LMFDB - Embedded newform 25.34.b.c.24.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,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, 34, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
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:	$172.457072203$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20265063301 x^{10} + \cdots + 39\!\cdots\!96 $ x^12 + 20265063301x^10 + 151877130254993985540x^8 + 529361026408998369955851761920x^6 + 862054500541443268723145801151954288640x^4 + 544606882049987247786598582768552479276511789056*x^2 + 39700341273686227371481766034965422500156905479886340096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{47}\cdot 3^{10}\cdot 5^{36}\cdot 7^{2}\cdot 11^{4} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.10
Root			$63200.4i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.c.24.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+126401. i q^{2} -8.63211e7i q^{3} -7.38725e9 q^{4} +1.09111e13 q^{6} -7.78650e13i q^{7} +1.52021e14i q^{8} -1.89228e15 q^{9} +O(q^{10})$	\(q+126401. i q^{2} -8.63211e7i q^{3} -7.38725e9 q^{4} +1.09111e13 q^{6} -7.78650e13i q^{7} +1.52021e14i q^{8} -1.89228e15 q^{9} +1.61939e17 q^{11} +6.37676e17i q^{12} -2.28706e18i q^{13} +9.84220e18 q^{14} -8.26715e19 q^{16} -2.46494e20i q^{17} -2.39186e20i q^{18} +1.53881e21 q^{19} -6.72140e21 q^{21} +2.04692e22i q^{22} -2.16284e22i q^{23} +1.31226e22 q^{24} +2.89086e23 q^{26} -3.16521e23i q^{27} +5.75208e23i q^{28} +2.07535e23 q^{29} +1.75532e24 q^{31} -9.14391e24i q^{32} -1.39788e25i q^{33} +3.11571e25 q^{34} +1.39787e25 q^{36} -8.12289e25i q^{37} +1.94506e26i q^{38} -1.97422e26 q^{39} -1.92486e26 q^{41} -8.49590e26i q^{42} +8.01003e26i q^{43} -1.19628e27 q^{44} +2.73385e27 q^{46} +7.53703e27i q^{47} +7.13630e27i q^{48} +1.66804e27 q^{49} -2.12777e28 q^{51} +1.68951e28i q^{52} +1.75257e28i q^{53} +4.00085e28 q^{54} +1.18371e28 q^{56} -1.32832e29i q^{57} +2.62326e28i q^{58} +2.97225e29 q^{59} -3.70944e29 q^{61} +2.21873e29i q^{62} +1.47342e29i q^{63} +4.45655e29 q^{64} +1.76693e30 q^{66} -8.43824e29i q^{67} +1.82091e30i q^{68} -1.86699e30 q^{69} +5.92473e30 q^{71} -2.87666e29i q^{72} +7.49289e30i q^{73} +1.02674e31 q^{74} -1.13675e31 q^{76} -1.26094e31i q^{77} -2.49543e31i q^{78} -6.07295e30 q^{79} -3.78417e31 q^{81} -2.43304e31i q^{82} +3.47153e31i q^{83} +4.96526e31 q^{84} -1.01248e32 q^{86} -1.79147e31i q^{87} +2.46181e31i q^{88} -1.80671e32 q^{89} -1.78082e32 q^{91} +1.59775e32i q^{92} -1.51521e32i q^{93} -9.52688e32 q^{94} -7.89312e32 q^{96} -1.09143e33i q^{97} +2.10841e32i q^{98} -3.06434e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) $ 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9	$ 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+ \cdots - 33\!\cdots\!32 q^{99}+O(q^{100}) $ 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9 + 301521793111780384 * q^11 + 14172220017979782912 * q^14 + 129023040011717337632 * q^16 - 3423168725199973224400 * q^19 - 21120795321652308296256 * q^21 - 423790032309447397723200 * q^24 - 723658493334872996337176 * q^26 - 2610446812821454716031400 * q^29 + 21650642793601151809506704 * q^31 - 17744819333309063470980248 * q^34 + 337428823503549785822326792 * q^36 - 1159928172465211851270376912 * q^39 + 896017159299045986791643864 * q^41 - 14343610684444535018100501728 * q^44 + 6987518581952661848987190144 * q^46 + 14346854147129333747058470516 * q^49 - 109840725610127342641737389776 * q^51 + 365294374336526194478458799200 * q^54 - 785146678781996293241501500800 * q^56 + 356630312442075454139067599600 * q^59 - 564635378121172028506416574616 * q^61 - 3875937069585082792868959215744 * q^64 + 10122417492310860521089546318528 * q^66 - 632254481633966368511307646272 * q^69 + 16902436063987485405313234340144 * q^71 - 40989454834346150858579084952968 * q^74 + 58820079845469675507259388916000 * q^76 + 44105010702804710887789495271200 * q^79 - 266327929778353521323811147439348 * q^81 + 471983223984448297035157677303552 * q^84 - 257647761243091711315108096211216 * q^86 + 672982716682338963896412426721800 * q^89 + 389267538804687732313205728966864 * q^91 - 2972282194336784425374584270690528 * q^94 + 6303457980346245345128406163058944 * q^96 - 3321764604884454158829134325248032 * 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 $

$2$	126401.i	1.36381i	0.731439	+	0.681907i	$0.238849\pi$
$2$	126401.i	1.36381i	−0.731439	+	0.681907i	$0.761151\pi$
$3$	− 8.63211e7i	− 1.15775i	−0.815415	−	0.578877i	$-0.803491\pi$
$3$	− 8.63211e7i	− 1.15775i	0.815415	−	0.578877i	$-0.196509\pi$
$4$	−7.38725e9	−0.859989
$5$	0	0
$5$	0	0
$6$	1.09111e13	1.57896
$7$	− 7.78650e13i	− 0.885573i	−0.896627	−	0.442787i	$-0.853990\pi$
$7$	− 7.78650e13i	− 0.885573i	0.896627	−	0.442787i	$-0.146010\pi$
$8$	1.52021e14i	0.190949i
$9$	−1.89228e15	−0.340396
$10$	0	0
$11$	1.61939e17	1.06260	0.531302	−	0.847182i	$-0.321703\pi$
$11$	1.61939e17	1.06260	0.531302	+	0.847182i	$0.321703\pi$
$12$	6.37676e17i	0.995656i
$13$	− 2.28706e18i	− 0.953262i	−0.879104	−	0.476631i	$-0.841858\pi$
$13$	− 2.28706e18i	− 0.953262i	0.879104	−	0.476631i	$-0.158142\pi$
$14$	9.84220e18	1.20776
$15$	0	0
$16$	−8.26715e19	−1.12041
$17$	− 2.46494e20i	− 1.22857i	−0.789085	−	0.614284i	$-0.789445\pi$
$17$	− 2.46494e20i	− 1.22857i	0.789085	−	0.614284i	$-0.210555\pi$
$18$	− 2.39186e20i	− 0.464236i
$19$	1.53881e21	1.22391	0.611955	−	0.790893i	$-0.290383\pi$
$19$	1.53881e21	1.22391	0.611955	+	0.790893i	$0.290383\pi$
$20$	0	0
$21$	−6.72140e21	−1.02528
$22$	2.04692e22i	1.44920i
$23$	− 2.16284e22i	− 0.735387i	−0.929947	−	0.367693i	$-0.880148\pi$
$23$	− 2.16284e22i	− 0.735387i	0.929947	−	0.367693i	$-0.119852\pi$
$24$	1.31226e22	0.221072
$25$	0	0
$26$	2.89086e23	1.30007
$27$	− 3.16521e23i	− 0.763660i
$28$	5.75208e23i	0.761583i
$29$	2.07535e23	0.154001	0.0770007	−	0.997031i	$-0.475466\pi$
$29$	2.07535e23	0.154001	0.0770007	+	0.997031i	$0.475466\pi$
$30$	0	0
$31$	1.75532e24	0.433398	0.216699	−	0.976238i	$-0.430471\pi$
$31$	1.75532e24	0.433398	0.216699	+	0.976238i	$0.430471\pi$
$32$	− 9.14391e24i	− 1.33708i
$33$	− 1.39788e25i	− 1.23024i
$34$	3.11571e25	1.67554
$35$	0	0
$36$	1.39787e25	0.292736
$37$	− 8.12289e25i	− 1.08239i	−0.840898	−	0.541193i	$-0.817973\pi$
$37$	− 8.12289e25i	− 1.08239i	0.840898	−	0.541193i	$-0.182027\pi$
$38$	1.94506e26i	1.66919i
$39$	−1.97422e26	−1.10364
$40$	0	0
$41$	−1.92486e26	−0.471483	−0.235741	−	0.971816i	$-0.575752\pi$
$41$	−1.92486e26	−0.471483	−0.235741	+	0.971816i	$0.575752\pi$
$42$	− 8.49590e26i	− 1.39829i
$43$	8.01003e26i	0.894139i	0.894499	+	0.447069i	$0.147532\pi$
$43$	8.01003e26i	0.894139i	−0.894499	+	0.447069i	$0.852468\pi$
$44$	−1.19628e27	−0.913828
$45$	0	0
$46$	2.73385e27	1.00293
$47$	7.53703e27i	1.93904i	0.245021	+	0.969518i	$0.421205\pi$
$47$	7.53703e27i	1.93904i	−0.245021	+	0.969518i	$0.578795\pi$
$48$	7.13630e27i	1.29716i
$49$	1.66804e27	0.215760
$50$	0	0
$51$	−2.12777e28	−1.42238
$52$	1.68951e28i	0.819795i
$53$	1.75257e28i	0.621047i	0.950566	+	0.310523i	$0.100504\pi$
$53$	1.75257e28i	0.621047i	−0.950566	+	0.310523i	$0.899496\pi$
$54$	4.00085e28	1.04149
$55$	0	0
$56$	1.18371e28	0.169100
$57$	− 1.32832e29i	− 1.41699i
$58$	2.62326e28i	0.210029i
$59$	2.97225e29	1.79484	0.897422	−	0.441172i	$-0.145437\pi$
$59$	2.97225e29	1.79484	0.897422	+	0.441172i	$0.145437\pi$
$60$	0	0
$61$	−3.70944e29	−1.29231	−0.646154	−	0.763207i	$-0.723624\pi$
$61$	−3.70944e29	−1.29231	−0.646154	+	0.763207i	$0.723624\pi$
$62$	2.21873e29i	0.591075i
$63$	1.47342e29i	0.301445i
$64$	4.45655e29	0.703119
$65$	0	0
$66$	1.76693e30	1.67781
$67$	− 8.43824e29i	− 0.625198i	−0.949885	−	0.312599i	$-0.898800\pi$
$67$	− 8.43824e29i	− 0.625198i	0.949885	−	0.312599i	$-0.101200\pi$
$68$	1.82091e30i	1.05656i
$69$	−1.86699e30	−0.851397
$70$	0	0
$71$	5.92473e30	1.68619	0.843094	−	0.537767i	$-0.180732\pi$
$71$	5.92473e30	1.68619	0.843094	+	0.537767i	$0.180732\pi$
$72$	− 2.87666e29i	− 0.0649982i
$73$	7.49289e30i	1.34841i	0.738544	+	0.674205i	$0.235514\pi$
$73$	7.49289e30i	1.34841i	−0.738544	+	0.674205i	$0.764486\pi$
$74$	1.02674e31	1.47617
$75$	0	0
$76$	−1.13675e31	−1.05255
$77$	− 1.26094e31i	− 0.941015i
$78$	− 2.49543e31i	− 1.50516i
$79$	−6.07295e30	−0.296861	−0.148430	−	0.988923i	$-0.547422\pi$
$79$	−6.07295e30	−0.296861	−0.148430	+	0.988923i	$0.547422\pi$
$80$	0	0
$81$	−3.78417e31	−1.22453
$82$	− 2.43304e31i	− 0.643015i
$83$	3.47153e31i	0.751160i	0.926790	+	0.375580i	$0.122556\pi$
$83$	3.47153e31i	0.751160i	−0.926790	+	0.375580i	$0.877444\pi$
$84$	4.96526e31	0.881727
$85$	0	0
$86$	−1.01248e32	−1.21944
$87$	− 1.79147e31i	− 0.178296i
$88$	2.46181e31i	0.202904i
$89$	−1.80671e32	−1.23582	−0.617909	−	0.786250i	$-0.712020\pi$
$89$	−1.80671e32	−1.23582	−0.617909	+	0.786250i	$0.712020\pi$
$90$	0	0
$91$	−1.78082e32	−0.844183
$92$	1.59775e32i	0.632424i
$93$	− 1.51521e32i	− 0.501769i
$94$	−9.52688e32	−2.64448
$95$	0	0
$96$	−7.89312e32	−1.54801
$97$	− 1.09143e33i	− 1.80411i	−0.431622	−	0.902055i	$-0.642058\pi$
$97$	− 1.09143e33i	− 1.80411i	0.431622	−	0.902055i	$-0.357942\pi$
$98$	2.10841e32i	0.294256i
$99$	−3.06434e32	−0.361706
$100$	0	0
$101$	−7.13542e32	−0.605504	−0.302752	−	0.953069i	$-0.597905\pi$
$101$	−7.13542e32	−0.605504	−0.302752	+	0.953069i	$0.597905\pi$
$102$	− 2.68952e33i	− 1.93986i
$103$	− 1.80265e33i	− 1.10687i	−0.832891	−	0.553437i	$-0.813316\pi$
$103$	− 1.80265e33i	− 1.10687i	0.832891	−	0.553437i	$-0.186684\pi$
$104$	3.47680e32	0.182025
$105$	0	0
$106$	−2.21527e33	−0.846992
$107$	− 4.02336e33i	− 1.31752i	−0.752354	−	0.658759i	$-0.771082\pi$
$107$	− 4.02336e33i	− 1.31752i	0.752354	−	0.658759i	$-0.228918\pi$
$108$	2.33822e33i	0.656739i
$109$	−2.00598e33	−0.483937	−0.241968	−	0.970284i	$-0.577793\pi$
$109$	−2.00598e33	−0.483937	−0.241968	+	0.970284i	$0.577793\pi$
$110$	0	0
$111$	−7.01177e33	−1.25314
$112$	6.43722e33i	0.992204i
$113$	− 6.69356e33i	− 0.890970i	−0.895289	−	0.445485i	$-0.853031\pi$
$113$	− 6.69356e33i	− 0.890970i	0.895289	−	0.445485i	$-0.146969\pi$
$114$	1.67900e34	1.93251
$115$	0	0
$116$	−1.53311e33	−0.132440
$117$	4.32776e33i	0.324486i
$118$	3.75695e34i	2.44783i
$119$	−1.91933e34	−1.08799
$120$	0	0
$121$	2.99905e33	0.129129
$122$	− 4.68877e34i	− 1.76247i
$123$	1.66156e34i	0.545861i
$124$	−1.29670e34	−0.372718
$125$	0	0
$126$	−1.86242e34	−0.411115
$127$	1.27300e34i	0.246643i	0.992367	+	0.123321i	$0.0393546\pi$
$127$	1.27300e34i	0.246643i	−0.992367	+	0.123321i	$0.960645\pi$
$128$	− 2.22144e34i	− 0.378155i
$129$	6.91435e34	1.03519
$130$	0	0
$131$	1.12002e35	1.30092	0.650461	−	0.759540i	$-0.274576\pi$
$131$	1.12002e35	1.30092	0.650461	+	0.759540i	$0.274576\pi$
$132$	1.03264e35i	1.05799i
$133$	− 1.19819e35i	− 1.08386i
$134$	1.06660e35	0.852653
$135$	0	0
$136$	3.74722e34	0.234594
$137$	− 7.78279e34i	− 0.431763i	−0.976420	−	0.215882i	$-0.930737\pi$
$137$	− 7.78279e34i	− 0.431763i	0.976420	−	0.215882i	$-0.0692626\pi$
$138$	− 2.35989e35i	− 1.16115i
$139$	−3.58047e35	−1.56385	−0.781925	−	0.623372i	$-0.785762\pi$
$139$	−3.58047e35	−1.56385	−0.781925	+	0.623372i	$0.785762\pi$
$140$	0	0
$141$	6.50605e35	2.24493
$142$	7.48891e35i	2.29965i
$143$	− 3.70364e35i	− 1.01294i
$144$	1.56438e35	0.381382
$145$	0	0
$146$	−9.47108e35	−1.83898
$147$	− 1.43987e35i	− 0.249797i
$148$	6.00058e35i	0.930840i
$149$	1.72179e35	0.239005	0.119502	−	0.992834i	$-0.461870\pi$
$149$	1.72179e35	0.239005	0.119502	+	0.992834i	$0.461870\pi$
$150$	0	0
$151$	1.08017e36	1.20330	0.601651	−	0.798759i	$-0.294510\pi$
$151$	1.08017e36	1.20330	0.601651	+	0.798759i	$0.294510\pi$
$152$	2.33930e35i	0.233705i
$153$	4.66436e35i	0.418199i
$154$	1.59384e36	1.28337
$155$	0	0
$156$	1.45840e36	0.949121
$157$	− 2.63407e36i	− 1.54271i	−0.636407	−	0.771353i	$-0.719580\pi$
$157$	− 2.63407e36i	− 1.54271i	0.636407	−	0.771353i	$-0.280420\pi$
$158$	− 7.67626e35i	− 0.404863i
$159$	1.51284e36	0.719019
$160$	0	0
$161$	−1.68410e36	−0.651239
$162$	− 4.78323e36i	− 1.67003i
$163$	5.17457e36i	1.63222i	0.577896	+	0.816111i	$0.303874\pi$
$163$	5.17457e36i	1.63222i	−0.577896	+	0.816111i	$0.696126\pi$
$164$	1.42194e36	0.405470
$165$	0	0
$166$	−4.38804e36	−1.02444
$167$	4.37605e36i	0.925252i	0.886553	+	0.462626i	$0.153093\pi$
$167$	4.37605e36i	0.925252i	−0.886553	+	0.462626i	$0.846907\pi$
$168$	− 1.02179e36i	− 0.195776i
$169$	5.25488e35	0.0912919
$170$	0	0
$171$	−2.91185e36	−0.416614
$172$	− 5.91721e36i	− 0.768949i
$173$	− 1.16497e37i	− 1.37580i	−0.725805	−	0.687900i	$-0.758533\pi$
$173$	− 1.16497e37i	− 1.37580i	0.725805	−	0.687900i	$-0.241467\pi$
$174$	2.26443e36	0.243162
$175$	0	0
$176$	−1.33877e37	−1.19055
$177$	− 2.56568e37i	− 2.07799i
$178$	− 2.28370e37i	− 1.68543i
$179$	−3.52955e36	−0.237490	−0.118745	−	0.992925i	$-0.537887\pi$
$179$	−3.52955e36	−0.237490	−0.118745	+	0.992925i	$0.537887\pi$
$180$	0	0
$181$	−1.74051e37	−0.974947	−0.487473	−	0.873138i	$-0.662081\pi$
$181$	−1.74051e37	−0.974947	−0.487473	+	0.873138i	$0.662081\pi$
$182$	− 2.25097e37i	− 1.15131i
$183$	3.20203e37i	1.49618i
$184$	3.28797e36	0.140421
$185$	0	0
$186$	1.91524e37	0.684320
$187$	− 3.99170e37i	− 1.30548i
$188$	− 5.56779e37i	− 1.66755i
$189$	−2.46459e37	−0.676277
$190$	0	0
$191$	−2.24606e36	−0.0518048	−0.0259024	−	0.999664i	$-0.508246\pi$
$191$	−2.24606e36	−0.0518048	−0.0259024	+	0.999664i	$0.508246\pi$
$192$	− 3.84694e37i	− 0.814040i
$193$	2.96630e37i	0.576129i	0.957611	+	0.288064i	$0.0930117\pi$
$193$	2.96630e37i	0.576129i	−0.957611	+	0.288064i	$0.906988\pi$
$194$	1.37958e38	2.46047
$195$	0	0
$196$	−1.23222e37	−0.185551
$197$	5.56817e37i	0.770939i	0.922721	+	0.385470i	$0.125961\pi$
$197$	5.56817e37i	0.770939i	−0.922721	+	0.385470i	$0.874039\pi$
$198$	− 3.87335e37i	− 0.493300i
$199$	6.53016e36	0.0765328	0.0382664	−	0.999268i	$-0.487816\pi$
$199$	6.53016e36	0.0765328	0.0382664	+	0.999268i	$0.487816\pi$
$200$	0	0
$201$	−7.28398e37	−0.723826
$202$	− 9.01924e37i	− 0.825795i
$203$	− 1.61597e37i	− 0.136380i
$204$	1.57183e38	1.22323
$205$	0	0
$206$	2.27857e38	1.50957
$207$	4.09270e37i	0.250322i
$208$	1.89075e38i	1.06804i
$209$	2.49193e38	1.30053
$210$	0	0
$211$	4.18954e38	1.86856	0.934278	−	0.356545i	$-0.116045\pi$
$211$	4.18954e38	1.86856	0.934278	+	0.356545i	$0.116045\pi$
$212$	− 1.29467e38i	− 0.534093i
$213$	− 5.11429e38i	− 1.95219i
$214$	5.08556e38	1.79685
$215$	0	0
$216$	4.81177e37	0.145820
$217$	− 1.36678e38i	− 0.383806i
$218$	− 2.53557e38i	− 0.660000i
$219$	6.46795e38	1.56113
$220$	0	0
$221$	−5.63747e38	−1.17115
$222$	− 8.86294e38i	− 1.70905i
$223$	− 1.62044e38i	− 0.290136i	−0.989422	−	0.145068i	$-0.953660\pi$
$223$	− 1.62044e38i	− 0.290136i	0.989422	−	0.145068i	$-0.0463402\pi$
$224$	−7.11990e38	−1.18408
$225$	0	0
$226$	8.46072e38	1.21512
$227$	− 9.68892e38i	− 1.29375i	−0.762598	−	0.646873i	$-0.776076\pi$
$227$	− 9.68892e38i	− 1.29375i	0.762598	−	0.646873i	$-0.223924\pi$
$228$	9.81259e38i	1.21859i
$229$	−4.72860e38	−0.546320	−0.273160	−	0.961969i	$-0.588069\pi$
$229$	−4.72860e38	−0.546320	−0.273160	+	0.961969i	$0.588069\pi$
$230$	0	0
$231$	−1.08846e39	−1.08946
$232$	3.15496e37i	0.0294065i
$233$	− 2.32086e38i	− 0.201501i	−0.994912	−	0.100750i	$-0.967876\pi$
$233$	− 2.32086e38i	− 0.201501i	0.994912	−	0.100750i	$-0.0321243\pi$
$234$	−5.47032e38	−0.442539
$235$	0	0
$236$	−2.19567e39	−1.54355
$237$	5.24224e38i	0.343692i
$238$	− 2.42605e39i	− 1.48381i
$239$	−1.78755e39	−1.02022	−0.510109	−	0.860110i	$-0.670395\pi$
$239$	−1.78755e39	−1.02022	−0.510109	+	0.860110i	$0.670395\pi$
$240$	0	0
$241$	−2.68792e39	−1.33701	−0.668506	−	0.743707i	$-0.733066\pi$
$241$	−2.68792e39	−1.33701	−0.668506	+	0.743707i	$0.733066\pi$
$242$	3.79082e38i	0.176108i
$243$	1.50698e39i	0.654041i
$244$	2.74026e39	1.11137
$245$	0	0
$246$	−2.10023e39	−0.744453
$247$	− 3.51934e39i	− 1.16671i
$248$	2.66844e38i	0.0827571i
$249$	2.99666e39	0.869659
$250$	0	0
$251$	2.18494e39	0.555677	0.277838	−	0.960628i	$-0.410382\pi$
$251$	2.18494e39	0.555677	0.277838	+	0.960628i	$0.410382\pi$
$252$	− 1.08845e39i	− 0.259240i
$253$	− 3.50248e39i	− 0.781426i
$254$	−1.60909e39	−0.336375
$255$	0	0
$256$	6.63606e39	1.21885
$257$	− 8.25568e39i	− 1.42186i	−0.703264	−	0.710929i	$-0.748275\pi$
$257$	− 8.25568e39i	− 1.42186i	0.703264	−	0.710929i	$-0.251725\pi$
$258$	8.73980e39i	1.41181i
$259$	−6.32489e39	−0.958532
$260$	0	0
$261$	−3.92715e38	−0.0524214
$262$	1.41572e40i	1.77422i
$263$	2.69949e39i	0.317697i	0.987303	+	0.158848i	$0.0507781\pi$
$263$	2.69949e39i	0.317697i	−0.987303	+	0.158848i	$0.949222\pi$
$264$	2.12506e39	0.234912
$265$	0	0
$266$	1.51452e40	1.47819
$267$	1.55958e40i	1.43077i
$268$	6.23353e39i	0.537663i
$269$	−1.21756e40	−0.987592	−0.493796	−	0.869578i	$-0.664391\pi$
$269$	−1.21756e40	−0.987592	−0.493796	+	0.869578i	$0.664391\pi$
$270$	0	0
$271$	−9.05453e39	−0.649939	−0.324969	−	0.945725i	$-0.605354\pi$
$271$	−9.05453e39	−0.649939	−0.324969	+	0.945725i	$0.605354\pi$
$272$	2.03781e40i	1.37650i
$273$	1.53722e40i	0.977357i
$274$	9.83751e39	0.588845
$275$	0	0
$276$	1.37919e40	0.732192
$277$	6.18766e39i	0.309464i	0.987956	+	0.154732i	$0.0494515\pi$
$277$	6.18766e39i	0.309464i	−0.987956	+	0.154732i	$0.950549\pi$
$278$	− 4.52574e40i	− 2.13280i
$279$	−3.32155e39	−0.147527
$280$	0	0
$281$	4.51611e39	0.178283	0.0891415	−	0.996019i	$-0.471588\pi$
$281$	4.51611e39	0.178283	0.0891415	+	0.996019i	$0.471588\pi$
$282$	8.22371e40i	3.06166i
$283$	3.25719e40i	1.14384i	0.820308	+	0.571921i	$0.193802\pi$
$283$	3.25719e40i	1.14384i	−0.820308	+	0.571921i	$0.806198\pi$
$284$	−4.37674e40	−1.45010
$285$	0	0
$286$	4.68143e40	1.38146
$287$	1.49879e40i	0.417533i
$288$	1.73028e40i	0.455136i
$289$	−2.05049e40	−0.509382
$290$	0	0
$291$	−9.42136e40	−2.08872
$292$	− 5.53518e40i	− 1.15962i
$293$	− 6.99032e40i	− 1.38414i	−0.721829	−	0.692072i	$-0.756698\pi$
$293$	− 6.99032e40i	− 1.38414i	0.721829	−	0.692072i	$-0.243302\pi$
$294$	1.82001e40	0.340676
$295$	0	0
$296$	1.23485e40	0.206681
$297$	− 5.12570e40i	− 0.811469i
$298$	2.17636e40i	0.325958i
$299$	−4.94655e40	−0.701016
$300$	0	0
$301$	6.23701e40	0.791825
$302$	1.36535e41i	1.64108i
$303$	6.15938e40i	0.701025i
$304$	−1.27215e41	−1.37128
$305$	0	0
$306$	−5.89579e40	−0.570346
$307$	− 1.35007e40i	− 0.123758i	−0.998084	−	0.0618788i	$-0.980291\pi$
$307$	− 1.35007e40i	− 0.123758i	0.998084	−	0.0618788i	$-0.0197092\pi$
$308$	9.31485e40i	0.809262i
$309$	−1.55607e41	−1.28149
$310$	0	0
$311$	5.12682e40	0.379579	0.189789	−	0.981825i	$-0.439220\pi$
$311$	5.12682e40	0.379579	0.189789	+	0.981825i	$0.439220\pi$
$312$	− 3.00122e40i	− 0.210740i
$313$	1.36507e39i	0.00909232i	0.999990	+	0.00454616i	$0.00144709\pi$
$313$	1.36507e39i	0.00909232i	−0.999990	+	0.00454616i	$0.998553\pi$
$314$	3.32949e41	2.10397
$315$	0	0
$316$	4.48624e40	0.255297
$317$	− 2.88324e41i	− 1.55741i	−0.627390	−	0.778705i	$-0.715877\pi$
$317$	− 2.88324e41i	− 1.55741i	0.627390	−	0.778705i	$-0.284123\pi$
$318$	1.91224e41i	0.980609i
$319$	3.36080e40	0.163643
$320$	0	0
$321$	−3.47301e41	−1.52536
$322$	− 2.12871e41i	− 0.888169i
$323$	− 3.79307e41i	− 1.50366i
$324$	2.79546e41	1.05308
$325$	0	0
$326$	−6.54070e41	−2.22605
$327$	1.73158e41i	0.560280i
$328$	− 2.92619e40i	− 0.0900292i
$329$	5.86871e41	1.71716
$330$	0	0
$331$	1.22306e41	0.323808	0.161904	−	0.986807i	$-0.448237\pi$
$331$	1.22306e41	0.323808	0.161904	+	0.986807i	$0.448237\pi$
$332$	− 2.56450e41i	− 0.645989i
$333$	1.53708e41i	0.368439i
$334$	−5.53136e41	−1.26187
$335$	0	0
$336$	5.55668e41	1.14873
$337$	− 1.95036e40i	− 0.0383902i	−0.999816	−	0.0191951i	$-0.993890\pi$
$337$	− 1.95036e40i	− 0.0383902i	0.999816	−	0.0191951i	$-0.00611037\pi$
$338$	6.64222e40i	0.124505i
$339$	−5.77796e41	−1.03152
$340$	0	0
$341$	2.84254e41	0.460531
$342$	− 3.68061e41i	− 0.568183i
$343$	− 7.31855e41i	− 1.07664i
$344$	−1.21769e41	−0.170735
$345$	0	0
$346$	1.47254e42	1.87634
$347$	8.38690e41i	1.01898i	0.860477	+	0.509490i	$0.170166\pi$
$347$	8.38690e41i	1.01898i	−0.860477	+	0.509490i	$0.829834\pi$
$348$	1.32340e41i	0.153333i
$349$	2.92359e40	0.0323070	0.0161535	−	0.999870i	$-0.494858\pi$
$349$	2.92359e40	0.0323070	0.0161535	+	0.999870i	$0.494858\pi$
$350$	0	0
$351$	−7.23902e41	−0.727968
$352$	− 1.48075e42i	− 1.42079i
$353$	− 1.88083e42i	− 1.72213i	−0.508492	−	0.861067i	$-0.669797\pi$
$353$	− 1.88083e42i	− 1.72213i	0.508492	−	0.861067i	$-0.330203\pi$
$354$	3.24304e42	2.83399
$355$	0	0
$356$	1.33466e42	1.06279
$357$	1.65679e42i	1.25962i
$358$	− 4.46139e41i	− 0.323892i
$359$	−1.60953e41	−0.111594	−0.0557968	−	0.998442i	$-0.517770\pi$
$359$	−1.60953e41	−0.111594	−0.0557968	+	0.998442i	$0.517770\pi$
$360$	0	0
$361$	7.87154e41	0.497956
$362$	− 2.20002e42i	− 1.32965i
$363$	− 2.58881e41i	− 0.149500i
$364$	1.31554e42	0.725988
$365$	0	0
$366$	−4.04740e42	−2.04051
$367$	− 2.15460e42i	− 1.03843i	−0.854645	−	0.519213i	$-0.826225\pi$
$367$	− 2.15460e42i	− 1.03843i	0.854645	−	0.519213i	$-0.173775\pi$
$368$	1.78806e42i	0.823933i
$369$	3.64238e41	0.160491
$370$	0	0
$371$	1.36464e42	0.549982
$372$	1.11932e42i	0.431516i
$373$	2.59028e42i	0.955325i	0.878543	+	0.477663i	$0.158516\pi$
$373$	2.59028e42i	0.955325i	−0.878543	+	0.477663i	$0.841484\pi$
$374$	5.04554e42	1.78044
$375$	0	0
$376$	−1.14578e42	−0.370257
$377$	− 4.74646e41i	− 0.146804i
$378$	− 3.11526e42i	− 0.922316i
$379$	−4.01905e42	−1.13914	−0.569568	−	0.821944i	$-0.692890\pi$
$379$	−4.01905e42	−1.13914	−0.569568	+	0.821944i	$0.692890\pi$
$380$	0	0
$381$	1.09887e42	0.285551
$382$	− 2.83904e41i	− 0.0706522i
$383$	5.03299e42i	1.19963i	0.800140	+	0.599813i	$0.204758\pi$
$383$	5.03299e42i	1.19963i	−0.800140	+	0.599813i	$0.795242\pi$
$384$	−1.91757e42	−0.437811
$385$	0	0
$386$	−3.74943e42	−0.785732
$387$	− 1.51572e42i	− 0.304361i
$388$	8.06268e42i	1.55151i
$389$	−4.14807e42	−0.765029	−0.382515	−	0.923949i	$-0.624942\pi$
$389$	−4.14807e42	−0.765029	−0.382515	+	0.923949i	$0.624942\pi$
$390$	0	0
$391$	−5.33128e42	−0.903473
$392$	2.53576e41i	0.0411991i
$393$	− 9.66818e42i	− 1.50615i
$394$	−7.03822e42	−1.05142
$395$	0	0
$396$	2.26370e42	0.311063
$397$	8.89168e42i	1.17203i	0.810299	+	0.586017i	$0.199305\pi$
$397$	8.89168e42i	1.17203i	−0.810299	+	0.586017i	$0.800695\pi$
$398$	8.25418e41i	0.104377i
$399$	−1.03429e43	−1.25485
$400$	0	0
$401$	1.71192e41	0.0191250	0.00956251	−	0.999954i	$-0.496956\pi$
$401$	1.71192e41	0.0191250	0.00956251	+	0.999954i	$0.496956\pi$
$402$	− 9.20702e42i	− 0.987163i
$403$	− 4.01451e42i	− 0.413142i
$404$	5.27111e42	0.520727
$405$	0	0
$406$	2.04260e42	0.185996
$407$	− 1.31541e43i	− 1.15015i
$408$	− 3.23464e42i	− 0.271603i
$409$	−1.40883e43	−1.13612	−0.568061	−	0.822986i	$-0.692306\pi$
$409$	−1.40883e43	−1.13612	−0.568061	+	0.822986i	$0.692306\pi$
$410$	0	0
$411$	−6.71819e42	−0.499876
$412$	1.33166e43i	0.951899i
$413$	− 2.31434e43i	− 1.58947i
$414$	−5.17321e42	−0.341393
$415$	0	0
$416$	−2.09127e43	−1.27459
$417$	3.09070e43i	1.81056i
$418$	3.14982e43i	1.77369i
$419$	2.03304e43	1.10056	0.550280	−	0.834980i	$-0.314521\pi$
$419$	2.03304e43	1.10056	0.550280	+	0.834980i	$0.314521\pi$
$420$	0	0
$421$	2.81610e43	1.40927	0.704633	−	0.709572i	$-0.251111\pi$
$421$	2.81610e43	1.40927	0.704633	+	0.709572i	$0.251111\pi$
$422$	5.29562e43i	2.54836i
$423$	− 1.42622e43i	− 0.660039i
$424$	−2.66427e42	−0.118588
$425$	0	0
$426$	6.46451e43	2.66243
$427$	2.88836e43i	1.14443i
$428$	2.97216e43i	1.13305i
$429$	−3.19702e43	−1.17274
$430$	0	0
$431$	−1.08445e43	−0.368412	−0.184206	−	0.982888i	$-0.558971\pi$
$431$	−1.08445e43	−0.368412	−0.184206	+	0.982888i	$0.558971\pi$
$432$	2.61673e43i	0.855611i
$433$	3.95138e43i	1.24365i	0.783156	+	0.621825i	$0.213608\pi$
$433$	3.95138e43i	1.24365i	−0.783156	+	0.621825i	$0.786392\pi$
$434$	1.72762e43	0.523440
$435$	0	0
$436$	1.48186e43	0.416180
$437$	− 3.32820e43i	− 0.900047i
$438$	8.17554e43i	2.12909i
$439$	−1.22543e43	−0.307342	−0.153671	−	0.988122i	$-0.549110\pi$
$439$	−1.22543e43	−0.307342	−0.153671	+	0.988122i	$0.549110\pi$
$440$	0	0
$441$	−3.15639e42	−0.0734436
$442$	− 7.12581e43i	− 1.59723i
$443$	− 5.64830e43i	− 1.21971i	−0.792513	−	0.609855i	$-0.791228\pi$
$443$	− 5.64830e43i	− 1.21971i	0.792513	−	0.609855i	$-0.208772\pi$
$444$	5.17977e43	1.07768
$445$	0	0
$446$	2.04825e43	0.395692
$447$	− 1.48627e43i	− 0.276709i
$448$	− 3.47009e43i	− 0.622664i
$449$	−2.63282e43	−0.455362	−0.227681	−	0.973736i	$-0.573114\pi$
$449$	−2.63282e43	−0.455362	−0.227681	+	0.973736i	$0.573114\pi$
$450$	0	0
$451$	−3.11710e43	−0.501000
$452$	4.94470e43i	0.766224i
$453$	− 9.32419e43i	− 1.39313i
$454$	1.22469e44	1.76443
$455$	0	0
$456$	2.01931e43	0.270573
$457$	4.92089e43i	0.635955i	0.948098	+	0.317977i	$0.103004\pi$
$457$	4.92089e43i	0.635955i	−0.948098	+	0.317977i	$0.896996\pi$
$458$	− 5.97700e43i	− 0.745079i
$459$	−7.80205e43	−0.938209
$460$	0	0
$461$	−1.35047e44	−1.51154	−0.755771	−	0.654836i	$-0.772737\pi$
$461$	−1.35047e44	−1.51154	−0.755771	+	0.654836i	$0.772737\pi$
$462$	− 1.37582e44i	− 1.48583i
$463$	9.98444e42i	0.104049i	0.998646	+	0.0520244i	$0.0165674\pi$
$463$	9.98444e42i	0.104049i	−0.998646	+	0.0520244i	$0.983433\pi$
$464$	−1.71573e43	−0.172544
$465$	0	0
$466$	2.93359e43	0.274810
$467$	− 1.53367e44i	− 1.38677i	−0.720568	−	0.693384i	$-0.756119\pi$
$467$	− 1.53367e44i	− 1.38677i	0.720568	−	0.693384i	$-0.243881\pi$
$468$	− 3.19702e43i	− 0.279054i
$469$	−6.57043e43	−0.553659
$470$	0	0
$471$	−2.27376e44	−1.78608
$472$	4.51843e43i	0.342724i
$473$	1.29714e44i	0.950116i
$474$	−6.62624e43	−0.468732
$475$	0	0
$476$	1.41785e44	0.935658
$477$	− 3.31636e43i	− 0.211401i
$478$	− 2.25948e44i	− 1.39139i
$479$	−5.80916e43	−0.345603	−0.172802	−	0.984957i	$-0.555282\pi$
$479$	−5.80916e43	−0.345603	−0.172802	+	0.984957i	$0.555282\pi$
$480$	0	0
$481$	−1.85775e44	−1.03180
$482$	− 3.39755e44i	− 1.82344i
$483$	1.45373e44i	0.753975i
$484$	−2.21547e43	−0.111050
$485$	0	0
$486$	−1.90484e44	−0.891990
$487$	− 6.21415e43i	− 0.281290i	−0.990060	−	0.140645i	$-0.955082\pi$
$487$	− 6.21415e43i	− 0.281290i	0.990060	−	0.140645i	$-0.0449176\pi$
$488$	− 5.63912e43i	− 0.246765i
$489$	4.46675e44	1.88971
$490$	0	0
$491$	1.52856e44	0.604557	0.302278	−	0.953220i	$-0.402253\pi$
$491$	1.52856e44	0.604557	0.302278	+	0.953220i	$0.402253\pi$
$492$	− 1.22744e44i	− 0.469435i
$493$	− 5.11562e43i	− 0.189201i
$494$	4.44848e44	1.59117
$495$	0	0
$496$	−1.45115e44	−0.485583
$497$	− 4.61329e44i	− 1.49324i
$498$	3.78781e44i	1.18605i
$499$	−9.99203e43	−0.302688	−0.151344	−	0.988481i	$-0.548360\pi$
$499$	−9.99203e43	−0.302688	−0.151344	+	0.988481i	$0.548360\pi$
$500$	0	0
$501$	3.77745e44	1.07122
$502$	2.76178e44i	0.757840i
$503$	9.03153e43i	0.239822i	0.992785	+	0.119911i	$0.0382610\pi$
$503$	9.03153e43i	0.239822i	−0.992785	+	0.119911i	$0.961739\pi$
$504$	−2.23991e43	−0.0575607
$505$	0	0
$506$	4.42717e44	1.06572
$507$	− 4.53607e43i	− 0.105694i
$508$	− 9.40399e43i	− 0.212110i
$509$	5.47217e44	1.19486	0.597429	−	0.801922i	$-0.296189\pi$
$509$	5.47217e44	1.19486	0.597429	+	0.801922i	$0.296189\pi$
$510$	0	0
$511$	5.83434e44	1.19412
$512$	6.47984e44i	1.28413i
$513$	− 4.87064e44i	− 0.934651i
$514$	1.04353e45	1.93915
$515$	0	0
$516$	−5.10780e44	−0.890254
$517$	1.22054e45i	2.06043i
$518$	− 7.99471e44i	− 1.30726i
$519$	−1.00562e45	−1.59284
$520$	0	0
$521$	1.19671e45	1.77897	0.889484	−	0.456966i	$-0.151064\pi$
$521$	1.19671e45	1.77897	0.889484	+	0.456966i	$0.151064\pi$
$522$	− 4.96395e43i	− 0.0714931i
$523$	− 6.44705e43i	− 0.0899670i	−0.998988	−	0.0449835i	$-0.985676\pi$
$523$	− 6.44705e43i	− 0.0899670i	0.998988	−	0.0449835i	$-0.0143235\pi$
$524$	−8.27390e44	−1.11878
$525$	0	0
$526$	−3.41218e44	−0.433279
$527$	− 4.32675e44i	− 0.532460i
$528$	1.15564e45i	1.37837i
$529$	3.97216e44	0.459206
$530$	0	0
$531$	−5.62432e44	−0.610957
$532$	8.85134e44i	0.932110i
$533$	4.40227e44i	0.449446i
$534$	−1.97132e45	−1.95131
$535$	0	0
$536$	1.28279e44	0.119381
$537$	3.04675e44i	0.274955i
$538$	− 1.53901e45i	− 1.34689i
$539$	2.70120e44	0.229267
$540$	0	0
$541$	−3.00892e44	−0.240246	−0.120123	−	0.992759i	$-0.538329\pi$
$541$	−3.00892e44	−0.240246	−0.120123	+	0.992759i	$0.538329\pi$
$542$	− 1.14450e45i	− 0.886396i
$543$	1.50243e45i	1.12875i
$544$	−2.25392e45	−1.64269
$545$	0	0
$546$	−1.94306e45	−1.33293
$547$	− 9.15780e44i	− 0.609537i	−0.952426	−	0.304769i	$-0.901421\pi$
$547$	− 9.15780e44i	− 0.609537i	0.952426	−	0.304769i	$-0.0985791\pi$
$548$	5.74934e44i	0.371312i
$549$	7.01930e44	0.439896
$550$	0	0
$551$	3.19357e44	0.188484
$552$	− 2.83821e44i	− 0.162574i
$553$	4.72870e44i	0.262892i
$554$	−7.82126e44	−0.422052
$555$	0	0
$556$	2.64498e45	1.34489
$557$	3.51921e45i	1.73714i	0.495568	+	0.868569i	$0.334960\pi$
$557$	3.51921e45i	1.73714i	−0.495568	+	0.868569i	$0.665040\pi$
$558$	− 4.19847e44i	− 0.201199i
$559$	1.83194e45	0.852348
$560$	0	0
$561$	−3.44568e45	−1.51143
$562$	5.70840e44i	0.243145i
$563$	1.25910e45i	0.520802i	0.965501	+	0.260401i	$0.0838547\pi$
$563$	1.25910e45i	0.520802i	−0.965501	+	0.260401i	$0.916145\pi$
$564$	−4.80618e45	−1.93061
$565$	0	0
$566$	−4.11711e45	−1.55999
$567$	2.94655e45i	1.08441i
$568$	9.00681e44i	0.321976i
$569$	1.60105e45	0.555972	0.277986	−	0.960585i	$-0.410333\pi$
$569$	1.60105e45	0.555972	0.277986	+	0.960585i	$0.410333\pi$
$570$	0	0
$571$	5.75140e44	0.188485	0.0942427	−	0.995549i	$-0.469957\pi$
$571$	5.75140e44	0.188485	0.0942427	+	0.995549i	$0.469957\pi$
$572$	2.73597e45i	0.871118i
$573$	1.93882e44i	0.0599773i
$574$	−1.89449e45	−0.569437
$575$	0	0
$576$	−8.43303e44	−0.239339
$577$	− 3.64572e45i	− 1.00550i	−0.864432	−	0.502750i	$-0.832321\pi$
$577$	− 3.64572e45i	− 1.00550i	0.864432	−	0.502750i	$-0.167679\pi$
$578$	− 2.59184e45i	− 0.694702i
$579$	2.56054e45	0.667016
$580$	0	0
$581$	2.70311e45	0.665207
$582$	− 1.19087e46i	− 2.84862i
$583$	2.83810e45i	0.659927i
$584$	−1.13907e45	−0.257478
$585$	0	0
$586$	8.83582e45	1.88771
$587$	2.48055e45i	0.515251i	0.966245	+	0.257626i	$0.0829401\pi$
$587$	2.48055e45i	0.515251i	−0.966245	+	0.257626i	$0.917060\pi$
$588$	1.06367e45i	0.214822i
$589$	2.70109e45	0.530441
$590$	0	0
$591$	4.80651e45	0.892558
$592$	6.71532e45i	1.21271i
$593$	2.97630e45i	0.522726i	0.965241	+	0.261363i	$0.0841720\pi$
$593$	2.97630e45i	0.522726i	−0.965241	+	0.261363i	$0.915828\pi$
$594$	6.47893e45	1.10669
$595$	0	0
$596$	−1.27193e45	−0.205541
$597$	− 5.63691e44i	− 0.0886062i
$598$	− 6.25249e45i	− 0.956056i
$599$	3.09884e45	0.460953	0.230476	−	0.973078i	$-0.425972\pi$
$599$	3.09884e45	0.460953	0.230476	+	0.973078i	$0.425972\pi$
$600$	0	0
$601$	−5.90335e45	−0.831132	−0.415566	−	0.909563i	$-0.636417\pi$
$601$	−5.90335e45	−0.831132	−0.415566	+	0.909563i	$0.636417\pi$
$602$	7.88364e45i	1.07990i
$603$	1.59675e45i	0.212815i
$604$	−7.97952e45	−1.03483
$605$	0	0
$606$	−7.78551e45	−0.956068
$607$	− 6.02204e45i	− 0.719664i	−0.933017	−	0.359832i	$-0.882834\pi$
$607$	− 6.02204e45i	− 0.719664i	0.933017	−	0.359832i	$-0.117166\pi$
$608$	− 1.40707e46i	− 1.63646i
$609$	−1.39493e45	−0.157894
$610$	0	0
$611$	1.72376e46	1.84841
$612$	− 3.44568e45i	− 0.359647i
$613$	7.92968e45i	0.805671i	0.915272	+	0.402836i	$0.131975\pi$
$613$	7.92968e45i	0.805671i	−0.915272	+	0.402836i	$0.868025\pi$
$614$	1.70650e45	0.168782
$615$	0	0
$616$	1.91688e45	0.179686
$617$	7.56919e45i	0.690787i	0.938458	+	0.345394i	$0.112255\pi$
$617$	7.56919e45i	0.690787i	−0.938458	+	0.345394i	$0.887745\pi$
$618$	− 1.96689e46i	− 1.74771i
$619$	4.72940e45	0.409176	0.204588	−	0.978848i	$-0.434415\pi$
$619$	4.72940e45	0.409176	0.204588	+	0.978848i	$0.434415\pi$
$620$	0	0
$621$	−6.84585e45	−0.561585
$622$	6.48035e45i	0.517675i
$623$	1.40680e46i	1.09441i
$624$	1.63211e46	1.23653
$625$	0	0
$626$	−1.72547e44	−0.0124002
$627$	− 2.15106e46i	− 1.50570i
$628$	1.94585e46i	1.32671i
$629$	−2.00225e46	−1.32979
$630$	0	0
$631$	−9.12534e45	−0.575128	−0.287564	−	0.957761i	$-0.592845\pi$
$631$	−9.12534e45	−0.575128	−0.287564	+	0.957761i	$0.592845\pi$
$632$	− 9.23213e44i	− 0.0566853i
$633$	− 3.61646e46i	− 2.16333i
$634$	3.64444e46	2.12402
$635$	0	0
$636$	−1.11757e46	−0.618349
$637$	− 3.81490e45i	− 0.205675i
$638$	4.24808e45i	0.223178i
$639$	−1.12112e46	−0.573971
$640$	0	0
$641$	−1.89987e46	−0.923774	−0.461887	−	0.886939i	$-0.652827\pi$
$641$	−1.89987e46	−0.923774	−0.461887	+	0.886939i	$0.652827\pi$
$642$	− 4.38992e46i	− 2.08031i
$643$	− 1.26235e46i	− 0.583040i	−0.956565	−	0.291520i	$-0.905839\pi$
$643$	− 1.26235e46i	− 0.583040i	0.956565	−	0.291520i	$-0.0941611\pi$
$644$	1.24408e46	0.560058
$645$	0	0
$646$	4.79447e46	2.05071
$647$	− 1.12690e46i	− 0.469855i	−0.972013	−	0.234927i	$-0.924515\pi$
$647$	− 1.12690e46i	− 0.469855i	0.972013	−	0.234927i	$-0.0754852\pi$
$648$	− 5.75272e45i	− 0.233822i
$649$	4.81323e46	1.90721
$650$	0	0
$651$	−1.17982e46	−0.444353
$652$	− 3.82258e46i	− 1.40369i
$653$	− 3.57189e45i	− 0.127888i	−0.997953	−	0.0639440i	$-0.979632\pi$
$653$	− 3.57189e45i	− 0.127888i	0.997953	−	0.0639440i	$-0.0203679\pi$
$654$	−2.18873e46	−0.764118
$655$	0	0
$656$	1.59131e46	0.528253
$657$	− 1.41786e46i	− 0.458993i
$658$	7.41810e46i	2.34189i
$659$	−4.26159e46	−1.31209	−0.656043	−	0.754723i	$-0.727771\pi$
$659$	−4.26159e46	−1.31209	−0.656043	+	0.754723i	$0.727771\pi$
$660$	0	0
$661$	−2.93053e46	−0.858268	−0.429134	−	0.903241i	$-0.641181\pi$
$661$	−2.93053e46	−0.858268	−0.429134	+	0.903241i	$0.641181\pi$
$662$	1.54596e46i	0.441613i
$663$	4.86633e46i	1.35590i
$664$	−5.27744e45	−0.143433
$665$	0	0
$666$	−1.94288e46	−0.502483
$667$	− 4.48866e45i	− 0.113251i
$668$	− 3.23269e46i	− 0.795707i
$669$	−1.39878e46	−0.335907
$670$	0	0
$671$	−6.00703e46	−1.37321
$672$	6.14598e46i	1.37088i
$673$	− 7.94628e44i	− 0.0172948i	−0.999963	−	0.00864740i	$-0.997247\pi$
$673$	− 7.94628e44i	− 0.0172948i	0.999963	−	0.00864740i	$-0.00275259\pi$
$674$	2.46527e45	0.0523571
$675$	0	0
$676$	−3.88191e45	−0.0785100
$677$	5.41689e46i	1.06915i	0.845122	+	0.534573i	$0.179527\pi$
$677$	5.41689e46i	1.06915i	−0.845122	+	0.534573i	$0.820473\pi$
$678$	− 7.30339e46i	− 1.40681i
$679$	−8.49843e46	−1.59767
$680$	0	0
$681$	−8.36359e46	−1.49784
$682$	3.59299e46i	0.628079i
$683$	4.80553e46i	0.819973i	0.912092	+	0.409986i	$0.134467\pi$
$683$	4.80553e46i	0.819973i	−0.912092	+	0.409986i	$0.865533\pi$
$684$	2.15106e46	0.358283
$685$	0	0
$686$	9.25072e46	1.46834
$687$	4.08178e46i	0.632505i
$688$	− 6.62202e46i	− 1.00180i
$689$	4.00824e46	0.592020
$690$	0	0
$691$	9.58471e46	1.34956	0.674779	−	0.738020i	$-0.264239\pi$
$691$	9.58471e46	1.34956	0.674779	+	0.738020i	$0.264239\pi$
$692$	8.60595e46i	1.18317i
$693$	2.38605e46i	0.320317i
$694$	−1.06011e47	−1.38970
$695$	0	0
$696$	2.72340e45	0.0340455
$697$	4.74467e46i	0.579249i
$698$	3.69544e45i	0.0440607i
$699$	−2.00340e46	−0.233288
$700$	0	0
$701$	3.14053e46	0.348863	0.174432	−	0.984669i	$-0.444191\pi$
$701$	3.14053e46	0.348863	0.174432	+	0.984669i	$0.444191\pi$
$702$	− 9.15018e46i	− 0.992813i
$703$	− 1.24996e47i	− 1.32474i
$704$	7.21688e46	0.747138
$705$	0	0
$706$	2.37738e47	2.34867
$707$	5.55600e46i	0.536218i
$708$	1.89533e47i	1.78705i
$709$	1.07691e47	0.992009	0.496005	−	0.868320i	$-0.334800\pi$
$709$	1.07691e47	0.992009	0.496005	+	0.868320i	$0.334800\pi$
$710$	0	0
$711$	1.14917e46	0.101050
$712$	− 2.74658e46i	− 0.235978i
$713$	− 3.79647e46i	− 0.318715i
$714$	−2.09419e47	−1.71789
$715$	0	0
$716$	2.60737e46	0.204239
$717$	1.54303e47i	1.18116i
$718$	− 2.03445e46i	− 0.152193i
$719$	−2.02046e47	−1.47715	−0.738573	−	0.674174i	$-0.764500\pi$
$719$	−2.02046e47	−1.47715	−0.738573	+	0.674174i	$0.764500\pi$
$720$	0	0
$721$	−1.40364e47	−0.980218
$722$	9.94970e46i	0.679120i
$723$	2.32024e47i	1.54793i
$724$	1.28576e47	0.838444
$725$	0	0
$726$	3.27228e46	0.203890
$727$	2.34830e47i	1.43033i	0.698957	+	0.715164i	$0.253648\pi$
$727$	2.34830e47i	1.43033i	−0.698957	+	0.715164i	$0.746352\pi$
$728$	− 2.70721e46i	− 0.161196i
$729$	−8.02799e46	−0.467308
$730$	0	0
$731$	1.97443e47	1.09851
$732$	− 2.36542e47i	− 1.28669i
$733$	7.07756e46i	0.376416i	0.982129	+	0.188208i	$0.0602679\pi$
$733$	7.07756e46i	0.376416i	−0.982129	+	0.188208i	$0.939732\pi$
$734$	2.72343e47	1.41622
$735$	0	0
$736$	−1.97768e47	−0.983270
$737$	− 1.36648e47i	− 0.664338i
$738$	4.60399e46i	0.218879i
$739$	3.25905e47	1.51516	0.757578	−	0.652744i	$-0.226382\pi$
$739$	3.25905e47	1.51516	0.757578	+	0.652744i	$0.226382\pi$
$740$	0	0
$741$	−3.03794e47	−1.35076
$742$	1.72492e47i	0.750074i
$743$	− 1.42154e47i	− 0.604568i	−0.953218	−	0.302284i	$-0.902251\pi$
$743$	− 1.42154e47i	− 0.604568i	0.953218	−	0.302284i	$-0.0977490\pi$
$744$	2.30343e46	0.0958124
$745$	0	0
$746$	−3.27414e47	−1.30289
$747$	− 6.56910e46i	− 0.255691i
$748$	2.94877e47i	1.12270i
$749$	−3.13279e47	−1.16676
$750$	0	0
$751$	−8.07948e45	−0.0287955	−0.0143978	−	0.999896i	$-0.504583\pi$
$751$	−8.07948e45	−0.0287955	−0.0143978	+	0.999896i	$0.504583\pi$
$752$	− 6.23098e47i	− 2.17251i
$753$	− 1.88606e47i	− 0.643338i
$754$	5.99956e46	0.200213
$755$	0	0
$756$	1.82065e47	0.581591
$757$	− 2.98356e47i	− 0.932509i	−0.884651	−	0.466255i	$-0.845603\pi$
$757$	− 2.98356e47i	− 0.932509i	0.884651	−	0.466255i	$-0.154397\pi$
$758$	− 5.08011e47i	− 1.55357i
$759$	−3.02338e47	−0.904699
$760$	0	0
$761$	8.91821e46	0.255524	0.127762	−	0.991805i	$-0.459221\pi$
$761$	8.91821e46	0.255524	0.127762	+	0.991805i	$0.459221\pi$
$762$	1.38898e47i	0.389439i
$763$	1.56195e47i	0.428562i
$764$	1.65922e46	0.0445516
$765$	0	0
$766$	−6.36174e47	−1.63607
$767$	− 6.79771e47i	− 1.71096i
$768$	− 5.72833e47i	− 1.41113i
$769$	3.11972e47	0.752195	0.376098	−	0.926580i	$-0.377266\pi$
$769$	3.11972e47	0.752195	0.376098	+	0.926580i	$0.377266\pi$
$770$	0	0
$771$	−7.12640e47	−1.64616
$772$	− 2.19128e47i	− 0.495464i
$773$	5.84176e47i	1.29295i	0.762935	+	0.646475i	$0.223758\pi$
$773$	5.84176e47i	1.29295i	−0.762935	+	0.646475i	$0.776242\pi$
$774$	1.91589e47	0.415092
$775$	0	0
$776$	1.65920e47	0.344493
$777$	5.45972e47i	1.10974i
$778$	− 5.24320e47i	− 1.04336i
$779$	−2.96199e47	−0.577053
$780$	0	0
$781$	9.59444e47	1.79175
$782$	− 6.73879e47i	− 1.23217i
$783$	− 6.56892e46i	− 0.117605i
$784$	−1.37899e47	−0.241739
$785$	0	0
$786$	1.22207e48	2.05411
$787$	− 3.46036e47i	− 0.569559i	−0.958593	−	0.284779i	$-0.908080\pi$
$787$	− 3.46036e47i	− 0.569559i	0.958593	−	0.284779i	$-0.0919203\pi$
$788$	− 4.11335e47i	− 0.662999i
$789$	2.33023e47	0.367815
$790$	0	0
$791$	−5.21194e47	−0.789019
$792$	− 4.65842e46i	− 0.0690675i
$793$	8.48371e47i	1.23191i
$794$	−1.12392e48	−1.59844
$795$	0	0
$796$	−4.82399e46	−0.0658174
$797$	8.43355e47i	1.12706i	0.826095	+	0.563532i	$0.190558\pi$
$797$	8.43355e47i	1.12706i	−0.826095	+	0.563532i	$0.809442\pi$
$798$	− 1.30735e48i	− 1.71138i
$799$	1.85784e48	2.38224
$800$	0	0
$801$	3.41881e47	0.420667
$802$	2.16388e46i	0.0260830i
$803$	1.21339e48i	1.43283i
$804$	5.38086e47	0.622482
$805$	0	0
$806$	5.07438e47	0.563449
$807$	1.05101e48i	1.14339i
$808$	− 1.08473e47i	− 0.115620i
$809$	1.87301e48	1.95609	0.978045	−	0.208392i	$-0.0668229\pi$
$809$	1.87301e48	1.95609	0.978045	+	0.208392i	$0.0668229\pi$
$810$	0	0
$811$	−1.53865e48	−1.54275	−0.771376	−	0.636380i	$-0.780431\pi$
$811$	−1.53865e48	−1.54275	−0.771376	+	0.636380i	$0.780431\pi$
$812$	1.19376e47i	0.117285i
$813$	7.81597e47i	0.752470i
$814$	1.66269e48	1.56859
$815$	0	0
$816$	1.75906e48	1.59365
$817$	1.23259e48i	1.09435i
$818$	− 1.78078e48i	− 1.54946i
$819$	3.36981e47	0.287356
$820$	0	0
$821$	−1.66705e48	−1.36548	−0.682742	−	0.730660i	$-0.739213\pi$
$821$	−1.66705e48	−1.36548	−0.682742	+	0.730660i	$0.739213\pi$
$822$	− 8.49185e47i	− 0.681738i
$823$	2.01297e48i	1.58394i	0.610557	+	0.791972i	$0.290945\pi$
$823$	2.01297e48i	1.58394i	−0.610557	+	0.791972i	$0.709055\pi$
$824$	2.74041e47	0.211357
$825$	0	0
$826$	2.92535e48	2.16774
$827$	− 1.15395e48i	− 0.838195i	−0.907941	−	0.419098i	$-0.862347\pi$
$827$	− 1.15395e48i	− 0.838195i	0.907941	−	0.419098i	$-0.137653\pi$
$828$	− 3.02338e47i	− 0.215274i
$829$	−1.78893e48	−1.24866	−0.624331	−	0.781160i	$-0.714628\pi$
$829$	−1.78893e48	−1.24866	−0.624331	+	0.781160i	$0.714628\pi$
$830$	0	0
$831$	5.34126e47	0.358284
$832$	− 1.01924e48i	− 0.670257i
$833$	− 4.11161e47i	− 0.265076i
$834$	−3.90667e48	−2.46926
$835$	0	0
$836$	−1.84085e48	−1.11844
$837$	− 5.55594e47i	− 0.330969i
$838$	2.56978e48i	1.50096i
$839$	−2.30591e48	−1.32059	−0.660297	−	0.751004i	$-0.729570\pi$
$839$	−2.30591e48	−1.32059	−0.660297	+	0.751004i	$0.729570\pi$
$840$	0	0
$841$	−1.77300e48	−0.976284
$842$	3.55957e48i	1.92198i
$843$	− 3.89835e47i	− 0.206408i
$844$	−3.09492e48	−1.60694
$845$	0	0
$846$	1.80275e48	0.900171
$847$	− 2.33521e47i	− 0.114354i
$848$	− 1.44888e48i	− 0.695826i
$849$	2.81164e48	1.32429
$850$	0	0
$851$	−1.75685e48	−0.795972
$852$	3.77806e48i	1.67886i
$853$	3.23565e48i	1.41027i	0.709073	+	0.705135i	$0.249114\pi$
$853$	3.23565e48i	1.41027i	−0.709073	+	0.705135i	$0.750886\pi$
$854$	−3.65091e48	−1.56080
$855$	0	0
$856$	6.11634e47	0.251579
$857$	− 1.13232e48i	− 0.456864i	−0.973560	−	0.228432i	$-0.926640\pi$
$857$	− 1.13232e48i	− 0.456864i	0.973560	−	0.228432i	$-0.0733598\pi$
$858$	− 4.04107e48i	− 1.59939i
$859$	1.69678e48	0.658777	0.329388	−	0.944195i	$-0.393157\pi$
$859$	1.69678e48	0.658777	0.329388	+	0.944195i	$0.393157\pi$
$860$	0	0
$861$	1.29378e48	0.483400
$862$	− 1.37075e48i	− 0.502445i
$863$	− 4.68742e48i	− 1.68561i	−0.538223	−	0.842803i	$-0.680904\pi$
$863$	− 4.68742e48i	− 1.68561i	0.538223	−	0.842803i	$-0.319096\pi$
$864$	−2.89424e48	−1.02107
$865$	0	0
$866$	−4.99457e48	−1.69611
$867$	1.77001e48i	0.589739i
$868$	1.00967e48i	0.330069i
$869$	−9.83446e47	−0.315446
$870$	0	0
$871$	−1.92987e48	−0.595977
$872$	− 3.04950e47i	− 0.0924073i
$873$	2.06529e48i	0.614111i
$874$	4.20687e48	1.22750
$875$	0	0
$876$	−4.77803e48	−1.34255
$877$	− 6.18989e48i	− 1.70683i	−0.521234	−	0.853414i	$-0.674528\pi$
$877$	− 6.18989e48i	− 1.70683i	0.521234	−	0.853414i	$-0.325472\pi$
$878$	− 1.54895e48i	− 0.419158i
$879$	−6.03412e48	−1.60250
$880$	0	0
$881$	2.27101e48	0.580919	0.290460	−	0.956887i	$-0.406192\pi$
$881$	2.27101e48	0.580919	0.290460	+	0.956887i	$0.406192\pi$
$882$	− 3.98971e47i	− 0.100163i
$883$	6.78750e48i	1.67247i	0.548372	+	0.836234i	$0.315248\pi$
$883$	6.78750e48i	1.67247i	−0.548372	+	0.836234i	$0.684752\pi$
$884$	4.16454e48	1.00717
$885$	0	0
$886$	7.13950e48	1.66346
$887$	6.24043e48i	1.42717i	0.700570	+	0.713583i	$0.252929\pi$
$887$	6.24043e48i	1.42717i	−0.700570	+	0.713583i	$0.747071\pi$
$888$	− 1.06593e48i	− 0.239285i
$889$	9.91224e47	0.218420
$890$	0	0
$891$	−6.12805e48	−1.30119
$892$	1.19706e48i	0.249514i
$893$	1.15980e49i	2.37321i
$894$	1.87866e48	0.377379
$895$	0	0
$896$	−1.72972e48	−0.334884
$897$	4.26992e48i	0.811605i
$898$	− 3.32791e48i	− 0.621030i
$899$	3.64290e47	0.0667440
$900$	0	0
$901$	4.31999e48	0.762998
$902$	− 3.94004e48i	− 0.683271i
$903$	− 5.38386e48i	− 0.916739i
$904$	1.01756e48	0.170130
$905$	0	0
$906$	1.17859e49	1.89997
$907$	6.86902e48i	1.08736i	0.839292	+	0.543681i	$0.182970\pi$
$907$	6.86902e48i	1.08736i	−0.839292	+	0.543681i	$0.817030\pi$
$908$	7.15745e48i	1.11261i
$909$	1.35022e48	0.206111
$910$	0	0
$911$	7.47750e48	1.10079	0.550393	−	0.834906i	$-0.314478\pi$
$911$	7.47750e48	1.10079	0.550393	+	0.834906i	$0.314478\pi$
$912$	1.09814e49i	1.58760i
$913$	5.62176e48i	0.798186i
$914$	−6.22004e48	−0.867324
$915$	0	0
$916$	3.49314e48	0.469829
$917$	− 8.72107e48i	− 1.15206i
$918$	− 9.86186e48i	− 1.27954i
$919$	1.28656e49	1.63955	0.819777	−	0.572683i	$-0.194097\pi$
$919$	1.28656e49	1.63955	0.819777	+	0.572683i	$0.194097\pi$
$920$	0	0
$921$	−1.16539e48	−0.143281
$922$	− 1.70701e49i	− 2.06146i
$923$	− 1.35502e49i	− 1.60738i
$924$	8.04069e48	0.936927
$925$	0	0
$926$	−1.26204e48	−0.141903
$927$	3.41112e48i	0.376775i
$928$	− 1.89768e48i	− 0.205912i
$929$	−8.12716e48	−0.866322	−0.433161	−	0.901316i	$-0.642602\pi$
$929$	−8.12716e48	−0.866322	−0.433161	+	0.901316i	$0.642602\pi$
$930$	0	0
$931$	2.56678e48	0.264070
$932$	1.71448e48i	0.173288i
$933$	− 4.42553e48i	− 0.439459i
$934$	1.93857e49	1.89129
$935$	0	0
$936$	−6.57908e47	−0.0619603
$937$	− 2.32824e48i	− 0.215439i	−0.994181	−	0.107720i	$-0.965645\pi$
$937$	− 2.32824e48i	− 0.215439i	0.994181	−	0.107720i	$-0.0343549\pi$
$938$	− 8.30508e48i	− 0.755087i
$939$	1.17835e47	0.0105267
$940$	0	0
$941$	3.65122e48	0.314926	0.157463	−	0.987525i	$-0.449668\pi$
$941$	3.65122e48	0.314926	0.157463	+	0.987525i	$0.449668\pi$
$942$	− 2.87405e49i	− 2.43588i
$943$	4.16317e48i	0.346722i
$944$	−2.45720e49	−2.01096
$945$	0	0
$946$	−1.63959e49	−1.29578
$947$	1.76048e49i	1.36728i	0.729821	+	0.683639i	$0.239604\pi$
$947$	1.76048e49i	1.36728i	−0.729821	+	0.683639i	$0.760396\pi$
$948$	− 3.87257e48i	− 0.295571i
$949$	1.71367e49	1.28539
$950$	0	0
$951$	−2.48885e49	−1.80310
$952$	− 2.91777e48i	− 0.207750i
$953$	− 1.48539e49i	− 1.03946i	−0.854330	−	0.519731i	$-0.826032\pi$
$953$	− 1.48539e49i	− 1.03946i	0.854330	−	0.519731i	$-0.173968\pi$
$954$	4.19190e48	0.288312
$955$	0	0
$956$	1.32051e49	0.877377
$957$	− 2.90108e48i	− 0.189458i
$958$	− 7.34283e48i	− 0.471338i
$959$	−6.06007e48	−0.382358
$960$	0	0
$961$	−1.33223e49	−0.812166
$962$	− 2.34822e49i	− 1.40718i
$963$	7.61332e48i	0.448477i
$964$	1.98563e49	1.14981
$965$	0	0
$966$	−1.83753e49	−1.02828
$967$	7.36558e47i	0.0405200i	0.999795	+	0.0202600i	$0.00644941\pi$
$967$	7.36558e47i	0.0405200i	−0.999795	+	0.0202600i	$0.993551\pi$
$968$	4.55917e47i	0.0246571i
$969$	−3.27422e49	−1.74087
$970$	0	0
$971$	−1.98790e49	−1.02159	−0.510797	−	0.859702i	$-0.670649\pi$
$971$	−1.98790e49	−1.02159	−0.510797	+	0.859702i	$0.670649\pi$
$972$	− 1.11325e49i	− 0.562468i
$973$	2.78793e49i	1.38490i
$974$	7.85474e48	0.383627
$975$	0	0
$976$	3.06665e49	1.44791
$977$	1.42950e49i	0.663626i	0.943345	+	0.331813i	$0.107660\pi$
$977$	1.42950e49i	0.663626i	−0.943345	+	0.331813i	$0.892340\pi$
$978$	5.64601e49i	2.57721i
$979$	−2.92577e49	−1.31319
$980$	0	0
$981$	3.79587e48	0.164730
$982$	1.93211e49i	0.824503i
$983$	− 1.85942e49i	− 0.780271i	−0.920757	−	0.390136i	$-0.872428\pi$
$983$	− 1.85942e49i	− 0.780271i	0.920757	−	0.390136i	$-0.127572\pi$
$984$	−2.52592e48	−0.104232
$985$	0	0
$986$	6.46619e48	0.258036
$987$	− 5.06594e49i	− 1.98805i
$988$	2.59983e49i	1.00335i
$989$	1.73245e49	0.657538
$990$	0	0
$991$	3.51455e49	1.29019	0.645095	−	0.764102i	$-0.276818\pi$
$991$	3.51455e49	1.29019	0.645095	+	0.764102i	$0.276818\pi$
$992$	− 1.60504e49i	− 0.579488i
$993$	− 1.05576e49i	− 0.374890i
$994$	5.83124e49	2.03651
$995$	0	0
$996$	−2.21371e49	−0.747897
$997$	− 2.49733e49i	− 0.829862i	−0.909853	−	0.414931i	$-0.863806\pi$
$997$	− 2.49733e49i	− 0.829862i	0.909853	−	0.414931i	$-0.136194\pi$
$998$	− 1.26300e49i	− 0.412810i
$999$	−2.57106e49	−0.826575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.c.24.10		12
5.2	odd	4		5.34.a.b.1.1	✓	6
5.3	odd	4		25.34.a.c.1.6		6
5.4	even	2	inner	25.34.b.c.24.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.1	✓	6	5.2	odd	4
25.34.a.c.1.6		6	5.3	odd	4
25.34.b.c.24.3		12	5.4	even	2	inner
25.34.b.c.24.10		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+126401. i q^{2} -8.63211e7i q^{3} -7.38725e9 q^{4} +1.09111e13 q^{6} -7.78650e13i q^{7} +1.52021e14i q^{8} -1.89228e15 q^{9} +O(q^{10})\)	\(q+126401. i q^{2} -8.63211e7i q^{3} -7.38725e9 q^{4} +1.09111e13 q^{6} -7.78650e13i q^{7} +1.52021e14i q^{8} -1.89228e15 q^{9} +1.61939e17 q^{11} +6.37676e17i q^{12} -2.28706e18i q^{13} +9.84220e18 q^{14} -8.26715e19 q^{16} -2.46494e20i q^{17} -2.39186e20i q^{18} +1.53881e21 q^{19} -6.72140e21 q^{21} +2.04692e22i q^{22} -2.16284e22i q^{23} +1.31226e22 q^{24} +2.89086e23 q^{26} -3.16521e23i q^{27} +5.75208e23i q^{28} +2.07535e23 q^{29} +1.75532e24 q^{31} -9.14391e24i q^{32} -1.39788e25i q^{33} +3.11571e25 q^{34} +1.39787e25 q^{36} -8.12289e25i q^{37} +1.94506e26i q^{38} -1.97422e26 q^{39} -1.92486e26 q^{41} -8.49590e26i q^{42} +8.01003e26i q^{43} -1.19628e27 q^{44} +2.73385e27 q^{46} +7.53703e27i q^{47} +7.13630e27i q^{48} +1.66804e27 q^{49} -2.12777e28 q^{51} +1.68951e28i q^{52} +1.75257e28i q^{53} +4.00085e28 q^{54} +1.18371e28 q^{56} -1.32832e29i q^{57} +2.62326e28i q^{58} +2.97225e29 q^{59} -3.70944e29 q^{61} +2.21873e29i q^{62} +1.47342e29i q^{63} +4.45655e29 q^{64} +1.76693e30 q^{66} -8.43824e29i q^{67} +1.82091e30i q^{68} -1.86699e30 q^{69} +5.92473e30 q^{71} -2.87666e29i q^{72} +7.49289e30i q^{73} +1.02674e31 q^{74} -1.13675e31 q^{76} -1.26094e31i q^{77} -2.49543e31i q^{78} -6.07295e30 q^{79} -3.78417e31 q^{81} -2.43304e31i q^{82} +3.47153e31i q^{83} +4.96526e31 q^{84} -1.01248e32 q^{86} -1.79147e31i q^{87} +2.46181e31i q^{88} -1.80671e32 q^{89} -1.78082e32 q^{91} +1.59775e32i q^{92} -1.51521e32i q^{93} -9.52688e32 q^{94} -7.89312e32 q^{96} -1.09143e33i q^{97} +2.10841e32i q^{98} -3.06434e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) \) 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+ \cdots - 33\!\cdots\!32 q^{99}+O(q^{100}) \) 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9 + 301521793111780384 * q^11 + 14172220017979782912 * q^14 + 129023040011717337632 * q^16 - 3423168725199973224400 * q^19 - 21120795321652308296256 * q^21 - 423790032309447397723200 * q^24 - 723658493334872996337176 * q^26 - 2610446812821454716031400 * q^29 + 21650642793601151809506704 * q^31 - 17744819333309063470980248 * q^34 + 337428823503549785822326792 * q^36 - 1159928172465211851270376912 * q^39 + 896017159299045986791643864 * q^41 - 14343610684444535018100501728 * q^44 + 6987518581952661848987190144 * q^46 + 14346854147129333747058470516 * q^49 - 109840725610127342641737389776 * q^51 + 365294374336526194478458799200 * q^54 - 785146678781996293241501500800 * q^56 + 356630312442075454139067599600 * q^59 - 564635378121172028506416574616 * q^61 - 3875937069585082792868959215744 * q^64 + 10122417492310860521089546318528 * q^66 - 632254481633966368511307646272 * q^69 + 16902436063987485405313234340144 * q^71 - 40989454834346150858579084952968 * q^74 + 58820079845469675507259388916000 * q^76 + 44105010702804710887789495271200 * q^79 - 266327929778353521323811147439348 * q^81 + 471983223984448297035157677303552 * q^84 - 257647761243091711315108096211216 * q^86 + 672982716682338963896412426721800 * q^89 + 389267538804687732313205728966864 * q^91 - 2972282194336784425374584270690528 * q^94 + 6303457980346245345128406163058944 * q^96 - 3321764604884454158829134325248032 * q^99

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