LMFDB - Embedded newform 350.10.c.j.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,10,Mod(99,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("350.99");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	350.c (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:	$180.262542657$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{2305})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1153x^{2} + 331776 $ x^4 + 1153*x^2 + 331776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$24.5052i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.10.c.j.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000i q^{2} +247.052i q^{3} -256.000 q^{4} +3952.83 q^{6} +2401.00i q^{7} +4096.00i q^{8} -41351.7 q^{9} +O(q^{10})$	\(q-16.0000i q^{2} +247.052i q^{3} -256.000 q^{4} +3952.83 q^{6} +2401.00i q^{7} +4096.00i q^{8} -41351.7 q^{9} -27940.9 q^{11} -63245.3i q^{12} -60943.3i q^{13} +38416.0 q^{14} +65536.0 q^{16} -358867. i q^{17} +661628. i q^{18} +391593. q^{19} -593172. q^{21} +447055. i q^{22} +302894. i q^{23} -1.01193e6 q^{24} -975093. q^{26} -5.35330e6i q^{27} -614656. i q^{28} -6.73993e6 q^{29} +2.98262e6 q^{31} -1.04858e6i q^{32} -6.90287e6i q^{33} -5.74188e6 q^{34} +1.05860e7 q^{36} -3.49582e6i q^{37} -6.26549e6i q^{38} +1.50562e7 q^{39} +3.43724e7 q^{41} +9.49075e6i q^{42} +1.45085e7i q^{43} +7.15288e6 q^{44} +4.84631e6 q^{46} -2.76485e7i q^{47} +1.61908e7i q^{48} -5.76480e6 q^{49} +8.86589e7 q^{51} +1.56015e7i q^{52} +2.39217e7i q^{53} -8.56529e7 q^{54} -9.83450e6 q^{56} +9.67439e7i q^{57} +1.07839e8i q^{58} +1.20580e8 q^{59} +7.23140e7 q^{61} -4.77219e7i q^{62} -9.92855e7i q^{63} -1.67772e7 q^{64} -1.10446e8 q^{66} +8.70377e7i q^{67} +9.18701e7i q^{68} -7.48307e7 q^{69} +2.19622e8 q^{71} -1.69377e8i q^{72} -2.67792e8i q^{73} -5.59331e7 q^{74} -1.00248e8 q^{76} -6.70862e7i q^{77} -2.40899e8i q^{78} -2.85350e7 q^{79} +5.08619e8 q^{81} -5.49959e8i q^{82} +3.83237e8i q^{83} +1.51852e8 q^{84} +2.32136e8 q^{86} -1.66511e9i q^{87} -1.14446e8i q^{88} -7.21581e8 q^{89} +1.46325e8 q^{91} -7.75410e7i q^{92} +7.36861e8i q^{93} -4.42377e8 q^{94} +2.59053e8 q^{96} -6.73736e8i q^{97} +9.22368e7i q^{98} +1.15541e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1024 q^{4} + 448 q^{6} - 151964 q^{9}+O(q^{10}) $ 4 * q - 1024 * q^4 + 448 * q^6 - 151964 * q^9	$ 4 q - 1024 q^{4} + 448 q^{6} - 151964 q^{9} + 89880 q^{11} + 153664 q^{14} + 262144 q^{16} - 1017548 q^{19} - 67228 q^{21} - 114688 q^{24} - 3209024 q^{26} - 4012656 q^{29} + 4377464 q^{31} - 27853056 q^{34} + 38902784 q^{36} + 11776448 q^{39} + 38033184 q^{41} - 23009280 q^{44} - 2553600 q^{46} - 23059204 q^{49} - 61113288 q^{51} - 59833984 q^{54} - 39337984 q^{56} + 267284724 q^{59} + 455603372 q^{61} - 67108864 q^{64} - 764413440 q^{66} - 328036800 q^{69} - 335971440 q^{71} - 663154432 q^{74} + 260492288 q^{76} - 539285552 q^{79} + 1277652956 q^{81} + 17210368 q^{84} - 134198912 q^{86} - 1583315496 q^{89} + 481554164 q^{91} - 2385360768 q^{94} + 29360128 q^{96} - 2736961080 q^{99}+O(q^{100}) $ 4 * q - 1024 * q^4 + 448 * q^6 - 151964 * q^9 + 89880 * q^11 + 153664 * q^14 + 262144 * q^16 - 1017548 * q^19 - 67228 * q^21 - 114688 * q^24 - 3209024 * q^26 - 4012656 * q^29 + 4377464 * q^31 - 27853056 * q^34 + 38902784 * q^36 + 11776448 * q^39 + 38033184 * q^41 - 23009280 * q^44 - 2553600 * q^46 - 23059204 * q^49 - 61113288 * q^51 - 59833984 * q^54 - 39337984 * q^56 + 267284724 * q^59 + 455603372 * q^61 - 67108864 * q^64 - 764413440 * q^66 - 328036800 * q^69 - 335971440 * q^71 - 663154432 * q^74 + 260492288 * q^76 - 539285552 * q^79 + 1277652956 * q^81 + 17210368 * q^84 - 134198912 * q^86 - 1583315496 * q^89 + 481554164 * q^91 - 2385360768 * q^94 + 29360128 * q^96 - 2736961080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 16.0000i	− 0.707107i
$2$	− 16.0000i	− 0.707107i
$3$	247.052i	1.76093i	0.474108	+	0.880467i	$0.342771\pi$
$3$	247.052i	1.76093i	−0.474108	+	0.880467i	$0.657229\pi$
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	3952.83	1.24517
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	4096.00i	0.353553i
$9$	−41351.7	−2.10089
$10$	0	0
$11$	−27940.9	−0.575405	−0.287703	−	0.957720i	$-0.592891\pi$
$11$	−27940.9	−0.575405	−0.287703	+	0.957720i	$0.592891\pi$
$12$	− 63245.3i	− 0.880467i
$13$	− 60943.3i	− 0.591808i	−0.955218	−	0.295904i	$-0.904379\pi$
$13$	− 60943.3i	− 0.591808i	0.955218	−	0.295904i	$-0.0956209\pi$
$14$	38416.0	0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	− 358867.i	− 1.04211i	−0.853523	−	0.521055i	$-0.825538\pi$
$17$	− 358867.i	− 1.04211i	0.853523	−	0.521055i	$-0.174462\pi$
$18$	661628.i	1.48555i
$19$	391593.	0.689356	0.344678	−	0.938721i	$-0.387988\pi$
$19$	391593.	0.689356	0.344678	+	0.938721i	$0.387988\pi$
$20$	0	0
$21$	−593172.	−0.665570
$22$	447055.i	0.406873i
$23$	302894.i	0.225692i	0.993612	+	0.112846i	$0.0359967\pi$
$23$	302894.i	0.225692i	−0.993612	+	0.112846i	$0.964003\pi$
$24$	−1.01193e6	−0.622584
$25$	0	0
$26$	−975093.	−0.418472
$27$	− 5.35330e6i	− 1.93859i
$28$	− 614656.i	− 0.188982i
$29$	−6.73993e6	−1.76956	−0.884778	−	0.466013i	$-0.845690\pi$
$29$	−6.73993e6	−1.76956	−0.884778	+	0.466013i	$0.845690\pi$
$30$	0	0
$31$	2.98262e6	0.580056	0.290028	−	0.957018i	$-0.406335\pi$
$31$	2.98262e6	0.580056	0.290028	+	0.957018i	$0.406335\pi$
$32$	− 1.04858e6i	− 0.176777i
$33$	− 6.90287e6i	− 1.01325i
$34$	−5.74188e6	−0.736884
$35$	0	0
$36$	1.05860e7	1.05044
$37$	− 3.49582e6i	− 0.306649i	−0.988176	−	0.153324i	$-0.951002\pi$
$37$	− 3.49582e6i	− 0.306649i	0.988176	−	0.153324i	$-0.0489979\pi$
$38$	− 6.26549e6i	− 0.487449i
$39$	1.50562e7	1.04214
$40$	0	0
$41$	3.43724e7	1.89969	0.949845	−	0.312722i	$-0.101241\pi$
$41$	3.43724e7	1.89969	0.949845	+	0.312722i	$0.101241\pi$
$42$	9.49075e6i	0.470629i
$43$	1.45085e7i	0.647164i	0.946200	+	0.323582i	$0.104887\pi$
$43$	1.45085e7i	0.647164i	−0.946200	+	0.323582i	$0.895113\pi$
$44$	7.15288e6	0.287703
$45$	0	0
$46$	4.84631e6	0.159588
$47$	− 2.76485e7i	− 0.826479i	−0.910622	−	0.413239i	$-0.864397\pi$
$47$	− 2.76485e7i	− 0.826479i	0.910622	−	0.413239i	$-0.135603\pi$
$48$	1.61908e7i	0.440233i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	8.86589e7	1.83509
$52$	1.56015e7i	0.295904i
$53$	2.39217e7i	0.416438i	0.978082	+	0.208219i	$0.0667666\pi$
$53$	2.39217e7i	0.416438i	−0.978082	+	0.208219i	$0.933233\pi$
$54$	−8.56529e7	−1.37079
$55$	0	0
$56$	−9.83450e6	−0.133631
$57$	9.67439e7i	1.21391i
$58$	1.07839e8i	1.25127i
$59$	1.20580e8	1.29551	0.647756	−	0.761848i	$-0.275707\pi$
$59$	1.20580e8	1.29551	0.647756	+	0.761848i	$0.275707\pi$
$60$	0	0
$61$	7.23140e7	0.668710	0.334355	−	0.942447i	$-0.391482\pi$
$61$	7.23140e7	0.668710	0.334355	+	0.942447i	$0.391482\pi$
$62$	− 4.77219e7i	− 0.410161i
$63$	− 9.92855e7i	− 0.794060i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	−1.10446e8	−0.716476
$67$	8.70377e7i	0.527680i	0.964566	+	0.263840i	$0.0849891\pi$
$67$	8.70377e7i	0.527680i	−0.964566	+	0.263840i	$0.915011\pi$
$68$	9.18701e7i	0.521055i
$69$	−7.48307e7	−0.397428
$70$	0	0
$71$	2.19622e8	1.02568	0.512842	−	0.858483i	$-0.328593\pi$
$71$	2.19622e8	1.02568	0.512842	+	0.858483i	$0.328593\pi$
$72$	− 1.69377e8i	− 0.742775i
$73$	− 2.67792e8i	− 1.10368i	−0.833949	−	0.551841i	$-0.813926\pi$
$73$	− 2.67792e8i	− 1.10368i	0.833949	−	0.551841i	$-0.186074\pi$
$74$	−5.59331e7	−0.216833
$75$	0	0
$76$	−1.00248e8	−0.344678
$77$	− 6.70862e7i	− 0.217483i
$78$	− 2.40899e8i	− 0.736901i
$79$	−2.85350e7	−0.0824243	−0.0412122	−	0.999150i	$-0.513122\pi$
$79$	−2.85350e7	−0.0824243	−0.0412122	+	0.999150i	$0.513122\pi$
$80$	0	0
$81$	5.08619e8	1.31283
$82$	− 5.49959e8i	− 1.34328i
$83$	3.83237e8i	0.886372i	0.896430	+	0.443186i	$0.146152\pi$
$83$	3.83237e8i	0.886372i	−0.896430	+	0.443186i	$0.853848\pi$
$84$	1.51852e8	0.332785
$85$	0	0
$86$	2.32136e8	0.457614
$87$	− 1.66511e9i	− 3.11607i
$88$	− 1.14446e8i	− 0.203437i
$89$	−7.21581e8	−1.21907	−0.609537	−	0.792757i	$-0.708645\pi$
$89$	−7.21581e8	−1.21907	−0.609537	+	0.792757i	$0.708645\pi$
$90$	0	0
$91$	1.46325e8	0.223683
$92$	− 7.75410e7i	− 0.112846i
$93$	7.36861e8i	1.02144i
$94$	−4.42377e8	−0.584409
$95$	0	0
$96$	2.59053e8	0.311292
$97$	− 6.73736e8i	− 0.772710i	−0.922350	−	0.386355i	$-0.873734\pi$
$97$	− 6.73736e8i	− 0.772710i	0.922350	−	0.386355i	$-0.126266\pi$
$98$	9.22368e7i	0.101015i
$99$	1.15541e9	1.20886
$100$	0	0
$101$	−1.04805e7	−0.0100216	−0.00501081	−	0.999987i	$-0.501595\pi$
$101$	−1.04805e7	−0.0100216	−0.00501081	+	0.999987i	$0.501595\pi$
$102$	− 1.41854e9i	− 1.29760i
$103$	− 1.39782e9i	− 1.22373i	−0.790963	−	0.611864i	$-0.790420\pi$
$103$	− 1.39782e9i	− 1.22373i	0.790963	−	0.611864i	$-0.209580\pi$
$104$	2.49624e8	0.209236
$105$	0	0
$106$	3.82747e8	0.294466
$107$	− 4.84414e8i	− 0.357264i	−0.983916	−	0.178632i	$-0.942833\pi$
$107$	− 4.84414e8i	− 0.357264i	0.983916	−	0.178632i	$-0.0571672\pi$
$108$	1.37045e9i	0.969293i
$109$	1.96298e8	0.133198	0.0665989	−	0.997780i	$-0.478785\pi$
$109$	1.96298e8	0.133198	0.0665989	+	0.997780i	$0.478785\pi$
$110$	0	0
$111$	8.63649e8	0.539988
$112$	1.57352e8i	0.0944911i
$113$	5.80849e8i	0.335128i	0.985861	+	0.167564i	$0.0535901\pi$
$113$	5.80849e8i	0.335128i	−0.985861	+	0.167564i	$0.946410\pi$
$114$	1.54790e9	0.858364
$115$	0	0
$116$	1.72542e9	0.884778
$117$	2.52011e9i	1.24332i
$118$	− 1.92928e9i	− 0.916066i
$119$	8.61641e8	0.393881
$120$	0	0
$121$	−1.57725e9	−0.668909
$122$	− 1.15702e9i	− 0.472850i
$123$	8.49178e9i	3.34523i
$124$	−7.63550e8	−0.290028
$125$	0	0
$126$	−1.58857e9	−0.561485
$127$	2.59088e9i	0.883751i	0.897076	+	0.441876i	$0.145687\pi$
$127$	2.59088e9i	0.883751i	−0.897076	+	0.441876i	$0.854313\pi$
$128$	2.68435e8i	0.0883883i
$129$	−3.58436e9	−1.13961
$130$	0	0
$131$	2.45598e9	0.728626	0.364313	−	0.931277i	$-0.381304\pi$
$131$	2.45598e9	0.728626	0.364313	+	0.931277i	$0.381304\pi$
$132$	1.76713e9i	0.506625i
$133$	9.40215e8i	0.260552i
$134$	1.39260e9	0.373126
$135$	0	0
$136$	1.46992e9	0.368442
$137$	6.08364e9i	1.47544i	0.675108	+	0.737719i	$0.264097\pi$
$137$	6.08364e9i	1.47544i	−0.675108	+	0.737719i	$0.735903\pi$
$138$	1.19729e9i	0.281024i
$139$	−2.25249e9	−0.511796	−0.255898	−	0.966704i	$-0.582371\pi$
$139$	−2.25249e9	−0.511796	−0.255898	+	0.966704i	$0.582371\pi$
$140$	0	0
$141$	6.83063e9	1.45537
$142$	− 3.51395e9i	− 0.725268i
$143$	1.70281e9i	0.340530i
$144$	−2.71003e9	−0.525221
$145$	0	0
$146$	−4.28466e9	−0.780421
$147$	− 1.42421e9i	− 0.251562i
$148$	8.94930e8i	0.153324i
$149$	3.13517e9	0.521103	0.260551	−	0.965460i	$-0.416096\pi$
$149$	3.13517e9	0.521103	0.260551	+	0.965460i	$0.416096\pi$
$150$	0	0
$151$	−6.20938e9	−0.971969	−0.485984	−	0.873968i	$-0.661539\pi$
$151$	−6.20938e9	−0.971969	−0.485984	+	0.873968i	$0.661539\pi$
$152$	1.60397e9i	0.243724i
$153$	1.48398e10i	2.18936i
$154$	−1.07338e9	−0.153784
$155$	0	0
$156$	−3.85438e9	−0.521068
$157$	1.33378e10i	1.75201i	0.482300	+	0.876006i	$0.339802\pi$
$157$	1.33378e10i	1.75201i	−0.482300	+	0.876006i	$0.660198\pi$
$158$	4.56560e8i	0.0582828i
$159$	−5.90990e9	−0.733319
$160$	0	0
$161$	−7.27249e8	−0.0853035
$162$	− 8.13790e9i	− 0.928314i
$163$	− 7.33621e9i	− 0.814006i	−0.913427	−	0.407003i	$-0.866574\pi$
$163$	− 7.33621e9i	− 0.814006i	0.913427	−	0.407003i	$-0.133426\pi$
$164$	−8.79934e9	−0.949845
$165$	0	0
$166$	6.13179e9	0.626760
$167$	− 6.42205e9i	− 0.638925i	−0.947599	−	0.319462i	$-0.896498\pi$
$167$	− 6.42205e9i	− 0.638925i	0.947599	−	0.319462i	$-0.103502\pi$
$168$	− 2.42963e9i	− 0.235315i
$169$	6.89041e9	0.649763
$170$	0	0
$171$	−1.61931e10	−1.44826
$172$	− 3.71418e9i	− 0.323582i
$173$	− 1.91846e10i	− 1.62834i	−0.580626	−	0.814171i	$-0.697192\pi$
$173$	− 1.91846e10i	− 1.62834i	0.580626	−	0.814171i	$-0.302808\pi$
$174$	−2.66418e10	−2.20339
$175$	0	0
$176$	−1.83114e9	−0.143851
$177$	2.97896e10i	2.28131i
$178$	1.15453e10i	0.862016i
$179$	−1.53377e10	−1.11666	−0.558330	−	0.829619i	$-0.688558\pi$
$179$	−1.53377e10	−1.11666	−0.558330	+	0.829619i	$0.688558\pi$
$180$	0	0
$181$	−1.73475e10	−1.20139	−0.600694	−	0.799479i	$-0.705109\pi$
$181$	−1.73475e10	−1.20139	−0.600694	+	0.799479i	$0.705109\pi$
$182$	− 2.34120e9i	− 0.158167i
$183$	1.78653e10i	1.17755i
$184$	−1.24066e9	−0.0797941
$185$	0	0
$186$	1.17898e10	0.722267
$187$	1.00271e10i	0.599636i
$188$	7.07802e9i	0.413239i
$189$	1.28533e10	0.732717
$190$	0	0
$191$	2.70138e10	1.46871	0.734355	−	0.678765i	$-0.237485\pi$
$191$	2.70138e10	1.46871	0.734355	+	0.678765i	$0.237485\pi$
$192$	− 4.14485e9i	− 0.220117i
$193$	− 2.70232e9i	− 0.140194i	−0.997540	−	0.0700970i	$-0.977669\pi$
$193$	− 2.70232e9i	− 0.140194i	0.997540	−	0.0700970i	$-0.0223309\pi$
$194$	−1.07798e10	−0.546389
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	2.39047e10i	1.13080i	0.824818	+	0.565399i	$0.191278\pi$
$197$	2.39047e10i	1.13080i	−0.824818	+	0.565399i	$0.808722\pi$
$198$	− 1.84865e10i	− 0.854794i
$199$	2.16111e9	0.0976872	0.0488436	−	0.998806i	$-0.484446\pi$
$199$	2.16111e9	0.0976872	0.0488436	+	0.998806i	$0.484446\pi$
$200$	0	0
$201$	−2.15028e10	−0.929209
$202$	1.67689e8i	0.00708635i
$203$	− 1.61826e10i	− 0.668829i
$204$	−2.26967e10	−0.917544
$205$	0	0
$206$	−2.23652e10	−0.865306
$207$	− 1.25252e10i	− 0.474153i
$208$	− 3.99398e9i	− 0.147952i
$209$	−1.09415e10	−0.396659
$210$	0	0
$211$	3.61055e9	0.125401	0.0627007	−	0.998032i	$-0.480029\pi$
$211$	3.61055e9	0.125401	0.0627007	+	0.998032i	$0.480029\pi$
$212$	− 6.12395e9i	− 0.208219i
$213$	5.42581e10i	1.80616i
$214$	−7.75062e9	−0.252624
$215$	0	0
$216$	2.19271e10	0.685394
$217$	7.16126e9i	0.219240i
$218$	− 3.14077e9i	− 0.0941851i
$219$	6.61585e10	1.94351
$220$	0	0
$221$	−2.18706e10	−0.616730
$222$	− 1.38184e10i	− 0.381829i
$223$	7.13001e10i	1.93072i	0.260929	+	0.965358i	$0.415971\pi$
$223$	7.13001e10i	1.93072i	−0.260929	+	0.965358i	$0.584029\pi$
$224$	2.51763e9	0.0668153
$225$	0	0
$226$	9.29359e9	0.236971
$227$	7.15361e10i	1.78817i	0.447896	+	0.894086i	$0.352173\pi$
$227$	7.15361e10i	1.78817i	−0.447896	+	0.894086i	$0.647827\pi$
$228$	− 2.47664e10i	− 0.606955i
$229$	3.56020e10	0.855491	0.427745	−	0.903899i	$-0.359308\pi$
$229$	3.56020e10	0.855491	0.427745	+	0.903899i	$0.359308\pi$
$230$	0	0
$231$	1.65738e10	0.382973
$232$	− 2.76067e10i	− 0.625633i
$233$	3.80069e10i	0.844814i	0.906406	+	0.422407i	$0.138815\pi$
$233$	3.80069e10i	0.844814i	−0.906406	+	0.422407i	$0.861185\pi$
$234$	4.03218e10	0.879161
$235$	0	0
$236$	−3.08685e10	−0.647756
$237$	− 7.04962e9i	− 0.145144i
$238$	− 1.37863e10i	− 0.278516i
$239$	8.67126e10	1.71906	0.859531	−	0.511083i	$-0.170756\pi$
$239$	8.67126e10	1.71906	0.859531	+	0.511083i	$0.170756\pi$
$240$	0	0
$241$	−8.18418e9	−0.156278	−0.0781391	−	0.996942i	$-0.524898\pi$
$241$	−8.18418e9	−0.156278	−0.0781391	+	0.996942i	$0.524898\pi$
$242$	2.52360e10i	0.472990i
$243$	2.02863e10i	0.373228i
$244$	−1.85124e10	−0.334355
$245$	0	0
$246$	1.35868e11	2.36543
$247$	− 2.38650e10i	− 0.407967i
$248$	1.22168e10i	0.205081i
$249$	−9.46795e10	−1.56084
$250$	0	0
$251$	9.75467e10	1.55125	0.775624	−	0.631196i	$-0.217435\pi$
$251$	9.75467e10	1.55125	0.775624	+	0.631196i	$0.217435\pi$
$252$	2.54171e10i	0.397030i
$253$	− 8.46315e9i	− 0.129864i
$254$	4.14540e10	0.624907
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	− 4.43042e9i	− 0.0633499i	−0.999498	−	0.0316750i	$-0.989916\pi$
$257$	− 4.43042e9i	− 0.0633499i	0.999498	−	0.0316750i	$-0.0100841\pi$
$258$	5.73497e10i	0.805828i
$259$	8.39346e9	0.115902
$260$	0	0
$261$	2.78708e11	3.71763
$262$	− 3.92957e10i	− 0.515216i
$263$	1.20620e11i	1.55460i	0.629129	+	0.777301i	$0.283412\pi$
$263$	1.20620e11i	1.55460i	−0.629129	+	0.777301i	$0.716588\pi$
$264$	2.82741e10	0.358238
$265$	0	0
$266$	1.50434e10	0.184238
$267$	− 1.78268e11i	− 2.14671i
$268$	− 2.22816e10i	− 0.263840i
$269$	−7.59025e10	−0.883835	−0.441917	−	0.897056i	$-0.645702\pi$
$269$	−7.59025e10	−0.883835	−0.441917	+	0.897056i	$0.645702\pi$
$270$	0	0
$271$	7.11397e10	0.801217	0.400608	−	0.916249i	$-0.368799\pi$
$271$	7.11397e10	0.801217	0.400608	+	0.916249i	$0.368799\pi$
$272$	− 2.35187e10i	− 0.260528i
$273$	3.61499e10i	0.393890i
$274$	9.73382e10	1.04329
$275$	0	0
$276$	1.91567e10	0.198714
$277$	8.61542e10i	0.879261i	0.898179	+	0.439630i	$0.144891\pi$
$277$	8.61542e10i	0.879261i	−0.898179	+	0.439630i	$0.855109\pi$
$278$	3.60399e10i	0.361894i
$279$	−1.23336e11	−1.21863
$280$	0	0
$281$	−1.00179e11	−0.958511	−0.479256	−	0.877675i	$-0.659093\pi$
$281$	−1.00179e11	−0.958511	−0.479256	+	0.877675i	$0.659093\pi$
$282$	− 1.09290e11i	− 1.02910i
$283$	4.57444e10i	0.423935i	0.977277	+	0.211967i	$0.0679871\pi$
$283$	4.57444e10i	0.423935i	−0.977277	+	0.211967i	$0.932013\pi$
$284$	−5.62233e10	−0.512842
$285$	0	0
$286$	2.72450e10	0.240791
$287$	8.25282e10i	0.718015i
$288$	4.33604e10i	0.371388i
$289$	−1.01980e10	−0.0859950
$290$	0	0
$291$	1.66448e11	1.36069
$292$	6.85546e10i	0.551841i
$293$	1.01615e10i	0.0805476i	0.999189	+	0.0402738i	$0.0128230\pi$
$293$	1.01615e10i	0.0805476i	−0.999189	+	0.0402738i	$0.987177\pi$
$294$	−2.27873e10	−0.177881
$295$	0	0
$296$	1.43189e10	0.108417
$297$	1.49576e11i	1.11547i
$298$	− 5.01628e10i	− 0.368475i
$299$	1.84594e10	0.133566
$300$	0	0
$301$	−3.48349e10	−0.244605
$302$	9.93501e10i	0.687286i
$303$	− 2.58924e9i	− 0.0176474i
$304$	2.56634e10	0.172339
$305$	0	0
$306$	2.37437e11	1.54811
$307$	− 3.68957e10i	− 0.237057i	−0.992951	−	0.118529i	$-0.962182\pi$
$307$	− 3.68957e10i	− 0.237057i	0.992951	−	0.118529i	$-0.0378178\pi$
$308$	1.71741e10i	0.108741i
$309$	3.45335e11	2.15490
$310$	0	0
$311$	1.88558e11	1.14294	0.571469	−	0.820624i	$-0.306374\pi$
$311$	1.88558e11	1.14294	0.571469	+	0.820624i	$0.306374\pi$
$312$	6.16701e10i	0.368450i
$313$	− 1.31778e11i	− 0.776058i	−0.921647	−	0.388029i	$-0.873156\pi$
$313$	− 1.31778e11i	− 0.776058i	0.921647	−	0.388029i	$-0.126844\pi$
$314$	2.13405e11	1.23886
$315$	0	0
$316$	7.30495e9	0.0412122
$317$	− 1.50686e11i	− 0.838118i	−0.907959	−	0.419059i	$-0.862360\pi$
$317$	− 1.50686e11i	− 0.838118i	0.907959	−	0.419059i	$-0.137640\pi$
$318$	9.45584e10i	0.518535i
$319$	1.88320e11	1.01821
$320$	0	0
$321$	1.19675e11	0.629118
$322$	1.16360e10i	0.0603187i
$323$	− 1.40530e11i	− 0.718386i
$324$	−1.30206e11	−0.656417
$325$	0	0
$326$	−1.17379e11	−0.575589
$327$	4.84959e10i	0.234552i
$328$	1.40789e11i	0.671642i
$329$	6.63841e10	0.312380
$330$	0	0
$331$	3.38877e10	0.155173	0.0775865	−	0.996986i	$-0.475279\pi$
$331$	3.38877e10	0.155173	0.0775865	+	0.996986i	$0.475279\pi$
$332$	− 9.81087e10i	− 0.443186i
$333$	1.44558e11i	0.644234i
$334$	−1.02753e11	−0.451788
$335$	0	0
$336$	−3.88741e10	−0.166393
$337$	1.98312e11i	0.837555i	0.908089	+	0.418778i	$0.137541\pi$
$337$	1.98312e11i	0.837555i	−0.908089	+	0.418778i	$0.862459\pi$
$338$	− 1.10247e11i	− 0.459452i
$339$	−1.43500e11	−0.590138
$340$	0	0
$341$	−8.33371e10	−0.333767
$342$	2.59089e11i	1.02407i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−5.94268e10	−0.228807
$345$	0	0
$346$	−3.06954e11	−1.15141
$347$	− 1.71762e11i	− 0.635981i	−0.948094	−	0.317990i	$-0.896992\pi$
$347$	− 1.71762e11i	− 0.635981i	0.948094	−	0.317990i	$-0.103008\pi$
$348$	4.26269e11i	1.55803i
$349$	1.88189e11	0.679014	0.339507	−	0.940603i	$-0.389740\pi$
$349$	1.88189e11	0.679014	0.339507	+	0.940603i	$0.389740\pi$
$350$	0	0
$351$	−3.26248e11	−1.14727
$352$	2.92982e10i	0.101718i
$353$	− 1.97995e11i	− 0.678686i	−0.940663	−	0.339343i	$-0.889795\pi$
$353$	− 1.97995e11i	− 0.678686i	0.940663	−	0.339343i	$-0.110205\pi$
$354$	4.76633e11	1.61313
$355$	0	0
$356$	1.84725e11	0.609537
$357$	2.12870e11i	0.693598i
$358$	2.45403e11i	0.789598i
$359$	−4.34669e11	−1.38113	−0.690563	−	0.723272i	$-0.742637\pi$
$359$	−4.34669e11	−1.38113	−0.690563	+	0.723272i	$0.742637\pi$
$360$	0	0
$361$	−1.69343e11	−0.524788
$362$	2.77560e11i	0.849510i
$363$	− 3.89663e11i	− 1.17790i
$364$	−3.74592e10	−0.111841
$365$	0	0
$366$	2.85845e11	0.832657
$367$	6.02066e10i	0.173240i	0.996241	+	0.0866198i	$0.0276065\pi$
$367$	6.02066e10i	0.173240i	−0.996241	+	0.0866198i	$0.972393\pi$
$368$	1.98505e10i	0.0564230i
$369$	−1.42136e12	−3.99103
$370$	0	0
$371$	−5.74359e10	−0.157399
$372$	− 1.88637e11i	− 0.510720i
$373$	6.85521e11i	1.83371i	0.399219	+	0.916855i	$0.369281\pi$
$373$	6.85521e11i	1.83371i	−0.399219	+	0.916855i	$0.630719\pi$
$374$	1.60433e11	0.424007
$375$	0	0
$376$	1.13248e11	0.292204
$377$	4.10754e11i	1.04724i
$378$	− 2.05653e11i	− 0.518109i
$379$	−5.05522e11	−1.25853	−0.629266	−	0.777190i	$-0.716644\pi$
$379$	−5.05522e11	−1.25853	−0.629266	+	0.777190i	$0.716644\pi$
$380$	0	0
$381$	−6.40082e11	−1.55623
$382$	− 4.32221e11i	− 1.03854i
$383$	− 2.02054e11i	− 0.479814i	−0.970796	−	0.239907i	$-0.922883\pi$
$383$	− 2.02054e11i	− 0.479814i	0.970796	−	0.239907i	$-0.0771170\pi$
$384$	−6.63175e10	−0.155646
$385$	0	0
$386$	−4.32371e10	−0.0991321
$387$	− 5.99952e11i	− 1.35962i
$388$	1.72476e11i	0.386355i
$389$	−5.51954e11	−1.22216	−0.611082	−	0.791567i	$-0.709265\pi$
$389$	−5.51954e11	−1.22216	−0.611082	+	0.791567i	$0.709265\pi$
$390$	0	0
$391$	1.08699e11	0.235196
$392$	− 2.36126e10i	− 0.0505076i
$393$	6.06756e11i	1.28306i
$394$	3.82475e11	0.799595
$395$	0	0
$396$	−2.95784e11	−0.604430
$397$	1.26816e11i	0.256222i	0.991760	+	0.128111i	$0.0408914\pi$
$397$	1.26816e11i	0.256222i	−0.991760	+	0.128111i	$0.959109\pi$
$398$	− 3.45777e10i	− 0.0690753i
$399$	−2.32282e11	−0.458815
$400$	0	0
$401$	5.86957e11	1.13359	0.566795	−	0.823859i	$-0.308183\pi$
$401$	5.86957e11	1.13359	0.566795	+	0.823859i	$0.308183\pi$
$402$	3.44045e11i	0.657050i
$403$	− 1.81771e11i	− 0.343282i
$404$	2.68302e9	0.00501081
$405$	0	0
$406$	−2.58921e11	−0.472934
$407$	9.76764e10i	0.176447i
$408$	3.63147e11i	0.648801i
$409$	9.08262e10	0.160493	0.0802465	−	0.996775i	$-0.474429\pi$
$409$	9.08262e10	0.160493	0.0802465	+	0.996775i	$0.474429\pi$
$410$	0	0
$411$	−1.50298e12	−2.59815
$412$	3.57843e11i	0.611864i
$413$	2.89513e11i	0.489658i
$414$	−2.00403e11	−0.335277
$415$	0	0
$416$	−6.39037e10	−0.104618
$417$	− 5.56483e11i	− 0.901238i
$418$	1.75064e11i	0.280481i
$419$	8.34669e11	1.32297	0.661487	−	0.749957i	$-0.269926\pi$
$419$	8.34669e11	1.32297	0.661487	+	0.749957i	$0.269926\pi$
$420$	0	0
$421$	−1.61360e10	−0.0250337	−0.0125169	−	0.999922i	$-0.503984\pi$
$421$	−1.61360e10	−0.0250337	−0.0125169	+	0.999922i	$0.503984\pi$
$422$	− 5.77688e10i	− 0.0886722i
$423$	1.14331e12i	1.73634i
$424$	−9.79832e10	−0.147233
$425$	0	0
$426$	8.68130e11	1.27715
$427$	1.73626e11i	0.252749i
$428$	1.24010e11i	0.178632i
$429$	−4.20684e11	−0.599650
$430$	0	0
$431$	−4.81935e11	−0.672730	−0.336365	−	0.941732i	$-0.609198\pi$
$431$	−4.81935e11	−0.672730	−0.336365	+	0.941732i	$0.609198\pi$
$432$	− 3.50834e11i	− 0.484646i
$433$	− 6.68314e11i	− 0.913661i	−0.889554	−	0.456830i	$-0.848985\pi$
$433$	− 6.68314e11i	− 0.913661i	0.889554	−	0.456830i	$-0.151015\pi$
$434$	1.14580e11	0.155026
$435$	0	0
$436$	−5.02523e10	−0.0665989
$437$	1.18611e11i	0.155582i
$438$	− 1.05854e12i	− 1.37427i
$439$	4.79819e11	0.616577	0.308288	−	0.951293i	$-0.400244\pi$
$439$	4.79819e11	0.616577	0.308288	+	0.951293i	$0.400244\pi$
$440$	0	0
$441$	2.38384e11	0.300126
$442$	3.49929e11i	0.436094i
$443$	6.53598e11i	0.806295i	0.915135	+	0.403148i	$0.132084\pi$
$443$	6.53598e11i	0.806295i	−0.915135	+	0.403148i	$0.867916\pi$
$444$	−2.21094e11	−0.269994
$445$	0	0
$446$	1.14080e12	1.36522
$447$	7.74551e11i	0.917627i
$448$	− 4.02821e10i	− 0.0472456i
$449$	1.88660e11	0.219064	0.109532	−	0.993983i	$-0.465065\pi$
$449$	1.88660e11	0.219064	0.109532	+	0.993983i	$0.465065\pi$
$450$	0	0
$451$	−9.60397e11	−1.09309
$452$	− 1.48697e11i	− 0.167564i
$453$	− 1.53404e12i	− 1.71157i
$454$	1.14458e12	1.26443
$455$	0	0
$456$	−3.96263e11	−0.429182
$457$	1.31205e12i	1.40711i	0.710639	+	0.703556i	$0.248406\pi$
$457$	1.31205e12i	1.40711i	−0.710639	+	0.703556i	$0.751594\pi$
$458$	− 5.69633e11i	− 0.604923i
$459$	−1.92113e12	−2.02022
$460$	0	0
$461$	1.16594e12	1.20233	0.601165	−	0.799125i	$-0.294703\pi$
$461$	1.16594e12	1.20233	0.601165	+	0.799125i	$0.294703\pi$
$462$	− 2.65181e11i	− 0.270803i
$463$	3.87318e10i	0.0391700i	0.999808	+	0.0195850i	$0.00623449\pi$
$463$	3.87318e10i	0.0391700i	−0.999808	+	0.0195850i	$0.993766\pi$
$464$	−4.41708e11	−0.442389
$465$	0	0
$466$	6.08111e11	0.597374
$467$	1.17150e11i	0.113977i	0.998375	+	0.0569883i	$0.0181498\pi$
$467$	1.17150e11i	0.113977i	−0.998375	+	0.0569883i	$0.981850\pi$
$468$	− 6.45149e11i	− 0.621661i
$469$	−2.08977e11	−0.199444
$470$	0	0
$471$	−3.29514e12	−3.08518
$472$	4.93896e11i	0.458033i
$473$	− 4.05381e11i	− 0.372382i
$474$	−1.12794e11	−0.102632
$475$	0	0
$476$	−2.20580e11	−0.196940
$477$	− 9.89203e11i	− 0.874888i
$478$	− 1.38740e12i	− 1.21556i
$479$	1.94734e12	1.69018	0.845089	−	0.534626i	$-0.179548\pi$
$479$	1.94734e12	1.69018	0.845089	+	0.534626i	$0.179548\pi$
$480$	0	0
$481$	−2.13047e11	−0.181477
$482$	1.30947e11i	0.110505i
$483$	− 1.79668e11i	− 0.150214i
$484$	4.03776e11	0.334454
$485$	0	0
$486$	3.24580e11	0.263912
$487$	− 1.95983e12i	− 1.57884i	−0.613852	−	0.789421i	$-0.710381\pi$
$487$	− 1.95983e12i	− 1.57884i	0.613852	−	0.789421i	$-0.289619\pi$
$488$	2.96198e11i	0.236425i
$489$	1.81243e12	1.43341
$490$	0	0
$491$	−2.93589e11	−0.227967	−0.113984	−	0.993483i	$-0.536361\pi$
$491$	−2.93589e11	−0.227967	−0.113984	+	0.993483i	$0.536361\pi$
$492$	− 2.17389e12i	− 1.67261i
$493$	2.41874e12i	1.84407i
$494$	−3.81840e11	−0.288476
$495$	0	0
$496$	1.95469e11	0.145014
$497$	5.27313e11i	0.387672i
$498$	1.51487e12i	1.10368i
$499$	−1.71390e12	−1.23746	−0.618732	−	0.785602i	$-0.712353\pi$
$499$	−1.71390e12	−1.23746	−0.618732	+	0.785602i	$0.712353\pi$
$500$	0	0
$501$	1.58658e12	1.12510
$502$	− 1.56075e12i	− 1.09690i
$503$	− 1.61385e12i	− 1.12411i	−0.827101	−	0.562053i	$-0.810012\pi$
$503$	− 1.61385e12i	− 1.12411i	0.827101	−	0.562053i	$-0.189988\pi$
$504$	4.06673e11	0.280743
$505$	0	0
$506$	−1.35410e11	−0.0918279
$507$	1.70229e12i	1.14419i
$508$	− 6.63265e11i	− 0.441876i
$509$	−1.17088e12	−0.773181	−0.386590	−	0.922252i	$-0.626347\pi$
$509$	−1.17088e12	−0.773181	−0.386590	+	0.922252i	$0.626347\pi$
$510$	0	0
$511$	6.42967e11	0.417153
$512$	− 6.87195e10i	− 0.0441942i
$513$	− 2.09632e12i	− 1.33638i
$514$	−7.08868e10	−0.0447952
$515$	0	0
$516$	9.17595e11	0.569807
$517$	7.72526e11i	0.475560i
$518$	− 1.34295e11i	− 0.0819553i
$519$	4.73960e12	2.86740
$520$	0	0
$521$	2.91339e12	1.73232	0.866161	−	0.499765i	$-0.166580\pi$
$521$	2.91339e12	1.73232	0.866161	+	0.499765i	$0.166580\pi$
$522$	− 4.45932e12i	− 2.62876i
$523$	− 2.53787e12i	− 1.48324i	−0.670820	−	0.741620i	$-0.734058\pi$
$523$	− 2.53787e12i	− 1.48324i	0.670820	−	0.741620i	$-0.265942\pi$
$524$	−6.28732e11	−0.364313
$525$	0	0
$526$	1.92992e12	1.09927
$527$	− 1.07036e12i	− 0.604482i
$528$	− 4.52386e11i	− 0.253313i
$529$	1.70941e12	0.949063
$530$	0	0
$531$	−4.98620e12	−2.72172
$532$	− 2.40695e11i	− 0.130276i
$533$	− 2.09477e12i	− 1.12425i
$534$	−2.85229e12	−1.51795
$535$	0	0
$536$	−3.56506e11	−0.186563
$537$	− 3.78920e12i	− 1.96636i
$538$	1.21444e12i	0.624965i
$539$	1.61074e11	0.0822008
$540$	0	0
$541$	1.11804e12	0.561136	0.280568	−	0.959834i	$-0.409477\pi$
$541$	1.11804e12	0.561136	0.280568	+	0.959834i	$0.409477\pi$
$542$	− 1.13823e12i	− 0.566546i
$543$	− 4.28574e12i	− 2.11556i
$544$	−3.76300e11	−0.184221
$545$	0	0
$546$	5.78398e11	0.278522
$547$	1.99438e12i	0.952500i	0.879310	+	0.476250i	$0.158004\pi$
$547$	1.99438e12i	0.952500i	−0.879310	+	0.476250i	$0.841996\pi$
$548$	− 1.55741e12i	− 0.737719i
$549$	−2.99031e12	−1.40488
$550$	0	0
$551$	−2.63931e12	−1.21985
$552$	− 3.06506e11i	− 0.140512i
$553$	− 6.85125e10i	− 0.0311535i
$554$	1.37847e12	0.621731
$555$	0	0
$556$	5.76638e11	0.255898
$557$	− 4.69088e11i	− 0.206493i	−0.994656	−	0.103247i	$-0.967077\pi$
$557$	− 4.69088e11i	− 0.206493i	0.994656	−	0.103247i	$-0.0329231\pi$
$558$	1.97338e12i	0.861702i
$559$	8.84197e11	0.382997
$560$	0	0
$561$	−2.47721e12	−1.05592
$562$	1.60286e12i	0.677770i
$563$	− 1.74518e12i	− 0.732069i	−0.930601	−	0.366034i	$-0.880715\pi$
$563$	− 1.74518e12i	− 0.732069i	0.930601	−	0.366034i	$-0.119285\pi$
$564$	−1.74864e12	−0.727687
$565$	0	0
$566$	7.31911e11	0.299767
$567$	1.22119e12i	0.496205i
$568$	8.99572e11i	0.362634i
$569$	4.13341e12	1.65311	0.826557	−	0.562853i	$-0.190296\pi$
$569$	4.13341e12	1.65311	0.826557	+	0.562853i	$0.190296\pi$
$570$	0	0
$571$	4.14262e12	1.63084	0.815422	−	0.578867i	$-0.196505\pi$
$571$	4.14262e12	1.63084	0.815422	+	0.578867i	$0.196505\pi$
$572$	− 4.35920e11i	− 0.170265i
$573$	6.67383e12i	2.58630i
$574$	1.32045e12	0.507713
$575$	0	0
$576$	6.93767e11	0.262611
$577$	4.27130e12i	1.60424i	0.597164	+	0.802120i	$0.296294\pi$
$577$	4.27130e12i	1.60424i	−0.597164	+	0.802120i	$0.703706\pi$
$578$	1.63167e11i	0.0608076i
$579$	6.67614e11	0.246872
$580$	0	0
$581$	−9.20152e11	−0.335017
$582$	− 2.66316e12i	− 0.962154i
$583$	− 6.68394e11i	− 0.239621i
$584$	1.09687e12	0.390211
$585$	0	0
$586$	1.62584e11	0.0569557
$587$	5.32282e12i	1.85042i	0.379455	+	0.925210i	$0.376111\pi$
$587$	5.32282e12i	1.85042i	−0.379455	+	0.925210i	$0.623889\pi$
$588$	3.64597e11i	0.125781i
$589$	1.16797e12	0.399865
$590$	0	0
$591$	−5.90570e12	−1.99126
$592$	− 2.29102e11i	− 0.0766622i
$593$	2.69262e11i	0.0894190i	0.999000	+	0.0447095i	$0.0142362\pi$
$593$	2.69262e11i	0.0894190i	−0.999000	+	0.0447095i	$0.985764\pi$
$594$	2.39322e12	0.788758
$595$	0	0
$596$	−8.02605e11	−0.260551
$597$	5.33906e11i	0.172021i
$598$	− 2.95350e11i	− 0.0944457i
$599$	−3.51807e12	−1.11657	−0.558283	−	0.829651i	$-0.688540\pi$
$599$	−3.51807e12	−1.11657	−0.558283	+	0.829651i	$0.688540\pi$
$600$	0	0
$601$	−1.97549e12	−0.617645	−0.308823	−	0.951120i	$-0.599935\pi$
$601$	−1.97549e12	−0.617645	−0.308823	+	0.951120i	$0.599935\pi$
$602$	5.57359e11i	0.172962i
$603$	− 3.59916e12i	− 1.10860i
$604$	1.58960e12	0.485984
$605$	0	0
$606$	−4.14279e10	−0.0124786
$607$	− 1.20562e12i	− 0.360464i	−0.983624	−	0.180232i	$-0.942315\pi$
$607$	− 1.20562e12i	− 0.360464i	0.983624	−	0.180232i	$-0.0576848\pi$
$608$	− 4.10615e11i	− 0.121862i
$609$	3.99794e12	1.17776
$610$	0	0
$611$	−1.68499e12	−0.489117
$612$	− 3.79899e12i	− 1.09468i
$613$	5.02026e11i	0.143600i	0.997419	+	0.0717999i	$0.0228743\pi$
$613$	5.02026e11i	0.143600i	−0.997419	+	0.0717999i	$0.977126\pi$
$614$	−5.90332e11	−0.167625
$615$	0	0
$616$	2.74785e11	0.0768918
$617$	5.17852e12i	1.43854i	0.694730	+	0.719271i	$0.255524\pi$
$617$	5.17852e12i	1.43854i	−0.694730	+	0.719271i	$0.744476\pi$
$618$	− 5.52536e12i	− 1.52375i
$619$	4.69963e12	1.28664	0.643318	−	0.765599i	$-0.277557\pi$
$619$	4.69963e12	1.28664	0.643318	+	0.765599i	$0.277557\pi$
$620$	0	0
$621$	1.62149e12	0.437523
$622$	− 3.01693e12i	− 0.808179i
$623$	− 1.73252e12i	− 0.460767i
$624$	9.86722e11	0.260534
$625$	0	0
$626$	−2.10845e12	−0.548756
$627$	− 2.70312e12i	− 0.698491i
$628$	− 3.41449e12i	− 0.876006i
$629$	−1.25454e12	−0.319562
$630$	0	0
$631$	−5.53678e12	−1.39035	−0.695177	−	0.718839i	$-0.744674\pi$
$631$	−5.53678e12	−1.39035	−0.695177	+	0.718839i	$0.744674\pi$
$632$	− 1.16879e11i	− 0.0291414i
$633$	8.91994e11i	0.220823i
$634$	−2.41097e12	−0.592639
$635$	0	0
$636$	1.51293e12	0.366660
$637$	3.51326e11i	0.0845441i
$638$	− 3.01312e12i	− 0.719985i
$639$	−9.08175e12	−2.15484
$640$	0	0
$641$	−2.85506e12	−0.667966	−0.333983	−	0.942579i	$-0.608393\pi$
$641$	−2.85506e12	−0.667966	−0.333983	+	0.942579i	$0.608393\pi$
$642$	− 1.91481e12i	− 0.444854i
$643$	7.48209e12i	1.72613i	0.505093	+	0.863065i	$0.331458\pi$
$643$	7.48209e12i	1.72613i	−0.505093	+	0.863065i	$0.668542\pi$
$644$	1.86176e11	0.0426518
$645$	0	0
$646$	−2.24848e12	−0.507976
$647$	− 3.83872e12i	− 0.861225i	−0.902537	−	0.430613i	$-0.858297\pi$
$647$	− 3.83872e12i	− 0.861225i	0.902537	−	0.430613i	$-0.141703\pi$
$648$	2.08330e12i	0.464157i
$649$	−3.36912e12	−0.745445
$650$	0	0
$651$	−1.76920e12	−0.386068
$652$	1.87807e12i	0.407003i
$653$	1.09261e11i	0.0235157i	0.999931	+	0.0117578i	$0.00374272\pi$
$653$	1.09261e11i	0.0235157i	−0.999931	+	0.0117578i	$0.996257\pi$
$654$	7.75934e11	0.165854
$655$	0	0
$656$	2.25263e12	0.474922
$657$	1.10736e13i	2.31871i
$658$	− 1.06215e12i	− 0.220886i
$659$	2.10319e12	0.434403	0.217202	−	0.976127i	$-0.430307\pi$
$659$	2.10319e12	0.434403	0.217202	+	0.976127i	$0.430307\pi$
$660$	0	0
$661$	−1.76045e12	−0.358688	−0.179344	−	0.983786i	$-0.557397\pi$
$661$	−1.76045e12	−0.358688	−0.179344	+	0.983786i	$0.557397\pi$
$662$	− 5.42203e11i	− 0.109724i
$663$	− 5.40317e12i	− 1.08602i
$664$	−1.56974e12	−0.313380
$665$	0	0
$666$	2.31293e12	0.455542
$667$	− 2.04149e12i	− 0.399374i
$668$	1.64404e12i	0.319462i
$669$	−1.76148e13	−3.39986
$670$	0	0
$671$	−2.02052e12	−0.384779
$672$	6.21986e11i	0.117657i
$673$	− 8.52389e12i	− 1.60166i	−0.598892	−	0.800830i	$-0.704392\pi$
$673$	− 8.52389e12i	− 1.60166i	0.598892	−	0.800830i	$-0.295608\pi$
$674$	3.17299e12	0.592241
$675$	0	0
$676$	−1.76394e12	−0.324881
$677$	− 2.88497e12i	− 0.527828i	−0.964546	−	0.263914i	$-0.914986\pi$
$677$	− 2.88497e12i	− 0.527828i	0.964546	−	0.263914i	$-0.0850135\pi$
$678$	2.29600e12i	0.417290i
$679$	1.61764e12	0.292057
$680$	0	0
$681$	−1.76732e13	−3.14885
$682$	1.33339e12i	0.236009i
$683$	− 1.03086e13i	− 1.81262i	−0.422616	−	0.906309i	$-0.638888\pi$
$683$	− 1.03086e13i	− 1.81262i	0.422616	−	0.906309i	$-0.361112\pi$
$684$	4.14542e12	0.724130
$685$	0	0
$686$	−2.21461e11	−0.0381802
$687$	8.79556e12i	1.50646i
$688$	9.50829e11i	0.161791i
$689$	1.45787e12	0.246451
$690$	0	0
$691$	7.85439e12	1.31057	0.655287	−	0.755380i	$-0.272548\pi$
$691$	7.85439e12	1.31057	0.655287	+	0.755380i	$0.272548\pi$
$692$	4.91126e12i	0.814171i
$693$	2.77413e12i	0.456906i
$694$	−2.74819e12	−0.449706
$695$	0	0
$696$	6.82030e12	1.10170
$697$	− 1.23351e13i	− 1.97969i
$698$	− 3.01102e12i	− 0.480136i
$699$	−9.38969e12	−1.48766
$700$	0	0
$701$	1.69579e12	0.265242	0.132621	−	0.991167i	$-0.457661\pi$
$701$	1.69579e12	0.265242	0.132621	+	0.991167i	$0.457661\pi$
$702$	5.21997e12i	0.811243i
$703$	− 1.36894e12i	− 0.211390i
$704$	4.68771e11	0.0719257
$705$	0	0
$706$	−3.16793e12	−0.479904
$707$	− 2.51638e10i	− 0.00378781i
$708$	− 7.62613e12i	− 1.14066i
$709$	2.20703e12	0.328020	0.164010	−	0.986459i	$-0.447557\pi$
$709$	2.20703e12	0.328020	0.164010	+	0.986459i	$0.447557\pi$
$710$	0	0
$711$	1.17997e12	0.173164
$712$	− 2.95560e12i	− 0.431008i
$713$	9.03417e11i	0.130914i
$714$	3.40592e12	0.490448
$715$	0	0
$716$	3.92644e12	0.558330
$717$	2.14225e13i	3.02715i
$718$	6.95470e12i	0.976604i
$719$	1.46869e12	0.204952	0.102476	−	0.994735i	$-0.467324\pi$
$719$	1.46869e12	0.204952	0.102476	+	0.994735i	$0.467324\pi$
$720$	0	0
$721$	3.35617e12	0.462525
$722$	2.70948e12i	0.371081i
$723$	− 2.02192e12i	− 0.275195i
$724$	4.44096e12	0.600694
$725$	0	0
$726$	−6.23461e12	−0.832904
$727$	− 4.97511e11i	− 0.0660538i	−0.999454	−	0.0330269i	$-0.989485\pi$
$727$	− 4.97511e11i	− 0.0660538i	0.999454	−	0.0330269i	$-0.0105147\pi$
$728$	5.99347e11i	0.0790837i
$729$	4.99938e12	0.655605
$730$	0	0
$731$	5.20663e12	0.674417
$732$	− 4.57352e12i	− 0.588777i
$733$	5.22437e12i	0.668445i	0.942494	+	0.334223i	$0.108474\pi$
$733$	5.22437e12i	0.668445i	−0.942494	+	0.334223i	$0.891526\pi$
$734$	9.63306e11	0.122499
$735$	0	0
$736$	3.17608e11	0.0398971
$737$	− 2.43191e12i	− 0.303630i
$738$	2.27417e13i	2.82208i
$739$	−7.35495e11	−0.0907152	−0.0453576	−	0.998971i	$-0.514443\pi$
$739$	−7.35495e11	−0.0907152	−0.0453576	+	0.998971i	$0.514443\pi$
$740$	0	0
$741$	5.89590e12	0.718403
$742$	9.18975e11i	0.111298i
$743$	1.12076e12i	0.134916i	0.997722	+	0.0674580i	$0.0214889\pi$
$743$	1.12076e12i	0.134916i	−0.997722	+	0.0674580i	$0.978511\pi$
$744$	−3.01818e12	−0.361133
$745$	0	0
$746$	1.09683e13	1.29663
$747$	− 1.58475e13i	− 1.86217i
$748$	− 2.56694e12i	− 0.299818i
$749$	1.16308e12	0.135033
$750$	0	0
$751$	−1.62183e12	−0.186049	−0.0930244	−	0.995664i	$-0.529653\pi$
$751$	−1.62183e12	−0.186049	−0.0930244	+	0.995664i	$0.529653\pi$
$752$	− 1.81197e12i	− 0.206620i
$753$	2.40991e13i	2.73164i
$754$	6.57206e12	0.740509
$755$	0	0
$756$	−3.29044e12	−0.366358
$757$	− 1.55150e12i	− 0.171720i	−0.996307	−	0.0858600i	$-0.972636\pi$
$757$	− 1.55150e12i	− 0.171720i	0.996307	−	0.0858600i	$-0.0273638\pi$
$758$	8.08836e12i	0.889916i
$759$	2.09084e12	0.228682
$760$	0	0
$761$	1.62863e13	1.76032	0.880159	−	0.474679i	$-0.157436\pi$
$761$	1.62863e13	1.76032	0.880159	+	0.474679i	$0.157436\pi$
$762$	1.02413e13i	1.10042i
$763$	4.71312e11i	0.0503440i
$764$	−6.91554e12	−0.734355
$765$	0	0
$766$	−3.23286e12	−0.339280
$767$	− 7.34856e12i	− 0.766695i
$768$	1.06108e12i	0.110058i
$769$	1.32915e13	1.37059	0.685293	−	0.728267i	$-0.259674\pi$
$769$	1.32915e13	1.37059	0.685293	+	0.728267i	$0.259674\pi$
$770$	0	0
$771$	1.09455e12	0.111555
$772$	6.91794e11i	0.0700970i
$773$	7.58593e12i	0.764190i	0.924123	+	0.382095i	$0.124797\pi$
$773$	7.58593e12i	0.764190i	−0.924123	+	0.382095i	$0.875203\pi$
$774$	−9.59923e12	−0.961395
$775$	0	0
$776$	2.75962e12	0.273194
$777$	2.07362e12i	0.204096i
$778$	8.83126e12i	0.864200i
$779$	1.34600e13	1.30956
$780$	0	0
$781$	−6.13645e12	−0.590184
$782$	− 1.73918e12i	− 0.166309i
$783$	3.60809e13i	3.43044i
$784$	−3.77802e11	−0.0357143
$785$	0	0
$786$	9.70809e12	0.907262
$787$	3.30985e12i	0.307554i	0.988106	+	0.153777i	$0.0491437\pi$
$787$	3.30985e12i	0.307554i	−0.988106	+	0.153777i	$0.950856\pi$
$788$	− 6.11960e12i	− 0.565399i
$789$	−2.97995e13	−2.73755
$790$	0	0
$791$	−1.39462e12	−0.126666
$792$	4.73254e12i	0.427397i
$793$	− 4.40706e12i	− 0.395748i
$794$	2.02906e12	0.181176
$795$	0	0
$796$	−5.53244e11	−0.0488436
$797$	− 3.26446e12i	− 0.286582i	−0.989681	−	0.143291i	$-0.954232\pi$
$797$	− 3.26446e12i	− 0.286582i	0.989681	−	0.143291i	$-0.0457685\pi$
$798$	3.71651e12i	0.324431i
$799$	−9.92216e12	−0.861283
$800$	0	0
$801$	2.98386e13	2.56114
$802$	− 9.39131e12i	− 0.801570i
$803$	7.48235e12i	0.635064i
$804$	5.50473e12	0.464605
$805$	0	0
$806$	−2.90833e12	−0.242737
$807$	− 1.87519e13i	− 1.55637i
$808$	− 4.29283e10i	− 0.00354318i
$809$	−3.46768e12	−0.284624	−0.142312	−	0.989822i	$-0.545454\pi$
$809$	−3.46768e12	−0.284624	−0.142312	+	0.989822i	$0.545454\pi$
$810$	0	0
$811$	1.02915e13	0.835381	0.417690	−	0.908589i	$-0.362840\pi$
$811$	1.02915e13	0.835381	0.417690	+	0.908589i	$0.362840\pi$
$812$	4.14274e12i	0.334415i
$813$	1.75752e13i	1.41089i
$814$	1.56282e12	0.124767
$815$	0	0
$816$	5.81035e12	0.458772
$817$	5.68143e12i	0.446127i
$818$	− 1.45322e12i	− 0.113486i
$819$	−6.05079e12	−0.469931
$820$	0	0
$821$	6.23700e12	0.479106	0.239553	−	0.970883i	$-0.422999\pi$
$821$	6.23700e12	0.479106	0.239553	+	0.970883i	$0.422999\pi$
$822$	2.40476e13i	1.83717i
$823$	− 2.46689e13i	− 1.87435i	−0.348860	−	0.937175i	$-0.613431\pi$
$823$	− 2.46689e13i	− 1.87435i	0.348860	−	0.937175i	$-0.386569\pi$
$824$	5.72548e12	0.432653
$825$	0	0
$826$	4.63221e12	0.346240
$827$	− 1.45027e13i	− 1.07814i	−0.842262	−	0.539068i	$-0.818776\pi$
$827$	− 1.45027e13i	− 1.07814i	0.842262	−	0.539068i	$-0.181224\pi$
$828$	3.20645e12i	0.237076i
$829$	1.07681e13	0.791854	0.395927	−	0.918282i	$-0.370423\pi$
$829$	1.07681e13	0.791854	0.395927	+	0.918282i	$0.370423\pi$
$830$	0	0
$831$	−2.12846e13	−1.54832
$832$	1.02246e12i	0.0739761i
$833$	2.06880e12i	0.148873i
$834$	−8.90373e12	−0.637272
$835$	0	0
$836$	2.80102e12	0.198330
$837$	− 1.59668e13i	− 1.12449i
$838$	− 1.33547e13i	− 0.935484i
$839$	2.36129e13	1.64521	0.822603	−	0.568616i	$-0.192521\pi$
$839$	2.36129e13	1.64521	0.822603	+	0.568616i	$0.192521\pi$
$840$	0	0
$841$	3.09195e13	2.13133
$842$	2.58176e11i	0.0177015i
$843$	− 2.47494e13i	− 1.68787i
$844$	−9.24301e11	−0.0627007
$845$	0	0
$846$	1.82930e13	1.22778
$847$	− 3.78698e12i	− 0.252824i
$848$	1.56773e12i	0.104109i
$849$	−1.13013e13	−0.746521
$850$	0	0
$851$	1.05886e12	0.0692081
$852$	− 1.38901e13i	− 0.903080i
$853$	1.67503e13i	1.08331i	0.840601	+	0.541655i	$0.182202\pi$
$853$	1.67503e13i	1.08331i	−0.840601	+	0.541655i	$0.817798\pi$
$854$	2.77801e12	0.178720
$855$	0	0
$856$	1.98416e12	0.126312
$857$	− 1.16182e13i	− 0.735742i	−0.929877	−	0.367871i	$-0.880087\pi$
$857$	− 1.16182e13i	− 0.735742i	0.929877	−	0.367871i	$-0.119913\pi$
$858$	6.73094e12i	0.424017i
$859$	−1.58818e13	−0.995246	−0.497623	−	0.867393i	$-0.665794\pi$
$859$	−1.58818e13	−0.995246	−0.497623	+	0.867393i	$0.665794\pi$
$860$	0	0
$861$	−2.03888e13	−1.26438
$862$	7.71096e12i	0.475692i
$863$	− 1.35971e13i	− 0.834446i	−0.908804	−	0.417223i	$-0.863003\pi$
$863$	− 1.35971e13i	− 0.834446i	0.908804	−	0.417223i	$-0.136997\pi$
$864$	−5.61335e12	−0.342697
$865$	0	0
$866$	−1.06930e13	−0.646056
$867$	− 2.51943e12i	− 0.151431i
$868$	− 1.83328e12i	− 0.109620i
$869$	7.97294e11	0.0474274
$870$	0	0
$871$	5.30437e12	0.312285
$872$	8.04037e11i	0.0470925i
$873$	2.78601e13i	1.62338i
$874$	1.89778e12	0.110013
$875$	0	0
$876$	−1.69366e13	−0.971755
$877$	3.40277e12i	0.194238i	0.995273	+	0.0971189i	$0.0309627\pi$
$877$	3.40277e12i	0.194238i	−0.995273	+	0.0971189i	$0.969037\pi$
$878$	− 7.67711e12i	− 0.435986i
$879$	−2.51041e12	−0.141839
$880$	0	0
$881$	9.30779e12	0.520541	0.260270	−	0.965536i	$-0.416188\pi$
$881$	9.30779e12	0.520541	0.260270	+	0.965536i	$0.416188\pi$
$882$	− 3.81415e12i	− 0.212221i
$883$	− 1.00154e13i	− 0.554430i	−0.960808	−	0.277215i	$-0.910589\pi$
$883$	− 1.00154e13i	− 0.554430i	0.960808	−	0.277215i	$-0.0894114\pi$
$884$	5.59887e12	0.308365
$885$	0	0
$886$	1.04576e13	0.570137
$887$	− 2.58440e13i	− 1.40186i	−0.713232	−	0.700928i	$-0.752769\pi$
$887$	− 2.58440e13i	− 1.40186i	0.713232	−	0.700928i	$-0.247231\pi$
$888$	3.53751e12i	0.190915i
$889$	−6.22070e12	−0.334027
$890$	0	0
$891$	−1.42113e13	−0.755412
$892$	− 1.82528e13i	− 0.965358i
$893$	− 1.08270e13i	− 0.569739i
$894$	1.23928e13	0.648860
$895$	0	0
$896$	−6.44514e11	−0.0334077
$897$	4.56043e12i	0.235201i
$898$	− 3.01855e12i	− 0.154901i
$899$	−2.01026e13	−1.02644
$900$	0	0
$901$	8.58471e12	0.433974
$902$	1.53664e13i	0.772932i
$903$	− 8.60604e12i	− 0.430733i
$904$	−2.37916e12	−0.118486
$905$	0	0
$906$	−2.45447e13	−1.21026
$907$	3.82049e13i	1.87451i	0.348650	+	0.937253i	$0.386640\pi$
$907$	3.82049e13i	1.87451i	−0.348650	+	0.937253i	$0.613360\pi$
$908$	− 1.83133e13i	− 0.894086i
$909$	4.33389e11	0.0210543
$910$	0	0
$911$	9.85478e12	0.474039	0.237020	−	0.971505i	$-0.423829\pi$
$911$	9.85478e12	0.474039	0.237020	+	0.971505i	$0.423829\pi$
$912$	6.34021e12i	0.303478i
$913$	− 1.07080e13i	− 0.510023i
$914$	2.09929e13	0.994979
$915$	0	0
$916$	−9.11412e12	−0.427745
$917$	5.89682e12i	0.275395i
$918$	3.07380e13i	1.42851i
$919$	−2.60834e13	−1.20627	−0.603135	−	0.797639i	$-0.706082\pi$
$919$	−2.60834e13	−1.20627	−0.603135	+	0.797639i	$0.706082\pi$
$920$	0	0
$921$	9.11517e12	0.417442
$922$	− 1.86551e13i	− 0.850176i
$923$	− 1.33845e13i	− 0.607008i
$924$	−4.24289e12	−0.191486
$925$	0	0
$926$	6.19709e11	0.0276974
$927$	5.78024e13i	2.57091i
$928$	7.06733e12i	0.312816i
$929$	3.60592e13	1.58835	0.794174	−	0.607690i	$-0.207904\pi$
$929$	3.60592e13	1.58835	0.794174	+	0.607690i	$0.207904\pi$
$930$	0	0
$931$	−2.25746e12	−0.0984795
$932$	− 9.72977e12i	− 0.422407i
$933$	4.65836e13i	2.01264i
$934$	1.87440e12	0.0805936
$935$	0	0
$936$	−1.03224e13	−0.439581
$937$	2.75358e13i	1.16700i	0.812114	+	0.583499i	$0.198317\pi$
$937$	2.75358e13i	1.16700i	−0.812114	+	0.583499i	$0.801683\pi$
$938$	3.34364e12i	0.141028i
$939$	3.25561e13	1.36659
$940$	0	0
$941$	−7.60157e12	−0.316046	−0.158023	−	0.987435i	$-0.550512\pi$
$941$	−7.60157e12	−0.316046	−0.158023	+	0.987435i	$0.550512\pi$
$942$	5.27223e13i	2.18155i
$943$	1.04112e13i	0.428745i
$944$	7.90234e12	0.323878
$945$	0	0
$946$	−6.48610e12	−0.263314
$947$	− 2.35269e13i	− 0.950582i	−0.879829	−	0.475291i	$-0.842343\pi$
$947$	− 2.35269e13i	− 0.950582i	0.879829	−	0.475291i	$-0.157657\pi$
$948$	1.80470e12i	0.0725719i
$949$	−1.63201e13	−0.653168
$950$	0	0
$951$	3.72272e13	1.47587
$952$	3.52928e12i	0.139258i
$953$	− 3.76056e12i	− 0.147684i	−0.997270	−	0.0738422i	$-0.976474\pi$
$953$	− 3.76056e12i	− 0.147684i	0.997270	−	0.0738422i	$-0.0235261\pi$
$954$	−1.58272e13	−0.618639
$955$	0	0
$956$	−2.21984e13	−0.859531
$957$	4.65248e13i	1.79300i
$958$	− 3.11575e13i	− 1.19514i
$959$	−1.46068e13	−0.557663
$960$	0	0
$961$	−1.75436e13	−0.663535
$962$	3.40875e12i	0.128324i
$963$	2.00313e13i	0.750571i
$964$	2.09515e12	0.0781391
$965$	0	0
$966$	−2.87470e12	−0.106217
$967$	3.59678e13i	1.32280i	0.750033	+	0.661400i	$0.230037\pi$
$967$	3.59678e13i	1.32280i	−0.750033	+	0.661400i	$0.769963\pi$
$968$	− 6.46042e12i	− 0.236495i
$969$	3.47182e13	1.26503
$970$	0	0
$971$	−1.20049e13	−0.433383	−0.216692	−	0.976240i	$-0.569527\pi$
$971$	−1.20049e13	−0.433383	−0.216692	+	0.976240i	$0.569527\pi$
$972$	− 5.19328e12i	− 0.186614i
$973$	− 5.40823e12i	− 0.193441i
$974$	−3.13573e13	−1.11641
$975$	0	0
$976$	4.73917e12	0.167178
$977$	− 4.59954e12i	− 0.161506i	−0.996734	−	0.0807530i	$-0.974268\pi$
$977$	− 4.59954e12i	− 0.161506i	0.996734	−	0.0807530i	$-0.0257325\pi$
$978$	− 2.89988e13i	− 1.01357i
$979$	2.01617e13	0.701462
$980$	0	0
$981$	−8.11727e12	−0.279833
$982$	4.69742e12i	0.161197i
$983$	3.13830e12i	0.107202i	0.998562	+	0.0536011i	$0.0170699\pi$
$983$	3.13830e12i	0.107202i	−0.998562	+	0.0536011i	$0.982930\pi$
$984$	−3.47823e13	−1.18272
$985$	0	0
$986$	3.86999e13	1.30396
$987$	1.64003e13i	0.550080i
$988$	6.10944e12i	0.203984i
$989$	−4.39454e12	−0.146060
$990$	0	0
$991$	1.38736e13	0.456939	0.228470	−	0.973551i	$-0.426628\pi$
$991$	1.38736e13	0.456939	0.228470	+	0.973551i	$0.426628\pi$
$992$	− 3.12750e12i	− 0.102540i
$993$	8.37203e12i	0.273249i
$994$	8.43700e12	0.274126
$995$	0	0
$996$	2.42380e13	0.780421
$997$	− 1.65453e13i	− 0.530331i	−0.964203	−	0.265166i	$-0.914573\pi$
$997$	− 1.65453e13i	− 0.530331i	0.964203	−	0.265166i	$-0.0854266\pi$
$998$	2.74224e13i	0.875019i
$999$	−1.87142e13	−0.594465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.10.c.j.99.2		4
5.2	odd	4		350.10.a.j.1.2		2
5.3	odd	4		14.10.a.c.1.1	✓	2
5.4	even	2	inner	350.10.c.j.99.3		4
15.8	even	4		126.10.a.o.1.2		2
20.3	even	4		112.10.a.c.1.2		2
35.3	even	12		98.10.c.h.79.1		4
35.13	even	4		98.10.a.e.1.2		2
35.18	odd	12		98.10.c.j.79.2		4
35.23	odd	12		98.10.c.j.67.2		4
35.33	even	12		98.10.c.h.67.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.c.1.1	✓	2	5.3	odd	4
98.10.a.e.1.2		2	35.13	even	4
98.10.c.h.67.1		4	35.33	even	12
98.10.c.h.79.1		4	35.3	even	12
98.10.c.j.67.2		4	35.23	odd	12
98.10.c.j.79.2		4	35.18	odd	12
112.10.a.c.1.2		2	20.3	even	4
126.10.a.o.1.2		2	15.8	even	4
350.10.a.j.1.2		2	5.2	odd	4
350.10.c.j.99.2		4	1.1	even	1	trivial
350.10.c.j.99.3		4	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-16.0000i q^{2} +247.052i q^{3} -256.000 q^{4} +3952.83 q^{6} +2401.00i q^{7} +4096.00i q^{8} -41351.7 q^{9} +O(q^{10})\)	\(q-16.0000i q^{2} +247.052i q^{3} -256.000 q^{4} +3952.83 q^{6} +2401.00i q^{7} +4096.00i q^{8} -41351.7 q^{9} -27940.9 q^{11} -63245.3i q^{12} -60943.3i q^{13} +38416.0 q^{14} +65536.0 q^{16} -358867. i q^{17} +661628. i q^{18} +391593. q^{19} -593172. q^{21} +447055. i q^{22} +302894. i q^{23} -1.01193e6 q^{24} -975093. q^{26} -5.35330e6i q^{27} -614656. i q^{28} -6.73993e6 q^{29} +2.98262e6 q^{31} -1.04858e6i q^{32} -6.90287e6i q^{33} -5.74188e6 q^{34} +1.05860e7 q^{36} -3.49582e6i q^{37} -6.26549e6i q^{38} +1.50562e7 q^{39} +3.43724e7 q^{41} +9.49075e6i q^{42} +1.45085e7i q^{43} +7.15288e6 q^{44} +4.84631e6 q^{46} -2.76485e7i q^{47} +1.61908e7i q^{48} -5.76480e6 q^{49} +8.86589e7 q^{51} +1.56015e7i q^{52} +2.39217e7i q^{53} -8.56529e7 q^{54} -9.83450e6 q^{56} +9.67439e7i q^{57} +1.07839e8i q^{58} +1.20580e8 q^{59} +7.23140e7 q^{61} -4.77219e7i q^{62} -9.92855e7i q^{63} -1.67772e7 q^{64} -1.10446e8 q^{66} +8.70377e7i q^{67} +9.18701e7i q^{68} -7.48307e7 q^{69} +2.19622e8 q^{71} -1.69377e8i q^{72} -2.67792e8i q^{73} -5.59331e7 q^{74} -1.00248e8 q^{76} -6.70862e7i q^{77} -2.40899e8i q^{78} -2.85350e7 q^{79} +5.08619e8 q^{81} -5.49959e8i q^{82} +3.83237e8i q^{83} +1.51852e8 q^{84} +2.32136e8 q^{86} -1.66511e9i q^{87} -1.14446e8i q^{88} -7.21581e8 q^{89} +1.46325e8 q^{91} -7.75410e7i q^{92} +7.36861e8i q^{93} -4.42377e8 q^{94} +2.59053e8 q^{96} -6.73736e8i q^{97} +9.22368e7i q^{98} +1.15541e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1024 q^{4} + 448 q^{6} - 151964 q^{9}+O(q^{10}) \) 4 * q - 1024 * q^4 + 448 * q^6 - 151964 * q^9	\( 4 q - 1024 q^{4} + 448 q^{6} - 151964 q^{9} + 89880 q^{11} + 153664 q^{14} + 262144 q^{16} - 1017548 q^{19} - 67228 q^{21} - 114688 q^{24} - 3209024 q^{26} - 4012656 q^{29} + 4377464 q^{31} - 27853056 q^{34} + 38902784 q^{36} + 11776448 q^{39} + 38033184 q^{41} - 23009280 q^{44} - 2553600 q^{46} - 23059204 q^{49} - 61113288 q^{51} - 59833984 q^{54} - 39337984 q^{56} + 267284724 q^{59} + 455603372 q^{61} - 67108864 q^{64} - 764413440 q^{66} - 328036800 q^{69} - 335971440 q^{71} - 663154432 q^{74} + 260492288 q^{76} - 539285552 q^{79} + 1277652956 q^{81} + 17210368 q^{84} - 134198912 q^{86} - 1583315496 q^{89} + 481554164 q^{91} - 2385360768 q^{94} + 29360128 q^{96} - 2736961080 q^{99}+O(q^{100}) \) 4 * q - 1024 * q^4 + 448 * q^6 - 151964 * q^9 + 89880 * q^11 + 153664 * q^14 + 262144 * q^16 - 1017548 * q^19 - 67228 * q^21 - 114688 * q^24 - 3209024 * q^26 - 4012656 * q^29 + 4377464 * q^31 - 27853056 * q^34 + 38902784 * q^36 + 11776448 * q^39 + 38033184 * q^41 - 23009280 * q^44 - 2553600 * q^46 - 23059204 * q^49 - 61113288 * q^51 - 59833984 * q^54 - 39337984 * q^56 + 267284724 * q^59 + 455603372 * q^61 - 67108864 * q^64 - 764413440 * q^66 - 328036800 * q^69 - 335971440 * q^71 - 663154432 * q^74 + 260492288 * q^76 - 539285552 * q^79 + 1277652956 * q^81 + 17210368 * q^84 - 134198912 * q^86 - 1583315496 * q^89 + 481554164 * q^91 - 2385360768 * q^94 + 29360128 * q^96 - 2736961080 * q^99

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