LMFDB - Embedded newform 25.18.b.b.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,18,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	25.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:	$45.8055218361$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{39})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 19x^{2} + 100 $ x^4 - 19*x^2 + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$3.12250 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.18.b.b.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-564.820i q^{2} -17180.6i q^{3} -187950. q^{4} -9.70397e6 q^{6} +2.21307e7i q^{7} +3.21256e7i q^{8} -1.66034e8 q^{9} +O(q^{10})$	\(q-564.820i q^{2} -17180.6i q^{3} -187950. q^{4} -9.70397e6 q^{6} +2.21307e7i q^{7} +3.21256e7i q^{8} -1.66034e8 q^{9} -7.27892e8 q^{11} +3.22909e9i q^{12} +3.52539e9i q^{13} +1.24998e10 q^{14} -6.48976e9 q^{16} -3.37530e10i q^{17} +9.37794e10i q^{18} +7.67459e10 q^{19} +3.80219e11 q^{21} +4.11128e11i q^{22} +5.48049e10i q^{23} +5.51938e11 q^{24} +1.99121e12 q^{26} +6.33861e11i q^{27} -4.15945e12i q^{28} +2.43412e12 q^{29} -8.21245e11 q^{31} +7.87631e12i q^{32} +1.25056e13i q^{33} -1.90644e13 q^{34} +3.12060e13 q^{36} +2.72120e13i q^{37} -4.33476e13i q^{38} +6.05685e13 q^{39} -7.17143e13 q^{41} -2.14755e14i q^{42} +2.55305e13i q^{43} +1.36807e14 q^{44} +3.09549e13 q^{46} -3.00475e12i q^{47} +1.11498e14i q^{48} -2.57136e14 q^{49} -5.79898e14 q^{51} -6.62596e14i q^{52} -6.88051e13i q^{53} +3.58017e14 q^{54} -7.10960e14 q^{56} -1.31854e15i q^{57} -1.37484e15i q^{58} +8.49663e14 q^{59} +1.42806e15 q^{61} +4.63855e14i q^{62} -3.67444e15i q^{63} +3.59807e15 q^{64} +7.06343e15 q^{66} +1.19425e15i q^{67} +6.34386e15i q^{68} +9.41583e14 q^{69} -1.19599e15 q^{71} -5.33394e15i q^{72} +9.91346e15i q^{73} +1.53699e16 q^{74} -1.44244e16 q^{76} -1.61087e16i q^{77} -3.42103e16i q^{78} -7.23279e15 q^{79} -1.05515e16 q^{81} +4.05057e16i q^{82} +2.82999e16i q^{83} -7.14620e16 q^{84} +1.44201e16 q^{86} -4.18197e16i q^{87} -2.33839e16i q^{88} -5.95425e15 q^{89} -7.80193e16 q^{91} -1.03006e16i q^{92} +1.41095e16i q^{93} -1.69714e15 q^{94} +1.35320e17 q^{96} +1.10249e17i q^{97} +1.45235e17i q^{98} +1.20855e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 140288 q^{4} - 17979552 q^{6} - 150683652 q^{9}+O(q^{10}) $ 4 * q - 140288 * q^4 - 17979552 * q^6 - 150683652 * q^9	$ 4 q - 140288 q^{4} - 17979552 q^{6} - 150683652 q^{9} - 2106710912 q^{11} + 25158636384 q^{14} + 11299057664 q^{16} - 13932982000 q^{19} + 751880425968 q^{21} + 1459367193600 q^{24} + 2793118146208 q^{26} + 8379197473000 q^{29} + 9224644833648 q^{31} - 40785137598496 q^{34} + 83780175135744 q^{36} + 185162581193616 q^{39} - 290945462384872 q^{41} + 196930878705664 q^{44} + 65916842739168 q^{46} - 49962773891828 q^{49} - 10\!\cdots\!92 q^{51}+ \cdots + 18\!\cdots\!56 q^{99}+O(q^{100}) $ 4 * q - 140288 * q^4 - 17979552 * q^6 - 150683652 * q^9 - 2106710912 * q^11 + 25158636384 * q^14 + 11299057664 * q^16 - 13932982000 * q^19 + 751880425968 * q^21 + 1459367193600 * q^24 + 2793118146208 * q^26 + 8379197473000 * q^29 + 9224644833648 * q^31 - 40785137598496 * q^34 + 83780175135744 * q^36 + 185162581193616 * q^39 - 290945462384872 * q^41 + 196930878705664 * q^44 + 65916842739168 * q^46 - 49962773891828 * q^49 - 1016789632544592 * q^51 + 1030039118827200 * q^54 - 1382359734604800 * q^56 + 6204826596098000 * q^59 + 927103175732488 * q^61 + 9190765145096192 * q^64 + 13661983636217856 * q^66 + 1667450401893936 * q^69 + 10242354790380368 * q^71 + 30129336083208544 * q^74 - 48572297066598400 * q^76 + 5218668194316000 * q^79 - 14583217294565676 * q^81 - 143932036192874496 * q^84 + 11392902743358688 * q^86 - 122385728353281000 * q^89 - 148913569441199472 * q^91 - 51660993199829536 * q^94 + 334574484314554368 * q^96 + 182675519501302656 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 564.820i	− 1.56011i	−0.625711	−	0.780055i	$-0.715191\pi$
$2$	− 564.820i	− 1.56011i	0.625711	−	0.780055i	$-0.284809\pi$
$3$	− 17180.6i	− 1.51185i	−0.654658	−	0.755925i	$-0.727188\pi$
$3$	− 17180.6i	− 1.51185i	0.654658	−	0.755925i	$-0.272812\pi$
$4$	−187950.	−1.43394
$5$	0	0
$5$	0	0
$6$	−9.70397e6	−2.35865
$7$	2.21307e7i	1.45098i	0.688233	+	0.725489i	$0.258387\pi$
$7$	2.21307e7i	1.45098i	−0.688233	+	0.725489i	$0.741613\pi$
$8$	3.21256e7i	0.676996i
$9$	−1.66034e8	−1.28569
$10$	0	0
$11$	−7.27892e8	−1.02383	−0.511916	−	0.859035i	$-0.671064\pi$
$11$	−7.27892e8	−1.02383	−0.511916	+	0.859035i	$0.671064\pi$
$12$	3.22909e9i	2.16790i
$13$	3.52539e9i	1.19864i	0.800509	+	0.599321i	$0.204563\pi$
$13$	3.52539e9i	1.19864i	−0.800509	+	0.599321i	$0.795437\pi$
$14$	1.24998e10	2.26369
$15$	0	0
$16$	−6.48976e9	−0.377754
$17$	− 3.37530e10i	− 1.17354i	−0.809755	−	0.586768i	$-0.800400\pi$
$17$	− 3.37530e10i	− 1.17354i	0.809755	−	0.586768i	$-0.199600\pi$
$18$	9.37794e10i	2.00582i
$19$	7.67459e10	1.03669	0.518346	−	0.855171i	$-0.326548\pi$
$19$	7.67459e10	1.03669	0.518346	+	0.855171i	$0.326548\pi$
$20$	0	0
$21$	3.80219e11	2.19366
$22$	4.11128e11i	1.59729i
$23$	5.48049e10i	0.145926i	0.997335	+	0.0729630i	$0.0232455\pi$
$23$	5.48049e10i	0.145926i	−0.997335	+	0.0729630i	$0.976754\pi$
$24$	5.51938e11	1.02352
$25$	0	0
$26$	1.99121e12	1.87001
$27$	6.33861e11i	0.431919i
$28$	− 4.15945e12i	− 2.08062i
$29$	2.43412e12	0.903564	0.451782	−	0.892128i	$-0.350788\pi$
$29$	2.43412e12	0.903564	0.451782	+	0.892128i	$0.350788\pi$
$30$	0	0
$31$	−8.21245e11	−0.172941	−0.0864705	−	0.996254i	$-0.527559\pi$
$31$	−8.21245e11	−0.172941	−0.0864705	+	0.996254i	$0.527559\pi$
$32$	7.87631e12i	1.26633i
$33$	1.25056e13i	1.54788i
$34$	−1.90644e13	−1.83084
$35$	0	0
$36$	3.12060e13	1.84360
$37$	2.72120e13i	1.27364i	0.771013	+	0.636819i	$0.219750\pi$
$37$	2.72120e13i	1.27364i	−0.771013	+	0.636819i	$0.780250\pi$
$38$	− 4.33476e13i	− 1.61735i
$39$	6.05685e13	1.81217
$40$	0	0
$41$	−7.17143e13	−1.40263	−0.701315	−	0.712852i	$-0.747403\pi$
$41$	−7.17143e13	−1.40263	−0.701315	+	0.712852i	$0.747403\pi$
$42$	− 2.14755e14i	− 3.42235i
$43$	2.55305e13i	0.333102i	0.986033	+	0.166551i	$0.0532631\pi$
$43$	2.55305e13i	0.333102i	−0.986033	+	0.166551i	$0.946737\pi$
$44$	1.36807e14	1.46812
$45$	0	0
$46$	3.09549e13	0.227661
$47$	− 3.00475e12i	− 0.0184067i	−0.999958	−	0.00920335i	$-0.997070\pi$
$47$	− 3.00475e12i	− 0.0184067i	0.999958	−	0.00920335i	$-0.00292956\pi$
$48$	1.11498e14i	0.571107i
$49$	−2.57136e14	−1.10534
$50$	0	0
$51$	−5.79898e14	−1.77421
$52$	− 6.62596e14i	− 1.71878i
$53$	− 6.88051e13i	− 0.151801i	−0.997115	−	0.0759006i	$-0.975817\pi$
$53$	− 6.88051e13i	− 0.151801i	0.997115	−	0.0759006i	$-0.0241832\pi$
$54$	3.58017e14	0.673841
$55$	0	0
$56$	−7.10960e14	−0.982307
$57$	− 1.31854e15i	− 1.56732i
$58$	− 1.37484e15i	− 1.40966i
$59$	8.49663e14	0.753364	0.376682	−	0.926343i	$-0.377065\pi$
$59$	8.49663e14	0.753364	0.376682	+	0.926343i	$0.377065\pi$
$60$	0	0
$61$	1.42806e15	0.953770	0.476885	−	0.878966i	$-0.341766\pi$
$61$	1.42806e15	0.953770	0.476885	+	0.878966i	$0.341766\pi$
$62$	4.63855e14i	0.269807i
$63$	− 3.67444e15i	− 1.86551i
$64$	3.59807e15	1.59786
$65$	0	0
$66$	7.06343e15	2.41486
$67$	1.19425e15i	0.359303i	0.983730	+	0.179651i	$0.0574970\pi$
$67$	1.19425e15i	0.359303i	−0.983730	+	0.179651i	$0.942503\pi$
$68$	6.34386e15i	1.68278i
$69$	9.41583e14	0.220618
$70$	0	0
$71$	−1.19599e15	−0.219802	−0.109901	−	0.993943i	$-0.535053\pi$
$71$	−1.19599e15	−0.219802	−0.109901	+	0.993943i	$0.535053\pi$
$72$	− 5.33394e15i	− 0.870406i
$73$	9.91346e15i	1.43873i	0.694630	+	0.719367i	$0.255568\pi$
$73$	9.91346e15i	1.43873i	−0.694630	+	0.719367i	$0.744432\pi$
$74$	1.53699e16	1.98702
$75$	0	0
$76$	−1.44244e16	−1.48656
$77$	− 1.61087e16i	− 1.48556i
$78$	− 3.42103e16i	− 2.82718i
$79$	−7.23279e15	−0.536384	−0.268192	−	0.963366i	$-0.586426\pi$
$79$	−7.23279e15	−0.536384	−0.268192	+	0.963366i	$0.586426\pi$
$80$	0	0
$81$	−1.05515e16	−0.632693
$82$	4.05057e16i	2.18825i
$83$	2.82999e16i	1.37918i	0.724200	+	0.689590i	$0.242209\pi$
$83$	2.82999e16i	1.37918i	−0.724200	+	0.689590i	$0.757791\pi$
$84$	−7.14620e16	−3.14558
$85$	0	0
$86$	1.44201e16	0.519676
$87$	− 4.18197e16i	− 1.36605i
$88$	− 2.33839e16i	− 0.693130i
$89$	−5.95425e15	−0.160329	−0.0801645	−	0.996782i	$-0.525545\pi$
$89$	−5.95425e15	−0.160329	−0.0801645	+	0.996782i	$0.525545\pi$
$90$	0	0
$91$	−7.80193e16	−1.73920
$92$	− 1.03006e16i	− 0.209249i
$93$	1.41095e16i	0.261461i
$94$	−1.69714e15	−0.0287165
$95$	0	0
$96$	1.35320e17	1.91450
$97$	1.10249e17i	1.42829i	0.700000	+	0.714143i	$0.253183\pi$
$97$	1.10249e17i	1.42829i	−0.700000	+	0.714143i	$0.746817\pi$
$98$	1.45235e17i	1.72445i
$99$	1.20855e17	1.31633
$100$	0	0
$101$	5.19625e16	0.477483	0.238742	−	0.971083i	$-0.423265\pi$
$101$	5.19625e16	0.477483	0.238742	+	0.971083i	$0.423265\pi$
$102$	3.27538e17i	2.76796i
$103$	7.41468e16i	0.576734i	0.957520	+	0.288367i	$0.0931124\pi$
$103$	7.41468e16i	0.576734i	−0.957520	+	0.288367i	$0.906888\pi$
$104$	−1.13255e17	−0.811475
$105$	0	0
$106$	−3.88625e16	−0.236827
$107$	9.50480e16i	0.534787i	0.963587	+	0.267393i	$0.0861624\pi$
$107$	9.50480e16i	0.534787i	−0.963587	+	0.267393i	$0.913838\pi$
$108$	− 1.19134e17i	− 0.619346i
$109$	5.57380e16	0.267933	0.133967	−	0.990986i	$-0.457229\pi$
$109$	5.57380e16	0.267933	0.133967	+	0.990986i	$0.457229\pi$
$110$	0	0
$111$	4.67520e17	1.92555
$112$	− 1.43623e17i	− 0.548113i
$113$	− 3.30512e17i	− 1.16956i	−0.811194	−	0.584778i	$-0.801182\pi$
$113$	− 3.30512e17i	− 1.16956i	0.811194	−	0.584778i	$-0.198818\pi$
$114$	−7.44740e17	−2.44519
$115$	0	0
$116$	−4.57492e17	−1.29566
$117$	− 5.85336e17i	− 1.54108i
$118$	− 4.79907e17i	− 1.17533i
$119$	7.46976e17	1.70278
$120$	0	0
$121$	2.43791e16	0.0482327
$122$	− 8.06598e17i	− 1.48799i
$123$	1.23210e18i	2.12056i
$124$	1.54353e17	0.247987
$125$	0	0
$126$	−2.07540e18	−2.91040
$127$	1.41324e18i	1.85304i	0.376241	+	0.926522i	$0.377216\pi$
$127$	1.41324e18i	1.85304i	−0.376241	+	0.926522i	$0.622784\pi$
$128$	− 9.99898e17i	− 1.22651i
$129$	4.38630e17	0.503600
$130$	0	0
$131$	4.77855e17	0.481382	0.240691	−	0.970602i	$-0.422626\pi$
$131$	4.77855e17	0.481382	0.240691	+	0.970602i	$0.422626\pi$
$132$	− 2.35043e18i	− 2.21957i
$133$	1.69844e18i	1.50422i
$134$	6.74538e17	0.560552
$135$	0	0
$136$	1.08433e18	0.794479
$137$	− 2.70610e18i	− 1.86303i	−0.363707	−	0.931514i	$-0.618489\pi$
$137$	− 2.70610e18i	− 1.86303i	0.363707	−	0.931514i	$-0.381511\pi$
$138$	− 5.31825e17i	− 0.344189i
$139$	1.60721e18	0.978241	0.489121	−	0.872216i	$-0.337318\pi$
$139$	1.60721e18	0.978241	0.489121	+	0.872216i	$0.337318\pi$
$140$	0	0
$141$	−5.16235e16	−0.0278282
$142$	6.75518e17i	0.342914i
$143$	− 2.56610e18i	− 1.22721i
$144$	1.07752e18	0.485674
$145$	0	0
$146$	5.59932e18	2.24458
$147$	4.41776e18i	1.67111i
$148$	− 5.11449e18i	− 1.82632i
$149$	−5.89349e17	−0.198742	−0.0993710	−	0.995050i	$-0.531683\pi$
$149$	−5.89349e17	−0.198742	−0.0993710	+	0.995050i	$0.531683\pi$
$150$	0	0
$151$	1.52832e18	0.460160	0.230080	−	0.973172i	$-0.426101\pi$
$151$	1.52832e18	0.460160	0.230080	+	0.973172i	$0.426101\pi$
$152$	2.46551e18i	0.701836i
$153$	5.60415e18i	1.50880i
$154$	−9.09853e18	−2.31763
$155$	0	0
$156$	−1.13838e19	−2.59854
$157$	3.25942e18i	0.704681i	0.935872	+	0.352341i	$0.114614\pi$
$157$	3.25942e18i	0.704681i	−0.935872	+	0.352341i	$0.885386\pi$
$158$	4.08522e18i	0.836817i
$159$	−1.18211e18	−0.229501
$160$	0	0
$161$	−1.21287e18	−0.211736
$162$	5.95971e18i	0.987070i
$163$	− 3.44735e18i	− 0.541865i	−0.962598	−	0.270933i	$-0.912668\pi$
$163$	− 3.44735e18i	− 0.541865i	0.962598	−	0.270933i	$-0.0873321\pi$
$164$	1.34787e19	2.01129
$165$	0	0
$166$	1.59843e19	2.15167
$167$	− 9.63268e18i	− 1.23213i	−0.787695	−	0.616066i	$-0.788726\pi$
$167$	− 9.63268e18i	− 1.23213i	0.787695	−	0.616066i	$-0.211274\pi$
$168$	1.22147e19i	1.48510i
$169$	−3.77799e18	−0.436741
$170$	0	0
$171$	−1.27424e19	−1.33286
$172$	− 4.79845e18i	− 0.477649i
$173$	1.48938e18i	0.141128i	0.997507	+	0.0705638i	$0.0224799\pi$
$173$	1.48938e18i	0.141128i	−0.997507	+	0.0705638i	$0.977520\pi$
$174$	−2.36206e19	−2.13119
$175$	0	0
$176$	4.72384e18	0.386756
$177$	− 1.45978e19i	− 1.13897i
$178$	3.36308e18i	0.250131i
$179$	−1.51604e18	−0.107513	−0.0537565	−	0.998554i	$-0.517119\pi$
$179$	−1.51604e18	−0.107513	−0.0537565	+	0.998554i	$0.517119\pi$
$180$	0	0
$181$	−2.24522e19	−1.44874	−0.724370	−	0.689411i	$-0.757869\pi$
$181$	−2.24522e19	−1.44874	−0.724370	+	0.689411i	$0.757869\pi$
$182$	4.40669e19i	2.71335i
$183$	− 2.45350e19i	− 1.44196i
$184$	−1.76064e18	−0.0987913
$185$	0	0
$186$	7.96933e18	0.407908
$187$	2.45685e19i	1.20150i
$188$	5.64741e17i	0.0263941i
$189$	−1.40278e19	−0.626705
$190$	0	0
$191$	−1.34669e19	−0.550156	−0.275078	−	0.961422i	$-0.588704\pi$
$191$	−1.34669e19	−0.550156	−0.275078	+	0.961422i	$0.588704\pi$
$192$	− 6.18171e19i	− 2.41573i
$193$	2.95630e19i	1.10538i	0.833387	+	0.552690i	$0.186399\pi$
$193$	2.95630e19i	1.10538i	−0.833387	+	0.552690i	$0.813601\pi$
$194$	6.22709e19	2.22828
$195$	0	0
$196$	4.83285e19	1.58499
$197$	2.82885e19i	0.888478i	0.895908	+	0.444239i	$0.146526\pi$
$197$	2.82885e19i	0.888478i	−0.895908	+	0.444239i	$0.853474\pi$
$198$	− 6.82612e19i	− 2.05362i
$199$	−4.75300e19	−1.36999	−0.684993	−	0.728549i	$-0.740195\pi$
$199$	−4.75300e19	−1.36999	−0.684993	+	0.728549i	$0.740195\pi$
$200$	0	0
$201$	2.05180e19	0.543212
$202$	− 2.93494e19i	− 0.744926i
$203$	5.38687e19i	1.31105i
$204$	1.08992e20	2.54411
$205$	0	0
$206$	4.18796e19	0.899769
$207$	− 9.09948e18i	− 0.187616i
$208$	− 2.28790e19i	− 0.452791i
$209$	−5.58627e19	−1.06140
$210$	0	0
$211$	−7.04136e19	−1.23383	−0.616916	−	0.787029i	$-0.711618\pi$
$211$	−7.04136e19	−1.23383	−0.616916	+	0.787029i	$0.711618\pi$
$212$	1.29319e19i	0.217674i
$213$	2.05478e19i	0.332307i
$214$	5.36850e19	0.834326
$215$	0	0
$216$	−2.03632e19	−0.292407
$217$	− 1.81747e19i	− 0.250934i
$218$	− 3.14819e19i	− 0.418005i
$219$	1.70319e20	2.17515
$220$	0	0
$221$	1.18993e20	1.40665
$222$	− 2.64065e20i	− 3.00407i
$223$	− 1.73587e20i	− 1.90075i	−0.311107	−	0.950375i	$-0.600700\pi$
$223$	− 1.73587e20i	− 1.90075i	0.311107	−	0.950375i	$-0.399300\pi$
$224$	−1.74308e20	−1.83742
$225$	0	0
$226$	−1.86680e20	−1.82463
$227$	2.97928e19i	0.280474i	0.990118	+	0.140237i	$0.0447864\pi$
$227$	2.97928e19i	0.280474i	−0.990118	+	0.140237i	$0.955214\pi$
$228$	2.47820e20i	2.24745i
$229$	7.83039e19	0.684198	0.342099	−	0.939664i	$-0.388862\pi$
$229$	7.83039e19	0.684198	0.342099	+	0.939664i	$0.388862\pi$
$230$	0	0
$231$	−2.76758e20	−2.24594
$232$	7.81975e19i	0.611709i
$233$	1.73319e20i	1.30714i	0.756868	+	0.653568i	$0.226729\pi$
$233$	1.73319e20i	1.30714i	−0.756868	+	0.653568i	$0.773271\pi$
$234$	−3.30609e20	−2.40425
$235$	0	0
$236$	−1.59694e20	−1.08028
$237$	1.24264e20i	0.810932i
$238$	− 4.21907e20i	− 2.65652i
$239$	−1.81871e20	−1.10505	−0.552524	−	0.833497i	$-0.686335\pi$
$239$	−1.81871e20	−1.10505	−0.552524	+	0.833497i	$0.686335\pi$
$240$	0	0
$241$	2.82549e20	1.59937	0.799685	−	0.600420i	$-0.205000\pi$
$241$	2.82549e20	1.59937	0.799685	+	0.600420i	$0.205000\pi$
$242$	− 1.37698e19i	− 0.0752484i
$243$	2.63139e20i	1.38846i
$244$	−2.68404e20	−1.36765
$245$	0	0
$246$	6.95913e20	3.30831
$247$	2.70560e20i	1.24262i
$248$	− 2.63830e19i	− 0.117080i
$249$	4.86210e20	2.08511
$250$	0	0
$251$	2.26036e19	0.0905629	0.0452814	−	0.998974i	$-0.485582\pi$
$251$	2.26036e19	0.0905629	0.0452814	+	0.998974i	$0.485582\pi$
$252$	6.90610e20i	2.67503i
$253$	− 3.98920e19i	− 0.149404i
$254$	7.98228e20	2.89095
$255$	0	0
$256$	−9.31562e19	−0.315626
$257$	− 1.93339e20i	− 0.633706i	−0.948475	−	0.316853i	$-0.897374\pi$
$257$	− 1.93339e20i	− 0.633706i	0.948475	−	0.316853i	$-0.102626\pi$
$258$	− 2.47747e20i	− 0.785672i
$259$	−6.02220e20	−1.84802
$260$	0	0
$261$	−4.04147e20	−1.16170
$262$	− 2.69902e20i	− 0.751009i
$263$	6.89343e20i	1.85700i	0.371335	+	0.928499i	$0.378900\pi$
$263$	6.89343e20i	1.85700i	−0.371335	+	0.928499i	$0.621100\pi$
$264$	−4.01751e20	−1.04791
$265$	0	0
$266$	9.59312e20	2.34674
$267$	1.02298e20i	0.242393i
$268$	− 2.24459e20i	− 0.515219i
$269$	8.00029e20	1.77915	0.889573	−	0.456794i	$-0.151002\pi$
$269$	8.00029e20	1.77915	0.889573	+	0.456794i	$0.151002\pi$
$270$	0	0
$271$	−4.68195e20	−0.977660	−0.488830	−	0.872379i	$-0.662576\pi$
$271$	−4.68195e20	−0.977660	−0.488830	+	0.872379i	$0.662576\pi$
$272$	2.19049e20i	0.443308i
$273$	1.34042e21i	2.62941i
$274$	−1.52846e21	−2.90653
$275$	0	0
$276$	−1.76970e20	−0.316354
$277$	1.67513e19i	0.0290383i	0.999895	+	0.0145192i	$0.00462175\pi$
$277$	1.67513e19i	0.0290383i	−0.999895	+	0.0145192i	$0.995378\pi$
$278$	− 9.07782e20i	− 1.52616i
$279$	1.36355e20	0.222348
$280$	0	0
$281$	−1.16305e21	−1.78482	−0.892409	−	0.451227i	$-0.850987\pi$
$281$	−1.16305e21	−1.78482	−0.892409	+	0.451227i	$0.850987\pi$
$282$	2.91580e19i	0.0434150i
$283$	− 1.10305e21i	− 1.59371i	−0.604172	−	0.796854i	$-0.706496\pi$
$283$	− 1.10305e21i	− 1.59371i	0.604172	−	0.796854i	$-0.293504\pi$
$284$	2.24785e20	0.315183
$285$	0	0
$286$	−1.44939e21	−1.91458
$287$	− 1.58708e21i	− 2.03519i
$288$	− 1.30774e21i	− 1.62811i
$289$	−3.12024e20	−0.377187
$290$	0	0
$291$	1.89415e21	2.15935
$292$	− 1.86323e21i	− 2.06306i
$293$	3.88758e20i	0.418124i	0.977902	+	0.209062i	$0.0670410\pi$
$293$	3.88758e20i	0.418124i	−0.977902	+	0.209062i	$0.932959\pi$
$294$	2.49524e21	2.60711
$295$	0	0
$296$	−8.74202e20	−0.862248
$297$	− 4.61382e20i	− 0.442213i
$298$	3.32876e20i	0.310059i
$299$	−1.93209e20	−0.174913
$300$	0	0
$301$	−5.65007e20	−0.483324
$302$	− 8.63223e20i	− 0.717900i
$303$	− 8.92749e20i	− 0.721883i
$304$	−4.98063e20	−0.391614
$305$	0	0
$306$	3.16533e21	2.35390
$307$	1.80153e21i	1.30306i	0.758621	+	0.651532i	$0.225873\pi$
$307$	1.80153e21i	1.30306i	−0.758621	+	0.651532i	$0.774127\pi$
$308$	3.02763e21i	2.13020i
$309$	1.27389e21	0.871935
$310$	0	0
$311$	−8.62093e20	−0.558587	−0.279293	−	0.960206i	$-0.590100\pi$
$311$	−8.62093e20	−0.558587	−0.279293	+	0.960206i	$0.590100\pi$
$312$	1.94580e21i	1.22683i
$313$	1.32283e21i	0.811668i	0.913947	+	0.405834i	$0.133019\pi$
$313$	1.32283e21i	0.811668i	−0.913947	+	0.405834i	$0.866981\pi$
$314$	1.84098e21	1.09938
$315$	0	0
$316$	1.35940e21	0.769143
$317$	1.89123e21i	1.04169i	0.853650	+	0.520847i	$0.174384\pi$
$317$	1.89123e21i	1.04169i	−0.853650	+	0.520847i	$0.825616\pi$
$318$	6.67682e20i	0.358046i
$319$	−1.77178e21	−0.925098
$320$	0	0
$321$	1.63298e21	0.808517
$322$	6.85053e20i	0.330331i
$323$	− 2.59040e21i	− 1.21660i
$324$	1.98316e21	0.907244
$325$	0	0
$326$	−1.94713e21	−0.845369
$327$	− 9.57615e20i	− 0.405075i
$328$	− 2.30386e21i	− 0.949574i
$329$	6.64970e19	0.0267077
$330$	0	0
$331$	9.83194e18	0.00375060	0.00187530	−	0.999998i	$-0.499403\pi$
$331$	9.83194e18	0.00375060	0.00187530	+	0.999998i	$0.499403\pi$
$332$	− 5.31895e21i	− 1.97766i
$333$	− 4.51813e21i	− 1.63750i
$334$	−5.44073e21	−1.92226
$335$	0	0
$336$	−2.46753e21	−0.828664
$337$	3.22406e21i	1.05572i	0.849331	+	0.527861i	$0.177006\pi$
$337$	3.22406e21i	1.05572i	−0.849331	+	0.527861i	$0.822994\pi$
$338$	2.13388e21i	0.681364i
$339$	−5.67841e21	−1.76819
$340$	0	0
$341$	5.97777e20	0.177063
$342$	7.19718e21i	2.07941i
$343$	− 5.42317e20i	− 0.152846i
$344$	−8.20182e20	−0.225509
$345$	0	0
$346$	8.41229e20	0.220175
$347$	4.53030e21i	1.15698i	0.815689	+	0.578490i	$0.196358\pi$
$347$	4.53030e21i	1.15698i	−0.815689	+	0.578490i	$0.803642\pi$
$348$	7.86000e21i	1.95884i
$349$	4.45189e21	1.08275	0.541375	−	0.840781i	$-0.317904\pi$
$349$	4.45189e21	1.08275	0.541375	+	0.840781i	$0.317904\pi$
$350$	0	0
$351$	−2.23461e21	−0.517716
$352$	− 5.73310e21i	− 1.29651i
$353$	5.07798e21i	1.12100i	0.828154	+	0.560501i	$0.189391\pi$
$353$	5.07798e21i	1.12100i	−0.828154	+	0.560501i	$0.810609\pi$
$354$	−8.24510e21	−1.77692
$355$	0	0
$356$	1.11910e21	0.229902
$357$	− 1.28335e22i	− 2.57434i
$358$	8.56292e20i	0.167732i
$359$	−7.66889e21	−1.46700	−0.733500	−	0.679690i	$-0.762114\pi$
$359$	−7.66889e21	−1.46700	−0.733500	+	0.679690i	$0.762114\pi$
$360$	0	0
$361$	4.09550e20	0.0747301
$362$	1.26814e22i	2.26019i
$363$	− 4.18848e20i	− 0.0729207i
$364$	1.46637e22	2.49392
$365$	0	0
$366$	−1.38579e22	−2.24961
$367$	− 4.94937e21i	− 0.785033i	−0.919745	−	0.392517i	$-0.871605\pi$
$367$	− 4.94937e21i	− 0.785033i	0.919745	−	0.392517i	$-0.128395\pi$
$368$	− 3.55671e20i	− 0.0551241i
$369$	1.19070e22	1.80335
$370$	0	0
$371$	1.52270e21	0.220260
$372$	− 2.65188e21i	− 0.374920i
$373$	− 3.93321e21i	− 0.543528i	−0.962364	−	0.271764i	$-0.912393\pi$
$373$	− 3.93321e21i	− 0.543528i	0.962364	−	0.271764i	$-0.0876069\pi$
$374$	1.38768e22	1.87448
$375$	0	0
$376$	9.65292e19	0.0124613
$377$	8.58124e21i	1.08305i
$378$	7.92316e21i	0.977729i
$379$	−1.21415e22	−1.46501	−0.732504	−	0.680763i	$-0.761648\pi$
$379$	−1.21415e22	−1.46501	−0.732504	+	0.680763i	$0.761648\pi$
$380$	0	0
$381$	2.42804e22	2.80152
$382$	7.60640e21i	0.858303i
$383$	− 1.46593e22i	− 1.61779i	−0.587952	−	0.808896i	$-0.700066\pi$
$383$	− 1.46593e22i	− 1.61779i	0.587952	−	0.808896i	$-0.299934\pi$
$384$	−1.71789e22	−1.85430
$385$	0	0
$386$	1.66978e22	1.72451
$387$	− 4.23893e21i	− 0.428266i
$388$	− 2.07213e22i	− 2.04808i
$389$	−1.63955e22	−1.58545	−0.792725	−	0.609579i	$-0.791338\pi$
$389$	−1.63955e22	−1.58545	−0.792725	+	0.609579i	$0.791338\pi$
$390$	0	0
$391$	1.84983e21	0.171249
$392$	− 8.26063e21i	− 0.748310i
$393$	− 8.20986e21i	− 0.727778i
$394$	1.59779e22	1.38612
$395$	0	0
$396$	−2.27146e22	−1.88754
$397$	3.76489e21i	0.306219i	0.988209	+	0.153110i	$0.0489288\pi$
$397$	3.76489e21i	0.306219i	−0.988209	+	0.153110i	$0.951071\pi$
$398$	2.68459e22i	2.13733i
$399$	2.91802e22	2.27415
$400$	0	0
$401$	−8.98376e21	−0.671013	−0.335506	−	0.942038i	$-0.608907\pi$
$401$	−8.98376e21	−0.671013	−0.335506	+	0.942038i	$0.608907\pi$
$402$	− 1.15890e22i	− 0.847470i
$403$	− 2.89521e21i	− 0.207294i
$404$	−9.76633e21	−0.684683
$405$	0	0
$406$	3.04261e22	2.04539
$407$	− 1.98074e22i	− 1.30399i
$408$	− 1.86296e22i	− 1.20113i
$409$	2.74380e22	1.73262	0.866311	−	0.499505i	$-0.166485\pi$
$409$	2.74380e22	1.73262	0.866311	+	0.499505i	$0.166485\pi$
$410$	0	0
$411$	−4.64925e22	−2.81662
$412$	− 1.39359e22i	− 0.827003i
$413$	1.88036e22i	1.09311i
$414$	−5.13957e21	−0.292701
$415$	0	0
$416$	−2.77671e22	−1.51788
$417$	− 2.76128e22i	− 1.47895i
$418$	3.15524e22i	1.65590i
$419$	5.84603e21	0.300636	0.150318	−	0.988638i	$-0.451970\pi$
$419$	5.84603e21	0.300636	0.150318	+	0.988638i	$0.451970\pi$
$420$	0	0
$421$	5.49695e21	0.271471	0.135736	−	0.990745i	$-0.456660\pi$
$421$	5.49695e21	0.271471	0.135736	+	0.990745i	$0.456660\pi$
$422$	3.97710e22i	1.92491i
$423$	4.98890e20i	0.0236653i
$424$	2.21040e21	0.102769
$425$	0	0
$426$	1.16058e22	0.518435
$427$	3.16040e22i	1.38390i
$428$	− 1.78642e22i	− 0.766853i
$429$	−4.40873e22	−1.85535
$430$	0	0
$431$	3.05715e22	1.23669	0.618343	−	0.785908i	$-0.287804\pi$
$431$	3.05715e22	1.23669	0.618343	+	0.785908i	$0.287804\pi$
$432$	− 4.11361e21i	− 0.163159i
$433$	3.52788e22i	1.37204i	0.727584	+	0.686019i	$0.240643\pi$
$433$	3.52788e22i	1.37204i	−0.727584	+	0.686019i	$0.759357\pi$
$434$	−1.02654e22	−0.391484
$435$	0	0
$436$	−1.04759e22	−0.384200
$437$	4.20605e21i	0.151280i
$438$	− 9.61998e22i	− 3.39347i
$439$	2.82873e22	0.978686	0.489343	−	0.872091i	$-0.337237\pi$
$439$	2.82873e22	0.978686	0.489343	+	0.872091i	$0.337237\pi$
$440$	0	0
$441$	4.26933e22	1.42112
$442$	− 6.72094e22i	− 2.19453i
$443$	2.21793e22i	0.710421i	0.934786	+	0.355211i	$0.115591\pi$
$443$	2.21793e22i	0.710421i	−0.934786	+	0.355211i	$0.884409\pi$
$444$	−8.78702e22	−2.76113
$445$	0	0
$446$	−9.80452e22	−2.96538
$447$	1.01254e22i	0.300468i
$448$	7.96277e22i	2.31847i
$449$	−2.11655e20	−0.00604692	−0.00302346	−	0.999995i	$-0.500962\pi$
$449$	−2.11655e20	−0.00604692	−0.00302346	+	0.999995i	$0.500962\pi$
$450$	0	0
$451$	5.22002e22	1.43606
$452$	6.21196e22i	1.67707i
$453$	− 2.62574e22i	− 0.695693i
$454$	1.68276e22	0.437570
$455$	0	0
$456$	4.23590e22	1.06107
$457$	2.66616e22i	0.655539i	0.944758	+	0.327770i	$0.106297\pi$
$457$	2.66616e22i	0.655539i	−0.944758	+	0.327770i	$0.893703\pi$
$458$	− 4.42276e22i	− 1.06742i
$459$	2.13947e22	0.506872
$460$	0	0
$461$	−3.51680e22	−0.802952	−0.401476	−	0.915869i	$-0.631503\pi$
$461$	−3.51680e22	−0.802952	−0.401476	+	0.915869i	$0.631503\pi$
$462$	1.56318e23i	3.50392i
$463$	− 6.26683e22i	− 1.37914i	−0.724217	−	0.689572i	$-0.757799\pi$
$463$	− 6.26683e22i	− 1.37914i	0.724217	−	0.689572i	$-0.242201\pi$
$464$	−1.57969e22	−0.341325
$465$	0	0
$466$	9.78940e22	2.03927
$467$	8.75525e21i	0.179092i	0.995983	+	0.0895458i	$0.0285415\pi$
$467$	8.75525e21i	0.179092i	−0.995983	+	0.0895458i	$0.971458\pi$
$468$	1.10014e23i	2.20982i
$469$	−2.64296e22	−0.521341
$470$	0	0
$471$	5.59988e22	1.06537
$472$	2.72959e22i	0.510024i
$473$	− 1.85834e22i	− 0.341041i
$474$	7.01868e22	1.26514
$475$	0	0
$476$	−1.40394e23	−2.44168
$477$	1.14240e22i	0.195169i
$478$	1.02724e23i	1.72400i
$479$	1.08139e22	0.178291	0.0891456	−	0.996019i	$-0.471586\pi$
$479$	1.08139e22	0.178291	0.0891456	+	0.996019i	$0.471586\pi$
$480$	0	0
$481$	−9.59331e22	−1.52664
$482$	− 1.59589e23i	− 2.49519i
$483$	2.08379e22i	0.320112i
$484$	−4.58204e21	−0.0691629
$485$	0	0
$486$	1.48626e23	2.16614
$487$	− 3.96471e22i	− 0.567826i	−0.958850	−	0.283913i	$-0.908367\pi$
$487$	− 3.96471e22i	− 0.567826i	0.958850	−	0.283913i	$-0.0916327\pi$
$488$	4.58773e22i	0.645698i
$489$	−5.92277e22	−0.819219
$490$	0	0
$491$	6.00195e22	0.801861	0.400931	−	0.916108i	$-0.368687\pi$
$491$	6.00195e22	0.801861	0.400931	+	0.916108i	$0.368687\pi$
$492$	− 2.31572e23i	− 3.04076i
$493$	− 8.21588e22i	− 1.06037i
$494$	1.52817e23	1.93863
$495$	0	0
$496$	5.32968e21	0.0653291
$497$	− 2.64680e22i	− 0.318927i
$498$	− 2.74621e23i	− 3.25300i
$499$	−4.84975e22	−0.564761	−0.282381	−	0.959302i	$-0.591124\pi$
$499$	−4.84975e22	−0.564761	−0.282381	+	0.959302i	$0.591124\pi$
$500$	0	0
$501$	−1.65495e23	−1.86280
$502$	− 1.27669e22i	− 0.141288i
$503$	1.48522e23i	1.61608i	0.589126	+	0.808041i	$0.299472\pi$
$503$	1.48522e23i	1.61608i	−0.589126	+	0.808041i	$0.700528\pi$
$504$	1.18044e23	1.26294
$505$	0	0
$506$	−2.25318e22	−0.233086
$507$	6.49083e22i	0.660287i
$508$	− 2.65619e23i	− 2.65716i
$509$	−1.06498e23	−1.04771	−0.523855	−	0.851807i	$-0.675507\pi$
$509$	−1.06498e23	−1.04771	−0.523855	+	0.851807i	$0.675507\pi$
$510$	0	0
$511$	−2.19391e23	−2.08757
$512$	− 7.84422e22i	− 0.734100i
$513$	4.86463e22i	0.447767i
$514$	−1.09202e23	−0.988650
$515$	0	0
$516$	−8.24404e22	−0.722133
$517$	2.18713e21i	0.0188454i
$518$	3.40146e23i	2.88312i
$519$	2.55884e22	0.213364
$520$	0	0
$521$	2.90787e21	0.0234668	0.0117334	−	0.999931i	$-0.496265\pi$
$521$	2.90787e21	0.0234668	0.0117334	+	0.999931i	$0.496265\pi$
$522$	2.28270e23i	1.81238i
$523$	1.05919e23i	0.827390i	0.910416	+	0.413695i	$0.135762\pi$
$523$	1.05919e23i	0.827390i	−0.910416	+	0.413695i	$0.864238\pi$
$524$	−8.98127e22	−0.690274
$525$	0	0
$526$	3.89355e23	2.89712
$527$	2.77195e22i	0.202953i
$528$	− 8.11586e22i	− 0.584718i
$529$	1.38046e23	0.978706
$530$	0	0
$531$	−1.41073e23	−0.968591
$532$	− 3.19221e23i	− 2.15696i
$533$	− 2.52821e23i	− 1.68125i
$534$	5.77798e22	0.378160
$535$	0	0
$536$	−3.83661e22	−0.243246
$537$	2.60466e22i	0.162544i
$538$	− 4.51872e23i	− 2.77566i
$539$	1.87167e23	1.13168
$540$	0	0
$541$	−2.58434e22	−0.151416	−0.0757081	−	0.997130i	$-0.524122\pi$
$541$	−2.58434e22	−0.151416	−0.0757081	+	0.997130i	$0.524122\pi$
$542$	2.64446e23i	1.52526i
$543$	3.85743e23i	2.19028i
$544$	2.65849e23	1.48609
$545$	0	0
$546$	7.57097e23	4.10217
$547$	− 1.74286e23i	− 0.929759i	−0.885374	−	0.464879i	$-0.846098\pi$
$547$	− 1.74286e23i	− 0.929759i	0.885374	−	0.464879i	$-0.153902\pi$
$548$	5.08610e23i	2.67147i
$549$	−2.37107e23	−1.22625
$550$	0	0
$551$	1.86809e23	0.936718
$552$	3.02489e22i	0.149358i
$553$	− 1.60066e23i	− 0.778282i
$554$	9.46148e21	0.0453029
$555$	0	0
$556$	−3.02074e23	−1.40274
$557$	2.23690e23i	1.02300i	0.859282	+	0.511502i	$0.170911\pi$
$557$	2.23690e23i	1.02300i	−0.859282	+	0.511502i	$0.829089\pi$
$558$	− 7.70158e22i	− 0.346888i
$559$	−9.00051e22	−0.399270
$560$	0	0
$561$	4.22103e23	1.81649
$562$	6.56913e23i	2.78451i
$563$	− 5.68895e22i	− 0.237526i	−0.992923	−	0.118763i	$-0.962107\pi$
$563$	− 5.68895e22i	− 0.237526i	0.992923	−	0.118763i	$-0.0378929\pi$
$564$	9.70261e21	0.0399040
$565$	0	0
$566$	−6.23022e23	−2.48636
$567$	− 2.33512e23i	− 0.918024i
$568$	− 3.84218e22i	− 0.148805i
$569$	−2.49161e23	−0.950662	−0.475331	−	0.879807i	$-0.657672\pi$
$569$	−2.49161e23	−0.950662	−0.475331	+	0.879807i	$0.657672\pi$
$570$	0	0
$571$	−1.59046e23	−0.589001	−0.294500	−	0.955651i	$-0.595153\pi$
$571$	−1.59046e23	−0.589001	−0.294500	+	0.955651i	$0.595153\pi$
$572$	4.82298e23i	1.75974i
$573$	2.31371e23i	0.831752i
$574$	−8.96417e23	−3.17511
$575$	0	0
$576$	−5.97402e23	−2.05436
$577$	5.53720e22i	0.187627i	0.995590	+	0.0938137i	$0.0299058\pi$
$577$	5.53720e22i	0.187627i	−0.995590	+	0.0938137i	$0.970094\pi$
$578$	1.76237e23i	0.588453i
$579$	5.07912e23	1.67117
$580$	0	0
$581$	−6.26296e23	−2.00116
$582$	− 1.06985e24i	− 3.36883i
$583$	5.00826e22i	0.155419i
$584$	−3.18475e23	−0.974018
$585$	0	0
$586$	2.19578e23	0.652318
$587$	− 2.87790e23i	− 0.842660i	−0.906907	−	0.421330i	$-0.861563\pi$
$587$	− 2.87790e23i	− 0.842660i	0.906907	−	0.421330i	$-0.138437\pi$
$588$	− 8.30315e23i	− 2.39627i
$589$	−6.30272e22	−0.179287
$590$	0	0
$591$	4.86014e23	1.34325
$592$	− 1.76600e23i	− 0.481122i
$593$	5.72587e23i	1.53772i	0.639419	+	0.768859i	$0.279175\pi$
$593$	5.72587e23i	1.53772i	−0.639419	+	0.768859i	$0.720825\pi$
$594$	−2.60598e23	−0.689900
$595$	0	0
$596$	1.10768e23	0.284984
$597$	8.16595e23i	2.07121i
$598$	1.09128e23i	0.272883i
$599$	9.84730e22	0.242767	0.121383	−	0.992606i	$-0.461267\pi$
$599$	9.84730e22	0.242767	0.121383	+	0.992606i	$0.461267\pi$
$600$	0	0
$601$	4.14229e23	0.992675	0.496337	−	0.868130i	$-0.334678\pi$
$601$	4.14229e23	0.992675	0.496337	+	0.868130i	$0.334678\pi$
$602$	3.19127e23i	0.754039i
$603$	− 1.98287e23i	− 0.461952i
$604$	−2.87246e23	−0.659843
$605$	0	0
$606$	−5.04242e23	−1.12622
$607$	− 3.86832e23i	− 0.851958i	−0.904733	−	0.425979i	$-0.859930\pi$
$607$	− 3.86832e23i	− 0.851958i	0.904733	−	0.425979i	$-0.140070\pi$
$608$	6.04475e23i	1.31280i
$609$	9.25499e23	1.98211
$610$	0	0
$611$	1.05929e22	0.0220630
$612$	− 1.05330e24i	− 2.16353i
$613$	− 4.00012e23i	− 0.810324i	−0.914245	−	0.405162i	$-0.867215\pi$
$613$	− 4.00012e23i	− 0.810324i	0.914245	−	0.405162i	$-0.132785\pi$
$614$	1.01754e24	2.03292
$615$	0	0
$616$	5.17502e23	1.00572
$617$	3.66504e23i	0.702513i	0.936279	+	0.351256i	$0.114245\pi$
$617$	3.66504e23i	0.702513i	−0.936279	+	0.351256i	$0.885755\pi$
$618$	− 7.19518e23i	− 1.36031i
$619$	−3.54711e23	−0.661460	−0.330730	−	0.943725i	$-0.607295\pi$
$619$	−3.54711e23	−0.661460	−0.330730	+	0.943725i	$0.607295\pi$
$620$	0	0
$621$	−3.47387e22	−0.0630282
$622$	4.86927e23i	0.871456i
$623$	− 1.31772e23i	− 0.232634i
$624$	−3.93075e23	−0.684552
$625$	0	0
$626$	7.47163e23	1.26629
$627$	9.59757e23i	1.60468i
$628$	− 6.12606e23i	− 1.01047i
$629$	9.18487e23	1.49466
$630$	0	0
$631$	2.16428e23	0.342817	0.171409	−	0.985200i	$-0.445168\pi$
$631$	2.16428e23	0.342817	0.171409	+	0.985200i	$0.445168\pi$
$632$	− 2.32358e23i	− 0.363130i
$633$	1.20975e24i	1.86537i
$634$	1.06820e24	1.62516
$635$	0	0
$636$	2.22178e23	0.329091
$637$	− 9.06505e23i	− 1.32491i
$638$	1.00073e24i	1.44325i
$639$	1.98575e23	0.282596
$640$	0	0
$641$	1.31951e23	0.182860	0.0914300	−	0.995812i	$-0.470856\pi$
$641$	1.31951e23	0.182860	0.0914300	+	0.995812i	$0.470856\pi$
$642$	− 9.22342e23i	− 1.26138i
$643$	− 5.55370e23i	− 0.749531i	−0.927120	−	0.374765i	$-0.877723\pi$
$643$	− 5.55370e23i	− 0.749531i	0.927120	−	0.374765i	$-0.122277\pi$
$644$	2.27958e23	0.303616
$645$	0	0
$646$	−1.46311e24	−1.89802
$647$	8.90545e22i	0.114017i	0.998374	+	0.0570085i	$0.0181562\pi$
$647$	8.90545e22i	0.114017i	−0.998374	+	0.0570085i	$0.981844\pi$
$648$	− 3.38974e23i	− 0.428330i
$649$	−6.18463e23	−0.771318
$650$	0	0
$651$	−3.12253e23	−0.379374
$652$	6.47929e23i	0.777003i
$653$	− 6.88691e23i	− 0.815197i	−0.913161	−	0.407598i	$-0.866366\pi$
$653$	− 6.88691e23i	− 0.815197i	0.913161	−	0.407598i	$-0.133634\pi$
$654$	−5.40880e23	−0.631961
$655$	0	0
$656$	4.65408e23	0.529848
$657$	− 1.64597e24i	− 1.84977i
$658$	− 3.75589e22i	− 0.0416670i
$659$	−8.62900e22	−0.0945005	−0.0472503	−	0.998883i	$-0.515046\pi$
$659$	−8.62900e22	−0.0945005	−0.0472503	+	0.998883i	$0.515046\pi$
$660$	0	0
$661$	1.26260e24	1.34757	0.673786	−	0.738927i	$-0.264667\pi$
$661$	1.26260e24	1.34757	0.673786	+	0.738927i	$0.264667\pi$
$662$	− 5.55328e21i	− 0.00585135i
$663$	− 2.04437e24i	− 2.12664i
$664$	−9.09150e23	−0.933699
$665$	0	0
$666$	−2.55193e24	−2.55468
$667$	1.33402e23i	0.131854i
$668$	1.81046e24i	1.76680i
$669$	−2.98233e24	−2.87365
$670$	0	0
$671$	−1.03947e24	−0.976500
$672$	2.99472e24i	2.77791i
$673$	− 1.39756e24i	− 1.28009i	−0.768336	−	0.640046i	$-0.778915\pi$
$673$	− 1.39756e24i	− 1.28009i	0.768336	−	0.640046i	$-0.221085\pi$
$674$	1.82102e24	1.64704
$675$	0	0
$676$	7.10072e23	0.626261
$677$	− 1.98205e24i	− 1.72628i	−0.504965	−	0.863140i	$-0.668495\pi$
$677$	− 1.98205e24i	− 1.72628i	0.504965	−	0.863140i	$-0.331505\pi$
$678$	3.20728e24i	2.75857i
$679$	−2.43989e24	−2.07241
$680$	0	0
$681$	5.11860e23	0.424034
$682$	− 3.37636e23i	− 0.276237i
$683$	− 1.91565e24i	− 1.54789i	−0.633252	−	0.773946i	$-0.718280\pi$
$683$	− 1.91565e24i	− 1.54789i	0.633252	−	0.773946i	$-0.281720\pi$
$684$	2.39494e24	1.91125
$685$	0	0
$686$	−3.06312e23	−0.238456
$687$	− 1.34531e24i	− 1.03440i
$688$	− 1.65687e23i	− 0.125831i
$689$	2.42565e23	0.181955
$690$	0	0
$691$	−9.32183e23	−0.682241	−0.341121	−	0.940020i	$-0.610806\pi$
$691$	−9.32183e23	−0.682241	−0.341121	+	0.940020i	$0.610806\pi$
$692$	− 2.79927e23i	− 0.202369i
$693$	2.67460e24i	1.90997i
$694$	2.55880e24	1.80502
$695$	0	0
$696$	1.34348e24	0.924812
$697$	2.42057e24i	1.64604i
$698$	− 2.51452e24i	− 1.68921i
$699$	2.97773e24	1.97619
$700$	0	0
$701$	−9.43006e23	−0.610817	−0.305408	−	0.952221i	$-0.598793\pi$
$701$	−9.43006e23	−0.610817	−0.305408	+	0.952221i	$0.598793\pi$
$702$	1.26215e24i	0.807693i
$703$	2.08841e24i	1.32037i
$704$	−2.61901e24	−1.63595
$705$	0	0
$706$	2.86815e24	1.74888
$707$	1.14996e24i	0.692818i
$708$	2.74364e24i	1.63322i
$709$	−8.30727e23	−0.488614	−0.244307	−	0.969698i	$-0.578560\pi$
$709$	−8.30727e23	−0.488614	−0.244307	+	0.969698i	$0.578560\pi$
$710$	0	0
$711$	1.20089e24	0.689623
$712$	− 1.91284e23i	− 0.108542i
$713$	− 4.50082e22i	− 0.0252366i
$714$	−7.24863e24	−4.01625
$715$	0	0
$716$	2.84940e23	0.154167
$717$	3.12466e24i	1.67067i
$718$	4.33154e24i	2.28868i
$719$	−2.57313e24	−1.34359	−0.671794	−	0.740738i	$-0.734476\pi$
$719$	−2.57313e24	−1.34359	−0.671794	+	0.740738i	$0.734476\pi$
$720$	0	0
$721$	−1.64092e24	−0.836829
$722$	− 2.31322e23i	− 0.116587i
$723$	− 4.85437e24i	− 2.41801i
$724$	4.21988e24	2.07741
$725$	0	0
$726$	−2.36574e23	−0.113764
$727$	1.02839e23i	0.0488783i	0.999701	+	0.0244391i	$0.00778000\pi$
$727$	1.02839e23i	0.0488783i	−0.999701	+	0.0244391i	$0.992220\pi$
$728$	− 2.50642e24i	− 1.17743i
$729$	3.15827e24	1.46644
$730$	0	0
$731$	8.61731e23	0.390907
$732$	4.61135e24i	2.06768i
$733$	2.97764e23i	0.131974i	0.997820	+	0.0659870i	$0.0210196\pi$
$733$	2.97764e23i	0.131974i	−0.997820	+	0.0659870i	$0.978980\pi$
$734$	−2.79550e24	−1.22474
$735$	0	0
$736$	−4.31660e23	−0.184791
$737$	− 8.69287e23i	− 0.367866i
$738$	− 6.72532e24i	− 2.81342i
$739$	3.64205e24	1.50615	0.753074	−	0.657936i	$-0.228570\pi$
$739$	3.64205e24	1.50615	0.753074	+	0.657936i	$0.228570\pi$
$740$	0	0
$741$	4.64839e24	1.87866
$742$	− 8.60052e23i	− 0.343630i
$743$	2.08027e24i	0.821701i	0.911703	+	0.410851i	$0.134768\pi$
$743$	2.08027e24i	0.821701i	−0.911703	+	0.410851i	$0.865232\pi$
$744$	−4.53276e23	−0.177008
$745$	0	0
$746$	−2.22155e24	−0.847962
$747$	− 4.69875e24i	− 1.77320i
$748$	− 4.61764e24i	− 1.72289i
$749$	−2.10348e24	−0.775965
$750$	0	0
$751$	−1.01283e24	−0.365256	−0.182628	−	0.983182i	$-0.558460\pi$
$751$	−1.01283e24	−0.365256	−0.182628	+	0.983182i	$0.558460\pi$
$752$	1.95001e22i	0.00695320i
$753$	− 3.88343e23i	− 0.136917i
$754$	4.84685e24	1.68968
$755$	0	0
$756$	2.63651e24	0.898659
$757$	− 1.79501e24i	− 0.604996i	−0.953150	−	0.302498i	$-0.902179\pi$
$757$	− 1.79501e24i	− 0.604996i	0.953150	−	0.302498i	$-0.0978205\pi$
$758$	6.85777e24i	2.28557i
$759$	−6.85370e23	−0.225876
$760$	0	0
$761$	−1.05630e23	−0.0340423	−0.0170212	−	0.999855i	$-0.505418\pi$
$761$	−1.05630e23	−0.0340423	−0.0170212	+	0.999855i	$0.505418\pi$
$762$	− 1.37141e25i	− 4.37068i
$763$	1.23352e24i	0.388765i
$764$	2.53111e24	0.788891
$765$	0	0
$766$	−8.27984e24	−2.52393
$767$	2.99540e24i	0.903013i
$768$	1.60048e24i	0.477178i
$769$	9.59386e23	0.282891	0.141446	−	0.989946i	$-0.454825\pi$
$769$	9.59386e23	0.282891	0.141446	+	0.989946i	$0.454825\pi$
$770$	0	0
$771$	−3.32169e24	−0.958068
$772$	− 5.55636e24i	− 1.58505i
$773$	− 8.69614e23i	− 0.245358i	−0.992446	−	0.122679i	$-0.960851\pi$
$773$	− 8.69614e23i	− 0.245358i	0.992446	−	0.122679i	$-0.0391486\pi$
$774$	−2.39423e24	−0.668142
$775$	0	0
$776$	−3.54182e24	−0.966944
$777$	1.03465e25i	2.79393i
$778$	9.26050e24i	2.47348i
$779$	−5.50378e24	−1.45409
$780$	0	0
$781$	8.70549e23	0.225040
$782$	− 1.04482e24i	− 0.267168i
$783$	1.54289e24i	0.390267i
$784$	1.66875e24	0.417546
$785$	0	0
$786$	−4.63709e24	−1.13541
$787$	− 6.67023e24i	− 1.61568i	−0.589401	−	0.807840i	$-0.700636\pi$
$787$	− 6.67023e24i	− 1.61568i	0.589401	−	0.807840i	$-0.299364\pi$
$788$	− 5.31681e24i	− 1.27403i
$789$	1.18433e25	2.80750
$790$	0	0
$791$	7.31446e24	1.69700
$792$	3.88253e24i	0.891150i
$793$	5.03448e24i	1.14323i
$794$	2.12648e24	0.477736
$795$	0	0
$796$	8.93324e24	1.96448
$797$	4.58059e24i	0.996612i	0.867001	+	0.498306i	$0.166044\pi$
$797$	4.58059e24i	0.996612i	−0.867001	+	0.498306i	$0.833956\pi$
$798$	− 1.64816e25i	− 3.54792i
$799$	−1.01419e23	−0.0216009
$800$	0	0
$801$	9.88609e23	0.206133
$802$	5.07421e24i	1.04685i
$803$	− 7.21592e24i	− 1.47302i
$804$	−3.85635e24	−0.778934
$805$	0	0
$806$	−1.63527e24	−0.323402
$807$	− 1.37450e25i	− 2.68980i
$808$	1.66932e24i	0.323254i
$809$	−3.33659e24	−0.639352	−0.319676	−	0.947527i	$-0.603574\pi$
$809$	−3.33659e24	−0.639352	−0.319676	+	0.947527i	$0.603574\pi$
$810$	0	0
$811$	−7.47175e24	−1.40199	−0.700995	−	0.713166i	$-0.747261\pi$
$811$	−7.47175e24	−1.40199	−0.700995	+	0.713166i	$0.747261\pi$
$812$	− 1.01246e25i	− 1.87997i
$813$	8.04389e24i	1.47808i
$814$	−1.11876e25	−2.03437
$815$	0	0
$816$	3.76340e24	0.670214
$817$	1.95936e24i	0.345324i
$818$	− 1.54975e25i	− 2.70308i
$819$	1.29539e25	2.23607
$820$	0	0
$821$	−1.52582e24	−0.257981	−0.128990	−	0.991646i	$-0.541174\pi$
$821$	−1.52582e24	−0.257981	−0.128990	+	0.991646i	$0.541174\pi$
$822$	2.62599e25i	4.39423i
$823$	6.12175e24i	1.01386i	0.861988	+	0.506929i	$0.169219\pi$
$823$	6.12175e24i	1.01386i	−0.861988	+	0.506929i	$0.830781\pi$
$824$	−2.38201e24	−0.390447
$825$	0	0
$826$	1.06207e25	1.70538
$827$	4.78747e24i	0.760868i	0.924808	+	0.380434i	$0.124225\pi$
$827$	4.78747e24i	0.760868i	−0.924808	+	0.380434i	$0.875775\pi$
$828$	1.71024e24i	0.269030i
$829$	−8.83452e24	−1.37553	−0.687764	−	0.725934i	$-0.741408\pi$
$829$	−8.83452e24	−1.37553	−0.687764	+	0.725934i	$0.741408\pi$
$830$	0	0
$831$	2.87798e23	0.0439015
$832$	1.26846e25i	1.91527i
$833$	8.67910e24i	1.29716i
$834$	−1.55963e25	−2.30733
$835$	0	0
$836$	1.04994e25	1.52198
$837$	− 5.20555e23i	− 0.0746965i
$838$	− 3.30195e24i	− 0.469026i
$839$	5.00324e24	0.703517	0.351759	−	0.936091i	$-0.385584\pi$
$839$	5.00324e24	0.703517	0.351759	+	0.936091i	$0.385584\pi$
$840$	0	0
$841$	−1.33221e24	−0.183571
$842$	− 3.10478e24i	− 0.423525i
$843$	1.99819e25i	2.69838i
$844$	1.32342e25	1.76924
$845$	0	0
$846$	2.81783e23	0.0369205
$847$	5.39526e23i	0.0699847i
$848$	4.46528e23i	0.0573435i
$849$	−1.89510e25	−2.40945
$850$	0	0
$851$	−1.49135e24	−0.185857
$852$	− 3.86196e24i	− 0.476509i
$853$	− 8.76800e24i	− 1.07111i	−0.844501	−	0.535554i	$-0.820103\pi$
$853$	− 8.76800e24i	− 1.07111i	0.844501	−	0.535554i	$-0.179897\pi$
$854$	1.78506e25	2.15904
$855$	0	0
$856$	−3.05347e24	−0.362049
$857$	9.35381e24i	1.09812i	0.835782	+	0.549062i	$0.185015\pi$
$857$	9.35381e24i	1.09812i	−0.835782	+	0.549062i	$0.814985\pi$
$858$	2.49014e25i	2.89455i
$859$	7.35462e24	0.846483	0.423241	−	0.906017i	$-0.360892\pi$
$859$	7.35462e24	0.846483	0.423241	+	0.906017i	$0.360892\pi$
$860$	0	0
$861$	−2.72671e25	−3.07689
$862$	− 1.72674e25i	− 1.92937i
$863$	− 8.81310e24i	− 0.975072i	−0.873103	−	0.487536i	$-0.837896\pi$
$863$	− 8.81310e24i	− 0.975072i	0.873103	−	0.487536i	$-0.162104\pi$
$864$	−4.99249e24	−0.546953
$865$	0	0
$866$	1.99261e25	2.14053
$867$	5.36077e24i	0.570250i
$868$	3.41592e24i	0.359824i
$869$	5.26469e24	0.549167
$870$	0	0
$871$	−4.21021e24	−0.430675
$872$	1.79062e24i	0.181390i
$873$	− 1.83051e25i	− 1.83633i
$874$	2.37566e24	0.236014
$875$	0	0
$876$	−3.20115e25	−3.11904
$877$	− 3.60902e24i	− 0.348252i	−0.984723	−	0.174126i	$-0.944290\pi$
$877$	− 3.60902e24i	− 0.348252i	0.984723	−	0.174126i	$-0.0557100\pi$
$878$	− 1.59772e25i	− 1.52686i
$879$	6.67911e24	0.632140
$880$	0	0
$881$	−1.96188e24	−0.182128	−0.0910639	−	0.995845i	$-0.529027\pi$
$881$	−1.96188e24	−0.182128	−0.0910639	+	0.995845i	$0.529027\pi$
$882$	− 2.41140e25i	− 2.21711i
$883$	− 7.10082e24i	− 0.646610i	−0.946295	−	0.323305i	$-0.895206\pi$
$883$	− 7.10082e24i	− 0.646610i	0.946295	−	0.323305i	$-0.104794\pi$
$884$	−2.23646e25	−2.01705
$885$	0	0
$886$	1.25273e25	1.10833
$887$	− 1.89470e25i	− 1.66031i	−0.557532	−	0.830156i	$-0.688252\pi$
$887$	− 1.89470e25i	− 1.66031i	0.557532	−	0.830156i	$-0.311748\pi$
$888$	1.50193e25i	1.30359i
$889$	−3.12760e25	−2.68873
$890$	0	0
$891$	7.68037e24	0.647771
$892$	3.26255e25i	2.72556i
$893$	− 2.30602e23i	− 0.0190821i
$894$	5.71903e24	0.468763
$895$	0	0
$896$	2.21284e25	1.77964
$897$	3.31945e24i	0.264442i
$898$	1.19547e23i	0.00943386i
$899$	−1.99901e24	−0.156263
$900$	0	0
$901$	−2.32238e24	−0.178144
$902$	− 2.94837e25i	− 2.24041i
$903$	9.70718e24i	0.730714i
$904$	1.06179e25	0.791784
$905$	0	0
$906$	−1.48307e25	−1.08536
$907$	7.47138e24i	0.541675i	0.962625	+	0.270837i	$0.0873006\pi$
$907$	7.47138e24i	0.541675i	−0.962625	+	0.270837i	$0.912699\pi$
$908$	− 5.59955e24i	− 0.402183i
$909$	−8.62754e24	−0.613895
$910$	0	0
$911$	1.50719e25	1.05260	0.526300	−	0.850299i	$-0.323579\pi$
$911$	1.50719e25	1.05260	0.526300	+	0.850299i	$0.323579\pi$
$912$	8.55703e24i	0.592062i
$913$	− 2.05993e25i	− 1.41205i
$914$	1.50590e25	1.02271
$915$	0	0
$916$	−1.47172e25	−0.981100
$917$	1.05753e25i	0.698476i
$918$	− 1.20842e25i	− 0.790776i
$919$	1.28199e25	0.831197	0.415599	−	0.909548i	$-0.363572\pi$
$919$	1.28199e25	0.831197	0.415599	+	0.909548i	$0.363572\pi$
$920$	0	0
$921$	3.09515e25	1.97004
$922$	1.98636e25i	1.25269i
$923$	− 4.21633e24i	− 0.263463i
$924$	5.20166e25	3.22055
$925$	0	0
$926$	−3.53963e25	−2.15161
$927$	− 1.23109e25i	− 0.741501i
$928$	1.91719e25i	1.14421i
$929$	1.41590e24	0.0837335	0.0418667	−	0.999123i	$-0.486670\pi$
$929$	1.41590e24	0.0837335	0.0418667	+	0.999123i	$0.486670\pi$
$930$	0	0
$931$	−1.97341e25	−1.14590
$932$	− 3.25752e25i	− 1.87436i
$933$	1.48113e25i	0.844499i
$934$	4.94514e24	0.279402
$935$	0	0
$936$	1.88042e25	1.04330
$937$	2.47144e24i	0.135883i	0.997689	+	0.0679414i	$0.0216431\pi$
$937$	2.47144e24i	0.135883i	−0.997689	+	0.0679414i	$0.978357\pi$
$938$	1.49280e25i	0.813348i
$939$	2.27271e25	1.22712
$940$	0	0
$941$	2.72156e25	1.44313	0.721567	−	0.692345i	$-0.243422\pi$
$941$	2.72156e25	1.44313	0.721567	+	0.692345i	$0.243422\pi$
$942$	− 3.16293e25i	− 1.66210i
$943$	− 3.93029e24i	− 0.204680i
$944$	−5.51411e24	−0.284586
$945$	0	0
$946$	−1.04963e25	−0.532061
$947$	4.52899e23i	0.0227524i	0.999935	+	0.0113762i	$0.00362123\pi$
$947$	4.52899e23i	0.0227524i	−0.999935	+	0.0113762i	$0.996379\pi$
$948$	− 2.33554e25i	− 1.16283i
$949$	−3.49488e25	−1.72453
$950$	0	0
$951$	3.24925e25	1.57489
$952$	2.39970e25i	1.15277i
$953$	9.70376e24i	0.462009i	0.972953	+	0.231004i	$0.0742012\pi$
$953$	9.70376e24i	0.462009i	−0.972953	+	0.231004i	$0.925799\pi$
$954$	6.45249e24	0.304485
$955$	0	0
$956$	3.41826e25	1.58457
$957$	3.04402e25i	1.39861i
$958$	− 6.10790e24i	− 0.278154i
$959$	5.98878e25	2.70321
$960$	0	0
$961$	−2.18757e25	−0.970091
$962$	5.41850e25i	2.38172i
$963$	− 1.57812e25i	− 0.687570i
$964$	−5.31049e25	−2.29340
$965$	0	0
$966$	1.17696e25	0.499410
$967$	− 3.03622e25i	− 1.27705i	−0.769601	−	0.638525i	$-0.779545\pi$
$967$	− 3.03622e25i	− 1.27705i	0.769601	−	0.638525i	$-0.220455\pi$
$968$	7.83193e23i	0.0326534i
$969$	−4.45048e25	−1.83931
$970$	0	0
$971$	−3.15755e25	−1.28229	−0.641145	−	0.767420i	$-0.721540\pi$
$971$	−3.15755e25	−1.28229	−0.641145	+	0.767420i	$0.721540\pi$
$972$	− 4.94568e25i	− 1.99096i
$973$	3.55686e25i	1.41941i
$974$	−2.23935e25	−0.885871
$975$	0	0
$976$	−9.26778e24	−0.360290
$977$	1.27985e25i	0.493238i	0.969113	+	0.246619i	$0.0793196\pi$
$977$	1.27985e25i	0.493238i	−0.969113	+	0.246619i	$0.920680\pi$
$978$	3.34530e25i	1.27807i
$979$	4.33405e24	0.164150
$980$	0	0
$981$	−9.25441e24	−0.344479
$982$	− 3.39002e25i	− 1.25099i
$983$	− 3.20093e25i	− 1.17104i	−0.810659	−	0.585519i	$-0.800891\pi$
$983$	− 3.20093e25i	− 1.17104i	0.810659	−	0.585519i	$-0.199109\pi$
$984$	−3.95818e25	−1.43561
$985$	0	0
$986$	−4.64050e25	−1.65429
$987$	− 1.14246e24i	− 0.0403781i
$988$	− 5.08516e25i	− 1.78185i
$989$	−1.39920e24	−0.0486083
$990$	0	0
$991$	−4.78103e25	−1.63266	−0.816330	−	0.577586i	$-0.803995\pi$
$991$	−4.78103e25	−1.63266	−0.816330	+	0.577586i	$0.803995\pi$
$992$	− 6.46838e24i	− 0.219001i
$993$	− 1.68919e23i	− 0.00567035i
$994$	−1.49497e25	−0.497562
$995$	0	0
$996$	−9.13830e25	−2.98993
$997$	− 3.63445e25i	− 1.17904i	−0.807753	−	0.589521i	$-0.799316\pi$
$997$	− 3.63445e25i	− 1.17904i	0.807753	−	0.589521i	$-0.200684\pi$
$998$	2.73924e25i	0.881089i
$999$	−1.72487e25	−0.550109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.18.b.b.24.1		4
5.2	odd	4		5.18.a.a.1.2	✓	2
5.3	odd	4		25.18.a.b.1.1		2
5.4	even	2	inner	25.18.b.b.24.4		4
15.2	even	4		45.18.a.a.1.1		2
20.7	even	4		80.18.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.18.a.a.1.2	✓	2	5.2	odd	4
25.18.a.b.1.1		2	5.3	odd	4
25.18.b.b.24.1		4	1.1	even	1	trivial
25.18.b.b.24.4		4	5.4	even	2	inner
45.18.a.a.1.1		2	15.2	even	4
80.18.a.f.1.2		2	20.7	even	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-564.820i q^{2} -17180.6i q^{3} -187950. q^{4} -9.70397e6 q^{6} +2.21307e7i q^{7} +3.21256e7i q^{8} -1.66034e8 q^{9} +O(q^{10})\)	\(q-564.820i q^{2} -17180.6i q^{3} -187950. q^{4} -9.70397e6 q^{6} +2.21307e7i q^{7} +3.21256e7i q^{8} -1.66034e8 q^{9} -7.27892e8 q^{11} +3.22909e9i q^{12} +3.52539e9i q^{13} +1.24998e10 q^{14} -6.48976e9 q^{16} -3.37530e10i q^{17} +9.37794e10i q^{18} +7.67459e10 q^{19} +3.80219e11 q^{21} +4.11128e11i q^{22} +5.48049e10i q^{23} +5.51938e11 q^{24} +1.99121e12 q^{26} +6.33861e11i q^{27} -4.15945e12i q^{28} +2.43412e12 q^{29} -8.21245e11 q^{31} +7.87631e12i q^{32} +1.25056e13i q^{33} -1.90644e13 q^{34} +3.12060e13 q^{36} +2.72120e13i q^{37} -4.33476e13i q^{38} +6.05685e13 q^{39} -7.17143e13 q^{41} -2.14755e14i q^{42} +2.55305e13i q^{43} +1.36807e14 q^{44} +3.09549e13 q^{46} -3.00475e12i q^{47} +1.11498e14i q^{48} -2.57136e14 q^{49} -5.79898e14 q^{51} -6.62596e14i q^{52} -6.88051e13i q^{53} +3.58017e14 q^{54} -7.10960e14 q^{56} -1.31854e15i q^{57} -1.37484e15i q^{58} +8.49663e14 q^{59} +1.42806e15 q^{61} +4.63855e14i q^{62} -3.67444e15i q^{63} +3.59807e15 q^{64} +7.06343e15 q^{66} +1.19425e15i q^{67} +6.34386e15i q^{68} +9.41583e14 q^{69} -1.19599e15 q^{71} -5.33394e15i q^{72} +9.91346e15i q^{73} +1.53699e16 q^{74} -1.44244e16 q^{76} -1.61087e16i q^{77} -3.42103e16i q^{78} -7.23279e15 q^{79} -1.05515e16 q^{81} +4.05057e16i q^{82} +2.82999e16i q^{83} -7.14620e16 q^{84} +1.44201e16 q^{86} -4.18197e16i q^{87} -2.33839e16i q^{88} -5.95425e15 q^{89} -7.80193e16 q^{91} -1.03006e16i q^{92} +1.41095e16i q^{93} -1.69714e15 q^{94} +1.35320e17 q^{96} +1.10249e17i q^{97} +1.45235e17i q^{98} +1.20855e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 140288 q^{4} - 17979552 q^{6} - 150683652 q^{9}+O(q^{10}) \) 4 * q - 140288 * q^4 - 17979552 * q^6 - 150683652 * q^9	\( 4 q - 140288 q^{4} - 17979552 q^{6} - 150683652 q^{9} - 2106710912 q^{11} + 25158636384 q^{14} + 11299057664 q^{16} - 13932982000 q^{19} + 751880425968 q^{21} + 1459367193600 q^{24} + 2793118146208 q^{26} + 8379197473000 q^{29} + 9224644833648 q^{31} - 40785137598496 q^{34} + 83780175135744 q^{36} + 185162581193616 q^{39} - 290945462384872 q^{41} + 196930878705664 q^{44} + 65916842739168 q^{46} - 49962773891828 q^{49} - 10\!\cdots\!92 q^{51}+ \cdots + 18\!\cdots\!56 q^{99}+O(q^{100}) \) 4 * q - 140288 * q^4 - 17979552 * q^6 - 150683652 * q^9 - 2106710912 * q^11 + 25158636384 * q^14 + 11299057664 * q^16 - 13932982000 * q^19 + 751880425968 * q^21 + 1459367193600 * q^24 + 2793118146208 * q^26 + 8379197473000 * q^29 + 9224644833648 * q^31 - 40785137598496 * q^34 + 83780175135744 * q^36 + 185162581193616 * q^39 - 290945462384872 * q^41 + 196930878705664 * q^44 + 65916842739168 * q^46 - 49962773891828 * q^49 - 1016789632544592 * q^51 + 1030039118827200 * q^54 - 1382359734604800 * q^56 + 6204826596098000 * q^59 + 927103175732488 * q^61 + 9190765145096192 * q^64 + 13661983636217856 * q^66 + 1667450401893936 * q^69 + 10242354790380368 * q^71 + 30129336083208544 * q^74 - 48572297066598400 * q^76 + 5218668194316000 * q^79 - 14583217294565676 * q^81 - 143932036192874496 * q^84 + 11392902743358688 * q^86 - 122385728353281000 * q^89 - 148913569441199472 * q^91 - 51660993199829536 * q^94 + 334574484314554368 * q^96 + 182675519501302656 * q^99

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