.128474i
$155$			1502.62i			0.778665i
$156$	24.1474	+	52.4224i	0.0123932	+	0.0269048i
$157$			936.231i			0.475920i	0.971275	+	0.237960i	$0.0764787\pi$
$157$			936.231i			0.475920i	−0.971275	+	0.237960i	$0.923521\pi$
$158$	688.972	−	1075.91i	0.346909	−	0.541741i
$159$	982.595			0.490093
$160$	866.326	−	262.066i	0.428057	−	0.129488i
$161$	−351.910			−0.172263
$162$	835.416	−	1304.60i	0.405163	−	0.632712i
$163$		−	2329.68i		−	1.11948i	−0.828670	−	0.559738i	$-0.810902\pi$
$163$		−	2329.68i		−	1.11948i	0.828670	−	0.559738i	$-0.189098\pi$
$164$	245.996	+	534.041i	0.117128	+	0.254278i
$165$		−	237.837i		−	0.112216i
$166$	−2324.98	−	1488.83i	−1.08707	−	0.696117i
$167$	2020.42			0.936195			0.468097	−	0.883677i	$-0.344940\pi$
$167$	2020.42			0.936195			0.468097	+	0.883677i	$0.344940\pi$
$168$	−24.2492	+	174.719i	−0.0111361	+	0.0802373i
$169$	2174.41			0.989716
$170$	−1288.07	−	824.828i	−0.581120	−	0.372126i
$171$			2219.99i			0.992788i
$172$	6.07459	−	2.79815i	0.00269292	−	0.00124045i
$173$			912.153i			0.400866i	0.979707	+	0.200433i	$0.0642348\pi$
$173$			912.153i			0.400866i	−0.979707	+	0.200433i	$0.935765\pi$
$174$	−38.3645	+	59.9108i	−0.0167150	+	0.0261024i
$175$	−128.405			−0.0554657
$176$	−1524.40	−	1303.59i	−0.652875	−	0.558307i
$177$	1143.91			0.485771
$178$	−1836.83	+	2868.43i	−0.773461	+	1.20785i
$179$		−	3226.95i		−	1.34745i	−0.738982	−	0.673726i	$-0.764693\pi$
$179$		−	3226.95i		−	1.34745i	0.738982	−	0.673726i	$-0.235307\pi$
$180$	−897.241	+	413.298i	−0.371536	+	0.171141i
$181$			1003.43i			0.412068i	0.978545	+	0.206034i	$0.0660557\pi$
$181$			1003.43i			0.412068i	−0.978545	+	0.206034i	$0.933944\pi$
$182$	−58.1530	−	37.2388i	−0.0236845	−	0.0151666i
$183$	441.426			0.178312
$184$	1535.61	+	213.127i	0.615255	+	0.0853909i
$185$	−1639.40			−0.651517
$186$	1086.45	+	695.721i	0.428294	+	0.274262i
$187$			3389.59i			1.32551i
$188$	−764.243	−	1659.12i	−0.296480	−	0.643637i
$189$		−	403.003i		−	0.155101i
$190$	685.547	−	1070.57i	0.261762	−	0.408774i
$191$	1272.08			0.481907			0.240953	−	0.970537i	$-0.422540\pi$
$191$	1272.08			0.481907			0.240953	+	0.970537i	$0.422540\pi$
$192$	211.630	−	747.727i	0.0795473	−	0.281055i
$193$	−730.914			−0.272603			−0.136301	−	0.990667i	$-0.543522\pi$
$193$	−730.914			−0.272603			−0.136301	+	0.990667i	$0.543522\pi$
$194$	−852.857	+	1331.84i	−0.315627	+	0.492890i
$195$			36.0729i			0.0132474i
$196$	1059.74	+	2300.61i	0.386201	+	0.838416i
$197$			3582.02i			1.29547i	0.761864	+	0.647737i	$0.224284\pi$
$197$			3582.02i			1.29547i	−0.761864	+	0.647737i	$0.775716\pi$
$198$	1843.58	+	1180.56i	0.661705	+	0.423729i
$199$	2007.64			0.715166			0.357583	−	0.933881i	$-0.383601\pi$
$199$	2007.64			0.715166			0.357583	+	0.933881i	$0.383601\pi$
$200$	560.315	+	77.7658i	0.198101	+	0.0274944i
$201$	−1216.95			−0.427051
$202$	1291.16	+	826.809i	0.449733	+	0.287991i
$203$		−	85.1165i		−	0.0294286i
$204$	−1192.77	+	549.427i	−0.409365	+	0.188567i
$205$			367.484i			0.125201i
$206$	−2692.08	+	4204.01i	−0.910514	+	1.42188i
$207$	−1692.09			−0.568156
$208$	231.207	+	197.717i	0.0770736	+	0.0659095i
$209$	−2817.22			−0.932398
$210$	−59.4522	+	92.8420i	−0.0195362	+	0.0305081i
$211$		−	1414.79i		−	0.461603i	−0.973001	−	0.230802i	$-0.925865\pi$
$211$		−	1414.79i		−	0.461603i	0.973001	−	0.230802i	$-0.0741349\pi$
$212$	4704.07	−	2166.84i	1.52395	−	0.701979i
$213$		−	1165.15i		−	0.374812i
$214$	1054.81	+	675.456i	0.336940	+	0.215763i
$215$	4.18004			0.00132594
$216$	−244.070	+	1758.57i	−0.0768837	+	0.553959i
$217$	−1543.55			−0.482870
$218$	−3685.31	−	2359.92i	−1.14496	−	0.733184i
$219$			73.3379i			0.0226288i
$220$	−524.485	−	1138.62i	−0.160731	−	0.348936i
$221$		−	514.100i		−	0.156480i
$222$	−759.050	+	1185.35i	−0.229478	+	0.358358i
$223$	1.69909			0.000510221			0.000255111	−	1.00000i	$-0.499919\pi$
$223$	1.69909			0.000510221			0.000255111		1.00000i	$0.499919\pi$
$224$	269.205	+	889.924i	0.0802990	+	0.265449i
$225$	−617.409			−0.182936
$226$	1202.72	−	1878.20i	0.353999	−	0.552813i
$227$		−	3374.87i		−	0.986775i	−0.869810	−	0.493387i	$-0.835759\pi$
$227$		−	3374.87i		−	0.986775i	0.869810	−	0.493387i	$-0.164241\pi$
$228$	−456.650	−	991.358i	−0.132642	−	0.287957i
$229$		−	1330.69i		−	0.383994i	−0.981396	−	0.191997i	$-0.938504\pi$
$229$		−	1330.69i		−	0.383994i	0.981396	−	0.191997i	$-0.0614964\pi$
$230$	815.992	+	522.528i	0.233935	+	0.149802i
$231$	244.316			0.0695879
$232$	−51.5491	+	371.419i	−0.0145878	+	0.105107i
$233$	−4373.02			−1.22955			−0.614776	−	0.788701i	$-0.710754\pi$
$233$	−4373.02			−1.22955			−0.614776	+	0.788701i	$0.710754\pi$
$234$	−279.617	−	179.055i	−0.0781160	−	0.0500223i
$235$		−	1141.67i		−	0.316913i
$236$	5476.34	−	2522.58i	1.51051	−	0.695787i
$237$		−	685.580i		−	0.187904i
$238$	847.296	−	1323.16i	0.230765	−	0.360367i
$239$	794.613			0.215060			0.107530	−	0.994202i	$-0.465706\pi$
$239$	794.613			0.215060			0.107530	+	0.994202i	$0.465706\pi$
$240$	315.657	−	369.124i	0.0848982	−	0.0992786i
$241$	617.471			0.165041			0.0825204	−	0.996589i	$-0.473703\pi$
$241$	617.471			0.165041			0.0825204	+	0.996589i	$0.473703\pi$
$242$	531.995	−	830.776i	0.141314	−	0.220679i
$243$		−	2949.81i		−	0.778727i
$244$	2113.28	−	973.444i	0.554463	−	0.255403i
$245$			1583.10i			0.412818i
$246$	265.706	+	170.147i	0.0688650	+	0.0440984i
$247$	427.289			0.110072
$248$	6735.51	+	934.817i	1.72462	+	0.239359i
$249$	−1481.50			−0.377052
$250$	297.739	+	190.660i	0.0753227	+	0.0482336i
$251$		−	907.026i		−	0.228092i	−0.993475	−	0.114046i	$-0.963619\pi$
$251$		−	907.026i		−	0.228092i	0.993475	−	0.114046i	$-0.0363811\pi$
$252$	−424.555	−	921.681i	−0.106129	−	0.230399i
$253$		−	2147.30i		−	0.533596i
$254$	−2354.92	+	3677.49i	−0.581735	+	0.908450i
$255$	−820.767			−0.201563
$256$	−635.751	−	4046.36i	−0.155213	−	0.987881i
$257$	−4350.70			−1.05599			−0.527994	−	0.849248i	$-0.677056\pi$
$257$	−4350.70			−1.05599			−0.527994	+	0.849248i	$0.677056\pi$
$258$	1.93538	−	3.02234i	0.000467022	−	0.000729313i
$259$		−	1684.05i		−	0.404022i
$260$	79.5489	+	172.695i	0.0189747	+	0.0411927i
$261$		−	409.266i		−	0.0970610i
$262$	−4604.85	−	2948.76i	−1.08583	−	0.695324i
$263$	3606.18			0.845499			0.422750	−	0.906246i	$-0.361065\pi$
$263$	3606.18			0.845499			0.422750	+	0.906246i	$0.361065\pi$
$264$	−1066.11	−	147.965i	−0.248540	−	0.0344947i
$265$	3236.96			0.750359
$266$	1099.73	+	704.221i	0.253491	+	0.162325i
$267$			1827.78i			0.418946i
$268$	−5826.03	+	2683.65i	−1.32792	+	0.611680i
$269$			6501.85i			1.47370i	0.676057	+	0.736849i	$0.263687\pi$
$269$			6501.85i			1.47370i	−0.676057	+	0.736849i	$0.736313\pi$
$270$	−598.393	+	934.464i	−0.134878	+	0.210629i
$271$	1011.82			0.226803			0.113401	−	0.993549i	$-0.463825\pi$
$271$	1011.82			0.226803			0.113401	+	0.993549i	$0.463825\pi$
$272$	−4498.65	+	5260.65i	−1.00283	+	1.17270i
$273$	−37.0555			−0.00821502
$274$	729.461	−	1139.14i	0.160833	−	0.251161i
$275$		−	783.508i		−	0.171808i
$276$	755.619	−	348.062i	0.164793	−	0.0759089i
$277$		−	2618.50i		−	0.567979i	−0.958827	−	0.283990i	$-0.908342\pi$
$277$		−	2618.50i		−	0.567979i	0.958827	−	0.283990i	$-0.0916582\pi$
$278$	4900.66	+	3138.19i	1.05727	+	0.677036i
$279$	−7421.84			−1.59259
$280$	−79.8840	+	575.577i	−0.0170499	+	0.122848i
$281$	2302.29			0.488766			0.244383	−	0.969679i	$-0.421415\pi$
$281$	2302.29			0.488766			0.244383	+	0.969679i	$0.421415\pi$
$282$	−825.476	−	528.602i	−0.174313	−	0.111623i
$283$			6591.42i			1.38452i	0.721648	+	0.692260i	$0.243385\pi$
$283$			6591.42i			1.38452i	−0.721648	+	0.692260i	$0.756615\pi$
$284$	−2569.43	−	5578.06i	−0.536857	−	1.16548i
$285$		−	682.172i		−	0.141784i
$286$	227.226	−	354.841i	0.0469795	−	0.0733643i
$287$	−377.494			−0.0776403
$288$	1294.42	+	4279.02i	0.264841	+	0.875499i
$289$	6784.33			1.38089
$290$	−126.384	+	197.364i	−0.0255915	+	0.0399642i
$291$			848.658i			0.170960i
$292$	161.727	+	351.098i	0.0324121	+	0.0703645i
$293$			4765.54i			0.950190i	0.879934	+	0.475095i	$0.157586\pi$
$293$			4765.54i			0.950190i	−0.879934	+	0.475095i	$0.842414\pi$
$294$	1144.64	+	732.984i	0.227065	+	0.145403i
$295$	3768.38			0.743741
$296$	−1019.91	+	7348.62i	−0.200274	+	1.44301i
$297$	2459.06			0.480436
$298$	−6762.00	−	4330.11i	−1.31447	−	0.841733i
$299$			325.682i			0.0629923i
$300$	275.710	−	127.001i	0.0530605	−	0.0244413i
$301$			4.29390i			0.000822247i
$302$	−3335.92	+	5209.45i	−0.635632	+	0.992617i
$303$	822.739			0.155990
$304$	−4372.34	−	3739.01i	−0.824903	−	0.705417i
$305$	1454.19			0.273005
$306$	4074.05	−	6362.13i	0.761105	−	1.18856i
$307$			117.958i			0.0219290i	0.999940	+	0.0109645i	$0.00349018\pi$
$307$			117.958i			0.0219290i	−0.999940	+	0.0109645i	$0.996510\pi$
$308$	1169.64	−	538.771i	0.216384	−	0.0996732i
$309$			2678.82i			0.493181i
$310$	3579.11	+	2291.91i	0.655740	+	0.419910i
$311$	4085.06			0.744832			0.372416	−	0.928066i	$-0.378530\pi$
$311$	4085.06			0.744832			0.372416	+	0.928066i	$0.378530\pi$
$312$	161.697	+	22.4419i	0.0293407	+	0.00407219i
$313$	904.680			0.163372			0.0816861	−	0.996658i	$-0.473969\pi$
$313$	904.680			0.163372			0.0816861	+	0.996658i	$0.473969\pi$
$314$	2230.02	+	1428.02i	0.400788	+	0.256648i
$315$		−	634.227i		−	0.113443i
$316$	−1511.86	−	3282.14i	−0.269141	−	0.584288i
$317$		−	5437.26i		−	0.963366i	−0.876346	−	0.481683i	$-0.840026\pi$
$317$		−	5437.26i		−	0.963366i	0.876346	−	0.481683i	$-0.159974\pi$
$318$	1498.73	−	2340.46i	0.264292	−	0.412724i
$319$	519.369			0.0911569
$320$	697.173	−	2463.24i	0.121791	−	0.430310i
$321$	672.131			0.116868
$322$	−536.762	+	838.219i	−0.0928961	+	0.145069i
$323$			9722.12i			1.67478i
$324$	−1833.21	−	3979.78i	−0.314337	−	0.682404i
$325$			118.835i			0.0202824i
$326$	−5549.10	−	3553.42i	−0.942749	−	0.603698i
$327$	−2348.30			−0.397130
$328$	1647.25	+	228.621i	0.277300	+	0.0384863i
$329$	1172.77			0.196526
$330$	−566.508	−	362.769i	−0.0945007	−	0.0605145i
$331$			5944.03i			0.987049i	0.869732	+	0.493525i	$0.164292\pi$
$331$			5944.03i			0.987049i	−0.869732	+	0.493525i	$0.835708\pi$
$332$	−7092.51	+	3267.03i	−1.17245	+	0.540066i
$333$		−	8097.42i		−	1.33254i
$334$	3081.71	−	4812.46i	0.504860	−	0.788401i
$335$	−4009.01			−0.653837
$336$	379.179	+	324.255i	0.0615652	+	0.0526475i
$337$	5636.91			0.911164			0.455582	−	0.890194i	$-0.349431\pi$
$337$	5636.91			0.911164			0.455582	+	0.890194i	$0.349431\pi$
$338$	3316.58	−	5179.25i	0.533722	−	0.833473i
$339$		−	1196.80i		−	0.191744i
$340$	−3929.34	+	1809.98i	−0.626760	+	0.288705i
$341$		−	9418.50i		−	1.49572i
$342$	5287.82	+	3386.11i	0.836060	+	0.535379i
$343$	−3387.93			−0.533327
$344$	2.60051	−	18.7371i	0.000407588	−	0.00293674i
$345$	519.956			0.0811405
$346$	2172.67	+	1391.29i	0.337582	+	0.216174i
$347$		−	7761.12i		−	1.20069i	−0.799742	−	0.600344i	$-0.795030\pi$
$347$		−	7761.12i		−	1.20069i	0.799742	−	0.600344i	$-0.204970\pi$
$348$	84.1858	+	182.762i	0.0129679	+	0.0281525i
$349$			8709.62i			1.33586i	0.744224	+	0.667930i	$0.232819\pi$
$349$			8709.62i			1.33586i	−0.744224	+	0.667930i	$0.767181\pi$
$350$	−195.854	+	305.849i	−0.0299109	+	0.0467095i
$351$	−372.968			−0.0567166
$352$	−5430.19	+	1642.65i	−0.822244	+	0.248731i
$353$	−986.323			−0.148716			−0.0743579	−	0.997232i	$-0.523691\pi$
$353$	−986.323			−0.148716			−0.0743579	+	0.997232i	$0.523691\pi$
$354$	1744.78	−	2724.69i	0.261961	−	0.409084i
$355$		−	3838.37i		−	0.573858i
$356$	4030.68	+	8750.33i	0.600072	+	1.30272i
$357$		−	843.124i		−	0.124994i
$358$	−7686.32	−	4922.01i	−1.13473	−	0.726638i
$359$	−11470.1			−1.68626			−0.843131	−	0.537708i	$-0.819290\pi$
$359$	−11470.1			−1.68626			−0.843131	+	0.537708i	$0.819290\pi$
$360$	−384.106	+	2767.55i	−0.0562339	+	0.405174i
$361$	−1221.44			−0.178078
$362$	2390.08	+	1530.51i	0.347016	+	0.222215i
$363$		−	529.376i		−	0.0765428i
$364$	−177.399	+	81.7157i	−0.0255447	+	0.0117667i
$365$			241.597i			0.0346459i
$366$	673.299	−	1051.44i	0.0961582	−	0.150163i
$367$	3330.42			0.473697			0.236848	−	0.971547i	$-0.423886\pi$
$367$	3330.42			0.473697			0.236848	+	0.971547i	$0.423886\pi$
$368$	2849.89	−	3332.62i	0.403698	−	0.472078i
$369$	−1815.10			−0.256072
$370$	−2500.54	+	3904.90i	−0.351343	+	0.548665i
$371$			3325.14i			0.465317i
$372$	3314.29	−	1526.67i	0.461931	−	0.212780i
$373$		−	9398.88i		−	1.30471i	−0.757915	−	0.652354i	$-0.773782\pi$
$373$		−	9398.88i		−	1.30471i	0.757915	−	0.652354i	$-0.226218\pi$
$374$	8073.70	+	5170.07i	1.11626	+	0.714808i
$375$	189.722			0.0261258
$376$	−5117.57	−	710.265i	−0.701911	−	0.0974178i
$377$	−78.7729			−0.0107613
$378$	−959.918	−	614.693i	−0.130616	−	0.0836413i
$379$		−	3840.58i		−	0.520521i	−0.965538	−	0.260260i	$-0.916192\pi$
$379$		−	3840.58i		−	0.520521i	0.965538	−	0.260260i	$-0.0838084\pi$
$380$	−1504.34	−	3265.83i	−0.203082	−	0.440878i
$381$			2343.32i			0.315097i
$382$	1940.27	−	3029.98i	0.259877	−	0.405830i
$383$	−2969.97			−0.396236			−0.198118	−	0.980178i	$-0.563483\pi$
$383$	−2969.97			−0.396236			−0.198118	+	0.980178i	$0.563483\pi$
$384$	−1458.23	−	1644.58i	−0.193789	−	0.218554i
$385$	804.850			0.106543
$386$	−1114.85	+	1740.98i	−0.147006	+	0.229568i
$387$			20.6464i			0.00271192i
$388$	1871.48	+	4062.86i	0.244872	+	0.531600i
$389$			8349.10i			1.08822i	0.839015	+	0.544108i	$0.183132\pi$
$389$			8349.10i			1.08822i	−0.839015	+	0.544108i	$0.816868\pi$
$390$	85.9226	+	55.0213i	0.0111560	+	0.00714388i
$391$	−7410.26			−0.958447
$392$	7096.26	+	984.886i	0.914325	+	0.126899i
$393$	−2934.24			−0.376623
$394$	8532.06	+	5463.59i	1.09096	+	0.698608i
$395$		−	2258.51i		−	0.287691i
$396$	5623.96	−	2590.57i	0.713674	−	0.328741i
$397$		−	4506.27i		−	0.569680i	−0.958575	−	0.284840i	$-0.908060\pi$
$397$		−	4506.27i		−	0.569680i	0.958575	−	0.284840i	$-0.0919405\pi$
$398$	3062.22	−	4782.03i	0.385666	−	0.602265i
$399$	700.754			0.0879238
$400$	1039.87	−	1216.01i	0.129984	−	0.152001i
$401$	−7654.44			−0.953228			−0.476614	−	0.879113i	$-0.658136\pi$
$401$	−7654.44			−0.953228			−0.476614	+	0.879113i	$0.658136\pi$
$402$	−1856.19	+	2898.68i	−0.230295	+	0.359634i
$403$			1428.51i			0.176573i
$404$	3938.78	−	1814.32i	0.485053	−	0.223431i
$405$		−	2738.56i		−	0.336001i
$406$	−202.740	−	129.827i	−0.0247828	−	0.0158699i
$407$	10275.8			1.25148
$408$	−510.621	+	3679.10i	−0.0619596	+	0.446428i
$409$	2603.53			0.314758			0.157379	−	0.987538i	$-0.449696\pi$
$409$	2603.53			0.314758			0.157379	+	0.987538i	$0.449696\pi$
$410$	875.316	+	560.517i	0.105436	+	0.0675170i
$411$		−	725.870i		−	0.0871156i
$412$	5907.41	+	12824.6i	0.706401	+	1.53355i
$413$			3871.03i			0.461212i
$414$	−2580.91	+	4030.41i	−0.306389	+	0.478463i
$415$	−4880.50			−0.577287
$416$	823.599	−	249.141i	0.0970680	−	0.0293633i
$417$	3122.74			0.366717
$418$	−4297.05	+	6710.38i	−0.502813	+	0.785204i
$419$		−	525.993i		−	0.0613280i	−0.999530	−	0.0306640i	$-0.990238\pi$
$419$		−	525.993i		−	0.0613280i	0.999530	−	0.0306640i	$-0.00976219\pi$
$420$	130.460	+	283.220i	0.0151567	+	0.0329041i
$421$			15126.1i			1.75107i	0.483157	+	0.875534i	$0.339490\pi$
$421$			15126.1i			1.75107i	−0.483157	+	0.875534i	$0.660510\pi$
$422$	−3369.91	−	2157.96i	−0.388732	−	0.248928i
$423$	5639.03			0.648178
$424$	2013.80	−	14509.7i	0.230658	−	1.66192i
$425$	−2703.86			−0.308603
$426$	−2775.30	−	1777.19i	−0.315642	−	0.202125i
$427$			1493.80i			0.169298i
$428$	3217.76	−	1482.20i	0.363402	−	0.167394i
$429$		−	226.107i		−	0.0254465i
$430$	6.37574	−	9.95650i	0.000715036	−	0.00111662i
$431$	4887.92			0.546271			0.273135	−	0.961976i	$-0.411939\pi$
$431$	4887.92			0.546271			0.273135	+	0.961976i	$0.411939\pi$
$432$	3816.48	+	3263.66i	0.425047	+	0.363479i
$433$	−6944.15			−0.770704			−0.385352	−	0.922770i	$-0.625920\pi$
$433$	−6944.15			−0.770704			−0.385352	+	0.922770i	$0.625920\pi$
$434$	−2354.34	+	3676.60i	−0.260397	+	0.406641i
$435$			125.762i			0.0138617i
$436$	−11242.3	+	5178.54i	−1.23488	+	0.568823i
$437$		−	6158.96i		−	0.674195i
$438$	174.684	+	111.861i	0.0190565	+	0.0122030i
$439$	577.528			0.0627879			0.0313940	−	0.999507i	$-0.490005\pi$
$439$	577.528			0.0627879			0.0313940	+	0.999507i	$0.490005\pi$
$440$	−3512.09	−	487.441i	−0.380528	−	0.0528132i
$441$	−7819.35			−0.844331
$442$	−1224.54	−	784.148i	−0.131777	−	0.0843848i
$443$			7039.42i			0.754973i	0.926015	+	0.377486i	$0.123211\pi$
$443$			7039.42i			0.754973i	−0.926015	+	0.377486i	$0.876789\pi$
$444$	1665.64	+	3615.98i	0.178035	+	0.386502i
$445$			6021.27i			0.641429i
$446$	2.59159	−	4.04708i	0.000275146	−	0.000429674i
$447$	−4308.79			−0.455926
$448$	2530.34	+	716.163i	0.266846	+	0.0755257i
$449$	6396.99			0.672366			0.336183	−	0.941797i	$-0.390864\pi$
$449$	6396.99			0.672366			0.336183	+	0.941797i	$0.390864\pi$
$450$	−941.723	+	1470.62i	−0.0986517	+	0.154057i
$451$		−	2303.41i		−	0.240496i
$452$	−2639.22	−	5729.56i	−0.274642	−	0.596230i
$453$			3319.50i			0.344291i
$454$	−8038.65	−	5147.62i	−0.830996	−	0.532136i
$455$	−122.072			−0.0125776
$456$	−3057.85	−	424.397i	−0.314028	−	0.0435838i
$457$	−7015.85			−0.718135			−0.359068	−	0.933312i	$-0.616905\pi$
$457$	−7015.85			−0.718135			−0.359068	+	0.933312i	$0.616905\pi$
$458$	−3169.60	−	2029.68i	−0.323374	−	0.207076i
$459$		−	8486.14i		−	0.862961i
$460$	2489.24	−	1146.62i	0.252307	−	0.116221i
$461$		−	13374.1i		−	1.35118i	−0.737279	−	0.675588i	$-0.763890\pi$
$461$		−	13374.1i		−	1.35118i	0.737279	−	0.675588i	$-0.236110\pi$
$462$	372.650	−	581.939i	0.0375265	−	0.0586023i
$463$	15414.3			1.54722			0.773611	−	0.633661i	$-0.218449\pi$
$463$	15414.3			1.54722			0.773611	+	0.633661i	$0.218449\pi$
$464$	806.062	+	689.304i	0.0806476	+	0.0689658i
$465$	2280.63			0.227445
$466$	−6670.08	+	10416.1i	−0.663059	+	1.03545i
$467$		−	1796.43i		−	0.178006i	−0.996031	−	0.0890032i	$-0.971632\pi$
$467$		−	1796.43i		−	0.178006i	0.996031	−	0.0890032i	$-0.0283681\pi$
$468$	−852.989	+	392.914i	−0.0842510	+	0.0388086i
$469$		−	4118.21i		−	0.405461i
$470$	−2719.37	−	1741.37i	−0.266883	−	0.170901i
$471$	1420.99			0.139014
$472$	2344.41	−	16891.8i	0.228623	−	1.64727i
$473$	−26.2008			−0.00254696
$474$	−1632.99	−	1045.70i	−0.158240	−	0.101331i
$475$		−	2247.28i		−	0.217079i
$476$	−1859.28	−	4036.37i	−0.179033	−	0.388670i
$477$			15988.3i			1.53470i
$478$	1212.01	−	1892.70i	0.115975	−	0.181109i
$479$	11789.0			1.12454			0.562270	−	0.826954i	$-0.309928\pi$
$479$	11789.0			1.12454			0.562270	+	0.826954i	$0.309928\pi$
$480$	−397.757	−	1314.89i	−0.0378230	−	0.125033i
$481$	−1558.54			−0.147741
$482$	941.818	−	1470.76i	0.0890013	−	0.138986i
$483$			534.119i			0.0503173i
$484$	−1167.39	−	2534.33i	−0.109635	−	0.238010i
$485$			2795.74i			0.261748i
$486$	−7026.20	−	4499.29i	−0.655792	−	0.419943i
$487$	18083.0			1.68258			0.841291	−	0.540582i	$-0.181796\pi$
$487$	18083.0			1.68258			0.841291	+	0.540582i	$0.181796\pi$
$488$	904.690	−	6518.43i	0.0839208	−	0.604663i
$489$	−3535.92			−0.326994
$490$	3770.80	+	2414.67i	0.347648	+	0.222620i
$491$		−	11259.2i		−	1.03487i	−0.855722	−	0.517435i	$-0.826887\pi$
$491$		−	11259.2i		−	1.03487i	0.855722	−	0.517435i	$-0.173113\pi$
$492$	810.553	−	373.366i	0.0742735	−	0.0342127i
$493$		−	1792.32i		−	0.163736i
$494$	651.736	−	1017.77i	0.0593583	−	0.0926953i
$495$	3869.96			0.351397
$496$	12500.2	−	14617.5i	1.13160	−	1.32328i
$497$	3942.92			0.355864
$498$	−2259.70	+	3528.80i	−0.203332	+	0.317529i
$499$			4589.82i			0.411761i	0.978577	+	0.205880i	$0.0660058\pi$
$499$			4589.82i			0.411761i	−0.978577	+	0.205880i	$0.933994\pi$
$500$	908.273	−	418.379i	0.0812384	−	0.0374209i
$501$		−	3066.53i		−	0.273458i
$502$	−2160.46	−	1383.47i	−0.192084	−	0.123003i
$503$	−5257.43			−0.466038			−0.233019	−	0.972472i	$-0.574860\pi$
$503$	−5257.43			−0.466038			−0.233019	+	0.972472i	$0.574860\pi$
$504$	−2842.93	−	394.569i	−0.251258	−	0.0348720i
$505$	2710.35			0.238830
$506$	−5114.69	−	3275.24i	−0.449359	−	0.287751i
$507$		−	3300.25i		−	0.289091i
$508$	5167.56	+	11218.4i	0.451325	+	0.979797i
$509$		−	2451.99i		−	0.213522i	−0.994285	−	0.106761i	$-0.965952\pi$
$509$		−	2451.99i		−	0.213522i	0.994285	−	0.106761i	$-0.0340479\pi$
$510$	−1251.90	+	1955.00i	−0.108696	+	0.169743i
$511$	−248.178			−0.0214848
$512$	−10607.8	−	4657.54i	−0.915629	−	0.402023i
$513$	7053.17			0.607027
$514$	−6636.04	+	10363.0i	−0.569461	+	0.889283i
$515$			8824.85i			0.755086i
$516$	−4.24695	−	9.21984i	−0.000362328	−	0.000786591i
$517$			7156.08i			0.608750i
$518$	−4011.26	−	2568.65i	−0.340241	−	0.217877i
$519$	1384.44			0.117091
$520$	532.680	+	73.9304i	0.0449222	+	0.00623473i
$521$	10677.6			0.897878			0.448939	−	0.893562i	$-0.351802\pi$
$521$	10677.6			0.897878			0.448939	+	0.893562i	$0.351802\pi$
$522$	−974.836	−	624.246i	−0.0817383	−	0.0523419i
$523$		−	19565.8i		−	1.63585i	−0.575323	−	0.817927i	$-0.695124\pi$
$523$		−	19565.8i		−	1.63585i	0.575323	−	0.817927i	$-0.304876\pi$
$524$	−14047.4	+	6470.67i	−1.17111	+	0.539451i
$525$			194.889i			0.0162013i
$526$	5500.43	−	8589.60i	0.455951	−	0.712024i
$527$	−32502.9			−2.68662
$528$	−1978.56	+	2313.69i	−0.163079	+	0.190702i
$529$	−7472.60			−0.614170
$530$	4937.28	−	7710.17i	0.404645	−	0.631903i
$531$			18613.1i			1.52116i
$532$	3354.79	−	1545.32i	0.273400	−	0.125936i
$533$			349.360i			0.0283911i
$534$	4353.63	+	2787.89i	0.352809	+	0.225924i
$535$	2214.20			0.178931
$536$	−2494.11	+	17970.4i	−0.200987	+	1.44814i
$537$	−4897.78			−0.393584
$538$	15486.9	+	9917.16i	1.24105	+	0.794719i
$539$		−	9922.95i		−	0.792972i
$540$	1313.10	+	2850.64i	0.104642	+	0.227171i
$541$			3313.01i			0.263286i	0.991297	+	0.131643i	$0.0420252\pi$
$541$			3313.01i			0.263286i	−0.991297	+	0.131643i	$0.957975\pi$
$542$	1543.31	−	2410.07i	0.122308	−	0.190998i
$543$	1522.98			0.120363
$544$	5668.71	+	18739.4i	0.446772	+	1.47692i
$545$	−7736.02			−0.608027
$546$	−56.5201	+	88.2630i	−0.00443010	+	0.00691815i
$547$			25040.9i			1.95735i	0.205414	+	0.978675i	$0.434146\pi$
$547$			25040.9i			1.95735i	−0.205414	+	0.978675i	$0.565854\pi$
$548$	−1600.71	−	3475.03i	−0.124779	−	0.270887i
$549$			7182.64i			0.558375i
$550$	−1866.25	−	1195.07i	−0.144686	−	0.0926508i
$551$	1489.67			0.115176
$552$	323.478	−	2330.71i	0.0249423	−	0.179713i
$553$	2320.03			0.178404
$554$	−6237.04	−	3993.95i	−0.478315	−	0.306293i
$555$			2488.23i			0.190305i
$556$	14949.8	−	6886.34i	1.14031	−	0.525263i
$557$			2708.11i			0.206008i	0.994681	+	0.103004i	$0.0328454\pi$
$557$			2708.11i			0.206008i	−0.994681	+	0.103004i	$0.967155\pi$
$558$	−11320.4	+	17678.2i	−0.858836	+	1.34118i
$559$	3.97388			0.000300675
$560$	1249.13	+	1068.19i	0.0942596	+	0.0806061i
$561$	5144.62			0.387177
$562$	3511.64	−	5483.86i	0.263576	−	0.411606i
$563$			9374.67i			0.701768i	0.936419	+	0.350884i	$0.114119\pi$
$563$			9374.67i			0.701768i	−0.936419	+	0.350884i	$0.885881\pi$
$564$	−2518.17	+	1159.95i	−0.188003	+	0.0866003i
$565$		−	3942.62i		−	0.293571i
$566$	15700.2	+	10053.8i	1.16595	+	0.746628i
$567$	2813.16			0.208363
$568$	−17205.6	−	2387.95i	−1.27100	−	0.176402i
$569$	12092.5			0.890938			0.445469	−	0.895297i	$-0.353037\pi$
$569$	12092.5			0.890938			0.445469	+	0.895297i	$0.353037\pi$
$570$	−1624.88	−	1040.51i	−0.119401	−	0.0764596i
$571$		−	10847.4i		−	0.795008i	−0.917601	−	0.397504i	$-0.869877\pi$
$571$		−	10847.4i		−	0.795008i	0.917601	−	0.397504i	$-0.130123\pi$
$572$	−498.617	−	1082.47i	−0.0364480	−	0.0791261i
$573$		−	1930.72i		−	0.140763i
$574$	−575.785	+	899.158i	−0.0418690	+	0.0653835i
$575$	1712.89			0.124230
$576$	12166.6	+	3443.53i	0.880108	+	0.249098i
$577$	−22325.8			−1.61080			−0.805402	−	0.592729i	$-0.798051\pi$
$577$	−22325.8			−1.61080			−0.805402	+	0.592729i	$0.798051\pi$
$578$	10348.0	−	16159.7i	0.744673	−	1.16290i
$579$			1109.36i			0.0796261i
$580$	277.333	+	602.072i	0.0198546	+	0.0431029i
$581$		−	5013.44i		−	0.357990i
$582$	2021.43	+	1294.44i	0.143971	+	0.0921931i
$583$	−20289.5			−1.44135
$584$	1082.96	+	150.304i	0.0767351	+	0.0106500i
$585$	−586.959			−0.0414833
$586$	11351.1	+	7268.79i	0.800187	+	0.512408i
$587$			281.244i			0.0197754i	0.999951	+	0.00988770i	$0.00314741\pi$
$587$			281.244i			0.0197754i	−0.999951	+	0.00988770i	$0.996853\pi$
$588$	3491.81	−	1608.44i	0.244898	−	0.112808i
$589$		−	27014.4i		−	1.88983i
$590$	5747.84	−	8975.95i	0.401076	−	0.626329i
$591$	5436.69			0.378402
$592$	15948.1	+	13638.1i	1.10720	+	0.946825i
$593$	−934.658			−0.0647248			−0.0323624	−	0.999476i	$-0.510303\pi$
$593$	−934.658			−0.0647248			−0.0323624	+	0.999476i	$0.510303\pi$
$594$	3750.77	−	5857.28i	0.259084	−	0.404591i
$595$		−	2777.51i		−	0.191372i
$596$	−20627.9	+	9501.86i	−1.41770	+	0.653039i
$597$		−	3047.14i		−	0.208897i
$598$	775.748	+	496.757i	0.0530480	+	0.0339698i
$599$	−15278.2			−1.04215			−0.521077	−	0.853510i	$-0.674470\pi$
$599$	−15278.2			−1.04215			−0.521077	+	0.853510i	$0.674470\pi$
$600$	118.031	−	850.430i	0.00803097	−	0.0578644i
$601$	10958.6			0.743780			0.371890	−	0.928277i	$-0.378710\pi$
$601$	10958.6			0.743780			0.371890	+	0.928277i	$0.378710\pi$
$602$	10.2277	+	6.54941i	0.000692442	+	0.000443412i
$603$		−	19801.6i		−	1.33728i
$604$	7320.24	+	15891.8i	0.493140	+	1.07057i
$605$		−	1743.92i		−	0.117191i
$606$	1254.91	−	1959.69i	0.0841207	−	0.131365i
$607$	−24850.2			−1.66167			−0.830837	−	0.556515i	$-0.812138\pi$
$607$	−24850.2			−1.66167			−0.830837	+	0.556515i	$0.812138\pi$
$608$	−15575.0	+	4711.49i	−1.03890	+	0.314270i
$609$	−129.187			−0.00859596
$610$	2218.05	−	3463.76i	0.147223	−	0.229907i
$611$		−	1085.37i		−	0.0718645i
$612$	−8939.97	−	19408.1i	−0.590485	−	1.28190i
$613$			3961.58i			0.261022i	0.991447	+	0.130511i	$0.0416618\pi$
$613$			3961.58i			0.261022i	−0.991447	+	0.130511i	$0.958338\pi$
$614$	280.965	+	179.919i	0.0184671	+	0.0118256i
$615$	557.757			0.0365706
$616$	500.718	−	3607.75i	0.0327508	−	0.235975i
$617$	20732.3			1.35275			0.676377	−	0.736555i	$-0.263549\pi$
$617$	20732.3			1.35275			0.676377	+	0.736555i	$0.263549\pi$
$618$	6380.73	+	4085.96i	0.415324	+	0.265957i
$619$			7801.96i			0.506603i	0.967387	+	0.253301i	$0.0815164\pi$
$619$			7801.96i			0.506603i	−0.967387	+	0.253301i	$0.918484\pi$
$620$	10918.3	−	5029.31i	0.707240	−	0.325777i
$621$			5375.97i			0.347391i
$622$	6230.87	−	9730.27i	0.401664	−	0.627248i
$623$	−6185.29			−0.397766
$624$	300.089	−	350.919i	0.0192519	−	0.0225128i
$625$	625.000			0.0400000
$626$	1379.89	−	2154.87i	0.0881015	−	0.137581i
$627$			4275.90i			0.272349i
$628$	6802.82	−	3133.59i	0.432265	−	0.199115i
$629$		−	35461.5i		−	2.24792i
$630$	−1510.67	−	967.375i	−0.0955344	−	0.0611764i
$631$	−9359.85			−0.590507			−0.295253	−	0.955419i	$-0.595404\pi$
$631$	−9359.85			−0.590507			−0.295253	+	0.955419i	$0.595404\pi$
$632$	−10123.8	−	1405.08i	−0.637188	−	0.0884350i
$633$	−2147.33			−0.134832
$634$	−12951.1	−	8293.36i	−0.811283	−	0.519513i
$635$			7719.61i			0.482431i
$636$	−3288.78	−	7139.71i	−0.205045	−	0.445138i
$637$			1505.02i			0.0936123i
$638$	792.183	−	1237.09i	0.0491581	−	0.0767663i
$639$	18958.8			1.17370
$640$	−4803.84	−	5417.74i	−0.296701	−	0.334617i
$641$	19129.1			1.17871			0.589356	−	0.807873i	$-0.299381\pi$
$641$	19129.1			1.17871			0.589356	+	0.807873i	$0.299381\pi$
$642$	1025.19	−	1600.96i	0.0630233	−	0.0984186i
$643$		−	11243.5i		−	0.689582i	−0.938680	−	0.344791i	$-0.887950\pi$
$643$		−	11243.5i		−	0.689582i	0.938680	−	0.344791i	$-0.112050\pi$
$644$	1177.85	+	2557.04i	0.0720713	+	0.156462i
$645$		−	6.34435i		−	0.000387300i
$646$	23157.3	+	14829.0i	1.41039	+	0.903155i
$647$	11887.6			0.722331			0.361166	−	0.932502i	$-0.382379\pi$
$647$	11887.6			0.722331			0.361166	+	0.932502i	$0.382379\pi$
$648$	−12275.7	−	1703.73i	−0.744187	−	0.103285i
$649$	−23620.4			−1.42863
$650$	283.055	+	181.257i	0.0170805	+	0.0109377i
$651$			2342.75i			0.141044i
$652$	−16927.9	+	7797.51i	−1.01679	+	0.468365i
$653$			5327.46i			0.319264i	0.987177	+	0.159632i	$0.0510308\pi$
$653$			5327.46i			0.319264i	−0.987177	+	0.159632i	$0.948969\pi$
$654$	−3581.82	+	5593.46i	−0.214160	+	0.334436i
$655$	−9666.28			−0.576630
$656$	3057.08	−	3574.91i	0.181950	−	0.212769i
$657$	−1193.31			−0.0708609
$658$	1788.81	−	2793.44i	0.105980	−	0.165501i
$659$			26016.2i			1.53786i	0.639334	+	0.768929i	$0.279210\pi$
$659$			26016.2i			1.53786i	−0.639334	+	0.768929i	$0.720790\pi$
$660$	−1728.17	+	796.049i	−0.101923	+	0.0469487i
$661$			5961.64i			0.350803i	0.984497	+	0.175401i	$0.0561224\pi$
$661$			5961.64i			0.350803i	−0.984497	+	0.175401i	$0.943878\pi$
$662$	14158.2	+	9066.32i	0.831228	+	0.532285i
$663$	−780.287			−0.0457071
$664$	−3036.28	+	21876.9i	−0.177456	+	1.27860i
$665$	2308.50			0.134616
$666$	−19287.4	−	12350.8i	−1.12218	−	0.718597i
$667$			1135.43i			0.0659134i
$668$	−6762.40	−	14680.7i	−0.391684	−	0.850320i
$669$		−	2.57883i		−	0.000149033i
$670$	−6114.87	+	9549.11i	−0.352594	+	0.550618i
$671$	−9114.95			−0.524410
$672$	1350.70	−	408.591i	0.0775364	−	0.0234550i
$673$	17544.1			1.00487			0.502435	−	0.864615i	$-0.332438\pi$
$673$	17544.1			1.00487			0.502435	+	0.864615i	$0.332438\pi$
$674$	8597.88	−	13426.6i	0.491362	−	0.767322i
$675$			1961.58i			0.111854i
$676$	−7277.80	−	15799.6i	−0.414076	−	0.898932i
$677$			17000.0i			0.965088i	0.875872	+	0.482544i	$0.160287\pi$
$677$			17000.0i			0.965088i	−0.875872	+	0.482544i	$0.839713\pi$
$678$	−2850.68	−	1825.46i	−0.161474	−	0.103402i
$679$	−2871.89			−0.162317
$680$	−1682.14	+	12120.1i	−0.0948634	+	0.683505i
$681$	−5122.28			−0.288232
$682$	−22434.1	−	14365.9i	−1.25960	−	0.806594i
$683$			5386.68i			0.301780i	0.988551	+	0.150890i	$0.0482139\pi$
$683$			5386.68i			0.301780i	−0.988551	+	0.150890i	$0.951786\pi$
$684$	16130.8	−	7430.37i	0.901722	−	0.415361i
$685$		−	2391.23i		−	0.133379i
$686$	−5167.55	+	8069.77i	−0.287607	+	0.449133i
$687$	−2019.69			−0.112163
$688$	−40.6637	−	34.7736i	−0.00225333	−	0.00192693i
$689$	3077.32			0.170155
$690$	793.079	−	1238.49i	0.0437565	−	0.0683312i
$691$		−	18049.0i		−	0.993658i	−0.867849	−	0.496829i	$-0.834498\pi$
$691$		−	18049.0i		−	0.993658i	0.867849	−	0.496829i	$-0.165502\pi$
$692$	6627.87	−	3053.01i	0.364095	−	0.167714i
$693$			3975.37i			0.217910i
$694$	−18486.3	−	11837.9i	−1.01114	−	0.647493i
$695$	10287.2			0.561464
$696$	563.730	+	78.2397i	0.0307013	+	0.00426102i
$697$	−7948.99			−0.431979
$698$	20745.6	+	13284.6i	1.12497	+	0.720387i
$699$			6637.24i			0.359147i
$700$	429.775	+	933.013i	0.0232057	+	0.0503780i
$701$			7991.13i			0.430558i	0.976553	+	0.215279i	$0.0690660\pi$
$701$			7991.13i			0.430558i	−0.976553	+	0.215279i	$0.930934\pi$
$702$	−568.881	+	888.377i	−0.0305855	+	0.0477630i
$703$	29473.5			1.58124
$704$	−4369.92	+	15439.7i	−0.233946	+	0.826573i
$705$	−1732.80			−0.0925688
$706$	−1504.42	+	2349.34i	−0.0801977	+	0.125239i
$707$			2784.18i			0.148104i
$708$	−3828.70	−	8311.84i	−0.203236	−	0.441212i
$709$			11306.8i			0.598920i	0.954109	+	0.299460i	$0.0968065\pi$
$709$			11306.8i			0.598920i	−0.954109	+	0.299460i	$0.903194\pi$
$710$	−9142.67	−	5854.59i	−0.483265	−	0.309463i
$711$	11155.4			0.588410
$712$	26990.5	+	3745.99i	1.42066	+	0.197173i
$713$	20590.6			1.08152
$714$	−2008.25	−	1286.00i	−0.105262	−	0.0674053i
$715$		−	744.865i		−	0.0389600i
$716$	−23447.6	+	10800.7i	−1.22385	+	0.563745i
$717$		−	1206.04i		−	0.0628180i
$718$	−17495.1	+	27320.8i	−0.909348	+	1.42006i
$719$	30968.9			1.60632			0.803160	−	0.595763i	$-0.203150\pi$
$719$	30968.9			1.60632			0.803160	+	0.595763i	$0.203150\pi$
$720$	6006.19	+	5136.20i	0.310885	+	0.265854i
$721$	−9065.23			−0.468248
$722$	−1863.04	+	2909.36i	−0.0960320	+	0.149966i
$723$		−	937.181i		−	0.0482076i
$724$	7291.09	−	3358.51i	0.374270	−	0.172400i
$725$			414.298i			0.0212229i
$726$	−1260.93	−	807.448i	−0.0644593	−	0.0412771i
$727$	26520.2			1.35293			0.676466	−	0.736474i	$-0.263511\pi$
$727$	26520.2			1.35293			0.676466	+	0.736474i	$0.263511\pi$
$728$	−75.9442	+	547.190i	−0.00386632	+	0.0278574i
$729$	10311.1			0.523858
$730$	575.463	+	368.504i	0.0291765	+	0.0186835i
$731$			90.4178i			0.00457486i
$732$	−1477.47	−	3207.48i	−0.0746021	−	0.161956i
$733$			15980.8i			0.805270i	0.915361	+	0.402635i	$0.131906\pi$
$733$			15980.8i			0.805270i	−0.915361	+	0.402635i	$0.868094\pi$
$734$	5079.83	−	7932.78i	0.255450	−	0.398916i
$735$	2402.78			0.120582
$736$	−3591.13	−	11871.4i	−0.179851	−	0.594545i
$737$	25128.7			1.25594
$738$	−2768.55	+	4323.42i	−0.138092	+	0.215647i
$739$			10163.8i			0.505927i	0.967476	+	0.252964i	$0.0814053\pi$
$739$			10163.8i			0.505927i	−0.967476	+	0.252964i	$0.918595\pi$
$740$	5487.11	+	11912.1i	0.272581	+	0.591755i
$741$		−	648.528i		−	0.0321515i
$742$	7920.19	+	5071.77i	0.391859	+	0.250931i
$743$	−37765.7			−1.86472			−0.932360	−	0.361530i	$-0.882254\pi$
$743$	−37765.7			−1.86472			−0.932360	+	0.361530i	$0.882254\pi$
$744$	1418.84	−	10223.0i	0.0699156	−	0.503753i
$745$	−14194.5			−0.698047
$746$	−22387.3	−	14335.9i	−1.09874	−	0.703588i
$747$		−	24106.1i		−	1.18072i
$748$	24629.3	−	11345.1i	1.20393	−	0.554567i
$749$			2274.51i			0.110960i
$750$	289.379	−	451.900i	0.0140888	−	0.0220014i
$751$	−20234.4			−0.983175			−0.491587	−	0.870828i	$-0.663583\pi$
$751$	−20234.4			−0.983175			−0.491587	+	0.870828i	$0.663583\pi$
$752$	−9497.52	+	11106.3i	−0.460557	+	0.538568i
$753$	−1376.66			−0.0666245
$754$	−120.151	+	187.630i	−0.00580323	+	0.00906245i
$755$			10935.4i			0.527127i
$756$	−2928.29	+	1348.86i	−0.140874	+	0.0648911i
$757$		−	27066.9i		−	1.29956i	−0.760124	−	0.649778i	$-0.774862\pi$
$757$		−	27066.9i		−	1.29956i	0.760124	−	0.649778i	$-0.225138\pi$
$758$	−9147.94	−	5857.97i	−0.438348	−	0.280701i
$759$	−3259.12			−0.155861
$760$	−10073.5	−	1398.09i	−0.480794	−	0.0667291i
$761$	−30797.4			−1.46702			−0.733512	−	0.679677i	$-0.762120\pi$
$761$	−30797.4			−1.46702			−0.733512	+	0.679677i	$0.762120\pi$
$762$	5581.59	+	3574.23i	0.265354	+	0.169922i
$763$		−	7946.74i		−	0.377053i
$764$	−4257.68	−	9243.13i	−0.201620	−	0.437703i
$765$		−	13355.1i		−	0.631182i
$766$	−4530.05	+	7074.22i	−0.213678	+	0.333684i
$767$	3582.52			0.168654
$768$	−6141.45	+	964.926i	−0.288556	+	0.0453369i
$769$	−35490.2			−1.66425			−0.832125	−	0.554588i	$-0.812876\pi$
$769$	−35490.2			−1.66425			−0.832125	+	0.554588i	$0.812876\pi$
$770$	1227.62	−	1917.08i	0.0574551	−	0.0897232i
$771$			6603.37i			0.308449i
$772$	2446.39	+	5310.96i	0.114051	+	0.247598i
$773$			37364.0i			1.73854i	0.494339	+	0.869269i	$0.335410\pi$
$773$			37364.0i			1.73854i	−0.494339	+	0.869269i	$0.664590\pi$
$774$	49.1779	+	31.4915i	0.00228380	+	0.00146245i
$775$	7513.09			0.348230
$776$	12531.9	+	1739.30i	0.579730	+	0.0804604i
$777$	−2556.01			−0.118013
$778$	19886.8	+	12734.7i	0.916424	+	0.586841i
$779$		−	6606.72i		−	0.303864i
$780$	262.112	−	120.737i	0.0120322	−	0.00554241i
$781$			24059.1i			1.10231i
$782$	−11302.7	+	17650.6i	−0.516860	+	0.807141i
$783$	−1300.29			−0.0593467
$784$	13169.7	−	15400.5i	0.599932	−	0.701551i
$785$	4681.16			0.212838
$786$	−4475.55	+	6989.11i	−0.203101	+	0.317167i
$787$		−	28529.7i		−	1.29222i	−0.763246	−	0.646108i	$-0.776395\pi$
$787$		−	28529.7i		−	1.29222i	0.763246	−	0.646108i	$-0.223605\pi$
$788$	26027.6	−	11989.1i	1.17664	−	0.541999i
$789$		−	5473.35i		−	0.246967i
$790$	−5379.57	−	3444.86i	−0.242274	−	0.155142i
$791$	4050.01			0.182051
$792$	2407.60	−	17347.2i	0.108018	−	0.778288i
$793$	1382.47			0.0619078
$794$	−10733.5	−	6873.33i	−0.479747	−	0.307211i
$795$		−	4912.98i		−	0.219176i
$796$	−6719.64	−	14587.9i	−0.299210	−	0.649565i
$797$		−	7130.44i		−	0.316905i	−0.987367	−	0.158452i	$-0.949350\pi$
$797$		−	7130.44i		−	0.316905i	0.987367	−	0.158452i	$-0.0506504\pi$
$798$	1068.85	−	1669.14i	0.0474145	−	0.0740436i
$799$	24695.3			1.09344
$800$	−1310.33	−	4331.63i	−0.0579090	−	0.191433i
$801$	−29740.7			−1.31191
$802$	−11675.2	+	18232.2i	−0.514046	+	0.802745i
$803$		−	1514.35i		−	0.0665505i
$804$	4073.18	+	8842.59i	0.178669	+	0.387878i
$805$			1759.55i			0.0770385i
$806$	3402.58	+	2178.88i	0.148698	+	0.0952204i
$807$	9868.33			0.430461
$808$	1686.18	−	12149.2i	0.0734153	−	0.528969i
$809$	−11060.3			−0.480665			−0.240333	−	0.970691i	$-0.577257\pi$
$809$	−11060.3			−0.480665			−0.240333	+	0.970691i	$0.577257\pi$
$810$	−6523.02	−	4177.08i	−0.282958	−	0.181195i
$811$		−	27381.5i		−	1.18557i	−0.805361	−	0.592784i	$-0.798029\pi$
$811$		−	27381.5i		−	1.18557i	0.805361	−	0.592784i	$-0.201971\pi$
$812$	−618.472	+	284.888i	−0.0267292	+	0.0123123i
$813$		−	1535.71i		−	0.0662481i
$814$	15673.5	−	24476.1i	0.674886	−	1.05392i
$815$	−11648.4			−0.500645
$816$	7984.47	+	6827.92i	0.342540	+	0.292923i
$817$	−75.1498			−0.00321807
$818$	3971.11	−	6201.38i	0.169739	−	0.265069i
$819$		−	602.947i		−	0.0257249i
$820$	2670.21	−	1229.98i	0.113717	−	0.0523815i
$821$		−	30033.9i		−	1.27672i	−0.769736	−	0.638362i	$-0.779612\pi$
$821$		−	30033.9i		−	1.27672i	0.769736	−	0.638362i	$-0.220388\pi$
$822$	−1728.96	−	1107.16i	−0.0733630	−	0.0469787i
$823$	3186.93			0.134981			0.0674906	−	0.997720i	$-0.478501\pi$
$823$	3186.93			0.134981			0.0674906	+	0.997720i	$0.478501\pi$
$824$	39557.5	+	5490.17i	1.67239	+	0.232111i
$825$	−1189.19			−0.0501844
$826$	9220.45	+	5904.40i	0.388403	+	0.248717i
$827$		−	18326.0i		−	0.770563i	−0.922799	−	0.385282i	$-0.874104\pi$
$827$		−	18326.0i		−	0.770563i	0.922799	−	0.385282i	$-0.125896\pi$
$828$	5663.47	+	12295.0i	0.237704	+	0.516040i
$829$			4370.27i			0.183095i	0.995801	+	0.0915475i	$0.0291813\pi$
$829$			4370.27i			0.183095i	−0.995801	+	0.0915475i	$0.970819\pi$
$830$	−7444.13	+	11624.9i	−0.311313	+	0.486153i
$831$	−3974.28			−0.165904
$832$	662.788	−	2341.75i	0.0276179	−	0.0975789i
$833$	−34243.7			−1.42434
$834$	4763.05	−	7438.09i	0.197759	−	0.308825i
$835$		−	10102.1i		−	0.418679i
$836$	9429.32	+	20470.4i	0.390096	+	0.846872i
$837$			23580.1i			0.973771i
$838$	−1252.87	−	802.288i	−0.0516464	−	0.0330723i
$839$	−29789.0			−1.22578			−0.612890	−	0.790168i	$-0.709993\pi$
$839$	−29789.0			−1.22578			−0.612890	+	0.790168i	$0.709993\pi$
$840$	873.595	+	121.246i	0.0358832	+	0.00498021i
$841$	24114.4			0.988740
$842$	36029.0	+	23071.5i	1.47463	+	0.944296i
$843$		−	3494.35i		−	0.142766i
$844$	−10280.1	+	4735.35i	−0.419262	+	0.193125i
$845$		−	10872.0i		−	0.442614i
$846$	8601.12	−	13431.7i	0.349542	−	0.545853i
$847$	1791.43			0.0726732
$848$	−31489.4	−	26928.2i	−1.27518	−	1.09047i
$849$	10004.3			0.404412
$850$	−4124.14	+	6440.35i	−0.166420	+	0.259885i
$851$			22464.9i			0.904918i
$852$	−8466.22	+	3899.81i	−0.340432	+	0.156814i
$853$		−	39023.7i		−	1.56641i	−0.621764	−	0.783205i	$-0.713584\pi$
$853$		−	39023.7i		−	1.56641i	0.621764	−	0.783205i	$-0.286416\pi$
$854$	3558.10	+	2278.47i	0.142571	+	0.0912969i
$855$	11099.9			0.443988
$856$	1377.51	−	9925.19i	0.0550028	−	0.396304i
$857$	−2749.52			−0.109594			−0.0547969	−	0.998498i	$-0.517451\pi$
$857$	−2749.52			−0.109594			−0.0547969	+	0.998498i	$0.517451\pi$
$858$	−538.568	−	344.877i	−0.0214294	−	0.0137225i
$859$			48225.6i			1.91553i	0.287559	+	0.957763i	$0.407156\pi$
$859$			48225.6i			1.91553i	−0.287559	+	0.957763i	$0.592844\pi$
$860$	−13.9907	−	30.3729i	−0.000554744	−	0.00120431i
$861$			572.950i			0.0226784i
$862$	7455.45	−	11642.6i	0.294587	−	0.460033i
$863$	−12421.1			−0.489942			−0.244971	−	0.969530i	$-0.578778\pi$
$863$	−12421.1			−0.489942			−0.244971	+	0.969530i	$0.578778\pi$
$864$	13595.0	−	4112.51i	0.535313	−	0.161934i
$865$	4560.77			0.179273
$866$	−10591.8	+	16540.4i	−0.415616	+	0.649036i
$867$		−	10297.1i		−	0.403353i
$868$	5166.30	+	11215.7i	0.202023	+	0.438578i
$869$			14156.5i			0.552618i
$870$	299.554	+	191.822i	0.0116734	+	0.00747515i
$871$	−3811.28			−0.148267
$872$	−4812.78	+	34676.8i	−0.186905	+	1.34668i
$873$	−13808.9			−0.535350
$874$	−14670.1	−	9394.15i	−0.567762	−	0.363572i
$875$			642.024i			0.0248050i
$876$	532.886	−	245.464i	0.0205531	−	0.00946742i
$877$		−	38301.8i		−	1.47475i	−0.675482	−	0.737377i	$-0.736064\pi$
$877$		−	38301.8i		−	1.47475i	0.675482	−	0.737377i	$-0.263936\pi$
$878$	880.892	−	1375.62i	0.0338595	−	0.0528758i
$879$	7233.00			0.277546
$880$	−6517.96	+	7622.01i	−0.249682	+	0.291975i
$881$	14792.0			0.565671			0.282836	−	0.959168i	$-0.408725\pi$
$881$	14792.0			0.565671			0.282836	+	0.959168i	$0.408725\pi$
$882$	−11926.7	+	18625.0i	−0.455321	+	0.711040i
$883$		−	2064.99i		−	0.0787002i	−0.999225	−	0.0393501i	$-0.987471\pi$
$883$		−	2064.99i		−	0.0787002i	0.999225	−	0.0393501i	$-0.0125288\pi$
$884$	−3735.55	+	1720.71i	−0.142127	+	0.0654680i
$885$		−	5719.54i		−	0.217243i
$886$	16767.3	+	10737.1i	0.635788	+	0.407133i
$887$	19268.8			0.729406			0.364703	−	0.931124i	$-0.381171\pi$
$887$	19268.8			0.729406			0.364703	+	0.931124i	$0.381171\pi$
$888$	11153.5	+	1547.99i	0.421495	+	0.0584991i
$889$	−7929.89			−0.299167
$890$	14342.2	+	9184.14i	0.540169	+	0.345902i
$891$			17165.5i			0.645415i
$892$	−5.68690	−	12.3459i	−0.000213466	−	0.000463420i
$893$			20525.3i			0.769152i
$894$	−6572.12	+	10263.2i	−0.245866	+	0.383951i
$895$	−16134.8			−0.602598
$896$	5565.31	−	4934.69i	0.207505	−	0.183992i
$897$	494.312			0.0183998
$898$	9757.21	−	15237.1i	0.362586	−	0.566223i
$899$			4980.24i			0.184761i
$900$	2066.49	+	4486.21i	0.0765366	+	0.166156i
$901$			70018.3i			2.58895i
$902$	−5486.53	−	3513.35i	−0.202529	−	0.129692i
$903$	6.51717			0.000240175
$904$	−17672.9	−	2452.81i	−0.650211	−	0.0902425i
$905$	5017.14			0.184282
$906$	7906.76	+	5063.17i	0.289939	+	0.185665i
$907$			46355.6i			1.69704i	0.529165	+	0.848519i	$0.322505\pi$
$907$			46355.6i			1.69704i	−0.529165	+	0.848519i	$0.677495\pi$
$908$	−24522.4	+	11295.8i	−0.896260	+	0.412846i
$909$			13387.2i			0.488475i
$910$	−186.194	+	290.765i	−0.00678272	+	0.0105920i
$911$	23365.5			0.849761			0.424881	−	0.905249i	$-0.360316\pi$
$911$	23365.5			0.849761			0.424881	+	0.905249i	$0.360316\pi$
$912$	−5674.96	+	6636.21i	−0.206049	+	0.240950i
$913$	30591.3			1.10890
$914$	−10701.2	+	16711.2i	−0.387268	+	0.604766i
$915$		−	2207.13i		−	0.0797436i
$916$	−9669.05	+	4453.87i	−0.348771	+	0.160655i
$917$		−	9929.58i		−	0.357583i
$918$	−20213.3	−	12943.8i	−0.726728	−	0.465368i
$919$	−36178.5			−1.29860			−0.649302	−	0.760530i	$-0.724939\pi$
$919$	−36178.5			−1.29860			−0.649302	+	0.760530i	$0.724939\pi$
$920$	1065.63	−	7678.07i	0.0381880	−	0.275150i
$921$	179.033			0.00640535
$922$	−31855.9	−	20399.2i	−1.13787	−	0.728647i
$923$		−	3649.06i		−	0.130130i
$924$	−817.732	−	1775.24i	−0.0291141	−	0.0632047i
$925$			8196.98i			0.291367i
$926$	23511.2	−	36715.5i	0.834368	−	1.30297i
$927$	−43588.4			−1.54437
$928$	2871.33	−	868.587i	0.101569	−	0.0307249i
$929$	17014.6			0.600895			0.300447	−	0.953798i	$-0.402864\pi$
$929$	17014.6			0.600895			0.300447	+	0.953798i	$0.402864\pi$
$930$	3478.60	−	5432.27i	0.122654	−	0.191539i
$931$		−	28461.3i		−	1.00191i
$932$	14636.6	+	31775.1i	0.514419	+	1.11677i
$933$		−	6200.20i		−	0.217562i
$934$	−4278.95	−	2740.07i	−0.149905	−	0.0959933i
$935$	16947.9			0.592788
$936$	−365.162	+	2631.05i	−0.0127518	+	0.0918789i
$937$	16898.8			0.589179			0.294589	−	0.955624i	$-0.404817\pi$
$937$	16898.8			0.589179			0.294589	+	0.955624i	$0.404817\pi$
$938$	−9809.22	−	6281.43i	−0.341452	−	0.218652i
$939$		−	1373.10i		−	0.0477203i
$940$	−8295.60	+	3821.22i	−0.287843	+	0.132590i
$941$		−	43995.9i		−	1.52415i	−0.647489	−	0.762074i	$-0.724181\pi$
$941$		−	43995.9i		−	1.52415i	0.647489	−	0.762074i	$-0.275819\pi$
$942$	2167.40	−	3384.67i	0.0749658	−	0.117068i
$943$	5035.68			0.173897
$944$	−36659.0	−	31349.0i	−1.26393	−	1.08085i
$945$	−2015.01			−0.0693634
$946$	−39.9635	+	62.4080i	−0.00137350	+	0.00214488i
$947$			2588.13i			0.0888099i	0.999014	+	0.0444050i	$0.0141392\pi$
$947$			2588.13i			0.0888099i	−0.999014	+	0.0444050i	$0.985861\pi$
$948$	−4981.54	+	2294.66i	−0.170668	+	0.0786149i
$949$			229.681i			0.00785646i
$950$	−5352.83	−	3427.74i	−0.182809	−	0.117064i
$951$	−8252.52			−0.281395
$952$	−12450.2	−	1727.96i	−0.423859	−	0.0588272i
$953$	7309.24			0.248447			0.124223	−	0.992254i	$-0.460356\pi$
$953$	7309.24			0.248447			0.124223	+	0.992254i	$0.460356\pi$
$954$	38082.7	+	24386.6i	1.29242	+	0.827615i
$955$		−	6360.38i		−	0.215515i
$956$	−2659.60	−	5773.80i	−0.0899764	−	0.195333i
$957$		−	788.283i		−	0.0266265i
$958$	17981.6	−	28080.5i	0.606429	−	0.947013i
$959$	2456.37			0.0827115
$960$	−3738.64	−	1058.15i	−0.125692	−	0.0355746i
$961$	60523.3			2.03160
$962$	−2377.21	+	3712.31i	−0.0796720	+	0.124418i
$963$			10936.5i			0.365966i
$964$	−2066.70	−	4486.66i	−0.0690496	−	0.149902i
$965$			3654.57i			0.121912i
$966$	1272.23	+	814.682i	0.0423739	+	0.0271345i
$967$	27600.6			0.917866			0.458933	−	0.888471i	$-0.348232\pi$
$967$	27600.6			0.917866			0.458933	+	0.888471i	$0.348232\pi$
$968$	−7817.17	−	1084.94i	−0.259559	−	0.0360241i
$969$	14756.0			0.489195
$970$	6659.20	+	4264.29i	0.220427	+	0.141153i
$971$			22638.5i			0.748201i	0.927388	+	0.374100i	$0.122048\pi$
$971$			22638.5i			0.748201i	−0.927388	+	0.374100i	$0.877952\pi$
$972$	−21433.9	+	9873.11i	−0.707296	+	0.325803i
$973$			10567.5i			0.348178i
$974$	27581.6	−	43072.1i	0.907364	−	1.41696i
$975$	180.364			0.00592440
$976$	−14146.4	−	12097.3i	−0.463951	−	0.396748i
$977$	−18390.3			−0.602208			−0.301104	−	0.953591i	$-0.597355\pi$
$977$	−18390.3			−0.602208			−0.301104	+	0.953591i	$0.597355\pi$
$978$	−5393.28	+	8422.27i	−0.176337	+	0.275373i
$979$		−	37741.7i		−	1.23210i
$980$	11503.1	−	5298.68i	0.374951	−	0.172714i
$981$		−	38210.3i		−	1.24359i
$982$	−26818.5	−	17173.5i	−0.871499	−	0.558073i
$983$	11139.1			0.361425			0.180712	−	0.983536i	$-0.442160\pi$
$983$	11139.1			0.361425			0.180712	+	0.983536i	$0.442160\pi$
$984$	346.995	−	2500.16i	0.0112417	−	0.0809980i
$985$	17910.1			0.579353
$986$	−4269.15	−	2733.79i	−0.137888	−	0.0882979i
$987$		−	1780.00i		−	0.0574043i
$988$	−1430.15	−	3104.76i	−0.0460518	−	0.0999753i
$989$		−	57.2797i		−	0.00184165i
$990$	5902.78	−	9217.91i	0.189498	−	0.295924i
$991$	30232.3			0.969083			0.484542	−	0.874768i	$-0.338986\pi$
$991$	30232.3			0.969083			0.484542	+	0.874768i	$0.338986\pi$
$992$	−15751.4	−	52070.3i	−0.504141	−	1.66657i
$993$	9021.68			0.288313
$994$	6014.07	−	9391.70i	0.191906	−	0.299685i
$995$		−	10038.2i		−	0.319832i
$996$	4958.62	+	10764.8i	0.157751	+	0.342466i
$997$		−	9623.78i		−	0.305705i	−0.988249	−	0.152853i	$-0.951154\pi$
$997$		−	9623.78i		−	0.305705i	0.988249	−	0.152853i	$-0.0488460\pi$
$998$	10932.6	+	7000.77i	0.346758	+	0.222050i
$999$	−25726.5			−0.814764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.d.a.21.7	✓	12
3.2	odd	2		360.4.k.c.181.6		12
4.3	odd	2		160.4.d.a.81.8		12
5.2	odd	4		200.4.f.b.149.12		12
5.3	odd	4		200.4.f.c.149.1		12
5.4	even	2		200.4.d.b.101.6		12
8.3	odd	2		160.4.d.a.81.5		12
8.5	even	2	inner	40.4.d.a.21.8	yes	12
12.11	even	2		1440.4.k.c.721.10		12
16.3	odd	4		1280.4.a.ba.1.3		6
16.5	even	4		1280.4.a.bb.1.3		6
16.11	odd	4		1280.4.a.bd.1.4		6
16.13	even	4		1280.4.a.bc.1.4		6
20.3	even	4		800.4.f.b.49.6		12
20.7	even	4		800.4.f.c.49.7		12
20.19	odd	2		800.4.d.d.401.5		12
24.5	odd	2		360.4.k.c.181.5		12
24.11	even	2		1440.4.k.c.721.4		12
40.3	even	4		800.4.f.c.49.8		12
40.13	odd	4		200.4.f.b.149.11		12
40.19	odd	2		800.4.d.d.401.8		12
40.27	even	4		800.4.f.b.49.5		12
40.29	even	2		200.4.d.b.101.5		12
40.37	odd	4		200.4.f.c.149.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.7	✓	12	1.1	even	1	trivial
40.4.d.a.21.8	yes	12	8.5	even	2	inner
160.4.d.a.81.5		12	8.3	odd	2
160.4.d.a.81.8		12	4.3	odd	2
200.4.d.b.101.5		12	40.29	even	2
200.4.d.b.101.6		12	5.4	even	2
200.4.f.b.149.11		12	40.13	odd	4
200.4.f.b.149.12		12	5.2	odd	4
200.4.f.c.149.1		12	5.3	odd	4
200.4.f.c.149.2		12	40.37	odd	4
360.4.k.c.181.5		12	24.5	odd	2
360.4.k.c.181.6		12	3.2	odd	2
800.4.d.d.401.5		12	20.19	odd	2
800.4.d.d.401.8		12	40.19	odd	2
800.4.f.b.49.5		12	40.27	even	4
800.4.f.b.49.6		12	20.3	even	4
800.4.f.c.49.7		12	20.7	even	4
800.4.f.c.49.8		12	40.3	even	4
1280.4.a.ba.1.3		6	16.3	odd	4
1280.4.a.bb.1.3		6	16.5	even	4
1280.4.a.bc.1.4		6	16.13	even	4
1280.4.a.bd.1.4		6	16.11	odd	4
1440.4.k.c.721.4		12	24.11	even	2
1440.4.k.c.721.10		12	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52528 - 2.38191i) q^{2} -1.51777i q^{3} +(-3.34703 - 7.26618i) q^{4} -5.00000i q^{5} +(-3.61520 - 2.31503i) q^{6} +5.13620 q^{7} +(-22.4126 - 3.11063i) q^{8} +24.6964 q^{9} +(-11.9096 - 7.62641i) q^{10} +31.3403i q^{11} +(-11.0284 + 5.08003i) q^{12} -4.75340i q^{13} +(7.83414 - 12.2340i) q^{14} -7.58886 q^{15} +(-41.5948 + 48.6403i) q^{16} +108.154 q^{17} +(37.6689 - 58.8246i) q^{18} +89.8913i q^{19} +(-36.3309 + 16.7352i) q^{20} -7.79558i q^{21} +(74.6499 + 47.8028i) q^{22} -68.5157 q^{23} +(-4.72123 + 34.0172i) q^{24} -25.0000 q^{25} +(-11.3222 - 7.25027i) q^{26} -78.4633i q^{27} +(-17.1910 - 37.3205i) q^{28} -16.5719i q^{29} +(-11.5752 + 18.0760i) q^{30} -300.523 q^{31} +(52.4132 + 173.265i) q^{32} +47.5675 q^{33} +(164.966 - 257.614i) q^{34} -25.6810i q^{35} +(-82.6595 - 179.448i) q^{36} -327.879i q^{37} +(214.113 + 137.109i) q^{38} -7.21458 q^{39} +(-15.5532 + 112.063i) q^{40} -73.4968 q^{41} +(-18.5684 - 11.8904i) q^{42} +0.836008i q^{43} +(227.724 - 104.897i) q^{44} -123.482i q^{45} +(-104.506 + 163.198i) q^{46} +228.335 q^{47} +(73.8249 + 63.1314i) q^{48} -316.619 q^{49} +(-38.1320 + 59.5479i) q^{50} -164.153i q^{51} +(-34.5391 + 15.9098i) q^{52} +647.393i q^{53} +(-186.893 - 119.679i) q^{54} +156.702 q^{55} +(-115.115 - 15.9768i) q^{56} +136.434 q^{57} +(-39.4728 - 25.2768i) q^{58} +753.676i q^{59} +(25.4002 + 55.1420i) q^{60} +290.838i q^{61} +(-458.383 + 715.821i) q^{62} +126.845 q^{63} +(492.648 + 139.435i) q^{64} -23.7670 q^{65} +(72.5538 - 113.302i) q^{66} -801.801i q^{67} +(-361.995 - 785.868i) q^{68} +103.991i q^{69} +(-61.1699 - 39.1707i) q^{70} +767.674 q^{71} +(-553.509 - 76.8213i) q^{72} -48.3194 q^{73} +(-780.980 - 500.108i) q^{74} +37.9443i q^{75} +(653.166 - 300.869i) q^{76} +160.970i q^{77} +(-11.0043 + 17.1845i) q^{78} +451.701 q^{79} +(243.201 + 207.974i) q^{80} +547.712 q^{81} +(-112.103 + 175.063i) q^{82} -976.099i q^{83} +(-56.6441 + 26.0920i) q^{84} -540.771i q^{85} +(1.99130 + 1.27515i) q^{86} -25.1524 q^{87} +(97.4881 - 702.417i) q^{88} -1204.25 q^{89} +(-294.123 - 188.345i) q^{90} -24.4144i q^{91} +(229.324 + 497.847i) q^{92} +456.126i q^{93} +(348.275 - 543.873i) q^{94} +449.456 q^{95} +(262.977 - 79.5513i) q^{96} -559.147 q^{97} +(-482.934 + 754.161i) q^{98} +773.992i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Introduction

L-functions

Modular forms

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Database

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