LMFDB - Embedded newform 75.20.b.b.49.4

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			49.4
Root			$148.386i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.20.b.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1238.32i q^{2} +19683.0i q^{3} -1.00914e6 q^{4} -2.43738e7 q^{6} +214621. i q^{7} -6.00397e8i q^{8} -3.87420e8 q^{9} +O(q^{10})$	\(q+1238.32i q^{2} +19683.0i q^{3} -1.00914e6 q^{4} -2.43738e7 q^{6} +214621. i q^{7} -6.00397e8i q^{8} -3.87420e8 q^{9} -1.30816e10 q^{11} -1.98629e10i q^{12} -1.34409e10i q^{13} -2.65768e8 q^{14} +2.14402e11 q^{16} -3.48802e11i q^{17} -4.79749e11i q^{18} +6.20630e11 q^{19} -4.22438e9 q^{21} -1.61991e13i q^{22} +2.65405e12i q^{23} +1.18176e13 q^{24} +1.66441e13 q^{26} -7.62560e12i q^{27} -2.16582e11i q^{28} -1.27229e14 q^{29} +2.32290e12 q^{31} -4.92835e13i q^{32} -2.57485e14i q^{33} +4.31927e14 q^{34} +3.90961e14 q^{36} -7.19096e14i q^{37} +7.68535e14i q^{38} +2.64557e14 q^{39} +1.72545e15 q^{41} -5.23112e12i q^{42} -2.48385e15i q^{43} +1.32011e16 q^{44} -3.28655e15 q^{46} +1.39689e15i q^{47} +4.22007e15i q^{48} +1.13988e16 q^{49} +6.86546e15 q^{51} +1.35637e16i q^{52} -1.05483e16i q^{53} +9.44290e15 q^{54} +1.28858e14 q^{56} +1.22159e16i q^{57} -1.57550e17i q^{58} +2.80846e16 q^{59} -3.60392e16 q^{61} +2.87648e15i q^{62} -8.31485e13i q^{63} +1.73437e17 q^{64} +3.18848e17 q^{66} +2.91862e17i q^{67} +3.51989e17i q^{68} -5.22397e16 q^{69} +3.20038e17 q^{71} +2.32606e17i q^{72} +3.15819e17i q^{73} +8.90467e17 q^{74} -6.26301e17 q^{76} -2.80758e15i q^{77} +3.27605e17i q^{78} -1.83029e18 q^{79} +1.50095e17 q^{81} +2.13665e18i q^{82} +1.64758e18i q^{83} +4.26298e15 q^{84} +3.07579e18 q^{86} -2.50426e18i q^{87} +7.85414e18i q^{88} -5.75855e18 q^{89} +2.88469e15 q^{91} -2.67830e18i q^{92} +4.57216e16i q^{93} -1.72979e18 q^{94} +9.70047e17 q^{96} +6.23309e18i q^{97} +1.41154e19i q^{98} +5.06808e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1238.32i	1.71020i	0.518465	+	0.855099i	$0.326504\pi$
$2$	1238.32i	1.71020i	−0.518465	+	0.855099i	$0.673496\pi$
$3$	19683.0i	0.577350i
$3$	19683.0i	0.577350i
$4$	−1.00914e6	−1.92478
$5$	0	0
$5$	0	0
$6$	−2.43738e7	−0.987383
$7$	214621.i	0.00201021i	0.999999	+	0.00100510i	$0.000319934\pi$
$7$	214621.i	0.00201021i	−0.999999	+	0.00100510i	$0.999680\pi$
$8$	− 6.00397e8i	− 1.58155i
$9$	−3.87420e8	−0.333333
$10$	0	0
$11$	−1.30816e10	−1.67275	−0.836373	−	0.548161i	$-0.815328\pi$
$11$	−1.30816e10	−1.67275	−0.836373	+	0.548161i	$0.815328\pi$
$12$	− 1.98629e10i	− 1.11127i
$13$	− 1.34409e10i	− 0.351533i	−0.984432	−	0.175766i	$-0.943760\pi$
$13$	− 1.34409e10i	− 0.351533i	0.984432	−	0.175766i	$-0.0562404\pi$
$14$	−2.65768e8	−0.00343785
$15$	0	0
$16$	2.14402e11	0.779990
$17$	− 3.48802e11i	− 0.713368i	−0.934225	−	0.356684i	$-0.883907\pi$
$17$	− 3.48802e11i	− 0.713368i	0.934225	−	0.356684i	$-0.116093\pi$
$18$	− 4.79749e11i	− 0.570066i
$19$	6.20630e11	0.441238	0.220619	−	0.975360i	$-0.429192\pi$
$19$	6.20630e11	0.441238	0.220619	+	0.975360i	$0.429192\pi$
$20$	0	0
$21$	−4.22438e9	−0.00116059
$22$	− 1.61991e13i	− 2.86073i
$23$	2.65405e12i	0.307252i	0.988129	+	0.153626i	$0.0490951\pi$
$23$	2.65405e12i	0.307252i	−0.988129	+	0.153626i	$0.950905\pi$
$24$	1.18176e13	0.913109
$25$	0	0
$26$	1.66441e13	0.601191
$27$	− 7.62560e12i	− 0.192450i
$28$	− 2.16582e11i	− 0.00386920i
$29$	−1.27229e14	−1.62857	−0.814286	−	0.580464i	$-0.802871\pi$
$29$	−1.27229e14	−1.62857	−0.814286	+	0.580464i	$0.802871\pi$
$30$	0	0
$31$	2.32290e12	0.0157795	0.00788977	−	0.999969i	$-0.497489\pi$
$31$	2.32290e12	0.0157795	0.00788977	+	0.999969i	$0.497489\pi$
$32$	− 4.92835e13i	− 0.247615i
$33$	− 2.57485e14i	− 0.965760i
$34$	4.31927e14	1.22000
$35$	0	0
$36$	3.90961e14	0.641592
$37$	− 7.19096e14i	− 0.909642i	−0.890583	−	0.454821i	$-0.849703\pi$
$37$	− 7.19096e14i	− 0.909642i	0.890583	−	0.454821i	$-0.150297\pi$
$38$	7.68535e14i	0.754605i
$39$	2.64557e14	0.202958
$40$	0	0
$41$	1.72545e15	0.823105	0.411553	−	0.911386i	$-0.364987\pi$
$41$	1.72545e15	0.823105	0.411553	+	0.911386i	$0.364987\pi$
$42$	− 5.23112e12i	− 0.00198484i
$43$	− 2.48385e15i	− 0.753660i	−0.926282	−	0.376830i	$-0.877014\pi$
$43$	− 2.48385e15i	− 0.753660i	0.926282	−	0.376830i	$-0.122986\pi$
$44$	1.32011e16	3.21966
$45$	0	0
$46$	−3.28655e15	−0.525462
$47$	1.39689e15i	0.182067i	0.995848	+	0.0910336i	$0.0290171\pi$
$47$	1.39689e15i	0.182067i	−0.995848	+	0.0910336i	$0.970983\pi$
$48$	4.22007e15i	0.450327i
$49$	1.13988e16	0.999996
$50$	0	0
$51$	6.86546e15	0.411863
$52$	1.35637e16i	0.676623i
$53$	− 1.05483e16i	− 0.439099i	−0.975601	−	0.219550i	$-0.929541\pi$
$53$	− 1.05483e16i	− 0.439099i	0.975601	−	0.219550i	$-0.0704588\pi$
$54$	9.44290e15	0.329128
$55$	0	0
$56$	1.28858e14	0.00317925
$57$	1.22159e16i	0.254749i
$58$	− 1.57550e17i	− 2.78518i
$59$	2.80846e16	0.422060	0.211030	−	0.977480i	$-0.432318\pi$
$59$	2.80846e16	0.422060	0.211030	+	0.977480i	$0.432318\pi$
$60$	0	0
$61$	−3.60392e16	−0.394586	−0.197293	−	0.980345i	$-0.563215\pi$
$61$	−3.60392e16	−0.394586	−0.197293	+	0.980345i	$0.563215\pi$
$62$	2.87648e15i	0.0269861i
$63$	− 8.31485e13i	0 0.000670069i
$64$	1.73437e17	1.20346
$65$	0	0
$66$	3.18848e17	1.65164
$67$	2.91862e17i	1.31059i	0.755373	+	0.655296i	$0.227456\pi$
$67$	2.91862e17i	1.31059i	−0.755373	+	0.655296i	$0.772544\pi$
$68$	3.51989e17i	1.37308i
$69$	−5.22397e16	−0.177392
$70$	0	0
$71$	3.20038e17	0.828414	0.414207	−	0.910183i	$-0.364059\pi$
$71$	3.20038e17	0.828414	0.414207	+	0.910183i	$0.364059\pi$
$72$	2.32606e17i	0.527184i
$73$	3.15819e17i	0.627873i	0.949444	+	0.313936i	$0.101648\pi$
$73$	3.15819e17i	0.627873i	−0.949444	+	0.313936i	$0.898352\pi$
$74$	8.90467e17	1.55567
$75$	0	0
$76$	−6.26301e17	−0.849286
$77$	− 2.80758e15i	− 0.00336256i
$78$	3.27605e17i	0.347098i
$79$	−1.83029e18	−1.71815	−0.859077	−	0.511846i	$-0.828962\pi$
$79$	−1.83029e18	−1.71815	−0.859077	+	0.511846i	$0.828962\pi$
$80$	0	0
$81$	1.50095e17	0.111111
$82$	2.13665e18i	1.40767i
$83$	1.64758e18i	0.967397i	0.875235	+	0.483698i	$0.160707\pi$
$83$	1.64758e18i	0.967397i	−0.875235	+	0.483698i	$0.839293\pi$
$84$	4.26298e15	0.00223388
$85$	0	0
$86$	3.07579e18	1.28891
$87$	− 2.50426e18i	− 0.940256i
$88$	7.85414e18i	2.64553i
$89$	−5.75855e18	−1.74224	−0.871120	−	0.491069i	$-0.836606\pi$
$89$	−5.75855e18	−1.74224	−0.871120	+	0.491069i	$0.836606\pi$
$90$	0	0
$91$	2.88469e15	0.000706654 0
$92$	− 2.67830e18i	− 0.591392i
$93$	4.57216e16i	0.00911032i
$94$	−1.72979e18	−0.311371
$95$	0	0
$96$	9.70047e17	0.142960
$97$	6.23309e18i	0.832477i	0.909256	+	0.416238i	$0.136652\pi$
$97$	6.23309e18i	0.832477i	−0.909256	+	0.416238i	$0.863348\pi$
$98$	1.41154e19i	1.71019i
$99$	5.06808e18	0.557582
$100$	0	0
$101$	8.80411e17	0.0801000	0.0400500	−	0.999198i	$-0.487248\pi$
$101$	8.80411e17	0.0801000	0.0400500	+	0.999198i	$0.487248\pi$
$102$	8.50161e18i	0.704368i
$103$	1.96998e19i	1.48767i	0.668361	+	0.743837i	$0.266996\pi$
$103$	1.96998e19i	1.48767i	−0.668361	+	0.743837i	$0.733004\pi$
$104$	−8.06987e18	−0.555968
$105$	0	0
$106$	1.30622e19	0.750946
$107$	2.58893e19i	1.36136i	0.732579	+	0.680682i	$0.238316\pi$
$107$	2.58893e19i	1.36136i	−0.732579	+	0.680682i	$0.761684\pi$
$108$	7.69528e18i	0.370424i
$109$	3.42533e19	1.51060	0.755302	−	0.655377i	$-0.227490\pi$
$109$	3.42533e19	1.51060	0.755302	+	0.655377i	$0.227490\pi$
$110$	0	0
$111$	1.41540e19	0.525182
$112$	4.60151e16i	0.00156794i
$113$	− 5.49844e19i	− 1.72185i	−0.508735	−	0.860923i	$-0.669887\pi$
$113$	− 5.49844e19i	− 1.72185i	0.508735	−	0.860923i	$-0.330113\pi$
$114$	−1.51271e19	−0.435671
$115$	0	0
$116$	1.28392e20	3.13464
$117$	5.20727e18i	0.117178i
$118$	3.47776e19i	0.721806i
$119$	7.48601e16	0.00143402
$120$	0	0
$121$	1.09969e20	1.79808
$122$	− 4.46279e19i	− 0.674821i
$123$	3.39620e19i	0.475220i
$124$	−2.34412e18	−0.0303721
$125$	0	0
$126$	1.02964e17	0.00114595
$127$	− 8.76640e19i	− 0.905078i	−0.891745	−	0.452539i	$-0.850518\pi$
$127$	− 8.76640e19i	− 0.905078i	0.891745	−	0.452539i	$-0.149482\pi$
$128$	1.88931e20i	1.81054i
$129$	4.88897e19	0.435126
$130$	0	0
$131$	−1.23083e20	−0.946497	−0.473249	−	0.880929i	$-0.656919\pi$
$131$	−1.23083e20	−0.946497	−0.473249	+	0.880929i	$0.656919\pi$
$132$	2.59838e20i	1.85887i
$133$	1.33200e17i	0 0.000886980i
$134$	−3.61418e20	−2.24137
$135$	0	0
$136$	−2.09419e20	−1.12823
$137$	− 1.10729e20i	− 0.556435i	−0.960518	−	0.278218i	$-0.910256\pi$
$137$	− 1.10729e20i	− 0.556435i	0.960518	−	0.278218i	$-0.0897437\pi$
$138$	− 6.46892e19i	− 0.303376i
$139$	2.36141e20	1.03402	0.517012	−	0.855978i	$-0.327044\pi$
$139$	2.36141e20	1.03402	0.517012	+	0.855978i	$0.327044\pi$
$140$	0	0
$141$	−2.74949e19	−0.105117
$142$	3.96308e20i	1.41675i
$143$	1.75828e20i	0.588025i
$144$	−8.30637e19	−0.259997
$145$	0	0
$146$	−3.91084e20	−1.07379
$147$	2.24364e20i	0.577348i
$148$	7.25666e20i	1.75086i
$149$	−2.05810e20	−0.465796	−0.232898	−	0.972501i	$-0.574821\pi$
$149$	−2.05810e20	−0.465796	−0.232898	+	0.972501i	$0.574821\pi$
$150$	0	0
$151$	−2.24449e20	−0.447546	−0.223773	−	0.974641i	$-0.571837\pi$
$151$	−2.24449e20	−0.447546	−0.223773	+	0.974641i	$0.571837\pi$
$152$	− 3.72624e20i	− 0.697842i
$153$	1.35133e20i	0.237789i
$154$	3.47667e18	0.00575065
$155$	0	0
$156$	−2.66974e20	−0.390648
$157$	3.13212e20i	0.431312i	0.976469	+	0.215656i	$0.0691889\pi$
$157$	3.13212e20i	0.431312i	−0.976469	+	0.215656i	$0.930811\pi$
$158$	− 2.26647e21i	− 2.93838i
$159$	2.07623e20	0.253514
$160$	0	0
$161$	−5.69615e17	−0.000617640 0
$162$	1.85865e20i	0.190022i
$163$	− 2.00591e20i	− 0.193432i	−0.995312	−	0.0967160i	$-0.969166\pi$
$163$	− 2.00591e20i	− 0.193432i	0.995312	−	0.0967160i	$-0.0308339\pi$
$164$	−1.74122e21	−1.58429
$165$	0	0
$166$	−2.04022e21	−1.65444
$167$	− 2.56060e21i	− 1.96126i	−0.195860	−	0.980632i	$-0.562750\pi$
$167$	− 2.56060e21i	− 1.96126i	0.195860	−	0.980632i	$-0.437250\pi$
$168$	2.53631e18i	0.00183554i
$169$	1.28126e21	0.876425
$170$	0	0
$171$	−2.40445e20	−0.147079
$172$	2.50655e21i	1.45063i
$173$	− 2.86308e21i	− 1.56818i	−0.620649	−	0.784089i	$-0.713131\pi$
$173$	− 2.86308e21i	− 1.56818i	0.620649	−	0.784089i	$-0.286869\pi$
$174$	3.10106e21	1.60802
$175$	0	0
$176$	−2.80472e21	−1.30472
$177$	5.52789e20i	0.243676i
$178$	− 7.13090e21i	− 2.97958i
$179$	−3.79065e20	−0.150179	−0.0750896	−	0.997177i	$-0.523924\pi$
$179$	−3.79065e20	−0.150179	−0.0750896	+	0.997177i	$0.523924\pi$
$180$	0	0
$181$	−3.15578e21	−1.12502	−0.562510	−	0.826790i	$-0.690164\pi$
$181$	−3.15578e21	−1.12502	−0.562510	+	0.826790i	$0.690164\pi$
$182$	3.57216e18i	0.00120852i
$183$	− 7.09360e20i	− 0.227814i
$184$	1.59348e21	0.485935
$185$	0	0
$186$	−5.66178e19	−0.0155805
$187$	4.56288e21i	1.19328i
$188$	− 1.40965e21i	− 0.350439i
$189$	1.63661e18	0.000386864 0
$190$	0	0
$191$	2.79667e21	0.598170	0.299085	−	0.954226i	$-0.403319\pi$
$191$	2.79667e21	0.598170	0.299085	+	0.954226i	$0.403319\pi$
$192$	3.41376e21i	0.694818i
$193$	7.34293e20i	0.142257i	0.997467	+	0.0711287i	$0.0226601\pi$
$193$	7.34293e20i	0.142257i	−0.997467	+	0.0711287i	$0.977340\pi$
$194$	−7.71854e21	−1.42370
$195$	0	0
$196$	−1.15030e22	−1.92477
$197$	− 5.32518e21i	− 0.848995i	−0.905429	−	0.424498i	$-0.860451\pi$
$197$	− 5.32518e21i	− 0.848995i	0.905429	−	0.424498i	$-0.139549\pi$
$198$	6.27588e21i	0.953576i
$199$	2.54553e21	0.368701	0.184350	−	0.982861i	$-0.440982\pi$
$199$	2.54553e21	0.368701	0.184350	+	0.982861i	$0.440982\pi$
$200$	0	0
$201$	−5.74472e21	−0.756670
$202$	1.09023e21i	0.136987i
$203$	− 2.73061e19i	− 0.00327376i
$204$	−6.92820e21	−0.792745
$205$	0	0
$206$	−2.43945e22	−2.54422
$207$	− 1.02823e21i	− 0.102417i
$208$	− 2.88175e21i	− 0.274192i
$209$	−8.11882e21	−0.738080
$210$	0	0
$211$	7.77610e21	0.645771	0.322886	−	0.946438i	$-0.395347\pi$
$211$	7.77610e21	0.645771	0.322886	+	0.946438i	$0.395347\pi$
$212$	1.06447e22i	0.845168i
$213$	6.29931e21i	0.478285i
$214$	−3.20591e22	−2.32820
$215$	0	0
$216$	−4.57838e21	−0.304370
$217$	4.98543e17i	0 3.17201e-5i
$218$	4.24164e22i	2.58343i
$219$	−6.21627e21	−0.362503
$220$	0	0
$221$	−4.68820e21	−0.250772
$222$	1.75271e22i	0.898165i
$223$	1.89249e22i	0.929259i	0.885505	+	0.464629i	$0.153812\pi$
$223$	1.89249e22i	0.929259i	−0.885505	+	0.464629i	$0.846188\pi$
$224$	1.05773e19	0.000497757 0
$225$	0	0
$226$	6.80881e22	2.94470
$227$	2.42145e22i	1.00422i	0.864803	+	0.502111i	$0.167443\pi$
$227$	2.42145e22i	1.00422i	−0.864803	+	0.502111i	$0.832557\pi$
$228$	− 1.23275e22i	− 0.490335i
$229$	3.29966e22	1.25902	0.629510	−	0.776992i	$-0.283256\pi$
$229$	3.29966e22	1.25902	0.629510	+	0.776992i	$0.283256\pi$
$230$	0	0
$231$	5.52616e19	0.00194138
$232$	7.63882e22i	2.57567i
$233$	8.99479e21i	0.291145i	0.989348	+	0.145573i	$0.0465025\pi$
$233$	8.99479e21i	0.291145i	−0.989348	+	0.145573i	$0.953498\pi$
$234$	−6.44825e21	−0.200397
$235$	0	0
$236$	−2.83412e22	−0.812371
$237$	− 3.60256e22i	− 0.991977i
$238$	9.27005e19i	0.00245245i
$239$	−1.22851e22	−0.312319	−0.156159	−	0.987732i	$-0.549911\pi$
$239$	−1.22851e22	−0.312319	−0.156159	+	0.987732i	$0.549911\pi$
$240$	0	0
$241$	−4.48313e22	−1.05298	−0.526489	−	0.850182i	$-0.676492\pi$
$241$	−4.48313e22	−1.05298	−0.526489	+	0.850182i	$0.676492\pi$
$242$	1.36176e23i	3.07507i
$243$	2.95431e21i	0.0641500i
$244$	3.63685e22	0.759491
$245$	0	0
$246$	−4.20557e22	−0.812720
$247$	− 8.34181e21i	− 0.155110i
$248$	− 1.39466e21i	− 0.0249562i
$249$	−3.24293e22	−0.558527
$250$	0	0
$251$	3.85123e22	0.614750	0.307375	−	0.951588i	$-0.400549\pi$
$251$	3.85123e22	0.614750	0.307375	+	0.951588i	$0.400549\pi$
$252$	8.39083e19i	0.00128973i
$253$	− 3.47192e22i	− 0.513955i
$254$	1.08556e23	1.54786
$255$	0	0
$256$	−1.43025e23	−1.89292
$257$	9.07321e22i	1.15717i	0.815623	+	0.578584i	$0.196394\pi$
$257$	9.07321e22i	1.15717i	−0.815623	+	0.578584i	$0.803606\pi$
$258$	6.05408e22i	0.744151i
$259$	1.54333e20	0.00182857
$260$	0	0
$261$	4.92913e22	0.542857
$262$	− 1.52415e23i	− 1.61870i
$263$	2.56086e21i	0.0262305i	0.999914	+	0.0131152i	$0.00417483\pi$
$263$	2.56086e21i	0.0262305i	−0.999914	+	0.0131152i	$0.995825\pi$
$264$	−1.54593e23	−1.52740
$265$	0	0
$266$	−1.64944e20	−0.00151691
$267$	− 1.13346e23i	− 1.00588i
$268$	− 2.94529e23i	− 2.52260i
$269$	−3.82577e22	−0.316281	−0.158140	−	0.987417i	$-0.550550\pi$
$269$	−3.82577e22	−0.316281	−0.158140	+	0.987417i	$0.550550\pi$
$270$	0	0
$271$	3.64857e22	0.281135	0.140567	−	0.990071i	$-0.455107\pi$
$271$	3.64857e22	0.281135	0.140567	+	0.990071i	$0.455107\pi$
$272$	− 7.47838e22i	− 0.556420i
$273$	5.67794e19i	0 0.000407987i
$274$	1.37117e23	0.951615
$275$	0	0
$276$	5.27170e22	0.341440
$277$	1.78571e23i	1.11752i	0.829331	+	0.558758i	$0.188722\pi$
$277$	1.78571e23i	1.11752i	−0.829331	+	0.558758i	$0.811278\pi$
$278$	2.92417e23i	1.76839i
$279$	−8.99939e20	−0.00525985
$280$	0	0
$281$	−2.28261e23	−1.24659	−0.623293	−	0.781989i	$-0.714205\pi$
$281$	−2.28261e23	−1.24659	−0.623293	+	0.781989i	$0.714205\pi$
$282$	− 3.40474e22i	− 0.179770i
$283$	− 1.87538e23i	− 0.957453i	−0.877964	−	0.478727i	$-0.841098\pi$
$283$	− 1.87538e23i	− 0.957453i	0.877964	−	0.478727i	$-0.158902\pi$
$284$	−3.22962e23	−1.59451
$285$	0	0
$286$	−2.17731e23	−1.00564
$287$	3.70317e20i	0.00165461i
$288$	1.90934e22i	0.0825383i
$289$	1.17410e23	0.491106
$290$	0	0
$291$	−1.22686e23	−0.480631
$292$	− 3.18705e23i	− 1.20852i
$293$	− 2.82617e23i	− 1.03742i	−0.854950	−	0.518711i	$-0.826412\pi$
$293$	− 2.82617e23i	− 1.03742i	0.854950	−	0.518711i	$-0.173588\pi$
$294$	−2.77833e23	−0.987379
$295$	0	0
$296$	−4.31743e23	−1.43865
$297$	9.97549e22i	0.321920i
$298$	− 2.54857e23i	− 0.796604i
$299$	3.56728e22	0.108009
$300$	0	0
$301$	5.33087e20	0.00151501
$302$	− 2.77939e23i	− 0.765392i
$303$	1.73291e22i	0.0462457i
$304$	1.33064e23	0.344162
$305$	0	0
$306$	−1.67337e23	−0.406667
$307$	− 2.47019e23i	− 0.581991i	−0.956724	−	0.290996i	$-0.906014\pi$
$307$	− 2.47019e23i	− 0.581991i	0.956724	−	0.290996i	$-0.0939865\pi$
$308$	2.83324e21i	0.00647219i
$309$	−3.87751e23	−0.858909
$310$	0	0
$311$	3.27126e23	0.681539	0.340770	−	0.940147i	$-0.389312\pi$
$311$	3.27126e23	0.681539	0.340770	+	0.940147i	$0.389312\pi$
$312$	− 1.58839e23i	− 0.320988i
$313$	− 3.73412e23i	− 0.732011i	−0.930613	−	0.366005i	$-0.880725\pi$
$313$	− 3.73412e23i	− 0.732011i	0.930613	−	0.366005i	$-0.119275\pi$
$314$	−3.87855e23	−0.737628
$315$	0	0
$316$	1.84701e24	3.30706
$317$	− 5.83518e22i	− 0.101389i	−0.998714	−	0.0506945i	$-0.983857\pi$
$317$	− 5.83518e22i	− 0.101389i	0.998714	−	0.0506945i	$-0.0161435\pi$
$318$	2.57102e23i	0.433559i
$319$	1.66436e24	2.72419
$320$	0	0
$321$	−5.09579e23	−0.785984
$322$	− 7.05363e20i	− 0.00105629i
$323$	− 2.16477e23i	− 0.314766i
$324$	−1.51466e23	−0.213864
$325$	0	0
$326$	2.48394e23	0.330807
$327$	6.74208e23i	0.872148i
$328$	− 1.03595e24i	− 1.30178i
$329$	−2.99801e20	−0.000365993 0
$330$	0	0
$331$	3.84253e23	0.442845	0.221422	−	0.975178i	$-0.428930\pi$
$331$	3.84253e23	0.442845	0.221422	+	0.975178i	$0.428930\pi$
$332$	− 1.66263e24i	− 1.86202i
$333$	2.78592e23i	0.303214i
$334$	3.17084e24	3.35415
$335$	0	0
$336$	−9.05716e20	−0.000905251 0
$337$	1.30128e24i	1.26440i	0.774803	+	0.632202i	$0.217849\pi$
$337$	1.30128e24i	1.26440i	−0.774803	+	0.632202i	$0.782151\pi$
$338$	1.58661e24i	1.49886i
$339$	1.08226e24	0.994109
$340$	0	0
$341$	−3.03872e22	−0.0263952
$342$	− 2.97746e23i	− 0.251535i
$343$	4.89287e21i	0.00402040i
$344$	−1.49130e24	−1.19195
$345$	0	0
$346$	3.54539e24	2.68189
$347$	− 8.56826e22i	− 0.0630613i	−0.999503	−	0.0315306i	$-0.989962\pi$
$347$	− 8.56826e22i	− 0.0630613i	0.999503	−	0.0315306i	$-0.0100382\pi$
$348$	2.52714e24i	1.80978i
$349$	1.11294e24	0.775586	0.387793	−	0.921746i	$-0.373237\pi$
$349$	1.11294e24	0.775586	0.387793	+	0.921746i	$0.373237\pi$
$350$	0	0
$351$	−1.02495e23	−0.0676526
$352$	6.44706e23i	0.414197i
$353$	2.23748e24i	1.39926i	0.714505	+	0.699631i	$0.246652\pi$
$353$	2.23748e24i	1.39926i	−0.714505	+	0.699631i	$0.753348\pi$
$354$	−6.84527e23	−0.416735
$355$	0	0
$356$	5.81117e24	3.35343
$357$	1.47347e21i	0 0.000827930i
$358$	− 4.69402e23i	− 0.256836i
$359$	−2.02884e24	−1.08106	−0.540531	−	0.841324i	$-0.681777\pi$
$359$	−2.02884e24	−1.08106	−0.540531	+	0.841324i	$0.681777\pi$
$360$	0	0
$361$	−1.59324e24	−0.805309
$362$	− 3.90785e24i	− 1.92401i
$363$	2.16452e24i	1.03812i
$364$	−2.91105e21	−0.00136015
$365$	0	0
$366$	8.78412e23	0.389608
$367$	− 2.03395e24i	− 0.879049i	−0.898230	−	0.439525i	$-0.855147\pi$
$367$	− 2.03395e24i	− 0.879049i	0.898230	−	0.439525i	$-0.144853\pi$
$368$	5.69034e23i	0.239654i
$369$	−6.68474e23	−0.274368
$370$	0	0
$371$	2.26389e21	0.000882680 0
$372$	− 4.61394e22i	− 0.0175353i
$373$	7.78333e23i	0.288358i	0.989552	+	0.144179i	$0.0460540\pi$
$373$	7.78333e23i	0.288358i	−0.989552	+	0.144179i	$0.953946\pi$
$374$	−5.65029e24	−2.04075
$375$	0	0
$376$	8.38687e23	0.287949
$377$	1.71008e24i	0.572497i
$378$	2.02664e21i	0 0.000661615i
$379$	−3.15677e24	−1.00501	−0.502505	−	0.864575i	$-0.667588\pi$
$379$	−3.15677e24	−1.00501	−0.502505	+	0.864575i	$0.667588\pi$
$380$	0	0
$381$	1.72549e24	0.522547
$382$	3.46316e24i	1.02299i
$383$	3.09305e24i	0.891249i	0.895220	+	0.445625i	$0.147018\pi$
$383$	3.09305e24i	0.891249i	−0.895220	+	0.445625i	$0.852982\pi$
$384$	−3.71873e24	−1.04532
$385$	0	0
$386$	−9.09286e23	−0.243288
$387$	9.62295e23i	0.251220i
$388$	− 6.29005e24i	− 1.60233i
$389$	4.58505e24	1.13978	0.569892	−	0.821719i	$-0.306985\pi$
$389$	4.58505e24	1.13978	0.569892	+	0.821719i	$0.306985\pi$
$390$	0	0
$391$	9.25738e23	0.219184
$392$	− 6.84383e24i	− 1.58155i
$393$	− 2.42263e24i	− 0.546460i
$394$	6.59426e24	1.45195
$395$	0	0
$396$	−5.11439e24	−1.07322
$397$	5.62169e24i	1.15175i	0.817539	+	0.575873i	$0.195338\pi$
$397$	5.62169e24i	1.15175i	−0.817539	+	0.575873i	$0.804662\pi$
$398$	3.15217e24i	0.630551i
$399$	−2.62178e21	−0.000512098 0
$400$	0	0
$401$	−8.34521e24	−1.55441	−0.777206	−	0.629247i	$-0.783364\pi$
$401$	−8.34521e24	−1.55441	−0.777206	+	0.629247i	$0.783364\pi$
$402$	− 7.11378e24i	− 1.29406i
$403$	− 3.12218e22i	− 0.00554703i
$404$	−8.88456e23	−0.154175
$405$	0	0
$406$	3.38136e22	0.00559878
$407$	9.40691e24i	1.52160i
$408$	− 4.12200e24i	− 0.651383i
$409$	1.09120e25	1.68474	0.842370	−	0.538900i	$-0.181160\pi$
$409$	1.09120e25	1.68474	0.842370	+	0.538900i	$0.181160\pi$
$410$	0	0
$411$	2.17947e24	0.321258
$412$	− 1.98798e25i	− 2.86344i
$413$	6.02754e21i	0 0.000848427i
$414$	1.27328e24	0.175154
$415$	0	0
$416$	−6.62414e23	−0.0870448
$417$	4.64796e24i	0.596994i
$418$	− 1.00537e25i	− 1.26226i
$419$	1.35175e25	1.65906	0.829529	−	0.558463i	$-0.188609\pi$
$419$	1.35175e25	1.65906	0.829529	+	0.558463i	$0.188609\pi$
$420$	0	0
$421$	9.91185e24	1.16272	0.581360	−	0.813647i	$-0.302521\pi$
$421$	9.91185e24	1.16272	0.581360	+	0.813647i	$0.302521\pi$
$422$	9.62927e24i	1.10440i
$423$	− 5.41183e23i	− 0.0606891i
$424$	−6.33318e24	−0.694458
$425$	0	0
$426$	−7.80053e24	−0.817962
$427$	− 7.73477e21i	0 0.000793200i
$428$	− 2.61259e25i	− 2.62032i
$429$	−3.46083e24	−0.339497
$430$	0	0
$431$	1.91272e24	0.179522	0.0897610	−	0.995963i	$-0.471390\pi$
$431$	1.91272e24	0.179522	0.0897610	+	0.995963i	$0.471390\pi$
$432$	− 1.63494e24i	− 0.150109i
$433$	− 5.77174e24i	− 0.518408i	−0.965823	−	0.259204i	$-0.916540\pi$
$433$	− 5.77174e24i	− 0.518408i	0.965823	−	0.259204i	$-0.0834602\pi$
$434$	−6.17353e20	−5.42477e−5 0
$435$	0	0
$436$	−3.45663e25	−2.90758
$437$	1.64718e24i	0.135571i
$438$	− 7.69771e24i	− 0.619951i
$439$	−8.11473e21	−0.000639530 0	−0.000319765	−	1.00000i	$-0.500102\pi$
$439$	−8.11473e21	−0.000639530 0	−0.000319765		1.00000i	$0.500102\pi$
$440$	0	0
$441$	−4.41615e24	−0.333332
$442$	− 5.80548e24i	− 0.428871i
$443$	− 2.51728e24i	− 0.182010i	−0.995850	−	0.0910051i	$-0.970992\pi$
$443$	− 2.51728e24i	− 0.182010i	0.995850	−	0.0910051i	$-0.0290079\pi$
$444$	−1.42833e25	−1.01086
$445$	0	0
$446$	−2.34350e25	−1.58922
$447$	− 4.05095e24i	− 0.268928i
$448$	3.72232e22i	0.00241920i
$449$	1.07451e25	0.683706	0.341853	−	0.939753i	$-0.388945\pi$
$449$	1.07451e25	0.683706	0.341853	+	0.939753i	$0.388945\pi$
$450$	0	0
$451$	−2.25716e25	−1.37685
$452$	5.54869e25i	3.31417i
$453$	− 4.41784e24i	− 0.258391i
$454$	−2.99852e25	−1.71742
$455$	0	0
$456$	7.33436e24	0.402899
$457$	8.09140e24i	0.435331i	0.976023	+	0.217665i	$0.0698442\pi$
$457$	8.09140e24i	0.435331i	−0.976023	+	0.217665i	$0.930156\pi$
$458$	4.08603e25i	2.15317i
$459$	−2.65982e24	−0.137288
$460$	0	0
$461$	1.48075e25	0.733368	0.366684	−	0.930346i	$-0.380493\pi$
$461$	1.48075e25	0.733368	0.366684	+	0.930346i	$0.380493\pi$
$462$	6.84313e22i	0.00332014i
$463$	2.65292e25i	1.26097i	0.776202	+	0.630485i	$0.217144\pi$
$463$	2.65292e25i	1.26097i	−0.776202	+	0.630485i	$0.782856\pi$
$464$	−2.72783e25	−1.27027
$465$	0	0
$466$	−1.11384e25	−0.497916
$467$	3.57468e25i	1.56576i	0.622170	+	0.782882i	$0.286251\pi$
$467$	3.57468e25i	1.56576i	−0.622170	+	0.782882i	$0.713749\pi$
$468$	− 5.25486e24i	− 0.225541i
$469$	−6.26397e22	−0.00263456
$470$	0	0
$471$	−6.16494e24	−0.249018
$472$	− 1.68619e25i	− 0.667510i
$473$	3.24927e25i	1.26068i
$474$	4.46110e25	1.69648
$475$	0	0
$476$	−7.55442e22	−0.00276016
$477$	4.08664e24i	0.146366i
$478$	− 1.52128e25i	− 0.534127i
$479$	2.88220e24	0.0992056	0.0496028	−	0.998769i	$-0.484204\pi$
$479$	2.88220e24	0.0992056	0.0496028	+	0.998769i	$0.484204\pi$
$480$	0	0
$481$	−9.66528e24	−0.319769
$482$	− 5.55152e25i	− 1.80080i
$483$	− 1.12117e22i	0 0.000356595i
$484$	−1.10974e26	−3.46090
$485$	0	0
$486$	−3.65837e24	−0.109709
$487$	6.03233e25i	1.77403i	0.461743	+	0.887014i	$0.347224\pi$
$487$	6.03233e25i	1.77403i	−0.461743	+	0.887014i	$0.652776\pi$
$488$	2.16378e25i	0.624059i
$489$	3.94822e24	0.111678
$490$	0	0
$491$	4.20599e25	1.14444	0.572222	−	0.820099i	$-0.306082\pi$
$491$	4.20599e25	1.14444	0.572222	+	0.820099i	$0.306082\pi$
$492$	− 3.42723e25i	− 0.914693i
$493$	4.43779e25i	1.16177i
$494$	1.03298e25	0.265269
$495$	0	0
$496$	4.98034e23	0.0123079
$497$	6.86869e22i	0.00166528i
$498$	− 4.01577e25i	− 0.955191i
$499$	3.96358e25	0.924979	0.462490	−	0.886625i	$-0.346956\pi$
$499$	3.96358e25	0.924979	0.462490	+	0.886625i	$0.346956\pi$
$500$	0	0
$501$	5.04004e25	1.13234
$502$	4.76904e25i	1.05134i
$503$	− 5.09940e25i	− 1.10312i	−0.834135	−	0.551561i	$-0.814032\pi$
$503$	− 5.09940e25i	− 1.10312i	0.834135	−	0.551561i	$-0.185968\pi$
$504$	−4.99221e22	−0.00105975
$505$	0	0
$506$	4.29933e25	0.878965
$507$	2.52191e25i	0.506004i
$508$	8.84651e25i	1.74207i
$509$	4.45056e25	0.860193	0.430096	−	0.902783i	$-0.358480\pi$
$509$	4.45056e25	0.860193	0.430096	+	0.902783i	$0.358480\pi$
$510$	0	0
$511$	−6.77814e22	−0.00126215
$512$	− 7.80561e25i	− 1.42673i
$513$	− 4.73267e24i	− 0.0849164i
$514$	−1.12355e26	−1.97899
$515$	0	0
$516$	−4.93364e25	−0.837520
$517$	− 1.82735e25i	− 0.304552i
$518$	1.91113e23i	0.00312721i
$519$	5.63540e25	0.905388
$520$	0	0
$521$	−1.65819e24	−0.0256847	−0.0128424	−	0.999918i	$-0.504088\pi$
$521$	−1.65819e24	−0.0256847	−0.0128424	+	0.999918i	$0.504088\pi$
$522$	6.10382e25i	0.928393i
$523$	4.69898e25i	0.701839i	0.936406	+	0.350920i	$0.114131\pi$
$523$	4.69898e25i	0.701839i	−0.936406	+	0.350920i	$0.885869\pi$
$524$	1.24207e26	1.82180
$525$	0	0
$526$	−3.17115e24	−0.0448593
$527$	− 8.10231e23i	− 0.0112566i
$528$	− 5.52053e25i	− 0.753283i
$529$	6.75715e25	0.905596
$530$	0	0
$531$	−1.08805e25	−0.140687
$532$	− 1.34417e23i	− 0.00170724i
$533$	− 2.31916e25i	− 0.289349i
$534$	1.40358e26	1.72026
$535$	0	0
$536$	1.75233e26	2.07277
$537$	− 7.46114e24i	− 0.0867060i
$538$	− 4.73752e25i	− 0.540903i
$539$	−1.49115e26	−1.67274
$540$	0	0
$541$	6.20242e25	0.671718	0.335859	−	0.941912i	$-0.390973\pi$
$541$	6.20242e25	0.671718	0.335859	+	0.941912i	$0.390973\pi$
$542$	4.51808e25i	0.480796i
$543$	− 6.21152e25i	− 0.649531i
$544$	−1.71902e25	−0.176641
$545$	0	0
$546$	−7.03109e22	−0.000697738 0
$547$	7.76624e25i	0.757410i	0.925517	+	0.378705i	$0.123630\pi$
$547$	7.76624e25i	0.757410i	−0.925517	+	0.378705i	$0.876370\pi$
$548$	1.11740e26i	1.07101i
$549$	1.39623e25	0.131529
$550$	0	0
$551$	−7.89624e25	−0.718588
$552$	3.13646e25i	0.280555i
$553$	− 3.92818e23i	− 0.00345384i
$554$	−2.21128e26	−1.91117
$555$	0	0
$556$	−2.38299e26	−1.99027
$557$	3.67420e25i	0.301675i	0.988559	+	0.150837i	$0.0481969\pi$
$557$	3.67420e25i	0.301675i	−0.988559	+	0.150837i	$0.951803\pi$
$558$	− 1.11441e24i	− 0.00899538i
$559$	−3.33852e25	−0.264936
$560$	0	0
$561$	−8.98112e25	−0.688943
$562$	− 2.82659e26i	− 2.13191i
$563$	− 1.24531e26i	− 0.923526i	−0.887003	−	0.461763i	$-0.847217\pi$
$563$	− 1.24531e26i	− 0.923526i	0.887003	−	0.461763i	$-0.152783\pi$
$564$	2.77462e25	0.202326
$565$	0	0
$566$	2.32231e26	1.63743
$567$	3.22134e22i	0 0.000223356i
$568$	− 1.92150e26i	− 1.31018i
$569$	5.63513e25	0.377866	0.188933	−	0.981990i	$-0.439497\pi$
$569$	5.63513e25	0.377866	0.188933	+	0.981990i	$0.439497\pi$
$570$	0	0
$571$	−1.23813e26	−0.803012	−0.401506	−	0.915856i	$-0.631513\pi$
$571$	−1.23813e26	−0.803012	−0.401506	+	0.915856i	$0.631513\pi$
$572$	− 1.77435e26i	− 1.13182i
$573$	5.50469e25i	0.345354i
$574$	−4.58570e23	−0.00282971
$575$	0	0
$576$	−6.71930e25	−0.401153
$577$	− 3.01722e26i	− 1.77189i	−0.463790	−	0.885945i	$-0.653511\pi$
$577$	− 3.01722e26i	− 1.77189i	0.463790	−	0.885945i	$-0.346489\pi$
$578$	1.45390e26i	0.839888i
$579$	−1.44531e25	−0.0821323
$580$	0	0
$581$	−3.53605e23	−0.00194467
$582$	− 1.51924e26i	− 0.821974i
$583$	1.37989e26i	0.734501i
$584$	1.89617e26	0.993014
$585$	0	0
$586$	3.49968e26	1.77420
$587$	− 6.00743e25i	− 0.299659i	−0.988712	−	0.149829i	$-0.952128\pi$
$587$	− 6.00743e25i	− 0.299659i	0.988712	−	0.149829i	$-0.0478724\pi$
$588$	− 2.26414e26i	− 1.11127i
$589$	1.44166e24	0.00696254
$590$	0	0
$591$	1.04816e26	0.490168
$592$	− 1.54176e26i	− 0.709511i
$593$	9.94196e25i	0.450248i	0.974330	+	0.225124i	$0.0722788\pi$
$593$	9.94196e25i	0.450248i	−0.974330	+	0.225124i	$0.927721\pi$
$594$	−1.23528e26	−0.550547
$595$	0	0
$596$	2.07690e26	0.896554
$597$	5.01037e25i	0.212869i
$598$	4.41742e25i	0.184717i
$599$	1.95677e26	0.805350	0.402675	−	0.915343i	$-0.368080\pi$
$599$	1.95677e26	0.805350	0.402675	+	0.915343i	$0.368080\pi$
$600$	0	0
$601$	−4.73445e26	−1.88782	−0.943912	−	0.330197i	$-0.892885\pi$
$601$	−4.73445e26	−1.88782	−0.943912	+	0.330197i	$0.892885\pi$
$602$	6.60129e23i	0.00259097i
$603$	− 1.13073e26i	− 0.436864i
$604$	2.26500e26	0.861426
$605$	0	0
$606$	−2.14589e25	−0.0790894
$607$	− 1.22707e26i	− 0.445222i	−0.974907	−	0.222611i	$-0.928542\pi$
$607$	− 1.22707e26i	− 0.445222i	0.974907	−	0.222611i	$-0.0714580\pi$
$608$	− 3.05868e25i	− 0.109257i
$609$	5.37466e23	0.00189011
$610$	0	0
$611$	1.87754e25	0.0640026
$612$	− 1.36368e26i	− 0.457692i
$613$	− 3.20354e26i	− 1.05866i	−0.848417	−	0.529329i	$-0.822444\pi$
$613$	− 3.20354e26i	− 1.05866i	0.848417	−	0.529329i	$-0.177556\pi$
$614$	3.05888e26	0.995320
$615$	0	0
$616$	−1.68566e24	−0.00531807
$617$	9.79781e25i	0.304383i	0.988351	+	0.152191i	$0.0486330\pi$
$617$	9.79781e25i	0.304383i	−0.988351	+	0.152191i	$0.951367\pi$
$618$	− 4.80158e26i	− 1.46890i
$619$	1.22713e25	0.0369682	0.0184841	−	0.999829i	$-0.494116\pi$
$619$	1.22713e25	0.0369682	0.0184841	+	0.999829i	$0.494116\pi$
$620$	0	0
$621$	2.02387e25	0.0591307
$622$	4.05085e26i	1.16557i
$623$	− 1.23591e24i	− 0.00350226i
$624$	5.67215e25	0.158305
$625$	0	0
$626$	4.62402e26	1.25188
$627$	− 1.59803e26i	− 0.426131i
$628$	− 3.16074e26i	− 0.830179i
$629$	−2.50822e26	−0.648909
$630$	0	0
$631$	4.30803e26	1.08143	0.540716	−	0.841205i	$-0.318153\pi$
$631$	4.30803e26	1.08143	0.540716	+	0.841205i	$0.318153\pi$
$632$	1.09890e27i	2.71735i
$633$	1.53057e26i	0.372836i
$634$	7.22579e25	0.173395
$635$	0	0
$636$	−2.09520e26	−0.487958
$637$	− 1.53211e26i	− 0.351532i
$638$	2.06101e27i	4.65890i
$639$	−1.23989e26	−0.276138
$640$	0	0
$641$	5.54923e26	1.19972	0.599862	−	0.800104i	$-0.295222\pi$
$641$	5.54923e26	1.19972	0.599862	+	0.800104i	$0.295222\pi$
$642$	− 6.31020e26i	− 1.34419i
$643$	− 6.72911e26i	− 1.41239i	−0.708019	−	0.706193i	$-0.750411\pi$
$643$	− 6.72911e26i	− 1.41239i	0.708019	−	0.706193i	$-0.249589\pi$
$644$	5.74820e23	0.00118882
$645$	0	0
$646$	2.68066e26	0.538311
$647$	− 3.57860e26i	− 0.708146i	−0.935218	−	0.354073i	$-0.884796\pi$
$647$	− 3.57860e26i	− 0.708146i	0.935218	−	0.354073i	$-0.115204\pi$
$648$	− 9.01163e25i	− 0.175728i
$649$	−3.67391e26	−0.705999
$650$	0	0
$651$	−9.81282e21	−1.83136e−5 0
$652$	2.02423e26i	0.372313i
$653$	− 5.10990e26i	− 0.926269i	−0.886288	−	0.463135i	$-0.846725\pi$
$653$	− 5.10990e26i	− 0.926269i	0.886288	−	0.463135i	$-0.153275\pi$
$654$	−8.34882e26	−1.49155
$655$	0	0
$656$	3.69940e26	0.642014
$657$	− 1.22355e26i	− 0.209291i
$658$	− 3.71249e23i	0 0.000625920i
$659$	6.67000e26	1.10844	0.554222	−	0.832369i	$-0.313016\pi$
$659$	6.67000e26	1.10844	0.554222	+	0.832369i	$0.313016\pi$
$660$	0	0
$661$	2.27178e26	0.366819	0.183410	−	0.983037i	$-0.441287\pi$
$661$	2.27178e26	0.366819	0.183410	+	0.983037i	$0.441287\pi$
$662$	4.75827e26i	0.757352i
$663$	− 9.22779e25i	− 0.144784i
$664$	9.89202e26	1.52999
$665$	0	0
$666$	−3.44985e26	−0.518556
$667$	− 3.37674e26i	− 0.500382i
$668$	2.58400e27i	3.77500i
$669$	−3.72498e26	−0.536508
$670$	0	0
$671$	4.71450e26	0.660043
$672$	2.08192e23i	0 0.000287380i
$673$	− 2.72017e26i	− 0.370214i	−0.982718	−	0.185107i	$-0.940737\pi$
$673$	− 2.72017e26i	− 0.370214i	0.982718	−	0.185107i	$-0.0592632\pi$
$674$	−1.61139e27	−2.16238
$675$	0	0
$676$	−1.29297e27	−1.68692
$677$	4.27674e26i	0.550200i	0.961416	+	0.275100i	$0.0887110\pi$
$677$	4.27674e26i	0.550200i	−0.961416	+	0.275100i	$0.911289\pi$
$678$	1.34018e27i	1.70012i
$679$	−1.33775e24	−0.00167345
$680$	0	0
$681$	−4.76614e26	−0.579788
$682$	− 3.76290e25i	− 0.0451409i
$683$	1.11866e26i	0.132344i	0.997808	+	0.0661719i	$0.0210786\pi$
$683$	1.11866e26i	0.132344i	−0.997808	+	0.0661719i	$0.978921\pi$
$684$	2.42642e26	0.283095
$685$	0	0
$686$	−6.05892e24	−0.00687569
$687$	6.49473e26i	0.726896i
$688$	− 5.32543e26i	− 0.587847i
$689$	−1.41779e26	−0.154358
$690$	0	0
$691$	1.82536e27	1.93333	0.966667	−	0.256037i	$-0.0824171\pi$
$691$	1.82536e27	1.93333	0.966667	+	0.256037i	$0.0824171\pi$
$692$	2.88924e27i	3.01839i
$693$	1.08771e24i	0.00112085i
$694$	1.06102e26	0.107847
$695$	0	0
$696$	−1.50355e27	−1.48706
$697$	− 6.01839e26i	− 0.587177i
$698$	1.37817e27i	1.32641i
$699$	−1.77045e26	−0.168093
$700$	0	0
$701$	−2.03227e27	−1.87785	−0.938924	−	0.344125i	$-0.888176\pi$
$701$	−2.03227e27	−1.87785	−0.938924	+	0.344125i	$0.888176\pi$
$702$	− 1.26921e26i	− 0.115699i
$703$	− 4.46292e26i	− 0.401369i
$704$	−2.26883e27	−2.01308
$705$	0	0
$706$	−2.77070e27	−2.39301
$707$	1.88955e23i	0 0.000161017i
$708$	− 5.57840e26i	− 0.469023i
$709$	1.86039e27	1.54335	0.771675	−	0.636017i	$-0.219419\pi$
$709$	1.86039e27	1.54335	0.771675	+	0.636017i	$0.219419\pi$
$710$	0	0
$711$	7.09091e26	0.572718
$712$	3.45742e27i	2.75544i
$713$	6.16510e24i	0.00484830i
$714$	−1.82462e24	−0.00141592
$715$	0	0
$716$	3.82529e26	0.289062
$717$	− 2.41807e26i	− 0.180317i
$718$	− 2.51234e27i	− 1.84883i
$719$	−1.92780e27	−1.40003	−0.700014	−	0.714129i	$-0.746823\pi$
$719$	−1.92780e27	−1.40003	−0.700014	+	0.714129i	$0.746823\pi$
$720$	0	0
$721$	−4.22798e24	−0.00299053
$722$	− 1.97293e27i	− 1.37724i
$723$	− 8.82414e26i	− 0.607937i
$724$	3.18462e27	2.16541
$725$	0	0
$726$	−2.68036e27	−1.77539
$727$	− 1.11559e27i	− 0.729339i	−0.931137	−	0.364670i	$-0.881182\pi$
$727$	− 1.11559e27i	− 0.729339i	0.931137	−	0.364670i	$-0.118818\pi$
$728$	− 1.73196e24i	− 0.00111761i
$729$	−5.81497e25	−0.0370370
$730$	0	0
$731$	−8.66372e26	−0.537637
$732$	7.15842e26i	0.438492i
$733$	− 2.04762e27i	− 1.23812i	−0.785344	−	0.619059i	$-0.787514\pi$
$733$	− 2.04762e27i	− 1.23812i	0.785344	−	0.619059i	$-0.212486\pi$
$734$	2.51868e27	1.50335
$735$	0	0
$736$	1.30801e26	0.0760802
$737$	− 3.81802e27i	− 2.19229i
$738$	− 8.27782e26i	− 0.469224i
$739$	−1.50373e27	−0.841486	−0.420743	−	0.907180i	$-0.638231\pi$
$739$	−1.50373e27	−0.841486	−0.420743	+	0.907180i	$0.638231\pi$
$740$	0	0
$741$	1.64192e26	0.0895527
$742$	2.80341e24i	0.00150956i
$743$	− 1.88836e27i	− 1.00390i	−0.864897	−	0.501950i	$-0.832616\pi$
$743$	− 1.88836e27i	− 1.00390i	0.864897	−	0.501950i	$-0.167384\pi$
$744$	2.74511e25	0.0144084
$745$	0	0
$746$	−9.63821e26	−0.493149
$747$	− 6.38306e26i	− 0.322466i
$748$	− 4.60457e27i	− 2.29681i
$749$	−5.55638e24	−0.00273662
$750$	0	0
$751$	8.19244e26	0.393400	0.196700	−	0.980464i	$-0.436978\pi$
$751$	8.19244e26	0.393400	0.196700	+	0.980464i	$0.436978\pi$
$752$	2.99495e26i	0.142011i
$753$	7.58037e26i	0.354926i
$754$	−2.11762e27	−0.979082
$755$	0	0
$756$	−1.65157e24	−0.000744628 0
$757$	1.94096e27i	0.864184i	0.901829	+	0.432092i	$0.142224\pi$
$757$	1.94096e27i	0.864184i	−0.901829	+	0.432092i	$0.857776\pi$
$758$	− 3.90907e27i	− 1.71876i
$759$	6.83378e26	0.296732
$760$	0	0
$761$	2.40135e27	1.01695	0.508477	−	0.861076i	$-0.330209\pi$
$761$	2.40135e27	1.01695	0.508477	+	0.861076i	$0.330209\pi$
$762$	2.13670e27i	0.893659i
$763$	7.35147e24i	0.00303663i
$764$	−2.82223e27	−1.15134
$765$	0	0
$766$	−3.83018e27	−1.52421
$767$	− 3.77482e26i	− 0.148368i
$768$	− 2.81516e27i	− 1.09288i
$769$	3.49979e27	1.34197	0.670984	−	0.741472i	$-0.265872\pi$
$769$	3.49979e27	1.34197	0.670984	+	0.741472i	$0.265872\pi$
$770$	0	0
$771$	−1.78588e27	−0.668091
$772$	− 7.41002e26i	− 0.273814i
$773$	3.84483e27i	1.40337i	0.712487	+	0.701685i	$0.247569\pi$
$773$	3.84483e27i	1.40337i	−0.712487	+	0.701685i	$0.752431\pi$
$774$	−1.19163e27	−0.429636
$775$	0	0
$776$	3.74233e27	1.31661
$777$	3.03774e24i	0.00105572i
$778$	5.67774e27i	1.94926i
$779$	1.07086e27	0.363186
$780$	0	0
$781$	−4.18661e27	−1.38573
$782$	1.14636e27i	0.374848i
$783$	9.70201e26i	0.313419i
$784$	2.44394e27	0.779987
$785$	0	0
$786$	2.99999e27	0.934556
$787$	4.22212e27i	1.29948i	0.760155	+	0.649741i	$0.225123\pi$
$787$	4.22212e27i	1.29948i	−0.760155	+	0.649741i	$0.774877\pi$
$788$	5.37384e27i	1.63413i
$789$	−5.04054e25	−0.0151442
$790$	0	0
$791$	1.18008e25	0.00346127
$792$	− 3.04286e27i	− 0.881845i
$793$	4.84399e26i	0.138710i
$794$	−6.96142e27	−1.96971
$795$	0	0
$796$	−2.56879e27	−0.709667
$797$	− 2.10706e27i	− 0.575205i	−0.957750	−	0.287602i	$-0.907142\pi$
$797$	− 2.10706e27i	− 0.575205i	0.957750	−	0.287602i	$-0.0928582\pi$
$798$	− 3.24659e24i	0 0.000875789i
$799$	4.87237e26	0.129881
$800$	0	0
$801$	2.23098e27	0.580747
$802$	− 1.03340e28i	− 2.65835i
$803$	− 4.13142e27i	− 1.05027i
$804$	5.79722e27	1.45642
$805$	0	0
$806$	3.86625e25	0.00948652
$807$	− 7.53027e26i	− 0.182605i
$808$	− 5.28596e26i	− 0.126682i
$809$	−2.31386e27	−0.548056	−0.274028	−	0.961722i	$-0.588356\pi$
$809$	−2.31386e27	−0.548056	−0.274028	+	0.961722i	$0.588356\pi$
$810$	0	0
$811$	2.32427e27	0.537760	0.268880	−	0.963174i	$-0.413347\pi$
$811$	2.32427e27	0.537760	0.268880	+	0.963174i	$0.413347\pi$
$812$	2.75556e25i	0.00630127i
$813$	7.18148e26i	0.162313i
$814$	−1.16487e28	−2.60224
$815$	0	0
$816$	1.47197e27	0.321249
$817$	− 1.54155e27i	− 0.332544i
$818$	1.35125e28i	2.88124i
$819$	−1.11759e24	−0.000235551 0
$820$	0	0
$821$	6.08231e27	1.25259	0.626295	−	0.779587i	$-0.284571\pi$
$821$	6.08231e27	1.25259	0.626295	+	0.779587i	$0.284571\pi$
$822$	2.69888e27i	0.549415i
$823$	3.84390e27i	0.773523i	0.922180	+	0.386762i	$0.126406\pi$
$823$	3.84390e27i	0.773523i	−0.922180	+	0.386762i	$0.873594\pi$
$824$	1.18277e28	2.35283
$825$	0	0
$826$	−7.46400e24	−0.00145098
$827$	5.47093e27i	1.05138i	0.850677	+	0.525689i	$0.176193\pi$
$827$	5.47093e27i	1.05138i	−0.850677	+	0.525689i	$0.823807\pi$
$828$	1.03763e27i	0.197131i
$829$	−8.53655e26	−0.160330	−0.0801649	−	0.996782i	$-0.525545\pi$
$829$	−8.53655e26	−0.160330	−0.0801649	+	0.996782i	$0.525545\pi$
$830$	0	0
$831$	−3.51482e27	−0.645198
$832$	− 2.33115e27i	− 0.423056i
$833$	− 3.97594e27i	− 0.713365i
$834$	−5.75564e27	−1.02098
$835$	0	0
$836$	8.19301e27	1.42064
$837$	− 1.77135e25i	− 0.00303677i
$838$	1.67389e28i	2.83732i
$839$	8.76504e27	1.46898	0.734489	−	0.678621i	$-0.237422\pi$
$839$	8.76504e27	1.46898	0.734489	+	0.678621i	$0.237422\pi$
$840$	0	0
$841$	1.00841e28	1.65224
$842$	1.22740e28i	1.98848i
$843$	− 4.49287e27i	− 0.719716i
$844$	−7.84716e27	−1.24297
$845$	0	0
$846$	6.70155e26	0.103790
$847$	2.36016e25i	0.00361451i
$848$	− 2.26158e27i	− 0.342493i
$849$	3.69131e27	0.552786
$850$	0	0
$851$	1.90852e27	0.279489
$852$	− 6.35687e27i	− 0.920592i
$853$	− 4.55754e27i	− 0.652702i	−0.945249	−	0.326351i	$-0.894181\pi$
$853$	− 4.55754e27i	− 0.652702i	0.945249	−	0.326351i	$-0.105819\pi$
$854$	9.57809e24	0.00135653
$855$	0	0
$856$	1.55438e28	2.15307
$857$	8.72531e27i	1.19526i	0.801771	+	0.597631i	$0.203891\pi$
$857$	8.72531e27i	1.19526i	−0.801771	+	0.597631i	$0.796109\pi$
$858$	− 4.28559e27i	− 0.580606i
$859$	6.82608e27	0.914610	0.457305	−	0.889310i	$-0.348815\pi$
$859$	6.82608e27	0.914610	0.457305	+	0.889310i	$0.348815\pi$
$860$	0	0
$861$	−7.28895e24	−0.000955290 0
$862$	2.36855e27i	0.307018i
$863$	− 1.70088e27i	− 0.218058i	−0.994039	−	0.109029i	$-0.965226\pi$
$863$	− 1.70088e27i	− 0.218058i	0.994039	−	0.109029i	$-0.0347741\pi$
$864$	−3.75816e26	−0.0476535
$865$	0	0
$866$	7.14723e27	0.886580
$867$	2.31098e27i	0.283540i
$868$	− 5.03098e23i	0 6.10542e-5i
$869$	2.39431e28	2.87404
$870$	0	0
$871$	3.92289e27	0.460716
$872$	− 2.05656e28i	− 2.38910i
$873$	− 2.41483e27i	− 0.277492i
$874$	−2.03973e27	−0.231854
$875$	0	0
$876$	6.27308e27	0.697737
$877$	− 9.69466e27i	− 1.06669i	−0.845899	−	0.533343i	$-0.820936\pi$
$877$	− 9.69466e27i	− 1.06669i	0.845899	−	0.533343i	$-0.179064\pi$
$878$	− 1.00486e25i	− 0.00109372i
$879$	5.56274e27	0.598955
$880$	0	0
$881$	−2.20901e27	−0.232769	−0.116385	−	0.993204i	$-0.537131\pi$
$881$	−2.20901e27	−0.232769	−0.116385	+	0.993204i	$0.537131\pi$
$882$	− 5.46858e27i	− 0.570064i
$883$	5.45945e27i	0.563018i	0.959559	+	0.281509i	$0.0908349\pi$
$883$	5.45945e27i	0.563018i	−0.959559	+	0.281509i	$0.909165\pi$
$884$	4.73104e27	0.482681
$885$	0	0
$886$	3.11718e27	0.311273
$887$	1.69664e28i	1.67616i	0.545546	+	0.838081i	$0.316322\pi$
$887$	1.69664e28i	1.67616i	−0.545546	+	0.838081i	$0.683678\pi$
$888$	− 8.49799e27i	− 0.830602i
$889$	1.88145e25	0.00181939
$890$	0	0
$891$	−1.96348e27	−0.185861
$892$	− 1.90978e28i	− 1.78862i
$893$	8.66950e26i	0.0803351i
$894$	5.01636e27	0.459920
$895$	0	0
$896$	−4.05485e25	−0.00363956
$897$	7.02148e26i	0.0623592i
$898$	1.33058e28i	1.16927i
$899$	−2.95541e26	−0.0256981
$900$	0	0
$901$	−3.67927e27	−0.313239
$902$	− 2.79508e28i	− 2.35468i
$903$	1.04927e25i	0 0.000874692i
$904$	−3.30125e28	−2.72319
$905$	0	0
$906$	5.47068e27	0.441899
$907$	1.06963e28i	0.854996i	0.904016	+	0.427498i	$0.140605\pi$
$907$	1.06963e28i	0.854996i	−0.904016	+	0.427498i	$0.859395\pi$
$908$	− 2.44357e28i	− 1.93290i
$909$	−3.41089e26	−0.0267000
$910$	0	0
$911$	−2.36272e28	−1.81129	−0.905645	−	0.424036i	$-0.860613\pi$
$911$	−2.36272e28	−1.81129	−0.905645	+	0.424036i	$0.860613\pi$
$912$	2.61910e27i	0.198702i
$913$	− 2.15530e28i	− 1.61821i
$914$	−1.00197e28	−0.744502
$915$	0	0
$916$	−3.32982e28	−2.42333
$917$	− 2.64161e25i	− 0.00190265i
$918$	− 3.29370e27i	− 0.234789i
$919$	−4.79736e27	−0.338458	−0.169229	−	0.985577i	$-0.554128\pi$
$919$	−4.79736e27	−0.338458	−0.169229	+	0.985577i	$0.554128\pi$
$920$	0	0
$921$	4.86208e27	0.336013
$922$	1.83363e28i	1.25420i
$923$	− 4.30160e27i	− 0.291215i
$924$	−5.57666e25	−0.00373672
$925$	0	0
$926$	−3.28515e28	−2.15651
$927$	− 7.63210e27i	− 0.495891i
$928$	6.27031e27i	0.403258i
$929$	4.77499e27	0.303965	0.151982	−	0.988383i	$-0.451434\pi$
$929$	4.77499e27	0.303965	0.151982	+	0.988383i	$0.451434\pi$
$930$	0	0
$931$	7.07446e27	0.441237
$932$	− 9.07699e27i	− 0.560390i
$933$	6.43881e27i	0.393487i
$934$	−4.42658e28	−2.67777
$935$	0	0
$936$	3.12643e27	0.185323
$937$	− 3.08658e27i	− 0.181114i	−0.995891	−	0.0905568i	$-0.971135\pi$
$937$	− 3.08658e27i	− 0.181114i	0.995891	−	0.0905568i	$-0.0288647\pi$
$938$	− 7.75677e25i	− 0.00450562i
$939$	7.34987e27	0.422627
$940$	0	0
$941$	2.51804e27	0.141893	0.0709466	−	0.997480i	$-0.477398\pi$
$941$	2.51804e27	0.141893	0.0709466	+	0.997480i	$0.477398\pi$
$942$	− 7.63414e27i	− 0.425870i
$943$	4.57943e27i	0.252901i
$944$	6.02139e27	0.329202
$945$	0	0
$946$	−4.02363e28	−2.15602
$947$	8.85552e27i	0.469774i	0.972023	+	0.234887i	$0.0754720\pi$
$947$	8.85552e27i	0.469774i	−0.972023	+	0.234887i	$0.924528\pi$
$948$	3.63547e28i	1.90933i
$949$	4.24489e27	0.220718
$950$	0	0
$951$	1.14854e27	0.0585370
$952$	− 4.49458e25i	− 0.00226797i
$953$	− 1.35516e28i	− 0.677030i	−0.940961	−	0.338515i	$-0.890075\pi$
$953$	− 1.35516e28i	− 0.677030i	0.940961	−	0.338515i	$-0.109925\pi$
$954$	−5.06055e27	−0.250315
$955$	0	0
$956$	1.23973e28	0.601144
$957$	3.27597e28i	1.57281i
$958$	3.56907e27i	0.169661i
$959$	2.37647e25	0.00111855
$960$	0	0
$961$	−2.16653e28	−0.999751
$962$	− 1.19687e28i	− 0.546868i
$963$	− 1.00300e28i	− 0.453788i
$964$	4.52409e28	2.02675
$965$	0	0
$966$	1.38837e25	0.000609848 0
$967$	5.51108e27i	0.239710i	0.992791	+	0.119855i	$0.0382429\pi$
$967$	5.51108e27i	0.239710i	−0.992791	+	0.119855i	$0.961757\pi$
$968$	− 6.60250e28i	− 2.84376i
$969$	4.26091e27	0.181730
$970$	0	0
$971$	2.37023e28	0.991308	0.495654	−	0.868520i	$-0.334928\pi$
$971$	2.37023e28	0.991308	0.495654	+	0.868520i	$0.334928\pi$
$972$	− 2.98131e27i	− 0.123475i
$973$	5.06808e25i	0.00207860i
$974$	−7.46993e28	−3.03394
$975$	0	0
$976$	−7.72688e27	−0.307773
$977$	− 6.97540e27i	− 0.275151i	−0.990491	−	0.137575i	$-0.956069\pi$
$977$	− 6.97540e27i	− 0.275151i	0.990491	−	0.137575i	$-0.0439309\pi$
$978$	4.88915e27i	0.190992i
$979$	7.53310e28	2.91433
$980$	0	0
$981$	−1.32704e28	−0.503535
$982$	5.20835e28i	1.95722i
$983$	− 1.96330e28i	− 0.730683i	−0.930874	−	0.365341i	$-0.880952\pi$
$983$	− 1.96330e28i	− 0.730683i	0.930874	−	0.365341i	$-0.119048\pi$
$984$	2.03907e28	0.751585
$985$	0	0
$986$	−5.49538e28	−1.98686
$987$	− 5.90099e24i	0 0.000211306i
$988$	8.41804e27i	0.298552i
$989$	6.59227e27	0.231564
$990$	0	0
$991$	4.20556e28	1.44918	0.724592	−	0.689178i	$-0.242028\pi$
$991$	4.20556e28	1.44918	0.724592	+	0.689178i	$0.242028\pi$
$992$	− 1.14481e26i	− 0.00390725i
$993$	7.56325e27i	0.255676i
$994$	−8.50560e25	−0.00284796
$995$	0	0
$996$	3.27256e28	1.07504
$997$	− 1.15418e28i	− 0.375551i	−0.982212	−	0.187776i	$-0.939872\pi$
$997$	− 1.15418e28i	− 0.375551i	0.982212	−	0.187776i	$-0.0601278\pi$
$998$	4.90816e28i	1.58190i
$999$	−5.48353e27	−0.175061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.20.b.b.49.4		4
5.2	odd	4		75.20.a.b.1.1		2
5.3	odd	4		3.20.a.b.1.2	✓	2
5.4	even	2	inner	75.20.b.b.49.1		4
15.8	even	4		9.20.a.c.1.1		2
20.3	even	4		48.20.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.20.a.b.1.2	✓	2	5.3	odd	4
9.20.a.c.1.1		2	15.8	even	4
48.20.a.j.1.2		2	20.3	even	4
75.20.a.b.1.1		2	5.2	odd	4
75.20.b.b.49.1		4	5.4	even	2	inner
75.20.b.b.49.4		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)

\(f(q)\)	\(=\)	\(q+1238.32i q^{2} +19683.0i q^{3} -1.00914e6 q^{4} -2.43738e7 q^{6} +214621. i q^{7} -6.00397e8i q^{8} -3.87420e8 q^{9} +O(q^{10})\)	\(q+1238.32i q^{2} +19683.0i q^{3} -1.00914e6 q^{4} -2.43738e7 q^{6} +214621. i q^{7} -6.00397e8i q^{8} -3.87420e8 q^{9} -1.30816e10 q^{11} -1.98629e10i q^{12} -1.34409e10i q^{13} -2.65768e8 q^{14} +2.14402e11 q^{16} -3.48802e11i q^{17} -4.79749e11i q^{18} +6.20630e11 q^{19} -4.22438e9 q^{21} -1.61991e13i q^{22} +2.65405e12i q^{23} +1.18176e13 q^{24} +1.66441e13 q^{26} -7.62560e12i q^{27} -2.16582e11i q^{28} -1.27229e14 q^{29} +2.32290e12 q^{31} -4.92835e13i q^{32} -2.57485e14i q^{33} +4.31927e14 q^{34} +3.90961e14 q^{36} -7.19096e14i q^{37} +7.68535e14i q^{38} +2.64557e14 q^{39} +1.72545e15 q^{41} -5.23112e12i q^{42} -2.48385e15i q^{43} +1.32011e16 q^{44} -3.28655e15 q^{46} +1.39689e15i q^{47} +4.22007e15i q^{48} +1.13988e16 q^{49} +6.86546e15 q^{51} +1.35637e16i q^{52} -1.05483e16i q^{53} +9.44290e15 q^{54} +1.28858e14 q^{56} +1.22159e16i q^{57} -1.57550e17i q^{58} +2.80846e16 q^{59} -3.60392e16 q^{61} +2.87648e15i q^{62} -8.31485e13i q^{63} +1.73437e17 q^{64} +3.18848e17 q^{66} +2.91862e17i q^{67} +3.51989e17i q^{68} -5.22397e16 q^{69} +3.20038e17 q^{71} +2.32606e17i q^{72} +3.15819e17i q^{73} +8.90467e17 q^{74} -6.26301e17 q^{76} -2.80758e15i q^{77} +3.27605e17i q^{78} -1.83029e18 q^{79} +1.50095e17 q^{81} +2.13665e18i q^{82} +1.64758e18i q^{83} +4.26298e15 q^{84} +3.07579e18 q^{86} -2.50426e18i q^{87} +7.85414e18i q^{88} -5.75855e18 q^{89} +2.88469e15 q^{91} -2.67830e18i q^{92} +4.57216e16i q^{93} -1.72979e18 q^{94} +9.70047e17 q^{96} +6.23309e18i q^{97} +1.41154e19i q^{98} +5.06808e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1544968 q^{4} - 27634932 q^{6} - 1549681956 q^{9}+O(q^{10}) \) 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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