LMFDB - Embedded newform 135.4.j.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(19,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("135.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	135.19
Dual form			135.4.j.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.35066 - 2.51186i) q^{2} +(8.61884 + 14.9283i) q^{4} +(11.1787 + 0.192474i) q^{5} +(4.66092 + 2.69099i) q^{7} -46.4074i q^{8} +O(q^{10})$	\(q+(-4.35066 - 2.51186i) q^{2} +(8.61884 + 14.9283i) q^{4} +(11.1787 + 0.192474i) q^{5} +(4.66092 + 2.69099i) q^{7} -46.4074i q^{8} +(-48.1512 - 28.9166i) q^{10} +(-19.5509 + 33.8631i) q^{11} +(-75.0212 + 43.3135i) q^{13} +(-13.5187 - 23.4151i) q^{14} +(-47.6180 + 82.4768i) q^{16} -15.4194i q^{17} +26.8412 q^{19} +(93.4739 + 168.537i) q^{20} +(170.119 - 98.2180i) q^{22} +(-96.2486 + 55.5692i) q^{23} +(124.926 + 4.30322i) q^{25} +435.189 q^{26} +92.7727i q^{28} +(-24.6174 + 42.6385i) q^{29} +(89.9383 + 155.778i) q^{31} +(92.8196 - 53.5894i) q^{32} +(-38.7312 + 67.0844i) q^{34} +(51.5851 + 30.9788i) q^{35} +293.496i q^{37} +(-116.777 - 67.4211i) q^{38} +(8.93223 - 518.774i) q^{40} +(13.8016 + 23.9051i) q^{41} +(52.3971 + 30.2515i) q^{43} -674.023 q^{44} +558.327 q^{46} +(83.3420 + 48.1175i) q^{47} +(-157.017 - 271.962i) q^{49} +(-532.701 - 332.518i) q^{50} +(-1293.19 - 746.625i) q^{52} +251.203i q^{53} +(-225.071 + 374.782i) q^{55} +(124.882 - 216.301i) q^{56} +(214.204 - 123.671i) q^{58} +(38.4231 + 66.5508i) q^{59} +(-245.045 + 424.431i) q^{61} -903.648i q^{62} +223.452 q^{64} +(-846.975 + 469.749i) q^{65} +(-206.738 + 119.360i) q^{67} +(230.184 - 132.897i) q^{68} +(-146.615 - 264.352i) q^{70} +640.447 q^{71} -769.257i q^{73} +(737.219 - 1276.90i) q^{74} +(231.340 + 400.692i) q^{76} +(-182.250 + 105.222i) q^{77} +(331.176 - 573.613i) q^{79} +(-548.181 + 912.817i) q^{80} -138.670i q^{82} +(1127.69 + 651.071i) q^{83} +(2.96783 - 172.368i) q^{85} +(-151.975 - 263.228i) q^{86} +(1571.50 + 907.306i) q^{88} -995.544 q^{89} -466.224 q^{91} +(-1659.10 - 957.883i) q^{92} +(-241.729 - 418.686i) q^{94} +(300.049 + 5.16623i) q^{95} +(705.677 + 407.423i) q^{97} +1577.62i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 54 q^{4} - 3 q^{5}+O(q^{10}) $ 32 * q + 54 * q^4 - 3 * q^5	$ 32 q + 54 q^{4} - 3 q^{5} - 20 q^{10} - 90 q^{11} + 102 q^{14} - 146 q^{16} - 8 q^{19} + 6 q^{20} + 71 q^{25} + 936 q^{26} + 516 q^{29} - 38 q^{31} + 212 q^{34} + 534 q^{35} + 44 q^{40} - 576 q^{41} - 3288 q^{44} - 580 q^{46} - 4 q^{49} - 558 q^{50} + 30 q^{55} - 2430 q^{56} + 2202 q^{59} - 20 q^{61} + 644 q^{64} - 339 q^{65} + 636 q^{70} + 5904 q^{71} + 4080 q^{74} + 396 q^{76} - 218 q^{79} - 2532 q^{80} - 704 q^{85} - 6108 q^{86} - 8148 q^{89} - 1884 q^{91} - 1078 q^{94} + 1692 q^{95}+O(q^{100}) $ 32 * q + 54 * q^4 - 3 * q^5 - 20 * q^10 - 90 * q^11 + 102 * q^14 - 146 * q^16 - 8 * q^19 + 6 * q^20 + 71 * q^25 + 936 * q^26 + 516 * q^29 - 38 * q^31 + 212 * q^34 + 534 * q^35 + 44 * q^40 - 576 * q^41 - 3288 * q^44 - 580 * q^46 - 4 * q^49 - 558 * q^50 + 30 * q^55 - 2430 * q^56 + 2202 * q^59 - 20 * q^61 + 644 * q^64 - 339 * q^65 + 636 * q^70 + 5904 * q^71 + 4080 * q^74 + 396 * q^76 - 218 * q^79 - 2532 * q^80 - 704 * q^85 - 6108 * q^86 - 8148 * q^89 - 1884 * q^91 - 1078 * q^94 + 1692 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−4.35066	−	2.51186i	−1.53819	−	0.888075i	−0.998945	−	0.0459269i	$-0.985376\pi$
$2$	−4.35066	−	2.51186i	−1.53819	−	0.888075i	−0.539246	−	0.842148i	$-0.681291\pi$
$3$		0			0
$3$		0			0
$4$	8.61884	+	14.9283i	1.07735	+	1.86603i
$5$	11.1787	+	0.192474i	0.999852	+	0.0172154i
$5$	11.1787	+	0.192474i	0.999852	+	0.0172154i
$6$		0			0
$7$	4.66092	+	2.69099i	0.251666	+	0.145300i	0.620527	−	0.784185i	$-0.286919\pi$
$7$	4.66092	+	2.69099i	0.251666	+	0.145300i	−0.368861	+	0.929485i	$0.620252\pi$
$8$		−	46.4074i		−	2.05094i
$9$		0			0
$10$	−48.1512	−	28.9166i	−1.52267	−	0.914424i
$11$	−19.5509	+	33.8631i	−0.535892	+	0.928192i	0.463227	+	0.886239i	$0.346691\pi$
$11$	−19.5509	+	33.8631i	−0.535892	+	0.928192i	−0.999120	+	0.0419529i	$0.986642\pi$
$12$		0			0
$13$	−75.0212	+	43.3135i	−1.60055	+	0.924078i	−0.609173	+	0.793037i	$0.708498\pi$
$13$	−75.0212	+	43.3135i	−1.60055	+	0.924078i	−0.991377	+	0.131040i	$0.958168\pi$
$14$	−13.5187	−	23.4151i	−0.258074	−	0.446997i
$15$		0			0
$16$	−47.6180	+	82.4768i	−0.744031	+	1.28870i
$17$		−	15.4194i		−	0.219985i	−0.993932	−	0.109993i	$-0.964917\pi$
$17$		−	15.4194i		−	0.219985i	0.993932	−	0.109993i	$-0.0350827\pi$
$18$		0			0
$19$	26.8412			0.324094			0.162047	−	0.986783i	$-0.448190\pi$
$19$	26.8412			0.324094			0.162047	+	0.986783i	$0.448190\pi$
$20$	93.4739	+	168.537i	1.04507	+	1.88430i
$21$		0			0
$22$	170.119	−	98.2180i	1.64861	−	0.951825i
$23$	−96.2486	+	55.5692i	−0.872575	+	0.503781i	−0.868203	−	0.496209i	$-0.834725\pi$
$23$	−96.2486	+	55.5692i	−0.872575	+	0.503781i	−0.00437188	+	0.999990i	$0.501392\pi$
$24$		0			0
$25$	124.926	+	4.30322i	0.999407	+	0.0344257i
$26$	435.189			3.28260
$27$		0			0
$28$			92.7727i			0.626157i
$29$	−24.6174	+	42.6385i	−0.157632	+	0.273027i	−0.934014	−	0.357236i	$-0.883719\pi$
$29$	−24.6174	+	42.6385i	−0.157632	+	0.273027i	0.776382	+	0.630262i	$0.217053\pi$
$30$		0			0
$31$	89.9383	+	155.778i	0.521077	+	0.902532i	0.999700	+	0.0245112i	$0.00780295\pi$
$31$	89.9383	+	155.778i	0.521077	+	0.902532i	−0.478622	+	0.878021i	$0.658864\pi$
$32$	92.8196	−	53.5894i	0.512761	−	0.296043i
$33$		0			0
$34$	−38.7312	+	67.0844i	−0.195363	+	0.338379i
$35$	51.5851	+	30.9788i	0.249128	+	0.149611i
$36$		0			0
$37$			293.496i			1.30407i	0.758191	+	0.652033i	$0.226084\pi$
$37$			293.496i			1.30407i	−0.758191	+	0.652033i	$0.773916\pi$
$38$	−116.777	−	67.4211i	−0.498518	−	0.287820i
$39$		0			0
$40$	8.93223	−	518.774i	0.0353077	−	2.05063i
$41$	13.8016	+	23.9051i	0.0525719	+	0.0910571i	0.891114	−	0.453780i	$-0.149925\pi$
$41$	13.8016	+	23.9051i	0.0525719	+	0.0910571i	−0.838542	+	0.544837i	$0.816591\pi$
$42$		0			0
$43$	52.3971	+	30.2515i	0.185825	+	0.107286i	0.590027	−	0.807384i	$-0.299117\pi$
$43$	52.3971	+	30.2515i	0.185825	+	0.107286i	−0.404201	+	0.914670i	$0.632451\pi$
$44$	−674.023			−2.30938
$45$		0			0
$46$	558.327			1.78958
$47$	83.3420	+	48.1175i	0.258653	+	0.149333i	0.623720	−	0.781648i	$-0.285621\pi$
$47$	83.3420	+	48.1175i	0.258653	+	0.149333i	−0.365067	+	0.930981i	$0.618954\pi$
$48$		0			0
$49$	−157.017	−	271.962i	−0.457776	−	0.792891i
$50$	−532.701	−	332.518i	−1.50671	−	0.940502i
$51$		0			0
$52$	−1293.19	−	746.625i	−3.44872	−	1.99112i
$53$			251.203i			0.651046i	0.945534	+	0.325523i	$0.105540\pi$
$53$			251.203i			0.651046i	−0.945534	+	0.325523i	$0.894460\pi$
$54$		0			0
$55$	−225.071	+	374.782i	−0.551792	+	0.918829i
$56$	124.882	−	216.301i	0.298000	−	0.516152i
$57$		0			0
$58$	214.204	−	123.671i	0.484937	−	0.279978i
$59$	38.4231	+	66.5508i	0.0847841	+	0.146850i	0.905299	−	0.424774i	$-0.139647\pi$
$59$	38.4231	+	66.5508i	0.0847841	+	0.146850i	−0.820515	+	0.571625i	$0.806313\pi$
$60$		0			0
$61$	−245.045	+	424.431i	−0.514342	+	0.890866i	0.485520	+	0.874226i	$0.338630\pi$
$61$	−245.045	+	424.431i	−0.514342	+	0.890866i	−0.999862	+	0.0166406i	$0.994703\pi$
$62$		−	903.648i		−	1.85102i
$63$		0			0
$64$	223.452			0.436430
$65$	−846.975	+	469.749i	−1.61622	+	0.896387i
$66$		0			0
$67$	−206.738	+	119.360i	−0.376972	+	0.217645i	−0.676500	−	0.736443i	$-0.736504\pi$
$67$	−206.738	+	119.360i	−0.376972	+	0.217645i	0.299528	+	0.954087i	$0.403171\pi$
$68$	230.184	−	132.897i	0.410499	−	0.237002i
$69$		0			0
$70$	−146.615	−	264.352i	−0.250340	−	0.451374i
$71$	640.447			1.07052			0.535261	−	0.844687i	$-0.320213\pi$
$71$	640.447			1.07052			0.535261	+	0.844687i	$0.320213\pi$
$72$		0			0
$73$		−	769.257i		−	1.23335i	−0.787217	−	0.616676i	$-0.788479\pi$
$73$		−	769.257i		−	1.23335i	0.787217	−	0.616676i	$-0.211521\pi$
$74$	737.219	−	1276.90i	1.15811	−	2.00590i
$75$		0			0
$76$	231.340	+	400.692i	0.349164	+	0.604770i
$77$	−182.250	+	105.222i	−0.269732	+	0.155730i
$78$		0			0
$79$	331.176	−	573.613i	0.471648	−	0.816918i	−0.527826	−	0.849353i	$-0.676993\pi$
$79$	331.176	−	573.613i	0.471648	−	0.816918i	0.999474	+	0.0324343i	$0.0103260\pi$
$80$	−548.181	+	912.817i	−0.766106	+	1.27570i
$81$		0			0
$82$		−	138.670i		−	0.186751i
$83$	1127.69	+	651.071i	1.49132	+	0.861016i	0.999951	−	0.00993336i	$-0.00316194\pi$
$83$	1127.69	+	651.071i	1.49132	+	0.861016i	0.491373	+	0.870949i	$0.336495\pi$
$84$		0			0
$85$	2.96783	−	172.368i	0.00378714	−	0.219952i
$86$	−151.975	−	263.228i	−0.190557	−	0.330054i
$87$		0			0
$88$	1571.50	+	907.306i	1.90366	+	1.09908i
$89$	−995.544			−1.18570			−0.592851	−	0.805312i	$-0.701998\pi$
$89$	−995.544			−1.18570			−0.592851	+	0.805312i	$0.701998\pi$
$90$		0			0
$91$	−466.224			−0.537073
$92$	−1659.10	−	957.883i	−1.88015	−	1.08550i
$93$		0			0
$94$	−241.729	−	418.686i	−0.265238	−	0.459406i
$95$	300.049	+	5.16623i	0.324046	+	0.00557942i
$96$		0			0
$97$	705.677	+	407.423i	0.738667	+	0.426470i	0.821584	−	0.570087i	$-0.193090\pi$
$97$	705.677	+	407.423i	0.738667	+	0.426470i	−0.0829175	+	0.996556i	$0.526424\pi$
$98$			1577.62i			1.62616i
$99$		0			0
$100$	1012.48	+	1902.02i	1.01248	+	1.90202i
$101$	−326.302	+	565.172i	−0.321468	+	0.556799i	−0.980791	−	0.195061i	$-0.937510\pi$
$101$	−326.302	+	565.172i	−0.321468	+	0.556799i	0.659323	+	0.751860i	$0.270843\pi$
$102$		0			0
$103$	−133.329	+	76.9776i	−0.127547	+	0.0736391i	−0.562416	−	0.826855i	$-0.690128\pi$
$103$	−133.329	+	76.9776i	−0.127547	+	0.0736391i	0.434869	+	0.900494i	$0.356795\pi$
$104$	2010.07	+	3481.54i	1.89523	+	3.28263i
$105$		0			0
$106$	630.987	−	1092.90i	0.578178	−	1.00143i
$107$		−	348.878i		−	0.315209i	−0.987502	−	0.157604i	$-0.949623\pi$
$107$		−	348.878i		−	0.315209i	0.987502	−	0.157604i	$-0.0503770\pi$
$108$		0			0
$109$	−1125.26			−0.988815			−0.494407	−	0.869230i	$-0.664615\pi$
$109$	−1125.26			−0.988815			−0.494407	+	0.869230i	$0.664615\pi$
$110$	1920.61	−	1065.20i	1.66475	−	0.923302i
$111$		0			0
$112$	−443.888	+	256.279i	−0.374495	+	0.216215i
$113$	304.907	−	176.038i	0.253834	−	0.146551i	−0.367685	−	0.929951i	$-0.619849\pi$
$113$	304.907	−	176.038i	0.253834	−	0.146551i	0.621518	+	0.783400i	$0.286516\pi$
$114$		0			0
$115$	−1086.63	+	602.665i	−0.881118	+	0.488685i
$116$	−848.692			−0.679303
$117$		0			0
$118$		−	386.053i		−	0.301179i
$119$	41.4933	−	71.8685i	0.0319637	−	0.0553628i
$120$		0			0
$121$	−98.9741	−	171.428i	−0.0743607	−	0.128797i
$122$	2132.22	−	1231.04i	1.58231	−	0.913549i
$123$		0			0
$124$	−1550.33	+	2685.24i	−1.12277	+	1.94469i
$125$	1395.68	+	72.1493i	0.998666	+	0.0516259i
$126$		0			0
$127$		−	1502.08i		−	1.04951i	−0.851252	−	0.524757i	$-0.824156\pi$
$127$		−	1502.08i		−	1.04951i	0.851252	−	0.524757i	$-0.175844\pi$
$128$	−1714.72	−	989.995i	−1.18407	−	0.683625i
$129$		0			0
$130$	4864.84	+	83.7628i	3.28212	+	0.0565114i
$131$	−787.356	−	1363.74i	−0.525127	−	0.909546i	−0.999572	−	0.0292609i	$-0.990685\pi$
$131$	−787.356	−	1363.74i	−0.525127	−	0.909546i	0.474445	−	0.880285i	$-0.342649\pi$
$132$		0			0
$133$	125.105	+	72.2292i	0.0815635	+	0.0470907i
$134$	1199.26			0.773140
$135$		0			0
$136$	−715.573			−0.451175
$137$	772.753	+	446.149i	0.481903	+	0.278227i	0.721209	−	0.692717i	$-0.243587\pi$
$137$	772.753	+	446.149i	0.481903	+	0.278227i	−0.239306	+	0.970944i	$0.576920\pi$
$138$		0			0
$139$	326.353	+	565.260i	0.199143	+	0.344926i	0.948251	−	0.317522i	$-0.102851\pi$
$139$	326.353	+	565.260i	0.199143	+	0.344926i	−0.749108	+	0.662448i	$0.769517\pi$
$140$	−17.8564	+	1037.08i	−0.0107796	+	0.626064i
$141$		0			0
$142$	−2786.37	−	1608.71i	−1.64667	−	0.950704i
$143$		−	3387.27i		−	1.98082i
$144$		0			0
$145$	−283.397	+	471.905i	−0.162309	+	0.270273i
$146$	−1932.26	+	3346.78i	−1.09531	+	1.89713i
$147$		0			0
$148$	−4381.38	+	2529.59i	−2.43343	+	1.40494i
$149$	−1718.93	−	2977.27i	−0.945101	−	1.63696i	−0.755550	−	0.655092i	$-0.772630\pi$
$149$	−1718.93	−	2977.27i	−0.945101	−	1.63696i	−0.189551	−	0.981871i	$-0.560703\pi$
$150$		0			0
$151$	−835.459	+	1447.06i	−0.450256	+	0.779867i	−0.998402	−	0.0565162i	$-0.982001\pi$
$151$	−835.459	+	1447.06i	−0.450256	+	0.779867i	0.548145	+	0.836383i	$0.315334\pi$
$152$		−	1245.63i		−	0.664696i
$153$		0			0
$154$	1057.21			0.553199
$155$	975.408	+	1758.70i	0.505462	+	0.911369i
$156$		0			0
$157$	−576.864	+	333.052i	−0.293240	+	0.169302i	−0.639402	−	0.768872i	$-0.720818\pi$
$157$	−576.864	+	333.052i	−0.293240	+	0.169302i	0.346162	+	0.938175i	$0.387485\pi$
$158$	−2881.67	+	1663.73i	−1.45097	+	0.837718i
$159$		0			0
$160$	1047.92	−	581.194i	0.517781	−	0.287171i
$161$	−598.143			−0.292797
$162$		0			0
$163$		−	889.255i		−	0.427312i	−0.976909	−	0.213656i	$-0.931463\pi$
$163$		−	889.255i		−	0.427312i	0.976909	−	0.213656i	$-0.0685371\pi$
$164$	−237.907	+	412.067i	−0.113277	+	0.196202i
$165$		0			0
$166$	−3270.79	−	5665.18i	−1.52929	−	2.64881i
$167$	−349.755	+	201.931i	−0.162065	+	0.0935683i	−0.578839	−	0.815442i	$-0.696494\pi$
$167$	−349.755	+	201.931i	−0.162065	+	0.0935683i	0.416774	+	0.909010i	$0.363161\pi$
$168$		0			0
$169$	2653.62	−	4596.21i	1.20784	−	2.09204i
$170$	−445.876	+	742.461i	−0.201160	+	0.334966i
$171$		0			0
$172$			1042.93i			0.462342i
$173$	−204.435	−	118.031i	−0.0898435	−	0.0518712i	0.454405	−	0.890795i	$-0.349852\pi$
$173$	−204.435	−	118.031i	−0.0898435	−	0.0518712i	−0.544249	+	0.838924i	$0.683185\pi$
$174$		0			0
$175$	570.690	+	356.231i	0.246515	+	0.153877i
$176$	−1861.95	−	3224.99i	−0.797441	−	1.38121i
$177$		0			0
$178$	4331.28	+	2500.66i	1.82384	+	1.05299i
$179$	2404.31			1.00395			0.501973	−	0.864883i	$-0.332608\pi$
$179$	2404.31			1.00395			0.501973	+	0.864883i	$0.332608\pi$
$180$		0			0
$181$	−1218.41			−0.500354			−0.250177	−	0.968200i	$-0.580489\pi$
$181$	−1218.41			−0.500354			−0.250177	+	0.968200i	$0.580489\pi$
$182$	2028.38	+	1171.09i	0.826120	+	0.476961i
$183$		0			0
$184$	2578.82	+	4466.65i	1.03322	+	1.78960i
$185$	−56.4904	+	3280.90i	−0.0224500	+	1.30387i
$186$		0			0
$187$	522.148	+	301.462i	0.204188	+	0.117888i
$188$			1658.87i			0.643539i
$189$		0			0
$190$	−1292.43	−	776.156i	−0.493490	−	0.296359i
$191$	87.9715	−	152.371i	0.0333267	−	0.0577235i	−0.848881	−	0.528584i	$-0.822723\pi$
$191$	87.9715	−	152.371i	0.0333267	−	0.0577235i	0.882208	+	0.470861i	$0.156056\pi$
$192$		0			0
$193$	−1918.47	+	1107.63i	−0.715516	+	0.413103i	−0.813100	−	0.582124i	$-0.802222\pi$
$193$	−1918.47	+	1107.63i	−0.715516	+	0.413103i	0.0975842	+	0.995227i	$0.468888\pi$
$194$	−2046.78	−	3545.12i	−0.757474	−	1.31198i
$195$		0			0
$196$	2706.61	−	4687.99i	0.986374	−	1.70845i
$197$			1054.08i			0.381218i	0.981666	+	0.190609i	$0.0610462\pi$
$197$			1054.08i			0.381218i	−0.981666	+	0.190609i	$0.938954\pi$
$198$		0			0
$199$	3484.04			1.24109			0.620546	−	0.784170i	$-0.286911\pi$
$199$	3484.04			1.24109			0.620546	+	0.784170i	$0.286911\pi$
$200$	199.701	−	5797.49i	0.0706050	−	2.04972i
$201$		0			0
$202$	2839.26	−	1639.25i	0.988958	−	0.570975i
$203$	−229.479	+	132.490i	−0.0793414	+	0.0458078i
$204$		0			0
$205$	149.682	+	269.883i	0.0509965	+	0.0919487i
$206$	773.426			0.261588
$207$		0			0
$208$		−	8250.01i		−	2.75017i
$209$	−524.768	+	908.926i	−0.173679	+	0.300822i
$210$		0			0
$211$	2098.45	+	3634.62i	0.684660	+	1.18587i	0.973544	+	0.228501i	$0.0733825\pi$
$211$	2098.45	+	3634.62i	0.684660	+	1.18587i	−0.288884	+	0.957364i	$0.593284\pi$
$212$	−3750.03	+	2165.08i	−1.21487	+	0.701408i
$213$		0			0
$214$	−876.331	+	1517.85i	−0.279929	+	0.484851i
$215$	579.908	+	348.257i	0.183951	+	0.110469i
$216$		0			0
$217$			968.091i			0.302849i
$218$	4895.65	+	2826.50i	1.52099	+	0.878142i
$219$		0			0
$220$	−7534.69	−	129.732i	−2.30904	−	0.0397570i
$221$	667.867	+	1156.78i	0.203283	+	0.352097i
$222$		0			0
$223$	2628.00	+	1517.28i	0.789166	+	0.455625i	0.839669	−	0.543098i	$-0.182749\pi$
$223$	2628.00	+	1517.28i	0.789166	+	0.455625i	−0.0505026	+	0.998724i	$0.516082\pi$
$224$	576.834			0.172059
$225$		0			0
$226$	−1768.73			−0.520593
$227$	−2802.60	−	1618.08i	−0.819450	−	0.473109i	0.0307770	−	0.999526i	$-0.490202\pi$
$227$	−2802.60	−	1618.08i	−0.819450	−	0.473109i	−0.850227	+	0.526417i	$0.823535\pi$
$228$		0			0
$229$	−1487.28	−	2576.04i	−0.429180	−	0.743361i	0.567621	−	0.823290i	$-0.307864\pi$
$229$	−1487.28	−	2576.04i	−0.429180	−	0.743361i	−0.996801	+	0.0799288i	$0.974531\pi$
$230$	6241.36	+	107.464i	1.78932	+	0.0308084i
$231$		0			0
$232$	1978.74	+	1142.43i	0.559961	+	0.323293i
$233$			2927.42i			0.823097i	0.911388	+	0.411549i	$0.135012\pi$
$233$			2927.42i			0.823097i	−0.911388	+	0.411549i	$0.864988\pi$
$234$		0			0
$235$	922.392	+	553.932i	0.256044	+	0.153764i
$236$	−662.325	+	1147.18i	−0.182685	+	0.316420i
$237$		0			0
$238$	−361.047	+	208.450i	−0.0983327	+	0.0567724i
$239$	−1439.35	−	2493.02i	−0.389555	−	0.674729i	0.602835	−	0.797866i	$-0.294038\pi$
$239$	−1439.35	−	2493.02i	−0.389555	−	0.674729i	−0.992390	+	0.123137i	$0.960705\pi$
$240$		0			0
$241$	558.792	−	967.856i	0.149357	−	0.258693i	−0.781633	−	0.623738i	$-0.785613\pi$
$241$	558.792	−	967.856i	0.149357	−	0.258693i	0.930990	+	0.365045i	$0.118946\pi$
$242$			994.435i			0.264152i
$243$		0			0
$244$	−8448.03			−2.21651
$245$	−1702.90	−	3070.40i	−0.444058	−	0.800655i
$246$		0			0
$247$	−2013.66	+	1162.59i	−0.518729	+	0.299488i
$248$	7229.24	−	4173.80i	1.85104	−	1.06870i
$249$		0			0
$250$	−5890.90	−	3819.64i	−1.49029	−	0.966301i
$251$	4612.00			1.15979			0.579894	−	0.814692i	$-0.303094\pi$
$251$	4612.00			1.15979			0.579894	+	0.814692i	$0.303094\pi$
$252$		0			0
$253$		−	4345.71i		−	1.07989i
$254$	−3773.02	+	6535.06i	−0.932048	+	1.61435i
$255$		0			0
$256$	4079.64	+	7066.14i	0.996006	+	1.72513i
$257$	−3280.26	+	1893.86i	−0.796176	+	0.459672i	−0.842132	−	0.539271i	$-0.818700\pi$
$257$	−3280.26	+	1893.86i	−0.796176	+	0.459672i	0.0459562	+	0.998943i	$0.485367\pi$
$258$		0			0
$259$	−789.793	+	1367.96i	−0.189480	+	0.328189i
$260$	−14312.5	−	8595.18i	−3.41393	−	2.05020i
$261$		0			0
$262$			7910.89i			1.86541i
$263$	−4321.08	−	2494.78i	−1.01312	−	0.584923i	−0.101013	−	0.994885i	$-0.532209\pi$
$263$	−4321.08	−	2494.78i	−1.01312	−	0.584923i	−0.912102	+	0.409962i	$0.865542\pi$
$264$		0			0
$265$	−48.3502	+	2808.12i	−0.0112080	+	0.650950i
$266$	−362.859	−	628.490i	−0.0836402	−	0.144869i
$267$		0			0
$268$	−3563.69	−	2057.50i	−0.812265	−	0.468961i
$269$	−5845.57			−1.32495			−0.662473	−	0.749086i	$-0.730493\pi$
$269$	−5845.57			−1.32495			−0.662473	+	0.749086i	$0.730493\pi$
$270$		0			0
$271$	2766.09			0.620030			0.310015	−	0.950732i	$-0.399666\pi$
$271$	2766.09			0.620030			0.310015	+	0.950732i	$0.399666\pi$
$272$	1271.74	+	734.239i	0.283495	+	0.163676i
$273$		0			0
$274$	−2241.32	−	3882.09i	−0.494173	−	0.855933i
$275$	−2588.13	+	4146.25i	−0.567528	+	0.909194i
$276$		0			0
$277$	1640.08	+	946.900i	0.355750	+	0.205393i	0.667215	−	0.744865i	$-0.267486\pi$
$277$	1640.08	+	946.900i	0.355750	+	0.205393i	−0.311465	+	0.950258i	$0.600820\pi$
$278$		−	3279.01i		−	0.707417i
$279$		0			0
$280$	1437.65	−	2393.93i	0.306842	−	0.510945i
$281$	2242.19	−	3883.58i	0.476006	−	0.824467i	−0.523616	−	0.851954i	$-0.675417\pi$
$281$	2242.19	−	3883.58i	0.476006	−	0.824467i	0.999622	+	0.0274877i	$0.00875069\pi$
$282$		0			0
$283$	5020.91	−	2898.82i	1.05464	−	0.608894i	0.130692	−	0.991423i	$-0.458280\pi$
$283$	5020.91	−	2898.82i	1.05464	−	0.608894i	0.923944	+	0.382529i	$0.124947\pi$
$284$	5519.91	+	9560.76i	1.15333	+	1.99763i
$285$		0			0
$286$	−8508.34	+	14736.9i	−1.75912	+	3.04689i
$287$			148.560i			0.0305547i
$288$		0			0
$289$	4675.24			0.951607
$290$	2418.32	−	1341.25i	0.489685	−	0.271588i
$291$		0			0
$292$	11483.7	−	6630.10i	2.30148	−	1.32876i
$293$	6850.49	−	3955.13i	1.36590	−	0.788605i	0.375502	−	0.926822i	$-0.377470\pi$
$293$	6850.49	−	3955.13i	1.36590	−	0.788605i	0.990402	+	0.138217i	$0.0441370\pi$
$294$		0			0
$295$	416.710	+	751.345i	0.0822434	+	0.148288i
$296$	13620.4			2.67456
$297$		0			0
$298$			17270.8i			3.35728i
$299$	4813.79	−	8337.74i	0.931066	−	1.61265i
$300$		0			0
$301$	162.813	+	282.000i	0.0311773	+	0.0540007i
$302$	7269.60	−	4197.11i	1.38516	−	0.799723i
$303$		0			0
$304$	−1278.12	+	2213.77i	−0.241136	+	0.417660i
$305$	−2820.98	+	4697.42i	−0.529602	+	0.881880i
$306$		0			0
$307$		−	4426.37i		−	0.822887i	−0.911435	−	0.411443i	$-0.865025\pi$
$307$		−	4426.37i		−	0.822887i	0.911435	−	0.411443i	$-0.134975\pi$
$308$	−3141.57	−	1813.79i	−0.581194	−	0.335552i
$309$		0			0
$310$	173.929	−	10101.6i	0.0318661	−	1.85075i
$311$	4848.62	+	8398.06i	0.884052	+	1.53122i	0.846797	+	0.531917i	$0.178528\pi$
$311$	4848.62	+	8398.06i	0.884052	+	1.53122i	0.0372549	+	0.999306i	$0.488139\pi$
$312$		0			0
$313$	−3917.11	−	2261.55i	−0.707375	−	0.408403i	0.102713	−	0.994711i	$-0.467248\pi$
$313$	−3917.11	−	2261.55i	−0.707375	−	0.408403i	−0.810088	+	0.586308i	$0.800581\pi$
$314$	3346.32			0.601413
$315$		0			0
$316$	11417.4			2.03253
$317$	4609.17	+	2661.10i	0.816646	+	0.471491i	0.849258	−	0.527977i	$-0.177049\pi$
$317$	4609.17	+	2661.10i	0.816646	+	0.471491i	−0.0326127	+	0.999468i	$0.510383\pi$
$318$		0			0
$319$	−962.583	−	1667.24i	−0.168948	−	0.292626i
$320$	2497.90	+	43.0088i	0.436365	+	0.00751333i
$321$		0			0
$322$	2602.32	+	1502.45i	0.450378	+	0.260026i
$323$		−	413.874i		−	0.0712958i
$324$		0			0
$325$	−9558.48	+	5088.15i	−1.63141	+	0.868430i
$326$	−2233.68	+	3868.85i	−0.379485	+	0.657287i
$327$		0			0
$328$	1109.37	−	640.496i	0.186752	−	0.107822i
$329$	258.967	+	448.544i	0.0433961	+	0.0751643i
$330$		0			0
$331$	3916.56	−	6783.67i	0.650373	−	1.12648i	−0.332660	−	0.943047i	$-0.607946\pi$
$331$	3916.56	−	6783.67i	0.650373	−	1.12648i	0.983032	−	0.183432i	$-0.0587207\pi$
$332$			22445.9i			3.71048i
$333$		0			0
$334$	2028.89			0.332383
$335$	−2334.04	+	1294.50i	−0.380663	+	0.211123i
$336$		0			0
$337$	−8597.97	+	4964.04i	−1.38980	+	0.802399i	−0.993292	−	0.115633i	$-0.963110\pi$
$337$	−8597.97	+	4964.04i	−1.38980	+	0.802399i	−0.396505	+	0.918033i	$0.629777\pi$
$338$	−23090.0	+	13331.0i	−3.71578	+	2.14530i
$339$		0			0
$340$	2598.74	−	1441.31i	0.414519	−	0.229900i
$341$	−7033.49			−1.11696
$342$		0			0
$343$		−	3536.14i		−	0.556658i
$344$	1403.89	−	2431.62i	0.220037	−	0.381116i
$345$		0			0
$346$	592.952	+	1027.02i	0.0921310	+	0.159576i
$347$	3499.03	−	2020.17i	0.541320	−	0.312531i	−0.204294	−	0.978910i	$-0.565490\pi$
$347$	3499.03	−	2020.17i	0.541320	−	0.312531i	0.745614	+	0.666379i	$0.232157\pi$
$348$		0			0
$349$	2399.86	−	4156.68i	0.368085	−	0.637541i	−0.621181	−	0.783667i	$-0.713347\pi$
$349$	2399.86	−	4156.68i	0.368085	−	0.637541i	0.989266	+	0.146125i	$0.0466803\pi$
$350$	−1588.08	−	2983.33i	−0.242533	−	0.455617i
$351$		0			0
$352$			4190.88i			0.634588i
$353$	2762.17	+	1594.74i	0.416474	+	0.240451i	0.693568	−	0.720391i	$-0.256038\pi$
$353$	2762.17	+	1594.74i	0.416474	+	0.240451i	−0.277094	+	0.960843i	$0.589371\pi$
$354$		0			0
$355$	7159.35	+	123.270i	1.07036	+	0.0184295i
$356$	−8580.43	−	14861.7i	−1.27742	−	2.21256i
$357$		0			0
$358$	−10460.3	−	6039.27i	−1.54426	−	0.891579i
$359$	−1159.83			−0.170511			−0.0852554	−	0.996359i	$-0.527171\pi$
$359$	−1159.83			−0.170511			−0.0852554	+	0.996359i	$0.527171\pi$
$360$		0			0
$361$	−6138.55			−0.894963
$362$	5300.91	+	3060.48i	0.769640	+	0.444352i
$363$		0			0
$364$	−4018.31	−	6959.92i	−0.578618	−	1.00220i
$365$	148.062	−	8599.28i	0.0212327	−	1.23317i
$366$		0			0
$367$	10284.2	+	5937.58i	1.46275	+	0.844520i	0.999138	−	0.0415170i	$-0.0132191\pi$
$367$	10284.2	+	5937.58i	1.46275	+	0.844520i	0.463614	+	0.886037i	$0.346552\pi$
$368$		−	10584.4i		−	1.49932i
$369$		0			0
$370$	8486.91	−	14132.2i	1.19247	−	1.98567i
$371$	−675.985	+	1170.84i	−0.0945968	+	0.163846i
$372$		0			0
$373$	−2289.13	+	1321.63i	−0.317766	+	0.183462i	−0.650396	−	0.759595i	$-0.725397\pi$
$373$	−2289.13	+	1321.63i	−0.317766	+	0.183462i	0.332631	+	0.943057i	$0.392064\pi$
$374$	−1514.46	−	2623.12i	−0.209387	−	0.362669i
$375$		0			0
$376$	2233.01	−	3867.69i	0.306273	−	0.530480i
$377$		−	4265.06i		−	0.582657i
$378$		0			0
$379$	−10452.7			−1.41667			−0.708335	−	0.705876i	$-0.750553\pi$
$379$	−10452.7			−1.41667			−0.708335	+	0.705876i	$0.750553\pi$
$380$	2508.95	+	4523.74i	0.338701	+	0.610691i
$381$		0			0
$382$	−765.468	+	441.943i	−0.102526	+	0.0591932i
$383$	9422.23	−	5439.92i	1.25706	−	0.725763i	0.284557	−	0.958659i	$-0.408154\pi$
$383$	9422.23	−	5439.92i	1.25706	−	0.725763i	0.972502	+	0.232896i	$0.0748203\pi$
$384$		0			0
$385$	−2057.57	+	1141.17i	−0.272373	+	0.151063i
$386$	11128.8			1.46747
$387$		0			0
$388$			14046.1i			1.83784i
$389$	−838.831	+	1452.90i	−0.109333	+	0.189370i	−0.915500	−	0.402318i	$-0.868205\pi$
$389$	−838.831	+	1452.90i	−0.109333	+	0.189370i	0.806167	+	0.591687i	$0.201538\pi$
$390$		0			0
$391$	856.841	+	1484.09i	0.110824	+	0.191953i
$392$	−12621.0	+	7286.76i	−1.62617	+	0.938870i
$393$		0			0
$394$	2647.69	−	4585.93i	0.338550	−	0.586385i
$395$	3812.52	−	6348.50i	0.485642	−	0.808678i
$396$		0			0
$397$		−	13147.5i		−	1.66210i	−0.556199	−	0.831049i	$-0.687741\pi$
$397$		−	13147.5i		−	1.66210i	0.556199	−	0.831049i	$-0.312259\pi$
$398$	−15157.9	−	8751.41i	−1.90904	−	1.10218i
$399$		0			0
$400$	−6303.64	+	10098.6i	−0.787955	+	1.26232i
$401$	−3260.95	−	5648.14i	−0.406095	−	0.703378i	0.588353	−	0.808604i	$-0.299777\pi$
$401$	−3260.95	−	5648.14i	−0.406095	−	0.703378i	−0.994448	+	0.105226i	$0.966443\pi$
$402$		0			0
$403$	−13494.6	−	7791.09i	−1.66802	−	0.963032i
$404$	−11249.4			−1.38534
$405$		0			0
$406$	1331.18			0.162723
$407$	−9938.69	−	5738.10i	−1.21042	−	0.698838i
$408$		0			0
$409$	2821.34	+	4886.70i	0.341091	+	0.590786i	0.984636	−	0.174622i	$-0.0558704\pi$
$409$	2821.34	+	4886.70i	0.341091	+	0.590786i	−0.643545	+	0.765408i	$0.722537\pi$
$410$	26.6905	−	1550.15i	0.00321500	−	0.186723i
$411$		0			0
$412$	−2298.28	−	1326.91i	−0.274826	−	0.158671i
$413$			413.584i			0.0492764i
$414$		0			0
$415$	12480.8	+	7495.17i	1.47628	+	0.886562i
$416$	−4642.30	+	8040.69i	−0.547133	+	0.947662i
$417$		0			0
$418$	4566.18	−	2636.29i	0.534304	−	0.308481i
$419$	4810.87	+	8332.66i	0.560922	+	0.971545i	0.997416	+	0.0718380i	$0.0228865\pi$
$419$	4810.87	+	8332.66i	0.560922	+	0.971545i	−0.436495	+	0.899707i	$0.643780\pi$
$420$		0			0
$421$	−5015.14	+	8686.47i	−0.580577	+	1.00559i	0.414834	+	0.909897i	$0.363840\pi$
$421$	−5015.14	+	8686.47i	−0.580577	+	1.00559i	−0.995411	+	0.0956916i	$0.969494\pi$
$422$		−	21084.0i		−	2.43212i
$423$		0			0
$424$	11657.7			1.33525
$425$	66.3529	−	1926.28i	0.00757315	−	0.219855i
$426$		0			0
$427$	−2284.28	+	1318.83i	−0.258885	+	0.149467i
$428$	5208.14	−	3006.92i	0.588189	−	0.339591i
$429$		0			0
$430$	−1648.21	−	2971.80i	−0.184846	−	0.333285i
$431$	−3867.23			−0.432200			−0.216100	−	0.976371i	$-0.569334\pi$
$431$	−3867.23			−0.432200			−0.216100	+	0.976371i	$0.569334\pi$
$432$		0			0
$433$		−	2345.27i		−	0.260292i	−0.991495	−	0.130146i	$-0.958455\pi$
$433$		−	2345.27i		−	0.260292i	0.991495	−	0.130146i	$-0.0415446\pi$
$434$	2431.70	−	4211.83i	0.268953	−	0.465840i
$435$		0			0
$436$	−9698.47	−	16798.2i	−1.06530	−	1.84516i
$437$	−2583.42	+	1491.54i	−0.282796	+	0.163273i
$438$		0			0
$439$	−7058.94	+	12226.4i	−0.767437	+	1.32924i	0.171512	+	0.985182i	$0.445135\pi$
$439$	−7058.94	+	12226.4i	−0.767437	+	1.32924i	−0.938949	+	0.344057i	$0.888199\pi$
$440$	17392.7	+	10445.0i	1.88446	+	1.13169i
$441$		0			0
$442$		−	6710.34i		−	0.722123i
$443$	15412.3	+	8898.31i	1.65296	+	0.954337i	0.975846	+	0.218460i	$0.0701033\pi$
$443$	15412.3	+	8898.31i	1.65296	+	0.954337i	0.677115	+	0.735877i	$0.263230\pi$
$444$		0			0
$445$	−11128.9	−	191.617i	−1.18553	−	0.0204124i
$446$	−7622.37	−	13202.3i	−0.809259	−	1.40168i
$447$		0			0
$448$	1041.49	+	601.307i	0.109835	+	0.0634131i
$449$	−11518.0			−1.21062			−0.605310	−	0.795990i	$-0.706951\pi$
$449$	−11518.0			−1.21062			−0.605310	+	0.795990i	$0.706951\pi$
$450$		0			0
$451$	−1079.33			−0.112691
$452$	5255.88	+	3034.49i	0.546938	+	0.315775i
$453$		0			0
$454$	8128.77	+	14079.4i	0.840313	+	1.45547i
$455$	−5211.78	−	89.7362i	−0.536993	−	0.00924593i
$456$		0			0
$457$	8537.03	+	4928.86i	0.873841	+	0.504512i	0.868623	−	0.495474i	$-0.165006\pi$
$457$	8537.03	+	4928.86i	0.873841	+	0.504512i	0.00521822	+	0.999986i	$0.498339\pi$
$458$			14943.3i			1.52458i
$459$		0			0
$460$	−18362.2	−	11027.2i	−1.86118	−	1.11771i
$461$	−8040.79	+	13927.1i	−0.812358	+	1.40704i	0.0988520	+	0.995102i	$0.468483\pi$
$461$	−8040.79	+	13927.1i	−0.812358	+	1.40704i	−0.911210	+	0.411943i	$0.864850\pi$
$462$		0			0
$463$	16364.2	−	9447.88i	1.64257	−	0.948338i	0.662653	−	0.748927i	$-0.269431\pi$
$463$	16364.2	−	9447.88i	1.64257	−	0.948338i	0.979916	−	0.199411i	$-0.0639028\pi$
$464$	−2344.46	−	4060.72i	−0.234566	−	0.406281i
$465$		0			0
$466$	7353.25	−	12736.2i	0.730972	−	1.26608i
$467$			10368.7i			1.02742i	0.857963	+	0.513712i	$0.171730\pi$
$467$			10368.7i			1.02742i	−0.857963	+	0.513712i	$0.828270\pi$
$468$		0			0
$469$	−1284.79			−0.126495
$470$	−2621.62	−	4726.89i	−0.257290	−	0.463904i
$471$		0			0
$472$	3088.45	−	1783.12i	0.301181	−	0.173887i
$473$	−2048.82	+	1182.89i	−0.199165	+	0.114988i
$474$		0			0
$475$	3353.16	+	115.503i	0.323902	+	0.0111572i
$476$	1430.50			0.137745
$477$		0			0
$478$			14461.7i			1.38382i
$479$	4777.01	−	8274.02i	0.455672	−	0.789248i	−0.543054	−	0.839698i	$-0.682732\pi$
$479$	4777.01	−	8274.02i	0.455672	−	0.789248i	0.998727	+	0.0504500i	$0.0160655\pi$
$480$		0			0
$481$	−12712.3	−	22018.4i	−1.20506	−	2.08722i
$482$	−4862.23	+	2807.21i	−0.459478	+	0.265280i
$483$		0			0
$484$	1706.08	−	2955.02i	0.160226	−	0.277519i
$485$	7810.13	+	4690.28i	0.731216	+	0.439123i
$486$		0			0
$487$			17514.2i			1.62966i	0.579699	+	0.814831i	$0.303170\pi$
$487$			17514.2i			1.62966i	−0.579699	+	0.814831i	$0.696830\pi$
$488$	19696.8	+	11371.9i	1.82711	+	1.05488i
$489$		0			0
$490$	−303.651	+	17635.7i	−0.0279950	+	1.62592i
$491$	−1933.27	−	3348.52i	−0.177693	−	0.307773i	0.763397	−	0.645929i	$-0.223530\pi$
$491$	−1933.27	−	3348.52i	−0.177693	−	0.307773i	−0.941090	+	0.338157i	$0.890197\pi$
$492$		0			0
$493$	657.459	+	379.584i	0.0600618	+	0.0346767i
$494$	11681.0			1.06387
$495$		0			0
$496$	−17130.7			−1.55079
$497$	2985.08	+	1723.43i	0.269414	+	0.155546i
$498$		0			0
$499$	2427.98	+	4205.39i	0.217818	+	0.377272i	0.954141	−	0.299358i	$-0.0967726\pi$
$499$	2427.98	+	4205.39i	0.217818	+	0.377272i	−0.736322	+	0.676631i	$0.763439\pi$
$500$	10952.1	+	21456.9i	0.979582	+	1.91916i
$501$		0			0
$502$	−20065.2	−	11584.7i	−1.78398	−	1.02998i
$503$		−	5481.79i		−	0.485927i	−0.970035	−	0.242963i	$-0.921881\pi$
$503$		−	5481.79i		−	0.485927i	0.970035	−	0.242963i	$-0.0781195\pi$
$504$		0			0
$505$	−3756.41	+	6255.07i	−0.331006	+	0.551182i
$506$	−10915.8	+	18906.7i	−0.959023	+	1.66108i
$507$		0			0
$508$	22423.5	−	12946.2i	1.95843	−	1.13070i
$509$	10213.5	+	17690.4i	0.889405	+	1.54049i	0.840580	+	0.541687i	$0.182214\pi$
$509$	10213.5	+	17690.4i	0.889405	+	1.54049i	0.0488251	+	0.998807i	$0.484452\pi$
$510$		0			0
$511$	2070.06	−	3585.45i	0.179206	−	0.310393i
$512$		−	25150.0i		−	2.17086i
$513$		0			0
$514$	19028.4			1.63289
$515$	−1505.26	+	834.846i	−0.128795	+	0.0714324i
$516$		0			0
$517$	−3258.82	+	1881.48i	−0.277220	+	0.160053i
$518$	6872.25	−	3967.69i	0.582914	−	0.336545i
$519$		0			0
$520$	21799.8	+	39305.9i	1.83843	+	3.31477i
$521$	5768.55			0.485076			0.242538	−	0.970142i	$-0.422020\pi$
$521$	5768.55			0.485076			0.242538	+	0.970142i	$0.422020\pi$
$522$		0			0
$523$			1753.72i			0.146625i	0.997309	+	0.0733126i	$0.0233571\pi$
$523$			1753.72i			0.146625i	−0.997309	+	0.0733126i	$0.976643\pi$
$524$	13572.2	−	23507.7i	1.13149	−	1.95981i
$525$		0			0
$526$	12533.1	+	21707.9i	1.03891	+	1.79945i
$527$	2401.99	−	1386.79i	0.198544	−	0.114629i
$528$		0			0
$529$	92.3641	−	159.979i	0.00759136	−	0.0131486i
$530$	7263.96	−	12095.7i	0.595332	−	0.991332i
$531$		0			0
$532$			2490.13i			0.202934i
$533$	−2070.82	−	1195.59i	−0.168288	−	0.0971610i
$534$		0			0
$535$	67.1501	−	3900.00i	0.00542645	−	0.315162i
$536$	5539.21	+	9594.19i	0.446376	+	0.773145i
$537$		0			0
$538$	25432.1	+	14683.2i	2.03802	+	1.17665i
$539$	12279.3			0.981274
$540$		0			0
$541$	7146.18			0.567908			0.283954	−	0.958838i	$-0.408354\pi$
$541$	7146.18			0.567908			0.283954	+	0.958838i	$0.408354\pi$
$542$	−12034.3	−	6948.03i	−0.953725	−	0.550633i
$543$		0			0
$544$	−826.315	−	1431.22i	−0.0651250	−	0.112800i
$545$	−12579.0	−	216.585i	−0.988668	−	0.0170229i
$546$		0			0
$547$	−6415.42	−	3703.95i	−0.501469	−	0.289523i	0.227851	−	0.973696i	$-0.426830\pi$
$547$	−6415.42	−	3703.95i	−0.501469	−	0.289523i	−0.729320	+	0.684173i	$0.760163\pi$
$548$			15381.1i			1.19900i
$549$		0			0
$550$	21674.9	−	11537.9i	1.68040	−	0.894506i
$551$	−660.759	+	1144.47i	−0.0510876	+	0.0884863i
$552$		0			0
$553$	3087.17	−	1782.38i	0.237396	−	0.137061i
$554$	−4756.95	−	8239.29i	−0.364808	−	0.631866i
$555$		0			0
$556$	−5625.57	+	9743.77i	−0.429096	+	0.743216i
$557$			11116.3i			0.845626i	0.906217	+	0.422813i	$0.138957\pi$
$557$			11116.3i			0.845626i	−0.906217	+	0.422813i	$0.861043\pi$
$558$		0			0
$559$	−5241.20			−0.396564
$560$	−5011.41	+	2779.42i	−0.378162	+	0.209736i
$561$		0			0
$562$	−19510.0	+	11264.1i	−1.46438	+	0.845458i
$563$	−9705.19	+	5603.29i	−0.726509	+	0.419450i	−0.817144	−	0.576434i	$-0.804444\pi$
$563$	−9705.19	+	5603.29i	−0.726509	+	0.419450i	0.0906344	+	0.995884i	$0.471111\pi$
$564$		0			0
$565$	3442.34	−	1909.19i	0.256319	−	0.142159i
$566$	−29125.7			−2.16298
$567$		0			0
$568$		−	29721.5i		−	2.19557i
$569$	−7936.88	+	13747.1i	−0.584765	+	1.01284i	0.410140	+	0.912023i	$0.365480\pi$
$569$	−7936.88	+	13747.1i	−0.584765	+	1.01284i	−0.994905	+	0.100820i	$0.967853\pi$
$570$		0			0
$571$	1194.23	+	2068.46i	0.0875250	+	0.151598i	0.906464	−	0.422282i	$-0.138771\pi$
$571$	1194.23	+	2068.46i	0.0875250	+	0.151598i	−0.818939	+	0.573880i	$0.805438\pi$
$572$	50566.1	−	29194.3i	3.69628	−	2.13405i
$573$		0			0
$574$	373.160	−	646.332i	0.0271348	−	0.0469989i
$575$	−12263.1	+	6527.85i	−0.889401	+	0.473444i
$576$		0			0
$577$		−	10429.0i		−	0.752455i	−0.926527	−	0.376227i	$-0.877221\pi$
$577$		−	10429.0i		−	0.752455i	0.926527	−	0.376227i	$-0.122779\pi$
$578$	−20340.4	−	11743.5i	−1.46375	−	0.845098i
$579$		0			0
$580$	−9487.26	−	163.351i	−0.679202	−	0.0116945i
$581$	3504.05	+	6069.19i	0.250211	+	0.433377i
$582$		0			0
$583$	−8506.54	−	4911.25i	−0.604296	−	0.348891i
$584$	−35699.2			−2.52953
$585$		0			0
$586$	−39738.9			−2.80136
$587$	−2726.29	−	1574.02i	−0.191697	−	0.110676i	0.401080	−	0.916043i	$-0.368635\pi$
$587$	−2726.29	−	1574.02i	−0.191697	−	0.110676i	−0.592777	+	0.805367i	$0.701968\pi$
$588$		0			0
$589$	2414.05	+	4181.25i	0.168878	+	0.292505i
$590$	74.3053	−	4315.57i	0.00518492	−	0.301134i
$591$		0			0
$592$	−24206.6	−	13975.7i	−1.68055	−	0.970265i
$593$		−	12123.4i		−	0.839542i	−0.907630	−	0.419771i	$-0.862110\pi$
$593$		−	12123.4i		−	0.839542i	0.907630	−	0.419771i	$-0.137890\pi$
$594$		0			0
$595$	477.673	−	795.409i	0.0329121	−	0.0548043i
$596$	29630.3	−	51321.2i	2.03642	−	3.52718i
$597$		0			0
$598$	−41886.4	+	24183.1i	−2.86432	+	1.65371i
$599$	7921.39	+	13720.3i	0.540333	+	0.935884i	0.998885	+	0.0472161i	$0.0150349\pi$
$599$	7921.39	+	13720.3i	0.540333	+	0.935884i	−0.458552	+	0.888668i	$0.651632\pi$
$600$		0			0
$601$	12845.1	−	22248.3i	0.871815	−	1.51003i	0.0116971	−	0.999932i	$-0.496277\pi$
$601$	12845.1	−	22248.3i	0.871815	−	1.51003i	0.860118	−	0.510096i	$-0.170390\pi$
$602$		−	1635.85i		−	0.110751i
$603$		0			0
$604$	−28802.8			−1.94034
$605$	−1073.40	−	1935.39i	−0.0721324	−	0.130058i
$606$		0			0
$607$	−12577.5	+	7261.64i	−0.841031	+	0.485570i	−0.857615	−	0.514293i	$-0.828054\pi$
$607$	−12577.5	+	7261.64i	−0.841031	+	0.485570i	0.0165834	+	0.999862i	$0.494721\pi$
$608$	2491.39	−	1438.40i	0.166183	−	0.0959456i
$609$		0			0
$610$	24072.4	−	13351.0i	1.59781	−	0.886173i
$611$	−8336.56			−0.551982
$612$		0			0
$613$			26426.7i			1.74121i	0.491981	+	0.870606i	$0.336273\pi$
$613$			26426.7i			1.74121i	−0.491981	+	0.870606i	$0.663727\pi$
$614$	−11118.4	+	19257.6i	−0.730785	+	1.26576i
$615$		0			0
$616$	4883.09	+	8457.77i	0.319392	+	0.553203i
$617$	−3254.33	+	1878.89i	−0.212341	+	0.122595i	−0.602399	−	0.798195i	$-0.705788\pi$
$617$	−3254.33	+	1878.89i	−0.212341	+	0.122595i	0.390058	+	0.920790i	$0.372455\pi$
$618$		0			0
$619$	−11740.3	+	20334.7i	−0.762327	+	1.32039i	0.179321	+	0.983791i	$0.442610\pi$
$619$	−11740.3	+	20334.7i	−0.762327	+	1.32039i	−0.941648	+	0.336599i	$0.890723\pi$
$620$	−17847.4	+	29719.1i	−1.15608	+	1.92508i
$621$		0			0
$622$		−	48716.1i		−	3.14042i
$623$	−4640.16	−	2679.00i	−0.298401	−	0.172282i
$624$		0			0
$625$	15588.0	+	1075.17i	0.997630	+	0.0688107i
$626$	11361.4	+	19678.5i	0.725385	+	1.25640i
$627$		0			0
$628$	−9943.79	−	5741.05i	−0.631848	−	0.364797i
$629$	4525.52			0.286875
$630$		0			0
$631$	8654.12			0.545983			0.272991	−	0.962016i	$-0.411987\pi$
$631$	8654.12			0.545983			0.272991	+	0.962016i	$0.411987\pi$
$632$	−26619.9	−	15369.0i	−1.67545	−	0.967320i
$633$		0			0
$634$	−13368.6	−	23155.1i	−0.837438	−	1.45049i
$635$	289.113	−	16791.3i	0.0180678	−	1.04936i
$636$		0			0
$637$	23559.2	+	13601.9i	1.46539	+	0.846041i
$638$			9671.48i			0.600153i
$639$		0			0
$640$	−18977.8	−	11396.9i	−1.17213	−	0.703908i
$641$	9588.81	−	16608.3i	0.590850	−	1.02338i	−0.403268	−	0.915082i	$-0.632126\pi$
$641$	9588.81	−	16608.3i	0.590850	−	1.02338i	0.994118	−	0.108301i	$-0.0345410\pi$
$642$		0			0
$643$	−8517.85	+	4917.78i	−0.522413	+	0.301615i	−0.737921	−	0.674887i	$-0.764192\pi$
$643$	−8517.85	+	4917.78i	−0.522413	+	0.301615i	0.215509	+	0.976502i	$0.430859\pi$
$644$	−5155.30	−	8929.24i	−0.315446	−	0.546369i
$645$		0			0
$646$	−1039.59	+	1800.62i	−0.0633160	+	0.109667i
$647$		−	7621.18i		−	0.463090i	−0.972824	−	0.231545i	$-0.925622\pi$
$647$		−	7621.18i		−	0.463090i	0.972824	−	0.231545i	$-0.0743781\pi$
$648$		0			0
$649$	−3004.82			−0.181741
$650$	54366.4	+	1872.71i	3.28066	+	0.113006i
$651$		0			0
$652$	13275.0	−	7664.34i	0.797378	−	0.460366i
$653$	−3807.33	+	2198.16i	−0.228166	+	0.131731i	−0.609726	−	0.792613i	$-0.708720\pi$
$653$	−3807.33	+	2198.16i	−0.228166	+	0.131731i	0.381560	+	0.924344i	$0.375387\pi$
$654$		0			0
$655$	−8539.11	−	15396.4i	−0.509391	−	0.918451i
$656$	−2628.82			−0.156460
$657$		0			0
$658$		−	2601.95i		−	0.154156i
$659$	−5410.13	+	9370.61i	−0.319801	+	0.553911i	−0.980446	−	0.196787i	$-0.936949\pi$
$659$	−5410.13	+	9370.61i	−0.319801	+	0.553911i	0.660646	+	0.750698i	$0.270283\pi$
$660$		0			0
$661$	14457.8	+	25041.6i	0.850744	+	1.47353i	0.880538	+	0.473975i	$0.157181\pi$
$661$	14457.8	+	25041.6i	0.850744	+	1.47353i	−0.0297946	+	0.999556i	$0.509485\pi$
$662$	−34079.2	+	19675.6i	−2.00080	+	1.15516i
$663$		0			0
$664$	30214.5	−	52333.1i	1.76589	−	3.05861i
$665$	1384.60	+	831.507i	0.0807407	+	0.0484879i
$666$		0			0
$667$		−	5471.87i		−	0.317649i
$668$	−6028.96	−	3480.82i	−0.349203	−	0.201612i
$669$		0			0
$670$	13406.2	+	230.828i	0.773025	+	0.0133099i
$671$	−9581.71	−	16596.0i	−0.551264	−	0.954817i
$672$		0			0
$673$	4383.09	+	2530.58i	0.251049	+	0.144943i	0.620244	−	0.784409i	$-0.287033\pi$
$673$	4383.09	+	2530.58i	0.251049	+	0.144943i	−0.369196	+	0.929352i	$0.620367\pi$
$674$	49875.8			2.85036
$675$		0			0
$676$	91484.6			5.20509
$677$	10443.6	+	6029.63i	0.592882	+	0.342300i	0.766236	−	0.642559i	$-0.222127\pi$
$677$	10443.6	+	6029.63i	0.592882	+	0.342300i	−0.173354	+	0.984860i	$0.555461\pi$
$678$		0			0
$679$	2192.74	+	3797.94i	0.123932	+	0.214656i
$680$	−7999.16	−	137.729i	−0.451109	−	0.00776718i
$681$		0			0
$682$	30600.3	+	17667.1i	1.71810	+	0.991948i
$683$		−	6110.33i		−	0.342321i	−0.985243	−	0.171160i	$-0.945248\pi$
$683$		−	6110.33i		−	0.342321i	0.985243	−	0.171160i	$-0.0547516\pi$
$684$		0			0
$685$	8552.49	+	5136.10i	0.477042	+	0.286482i
$686$	−8882.27	+	15384.6i	−0.494354	+	0.856246i
$687$		0			0
$688$	−4990.09	+	2881.03i	−0.276520	+	0.159649i
$689$	−10880.5	−	18845.6i	−0.601617	−	1.04203i
$690$		0			0
$691$	−13604.9	+	23564.3i	−0.748991	+	1.29729i	0.199315	+	0.979935i	$0.436128\pi$
$691$	−13604.9	+	23564.3i	−0.748991	+	1.29729i	−0.948307	+	0.317356i	$0.897205\pi$
$692$		−	4069.15i		−	0.223535i
$693$		0			0
$694$	−20297.5			−1.11020
$695$	3539.40	+	6381.68i	0.193176	+	0.348303i
$696$		0			0
$697$	368.601	−	212.812i	0.0200312	−	0.0115650i
$698$	−20882.0	+	12056.2i	−1.13237	+	0.653774i
$699$		0			0
$700$	−399.221	+	11589.7i	−0.0215559	+	0.625786i
$701$	30424.7			1.63927			0.819633	−	0.572888i	$-0.194177\pi$
$701$	30424.7			1.63927			0.819633	+	0.572888i	$0.194177\pi$
$702$		0			0
$703$			7877.77i			0.422640i
$704$	−4368.69	+	7566.79i	−0.233879	+	0.405091i
$705$		0			0
$706$	−8011.51	−	13876.3i	−0.427078	−	0.739721i
$707$	−3041.74	+	1756.15i	−0.161805	+	0.0934183i
$708$		0			0
$709$	923.205	−	1599.04i	0.0489022	−	0.0847012i	−0.840538	−	0.541752i	$-0.817761\pi$
$709$	923.205	−	1599.04i	0.0489022	−	0.0847012i	0.889440	+	0.457051i	$0.151094\pi$
$710$	−30838.3	−	18519.6i	−1.63006	−	0.978911i
$711$		0			0
$712$			46200.6i			2.43180i
$713$	−17312.9	−	9995.59i	−0.909358	−	0.525018i
$714$		0			0
$715$	651.963	−	37865.2i	0.0341007	−	1.98053i
$716$	20722.3	+	35892.1i	1.08161	+	1.87340i
$717$		0			0
$718$	5046.02	+	2913.32i	0.262278	+	0.151426i
$719$	13301.3			0.689923			0.344961	−	0.938617i	$-0.387892\pi$
$719$	13301.3			0.689923			0.344961	+	0.938617i	$0.387892\pi$
$720$		0			0
$721$	−828.583			−0.0427989
$722$	26706.8	+	15419.2i	1.37662	+	0.794794i
$723$		0			0
$724$	−10501.3	−	18188.8i	−0.539058	−	0.933676i
$725$	−3258.83	+	5220.72i	−0.166938	+	0.267438i
$726$		0			0
$727$	−22443.2	−	12957.6i	−1.14494	−	0.661031i	−0.197290	−	0.980345i	$-0.563214\pi$
$727$	−22443.2	−	12957.6i	−1.14494	−	0.661031i	−0.947649	+	0.319314i	$0.896548\pi$
$728$			21636.3i			1.10150i
$729$		0			0
$730$	−22244.3	+	37040.6i	−1.12781	+	1.87799i
$731$	466.459	−	807.931i	0.0236014	−	0.0408788i
$732$		0			0
$733$	19267.1	−	11123.9i	0.970871	−	0.560532i	0.0713691	−	0.997450i	$-0.477263\pi$
$733$	19267.1	−	11123.9i	0.970871	−	0.560532i	0.899502	+	0.436918i	$0.143930\pi$
$734$	−29828.7	−	51664.8i	−1.49999	−	2.59807i
$735$		0			0
$736$	−5955.84	+	10315.8i	−0.298282	+	0.516639i
$737$		−	9334.41i		−	0.466536i
$738$		0			0
$739$	23675.6			1.17851			0.589256	−	0.807947i	$-0.299421\pi$
$739$	23675.6			1.17851			0.589256	+	0.807947i	$0.299421\pi$
$740$	−49465.0	+	27434.2i	−2.45726	+	1.36284i
$741$		0			0
$742$	5881.96	−	3395.95i	0.291016	−	0.168018i
$743$	29059.6	−	16777.6i	1.43485	−	0.828411i	0.437365	−	0.899284i	$-0.355912\pi$
$743$	29059.6	−	16777.6i	1.43485	−	0.828411i	0.997485	+	0.0708729i	$0.0225785\pi$
$744$		0			0
$745$	−18642.3	−	33612.8i	−0.916780	−	1.65299i
$746$	13279.0			0.651713
$747$		0			0
$748$			10393.0i			0.508030i
$749$	938.826	−	1626.09i	0.0457997	−	0.0793274i
$750$		0			0
$751$	−10944.9	−	18957.1i	−0.531804	−	0.921111i	−0.999311	−	0.0371219i	$-0.988181\pi$
$751$	−10944.9	−	18957.1i	−0.531804	−	0.921111i	0.467507	−	0.883989i	$-0.345152\pi$
$752$	−7937.16	+	4582.52i	−0.384891	+	0.222217i
$753$		0			0
$754$	−10713.2	+	18555.8i	−0.517444	+	0.896238i
$755$	−9617.86	+	16015.4i	−0.463615	+	0.772000i
$756$		0			0
$757$		−	24362.3i		−	1.16970i	−0.811141	−	0.584851i	$-0.801153\pi$
$757$		−	24362.3i		−	1.16970i	0.811141	−	0.584851i	$-0.198847\pi$
$758$	45476.1	+	26255.6i	2.17911	+	1.25811i
$759$		0			0
$760$	239.752	−	13924.5i	0.0114430	−	0.664598i
$761$	−13842.7	−	23976.2i	−0.659391	−	1.14210i	−0.980774	−	0.195149i	$-0.937481\pi$
$761$	−13842.7	−	23976.2i	−0.659391	−	1.14210i	0.321383	−	0.946949i	$-0.395852\pi$
$762$		0			0
$763$	−5244.77	−	3028.07i	−0.248851	−	0.143674i
$764$	3032.85			0.143619
$765$		0			0
$766$	−54657.2			−2.57813
$767$	−5765.10	−	3328.48i	−0.271402	−	0.156694i
$768$		0			0
$769$	−3498.05	−	6058.81i	−0.164035	−	0.284117i	0.772277	−	0.635286i	$-0.219118\pi$
$769$	−3498.05	−	6058.81i	−0.164035	−	0.284117i	−0.936312	+	0.351169i	$0.885784\pi$
$770$	11818.2	+	203.486i	0.553117	+	0.00952356i
$771$		0			0
$772$	−33070.0	−	19093.0i	−1.54173	−	0.890117i
$773$		−	19650.7i		−	0.914342i	−0.889379	−	0.457171i	$-0.848863\pi$
$773$		−	19650.7i		−	0.914342i	0.889379	−	0.457171i	$-0.151137\pi$
$774$		0			0
$775$	10565.3	+	19847.7i	0.489698	+	0.919936i
$776$	18907.4	−	32748.7i	0.874662	−	1.51496i
$777$		0			0
$778$	7298.94	−	4214.04i	0.336349	−	0.194191i
$779$	370.451	+	641.639i	0.0170382	+	0.0295111i
$780$		0			0
$781$	−12521.3	+	21687.5i	−0.573684	+	0.993651i
$782$		−	8609.05i		−	0.393681i
$783$		0			0
$784$	29907.4			1.36240
$785$	−6512.68	+	3612.06i	−0.296112	+	0.164229i
$786$		0			0
$787$	−1137.06	+	656.480i	−0.0515016	+	0.0297344i	−0.525530	−	0.850775i	$-0.676133\pi$
$787$	−1137.06	+	656.480i	−0.0515016	+	0.0297344i	0.474028	+	0.880510i	$0.342799\pi$
$788$	−15735.5	+	9084.91i	−0.711364	+	0.410706i
$789$		0			0
$790$	−32533.5	+	18043.7i	−1.46518	+	0.812615i
$791$	1894.86			0.0851752
$792$		0			0
$793$		−	42455.1i		−	1.90117i
$794$	−33024.6	+	57200.2i	−1.47607	+	2.55662i
$795$		0			0
$796$	30028.4	+	52010.7i	1.33710	+	2.31592i
$797$	2071.21	−	1195.82i	0.0920529	−	0.0531468i	−0.453267	−	0.891375i	$-0.649742\pi$
$797$	2071.21	−	1195.82i	0.0920529	−	0.0531468i	0.545320	+	0.838228i	$0.316408\pi$
$798$		0			0
$799$	741.942	−	1285.08i	0.0328511	−	0.0568997i
$800$	11826.2	−	6295.29i	0.522648	−	0.278215i
$801$		0			0
$802$			32764.2i			1.44257i
$803$	26049.4	+	15039.7i	1.14479	+	0.660944i
$804$		0			0
$805$	−6686.46	−	115.127i	−0.292754	−	0.00504062i
$806$	39140.2	+	67792.8i	1.71049	+	2.96265i
$807$		0			0
$808$	26228.2	+	15142.8i	1.14196	+	0.659311i
$809$	−7059.58			−0.306801			−0.153400	−	0.988164i	$-0.549022\pi$
$809$	−7059.58			−0.306801			−0.153400	+	0.988164i	$0.549022\pi$
$810$		0			0
$811$	12699.2			0.549849			0.274925	−	0.961466i	$-0.411347\pi$
$811$	12699.2			0.549849			0.274925	+	0.961466i	$0.411347\pi$
$812$	−3955.69	−	2283.82i	−0.170958	−	0.0987024i
$813$		0			0
$814$	28826.6	+	49929.1i	1.24124	+	2.14989i
$815$	171.159	−	9940.70i	0.00735635	−	0.427248i
$816$		0			0
$817$	1406.40	+	811.986i	0.0602249	+	0.0347708i
$818$		−	28347.1i		−	1.21166i
$819$		0			0
$820$	−2738.80	+	4560.58i	−0.116638	+	0.194222i
$821$	812.003	−	1406.43i	0.0345178	−	0.0597865i	−0.848250	−	0.529595i	$-0.822344\pi$
$821$	812.003	−	1406.43i	0.0345178	−	0.0597865i	0.882768	+	0.469809i	$0.155677\pi$
$822$		0			0
$823$	18317.9	−	10575.8i	0.775846	−	0.447935i	−0.0591102	−	0.998251i	$-0.518826\pi$
$823$	18317.9	−	10575.8i	0.775846	−	0.447935i	0.834956	+	0.550317i	$0.185493\pi$
$824$	3572.33	+	6187.46i	0.151029	+	0.261590i
$825$		0			0
$826$	1038.86	−	1799.36i	0.0437611	−	0.0757965i
$827$		−	18269.2i		−	0.768178i	−0.923296	−	0.384089i	$-0.874516\pi$
$827$		−	18269.2i		−	0.768178i	0.923296	−	0.384089i	$-0.125484\pi$
$828$		0			0
$829$	−19893.4			−0.833446			−0.416723	−	0.909034i	$-0.636821\pi$
$829$	−19893.4			−0.833446			−0.416723	+	0.909034i	$0.636821\pi$
$830$	−35472.8	−	63958.8i	−1.48347	−	2.67475i
$831$		0			0
$832$	−16763.7	+	9678.50i	−0.698528	+	0.403295i
$833$	−4193.48	+	2421.11i	−0.174424	+	0.100704i
$834$		0			0
$835$	−3948.67	+	2190.01i	−0.163652	+	0.0907644i
$836$	−18091.6			−0.748457
$837$		0			0
$838$		−	48336.8i		−	1.99256i
$839$	5852.88	−	10137.5i	0.240839	−	0.417145i	−0.720115	−	0.693855i	$-0.755911\pi$
$839$	5852.88	−	10137.5i	0.240839	−	0.417145i	0.960954	+	0.276710i	$0.0892441\pi$
$840$		0			0
$841$	10982.5	+	19022.2i	0.450304	+	0.779950i
$842$	43638.3	−	25194.6i	1.78608	−	1.03119i
$843$		0			0
$844$	−36172.4	+	62652.4i	−1.47524	+	2.55519i
$845$	30548.7	−	50868.8i	1.24368	−	2.07094i
$846$		0			0
$847$		−	1065.35i		−	0.0432183i
$848$	−20718.5	−	11961.8i	−0.839003	−	0.484399i
$849$		0			0
$850$	−5127.21	+	8213.92i	−0.206896	+	0.331453i
$851$	−16309.3	−	28248.6i	−0.656964	−	1.13790i
$852$		0			0
$853$	−916.495	−	529.139i	−0.0367880	−	0.0212396i	0.481493	−	0.876450i	$-0.340095\pi$
$853$	−916.495	−	529.139i	−0.0367880	−	0.0212396i	−0.518281	+	0.855210i	$0.673428\pi$
$854$	13250.8			0.530953
$855$		0			0
$856$	−16190.5			−0.646473
$857$	20815.2	+	12017.7i	0.829678	+	0.479015i	0.853742	−	0.520695i	$-0.174327\pi$
$857$	20815.2	+	12017.7i	0.829678	+	0.479015i	−0.0240642	+	0.999710i	$0.507661\pi$
$858$		0			0
$859$	−17547.1	−	30392.5i	−0.696973	−	1.20719i	−0.969511	−	0.245047i	$-0.921196\pi$
$859$	−17547.1	−	30392.5i	−0.696973	−	1.20719i	0.272538	−	0.962145i	$-0.412137\pi$
$860$	−200.737	+	11658.6i	−0.00795941	+	0.462273i
$861$		0			0
$862$	16825.0	+	9713.93i	0.664805	+	0.383826i
$863$			41958.9i			1.65504i	0.561439	+	0.827518i	$0.310248\pi$
$863$			41958.9i			1.65504i	−0.561439	+	0.827518i	$0.689752\pi$
$864$		0			0
$865$	−2262.60	−	1358.78i	−0.0889372	−	0.0534102i
$866$	−5890.98	+	10203.5i	−0.231159	+	0.400379i
$867$		0			0
$868$	−14451.9	+	8343.81i	−0.565127	+	0.326276i
$869$	12949.6	+	22429.3i	0.505505	+	0.875560i
$870$		0			0
$871$	10339.8	−	17909.1i	0.402241	−	0.696703i
$872$			52220.6i			2.02800i
$873$		0			0
$874$	14986.1			0.579993
$875$	6311.00	+	4092.04i	0.243829	+	0.158098i
$876$		0			0
$877$	16983.7	−	9805.55i	0.653933	−	0.377548i	−0.136028	−	0.990705i	$-0.543434\pi$
$877$	16983.7	−	9805.55i	0.653933	−	0.377548i	0.789961	+	0.613157i	$0.210101\pi$
$878$	61422.1	−	35462.1i	2.36093	−	1.36308i
$879$		0			0
$880$	−20193.4	−	36409.5i	−0.773545	−	1.39473i
$881$	−10465.2			−0.400204			−0.200102	−	0.979775i	$-0.564127\pi$
$881$	−10465.2			−0.400204			−0.200102	+	0.979775i	$0.564127\pi$
$882$		0			0
$883$			10812.2i			0.412074i	0.978544	+	0.206037i	$0.0660567\pi$
$883$			10812.2i			0.412074i	−0.978544	+	0.206037i	$0.933943\pi$
$884$	−11512.5	+	19940.2i	−0.438016	+	0.758667i
$885$		0			0
$886$	−44702.5	−	77427.1i	−1.69505	−	2.93591i
$887$	−31177.4	+	18000.3i	−1.18020	+	0.681387i	−0.956060	−	0.293171i	$-0.905289\pi$
$887$	−31177.4	+	18000.3i	−1.18020	+	0.681387i	−0.224137	+	0.974558i	$0.571956\pi$
$888$		0			0
$889$	4042.09	−	7001.10i	0.152494	−	0.264127i
$890$	47936.7	+	28787.8i	1.80544	+	1.08423i
$891$		0			0
$892$			52308.7i			1.96348i
$893$	2237.00	+	1291.53i	0.0838278	+	0.0483980i
$894$		0			0
$895$	26877.0	+	462.767i	1.00380	+	0.0172834i
$896$	−5328.13	−	9228.58i	−0.198661	−	0.344091i
$897$		0			0
$898$	50110.9	+	28931.6i	1.86216	+	1.07512i
$899$	−8856.18			−0.328554
$900$		0			0
$901$	3873.40			0.143220
$902$	4695.81	+	2711.13i	0.173341	+	0.100078i
$903$		0			0
$904$	−8169.47	−	14149.9i	−0.300567	−	0.520597i
$905$	−13620.3	−	234.513i	−0.500280	−	0.00861380i
$906$		0			0
$907$	4513.41	+	2605.82i	0.165232	+	0.0953968i	0.580336	−	0.814377i	$-0.302921\pi$
$907$	4513.41	+	2605.82i	0.165232	+	0.0953968i	−0.415104	+	0.909774i	$0.636255\pi$
$908$		−	55783.9i		−	2.03883i
$909$		0			0
$910$	22449.3	+	13481.6i	0.817787	+	0.491112i
$911$	−8366.56	+	14491.3i	−0.304277	+	0.527024i	−0.977100	−	0.212780i	$-0.931748\pi$
$911$	−8366.56	+	14491.3i	−0.304277	+	0.527024i	0.672823	+	0.739804i	$0.265082\pi$
$912$		0			0
$913$	−44094.6	+	25458.0i	−1.59838	+	0.922823i
$914$	−24761.1	−	42887.6i	−0.896090	−	1.55207i
$915$		0			0
$916$	25637.2	−	44405.0i	0.924758	−	1.60173i
$917$		−	8475.05i		−	0.305203i
$918$		0			0
$919$	−16722.8			−0.600255			−0.300127	−	0.953899i	$-0.597029\pi$
$919$	−16722.8			−0.600255			−0.300127	+	0.953899i	$0.597029\pi$
$920$	27968.1	+	50427.6i	1.00226	+	1.80712i
$921$		0			0
$922$	69965.5	−	40394.6i	2.49912	−	1.44287i
$923$	−48047.1	+	27740.0i	−1.71342	+	0.989246i
$924$		0			0
$925$	−1262.98	+	36665.2i	−0.0448934	+	1.30329i
$926$	−94926.8			−3.36878
$927$		0			0
$928$			5276.93i			0.186663i
$929$	17672.3	−	30609.2i	0.624120	−	1.08101i	−0.364590	−	0.931168i	$-0.618791\pi$
$929$	17672.3	−	30609.2i	0.624120	−	1.08101i	0.988710	−	0.149840i	$-0.0478759\pi$
$930$		0			0
$931$	−4214.52	−	7299.77i	−0.148362	−	0.256971i
$932$	−43701.3	+	25230.9i	−1.53593	+	0.886767i
$933$		0			0
$934$	26044.7	−	45110.8i	0.912430	−	1.58037i
$935$	5778.90	+	3470.45i	0.202129	+	0.121386i
$936$		0			0
$937$		−	2015.96i		−	0.0702867i	−0.999382	−	0.0351433i	$-0.988811\pi$
$937$		−	2015.96i		−	0.0702867i	0.999382	−	0.0351433i	$-0.0111888\pi$
$938$	5589.68	+	3227.21i	0.194573	+	0.112337i
$939$		0			0
$940$	−319.290	+	18544.0i	−0.0110788	+	0.643444i
$941$	19940.2	+	34537.4i	0.690787	+	1.19648i	0.971580	+	0.236710i	$0.0760690\pi$
$941$	19940.2	+	34537.4i	0.690787	+	1.19648i	−0.280794	+	0.959768i	$0.590598\pi$
$942$		0			0
$943$	−2656.77	−	1533.89i	−0.0917458	−	0.0529694i
$944$	−7318.52			−0.252328
$945$		0			0
$946$	11885.0			0.408471
$947$	−30319.7	−	17505.1i	−1.04040	−	0.600675i	−0.120453	−	0.992719i	$-0.538435\pi$
$947$	−30319.7	−	17505.1i	−1.04040	−	0.600675i	−0.919947	+	0.392044i	$0.871768\pi$
$948$		0			0
$949$	33319.2	+	57710.6i	1.13971	+	1.97404i
$950$	−14298.3	−	8925.16i	−0.488315	−	0.304811i
$951$		0			0
$952$	−3335.23	−	1925.60i	−0.113546	−	0.0655556i
$953$			49213.8i			1.67281i	0.548109	+	0.836407i	$0.315348\pi$
$953$			49213.8i			1.67281i	−0.548109	+	0.836407i	$0.684652\pi$
$954$		0			0
$955$	1012.73	−	1686.38i	0.0343155	−	0.0571412i
$956$	24811.0	−	42973.9i	0.839378	−	1.45384i
$957$		0			0
$958$	−41566.3	+	23998.3i	−1.40182	+	0.809342i
$959$	2401.16	+	4158.94i	0.0808525	+	0.140041i
$960$		0			0
$961$	−1282.29	+	2220.98i	−0.0430427	+	0.0745522i
$962$			127726.i			4.28073i
$963$		0			0
$964$	19264.5			0.643640
$965$	−21659.2	+	12012.6i	−0.722522	+	0.400724i
$966$		0			0
$967$	1055.98	−	609.670i	0.0351169	−	0.0202747i	−0.482339	−	0.875985i	$-0.660213\pi$
$967$	1055.98	−	609.670i	0.0351169	−	0.0202747i	0.517456	+	0.855710i	$0.326879\pi$
$968$	−7955.54	+	4593.13i	−0.264154	+	0.152509i
$969$		0			0
$970$	−22197.9	−	40023.7i	−0.734775	−	1.32483i
$971$	1660.33			0.0548740			0.0274370	−	0.999624i	$-0.491265\pi$
$971$	1660.33			0.0548740			0.0274370	+	0.999624i	$0.491265\pi$
$972$		0			0
$973$			3512.85i			0.115742i
$974$	43993.2	−	76198.5i	1.44726	−	2.50673i
$975$		0			0
$976$	−23337.1	−	40421.1i	−0.765373	−	1.32566i
$977$	40969.7	−	23653.9i	1.34159	−	0.774569i	0.354552	−	0.935036i	$-0.384633\pi$
$977$	40969.7	−	23653.9i	1.34159	−	0.774569i	0.987041	+	0.160467i	$0.0512999\pi$
$978$		0			0
$979$	19463.8	−	33712.2i	0.635408	−	1.10056i
$980$	31158.7	−	51884.6i	1.01564	−	1.69122i
$981$		0			0
$982$			19424.4i			0.631218i
$983$	−35682.9	−	20601.5i	−1.15779	−	0.668450i	−0.207016	−	0.978338i	$-0.566375\pi$
$983$	−35682.9	−	20601.5i	−1.15779	−	0.668450i	−0.950773	+	0.309888i	$0.899709\pi$
$984$		0			0
$985$	−202.883	+	11783.2i	−0.00656282	+	0.381161i
$986$	−1906.92	−	3302.89i	−0.0615910	−	0.106679i
$987$		0			0
$988$	−34710.8	−	20040.3i	−1.11771	−	0.645310i
$989$	−6724.20			−0.216195
$990$		0			0
$991$	−29805.3			−0.955395			−0.477698	−	0.878524i	$-0.658529\pi$
$991$	−29805.3			−0.955395			−0.477698	+	0.878524i	$0.658529\pi$
$992$	16696.1	+	9639.48i	0.534376	+	0.308522i
$993$		0			0
$994$	−8658.04	−	14996.2i	−0.276274	−	0.478520i
$995$	38947.0	+	670.589i	1.24091	+	0.0213659i
$996$		0			0
$997$	34496.2	+	19916.4i	1.09579	+	0.632657i	0.935113	−	0.354350i	$-0.115298\pi$
$997$	34496.2	+	19916.4i	1.09579	+	0.632657i	0.160680	+	0.987006i	$0.448631\pi$
$998$		−	24395.0i		−	0.773756i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.j.a.19.2		32
3.2	odd	2		45.4.j.a.34.15	yes	32
5.4	even	2	inner	135.4.j.a.19.15		32
9.2	odd	6		405.4.b.e.244.2		16
9.4	even	3	inner	135.4.j.a.64.15		32
9.5	odd	6		45.4.j.a.4.2	✓	32
9.7	even	3		405.4.b.f.244.15		16
15.2	even	4		225.4.e.g.151.2		32
15.8	even	4		225.4.e.g.151.15		32
15.14	odd	2		45.4.j.a.34.2	yes	32
45.2	even	12		2025.4.a.bk.1.15		16
45.4	even	6	inner	135.4.j.a.64.2		32
45.7	odd	12		2025.4.a.bl.1.2		16
45.14	odd	6		45.4.j.a.4.15	yes	32
45.23	even	12		225.4.e.g.76.15		32
45.29	odd	6		405.4.b.e.244.15		16
45.32	even	12		225.4.e.g.76.2		32
45.34	even	6		405.4.b.f.244.2		16
45.38	even	12		2025.4.a.bk.1.2		16
45.43	odd	12		2025.4.a.bl.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.2	✓	32	9.5	odd	6
45.4.j.a.4.15	yes	32	45.14	odd	6
45.4.j.a.34.2	yes	32	15.14	odd	2
45.4.j.a.34.15	yes	32	3.2	odd	2
135.4.j.a.19.2		32	1.1	even	1	trivial
135.4.j.a.19.15		32	5.4	even	2	inner
135.4.j.a.64.2		32	45.4	even	6	inner
135.4.j.a.64.15		32	9.4	even	3	inner
225.4.e.g.76.2		32	45.32	even	12
225.4.e.g.76.15		32	45.23	even	12
225.4.e.g.151.2		32	15.2	even	4
225.4.e.g.151.15		32	15.8	even	4
405.4.b.e.244.2		16	9.2	odd	6
405.4.b.e.244.15		16	45.29	odd	6
405.4.b.f.244.2		16	45.34	even	6
405.4.b.f.244.15		16	9.7	even	3
2025.4.a.bk.1.2		16	45.38	even	12
2025.4.a.bk.1.15		16	45.2	even	12
2025.4.a.bl.1.2		16	45.7	odd	12
2025.4.a.bl.1.15		16	45.43	odd	12

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.35066 - 2.51186i) q^{2} +(8.61884 + 14.9283i) q^{4} +(11.1787 + 0.192474i) q^{5} +(4.66092 + 2.69099i) q^{7} -46.4074i q^{8} +O(q^{10})\)	\(q+(-4.35066 - 2.51186i) q^{2} +(8.61884 + 14.9283i) q^{4} +(11.1787 + 0.192474i) q^{5} +(4.66092 + 2.69099i) q^{7} -46.4074i q^{8} +(-48.1512 - 28.9166i) q^{10} +(-19.5509 + 33.8631i) q^{11} +(-75.0212 + 43.3135i) q^{13} +(-13.5187 - 23.4151i) q^{14} +(-47.6180 + 82.4768i) q^{16} -15.4194i q^{17} +26.8412 q^{19} +(93.4739 + 168.537i) q^{20} +(170.119 - 98.2180i) q^{22} +(-96.2486 + 55.5692i) q^{23} +(124.926 + 4.30322i) q^{25} +435.189 q^{26} +92.7727i q^{28} +(-24.6174 + 42.6385i) q^{29} +(89.9383 + 155.778i) q^{31} +(92.8196 - 53.5894i) q^{32} +(-38.7312 + 67.0844i) q^{34} +(51.5851 + 30.9788i) q^{35} +293.496i q^{37} +(-116.777 - 67.4211i) q^{38} +(8.93223 - 518.774i) q^{40} +(13.8016 + 23.9051i) q^{41} +(52.3971 + 30.2515i) q^{43} -674.023 q^{44} +558.327 q^{46} +(83.3420 + 48.1175i) q^{47} +(-157.017 - 271.962i) q^{49} +(-532.701 - 332.518i) q^{50} +(-1293.19 - 746.625i) q^{52} +251.203i q^{53} +(-225.071 + 374.782i) q^{55} +(124.882 - 216.301i) q^{56} +(214.204 - 123.671i) q^{58} +(38.4231 + 66.5508i) q^{59} +(-245.045 + 424.431i) q^{61} -903.648i q^{62} +223.452 q^{64} +(-846.975 + 469.749i) q^{65} +(-206.738 + 119.360i) q^{67} +(230.184 - 132.897i) q^{68} +(-146.615 - 264.352i) q^{70} +640.447 q^{71} -769.257i q^{73} +(737.219 - 1276.90i) q^{74} +(231.340 + 400.692i) q^{76} +(-182.250 + 105.222i) q^{77} +(331.176 - 573.613i) q^{79} +(-548.181 + 912.817i) q^{80} -138.670i q^{82} +(1127.69 + 651.071i) q^{83} +(2.96783 - 172.368i) q^{85} +(-151.975 - 263.228i) q^{86} +(1571.50 + 907.306i) q^{88} -995.544 q^{89} -466.224 q^{91} +(-1659.10 - 957.883i) q^{92} +(-241.729 - 418.686i) q^{94} +(300.049 + 5.16623i) q^{95} +(705.677 + 407.423i) q^{97} +1577.62i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 54 q^{4} - 3 q^{5}+O(q^{10}) \) 32 * q + 54 * q^4 - 3 * q^5	\( 32 q + 54 q^{4} - 3 q^{5} - 20 q^{10} - 90 q^{11} + 102 q^{14} - 146 q^{16} - 8 q^{19} + 6 q^{20} + 71 q^{25} + 936 q^{26} + 516 q^{29} - 38 q^{31} + 212 q^{34} + 534 q^{35} + 44 q^{40} - 576 q^{41} - 3288 q^{44} - 580 q^{46} - 4 q^{49} - 558 q^{50} + 30 q^{55} - 2430 q^{56} + 2202 q^{59} - 20 q^{61} + 644 q^{64} - 339 q^{65} + 636 q^{70} + 5904 q^{71} + 4080 q^{74} + 396 q^{76} - 218 q^{79} - 2532 q^{80} - 704 q^{85} - 6108 q^{86} - 8148 q^{89} - 1884 q^{91} - 1078 q^{94} + 1692 q^{95}+O(q^{100}) \) 32 * q + 54 * q^4 - 3 * q^5 - 20 * q^10 - 90 * q^11 + 102 * q^14 - 146 * q^16 - 8 * q^19 + 6 * q^20 + 71 * q^25 + 936 * q^26 + 516 * q^29 - 38 * q^31 + 212 * q^34 + 534 * q^35 + 44 * q^40 - 576 * q^41 - 3288 * q^44 - 580 * q^46 - 4 * q^49 - 558 * q^50 + 30 * q^55 - 2430 * q^56 + 2202 * q^59 - 20 * q^61 + 644 * q^64 - 339 * q^65 + 636 * q^70 + 5904 * q^71 + 4080 * q^74 + 396 * q^76 - 218 * q^79 - 2532 * q^80 - 704 * q^85 - 6108 * q^86 - 8148 * q^89 - 1884 * q^91 - 1078 * q^94 + 1692 * q^95

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