LMFDB - Embedded newform 75.10.b.g.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,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, 10, names="a")

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

chi := DirichletCharacter("75.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{79})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 39x^{2} + 400 $ x^4 - 39*x^2 + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-4.44410 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.10.b.g.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.223611i q^{2} -81.0000i q^{3} +511.950 q^{4} -18.1125 q^{6} -580.825i q^{7} -228.967i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-0.223611i q^{2} -81.0000i q^{3} +511.950 q^{4} -18.1125 q^{6} -580.825i q^{7} -228.967i q^{8} -6561.00 q^{9} +47275.7 q^{11} -41467.9i q^{12} -22367.7i q^{13} -129.879 q^{14} +262067. q^{16} -244880. i q^{17} +1467.11i q^{18} +248536. q^{19} -47046.8 q^{21} -10571.4i q^{22} +990208. i q^{23} -18546.3 q^{24} -5001.67 q^{26} +531441. i q^{27} -297353. i q^{28} +4.35002e6 q^{29} -5.60419e6 q^{31} -175832. i q^{32} -3.82933e6i q^{33} -54758.0 q^{34} -3.35890e6 q^{36} -4.73703e6i q^{37} -55575.5i q^{38} -1.81178e6 q^{39} +6.11568e6 q^{41} +10520.2i q^{42} -3.89014e7i q^{43} +2.42028e7 q^{44} +221422. q^{46} -5.09738e7i q^{47} -2.12274e7i q^{48} +4.00162e7 q^{49} -1.98353e7 q^{51} -1.14511e7i q^{52} +1.16798e7i q^{53} +118836. q^{54} -132990. q^{56} -2.01314e7i q^{57} -972713. i q^{58} +1.79748e8 q^{59} -1.24120e8 q^{61} +1.25316e6i q^{62} +3.81079e6i q^{63} +1.34139e8 q^{64} -856281. q^{66} -1.90142e8i q^{67} -1.25366e8i q^{68} +8.02068e7 q^{69} -1.13551e8 q^{71} +1.50225e6i q^{72} -1.03304e8i q^{73} -1.05925e6 q^{74} +1.27238e8 q^{76} -2.74589e7i q^{77} +405135. i q^{78} +1.94841e7 q^{79} +4.30467e7 q^{81} -1.36753e6i q^{82} -5.52722e8i q^{83} -2.40856e7 q^{84} -8.69878e6 q^{86} -3.52351e8i q^{87} -1.08246e7i q^{88} -3.25690e8 q^{89} -1.29917e7 q^{91} +5.06937e8i q^{92} +4.53939e8i q^{93} -1.13983e7 q^{94} -1.42424e7 q^{96} +1.33561e8i q^{97} -8.94808e6i q^{98} -3.10176e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 512 q^{4} - 5832 q^{6} - 26244 q^{9}+O(q^{10}) $ 4 * q - 512 * q^4 - 5832 * q^6 - 26244 * q^9	$ 4 q - 512 q^{4} - 5832 q^{6} - 26244 q^{9} + 48456 q^{11} + 278712 q^{14} + 392960 q^{16} + 2697692 q^{19} + 537516 q^{21} + 1446336 q^{24} + 8097048 q^{26} + 8566344 q^{29} + 2353164 q^{31} + 26301776 q^{34} + 3359232 q^{36} + 14731308 q^{39} - 57776976 q^{41} + 83804544 q^{44} - 94053456 q^{46} + 130338040 q^{49} + 20126232 q^{51} + 38263752 q^{54} - 71668800 q^{56} + 230300568 q^{59} - 462988820 q^{61} + 704479232 q^{64} + 131866704 q^{66} - 53531928 q^{69} + 223584048 q^{71} + 709452432 q^{74} - 1435489408 q^{76} + 668892000 q^{79} + 172186884 q^{81} - 533215872 q^{84} + 1809396936 q^{86} + 493342272 q^{89} - 909470436 q^{91} - 1130811472 q^{94} + 1111159296 q^{96} - 317919816 q^{99}+O(q^{100}) $ 4 * q - 512 * q^4 - 5832 * q^6 - 26244 * q^9 + 48456 * q^11 + 278712 * q^14 + 392960 * q^16 + 2697692 * q^19 + 537516 * q^21 + 1446336 * q^24 + 8097048 * q^26 + 8566344 * q^29 + 2353164 * q^31 + 26301776 * q^34 + 3359232 * q^36 + 14731308 * q^39 - 57776976 * q^41 + 83804544 * q^44 - 94053456 * q^46 + 130338040 * q^49 + 20126232 * q^51 + 38263752 * q^54 - 71668800 * q^56 + 230300568 * q^59 - 462988820 * q^61 + 704479232 * q^64 + 131866704 * q^66 - 53531928 * q^69 + 223584048 * q^71 + 709452432 * q^74 - 1435489408 * q^76 + 668892000 * q^79 + 172186884 * q^81 - 533215872 * q^84 + 1809396936 * q^86 + 493342272 * q^89 - 909470436 * q^91 - 1130811472 * q^94 + 1111159296 * q^96 - 317919816 * 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 $

$2$	− 0.223611i	− 0.00988231i	−0.999988	−	0.00494116i	$-0.998427\pi$
$2$	− 0.223611i	− 0.00988231i	0.999988	−	0.00494116i	$-0.00157282\pi$
$3$	− 81.0000i	− 0.577350i
$3$	− 81.0000i	− 0.577350i
$4$	511.950	0.999902
$5$	0	0
$5$	0	0
$6$	−18.1125	−0.00570555
$7$	− 580.825i	− 0.0914332i	−0.998954	−	0.0457166i	$-0.985443\pi$
$7$	− 580.825i	− 0.0914332i	0.998954	−	0.0457166i	$-0.0145571\pi$
$8$	− 228.967i	− 0.0197637i
$9$	−6561.00	−0.333333
$10$	0	0
$11$	47275.7	0.973578	0.486789	−	0.873520i	$-0.338168\pi$
$11$	47275.7	0.973578	0.486789	+	0.873520i	$0.338168\pi$
$12$	− 41467.9i	− 0.577294i
$13$	− 22367.7i	− 0.217208i	−0.994085	−	0.108604i	$-0.965362\pi$
$13$	− 22367.7i	− 0.217208i	0.994085	−	0.108604i	$-0.0346381\pi$
$14$	−129.879	−0.000903572 0
$15$	0	0
$16$	262067.	0.999707
$17$	− 244880.i	− 0.711105i	−0.934656	−	0.355552i	$-0.884293\pi$
$17$	− 244880.i	− 0.711105i	0.934656	−	0.355552i	$-0.115707\pi$
$18$	1467.11i	0.00329410i
$19$	248536.	0.437521	0.218760	−	0.975779i	$-0.429799\pi$
$19$	248536.	0.437521	0.218760	+	0.975779i	$0.429799\pi$
$20$	0	0
$21$	−47046.8	−0.0527890
$22$	− 10571.4i	− 0.00962120i
$23$	990208.i	0.737821i	0.929465	+	0.368911i	$0.120269\pi$
$23$	990208.i	0.737821i	−0.929465	+	0.368911i	$0.879731\pi$
$24$	−18546.3	−0.0114106
$25$	0	0
$26$	−5001.67	−0.00214652
$27$	531441.i	0.192450i
$28$	− 297353.i	− 0.0914243i
$29$	4.35002e6	1.14209	0.571045	−	0.820919i	$-0.306538\pi$
$29$	4.35002e6	1.14209	0.571045	+	0.820919i	$0.306538\pi$
$30$	0	0
$31$	−5.60419e6	−1.08990	−0.544948	−	0.838470i	$-0.683451\pi$
$31$	−5.60419e6	−1.08990	−0.544948	+	0.838470i	$0.683451\pi$
$32$	− 175832.i	− 0.0296431i
$33$	− 3.82933e6i	− 0.562096i
$34$	−54758.0	−0.00702736
$35$	0	0
$36$	−3.35890e6	−0.333301
$37$	− 4.73703e6i	− 0.415526i	−0.978179	−	0.207763i	$-0.933382\pi$
$37$	− 4.73703e6i	− 0.415526i	0.978179	−	0.207763i	$-0.0666183\pi$
$38$	− 55575.5i	− 0.00432372i
$39$	−1.81178e6	−0.125405
$40$	0	0
$41$	6.11568e6	0.338000	0.169000	−	0.985616i	$-0.445946\pi$
$41$	6.11568e6	0.338000	0.169000	+	0.985616i	$0.445946\pi$
$42$	10520.2i	0 0.000521677i
$43$	− 3.89014e7i	− 1.73523i	−0.497238	−	0.867614i	$-0.665652\pi$
$43$	− 3.89014e7i	− 1.73523i	0.497238	−	0.867614i	$-0.334348\pi$
$44$	2.42028e7	0.973483
$45$	0	0
$46$	221422.	0.00729138
$47$	− 5.09738e7i	− 1.52372i	−0.647739	−	0.761862i	$-0.724285\pi$
$47$	− 5.09738e7i	− 1.52372i	0.647739	−	0.761862i	$-0.275715\pi$
$48$	− 2.12274e7i	− 0.577181i
$49$	4.00162e7	0.991640
$50$	0	0
$51$	−1.98353e7	−0.410557
$52$	− 1.14511e7i	− 0.217187i
$53$	1.16798e7i	0.203327i	0.994819	+	0.101664i	$0.0324166\pi$
$53$	1.16798e7i	0.203327i	−0.994819	+	0.101664i	$0.967583\pi$
$54$	118836.	0.00190185
$55$	0	0
$56$	−132990.	−0.00180706
$57$	− 2.01314e7i	− 0.252603i
$58$	− 972713.i	− 0.0112865i
$59$	1.79748e8	1.93121	0.965607	−	0.260006i	$-0.0837247\pi$
$59$	1.79748e8	1.93121	0.965607	+	0.260006i	$0.0837247\pi$
$60$	0	0
$61$	−1.24120e8	−1.14777	−0.573887	−	0.818935i	$-0.694565\pi$
$61$	−1.24120e8	−1.14777	−0.573887	+	0.818935i	$0.694565\pi$
$62$	1.25316e6i	0.0107707i
$63$	3.81079e6i	0.0304777i
$64$	1.34139e8	0.999414
$65$	0	0
$66$	−856281.	−0.00555480
$67$	− 1.90142e8i	− 1.15277i	−0.817180	−	0.576383i	$-0.804464\pi$
$67$	− 1.90142e8i	− 1.15277i	0.817180	−	0.576383i	$-0.195536\pi$
$68$	− 1.25366e8i	− 0.711035i
$69$	8.02068e7	0.425981
$70$	0	0
$71$	−1.13551e8	−0.530309	−0.265155	−	0.964206i	$-0.585423\pi$
$71$	−1.13551e8	−0.530309	−0.265155	+	0.964206i	$0.585423\pi$
$72$	1.50225e6i	0.00658789i
$73$	− 1.03304e8i	− 0.425761i	−0.977078	−	0.212881i	$-0.931715\pi$
$73$	− 1.03304e8i	− 0.425761i	0.977078	−	0.212881i	$-0.0682846\pi$
$74$	−1.05925e6	−0.00410636
$75$	0	0
$76$	1.27238e8	0.437478
$77$	− 2.74589e7i	− 0.0890174i
$78$	405135.i	0.00123929i
$79$	1.94841e7	0.0562807	0.0281403	−	0.999604i	$-0.491041\pi$
$79$	1.94841e7	0.0562807	0.0281403	+	0.999604i	$0.491041\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	− 1.36753e6i	− 0.00334023i
$83$	− 5.52722e8i	− 1.27837i	−0.769055	−	0.639183i	$-0.779273\pi$
$83$	− 5.52722e8i	− 1.27837i	0.769055	−	0.639183i	$-0.220727\pi$
$84$	−2.40856e7	−0.0527839
$85$	0	0
$86$	−8.69878e6	−0.0171481
$87$	− 3.52351e8i	− 0.659386i
$88$	− 1.08246e7i	− 0.0192415i
$89$	−3.25690e8	−0.550237	−0.275119	−	0.961410i	$-0.588717\pi$
$89$	−3.25690e8	−0.550237	−0.275119	+	0.961410i	$0.588717\pi$
$90$	0	0
$91$	−1.29917e7	−0.0198601
$92$	5.06937e8i	0.737749i
$93$	4.53939e8i	0.629251i
$94$	−1.13983e7	−0.0150579
$95$	0	0
$96$	−1.42424e7	−0.0171144
$97$	1.33561e8i	0.153182i	0.997063	+	0.0765910i	$0.0244036\pi$
$97$	1.33561e8i	0.153182i	−0.997063	+	0.0765910i	$0.975596\pi$
$98$	− 8.94808e6i	− 0.00979969i
$99$	−3.10176e8	−0.324526
$100$	0	0
$101$	1.72460e8	0.164908	0.0824542	−	0.996595i	$-0.473724\pi$
$101$	1.72460e8	0.164908	0.0824542	+	0.996595i	$0.473724\pi$
$102$	4.43539e6i	0.00405725i
$103$	1.72881e9i	1.51349i	0.653710	+	0.756746i	$0.273212\pi$
$103$	1.72881e9i	1.51349i	−0.653710	+	0.756746i	$0.726788\pi$
$104$	−5.12146e6	−0.00429283
$105$	0	0
$106$	2.61174e6	0.00200934
$107$	2.12656e9i	1.56838i	0.620521	+	0.784190i	$0.286921\pi$
$107$	2.12656e9i	1.56838i	−0.620521	+	0.784190i	$0.713079\pi$
$108$	2.72071e8i	0.192431i
$109$	−1.65766e9	−1.12480	−0.562402	−	0.826864i	$-0.690123\pi$
$109$	−1.65766e9	−1.12480	−0.562402	+	0.826864i	$0.690123\pi$
$110$	0	0
$111$	−3.83700e8	−0.239904
$112$	− 1.52215e8i	− 0.0914065i
$113$	1.83857e9i	1.06079i	0.847752	+	0.530394i	$0.177956\pi$
$113$	1.83857e9i	1.06079i	−0.847752	+	0.530394i	$0.822044\pi$
$114$	−4.50161e6	−0.00249630
$115$	0	0
$116$	2.22699e9	1.14198
$117$	1.46754e8i	0.0724027i
$118$	− 4.01937e7i	− 0.0190849i
$119$	−1.42233e8	−0.0650186
$120$	0	0
$121$	−1.22956e8	−0.0521454
$122$	2.77545e7i	0.0113427i
$123$	− 4.95370e8i	− 0.195145i
$124$	−2.86906e9	−1.08979
$125$	0	0
$126$	852136.	0.000301191 0
$127$	− 7.74572e7i	− 0.0264207i	−0.999913	−	0.0132104i	$-0.995795\pi$
$127$	− 7.74572e7i	− 0.0264207i	0.999913	−	0.0132104i	$-0.00420511\pi$
$128$	− 1.20021e8i	− 0.0395196i
$129$	−3.15101e9	−1.00183
$130$	0	0
$131$	4.50478e9	1.33645	0.668225	−	0.743960i	$-0.267055\pi$
$131$	4.50478e9	1.33645	0.668225	+	0.743960i	$0.267055\pi$
$132$	− 1.96043e9i	− 0.562041i
$133$	− 1.44356e8i	− 0.0400039i
$134$	−4.25178e7	−0.0113920
$135$	0	0
$136$	−5.60694e7	−0.0140540
$137$	6.80091e9i	1.64939i	0.565575	+	0.824697i	$0.308654\pi$
$137$	6.80091e9i	1.64939i	−0.565575	+	0.824697i	$0.691346\pi$
$138$	− 1.79351e7i	− 0.00420968i
$139$	−1.95054e9	−0.443187	−0.221594	−	0.975139i	$-0.571126\pi$
$139$	−1.95054e9	−0.443187	−0.221594	+	0.975139i	$0.571126\pi$
$140$	0	0
$141$	−4.12888e9	−0.879723
$142$	2.53913e7i	0.00524068i
$143$	− 1.05745e9i	− 0.211469i
$144$	−1.71942e9	−0.333236
$145$	0	0
$146$	−2.31000e7	−0.00420751
$147$	− 3.24132e9i	− 0.572524i
$148$	− 2.42512e9i	− 0.415486i
$149$	1.06040e10	1.76251	0.881257	−	0.472637i	$-0.156698\pi$
$149$	1.06040e10	1.76251	0.881257	+	0.472637i	$0.156698\pi$
$150$	0	0
$151$	−6.54596e9	−1.02465	−0.512327	−	0.858791i	$-0.671216\pi$
$151$	−6.54596e9	−1.02465	−0.512327	+	0.858791i	$0.671216\pi$
$152$	− 5.69065e7i	− 0.00864701i
$153$	1.60666e9i	0.237035i
$154$	−6.14012e6	−0.000879698 0
$155$	0	0
$156$	−9.27543e8	−0.125393
$157$	− 4.83783e9i	− 0.635480i	−0.948178	−	0.317740i	$-0.897076\pi$
$157$	− 4.83783e9i	− 0.635480i	0.948178	−	0.317740i	$-0.102924\pi$
$158$	− 4.35687e6i	0 0.000556183i
$159$	9.46068e8	0.117391
$160$	0	0
$161$	5.75137e8	0.0674614
$162$	− 9.62573e6i	− 0.00109803i
$163$	5.42724e9i	0.602191i	0.953594	+	0.301096i	$0.0973524\pi$
$163$	5.42724e9i	0.602191i	−0.953594	+	0.301096i	$0.902648\pi$
$164$	3.13092e9	0.337967
$165$	0	0
$166$	−1.23595e8	−0.0126332
$167$	1.36699e10i	1.36000i	0.733210	+	0.680002i	$0.238021\pi$
$167$	1.36699e10i	1.36000i	−0.733210	+	0.680002i	$0.761979\pi$
$168$	1.07722e7i	0.00104330i
$169$	1.01042e10	0.952821
$170$	0	0
$171$	−1.63065e9	−0.145840
$172$	− 1.99156e10i	− 1.73506i
$173$	− 1.84099e10i	− 1.56259i	−0.624163	−	0.781294i	$-0.714560\pi$
$173$	− 1.84099e10i	− 1.56259i	0.624163	−	0.781294i	$-0.285440\pi$
$174$	−7.87897e7	−0.00651625
$175$	0	0
$176$	1.23894e10	0.973293
$177$	− 1.45596e10i	− 1.11499i
$178$	7.28280e7i	0.00543762i
$179$	2.21847e10	1.61516	0.807580	−	0.589758i	$-0.200777\pi$
$179$	2.21847e10	1.61516	0.807580	+	0.589758i	$0.200777\pi$
$180$	0	0
$181$	−1.26287e10	−0.874593	−0.437297	−	0.899317i	$-0.644064\pi$
$181$	−1.26287e10	−0.874593	−0.437297	+	0.899317i	$0.644064\pi$
$182$	2.90509e6i	0 0.000196263i
$183$	1.00537e10i	0.662668i
$184$	2.26725e8	0.0145820
$185$	0	0
$186$	1.01506e8	0.00621846
$187$	− 1.15769e10i	− 0.692316i
$188$	− 2.60960e10i	− 1.52358i
$189$	3.08674e8	0.0175963
$190$	0	0
$191$	−3.00606e9	−0.163436	−0.0817179	−	0.996655i	$-0.526041\pi$
$191$	−3.00606e9	−0.163436	−0.0817179	+	0.996655i	$0.526041\pi$
$192$	− 1.08653e10i	− 0.577012i
$193$	− 3.17884e9i	− 0.164915i	−0.996595	−	0.0824576i	$-0.973723\pi$
$193$	− 3.17884e9i	− 0.164915i	0.996595	−	0.0824576i	$-0.0262769\pi$
$194$	2.98658e7	0.00151379
$195$	0	0
$196$	2.04863e10	0.991543
$197$	2.67639e10i	1.26605i	0.774131	+	0.633026i	$0.218187\pi$
$197$	2.67639e10i	1.26605i	−0.774131	+	0.633026i	$0.781813\pi$
$198$	6.93588e7i	0.00320707i
$199$	−3.55476e8	−0.0160684	−0.00803419	−	0.999968i	$-0.502557\pi$
$199$	−3.55476e8	−0.0160684	−0.00803419	+	0.999968i	$0.502557\pi$
$200$	0	0
$201$	−1.54015e10	−0.665550
$202$	− 3.85640e7i	− 0.00162968i
$203$	− 2.52660e9i	− 0.104425i
$204$	−1.01547e10	−0.410516
$205$	0	0
$206$	3.86581e8	0.0149568
$207$	− 6.49675e9i	− 0.245940i
$208$	− 5.86184e9i	− 0.217145i
$209$	1.17497e10	0.425961
$210$	0	0
$211$	−3.90979e10	−1.35795	−0.678973	−	0.734164i	$-0.737574\pi$
$211$	−3.90979e10	−1.35795	−0.678973	+	0.734164i	$0.737574\pi$
$212$	5.97950e9i	0.203307i
$213$	9.19765e9i	0.306174i
$214$	4.75523e8	0.0154992
$215$	0	0
$216$	1.21682e8	0.00380352
$217$	3.25505e9i	0.0996527i
$218$	3.70672e8i	0.0111157i
$219$	−8.36766e9	−0.245813
$220$	0	0
$221$	−5.47741e9	−0.154458
$222$	8.57995e7i	0.00237081i
$223$	3.00688e10i	0.814225i	0.913378	+	0.407112i	$0.133464\pi$
$223$	3.00688e10i	0.814225i	−0.913378	+	0.407112i	$0.866536\pi$
$224$	−1.02128e8	−0.00271036
$225$	0	0
$226$	4.11126e8	0.0104830
$227$	5.17270e10i	1.29301i	0.762911	+	0.646503i	$0.223769\pi$
$227$	5.17270e10i	1.29301i	−0.762911	+	0.646503i	$0.776231\pi$
$228$	− 1.03063e10i	− 0.252578i
$229$	−4.39043e10	−1.05499	−0.527494	−	0.849559i	$-0.676868\pi$
$229$	−4.39043e10	−1.05499	−0.527494	+	0.849559i	$0.676868\pi$
$230$	0	0
$231$	−2.22417e9	−0.0513942
$232$	− 9.96009e8i	− 0.0225719i
$233$	5.20811e10i	1.15765i	0.815451	+	0.578826i	$0.196489\pi$
$233$	5.20811e10i	1.15765i	−0.815451	+	0.578826i	$0.803511\pi$
$234$	3.28159e7	0.000715506 0
$235$	0	0
$236$	9.20221e10	1.93103
$237$	− 1.57822e9i	− 0.0324937i
$238$	3.18048e7i	0 0.000642534i
$239$	−1.25028e9	−0.0247866	−0.0123933	−	0.999923i	$-0.503945\pi$
$239$	−1.25028e9	−0.0247866	−0.0123933	+	0.999923i	$0.503945\pi$
$240$	0	0
$241$	5.39086e9	0.102939	0.0514696	−	0.998675i	$-0.483609\pi$
$241$	5.39086e9	0.102939	0.0514696	+	0.998675i	$0.483609\pi$
$242$	2.74944e7i	0 0.000515317i
$243$	− 3.48678e9i	− 0.0641500i
$244$	−6.35431e10	−1.14766
$245$	0	0
$246$	−1.10770e8	−0.00192848
$247$	− 5.55918e9i	− 0.0950331i
$248$	1.28317e9i	0.0215403i
$249$	−4.47705e10	−0.738065
$250$	0	0
$251$	3.79306e10	0.603196	0.301598	−	0.953435i	$-0.402480\pi$
$251$	3.79306e10	0.603196	0.301598	+	0.953435i	$0.402480\pi$
$252$	1.95094e9i	0.0304748i
$253$	4.68128e10i	0.718327i
$254$	−1.73203e7	−0.000261098 0
$255$	0	0
$256$	6.86524e10	0.999024
$257$	1.23297e10i	0.176301i	0.996107	+	0.0881504i	$0.0280956\pi$
$257$	1.23297e10i	0.176301i	−0.996107	+	0.0881504i	$0.971904\pi$
$258$	7.04601e8i	0.00990044i
$259$	−2.75139e9	−0.0379929
$260$	0	0
$261$	−2.85405e10	−0.380696
$262$	− 1.00732e9i	− 0.0132072i
$263$	8.86491e10i	1.14255i	0.820760	+	0.571273i	$0.193550\pi$
$263$	8.86491e10i	1.14255i	−0.820760	+	0.571273i	$0.806450\pi$
$264$	−8.76789e8	−0.0111091
$265$	0	0
$266$	−3.22796e7	−0.000395331 0
$267$	2.63809e10i	0.317680i
$268$	− 9.73431e10i	− 1.15265i
$269$	−6.53334e10	−0.760764	−0.380382	−	0.924829i	$-0.624207\pi$
$269$	−6.53334e10	−0.760764	−0.380382	+	0.924829i	$0.624207\pi$
$270$	0	0
$271$	−4.43373e10	−0.499353	−0.249676	−	0.968329i	$-0.580324\pi$
$271$	−4.43373e10	−0.499353	−0.249676	+	0.968329i	$0.580324\pi$
$272$	− 6.41751e10i	− 0.710896i
$273$	1.05233e9i	0.0114662i
$274$	1.52076e9	0.0162998
$275$	0	0
$276$	4.10619e10	0.425940
$277$	1.89388e11i	1.93283i	0.256984	+	0.966416i	$0.417271\pi$
$277$	1.89388e11i	1.93283i	−0.256984	+	0.966416i	$0.582729\pi$
$278$	4.36162e8i	0.00437972i
$279$	3.67691e10	0.363298
$280$	0	0
$281$	−1.59371e11	−1.52486	−0.762432	−	0.647068i	$-0.775995\pi$
$281$	−1.59371e11	−1.52486	−0.762432	+	0.647068i	$0.775995\pi$
$282$	9.23263e8i	0.00869369i
$283$	9.23708e10i	0.856043i	0.903769	+	0.428022i	$0.140789\pi$
$283$	9.23708e10i	0.856043i	−0.903769	+	0.428022i	$0.859211\pi$
$284$	−5.81325e10	−0.530257
$285$	0	0
$286$	−2.36457e8	−0.00208980
$287$	− 3.55214e9i	− 0.0309045i
$288$	1.15363e9i	0.00988102i
$289$	5.86215e10	0.494330
$290$	0	0
$291$	1.08185e10	0.0884396
$292$	− 5.28867e10i	− 0.425720i
$293$	− 1.47354e11i	− 1.16804i	−0.811740	−	0.584018i	$-0.801480\pi$
$293$	− 1.47354e11i	− 1.16804i	0.811740	−	0.584018i	$-0.198520\pi$
$294$	−7.24794e8	−0.00565786
$295$	0	0
$296$	−1.08462e9	−0.00821232
$297$	2.51242e10i	0.187365i
$298$	− 2.37118e9i	− 0.0174177i
$299$	2.21487e10	0.160261
$300$	0	0
$301$	−2.25949e10	−0.158658
$302$	1.46375e9i	0.0101259i
$303$	− 1.39693e10i	− 0.0952099i
$304$	6.51332e10	0.437392
$305$	0	0
$306$	3.59267e8	0.00234245
$307$	− 1.85136e11i	− 1.18951i	−0.803907	−	0.594755i	$-0.797249\pi$
$307$	− 1.85136e11i	− 1.18951i	0.803907	−	0.594755i	$-0.202751\pi$
$308$	− 1.40576e10i	− 0.0890087i
$309$	1.40034e11	0.873814
$310$	0	0
$311$	−1.63232e11	−0.989429	−0.494715	−	0.869055i	$-0.664727\pi$
$311$	−1.63232e11	−0.989429	−0.494715	+	0.869055i	$0.664727\pi$
$312$	4.14838e8i	0.00247847i
$313$	− 1.58814e11i	− 0.935272i	−0.883921	−	0.467636i	$-0.845106\pi$
$313$	− 1.58814e11i	− 0.935272i	0.883921	−	0.467636i	$-0.154894\pi$
$314$	−1.08179e9	−0.00628001
$315$	0	0
$316$	9.97491e9	0.0562752
$317$	− 2.22998e11i	− 1.24032i	−0.784474	−	0.620161i	$-0.787067\pi$
$317$	− 2.22998e11i	− 1.24032i	0.784474	−	0.620161i	$-0.212933\pi$
$318$	− 2.11551e8i	− 0.00116010i
$319$	2.05650e11	1.11191
$320$	0	0
$321$	1.72252e11	0.905504
$322$	− 1.28607e8i	0 0.000666674i
$323$	− 6.08616e10i	− 0.311123i
$324$	2.20378e10	0.111100
$325$	0	0
$326$	1.21359e9	0.00595104
$327$	1.34271e11i	0.649406i
$328$	− 1.40029e9i	− 0.00668012i
$329$	−2.96068e10	−0.139319
$330$	0	0
$331$	2.64535e11	1.21131	0.605657	−	0.795725i	$-0.292910\pi$
$331$	2.64535e11	1.21131	0.605657	+	0.795725i	$0.292910\pi$
$332$	− 2.82966e11i	− 1.27824i
$333$	3.10797e10i	0.138509i
$334$	3.05674e9	0.0134400
$335$	0	0
$336$	−1.23294e10	−0.0527735
$337$	1.13648e11i	0.479986i	0.970775	+	0.239993i	$0.0771451\pi$
$337$	1.13648e11i	0.479986i	−0.970775	+	0.239993i	$0.922855\pi$
$338$	− 2.25941e9i	− 0.00941607i
$339$	1.48925e11	0.612446
$340$	0	0
$341$	−2.64942e11	−1.06110
$342$	3.64631e8i	0.00144124i
$343$	− 4.66808e10i	− 0.182102i
$344$	−8.90711e9	−0.0342945
$345$	0	0
$346$	−4.11667e9	−0.0154420
$347$	− 3.78341e11i	− 1.40088i	−0.713711	−	0.700441i	$-0.752987\pi$
$347$	− 3.78341e11i	− 1.40088i	0.713711	−	0.700441i	$-0.247013\pi$
$348$	− 1.80386e11i	− 0.659321i
$349$	4.60370e11	1.66109	0.830545	−	0.556952i	$-0.188029\pi$
$349$	4.60370e11	1.66109	0.830545	+	0.556952i	$0.188029\pi$
$350$	0	0
$351$	1.18871e10	0.0418017
$352$	− 8.31258e9i	− 0.0288598i
$353$	1.01736e11i	0.348728i	0.984681	+	0.174364i	$0.0557870\pi$
$353$	1.01736e11i	0.348728i	−0.984681	+	0.174364i	$0.944213\pi$
$354$	−3.25569e9	−0.0110186
$355$	0	0
$356$	−1.66737e11	−0.550184
$357$	1.15208e10i	0.0375385i
$358$	− 4.96075e9i	− 0.0159615i
$359$	−6.76144e10	−0.214839	−0.107420	−	0.994214i	$-0.534259\pi$
$359$	−6.76144e10	−0.214839	−0.107420	+	0.994214i	$0.534259\pi$
$360$	0	0
$361$	−2.60917e11	−0.808576
$362$	2.82392e9i	0.00864300i
$363$	9.95945e9i	0.0301062i
$364$	−6.65111e9	−0.0198581
$365$	0	0
$366$	2.24812e9	0.00654869
$367$	5.81071e11i	1.67198i	0.548743	+	0.835991i	$0.315107\pi$
$367$	5.81071e11i	1.67198i	−0.548743	+	0.835991i	$0.684893\pi$
$368$	2.59501e11i	0.737605i
$369$	−4.01250e10	−0.112667
$370$	0	0
$371$	6.78395e9	0.0185909
$372$	2.32394e11i	0.629190i
$373$	− 3.30933e11i	− 0.885219i	−0.896714	−	0.442610i	$-0.854053\pi$
$373$	− 3.30933e11i	− 0.885219i	0.896714	−	0.442610i	$-0.145947\pi$
$374$	−2.58872e9	−0.00684168
$375$	0	0
$376$	−1.16713e10	−0.0301144
$377$	− 9.72999e10i	− 0.248071i
$378$	− 6.90230e7i	0 0.000173892i
$379$	−5.19853e11	−1.29421	−0.647104	−	0.762401i	$-0.724020\pi$
$379$	−5.19853e11	−1.29421	−0.647104	+	0.762401i	$0.724020\pi$
$380$	0	0
$381$	−6.27403e9	−0.0152540
$382$	6.72188e8i	0.00161512i
$383$	4.51303e11i	1.07170i	0.844313	+	0.535850i	$0.180009\pi$
$383$	4.51303e11i	1.07170i	−0.844313	+	0.535850i	$0.819991\pi$
$384$	−9.72170e9	−0.0228166
$385$	0	0
$386$	−7.10824e8	−0.00162974
$387$	2.55232e11i	0.578410i
$388$	6.83767e10i	0.153167i
$389$	−4.61900e11	−1.02276	−0.511381	−	0.859354i	$-0.670866\pi$
$389$	−4.61900e11	−1.02276	−0.511381	+	0.859354i	$0.670866\pi$
$390$	0	0
$391$	2.42482e11	0.524668
$392$	− 9.16239e9i	− 0.0195984i
$393$	− 3.64887e11i	− 0.771599i
$394$	5.98471e9	0.0125115
$395$	0	0
$396$	−1.58795e11	−0.324494
$397$	− 4.81112e11i	− 0.972052i	−0.873944	−	0.486026i	$-0.838446\pi$
$397$	− 4.81112e11i	− 0.972052i	0.873944	−	0.486026i	$-0.161554\pi$
$398$	7.94885e7i	0 0.000158793i
$399$	−1.16928e10	−0.0230963
$400$	0	0
$401$	4.12911e11	0.797457	0.398728	−	0.917069i	$-0.369452\pi$
$401$	4.12911e11	0.797457	0.398728	+	0.917069i	$0.369452\pi$
$402$	3.44395e9i	0.00657717i
$403$	1.25353e11i	0.236734i
$404$	8.82910e10	0.164892
$405$	0	0
$406$	−5.64976e8	−0.00103196
$407$	− 2.23947e11i	− 0.404547i
$408$	4.54162e9i	0.00811410i
$409$	−6.65886e11	−1.17664	−0.588322	−	0.808627i	$-0.700211\pi$
$409$	−6.65886e11	−1.17664	−0.588322	+	0.808627i	$0.700211\pi$
$410$	0	0
$411$	5.50874e11	0.952278
$412$	8.85064e11i	1.51334i
$413$	− 1.04402e11i	− 0.176577i
$414$	−1.45275e9	−0.00243046
$415$	0	0
$416$	−3.93296e9	−0.00643872
$417$	1.57993e11i	0.255874i
$418$	− 2.62737e9i	− 0.00420948i
$419$	−7.79778e11	−1.23597	−0.617985	−	0.786190i	$-0.712051\pi$
$419$	−7.79778e11	−1.23597	−0.617985	+	0.786190i	$0.712051\pi$
$420$	0	0
$421$	9.59110e11	1.48799	0.743994	−	0.668187i	$-0.232929\pi$
$421$	9.59110e11	1.48799	0.743994	+	0.668187i	$0.232929\pi$
$422$	8.74272e9i	0.0134196i
$423$	3.34439e11i	0.507908i
$424$	2.67430e9	0.00401849
$425$	0	0
$426$	2.05670e9	0.00302571
$427$	7.20918e10i	0.104945i
$428$	1.08869e12i	1.56823i
$429$	−8.56533e10	−0.122092
$430$	0	0
$431$	1.89582e10	0.0264636	0.0132318	−	0.999912i	$-0.495788\pi$
$431$	1.89582e10	0.0264636	0.0132318	+	0.999912i	$0.495788\pi$
$432$	1.39273e11i	0.192394i
$433$	8.39898e11i	1.14824i	0.818773	+	0.574118i	$0.194655\pi$
$433$	8.39898e11i	1.14824i	−0.818773	+	0.574118i	$0.805345\pi$
$434$	7.27866e8	0.000984799 0
$435$	0	0
$436$	−8.48641e11	−1.12469
$437$	2.46103e11i	0.322812i
$438$	1.87110e9i	0.00242920i
$439$	3.74391e11	0.481100	0.240550	−	0.970637i	$-0.422672\pi$
$439$	3.74391e11	0.481100	0.240550	+	0.970637i	$0.422672\pi$
$440$	0	0
$441$	−2.62547e11	−0.330547
$442$	1.22481e9i	0.00152640i
$443$	− 7.04057e11i	− 0.868542i	−0.900782	−	0.434271i	$-0.857006\pi$
$443$	− 7.04057e11i	− 0.868542i	0.900782	−	0.434271i	$-0.142994\pi$
$444$	−1.96435e11	−0.239881
$445$	0	0
$446$	6.72372e9	0.00804642
$447$	− 8.58926e11i	− 1.01759i
$448$	− 7.79113e10i	− 0.0913797i
$449$	−3.02133e11	−0.350824	−0.175412	−	0.984495i	$-0.556126\pi$
$449$	−3.02133e11	−0.350824	−0.175412	+	0.984495i	$0.556126\pi$
$450$	0	0
$451$	2.89123e11	0.329070
$452$	9.41258e11i	1.06068i
$453$	5.30223e11i	0.591584i
$454$	1.15667e10	0.0127779
$455$	0	0
$456$	−4.60943e9	−0.00499235
$457$	− 2.44866e11i	− 0.262607i	−0.991342	−	0.131303i	$-0.958084\pi$
$457$	− 2.44866e11i	− 0.262607i	0.991342	−	0.131303i	$-0.0419162\pi$
$458$	9.81749e9i	0.0104257i
$459$	1.30139e11	0.136852
$460$	0	0
$461$	−5.68075e11	−0.585803	−0.292902	−	0.956143i	$-0.594621\pi$
$461$	−5.68075e11	−0.585803	−0.292902	+	0.956143i	$0.594621\pi$
$462$	4.97350e8i	0 0.000507894i
$463$	3.27020e11i	0.330720i	0.986233	+	0.165360i	$0.0528785\pi$
$463$	3.27020e11i	0.330720i	−0.986233	+	0.165360i	$0.947121\pi$
$464$	1.14000e12	1.14175
$465$	0	0
$466$	1.16459e10	0.0114403
$467$	7.11477e11i	0.692205i	0.938197	+	0.346102i	$0.112495\pi$
$467$	7.11477e11i	0.692205i	−0.938197	+	0.346102i	$0.887505\pi$
$468$	7.51310e10i	0.0723957i
$469$	−1.10439e11	−0.105401
$470$	0	0
$471$	−3.91864e11	−0.366894
$472$	− 4.11563e10i	− 0.0381678i
$473$	− 1.83909e12i	− 1.68938i
$474$	−3.52907e8	−0.000321113 0
$475$	0	0
$476$	−7.28160e10	−0.0650123
$477$	− 7.66315e10i	− 0.0677758i
$478$	2.79577e8i	0 0.000244949i
$479$	−3.36653e11	−0.292195	−0.146098	−	0.989270i	$-0.546671\pi$
$479$	−3.36653e11	−0.292195	−0.146098	+	0.989270i	$0.546671\pi$
$480$	0	0
$481$	−1.05957e11	−0.0902557
$482$	− 1.20546e9i	− 0.00101728i
$483$	− 4.65861e10i	− 0.0389488i
$484$	−6.29474e10	−0.0521403
$485$	0	0
$486$	−7.79684e8	−0.000633951 0
$487$	− 1.66615e12i	− 1.34225i	−0.741342	−	0.671127i	$-0.765810\pi$
$487$	− 1.66615e12i	− 1.34225i	0.741342	−	0.671127i	$-0.234190\pi$
$488$	2.84193e10i	0.0226842i
$489$	4.39606e11	0.347675
$490$	0	0
$491$	7.80759e11	0.606248	0.303124	−	0.952951i	$-0.401970\pi$
$491$	7.80759e11	0.606248	0.303124	+	0.952951i	$0.401970\pi$
$492$	− 2.53605e11i	− 0.195126i
$493$	− 1.06523e12i	− 0.812145i
$494$	−1.24310e9	−0.000939146 0
$495$	0	0
$496$	−1.46867e12	−1.08958
$497$	6.59534e10i	0.0484879i
$498$	1.00112e10i	0.00729378i
$499$	5.98100e11	0.431838	0.215919	−	0.976411i	$-0.430725\pi$
$499$	5.98100e11	0.431838	0.215919	+	0.976411i	$0.430725\pi$
$500$	0	0
$501$	1.10726e12	0.785199
$502$	− 8.48171e9i	− 0.00596097i
$503$	− 2.15422e12i	− 1.50050i	−0.661156	−	0.750248i	$-0.729934\pi$
$503$	− 2.15422e12i	− 1.50050i	0.661156	−	0.750248i	$-0.270066\pi$
$504$	8.72544e8	0.000602352 0
$505$	0	0
$506$	1.04679e10	0.00709873
$507$	− 8.18439e11i	− 0.550111i
$508$	− 3.96542e10i	− 0.0264181i
$509$	2.28931e12	1.51173	0.755866	−	0.654726i	$-0.227216\pi$
$509$	2.28931e12	1.51173	0.755866	+	0.654726i	$0.227216\pi$
$510$	0	0
$511$	−6.00018e10	−0.0389287
$512$	− 7.68022e10i	− 0.0493923i
$513$	1.32082e11i	0.0842009i
$514$	2.75706e9	0.00174226
$515$	0	0
$516$	−1.61316e12	−1.00174
$517$	− 2.40982e12i	− 1.48347i
$518$	6.15241e8i	0 0.000375458i
$519$	−1.49120e12	−0.902161
$520$	0	0
$521$	1.81335e12	1.07823	0.539114	−	0.842233i	$-0.318759\pi$
$521$	1.81335e12	1.07823	0.539114	+	0.842233i	$0.318759\pi$
$522$	6.38197e9i	0.00376216i
$523$	− 2.18455e11i	− 0.127675i	−0.997960	−	0.0638373i	$-0.979666\pi$
$523$	− 2.18455e11i	− 0.127675i	0.997960	−	0.0638373i	$-0.0203339\pi$
$524$	2.30622e12	1.33632
$525$	0	0
$526$	1.98229e10	0.0112910
$527$	1.37235e12i	0.775030i
$528$	− 1.00354e12i	− 0.561931i
$529$	8.20641e11	0.455620
$530$	0	0
$531$	−1.17933e12	−0.643738
$532$	− 7.39031e10i	− 0.0400000i
$533$	− 1.36794e11i	− 0.0734165i
$534$	5.89907e9	0.00313941
$535$	0	0
$536$	−4.35361e10	−0.0227829
$537$	− 1.79696e12i	− 0.932513i
$538$	1.46093e10i	0.00751811i
$539$	1.89180e12	0.965439
$540$	0	0
$541$	−1.00780e12	−0.505811	−0.252906	−	0.967491i	$-0.581386\pi$
$541$	−1.00780e12	−0.505811	−0.252906	+	0.967491i	$0.581386\pi$
$542$	9.91431e9i	0.00493476i
$543$	1.02293e12i	0.504947i
$544$	−4.30578e10	−0.0210793
$545$	0	0
$546$	2.35313e8	0.000113313 0
$547$	1.06674e12i	0.509468i	0.967011	+	0.254734i	$0.0819880\pi$
$547$	1.06674e12i	0.509468i	−0.967011	+	0.254734i	$0.918012\pi$
$548$	3.48173e12i	1.64923i
$549$	8.14349e11	0.382591
$550$	0	0
$551$	1.08114e12	0.499688
$552$	− 1.83647e10i	− 0.00841895i
$553$	− 1.13169e10i	− 0.00514593i
$554$	4.23493e10	0.0191008
$555$	0	0
$556$	−9.98577e11	−0.443144
$557$	2.02018e12i	0.889286i	0.895708	+	0.444643i	$0.146669\pi$
$557$	2.02018e12i	0.889286i	−0.895708	+	0.444643i	$0.853331\pi$
$558$	− 8.22197e9i	− 0.00359023i
$559$	−8.70134e11	−0.376906
$560$	0	0
$561$	−9.37728e11	−0.399709
$562$	3.56372e10i	0.0150692i
$563$	− 5.92218e11i	− 0.248424i	−0.992256	−	0.124212i	$-0.960360\pi$
$563$	− 5.92218e11i	− 0.248424i	0.992256	−	0.124212i	$-0.0396403\pi$
$564$	−2.11378e12	−0.879637
$565$	0	0
$566$	2.06551e10	0.00845968
$567$	− 2.50026e10i	− 0.0101592i
$568$	2.59994e10i	0.0104808i
$569$	1.47778e12	0.591025	0.295512	−	0.955339i	$-0.404510\pi$
$569$	1.47778e12	0.591025	0.295512	+	0.955339i	$0.404510\pi$
$570$	0	0
$571$	1.63251e11	0.0642677	0.0321339	−	0.999484i	$-0.489770\pi$
$571$	1.63251e11	0.0642677	0.0321339	+	0.999484i	$0.489770\pi$
$572$	− 5.41361e11i	− 0.211449i
$573$	2.43491e11i	0.0943597i
$574$	−7.94298e8	−0.000305408 0
$575$	0	0
$576$	−8.80087e11	−0.333138
$577$	− 1.06656e12i	− 0.400584i	−0.979736	−	0.200292i	$-0.935811\pi$
$577$	− 1.06656e12i	− 0.400584i	0.979736	−	0.200292i	$-0.0641891\pi$
$578$	− 1.31084e10i	− 0.00488512i
$579$	−2.57486e11	−0.0952138
$580$	0	0
$581$	−3.21035e11	−0.116885
$582$	− 2.41913e9i	0 0.000873988i
$583$	5.52173e11i	0.197955i
$584$	−2.36533e10	−0.00841460
$585$	0	0
$586$	−3.29499e10	−0.0115429
$587$	2.49441e12i	0.867153i	0.901117	+	0.433577i	$0.142749\pi$
$587$	2.49441e12i	0.867153i	−0.901117	+	0.433577i	$0.857251\pi$
$588$	− 1.65939e12i	− 0.572468i
$589$	−1.39284e12	−0.476852
$590$	0	0
$591$	2.16788e12	0.730955
$592$	− 1.24142e12i	− 0.415405i
$593$	− 1.76944e12i	− 0.587610i	−0.955865	−	0.293805i	$-0.905078\pi$
$593$	− 1.76944e12i	− 0.587610i	0.955865	−	0.293805i	$-0.0949217\pi$
$594$	5.61806e9	0.00185160
$595$	0	0
$596$	5.42873e12	1.76234
$597$	2.87936e10i	0.00927708i
$598$	− 4.95269e9i	− 0.00158375i
$599$	−5.49741e12	−1.74477	−0.872383	−	0.488823i	$-0.837426\pi$
$599$	−5.49741e12	−1.74477	−0.872383	+	0.488823i	$0.837426\pi$
$600$	0	0
$601$	4.24474e11	0.132714	0.0663569	−	0.997796i	$-0.478862\pi$
$601$	4.24474e11	0.132714	0.0663569	+	0.997796i	$0.478862\pi$
$602$	5.05247e9i	0.00156790i
$603$	1.24752e12i	0.384255i
$604$	−3.35120e12	−1.02455
$605$	0	0
$606$	−3.12369e9	−0.000940894 0
$607$	2.57263e12i	0.769181i	0.923087	+	0.384590i	$0.125657\pi$
$607$	2.57263e12i	0.769181i	−0.923087	+	0.384590i	$0.874343\pi$
$608$	− 4.37006e10i	− 0.0129695i
$609$	−2.04655e11	−0.0602898
$610$	0	0
$611$	−1.14017e12	−0.330965
$612$	8.22529e11i	0.237012i
$613$	3.01773e12i	0.863194i	0.902066	+	0.431597i	$0.142050\pi$
$613$	3.01773e12i	0.863194i	−0.902066	+	0.431597i	$0.857950\pi$
$614$	−4.13985e10	−0.0117551
$615$	0	0
$616$	−6.28717e9	−0.00175931
$617$	2.87854e12i	0.799631i	0.916596	+	0.399816i	$0.130926\pi$
$617$	2.87854e12i	0.799631i	−0.916596	+	0.399816i	$0.869074\pi$
$618$	− 3.13131e10i	− 0.00863531i
$619$	−5.36553e12	−1.46894	−0.734471	−	0.678640i	$-0.762569\pi$
$619$	−5.36553e12	−1.46894	−0.734471	+	0.678640i	$0.762569\pi$
$620$	0	0
$621$	−5.26237e11	−0.141994
$622$	3.65006e10i	0.00977785i
$623$	1.89169e11i	0.0503100i
$624$	−4.74809e11	−0.125368
$625$	0	0
$626$	−3.55125e10	−0.00924265
$627$	− 9.51728e11i	− 0.245928i
$628$	− 2.47672e12i	− 0.635418i
$629$	−1.16001e12	−0.295483
$630$	0	0
$631$	3.28798e12	0.825653	0.412826	−	0.910810i	$-0.364542\pi$
$631$	3.28798e12	0.825653	0.412826	+	0.910810i	$0.364542\pi$
$632$	− 4.46122e9i	− 0.00111231i
$633$	3.16693e12i	0.784010i
$634$	−4.98649e10	−0.0122573
$635$	0	0
$636$	4.84339e11	0.117380
$637$	− 8.95071e11i	− 0.215392i
$638$	− 4.59857e10i	− 0.0109883i
$639$	7.45009e11	0.176770
$640$	0	0
$641$	−4.40972e12	−1.03169	−0.515846	−	0.856681i	$-0.672522\pi$
$641$	−4.40972e12	−1.03169	−0.515846	+	0.856681i	$0.672522\pi$
$642$	− 3.85174e10i	− 0.00894848i
$643$	4.91168e12i	1.13313i	0.824016	+	0.566566i	$0.191728\pi$
$643$	4.91168e12i	1.13313i	−0.824016	+	0.566566i	$0.808272\pi$
$644$	2.94442e11	0.0674548
$645$	0	0
$646$	−1.36093e10	−0.00307461
$647$	2.80990e12i	0.630408i	0.949024	+	0.315204i	$0.102073\pi$
$647$	2.80990e12i	0.630408i	−0.949024	+	0.315204i	$0.897927\pi$
$648$	− 9.85626e9i	− 0.00219596i
$649$	8.49772e12	1.88019
$650$	0	0
$651$	2.63659e11	0.0575345
$652$	2.77847e12i	0.602133i
$653$	− 2.56025e12i	− 0.551028i	−0.961297	−	0.275514i	$-0.911152\pi$
$653$	− 2.56025e12i	− 0.551028i	0.961297	−	0.275514i	$-0.0888480\pi$
$654$	3.00244e10	0.00641763
$655$	0	0
$656$	1.60272e12	0.337901
$657$	6.77781e11i	0.141920i
$658$	6.62042e9i	0.00137679i
$659$	−8.27996e12	−1.71019	−0.855094	−	0.518472i	$-0.826501\pi$
$659$	−8.27996e12	−1.71019	−0.855094	+	0.518472i	$0.826501\pi$
$660$	0	0
$661$	−3.18671e11	−0.0649286	−0.0324643	−	0.999473i	$-0.510336\pi$
$661$	−3.18671e11	−0.0649286	−0.0324643	+	0.999473i	$0.510336\pi$
$662$	− 5.91530e10i	− 0.0119706i
$663$	4.43670e11i	0.0891762i
$664$	−1.26555e11	−0.0252652
$665$	0	0
$666$	6.94976e9	0.00136879
$667$	4.30742e12i	0.842658i
$668$	6.99829e12i	1.35987i
$669$	2.43557e12	0.470093
$670$	0	0
$671$	−5.86784e12	−1.11745
$672$	8.27234e9i	0.00156483i
$673$	6.44097e12i	1.21027i	0.796122	+	0.605136i	$0.206881\pi$
$673$	6.44097e12i	1.21027i	−0.796122	+	0.605136i	$0.793119\pi$
$674$	2.54130e10	0.00474337
$675$	0	0
$676$	5.17284e12	0.952728
$677$	− 7.45494e12i	− 1.36394i	−0.731381	−	0.681969i	$-0.761124\pi$
$677$	− 7.45494e12i	− 1.36394i	0.731381	−	0.681969i	$-0.238876\pi$
$678$	− 3.33012e10i	− 0.00605238i
$679$	7.75757e10	0.0140059
$680$	0	0
$681$	4.18989e12	0.746518
$682$	5.92439e10i	0.0104861i
$683$	− 1.88685e11i	− 0.0331776i	−0.999862	−	0.0165888i	$-0.994719\pi$
$683$	− 1.88685e11i	− 0.0331776i	0.999862	−	0.0165888i	$-0.00528062\pi$
$684$	−8.34809e11	−0.145826
$685$	0	0
$686$	−1.04384e10	−0.00179959
$687$	3.55625e12i	0.609097i
$688$	− 1.01948e13i	− 1.73472i
$689$	2.61251e11	0.0441644
$690$	0	0
$691$	−4.12572e12	−0.688412	−0.344206	−	0.938894i	$-0.611852\pi$
$691$	−4.12572e12	−0.688412	−0.344206	+	0.938894i	$0.611852\pi$
$692$	− 9.42497e12i	− 1.56244i
$693$	1.80158e11i	0.0296725i
$694$	−8.46014e10	−0.0138439
$695$	0	0
$696$	−8.06767e10	−0.0130319
$697$	− 1.49761e12i	− 0.240354i
$698$	− 1.02944e11i	− 0.0164154i
$699$	4.21857e12	0.668371
$700$	0	0
$701$	−6.26038e12	−0.979196	−0.489598	−	0.871948i	$-0.662857\pi$
$701$	−6.26038e12	−0.979196	−0.489598	+	0.871948i	$0.662857\pi$
$702$	− 2.65809e9i	0 0.000413098i
$703$	− 1.17732e12i	− 0.181801i
$704$	6.34152e12	0.973008
$705$	0	0
$706$	2.27492e10	0.00344624
$707$	− 1.00169e11i	− 0.0150781i
$708$	− 7.45379e12i	− 1.11488i
$709$	8.40293e12	1.24888	0.624442	−	0.781071i	$-0.285326\pi$
$709$	8.40293e12	1.24888	0.624442	+	0.781071i	$0.285326\pi$
$710$	0	0
$711$	−1.27835e11	−0.0187602
$712$	7.45723e10i	0.0108747i
$713$	− 5.54931e12i	− 0.804148i
$714$	2.57619e9	0.000370967 0
$715$	0	0
$716$	1.13575e13	1.61500
$717$	1.01273e11i	0.0143105i
$718$	1.51193e10i	0.00212311i
$719$	3.44185e11	0.0480300	0.0240150	−	0.999712i	$-0.492355\pi$
$719$	3.44185e11	0.0480300	0.0240150	+	0.999712i	$0.492355\pi$
$720$	0	0
$721$	1.00414e12	0.138383
$722$	5.83440e10i	0.00799060i
$723$	− 4.36659e11i	− 0.0594320i
$724$	−6.46528e12	−0.874508
$725$	0	0
$726$	2.22704e9	0.000297519 0
$727$	− 8.67049e12i	− 1.15117i	−0.817743	−	0.575584i	$-0.804775\pi$
$727$	− 8.67049e12i	− 1.15117i	0.817743	−	0.575584i	$-0.195225\pi$
$728$	2.97467e9i	0 0.000392507i
$729$	−2.82430e11	−0.0370370
$730$	0	0
$731$	−9.52617e12	−1.23393
$732$	5.14699e12i	0.662603i
$733$	− 1.10927e13i	− 1.41929i	−0.704561	−	0.709644i	$-0.748856\pi$
$733$	− 1.10927e13i	− 1.41929i	0.704561	−	0.709644i	$-0.251144\pi$
$734$	1.29934e11	0.0165230
$735$	0	0
$736$	1.74110e11	0.0218713
$737$	− 8.98909e12i	− 1.12231i
$738$	8.97239e9i	0.00111341i
$739$	6.37409e12	0.786173	0.393087	−	0.919501i	$-0.371407\pi$
$739$	6.37409e12	0.786173	0.393087	+	0.919501i	$0.371407\pi$
$740$	0	0
$741$	−4.50294e11	−0.0548674
$742$	− 1.51697e9i	0 0.000183721i
$743$	6.36760e12i	0.766525i	0.923639	+	0.383263i	$0.125200\pi$
$743$	6.36760e12i	0.766525i	−0.923639	+	0.383263i	$0.874800\pi$
$744$	1.03937e11	0.0124363
$745$	0	0
$746$	−7.40004e10	−0.00874801
$747$	3.62641e12i	0.426122i
$748$	− 5.92679e12i	− 0.692249i
$749$	1.23516e12	0.143402
$750$	0	0
$751$	−3.40024e12	−0.390058	−0.195029	−	0.980797i	$-0.562480\pi$
$751$	−3.40024e12	−0.390058	−0.195029	+	0.980797i	$0.562480\pi$
$752$	− 1.33586e13i	− 1.52328i
$753$	− 3.07238e12i	− 0.348255i
$754$	−2.17573e10	−0.00245152
$755$	0	0
$756$	1.58026e11	0.0175946
$757$	1.38522e13i	1.53316i	0.642148	+	0.766581i	$0.278044\pi$
$757$	1.38522e13i	1.53316i	−0.642148	+	0.766581i	$0.721956\pi$
$758$	1.16245e11i	0.0127898i
$759$	3.79183e12	0.414726
$760$	0	0
$761$	−1.25728e13	−1.35894	−0.679471	−	0.733703i	$-0.737790\pi$
$761$	−1.25728e13	−1.35894	−0.679471	+	0.733703i	$0.737790\pi$
$762$	1.40294e9i	0 0.000150745i
$763$	9.62812e11i	0.102845i
$764$	−1.53895e12	−0.163420
$765$	0	0
$766$	1.00916e11	0.0105909
$767$	− 4.02055e12i	− 0.419475i
$768$	− 5.56084e12i	− 0.576787i
$769$	1.11440e13	1.14914	0.574569	−	0.818456i	$-0.305170\pi$
$769$	1.11440e13	1.14914	0.574569	+	0.818456i	$0.305170\pi$
$770$	0	0
$771$	9.98707e11	0.101787
$772$	− 1.62741e12i	− 0.164899i
$773$	4.40857e12i	0.444110i	0.975034	+	0.222055i	$0.0712764\pi$
$773$	4.40857e12i	0.444110i	−0.975034	+	0.222055i	$0.928724\pi$
$774$	5.70727e10	0.00571602
$775$	0	0
$776$	3.05811e10	0.00302744
$777$	2.22862e11i	0.0219352i
$778$	1.03286e11i	0.0101073i
$779$	1.51997e12	0.147882
$780$	0	0
$781$	−5.36821e12	−0.516297
$782$	− 5.42217e10i	− 0.00518493i
$783$	2.31178e12i	0.219795i
$784$	1.04869e13	0.991349
$785$	0	0
$786$	−8.15928e10	−0.00762518
$787$	1.39083e13i	1.29237i	0.763180	+	0.646186i	$0.223637\pi$
$787$	1.39083e13i	1.29237i	−0.763180	+	0.646186i	$0.776363\pi$
$788$	1.37018e13i	1.26593i
$789$	7.18057e12	0.659649
$790$	0	0
$791$	1.06789e12	0.0969912
$792$	7.10199e10i	0.00641382i
$793$	2.77627e12i	0.249306i
$794$	−1.07582e11	−0.00960612
$795$	0	0
$796$	−1.81986e11	−0.0160668
$797$	− 1.11093e13i	− 0.975266i	−0.873049	−	0.487633i	$-0.837861\pi$
$797$	− 1.11093e13i	− 0.975266i	0.873049	−	0.487633i	$-0.162139\pi$
$798$	2.61465e9i	0 0.000228245i
$799$	−1.24825e13	−1.08353
$800$	0	0
$801$	2.13686e12	0.183412
$802$	− 9.23316e10i	− 0.00788072i
$803$	− 4.88379e12i	− 0.414512i
$804$	−7.88479e12	−0.665485
$805$	0	0
$806$	2.80303e10	0.00233948
$807$	5.29201e12i	0.439227i
$808$	− 3.94876e10i	− 0.00325919i
$809$	−8.47032e12	−0.695235	−0.347617	−	0.937636i	$-0.613009\pi$
$809$	−8.47032e12	−0.695235	−0.347617	+	0.937636i	$0.613009\pi$
$810$	0	0
$811$	1.98968e13	1.61506	0.807532	−	0.589823i	$-0.200803\pi$
$811$	1.98968e13	1.61506	0.807532	+	0.589823i	$0.200803\pi$
$812$	− 1.29349e12i	− 0.104415i
$813$	3.59132e12i	0.288301i
$814$	−5.00769e10	−0.00399786
$815$	0	0
$816$	−5.19818e12	−0.410436
$817$	− 9.66840e12i	− 0.759198i
$818$	1.48900e11i	0.0116280i
$819$	8.52387e10	0.00662002
$820$	0	0
$821$	−7.94161e11	−0.0610049	−0.0305024	−	0.999535i	$-0.509711\pi$
$821$	−7.94161e11	−0.0610049	−0.0305024	+	0.999535i	$0.509711\pi$
$822$	− 1.23182e11i	− 0.00941071i
$823$	1.36089e13i	1.03401i	0.855983	+	0.517004i	$0.172953\pi$
$823$	1.36089e13i	1.03401i	−0.855983	+	0.517004i	$0.827047\pi$
$824$	3.95840e11	0.0299121
$825$	0	0
$826$	−2.33455e10	−0.00174499
$827$	1.79571e13i	1.33494i	0.744637	+	0.667470i	$0.232623\pi$
$827$	1.79571e13i	1.33494i	−0.744637	+	0.667470i	$0.767377\pi$
$828$	− 3.32601e12i	− 0.245916i
$829$	3.69953e12	0.272052	0.136026	−	0.990705i	$-0.456567\pi$
$829$	3.69953e12	0.272052	0.136026	+	0.990705i	$0.456567\pi$
$830$	0	0
$831$	1.53404e13	1.11592
$832$	− 3.00038e12i	− 0.217081i
$833$	− 9.79919e12i	− 0.705160i
$834$	3.53291e10	0.00252863
$835$	0	0
$836$	6.01527e12	0.425919
$837$	− 2.97829e12i	− 0.209750i
$838$	1.74367e11i	0.0122142i
$839$	−2.50920e13	−1.74826	−0.874132	−	0.485688i	$-0.838569\pi$
$839$	−2.50920e13	−1.74826	−0.874132	+	0.485688i	$0.838569\pi$
$840$	0	0
$841$	4.41551e12	0.304368
$842$	− 2.14468e11i	− 0.0147048i
$843$	1.29091e13i	0.880381i
$844$	−2.00162e13	−1.35781
$845$	0	0
$846$	7.47843e10	0.00501931
$847$	7.14160e10i	0.00476782i
$848$	3.06091e12i	0.203268i
$849$	7.48203e12	0.494237
$850$	0	0
$851$	4.69065e12	0.306584
$852$	4.70874e12i	0.306144i
$853$	− 6.79534e12i	− 0.439481i	−0.975558	−	0.219741i	$-0.929479\pi$
$853$	− 6.79534e12i	− 0.439481i	0.975558	−	0.219741i	$-0.0705211\pi$
$854$	1.61205e10	0.00103710
$855$	0	0
$856$	4.86912e11	0.0309969
$857$	1.31867e13i	0.835070i	0.908661	+	0.417535i	$0.137106\pi$
$857$	1.31867e13i	0.835070i	−0.908661	+	0.417535i	$0.862894\pi$
$858$	1.91530e10i	0.00120655i
$859$	−1.27461e13	−0.798747	−0.399374	−	0.916788i	$-0.630772\pi$
$859$	−1.27461e13	−0.798747	−0.399374	+	0.916788i	$0.630772\pi$
$860$	0	0
$861$	−2.87723e11	−0.0178427
$862$	− 4.23926e9i	0 0.000261522i
$863$	− 8.12433e12i	− 0.498585i	−0.968428	−	0.249292i	$-0.919802\pi$
$863$	− 8.12433e12i	− 0.498585i	0.968428	−	0.249292i	$-0.0801980\pi$
$864$	9.34444e10	0.00570481
$865$	0	0
$866$	1.87811e11	0.0113472
$867$	− 4.74835e12i	− 0.285402i
$868$	1.66642e12i	0.0996429i
$869$	9.21126e11	0.0547937
$870$	0	0
$871$	−4.25304e12	−0.250390
$872$	3.79550e11i	0.0222303i
$873$	− 8.76295e11i	− 0.0510607i
$874$	5.50313e10	0.00319013
$875$	0	0
$876$	−4.28382e12	−0.245789
$877$	6.46585e12i	0.369086i	0.982824	+	0.184543i	$0.0590805\pi$
$877$	6.46585e12i	0.369086i	−0.982824	+	0.184543i	$0.940920\pi$
$878$	− 8.37180e10i	− 0.00475438i
$879$	−1.19356e13	−0.674366
$880$	0	0
$881$	−1.69271e13	−0.946653	−0.473326	−	0.880887i	$-0.656947\pi$
$881$	−1.69271e13	−0.946653	−0.473326	+	0.880887i	$0.656947\pi$
$882$	5.87084e10i	0.00326656i
$883$	3.56100e13i	1.97128i	0.168846	+	0.985642i	$0.445996\pi$
$883$	3.56100e13i	1.97128i	−0.168846	+	0.985642i	$0.554004\pi$
$884$	−2.80416e12	−0.154443
$885$	0	0
$886$	−1.57435e11	−0.00858321
$887$	2.18278e13i	1.18400i	0.805936	+	0.592002i	$0.201662\pi$
$887$	2.18278e13i	1.18400i	−0.805936	+	0.592002i	$0.798338\pi$
$888$	8.78544e10i	0.00474139i
$889$	−4.49891e10	−0.00241573
$890$	0	0
$891$	2.03506e12	0.108175
$892$	1.53937e13i	0.814145i
$893$	− 1.26688e13i	− 0.666661i
$894$	−1.92066e11	−0.0100561
$895$	0	0
$896$	−6.97112e10	−0.00361340
$897$	− 1.79404e12i	− 0.0925266i
$898$	6.75602e10i	0.00346695i
$899$	−2.43783e13	−1.24476
$900$	0	0
$901$	2.86016e12	0.144587
$902$	− 6.46511e10i	− 0.00325197i
$903$	1.83019e12i	0.0916010i
$904$	4.20972e11	0.0209650
$905$	0	0
$906$	1.18564e11	0.00584622
$907$	4.79737e12i	0.235380i	0.993050	+	0.117690i	$0.0375490\pi$
$907$	4.79737e12i	0.235380i	−0.993050	+	0.117690i	$0.962451\pi$
$908$	2.64816e13i	1.29288i
$909$	−1.13151e12	−0.0549695
$910$	0	0
$911$	1.70045e13	0.817957	0.408979	−	0.912544i	$-0.365885\pi$
$911$	1.70045e13	0.817957	0.408979	+	0.912544i	$0.365885\pi$
$912$	− 5.27579e12i	− 0.252529i
$913$	− 2.61303e13i	− 1.24459i
$914$	−5.47549e10	−0.00259516
$915$	0	0
$916$	−2.24768e13	−1.05488
$917$	− 2.61649e12i	− 0.122196i
$918$	− 2.91006e10i	− 0.00135242i
$919$	1.12820e12	0.0521756	0.0260878	−	0.999660i	$-0.491695\pi$
$919$	1.12820e12	0.0521756	0.0260878	+	0.999660i	$0.491695\pi$
$920$	0	0
$921$	−1.49960e13	−0.686764
$922$	1.27028e11i	0.00578909i
$923$	2.53988e12i	0.115188i
$924$	−1.13866e12	−0.0513892
$925$	0	0
$926$	7.31253e10	0.00326827
$927$	− 1.13427e13i	− 0.504497i
$928$	− 7.64873e11i	− 0.0338550i
$929$	3.97727e13	1.75192	0.875960	−	0.482384i	$-0.160229\pi$
$929$	3.97727e13	1.75192	0.875960	+	0.482384i	$0.160229\pi$
$930$	0	0
$931$	9.94549e12	0.433863
$932$	2.66629e13i	1.15754i
$933$	1.32218e13i	0.571247i
$934$	1.59094e11	0.00684058
$935$	0	0
$936$	3.36019e10	0.00143094
$937$	− 3.91551e13i	− 1.65944i	−0.558184	−	0.829718i	$-0.688501\pi$
$937$	− 3.91551e13i	− 1.65944i	0.558184	−	0.829718i	$-0.311499\pi$
$938$	2.46954e10i	0.00104161i
$939$	−1.28639e13	−0.539980
$940$	0	0
$941$	2.55120e13	1.06070	0.530348	−	0.847780i	$-0.322061\pi$
$941$	2.55120e13	1.06070	0.530348	+	0.847780i	$0.322061\pi$
$942$	8.76251e10i	0.00362577i
$943$	6.05579e12i	0.249384i
$944$	4.71061e13	1.93065
$945$	0	0
$946$	−4.11241e11	−0.0166950
$947$	− 1.92093e12i	− 0.0776133i	−0.999247	−	0.0388066i	$-0.987644\pi$
$947$	− 1.92093e12i	− 0.0776133i	0.999247	−	0.0388066i	$-0.0123556\pi$
$948$	− 8.07967e11i	− 0.0324905i
$949$	−2.31068e12	−0.0924789
$950$	0	0
$951$	−1.80629e13	−0.716101
$952$	3.25665e10i	0.00128501i
$953$	− 3.70640e13i	− 1.45558i	−0.685802	−	0.727788i	$-0.740549\pi$
$953$	− 3.70640e13i	− 1.45558i	0.685802	−	0.727788i	$-0.259451\pi$
$954$	−1.71357e10	−0.000669781 0
$955$	0	0
$956$	−6.40081e11	−0.0247842
$957$	− 1.66577e13i	− 0.641963i
$958$	7.52794e10i	0.00288756i
$959$	3.95014e12	0.150809
$960$	0	0
$961$	4.96727e12	0.187872
$962$	2.36931e10i	0 0.000891935i
$963$	− 1.39524e13i	− 0.522793i
$964$	2.75985e12	0.102929
$965$	0	0
$966$	−1.04172e10	−0.000384905 0
$967$	− 2.97114e13i	− 1.09271i	−0.837555	−	0.546353i	$-0.816016\pi$
$967$	− 2.97114e13i	− 1.09271i	0.837555	−	0.546353i	$-0.183984\pi$
$968$	2.81529e10i	0.00103058i
$969$	−4.92979e12	−0.179627
$970$	0	0
$971$	4.42639e13	1.59795	0.798975	−	0.601364i	$-0.205376\pi$
$971$	4.42639e13	1.59795	0.798975	+	0.601364i	$0.205376\pi$
$972$	− 1.78506e12i	− 0.0641438i
$973$	1.13292e12i	0.0405221i
$974$	−3.72571e11	−0.0132646
$975$	0	0
$976$	−3.25277e13	−1.14744
$977$	− 3.02165e12i	− 0.106101i	−0.998592	−	0.0530503i	$-0.983106\pi$
$977$	− 3.02165e12i	− 0.106101i	0.998592	−	0.0530503i	$-0.0168944\pi$
$978$	− 9.83008e10i	− 0.00343584i
$979$	−1.53972e13	−0.535699
$980$	0	0
$981$	1.08759e13	0.374935
$982$	− 1.74586e11i	− 0.00599113i
$983$	2.56151e13i	0.874994i	0.899220	+	0.437497i	$0.144135\pi$
$983$	2.56151e13i	0.874994i	−0.899220	+	0.437497i	$0.855865\pi$
$984$	−1.13423e11	−0.00385677
$985$	0	0
$986$	−2.38198e11	−0.00802587
$987$	2.39815e12i	0.0804359i
$988$	− 2.84602e12i	− 0.0950238i
$989$	3.85204e13	1.28029
$990$	0	0
$991$	4.40641e12	0.145129	0.0725644	−	0.997364i	$-0.476882\pi$
$991$	4.40641e12	0.145129	0.0725644	+	0.997364i	$0.476882\pi$
$992$	9.85396e11i	0.0323079i
$993$	− 2.14273e13i	− 0.699353i
$994$	1.47479e10	0.000479172 0
$995$	0	0
$996$	−2.29202e13	−0.737993
$997$	− 4.49122e13i	− 1.43958i	−0.694192	−	0.719790i	$-0.744238\pi$
$997$	− 4.49122e13i	− 1.43958i	0.694192	−	0.719790i	$-0.255762\pi$
$998$	− 1.33742e11i	− 0.00426756i
$999$	2.51745e12	0.0799681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.b.g.49.2		4
3.2	odd	2		225.10.b.j.199.3		4
5.2	odd	4		75.10.a.h.1.1	yes	2
5.3	odd	4		75.10.a.e.1.2	✓	2
5.4	even	2	inner	75.10.b.g.49.3		4
15.2	even	4		225.10.a.g.1.2		2
15.8	even	4		225.10.a.l.1.1		2
15.14	odd	2		225.10.b.j.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.a.e.1.2	✓	2	5.3	odd	4
75.10.a.h.1.1	yes	2	5.2	odd	4
75.10.b.g.49.2		4	1.1	even	1	trivial
75.10.b.g.49.3		4	5.4	even	2	inner
225.10.a.g.1.2		2	15.2	even	4
225.10.a.l.1.1		2	15.8	even	4
225.10.b.j.199.2		4	15.14	odd	2
225.10.b.j.199.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.223611i q^{2} -81.0000i q^{3} +511.950 q^{4} -18.1125 q^{6} -580.825i q^{7} -228.967i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-0.223611i q^{2} -81.0000i q^{3} +511.950 q^{4} -18.1125 q^{6} -580.825i q^{7} -228.967i q^{8} -6561.00 q^{9} +47275.7 q^{11} -41467.9i q^{12} -22367.7i q^{13} -129.879 q^{14} +262067. q^{16} -244880. i q^{17} +1467.11i q^{18} +248536. q^{19} -47046.8 q^{21} -10571.4i q^{22} +990208. i q^{23} -18546.3 q^{24} -5001.67 q^{26} +531441. i q^{27} -297353. i q^{28} +4.35002e6 q^{29} -5.60419e6 q^{31} -175832. i q^{32} -3.82933e6i q^{33} -54758.0 q^{34} -3.35890e6 q^{36} -4.73703e6i q^{37} -55575.5i q^{38} -1.81178e6 q^{39} +6.11568e6 q^{41} +10520.2i q^{42} -3.89014e7i q^{43} +2.42028e7 q^{44} +221422. q^{46} -5.09738e7i q^{47} -2.12274e7i q^{48} +4.00162e7 q^{49} -1.98353e7 q^{51} -1.14511e7i q^{52} +1.16798e7i q^{53} +118836. q^{54} -132990. q^{56} -2.01314e7i q^{57} -972713. i q^{58} +1.79748e8 q^{59} -1.24120e8 q^{61} +1.25316e6i q^{62} +3.81079e6i q^{63} +1.34139e8 q^{64} -856281. q^{66} -1.90142e8i q^{67} -1.25366e8i q^{68} +8.02068e7 q^{69} -1.13551e8 q^{71} +1.50225e6i q^{72} -1.03304e8i q^{73} -1.05925e6 q^{74} +1.27238e8 q^{76} -2.74589e7i q^{77} +405135. i q^{78} +1.94841e7 q^{79} +4.30467e7 q^{81} -1.36753e6i q^{82} -5.52722e8i q^{83} -2.40856e7 q^{84} -8.69878e6 q^{86} -3.52351e8i q^{87} -1.08246e7i q^{88} -3.25690e8 q^{89} -1.29917e7 q^{91} +5.06937e8i q^{92} +4.53939e8i q^{93} -1.13983e7 q^{94} -1.42424e7 q^{96} +1.33561e8i q^{97} -8.94808e6i q^{98} -3.10176e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 512 q^{4} - 5832 q^{6} - 26244 q^{9}+O(q^{10}) \) 4 * q - 512 * q^4 - 5832 * q^6 - 26244 * q^9	\( 4 q - 512 q^{4} - 5832 q^{6} - 26244 q^{9} + 48456 q^{11} + 278712 q^{14} + 392960 q^{16} + 2697692 q^{19} + 537516 q^{21} + 1446336 q^{24} + 8097048 q^{26} + 8566344 q^{29} + 2353164 q^{31} + 26301776 q^{34} + 3359232 q^{36} + 14731308 q^{39} - 57776976 q^{41} + 83804544 q^{44} - 94053456 q^{46} + 130338040 q^{49} + 20126232 q^{51} + 38263752 q^{54} - 71668800 q^{56} + 230300568 q^{59} - 462988820 q^{61} + 704479232 q^{64} + 131866704 q^{66} - 53531928 q^{69} + 223584048 q^{71} + 709452432 q^{74} - 1435489408 q^{76} + 668892000 q^{79} + 172186884 q^{81} - 533215872 q^{84} + 1809396936 q^{86} + 493342272 q^{89} - 909470436 q^{91} - 1130811472 q^{94} + 1111159296 q^{96} - 317919816 q^{99}+O(q^{100}) \) 4 * q - 512 * q^4 - 5832 * q^6 - 26244 * q^9 + 48456 * q^11 + 278712 * q^14 + 392960 * q^16 + 2697692 * q^19 + 537516 * q^21 + 1446336 * q^24 + 8097048 * q^26 + 8566344 * q^29 + 2353164 * q^31 + 26301776 * q^34 + 3359232 * q^36 + 14731308 * q^39 - 57776976 * q^41 + 83804544 * q^44 - 94053456 * q^46 + 130338040 * q^49 + 20126232 * q^51 + 38263752 * q^54 - 71668800 * q^56 + 230300568 * q^59 - 462988820 * q^61 + 704479232 * q^64 + 131866704 * q^66 - 53531928 * q^69 + 223584048 * q^71 + 709452432 * q^74 - 1435489408 * q^76 + 668892000 * q^79 + 172186884 * q^81 - 533215872 * q^84 + 1809396936 * q^86 + 493342272 * q^89 - 909470436 * q^91 - 1130811472 * q^94 + 1111159296 * q^96 - 317919816 * q^99

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