LMFDB - Embedded newform 25.34.b.c.24.11

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			24.11
Root			$66460.8i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.c.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+132922. i q^{2} +1.17526e8i q^{3} -9.07819e9 q^{4} -1.56217e13 q^{6} -1.34853e13i q^{7} -6.49000e13i q^{8} -8.25322e15 q^{9} +O(q^{10})$	\(q+132922. i q^{2} +1.17526e8i q^{3} -9.07819e9 q^{4} -1.56217e13 q^{6} -1.34853e13i q^{7} -6.49000e13i q^{8} -8.25322e15 q^{9} -7.96470e16 q^{11} -1.06692e18i q^{12} +1.16823e18i q^{13} +1.79249e18 q^{14} -6.93545e19 q^{16} +3.27833e20i q^{17} -1.09703e21i q^{18} -2.21358e21 q^{19} +1.58487e21 q^{21} -1.05868e22i q^{22} -3.93052e22i q^{23} +7.62742e21 q^{24} -1.55283e23 q^{26} -3.16633e23i q^{27} +1.22422e23i q^{28} -1.59428e24 q^{29} +2.07133e24 q^{31} -9.77619e24i q^{32} -9.36057e24i q^{33} -4.35761e25 q^{34} +7.49243e25 q^{36} -4.76387e25i q^{37} -2.94233e26i q^{38} -1.37297e26 q^{39} -6.39281e26 q^{41} +2.10663e26i q^{42} +2.16469e26i q^{43} +7.23051e26 q^{44} +5.22451e27 q^{46} +7.45743e27i q^{47} -8.15093e27i q^{48} +7.54914e27 q^{49} -3.85288e28 q^{51} -1.06055e28i q^{52} -1.70592e28i q^{53} +4.20873e28 q^{54} -8.75196e26 q^{56} -2.60153e29i q^{57} -2.11913e29i q^{58} +5.91397e28 q^{59} +2.18117e29 q^{61} +2.75325e29i q^{62} +1.11297e29i q^{63} +7.03715e29 q^{64} +1.24422e30 q^{66} +2.21631e30i q^{67} -2.97613e30i q^{68} +4.61937e30 q^{69} +2.87498e30 q^{71} +5.35634e29i q^{72} +3.41825e30i q^{73} +6.33220e30 q^{74} +2.00953e31 q^{76} +1.07406e30i q^{77} -1.82498e31i q^{78} -5.87385e30 q^{79} -8.66769e30 q^{81} -8.49743e31i q^{82} +2.11211e31i q^{83} -1.43877e31 q^{84} -2.87734e31 q^{86} -1.87368e32i q^{87} +5.16909e30i q^{88} +2.67672e32 q^{89} +1.57540e31 q^{91} +3.56821e32i q^{92} +2.43435e32i q^{93} -9.91253e32 q^{94} +1.14895e33 q^{96} +1.07066e31i q^{97} +1.00344e33i q^{98} +6.57344e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	132922.i	1.43417i	0.696986	+	0.717085i	$0.254524\pi$
$2$	132922.i	1.43417i	−0.696986	+	0.717085i	$0.745476\pi$
$3$	1.17526e8i	1.57627i	0.615499	+	0.788137i	$0.288954\pi$
$3$	1.17526e8i	1.57627i	−0.615499	+	0.788137i	$0.711046\pi$
$4$	−9.07819e9	−1.05684
$5$	0	0
$5$	0	0
$6$	−1.56217e13	−2.26064
$7$	− 1.34853e13i	− 0.153371i	−0.997055	−	0.0766854i	$-0.975566\pi$
$7$	− 1.34853e13i	− 0.153371i	0.997055	−	0.0766854i	$-0.0244337\pi$
$8$	− 6.49000e13i	− 0.0815192i
$9$	−8.25322e15	−1.48464
$10$	0	0
$11$	−7.96470e16	−0.522625	−0.261313	−	0.965254i	$-0.584155\pi$
$11$	−7.96470e16	−0.522625	−0.261313	+	0.965254i	$0.584155\pi$
$12$	− 1.06692e18i	− 1.66587i
$13$	1.16823e18i	0.486928i	0.969910	+	0.243464i	$0.0782838\pi$
$13$	1.16823e18i	0.486928i	−0.969910	+	0.243464i	$0.921716\pi$
$14$	1.79249e18	0.219960
$15$	0	0
$16$	−6.93545e19	−0.939928
$17$	3.27833e20i	1.63398i	0.576654	+	0.816988i	$0.304358\pi$
$17$	3.27833e20i	1.63398i	−0.576654	+	0.816988i	$0.695642\pi$
$18$	− 1.09703e21i	− 2.12923i
$19$	−2.21358e21	−1.76060	−0.880301	−	0.474416i	$-0.842659\pi$
$19$	−2.21358e21	−1.76060	−0.880301	+	0.474416i	$0.842659\pi$
$20$	0	0
$21$	1.58487e21	0.241755
$22$	− 1.05868e22i	− 0.749533i
$23$	− 3.93052e22i	− 1.33641i	−0.743975	−	0.668207i	$-0.767062\pi$
$23$	− 3.93052e22i	− 1.33641i	0.743975	−	0.668207i	$-0.232938\pi$
$24$	7.62742e21	0.128497
$25$	0	0
$26$	−1.55283e23	−0.698337
$27$	− 3.16633e23i	− 0.763930i
$28$	1.22422e23i	0.162089i
$29$	−1.59428e24	−1.18303	−0.591516	−	0.806293i	$-0.701470\pi$
$29$	−1.59428e24	−1.18303	−0.591516	+	0.806293i	$0.701470\pi$
$30$	0	0
$31$	2.07133e24	0.511425	0.255712	−	0.966753i	$-0.417690\pi$
$31$	2.07133e24	0.511425	0.255712	+	0.966753i	$0.417690\pi$
$32$	− 9.77619e24i	− 1.42954i
$33$	− 9.36057e24i	− 0.823801i
$34$	−4.35761e25	−2.34340
$35$	0	0
$36$	7.49243e25	1.56903
$37$	− 4.76387e25i	− 0.634792i	−0.948293	−	0.317396i	$-0.897192\pi$
$37$	− 4.76387e25i	− 0.634792i	0.948293	−	0.317396i	$-0.102808\pi$
$38$	− 2.94233e26i	− 2.52500i
$39$	−1.37297e26	−0.767532
$40$	0	0
$41$	−6.39281e26	−1.56588	−0.782940	−	0.622097i	$-0.786281\pi$
$41$	−6.39281e26	−1.56588	−0.782940	+	0.622097i	$0.786281\pi$
$42$	2.10663e26i	0.346717i
$43$	2.16469e26i	0.241639i	0.992674	+	0.120819i	$0.0385522\pi$
$43$	2.16469e26i	0.241639i	−0.992674	+	0.120819i	$0.961448\pi$
$44$	7.23051e26	0.552331
$45$	0	0
$46$	5.22451e27	1.91664
$47$	7.45743e27i	1.91856i	0.282462	+	0.959278i	$0.408849\pi$
$47$	7.45743e27i	1.91856i	−0.282462	+	0.959278i	$0.591151\pi$
$48$	− 8.15093e27i	− 1.48159i
$49$	7.54914e27	0.976477
$50$	0	0
$51$	−3.85288e28	−2.57560
$52$	− 1.06055e28i	− 0.514605i
$53$	− 1.70592e28i	− 0.604513i	−0.953227	−	0.302257i	$-0.902260\pi$
$53$	− 1.70592e28i	− 0.604513i	0.953227	−	0.302257i	$-0.0977399\pi$
$54$	4.20873e28	1.09560
$55$	0	0
$56$	−8.75196e26	−0.0125027
$57$	− 2.60153e29i	− 2.77519i
$58$	− 2.11913e29i	− 1.69667i
$59$	5.91397e28	0.357126	0.178563	−	0.983928i	$-0.442855\pi$
$59$	5.91397e28	0.357126	0.178563	+	0.983928i	$0.442855\pi$
$60$	0	0
$61$	2.18117e29	0.759884	0.379942	−	0.925010i	$-0.375944\pi$
$61$	2.18117e29	0.759884	0.379942	+	0.925010i	$0.375944\pi$
$62$	2.75325e29i	0.733470i
$63$	1.11297e29i	0.227701i
$64$	7.03715e29	1.11027
$65$	0	0
$66$	1.24422e30	1.18147
$67$	2.21631e30i	1.64209i	0.570865	+	0.821044i	$0.306608\pi$
$67$	2.21631e30i	1.64209i	−0.570865	+	0.821044i	$0.693392\pi$
$68$	− 2.97613e30i	− 1.72685i
$69$	4.61937e30	2.10656
$70$	0	0
$71$	2.87498e30	0.818223	0.409112	−	0.912484i	$-0.365839\pi$
$71$	2.87498e30	0.818223	0.409112	+	0.912484i	$0.365839\pi$
$72$	5.35634e29i	0.121027i
$73$	3.41825e30i	0.615143i	0.951525	+	0.307571i	$0.0995163\pi$
$73$	3.41825e30i	0.615143i	−0.951525	+	0.307571i	$0.900484\pi$
$74$	6.33220e30	0.910398
$75$	0	0
$76$	2.00953e31	1.86068
$77$	1.07406e30i	0.0801555i
$78$	− 1.82498e31i	− 1.10077i
$79$	−5.87385e30	−0.287128	−0.143564	−	0.989641i	$-0.545856\pi$
$79$	−5.87385e30	−0.287128	−0.143564	+	0.989641i	$0.545856\pi$
$80$	0	0
$81$	−8.66769e30	−0.280479
$82$	− 8.49743e31i	− 2.24574i
$83$	2.11211e31i	0.457013i	0.973542	+	0.228507i	$0.0733843\pi$
$83$	2.11211e31i	0.457013i	−0.973542	+	0.228507i	$0.926616\pi$
$84$	−1.43877e31	−0.255496
$85$	0	0
$86$	−2.87734e31	−0.346551
$87$	− 1.87368e32i	− 1.86478i
$88$	5.16909e30i	0.0426040i
$89$	2.67672e32	1.83092	0.915458	−	0.402413i	$-0.131828\pi$
$89$	2.67672e32	1.83092	0.915458	+	0.402413i	$0.131828\pi$
$90$	0	0
$91$	1.57540e31	0.0746806
$92$	3.56821e32i	1.41238i
$93$	2.43435e32i	0.806146i
$94$	−9.91253e32	−2.75153
$95$	0	0
$96$	1.14895e33	2.25334
$97$	1.07066e31i	0.0176977i	0.999961	+	0.00884885i	$0.00281671\pi$
$97$	1.07066e31i	0.0176977i	−0.999961	+	0.00884885i	$0.997183\pi$
$98$	1.00344e33i	1.40043i
$99$	6.57344e32	0.775911
$100$	0	0
$101$	1.55093e33	1.31610	0.658051	−	0.752974i	$-0.271381\pi$
$101$	1.55093e33	1.31610	0.658051	+	0.752974i	$0.271381\pi$
$102$	− 5.12131e33i	− 3.69384i
$103$	− 6.99665e32i	− 0.429612i	−0.976657	−	0.214806i	$-0.931088\pi$
$103$	− 6.99665e32i	− 0.429612i	0.976657	−	0.214806i	$-0.0689119\pi$
$104$	7.58184e31	0.0396940
$105$	0	0
$106$	2.26753e33	0.866974
$107$	− 6.35208e32i	− 0.208010i	−0.994577	−	0.104005i	$-0.966834\pi$
$107$	− 6.35208e32i	− 0.208010i	0.994577	−	0.104005i	$-0.0331658\pi$
$108$	2.87445e33i	0.807352i
$109$	−2.09396e33	−0.505163	−0.252581	−	0.967576i	$-0.581280\pi$
$109$	−2.09396e33	−0.505163	−0.252581	+	0.967576i	$0.581280\pi$
$110$	0	0
$111$	5.59876e33	1.00061
$112$	9.35266e32i	0.144158i
$113$	− 7.28662e33i	− 0.969910i	−0.874539	−	0.484955i	$-0.838836\pi$
$113$	− 7.28662e33i	− 0.969910i	0.874539	−	0.484955i	$-0.161164\pi$
$114$	3.45799e34	3.98009
$115$	0	0
$116$	1.44731e34	1.25028
$117$	− 9.64169e33i	− 0.722914i
$118$	7.86094e33i	0.512179i
$119$	4.42093e33	0.250604
$120$	0	0
$121$	−1.68815e34	−0.726863
$122$	2.89924e34i	1.08980i
$123$	− 7.51320e34i	− 2.46826i
$124$	−1.88040e34	−0.540495
$125$	0	0
$126$	−1.47938e34	−0.326562
$127$	− 4.47086e34i	− 0.866222i	−0.901341	−	0.433111i	$-0.857416\pi$
$127$	− 4.47086e34i	− 0.866222i	0.901341	−	0.433111i	$-0.142584\pi$
$128$	9.56208e33i	0.162775i
$129$	−2.54407e34	−0.380889
$130$	0	0
$131$	−2.63964e34	−0.306597	−0.153298	−	0.988180i	$-0.548990\pi$
$131$	−2.63964e34	−0.306597	−0.153298	+	0.988180i	$0.548990\pi$
$132$	8.49770e34i	0.870626i
$133$	2.98508e34i	0.270025i
$134$	−2.94595e35	−2.35503
$135$	0	0
$136$	2.12764e34	0.133201
$137$	1.03805e35i	0.575874i	0.957649	+	0.287937i	$0.0929694\pi$
$137$	1.03805e35i	0.575874i	−0.957649	+	0.287937i	$0.907031\pi$
$138$	6.14014e35i	3.02116i
$139$	1.77157e34	0.0773774	0.0386887	−	0.999251i	$-0.487682\pi$
$139$	1.77157e34	0.0773774	0.0386887	+	0.999251i	$0.487682\pi$
$140$	0	0
$141$	−8.76440e35	−3.02417
$142$	3.82147e35i	1.17347i
$143$	− 9.30464e34i	− 0.254481i
$144$	5.72398e35	1.39546
$145$	0	0
$146$	−4.54358e35	−0.882219
$147$	8.87218e35i	1.53920i
$148$	4.32473e35i	0.670874i
$149$	−9.39618e35	−1.30430	−0.652151	−	0.758089i	$-0.726133\pi$
$149$	−9.39618e35	−1.30430	−0.652151	+	0.758089i	$0.726133\pi$
$150$	0	0
$151$	4.46650e35	0.497563	0.248781	−	0.968560i	$-0.419970\pi$
$151$	4.46650e35	0.497563	0.248781	+	0.968560i	$0.419970\pi$
$152$	1.43661e35i	0.143523i
$153$	− 2.70568e36i	− 2.42587i
$154$	−1.42766e35	−0.114956
$155$	0	0
$156$	1.24641e36	0.811159
$157$	− 7.30629e35i	− 0.427910i	−0.976843	−	0.213955i	$-0.931365\pi$
$157$	− 7.30629e35i	− 0.427910i	0.976843	−	0.213955i	$-0.0686346\pi$
$158$	− 7.80761e35i	− 0.411791i
$159$	2.00489e36	0.952879
$160$	0	0
$161$	−5.30043e35	−0.204967
$162$	− 1.15212e36i	− 0.402254i
$163$	2.77089e35i	0.0874026i	0.999045	+	0.0437013i	$0.0139150\pi$
$163$	2.77089e35i	0.0874026i	−0.999045	+	0.0437013i	$0.986085\pi$
$164$	5.80352e36	1.65489
$165$	0	0
$166$	−2.80745e36	−0.655434
$167$	5.22919e36i	1.10564i	0.833302	+	0.552818i	$0.186448\pi$
$167$	5.22919e36i	1.10564i	−0.833302	+	0.552818i	$0.813552\pi$
$168$	− 1.02858e35i	− 0.0197077i
$169$	4.39136e36	0.762901
$170$	0	0
$171$	1.82692e37	2.61386
$172$	− 1.96515e36i	− 0.255374i
$173$	5.38814e36i	0.636324i	0.948036	+	0.318162i	$0.103066\pi$
$173$	5.38814e36i	0.636324i	−0.948036	+	0.318162i	$0.896934\pi$
$174$	2.49053e37	2.67441
$175$	0	0
$176$	5.52388e36	0.491230
$177$	6.95044e36i	0.562928i
$178$	3.55794e37i	2.62584i
$179$	−2.52793e37	−1.70094	−0.850472	−	0.526020i	$-0.823684\pi$
$179$	−2.52793e37	−1.70094	−0.850472	+	0.526020i	$0.823684\pi$
$180$	0	0
$181$	1.65835e36	0.0928924	0.0464462	−	0.998921i	$-0.485210\pi$
$181$	1.65835e36	0.0928924	0.0464462	+	0.998921i	$0.485210\pi$
$182$	2.09404e36i	0.107105i
$183$	2.56343e37i	1.19779i
$184$	−2.55091e36	−0.108943
$185$	0	0
$186$	−3.23577e37	−1.15615
$187$	− 2.61109e37i	− 0.853957i
$188$	− 6.77000e37i	− 2.02761i
$189$	−4.26989e36	−0.117165
$190$	0	0
$191$	6.04480e37	1.39422	0.697110	−	0.716964i	$-0.254469\pi$
$191$	6.04480e37	1.39422	0.697110	+	0.716964i	$0.254469\pi$
$192$	8.27046e37i	1.75009i
$193$	− 6.49082e36i	− 0.126068i	−0.998011	−	0.0630339i	$-0.979922\pi$
$193$	− 6.49082e36i	− 0.126068i	0.998011	−	0.0630339i	$-0.0200776\pi$
$194$	−1.42313e36	−0.0253815
$195$	0	0
$196$	−6.85326e37	−1.03198
$197$	9.24040e37i	1.27938i	0.768635	+	0.639688i	$0.220936\pi$
$197$	9.24040e37i	1.27938i	−0.768635	+	0.639688i	$0.779064\pi$
$198$	8.73752e37i	1.11279i
$199$	1.09203e38	1.27985	0.639925	−	0.768437i	$-0.278965\pi$
$199$	1.09203e38	1.27985	0.639925	+	0.768437i	$0.278965\pi$
$200$	0	0
$201$	−2.60473e38	−2.58838
$202$	2.06152e38i	1.88751i
$203$	2.14993e37i	0.181443i
$204$	3.49772e38	2.72200
$205$	0	0
$206$	9.30006e37	0.616136
$207$	3.24395e38i	1.98410i
$208$	− 8.10223e37i	− 0.457677i
$209$	1.76305e38	0.920134
$210$	0	0
$211$	−6.11672e37	−0.272808	−0.136404	−	0.990653i	$-0.543555\pi$
$211$	−6.11672e37	−0.272808	−0.136404	+	0.990653i	$0.543555\pi$
$212$	1.54866e38i	0.638874i
$213$	3.37884e38i	1.28974i
$214$	8.44328e37	0.298321
$215$	0	0
$216$	−2.05495e37	−0.0622750
$217$	− 2.79325e37i	− 0.0784377i
$218$	− 2.78332e38i	− 0.724489i
$219$	−4.01731e38	−0.969634
$220$	0	0
$221$	−3.82986e38	−0.795629
$222$	7.44196e38i	1.43504i
$223$	− 9.45280e38i	− 1.69251i	−0.532781	−	0.846253i	$-0.678853\pi$
$223$	− 9.45280e38i	− 1.69251i	0.532781	−	0.846253i	$-0.321147\pi$
$224$	−1.31835e38	−0.219249
$225$	0	0
$226$	9.68548e38	1.39102
$227$	4.90469e38i	0.654914i	0.944866	+	0.327457i	$0.106192\pi$
$227$	4.90469e38i	0.654914i	−0.944866	+	0.327457i	$0.893808\pi$
$228$	2.36172e39i	2.93294i
$229$	4.57241e38	0.528275	0.264137	−	0.964485i	$-0.414913\pi$
$229$	4.57241e38	0.528275	0.264137	+	0.964485i	$0.414913\pi$
$230$	0	0
$231$	−1.26230e38	−0.126347
$232$	1.03468e38i	0.0964398i
$233$	8.69571e38i	0.754975i	0.926015	+	0.377487i	$0.123212\pi$
$233$	8.69571e38i	0.754975i	−0.926015	+	0.377487i	$0.876788\pi$
$234$	1.28159e39	1.03678
$235$	0	0
$236$	−5.36882e38	−0.377425
$237$	− 6.90328e38i	− 0.452593i
$238$	5.87637e38i	0.359409i
$239$	1.38618e39	0.791140	0.395570	−	0.918436i	$-0.370547\pi$
$239$	1.38618e39	0.791140	0.395570	+	0.918436i	$0.370547\pi$
$240$	0	0
$241$	−2.94732e39	−1.46604	−0.733019	−	0.680208i	$-0.761890\pi$
$241$	−2.94732e39	−1.46604	−0.733019	+	0.680208i	$0.761890\pi$
$242$	− 2.24392e39i	− 1.04244i
$243$	− 2.77886e39i	− 1.20604i
$244$	−1.98011e39	−0.803076
$245$	0	0
$246$	9.98665e39	3.53990
$247$	− 2.58598e39i	− 0.857286i
$248$	− 1.34430e38i	− 0.0416910i
$249$	−2.48228e39	−0.720379
$250$	0	0
$251$	−5.17168e39	−1.31527	−0.657636	−	0.753336i	$-0.728444\pi$
$251$	−5.17168e39	−1.31527	−0.657636	+	0.753336i	$0.728444\pi$
$252$	− 1.01038e39i	− 0.240644i
$253$	3.13055e39i	0.698444i
$254$	5.94273e39	1.24231
$255$	0	0
$256$	4.77386e39	0.876820
$257$	− 4.09624e39i	− 0.705488i	−0.935720	−	0.352744i	$-0.885249\pi$
$257$	− 4.09624e39i	− 0.705488i	0.935720	−	0.352744i	$-0.114751\pi$
$258$	− 3.38162e39i	− 0.546260i
$259$	−6.42422e38	−0.0973585
$260$	0	0
$261$	1.31579e40	1.75638
$262$	− 3.50865e39i	− 0.439712i
$263$	− 2.59968e39i	− 0.305950i	−0.988230	−	0.152975i	$-0.951115\pi$
$263$	− 2.59968e39i	− 0.305950i	0.988230	−	0.152975i	$-0.0488854\pi$
$264$	−6.07501e38	−0.0671556
$265$	0	0
$266$	−3.96781e39	−0.387262
$267$	3.14584e40i	2.88603i
$268$	− 2.01201e40i	− 1.73543i
$269$	−7.20422e39	−0.584351	−0.292176	−	0.956365i	$-0.594379\pi$
$269$	−7.20422e39	−0.584351	−0.292176	+	0.956365i	$0.594379\pi$
$270$	0	0
$271$	−1.89743e40	−1.36199	−0.680993	−	0.732290i	$-0.738451\pi$
$271$	−1.89743e40	−1.36199	−0.680993	+	0.732290i	$0.738451\pi$
$272$	− 2.27367e40i	− 1.53582i
$273$	1.85150e39i	0.117717i
$274$	−1.37979e40	−0.825901
$275$	0	0
$276$	−4.19356e40	−2.22629
$277$	3.08340e40i	1.54211i	0.636771	+	0.771053i	$0.280270\pi$
$277$	3.08340e40i	1.54211i	−0.636771	+	0.771053i	$0.719730\pi$
$278$	2.35480e39i	0.110972i
$279$	−1.70952e40	−0.759283
$280$	0	0
$281$	−1.56575e40	−0.618112	−0.309056	−	0.951044i	$-0.600013\pi$
$281$	−1.56575e40	−0.618112	−0.309056	+	0.951044i	$0.600013\pi$
$282$	− 1.16498e41i	− 4.33718i
$283$	− 7.24188e39i	− 0.254317i	−0.991882	−	0.127158i	$-0.959414\pi$
$283$	− 7.24188e39i	− 0.254317i	0.991882	−	0.127158i	$-0.0405857\pi$
$284$	−2.60996e40	−0.864732
$285$	0	0
$286$	1.23679e40	0.364968
$287$	8.62090e39i	0.240160i
$288$	8.06850e40i	2.12235i
$289$	−6.72202e40	−1.66988
$290$	0	0
$291$	−1.25830e39	−0.0278964
$292$	− 3.10315e40i	− 0.650108i
$293$	− 7.67091e40i	− 1.51891i	−0.650562	−	0.759453i	$-0.725467\pi$
$293$	− 7.67091e40i	− 1.51891i	0.650562	−	0.759453i	$-0.274533\pi$
$294$	−1.17930e41	−2.20747
$295$	0	0
$296$	−3.09175e39	−0.0517477
$297$	2.52188e40i	0.399249i
$298$	− 1.24895e41i	− 1.87059i
$299$	4.59177e40	0.650737
$300$	0	0
$301$	2.91915e39	0.0370604
$302$	5.93694e40i	0.713589i
$303$	1.82274e41i	2.07454i
$304$	1.53522e41	1.65484
$305$	0	0
$306$	3.59643e41	3.47911
$307$	− 1.29298e41i	− 1.18525i	−0.805478	−	0.592625i	$-0.798091\pi$
$307$	− 1.29298e41i	− 1.18525i	0.805478	−	0.592625i	$-0.201909\pi$
$308$	− 9.75056e39i	− 0.0847116i
$309$	8.22286e40	0.677186
$310$	0	0
$311$	−5.39990e40	−0.399797	−0.199898	−	0.979817i	$-0.564061\pi$
$311$	−5.39990e40	−0.399797	−0.199898	+	0.979817i	$0.564061\pi$
$312$	8.91061e39i	0.0625686i
$313$	− 1.08588e41i	− 0.723270i	−0.932320	−	0.361635i	$-0.882219\pi$
$313$	− 1.08588e41i	− 0.723270i	0.932320	−	0.361635i	$-0.117781\pi$
$314$	9.71163e40	0.613696
$315$	0	0
$316$	5.33240e40	0.303449
$317$	− 1.38129e41i	− 0.746117i	−0.927808	−	0.373059i	$-0.878309\pi$
$317$	− 1.38129e41i	− 0.746117i	0.927808	−	0.373059i	$-0.121691\pi$
$318$	2.66493e41i	1.36659i
$319$	1.26979e41	0.618282
$320$	0	0
$321$	7.46533e40	0.327881
$322$	− 7.04541e40i	− 0.293957i
$323$	− 7.25686e41i	− 2.87678i
$324$	7.86869e40	0.296422
$325$	0	0
$326$	−3.68311e40	−0.125350
$327$	− 2.46094e41i	− 0.796275i
$328$	4.14894e40i	0.127649i
$329$	1.00566e41	0.294251
$330$	0	0
$331$	−4.29457e41	−1.13699	−0.568496	−	0.822686i	$-0.692474\pi$
$331$	−4.29457e41	−1.13699	−0.568496	+	0.822686i	$0.692474\pi$
$332$	− 1.91742e41i	− 0.482990i
$333$	3.93172e41i	0.942439i
$334$	−6.95072e41	−1.58567
$335$	0	0
$336$	−1.09918e41	−0.227232
$337$	6.97107e41i	1.37216i	0.727524	+	0.686082i	$0.240671\pi$
$337$	6.97107e41i	1.37216i	−0.727524	+	0.686082i	$0.759329\pi$
$338$	5.83706e41i	1.09413i
$339$	8.56364e41	1.52885
$340$	0	0
$341$	−1.64975e41	−0.267284
$342$	2.42837e42i	3.74872i
$343$	− 2.06057e41i	− 0.303134i
$344$	1.40489e40	0.0196982
$345$	0	0
$346$	−7.16200e41	−0.912596
$347$	7.56830e41i	0.919522i	0.888043	+	0.459761i	$0.152065\pi$
$347$	7.56830e41i	0.919522i	−0.888043	+	0.459761i	$0.847935\pi$
$348$	1.70096e42i	1.97078i
$349$	−4.06051e41	−0.448705	−0.224353	−	0.974508i	$-0.572027\pi$
$349$	−4.06051e41	−0.448705	−0.224353	+	0.974508i	$0.572027\pi$
$350$	0	0
$351$	3.69901e41	0.371979
$352$	7.78644e41i	0.747111i
$353$	1.97994e42i	1.81288i	0.422336	+	0.906439i	$0.361210\pi$
$353$	1.97994e42i	1.81288i	−0.422336	+	0.906439i	$0.638790\pi$
$354$	−9.23863e41	−0.807335
$355$	0	0
$356$	−2.42998e42	−1.93499
$357$	5.19573e41i	0.395022i
$358$	− 3.36016e42i	− 2.43944i
$359$	6.70289e41	0.464733	0.232366	−	0.972628i	$-0.425353\pi$
$359$	6.70289e41	0.464733	0.232366	+	0.972628i	$0.425353\pi$
$360$	0	0
$361$	3.31917e42	2.09972
$362$	2.20431e41i	0.133223i
$363$	− 1.98401e42i	− 1.14574i
$364$	−1.43018e41	−0.0789255
$365$	0	0
$366$	−3.40736e42	−1.71783
$367$	− 1.36571e42i	− 0.658215i	−0.944292	−	0.329108i	$-0.893252\pi$
$367$	− 1.36571e42i	− 0.658215i	0.944292	−	0.329108i	$-0.106748\pi$
$368$	2.72599e42i	1.25613i
$369$	5.27613e42	2.32477
$370$	0	0
$371$	−2.30048e41	−0.0927147
$372$	− 2.20995e42i	− 0.851968i
$373$	− 3.32617e41i	− 0.122673i	−0.998117	−	0.0613364i	$-0.980464\pi$
$373$	− 3.32617e41i	− 0.122673i	0.998117	−	0.0613364i	$-0.0195363\pi$
$374$	3.47071e42	1.22472
$375$	0	0
$376$	4.83988e41	0.156399
$377$	− 1.86249e42i	− 0.576051i
$378$	− 5.67560e41i	− 0.168034i
$379$	−1.32387e42	−0.375230	−0.187615	−	0.982243i	$-0.560076\pi$
$379$	−1.32387e42	−0.375230	−0.187615	+	0.982243i	$0.560076\pi$
$380$	0	0
$381$	5.25440e42	1.36540
$382$	8.03484e42i	1.99955i
$383$	− 5.38010e42i	− 1.28236i	−0.767390	−	0.641181i	$-0.778445\pi$
$383$	− 5.38010e42i	− 1.28236i	0.767390	−	0.641181i	$-0.221555\pi$
$384$	−1.12379e42	−0.256578
$385$	0	0
$386$	8.62770e41	0.180803
$387$	− 1.78657e42i	− 0.358747i
$388$	− 9.71963e40i	− 0.0187036i
$389$	6.93155e42	1.27839	0.639193	−	0.769046i	$-0.279269\pi$
$389$	6.93155e42	1.27839	0.639193	+	0.769046i	$0.279269\pi$
$390$	0	0
$391$	1.28856e43	2.18367
$392$	− 4.89939e41i	− 0.0796017i
$393$	− 3.10225e42i	− 0.483281i
$394$	−1.22825e43	−1.83484
$395$	0	0
$396$	−5.96750e42	−0.820015
$397$	− 9.33530e42i	− 1.23051i	−0.788329	−	0.615254i	$-0.789053\pi$
$397$	− 9.33530e42i	− 1.23051i	0.788329	−	0.615254i	$-0.210947\pi$
$398$	1.45154e43i	1.83552i
$399$	−3.50824e42	−0.425634
$400$	0	0
$401$	3.40931e42	0.380877	0.190438	−	0.981699i	$-0.439009\pi$
$401$	3.40931e42	0.380877	0.190438	+	0.981699i	$0.439009\pi$
$402$	− 3.46225e43i	− 3.71218i
$403$	2.41980e42i	0.249027i
$404$	−1.40796e43	−1.39091
$405$	0	0
$406$	−2.85772e42	−0.260219
$407$	3.79428e42i	0.331758i
$408$	2.50052e42i	0.209961i
$409$	−3.12051e42	−0.251646	−0.125823	−	0.992053i	$-0.540157\pi$
$409$	−3.12051e42	−0.251646	−0.125823	+	0.992053i	$0.540157\pi$
$410$	0	0
$411$	−1.21997e43	−0.907736
$412$	6.35170e42i	0.454031i
$413$	− 7.97517e41i	− 0.0547727i
$414$	−4.31190e43	−2.84553
$415$	0	0
$416$	1.14209e43	0.696081
$417$	2.08205e42i	0.121968i
$418$	2.34347e43i	1.31963i
$419$	3.20466e43	1.73480	0.867402	−	0.497608i	$-0.165788\pi$
$419$	3.20466e43	1.73480	0.867402	+	0.497608i	$0.165788\pi$
$420$	0	0
$421$	5.44061e42	0.272266	0.136133	−	0.990691i	$-0.456533\pi$
$421$	5.44061e42	0.272266	0.136133	+	0.990691i	$0.456533\pi$
$422$	− 8.13043e42i	− 0.391253i
$423$	− 6.15478e43i	− 2.84837i
$424$	−1.10714e42	−0.0492794
$425$	0	0
$426$	−4.49120e43	−1.84971
$427$	− 2.94137e42i	− 0.116544i
$428$	5.76654e42i	0.219833i
$429$	1.09353e43	0.401132
$430$	0	0
$431$	−3.50771e43	−1.19165	−0.595826	−	0.803114i	$-0.703175\pi$
$431$	−3.50771e43	−1.19165	−0.595826	+	0.803114i	$0.703175\pi$
$432$	2.19599e43i	0.718039i
$433$	− 4.30567e43i	− 1.35516i	−0.735449	−	0.677580i	$-0.763029\pi$
$433$	− 4.30567e43i	− 1.35516i	0.735449	−	0.677580i	$-0.236971\pi$
$434$	3.71284e42	0.112493
$435$	0	0
$436$	1.90094e43	0.533876
$437$	8.70054e43i	2.35289i
$438$	− 5.33988e43i	− 1.39062i
$439$	1.81689e43	0.455685	0.227843	−	0.973698i	$-0.426833\pi$
$439$	1.81689e43	0.455685	0.227843	+	0.973698i	$0.426833\pi$
$440$	0	0
$441$	−6.23047e43	−1.44972
$442$	− 5.09071e43i	− 1.14107i
$443$	2.81575e43i	0.608040i	0.952666	+	0.304020i	$0.0983290\pi$
$443$	2.81575e43i	0.608040i	−0.952666	+	0.304020i	$0.901671\pi$
$444$	−5.08267e43	−1.05748
$445$	0	0
$446$	1.25648e44	2.42734
$447$	− 1.10429e44i	− 2.05594i
$448$	− 9.48981e42i	− 0.170283i
$449$	−2.21288e43	−0.382731	−0.191365	−	0.981519i	$-0.561292\pi$
$449$	−2.21288e43	−0.382731	−0.191365	+	0.981519i	$0.561292\pi$
$450$	0	0
$451$	5.09169e43	0.818368
$452$	6.61493e43i	1.02504i
$453$	5.24928e43i	0.784295i
$454$	−6.51938e43	−0.939258
$455$	0	0
$456$	−1.68839e43	−0.226231
$457$	− 6.39404e43i	− 0.826339i	−0.910654	−	0.413169i	$-0.864422\pi$
$457$	− 6.39404e43i	− 0.826339i	0.910654	−	0.413169i	$-0.135578\pi$
$458$	6.07772e43i	0.757636i
$459$	1.03803e44	1.24824
$460$	0	0
$461$	8.79013e42	0.0983853	0.0491926	−	0.998789i	$-0.484335\pi$
$461$	8.79013e42	0.0983853	0.0491926	+	0.998789i	$0.484335\pi$
$462$	− 1.67787e43i	− 0.181203i
$463$	1.18763e44i	1.23764i	0.785532	+	0.618821i	$0.212389\pi$
$463$	1.18763e44i	1.23764i	−0.785532	+	0.618821i	$0.787611\pi$
$464$	1.10570e44	1.11196
$465$	0	0
$466$	−1.15585e44	−1.08276
$467$	1.78679e44i	1.61564i	0.589431	+	0.807819i	$0.299352\pi$
$467$	1.78679e44i	1.61564i	−0.589431	+	0.807819i	$0.700648\pi$
$468$	8.75291e43i	0.764005i
$469$	2.98876e43	0.251849
$470$	0	0
$471$	8.58677e43	0.674504
$472$	− 3.83817e42i	− 0.0291126i
$473$	− 1.72411e43i	− 0.126287i
$474$	9.17595e43	0.649095
$475$	0	0
$476$	−4.01341e43	−0.264849
$477$	1.40793e44i	0.897486i
$478$	1.84253e44i	1.13463i
$479$	−1.06259e44	−0.632165	−0.316082	−	0.948732i	$-0.602368\pi$
$479$	−1.06259e44	−0.632165	−0.316082	+	0.948732i	$0.602368\pi$
$480$	0	0
$481$	5.56531e43	0.309098
$482$	− 3.91762e44i	− 2.10255i
$483$	− 6.22936e43i	− 0.323084i
$484$	1.53254e44	0.768178
$485$	0	0
$486$	3.69370e44	1.72967
$487$	1.85504e44i	0.839700i	0.907593	+	0.419850i	$0.137917\pi$
$487$	1.85504e44i	0.839700i	−0.907593	+	0.419850i	$0.862083\pi$
$488$	− 1.41558e43i	− 0.0619451i
$489$	−3.25651e43	−0.137771
$490$	0	0
$491$	8.88210e43	0.351294	0.175647	−	0.984453i	$-0.443798\pi$
$491$	8.88210e43	0.351294	0.175647	+	0.984453i	$0.443798\pi$
$492$	6.82062e44i	2.60855i
$493$	− 5.22657e44i	− 1.93305i
$494$	3.43733e44	1.22949
$495$	0	0
$496$	−1.43656e44	−0.480703
$497$	− 3.87700e43i	− 0.125492i
$498$	− 3.29948e44i	− 1.03314i
$499$	−2.77853e44	−0.841699	−0.420849	−	0.907131i	$-0.638268\pi$
$499$	−2.77853e44	−0.841699	−0.420849	+	0.907131i	$0.638268\pi$
$500$	0	0
$501$	−6.14564e44	−1.74279
$502$	− 6.87428e44i	− 1.88632i
$503$	− 8.80760e41i	− 0.00233876i	−0.999999	−	0.00116938i	$-0.999628\pi$
$503$	− 8.80760e41i	− 0.00233876i	0.999999	−	0.00116938i	$-0.000372226\pi$
$504$	7.22319e42	0.0185620
$505$	0	0
$506$	−4.16117e44	−1.00169
$507$	5.16097e44i	1.20254i
$508$	4.05873e44i	0.915459i
$509$	8.68803e44	1.89705	0.948523	−	0.316709i	$-0.102578\pi$
$509$	8.68803e44	1.89705	0.948523	+	0.316709i	$0.102578\pi$
$510$	0	0
$511$	4.60961e43	0.0943450
$512$	7.16687e44i	1.42028i
$513$	7.00892e44i	1.34498i
$514$	5.44479e44	1.01179
$515$	0	0
$516$	2.30956e44	0.402539
$517$	− 5.93962e44i	− 1.00269i
$518$	− 8.53917e43i	− 0.139629i
$519$	−6.33245e44	−1.00302
$520$	0	0
$521$	−2.56437e44	−0.381205	−0.190602	−	0.981667i	$-0.561044\pi$
$521$	−2.56437e44	−0.381205	−0.190602	+	0.981667i	$0.561044\pi$
$522$	1.74897e45i	2.51894i
$523$	6.37079e43i	0.0889028i	0.999012	+	0.0444514i	$0.0141540\pi$
$523$	6.37079e43i	0.0889028i	−0.999012	+	0.0444514i	$0.985846\pi$
$524$	2.39631e44	0.324024
$525$	0	0
$526$	3.45554e44	0.438784
$527$	6.79052e44i	0.835657i
$528$	6.49197e44i	0.774314i
$529$	−6.79897e44	−0.786004
$530$	0	0
$531$	−4.88093e44	−0.530204
$532$	− 2.70991e44i	− 0.285373i
$533$	− 7.46830e44i	− 0.762471i
$534$	−4.18149e45	−4.13905
$535$	0	0
$536$	1.43839e44	0.133862
$537$	− 2.97097e45i	− 2.68116i
$538$	− 9.57595e44i	− 0.838059i
$539$	−6.01267e44	−0.510332
$540$	0	0
$541$	−1.56706e45	−1.25121	−0.625605	−	0.780140i	$-0.715148\pi$
$541$	−1.56706e45	−1.25121	−0.625605	+	0.780140i	$0.715148\pi$
$542$	− 2.52209e45i	− 1.95332i
$543$	1.94899e44i	0.146424i
$544$	3.20496e45	2.33583
$545$	0	0
$546$	−2.46104e44	−0.168826
$547$	− 2.05395e45i	− 1.36710i	−0.729905	−	0.683548i	$-0.760436\pi$
$547$	− 2.05395e45i	− 1.36710i	0.729905	−	0.683548i	$-0.239564\pi$
$548$	− 9.42359e44i	− 0.608607i
$549$	−1.80017e45	−1.12816
$550$	0	0
$551$	3.52906e45	2.08285
$552$	− 2.99797e44i	− 0.171725i
$553$	7.92107e43i	0.0440371i
$554$	−4.09851e45	−2.21164
$555$	0	0
$556$	−1.60827e44	−0.0817756
$557$	3.02985e44i	0.149558i	0.997200	+	0.0747792i	$0.0238252\pi$
$557$	3.02985e44i	0.149558i	−0.997200	+	0.0747792i	$0.976175\pi$
$558$	− 2.27231e45i	− 1.08894i
$559$	−2.52887e44	−0.117661
$560$	0	0
$561$	3.06871e45	1.34607
$562$	− 2.08122e45i	− 0.886478i
$563$	2.25447e45i	0.932514i	0.884649	+	0.466257i	$0.154398\pi$
$563$	2.25447e45i	0.932514i	−0.884649	+	0.466257i	$0.845602\pi$
$564$	7.95649e45	3.19607
$565$	0	0
$566$	9.62602e44	0.364733
$567$	1.16886e44i	0.0430173i
$568$	− 1.86586e44i	− 0.0667009i
$569$	3.27232e45	1.13633	0.568163	−	0.822916i	$-0.307654\pi$
$569$	3.27232e45	1.13633	0.568163	+	0.822916i	$0.307654\pi$
$570$	0	0
$571$	3.07381e45	1.00735	0.503675	−	0.863893i	$-0.331981\pi$
$571$	3.07381e45	1.00735	0.503675	+	0.863893i	$0.331981\pi$
$572$	8.44693e44i	0.268946i
$573$	7.10419e45i	2.19768i
$574$	−1.14590e45	−0.344431
$575$	0	0
$576$	−5.80792e45	−1.64835
$577$	− 6.81899e43i	− 0.0188070i	−0.999956	−	0.00940349i	$-0.997007\pi$
$577$	− 6.81899e43i	− 0.0188070i	0.999956	−	0.00940349i	$-0.00299327\pi$
$578$	− 8.93501e45i	− 2.39489i
$579$	7.62838e44	0.198718
$580$	0	0
$581$	2.84825e44	0.0700926
$582$	− 1.67255e44i	− 0.0400082i
$583$	1.35871e45i	0.315934i
$584$	2.21844e44	0.0501460
$585$	0	0
$586$	1.01963e46	2.17837
$587$	− 8.96797e45i	− 1.86280i	−0.364002	−	0.931398i	$-0.618590\pi$
$587$	− 8.96797e45i	− 1.86280i	0.364002	−	0.931398i	$-0.381410\pi$
$588$	− 8.05433e45i	− 1.62669i
$589$	−4.58506e45	−0.900416
$590$	0	0
$591$	−1.08598e46	−2.01665
$592$	3.30395e45i	0.596659i
$593$	3.75910e45i	0.660209i	0.943944	+	0.330104i	$0.107084\pi$
$593$	3.75910e45i	0.660209i	−0.943944	+	0.330104i	$0.892916\pi$
$594$	−3.35213e45	−0.572590
$595$	0	0
$596$	8.53004e45	1.37844
$597$	1.28342e46i	2.01740i
$598$	6.10345e45i	0.933268i
$599$	−8.80446e45	−1.30966	−0.654832	−	0.755774i	$-0.727261\pi$
$599$	−8.80446e45	−1.30966	−0.654832	+	0.755774i	$0.727261\pi$
$600$	0	0
$601$	−4.53048e45	−0.637846	−0.318923	−	0.947781i	$-0.603321\pi$
$601$	−4.53048e45	−0.637846	−0.318923	+	0.947781i	$0.603321\pi$
$602$	3.88018e44i	0.0531508i
$603$	− 1.82917e46i	− 2.43791i
$604$	−4.05477e45	−0.525844
$605$	0	0
$606$	−2.42281e46	−2.97524
$607$	1.02463e46i	1.22448i	0.790671	+	0.612242i	$0.209732\pi$
$607$	1.02463e46i	1.22448i	−0.790671	+	0.612242i	$0.790268\pi$
$608$	2.16404e46i	2.51684i
$609$	−2.52672e45	−0.286003
$610$	0	0
$611$	−8.71203e45	−0.934199
$612$	2.45627e46i	2.56376i
$613$	4.85425e45i	0.493201i	0.969117	+	0.246601i	$0.0793136\pi$
$613$	4.85425e45i	0.493201i	−0.969117	+	0.246601i	$0.920686\pi$
$614$	1.71865e46	1.69985
$615$	0	0
$616$	6.97068e43	0.00653421
$617$	− 1.62668e46i	− 1.48455i	−0.670093	−	0.742277i	$-0.733746\pi$
$617$	− 1.62668e46i	− 1.48455i	0.670093	−	0.742277i	$-0.266254\pi$
$618$	1.09300e46i	0.971200i
$619$	2.50157e45	0.216430	0.108215	−	0.994128i	$-0.465486\pi$
$619$	2.50157e45	0.216430	0.108215	+	0.994128i	$0.465486\pi$
$620$	0	0
$621$	−1.24453e46	−1.02093
$622$	− 7.17763e45i	− 0.573376i
$623$	− 3.60964e45i	− 0.280809i
$624$	9.52220e45	0.721425
$625$	0	0
$626$	1.44337e46	1.03729
$627$	2.07204e46i	1.45038i
$628$	6.63279e45i	0.452233i
$629$	1.56175e46	1.03723
$630$	0	0
$631$	6.94339e45	0.437610	0.218805	−	0.975769i	$-0.429784\pi$
$631$	6.94339e45	0.437610	0.218805	+	0.975769i	$0.429784\pi$
$632$	3.81213e44i	0.0234065i
$633$	− 7.18871e45i	− 0.430021i
$634$	1.83603e46	1.07006
$635$	0	0
$636$	−1.82008e46	−1.00704
$637$	8.81916e45i	0.475474i
$638$	1.68783e46i	0.886721i
$639$	−2.37278e46	−1.21477
$640$	0	0
$641$	4.34529e45	0.211282	0.105641	−	0.994404i	$-0.466311\pi$
$641$	4.34529e45	0.211282	0.105641	+	0.994404i	$0.466311\pi$
$642$	9.92303e45i	0.470236i
$643$	− 2.56764e46i	− 1.18591i	−0.805235	−	0.592956i	$-0.797961\pi$
$643$	− 2.56764e46i	− 1.18591i	0.805235	−	0.592956i	$-0.202039\pi$
$644$	4.81183e45	0.216618
$645$	0	0
$646$	9.64592e46	4.12579
$647$	− 1.55928e46i	− 0.650136i	−0.945691	−	0.325068i	$-0.894613\pi$
$647$	− 1.55928e46i	− 0.650136i	0.945691	−	0.325068i	$-0.105387\pi$
$648$	5.62533e44i	0.0228644i
$649$	−4.71030e45	−0.186643
$650$	0	0
$651$	3.28279e45	0.123639
$652$	− 2.51547e45i	− 0.0923706i
$653$	− 1.54838e45i	− 0.0554384i	−0.999616	−	0.0277192i	$-0.991176\pi$
$653$	− 1.54838e45i	− 0.0554384i	0.999616	−	0.0277192i	$-0.00882442\pi$
$654$	3.27112e46	1.14199
$655$	0	0
$656$	4.43370e46	1.47182
$657$	− 2.82115e46i	− 0.913267i
$658$	1.33673e46i	0.422005i
$659$	1.05260e46	0.324080	0.162040	−	0.986784i	$-0.448193\pi$
$659$	1.05260e46	0.324080	0.162040	+	0.986784i	$0.448193\pi$
$660$	0	0
$661$	−1.48865e46	−0.435981	−0.217990	−	0.975951i	$-0.569950\pi$
$661$	−1.48865e46	−0.435981	−0.217990	+	0.975951i	$0.569950\pi$
$662$	− 5.70840e46i	− 1.63064i
$663$	− 4.50107e46i	− 1.25413i
$664$	1.37076e45	0.0372554
$665$	0	0
$666$	−5.22611e46	−1.35162
$667$	6.26634e46i	1.58102i
$668$	− 4.74716e46i	− 1.16848i
$669$	1.11095e47	2.66786
$670$	0	0
$671$	−1.73724e46	−0.397134
$672$	− 1.54940e46i	− 0.345597i
$673$	2.78172e46i	0.605432i	0.953081	+	0.302716i	$0.0978933\pi$
$673$	2.78172e46i	0.605432i	−0.953081	+	0.302716i	$0.902107\pi$
$674$	−9.26605e46	−1.96791
$675$	0	0
$676$	−3.98656e46	−0.806265
$677$	− 9.09948e45i	− 0.179599i	−0.995960	−	0.0897995i	$-0.971377\pi$
$677$	− 9.09948e45i	− 0.179599i	0.995960	−	0.0897995i	$-0.0286226\pi$
$678$	1.13829e47i	2.19262i
$679$	1.44381e44	0.00271431
$680$	0	0
$681$	−5.76426e46	−1.03233
$682$	− 2.19288e46i	− 0.383330i
$683$	− 2.07397e46i	− 0.353883i	−0.984221	−	0.176942i	$-0.943380\pi$
$683$	− 2.07397e46i	− 0.353883i	0.984221	−	0.176942i	$-0.0566204\pi$
$684$	−1.65851e47	−2.76244
$685$	0	0
$686$	2.73894e46	0.434746
$687$	5.37376e46i	0.832707i
$688$	− 1.50131e46i	− 0.227123i
$689$	1.99291e46	0.294354
$690$	0	0
$691$	7.80876e46	1.09950	0.549749	−	0.835330i	$-0.314723\pi$
$691$	7.80876e46	1.09950	0.549749	+	0.835330i	$0.314723\pi$
$692$	− 4.89146e46i	− 0.672493i
$693$	− 8.86448e45i	− 0.119002i
$694$	−1.00599e47	−1.31875
$695$	0	0
$696$	−1.21602e46	−0.152016
$697$	− 2.09578e47i	− 2.55861i
$698$	− 5.39729e46i	− 0.643519i
$699$	−1.02197e47	−1.19005
$700$	0	0
$701$	−7.28838e46	−0.809624	−0.404812	−	0.914400i	$-0.632663\pi$
$701$	−7.28838e46	−0.809624	−0.404812	+	0.914400i	$0.632663\pi$
$702$	4.91678e46i	0.533480i
$703$	1.05452e47i	1.11761i
$704$	−5.60488e46	−0.580253
$705$	0	0
$706$	−2.63176e47	−2.59997
$707$	− 2.09147e46i	− 0.201852i
$708$	− 6.30974e46i	− 0.594926i
$709$	−4.67334e46	−0.430491	−0.215246	−	0.976560i	$-0.569055\pi$
$709$	−4.67334e46	−0.430491	−0.215246	+	0.976560i	$0.569055\pi$
$710$	0	0
$711$	4.84782e46	0.426283
$712$	− 1.73719e46i	− 0.149255i
$713$	− 8.14142e46i	− 0.683476i
$714$	−6.90624e46	−0.566528
$715$	0	0
$716$	2.29490e47	1.79763
$717$	1.62911e47i	1.24705i
$718$	8.90958e46i	0.666506i
$719$	1.27931e47	0.935299	0.467649	−	0.883914i	$-0.345101\pi$
$719$	1.27931e47	0.935299	0.467649	+	0.883914i	$0.345101\pi$
$720$	0	0
$721$	−9.43520e45	−0.0658899
$722$	4.41189e47i	3.01135i
$723$	− 3.46385e47i	− 2.31088i
$724$	−1.50548e46	−0.0981725
$725$	0	0
$726$	2.63718e47	1.64318
$727$	− 1.68652e47i	− 1.02724i	−0.858017	−	0.513621i	$-0.828304\pi$
$727$	− 1.68652e47i	− 1.02724i	0.858017	−	0.513621i	$-0.171696\pi$
$728$	− 1.02243e45i	− 0.00608790i
$729$	2.78403e47	1.62057
$730$	0	0
$731$	−7.09659e46	−0.394832
$732$	− 2.32713e47i	− 1.26587i
$733$	− 3.19951e47i	− 1.70164i	−0.525456	−	0.850821i	$-0.676105\pi$
$733$	− 3.19951e47i	− 1.70164i	0.525456	−	0.850821i	$-0.323895\pi$
$734$	1.81532e47	0.943992
$735$	0	0
$736$	−3.84255e47	−1.91045
$737$	− 1.76523e47i	− 0.858196i
$738$	7.01311e47i	3.33412i
$739$	1.33356e47	0.619980	0.309990	−	0.950740i	$-0.399674\pi$
$739$	1.33356e47	0.619980	0.309990	+	0.950740i	$0.399674\pi$
$740$	0	0
$741$	3.03919e47	1.35132
$742$	− 3.05783e46i	− 0.132969i
$743$	− 3.22840e46i	− 0.137300i	−0.997641	−	0.0686502i	$-0.978131\pi$
$743$	− 3.22840e46i	− 0.137300i	0.997641	−	0.0686502i	$-0.0218692\pi$
$744$	1.57989e46	0.0657164
$745$	0	0
$746$	4.42119e46	0.175934
$747$	− 1.74317e47i	− 0.678502i
$748$	2.37040e47i	0.902497i
$749$	−8.56597e45	−0.0319027
$750$	0	0
$751$	2.39672e46	0.0854196	0.0427098	−	0.999088i	$-0.486401\pi$
$751$	2.39672e46	0.0854196	0.0427098	+	0.999088i	$0.486401\pi$
$752$	− 5.17206e47i	− 1.80331i
$753$	− 6.07806e47i	− 2.07323i
$754$	2.47565e47	0.826154
$755$	0	0
$756$	3.87628e46	0.123824
$757$	− 6.92584e46i	− 0.216466i	−0.994126	−	0.108233i	$-0.965481\pi$
$757$	− 6.92584e46i	− 0.216466i	0.994126	−	0.108233i	$-0.0345193\pi$
$758$	− 1.75970e47i	− 0.538143i
$759$	−3.67919e47	−1.10094
$760$	0	0
$761$	−4.97287e47	−1.42482	−0.712411	−	0.701763i	$-0.752397\pi$
$761$	−4.97287e47	−1.42482	−0.712411	+	0.701763i	$0.752397\pi$
$762$	6.98423e47i	1.95822i
$763$	2.82377e46i	0.0774773i
$764$	−5.48759e47	−1.47347
$765$	0	0
$766$	7.15131e47	1.83912
$767$	6.90891e46i	0.173895i
$768$	5.61051e47i	1.38211i
$769$	−2.89778e47	−0.698683	−0.349342	−	0.936995i	$-0.613595\pi$
$769$	−2.89778e47	−0.698683	−0.349342	+	0.936995i	$0.613595\pi$
$770$	0	0
$771$	4.81414e47	1.11204
$772$	5.89249e46i	0.133234i
$773$	5.10656e47i	1.13023i	0.825012	+	0.565115i	$0.191168\pi$
$773$	5.10656e47i	1.13023i	−0.825012	+	0.565115i	$0.808832\pi$
$774$	2.37473e47	0.514504
$775$	0	0
$776$	6.94857e44	0.00144270
$777$	− 7.55010e46i	− 0.153464i
$778$	9.21352e47i	1.83342i
$779$	1.41510e48	2.75689
$780$	0	0
$781$	−2.28983e47	−0.427624
$782$	1.71277e48i	3.13175i
$783$	5.04799e47i	0.903753i
$784$	−5.23567e47	−0.917819
$785$	0	0
$786$	4.12356e47	0.693107
$787$	3.90010e47i	0.641938i	0.947090	+	0.320969i	$0.104009\pi$
$787$	3.90010e47i	0.641938i	−0.947090	+	0.320969i	$0.895991\pi$
$788$	− 8.38862e47i	− 1.35210i
$789$	3.05529e47	0.482261
$790$	0	0
$791$	−9.82622e46	−0.148756
$792$	− 4.26617e46i	− 0.0632517i
$793$	2.54812e47i	0.370009i
$794$	1.24086e48	1.76476
$795$	0	0
$796$	−9.91367e47	−1.35260
$797$	6.38986e47i	0.853943i	0.904265	+	0.426972i	$0.140420\pi$
$797$	6.38986e47i	0.853943i	−0.904265	+	0.426972i	$0.859580\pi$
$798$	− 4.66320e47i	− 0.610431i
$799$	−2.44479e48	−3.13488
$800$	0	0
$801$	−2.20916e48	−2.71826
$802$	4.53171e47i	0.546242i
$803$	− 2.72253e47i	− 0.321489i
$804$	2.36463e48	2.73551
$805$	0	0
$806$	−3.21644e47	−0.357147
$807$	− 8.46680e47i	− 0.921098i
$808$	− 1.00655e47i	− 0.107288i
$809$	3.00339e47	0.313661	0.156831	−	0.987626i	$-0.449872\pi$
$809$	3.00339e47	0.313661	0.156831	+	0.987626i	$0.449872\pi$
$810$	0	0
$811$	−1.57205e48	−1.57624	−0.788121	−	0.615521i	$-0.788946\pi$
$811$	−1.57205e48	−1.57624	−0.788121	+	0.615521i	$0.788946\pi$
$812$	− 1.95175e47i	− 0.191756i
$813$	− 2.22997e48i	− 2.14686i
$814$	−5.04341e47	−0.475797
$815$	0	0
$816$	2.67215e48	2.42088
$817$	− 4.79172e47i	− 0.425430i
$818$	− 4.14782e47i	− 0.360903i
$819$	−1.30021e47	−0.110874
$820$	0	0
$821$	2.23751e48	1.83275	0.916374	−	0.400324i	$-0.131102\pi$
$821$	2.23751e48	1.83275	0.916374	+	0.400324i	$0.131102\pi$
$822$	− 1.62160e48i	− 1.30185i
$823$	5.02472e47i	0.395380i	0.980265	+	0.197690i	$0.0633439\pi$
$823$	5.02472e47i	0.395380i	−0.980265	+	0.197690i	$0.936656\pi$
$824$	−4.54083e46	−0.0350216
$825$	0	0
$826$	1.06007e47	0.0785533
$827$	1.52395e48i	1.10695i	0.832865	+	0.553475i	$0.186699\pi$
$827$	1.52395e48i	1.10695i	−0.832865	+	0.553475i	$0.813301\pi$
$828$	− 2.94492e48i	− 2.09688i
$829$	−7.14872e47	−0.498975	−0.249487	−	0.968378i	$-0.580262\pi$
$829$	−7.14872e47	−0.498975	−0.249487	+	0.968378i	$0.580262\pi$
$830$	0	0
$831$	−3.62379e48	−2.43078
$832$	8.22104e47i	0.540620i
$833$	2.47486e48i	1.59554i
$834$	−2.76749e47	−0.174923
$835$	0	0
$836$	−1.60053e48	−0.972436
$837$	− 6.55851e47i	− 0.390693i
$838$	4.25968e48i	2.48800i
$839$	−2.41800e48	−1.38479	−0.692394	−	0.721519i	$-0.743444\pi$
$839$	−2.41800e48	−1.38479	−0.692394	+	0.721519i	$0.743444\pi$
$840$	0	0
$841$	7.25637e47	0.399563
$842$	7.23174e47i	0.390475i
$843$	− 1.84015e48i	− 0.974315i
$844$	5.55287e47	0.288315
$845$	0	0
$846$	8.18103e48	4.08505
$847$	2.27652e47i	0.111480i
$848$	1.18313e48i	0.568199i
$849$	8.51107e47	0.400873
$850$	0	0
$851$	−1.87245e48	−0.848345
$852$	− 3.06737e48i	− 1.36306i
$853$	− 5.58595e47i	− 0.243466i	−0.992563	−	0.121733i	$-0.961155\pi$
$853$	− 5.58595e47i	− 0.243466i	0.992563	−	0.121733i	$-0.0388452\pi$
$854$	3.90972e47	0.167144
$855$	0	0
$856$	−4.12250e46	−0.0169568
$857$	− 7.99378e47i	− 0.322529i	−0.986911	−	0.161264i	$-0.948443\pi$
$857$	− 7.99378e47i	− 0.322529i	0.986911	−	0.161264i	$-0.0515572\pi$
$858$	1.45354e48i	0.575290i
$859$	−3.21299e48	−1.24745	−0.623723	−	0.781646i	$-0.714381\pi$
$859$	−3.21299e48	−1.24745	−0.623723	+	0.781646i	$0.714381\pi$
$860$	0	0
$861$	−1.01318e48	−0.378559
$862$	− 4.66251e48i	− 1.70903i
$863$	− 2.15382e48i	− 0.774519i	−0.921971	−	0.387259i	$-0.873422\pi$
$863$	− 2.15382e48i	− 0.774519i	0.921971	−	0.387259i	$-0.126578\pi$
$864$	−3.09546e48	−1.09206
$865$	0	0
$866$	5.72316e48	1.94353
$867$	− 7.90010e48i	− 2.63219i
$868$	2.53577e47i	0.0828962i
$869$	4.67835e47	0.150060
$870$	0	0
$871$	−2.58917e48	−0.799578
$872$	1.35898e47i	0.0411805i
$873$	− 8.83637e46i	− 0.0262748i
$874$	−1.15649e49	−3.37445
$875$	0	0
$876$	3.64700e48	1.02475
$877$	4.36089e48i	1.20249i	0.799064	+	0.601245i	$0.205329\pi$
$877$	4.36089e48i	1.20249i	−0.799064	+	0.601245i	$0.794671\pi$
$878$	2.41504e48i	0.653530i
$879$	9.01528e48	2.39421
$880$	0	0
$881$	−4.71885e48	−1.20707	−0.603537	−	0.797335i	$-0.706242\pi$
$881$	−4.71885e48	−1.20707	−0.603537	+	0.797335i	$0.706242\pi$
$882$	− 8.28163e48i	− 2.07914i
$883$	2.47214e48i	0.609146i	0.952489	+	0.304573i	$0.0985138\pi$
$883$	2.47214e48i	0.609146i	−0.952489	+	0.304573i	$0.901486\pi$
$884$	3.47682e48	0.840853
$885$	0	0
$886$	−3.74274e48	−0.872033
$887$	− 6.65983e48i	− 1.52308i	−0.648116	−	0.761542i	$-0.724443\pi$
$887$	− 6.65983e48i	− 1.52308i	0.648116	−	0.761542i	$-0.275557\pi$
$888$	− 3.63360e47i	− 0.0815686i
$889$	−6.02908e47	−0.132853
$890$	0	0
$891$	6.90355e47	0.146585
$892$	8.58144e48i	1.78871i
$893$	− 1.65076e49i	− 3.37781i
$894$	1.46784e49	2.94856
$895$	0	0
$896$	1.28948e47	0.0249650
$897$	5.39651e48i	1.02574i
$898$	− 2.94139e48i	− 0.548901i
$899$	−3.30227e48	−0.605032
$900$	0	0
$901$	5.59256e48	0.987760
$902$	6.76795e48i	1.17368i
$903$	3.43075e47i	0.0584173i
$904$	−4.72902e47	−0.0790663
$905$	0	0
$906$	−6.97743e48	−1.12481
$907$	4.30056e48i	0.680777i	0.940285	+	0.340388i	$0.110559\pi$
$907$	4.30056e48i	0.680777i	−0.940285	+	0.340388i	$0.889441\pi$
$908$	− 4.45257e48i	− 0.692140i
$909$	−1.28002e49	−1.95394
$910$	0	0
$911$	−2.43257e48	−0.358106	−0.179053	−	0.983839i	$-0.557303\pi$
$911$	−2.43257e48	−0.358106	−0.179053	+	0.983839i	$0.557303\pi$
$912$	1.80427e49i	2.60848i
$913$	− 1.68224e48i	− 0.238847i
$914$	8.49906e48	1.18511
$915$	0	0
$916$	−4.15093e48	−0.558303
$917$	3.55963e47i	0.0470230i
$918$	1.37976e49i	1.79019i
$919$	−1.59035e48	−0.202669	−0.101334	−	0.994852i	$-0.532311\pi$
$919$	−1.59035e48	−0.202669	−0.101334	+	0.994852i	$0.532311\pi$
$920$	0	0
$921$	1.51959e49	1.86828
$922$	1.16840e48i	0.141101i
$923$	3.35865e48i	0.398416i
$924$	1.14594e48	0.133529
$925$	0	0
$926$	−1.57862e49	−1.77499
$927$	5.77449e48i	0.637820i
$928$	1.55859e49i	1.69119i
$929$	1.48456e49	1.58248	0.791239	−	0.611507i	$-0.209436\pi$
$929$	1.48456e49	1.58248	0.791239	+	0.611507i	$0.209436\pi$
$930$	0	0
$931$	−1.67106e49	−1.71919
$932$	− 7.89414e48i	− 0.797888i
$933$	− 6.34627e48i	− 0.630190i
$934$	−2.37502e49	−2.31710
$935$	0	0
$936$	−6.25746e47	−0.0589314
$937$	− 1.00831e49i	− 0.933020i	−0.884516	−	0.466510i	$-0.845511\pi$
$937$	− 1.00831e49i	− 0.933020i	0.884516	−	0.466510i	$-0.154489\pi$
$938$	3.97271e48i	0.361193i
$939$	1.27619e49	1.14007
$940$	0	0
$941$	9.04832e48	0.780440	0.390220	−	0.920722i	$-0.372399\pi$
$941$	9.04832e48	0.780440	0.390220	+	0.920722i	$0.372399\pi$
$942$	1.14137e49i	0.967353i
$943$	2.51271e49i	2.09266i
$944$	−4.10161e48	−0.335673
$945$	0	0
$946$	2.29172e48	0.181116
$947$	− 9.36347e48i	− 0.727214i	−0.931552	−	0.363607i	$-0.881545\pi$
$947$	− 9.36347e48i	− 0.727214i	0.931552	−	0.363607i	$-0.118455\pi$
$948$	6.26693e48i	0.478319i
$949$	−3.99331e48	−0.299530
$950$	0	0
$951$	1.62337e49	1.17609
$952$	− 2.86919e47i	− 0.0204291i
$953$	− 1.92193e49i	− 1.34494i	−0.740123	−	0.672472i	$-0.765233\pi$
$953$	− 1.92193e49i	− 1.34494i	0.740123	−	0.672472i	$-0.234767\pi$
$954$	−1.87144e49	−1.28715
$955$	0	0
$956$	−1.25840e49	−0.836109
$957$	1.49233e49i	0.974582i
$958$	− 1.41241e49i	− 0.906631i
$959$	1.39984e48	0.0883223
$960$	0	0
$961$	−1.21131e49	−0.738444
$962$	7.39750e48i	0.443298i
$963$	5.24251e48i	0.308820i
$964$	2.67563e49	1.54937
$965$	0	0
$966$	8.28017e48	0.463358
$967$	− 1.11182e49i	− 0.611642i	−0.952089	−	0.305821i	$-0.901069\pi$
$967$	− 1.11182e49i	− 0.611642i	0.952089	−	0.305821i	$-0.0989309\pi$
$968$	1.09561e48i	0.0592533i
$969$	8.52867e49	4.53460
$970$	0	0
$971$	1.55536e49	0.799308	0.399654	−	0.916666i	$-0.369130\pi$
$971$	1.55536e49	0.799308	0.399654	+	0.916666i	$0.369130\pi$
$972$	2.52270e49i	1.27459i
$973$	− 2.38902e47i	− 0.0118674i
$974$	−2.46574e49	−1.20427
$975$	0	0
$976$	−1.51274e49	−0.714236
$977$	− 2.43707e49i	− 1.13138i	−0.824618	−	0.565690i	$-0.808610\pi$
$977$	− 2.43707e49i	− 1.13138i	0.824618	−	0.565690i	$-0.191390\pi$
$978$	− 4.32860e48i	− 0.197586i
$979$	−2.13193e49	−0.956883
$980$	0	0
$981$	1.72819e49	0.749986
$982$	1.18062e49i	0.503815i
$983$	− 1.27767e48i	− 0.0536148i	−0.999641	−	0.0268074i	$-0.991466\pi$
$983$	− 1.27767e48i	− 0.0536148i	0.999641	−	0.0268074i	$-0.00853409\pi$
$984$	−4.87607e48	−0.201210
$985$	0	0
$986$	6.94723e49	2.77231
$987$	1.18191e49i	0.463820i
$988$	2.34760e49i	0.906015i
$989$	8.50838e48	0.322930
$990$	0	0
$991$	−8.47131e48	−0.310982	−0.155491	−	0.987837i	$-0.549696\pi$
$991$	−8.47131e48	−0.310982	−0.155491	+	0.987837i	$0.549696\pi$
$992$	− 2.02497e49i	− 0.731100i
$993$	− 5.04722e49i	− 1.79221i
$994$	5.15336e48	0.179976
$995$	0	0
$996$	2.25346e49	0.761326
$997$	− 4.23201e49i	− 1.40629i	−0.711045	−	0.703147i	$-0.751778\pi$
$997$	− 4.23201e49i	− 1.40629i	0.711045	−	0.703147i	$-0.248222\pi$
$998$	− 3.69327e49i	− 1.20714i
$999$	−1.50840e49	−0.484936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.c.24.11		12
5.2	odd	4		25.34.a.c.1.2		6
5.3	odd	4		5.34.a.b.1.5	✓	6
5.4	even	2	inner	25.34.b.c.24.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.5	✓	6	5.3	odd	4
25.34.a.c.1.2		6	5.2	odd	4
25.34.b.c.24.2		12	5.4	even	2	inner
25.34.b.c.24.11		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)

\(f(q)\)	\(=\)	\(q+132922. i q^{2} +1.17526e8i q^{3} -9.07819e9 q^{4} -1.56217e13 q^{6} -1.34853e13i q^{7} -6.49000e13i q^{8} -8.25322e15 q^{9} +O(q^{10})\)	\(q+132922. i q^{2} +1.17526e8i q^{3} -9.07819e9 q^{4} -1.56217e13 q^{6} -1.34853e13i q^{7} -6.49000e13i q^{8} -8.25322e15 q^{9} -7.96470e16 q^{11} -1.06692e18i q^{12} +1.16823e18i q^{13} +1.79249e18 q^{14} -6.93545e19 q^{16} +3.27833e20i q^{17} -1.09703e21i q^{18} -2.21358e21 q^{19} +1.58487e21 q^{21} -1.05868e22i q^{22} -3.93052e22i q^{23} +7.62742e21 q^{24} -1.55283e23 q^{26} -3.16633e23i q^{27} +1.22422e23i q^{28} -1.59428e24 q^{29} +2.07133e24 q^{31} -9.77619e24i q^{32} -9.36057e24i q^{33} -4.35761e25 q^{34} +7.49243e25 q^{36} -4.76387e25i q^{37} -2.94233e26i q^{38} -1.37297e26 q^{39} -6.39281e26 q^{41} +2.10663e26i q^{42} +2.16469e26i q^{43} +7.23051e26 q^{44} +5.22451e27 q^{46} +7.45743e27i q^{47} -8.15093e27i q^{48} +7.54914e27 q^{49} -3.85288e28 q^{51} -1.06055e28i q^{52} -1.70592e28i q^{53} +4.20873e28 q^{54} -8.75196e26 q^{56} -2.60153e29i q^{57} -2.11913e29i q^{58} +5.91397e28 q^{59} +2.18117e29 q^{61} +2.75325e29i q^{62} +1.11297e29i q^{63} +7.03715e29 q^{64} +1.24422e30 q^{66} +2.21631e30i q^{67} -2.97613e30i q^{68} +4.61937e30 q^{69} +2.87498e30 q^{71} +5.35634e29i q^{72} +3.41825e30i q^{73} +6.33220e30 q^{74} +2.00953e31 q^{76} +1.07406e30i q^{77} -1.82498e31i q^{78} -5.87385e30 q^{79} -8.66769e30 q^{81} -8.49743e31i q^{82} +2.11211e31i q^{83} -1.43877e31 q^{84} -2.87734e31 q^{86} -1.87368e32i q^{87} +5.16909e30i q^{88} +2.67672e32 q^{89} +1.57540e31 q^{91} +3.56821e32i q^{92} +2.43435e32i q^{93} -9.91253e32 q^{94} +1.14895e33 q^{96} +1.07066e31i q^{97} +1.00344e33i q^{98} +6.57344e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) \) 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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