LMFDB - Embedded newform 325.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.a (trivial)

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:	yes
Analytic conductor:	$167.386646753$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 $ x^5 - 1438x^3 - 4164x^2 + 396957*x - 59580
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$35.1685$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-38.1685 q^{2} -47.8784 q^{3} +944.833 q^{4} +1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} +O(q^{10})$	\(q-38.1685 q^{2} -47.8784 q^{3} +944.833 q^{4} +1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} -25205.7 q^{11} -45237.1 q^{12} -28561.0 q^{13} +227005. q^{14} +146811. q^{16} -109318. q^{17} +663775. q^{18} -904609. q^{19} +284754. q^{21} +962062. q^{22} +435749. q^{23} +790979. q^{24} +1.09013e6 q^{26} +1.77503e6 q^{27} -5.61934e6 q^{28} +6.44791e6 q^{29} +6.62308e6 q^{31} +2.85499e6 q^{32} +1.20681e6 q^{33} +4.17250e6 q^{34} -1.64313e7 q^{36} -4.14357e6 q^{37} +3.45275e7 q^{38} +1.36745e6 q^{39} +1.49568e7 q^{41} -1.08686e7 q^{42} -4.01789e7 q^{43} -2.38151e7 q^{44} -1.66319e7 q^{46} -6.30151e6 q^{47} -7.02907e6 q^{48} -4.98153e6 q^{49} +5.23397e6 q^{51} -2.69854e7 q^{52} -1.53111e7 q^{53} -6.77501e7 q^{54} +9.82552e7 q^{56} +4.33112e7 q^{57} -2.46107e8 q^{58} -1.52760e8 q^{59} +8.66321e7 q^{61} -2.52793e8 q^{62} +1.03430e8 q^{63} -1.84138e8 q^{64} -4.60620e7 q^{66} +1.01034e8 q^{67} -1.03287e8 q^{68} -2.08630e7 q^{69} +4.13122e8 q^{71} +2.87304e8 q^{72} +3.14453e8 q^{73} +1.58154e8 q^{74} -8.54704e8 q^{76} +1.49909e8 q^{77} -5.21937e7 q^{78} -2.00580e8 q^{79} +2.57315e8 q^{81} -5.70879e8 q^{82} -6.34578e7 q^{83} +2.69045e8 q^{84} +1.53357e9 q^{86} -3.08715e8 q^{87} +4.16412e8 q^{88} +3.47074e7 q^{89} +1.69865e8 q^{91} +4.11710e8 q^{92} -3.17102e8 q^{93} +2.40519e8 q^{94} -1.36692e8 q^{96} +1.25403e9 q^{97} +1.90137e8 q^{98} +4.38343e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 15 q^{2} - 161 q^{3} + 361 q^{4} + 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9}+O(q^{10}) $ 5 * q - 15 * q^2 - 161 * q^3 + 361 * q^4 + 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9	\( 5 q - 15 q^{2} - 161 q^{3} + 361 q^{4} + 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9} + 121746 q^{11} - 113389 q^{12} - 142805 q^{13} + 8475 q^{14} - 322463 q^{16} + 495669 q^{17} + 656228 q^{18} - 840738 q^{19} - 1599467 q^{21} + 2023594 q^{22} + 592152 q^{23} - 2295657 q^{24} + 428415 q^{26} - 6847883 q^{27} - 2587955 q^{28} + 10678182 q^{29} + 12885296 q^{31} - 3282927 q^{32} - 17278298 q^{33} - 9934079 q^{34} - 20483302 q^{36} - 7171823 q^{37} + 25568814 q^{38} + 4598321 q^{39} + 9294012 q^{41} + 69520457 q^{42} - 12831975 q^{43} - 41479074 q^{44} - 59319696 q^{46} - 43354215 q^{47} + 86874671 q^{48} + 25249488 q^{49} + 16905901 q^{51} - 10310521 q^{52} - 93231780 q^{53} + 58983719 q^{54} + 199599225 q^{56} - 90173382 q^{57} - 151020970 q^{58} + 246496182 q^{59} - 132232612 q^{61} - 158135724 q^{62} + 416955202 q^{63} + 91019105 q^{64} - 323733130 q^{66} + 369388534 q^{67} - 238172073 q^{68} - 579986760 q^{69} + 212150457 q^{71} + 415774278 q^{72} + 252729806 q^{73} + 192105957 q^{74} - 953775990 q^{76} - 449666118 q^{77} - 162597773 q^{78} - 1247271728 q^{79} - 317713115 q^{81} - 169559388 q^{82} - 1696894296 q^{83} + 1247983739 q^{84} + 3291621459 q^{86} + 614530466 q^{87} + 220227222 q^{88} - 753854382 q^{89} + 288437539 q^{91} - 13876128 q^{92} + 892784668 q^{93} + 272071215 q^{94} + 930612847 q^{96} - 3824606 q^{97} - 1570614816 q^{98} + 3016199848 q^{99}+O(q^{100}) \) 5 * q - 15 * q^2 - 161 * q^3 + 361 * q^4 + 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9 + 121746 * q^11 - 113389 * q^12 - 142805 * q^13 + 8475 * q^14 - 322463 * q^16 + 495669 * q^17 + 656228 * q^18 - 840738 * q^19 - 1599467 * q^21 + 2023594 * q^22 + 592152 * q^23 - 2295657 * q^24 + 428415 * q^26 - 6847883 * q^27 - 2587955 * q^28 + 10678182 * q^29 + 12885296 * q^31 - 3282927 * q^32 - 17278298 * q^33 - 9934079 * q^34 - 20483302 * q^36 - 7171823 * q^37 + 25568814 * q^38 + 4598321 * q^39 + 9294012 * q^41 + 69520457 * q^42 - 12831975 * q^43 - 41479074 * q^44 - 59319696 * q^46 - 43354215 * q^47 + 86874671 * q^48 + 25249488 * q^49 + 16905901 * q^51 - 10310521 * q^52 - 93231780 * q^53 + 58983719 * q^54 + 199599225 * q^56 - 90173382 * q^57 - 151020970 * q^58 + 246496182 * q^59 - 132232612 * q^61 - 158135724 * q^62 + 416955202 * q^63 + 91019105 * q^64 - 323733130 * q^66 + 369388534 * q^67 - 238172073 * q^68 - 579986760 * q^69 + 212150457 * q^71 + 415774278 * q^72 + 252729806 * q^73 + 192105957 * q^74 - 953775990 * q^76 - 449666118 * q^77 - 162597773 * q^78 - 1247271728 * q^79 - 317713115 * q^81 - 169559388 * q^82 - 1696894296 * q^83 + 1247983739 * q^84 + 3291621459 * q^86 + 614530466 * q^87 + 220227222 * q^88 - 753854382 * q^89 + 288437539 * q^91 - 13876128 * q^92 + 892784668 * q^93 + 272071215 * q^94 + 930612847 * q^96 - 3824606 * q^97 - 1570614816 * q^98 + 3016199848 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−38.1685	−1.68682	−0.843412	−	0.537267i	$-0.819457\pi$
$2$	−38.1685	−1.68682	−0.843412	+	0.537267i	$0.819457\pi$
$3$	−47.8784	−0.341267	−0.170633	−	0.985335i	$-0.554581\pi$
$3$	−47.8784	−0.341267	−0.170633	+	0.985335i	$0.554581\pi$
$4$	944.833	1.84538
$5$	0	0
$5$	0	0
$6$	1827.45	0.575657
$7$	−5947.44	−0.936244	−0.468122	−	0.883664i	$-0.655069\pi$
$7$	−5947.44	−0.936244	−0.468122	+	0.883664i	$0.655069\pi$
$8$	−16520.6	−1.42600
$9$	−17390.7	−0.883537
$10$	0	0
$11$	−25205.7	−0.519076	−0.259538	−	0.965733i	$-0.583570\pi$
$11$	−25205.7	−0.519076	−0.259538	+	0.965733i	$0.583570\pi$
$12$	−45237.1	−0.629766
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	227005.	1.57928
$15$	0	0
$16$	146811.	0.560039
$17$	−109318.	−0.317447	−0.158724	−	0.987323i	$-0.550738\pi$
$17$	−109318.	−0.317447	−0.158724	+	0.987323i	$0.550738\pi$
$18$	663775.	1.49037
$19$	−904609.	−1.59246	−0.796232	−	0.604992i	$-0.793176\pi$
$19$	−904609.	−1.59246	−0.796232	+	0.604992i	$0.793176\pi$
$20$	0	0
$21$	284754.	0.319509
$22$	962062.	0.875590
$23$	435749.	0.324684	0.162342	−	0.986735i	$-0.448095\pi$
$23$	435749.	0.324684	0.162342	+	0.986735i	$0.448095\pi$
$24$	790979.	0.486647
$25$	0	0
$26$	1.09013e6	0.467841
$27$	1.77503e6	0.642789
$28$	−5.61934e6	−1.72772
$29$	6.44791e6	1.69289	0.846443	−	0.532479i	$-0.178740\pi$
$29$	6.44791e6	1.69289	0.846443	+	0.532479i	$0.178740\pi$
$30$	0	0
$31$	6.62308e6	1.28805	0.644024	−	0.765005i	$-0.277264\pi$
$31$	6.62308e6	1.28805	0.644024	+	0.765005i	$0.277264\pi$
$32$	2.85499e6	0.481315
$33$	1.20681e6	0.177143
$34$	4.17250e6	0.535477
$35$	0	0
$36$	−1.64313e7	−1.63046
$37$	−4.14357e6	−0.363469	−0.181734	−	0.983348i	$-0.558171\pi$
$37$	−4.14357e6	−0.363469	−0.181734	+	0.983348i	$0.558171\pi$
$38$	3.45275e7	2.68621
$39$	1.36745e6	0.0946504
$40$	0	0
$41$	1.49568e7	0.826632	0.413316	−	0.910588i	$-0.364370\pi$
$41$	1.49568e7	0.826632	0.413316	+	0.910588i	$0.364370\pi$
$42$	−1.08686e7	−0.538956
$43$	−4.01789e7	−1.79221	−0.896107	−	0.443838i	$-0.853616\pi$
$43$	−4.01789e7	−1.79221	−0.896107	+	0.443838i	$0.853616\pi$
$44$	−2.38151e7	−0.957891
$45$	0	0
$46$	−1.66319e7	−0.547685
$47$	−6.30151e6	−0.188367	−0.0941834	−	0.995555i	$-0.530024\pi$
$47$	−6.30151e6	−0.188367	−0.0941834	+	0.995555i	$0.530024\pi$
$48$	−7.02907e6	−0.191123
$49$	−4.98153e6	−0.123447
$50$	0	0
$51$	5.23397e6	0.108334
$52$	−2.69854e7	−0.511815
$53$	−1.53111e7	−0.266542	−0.133271	−	0.991080i	$-0.542548\pi$
$53$	−1.53111e7	−0.266542	−0.133271	+	0.991080i	$0.542548\pi$
$54$	−6.77501e7	−1.08427
$55$	0	0
$56$	9.82552e7	1.33509
$57$	4.33112e7	0.543455
$58$	−2.46107e8	−2.85560
$59$	−1.52760e8	−1.64126	−0.820629	−	0.571462i	$-0.806376\pi$
$59$	−1.52760e8	−1.64126	−0.820629	+	0.571462i	$0.806376\pi$
$60$	0	0
$61$	8.66321e7	0.801114	0.400557	−	0.916272i	$-0.368817\pi$
$61$	8.66321e7	0.801114	0.400557	+	0.916272i	$0.368817\pi$
$62$	−2.52793e8	−2.17271
$63$	1.03430e8	0.827206
$64$	−1.84138e8	−1.37193
$65$	0	0
$66$	−4.60620e7	−0.298810
$67$	1.01034e8	0.612537	0.306268	−	0.951945i	$-0.400920\pi$
$67$	1.01034e8	0.612537	0.306268	+	0.951945i	$0.400920\pi$
$68$	−1.03287e8	−0.585809
$69$	−2.08630e7	−0.110804
$70$	0	0
$71$	4.13122e8	1.92937	0.964685	−	0.263406i	$-0.0848458\pi$
$71$	4.13122e8	1.92937	0.964685	+	0.263406i	$0.0848458\pi$
$72$	2.87304e8	1.25993
$73$	3.14453e8	1.29599	0.647997	−	0.761643i	$-0.275607\pi$
$73$	3.14453e8	1.29599	0.647997	+	0.761643i	$0.275607\pi$
$74$	1.58154e8	0.613108
$75$	0	0
$76$	−8.54704e8	−2.93870
$77$	1.49909e8	0.485982
$78$	−5.21937e7	−0.159659
$79$	−2.00580e8	−0.579383	−0.289692	−	0.957120i	$-0.593553\pi$
$79$	−2.00580e8	−0.579383	−0.289692	+	0.957120i	$0.593553\pi$
$80$	0	0
$81$	2.57315e8	0.664175
$82$	−5.70879e8	−1.39438
$83$	−6.34578e7	−0.146769	−0.0733843	−	0.997304i	$-0.523380\pi$
$83$	−6.34578e7	−0.146769	−0.0733843	+	0.997304i	$0.523380\pi$
$84$	2.69045e8	0.589614
$85$	0	0
$86$	1.53357e9	3.02315
$87$	−3.08715e8	−0.577726
$88$	4.16412e8	0.740204
$89$	3.47074e7	0.0586364	0.0293182	−	0.999570i	$-0.490666\pi$
$89$	3.47074e7	0.0586364	0.0293182	+	0.999570i	$0.490666\pi$
$90$	0	0
$91$	1.69865e8	0.259667
$92$	4.11710e8	0.599164
$93$	−3.17102e8	−0.439568
$94$	2.40519e8	0.317742
$95$	0	0
$96$	−1.36692e8	−0.164257
$97$	1.25403e9	1.43825	0.719127	−	0.694879i	$-0.244542\pi$
$97$	1.25403e9	1.43825	0.719127	+	0.694879i	$0.244542\pi$
$98$	1.90137e8	0.208233
$99$	4.38343e8	0.458623
$100$	0	0
$101$	−9.06459e8	−0.866766	−0.433383	−	0.901210i	$-0.642680\pi$
$101$	−9.06459e8	−0.866766	−0.433383	+	0.901210i	$0.642680\pi$
$102$	−1.99773e8	−0.182741
$103$	4.17013e8	0.365075	0.182537	−	0.983199i	$-0.441569\pi$
$103$	4.17013e8	0.365075	0.182537	+	0.983199i	$0.441569\pi$
$104$	4.71844e8	0.395502
$105$	0	0
$106$	5.84402e8	0.449610
$107$	−6.71636e8	−0.495344	−0.247672	−	0.968844i	$-0.579666\pi$
$107$	−6.71636e8	−0.495344	−0.247672	+	0.968844i	$0.579666\pi$
$108$	1.67710e9	1.18619
$109$	1.66748e9	1.13147	0.565734	−	0.824588i	$-0.308593\pi$
$109$	1.66748e9	1.13147	0.565734	+	0.824588i	$0.308593\pi$
$110$	0	0
$111$	1.98387e8	0.124040
$112$	−8.73149e8	−0.524333
$113$	1.84580e9	1.06496	0.532478	−	0.846444i	$-0.321261\pi$
$113$	1.84580e9	1.06496	0.532478	+	0.846444i	$0.321261\pi$
$114$	−1.65312e9	−0.916713
$115$	0	0
$116$	6.09219e9	3.12401
$117$	4.96695e8	0.245049
$118$	5.83063e9	2.76851
$119$	6.50162e8	0.297208
$120$	0	0
$121$	−1.72262e9	−0.730560
$122$	−3.30661e9	−1.35134
$123$	−7.16109e8	−0.282102
$124$	6.25770e9	2.37694
$125$	0	0
$126$	−3.94776e9	−1.39535
$127$	−1.87922e9	−0.641006	−0.320503	−	0.947248i	$-0.603852\pi$
$127$	−1.87922e9	−0.641006	−0.320503	+	0.947248i	$0.603852\pi$
$128$	5.56650e9	1.83290
$129$	1.92370e9	0.611623
$130$	0	0
$131$	3.46045e9	1.02663	0.513313	−	0.858201i	$-0.328418\pi$
$131$	3.46045e9	1.02663	0.513313	+	0.858201i	$0.328418\pi$
$132$	1.14023e9	0.326896
$133$	5.38011e9	1.49093
$134$	−3.85632e9	−1.03324
$135$	0	0
$136$	1.80600e9	0.452680
$137$	−5.04786e9	−1.22424	−0.612118	−	0.790766i	$-0.709682\pi$
$137$	−5.04786e9	−1.22424	−0.612118	+	0.790766i	$0.709682\pi$
$138$	7.96307e8	0.186907
$139$	3.59716e9	0.817322	0.408661	−	0.912686i	$-0.365996\pi$
$139$	3.59716e9	0.817322	0.408661	+	0.912686i	$0.365996\pi$
$140$	0	0
$141$	3.01706e8	0.0642833
$142$	−1.57682e10	−3.25451
$143$	7.19899e8	0.143966
$144$	−2.55314e9	−0.494815
$145$	0	0
$146$	−1.20022e10	−2.18611
$147$	2.38508e8	0.0421283
$148$	−3.91498e9	−0.670736
$149$	1.27561e9	0.212022	0.106011	−	0.994365i	$-0.466192\pi$
$149$	1.27561e9	0.212022	0.106011	+	0.994365i	$0.466192\pi$
$150$	0	0
$151$	4.35273e9	0.681342	0.340671	−	0.940183i	$-0.389346\pi$
$151$	4.35273e9	0.681342	0.340671	+	0.940183i	$0.389346\pi$
$152$	1.49447e10	2.27086
$153$	1.90111e9	0.280476
$154$	−5.72181e9	−0.819766
$155$	0	0
$156$	1.29202e9	0.174666
$157$	1.41002e10	1.85215	0.926075	−	0.377339i	$-0.123161\pi$
$157$	1.41002e10	1.85215	0.926075	+	0.377339i	$0.123161\pi$
$158$	7.65584e9	0.977318
$159$	7.33072e8	0.0909619
$160$	0	0
$161$	−2.59159e9	−0.303983
$162$	−9.82132e9	−1.12035
$163$	−7.24812e8	−0.0804231	−0.0402116	−	0.999191i	$-0.512803\pi$
$163$	−7.24812e8	−0.0804231	−0.0402116	+	0.999191i	$0.512803\pi$
$164$	1.41317e10	1.52545
$165$	0	0
$166$	2.42209e9	0.247573
$167$	8.33031e8	0.0828776	0.0414388	−	0.999141i	$-0.486806\pi$
$167$	8.33031e8	0.0828776	0.0414388	+	0.999141i	$0.486806\pi$
$168$	−4.70430e9	−0.455621
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	1.57317e10	1.40700
$172$	−3.79623e10	−3.30731
$173$	−5.77955e8	−0.0490553	−0.0245277	−	0.999699i	$-0.507808\pi$
$173$	−5.77955e8	−0.0490553	−0.0245277	+	0.999699i	$0.507808\pi$
$174$	1.17832e10	0.974522
$175$	0	0
$176$	−3.70046e9	−0.290703
$177$	7.31392e9	0.560106
$178$	−1.32473e9	−0.0989094
$179$	−1.56569e10	−1.13990	−0.569952	−	0.821678i	$-0.693038\pi$
$179$	−1.56569e10	−1.13990	−0.569952	+	0.821678i	$0.693038\pi$
$180$	0	0
$181$	−2.18552e10	−1.51356	−0.756781	−	0.653668i	$-0.773229\pi$
$181$	−2.18552e10	−1.51356	−0.756781	+	0.653668i	$0.773229\pi$
$182$	−6.48349e9	−0.438013
$183$	−4.14780e9	−0.273394
$184$	−7.19882e9	−0.463000
$185$	0	0
$186$	1.21033e10	0.741474
$187$	2.75543e9	0.164779
$188$	−5.95388e9	−0.347608
$189$	−1.05569e10	−0.601807
$190$	0	0
$191$	1.67784e10	0.912222	0.456111	−	0.889923i	$-0.349242\pi$
$191$	1.67784e10	0.912222	0.456111	+	0.889923i	$0.349242\pi$
$192$	8.81622e9	0.468195
$193$	2.70036e10	1.40092	0.700462	−	0.713690i	$-0.252977\pi$
$193$	2.70036e10	1.40092	0.700462	+	0.713690i	$0.252977\pi$
$194$	−4.78645e10	−2.42608
$195$	0	0
$196$	−4.70671e9	−0.227806
$197$	−1.58277e10	−0.748720	−0.374360	−	0.927283i	$-0.622138\pi$
$197$	−1.58277e10	−0.748720	−0.374360	+	0.927283i	$0.622138\pi$
$198$	−1.67309e10	−0.773616
$199$	8.80397e9	0.397960	0.198980	−	0.980004i	$-0.436237\pi$
$199$	8.80397e9	0.397960	0.198980	+	0.980004i	$0.436237\pi$
$200$	0	0
$201$	−4.83736e9	−0.209038
$202$	3.45982e10	1.46208
$203$	−3.83485e10	−1.58495
$204$	4.94523e9	0.199917
$205$	0	0
$206$	−1.59167e10	−0.615817
$207$	−7.57796e9	−0.286870
$208$	−4.19306e9	−0.155327
$209$	2.28013e10	0.826610
$210$	0	0
$211$	−1.82054e10	−0.632308	−0.316154	−	0.948708i	$-0.602392\pi$
$211$	−1.82054e10	−0.632308	−0.316154	+	0.948708i	$0.602392\pi$
$212$	−1.44665e10	−0.491870
$213$	−1.97796e10	−0.658430
$214$	2.56353e10	0.835558
$215$	0	0
$216$	−2.93245e10	−0.916618
$217$	−3.93904e10	−1.20593
$218$	−6.36453e10	−1.90859
$219$	−1.50555e10	−0.442280
$220$	0	0
$221$	3.12223e9	0.0880440
$222$	−7.57215e9	−0.209233
$223$	−1.53511e10	−0.415688	−0.207844	−	0.978162i	$-0.566645\pi$
$223$	−1.53511e10	−0.415688	−0.207844	+	0.978162i	$0.566645\pi$
$224$	−1.69799e10	−0.450628
$225$	0	0
$226$	−7.04514e10	−1.79639
$227$	−4.20620e10	−1.05141	−0.525707	−	0.850666i	$-0.676199\pi$
$227$	−4.20620e10	−1.05141	−0.525707	+	0.850666i	$0.676199\pi$
$228$	4.09219e10	1.00288
$229$	−6.68760e10	−1.60698	−0.803490	−	0.595318i	$-0.797026\pi$
$229$	−6.68760e10	−1.60698	−0.803490	+	0.595318i	$0.797026\pi$
$230$	0	0
$231$	−7.17741e9	−0.165849
$232$	−1.06523e11	−2.41406
$233$	5.19268e10	1.15422	0.577112	−	0.816665i	$-0.304180\pi$
$233$	5.19268e10	1.15422	0.577112	+	0.816665i	$0.304180\pi$
$234$	−1.89581e10	−0.413355
$235$	0	0
$236$	−1.44333e11	−3.02874
$237$	9.60345e9	0.197724
$238$	−2.48157e10	−0.501338
$239$	7.45881e10	1.47870	0.739348	−	0.673323i	$-0.235134\pi$
$239$	7.45881e10	1.47870	0.739348	+	0.673323i	$0.235134\pi$
$240$	0	0
$241$	5.74852e10	1.09769	0.548845	−	0.835924i	$-0.315068\pi$
$241$	5.74852e10	1.09769	0.548845	+	0.835924i	$0.315068\pi$
$242$	6.57499e10	1.23233
$243$	−4.72577e10	−0.869449
$244$	8.18528e10	1.47836
$245$	0	0
$246$	2.73328e10	0.475857
$247$	2.58365e10	0.441670
$248$	−1.09417e11	−1.83676
$249$	3.03826e9	0.0500873
$250$	0	0
$251$	−1.07873e11	−1.71546	−0.857732	−	0.514097i	$-0.828127\pi$
$251$	−1.07873e11	−1.71546	−0.857732	+	0.514097i	$0.828127\pi$
$252$	9.77240e10	1.52651
$253$	−1.09833e10	−0.168536
$254$	7.17272e10	1.08126
$255$	0	0
$256$	−1.18186e11	−1.71984
$257$	6.64074e10	0.949550	0.474775	−	0.880107i	$-0.342530\pi$
$257$	6.64074e10	0.949550	0.474775	+	0.880107i	$0.342530\pi$
$258$	−7.34247e10	−1.03170
$259$	2.46436e10	0.340295
$260$	0	0
$261$	−1.12133e11	−1.49573
$262$	−1.32080e11	−1.73174
$263$	8.15356e10	1.05086	0.525432	−	0.850836i	$-0.323904\pi$
$263$	8.15356e10	1.05086	0.525432	+	0.850836i	$0.323904\pi$
$264$	−1.99371e10	−0.252607
$265$	0	0
$266$	−2.05351e11	−2.51494
$267$	−1.66174e9	−0.0200107
$268$	9.54605e10	1.13036
$269$	1.00568e11	1.17105	0.585523	−	0.810656i	$-0.300889\pi$
$269$	1.00568e11	1.17105	0.585523	+	0.810656i	$0.300889\pi$
$270$	0	0
$271$	−2.98757e10	−0.336477	−0.168239	−	0.985746i	$-0.553808\pi$
$271$	−2.98757e10	−0.336477	−0.168239	+	0.985746i	$0.553808\pi$
$272$	−1.60491e10	−0.177783
$273$	−8.13286e9	−0.0886158
$274$	1.92669e11	2.06507
$275$	0	0
$276$	−1.97120e10	−0.204475
$277$	3.17195e10	0.323718	0.161859	−	0.986814i	$-0.448251\pi$
$277$	3.17195e10	0.323718	0.161859	+	0.986814i	$0.448251\pi$
$278$	−1.37298e11	−1.37868
$279$	−1.15180e11	−1.13804
$280$	0	0
$281$	9.86953e10	0.944318	0.472159	−	0.881513i	$-0.343475\pi$
$281$	9.86953e10	0.944318	0.472159	+	0.881513i	$0.343475\pi$
$282$	−1.15157e10	−0.108435
$283$	1.06164e11	0.983871	0.491935	−	0.870632i	$-0.336290\pi$
$283$	1.06164e11	0.983871	0.491935	+	0.870632i	$0.336290\pi$
$284$	3.90331e11	3.56042
$285$	0	0
$286$	−2.74774e10	−0.242845
$287$	−8.89549e10	−0.773929
$288$	−4.96501e10	−0.425260
$289$	−1.06637e11	−0.899227
$290$	0	0
$291$	−6.00410e10	−0.490828
$292$	2.97106e11	2.39160
$293$	−2.26355e11	−1.79426	−0.897132	−	0.441763i	$-0.854353\pi$
$293$	−2.26355e11	−1.79426	−0.897132	+	0.441763i	$0.854353\pi$
$294$	−9.10348e9	−0.0710631
$295$	0	0
$296$	6.84541e10	0.518307
$297$	−4.47407e10	−0.333656
$298$	−4.86881e10	−0.357643
$299$	−1.24454e10	−0.0900511
$300$	0	0
$301$	2.38962e11	1.67795
$302$	−1.66137e11	−1.14930
$303$	4.33998e10	0.295798
$304$	−1.32806e11	−0.891841
$305$	0	0
$306$	−7.25625e10	−0.473114
$307$	2.23009e10	0.143285	0.0716424	−	0.997430i	$-0.477176\pi$
$307$	2.23009e10	0.143285	0.0716424	+	0.997430i	$0.477176\pi$
$308$	1.41639e11	0.896820
$309$	−1.99659e10	−0.124588
$310$	0	0
$311$	−2.71805e11	−1.64754	−0.823770	−	0.566925i	$-0.808133\pi$
$311$	−2.71805e11	−1.64754	−0.823770	+	0.566925i	$0.808133\pi$
$312$	−2.25911e10	−0.134972
$313$	7.90775e10	0.465697	0.232849	−	0.972513i	$-0.425195\pi$
$313$	7.90775e10	0.465697	0.232849	+	0.972513i	$0.425195\pi$
$314$	−5.38183e11	−3.12425
$315$	0	0
$316$	−1.89515e11	−1.06918
$317$	−2.03032e11	−1.12927	−0.564636	−	0.825340i	$-0.690983\pi$
$317$	−2.03032e11	−1.12927	−0.564636	+	0.825340i	$0.690983\pi$
$318$	−2.79802e10	−0.153437
$319$	−1.62524e11	−0.878736
$320$	0	0
$321$	3.21568e10	0.169044
$322$	9.89171e10	0.512767
$323$	9.88899e10	0.505523
$324$	2.43120e11	1.22565
$325$	0	0
$326$	2.76650e10	0.135660
$327$	−7.98365e10	−0.386132
$328$	−2.47095e11	−1.17878
$329$	3.74779e10	0.176357
$330$	0	0
$331$	3.24137e11	1.48424	0.742118	−	0.670270i	$-0.233822\pi$
$331$	3.24137e11	1.48424	0.742118	+	0.670270i	$0.233822\pi$
$332$	−5.99570e10	−0.270844
$333$	7.20594e10	0.321138
$334$	−3.17955e10	−0.139800
$335$	0	0
$336$	4.18050e10	0.178937
$337$	−2.68510e11	−1.13403	−0.567017	−	0.823706i	$-0.691903\pi$
$337$	−2.68510e11	−1.13403	−0.567017	+	0.823706i	$0.691903\pi$
$338$	−3.11352e10	−0.129756
$339$	−8.83739e10	−0.363434
$340$	0	0
$341$	−1.66939e11	−0.668595
$342$	−6.00457e11	−2.37336
$343$	2.69628e11	1.05182
$344$	6.63778e11	2.55570
$345$	0	0
$346$	2.20597e10	0.0827478
$347$	−2.74715e11	−1.01719	−0.508593	−	0.861007i	$-0.669834\pi$
$347$	−2.74715e11	−1.01719	−0.508593	+	0.861007i	$0.669834\pi$
$348$	−2.91684e11	−1.06612
$349$	−3.54006e11	−1.27731	−0.638655	−	0.769494i	$-0.720509\pi$
$349$	−3.54006e11	−1.27731	−0.638655	+	0.769494i	$0.720509\pi$
$350$	0	0
$351$	−5.06966e10	−0.178277
$352$	−7.19619e10	−0.249839
$353$	2.25650e11	0.773481	0.386741	−	0.922189i	$-0.373601\pi$
$353$	2.25650e11	0.773481	0.386741	+	0.922189i	$0.373601\pi$
$354$	−2.79161e11	−0.944801
$355$	0	0
$356$	3.27927e10	0.108206
$357$	−3.11287e10	−0.101427
$358$	5.97602e11	1.92282
$359$	3.39022e10	0.107722	0.0538608	−	0.998548i	$-0.482847\pi$
$359$	3.39022e10	0.107722	0.0538608	+	0.998548i	$0.482847\pi$
$360$	0	0
$361$	4.95629e11	1.53594
$362$	8.34178e11	2.55312
$363$	8.24764e10	0.249316
$364$	1.60494e11	0.479184
$365$	0	0
$366$	1.58315e11	0.461167
$367$	7.74387e10	0.222823	0.111412	−	0.993774i	$-0.464463\pi$
$367$	7.74387e10	0.222823	0.111412	+	0.993774i	$0.464463\pi$
$368$	6.39726e10	0.181836
$369$	−2.60109e11	−0.730360
$370$	0	0
$371$	9.10620e10	0.249548
$372$	−2.99609e11	−0.811169
$373$	−6.50821e11	−1.74089	−0.870446	−	0.492264i	$-0.836169\pi$
$373$	−6.50821e11	−1.74089	−0.870446	+	0.492264i	$0.836169\pi$
$374$	−1.05171e11	−0.277954
$375$	0	0
$376$	1.04105e11	0.268612
$377$	−1.84159e11	−0.469522
$378$	4.02940e11	1.01514
$379$	1.93989e11	0.482948	0.241474	−	0.970407i	$-0.422369\pi$
$379$	1.93989e11	0.482948	0.241474	+	0.970407i	$0.422369\pi$
$380$	0	0
$381$	8.99743e10	0.218754
$382$	−6.40406e11	−1.53876
$383$	−4.44645e11	−1.05589	−0.527946	−	0.849278i	$-0.677037\pi$
$383$	−4.44645e11	−1.05589	−0.527946	+	0.849278i	$0.677037\pi$
$384$	−2.66515e11	−0.625506
$385$	0	0
$386$	−1.03069e12	−2.36311
$387$	6.98737e11	1.58349
$388$	1.18485e12	2.65412
$389$	−1.69623e11	−0.375589	−0.187794	−	0.982208i	$-0.560134\pi$
$389$	−1.69623e11	−0.375589	−0.187794	+	0.982208i	$0.560134\pi$
$390$	0	0
$391$	−4.76352e10	−0.103070
$392$	8.22978e10	0.176036
$393$	−1.65681e11	−0.350353
$394$	6.04119e11	1.26296
$395$	0	0
$396$	4.14161e11	0.846332
$397$	−2.94468e11	−0.594951	−0.297476	−	0.954729i	$-0.596145\pi$
$397$	−2.94468e11	−0.594951	−0.297476	+	0.954729i	$0.596145\pi$
$398$	−3.36034e11	−0.671289
$399$	−2.57591e11	−0.508806
$400$	0	0
$401$	4.43362e11	0.856265	0.428133	−	0.903716i	$-0.359172\pi$
$401$	4.43362e11	0.856265	0.428133	+	0.903716i	$0.359172\pi$
$402$	1.84635e11	0.352611
$403$	−1.89162e11	−0.357240
$404$	−8.56452e11	−1.59951
$405$	0	0
$406$	1.46371e12	2.67354
$407$	1.04441e11	0.188668
$408$	−8.64682e10	−0.154485
$409$	−1.01253e11	−0.178918	−0.0894592	−	0.995990i	$-0.528514\pi$
$409$	−1.01253e11	−0.178918	−0.0894592	+	0.995990i	$0.528514\pi$
$410$	0	0
$411$	2.41684e11	0.417791
$412$	3.94007e11	0.673700
$413$	9.08533e11	1.53662
$414$	2.89239e11	0.483900
$415$	0	0
$416$	−8.15413e10	−0.133493
$417$	−1.72226e11	−0.278925
$418$	−8.70289e11	−1.39435
$419$	7.93982e10	0.125848	0.0629242	−	0.998018i	$-0.479957\pi$
$419$	7.93982e10	0.125848	0.0629242	+	0.998018i	$0.479957\pi$
$420$	0	0
$421$	−6.06765e11	−0.941350	−0.470675	−	0.882307i	$-0.655990\pi$
$421$	−6.06765e11	−0.941350	−0.470675	+	0.882307i	$0.655990\pi$
$422$	6.94871e11	1.06659
$423$	1.09587e11	0.166429
$424$	2.52949e11	0.380089
$425$	0	0
$426$	7.54958e11	1.11066
$427$	−5.15239e11	−0.750038
$428$	−6.34583e11	−0.914096
$429$	−3.44676e10	−0.0491307
$430$	0	0
$431$	−2.72544e11	−0.380442	−0.190221	−	0.981741i	$-0.560920\pi$
$431$	−2.72544e11	−0.380442	−0.190221	+	0.981741i	$0.560920\pi$
$432$	2.60593e11	0.359987
$433$	1.15522e12	1.57931	0.789655	−	0.613551i	$-0.210260\pi$
$433$	1.15522e12	1.57931	0.789655	+	0.613551i	$0.210260\pi$
$434$	1.50347e12	2.03419
$435$	0	0
$436$	1.57549e12	2.08799
$437$	−3.94182e11	−0.517047
$438$	5.74646e11	0.746048
$439$	1.78053e11	0.228801	0.114401	−	0.993435i	$-0.463505\pi$
$439$	1.78053e11	0.228801	0.114401	+	0.993435i	$0.463505\pi$
$440$	0	0
$441$	8.66321e10	0.109070
$442$	−1.19171e11	−0.148515
$443$	6.55260e10	0.0808345	0.0404173	−	0.999183i	$-0.487131\pi$
$443$	6.55260e10	0.0808345	0.0404173	+	0.999183i	$0.487131\pi$
$444$	1.87443e11	0.228900
$445$	0	0
$446$	5.85928e11	0.701192
$447$	−6.10742e10	−0.0723559
$448$	1.09515e12	1.28446
$449$	−7.98150e11	−0.926779	−0.463390	−	0.886155i	$-0.653367\pi$
$449$	−7.98150e11	−0.926779	−0.463390	+	0.886155i	$0.653367\pi$
$450$	0	0
$451$	−3.76997e11	−0.429085
$452$	1.74397e12	1.96525
$453$	−2.08402e11	−0.232519
$454$	1.60544e12	1.77355
$455$	0	0
$456$	−7.15526e11	−0.774968
$457$	8.92736e11	0.957415	0.478708	−	0.877974i	$-0.341105\pi$
$457$	8.92736e11	0.957415	0.478708	+	0.877974i	$0.341105\pi$
$458$	2.55256e12	2.71069
$459$	−1.94042e11	−0.204051
$460$	0	0
$461$	2.32490e11	0.239745	0.119872	−	0.992789i	$-0.461751\pi$
$461$	2.32490e11	0.239745	0.119872	+	0.992789i	$0.461751\pi$
$462$	2.73951e11	0.279759
$463$	1.54421e12	1.56168	0.780841	−	0.624730i	$-0.214791\pi$
$463$	1.54421e12	1.56168	0.780841	+	0.624730i	$0.214791\pi$
$464$	9.46622e11	0.948082
$465$	0	0
$466$	−1.98197e12	−1.94697
$467$	−1.63317e12	−1.58893	−0.794465	−	0.607310i	$-0.792249\pi$
$467$	−1.63317e12	−1.58893	−0.794465	+	0.607310i	$0.792249\pi$
$468$	4.69293e11	0.452208
$469$	−6.00895e11	−0.573484
$470$	0	0
$471$	−6.75094e11	−0.632077
$472$	2.52369e12	2.34044
$473$	1.01274e12	0.930295
$474$	−3.66549e11	−0.333526
$475$	0	0
$476$	6.14295e11	0.548461
$477$	2.66271e11	0.235500
$478$	−2.84692e12	−2.49430
$479$	1.54414e12	1.34022	0.670112	−	0.742260i	$-0.266246\pi$
$479$	1.54414e12	1.34022	0.670112	+	0.742260i	$0.266246\pi$
$480$	0	0
$481$	1.18344e11	0.100808
$482$	−2.19412e12	−1.85161
$483$	1.24081e11	0.103739
$484$	−1.62759e12	−1.34816
$485$	0	0
$486$	1.80375e12	1.46661
$487$	−2.55439e11	−0.205782	−0.102891	−	0.994693i	$-0.532809\pi$
$487$	−2.55439e11	−0.205782	−0.102891	+	0.994693i	$0.532809\pi$
$488$	−1.43121e12	−1.14239
$489$	3.47028e10	0.0274457
$490$	0	0
$491$	1.58407e12	1.23000	0.615002	−	0.788526i	$-0.289155\pi$
$491$	1.58407e12	1.23000	0.615002	+	0.788526i	$0.289155\pi$
$492$	−6.76603e11	−0.520584
$493$	−7.04872e11	−0.537402
$494$	−9.86141e11	−0.745020
$495$	0	0
$496$	9.72340e11	0.721357
$497$	−2.45702e12	−1.80636
$498$	−1.15966e11	−0.0844884
$499$	−6.29948e11	−0.454833	−0.227417	−	0.973798i	$-0.573028\pi$
$499$	−6.29948e11	−0.454833	−0.227417	+	0.973798i	$0.573028\pi$
$500$	0	0
$501$	−3.98842e10	−0.0282834
$502$	4.11736e12	2.89369
$503$	−5.49263e11	−0.382582	−0.191291	−	0.981533i	$-0.561267\pi$
$503$	−5.49263e11	−0.382582	−0.191291	+	0.981533i	$0.561267\pi$
$504$	−1.70872e12	−1.17960
$505$	0	0
$506$	4.19217e11	0.284290
$507$	−3.90559e10	−0.0262513
$508$	−1.77555e12	−1.18290
$509$	1.36923e11	0.0904165	0.0452083	−	0.998978i	$-0.485605\pi$
$509$	1.36923e11	0.0904165	0.0452083	+	0.998978i	$0.485605\pi$
$510$	0	0
$511$	−1.87019e12	−1.21337
$512$	1.66095e12	1.06817
$513$	−1.60570e12	−1.02362
$514$	−2.53467e12	−1.60172
$515$	0	0
$516$	1.81758e12	1.12867
$517$	1.58834e11	0.0977767
$518$	−9.40610e11	−0.574018
$519$	2.76715e10	0.0167410
$520$	0	0
$521$	−1.66627e12	−0.990779	−0.495389	−	0.868671i	$-0.664975\pi$
$521$	−1.66627e12	−0.990779	−0.495389	+	0.868671i	$0.664975\pi$
$522$	4.27996e12	2.52303
$523$	−1.97187e12	−1.15244	−0.576222	−	0.817293i	$-0.695474\pi$
$523$	−1.97187e12	−1.15244	−0.576222	+	0.817293i	$0.695474\pi$
$524$	3.26955e12	1.89451
$525$	0	0
$526$	−3.11209e12	−1.77262
$527$	−7.24021e11	−0.408887
$528$	1.77172e11	0.0992072
$529$	−1.61128e12	−0.894580
$530$	0	0
$531$	2.65660e12	1.45011
$532$	5.08330e12	2.75134
$533$	−4.27182e11	−0.229266
$534$	6.34260e10	0.0337545
$535$	0	0
$536$	−1.66914e12	−0.873479
$537$	7.49629e11	0.389011
$538$	−3.83852e12	−1.97535
$539$	1.25563e11	0.0640784
$540$	0	0
$541$	1.54916e12	0.777513	0.388756	−	0.921341i	$-0.372905\pi$
$541$	1.54916e12	0.777513	0.388756	+	0.921341i	$0.372905\pi$
$542$	1.14031e12	0.567578
$543$	1.04639e12	0.516529
$544$	−3.12101e11	−0.152792
$545$	0	0
$546$	3.10419e11	0.149479
$547$	−1.98052e12	−0.945879	−0.472939	−	0.881095i	$-0.656807\pi$
$547$	−1.98052e12	−0.945879	−0.472939	+	0.881095i	$0.656807\pi$
$548$	−4.76939e12	−2.25918
$549$	−1.50659e12	−0.707814
$550$	0	0
$551$	−5.83283e12	−2.69586
$552$	3.44668e11	0.158007
$553$	1.19294e12	0.542444
$554$	−1.21068e12	−0.546056
$555$	0	0
$556$	3.39871e12	1.50827
$557$	−8.86577e11	−0.390273	−0.195136	−	0.980776i	$-0.562515\pi$
$557$	−8.86577e11	−0.390273	−0.195136	+	0.980776i	$0.562515\pi$
$558$	4.39623e12	1.91967
$559$	1.14755e12	0.497071
$560$	0	0
$561$	−1.31926e11	−0.0562336
$562$	−3.76705e12	−1.59290
$563$	−3.89786e12	−1.63508	−0.817539	−	0.575873i	$-0.804662\pi$
$563$	−3.89786e12	−1.63508	−0.817539	+	0.575873i	$0.804662\pi$
$564$	2.85062e11	0.118627
$565$	0	0
$566$	−4.05212e12	−1.65962
$567$	−1.53037e12	−0.621830
$568$	−6.82501e12	−2.75129
$569$	−2.26590e12	−0.906223	−0.453112	−	0.891454i	$-0.649686\pi$
$569$	−2.26590e12	−0.906223	−0.453112	+	0.891454i	$0.649686\pi$
$570$	0	0
$571$	−3.09546e12	−1.21860	−0.609302	−	0.792938i	$-0.708550\pi$
$571$	−3.09546e12	−1.21860	−0.609302	+	0.792938i	$0.708550\pi$
$572$	6.80184e11	0.265671
$573$	−8.03323e11	−0.311311
$574$	3.39527e12	1.30548
$575$	0	0
$576$	3.20228e12	1.21215
$577$	3.23415e12	1.21470	0.607350	−	0.794434i	$-0.292233\pi$
$577$	3.23415e12	1.21470	0.607350	+	0.794434i	$0.292233\pi$
$578$	4.07019e12	1.51684
$579$	−1.29289e12	−0.478089
$580$	0	0
$581$	3.77411e11	0.137411
$582$	2.29167e12	0.827941
$583$	3.85927e11	0.138356
$584$	−5.19495e12	−1.84809
$585$	0	0
$586$	8.63964e12	3.02661
$587$	8.78491e11	0.305398	0.152699	−	0.988273i	$-0.451204\pi$
$587$	8.78491e11	0.305398	0.152699	+	0.988273i	$0.451204\pi$
$588$	2.25350e11	0.0777427
$589$	−5.99129e12	−2.05117
$590$	0	0
$591$	7.57805e11	0.255513
$592$	−6.08321e11	−0.203556
$593$	1.91730e12	0.636712	0.318356	−	0.947971i	$-0.396869\pi$
$593$	1.91730e12	0.636712	0.318356	+	0.947971i	$0.396869\pi$
$594$	1.70769e12	0.562819
$595$	0	0
$596$	1.20524e12	0.391260
$597$	−4.21520e11	−0.135811
$598$	4.75023e11	0.151900
$599$	−5.10464e12	−1.62011	−0.810054	−	0.586355i	$-0.800562\pi$
$599$	−5.10464e12	−1.62011	−0.810054	+	0.586355i	$0.800562\pi$
$600$	0	0
$601$	3.00419e12	0.939273	0.469636	−	0.882860i	$-0.344385\pi$
$601$	3.00419e12	0.939273	0.469636	+	0.882860i	$0.344385\pi$
$602$	−9.12080e12	−2.83041
$603$	−1.75705e12	−0.541199
$604$	4.11260e12	1.25733
$605$	0	0
$606$	−1.65650e12	−0.498960
$607$	−1.18434e12	−0.354101	−0.177051	−	0.984202i	$-0.556656\pi$
$607$	−1.18434e12	−0.354101	−0.177051	+	0.984202i	$0.556656\pi$
$608$	−2.58265e12	−0.766477
$609$	1.83607e12	0.540892
$610$	0	0
$611$	1.79978e11	0.0522436
$612$	1.79623e12	0.517584
$613$	−6.42597e11	−0.183809	−0.0919045	−	0.995768i	$-0.529295\pi$
$613$	−6.42597e11	−0.183809	−0.0919045	+	0.995768i	$0.529295\pi$
$614$	−8.51193e11	−0.241696
$615$	0	0
$616$	−2.47659e12	−0.693011
$617$	−5.05474e12	−1.40416	−0.702078	−	0.712100i	$-0.747744\pi$
$617$	−5.05474e12	−1.40416	−0.702078	+	0.712100i	$0.747744\pi$
$618$	7.62068e11	0.210158
$619$	−3.09492e11	−0.0847308	−0.0423654	−	0.999102i	$-0.513489\pi$
$619$	−3.09492e11	−0.0847308	−0.0423654	+	0.999102i	$0.513489\pi$
$620$	0	0
$621$	7.73466e11	0.208703
$622$	1.03744e13	2.77911
$623$	−2.06421e11	−0.0548980
$624$	2.00757e11	0.0530079
$625$	0	0
$626$	−3.01827e12	−0.785549
$627$	−1.09169e12	−0.282094
$628$	1.33223e13	3.41792
$629$	4.52966e11	0.115382
$630$	0	0
$631$	−7.94237e11	−0.199443	−0.0997214	−	0.995015i	$-0.531795\pi$
$631$	−7.94237e11	−0.199443	−0.0997214	+	0.995015i	$0.531795\pi$
$632$	3.31370e12	0.826202
$633$	8.71644e11	0.215786
$634$	7.74944e12	1.90488
$635$	0	0
$636$	6.92631e11	0.167859
$637$	1.42278e11	0.0342380
$638$	6.20328e12	1.48227
$639$	−7.18446e12	−1.70467
$640$	0	0
$641$	2.30298e12	0.538802	0.269401	−	0.963028i	$-0.413174\pi$
$641$	2.30298e12	0.538802	0.269401	+	0.963028i	$0.413174\pi$
$642$	−1.22738e12	−0.285148
$643$	2.54593e12	0.587350	0.293675	−	0.955905i	$-0.405122\pi$
$643$	2.54593e12	0.587350	0.293675	+	0.955905i	$0.405122\pi$
$644$	−2.44862e12	−0.560964
$645$	0	0
$646$	−3.77448e12	−0.852728
$647$	2.74568e11	0.0616001	0.0308000	−	0.999526i	$-0.490194\pi$
$647$	2.74568e11	0.0616001	0.0308000	+	0.999526i	$0.490194\pi$
$648$	−4.25099e12	−0.947115
$649$	3.85043e12	0.851937
$650$	0	0
$651$	1.88595e12	0.411543
$652$	−6.84826e11	−0.148411
$653$	6.05719e12	1.30365	0.651826	−	0.758369i	$-0.274003\pi$
$653$	6.05719e12	1.30365	0.651826	+	0.758369i	$0.274003\pi$
$654$	3.04724e12	0.651338
$655$	0	0
$656$	2.19582e12	0.462946
$657$	−5.46855e12	−1.14506
$658$	−1.43047e12	−0.297484
$659$	4.97718e12	1.02801	0.514007	−	0.857786i	$-0.328160\pi$
$659$	4.97718e12	1.02801	0.514007	+	0.857786i	$0.328160\pi$
$660$	0	0
$661$	1.79834e12	0.366409	0.183204	−	0.983075i	$-0.441353\pi$
$661$	1.79834e12	0.366409	0.183204	+	0.983075i	$0.441353\pi$
$662$	−1.23718e13	−2.50364
$663$	−1.49487e11	−0.0300465
$664$	1.04836e12	0.209292
$665$	0	0
$666$	−2.75040e12	−0.541703
$667$	2.80967e12	0.549653
$668$	7.87076e11	0.152940
$669$	7.34986e11	0.141860
$670$	0	0
$671$	−2.18362e12	−0.415839
$672$	8.12969e11	0.153784
$673$	−1.37693e12	−0.258728	−0.129364	−	0.991597i	$-0.541294\pi$
$673$	−1.37693e12	−0.258728	−0.129364	+	0.991597i	$0.541294\pi$
$674$	1.02486e13	1.91292
$675$	0	0
$676$	7.70729e11	0.141952
$677$	−6.49642e11	−0.118857	−0.0594285	−	0.998233i	$-0.518928\pi$
$677$	−6.49642e11	−0.118857	−0.0594285	+	0.998233i	$0.518928\pi$
$678$	3.37310e12	0.613049
$679$	−7.45828e12	−1.34656
$680$	0	0
$681$	2.01386e12	0.358813
$682$	6.37181e12	1.12780
$683$	1.10011e12	0.193438	0.0967190	−	0.995312i	$-0.469165\pi$
$683$	1.10011e12	0.193438	0.0967190	+	0.995312i	$0.469165\pi$
$684$	1.48639e13	2.59645
$685$	0	0
$686$	−1.02913e13	−1.77424
$687$	3.20192e12	0.548409
$688$	−5.89869e12	−1.00371
$689$	4.37301e11	0.0739254
$690$	0	0
$691$	7.72289e12	1.28863	0.644315	−	0.764760i	$-0.277142\pi$
$691$	7.72289e12	1.28863	0.644315	+	0.764760i	$0.277142\pi$
$692$	−5.46071e11	−0.0905256
$693$	−2.60702e12	−0.429383
$694$	1.04855e13	1.71581
$695$	0	0
$696$	5.10016e12	0.823838
$697$	−1.63505e12	−0.262412
$698$	1.35119e13	2.15460
$699$	−2.48617e12	−0.393898
$700$	0	0
$701$	1.40436e12	0.219658	0.109829	−	0.993950i	$-0.464970\pi$
$701$	1.40436e12	0.219658	0.109829	+	0.993950i	$0.464970\pi$
$702$	1.93501e12	0.300723
$703$	3.74831e12	0.578810
$704$	4.64131e12	0.712137
$705$	0	0
$706$	−8.61273e12	−1.30473
$707$	5.39111e12	0.811505
$708$	6.91043e12	1.03361
$709$	5.19764e12	0.772499	0.386250	−	0.922394i	$-0.373770\pi$
$709$	5.19764e12	0.772499	0.386250	+	0.922394i	$0.373770\pi$
$710$	0	0
$711$	3.48822e12	0.511907
$712$	−5.73387e11	−0.0836157
$713$	2.88600e12	0.418209
$714$	1.18814e12	0.171090
$715$	0	0
$716$	−1.47932e13	−2.10355
$717$	−3.57116e12	−0.504630
$718$	−1.29400e12	−0.181707
$719$	−1.27042e13	−1.77284	−0.886418	−	0.462886i	$-0.846814\pi$
$719$	−1.27042e13	−1.77284	−0.886418	+	0.462886i	$0.846814\pi$
$720$	0	0
$721$	−2.48016e12	−0.341799
$722$	−1.89174e13	−2.59086
$723$	−2.75230e12	−0.374605
$724$	−2.06495e13	−2.79309
$725$	0	0
$726$	−3.14800e12	−0.420552
$727$	−9.91998e11	−0.131706	−0.0658531	−	0.997829i	$-0.520977\pi$
$727$	−9.91998e11	−0.131706	−0.0658531	+	0.997829i	$0.520977\pi$
$728$	−2.80627e12	−0.370286
$729$	−2.80211e12	−0.367461
$730$	0	0
$731$	4.39227e12	0.568933
$732$	−3.91898e12	−0.504514
$733$	−5.54849e12	−0.709916	−0.354958	−	0.934882i	$-0.615505\pi$
$733$	−5.54849e12	−0.709916	−0.354958	+	0.934882i	$0.615505\pi$
$734$	−2.95572e12	−0.375864
$735$	0	0
$736$	1.24406e12	0.156275
$737$	−2.54663e12	−0.317953
$738$	9.92797e12	1.23199
$739$	8.78597e12	1.08365	0.541826	−	0.840491i	$-0.317733\pi$
$739$	8.78597e12	1.08365	0.541826	+	0.840491i	$0.317733\pi$
$740$	0	0
$741$	−1.23701e12	−0.150727
$742$	−3.47570e12	−0.420944
$743$	−4.04326e12	−0.486724	−0.243362	−	0.969936i	$-0.578250\pi$
$743$	−4.04326e12	−0.486724	−0.243362	+	0.969936i	$0.578250\pi$
$744$	5.23871e12	0.626825
$745$	0	0
$746$	2.48408e13	2.93658
$747$	1.10357e12	0.129676
$748$	2.60342e12	0.304080
$749$	3.99451e12	0.463763
$750$	0	0
$751$	−2.52936e11	−0.0290156	−0.0145078	−	0.999895i	$-0.504618\pi$
$751$	−2.52936e11	−0.0290156	−0.0145078	+	0.999895i	$0.504618\pi$
$752$	−9.25130e11	−0.105493
$753$	5.16479e12	0.585431
$754$	7.02906e12	0.792001
$755$	0	0
$756$	−9.97448e12	−1.11056
$757$	−9.99638e12	−1.10640	−0.553199	−	0.833049i	$-0.686593\pi$
$757$	−9.99638e12	−1.10640	−0.553199	+	0.833049i	$0.686593\pi$
$758$	−7.40426e12	−0.814649
$759$	5.25864e11	0.0575156
$760$	0	0
$761$	−2.98848e12	−0.323013	−0.161507	−	0.986872i	$-0.551635\pi$
$761$	−2.98848e12	−0.323013	−0.161507	+	0.986872i	$0.551635\pi$
$762$	−3.43418e12	−0.369000
$763$	−9.91726e12	−1.05933
$764$	1.58528e13	1.68339
$765$	0	0
$766$	1.69714e13	1.78110
$767$	4.36299e12	0.455203
$768$	5.65858e12	0.586924
$769$	1.54887e13	1.59715	0.798576	−	0.601894i	$-0.205587\pi$
$769$	1.54887e13	1.59715	0.798576	+	0.601894i	$0.205587\pi$
$770$	0	0
$771$	−3.17948e12	−0.324050
$772$	2.55139e13	2.58523
$773$	−1.07589e13	−1.08383	−0.541915	−	0.840434i	$-0.682300\pi$
$773$	−1.07589e13	−1.08383	−0.541915	+	0.840434i	$0.682300\pi$
$774$	−2.66697e13	−2.67106
$775$	0	0
$776$	−2.07173e13	−2.05095
$777$	−1.17990e12	−0.116131
$778$	6.47427e12	0.633552
$779$	−1.35301e13	−1.31638
$780$	0	0
$781$	−1.04130e13	−1.00149
$782$	1.81816e12	0.173861
$783$	1.14452e13	1.08817
$784$	−7.31343e11	−0.0691351
$785$	0	0
$786$	6.32379e12	0.590985
$787$	−1.29304e13	−1.20151	−0.600755	−	0.799433i	$-0.705133\pi$
$787$	−1.29304e13	−1.20151	−0.600755	+	0.799433i	$0.705133\pi$
$788$	−1.49545e13	−1.38167
$789$	−3.90379e12	−0.358625
$790$	0	0
$791$	−1.09778e13	−0.997059
$792$	−7.24168e12	−0.653997
$793$	−2.47430e12	−0.222189
$794$	1.12394e13	1.00358
$795$	0	0
$796$	8.31828e12	0.734387
$797$	−1.24713e13	−1.09484	−0.547418	−	0.836859i	$-0.684389\pi$
$797$	−1.24713e13	−1.09484	−0.547418	+	0.836859i	$0.684389\pi$
$798$	9.83185e12	0.858267
$799$	6.88868e11	0.0597965
$800$	0	0
$801$	−6.03585e11	−0.0518075
$802$	−1.69224e13	−1.44437
$803$	−7.92600e12	−0.672719
$804$	−4.57049e12	−0.385755
$805$	0	0
$806$	7.22002e12	0.602602
$807$	−4.81502e12	−0.399639
$808$	1.49752e13	1.23601
$809$	−2.40763e13	−1.97616	−0.988079	−	0.153948i	$-0.950801\pi$
$809$	−2.40763e13	−1.97616	−0.988079	+	0.153948i	$0.950801\pi$
$810$	0	0
$811$	1.14686e13	0.930928	0.465464	−	0.885067i	$-0.345888\pi$
$811$	1.14686e13	0.930928	0.465464	+	0.885067i	$0.345888\pi$
$812$	−3.62330e13	−2.92484
$813$	1.43040e12	0.114829
$814$	−3.98637e12	−0.318249
$815$	0	0
$816$	7.68403e11	0.0606713
$817$	3.63462e13	2.85403
$818$	3.86469e12	0.301804
$819$	−2.95406e12	−0.229426
$820$	0	0
$821$	−2.50113e13	−1.92129	−0.960643	−	0.277786i	$-0.910399\pi$
$821$	−2.50113e13	−1.92129	−0.960643	+	0.277786i	$0.910399\pi$
$822$	−9.22470e12	−0.704740
$823$	−1.29351e13	−0.982808	−0.491404	−	0.870932i	$-0.663516\pi$
$823$	−1.29351e13	−0.982808	−0.491404	+	0.870932i	$0.663516\pi$
$824$	−6.88929e12	−0.520597
$825$	0	0
$826$	−3.46773e13	−2.59200
$827$	−1.00464e13	−0.746851	−0.373425	−	0.927660i	$-0.621817\pi$
$827$	−1.00464e13	−0.746851	−0.373425	+	0.927660i	$0.621817\pi$
$828$	−7.15990e12	−0.529384
$829$	8.77304e12	0.645141	0.322570	−	0.946545i	$-0.395453\pi$
$829$	8.77304e12	0.645141	0.322570	+	0.946545i	$0.395453\pi$
$830$	0	0
$831$	−1.51868e12	−0.110474
$832$	5.25916e12	0.380506
$833$	5.44571e11	0.0391879
$834$	6.57361e12	0.470497
$835$	0	0
$836$	2.15434e13	1.52541
$837$	1.17561e13	0.827943
$838$	−3.03051e12	−0.212284
$839$	−1.54259e13	−1.07478	−0.537392	−	0.843332i	$-0.680590\pi$
$839$	−1.54259e13	−1.07478	−0.537392	+	0.843332i	$0.680590\pi$
$840$	0	0
$841$	2.70683e13	1.86586
$842$	2.31593e13	1.58789
$843$	−4.72537e12	−0.322264
$844$	−1.72010e13	−1.16685
$845$	0	0
$846$	−4.18279e12	−0.280737
$847$	1.02452e13	0.683983
$848$	−2.24784e12	−0.149274
$849$	−5.08296e12	−0.335762
$850$	0	0
$851$	−1.80556e12	−0.118012
$852$	−1.86884e13	−1.21505
$853$	1.84928e12	0.119600	0.0598002	−	0.998210i	$-0.480954\pi$
$853$	1.84928e12	0.119600	0.0598002	+	0.998210i	$0.480954\pi$
$854$	1.96659e13	1.26518
$855$	0	0
$856$	1.10958e13	0.706361
$857$	2.34715e13	1.48637	0.743185	−	0.669086i	$-0.233314\pi$
$857$	2.34715e13	1.48637	0.743185	+	0.669086i	$0.233314\pi$
$858$	1.31558e12	0.0828749
$859$	1.25121e12	0.0784079	0.0392039	−	0.999231i	$-0.487518\pi$
$859$	1.25121e12	0.0784079	0.0392039	+	0.999231i	$0.487518\pi$
$860$	0	0
$861$	4.25902e12	0.264116
$862$	1.04026e13	0.641739
$863$	−2.38217e13	−1.46192	−0.730961	−	0.682419i	$-0.760928\pi$
$863$	−2.38217e13	−1.46192	−0.730961	+	0.682419i	$0.760928\pi$
$864$	5.06768e12	0.309384
$865$	0	0
$866$	−4.40928e13	−2.66402
$867$	5.10563e12	0.306876
$868$	−3.72173e13	−2.22539
$869$	5.05575e12	0.300744
$870$	0	0
$871$	−2.88564e12	−0.169887
$872$	−2.75478e13	−1.61348
$873$	−2.18084e13	−1.27075
$874$	1.50453e13	0.872168
$875$	0	0
$876$	−1.42249e13	−0.816173
$877$	1.35717e13	0.774707	0.387353	−	0.921931i	$-0.373389\pi$
$877$	1.35717e13	0.774707	0.387353	+	0.921931i	$0.373389\pi$
$878$	−6.79601e12	−0.385948
$879$	1.08375e13	0.612323
$880$	0	0
$881$	2.38436e12	0.133346	0.0666730	−	0.997775i	$-0.478762\pi$
$881$	2.38436e12	0.133346	0.0666730	+	0.997775i	$0.478762\pi$
$882$	−3.30662e12	−0.183982
$883$	5.99779e11	0.0332023	0.0166011	−	0.999862i	$-0.494715\pi$
$883$	5.99779e11	0.0332023	0.0166011	+	0.999862i	$0.494715\pi$
$884$	2.94999e12	0.162474
$885$	0	0
$886$	−2.50103e12	−0.136354
$887$	−1.02483e13	−0.555897	−0.277949	−	0.960596i	$-0.589654\pi$
$887$	−1.02483e13	−0.555897	−0.277949	+	0.960596i	$0.589654\pi$
$888$	−3.27747e12	−0.176881
$889$	1.11766e13	0.600138
$890$	0	0
$891$	−6.48579e12	−0.344757
$892$	−1.45042e13	−0.767101
$893$	5.70040e12	0.299967
$894$	2.33111e12	0.122052
$895$	0	0
$896$	−3.31065e13	−1.71604
$897$	5.95867e11	0.0307315
$898$	3.04642e13	1.56331
$899$	4.27050e13	2.18052
$900$	0	0
$901$	1.67378e12	0.0846130
$902$	1.43894e13	0.723791
$903$	−1.14411e13	−0.572628
$904$	−3.04937e13	−1.51863
$905$	0	0
$906$	7.95437e12	0.392219
$907$	2.43855e13	1.19646	0.598231	−	0.801323i	$-0.295870\pi$
$907$	2.43855e13	1.19646	0.598231	+	0.801323i	$0.295870\pi$
$908$	−3.97416e13	−1.94026
$909$	1.57639e13	0.765820
$910$	0	0
$911$	2.90386e13	1.39683	0.698415	−	0.715693i	$-0.253889\pi$
$911$	2.90386e13	1.39683	0.698415	+	0.715693i	$0.253889\pi$
$912$	6.35855e12	0.304356
$913$	1.59949e12	0.0761841
$914$	−3.40744e13	−1.61499
$915$	0	0
$916$	−6.31867e13	−2.96549
$917$	−2.05809e13	−0.961173
$918$	7.40630e12	0.344199
$919$	−1.41793e13	−0.655746	−0.327873	−	0.944722i	$-0.606332\pi$
$919$	−1.41793e13	−0.655746	−0.327873	+	0.944722i	$0.606332\pi$
$920$	0	0
$921$	−1.06773e12	−0.0488984
$922$	−8.87378e12	−0.404408
$923$	−1.17992e13	−0.535111
$924$	−6.78146e12	−0.306055
$925$	0	0
$926$	−5.89402e13	−2.63428
$927$	−7.25212e12	−0.322557
$928$	1.84087e13	0.814812
$929$	−3.56246e13	−1.56920	−0.784601	−	0.620001i	$-0.787132\pi$
$929$	−3.56246e13	−1.56920	−0.784601	+	0.620001i	$0.787132\pi$
$930$	0	0
$931$	4.50634e12	0.196585
$932$	4.90621e13	2.12998
$933$	1.30136e13	0.562250
$934$	6.23355e13	2.68025
$935$	0	0
$936$	−8.20568e12	−0.349441
$937$	−9.35575e12	−0.396506	−0.198253	−	0.980151i	$-0.563527\pi$
$937$	−9.35575e12	−0.396506	−0.198253	+	0.980151i	$0.563527\pi$
$938$	2.29353e13	0.967366
$939$	−3.78610e12	−0.158927
$940$	0	0
$941$	1.23413e13	0.513106	0.256553	−	0.966530i	$-0.417413\pi$
$941$	1.23413e13	0.513106	0.256553	+	0.966530i	$0.417413\pi$
$942$	2.57673e13	1.06620
$943$	6.51742e12	0.268394
$944$	−2.24269e13	−0.919168
$945$	0	0
$946$	−3.86546e13	−1.56924
$947$	−2.93722e12	−0.118676	−0.0593379	−	0.998238i	$-0.518899\pi$
$947$	−2.93722e12	−0.118676	−0.0593379	+	0.998238i	$0.518899\pi$
$948$	9.07366e12	0.364876
$949$	−8.98110e12	−0.359444
$950$	0	0
$951$	9.72086e12	0.385383
$952$	−1.07411e13	−0.423819
$953$	3.90544e12	0.153374	0.0766870	−	0.997055i	$-0.475566\pi$
$953$	3.90544e12	0.153374	0.0766870	+	0.997055i	$0.475566\pi$
$954$	−1.01631e13	−0.397247
$955$	0	0
$956$	7.04733e13	2.72875
$957$	7.78137e12	0.299883
$958$	−5.89375e13	−2.26072
$959$	3.00219e13	1.14618
$960$	0	0
$961$	1.74255e13	0.659069
$962$	−4.51703e12	−0.170045
$963$	1.16802e13	0.437655
$964$	5.43139e13	2.02565
$965$	0	0
$966$	−4.73599e12	−0.174990
$967$	1.06697e13	0.392405	0.196203	−	0.980563i	$-0.437139\pi$
$967$	1.06697e13	0.392405	0.196203	+	0.980563i	$0.437139\pi$
$968$	2.84587e13	1.04178
$969$	−4.73469e12	−0.172518
$970$	0	0
$971$	−3.10264e12	−0.112007	−0.0560034	−	0.998431i	$-0.517836\pi$
$971$	−3.10264e12	−0.112007	−0.0560034	+	0.998431i	$0.517836\pi$
$972$	−4.46506e13	−1.60446
$973$	−2.13939e13	−0.765213
$974$	9.74972e12	0.347118
$975$	0	0
$976$	1.27185e13	0.448655
$977$	4.66167e13	1.63688	0.818438	−	0.574594i	$-0.194840\pi$
$977$	4.66167e13	1.63688	0.818438	+	0.574594i	$0.194840\pi$
$978$	−1.32455e12	−0.0462961
$979$	−8.74824e11	−0.0304368
$980$	0	0
$981$	−2.89986e13	−0.999694
$982$	−6.04614e13	−2.07480
$983$	3.22316e13	1.10101	0.550505	−	0.834832i	$-0.314435\pi$
$983$	3.22316e13	1.10101	0.550505	+	0.834832i	$0.314435\pi$
$984$	1.18305e13	0.402278
$985$	0	0
$986$	2.69039e13	0.906502
$987$	−1.79438e12	−0.0601849
$988$	2.44112e13	0.815047
$989$	−1.75079e13	−0.581903
$990$	0	0
$991$	−2.25008e13	−0.741081	−0.370540	−	0.928816i	$-0.620828\pi$
$991$	−2.25008e13	−0.741081	−0.370540	+	0.928816i	$0.620828\pi$
$992$	1.89088e13	0.619957
$993$	−1.55192e13	−0.506520
$994$	9.37807e13	3.04701
$995$	0	0
$996$	2.87064e12	0.0924299
$997$	3.13756e13	1.00569	0.502844	−	0.864377i	$-0.332287\pi$
$997$	3.13756e13	1.00569	0.502844	+	0.864377i	$0.332287\pi$
$998$	2.40442e13	0.767224
$999$	−7.35495e12	−0.233633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.b.1.1		5
5.4	even	2		13.10.a.b.1.5	✓	5
15.14	odd	2		117.10.a.e.1.1		5
20.19	odd	2		208.10.a.h.1.3		5
65.64	even	2		169.10.a.b.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.5	✓	5	5.4	even	2
117.10.a.e.1.1		5	15.14	odd	2
169.10.a.b.1.1		5	65.64	even	2
208.10.a.h.1.3		5	20.19	odd	2
325.10.a.b.1.1		5	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-38.1685 q^{2} -47.8784 q^{3} +944.833 q^{4} +1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} +O(q^{10})\)	\(q-38.1685 q^{2} -47.8784 q^{3} +944.833 q^{4} +1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} -25205.7 q^{11} -45237.1 q^{12} -28561.0 q^{13} +227005. q^{14} +146811. q^{16} -109318. q^{17} +663775. q^{18} -904609. q^{19} +284754. q^{21} +962062. q^{22} +435749. q^{23} +790979. q^{24} +1.09013e6 q^{26} +1.77503e6 q^{27} -5.61934e6 q^{28} +6.44791e6 q^{29} +6.62308e6 q^{31} +2.85499e6 q^{32} +1.20681e6 q^{33} +4.17250e6 q^{34} -1.64313e7 q^{36} -4.14357e6 q^{37} +3.45275e7 q^{38} +1.36745e6 q^{39} +1.49568e7 q^{41} -1.08686e7 q^{42} -4.01789e7 q^{43} -2.38151e7 q^{44} -1.66319e7 q^{46} -6.30151e6 q^{47} -7.02907e6 q^{48} -4.98153e6 q^{49} +5.23397e6 q^{51} -2.69854e7 q^{52} -1.53111e7 q^{53} -6.77501e7 q^{54} +9.82552e7 q^{56} +4.33112e7 q^{57} -2.46107e8 q^{58} -1.52760e8 q^{59} +8.66321e7 q^{61} -2.52793e8 q^{62} +1.03430e8 q^{63} -1.84138e8 q^{64} -4.60620e7 q^{66} +1.01034e8 q^{67} -1.03287e8 q^{68} -2.08630e7 q^{69} +4.13122e8 q^{71} +2.87304e8 q^{72} +3.14453e8 q^{73} +1.58154e8 q^{74} -8.54704e8 q^{76} +1.49909e8 q^{77} -5.21937e7 q^{78} -2.00580e8 q^{79} +2.57315e8 q^{81} -5.70879e8 q^{82} -6.34578e7 q^{83} +2.69045e8 q^{84} +1.53357e9 q^{86} -3.08715e8 q^{87} +4.16412e8 q^{88} +3.47074e7 q^{89} +1.69865e8 q^{91} +4.11710e8 q^{92} -3.17102e8 q^{93} +2.40519e8 q^{94} -1.36692e8 q^{96} +1.25403e9 q^{97} +1.90137e8 q^{98} +4.38343e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} - 161 q^{3} + 361 q^{4} + 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9}+O(q^{10}) \) 5 * q - 15 * q^2 - 161 * q^3 + 361 * q^4 + 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9	\( 5 q - 15 q^{2} - 161 q^{3} + 361 q^{4} + 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9} + 121746 q^{11} - 113389 q^{12} - 142805 q^{13} + 8475 q^{14} - 322463 q^{16} + 495669 q^{17} + 656228 q^{18} - 840738 q^{19} - 1599467 q^{21} + 2023594 q^{22} + 592152 q^{23} - 2295657 q^{24} + 428415 q^{26} - 6847883 q^{27} - 2587955 q^{28} + 10678182 q^{29} + 12885296 q^{31} - 3282927 q^{32} - 17278298 q^{33} - 9934079 q^{34} - 20483302 q^{36} - 7171823 q^{37} + 25568814 q^{38} + 4598321 q^{39} + 9294012 q^{41} + 69520457 q^{42} - 12831975 q^{43} - 41479074 q^{44} - 59319696 q^{46} - 43354215 q^{47} + 86874671 q^{48} + 25249488 q^{49} + 16905901 q^{51} - 10310521 q^{52} - 93231780 q^{53} + 58983719 q^{54} + 199599225 q^{56} - 90173382 q^{57} - 151020970 q^{58} + 246496182 q^{59} - 132232612 q^{61} - 158135724 q^{62} + 416955202 q^{63} + 91019105 q^{64} - 323733130 q^{66} + 369388534 q^{67} - 238172073 q^{68} - 579986760 q^{69} + 212150457 q^{71} + 415774278 q^{72} + 252729806 q^{73} + 192105957 q^{74} - 953775990 q^{76} - 449666118 q^{77} - 162597773 q^{78} - 1247271728 q^{79} - 317713115 q^{81} - 169559388 q^{82} - 1696894296 q^{83} + 1247983739 q^{84} + 3291621459 q^{86} + 614530466 q^{87} + 220227222 q^{88} - 753854382 q^{89} + 288437539 q^{91} - 13876128 q^{92} + 892784668 q^{93} + 272071215 q^{94} + 930612847 q^{96} - 3824606 q^{97} - 1570614816 q^{98} + 3016199848 q^{99}+O(q^{100}) \) 5 * q - 15 * q^2 - 161 * q^3 + 361 * q^4 + 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9 + 121746 * q^11 - 113389 * q^12 - 142805 * q^13 + 8475 * q^14 - 322463 * q^16 + 495669 * q^17 + 656228 * q^18 - 840738 * q^19 - 1599467 * q^21 + 2023594 * q^22 + 592152 * q^23 - 2295657 * q^24 + 428415 * q^26 - 6847883 * q^27 - 2587955 * q^28 + 10678182 * q^29 + 12885296 * q^31 - 3282927 * q^32 - 17278298 * q^33 - 9934079 * q^34 - 20483302 * q^36 - 7171823 * q^37 + 25568814 * q^38 + 4598321 * q^39 + 9294012 * q^41 + 69520457 * q^42 - 12831975 * q^43 - 41479074 * q^44 - 59319696 * q^46 - 43354215 * q^47 + 86874671 * q^48 + 25249488 * q^49 + 16905901 * q^51 - 10310521 * q^52 - 93231780 * q^53 + 58983719 * q^54 + 199599225 * q^56 - 90173382 * q^57 - 151020970 * q^58 + 246496182 * q^59 - 132232612 * q^61 - 158135724 * q^62 + 416955202 * q^63 + 91019105 * q^64 - 323733130 * q^66 + 369388534 * q^67 - 238172073 * q^68 - 579986760 * q^69 + 212150457 * q^71 + 415774278 * q^72 + 252729806 * q^73 + 192105957 * q^74 - 953775990 * q^76 - 449666118 * q^77 - 162597773 * q^78 - 1247271728 * q^79 - 317713115 * q^81 - 169559388 * q^82 - 1696894296 * q^83 + 1247983739 * q^84 + 3291621459 * q^86 + 614530466 * q^87 + 220227222 * q^88 - 753854382 * q^89 + 288437539 * q^91 - 13876128 * q^92 + 892784668 * q^93 + 272071215 * q^94 + 930612847 * q^96 - 3824606 * q^97 - 1570614816 * q^98 + 3016199848 * q^99

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