LMFDB - Embedded newform 25.34.b.c.24.12

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			24.12
Root			$89431.3i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.c.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+178863. i q^{2} -8.55112e7i q^{3} -2.34019e10 q^{4} +1.52948e13 q^{6} -8.09549e13i q^{7} -2.64931e15i q^{8} -1.75311e15 q^{9} +O(q^{10})$	\(q+178863. i q^{2} -8.55112e7i q^{3} -2.34019e10 q^{4} +1.52948e13 q^{6} -8.09549e13i q^{7} -2.64931e15i q^{8} -1.75311e15 q^{9} +1.95800e17 q^{11} +2.00113e18i q^{12} +2.59207e18i q^{13} +1.44798e19 q^{14} +2.72841e20 q^{16} -1.52177e20i q^{17} -3.13565e20i q^{18} -1.39526e21 q^{19} -6.92255e21 q^{21} +3.50214e22i q^{22} +3.40316e22i q^{23} -2.26546e23 q^{24} -4.63625e23 q^{26} -3.25452e23i q^{27} +1.89450e24i q^{28} +1.49246e24 q^{29} -1.38398e24 q^{31} +2.60438e25i q^{32} -1.67431e25i q^{33} +2.72188e25 q^{34} +4.10261e25 q^{36} +1.15380e26i q^{37} -2.49559e26i q^{38} +2.21651e26 q^{39} -6.35087e25 q^{41} -1.23819e27i q^{42} +2.64294e26i q^{43} -4.58211e27 q^{44} -6.08698e27 q^{46} +1.03700e27i q^{47} -2.33310e28i q^{48} +1.17730e27 q^{49} -1.30128e28 q^{51} -6.06594e28i q^{52} -5.20280e28i q^{53} +5.82111e28 q^{54} -2.14475e29 q^{56} +1.19310e29i q^{57} +2.66946e29i q^{58} +6.17754e28 q^{59} -1.21654e29 q^{61} -2.47543e29i q^{62} +1.41923e29i q^{63} -2.31456e30 q^{64} +2.99472e30 q^{66} -2.87484e29i q^{67} +3.56123e30i q^{68} +2.91008e30 q^{69} -2.84409e30 q^{71} +4.64452e30i q^{72} +2.67045e30i q^{73} -2.06372e31 q^{74} +3.26517e31 q^{76} -1.58510e31i q^{77} +3.96451e31i q^{78} +7.84640e30 q^{79} -3.75754e31 q^{81} -1.13593e31i q^{82} -1.28723e31i q^{83} +1.62001e32 q^{84} -4.72724e31 q^{86} -1.27622e32i q^{87} -5.18736e32i q^{88} +1.56902e32 q^{89} +2.09841e32 q^{91} -7.96404e32i q^{92} +1.18346e32i q^{93} -1.85481e32 q^{94} +2.22703e33 q^{96} +4.84738e32i q^{97} +2.10574e32i q^{98} -3.43259e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	178863.i	1.92986i	0.262516	+	0.964928i	$0.415448\pi$
$2$	178863.i	1.92986i	−0.262516	+	0.964928i	$0.584552\pi$
$3$	− 8.55112e7i	− 1.14689i	−0.819243	−	0.573446i	$-0.805606\pi$
$3$	− 8.55112e7i	− 1.14689i	0.819243	−	0.573446i	$-0.194394\pi$
$4$	−2.34019e10	−2.72434
$5$	0	0
$5$	0	0
$6$	1.52948e13	2.21333
$7$	− 8.09549e13i	− 0.920716i	−0.887733	−	0.460358i	$-0.847721\pi$
$7$	− 8.09549e13i	− 0.920716i	0.887733	−	0.460358i	$-0.152279\pi$
$8$	− 2.64931e15i	− 3.32773i
$9$	−1.75311e15	−0.315360
$10$	0	0
$11$	1.95800e17	1.28480	0.642398	−	0.766371i	$-0.277939\pi$
$11$	1.95800e17	1.28480	0.642398	+	0.766371i	$0.277939\pi$
$12$	2.00113e18i	3.12452i
$13$	2.59207e18i	1.08039i	0.841539	+	0.540197i	$0.181650\pi$
$13$	2.59207e18i	1.08039i	−0.841539	+	0.540197i	$0.818350\pi$
$14$	1.44798e19	1.77685
$15$	0	0
$16$	2.72841e20	3.69769
$17$	− 1.52177e20i	− 0.758475i	−0.925299	−	0.379238i	$-0.876186\pi$
$17$	− 1.52177e20i	− 0.758475i	0.925299	−	0.379238i	$-0.123814\pi$
$18$	− 3.13565e20i	− 0.608600i
$19$	−1.39526e21	−1.10974	−0.554868	−	0.831938i	$-0.687231\pi$
$19$	−1.39526e21	−1.10974	−0.554868	+	0.831938i	$0.687231\pi$
$20$	0	0
$21$	−6.92255e21	−1.05596
$22$	3.50214e22i	2.47947i
$23$	3.40316e22i	1.15711i	0.815645	+	0.578553i	$0.196382\pi$
$23$	3.40316e22i	1.15711i	−0.815645	+	0.578553i	$0.803618\pi$
$24$	−2.26546e23	−3.81654
$25$	0	0
$26$	−4.63625e23	−2.08500
$27$	− 3.25452e23i	− 0.785207i
$28$	1.89450e24i	2.50834i
$29$	1.49246e24	1.10748	0.553741	−	0.832689i	$-0.313200\pi$
$29$	1.49246e24	1.10748	0.553741	+	0.832689i	$0.313200\pi$
$30$	0	0
$31$	−1.38398e24	−0.341714	−0.170857	−	0.985296i	$-0.554654\pi$
$31$	−1.38398e24	−0.341714	−0.170857	+	0.985296i	$0.554654\pi$
$32$	2.60438e25i	3.80828i
$33$	− 1.67431e25i	− 1.47352i
$34$	2.72188e25	1.46375
$35$	0	0
$36$	4.10261e25	0.859149
$37$	1.15380e26i	1.53745i	0.639577	+	0.768727i	$0.279109\pi$
$37$	1.15380e26i	1.53745i	−0.639577	+	0.768727i	$0.720891\pi$
$38$	− 2.49559e26i	− 2.14163i
$39$	2.21651e26	1.23909
$40$	0	0
$41$	−6.35087e25	−0.155561	−0.0777804	−	0.996971i	$-0.524783\pi$
$41$	−6.35087e25	−0.155561	−0.0777804	+	0.996971i	$0.524783\pi$
$42$	− 1.23819e27i	− 2.03785i
$43$	2.64294e26i	0.295025i	0.989060	+	0.147512i	$0.0471266\pi$
$43$	2.64294e26i	0.295025i	−0.989060	+	0.147512i	$0.952873\pi$
$44$	−4.58211e27	−3.50022
$45$	0	0
$46$	−6.08698e27	−2.23305
$47$	1.03700e27i	0.266788i	0.991063	+	0.133394i	$0.0425875\pi$
$47$	1.03700e27i	0.266788i	−0.991063	+	0.133394i	$0.957412\pi$
$48$	− 2.33310e28i	− 4.24085i
$49$	1.17730e27	0.152283
$50$	0	0
$51$	−1.30128e28	−0.869889
$52$	− 6.06594e28i	− 2.94336i
$53$	− 5.20280e28i	− 1.84368i	−0.387574	−	0.921839i	$-0.626687\pi$
$53$	− 5.20280e28i	− 1.84368i	0.387574	−	0.921839i	$-0.373313\pi$
$54$	5.82111e28	1.51534
$55$	0	0
$56$	−2.14475e29	−3.06389
$57$	1.19310e29i	1.27275i
$58$	2.66946e29i	2.13728i
$59$	6.17754e28	0.373042	0.186521	−	0.982451i	$-0.440279\pi$
$59$	6.17754e28	0.373042	0.186521	+	0.982451i	$0.440279\pi$
$60$	0	0
$61$	−1.21654e29	−0.423822	−0.211911	−	0.977289i	$-0.567969\pi$
$61$	−1.21654e29	−0.423822	−0.211911	+	0.977289i	$0.567969\pi$
$62$	− 2.47543e29i	− 0.659458i
$63$	1.41923e29i	0.290357i
$64$	−2.31456e30	−3.65174
$65$	0	0
$66$	2.99472e30	2.84369
$67$	− 2.87484e29i	− 0.213000i	−0.994313	−	0.106500i	$-0.966036\pi$
$67$	− 2.87484e29i	− 0.213000i	0.994313	−	0.106500i	$-0.0339644\pi$
$68$	3.56123e30i	2.06634i
$69$	2.91008e30	1.32707
$70$	0	0
$71$	−2.84409e30	−0.809432	−0.404716	−	0.914442i	$-0.632630\pi$
$71$	−2.84409e30	−0.809432	−0.404716	+	0.914442i	$0.632630\pi$
$72$	4.64452e30i	1.04943i
$73$	2.67045e30i	0.480570i	0.970702	+	0.240285i	$0.0772410\pi$
$73$	2.67045e30i	0.480570i	−0.970702	+	0.240285i	$0.922759\pi$
$74$	−2.06372e31	−2.96706
$75$	0	0
$76$	3.26517e31	3.02330
$77$	− 1.58510e31i	− 1.18293i
$78$	3.96451e31i	2.39127i
$79$	7.84640e30	0.383551	0.191776	−	0.981439i	$-0.438575\pi$
$79$	7.84640e30	0.383551	0.191776	+	0.981439i	$0.438575\pi$
$80$	0	0
$81$	−3.75754e31	−1.21591
$82$	− 1.13593e31i	− 0.300210i
$83$	− 1.28723e31i	− 0.278527i	−0.990255	−	0.139263i	$-0.955527\pi$
$83$	− 1.28723e31i	− 0.278527i	0.990255	−	0.139263i	$-0.0444735\pi$
$84$	1.62001e32	2.87680
$85$	0	0
$86$	−4.72724e31	−0.569355
$87$	− 1.27622e32i	− 1.27016i
$88$	− 5.18736e32i	− 4.27545i
$89$	1.56902e32	1.07323	0.536616	−	0.843826i	$-0.319702\pi$
$89$	1.56902e32	1.07323	0.536616	+	0.843826i	$0.319702\pi$
$90$	0	0
$91$	2.09841e32	0.994735
$92$	− 7.96404e32i	− 3.15235i
$93$	1.18346e32i	0.391909i
$94$	−1.85481e32	−0.514862
$95$	0	0
$96$	2.22703e33	4.36769
$97$	4.84738e32i	0.801259i	0.916240	+	0.400630i	$0.131209\pi$
$97$	4.84738e32i	0.801259i	−0.916240	+	0.400630i	$0.868791\pi$
$98$	2.10574e32i	0.293883i
$99$	−3.43259e32	−0.405174
$100$	0	0
$101$	2.51128e32	0.213105	0.106552	−	0.994307i	$-0.466019\pi$
$101$	2.51128e32	0.213105	0.106552	+	0.994307i	$0.466019\pi$
$102$	− 2.32751e33i	− 1.67876i
$103$	2.60164e33i	1.59747i	0.601681	+	0.798737i	$0.294498\pi$
$103$	2.60164e33i	1.59747i	−0.601681	+	0.798737i	$0.705502\pi$
$104$	6.86720e33	3.59525
$105$	0	0
$106$	9.30586e33	3.55803
$107$	3.74478e33i	1.22629i	0.789970	+	0.613146i	$0.210096\pi$
$107$	3.74478e33i	1.22629i	−0.789970	+	0.613146i	$0.789904\pi$
$108$	7.61619e33i	2.13917i
$109$	2.76732e33	0.667609	0.333805	−	0.942642i	$-0.391667\pi$
$109$	2.76732e33	0.667609	0.333805	+	0.942642i	$0.391667\pi$
$110$	0	0
$111$	9.86628e33	1.76329
$112$	− 2.20879e34i	− 3.40452i
$113$	− 1.26307e34i	− 1.68125i	−0.541617	−	0.840626i	$-0.682188\pi$
$113$	− 1.26307e34i	− 1.68125i	0.541617	−	0.840626i	$-0.317812\pi$
$114$	−2.13401e34	−2.45622
$115$	0	0
$116$	−3.49265e34	−3.01716
$117$	− 4.54418e33i	− 0.340713i
$118$	1.10493e34i	0.719917i
$119$	−1.23195e34	−0.698340
$120$	0	0
$121$	1.51127e34	0.650703
$122$	− 2.17593e34i	− 0.817915i
$123$	5.43071e33i	0.178411i
$124$	3.23878e34	0.930945
$125$	0	0
$126$	−2.53847e34	−0.560348
$127$	− 2.24824e33i	− 0.0435594i	−0.999763	−	0.0217797i	$-0.993067\pi$
$127$	− 2.24824e33i	− 0.0435594i	0.999763	−	0.0217797i	$-0.00693324\pi$
$128$	− 1.90275e35i	− 3.23905i
$129$	2.26001e34	0.338361
$130$	0	0
$131$	7.19207e34	0.835368	0.417684	−	0.908592i	$-0.362842\pi$
$131$	7.19207e34	0.835368	0.417684	+	0.908592i	$0.362842\pi$
$132$	3.91821e35i	4.01438i
$133$	1.12953e35i	1.02175i
$134$	5.14202e34	0.411059
$135$	0	0
$136$	−4.03163e35	−2.52400
$137$	2.56636e35i	1.42373i	0.702314	+	0.711867i	$0.252150\pi$
$137$	2.56636e35i	1.42373i	−0.702314	+	0.711867i	$0.747850\pi$
$138$	5.20505e35i	2.56106i
$139$	−7.81097e34	−0.341162	−0.170581	−	0.985344i	$-0.554564\pi$
$139$	−7.81097e34	−0.341162	−0.170581	+	0.985344i	$0.554564\pi$
$140$	0	0
$141$	8.86755e34	0.305977
$142$	− 5.08701e35i	− 1.56209i
$143$	5.07529e35i	1.38809i
$144$	−4.78320e35	−1.16611
$145$	0	0
$146$	−4.77643e35	−0.927431
$147$	− 1.00672e35i	− 0.174652i
$148$	− 2.70011e36i	− 4.18855i
$149$	1.40823e35	0.195479	0.0977397	−	0.995212i	$-0.468839\pi$
$149$	1.40823e35	0.195479	0.0977397	+	0.995212i	$0.468839\pi$
$150$	0	0
$151$	4.46232e35	0.497097	0.248548	−	0.968619i	$-0.420046\pi$
$151$	4.46232e35	0.497097	0.248548	+	0.968619i	$0.420046\pi$
$152$	3.69647e36i	3.69290i
$153$	2.66782e35i	0.239193i
$154$	2.83515e36	2.28289
$155$	0	0
$156$	−5.18706e36	−3.37571
$157$	7.61070e35i	0.445739i	0.974848	+	0.222869i	$0.0715424\pi$
$157$	7.61070e35i	0.445739i	−0.974848	+	0.222869i	$0.928458\pi$
$158$	1.40343e36i	0.740199i
$159$	−4.44897e36	−2.11450
$160$	0	0
$161$	2.75502e36	1.06537
$162$	− 6.72084e36i	− 2.34653i
$163$	− 1.95336e36i	− 0.616152i	−0.951362	−	0.308076i	$-0.900315\pi$
$163$	− 1.95336e36i	− 0.616152i	0.951362	−	0.308076i	$-0.0996851\pi$
$164$	1.48623e36	0.423800
$165$	0	0
$166$	2.30237e36	0.537516
$167$	2.87170e36i	0.607180i	0.952803	+	0.303590i	$0.0981854\pi$
$167$	2.87170e36i	0.607180i	−0.952803	+	0.303590i	$0.901815\pi$
$168$	1.83400e37i	3.51395i
$169$	−9.62710e35	−0.167249
$170$	0	0
$171$	2.44604e36	0.349967
$172$	− 6.18499e36i	− 0.803748i
$173$	− 1.61105e37i	− 1.90261i	−0.308258	−	0.951303i	$-0.599746\pi$
$173$	− 1.61105e37i	− 1.90261i	0.308258	−	0.951303i	$-0.400254\pi$
$174$	2.28269e37	2.45123
$175$	0	0
$176$	5.34225e37	4.75078
$177$	− 5.28249e36i	− 0.427839i
$178$	2.80639e37i	2.07118i
$179$	−9.06671e33	−0.000610063 0	−0.000305031	−	1.00000i	$-0.500097\pi$
$179$	−9.06671e33	−0.000610063 0	−0.000305031		1.00000i	$0.500097\pi$
$180$	0	0
$181$	1.89723e36	0.106273	0.0531364	−	0.998587i	$-0.483078\pi$
$181$	1.89723e36	0.106273	0.0531364	+	0.998587i	$0.483078\pi$
$182$	3.75327e37i	1.91969i
$183$	1.04028e37i	0.486078i
$184$	9.01602e37	3.85053
$185$	0	0
$186$	−2.11677e37	−0.756327
$187$	− 2.97963e37i	− 0.974487i
$188$	− 2.42679e37i	− 0.726821i
$189$	−2.63469e37	−0.722953
$190$	0	0
$191$	−6.88314e37	−1.58758	−0.793790	−	0.608192i	$-0.791895\pi$
$191$	−6.88314e37	−1.58758	−0.793790	+	0.608192i	$0.791895\pi$
$192$	1.97921e38i	4.18815i
$193$	− 5.10528e37i	− 0.991571i	−0.868445	−	0.495786i	$-0.834880\pi$
$193$	− 5.10528e37i	− 0.991571i	0.868445	−	0.495786i	$-0.165120\pi$
$194$	−8.67015e37	−1.54631
$195$	0	0
$196$	−2.75510e37	−0.414869
$197$	− 6.02889e37i	− 0.834727i	−0.908740	−	0.417364i	$-0.862954\pi$
$197$	− 6.02889e37i	− 0.834727i	0.908740	−	0.417364i	$-0.137046\pi$
$198$	− 6.13963e37i	− 0.781927i
$199$	1.42678e38	1.67218	0.836089	−	0.548594i	$-0.184837\pi$
$199$	1.42678e38	1.67218	0.836089	+	0.548594i	$0.184837\pi$
$200$	0	0
$201$	−2.45831e37	−0.244288
$202$	4.49175e37i	0.411261i
$203$	− 1.20822e38i	− 1.01968i
$204$	3.04525e38	2.36987
$205$	0	0
$206$	−4.65337e38	−3.08289
$207$	− 5.96610e37i	− 0.364905i
$208$	7.07225e38i	3.99496i
$209$	−2.73192e38	−1.42579
$210$	0	0
$211$	3.27612e38	1.46116	0.730582	−	0.682825i	$-0.239249\pi$
$211$	3.27612e38	1.46116	0.730582	+	0.682825i	$0.239249\pi$
$212$	1.21755e39i	5.02280i
$213$	2.43201e38i	0.928331i
$214$	−6.69801e38	−2.36656
$215$	0	0
$216$	−8.62222e38	−2.61296
$217$	1.12040e38i	0.314621i
$218$	4.94971e38i	1.28839i
$219$	2.28353e38	0.551162
$220$	0	0
$221$	3.94453e38	0.819451
$222$	1.76471e39i	3.40290i
$223$	3.22330e38i	0.577126i	0.957461	+	0.288563i	$0.0931774\pi$
$223$	3.22330e38i	0.577126i	−0.957461	+	0.288563i	$0.906823\pi$
$224$	2.10837e39	3.50634
$225$	0	0
$226$	2.25916e39	3.24457
$227$	− 6.02003e38i	− 0.803845i	−0.915674	−	0.401922i	$-0.868342\pi$
$227$	− 6.02003e38i	− 0.803845i	0.915674	−	0.401922i	$-0.131658\pi$
$228$	− 2.79209e39i	− 3.46740i
$229$	3.71091e38	0.428741	0.214370	−	0.976752i	$-0.431230\pi$
$229$	3.71091e38	0.428741	0.214370	+	0.976752i	$0.431230\pi$
$230$	0	0
$231$	−1.35544e39	−1.35670
$232$	− 3.95400e39i	− 3.68540i
$233$	3.81211e38i	0.330973i	0.986212	+	0.165486i	$0.0529194\pi$
$233$	3.81211e38i	0.330973i	−0.986212	+	0.165486i	$0.947081\pi$
$234$	8.12784e38	0.657527
$235$	0	0
$236$	−1.44566e39	−1.01629
$237$	− 6.70955e38i	− 0.439892i
$238$	− 2.20349e39i	− 1.34770i
$239$	−8.52350e38	−0.486466	−0.243233	−	0.969968i	$-0.578208\pi$
$239$	−8.52350e38	−0.486466	−0.243233	+	0.969968i	$0.578208\pi$
$240$	0	0
$241$	3.41820e39	1.70027	0.850133	−	0.526568i	$-0.176522\pi$
$241$	3.41820e39	1.70027	0.850133	+	0.526568i	$0.176522\pi$
$242$	2.70309e39i	1.25576i
$243$	1.40391e39i	0.609308i
$244$	2.84693e39	1.15464
$245$	0	0
$246$	−9.71351e38	−0.344308
$247$	− 3.61661e39i	− 1.19895i
$248$	3.66660e39i	1.13713i
$249$	−1.10072e39	−0.319440
$250$	0	0
$251$	2.52321e39	0.641706	0.320853	−	0.947129i	$-0.396030\pi$
$251$	2.52321e39	0.641706	0.320853	+	0.947129i	$0.396030\pi$
$252$	− 3.32126e39i	− 0.791032i
$253$	6.66340e39i	1.48665i
$254$	4.02127e38	0.0840633
$255$	0	0
$256$	1.41511e40	2.59915
$257$	4.18511e39i	0.720793i	0.932799	+	0.360396i	$0.117359\pi$
$257$	4.18511e39i	0.720793i	−0.932799	+	0.360396i	$0.882641\pi$
$258$	4.04232e39i	0.652988i
$259$	9.34058e39	1.41556
$260$	0	0
$261$	−2.61645e39	−0.349256
$262$	1.28639e40i	1.61214i
$263$	− 1.15657e40i	− 1.36114i	−0.732683	−	0.680570i	$-0.761732\pi$
$263$	− 1.15657e40i	− 1.36114i	0.732683	−	0.680570i	$-0.238268\pi$
$264$	−4.43577e40	−4.90348
$265$	0	0
$266$	−2.02031e40	−1.97183
$267$	− 1.34169e40i	− 1.23088i
$268$	6.72768e39i	0.580284i
$269$	7.21991e39	0.585624	0.292812	−	0.956170i	$-0.405409\pi$
$269$	7.21991e39	0.585624	0.292812	+	0.956170i	$0.405409\pi$
$270$	0	0
$271$	2.28804e40	1.64237	0.821183	−	0.570665i	$-0.193315\pi$
$271$	2.28804e40	1.64237	0.821183	+	0.570665i	$0.193315\pi$
$272$	− 4.15202e40i	− 2.80461i
$273$	− 1.79438e40i	− 1.14085i
$274$	−4.59026e40	−2.74760
$275$	0	0
$276$	−6.81015e40	−3.61540
$277$	2.67522e40i	1.33796i	0.743279	+	0.668981i	$0.233269\pi$
$277$	2.67522e40i	1.33796i	−0.743279	+	0.668981i	$0.766731\pi$
$278$	− 1.39709e40i	− 0.658394i
$279$	2.42627e39	0.107763
$280$	0	0
$281$	−2.51780e40	−0.993955	−0.496977	−	0.867763i	$-0.665557\pi$
$281$	−2.51780e40	−0.993955	−0.496977	+	0.867763i	$0.665557\pi$
$282$	1.58607e40i	0.590490i
$283$	− 4.17854e40i	− 1.46740i	−0.679475	−	0.733699i	$-0.737792\pi$
$283$	− 4.17854e40i	− 1.46740i	0.679475	−	0.733699i	$-0.262208\pi$
$284$	6.65571e40	2.20517
$285$	0	0
$286$	−9.07780e40	−2.67880
$287$	5.14135e39i	0.143227i
$288$	− 4.56575e40i	− 1.20098i
$289$	1.70967e40	0.424715
$290$	0	0
$291$	4.14505e40	0.918958
$292$	− 6.24936e40i	− 1.30924i
$293$	1.81801e40i	0.359981i	0.983668	+	0.179991i	$0.0576068\pi$
$293$	1.81801e40i	0.359981i	−0.983668	+	0.179991i	$0.942393\pi$
$294$	1.80064e40	0.337052
$295$	0	0
$296$	3.05677e41	5.11623
$297$	− 6.37236e40i	− 1.00883i
$298$	2.51880e40i	0.377247i
$299$	−8.82124e40	−1.25013
$300$	0	0
$301$	2.13959e40	0.271634
$302$	7.98142e40i	0.959325i
$303$	− 2.14743e40i	− 0.244408i
$304$	−3.80684e41	−4.10346
$305$	0	0
$306$	−4.77174e40	−0.461608
$307$	− 1.04678e40i	− 0.0959564i	−0.998848	−	0.0479782i	$-0.984722\pi$
$307$	− 1.04678e40i	− 0.0959564i	0.998848	−	0.0479782i	$-0.0152778\pi$
$308$	3.70944e41i	3.22271i
$309$	2.22470e41	1.83213
$310$	0	0
$311$	1.01794e41	0.753660	0.376830	−	0.926282i	$-0.377014\pi$
$311$	1.01794e41	0.753660	0.376830	+	0.926282i	$0.377014\pi$
$312$	− 5.87223e41i	− 4.12337i
$313$	2.12567e41i	1.41584i	0.706292	+	0.707921i	$0.250367\pi$
$313$	2.12567e41i	1.41584i	−0.706292	+	0.707921i	$0.749633\pi$
$314$	−1.36127e41	−0.860212
$315$	0	0
$316$	−1.83621e41	−1.04492
$317$	5.12986e40i	0.277094i	0.990356	+	0.138547i	$0.0442433\pi$
$317$	5.12986e40i	0.277094i	−0.990356	+	0.138547i	$0.955757\pi$
$318$	− 7.95755e41i	− 4.08067i
$319$	2.92225e41	1.42289
$320$	0	0
$321$	3.20220e41	1.40642
$322$	4.92771e41i	2.05600i
$323$	2.12326e41i	0.841708i
$324$	8.79336e41	3.31255
$325$	0	0
$326$	3.49384e41	1.18908
$327$	− 2.36637e41i	− 0.765676i
$328$	1.68254e41i	0.517664i
$329$	8.39506e40	0.245636
$330$	0	0
$331$	−4.71143e41	−1.24736	−0.623679	−	0.781681i	$-0.714363\pi$
$331$	−4.71143e41	−1.24736	−0.623679	+	0.781681i	$0.714363\pi$
$332$	3.01236e41i	0.758802i
$333$	− 2.02274e41i	− 0.484852i
$334$	−5.13640e41	−1.17177
$335$	0	0
$336$	−1.88876e42	−3.90462
$337$	8.62495e40i	0.169771i	0.996391	+	0.0848854i	$0.0270524\pi$
$337$	8.62495e40i	0.169771i	−0.996391	+	0.0848854i	$0.972948\pi$
$338$	− 1.72193e41i	− 0.322767i
$339$	−1.08007e42	−1.92821
$340$	0	0
$341$	−2.70984e41	−0.439033
$342$	4.37505e41i	0.675386i
$343$	− 7.21170e41i	− 1.06092i
$344$	7.00197e41	0.981762
$345$	0	0
$346$	2.88157e42	3.67175
$347$	2.78000e41i	0.337760i	0.985637	+	0.168880i	$0.0540151\pi$
$347$	2.78000e41i	0.337760i	−0.985637	+	0.168880i	$0.945985\pi$
$348$	2.98661e42i	3.46036i
$349$	1.12911e42	1.24772	0.623860	−	0.781536i	$-0.285563\pi$
$349$	1.12911e42	1.24772	0.623860	+	0.781536i	$0.285563\pi$
$350$	0	0
$351$	8.43594e41	0.848333
$352$	5.09938e42i	4.89287i
$353$	− 1.75490e42i	− 1.60683i	−0.595422	−	0.803413i	$-0.703015\pi$
$353$	− 1.75490e42i	− 1.60683i	0.595422	−	0.803413i	$-0.296985\pi$
$354$	9.44841e41	0.825667
$355$	0	0
$356$	−3.67181e42	−2.92385
$357$	1.05345e42i	0.800920i
$358$	− 1.62170e39i	− 0.00117733i
$359$	2.42990e42	1.68473	0.842365	−	0.538907i	$-0.181163\pi$
$359$	2.42990e42	1.68473	0.842365	+	0.538907i	$0.181163\pi$
$360$	0	0
$361$	3.65974e41	0.231516
$362$	3.39343e41i	0.205091i
$363$	− 1.29230e42i	− 0.746286i
$364$	−4.91068e42	−2.71000
$365$	0	0
$366$	−1.86067e42	−0.938060
$367$	− 2.37509e42i	− 1.14470i	−0.820010	−	0.572349i	$-0.806032\pi$
$367$	− 2.37509e42i	− 1.14470i	0.820010	−	0.572349i	$-0.193968\pi$
$368$	9.28523e42i	4.27862i
$369$	1.11338e41	0.0490577
$370$	0	0
$371$	−4.21192e42	−1.69750
$372$	− 2.76952e42i	− 1.06769i
$373$	− 1.58778e42i	− 0.585592i	−0.956175	−	0.292796i	$-0.905414\pi$
$373$	− 1.58778e42i	− 0.585592i	0.956175	−	0.292796i	$-0.0945856\pi$
$374$	5.32944e42	1.88062
$375$	0	0
$376$	2.74734e42	0.887797
$377$	3.86858e42i	1.19652i
$378$	− 4.71248e42i	− 1.39519i
$379$	2.74032e42	0.776703	0.388351	−	0.921511i	$-0.373045\pi$
$379$	2.74032e42	0.776703	0.388351	+	0.921511i	$0.373045\pi$
$380$	0	0
$381$	−1.92250e41	−0.0499579
$382$	− 1.23114e43i	− 3.06380i
$383$	− 3.57273e42i	− 0.851570i	−0.904824	−	0.425785i	$-0.859998\pi$
$383$	− 3.57273e42i	− 0.851570i	0.904824	−	0.425785i	$-0.140002\pi$
$384$	−1.62706e43	−3.71483
$385$	0	0
$386$	9.13144e42	1.91359
$387$	− 4.63336e41i	− 0.0930391i
$388$	− 1.13438e43i	− 2.18290i
$389$	2.24258e42	0.413599	0.206799	−	0.978383i	$-0.433695\pi$
$389$	2.24258e42	0.413599	0.206799	+	0.978383i	$0.433695\pi$
$390$	0	0
$391$	5.17882e42	0.877636
$392$	− 3.11902e42i	− 0.506755i
$393$	− 6.15003e42i	− 0.958077i
$394$	1.07834e43	1.61090
$395$	0	0
$396$	8.03292e42	1.10383
$397$	− 8.69665e41i	− 0.114633i	−0.998356	−	0.0573164i	$-0.981746\pi$
$397$	− 8.69665e41i	− 0.114633i	0.998356	−	0.0573164i	$-0.0182544\pi$
$398$	2.55198e43i	3.22706i
$399$	9.65875e42	1.17184
$400$	0	0
$401$	1.79590e41	0.0200632	0.0100316	−	0.999950i	$-0.496807\pi$
$401$	1.79590e41	0.0200632	0.0100316	+	0.999950i	$0.496807\pi$
$402$	− 4.39700e42i	− 0.471440i
$403$	− 3.58738e42i	− 0.369185i
$404$	−5.87688e42	−0.580569
$405$	0	0
$406$	2.16106e43	1.96783
$407$	2.25915e43i	1.97532i
$408$	3.44750e43i	2.89475i
$409$	−1.72895e43	−1.39427	−0.697136	−	0.716939i	$-0.745543\pi$
$409$	−1.72895e43	−1.39427	−0.697136	+	0.716939i	$0.745543\pi$
$410$	0	0
$411$	2.19453e43	1.63287
$412$	− 6.08834e43i	− 4.35206i
$413$	− 5.00103e42i	− 0.343466i
$414$	1.06711e43	0.704214
$415$	0	0
$416$	−6.75073e43	−4.11444
$417$	6.67926e42i	0.391276i
$418$	− 4.88639e43i	− 2.75156i
$419$	3.07423e43	1.66420	0.832099	−	0.554628i	$-0.187139\pi$
$419$	3.07423e43	1.66420	0.832099	+	0.554628i	$0.187139\pi$
$420$	0	0
$421$	−1.46291e43	−0.732090	−0.366045	−	0.930597i	$-0.619288\pi$
$421$	−1.46291e43	−0.732090	−0.366045	+	0.930597i	$0.619288\pi$
$422$	5.85975e43i	2.81983i
$423$	− 1.81798e42i	− 0.0841343i
$424$	−1.37838e44	−6.13526
$425$	0	0
$426$	−4.34997e43	−1.79154
$427$	9.84848e42i	0.390220i
$428$	− 8.76349e43i	− 3.34083i
$429$	4.33994e43	1.59198
$430$	0	0
$431$	3.24328e43	1.10182	0.550909	−	0.834565i	$-0.314281\pi$
$431$	3.24328e43	1.10182	0.550909	+	0.834565i	$0.314281\pi$
$432$	− 8.87967e43i	− 2.90345i
$433$	2.61817e42i	0.0824040i	0.999151	+	0.0412020i	$0.0131187\pi$
$433$	2.61817e42i	0.0824040i	−0.999151	+	0.0412020i	$0.986881\pi$
$434$	−2.00398e43	−0.607174
$435$	0	0
$436$	−6.47606e43	−1.81880
$437$	− 4.74828e43i	− 1.28408i
$438$	4.08439e43i	1.06366i
$439$	6.39695e43	1.60438	0.802192	−	0.597066i	$-0.203667\pi$
$439$	6.39695e43	1.60438	0.802192	+	0.597066i	$0.203667\pi$
$440$	0	0
$441$	−2.06393e42	−0.0480239
$442$	7.05530e43i	1.58142i
$443$	− 1.30321e43i	− 0.281418i	−0.990051	−	0.140709i	$-0.955062\pi$
$443$	− 1.30321e43i	− 0.281418i	0.990051	−	0.140709i	$-0.0449382\pi$
$444$	−2.30890e44	−4.80381
$445$	0	0
$446$	−5.76528e43	−1.11377
$447$	− 1.20420e43i	− 0.224194i
$448$	1.87375e44i	3.36221i
$449$	9.56472e43	1.65428	0.827138	−	0.561999i	$-0.189968\pi$
$449$	9.56472e43	1.65428	0.827138	+	0.561999i	$0.189968\pi$
$450$	0	0
$451$	−1.24350e43	−0.199864
$452$	2.95582e44i	4.58030i
$453$	− 3.81578e43i	− 0.570116i
$454$	1.07676e44	1.55130
$455$	0	0
$456$	3.16090e44	4.23536
$457$	− 3.78578e42i	− 0.0489258i	−0.999701	−	0.0244629i	$-0.992212\pi$
$457$	− 3.78578e42i	− 0.0489258i	0.999701	−	0.0244629i	$-0.00778755\pi$
$458$	6.63743e43i	0.827408i
$459$	−4.95262e43	−0.595560
$460$	0	0
$461$	7.04190e43	0.788179	0.394089	−	0.919072i	$-0.371060\pi$
$461$	7.04190e43	0.788179	0.394089	+	0.919072i	$0.371060\pi$
$462$	− 2.42437e44i	− 2.61823i
$463$	− 1.41714e44i	− 1.47682i	−0.674353	−	0.738409i	$-0.735577\pi$
$463$	− 1.41714e44i	− 1.47682i	0.674353	−	0.738409i	$-0.264423\pi$
$464$	4.07206e44	4.09513
$465$	0	0
$466$	−6.81843e43	−0.638729
$467$	− 1.83277e44i	− 1.65721i	−0.559831	−	0.828606i	$-0.689134\pi$
$467$	− 1.83277e44i	− 1.65721i	0.559831	−	0.828606i	$-0.310866\pi$
$468$	1.06343e44i	0.928219i
$469$	−2.32732e43	−0.196112
$470$	0	0
$471$	6.50801e43	0.511214
$472$	− 1.63662e44i	− 1.24138i
$473$	5.17490e43i	0.379047i
$474$	1.20009e44	0.848928
$475$	0	0
$476$	2.88299e44	1.90252
$477$	9.12106e43i	0.581423i
$478$	− 1.52454e44i	− 0.938809i
$479$	6.67837e43	0.397314	0.198657	−	0.980069i	$-0.436342\pi$
$479$	6.67837e43	0.397314	0.198657	+	0.980069i	$0.436342\pi$
$480$	0	0
$481$	−2.99073e44	−1.66105
$482$	6.11389e44i	3.28127i
$483$	− 2.35586e44i	− 1.22186i
$484$	−3.53666e44	−1.77274
$485$	0	0
$486$	−2.51108e44	−1.17588
$487$	− 1.75263e44i	− 0.793345i	−0.917960	−	0.396673i	$-0.870165\pi$
$487$	− 1.75263e44i	− 0.793345i	0.917960	−	0.396673i	$-0.129835\pi$
$488$	3.22299e44i	1.41036i
$489$	−1.67035e44	−0.706659
$490$	0	0
$491$	3.92240e44	1.55134	0.775670	−	0.631139i	$-0.217412\pi$
$491$	3.92240e44	1.55134	0.775670	+	0.631139i	$0.217412\pi$
$492$	− 1.27089e44i	− 0.486053i
$493$	− 2.27118e44i	− 0.839998i
$494$	6.46876e44	2.31380
$495$	0	0
$496$	−3.77608e44	−1.26355
$497$	2.30243e44i	0.745257i
$498$	− 1.96878e44i	− 0.616473i
$499$	−7.64433e43	−0.231569	−0.115785	−	0.993274i	$-0.536938\pi$
$499$	−7.64433e43	−0.231569	−0.115785	+	0.993274i	$0.536938\pi$
$500$	0	0
$501$	2.45563e44	0.696370
$502$	4.51307e44i	1.23840i
$503$	4.88916e44i	1.29826i	0.760676	+	0.649132i	$0.224868\pi$
$503$	4.88916e44i	1.29826i	−0.760676	+	0.649132i	$0.775132\pi$
$504$	3.75997e44	0.966230
$505$	0	0
$506$	−1.19183e45	−2.86901
$507$	8.23225e43i	0.191817i
$508$	5.26132e43i	0.118671i
$509$	3.35020e44	0.731522	0.365761	−	0.930709i	$-0.380809\pi$
$509$	3.35020e44	0.731522	0.365761	+	0.930709i	$0.380809\pi$
$510$	0	0
$511$	2.16186e44	0.442469
$512$	8.96657e44i	1.77694i
$513$	4.54089e44i	0.871374i
$514$	−7.48560e44	−1.39103
$515$	0	0
$516$	−5.28886e44	−0.921812
$517$	2.03046e44i	0.342768i
$518$	1.67068e45i	2.73182i
$519$	−1.37763e45	−2.18208
$520$	0	0
$521$	−5.22367e44	−0.776521	−0.388261	−	0.921550i	$-0.626924\pi$
$521$	−5.22367e44	−0.776521	−0.388261	+	0.921550i	$0.626924\pi$
$522$	− 4.67985e44i	− 0.674014i
$523$	1.10438e45i	1.54113i	0.637360	+	0.770566i	$0.280026\pi$
$523$	1.10438e45i	1.54113i	−0.637360	+	0.770566i	$0.719974\pi$
$524$	−1.68308e45	−2.27583
$525$	0	0
$526$	2.06868e45	2.62680
$527$	2.10610e44i	0.259182i
$528$	− 4.56822e45i	− 5.44863i
$529$	−2.93144e44	−0.338893
$530$	0	0
$531$	−1.08299e44	−0.117643
$532$	− 2.64332e45i	− 2.78360i
$533$	− 1.64619e44i	− 0.168067i
$534$	2.39978e45	2.37542
$535$	0	0
$536$	−7.61634e44	−0.708806
$537$	7.75305e41i	0 0.000699676i
$538$	1.29137e45i	1.13017i
$539$	2.30515e44	0.195652
$540$	0	0
$541$	−1.40716e45	−1.12354	−0.561772	−	0.827292i	$-0.689880\pi$
$541$	−1.40716e45	−1.12354	−0.561772	+	0.827292i	$0.689880\pi$
$542$	4.09244e45i	3.16953i
$543$	− 1.62234e44i	− 0.121883i
$544$	3.96326e45	2.88849
$545$	0	0
$546$	3.20947e45	2.20168
$547$	− 1.00599e45i	− 0.669579i	−0.942293	−	0.334789i	$-0.891335\pi$
$547$	− 1.00599e45i	− 0.669579i	0.942293	−	0.334789i	$-0.108665\pi$
$548$	− 6.00578e45i	− 3.87874i
$549$	2.13272e44	0.133657
$550$	0	0
$551$	−2.08237e45	−1.22901
$552$	− 7.70971e45i	− 4.41614i
$553$	− 6.35205e44i	− 0.353142i
$554$	−4.78498e45	−2.58207
$555$	0	0
$556$	1.82792e45	0.929442
$557$	6.35386e44i	0.313637i	0.987627	+	0.156818i	$0.0501238\pi$
$557$	6.35386e44i	0.313637i	−0.987627	+	0.156818i	$0.949876\pi$
$558$	4.33969e44i	0.207967i
$559$	−6.85070e44	−0.318743
$560$	0	0
$561$	−2.54792e45	−1.11763
$562$	− 4.50340e45i	− 1.91819i
$563$	1.73714e45i	0.718534i	0.933235	+	0.359267i	$0.116973\pi$
$563$	1.73714e45i	0.718534i	−0.933235	+	0.359267i	$0.883027\pi$
$564$	−2.07518e45	−0.833584
$565$	0	0
$566$	7.47384e45	2.83187
$567$	3.04191e45i	1.11951i
$568$	7.53487e45i	2.69357i
$569$	−3.27076e45	−1.13579	−0.567894	−	0.823102i	$-0.692241\pi$
$569$	−3.27076e45	−1.13579	−0.567894	+	0.823102i	$0.692241\pi$
$570$	0	0
$571$	2.07979e45	0.681591	0.340795	−	0.940137i	$-0.389304\pi$
$571$	2.07979e45	0.681591	0.340795	+	0.940137i	$0.389304\pi$
$572$	− 1.18771e46i	− 3.78162i
$573$	5.88585e45i	1.82078i
$574$	−9.19595e44	−0.276408
$575$	0	0
$576$	4.05768e45	1.15161
$577$	− 2.30164e45i	− 0.634800i	−0.948292	−	0.317400i	$-0.897190\pi$
$577$	− 2.30164e45i	− 0.634800i	0.948292	−	0.317400i	$-0.102810\pi$
$578$	3.05796e45i	0.819639i
$579$	−4.36559e45	−1.13722
$580$	0	0
$581$	−1.04207e45	−0.256444
$582$	7.41395e45i	1.77346i
$583$	− 1.01871e46i	− 2.36875i
$584$	7.07484e45	1.59921
$585$	0	0
$586$	−3.25174e45	−0.694712
$587$	1.99372e45i	0.414128i	0.978327	+	0.207064i	$0.0663909\pi$
$587$	1.99372e45i	0.414128i	−0.978327	+	0.207064i	$0.933609\pi$
$588$	2.35592e45i	0.475810i
$589$	1.93101e45	0.379213
$590$	0	0
$591$	−5.15538e45	−0.957341
$592$	3.14804e46i	5.68503i
$593$	6.54556e45i	1.14959i	0.818296	+	0.574797i	$0.194919\pi$
$593$	6.54556e45i	1.14959i	−0.818296	+	0.574797i	$0.805081\pi$
$594$	1.13978e46	1.94690
$595$	0	0
$596$	−3.29553e45	−0.532553
$597$	− 1.22006e46i	− 1.91781i
$598$	− 1.57779e46i	− 2.41257i
$599$	−1.89735e45	−0.282231	−0.141115	−	0.989993i	$-0.545069\pi$
$599$	−1.89735e45	−0.282231	−0.141115	+	0.989993i	$0.545069\pi$
$600$	0	0
$601$	−8.66013e45	−1.21926	−0.609629	−	0.792687i	$-0.708681\pi$
$601$	−8.66013e45	−1.21926	−0.609629	+	0.792687i	$0.708681\pi$
$602$	3.82693e45i	0.524214i
$603$	5.03991e44i	0.0671718i
$604$	−1.04427e46	−1.35426
$605$	0	0
$606$	3.84095e45	0.471672
$607$	8.81789e45i	1.05378i	0.849932	+	0.526892i	$0.176643\pi$
$607$	8.81789e45i	1.05378i	−0.849932	+	0.526892i	$0.823357\pi$
$608$	− 3.63378e46i	− 4.22619i
$609$	−1.03317e46	−1.16946
$610$	0	0
$611$	−2.68799e45	−0.288236
$612$	− 6.24322e45i	− 0.651643i
$613$	1.91712e46i	1.94783i	0.226912	+	0.973915i	$0.427137\pi$
$613$	1.91712e46i	1.94783i	−0.226912	+	0.973915i	$0.572863\pi$
$614$	1.87231e45	0.185182
$615$	0	0
$616$	−4.19942e46	−3.93648
$617$	− 1.53369e46i	− 1.39969i	−0.714295	−	0.699844i	$-0.753253\pi$
$617$	− 1.53369e46i	− 1.39969i	0.714295	−	0.699844i	$-0.246747\pi$
$618$	3.97915e46i	3.53574i
$619$	−8.04204e45	−0.695778	−0.347889	−	0.937536i	$-0.613101\pi$
$619$	−8.04204e45	−0.695778	−0.347889	+	0.937536i	$0.613101\pi$
$620$	0	0
$621$	1.10756e46	0.908568
$622$	1.82071e46i	1.45446i
$623$	− 1.27020e46i	− 0.988142i
$624$	6.04757e46	4.58179
$625$	0	0
$626$	−3.80203e46	−2.73237
$627$	2.33610e46i	1.63522i
$628$	− 1.78105e46i	− 1.21434i
$629$	1.75582e46	1.16612
$630$	0	0
$631$	2.52921e46	1.59405	0.797023	−	0.603949i	$-0.206407\pi$
$631$	2.52921e46	1.59405	0.797023	+	0.603949i	$0.206407\pi$
$632$	− 2.07875e46i	− 1.27635i
$633$	− 2.80145e46i	− 1.67580i
$634$	−9.17540e45	−0.534752
$635$	0	0
$636$	1.04114e47	5.76061
$637$	3.05163e45i	0.164525i
$638$	5.22682e46i	2.74597i
$639$	4.98599e45	0.255263
$640$	0	0
$641$	2.51177e46	1.22130	0.610651	−	0.791900i	$-0.290908\pi$
$641$	2.51177e46	1.22130	0.610651	+	0.791900i	$0.290908\pi$
$642$	5.72755e46i	2.71419i
$643$	1.47547e46i	0.681473i	0.940159	+	0.340736i	$0.110676\pi$
$643$	1.47547e46i	0.681473i	−0.940159	+	0.340736i	$0.889324\pi$
$644$	−6.44728e46	−2.90242
$645$	0	0
$646$	−3.79772e46	−1.62437
$647$	− 4.64548e46i	− 1.93691i	−0.249182	−	0.968457i	$-0.580162\pi$
$647$	− 4.64548e46i	− 1.93691i	0.249182	−	0.968457i	$-0.419838\pi$
$648$	9.95488e46i	4.04621i
$649$	1.20957e46	0.479283
$650$	0	0
$651$	9.58069e45	0.360837
$652$	4.57124e46i	1.67861i
$653$	− 3.12135e46i	− 1.11757i	−0.829312	−	0.558786i	$-0.811267\pi$
$653$	− 3.12135e46i	− 1.11757i	0.829312	−	0.558786i	$-0.188733\pi$
$654$	4.23255e46	1.47764
$655$	0	0
$656$	−1.73278e46	−0.575215
$657$	− 4.68158e45i	− 0.151553i
$658$	1.50156e46i	0.474041i
$659$	−1.16512e46	−0.358724	−0.179362	−	0.983783i	$-0.557403\pi$
$659$	−1.16512e46	−0.358724	−0.179362	+	0.983783i	$0.557403\pi$
$660$	0	0
$661$	−1.14126e46	−0.334241	−0.167121	−	0.985936i	$-0.553447\pi$
$661$	−1.14126e46	−0.334241	−0.167121	+	0.985936i	$0.553447\pi$
$662$	− 8.42699e46i	− 2.40722i
$663$	− 3.37302e46i	− 0.939822i
$664$	−3.41026e46	−0.926861
$665$	0	0
$666$	3.61792e46	0.935694
$667$	5.07909e46i	1.28147i
$668$	− 6.72033e46i	− 1.65417i
$669$	2.75628e46	0.661901
$670$	0	0
$671$	−2.38199e46	−0.544525
$672$	− 1.80289e47i	− 4.02140i
$673$	− 4.26138e45i	− 0.0927475i	−0.998924	−	0.0463737i	$-0.985233\pi$
$673$	− 4.26138e45i	− 0.0927475i	0.998924	−	0.0463737i	$-0.0147665\pi$
$674$	−1.54268e46	−0.327633
$675$	0	0
$676$	2.25292e46	0.455644
$677$	− 6.45770e46i	− 1.27457i	−0.770627	−	0.637287i	$-0.780057\pi$
$677$	− 6.45770e46i	− 1.27457i	0.770627	−	0.637287i	$-0.219943\pi$
$678$	− 1.93183e47i	− 3.72117i
$679$	3.92419e46	0.737732
$680$	0	0
$681$	−5.14780e46	−0.921923
$682$	− 4.84690e46i	− 0.847270i
$683$	− 3.35691e46i	− 0.572794i	−0.958111	−	0.286397i	$-0.907542\pi$
$683$	− 3.35691e46i	− 0.572794i	0.958111	−	0.286397i	$-0.0924577\pi$
$684$	−5.72419e46	−0.953430
$685$	0	0
$686$	1.28990e47	2.04743
$687$	− 3.17324e46i	− 0.491719i
$688$	7.21105e46i	1.09091i
$689$	1.34860e47	1.99190
$690$	0	0
$691$	−4.55000e46	−0.640654	−0.320327	−	0.947307i	$-0.603793\pi$
$691$	−4.55000e46	−0.640654	−0.320327	+	0.947307i	$0.603793\pi$
$692$	3.77017e47i	5.18334i
$693$	2.77885e46i	0.373050i
$694$	−4.97238e46	−0.651828
$695$	0	0
$696$	−3.38111e47	−4.22676
$697$	9.66456e45i	0.117989i
$698$	2.01956e47i	2.40792i
$699$	3.25978e46	0.379590
$700$	0	0
$701$	−1.37611e47	−1.52864	−0.764320	−	0.644837i	$-0.776925\pi$
$701$	−1.37611e47	−1.52864	−0.764320	+	0.644837i	$0.776925\pi$
$702$	1.50888e47i	1.63716i
$703$	− 1.60985e47i	− 1.70617i
$704$	−4.53193e47	−4.69174
$705$	0	0
$706$	3.13885e47	3.10094
$707$	− 2.03301e46i	− 0.196209i
$708$	1.23620e47i	1.16558i
$709$	1.72099e47	1.58531	0.792656	−	0.609670i	$-0.208698\pi$
$709$	1.72099e47	1.58531	0.792656	+	0.609670i	$0.208698\pi$
$710$	0	0
$711$	−1.37556e46	−0.120957
$712$	− 4.15682e47i	− 3.57143i
$713$	− 4.70991e46i	− 0.395399i
$714$	−1.88423e47	−1.54566
$715$	0	0
$716$	2.12178e44	0.00166202
$717$	7.28855e46i	0.557924i
$718$	4.34619e47i	3.25128i
$719$	−1.00489e47	−0.734667	−0.367334	−	0.930089i	$-0.619729\pi$
$719$	−1.00489e47	−0.734667	−0.367334	+	0.930089i	$0.619729\pi$
$720$	0	0
$721$	2.10616e47	1.47082
$722$	6.54591e46i	0.446793i
$723$	− 2.92295e47i	− 1.95002i
$724$	−4.43987e46	−0.289524
$725$	0	0
$726$	2.31145e47	1.44022
$727$	1.79204e47i	1.09151i	0.837944	+	0.545757i	$0.183758\pi$
$727$	1.79204e47i	1.09151i	−0.837944	+	0.545757i	$0.816242\pi$
$728$	− 5.55934e47i	− 3.31021i
$729$	−8.88336e46	−0.517098
$730$	0	0
$731$	4.02195e46	0.223769
$732$	− 2.43445e47i	− 1.32424i
$733$	− 1.91032e46i	− 0.101599i	−0.998709	−	0.0507996i	$-0.983823\pi$
$733$	− 1.91032e46i	− 0.101599i	0.998709	−	0.0507996i	$-0.0161770\pi$
$734$	4.24816e47	2.20910
$735$	0	0
$736$	−8.86310e47	−4.40658
$737$	− 5.62895e46i	− 0.273662i
$738$	1.99141e46i	0.0946742i
$739$	−2.81727e47	−1.30977	−0.654886	−	0.755728i	$-0.727283\pi$
$739$	−2.81727e47	−1.30977	−0.654886	+	0.755728i	$0.727283\pi$
$740$	0	0
$741$	−3.09261e47	−1.37507
$742$	− 7.53355e47i	− 3.27593i
$743$	5.77441e46i	0.245580i	0.992433	+	0.122790i	$0.0391841\pi$
$743$	5.77441e46i	0.245580i	−0.992433	+	0.122790i	$0.960816\pi$
$744$	3.13535e47	1.30417
$745$	0	0
$746$	2.83995e47	1.13011
$747$	2.25665e46i	0.0878363i
$748$	6.97290e47i	2.65483i
$749$	3.03158e47	1.12907
$750$	0	0
$751$	2.71539e47	0.967772	0.483886	−	0.875131i	$-0.339225\pi$
$751$	2.71539e47	0.967772	0.483886	+	0.875131i	$0.339225\pi$
$752$	2.82938e47i	0.986498i
$753$	− 2.15762e47i	− 0.735968i
$754$	−6.91944e47	−2.30910
$755$	0	0
$756$	6.16568e47	1.96957
$757$	2.34370e47i	0.732521i	0.930512	+	0.366260i	$0.119362\pi$
$757$	2.34370e47i	0.732521i	−0.930512	+	0.366260i	$0.880638\pi$
$758$	4.90141e47i	1.49892i
$759$	5.69796e47	1.70502
$760$	0	0
$761$	−3.85769e47	−1.10530	−0.552651	−	0.833413i	$-0.686384\pi$
$761$	−3.85769e47	−1.10530	−0.552651	+	0.833413i	$0.686384\pi$
$762$	− 3.43863e46i	− 0.0964115i
$763$	− 2.24028e47i	− 0.614679i
$764$	1.61079e48	4.32511
$765$	0	0
$766$	6.39028e47	1.64341
$767$	1.60126e47i	0.403032i
$768$	− 1.21008e48i	− 2.98094i
$769$	−5.88677e47	−1.41936	−0.709679	−	0.704525i	$-0.751160\pi$
$769$	−5.88677e47	−1.41936	−0.709679	+	0.704525i	$0.751160\pi$
$770$	0	0
$771$	3.57874e47	0.826671
$772$	1.19473e48i	2.70138i
$773$	4.68346e47i	1.03659i	0.855203	+	0.518293i	$0.173432\pi$
$773$	4.68346e47i	1.03659i	−0.855203	+	0.518293i	$0.826568\pi$
$774$	8.28736e46	0.179552
$775$	0	0
$776$	1.28422e48	2.66637
$777$	− 7.98724e47i	− 1.62349i
$778$	4.01113e47i	0.798185i
$779$	8.86111e46	0.172631
$780$	0	0
$781$	−5.56874e47	−1.03996
$782$	9.26297e47i	1.69371i
$783$	− 4.85725e47i	− 0.869604i
$784$	3.21215e47	0.563094
$785$	0	0
$786$	1.10001e48	1.84895
$787$	− 3.57150e47i	− 0.587851i	−0.955828	−	0.293926i	$-0.905038\pi$
$787$	− 3.57150e47i	− 0.587851i	0.955828	−	0.293926i	$-0.0949618\pi$
$788$	1.41087e48i	2.27408i
$789$	−9.88999e47	−1.56108
$790$	0	0
$791$	−1.02252e48	−1.54795
$792$	9.09400e47i	1.34831i
$793$	− 3.15336e47i	− 0.457895i
$794$	1.55551e47	0.221225
$795$	0	0
$796$	−3.33895e48	−4.55558
$797$	− 3.36343e47i	− 0.449490i	−0.974418	−	0.224745i	$-0.927845\pi$
$797$	− 3.36343e47i	− 0.449490i	0.974418	−	0.224745i	$-0.0721549\pi$
$798$	1.72759e48i	2.26148i
$799$	1.57808e47	0.202352
$800$	0	0
$801$	−2.75066e47	−0.338455
$802$	3.21219e46i	0.0387190i
$803$	5.22875e47i	0.617435i
$804$	5.75292e47	0.665523
$805$	0	0
$806$	6.41649e47	0.712474
$807$	− 6.17383e47i	− 0.671647i
$808$	− 6.65316e47i	− 0.709154i
$809$	−8.08353e47	−0.844210	−0.422105	−	0.906547i	$-0.638709\pi$
$809$	−8.08353e47	−0.844210	−0.422105	+	0.906547i	$0.638709\pi$
$810$	0	0
$811$	−1.18729e48	−1.19045	−0.595225	−	0.803559i	$-0.702937\pi$
$811$	−1.18729e48	−1.19045	−0.595225	+	0.803559i	$0.702937\pi$
$812$	2.82747e48i	2.77795i
$813$	− 1.95653e48i	− 1.88362i
$814$	−4.04077e48	−3.81207
$815$	0	0
$816$	−3.55044e48	−3.21658
$817$	− 3.68759e47i	− 0.327400i
$818$	− 3.09244e48i	− 2.69074i
$819$	−3.67874e47	−0.313700
$820$	0	0
$821$	−1.55006e48	−1.26966	−0.634829	−	0.772653i	$-0.718929\pi$
$821$	−1.55006e48	−1.26966	−0.634829	+	0.772653i	$0.718929\pi$
$822$	3.92519e48i	3.15120i
$823$	− 2.91534e47i	− 0.229399i	−0.993400	−	0.114700i	$-0.963409\pi$
$823$	− 2.91534e47i	− 0.229399i	0.993400	−	0.114700i	$-0.0365905\pi$
$824$	6.89256e48	5.31596
$825$	0	0
$826$	8.94497e47	0.662839
$827$	− 1.33839e48i	− 0.972166i	−0.873913	−	0.486083i	$-0.838425\pi$
$827$	− 1.33839e48i	− 0.972166i	0.873913	−	0.486083i	$-0.161575\pi$
$828$	1.39618e48i	0.994126i
$829$	2.06685e47	0.144264	0.0721321	−	0.997395i	$-0.477020\pi$
$829$	2.06685e47	0.144264	0.0721321	+	0.997395i	$0.477020\pi$
$830$	0	0
$831$	2.28762e48	1.53450
$832$	− 5.99952e48i	− 3.94531i
$833$	− 1.79157e47i	− 0.115502i
$834$	−1.19467e48	−0.755106
$835$	0	0
$836$	6.39322e48	3.88433
$837$	4.50419e47i	0.268316i
$838$	5.49865e48i	3.21166i
$839$	1.80225e48	1.03215	0.516075	−	0.856544i	$-0.327393\pi$
$839$	1.80225e48	1.03215	0.516075	+	0.856544i	$0.327393\pi$
$840$	0	0
$841$	4.11374e47	0.226518
$842$	− 2.61661e48i	− 1.41283i
$843$	2.15300e48i	1.13996i
$844$	−7.66674e48	−3.98071
$845$	0	0
$846$	3.25169e47	0.162367
$847$	− 1.22345e48i	− 0.599113i
$848$	− 1.41954e49i	− 6.81735i
$849$	−3.57312e48	−1.68295
$850$	0	0
$851$	−3.92656e48	−1.77900
$852$	− 5.69138e48i	− 2.52909i
$853$	3.50343e48i	1.52699i	0.645816	+	0.763493i	$0.276517\pi$
$853$	3.50343e48i	1.52699i	−0.645816	+	0.763493i	$0.723483\pi$
$854$	−1.76153e48	−0.753068
$855$	0	0
$856$	9.92107e48	4.08076
$857$	4.03540e48i	1.62818i	0.580737	+	0.814091i	$0.302764\pi$
$857$	4.03540e48i	1.62818i	−0.580737	+	0.814091i	$0.697236\pi$
$858$	7.76254e48i	3.07230i
$859$	4.93399e46	0.0191563	0.00957813	−	0.999954i	$-0.496951\pi$
$859$	4.93399e46	0.0191563	0.00957813	+	0.999954i	$0.496951\pi$
$860$	0	0
$861$	4.39643e47	0.164266
$862$	5.80102e48i	2.12635i
$863$	5.86818e47i	0.211021i	0.994418	+	0.105510i	$0.0336476\pi$
$863$	5.86818e47i	0.211021i	−0.994418	+	0.105510i	$0.966352\pi$
$864$	8.47598e48	2.99029
$865$	0	0
$866$	−4.68294e47	−0.159028
$867$	− 1.46196e48i	− 0.487103i
$868$	− 2.62195e48i	− 0.857136i
$869$	1.53633e48	0.492786
$870$	0	0
$871$	7.45180e47	0.230124
$872$	− 7.33149e48i	− 2.22162i
$873$	− 8.49797e47i	− 0.252686i
$874$	8.49291e48	2.47809
$875$	0	0
$876$	−5.34390e48	−1.50155
$877$	− 5.15342e48i	− 1.42103i	−0.703683	−	0.710514i	$-0.748463\pi$
$877$	− 5.15342e48i	− 1.42103i	0.703683	−	0.710514i	$-0.251537\pi$
$878$	1.14418e49i	3.09623i
$879$	1.55460e48	0.412860
$880$	0	0
$881$	7.21570e48	1.84576	0.922882	−	0.385084i	$-0.125827\pi$
$881$	7.21570e48	1.84576	0.922882	+	0.385084i	$0.125827\pi$
$882$	− 3.69159e47i	− 0.0926791i
$883$	− 7.21502e48i	− 1.77781i	−0.458089	−	0.888906i	$-0.651466\pi$
$883$	− 7.21502e48i	− 1.77781i	0.458089	−	0.888906i	$-0.348534\pi$
$884$	−9.23096e48	−2.23246
$885$	0	0
$886$	2.33095e48	0.543097
$887$	− 2.04483e48i	− 0.467647i	−0.972279	−	0.233824i	$-0.924876\pi$
$887$	− 2.04483e48i	− 0.467647i	0.972279	−	0.233824i	$-0.0751238\pi$
$888$	− 2.61388e49i	− 5.86776i
$889$	−1.82006e47	−0.0401058
$890$	0	0
$891$	−7.35728e48	−1.56220
$892$	− 7.54314e48i	− 1.57229i
$893$	− 1.44689e48i	− 0.296064i
$894$	2.15386e48	0.432661
$895$	0	0
$896$	−1.54037e49	−2.98224
$897$	7.54315e48i	1.43376i
$898$	1.71077e49i	3.19251i
$899$	−2.06554e48	−0.378442
$900$	0	0
$901$	−7.91745e48	−1.39838
$902$	− 2.22416e48i	− 0.385708i
$903$	− 1.82959e48i	− 0.311535i
$904$	−3.34626e49	−5.59475
$905$	0	0
$906$	6.82501e48	1.10024
$907$	4.33823e48i	0.686739i	0.939200	+	0.343370i	$0.111568\pi$
$907$	4.33823e48i	0.686739i	−0.939200	+	0.343370i	$0.888432\pi$
$908$	1.40880e49i	2.18995i
$909$	−4.40255e47	−0.0672048
$910$	0	0
$911$	−1.54797e48	−0.227882	−0.113941	−	0.993488i	$-0.536348\pi$
$911$	−1.54797e48	−0.227882	−0.113941	+	0.993488i	$0.536348\pi$
$912$	3.25528e49i	4.70623i
$913$	− 2.52040e48i	− 0.357850i
$914$	6.77134e47	0.0944196
$915$	0	0
$916$	−8.68424e48	−1.16804
$917$	− 5.82234e48i	− 0.769136i
$918$	− 8.85839e48i	− 1.14935i
$919$	−4.44681e48	−0.566686	−0.283343	−	0.959019i	$-0.591443\pi$
$919$	−4.44681e48	−0.566686	−0.283343	+	0.959019i	$0.591443\pi$
$920$	0	0
$921$	−8.95118e47	−0.110052
$922$	1.25953e49i	1.52107i
$923$	− 7.37208e48i	− 0.874505i
$924$	3.17199e49	3.69610
$925$	0	0
$926$	2.53474e49	2.85005
$927$	− 4.56096e48i	− 0.503780i
$928$	3.88694e49i	4.21760i
$929$	−7.81292e48	−0.832826	−0.416413	−	0.909176i	$-0.636713\pi$
$929$	−7.81292e48	−0.832826	−0.416413	+	0.909176i	$0.636713\pi$
$930$	0	0
$931$	−1.64263e48	−0.168994
$932$	− 8.92105e48i	− 0.901682i
$933$	− 8.70453e48i	− 0.864367i
$934$	3.27813e49	3.19818
$935$	0	0
$936$	−1.20389e49	−1.13380
$937$	1.29441e49i	1.19776i	0.800839	+	0.598880i	$0.204387\pi$
$937$	1.29441e49i	1.19776i	−0.800839	+	0.598880i	$0.795613\pi$
$938$	− 4.16271e48i	− 0.378469i
$939$	1.81769e49	1.62382
$940$	0	0
$941$	−5.82381e47	−0.0502318	−0.0251159	−	0.999685i	$-0.507995\pi$
$941$	−5.82381e47	−0.0502318	−0.0251159	+	0.999685i	$0.507995\pi$
$942$	1.16404e49i	0.986569i
$943$	− 2.16130e48i	− 0.180000i
$944$	1.68549e49	1.37939
$945$	0	0
$946$	−9.25596e48	−0.731505
$947$	1.87865e49i	1.45905i	0.683953	+	0.729526i	$0.260259\pi$
$947$	1.87865e49i	1.45905i	−0.683953	+	0.729526i	$0.739741\pi$
$948$	1.57016e49i	1.19842i
$949$	−6.92200e48	−0.519205
$950$	0	0
$951$	4.38661e48	0.317797
$952$	3.26381e49i	2.32389i
$953$	− 1.71040e49i	− 1.19692i	−0.801154	−	0.598459i	$-0.795780\pi$
$953$	− 1.71040e49i	− 1.19692i	0.801154	−	0.598459i	$-0.204220\pi$
$954$	−1.63142e49	−1.12206
$955$	0	0
$956$	1.99466e49	1.32530
$957$	− 2.49885e49i	− 1.63190i
$958$	1.19451e49i	0.766759i
$959$	2.07760e49	1.31085
$960$	0	0
$961$	−1.44881e49	−0.883232
$962$	− 5.34930e49i	− 3.20559i
$963$	− 6.56500e48i	− 0.386724i
$964$	−7.99925e49	−4.63210
$965$	0	0
$966$	4.21374e49	2.35801
$967$	− 3.31445e49i	− 1.82337i	−0.410893	−	0.911683i	$-0.634783\pi$
$967$	− 3.31445e49i	− 1.82337i	0.410893	−	0.911683i	$-0.365217\pi$
$968$	− 4.00382e49i	− 2.16536i
$969$	1.81562e49	0.965348
$970$	0	0
$971$	−1.48405e49	−0.762662	−0.381331	−	0.924439i	$-0.624534\pi$
$971$	−1.48405e49	−0.762662	−0.381331	+	0.924439i	$0.624534\pi$
$972$	− 3.28542e49i	− 1.65996i
$973$	6.32337e48i	0.314113i
$974$	3.13480e49	1.53104
$975$	0	0
$976$	−3.31922e49	−1.56716
$977$	− 7.11883e47i	− 0.0330482i	−0.999863	−	0.0165241i	$-0.994740\pi$
$977$	− 7.11883e47i	− 0.0330482i	0.999863	−	0.0165241i	$-0.00526003\pi$
$978$	− 2.98762e49i	− 1.36375i
$979$	3.07215e49	1.37889
$980$	0	0
$981$	−4.85141e48	−0.210538
$982$	7.01570e49i	2.99386i
$983$	− 3.13902e49i	− 1.31723i	−0.752481	−	0.658614i	$-0.771143\pi$
$983$	− 3.13902e49i	− 1.31723i	0.752481	−	0.658614i	$-0.228857\pi$
$984$	1.43876e49	0.593704
$985$	0	0
$986$	4.06230e49	1.62107
$987$	− 7.17872e48i	− 0.281717i
$988$	8.46356e49i	3.26635i
$989$	−8.99436e48	−0.341375
$990$	0	0
$991$	2.53674e49	0.931239	0.465619	−	0.884985i	$-0.345832\pi$
$991$	2.53674e49	0.931239	0.465619	+	0.884985i	$0.345832\pi$
$992$	− 3.60441e49i	− 1.30134i
$993$	4.02880e49i	1.43058i
$994$	−4.11819e49	−1.43824
$995$	0	0
$996$	2.57590e49	0.870263
$997$	4.24313e48i	0.140999i	0.997512	+	0.0704995i	$0.0224593\pi$
$997$	4.24313e48i	0.140999i	−0.997512	+	0.0704995i	$0.977541\pi$
$998$	− 1.36729e49i	− 0.446895i
$999$	3.75506e49	1.20722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.c.24.12		12
5.2	odd	4		25.34.a.c.1.1		6
5.3	odd	4		5.34.a.b.1.6	✓	6
5.4	even	2	inner	25.34.b.c.24.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.6	✓	6	5.3	odd	4
25.34.a.c.1.1		6	5.2	odd	4
25.34.b.c.24.1		12	5.4	even	2	inner
25.34.b.c.24.12		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)

\(f(q)\)	\(=\)	\(q+178863. i q^{2} -8.55112e7i q^{3} -2.34019e10 q^{4} +1.52948e13 q^{6} -8.09549e13i q^{7} -2.64931e15i q^{8} -1.75311e15 q^{9} +O(q^{10})\)	\(q+178863. i q^{2} -8.55112e7i q^{3} -2.34019e10 q^{4} +1.52948e13 q^{6} -8.09549e13i q^{7} -2.64931e15i q^{8} -1.75311e15 q^{9} +1.95800e17 q^{11} +2.00113e18i q^{12} +2.59207e18i q^{13} +1.44798e19 q^{14} +2.72841e20 q^{16} -1.52177e20i q^{17} -3.13565e20i q^{18} -1.39526e21 q^{19} -6.92255e21 q^{21} +3.50214e22i q^{22} +3.40316e22i q^{23} -2.26546e23 q^{24} -4.63625e23 q^{26} -3.25452e23i q^{27} +1.89450e24i q^{28} +1.49246e24 q^{29} -1.38398e24 q^{31} +2.60438e25i q^{32} -1.67431e25i q^{33} +2.72188e25 q^{34} +4.10261e25 q^{36} +1.15380e26i q^{37} -2.49559e26i q^{38} +2.21651e26 q^{39} -6.35087e25 q^{41} -1.23819e27i q^{42} +2.64294e26i q^{43} -4.58211e27 q^{44} -6.08698e27 q^{46} +1.03700e27i q^{47} -2.33310e28i q^{48} +1.17730e27 q^{49} -1.30128e28 q^{51} -6.06594e28i q^{52} -5.20280e28i q^{53} +5.82111e28 q^{54} -2.14475e29 q^{56} +1.19310e29i q^{57} +2.66946e29i q^{58} +6.17754e28 q^{59} -1.21654e29 q^{61} -2.47543e29i q^{62} +1.41923e29i q^{63} -2.31456e30 q^{64} +2.99472e30 q^{66} -2.87484e29i q^{67} +3.56123e30i q^{68} +2.91008e30 q^{69} -2.84409e30 q^{71} +4.64452e30i q^{72} +2.67045e30i q^{73} -2.06372e31 q^{74} +3.26517e31 q^{76} -1.58510e31i q^{77} +3.96451e31i q^{78} +7.84640e30 q^{79} -3.75754e31 q^{81} -1.13593e31i q^{82} -1.28723e31i q^{83} +1.62001e32 q^{84} -4.72724e31 q^{86} -1.27622e32i q^{87} -5.18736e32i q^{88} +1.56902e32 q^{89} +2.09841e32 q^{91} -7.96404e32i q^{92} +1.18346e32i q^{93} -1.85481e32 q^{94} +2.22703e33 q^{96} +4.84738e32i q^{97} +2.10574e32i q^{98} -3.43259e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) \) 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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