LMFDB - Embedded newform 75.22.b.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,22,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, 22, names="a")

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

chi := DirichletCharacter("75.49");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
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:	$209.608008215$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.22.b.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2844.00i q^{2} -59049.0i q^{3} -5.99118e6 q^{4} +1.67935e8 q^{6} -3.63304e8i q^{7} -1.10746e10i q^{8} -3.48678e9 q^{9} +O(q^{10})$	\(q+2844.00i q^{2} -59049.0i q^{3} -5.99118e6 q^{4} +1.67935e8 q^{6} -3.63304e8i q^{7} -1.10746e10i q^{8} -3.48678e9 q^{9} +1.45818e10 q^{11} +3.53773e11i q^{12} +1.13351e11i q^{13} +1.03324e12 q^{14} +1.89318e13 q^{16} +8.58939e12i q^{17} -9.91641e12i q^{18} +2.92029e13 q^{19} -2.14527e13 q^{21} +4.14707e13i q^{22} -1.55899e14i q^{23} -6.53946e14 q^{24} -3.22370e14 q^{26} +2.05891e14i q^{27} +2.17662e15i q^{28} -2.40079e15 q^{29} +2.23982e15 q^{31} +3.06169e16i q^{32} -8.61043e14i q^{33} -2.44282e16 q^{34} +2.08900e16 q^{36} +3.07851e16i q^{37} +8.30532e16i q^{38} +6.69325e15 q^{39} -1.03208e17 q^{41} -6.10116e16i q^{42} -1.65557e17i q^{43} -8.73624e16 q^{44} +4.43377e17 q^{46} +6.65872e16i q^{47} -1.11790e18i q^{48} +4.26556e17 q^{49} +5.07195e17 q^{51} -6.79105e17i q^{52} +4.35423e17i q^{53} -5.85554e17 q^{54} -4.02346e18 q^{56} -1.72440e18i q^{57} -6.82784e18i q^{58} -5.53437e18 q^{59} -7.17621e18 q^{61} +6.37005e18i q^{62} +1.26676e18i q^{63} -4.73716e19 q^{64} +2.44881e18 q^{66} +1.57554e19i q^{67} -5.14606e19i q^{68} -9.20569e18 q^{69} +2.64579e19 q^{71} +3.86148e19i q^{72} +1.34712e19i q^{73} -8.75527e19 q^{74} -1.74960e20 q^{76} -5.29764e18i q^{77} +1.90356e19i q^{78} +1.68861e19 q^{79} +1.21577e19 q^{81} -2.93522e20i q^{82} -1.70688e20i q^{83} +1.28527e20 q^{84} +4.70845e20 q^{86} +1.41764e20i q^{87} -1.61488e20i q^{88} +3.12592e20 q^{89} +4.11808e19 q^{91} +9.34021e20i q^{92} -1.32259e20i q^{93} -1.89374e20 q^{94} +1.80790e21 q^{96} -9.49015e20i q^{97} +1.21313e21i q^{98} -5.08437e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 11982368 q^{4} + 335870712 q^{6} - 6973568802 q^{9}+O(q^{10}) $ 2 * q - 11982368 * q^4 + 335870712 * q^6 - 6973568802 * q^9	$ 2 q - 11982368 q^{4} + 335870712 q^{6} - 6973568802 q^{9} + 29163666312 q^{11} + 2066472696960 q^{14} + 37863631405568 q^{16} + 58405878547592 q^{19} - 42905466344160 q^{21} - 13\!\cdots\!84 q^{24}+ \cdots - 10\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 11982368 * q^4 + 335870712 * q^6 - 6973568802 * q^9 + 29163666312 * q^11 + 2066472696960 * q^14 + 37863631405568 * q^16 + 58405878547592 * q^19 - 42905466344160 * q^21 - 1307891300390784 * q^24 - 644739297512976 * q^26 - 4801577414181516 * q^29 + 4479641353894000 * q^31 - 48856448033321616 * q^34 + 41779933829441568 * q^36 + 13386501680324796 * q^39 - 206415142082562060 * q^41 - 174724890989793408 * q^44 + 886754734659944640 * q^46 + 853112251591835214 * q^49 + 1014389732742478236 * q^51 - 1171108759354363512 * q^54 - 8046910809088542720 * q^56 - 11068731596518162632 * q^59 - 14352410329445922404 * q^61 - 94743180552322555904 * q^64 + 4897610684370927072 * q^66 - 18411385487670559440 * q^69 + 52915709748518752464 * q^71 - 175105474652204086320 * q^74 - 349920365060276428928 * q^76 + 33772250171051973680 * q^79 + 24315330918113857602 * q^81 + 257054543473669885440 * q^84 + 941689755272272449312 * q^86 + 625184973879174087372 * q^89 + 82361573194272303680 * q^91 - 378748085896203496704 * q^94 + 3615795563149709015040 * q^96 - 101687416772650799112 * 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 $

$2$	2844.00i	1.96388i	0.189196	+	0.981939i	$0.439412\pi$
$2$	2844.00i	1.96388i	−0.189196	+	0.981939i	$0.560588\pi$
$3$	− 59049.0i	− 0.577350i
$3$	− 59049.0i	− 0.577350i
$4$	−5.99118e6	−2.85682
$5$	0	0
$5$	0	0
$6$	1.67935e8	1.13385
$7$	− 3.63304e8i	− 0.486117i	−0.970012	−	0.243058i	$-0.921849\pi$
$7$	− 3.63304e8i	− 0.486117i	0.970012	−	0.243058i	$-0.0781507\pi$
$8$	− 1.10746e10i	− 3.64657i
$9$	−3.48678e9	−0.333333
$10$	0	0
$11$	1.45818e10	0.169508	0.0847538	−	0.996402i	$-0.472990\pi$
$11$	1.45818e10	0.169508	0.0847538	+	0.996402i	$0.472990\pi$
$12$	3.53773e11i	1.64939i
$13$	1.13351e11i	0.228044i	0.993478	+	0.114022i	$0.0363735\pi$
$13$	1.13351e11i	0.228044i	−0.993478	+	0.114022i	$0.963627\pi$
$14$	1.03324e12	0.954674
$15$	0	0
$16$	1.89318e13	4.30460
$17$	8.58939e12i	1.03335i	0.856181	+	0.516676i	$0.172831\pi$
$17$	8.58939e12i	1.03335i	−0.856181	+	0.516676i	$0.827169\pi$
$18$	− 9.91641e12i	− 0.654626i
$19$	2.92029e13	1.09273	0.546366	−	0.837546i	$-0.316011\pi$
$19$	2.92029e13	1.09273	0.546366	+	0.837546i	$0.316011\pi$
$20$	0	0
$21$	−2.14527e13	−0.280660
$22$	4.14707e13i	0.332892i
$23$	− 1.55899e14i	− 0.784696i	−0.919817	−	0.392348i	$-0.871663\pi$
$23$	− 1.55899e14i	− 0.784696i	0.919817	−	0.392348i	$-0.128337\pi$
$24$	−6.53946e14	−2.10535
$25$	0	0
$26$	−3.22370e14	−0.447851
$27$	2.05891e14i	0.192450i
$28$	2.17662e15i	1.38875i
$29$	−2.40079e15	−1.05968	−0.529840	−	0.848097i	$-0.677748\pi$
$29$	−2.40079e15	−1.05968	−0.529840	+	0.848097i	$0.677748\pi$
$30$	0	0
$31$	2.23982e15	0.490812	0.245406	−	0.969420i	$-0.421079\pi$
$31$	2.23982e15	0.490812	0.245406	+	0.969420i	$0.421079\pi$
$32$	3.06169e16i	4.80714i
$33$	− 8.61043e14i	− 0.0978652i
$34$	−2.44282e16	−2.02938
$35$	0	0
$36$	2.08900e16	0.952273
$37$	3.07851e16i	1.05250i	0.850330	+	0.526250i	$0.176402\pi$
$37$	3.07851e16i	1.05250i	−0.850330	+	0.526250i	$0.823598\pi$
$38$	8.30532e16i	2.14599i
$39$	6.69325e15	0.131661
$40$	0	0
$41$	−1.03208e17	−1.20083	−0.600414	−	0.799689i	$-0.704998\pi$
$41$	−1.03208e17	−1.20083	−0.600414	+	0.799689i	$0.704998\pi$
$42$	− 6.10116e16i	− 0.551182i
$43$	− 1.65557e17i	− 1.16823i	−0.811670	−	0.584117i	$-0.801441\pi$
$43$	− 1.65557e17i	− 1.16823i	0.811670	−	0.584117i	$-0.198559\pi$
$44$	−8.73624e16	−0.484252
$45$	0	0
$46$	4.43377e17	1.54105
$47$	6.65872e16i	0.184656i	0.995729	+	0.0923280i	$0.0294308\pi$
$47$	6.65872e16i	0.184656i	−0.995729	+	0.0923280i	$0.970569\pi$
$48$	− 1.11790e18i	− 2.48526i
$49$	4.26556e17	0.763690
$50$	0	0
$51$	5.07195e17	0.596607
$52$	− 6.79105e17i	− 0.651482i
$53$	4.35423e17i	0.341991i	0.985272	+	0.170995i	$0.0546983\pi$
$53$	4.35423e17i	0.341991i	−0.985272	+	0.170995i	$0.945302\pi$
$54$	−5.85554e17	−0.377949
$55$	0	0
$56$	−4.02346e18	−1.77266
$57$	− 1.72440e18i	− 0.630889i
$58$	− 6.82784e18i	− 2.08108i
$59$	−5.53437e18	−1.40968	−0.704842	−	0.709364i	$-0.748982\pi$
$59$	−5.53437e18	−1.40968	−0.704842	+	0.709364i	$0.748982\pi$
$60$	0	0
$61$	−7.17621e18	−1.28805	−0.644023	−	0.765006i	$-0.722736\pi$
$61$	−7.17621e18	−1.28805	−0.644023	+	0.765006i	$0.722736\pi$
$62$	6.37005e18i	0.963896i
$63$	1.26676e18i	0.162039i
$64$	−4.73716e19	−5.13604
$65$	0	0
$66$	2.44881e18	0.192195
$67$	1.57554e19i	1.05595i	0.849258	+	0.527977i	$0.177049\pi$
$67$	1.57554e19i	1.05595i	−0.849258	+	0.527977i	$0.822951\pi$
$68$	− 5.14606e19i	− 2.95210i
$69$	−9.20569e18	−0.453045
$70$	0	0
$71$	2.64579e19	0.964588	0.482294	−	0.876009i	$-0.339804\pi$
$71$	2.64579e19	0.964588	0.482294	+	0.876009i	$0.339804\pi$
$72$	3.86148e19i	1.21552i
$73$	1.34712e19i	0.366875i	0.983031	+	0.183437i	$0.0587225\pi$
$73$	1.34712e19i	0.366875i	−0.983031	+	0.183437i	$0.941278\pi$
$74$	−8.75527e19	−2.06698
$75$	0	0
$76$	−1.74960e20	−3.12174
$77$	− 5.29764e18i	− 0.0824005i
$78$	1.90356e19i	0.258567i
$79$	1.68861e19	0.200653	0.100326	−	0.994955i	$-0.468011\pi$
$79$	1.68861e19	0.200653	0.100326	+	0.994955i	$0.468011\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	− 2.93522e20i	− 2.35828i
$83$	− 1.70688e20i	− 1.20749i	−0.797178	−	0.603744i	$-0.793675\pi$
$83$	− 1.70688e20i	− 1.20749i	0.797178	−	0.603744i	$-0.206325\pi$
$84$	1.28527e20	0.801794
$85$	0	0
$86$	4.70845e20	2.29427
$87$	1.41764e20i	0.611807i
$88$	− 1.61488e20i	− 0.618121i
$89$	3.12592e20	1.06263	0.531317	−	0.847173i	$-0.321697\pi$
$89$	3.12592e20	1.06263	0.531317	+	0.847173i	$0.321697\pi$
$90$	0	0
$91$	4.11808e19	0.110856
$92$	9.34021e20i	2.24174i
$93$	− 1.32259e20i	− 0.283371i
$94$	−1.89374e20	−0.362642
$95$	0	0
$96$	1.80790e21	2.77540
$97$	− 9.49015e20i	− 1.30668i	−0.757064	−	0.653341i	$-0.773367\pi$
$97$	− 9.49015e20i	− 1.30668i	0.757064	−	0.653341i	$-0.226633\pi$
$98$	1.21313e21i	1.49980i
$99$	−5.08437e19	−0.0565025
$100$	0	0
$101$	1.44798e20	0.130433	0.0652166	−	0.997871i	$-0.479226\pi$
$101$	1.44798e20	0.130433	0.0652166	+	0.997871i	$0.479226\pi$
$102$	1.44246e21i	1.17166i
$103$	2.19627e21i	1.61025i	0.593102	+	0.805127i	$0.297903\pi$
$103$	2.19627e21i	1.61025i	−0.593102	+	0.805127i	$0.702097\pi$
$104$	1.25532e21	0.831579
$105$	0	0
$106$	−1.23834e21	−0.671629
$107$	1.63087e20i	0.0801473i	0.999197	+	0.0400737i	$0.0127593\pi$
$107$	1.63087e20i	0.0801473i	−0.999197	+	0.0400737i	$0.987241\pi$
$108$	− 1.23353e21i	− 0.549795i
$109$	−2.24852e20	−0.0909743	−0.0454871	−	0.998965i	$-0.514484\pi$
$109$	−2.24852e20	−0.0909743	−0.0454871	+	0.998965i	$0.514484\pi$
$110$	0	0
$111$	1.81783e21	0.607661
$112$	− 6.87800e21i	− 2.09254i
$113$	− 4.24118e21i	− 1.17534i	−0.809101	−	0.587670i	$-0.800045\pi$
$113$	− 4.24118e21i	− 1.17534i	0.809101	−	0.587670i	$-0.199955\pi$
$114$	4.90421e21	1.23899
$115$	0	0
$116$	1.43836e22	3.02732
$117$	− 3.95230e20i	− 0.0760148i
$118$	− 1.57397e22i	− 2.76845i
$119$	3.12056e21	0.502330
$120$	0	0
$121$	−7.18762e21	−0.971267
$122$	− 2.04091e22i	− 2.52957i
$123$	6.09430e21i	0.693299i
$124$	−1.34192e22	−1.40216
$125$	0	0
$126$	−3.60267e21	−0.318225
$127$	− 1.66312e21i	− 0.135202i	−0.997712	−	0.0676012i	$-0.978465\pi$
$127$	− 1.66312e21i	− 0.135202i	0.997712	−	0.0676012i	$-0.0215346\pi$
$128$	− 7.05165e22i	− 5.27942i
$129$	−9.77599e21	−0.674480
$130$	0	0
$131$	6.40663e21	0.376081	0.188040	−	0.982161i	$-0.439786\pi$
$131$	6.40663e21	0.376081	0.188040	+	0.982161i	$0.439786\pi$
$132$	5.15867e21i	0.279583i
$133$	− 1.06095e22i	− 0.531196i
$134$	−4.48085e22	−2.07377
$135$	0	0
$136$	9.51243e22	3.76819
$137$	1.98314e22i	0.727423i	0.931512	+	0.363711i	$0.118491\pi$
$137$	1.98314e22i	0.727423i	−0.931512	+	0.363711i	$0.881509\pi$
$138$	− 2.61810e22i	− 0.889725i
$139$	5.20143e21	0.163858	0.0819290	−	0.996638i	$-0.473892\pi$
$139$	5.20143e21	0.163858	0.0819290	+	0.996638i	$0.473892\pi$
$140$	0	0
$141$	3.93191e21	0.106611
$142$	7.52461e22i	1.89433i
$143$	1.65286e21i	0.0386552i
$144$	−6.60112e22	−1.43487
$145$	0	0
$146$	−3.83122e22	−0.720498
$147$	− 2.51877e22i	− 0.440917i
$148$	− 1.84439e23i	− 3.00680i
$149$	7.47631e22	1.13562	0.567808	−	0.823161i	$-0.307792\pi$
$149$	7.47631e22	1.13562	0.567808	+	0.823161i	$0.307792\pi$
$150$	0	0
$151$	1.11044e23	1.46635	0.733174	−	0.680042i	$-0.238038\pi$
$151$	1.11044e23	1.46635	0.733174	+	0.680042i	$0.238038\pi$
$152$	− 3.23412e23i	− 3.98472i
$153$	− 2.99493e22i	− 0.344451i
$154$	1.50665e22	0.161824
$155$	0	0
$156$	−4.01005e22	−0.376133
$157$	− 4.36563e22i	− 0.382913i	−0.981501	−	0.191457i	$-0.938679\pi$
$157$	− 4.36563e22i	− 0.382913i	0.981501	−	0.191457i	$-0.0613211\pi$
$158$	4.80241e22i	0.394058i
$159$	2.57113e22	0.197449
$160$	0	0
$161$	−5.66388e22	−0.381454
$162$	3.45764e22i	0.218209i
$163$	2.85661e23i	1.68998i	0.534783	+	0.844989i	$0.320393\pi$
$163$	2.85661e23i	1.68998i	−0.534783	+	0.844989i	$0.679607\pi$
$164$	6.18336e23	3.43055
$165$	0	0
$166$	4.85437e23	2.37136
$167$	− 2.66950e23i	− 1.22435i	−0.790720	−	0.612177i	$-0.790294\pi$
$167$	− 2.66950e23i	− 1.22435i	0.790720	−	0.612177i	$-0.209706\pi$
$168$	2.37581e23i	1.02344i
$169$	2.34216e23	0.947996
$170$	0	0
$171$	−1.01824e23	−0.364244
$172$	9.91884e23i	3.33743i
$173$	− 2.28496e23i	− 0.723425i	−0.932290	−	0.361713i	$-0.882192\pi$
$173$	− 2.28496e23i	− 0.723425i	0.932290	−	0.361713i	$-0.117808\pi$
$174$	−4.03177e23	−1.20151
$175$	0	0
$176$	2.76061e23	0.729661
$177$	3.26799e23i	0.813881i
$178$	8.89013e23i	2.08688i
$179$	1.29151e22	0.0285852	0.0142926	−	0.999898i	$-0.495450\pi$
$179$	1.29151e22	0.0285852	0.0142926	+	0.999898i	$0.495450\pi$
$180$	0	0
$181$	−8.75338e23	−1.72405	−0.862026	−	0.506863i	$-0.830805\pi$
$181$	−8.75338e23	−1.72405	−0.862026	+	0.506863i	$0.830805\pi$
$182$	1.17118e23i	0.217708i
$183$	4.23748e23i	0.743654i
$184$	−1.72653e24	−2.86145
$185$	0	0
$186$	3.76145e23	0.556506
$187$	1.25249e23i	0.175161i
$188$	− 3.98936e23i	− 0.527529i
$189$	7.48011e22	0.0935532
$190$	0	0
$191$	1.33961e24	1.50013	0.750066	−	0.661363i	$-0.230022\pi$
$191$	1.33961e24	1.50013	0.750066	+	0.661363i	$0.230022\pi$
$192$	2.79725e24i	2.96529i
$193$	− 2.13970e23i	− 0.214783i	−0.994217	−	0.107392i	$-0.965750\pi$
$193$	− 2.13970e23i	− 0.214783i	0.994217	−	0.107392i	$-0.0342499\pi$
$194$	2.69900e24	2.56616
$195$	0	0
$196$	−2.55558e24	−2.18173
$197$	− 1.42895e24i	− 1.15644i	−0.815881	−	0.578220i	$-0.803748\pi$
$197$	− 1.42895e24i	− 1.15644i	0.815881	−	0.578220i	$-0.196252\pi$
$198$	− 1.44600e23i	− 0.110964i
$199$	−7.45856e23	−0.542872	−0.271436	−	0.962456i	$-0.587499\pi$
$199$	−7.45856e23	−0.542872	−0.271436	+	0.962456i	$0.587499\pi$
$200$	0	0
$201$	9.30344e23	0.609656
$202$	4.11805e23i	0.256155i
$203$	8.72216e23i	0.515129i
$204$	−3.03870e24	−1.70440
$205$	0	0
$206$	−6.24619e24	−3.16234
$207$	5.43587e23i	0.261565i
$208$	2.14594e24i	0.981639i
$209$	4.25832e23	0.185226
$210$	0	0
$211$	−2.65090e24	−1.04334	−0.521671	−	0.853147i	$-0.674691\pi$
$211$	−2.65090e24	−1.04334	−0.521671	+	0.853147i	$0.674691\pi$
$212$	− 2.60870e24i	− 0.977006i
$213$	− 1.56231e24i	− 0.556905i
$214$	−4.63819e23	−0.157400
$215$	0	0
$216$	2.28017e24	0.701782
$217$	− 8.13736e23i	− 0.238592i
$218$	− 6.39479e23i	− 0.178662i
$219$	7.95464e23	0.211815
$220$	0	0
$221$	−9.73614e23	−0.235650
$222$	5.16990e24i	1.19337i
$223$	3.97174e24i	0.874539i	0.899330	+	0.437270i	$0.144054\pi$
$223$	3.97174e24i	0.874539i	−0.899330	+	0.437270i	$0.855946\pi$
$224$	1.11232e25	2.33683
$225$	0	0
$226$	1.20619e25	2.30823
$227$	2.14690e24i	0.392229i	0.980581	+	0.196114i	$0.0628324\pi$
$227$	2.14690e24i	0.392229i	−0.980581	+	0.196114i	$0.937168\pi$
$228$	1.03312e25i	1.80234i
$229$	−3.66024e24	−0.609869	−0.304934	−	0.952373i	$-0.598635\pi$
$229$	−3.66024e24	−0.609869	−0.304934	+	0.952373i	$0.598635\pi$
$230$	0	0
$231$	−3.12820e23	−0.0475739
$232$	2.65878e25i	3.86420i
$233$	− 2.90921e24i	− 0.404145i	−0.979371	−	0.202073i	$-0.935232\pi$
$233$	− 2.90921e24i	− 0.404145i	0.979371	−	0.202073i	$-0.0647677\pi$
$234$	1.12403e24	0.149284
$235$	0	0
$236$	3.31574e25	4.02721
$237$	− 9.97109e23i	− 0.115847i
$238$	8.87487e24i	0.986516i
$239$	4.80224e24	0.510818	0.255409	−	0.966833i	$-0.417790\pi$
$239$	4.80224e24	0.510818	0.255409	+	0.966833i	$0.417790\pi$
$240$	0	0
$241$	7.86263e24	0.766282	0.383141	−	0.923690i	$-0.374842\pi$
$241$	7.86263e24	0.766282	0.383141	+	0.923690i	$0.374842\pi$
$242$	− 2.04416e25i	− 1.90745i
$243$	− 7.17898e23i	− 0.0641500i
$244$	4.29940e25	3.67972
$245$	0	0
$246$	−1.73322e25	−1.36155
$247$	3.31018e24i	0.249191i
$248$	− 2.48052e25i	− 1.78978i
$249$	−1.00790e25	−0.697144
$250$	0	0
$251$	−1.99525e25	−1.26889	−0.634443	−	0.772969i	$-0.718771\pi$
$251$	−1.99525e25	−1.26889	−0.634443	+	0.772969i	$0.718771\pi$
$252$	− 7.58941e24i	− 0.462916i
$253$	− 2.27330e24i	− 0.133012i
$254$	4.72991e24	0.265521
$255$	0	0
$256$	1.01203e26	5.23210
$257$	− 1.33580e25i	− 0.662894i	−0.943474	−	0.331447i	$-0.892463\pi$
$257$	− 1.33580e25i	− 0.662894i	0.943474	−	0.331447i	$-0.107537\pi$
$258$	− 2.78029e25i	− 1.32460i
$259$	1.11843e25	0.511638
$260$	0	0
$261$	8.37103e24	0.353227
$262$	1.82204e25i	0.738576i
$263$	− 5.83637e24i	− 0.227304i	−0.993521	−	0.113652i	$-0.963745\pi$
$263$	− 5.83637e24i	− 0.227304i	0.993521	−	0.113652i	$-0.0362549\pi$
$264$	−9.53573e24	−0.356872
$265$	0	0
$266$	3.01735e25	1.04320
$267$	− 1.84583e25i	− 0.613512i
$268$	− 9.43938e25i	− 3.01667i
$269$	−5.35297e25	−1.64511	−0.822557	−	0.568683i	$-0.807453\pi$
$269$	−5.35297e25	−1.64511	−0.822557	+	0.568683i	$0.807453\pi$
$270$	0	0
$271$	−1.04403e25	−0.296849	−0.148425	−	0.988924i	$-0.547420\pi$
$271$	−1.04403e25	−0.296849	−0.148425	+	0.988924i	$0.547420\pi$
$272$	1.62613e26i	4.44817i
$273$	− 2.43168e24i	− 0.0640029i
$274$	−5.64004e25	−1.42857
$275$	0	0
$276$	5.51530e25	1.29427
$277$	− 3.14884e25i	− 0.711399i	−0.934600	−	0.355699i	$-0.884243\pi$
$277$	− 3.14884e25i	− 0.711399i	0.934600	−	0.355699i	$-0.115757\pi$
$278$	1.47929e25i	0.321797i
$279$	−7.80977e24	−0.163604
$280$	0	0
$281$	−1.15887e25	−0.225225	−0.112613	−	0.993639i	$-0.535922\pi$
$281$	−1.15887e25	−0.225225	−0.112613	+	0.993639i	$0.535922\pi$
$282$	1.11823e25i	0.209371i
$283$	− 4.80399e25i	− 0.866652i	−0.901237	−	0.433326i	$-0.857340\pi$
$283$	− 4.80399e25i	− 0.866652i	0.901237	−	0.433326i	$-0.142660\pi$
$284$	−1.58514e26	−2.75565
$285$	0	0
$286$	−4.70074e24	−0.0759142
$287$	3.74957e25i	0.583743i
$288$	− 1.06755e26i	− 1.60238i
$289$	−4.68568e24	−0.0678180
$290$	0	0
$291$	−5.60384e25	−0.754413
$292$	− 8.07087e25i	− 1.04809i
$293$	− 7.96714e25i	− 0.998142i	−0.866561	−	0.499071i	$-0.833675\pi$
$293$	− 7.96714e25i	− 0.998142i	0.866561	−	0.499071i	$-0.166325\pi$
$294$	7.16339e25	0.865907
$295$	0	0
$296$	3.40933e26	3.83801
$297$	3.00227e24i	0.0326217i
$298$	2.12626e26i	2.23021i
$299$	1.76713e25	0.178946
$300$	0	0
$301$	−6.01476e25	−0.567898
$302$	3.15809e26i	2.87973i
$303$	− 8.55018e24i	− 0.0753056i
$304$	5.52865e26	4.70377
$305$	0	0
$306$	8.51760e25	0.676460
$307$	− 1.51498e26i	− 1.16266i	−0.813666	−	0.581332i	$-0.802532\pi$
$307$	− 1.51498e26i	− 1.16266i	0.813666	−	0.581332i	$-0.197468\pi$
$308$	3.17391e25i	0.235403i
$309$	1.29687e26	0.929681
$310$	0	0
$311$	1.41406e26	0.947292	0.473646	−	0.880715i	$-0.342938\pi$
$311$	1.41406e26	0.947292	0.473646	+	0.880715i	$0.342938\pi$
$312$	− 7.41253e25i	− 0.480112i
$313$	4.99598e25i	0.312899i	0.987686	+	0.156450i	$0.0500049\pi$
$313$	4.99598e25i	0.312899i	−0.987686	+	0.156450i	$0.949995\pi$
$314$	1.24158e26	0.751995
$315$	0	0
$316$	−1.01168e26	−0.573229
$317$	− 1.81535e26i	− 0.995033i	−0.867454	−	0.497517i	$-0.834245\pi$
$317$	− 1.81535e26i	− 0.995033i	0.867454	−	0.497517i	$-0.165755\pi$
$318$	7.31229e25i	0.387765i
$319$	−3.50079e25	−0.179624
$320$	0	0
$321$	9.63011e24	0.0462731
$322$	− 1.61081e26i	− 0.749130i
$323$	2.50835e26i	1.12918i
$324$	−7.28388e25	−0.317424
$325$	0	0
$326$	−8.12420e26	−3.31891
$327$	1.32773e25i	0.0525240i
$328$	1.14299e27i	4.37890i
$329$	2.41914e25	0.0897644
$330$	0	0
$331$	1.44090e26	0.501695	0.250848	−	0.968027i	$-0.419291\pi$
$331$	1.44090e26	0.501695	0.250848	+	0.968027i	$0.419291\pi$
$332$	1.02262e27i	3.44958i
$333$	− 1.07341e26i	− 0.350833i
$334$	7.59206e26	2.40448
$335$	0	0
$336$	−4.06139e26	−1.20813
$337$	3.63051e26i	1.04678i	0.852095	+	0.523388i	$0.175332\pi$
$337$	3.63051e26i	1.04678i	−0.852095	+	0.523388i	$0.824668\pi$
$338$	6.66111e26i	1.86175i
$339$	−2.50438e26	−0.678583
$340$	0	0
$341$	3.26607e25	0.0831964
$342$	− 2.89588e26i	− 0.715331i
$343$	− 3.57891e26i	− 0.857360i
$344$	−1.83349e27	−4.26004
$345$	0	0
$346$	6.49841e26	1.42072
$347$	7.09622e25i	0.150511i	0.997164	+	0.0752554i	$0.0239772\pi$
$347$	7.09622e25i	0.150511i	−0.997164	+	0.0752554i	$0.976023\pi$
$348$	− 8.49335e26i	− 1.74782i
$349$	7.03939e26	1.40562	0.702810	−	0.711378i	$-0.251928\pi$
$349$	7.03939e26	1.40562	0.702810	+	0.711378i	$0.251928\pi$
$350$	0	0
$351$	−2.33379e25	−0.0438872
$352$	4.46451e26i	0.814846i
$353$	− 1.08085e26i	− 0.191483i	−0.995406	−	0.0957414i	$-0.969478\pi$
$353$	− 1.08085e26i	− 0.191483i	0.995406	−	0.0957414i	$-0.0305222\pi$
$354$	−9.29416e26	−1.59836
$355$	0	0
$356$	−1.87280e27	−3.03575
$357$	− 1.84266e26i	− 0.290020i
$358$	3.67305e25i	0.0561378i
$359$	1.67492e26	0.248601	0.124301	−	0.992245i	$-0.460331\pi$
$359$	1.67492e26	0.248601	0.124301	+	0.992245i	$0.460331\pi$
$360$	0	0
$361$	1.38602e26	0.194064
$362$	− 2.48946e27i	− 3.38583i
$363$	4.24422e26i	0.560761i
$364$	−2.46722e26	−0.316696
$365$	0	0
$366$	−1.20514e27	−1.46045
$367$	− 9.83667e26i	− 1.15839i	−0.815190	−	0.579194i	$-0.803367\pi$
$367$	− 9.83667e26i	− 1.15839i	0.815190	−	0.579194i	$-0.196633\pi$
$368$	− 2.95146e27i	− 3.37780i
$369$	3.59863e26	0.400276
$370$	0	0
$371$	1.58191e26	0.166248
$372$	7.92389e26i	0.809539i
$373$	1.00058e26i	0.0993824i	0.998765	+	0.0496912i	$0.0158237\pi$
$373$	1.00058e26i	0.0993824i	−0.998765	+	0.0496912i	$0.984176\pi$
$374$	−3.56208e26	−0.343995
$375$	0	0
$376$	7.37429e26	0.673360
$377$	− 2.72131e26i	− 0.241654i
$378$	2.12734e26i	0.183727i
$379$	−9.23905e25	−0.0776096	−0.0388048	−	0.999247i	$-0.512355\pi$
$379$	−9.23905e25	−0.0776096	−0.0388048	+	0.999247i	$0.512355\pi$
$380$	0	0
$381$	−9.82055e25	−0.0780591
$382$	3.80986e27i	2.94608i
$383$	− 2.13677e27i	− 1.60757i	−0.594919	−	0.803786i	$-0.702816\pi$
$383$	− 2.13677e27i	− 1.60757i	0.594919	−	0.803786i	$-0.297184\pi$
$384$	−4.16393e27	−3.04807
$385$	0	0
$386$	6.08530e26	0.421809
$387$	5.77263e26i	0.389411i
$388$	5.68572e27i	3.73295i
$389$	1.25581e27	0.802516	0.401258	−	0.915965i	$-0.368573\pi$
$389$	1.25581e27	0.802516	0.401258	+	0.915965i	$0.368573\pi$
$390$	0	0
$391$	1.33908e27	0.810868
$392$	− 4.72395e27i	− 2.78485i
$393$	− 3.78305e26i	− 0.217130i
$394$	4.06394e27	2.27111
$395$	0	0
$396$	3.04614e26	0.161417
$397$	− 1.78165e27i	− 0.919439i	−0.888064	−	0.459719i	$-0.847950\pi$
$397$	− 1.78165e27i	− 0.919439i	0.888064	−	0.459719i	$-0.152050\pi$
$398$	− 2.12121e27i	− 1.06614i
$399$	−6.26483e26	−0.306686
$400$	0	0
$401$	1.40181e27	0.651141	0.325570	−	0.945518i	$-0.394444\pi$
$401$	1.40181e27	0.651141	0.325570	+	0.945518i	$0.394444\pi$
$402$	2.64590e27i	1.19729i
$403$	2.53885e26i	0.111927i
$404$	−8.67511e26	−0.372624
$405$	0	0
$406$	−2.48058e27	−1.01165
$407$	4.48903e26i	0.178407i
$408$	− 5.61699e27i	− 2.17557i
$409$	−2.17493e27	−0.821015	−0.410507	−	0.911857i	$-0.634648\pi$
$409$	−2.17493e27	−0.821015	−0.410507	+	0.911857i	$0.634648\pi$
$410$	0	0
$411$	1.17102e27	0.419978
$412$	− 1.31582e28i	− 4.60021i
$413$	2.01066e27i	0.685271i
$414$	−1.54596e27	−0.513683
$415$	0	0
$416$	−3.47045e27	−1.09624
$417$	− 3.07139e26i	− 0.0946034i
$418$	1.21107e27i	0.363762i
$419$	6.07636e27	1.77990	0.889952	−	0.456055i	$-0.150738\pi$
$419$	6.07636e27	1.77990	0.889952	+	0.456055i	$0.150738\pi$
$420$	0	0
$421$	−1.89993e27	−0.529389	−0.264695	−	0.964332i	$-0.585271\pi$
$421$	−1.89993e27	−0.529389	−0.264695	+	0.964332i	$0.585271\pi$
$422$	− 7.53915e27i	− 2.04900i
$423$	− 2.32175e26i	− 0.0615520i
$424$	4.82214e27	1.24709
$425$	0	0
$426$	4.44321e27	1.09369
$427$	2.60714e27i	0.626141i
$428$	− 9.77083e26i	− 0.228966i
$429$	9.75999e25	0.0223176
$430$	0	0
$431$	−8.08572e24	−0.00176079	−0.000880395	−	1.00000i	$-0.500280\pi$
$431$	−8.08572e24	−0.00176079	−0.000880395		1.00000i	$0.500280\pi$
$432$	3.89789e27i	0.828420i
$433$	− 5.60439e27i	− 1.16253i	−0.813713	−	0.581267i	$-0.802557\pi$
$433$	− 5.60439e27i	− 1.16253i	0.813713	−	0.581267i	$-0.197443\pi$
$434$	2.31426e27	0.468566
$435$	0	0
$436$	1.34713e27	0.259897
$437$	− 4.55272e27i	− 0.857463i
$438$	2.26230e27i	0.415979i
$439$	8.51110e27	1.52795	0.763973	−	0.645248i	$-0.223246\pi$
$439$	8.51110e27	1.52795	0.763973	+	0.645248i	$0.223246\pi$
$440$	0	0
$441$	−1.48731e27	−0.254563
$442$	− 2.76896e27i	− 0.462789i
$443$	− 6.63134e27i	− 1.08234i	−0.840915	−	0.541168i	$-0.817982\pi$
$443$	− 6.63134e27i	− 1.08234i	0.840915	−	0.541168i	$-0.182018\pi$
$444$	−1.08909e28	−1.73598
$445$	0	0
$446$	−1.12956e28	−1.71749
$447$	− 4.41468e27i	− 0.655648i
$448$	1.72103e28i	2.49671i
$449$	−1.30394e28	−1.84787	−0.923933	−	0.382555i	$-0.875044\pi$
$449$	−1.30394e28	−1.84787	−0.923933	+	0.382555i	$0.875044\pi$
$450$	0	0
$451$	−1.50496e27	−0.203549
$452$	2.54097e28i	3.35773i
$453$	− 6.55703e27i	− 0.846596i
$454$	−6.10577e27	−0.770289
$455$	0	0
$456$	−1.90971e28	−2.30058
$457$	− 4.72949e27i	− 0.556793i	−0.960466	−	0.278397i	$-0.910197\pi$
$457$	− 4.72949e27i	− 0.556793i	0.960466	−	0.278397i	$-0.0898030\pi$
$458$	− 1.04097e28i	− 1.19771i
$459$	−1.76848e27	−0.198869
$460$	0	0
$461$	4.92722e27	0.529349	0.264675	−	0.964338i	$-0.414735\pi$
$461$	4.92722e27	0.529349	0.264675	+	0.964338i	$0.414735\pi$
$462$	− 8.89661e26i	− 0.0934294i
$463$	1.20207e28i	1.23404i	0.786947	+	0.617021i	$0.211661\pi$
$463$	1.20207e28i	1.23404i	−0.786947	+	0.617021i	$0.788339\pi$
$464$	−4.54513e28	−4.56150
$465$	0	0
$466$	8.27379e27	0.793693
$467$	− 1.09969e28i	− 1.03144i	−0.856758	−	0.515719i	$-0.827525\pi$
$467$	− 1.09969e28i	− 1.03144i	0.856758	−	0.515719i	$-0.172475\pi$
$468$	2.36789e27i	0.217161i
$469$	5.72402e27	0.513317
$470$	0	0
$471$	−2.57786e27	−0.221075
$472$	6.12910e28i	5.14051i
$473$	− 2.41413e27i	− 0.198024i
$474$	2.83578e27	0.227510
$475$	0	0
$476$	−1.86958e28	−1.43507
$477$	− 1.51823e27i	− 0.113997i
$478$	1.36576e28i	1.00318i
$479$	1.32717e28	0.953684	0.476842	−	0.878989i	$-0.341781\pi$
$479$	1.32717e28	0.953684	0.476842	+	0.878989i	$0.341781\pi$
$480$	0	0
$481$	−3.48951e27	−0.240017
$482$	2.23613e28i	1.50489i
$483$	3.34446e27i	0.220233i
$484$	4.30624e28	2.77473
$485$	0	0
$486$	2.04170e27	0.125983
$487$	− 2.62576e28i	− 1.58563i	−0.609466	−	0.792813i	$-0.708616\pi$
$487$	− 2.62576e28i	− 1.58563i	0.609466	−	0.792813i	$-0.291384\pi$
$488$	7.94738e28i	4.69695i
$489$	1.68680e28	0.975710
$490$	0	0
$491$	−2.54066e28	−1.40796	−0.703982	−	0.710218i	$-0.748596\pi$
$491$	−2.54066e28	−1.40796	−0.703982	+	0.710218i	$0.748596\pi$
$492$	− 3.65121e28i	− 1.98063i
$493$	− 2.06213e28i	− 1.09502i
$494$	−9.41414e27	−0.489382
$495$	0	0
$496$	4.24039e28	2.11275
$497$	− 9.61224e27i	− 0.468903i
$498$	− 2.86645e28i	− 1.36911i
$499$	1.30048e28	0.608204	0.304102	−	0.952640i	$-0.401644\pi$
$499$	1.30048e28	0.608204	0.304102	+	0.952640i	$0.401644\pi$
$500$	0	0
$501$	−1.57631e28	−0.706882
$502$	− 5.67449e28i	− 2.49194i
$503$	1.34993e27i	0.0580559i	0.999579	+	0.0290280i	$0.00924119\pi$
$503$	1.34993e27i	0.0580559i	−0.999579	+	0.0290280i	$0.990759\pi$
$504$	1.40289e28	0.590886
$505$	0	0
$506$	6.46525e27	0.261219
$507$	− 1.38302e28i	− 0.547326i
$508$	9.96406e27i	0.386249i
$509$	4.04902e28	1.53749	0.768746	−	0.639554i	$-0.220881\pi$
$509$	4.04902e28	1.53749	0.768746	+	0.639554i	$0.220881\pi$
$510$	0	0
$511$	4.89416e27	0.178344
$512$	1.39939e29i	4.99579i
$513$	6.01263e27i	0.210296i
$514$	3.79902e28	1.30184
$515$	0	0
$516$	5.85698e28	1.92687
$517$	9.70964e26i	0.0313006i
$518$	3.18083e28i	1.00479i
$519$	−1.34924e28	−0.417670
$520$	0	0
$521$	5.40378e28	1.60658	0.803289	−	0.595590i	$-0.203082\pi$
$521$	5.40378e28	1.60658	0.803289	+	0.595590i	$0.203082\pi$
$522$	2.38072e28i	0.693695i
$523$	1.54066e28i	0.439988i	0.975501	+	0.219994i	$0.0706037\pi$
$523$	1.54066e28i	0.439988i	−0.975501	+	0.219994i	$0.929396\pi$
$524$	−3.83833e28	−1.07439
$525$	0	0
$526$	1.65986e28	0.446398
$527$	1.92387e28i	0.507182i
$528$	− 1.63011e28i	− 0.421270i
$529$	1.51670e28	0.384252
$530$	0	0
$531$	1.92971e28	0.469895
$532$	6.35637e28i	1.51753i
$533$	− 1.16987e28i	− 0.273842i
$534$	5.24953e28	1.20486
$535$	0	0
$536$	1.74486e29	3.85061
$537$	− 7.62623e26i	− 0.0165037i
$538$	− 1.52238e29i	− 3.23080i
$539$	6.21997e27	0.129451
$540$	0	0
$541$	−7.54478e28	−1.51034	−0.755171	−	0.655528i	$-0.772446\pi$
$541$	−7.54478e28	−1.51034	−0.755171	+	0.655528i	$0.772446\pi$
$542$	− 2.96923e28i	− 0.582976i
$543$	5.16878e28i	0.995382i
$544$	−2.62981e29	−4.96747
$545$	0	0
$546$	6.91571e27	0.125694
$547$	− 7.90524e28i	− 1.40944i	−0.709483	−	0.704722i	$-0.751072\pi$
$547$	− 7.90524e28i	− 1.40944i	0.709483	−	0.704722i	$-0.248928\pi$
$548$	− 1.18813e29i	− 2.07812i
$549$	2.50219e28	0.429349
$550$	0	0
$551$	−7.01101e28	−1.15795
$552$	1.01950e29i	1.65206i
$553$	− 6.13480e27i	− 0.0975408i
$554$	8.95531e28	1.39710
$555$	0	0
$556$	−3.11627e28	−0.468113
$557$	− 1.17729e29i	− 1.73541i	−0.497075	−	0.867707i	$-0.665593\pi$
$557$	− 1.17729e29i	− 1.73541i	0.497075	−	0.867707i	$-0.334407\pi$
$558$	− 2.22110e28i	− 0.321299i
$559$	1.87660e28	0.266409
$560$	0	0
$561$	7.39583e27	0.101129
$562$	− 3.29582e28i	− 0.442315i
$563$	− 9.20807e28i	− 1.21291i	−0.795116	−	0.606457i	$-0.792590\pi$
$563$	− 9.20807e28i	− 1.21291i	0.795116	−	0.606457i	$-0.207410\pi$
$564$	−2.35568e28	−0.304569
$565$	0	0
$566$	1.36626e29	1.70200
$567$	− 4.41693e27i	− 0.0540130i
$568$	− 2.93011e29i	− 3.51744i
$569$	2.71795e27	0.0320304	0.0160152	−	0.999872i	$-0.494902\pi$
$569$	2.71795e27	0.0320304	0.0160152	+	0.999872i	$0.494902\pi$
$570$	0	0
$571$	1.28086e28	0.145487	0.0727434	−	0.997351i	$-0.476825\pi$
$571$	1.28086e28	0.145487	0.0727434	+	0.997351i	$0.476825\pi$
$572$	− 9.90260e27i	− 0.110431i
$573$	− 7.91029e28i	− 0.866102i
$574$	−1.06638e29	−1.14640
$575$	0	0
$576$	1.65175e29	1.71201
$577$	− 1.49329e29i	− 1.51984i	−0.650015	−	0.759922i	$-0.725237\pi$
$577$	− 1.49329e29i	− 1.51984i	0.650015	−	0.759922i	$-0.274763\pi$
$578$	− 1.33261e28i	− 0.133186i
$579$	−1.26347e28	−0.124005
$580$	0	0
$581$	−6.20116e28	−0.586980
$582$	− 1.59373e29i	− 1.48158i
$583$	6.34926e27i	0.0579700i
$584$	1.49189e29	1.33783
$585$	0	0
$586$	2.26586e29	1.96023
$587$	− 2.62975e28i	− 0.223468i	−0.993738	−	0.111734i	$-0.964360\pi$
$587$	− 2.62975e28i	− 0.223468i	0.993738	−	0.111734i	$-0.0356404\pi$
$588$	1.50904e29i	1.25962i
$589$	6.54093e28	0.536326
$590$	0	0
$591$	−8.43783e28	−0.667671
$592$	5.82817e29i	4.53059i
$593$	1.92294e29i	1.46856i	0.678849	+	0.734278i	$0.262479\pi$
$593$	1.92294e29i	1.46856i	−0.678849	+	0.734278i	$0.737521\pi$
$594$	−8.53846e27	−0.0640651
$595$	0	0
$596$	−4.47919e29	−3.24425
$597$	4.40421e28i	0.313428i
$598$	5.02572e28i	0.351427i
$599$	2.45874e29	1.68940	0.844699	−	0.535242i	$-0.179780\pi$
$599$	2.45874e29	1.68940	0.844699	+	0.535242i	$0.179780\pi$
$600$	0	0
$601$	7.47252e28	0.495776	0.247888	−	0.968789i	$-0.420264\pi$
$601$	7.47252e28	0.495776	0.247888	+	0.968789i	$0.420264\pi$
$602$	− 1.71060e29i	− 1.11528i
$603$	− 5.49359e28i	− 0.351985i
$604$	−6.65285e29	−4.18909
$605$	0	0
$606$	2.43167e28	0.147891
$607$	1.23466e29i	0.738016i	0.929426	+	0.369008i	$0.120302\pi$
$607$	1.23466e29i	0.738016i	−0.929426	+	0.369008i	$0.879698\pi$
$608$	8.94104e29i	5.25291i
$609$	5.15035e28	0.297410
$610$	0	0
$611$	−7.54771e27	−0.0421098
$612$	1.79432e29i	0.984034i
$613$	− 1.59244e29i	− 0.858476i	−0.903191	−	0.429238i	$-0.858782\pi$
$613$	− 1.59244e29i	− 0.858476i	0.903191	−	0.429238i	$-0.141218\pi$
$614$	4.30861e29	2.28333
$615$	0	0
$616$	−5.86694e28	−0.300479
$617$	− 1.23256e29i	− 0.620602i	−0.950638	−	0.310301i	$-0.899570\pi$
$617$	− 1.23256e29i	− 0.620602i	0.950638	−	0.310301i	$-0.100430\pi$
$618$	3.68831e29i	1.82578i
$619$	5.18990e28	0.252585	0.126292	−	0.991993i	$-0.459692\pi$
$619$	5.18990e28	0.252585	0.126292	+	0.991993i	$0.459692\pi$
$620$	0	0
$621$	3.20983e28	0.151015
$622$	4.02159e29i	1.86037i
$623$	− 1.13566e29i	− 0.516564i
$624$	1.26715e29	0.566750
$625$	0	0
$626$	−1.42086e29	−0.614497
$627$	− 2.51450e28i	− 0.106940i
$628$	2.61553e29i	1.09391i
$629$	−2.64425e29	−1.08760
$630$	0	0
$631$	−2.05208e28	−0.0816366	−0.0408183	−	0.999167i	$-0.512996\pi$
$631$	−2.05208e28	−0.0816366	−0.0408183	+	0.999167i	$0.512996\pi$
$632$	− 1.87008e29i	− 0.731694i
$633$	1.56533e29i	0.602374i
$634$	5.16285e29	1.95412
$635$	0	0
$636$	−1.54041e29	−0.564075
$637$	4.83505e28i	0.174155i
$638$	− 9.95625e28i	− 0.352759i
$639$	−9.22528e28	−0.321529
$640$	0	0
$641$	5.14342e29	1.73477	0.867386	−	0.497636i	$-0.165798\pi$
$641$	5.14342e29	1.73477	0.867386	+	0.497636i	$0.165798\pi$
$642$	2.73880e28i	0.0908747i
$643$	− 8.85766e28i	− 0.289137i	−0.989495	−	0.144569i	$-0.953821\pi$
$643$	− 8.85766e28i	− 0.289137i	0.989495	−	0.144569i	$-0.0461794\pi$
$644$	3.39333e29	1.08975
$645$	0	0
$646$	−7.13376e29	−2.21757
$647$	− 5.46916e29i	− 1.67273i	−0.548174	−	0.836364i	$-0.684677\pi$
$647$	− 5.46916e29i	− 1.67273i	0.548174	−	0.836364i	$-0.315323\pi$
$648$	− 1.34642e29i	− 0.405174i
$649$	−8.07012e28	−0.238952
$650$	0	0
$651$	−4.80503e28	−0.137751
$652$	− 1.71145e30i	− 4.82796i
$653$	− 5.66153e29i	− 1.57161i	−0.618473	−	0.785806i	$-0.712248\pi$
$653$	− 5.66153e29i	− 1.57161i	0.618473	−	0.785806i	$-0.287752\pi$
$654$	−3.77606e28	−0.103151
$655$	0	0
$656$	−1.95391e30	−5.16908
$657$	− 4.69713e28i	− 0.122292i
$658$	6.88003e28i	0.176286i
$659$	1.48653e29	0.374867	0.187434	−	0.982277i	$-0.439983\pi$
$659$	1.48653e29	0.374867	0.187434	+	0.982277i	$0.439983\pi$
$660$	0	0
$661$	−4.04669e29	−0.988517	−0.494259	−	0.869315i	$-0.664560\pi$
$661$	−4.04669e29	−0.988517	−0.494259	+	0.869315i	$0.664560\pi$
$662$	4.09792e29i	0.985268i
$663$	5.74909e28i	0.136053i
$664$	−1.89031e30	−4.40319
$665$	0	0
$666$	3.05278e29	0.688994
$667$	3.74281e29i	0.831527i
$668$	1.59935e30i	3.49776i
$669$	2.34527e29	0.504916
$670$	0	0
$671$	−1.04642e29	−0.218334
$672$	− 6.56816e29i	− 1.34917i
$673$	− 1.54590e29i	− 0.312625i	−0.987708	−	0.156313i	$-0.950039\pi$
$673$	− 1.54590e29i	− 0.312625i	0.987708	−	0.156313i	$-0.0499608\pi$
$674$	−1.03252e30	−2.05574
$675$	0	0
$676$	−1.40323e30	−2.70825
$677$	9.88421e29i	1.87828i	0.343530	+	0.939142i	$0.388377\pi$
$677$	9.88421e29i	1.87828i	−0.343530	+	0.939142i	$0.611623\pi$
$678$	− 7.12245e29i	− 1.33265i
$679$	−3.44781e29	−0.635200
$680$	0	0
$681$	1.26772e29	0.226453
$682$	9.28870e28i	0.163388i
$683$	− 1.41169e29i	− 0.244524i	−0.992498	−	0.122262i	$-0.960985\pi$
$683$	− 1.41169e29i	− 0.244524i	0.992498	−	0.122262i	$-0.0390147\pi$
$684$	6.10048e29	1.04058
$685$	0	0
$686$	1.01784e30	1.68375
$687$	2.16133e29i	0.352108i
$688$	− 3.13430e30i	− 5.02877i
$689$	−4.93555e28	−0.0779891
$690$	0	0
$691$	7.11585e29	1.09070	0.545352	−	0.838207i	$-0.316396\pi$
$691$	7.11585e29	1.09070	0.545352	+	0.838207i	$0.316396\pi$
$692$	1.36896e30i	2.06669i
$693$	1.84717e28i	0.0274668i
$694$	−2.01817e29	−0.295585
$695$	0	0
$696$	1.56999e30	2.23099
$697$	− 8.86490e29i	− 1.24088i
$698$	2.00200e30i	2.76047i
$699$	−1.71786e29	−0.233334
$700$	0	0
$701$	−8.80754e29	−1.16096	−0.580478	−	0.814276i	$-0.697134\pi$
$701$	−8.80754e29	−1.16096	−0.580478	+	0.814276i	$0.697134\pi$
$702$	− 6.63731e28i	− 0.0861891i
$703$	8.99015e29i	1.15010i
$704$	−6.90765e29	−0.870597
$705$	0	0
$706$	3.07393e29	0.376049
$707$	− 5.26057e28i	− 0.0634058i
$708$	− 1.95791e30i	− 2.32511i
$709$	2.79000e29	0.326452	0.163226	−	0.986589i	$-0.447810\pi$
$709$	2.79000e29	0.326452	0.163226	+	0.986589i	$0.447810\pi$
$710$	0	0
$711$	−5.88783e28	−0.0668843
$712$	− 3.46185e30i	− 3.87496i
$713$	− 3.49186e29i	− 0.385139i
$714$	5.24052e29	0.569565
$715$	0	0
$716$	−7.73767e28	−0.0816626
$717$	− 2.83568e29i	− 0.294921i
$718$	4.76349e29i	0.488223i
$719$	−1.21404e30	−1.22625	−0.613124	−	0.789987i	$-0.710087\pi$
$719$	−1.21404e30	−1.22625	−0.613124	+	0.789987i	$0.710087\pi$
$720$	0	0
$721$	7.97913e29	0.782772
$722$	3.94185e29i	0.381118i
$723$	− 4.64280e29i	− 0.442413i
$724$	5.24431e30	4.92531
$725$	0	0
$726$	−1.20706e30	−1.10127
$727$	6.54831e29i	0.588868i	0.955672	+	0.294434i	$0.0951311\pi$
$727$	6.54831e29i	0.588868i	−0.955672	+	0.294434i	$0.904869\pi$
$728$	− 4.56062e29i	− 0.404245i
$729$	−4.23912e28	−0.0370370
$730$	0	0
$731$	1.42204e30	1.20720
$732$	− 2.53875e30i	− 2.12449i
$733$	2.20665e29i	0.182029i	0.995850	+	0.0910147i	$0.0290110\pi$
$733$	2.20665e29i	0.182029i	−0.995850	+	0.0910147i	$0.970989\pi$
$734$	2.79755e30	2.27493
$735$	0	0
$736$	4.77315e30	3.77214
$737$	2.29743e29i	0.178992i
$738$	1.02345e30i	0.786094i
$739$	4.07297e29	0.308422	0.154211	−	0.988038i	$-0.450717\pi$
$739$	4.07297e29	0.308422	0.154211	+	0.988038i	$0.450717\pi$
$740$	0	0
$741$	1.95463e29	0.143871
$742$	4.49895e29i	0.326490i
$743$	3.97218e29i	0.284214i	0.989851	+	0.142107i	$0.0453878\pi$
$743$	3.97218e29i	0.284214i	−0.989851	+	0.142107i	$0.954612\pi$
$744$	−1.46472e30	−1.03333
$745$	0	0
$746$	−2.84565e29	−0.195175
$747$	5.95152e29i	0.402496i
$748$	− 7.50390e29i	− 0.500403i
$749$	5.92500e28	0.0389610
$750$	0	0
$751$	−1.86890e30	−1.19500	−0.597498	−	0.801871i	$-0.703838\pi$
$751$	−1.86890e30	−1.19500	−0.597498	+	0.801871i	$0.703838\pi$
$752$	1.26062e30i	0.794869i
$753$	1.17817e30i	0.732592i
$754$	7.73941e29	0.474579
$755$	0	0
$756$	−4.48147e29	−0.267265
$757$	2.99103e30i	1.75919i	0.475720	+	0.879597i	$0.342188\pi$
$757$	2.99103e30i	1.75919i	−0.475720	+	0.879597i	$0.657812\pi$
$758$	− 2.62759e29i	− 0.152416i
$759$	−1.34236e29	−0.0767945
$760$	0	0
$761$	1.51341e30	0.842206	0.421103	−	0.907013i	$-0.361643\pi$
$761$	1.51341e30	0.842206	0.421103	+	0.907013i	$0.361643\pi$
$762$	− 2.79297e29i	− 0.153299i
$763$	8.16896e28i	0.0442241i
$764$	−8.02588e30	−4.28561
$765$	0	0
$766$	6.07697e30	3.15707
$767$	− 6.27325e29i	− 0.321470i
$768$	− 5.97596e30i	− 3.02075i
$769$	−2.53401e30	−1.26352	−0.631759	−	0.775165i	$-0.717667\pi$
$769$	−2.53401e30	−1.26352	−0.631759	+	0.775165i	$0.717667\pi$
$770$	0	0
$771$	−7.88777e29	−0.382722
$772$	1.28193e30i	0.613598i
$773$	− 1.69545e30i	− 0.800571i	−0.916390	−	0.400285i	$-0.868911\pi$
$773$	− 1.69545e30i	− 0.800571i	0.916390	−	0.400285i	$-0.131089\pi$
$774$	−1.64173e30	−0.764756
$775$	0	0
$776$	−1.05100e31	−4.76490
$777$	− 6.60424e29i	− 0.295394i
$778$	3.57153e30i	1.57604i
$779$	−3.01396e30	−1.31218
$780$	0	0
$781$	3.85804e29	0.163505
$782$	3.80834e30i	1.59245i
$783$	− 4.94301e29i	− 0.203936i
$784$	8.07548e30	3.28738
$785$	0	0
$786$	1.07590e30	0.426417
$787$	1.87332e30i	0.732616i	0.930494	+	0.366308i	$0.119378\pi$
$787$	1.87332e30i	0.732616i	−0.930494	+	0.366308i	$0.880622\pi$
$788$	8.56113e30i	3.30374i
$789$	−3.44632e29	−0.131234
$790$	0	0
$791$	−1.54084e30	−0.571353
$792$	5.63075e29i	0.206040i
$793$	− 8.13429e29i	− 0.293732i
$794$	5.06702e30	1.80567
$795$	0	0
$796$	4.46856e30	1.55089
$797$	7.79664e29i	0.267051i	0.991045	+	0.133526i	$0.0426299\pi$
$797$	7.79664e29i	0.267051i	−0.991045	+	0.133526i	$0.957370\pi$
$798$	− 1.78172e30i	− 0.602294i
$799$	−5.71944e29	−0.190815
$800$	0	0
$801$	−1.08994e30	−0.354211
$802$	3.98676e30i	1.27876i
$803$	1.96436e29i	0.0621880i
$804$	−5.57386e30	−1.74168
$805$	0	0
$806$	−7.22050e29	−0.219811
$807$	3.16088e30i	0.949807i
$808$	− 1.60358e30i	− 0.475633i
$809$	−8.82262e29	−0.258308	−0.129154	−	0.991625i	$-0.541226\pi$
$809$	−8.82262e29	−0.258308	−0.129154	+	0.991625i	$0.541226\pi$
$810$	0	0
$811$	−2.06044e30	−0.587815	−0.293907	−	0.955834i	$-0.594956\pi$
$811$	−2.06044e30	−0.587815	−0.293907	+	0.955834i	$0.594956\pi$
$812$	− 5.22561e30i	− 1.47163i
$813$	6.16490e29i	0.171386i
$814$	−1.27668e30	−0.350369
$815$	0	0
$816$	9.60212e30	2.56815
$817$	− 4.83476e30i	− 1.27657i
$818$	− 6.18551e30i	− 1.61237i
$819$	−1.43589e29	−0.0369521
$820$	0	0
$821$	−1.83846e30	−0.461160	−0.230580	−	0.973053i	$-0.574062\pi$
$821$	−1.83846e30	−0.461160	−0.230580	+	0.973053i	$0.574062\pi$
$822$	3.33039e30i	0.824785i
$823$	7.73766e29i	0.189196i	0.995516	+	0.0945979i	$0.0301565\pi$
$823$	7.73766e29i	0.189196i	−0.995516	+	0.0945979i	$0.969843\pi$
$824$	2.43229e31	5.87190
$825$	0	0
$826$	−5.71831e30	−1.34579
$827$	4.59989e30i	1.06891i	0.845198	+	0.534453i	$0.179482\pi$
$827$	4.59989e30i	1.06891i	−0.845198	+	0.534453i	$0.820518\pi$
$828$	− 3.25673e30i	− 0.747245i
$829$	−7.93000e30	−1.79660	−0.898298	−	0.439386i	$-0.855196\pi$
$829$	−7.93000e30	−1.79660	−0.898298	+	0.439386i	$0.855196\pi$
$830$	0	0
$831$	−1.85936e30	−0.410726
$832$	− 5.36961e30i	− 1.17124i
$833$	3.66386e30i	0.789162i
$834$	8.73504e29	0.185790
$835$	0	0
$836$	−2.55124e30	−0.529158
$837$	4.61159e29i	0.0944569i
$838$	1.72812e31i	3.49551i
$839$	−4.84033e30	−0.966884	−0.483442	−	0.875376i	$-0.660614\pi$
$839$	−4.84033e30	−0.966884	−0.483442	+	0.875376i	$0.660614\pi$
$840$	0	0
$841$	6.30944e29	0.122923
$842$	− 5.40340e30i	− 1.03966i
$843$	6.84300e29i	0.130034i
$844$	1.58820e31	2.98064
$845$	0	0
$846$	6.60306e29	0.120881
$847$	2.61129e30i	0.472149i
$848$	8.24334e30i	1.47213i
$849$	−2.83671e30	−0.500362
$850$	0	0
$851$	4.79937e30	0.825893
$852$	9.36009e30i	1.59098i
$853$	2.96903e30i	0.498483i	0.968441	+	0.249242i	$0.0801813\pi$
$853$	2.96903e30i	0.498483i	−0.968441	+	0.249242i	$0.919819\pi$
$854$	−7.41472e30	−1.22967
$855$	0	0
$856$	1.80612e30	0.292263
$857$	3.70009e30i	0.591444i	0.955274	+	0.295722i	$0.0955602\pi$
$857$	3.70009e30i	0.591444i	−0.955274	+	0.295722i	$0.904440\pi$
$858$	2.77574e29i	0.0438291i
$859$	−7.75385e29	−0.120945	−0.0604726	−	0.998170i	$-0.519261\pi$
$859$	−7.75385e29	−0.120945	−0.0604726	+	0.998170i	$0.519261\pi$
$860$	0	0
$861$	2.21408e30	0.337024
$862$	− 2.29958e28i	− 0.00345798i
$863$	− 1.29544e31i	− 1.92443i	−0.272283	−	0.962217i	$-0.587779\pi$
$863$	− 1.29544e31i	− 1.92443i	0.272283	−	0.962217i	$-0.412221\pi$
$864$	−6.30375e30	−0.925134
$865$	0	0
$866$	1.59389e31	2.28307
$867$	2.76685e29i	0.0391548i
$868$	4.87524e30i	0.681615i
$869$	2.46231e29	0.0340122
$870$	0	0
$871$	−1.78589e30	−0.240805
$872$	2.49015e30i	0.331744i
$873$	3.30901e30i	0.435560i
$874$	1.29479e31	1.68395
$875$	0	0
$876$	−4.76577e30	−0.605118
$877$	1.57355e31i	1.97417i	0.160207	+	0.987083i	$0.448784\pi$
$877$	1.57355e31i	1.97417i	−0.160207	+	0.987083i	$0.551216\pi$
$878$	2.42056e31i	3.00070i
$879$	−4.70452e30	−0.576278
$880$	0	0
$881$	−1.47526e31	−1.76450	−0.882252	−	0.470778i	$-0.843973\pi$
$881$	−1.47526e31	−1.76450	−0.882252	+	0.470778i	$0.843973\pi$
$882$	− 4.22991e30i	− 0.499932i
$883$	− 5.64453e30i	− 0.659235i	−0.944115	−	0.329617i	$-0.893080\pi$
$883$	− 5.64453e30i	− 0.659235i	0.944115	−	0.329617i	$-0.106920\pi$
$884$	5.83310e30	0.673210
$885$	0	0
$886$	1.88595e31	2.12558
$887$	− 5.89300e30i	− 0.656354i	−0.944616	−	0.328177i	$-0.893566\pi$
$887$	− 5.89300e30i	− 0.656354i	0.944616	−	0.328177i	$-0.106434\pi$
$888$	− 2.01318e31i	− 2.21588i
$889$	−6.04218e29	−0.0657242
$890$	0	0
$891$	1.77281e29	0.0188342
$892$	− 2.37954e31i	− 2.49840i
$893$	1.94454e30i	0.201780i
$894$	1.25554e31	1.28761
$895$	0	0
$896$	−2.56189e31	−2.56641
$897$	− 1.04347e30i	− 0.103314i
$898$	− 3.70840e31i	− 3.62898i
$899$	−5.37734e30	−0.520104
$900$	0	0
$901$	−3.74002e30	−0.353397
$902$	− 4.28009e30i	− 0.399746i
$903$	3.55166e30i	0.327876i
$904$	−4.69695e31	−4.28596
$905$	0	0
$906$	1.86482e31	1.66261
$907$	− 8.32782e30i	− 0.733931i	−0.930235	−	0.366965i	$-0.880397\pi$
$907$	− 8.32782e30i	− 0.733931i	0.930235	−	0.366965i	$-0.119603\pi$
$908$	− 1.28624e31i	− 1.12053i
$909$	−5.04879e29	−0.0434777
$910$	0	0
$911$	1.08086e31	0.909548	0.454774	−	0.890607i	$-0.349720\pi$
$911$	1.08086e31	0.909548	0.454774	+	0.890607i	$0.349720\pi$
$912$	− 3.26461e31i	− 2.71572i
$913$	− 2.48894e30i	− 0.204678i
$914$	1.34507e31	1.09347
$915$	0	0
$916$	2.19291e31	1.74229
$917$	− 2.32755e30i	− 0.182819i
$918$	− 5.02955e30i	− 0.390554i
$919$	−6.55205e30	−0.502996	−0.251498	−	0.967858i	$-0.580923\pi$
$919$	−6.55205e30	−0.502996	−0.251498	+	0.967858i	$0.580923\pi$
$920$	0	0
$921$	−8.94582e30	−0.671265
$922$	1.40130e31i	1.03958i
$923$	2.99902e30i	0.219969i
$924$	1.87416e30	0.135910
$925$	0	0
$926$	−3.41869e31	−2.42351
$927$	− 7.65791e30i	− 0.536752i
$928$	− 7.35047e31i	− 5.09403i
$929$	−1.04036e31	−0.712883	−0.356442	−	0.934318i	$-0.616010\pi$
$929$	−1.04036e31	−0.712883	−0.356442	+	0.934318i	$0.616010\pi$
$930$	0	0
$931$	1.24567e31	0.834509
$932$	1.74296e31i	1.15457i
$933$	− 8.34989e30i	− 0.546919i
$934$	3.12752e31	2.02562
$935$	0	0
$936$	−4.37702e30	−0.277193
$937$	2.09831e31i	1.31402i	0.753880	+	0.657012i	$0.228180\pi$
$937$	2.09831e31i	1.31402i	−0.753880	+	0.657012i	$0.771820\pi$
$938$	1.62791e31i	1.00809i
$939$	2.95007e30	0.180653
$940$	0	0
$941$	2.20967e31	1.32323	0.661617	−	0.749842i	$-0.269870\pi$
$941$	2.20967e31	1.32323	0.661617	+	0.749842i	$0.269870\pi$
$942$	− 7.33143e30i	− 0.434165i
$943$	1.60900e31i	0.942286i
$944$	−1.04776e32	−6.06812
$945$	0	0
$946$	6.86578e30	0.388896
$947$	2.59604e31i	1.45424i	0.686509	+	0.727121i	$0.259142\pi$
$947$	2.59604e31i	1.45424i	−0.686509	+	0.727121i	$0.740858\pi$
$948$	5.97386e30i	0.330954i
$949$	−1.52698e30	−0.0836637
$950$	0	0
$951$	−1.07194e31	−0.574483
$952$	− 3.45590e31i	− 1.83178i
$953$	− 2.94729e31i	− 1.54507i	−0.634973	−	0.772535i	$-0.718989\pi$
$953$	− 2.94729e31i	− 1.54507i	0.634973	−	0.772535i	$-0.281011\pi$
$954$	4.31783e30	0.223876
$955$	0	0
$956$	−2.87711e31	−1.45931
$957$	2.06718e30i	0.103706i
$958$	3.77448e31i	1.87292i
$959$	7.20482e30	0.353612
$960$	0	0
$961$	−1.58087e31	−0.759103
$962$	− 9.92417e30i	− 0.471364i
$963$	− 5.68648e29i	− 0.0267158i
$964$	−4.71064e31	−2.18913
$965$	0	0
$966$	−9.51166e30	−0.432510
$967$	− 6.98077e30i	− 0.313997i	−0.987599	−	0.156998i	$-0.949818\pi$
$967$	− 6.98077e30i	− 0.313997i	0.987599	−	0.156998i	$-0.0501818\pi$
$968$	7.96002e31i	3.54179i
$969$	1.48116e31	0.651931
$970$	0	0
$971$	−1.30234e30	−0.0560946	−0.0280473	−	0.999607i	$-0.508929\pi$
$971$	−1.30234e30	−0.0560946	−0.0280473	+	0.999607i	$0.508929\pi$
$972$	4.30106e30i	0.183265i
$973$	− 1.88970e30i	− 0.0796541i
$974$	7.46765e31	3.11398
$975$	0	0
$976$	−1.35859e32	−5.54452
$977$	− 3.06599e31i	− 1.23788i	−0.785439	−	0.618939i	$-0.787563\pi$
$977$	− 3.06599e31i	− 1.23788i	0.785439	−	0.618939i	$-0.212437\pi$
$978$	4.79726e31i	1.91618i
$979$	4.55817e30	0.180124
$980$	0	0
$981$	7.84011e29	0.0303248
$982$	− 7.22564e31i	− 2.76507i
$983$	8.31325e30i	0.314745i	0.987539	+	0.157373i	$0.0503023\pi$
$983$	8.31325e30i	0.314745i	−0.987539	+	0.157373i	$0.949698\pi$
$984$	6.74921e31	2.52816
$985$	0	0
$986$	5.86470e31	2.15049
$987$	− 1.42848e30i	− 0.0518255i
$988$	− 1.98319e31i	− 0.711895i
$989$	−2.58102e31	−0.916708
$990$	0	0
$991$	−1.32568e31	−0.460962	−0.230481	−	0.973077i	$-0.574030\pi$
$991$	−1.32568e31	−0.460962	−0.230481	+	0.973077i	$0.574030\pi$
$992$	6.85764e31i	2.35940i
$993$	− 8.50837e30i	− 0.289654i
$994$	2.73372e31	0.920868
$995$	0	0
$996$	6.03849e31	1.99161
$997$	− 3.42048e31i	− 1.11632i	−0.829734	−	0.558159i	$-0.811508\pi$
$997$	− 3.42048e31i	− 1.11632i	0.829734	−	0.558159i	$-0.188492\pi$
$998$	3.69857e31i	1.19444i
$999$	−6.33837e30	−0.202554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.b.a.49.2		2
5.2	odd	4		3.22.a.a.1.1	✓	1
5.3	odd	4		75.22.a.c.1.1		1
5.4	even	2	inner	75.22.b.a.49.1		2
15.2	even	4		9.22.a.d.1.1		1
20.7	even	4		48.22.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.a.1.1	✓	1	5.2	odd	4
9.22.a.d.1.1		1	15.2	even	4
48.22.a.e.1.1		1	20.7	even	4
75.22.a.c.1.1		1	5.3	odd	4
75.22.b.a.49.1		2	5.4	even	2	inner
75.22.b.a.49.2		2	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:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2844.00i q^{2} -59049.0i q^{3} -5.99118e6 q^{4} +1.67935e8 q^{6} -3.63304e8i q^{7} -1.10746e10i q^{8} -3.48678e9 q^{9} +O(q^{10})\)	\(q+2844.00i q^{2} -59049.0i q^{3} -5.99118e6 q^{4} +1.67935e8 q^{6} -3.63304e8i q^{7} -1.10746e10i q^{8} -3.48678e9 q^{9} +1.45818e10 q^{11} +3.53773e11i q^{12} +1.13351e11i q^{13} +1.03324e12 q^{14} +1.89318e13 q^{16} +8.58939e12i q^{17} -9.91641e12i q^{18} +2.92029e13 q^{19} -2.14527e13 q^{21} +4.14707e13i q^{22} -1.55899e14i q^{23} -6.53946e14 q^{24} -3.22370e14 q^{26} +2.05891e14i q^{27} +2.17662e15i q^{28} -2.40079e15 q^{29} +2.23982e15 q^{31} +3.06169e16i q^{32} -8.61043e14i q^{33} -2.44282e16 q^{34} +2.08900e16 q^{36} +3.07851e16i q^{37} +8.30532e16i q^{38} +6.69325e15 q^{39} -1.03208e17 q^{41} -6.10116e16i q^{42} -1.65557e17i q^{43} -8.73624e16 q^{44} +4.43377e17 q^{46} +6.65872e16i q^{47} -1.11790e18i q^{48} +4.26556e17 q^{49} +5.07195e17 q^{51} -6.79105e17i q^{52} +4.35423e17i q^{53} -5.85554e17 q^{54} -4.02346e18 q^{56} -1.72440e18i q^{57} -6.82784e18i q^{58} -5.53437e18 q^{59} -7.17621e18 q^{61} +6.37005e18i q^{62} +1.26676e18i q^{63} -4.73716e19 q^{64} +2.44881e18 q^{66} +1.57554e19i q^{67} -5.14606e19i q^{68} -9.20569e18 q^{69} +2.64579e19 q^{71} +3.86148e19i q^{72} +1.34712e19i q^{73} -8.75527e19 q^{74} -1.74960e20 q^{76} -5.29764e18i q^{77} +1.90356e19i q^{78} +1.68861e19 q^{79} +1.21577e19 q^{81} -2.93522e20i q^{82} -1.70688e20i q^{83} +1.28527e20 q^{84} +4.70845e20 q^{86} +1.41764e20i q^{87} -1.61488e20i q^{88} +3.12592e20 q^{89} +4.11808e19 q^{91} +9.34021e20i q^{92} -1.32259e20i q^{93} -1.89374e20 q^{94} +1.80790e21 q^{96} -9.49015e20i q^{97} +1.21313e21i q^{98} -5.08437e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 11982368 q^{4} + 335870712 q^{6} - 6973568802 q^{9}+O(q^{10}) \) 2 * q - 11982368 * q^4 + 335870712 * q^6 - 6973568802 * q^9	\( 2 q - 11982368 q^{4} + 335870712 q^{6} - 6973568802 q^{9} + 29163666312 q^{11} + 2066472696960 q^{14} + 37863631405568 q^{16} + 58405878547592 q^{19} - 42905466344160 q^{21} - 13\!\cdots\!84 q^{24}+ \cdots - 10\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 11982368 * q^4 + 335870712 * q^6 - 6973568802 * q^9 + 29163666312 * q^11 + 2066472696960 * q^14 + 37863631405568 * q^16 + 58405878547592 * q^19 - 42905466344160 * q^21 - 1307891300390784 * q^24 - 644739297512976 * q^26 - 4801577414181516 * q^29 + 4479641353894000 * q^31 - 48856448033321616 * q^34 + 41779933829441568 * q^36 + 13386501680324796 * q^39 - 206415142082562060 * q^41 - 174724890989793408 * q^44 + 886754734659944640 * q^46 + 853112251591835214 * q^49 + 1014389732742478236 * q^51 - 1171108759354363512 * q^54 - 8046910809088542720 * q^56 - 11068731596518162632 * q^59 - 14352410329445922404 * q^61 - 94743180552322555904 * q^64 + 4897610684370927072 * q^66 - 18411385487670559440 * q^69 + 52915709748518752464 * q^71 - 175105474652204086320 * q^74 - 349920365060276428928 * q^76 + 33772250171051973680 * q^79 + 24315330918113857602 * q^81 + 257054543473669885440 * q^84 + 941689755272272449312 * q^86 + 625184973879174087372 * q^89 + 82361573194272303680 * q^91 - 378748085896203496704 * q^94 + 3615795563149709015040 * q^96 - 101687416772650799112 * q^99

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