LMFDB - Embedded newform 75.20.b.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,20,Mod(49,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("75.49");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	75.b (of order $2$, degree $1$, 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:	$171.612522417$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 43741x^{2} + 478296900 $ x^4 + 43741*x^2 + 478296900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.3
Root			$147.386i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.20.b.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+536.316i q^{2} -19683.0i q^{3} +236654. q^{4} +1.05563e7 q^{6} -1.13677e8i q^{7} +4.08105e8i q^{8} -3.87420e8 q^{9} +O(q^{10})$	\(q+536.316i q^{2} -19683.0i q^{3} +236654. q^{4} +1.05563e7 q^{6} -1.13677e8i q^{7} +4.08105e8i q^{8} -3.87420e8 q^{9} +6.43152e9 q^{11} -4.65805e9i q^{12} -5.75132e10i q^{13} +6.09670e10 q^{14} -9.47984e10 q^{16} -6.85083e11i q^{17} -2.07780e11i q^{18} -1.22275e12 q^{19} -2.23751e12 q^{21} +3.44932e12i q^{22} +5.02230e12i q^{23} +8.03273e12 q^{24} +3.08453e13 q^{26} +7.62560e12i q^{27} -2.69022e13i q^{28} -1.53748e14 q^{29} +3.92872e13 q^{31} +1.63123e14i q^{32} -1.26592e14i q^{33} +3.67421e14 q^{34} -9.16844e13 q^{36} -1.35709e15i q^{37} -6.55779e14i q^{38} -1.13203e15 q^{39} -5.75410e14 q^{41} -1.20001e15i q^{42} +3.36667e14i q^{43} +1.52204e15 q^{44} -2.69354e15 q^{46} +6.99998e15i q^{47} +1.86592e15i q^{48} -1.52367e15 q^{49} -1.34845e16 q^{51} -1.36107e16i q^{52} +1.69895e16i q^{53} -4.08973e15 q^{54} +4.63923e16 q^{56} +2.40674e16i q^{57} -8.24573e16i q^{58} +2.70689e16 q^{59} -5.11533e16 q^{61} +2.10704e16i q^{62} +4.40410e16i q^{63} -1.37187e17 q^{64} +6.78930e16 q^{66} -2.07437e17i q^{67} -1.62127e17i q^{68} +9.88540e16 q^{69} -2.35123e17 q^{71} -1.58108e17i q^{72} +7.43858e16i q^{73} +7.27828e17 q^{74} -2.89368e17 q^{76} -7.31118e17i q^{77} -6.07127e17i q^{78} +6.98697e17 q^{79} +1.50095e17 q^{81} -3.08601e17i q^{82} +3.25532e18i q^{83} -5.29515e17 q^{84} -1.80560e17 q^{86} +3.02622e18i q^{87} +2.62473e18i q^{88} +1.43575e18 q^{89} -6.53796e18 q^{91} +1.18855e18i q^{92} -7.73291e17i q^{93} -3.75420e18 q^{94} +3.21074e18 q^{96} -1.66911e18i q^{97} -8.17166e17i q^{98} -2.49170e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1544968 q^{4} - 27634932 q^{6} - 1549681956 q^{9}+O(q^{10}) $ 4 * q - 1544968 * q^4 - 27634932 * q^6 - 1549681956 * q^9	$ 4 q - 1544968 q^{4} - 27634932 q^{6} - 1549681956 q^{9} - 13300142544 q^{11} + 121402438848 q^{14} + 239207241760 q^{16} - 1204237850192 q^{19} - 4483474991424 q^{21} + 39700674930384 q^{24} + 94978619578728 q^{26} - 561954503940984 q^{29} + 83220298507424 q^{31} + 15\!\cdots\!64 q^{34}+ \cdots + 51\!\cdots\!16 q^{99}+O(q^{100}) $ 4 * q - 1544968 * q^4 - 27634932 * q^6 - 1549681956 * q^9 - 13300142544 * q^11 + 121402438848 * q^14 + 239207241760 * q^16 - 1204237850192 * q^19 - 4483474991424 * q^21 + 39700674930384 * q^24 + 94978619578728 * q^26 - 561954503940984 * q^29 + 83220298507424 * q^31 + 1598694698342664 * q^34 + 598552258049352 * q^36 - 1734952372122168 * q^39 + 2300076860561064 * q^41 + 29446328828101536 * q^44 - 11960188021600416 * q^46 + 19750366460386140 * q^49 - 13238056416831768 * q^51 + 10706338868921748 * q^54 + 93042345123175680 * q^56 + 110306948843671632 * q^59 - 174385138132411240 * q^61 + 72500092437262208 * q^64 + 773481249856604304 * q^66 + 93228614765496288 * q^69 + 169830096873941088 * q^71 + 3236591734880155128 * q^74 - 1831337138947140448 * q^76 - 2263182932067046880 * q^79 + 600378541187996484 * q^81 - 1050504928298587008 * q^84 + 5790466823989672656 * q^86 - 8645595252739152552 * q^89 - 13070147362624689536 * q^91 - 10967971360190514048 * q^94 + 8361578887023750336 * q^96 + 5152747728166184016 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$-1$

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 $

$2$	536.316i	0.740688i	0.928895	+	0.370344i	$0.120760\pi$
$2$	536.316i	0.740688i	−0.928895	+	0.370344i	$0.879240\pi$
$3$	− 19683.0i	− 0.577350i
$3$	− 19683.0i	− 0.577350i
$4$	236654.	0.451381
$5$	0	0
$5$	0	0
$6$	1.05563e7	0.427637
$7$	− 1.13677e8i	− 1.06474i	−0.846512	−	0.532369i	$-0.821302\pi$
$7$	− 1.13677e8i	− 1.06474i	0.846512	−	0.532369i	$-0.178698\pi$
$8$	4.08105e8i	1.07502i
$9$	−3.87420e8	−0.333333
$10$	0	0
$11$	6.43152e9	0.822400	0.411200	−	0.911545i	$-0.365110\pi$
$11$	6.43152e9	0.822400	0.411200	+	0.911545i	$0.365110\pi$
$12$	− 4.65805e9i	− 0.260605i
$13$	− 5.75132e10i	− 1.50420i	−0.659048	−	0.752101i	$-0.729041\pi$
$13$	− 5.75132e10i	− 1.50420i	0.659048	−	0.752101i	$-0.270959\pi$
$14$	6.09670e10	0.788639
$15$	0	0
$16$	−9.47984e10	−0.344874
$17$	− 6.85083e11i	− 1.40113i	−0.713588	−	0.700565i	$-0.752931\pi$
$17$	− 6.85083e11i	− 1.40113i	0.713588	−	0.700565i	$-0.247069\pi$
$18$	− 2.07780e11i	− 0.246896i
$19$	−1.22275e12	−0.869317	−0.434658	−	0.900595i	$-0.643131\pi$
$19$	−1.22275e12	−0.869317	−0.434658	+	0.900595i	$0.643131\pi$
$20$	0	0
$21$	−2.23751e12	−0.614727
$22$	3.44932e12i	0.609142i
$23$	5.02230e12i	0.581418i	0.956811	+	0.290709i	$0.0938912\pi$
$23$	5.02230e12i	0.581418i	−0.956811	+	0.290709i	$0.906109\pi$
$24$	8.03273e12	0.620664
$25$	0	0
$26$	3.08453e13	1.11414
$27$	7.62560e12i	0.192450i
$28$	− 2.69022e13i	− 0.480603i
$29$	−1.53748e14	−1.96801	−0.984006	−	0.178134i	$-0.942994\pi$
$29$	−1.53748e14	−1.96801	−0.984006	+	0.178134i	$0.942994\pi$
$30$	0	0
$31$	3.92872e13	0.266880	0.133440	−	0.991057i	$-0.457398\pi$
$31$	3.92872e13	0.266880	0.133440	+	0.991057i	$0.457398\pi$
$32$	1.63123e14i	0.819576i
$33$	− 1.26592e14i	− 0.474813i
$34$	3.67421e14	1.03780
$35$	0	0
$36$	−9.16844e13	−0.150460
$37$	− 1.35709e15i	− 1.71669i	−0.513072	−	0.858346i	$-0.671493\pi$
$37$	− 1.35709e15i	− 1.71669i	0.513072	−	0.858346i	$-0.328507\pi$
$38$	− 6.55779e14i	− 0.643893i
$39$	−1.13203e15	−0.868451
$40$	0	0
$41$	−5.75410e14	−0.274493	−0.137246	−	0.990537i	$-0.543825\pi$
$41$	−5.75410e14	−0.274493	−0.137246	+	0.990537i	$0.543825\pi$
$42$	− 1.20001e15i	− 0.455321i
$43$	3.36667e14i	0.102153i	0.998695	+	0.0510763i	$0.0162652\pi$
$43$	3.36667e14i	0.102153i	−0.998695	+	0.0510763i	$0.983735\pi$
$44$	1.52204e15	0.371215
$45$	0	0
$46$	−2.69354e15	−0.430650
$47$	6.99998e15i	0.912362i	0.889887	+	0.456181i	$0.150783\pi$
$47$	6.99998e15i	0.912362i	−0.889887	+	0.456181i	$0.849217\pi$
$48$	1.86592e15i	0.199113i
$49$	−1.52367e15	−0.133668
$50$	0	0
$51$	−1.34845e16	−0.808943
$52$	− 1.36107e16i	− 0.678968i
$53$	1.69895e16i	0.707231i	0.935391	+	0.353615i	$0.115048\pi$
$53$	1.69895e16i	0.707231i	−0.935391	+	0.353615i	$0.884952\pi$
$54$	−4.08973e15	−0.142546
$55$	0	0
$56$	4.63923e16	1.14462
$57$	2.40674e16i	0.501900i
$58$	− 8.24573e16i	− 1.45768i
$59$	2.70689e16	0.406796	0.203398	−	0.979096i	$-0.434802\pi$
$59$	2.70689e16	0.406796	0.203398	+	0.979096i	$0.434802\pi$
$60$	0	0
$61$	−5.11533e16	−0.560068	−0.280034	−	0.959990i	$-0.590346\pi$
$61$	−5.11533e16	−0.560068	−0.280034	+	0.959990i	$0.590346\pi$
$62$	2.10704e16i	0.197675i
$63$	4.40410e16i	0.354913i
$64$	−1.37187e17	−0.951925
$65$	0	0
$66$	6.78930e16	0.351688
$67$	− 2.07437e17i	− 0.931487i	−0.884920	−	0.465743i	$-0.845787\pi$
$67$	− 2.07437e17i	− 0.931487i	0.884920	−	0.465743i	$-0.154213\pi$
$68$	− 1.62127e17i	− 0.632443i
$69$	9.88540e16	0.335682
$70$	0	0
$71$	−2.35123e17	−0.608613	−0.304306	−	0.952574i	$-0.598425\pi$
$71$	−2.35123e17	−0.608613	−0.304306	+	0.952574i	$0.598425\pi$
$72$	− 1.58108e17i	− 0.358340i
$73$	7.43858e16i	0.147885i	0.997263	+	0.0739423i	$0.0235580\pi$
$73$	7.43858e16i	0.147885i	−0.997263	+	0.0739423i	$0.976442\pi$
$74$	7.27828e17	1.27153
$75$	0	0
$76$	−2.89368e17	−0.392393
$77$	− 7.31118e17i	− 0.875641i
$78$	− 6.07127e17i	− 0.643252i
$79$	6.98697e17	0.655890	0.327945	−	0.944697i	$-0.393644\pi$
$79$	6.98697e17	0.655890	0.327945	+	0.944697i	$0.393644\pi$
$80$	0	0
$81$	1.50095e17	0.111111
$82$	− 3.08601e17i	− 0.203314i
$83$	3.25532e18i	1.91140i	0.294338	+	0.955701i	$0.404901\pi$
$83$	3.25532e18i	1.91140i	−0.294338	+	0.955701i	$0.595099\pi$
$84$	−5.29515e17	−0.277476
$85$	0	0
$86$	−1.80560e17	−0.0756633
$87$	3.02622e18i	1.13623i
$88$	2.62473e18i	0.884097i
$89$	1.43575e18	0.434385	0.217193	−	0.976129i	$-0.430310\pi$
$89$	1.43575e18	0.434385	0.217193	+	0.976129i	$0.430310\pi$
$90$	0	0
$91$	−6.53796e18	−1.60158
$92$	1.18855e18i	0.262441i
$93$	− 7.73291e17i	− 0.154083i
$94$	−3.75420e18	−0.675776
$95$	0	0
$96$	3.21074e18	0.473183
$97$	− 1.66911e18i	− 0.222922i	−0.993769	−	0.111461i	$-0.964447\pi$
$97$	− 1.66911e18i	− 0.222922i	0.993769	−	0.111461i	$-0.0355530\pi$
$98$	− 8.17166e17i	− 0.0990062i
$99$	−2.49170e18	−0.274133
$100$	0	0
$101$	9.99068e18	0.908955	0.454477	−	0.890758i	$-0.349826\pi$
$101$	9.99068e18	0.908955	0.454477	+	0.890758i	$0.349826\pi$
$102$	− 7.23194e18i	− 0.599175i
$103$	1.17501e18i	0.0887333i	0.999015	+	0.0443666i	$0.0141270\pi$
$103$	1.17501e18i	0.0887333i	−0.999015	+	0.0443666i	$0.985873\pi$
$104$	2.34714e19	1.61705
$105$	0	0
$106$	−9.11176e18	−0.523837
$107$	1.73164e19i	0.910568i	0.890346	+	0.455284i	$0.150462\pi$
$107$	1.73164e19i	0.910568i	−0.890346	+	0.455284i	$0.849538\pi$
$108$	1.80462e18i	0.0868683i
$109$	−1.57748e19	−0.695685	−0.347842	−	0.937553i	$-0.613086\pi$
$109$	−1.57748e19	−0.695685	−0.347842	+	0.937553i	$0.613086\pi$
$110$	0	0
$111$	−2.67116e19	−0.991132
$112$	1.07764e19i	0.367201i
$113$	4.78817e19i	1.49942i	0.661764	+	0.749712i	$0.269808\pi$
$113$	4.78817e19i	1.49942i	−0.661764	+	0.749712i	$0.730192\pi$
$114$	−1.29077e19	−0.371752
$115$	0	0
$116$	−3.63850e19	−0.888323
$117$	2.22818e19i	0.501400i
$118$	1.45175e19i	0.301309i
$119$	−7.78785e19	−1.49184
$120$	0	0
$121$	−1.97947e19	−0.323659
$122$	− 2.74343e19i	− 0.414836i
$123$	1.13258e19i	0.158478i
$124$	9.29747e18	0.120464
$125$	0	0
$126$	−2.36199e19	−0.262880
$127$	1.25232e20i	1.29294i	0.762938	+	0.646472i	$0.223756\pi$
$127$	1.25232e20i	1.29294i	−0.762938	+	0.646472i	$0.776244\pi$
$128$	1.19478e19i	0.114497i
$129$	6.62661e18	0.0589779
$130$	0	0
$131$	−2.09329e20	−1.60972	−0.804862	−	0.593462i	$-0.797761\pi$
$131$	−2.09329e20	−1.60972	−0.804862	+	0.593462i	$0.797761\pi$
$132$	− 2.99583e19i	− 0.214321i
$133$	1.38999e20i	0.925595i
$134$	1.11252e20	0.689941
$135$	0	0
$136$	2.79586e20	1.50624
$137$	− 1.53205e20i	− 0.769888i	−0.922940	−	0.384944i	$-0.874221\pi$
$137$	− 1.53205e20i	− 0.769888i	0.922940	−	0.384944i	$-0.125779\pi$
$138$	5.30169e19i	0.248636i
$139$	2.54374e19	0.111386	0.0556932	−	0.998448i	$-0.482263\pi$
$139$	2.54374e19	0.111386	0.0556932	+	0.998448i	$0.482263\pi$
$140$	0	0
$141$	1.37781e20	0.526752
$142$	− 1.26100e20i	− 0.450792i
$143$	− 3.69897e20i	− 1.23705i
$144$	3.67268e19	0.114958
$145$	0	0
$146$	−3.98942e19	−0.109536
$147$	2.99903e19i	0.0771732i
$148$	− 3.21160e20i	− 0.774882i
$149$	−1.67659e20	−0.379453	−0.189727	−	0.981837i	$-0.560760\pi$
$149$	−1.67659e20	−0.379453	−0.189727	+	0.981837i	$0.560760\pi$
$150$	0	0
$151$	−4.29868e20	−0.857144	−0.428572	−	0.903508i	$-0.640983\pi$
$151$	−4.29868e20	−0.857144	−0.428572	+	0.903508i	$0.640983\pi$
$152$	− 4.99010e20i	− 0.934533i
$153$	2.65415e20i	0.467043i
$154$	3.92110e20	0.648577
$155$	0	0
$156$	−2.67900e20	−0.392002
$157$	− 9.16306e20i	− 1.26181i	−0.775860	−	0.630905i	$-0.782684\pi$
$157$	− 9.16306e20i	− 1.26181i	0.775860	−	0.630905i	$-0.217316\pi$
$158$	3.74722e20i	0.485810i
$159$	3.34405e20	0.408320
$160$	0	0
$161$	5.70923e20	0.619058
$162$	8.04981e19i	0.0822987i
$163$	4.50070e20i	0.434008i	0.976171	+	0.217004i	$0.0696284\pi$
$163$	4.50070e20i	0.434008i	−0.976171	+	0.217004i	$0.930372\pi$
$164$	−1.36173e20	−0.123901
$165$	0	0
$166$	−1.74588e21	−1.41575
$167$	1.62414e20i	0.124399i	0.998064	+	0.0621993i	$0.0198115\pi$
$167$	1.62414e20i	0.124399i	−0.998064	+	0.0621993i	$0.980189\pi$
$168$	− 9.13140e20i	− 0.660844i
$169$	−1.84585e21	−1.26262
$170$	0	0
$171$	4.73718e20	0.289772
$172$	7.96734e19i	0.0461098i
$173$	− 3.29538e21i	− 1.80496i	−0.430731	−	0.902481i	$-0.641744\pi$
$173$	− 3.29538e21i	− 1.80496i	0.430731	−	0.902481i	$-0.358256\pi$
$174$	−1.62301e21	−0.841594
$175$	0	0
$176$	−6.09697e20	−0.283625
$177$	− 5.32797e20i	− 0.234864i
$178$	7.70017e20i	0.321744i
$179$	9.81720e20	0.388941	0.194471	−	0.980908i	$-0.437701\pi$
$179$	9.81720e20	0.388941	0.194471	+	0.980908i	$0.437701\pi$
$180$	0	0
$181$	1.51701e20	0.0540807	0.0270403	−	0.999634i	$-0.491392\pi$
$181$	1.51701e20	0.0540807	0.0270403	+	0.999634i	$0.491392\pi$
$182$	− 3.50641e21i	− 1.18627i
$183$	1.00685e21i	0.323355i
$184$	−2.04963e21	−0.625037
$185$	0	0
$186$	4.14728e20	0.114128
$187$	− 4.40612e21i	− 1.15229i
$188$	1.65657e21i	0.411823i
$189$	8.66858e20	0.204909
$190$	0	0
$191$	−5.13044e21	−1.09733	−0.548666	−	0.836042i	$-0.684864\pi$
$191$	−5.13044e21	−1.09733	−0.548666	+	0.836042i	$0.684864\pi$
$192$	2.70025e21i	0.549594i
$193$	− 9.72873e21i	− 1.88478i	−0.334510	−	0.942392i	$-0.608571\pi$
$193$	− 9.72873e21i	− 1.88478i	0.334510	−	0.942392i	$-0.391429\pi$
$194$	8.95169e20	0.165116
$195$	0	0
$196$	−3.60581e20	−0.0603351
$197$	− 7.68506e21i	− 1.22523i	−0.790381	−	0.612616i	$-0.790117\pi$
$197$	− 7.68506e21i	− 1.22523i	0.790381	−	0.612616i	$-0.209883\pi$
$198$	− 1.33634e21i	− 0.203047i
$199$	−4.55786e21	−0.660172	−0.330086	−	0.943951i	$-0.607078\pi$
$199$	−4.55786e21	−0.660172	−0.330086	+	0.943951i	$0.607078\pi$
$200$	0	0
$201$	−4.08299e21	−0.537794
$202$	5.35816e21i	0.673252i
$203$	1.74777e22i	2.09542i
$204$	−3.19115e21	−0.365141
$205$	0	0
$206$	−6.30174e20	−0.0657237
$207$	− 1.94574e21i	− 0.193806i
$208$	5.45216e21i	0.518761i
$209$	−7.86413e21	−0.714926
$210$	0	0
$211$	−1.71334e22	−1.42285	−0.711426	−	0.702761i	$-0.751950\pi$
$211$	−1.71334e22	−1.42285	−0.711426	+	0.702761i	$0.751950\pi$
$212$	4.02064e21i	0.319230i
$213$	4.62793e21i	0.351383i
$214$	−9.28707e21	−0.674447
$215$	0	0
$216$	−3.11204e21	−0.206888
$217$	− 4.46607e21i	− 0.284157i
$218$	− 8.46028e21i	− 0.515286i
$219$	1.46414e21	0.0853812
$220$	0	0
$221$	−3.94014e22	−2.10758
$222$	− 1.43258e22i	− 0.734120i
$223$	3.17895e22i	1.56095i	0.625189	+	0.780473i	$0.285022\pi$
$223$	3.17895e22i	1.56095i	−0.625189	+	0.780473i	$0.714978\pi$
$224$	1.85434e22	0.872634
$225$	0	0
$226$	−2.56797e22	−1.11061
$227$	− 2.55774e22i	− 1.06074i	−0.847765	−	0.530372i	$-0.822052\pi$
$227$	− 2.55774e22i	− 1.06074i	0.847765	−	0.530372i	$-0.177948\pi$
$228$	5.69563e21i	0.226548i
$229$	2.23445e22	0.852576	0.426288	−	0.904588i	$-0.359821\pi$
$229$	2.23445e22	0.852576	0.426288	+	0.904588i	$0.359821\pi$
$230$	0	0
$231$	−1.43906e22	−0.505551
$232$	− 6.27452e22i	− 2.11565i
$233$	− 2.52369e21i	− 0.0816874i	−0.999166	−	0.0408437i	$-0.986995\pi$
$233$	− 2.52369e21i	− 0.0816874i	0.999166	−	0.0408437i	$-0.0130046\pi$
$234$	−1.19501e22	−0.371381
$235$	0	0
$236$	6.40595e21	0.183620
$237$	− 1.37524e22i	− 0.378678i
$238$	− 4.17675e22i	− 1.10499i
$239$	−3.93020e22	−0.999158	−0.499579	−	0.866268i	$-0.666512\pi$
$239$	−3.93020e22	−0.999158	−0.499579	+	0.866268i	$0.666512\pi$
$240$	0	0
$241$	−1.99943e22	−0.469618	−0.234809	−	0.972042i	$-0.575447\pi$
$241$	−1.99943e22	−0.469618	−0.234809	+	0.972042i	$0.575447\pi$
$242$	− 1.06162e22i	− 0.239730i
$243$	− 2.95431e21i	− 0.0641500i
$244$	−1.21056e22	−0.252804
$245$	0	0
$246$	−6.07420e21	−0.117383
$247$	7.03242e22i	1.30763i
$248$	1.60333e22i	0.286901i
$249$	6.40745e22	1.10355
$250$	0	0
$251$	−4.94152e22	−0.788788	−0.394394	−	0.918942i	$-0.629045\pi$
$251$	−4.94152e22	−0.788788	−0.394394	+	0.918942i	$0.629045\pi$
$252$	1.04225e22i	0.160201i
$253$	3.23010e22i	0.478158i
$254$	−6.71638e22	−0.957668
$255$	0	0
$256$	−7.83332e22	−1.03673
$257$	− 1.79354e22i	− 0.228742i	−0.993438	−	0.114371i	$-0.963515\pi$
$257$	− 1.79354e22i	− 0.228742i	0.993438	−	0.114371i	$-0.0364853\pi$
$258$	3.55395e21i	0.0436842i
$259$	−1.54271e23	−1.82783
$260$	0	0
$261$	5.95650e22	0.656004
$262$	− 1.12266e23i	− 1.19230i
$263$	2.64384e22i	0.270804i	0.990791	+	0.135402i	$0.0432327\pi$
$263$	2.64384e22i	0.270804i	−0.990791	+	0.135402i	$0.956767\pi$
$264$	5.16626e22	0.510434
$265$	0	0
$266$	−7.45473e22	−0.685577
$267$	− 2.82599e22i	− 0.250792i
$268$	− 4.90908e22i	− 0.420455i
$269$	6.26512e22	0.517944	0.258972	−	0.965885i	$-0.416616\pi$
$269$	6.26512e22	0.517944	0.258972	+	0.965885i	$0.416616\pi$
$270$	0	0
$271$	−8.23488e22	−0.634525	−0.317263	−	0.948338i	$-0.602764\pi$
$271$	−8.23488e22	−0.634525	−0.317263	+	0.948338i	$0.602764\pi$
$272$	6.49448e22i	0.483214i
$273$	1.28687e23i	0.924673i
$274$	8.21662e22	0.570247
$275$	0	0
$276$	2.33942e22	0.151520
$277$	− 1.42704e23i	− 0.893057i	−0.894769	−	0.446528i	$-0.852660\pi$
$277$	− 1.42704e23i	− 0.893057i	0.894769	−	0.446528i	$-0.147340\pi$
$278$	1.36425e22i	0.0825026i
$279$	−1.52207e22	−0.0889599
$280$	0	0
$281$	4.36986e22	0.238648	0.119324	−	0.992855i	$-0.461927\pi$
$281$	4.36986e22	0.238648	0.119324	+	0.992855i	$0.461927\pi$
$282$	7.38939e22i	0.390159i
$283$	− 2.42461e23i	− 1.23786i	−0.785447	−	0.618929i	$-0.787567\pi$
$283$	− 2.42461e23i	− 1.23786i	0.785447	−	0.618929i	$-0.212433\pi$
$284$	−5.56427e22	−0.274716
$285$	0	0
$286$	1.98382e23	0.916272
$287$	6.54112e22i	0.292263i
$288$	− 6.31970e22i	− 0.273192i
$289$	−2.30266e23	−0.963166
$290$	0	0
$291$	−3.28531e22	−0.128704
$292$	1.76037e22i	0.0667522i
$293$	1.65262e22i	0.0606638i	0.999540	+	0.0303319i	$0.00965643\pi$
$293$	1.65262e22i	0.0606638i	−0.999540	+	0.0303319i	$0.990344\pi$
$294$	−1.60843e22	−0.0571613
$295$	0	0
$296$	5.53835e23	1.84548
$297$	4.90442e22i	0.158271i
$298$	− 8.99184e22i	− 0.281057i
$299$	2.88849e23	0.874570
$300$	0	0
$301$	3.82714e22	0.108766
$302$	− 2.30545e23i	− 0.634876i
$303$	− 1.96647e23i	− 0.524785i
$304$	1.15915e23	0.299805
$305$	0	0
$306$	−1.42346e23	−0.345934
$307$	7.14354e23i	1.68306i	0.540213	+	0.841528i	$0.318344\pi$
$307$	7.14354e23i	1.68306i	−0.540213	+	0.841528i	$0.681656\pi$
$308$	− 1.73022e23i	− 0.395247i
$309$	2.31276e22	0.0512302
$310$	0	0
$311$	3.74882e23	0.781037	0.390518	−	0.920595i	$-0.372296\pi$
$311$	3.74882e23	0.781037	0.390518	+	0.920595i	$0.372296\pi$
$312$	− 4.61988e23i	− 0.933603i
$313$	− 2.04132e23i	− 0.400166i	−0.979779	−	0.200083i	$-0.935879\pi$
$313$	− 2.04132e23i	− 0.400166i	0.979779	−	0.200083i	$-0.0641211\pi$
$314$	4.91429e23	0.934607
$315$	0	0
$316$	1.65349e23	0.296056
$317$	2.74437e23i	0.476848i	0.971161	+	0.238424i	$0.0766308\pi$
$317$	2.74437e23i	0.476848i	−0.971161	+	0.238424i	$0.923369\pi$
$318$	1.79347e23i	0.302438i
$319$	−9.88832e23	−1.61849
$320$	0	0
$321$	3.40839e23	0.525717
$322$	3.06195e23i	0.458529i
$323$	8.37684e23i	1.21803i
$324$	3.55204e22	0.0501534
$325$	0	0
$326$	−2.41379e23	−0.321464
$327$	3.10496e23i	0.401654i
$328$	− 2.34828e23i	− 0.295085i
$329$	7.95740e23	0.971427
$330$	0	0
$331$	−2.31592e23	−0.266906	−0.133453	−	0.991055i	$-0.542607\pi$
$331$	−2.31592e23	−0.266906	−0.133453	+	0.991055i	$0.542607\pi$
$332$	7.70384e23i	0.862771i
$333$	5.25764e23i	0.572230i
$334$	−8.71049e22	−0.0921406
$335$	0	0
$336$	2.12113e23	0.212004
$337$	1.11237e23i	0.108085i	0.998539	+	0.0540425i	$0.0172106\pi$
$337$	1.11237e23i	0.108085i	−0.998539	+	0.0540425i	$0.982789\pi$
$338$	− 9.89960e23i	− 0.935209i
$339$	9.42456e23	0.865693
$340$	0	0
$341$	2.52677e23	0.219482
$342$	2.54062e23i	0.214631i
$343$	− 1.12259e24i	− 0.922417i
$344$	−1.37395e23	−0.109816
$345$	0	0
$346$	1.76737e24	1.33691
$347$	− 2.05609e24i	− 1.51326i	−0.653844	−	0.756629i	$-0.726845\pi$
$347$	− 2.05609e24i	− 1.51326i	0.653844	−	0.756629i	$-0.273155\pi$
$348$	7.16165e23i	0.512874i
$349$	1.75492e24	1.22297	0.611487	−	0.791255i	$-0.290572\pi$
$349$	1.75492e24	1.22297	0.611487	+	0.791255i	$0.290572\pi$
$350$	0	0
$351$	4.38573e23	0.289484
$352$	1.04913e24i	0.674019i
$353$	8.21430e23i	0.513702i	0.966451	+	0.256851i	$0.0826849\pi$
$353$	8.21430e23i	0.513702i	−0.966451	+	0.256851i	$0.917315\pi$
$354$	2.85747e23	0.173961
$355$	0	0
$356$	3.39776e23	0.196073
$357$	1.53288e24i	0.861313i
$358$	5.26512e23i	0.288084i
$359$	−5.29683e23	−0.282240	−0.141120	−	0.989992i	$-0.545070\pi$
$359$	−5.29683e23	−0.282240	−0.141120	+	0.989992i	$0.545070\pi$
$360$	0	0
$361$	−4.83305e23	−0.244289
$362$	8.13596e22i	0.0400569i
$363$	3.89618e23i	0.186864i
$364$	−1.54723e24	−0.722923
$365$	0	0
$366$	−5.39990e23	−0.239505
$367$	2.30180e24i	0.994809i	0.867519	+	0.497404i	$0.165713\pi$
$367$	2.30180e24i	0.994809i	−0.867519	+	0.497404i	$0.834287\pi$
$368$	− 4.76106e23i	− 0.200516i
$369$	2.22926e23	0.0914976
$370$	0	0
$371$	1.93133e24	0.753016
$372$	− 1.83002e23i	− 0.0695501i
$373$	1.64953e24i	0.611120i	0.952173	+	0.305560i	$0.0988437\pi$
$373$	1.64953e24i	0.611120i	−0.952173	+	0.305560i	$0.901156\pi$
$374$	2.36307e24	0.853487
$375$	0	0
$376$	−2.85673e24	−0.980808
$377$	8.84253e24i	2.96029i
$378$	4.64910e23i	0.151774i
$379$	−3.36454e24	−1.07116	−0.535579	−	0.844485i	$-0.679906\pi$
$379$	−3.36454e24	−1.07116	−0.535579	+	0.844485i	$0.679906\pi$
$380$	0	0
$381$	2.46494e24	0.746482
$382$	− 2.75154e24i	− 0.812780i
$383$	1.55219e24i	0.447257i	0.974674	+	0.223628i	$0.0717902\pi$
$383$	1.55219e24i	0.447257i	−0.974674	+	0.223628i	$0.928210\pi$
$384$	2.35168e23	0.0661046
$385$	0	0
$386$	5.21767e24	1.39604
$387$	− 1.30432e23i	− 0.0340509i
$388$	− 3.95000e23i	− 0.100623i
$389$	1.19996e23	0.0298295	0.0149148	−	0.999889i	$-0.495252\pi$
$389$	1.19996e23	0.0298295	0.0149148	+	0.999889i	$0.495252\pi$
$390$	0	0
$391$	3.44070e24	0.814643
$392$	− 6.21815e23i	− 0.143696i
$393$	4.12022e24i	0.929375i
$394$	4.12162e24	0.907515
$395$	0	0
$396$	−5.89670e23	−0.123738
$397$	1.23812e24i	0.253661i	0.991924	+	0.126831i	$0.0404805\pi$
$397$	1.23812e24i	0.253661i	−0.991924	+	0.126831i	$0.959520\pi$
$398$	− 2.44445e24i	− 0.488981i
$399$	2.73592e24	0.534392
$400$	0	0
$401$	−6.55287e24	−1.22056	−0.610281	−	0.792185i	$-0.708943\pi$
$401$	−6.55287e24	−1.22056	−0.610281	+	0.792185i	$0.708943\pi$
$402$	− 2.18977e24i	− 0.398338i
$403$	− 2.25954e24i	− 0.401441i
$404$	2.36433e24	0.410285
$405$	0	0
$406$	−9.37354e24	−1.55205
$407$	− 8.72815e24i	− 1.41181i
$408$	− 5.50309e24i	− 0.869631i
$409$	−8.56848e24	−1.32292	−0.661458	−	0.749982i	$-0.730062\pi$
$409$	−8.56848e24	−1.32292	−0.661458	+	0.749982i	$0.730062\pi$
$410$	0	0
$411$	−3.01553e24	−0.444495
$412$	2.78069e23i	0.0400525i
$413$	− 3.07712e24i	− 0.433131i
$414$	1.04353e24	0.143550
$415$	0	0
$416$	9.38171e24	1.23281
$417$	− 5.00685e23i	− 0.0643090i
$418$	− 4.21766e24i	− 0.529537i
$419$	−8.09987e24	−0.994134	−0.497067	−	0.867712i	$-0.665590\pi$
$419$	−8.09987e24	−0.994134	−0.497067	+	0.867712i	$0.665590\pi$
$420$	0	0
$421$	9.99748e24	1.17276	0.586382	−	0.810035i	$-0.300552\pi$
$421$	9.99748e24	1.17276	0.586382	+	0.810035i	$0.300552\pi$
$422$	− 9.18890e24i	− 1.05389i
$423$	− 2.71194e24i	− 0.304121i
$424$	−6.93352e24	−0.760288
$425$	0	0
$426$	−2.48203e24	−0.260265
$427$	5.81498e24i	0.596326i
$428$	4.09799e24i	0.411013i
$429$	−7.28069e24	−0.714214
$430$	0	0
$431$	−4.59733e24	−0.431491	−0.215745	−	0.976450i	$-0.569218\pi$
$431$	−4.59733e24	−0.431491	−0.215745	+	0.976450i	$0.569218\pi$
$432$	− 7.22894e23i	− 0.0663711i
$433$	− 7.51468e24i	− 0.674956i	−0.941333	−	0.337478i	$-0.890426\pi$
$433$	− 7.51468e24i	− 0.674956i	0.941333	−	0.337478i	$-0.109574\pi$
$434$	2.39523e24	0.210472
$435$	0	0
$436$	−3.73317e24	−0.314019
$437$	− 6.14102e24i	− 0.505436i
$438$	7.85238e23i	0.0632408i
$439$	2.04197e25	1.60930	0.804649	−	0.593751i	$-0.202353\pi$
$439$	2.04197e25	1.60930	0.804649	+	0.593751i	$0.202353\pi$
$440$	0	0
$441$	5.90299e23	0.0445560
$442$	− 2.11316e25i	− 1.56106i
$443$	− 1.84340e25i	− 1.33286i	−0.745569	−	0.666428i	$-0.767822\pi$
$443$	− 1.84340e25i	− 1.33286i	0.745569	−	0.666428i	$-0.232178\pi$
$444$	−6.32140e24	−0.447378
$445$	0	0
$446$	−1.70492e25	−1.15617
$447$	3.30004e24i	0.219077i
$448$	1.55951e25i	1.01355i
$449$	−7.82616e24	−0.497976	−0.248988	−	0.968507i	$-0.580098\pi$
$449$	−7.82616e24	−0.497976	−0.248988	+	0.968507i	$0.580098\pi$
$450$	0	0
$451$	−3.70076e24	−0.225743
$452$	1.13314e25i	0.676811i
$453$	8.46108e24i	0.494872i
$454$	1.37176e25	0.785681
$455$	0	0
$456$	−9.82201e24	−0.539553
$457$	− 2.15612e25i	− 1.16003i	−0.814606	−	0.580015i	$-0.803047\pi$
$457$	− 2.15612e25i	− 1.16003i	0.814606	−	0.580015i	$-0.196953\pi$
$458$	1.19837e25i	0.631493i
$459$	5.22417e24	0.269648
$460$	0	0
$461$	4.52754e24	0.224235	0.112118	−	0.993695i	$-0.464237\pi$
$461$	4.52754e24	0.224235	0.112118	+	0.993695i	$0.464237\pi$
$462$	− 7.71791e24i	− 0.374456i
$463$	1.12552e25i	0.534974i	0.963562	+	0.267487i	$0.0861932\pi$
$463$	1.12552e25i	0.534974i	−0.963562	+	0.267487i	$0.913807\pi$
$464$	1.45750e25	0.678717
$465$	0	0
$466$	1.35350e24	0.0605049
$467$	− 1.73792e25i	− 0.761237i	−0.924732	−	0.380618i	$-0.875711\pi$
$467$	− 1.73792e25i	− 0.761237i	0.924732	−	0.380618i	$-0.124289\pi$
$468$	5.27307e24i	0.226323i
$469$	−2.35810e25	−0.991790
$470$	0	0
$471$	−1.80356e25	−0.728506
$472$	1.10469e25i	0.437314i
$473$	2.16528e24i	0.0840104i
$474$	7.37565e24	0.280483
$475$	0	0
$476$	−1.84302e25	−0.673387
$477$	− 6.58210e24i	− 0.235744i
$478$	− 2.10783e25i	− 0.740065i
$479$	−4.26798e25	−1.46904	−0.734522	−	0.678585i	$-0.762593\pi$
$479$	−4.26798e25	−1.46904	−0.734522	+	0.678585i	$0.762593\pi$
$480$	0	0
$481$	−7.80506e25	−2.58225
$482$	− 1.07233e25i	− 0.347841i
$483$	− 1.12375e25i	− 0.357413i
$484$	−4.68448e24	−0.146093
$485$	0	0
$486$	1.58444e24	0.0475152
$487$	6.57071e24i	0.193236i	0.995322	+	0.0966178i	$0.0308024\pi$
$487$	6.57071e24i	0.193236i	−0.995322	+	0.0966178i	$0.969198\pi$
$488$	− 2.08759e25i	− 0.602085i
$489$	8.85872e24	0.250574
$490$	0	0
$491$	5.24168e25	1.42625	0.713126	−	0.701035i	$-0.247279\pi$
$491$	5.24168e25	1.42625	0.713126	+	0.701035i	$0.247279\pi$
$492$	2.68029e24i	0.0715342i
$493$	1.05330e26i	2.75744i
$494$	−3.77160e25	−0.968544
$495$	0	0
$496$	−3.72437e24	−0.0920400
$497$	2.67282e25i	0.648013i
$498$	3.43642e25i	0.817386i
$499$	2.55146e25	0.595434	0.297717	−	0.954654i	$-0.403775\pi$
$499$	2.55146e25	0.595434	0.297717	+	0.954654i	$0.403775\pi$
$500$	0	0
$501$	3.19679e24	0.0718216
$502$	− 2.65021e25i	− 0.584246i
$503$	− 5.69466e25i	− 1.23189i	−0.787789	−	0.615945i	$-0.788775\pi$
$503$	− 5.69466e25i	− 1.23189i	0.787789	−	0.615945i	$-0.211225\pi$
$504$	−1.79733e25	−0.381539
$505$	0	0
$506$	−1.73236e25	−0.354166
$507$	3.63319e25i	0.728975i
$508$	2.96366e25i	0.583610i
$509$	3.26878e25	0.631781	0.315891	−	0.948796i	$-0.397697\pi$
$509$	3.26878e25	0.631781	0.315891	+	0.948796i	$0.397697\pi$
$510$	0	0
$511$	8.45598e24	0.157458
$512$	− 3.57472e25i	− 0.653398i
$513$	− 9.32419e24i	− 0.167300i
$514$	9.61903e24	0.169427
$515$	0	0
$516$	1.56821e24	0.0266215
$517$	4.50205e25i	0.750326i
$518$	− 8.27377e25i	− 1.35385i
$519$	−6.48630e25	−1.04209
$520$	0	0
$521$	−9.30404e25	−1.44116	−0.720581	−	0.693370i	$-0.756125\pi$
$521$	−9.30404e25	−1.44116	−0.720581	+	0.693370i	$0.756125\pi$
$522$	3.19457e25i	0.485895i
$523$	4.88002e25i	0.728879i	0.931227	+	0.364440i	$0.118739\pi$
$523$	4.88002e25i	0.728879i	−0.931227	+	0.364440i	$0.881261\pi$
$524$	−4.95384e25	−0.726599
$525$	0	0
$526$	−1.41793e25	−0.200582
$527$	− 2.69150e25i	− 0.373933i
$528$	1.20007e25i	0.163751i
$529$	4.93919e25	0.661953
$530$	0	0
$531$	−1.04870e25	−0.135599
$532$	3.28946e25i	0.417796i
$533$	3.30937e25i	0.412892i
$534$	1.51562e25	0.185759
$535$	0	0
$536$	8.46562e25	1.00137
$537$	− 1.93232e25i	− 0.224555i
$538$	3.36008e25i	0.383635i
$539$	−9.79948e24	−0.109928
$540$	0	0
$541$	8.45858e25	0.916059	0.458030	−	0.888937i	$-0.348555\pi$
$541$	8.45858e25	0.916059	0.458030	+	0.888937i	$0.348555\pi$
$542$	− 4.41649e25i	− 0.469985i
$543$	− 2.98593e24i	− 0.0312235i
$544$	1.11753e26	1.14833
$545$	0	0
$546$	−6.90167e25	−0.684895
$547$	2.08591e25i	0.203430i	0.994814	+	0.101715i	$0.0324330\pi$
$547$	2.08591e25i	0.203430i	−0.994814	+	0.101715i	$0.967567\pi$
$548$	− 3.62565e25i	− 0.347513i
$549$	1.98179e25	0.186689
$550$	0	0
$551$	1.87995e26	1.71083
$552$	4.03428e25i	0.360865i
$553$	− 7.94260e25i	− 0.698352i
$554$	7.65345e25	0.661477
$555$	0	0
$556$	6.01985e24	0.0502777
$557$	1.19573e25i	0.0981768i	0.998794	+	0.0490884i	$0.0156316\pi$
$557$	1.19573e25i	0.0981768i	−0.998794	+	0.0490884i	$0.984368\pi$
$558$	− 8.16309e24i	− 0.0658916i
$559$	1.93628e25	0.153658
$560$	0	0
$561$	−8.67257e25	−0.665274
$562$	2.34362e25i	0.176764i
$563$	− 1.51109e26i	− 1.12063i	−0.828281	−	0.560313i	$-0.810681\pi$
$563$	− 1.51109e26i	− 1.12063i	0.828281	−	0.560313i	$-0.189319\pi$
$564$	3.26063e25	0.237766
$565$	0	0
$566$	1.30036e26	0.916866
$567$	− 1.70624e25i	− 0.118304i
$568$	− 9.59549e25i	− 0.654271i
$569$	1.31930e26	0.884661	0.442331	−	0.896852i	$-0.354152\pi$
$569$	1.31930e26	0.884661	0.442331	+	0.896852i	$0.354152\pi$
$570$	0	0
$571$	2.65239e26	1.72026	0.860130	−	0.510076i	$-0.170383\pi$
$571$	2.65239e26	1.72026	0.860130	+	0.510076i	$0.170383\pi$
$572$	− 8.75375e25i	− 0.558383i
$573$	1.00982e26i	0.633544i
$574$	−3.50810e25	−0.216476
$575$	0	0
$576$	5.31490e25	0.317308
$577$	9.99355e25i	0.586880i	0.955977	+	0.293440i	$0.0948001\pi$
$577$	9.99355e25i	0.586880i	−0.955977	+	0.293440i	$0.905200\pi$
$578$	− 1.23496e26i	− 0.713406i
$579$	−1.91491e26	−1.08818
$580$	0	0
$581$	3.70057e26	2.03514
$582$	− 1.76196e25i	− 0.0953296i
$583$	1.09269e26i	0.581626i
$584$	−3.03572e25	−0.158979
$585$	0	0
$586$	−8.86324e24	−0.0449330
$587$	1.90494e26i	0.950209i	0.879930	+	0.475104i	$0.157590\pi$
$587$	1.90494e26i	0.950209i	−0.879930	+	0.475104i	$0.842410\pi$
$588$	7.09732e24i	0.0348345i
$589$	−4.80384e25	−0.232003
$590$	0	0
$591$	−1.51265e26	−0.707388
$592$	1.28650e26i	0.592043i
$593$	− 2.37669e26i	− 1.07635i	−0.842834	−	0.538173i	$-0.819115\pi$
$593$	− 2.37669e26i	− 1.07635i	0.842834	−	0.538173i	$-0.180885\pi$
$594$	−2.63032e25	−0.117229
$595$	0	0
$596$	−3.96772e25	−0.171278
$597$	8.97124e25i	0.381150i
$598$	1.54914e26i	0.647784i
$599$	3.08975e26	1.27165	0.635826	−	0.771832i	$-0.280659\pi$
$599$	3.08975e26	1.27165	0.635826	+	0.771832i	$0.280659\pi$
$600$	0	0
$601$	−2.61533e26	−1.04284	−0.521421	−	0.853299i	$-0.674598\pi$
$601$	−2.61533e26	−1.04284	−0.521421	+	0.853299i	$0.674598\pi$
$602$	2.05256e25i	0.0805616i
$603$	8.03655e25i	0.310496i
$604$	−1.01730e26	−0.386898
$605$	0	0
$606$	1.05465e26	0.388702
$607$	− 5.37620e25i	− 0.195067i	−0.995232	−	0.0975334i	$-0.968905\pi$
$607$	− 5.37620e25i	− 0.195067i	0.995232	−	0.0975334i	$-0.0310953\pi$
$608$	− 1.99458e26i	− 0.712471i
$609$	3.44013e26	1.20979
$610$	0	0
$611$	4.02591e26	1.37238
$612$	6.28115e25i	0.210814i
$613$	3.16087e26i	1.04456i	0.852775	+	0.522278i	$0.174918\pi$
$613$	3.16087e26i	1.04456i	−0.852775	+	0.522278i	$0.825082\pi$
$614$	−3.83119e26	−1.24662
$615$	0	0
$616$	2.98373e26	0.941332
$617$	− 1.98562e26i	− 0.616862i	−0.951247	−	0.308431i	$-0.900196\pi$
$617$	− 1.98562e26i	− 0.616862i	0.951247	−	0.308431i	$-0.0998038\pi$
$618$	1.24037e25i	0.0379456i
$619$	4.82992e26	1.45505	0.727527	−	0.686080i	$-0.240670\pi$
$619$	4.82992e26	1.45505	0.727527	+	0.686080i	$0.240670\pi$
$620$	0	0
$621$	−3.82981e25	−0.111894
$622$	2.01055e26i	0.578505i
$623$	− 1.63213e26i	− 0.462507i
$624$	1.07315e26	0.299507
$625$	0	0
$626$	1.09479e26	0.296398
$627$	1.54790e26i	0.412763i
$628$	− 2.16847e26i	− 0.569556i
$629$	−9.29719e26	−2.40531
$630$	0	0
$631$	−6.27693e26	−1.57568	−0.787841	−	0.615879i	$-0.788801\pi$
$631$	−6.27693e26	−1.57568	−0.787841	+	0.615879i	$0.788801\pi$
$632$	2.85141e26i	0.705096i
$633$	3.37236e26i	0.821484i
$634$	−1.47185e26	−0.353196
$635$	0	0
$636$	7.91382e25	0.184308
$637$	8.76310e25i	0.201063i
$638$	− 5.30326e26i	− 1.19880i
$639$	9.10915e25	0.202871
$640$	0	0
$641$	2.15915e26	0.466800	0.233400	−	0.972381i	$-0.425015\pi$
$641$	2.15915e26	0.466800	0.233400	+	0.972381i	$0.425015\pi$
$642$	1.82797e26i	0.389392i
$643$	4.68779e26i	0.983929i	0.870615	+	0.491964i	$0.163721\pi$
$643$	4.68779e26i	0.983929i	−0.870615	+	0.491964i	$0.836279\pi$
$644$	1.35111e26	0.279431
$645$	0	0
$646$	−4.49263e26	−0.902177
$647$	2.10829e26i	0.417196i	0.978001	+	0.208598i	$0.0668900\pi$
$647$	2.10829e26i	0.417196i	−0.978001	+	0.208598i	$0.933110\pi$
$648$	6.12543e25i	0.119447i
$649$	1.74094e26	0.334549
$650$	0	0
$651$	−8.79057e25	−0.164058
$652$	1.06511e26i	0.195903i
$653$	2.88194e26i	0.522408i	0.965284	+	0.261204i	$0.0841195\pi$
$653$	2.88194e26i	0.522408i	−0.965284	+	0.261204i	$0.915880\pi$
$654$	−1.66524e26	−0.297500
$655$	0	0
$656$	5.45480e25	0.0946656
$657$	− 2.88186e25i	− 0.0492948i
$658$	4.26768e26i	0.719524i
$659$	7.36091e26	1.22326	0.611632	−	0.791143i	$-0.290514\pi$
$659$	7.36091e26	1.22326	0.611632	+	0.791143i	$0.290514\pi$
$660$	0	0
$661$	3.05440e25	0.0493187	0.0246594	−	0.999696i	$-0.492150\pi$
$661$	3.05440e25	0.0493187	0.0246594	+	0.999696i	$0.492150\pi$
$662$	− 1.24207e26i	− 0.197694i
$663$	7.75537e26i	1.21681i
$664$	−1.32851e27	−2.05480
$665$	0	0
$666$	−2.81976e26	−0.423844
$667$	− 7.72168e26i	− 1.14424i
$668$	3.84357e25i	0.0561512i
$669$	6.25713e26	0.901213
$670$	0	0
$671$	−3.28994e26	−0.460600
$672$	− 3.64989e26i	− 0.503816i
$673$	− 9.62645e26i	− 1.31016i	−0.755561	−	0.655078i	$-0.772636\pi$
$673$	− 9.62645e26i	− 1.31016i	0.755561	−	0.655078i	$-0.227364\pi$
$674$	−5.96582e25	−0.0800573
$675$	0	0
$676$	−4.36828e26	−0.569923
$677$	− 1.18974e27i	− 1.53059i	−0.643680	−	0.765295i	$-0.722593\pi$
$677$	− 1.18974e27i	− 1.53059i	0.643680	−	0.765295i	$-0.277407\pi$
$678$	5.05454e26i	0.641208i
$679$	−1.89740e26	−0.237354
$680$	0	0
$681$	−5.03440e26	−0.612421
$682$	1.35514e26i	0.162568i
$683$	− 1.51240e27i	− 1.78925i	−0.446819	−	0.894624i	$-0.647443\pi$
$683$	− 1.51240e27i	− 1.78925i	0.446819	−	0.894624i	$-0.352557\pi$
$684$	1.12107e26	0.130798
$685$	0	0
$686$	6.02063e26	0.683224
$687$	− 4.39806e26i	− 0.492235i
$688$	− 3.19155e25i	− 0.0352299i
$689$	9.77124e26	1.06382
$690$	0	0
$691$	−1.40247e27	−1.48543	−0.742716	−	0.669606i	$-0.766463\pi$
$691$	−1.40247e27	−1.48543	−0.742716	+	0.669606i	$0.766463\pi$
$692$	− 7.79864e26i	− 0.814725i
$693$	2.83250e26i	0.291880i
$694$	1.10272e27	1.12085
$695$	0	0
$696$	−1.23501e27	−1.22147
$697$	3.94204e26i	0.384600i
$698$	9.41194e26i	0.905842i
$699$	−4.96738e25	−0.0471622
$700$	0	0
$701$	6.64167e26	0.613700	0.306850	−	0.951758i	$-0.400725\pi$
$701$	6.64167e26	0.613700	0.306850	+	0.951758i	$0.400725\pi$
$702$	2.35213e26i	0.214417i
$703$	1.65938e27i	1.49235i
$704$	−8.82320e26	−0.782863
$705$	0	0
$706$	−4.40546e26	−0.380493
$707$	− 1.13572e27i	− 0.967799i
$708$	− 1.26088e26i	− 0.106013i
$709$	−1.03445e27	−0.858163	−0.429081	−	0.903266i	$-0.641163\pi$
$709$	−1.03445e27	−0.858163	−0.429081	+	0.903266i	$0.641163\pi$
$710$	0	0
$711$	−2.70689e26	−0.218630
$712$	5.85938e26i	0.466973i
$713$	1.97313e26i	0.155169i
$714$	−8.22109e26	−0.637964
$715$	0	0
$716$	2.32328e26	0.175561
$717$	7.73581e26i	0.576864i
$718$	− 2.84077e26i	− 0.209052i
$719$	1.59383e26	0.115749	0.0578744	−	0.998324i	$-0.481568\pi$
$719$	1.59383e26	0.115749	0.0578744	+	0.998324i	$0.481568\pi$
$720$	0	0
$721$	1.33572e26	0.0944777
$722$	− 2.59204e26i	− 0.180942i
$723$	3.93548e26i	0.271134i
$724$	3.59006e25	0.0244110
$725$	0	0
$726$	−2.08958e26	−0.138408
$727$	− 1.66059e27i	− 1.08564i	−0.839850	−	0.542819i	$-0.817357\pi$
$727$	− 1.66059e27i	− 1.08564i	0.839850	−	0.542819i	$-0.182643\pi$
$728$	− 2.66817e27i	− 1.72173i
$729$	−5.81497e25	−0.0370370
$730$	0	0
$731$	2.30645e26	0.143129
$732$	2.38275e26i	0.145956i
$733$	− 1.36074e27i	− 0.822786i	−0.911458	−	0.411393i	$-0.865042\pi$
$733$	− 1.36074e27i	− 0.822786i	0.911458	−	0.411393i	$-0.134958\pi$
$734$	−1.23449e27	−0.736843
$735$	0	0
$736$	−8.19251e26	−0.476517
$737$	− 1.33414e27i	− 0.766054i
$738$	1.19559e26i	0.0677712i
$739$	−9.59784e26	−0.537095	−0.268548	−	0.963266i	$-0.586544\pi$
$739$	−9.59784e26	−0.537095	−0.268548	+	0.963266i	$0.586544\pi$
$740$	0	0
$741$	1.38419e27	0.754959
$742$	1.03580e27i	0.557750i
$743$	− 1.18287e27i	− 0.628846i	−0.949283	−	0.314423i	$-0.898189\pi$
$743$	− 1.18287e27i	− 0.628846i	0.949283	−	0.314423i	$-0.101811\pi$
$744$	3.15584e26	0.165643
$745$	0	0
$746$	−8.84670e26	−0.452650
$747$	− 1.26118e27i	− 0.637134i
$748$	− 1.04273e27i	− 0.520121i
$749$	1.96849e27	0.969516
$750$	0	0
$751$	−1.02382e27	−0.491637	−0.245819	−	0.969316i	$-0.579057\pi$
$751$	−1.02382e27	−0.491637	−0.245819	+	0.969316i	$0.579057\pi$
$752$	− 6.63587e26i	− 0.314650i
$753$	9.72639e26i	0.455407i
$754$	−4.74239e27	−2.19265
$755$	0	0
$756$	2.05145e26	0.0924920
$757$	− 2.74415e25i	− 0.0122179i	−0.999981	−	0.00610897i	$-0.998055\pi$
$757$	− 2.74415e25i	− 0.0122179i	0.999981	−	0.00610897i	$-0.00194456\pi$
$758$	− 1.80446e27i	− 0.793394i
$759$	6.35781e26	0.276065
$760$	0	0
$761$	1.89240e27	0.801416	0.400708	−	0.916206i	$-0.368764\pi$
$761$	1.89240e27	0.801416	0.400708	+	0.916206i	$0.368764\pi$
$762$	1.32199e27i	0.552910i
$763$	1.79324e27i	0.740722i
$764$	−1.21414e27	−0.495314
$765$	0	0
$766$	−8.32465e26	−0.331278
$767$	− 1.55682e27i	− 0.611902i
$768$	1.54183e27i	0.598557i
$769$	1.93865e27	0.743359	0.371679	−	0.928361i	$-0.378782\pi$
$769$	1.93865e27	0.743359	0.371679	+	0.928361i	$0.378782\pi$
$770$	0	0
$771$	−3.53022e26	−0.132064
$772$	− 2.30234e27i	− 0.850756i
$773$	− 7.63732e24i	− 0.00278764i	−0.999999	−	0.00139382i	$-0.999556\pi$
$773$	− 7.63732e24i	− 0.00278764i	0.999999	−	0.00139382i	$-0.000443666\pi$
$774$	6.99525e25	0.0252211
$775$	0	0
$776$	6.81171e26	0.239646
$777$	3.03651e27i	1.05530i
$778$	6.43559e25i	0.0220944i
$779$	7.03582e26	0.238621
$780$	0	0
$781$	−1.51220e27	−0.500523
$782$	1.84530e27i	0.603396i
$783$	− 1.17242e27i	− 0.378744i
$784$	1.44441e26	0.0460986
$785$	0	0
$786$	−2.20974e27	−0.688377
$787$	4.61341e27i	1.41991i	0.704246	+	0.709956i	$0.251285\pi$
$787$	4.61341e27i	1.41991i	−0.704246	+	0.709956i	$0.748715\pi$
$788$	− 1.81870e27i	− 0.553046i
$789$	5.20387e26	0.156349
$790$	0	0
$791$	5.44307e27	1.59649
$792$	− 1.01688e27i	− 0.294699i
$793$	2.94199e27i	0.842455i
$794$	−6.64025e26	−0.187884
$795$	0	0
$796$	−1.07863e27	−0.297989
$797$	− 1.01219e27i	− 0.276316i	−0.990410	−	0.138158i	$-0.955882\pi$
$797$	− 1.01219e27i	− 0.276316i	0.990410	−	0.138158i	$-0.0441182\pi$
$798$	1.46731e27i	0.395818i
$799$	4.79557e27	1.27834
$800$	0	0
$801$	−5.56240e26	−0.144795
$802$	− 3.51440e27i	− 0.904056i
$803$	4.78413e26i	0.121620i
$804$	−9.66255e26	−0.242750
$805$	0	0
$806$	1.21183e27	0.297343
$807$	− 1.23316e27i	− 0.299035i
$808$	4.07725e27i	0.977145i
$809$	−3.00853e27	−0.712597	−0.356298	−	0.934372i	$-0.615961\pi$
$809$	−3.00853e27	−0.712597	−0.356298	+	0.934372i	$0.615961\pi$
$810$	0	0
$811$	3.54753e27	0.820782	0.410391	−	0.911910i	$-0.365392\pi$
$811$	3.54753e27	0.820782	0.410391	+	0.911910i	$0.365392\pi$
$812$	4.13615e27i	0.945832i
$813$	1.62087e27i	0.366343i
$814$	4.68104e27	1.04571
$815$	0	0
$816$	1.27831e27	0.278984
$817$	− 4.11659e26i	− 0.0888030i
$818$	− 4.59541e27i	− 0.979869i
$819$	2.53294e27	0.533860
$820$	0	0
$821$	−4.28797e27	−0.883063	−0.441532	−	0.897246i	$-0.645565\pi$
$821$	−4.28797e27	−0.883063	−0.441532	+	0.897246i	$0.645565\pi$
$822$	− 1.61728e27i	− 0.329232i
$823$	3.20459e27i	0.644874i	0.946591	+	0.322437i	$0.104502\pi$
$823$	3.20459e27i	0.644874i	−0.946591	+	0.322437i	$0.895498\pi$
$824$	−4.79526e26	−0.0953901
$825$	0	0
$826$	1.65031e27	0.320815
$827$	4.02192e27i	0.772914i	0.922308	+	0.386457i	$0.126301\pi$
$827$	4.02192e27i	0.772914i	−0.922308	+	0.386457i	$0.873699\pi$
$828$	− 4.60467e26i	− 0.0874803i
$829$	1.58908e27	0.298455	0.149227	−	0.988803i	$-0.452321\pi$
$829$	1.58908e27	0.298455	0.149227	+	0.988803i	$0.452321\pi$
$830$	0	0
$831$	−2.80885e27	−0.515607
$832$	7.89006e27i	1.43189i
$833$	1.04384e27i	0.187286i
$834$	2.68525e26	0.0476329
$835$	0	0
$836$	−1.86107e27	−0.322704
$837$	2.99589e26i	0.0513610i
$838$	− 4.34409e27i	− 0.736343i
$839$	5.31813e27	0.891293	0.445646	−	0.895209i	$-0.352974\pi$
$839$	5.31813e27	0.891293	0.445646	+	0.895209i	$0.352974\pi$
$840$	0	0
$841$	1.75351e28	2.87307
$842$	5.36180e27i	0.868652i
$843$	− 8.60120e26i	− 0.137783i
$844$	−4.05467e27	−0.642248
$845$	0	0
$846$	1.45445e27	0.225259
$847$	2.25021e27i	0.344612i
$848$	− 1.61058e27i	− 0.243906i
$849$	−4.77236e27	−0.714677
$850$	0	0
$851$	6.81572e27	0.998115
$852$	1.09522e27i	0.158607i
$853$	− 1.60722e27i	− 0.230176i	−0.993355	−	0.115088i	$-0.963285\pi$
$853$	− 1.60722e27i	− 0.230176i	0.993355	−	0.115088i	$-0.0367150\pi$
$854$	−3.11867e27	−0.441691
$855$	0	0
$856$	−7.06692e27	−0.978879
$857$	− 8.25782e27i	− 1.13122i	−0.824672	−	0.565611i	$-0.808641\pi$
$857$	− 8.25782e27i	− 1.13122i	0.824672	−	0.565611i	$-0.191359\pi$
$858$	− 3.90475e27i	− 0.529010i
$859$	9.31408e27	1.24797	0.623986	−	0.781436i	$-0.285512\pi$
$859$	9.31408e27	1.24797	0.623986	+	0.781436i	$0.285512\pi$
$860$	0	0
$861$	1.28749e27	0.168738
$862$	− 2.46562e27i	− 0.319600i
$863$	6.65457e27i	0.853134i	0.904456	+	0.426567i	$0.140277\pi$
$863$	6.65457e27i	0.853134i	−0.904456	+	0.426567i	$0.859723\pi$
$864$	−1.24391e27	−0.157728
$865$	0	0
$866$	4.03024e27	0.499932
$867$	4.53234e27i	0.556084i
$868$	− 1.05691e27i	− 0.128263i
$869$	4.49368e27	0.539404
$870$	0	0
$871$	−1.19304e28	−1.40114
$872$	− 6.43778e27i	− 0.747876i
$873$	6.46647e26i	0.0743074i
$874$	3.29352e27	0.374371
$875$	0	0
$876$	3.46493e26	0.0385394
$877$	1.08073e27i	0.118911i	0.998231	+	0.0594554i	$0.0189364\pi$
$877$	1.08073e27i	0.118911i	−0.998231	+	0.0594554i	$0.981064\pi$
$878$	1.09514e28i	1.19199i
$879$	3.25285e26	0.0350243
$880$	0	0
$881$	−1.38540e28	−1.45983	−0.729916	−	0.683536i	$-0.760441\pi$
$881$	−1.38540e28	−1.45983	−0.729916	+	0.683536i	$0.760441\pi$
$882$	3.16587e26i	0.0330021i
$883$	6.76336e27i	0.697487i	0.937218	+	0.348743i	$0.113392\pi$
$883$	6.76336e27i	0.697487i	−0.937218	+	0.348743i	$0.886608\pi$
$884$	−9.32447e27	−0.951322
$885$	0	0
$886$	9.88642e27	0.987231
$887$	1.60903e28i	1.58960i	0.606869	+	0.794802i	$0.292425\pi$
$887$	1.60903e28i	1.58960i	−0.606869	+	0.794802i	$0.707575\pi$
$888$	− 1.09011e28i	− 1.06549i
$889$	1.42360e28	1.37665
$890$	0	0
$891$	9.65336e26	0.0913777
$892$	7.52311e27i	0.704581i
$893$	− 8.55921e27i	− 0.793131i
$894$	−1.76986e27	−0.162268
$895$	0	0
$896$	1.35819e27	0.121909
$897$	− 5.68541e27i	− 0.504933i
$898$	− 4.19729e27i	− 0.368845i
$899$	−6.04033e27	−0.525223
$900$	0	0
$901$	1.16393e28	0.990922
$902$	− 1.98478e27i	− 0.167205i
$903$	− 7.53296e26i	− 0.0627960i
$904$	−1.95408e28	−1.61191
$905$	0	0
$906$	−4.53781e27	−0.366546
$907$	4.87731e26i	0.0389862i	0.999810	+	0.0194931i	$0.00620524\pi$
$907$	4.87731e26i	0.0389862i	−0.999810	+	0.0194931i	$0.993795\pi$
$908$	− 6.05299e27i	− 0.478800i
$909$	−3.87060e27	−0.302985
$910$	0	0
$911$	2.04975e28	1.57136	0.785680	−	0.618634i	$-0.212313\pi$
$911$	2.04975e28	1.57136	0.785680	+	0.618634i	$0.212313\pi$
$912$	− 2.28155e27i	− 0.173093i
$913$	2.09367e28i	1.57194i
$914$	1.15636e28	0.859221
$915$	0	0
$916$	5.28790e27	0.384836
$917$	2.37960e28i	1.71394i
$918$	2.80180e27i	0.199725i
$919$	−7.36209e27	−0.519402	−0.259701	−	0.965689i	$-0.583624\pi$
$919$	−7.36209e27	−0.519402	−0.259701	+	0.965689i	$0.583624\pi$
$920$	0	0
$921$	1.40606e28	0.971713
$922$	2.42819e27i	0.166088i
$923$	1.35227e28i	0.915476i
$924$	−3.40559e27	−0.228196
$925$	0	0
$926$	−6.03632e27	−0.396249
$927$	− 4.55222e26i	− 0.0295778i
$928$	− 2.50797e28i	− 1.61294i
$929$	9.18844e27	0.584915	0.292457	−	0.956279i	$-0.405527\pi$
$929$	9.18844e27	0.584915	0.292457	+	0.956279i	$0.405527\pi$
$930$	0	0
$931$	1.86306e27	0.116200
$932$	− 5.97241e26i	− 0.0368721i
$933$	− 7.37881e27i	− 0.450932i
$934$	9.32074e27	0.563839
$935$	0	0
$936$	−9.09331e27	−0.539016
$937$	− 1.55615e28i	− 0.913113i	−0.889694	−	0.456557i	$-0.849083\pi$
$937$	− 1.55615e28i	− 0.913113i	0.889694	−	0.456557i	$-0.150917\pi$
$938$	− 1.26468e28i	− 0.734607i
$939$	−4.01793e27	−0.231036
$940$	0	0
$941$	−4.21264e27	−0.237385	−0.118693	−	0.992931i	$-0.537870\pi$
$941$	−4.21264e27	−0.237385	−0.118693	+	0.992931i	$0.537870\pi$
$942$	− 9.67280e27i	− 0.539596i
$943$	− 2.88989e27i	− 0.159595i
$944$	−2.56609e27	−0.140293
$945$	0	0
$946$	−1.16127e27	−0.0622255
$947$	− 1.60906e27i	− 0.0853584i	−0.999089	−	0.0426792i	$-0.986411\pi$
$947$	− 1.60906e27i	− 0.0853584i	0.999089	−	0.0426792i	$-0.0135893\pi$
$948$	− 3.25456e27i	− 0.170928i
$949$	4.27817e27	0.222448
$950$	0	0
$951$	5.40175e27	0.275308
$952$	− 3.17826e28i	− 1.60376i
$953$	2.00721e28i	1.00279i	0.865218	+	0.501396i	$0.167180\pi$
$953$	2.00721e28i	1.00279i	−0.865218	+	0.501396i	$0.832820\pi$
$954$	3.53008e27	0.174612
$955$	0	0
$956$	−9.30095e27	−0.451001
$957$	1.94632e28i	0.934437i
$958$	− 2.28898e28i	− 1.08810i
$959$	−1.74160e28	−0.819729
$960$	0	0
$961$	−2.01272e28	−0.928775
$962$	− 4.18598e28i	− 1.91264i
$963$	− 6.70874e27i	− 0.303523i
$964$	−4.73173e27	−0.211977
$965$	0	0
$966$	6.02683e27	0.264732
$967$	− 3.69606e28i	− 1.60764i	−0.594876	−	0.803818i	$-0.702799\pi$
$967$	− 3.69606e28i	− 1.60764i	0.594876	−	0.803818i	$-0.297201\pi$
$968$	− 8.07830e27i	− 0.347940i
$969$	1.64881e28	0.703228
$970$	0	0
$971$	−2.54073e28	−1.06261	−0.531306	−	0.847180i	$-0.678299\pi$
$971$	−2.54073e28	−1.06261	−0.531306	+	0.847180i	$0.678299\pi$
$972$	− 6.99149e26i	− 0.0289561i
$973$	− 2.89166e27i	− 0.118597i
$974$	−3.52397e27	−0.143127
$975$	0	0
$976$	4.84925e27	0.193153
$977$	− 8.52403e27i	− 0.336238i	−0.985767	−	0.168119i	$-0.946231\pi$
$977$	− 8.52403e27i	− 0.336238i	0.985767	−	0.168119i	$-0.0537693\pi$
$978$	4.75107e27i	0.185598i
$979$	9.23408e27	0.357238
$980$	0	0
$981$	6.11149e27	0.231895
$982$	2.81120e28i	1.05641i
$983$	3.09592e28i	1.15221i	0.817376	+	0.576105i	$0.195428\pi$
$983$	3.09592e28i	1.15221i	−0.817376	+	0.576105i	$0.804572\pi$
$984$	−4.62211e27	−0.170368
$985$	0	0
$986$	−5.64901e28	−2.04240
$987$	− 1.56625e28i	− 0.560853i
$988$	1.66425e28i	0.590238i
$989$	−1.69084e27	−0.0593934
$990$	0	0
$991$	−2.94856e28	−1.01604	−0.508020	−	0.861345i	$-0.669622\pi$
$991$	−2.94856e28	−1.01604	−0.508020	+	0.861345i	$0.669622\pi$
$992$	6.40864e27i	0.218728i
$993$	4.55843e27i	0.154098i
$994$	−1.43347e28	−0.479976
$995$	0	0
$996$	1.51635e28	0.498121
$997$	3.29038e28i	1.07064i	0.844650	+	0.535318i	$0.179808\pi$
$997$	3.29038e28i	1.07064i	−0.844650	+	0.535318i	$0.820192\pi$
$998$	1.36839e28i	0.441031i
$999$	1.03486e28	0.330377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.20.b.b.49.3		4
5.2	odd	4		3.20.a.b.1.1	✓	2
5.3	odd	4		75.20.a.b.1.2		2
5.4	even	2	inner	75.20.b.b.49.2		4
15.2	even	4		9.20.a.c.1.2		2
20.7	even	4		48.20.a.j.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.20.a.b.1.1	✓	2	5.2	odd	4
9.20.a.c.1.2		2	15.2	even	4
48.20.a.j.1.1		2	20.7	even	4
75.20.a.b.1.2		2	5.3	odd	4
75.20.b.b.49.2		4	5.4	even	2	inner
75.20.b.b.49.3		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+536.316i q^{2} -19683.0i q^{3} +236654. q^{4} +1.05563e7 q^{6} -1.13677e8i q^{7} +4.08105e8i q^{8} -3.87420e8 q^{9} +O(q^{10})\)	\(q+536.316i q^{2} -19683.0i q^{3} +236654. q^{4} +1.05563e7 q^{6} -1.13677e8i q^{7} +4.08105e8i q^{8} -3.87420e8 q^{9} +6.43152e9 q^{11} -4.65805e9i q^{12} -5.75132e10i q^{13} +6.09670e10 q^{14} -9.47984e10 q^{16} -6.85083e11i q^{17} -2.07780e11i q^{18} -1.22275e12 q^{19} -2.23751e12 q^{21} +3.44932e12i q^{22} +5.02230e12i q^{23} +8.03273e12 q^{24} +3.08453e13 q^{26} +7.62560e12i q^{27} -2.69022e13i q^{28} -1.53748e14 q^{29} +3.92872e13 q^{31} +1.63123e14i q^{32} -1.26592e14i q^{33} +3.67421e14 q^{34} -9.16844e13 q^{36} -1.35709e15i q^{37} -6.55779e14i q^{38} -1.13203e15 q^{39} -5.75410e14 q^{41} -1.20001e15i q^{42} +3.36667e14i q^{43} +1.52204e15 q^{44} -2.69354e15 q^{46} +6.99998e15i q^{47} +1.86592e15i q^{48} -1.52367e15 q^{49} -1.34845e16 q^{51} -1.36107e16i q^{52} +1.69895e16i q^{53} -4.08973e15 q^{54} +4.63923e16 q^{56} +2.40674e16i q^{57} -8.24573e16i q^{58} +2.70689e16 q^{59} -5.11533e16 q^{61} +2.10704e16i q^{62} +4.40410e16i q^{63} -1.37187e17 q^{64} +6.78930e16 q^{66} -2.07437e17i q^{67} -1.62127e17i q^{68} +9.88540e16 q^{69} -2.35123e17 q^{71} -1.58108e17i q^{72} +7.43858e16i q^{73} +7.27828e17 q^{74} -2.89368e17 q^{76} -7.31118e17i q^{77} -6.07127e17i q^{78} +6.98697e17 q^{79} +1.50095e17 q^{81} -3.08601e17i q^{82} +3.25532e18i q^{83} -5.29515e17 q^{84} -1.80560e17 q^{86} +3.02622e18i q^{87} +2.62473e18i q^{88} +1.43575e18 q^{89} -6.53796e18 q^{91} +1.18855e18i q^{92} -7.73291e17i q^{93} -3.75420e18 q^{94} +3.21074e18 q^{96} -1.66911e18i q^{97} -8.17166e17i q^{98} -2.49170e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1544968 q^{4} - 27634932 q^{6} - 1549681956 q^{9}+O(q^{10}) \) 4 * q - 1544968 * q^4 - 27634932 * q^6 - 1549681956 * q^9	\( 4 q - 1544968 q^{4} - 27634932 q^{6} - 1549681956 q^{9} - 13300142544 q^{11} + 121402438848 q^{14} + 239207241760 q^{16} - 1204237850192 q^{19} - 4483474991424 q^{21} + 39700674930384 q^{24} + 94978619578728 q^{26} - 561954503940984 q^{29} + 83220298507424 q^{31} + 15\!\cdots\!64 q^{34}+ \cdots + 51\!\cdots\!16 q^{99}+O(q^{100}) \) 4 * q - 1544968 * q^4 - 27634932 * q^6 - 1549681956 * q^9 - 13300142544 * q^11 + 121402438848 * q^14 + 239207241760 * q^16 - 1204237850192 * q^19 - 4483474991424 * q^21 + 39700674930384 * q^24 + 94978619578728 * q^26 - 561954503940984 * q^29 + 83220298507424 * q^31 + 1598694698342664 * q^34 + 598552258049352 * q^36 - 1734952372122168 * q^39 + 2300076860561064 * q^41 + 29446328828101536 * q^44 - 11960188021600416 * q^46 + 19750366460386140 * q^49 - 13238056416831768 * q^51 + 10706338868921748 * q^54 + 93042345123175680 * q^56 + 110306948843671632 * q^59 - 174385138132411240 * q^61 + 72500092437262208 * q^64 + 773481249856604304 * q^66 + 93228614765496288 * q^69 + 169830096873941088 * q^71 + 3236591734880155128 * q^74 - 1831337138947140448 * q^76 - 2263182932067046880 * q^79 + 600378541187996484 * q^81 - 1050504928298587008 * q^84 + 5790466823989672656 * q^86 - 8645595252739152552 * q^89 - 13070147362624689536 * q^91 - 10967971360190514048 * q^94 + 8361578887023750336 * q^96 + 5152747728166184016 * q^99

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