LMFDB - Embedded newform 325.10.a.b.1.2

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			1.2
Root			$16.7176$ 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)

$f(q)$	$=$	$q-19.7176 q^{2} -250.479 q^{3} -123.217 q^{4} +4938.84 q^{6} +8329.39 q^{7} +12524.9 q^{8} +43056.6 q^{9} +O(q^{10})$	\(q-19.7176 q^{2} -250.479 q^{3} -123.217 q^{4} +4938.84 q^{6} +8329.39 q^{7} +12524.9 q^{8} +43056.6 q^{9} +30751.5 q^{11} +30863.2 q^{12} -28561.0 q^{13} -164236. q^{14} -183875. q^{16} +637455. q^{17} -848973. q^{18} +105834. q^{19} -2.08634e6 q^{21} -606345. q^{22} +511169. q^{23} -3.13723e6 q^{24} +563154. q^{26} -5.85460e6 q^{27} -1.02632e6 q^{28} +781868. q^{29} -2.83285e6 q^{31} -2.78721e6 q^{32} -7.70259e6 q^{33} -1.25691e7 q^{34} -5.30530e6 q^{36} -1.22183e7 q^{37} -2.08680e6 q^{38} +7.15392e6 q^{39} -6.83367e6 q^{41} +4.11375e7 q^{42} -3.84656e7 q^{43} -3.78910e6 q^{44} -1.00790e7 q^{46} +1.30402e7 q^{47} +4.60567e7 q^{48} +2.90252e7 q^{49} -1.59669e8 q^{51} +3.51920e6 q^{52} +2.42871e7 q^{53} +1.15439e8 q^{54} +1.04325e8 q^{56} -2.65092e7 q^{57} -1.54166e7 q^{58} +1.63738e8 q^{59} +1.90751e7 q^{61} +5.58569e7 q^{62} +3.58636e8 q^{63} +1.49101e8 q^{64} +1.51876e8 q^{66} +7.22869e7 q^{67} -7.85452e7 q^{68} -1.28037e8 q^{69} +2.65461e7 q^{71} +5.39282e8 q^{72} -2.42850e8 q^{73} +2.40916e8 q^{74} -1.30406e7 q^{76} +2.56141e8 q^{77} -1.41058e8 q^{78} -4.64290e8 q^{79} +6.18969e8 q^{81} +1.34744e8 q^{82} -5.46643e8 q^{83} +2.57072e8 q^{84} +7.58449e8 q^{86} -1.95841e8 q^{87} +3.85160e8 q^{88} +3.65672e8 q^{89} -2.37896e8 q^{91} -6.29847e7 q^{92} +7.09568e8 q^{93} -2.57121e8 q^{94} +6.98137e8 q^{96} -9.98914e7 q^{97} -5.72307e8 q^{98} +1.32405e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.7176	−0.871402	−0.435701	−	0.900091i	$-0.643500\pi$
$2$	−19.7176	−0.871402	−0.435701	+	0.900091i	$0.643500\pi$
$3$	−250.479	−1.78536	−0.892679	−	0.450693i	$-0.851177\pi$
$3$	−250.479	−1.78536	−0.892679	+	0.450693i	$0.851177\pi$
$4$	−123.217	−0.240658
$5$	0	0
$5$	0	0
$6$	4938.84	1.55577
$7$	8329.39	1.31121	0.655605	−	0.755104i	$-0.272414\pi$
$7$	8329.39	1.31121	0.655605	+	0.755104i	$0.272414\pi$
$8$	12524.9	1.08111
$9$	43056.6	2.18750
$10$	0	0
$11$	30751.5	0.633284	0.316642	−	0.948545i	$-0.397445\pi$
$11$	30751.5	0.633284	0.316642	+	0.948545i	$0.397445\pi$
$12$	30863.2	0.429661
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−164236.	−1.14259
$15$	0	0
$16$	−183875.	−0.701426
$17$	637455.	1.85110	0.925549	−	0.378629i	$-0.123604\pi$
$17$	637455.	1.85110	0.925549	+	0.378629i	$0.123604\pi$
$18$	−848973.	−1.90620
$19$	105834.	0.186310	0.0931548	−	0.995652i	$-0.470305\pi$
$19$	105834.	0.186310	0.0931548	+	0.995652i	$0.470305\pi$
$20$	0	0
$21$	−2.08634e6	−2.34098
$22$	−606345.	−0.551845
$23$	511169.	0.380881	0.190441	−	0.981699i	$-0.439008\pi$
$23$	511169.	0.380881	0.190441	+	0.981699i	$0.439008\pi$
$24$	−3.13723e6	−1.93017
$25$	0	0
$26$	563154.	0.241684
$27$	−5.85460e6	−2.12012
$28$	−1.02632e6	−0.315553
$29$	781868.	0.205278	0.102639	−	0.994719i	$-0.467271\pi$
$29$	781868.	0.205278	0.102639	+	0.994719i	$0.467271\pi$
$30$	0	0
$31$	−2.83285e6	−0.550929	−0.275464	−	0.961311i	$-0.588832\pi$
$31$	−2.83285e6	−0.550929	−0.275464	+	0.961311i	$0.588832\pi$
$32$	−2.78721e6	−0.469888
$33$	−7.70259e6	−1.13064
$34$	−1.25691e7	−1.61305
$35$	0	0
$36$	−5.30530e6	−0.526440
$37$	−1.22183e7	−1.07178	−0.535889	−	0.844289i	$-0.680023\pi$
$37$	−1.22183e7	−1.07178	−0.535889	+	0.844289i	$0.680023\pi$
$38$	−2.08680e6	−0.162351
$39$	7.15392e6	0.495169
$40$	0	0
$41$	−6.83367e6	−0.377682	−0.188841	−	0.982008i	$-0.560473\pi$
$41$	−6.83367e6	−0.377682	−0.188841	+	0.982008i	$0.560473\pi$
$42$	4.11375e7	2.03993
$43$	−3.84656e7	−1.71579	−0.857896	−	0.513823i	$-0.828229\pi$
$43$	−3.84656e7	−1.71579	−0.857896	+	0.513823i	$0.828229\pi$
$44$	−3.78910e6	−0.152405
$45$	0	0
$46$	−1.00790e7	−0.331901
$47$	1.30402e7	0.389802	0.194901	−	0.980823i	$-0.437561\pi$
$47$	1.30402e7	0.389802	0.194901	+	0.980823i	$0.437561\pi$
$48$	4.60567e7	1.25230
$49$	2.90252e7	0.719272
$50$	0	0
$51$	−1.59669e8	−3.30487
$52$	3.51920e6	0.0667465
$53$	2.42871e7	0.422800	0.211400	−	0.977400i	$-0.432198\pi$
$53$	2.42871e7	0.422800	0.211400	+	0.977400i	$0.432198\pi$
$54$	1.15439e8	1.84748
$55$	0	0
$56$	1.04325e8	1.41757
$57$	−2.65092e7	−0.332629
$58$	−1.54166e7	−0.178880
$59$	1.63738e8	1.75920	0.879599	−	0.475716i	$-0.157811\pi$
$59$	1.63738e8	1.75920	0.879599	+	0.475716i	$0.157811\pi$
$60$	0	0
$61$	1.90751e7	0.176394	0.0881968	−	0.996103i	$-0.471890\pi$
$61$	1.90751e7	0.176394	0.0881968	+	0.996103i	$0.471890\pi$
$62$	5.58569e7	0.480081
$63$	3.58636e8	2.86828
$64$	1.49101e8	1.11089
$65$	0	0
$66$	1.51876e8	0.985242
$67$	7.22869e7	0.438251	0.219125	−	0.975697i	$-0.429680\pi$
$67$	7.22869e7	0.438251	0.219125	+	0.975697i	$0.429680\pi$
$68$	−7.85452e7	−0.445481
$69$	−1.28037e8	−0.680009
$70$	0	0
$71$	2.65461e7	0.123976	0.0619880	−	0.998077i	$-0.480256\pi$
$71$	2.65461e7	0.123976	0.0619880	+	0.998077i	$0.480256\pi$
$72$	5.39282e8	2.36494
$73$	−2.42850e8	−1.00089	−0.500445	−	0.865769i	$-0.666830\pi$
$73$	−2.42850e8	−1.00089	−0.500445	+	0.865769i	$0.666830\pi$
$74$	2.40916e8	0.933950
$75$	0	0
$76$	−1.30406e7	−0.0448369
$77$	2.56141e8	0.830369
$78$	−1.41058e8	−0.431492
$79$	−4.64290e8	−1.34112	−0.670560	−	0.741855i	$-0.733946\pi$
$79$	−4.64290e8	−1.34112	−0.670560	+	0.741855i	$0.733946\pi$
$80$	0	0
$81$	6.18969e8	1.59767
$82$	1.34744e8	0.329113
$83$	−5.46643e8	−1.26431	−0.632153	−	0.774843i	$-0.717829\pi$
$83$	−5.46643e8	−1.26431	−0.632153	+	0.774843i	$0.717829\pi$
$84$	2.57072e8	0.563375
$85$	0	0
$86$	7.58449e8	1.49515
$87$	−1.95841e8	−0.366495
$88$	3.85160e8	0.684651
$89$	3.65672e8	0.617783	0.308892	−	0.951097i	$-0.400042\pi$
$89$	3.65672e8	0.617783	0.308892	+	0.951097i	$0.400042\pi$
$90$	0	0
$91$	−2.37896e8	−0.363664
$92$	−6.29847e7	−0.0916621
$93$	7.09568e8	0.983605
$94$	−2.57121e8	−0.339674
$95$	0	0
$96$	6.98137e8	0.838919
$97$	−9.98914e7	−0.114566	−0.0572830	−	0.998358i	$-0.518244\pi$
$97$	−9.98914e7	−0.114566	−0.0572830	+	0.998358i	$0.518244\pi$
$98$	−5.72307e8	−0.626775
$99$	1.32405e9	1.38531
$100$	0	0
$101$	−6.76155e8	−0.646547	−0.323273	−	0.946306i	$-0.604783\pi$
$101$	−6.76155e8	−0.646547	−0.323273	+	0.946306i	$0.604783\pi$
$102$	3.14829e9	2.87987
$103$	1.73267e8	0.151687	0.0758434	−	0.997120i	$-0.475835\pi$
$103$	1.73267e8	0.151687	0.0758434	+	0.997120i	$0.475835\pi$
$104$	−3.57725e8	−0.299847
$105$	0	0
$106$	−4.78883e8	−0.368429
$107$	−1.23684e9	−0.912191	−0.456095	−	0.889931i	$-0.650752\pi$
$107$	−1.23684e9	−0.912191	−0.456095	+	0.889931i	$0.650752\pi$
$108$	7.21385e8	0.510223
$109$	−1.04481e9	−0.708956	−0.354478	−	0.935064i	$-0.615341\pi$
$109$	−1.04481e9	−0.708956	−0.354478	+	0.935064i	$0.615341\pi$
$110$	0	0
$111$	3.06044e9	1.91351
$112$	−1.53156e9	−0.919716
$113$	1.17492e9	0.677884	0.338942	−	0.940807i	$-0.389931\pi$
$113$	1.17492e9	0.677884	0.338942	+	0.940807i	$0.389931\pi$
$114$	5.22698e8	0.289854
$115$	0	0
$116$	−9.63394e7	−0.0494018
$117$	−1.22974e9	−0.606704
$118$	−3.22851e9	−1.53297
$119$	5.30961e9	2.42718
$120$	0	0
$121$	−1.41230e9	−0.598951
$122$	−3.76115e8	−0.153710
$123$	1.71169e9	0.674298
$124$	3.49055e8	0.132585
$125$	0	0
$126$	−7.07143e9	−2.49942
$127$	−6.34961e8	−0.216586	−0.108293	−	0.994119i	$-0.534538\pi$
$127$	−6.34961e8	−0.216586	−0.108293	+	0.994119i	$0.534538\pi$
$128$	−1.51286e9	−0.498142
$129$	9.63482e9	3.06330
$130$	0	0
$131$	−5.68611e9	−1.68692	−0.843459	−	0.537193i	$-0.819485\pi$
$131$	−5.68611e9	−1.68692	−0.843459	+	0.537193i	$0.819485\pi$
$132$	9.49089e8	0.272097
$133$	8.81536e8	0.244291
$134$	−1.42532e9	−0.381893
$135$	0	0
$136$	7.98408e9	2.00124
$137$	−4.47162e9	−1.08448	−0.542241	−	0.840223i	$-0.682424\pi$
$137$	−4.47162e9	−1.08448	−0.542241	+	0.840223i	$0.682424\pi$
$138$	2.52458e9	0.592562
$139$	−8.63285e9	−1.96150	−0.980748	−	0.195275i	$-0.937440\pi$
$139$	−8.63285e9	−1.96150	−0.980748	+	0.195275i	$0.937440\pi$
$140$	0	0
$141$	−3.26629e9	−0.695936
$142$	−5.23424e8	−0.108033
$143$	−8.78292e8	−0.175641
$144$	−7.91702e9	−1.53437
$145$	0	0
$146$	4.78842e9	0.872177
$147$	−7.27020e9	−1.28416
$148$	1.50551e9	0.257932
$149$	−6.88630e9	−1.14458	−0.572292	−	0.820050i	$-0.693946\pi$
$149$	−6.88630e9	−1.14458	−0.572292	+	0.820050i	$0.693946\pi$
$150$	0	0
$151$	4.01063e9	0.627792	0.313896	−	0.949457i	$-0.398366\pi$
$151$	4.01063e9	0.627792	0.313896	+	0.949457i	$0.398366\pi$
$152$	1.32557e9	0.201422
$153$	2.74467e10	4.04928
$154$	−5.05048e9	−0.723585
$155$	0	0
$156$	−8.81484e8	−0.119166
$157$	−9.39913e9	−1.23464	−0.617318	−	0.786714i	$-0.711781\pi$
$157$	−9.39913e9	−1.23464	−0.617318	+	0.786714i	$0.711781\pi$
$158$	9.15469e9	1.16866
$159$	−6.08341e9	−0.754849
$160$	0	0
$161$	4.25773e9	0.499415
$162$	−1.22046e10	−1.39221
$163$	−3.72144e9	−0.412920	−0.206460	−	0.978455i	$-0.566194\pi$
$163$	−3.72144e9	−0.412920	−0.206460	+	0.978455i	$0.566194\pi$
$164$	8.42024e8	0.0908923
$165$	0	0
$166$	1.07785e10	1.10172
$167$	4.48607e9	0.446315	0.223158	−	0.974782i	$-0.428364\pi$
$167$	4.48607e9	0.446315	0.223158	+	0.974782i	$0.428364\pi$
$168$	−2.61312e10	−2.53086
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	4.55687e9	0.407553
$172$	4.73962e9	0.412919
$173$	1.69286e10	1.43686	0.718428	−	0.695602i	$-0.244862\pi$
$173$	1.69286e10	1.43686	0.718428	+	0.695602i	$0.244862\pi$
$174$	3.86152e9	0.319364
$175$	0	0
$176$	−5.65441e9	−0.444202
$177$	−4.10128e10	−3.14080
$178$	−7.21016e9	−0.538338
$179$	1.23127e10	0.896428	0.448214	−	0.893926i	$-0.352060\pi$
$179$	1.23127e10	0.896428	0.448214	+	0.893926i	$0.352060\pi$
$180$	0	0
$181$	−2.43748e10	−1.68806	−0.844030	−	0.536295i	$-0.819823\pi$
$181$	−2.43748e10	−1.68806	−0.844030	+	0.536295i	$0.819823\pi$
$182$	4.69073e9	0.316898
$183$	−4.77791e9	−0.314926
$184$	6.40237e9	0.411775
$185$	0	0
$186$	−1.39910e10	−0.857116
$187$	1.96027e10	1.17227
$188$	−1.60677e9	−0.0938089
$189$	−4.87653e10	−2.77992
$190$	0	0
$191$	−8.67702e9	−0.471759	−0.235880	−	0.971782i	$-0.575797\pi$
$191$	−8.67702e9	−0.471759	−0.235880	+	0.971782i	$0.575797\pi$
$192$	−3.73466e10	−1.98333
$193$	2.33509e10	1.21142	0.605712	−	0.795684i	$-0.292888\pi$
$193$	2.33509e10	1.21142	0.605712	+	0.795684i	$0.292888\pi$
$194$	1.96962e9	0.0998330
$195$	0	0
$196$	−3.57640e9	−0.173098
$197$	2.62332e9	0.124095	0.0620473	−	0.998073i	$-0.480237\pi$
$197$	2.62332e9	0.124095	0.0620473	+	0.998073i	$0.480237\pi$
$198$	−2.61071e10	−1.20716
$199$	8.36775e9	0.378242	0.189121	−	0.981954i	$-0.439436\pi$
$199$	8.36775e9	0.378242	0.189121	+	0.981954i	$0.439436\pi$
$200$	0	0
$201$	−1.81063e10	−0.782435
$202$	1.33321e10	0.563403
$203$	6.51249e9	0.269163
$204$	1.96739e10	0.795344
$205$	0	0
$206$	−3.41640e9	−0.132180
$207$	2.20092e10	0.833179
$208$	5.25164e9	0.194541
$209$	3.25456e9	0.117987
$210$	0	0
$211$	3.66318e10	1.27229	0.636147	−	0.771568i	$-0.280527\pi$
$211$	3.66318e10	1.27229	0.636147	+	0.771568i	$0.280527\pi$
$212$	−2.99258e9	−0.101750
$213$	−6.64923e9	−0.221342
$214$	2.43874e10	0.794885
$215$	0	0
$216$	−7.33285e10	−2.29209
$217$	−2.35959e10	−0.722383
$218$	2.06012e10	0.617786
$219$	6.08289e10	1.78695
$220$	0	0
$221$	−1.82063e10	−0.513402
$222$	−6.03444e10	−1.66743
$223$	−6.22383e10	−1.68533	−0.842667	−	0.538435i	$-0.819016\pi$
$223$	−6.22383e10	−1.68533	−0.842667	+	0.538435i	$0.819016\pi$
$224$	−2.32158e10	−0.616122
$225$	0	0
$226$	−2.31666e10	−0.590710
$227$	−4.00531e10	−1.00120	−0.500599	−	0.865679i	$-0.666887\pi$
$227$	−4.00531e10	−1.00120	−0.500599	+	0.865679i	$0.666887\pi$
$228$	3.26639e9	0.0800499
$229$	4.61622e10	1.10924	0.554621	−	0.832103i	$-0.312863\pi$
$229$	4.61622e10	1.10924	0.554621	+	0.832103i	$0.312863\pi$
$230$	0	0
$231$	−6.41579e10	−1.48251
$232$	9.79285e9	0.221929
$233$	2.82042e10	0.626920	0.313460	−	0.949601i	$-0.398512\pi$
$233$	2.82042e10	0.626920	0.313460	+	0.949601i	$0.398512\pi$
$234$	2.42475e10	0.528683
$235$	0	0
$236$	−2.01753e10	−0.423365
$237$	1.16295e11	2.39438
$238$	−1.04693e11	−2.11505
$239$	7.93923e9	0.157394	0.0786969	−	0.996899i	$-0.474924\pi$
$239$	7.93923e9	0.157394	0.0786969	+	0.996899i	$0.474924\pi$
$240$	0	0
$241$	−4.33069e10	−0.826953	−0.413476	−	0.910515i	$-0.635686\pi$
$241$	−4.33069e10	−0.826953	−0.413476	+	0.910515i	$0.635686\pi$
$242$	2.78471e10	0.521927
$243$	−3.98026e10	−0.732290
$244$	−2.35037e9	−0.0424505
$245$	0	0
$246$	−3.37504e10	−0.587585
$247$	−3.02273e9	−0.0516730
$248$	−3.54812e10	−0.595616
$249$	1.36922e11	2.25724
$250$	0	0
$251$	3.48447e10	0.554121	0.277061	−	0.960852i	$-0.410640\pi$
$251$	3.48447e10	0.554121	0.277061	+	0.960852i	$0.410640\pi$
$252$	−4.41900e10	−0.690274
$253$	1.57192e10	0.241206
$254$	1.25199e10	0.188733
$255$	0	0
$256$	−4.65097e10	−0.676806
$257$	−6.17149e10	−0.882452	−0.441226	−	0.897396i	$-0.645456\pi$
$257$	−6.17149e10	−0.882452	−0.441226	+	0.897396i	$0.645456\pi$
$258$	−1.89975e11	−2.66937
$259$	−1.01771e11	−1.40533
$260$	0	0
$261$	3.36646e10	0.449046
$262$	1.12116e11	1.46999
$263$	1.78558e10	0.230132	0.115066	−	0.993358i	$-0.463292\pi$
$263$	1.78558e10	0.230132	0.115066	+	0.993358i	$0.463292\pi$
$264$	−9.64745e10	−1.22235
$265$	0	0
$266$	−1.73818e10	−0.212876
$267$	−9.15930e10	−1.10296
$268$	−8.90696e9	−0.105469
$269$	−5.24399e10	−0.610628	−0.305314	−	0.952252i	$-0.598761\pi$
$269$	−5.24399e10	−0.610628	−0.305314	+	0.952252i	$0.598761\pi$
$270$	0	0
$271$	−5.03988e10	−0.567621	−0.283811	−	0.958880i	$-0.591599\pi$
$271$	−5.03988e10	−0.567621	−0.283811	+	0.958880i	$0.591599\pi$
$272$	−1.17212e11	−1.29841
$273$	5.95879e10	0.649271
$274$	8.81695e10	0.945020
$275$	0	0
$276$	1.57763e10	0.163650
$277$	1.58677e11	1.61941	0.809703	−	0.586840i	$-0.199628\pi$
$277$	1.58677e11	1.61941	0.809703	+	0.586840i	$0.199628\pi$
$278$	1.70219e11	1.70925
$279$	−1.21973e11	−1.20516
$280$	0	0
$281$	3.04536e10	0.291381	0.145690	−	0.989330i	$-0.453460\pi$
$281$	3.04536e10	0.291381	0.145690	+	0.989330i	$0.453460\pi$
$282$	6.44034e10	0.606440
$283$	−4.21589e10	−0.390706	−0.195353	−	0.980733i	$-0.562585\pi$
$283$	−4.21589e10	−0.390706	−0.195353	+	0.980733i	$0.562585\pi$
$284$	−3.27092e9	−0.0298358
$285$	0	0
$286$	1.73178e10	0.153054
$287$	−5.69204e10	−0.495221
$288$	−1.20008e11	−1.02788
$289$	2.87761e11	2.42656
$290$	0	0
$291$	2.50207e10	0.204541
$292$	2.99233e10	0.240872
$293$	−9.73493e10	−0.771665	−0.385832	−	0.922569i	$-0.626086\pi$
$293$	−9.73493e10	−0.771665	−0.385832	+	0.922569i	$0.626086\pi$
$294$	1.43351e11	1.11902
$295$	0	0
$296$	−1.53034e11	−1.15871
$297$	−1.80037e11	−1.34264
$298$	1.35781e11	0.997393
$299$	−1.45995e10	−0.105637
$300$	0	0
$301$	−3.20395e11	−2.24976
$302$	−7.90799e10	−0.547060
$303$	1.69362e11	1.15432
$304$	−1.94602e10	−0.130682
$305$	0	0
$306$	−5.41182e11	−3.52855
$307$	1.62669e11	1.04516	0.522578	−	0.852591i	$-0.324970\pi$
$307$	1.62669e11	1.04516	0.522578	+	0.852591i	$0.324970\pi$
$308$	−3.15609e10	−0.199835
$309$	−4.33996e10	−0.270815
$310$	0	0
$311$	1.80301e11	1.09289	0.546445	−	0.837495i	$-0.315981\pi$
$311$	1.80301e11	1.09289	0.546445	+	0.837495i	$0.315981\pi$
$312$	8.96025e10	0.535334
$313$	6.08927e10	0.358605	0.179302	−	0.983794i	$-0.442616\pi$
$313$	6.08927e10	0.358605	0.179302	+	0.983794i	$0.442616\pi$
$314$	1.85328e11	1.07586
$315$	0	0
$316$	5.72084e10	0.322751
$317$	−4.75152e10	−0.264281	−0.132140	−	0.991231i	$-0.542185\pi$
$317$	−4.75152e10	−0.264281	−0.132140	+	0.991231i	$0.542185\pi$
$318$	1.19950e11	0.657777
$319$	2.40436e10	0.129999
$320$	0	0
$321$	3.09802e11	1.62859
$322$	−8.39522e10	−0.435192
$323$	6.74646e10	0.344877
$324$	−7.62674e10	−0.384491
$325$	0	0
$326$	7.33777e10	0.359820
$327$	2.61704e11	1.26574
$328$	−8.55914e10	−0.408317
$329$	1.08617e11	0.511112
$330$	0	0
$331$	−8.96236e10	−0.410390	−0.205195	−	0.978721i	$-0.565783\pi$
$331$	−8.96236e10	−0.410390	−0.205195	+	0.978721i	$0.565783\pi$
$332$	6.73557e10	0.304265
$333$	−5.26081e11	−2.34452
$334$	−8.84544e10	−0.388920
$335$	0	0
$336$	3.83624e11	1.64202
$337$	−2.05747e11	−0.868957	−0.434478	−	0.900682i	$-0.643067\pi$
$337$	−2.05747e11	−0.868957	−0.434478	+	0.900682i	$0.643067\pi$
$338$	−1.60842e10	−0.0670309
$339$	−2.94293e11	−1.21027
$340$	0	0
$341$	−8.71142e10	−0.348894
$342$	−8.98504e10	−0.355143
$343$	−9.43587e10	−0.368094
$344$	−4.81780e11	−1.85496
$345$	0	0
$346$	−3.33791e11	−1.25208
$347$	−3.41311e11	−1.26377	−0.631884	−	0.775063i	$-0.717718\pi$
$347$	−3.41311e11	−1.26377	−0.631884	+	0.775063i	$0.717718\pi$
$348$	2.41310e10	0.0881999
$349$	−4.15352e11	−1.49866	−0.749328	−	0.662198i	$-0.769624\pi$
$349$	−4.15352e11	−1.49866	−0.749328	+	0.662198i	$0.769624\pi$
$350$	0	0
$351$	1.67213e11	0.588015
$352$	−8.57107e10	−0.297573
$353$	1.00300e11	0.343806	0.171903	−	0.985114i	$-0.445008\pi$
$353$	1.00300e11	0.343806	0.171903	+	0.985114i	$0.445008\pi$
$354$	8.08674e11	2.73690
$355$	0	0
$356$	−4.50569e10	−0.148675
$357$	−1.32995e12	−4.33338
$358$	−2.42777e11	−0.781149
$359$	−3.35856e11	−1.06716	−0.533578	−	0.845751i	$-0.679153\pi$
$359$	−3.35856e11	−1.06716	−0.533578	+	0.845751i	$0.679153\pi$
$360$	0	0
$361$	−3.11487e11	−0.965289
$362$	4.80613e11	1.47098
$363$	3.53750e11	1.06934
$364$	2.93128e10	0.0875187
$365$	0	0
$366$	9.42088e10	0.274427
$367$	−3.43252e11	−0.987679	−0.493839	−	0.869553i	$-0.664407\pi$
$367$	−3.43252e11	−0.987679	−0.493839	+	0.869553i	$0.664407\pi$
$368$	−9.39910e10	−0.267160
$369$	−2.94235e11	−0.826182
$370$	0	0
$371$	2.02297e11	0.554379
$372$	−8.74308e10	−0.236712
$373$	3.20544e11	0.857428	0.428714	−	0.903440i	$-0.358967\pi$
$373$	3.20544e11	0.857428	0.428714	+	0.903440i	$0.358967\pi$
$374$	−3.86517e11	−1.02152
$375$	0	0
$376$	1.63328e11	0.421420
$377$	−2.23309e10	−0.0569339
$378$	9.61533e11	2.42243
$379$	5.59129e11	1.39199	0.695994	−	0.718047i	$-0.254964\pi$
$379$	5.59129e11	1.39199	0.695994	+	0.718047i	$0.254964\pi$
$380$	0	0
$381$	1.59044e11	0.386683
$382$	1.71090e11	0.411092
$383$	1.14158e11	0.271089	0.135544	−	0.990771i	$-0.456722\pi$
$383$	1.14158e11	0.271089	0.135544	+	0.990771i	$0.456722\pi$
$384$	3.78938e11	0.889361
$385$	0	0
$386$	−4.60424e11	−1.05564
$387$	−1.65620e12	−3.75330
$388$	1.23083e10	0.0275712
$389$	−1.10883e11	−0.245522	−0.122761	−	0.992436i	$-0.539175\pi$
$389$	−1.10883e11	−0.245522	−0.122761	+	0.992436i	$0.539175\pi$
$390$	0	0
$391$	3.25847e11	0.705048
$392$	3.63539e11	0.777613
$393$	1.42425e12	3.01175
$394$	−5.17255e10	−0.108136
$395$	0	0
$396$	−1.63146e11	−0.333386
$397$	−2.31687e11	−0.468107	−0.234053	−	0.972224i	$-0.575199\pi$
$397$	−2.31687e11	−0.468107	−0.234053	+	0.972224i	$0.575199\pi$
$398$	−1.64992e11	−0.329601
$399$	−2.20806e11	−0.436147
$400$	0	0
$401$	5.44480e10	0.105156	0.0525778	−	0.998617i	$-0.483256\pi$
$401$	5.44480e10	0.105156	0.0525778	+	0.998617i	$0.483256\pi$
$402$	3.57013e11	0.681815
$403$	8.09089e10	0.152800
$404$	8.33137e10	0.155597
$405$	0	0
$406$	−1.28411e11	−0.234549
$407$	−3.75732e11	−0.678740
$408$	−1.99984e12	−3.57294
$409$	2.35793e11	0.416654	0.208327	−	0.978059i	$-0.433198\pi$
$409$	2.35793e11	0.416654	0.208327	+	0.978059i	$0.433198\pi$
$410$	0	0
$411$	1.12005e12	1.93619
$412$	−2.13494e10	−0.0365046
$413$	1.36384e12	2.30668
$414$	−4.33969e11	−0.726034
$415$	0	0
$416$	7.96055e10	0.130324
$417$	2.16235e12	3.50197
$418$	−6.41721e10	−0.102814
$419$	5.43639e11	0.861682	0.430841	−	0.902428i	$-0.358217\pi$
$419$	5.43639e11	0.861682	0.430841	+	0.902428i	$0.358217\pi$
$420$	0	0
$421$	2.70622e11	0.419849	0.209925	−	0.977718i	$-0.432678\pi$
$421$	2.70622e11	0.419849	0.209925	+	0.977718i	$0.432678\pi$
$422$	−7.22291e11	−1.10868
$423$	5.61467e11	0.852693
$424$	3.04195e11	0.457094
$425$	0	0
$426$	1.31107e11	0.192878
$427$	1.58884e11	0.231289
$428$	1.52399e11	0.219526
$429$	2.19994e11	0.313583
$430$	0	0
$431$	−1.07553e12	−1.50132	−0.750662	−	0.660687i	$-0.770265\pi$
$431$	−1.07553e12	−1.50132	−0.750662	+	0.660687i	$0.770265\pi$
$432$	1.07651e12	1.48711
$433$	2.63085e11	0.359667	0.179833	−	0.983697i	$-0.442444\pi$
$433$	2.63085e11	0.359667	0.179833	+	0.983697i	$0.442444\pi$
$434$	4.65254e11	0.629486
$435$	0	0
$436$	1.28739e11	0.170616
$437$	5.40992e10	0.0709618
$438$	−1.19940e12	−1.55715
$439$	−8.20045e11	−1.05377	−0.526887	−	0.849935i	$-0.676641\pi$
$439$	−8.20045e11	−1.05377	−0.526887	+	0.849935i	$0.676641\pi$
$440$	0	0
$441$	1.24973e12	1.57341
$442$	3.58985e11	0.447380
$443$	1.77977e10	0.0219557	0.0109779	−	0.999940i	$-0.496506\pi$
$443$	1.77977e10	0.0219557	0.0109779	+	0.999940i	$0.496506\pi$
$444$	−3.77098e11	−0.460501
$445$	0	0
$446$	1.22719e12	1.46860
$447$	1.72487e12	2.04349
$448$	1.24192e12	1.45661
$449$	1.15873e12	1.34547	0.672734	−	0.739885i	$-0.265120\pi$
$449$	1.15873e12	1.34547	0.672734	+	0.739885i	$0.265120\pi$
$450$	0	0
$451$	−2.10145e11	−0.239180
$452$	−1.44770e11	−0.163138
$453$	−1.00458e12	−1.12083
$454$	7.89751e11	0.872446
$455$	0	0
$456$	−3.32027e11	−0.359610
$457$	9.23583e11	0.990497	0.495249	−	0.868751i	$-0.335077\pi$
$457$	9.23583e11	0.990497	0.495249	+	0.868751i	$0.335077\pi$
$458$	−9.10207e11	−0.966597
$459$	−3.73204e12	−3.92455
$460$	0	0
$461$	6.32718e11	0.652464	0.326232	−	0.945290i	$-0.394221\pi$
$461$	6.32718e11	0.652464	0.326232	+	0.945290i	$0.394221\pi$
$462$	1.26504e12	1.29186
$463$	−2.14607e11	−0.217035	−0.108517	−	0.994095i	$-0.534610\pi$
$463$	−2.14607e11	−0.217035	−0.108517	+	0.994095i	$0.534610\pi$
$464$	−1.43766e11	−0.143987
$465$	0	0
$466$	−5.56119e11	−0.546300
$467$	−5.49922e11	−0.535026	−0.267513	−	0.963554i	$-0.586202\pi$
$467$	−5.49922e11	−0.535026	−0.267513	+	0.963554i	$0.586202\pi$
$468$	1.51525e11	0.146008
$469$	6.02106e11	0.574639
$470$	0	0
$471$	2.35428e12	2.20427
$472$	2.05081e12	1.90189
$473$	−1.18287e12	−1.08658
$474$	−2.29305e12	−2.08647
$475$	0	0
$476$	−6.54234e11	−0.584120
$477$	1.04572e12	0.924875
$478$	−1.56542e11	−0.137153
$479$	1.60843e12	1.39602	0.698010	−	0.716088i	$-0.254069\pi$
$479$	1.60843e12	1.39602	0.698010	+	0.716088i	$0.254069\pi$
$480$	0	0
$481$	3.48968e11	0.297258
$482$	8.53908e11	0.720609
$483$	−1.06647e12	−0.891635
$484$	1.74019e11	0.144142
$485$	0	0
$486$	7.84810e11	0.638119
$487$	1.40030e12	1.12808	0.564040	−	0.825747i	$-0.309246\pi$
$487$	1.40030e12	1.12808	0.564040	+	0.825747i	$0.309246\pi$
$488$	2.38915e11	0.190701
$489$	9.32141e11	0.737211
$490$	0	0
$491$	1.31274e12	1.01932	0.509661	−	0.860376i	$-0.329771\pi$
$491$	1.31274e12	1.01932	0.509661	+	0.860376i	$0.329771\pi$
$492$	−2.10909e11	−0.162275
$493$	4.98406e11	0.379990
$494$	5.96010e10	0.0450280
$495$	0	0
$496$	5.20888e11	0.386436
$497$	2.21113e11	0.162559
$498$	−2.69978e12	−1.96696
$499$	−3.50247e11	−0.252885	−0.126442	−	0.991974i	$-0.540356\pi$
$499$	−3.50247e11	−0.252885	−0.126442	+	0.991974i	$0.540356\pi$
$500$	0	0
$501$	−1.12366e12	−0.796833
$502$	−6.87053e11	−0.482863
$503$	−2.62962e12	−1.83163	−0.915815	−	0.401601i	$-0.868454\pi$
$503$	−2.62962e12	−1.83163	−0.915815	+	0.401601i	$0.868454\pi$
$504$	4.49189e12	3.10093
$505$	0	0
$506$	−3.09945e11	−0.210187
$507$	−2.04323e11	−0.137335
$508$	7.82379e10	0.0521231
$509$	4.07673e11	0.269204	0.134602	−	0.990900i	$-0.457024\pi$
$509$	4.07673e11	0.269204	0.134602	+	0.990900i	$0.457024\pi$
$510$	0	0
$511$	−2.02280e12	−1.31238
$512$	1.69164e12	1.08791
$513$	−6.19617e11	−0.394998
$514$	1.21687e12	0.768970
$515$	0	0
$516$	−1.18717e12	−0.737209
$517$	4.01005e11	0.246855
$518$	2.00669e12	1.22460
$519$	−4.24025e12	−2.56530
$520$	0	0
$521$	−1.90638e12	−1.13355	−0.566773	−	0.823874i	$-0.691808\pi$
$521$	−1.90638e12	−1.13355	−0.566773	+	0.823874i	$0.691808\pi$
$522$	−6.63785e11	−0.391300
$523$	6.84980e11	0.400332	0.200166	−	0.979762i	$-0.435852\pi$
$523$	6.84980e11	0.400332	0.200166	+	0.979762i	$0.435852\pi$
$524$	7.00624e11	0.405971
$525$	0	0
$526$	−3.52073e11	−0.200538
$527$	−1.80581e12	−1.01982
$528$	1.41631e12	0.793059
$529$	−1.53986e12	−0.854930
$530$	0	0
$531$	7.04999e12	3.84825
$532$	−1.08620e11	−0.0587906
$533$	1.95177e11	0.104750
$534$	1.80599e12	0.961126
$535$	0	0
$536$	9.05389e11	0.473798
$537$	−3.08407e12	−1.60044
$538$	1.03399e12	0.532103
$539$	8.92568e11	0.455503
$540$	0	0
$541$	−1.99962e12	−1.00360	−0.501798	−	0.864985i	$-0.667328\pi$
$541$	−1.99962e12	−1.00360	−0.501798	+	0.864985i	$0.667328\pi$
$542$	9.93743e11	0.494626
$543$	6.10538e12	3.01379
$544$	−1.77672e12	−0.869809
$545$	0	0
$546$	−1.17493e12	−0.565776
$547$	−2.19967e12	−1.05055	−0.525273	−	0.850933i	$-0.676037\pi$
$547$	−2.19967e12	−1.05055	−0.525273	+	0.850933i	$0.676037\pi$
$548$	5.50979e11	0.260989
$549$	8.21310e11	0.385861
$550$	0	0
$551$	8.27485e10	0.0382453
$552$	−1.60366e12	−0.735166
$553$	−3.86726e12	−1.75849
$554$	−3.12873e12	−1.41115
$555$	0	0
$556$	1.06371e12	0.472050
$557$	−2.10846e12	−0.928148	−0.464074	−	0.885797i	$-0.653613\pi$
$557$	−2.10846e12	−0.928148	−0.464074	+	0.885797i	$0.653613\pi$
$558$	2.40501e12	1.05018
$559$	1.09862e12	0.475875
$560$	0	0
$561$	−4.91005e12	−2.09292
$562$	−6.00472e11	−0.253910
$563$	−2.49136e12	−1.04508	−0.522540	−	0.852615i	$-0.675015\pi$
$563$	−2.49136e12	−1.04508	−0.522540	+	0.852615i	$0.675015\pi$
$564$	4.02462e11	0.167483
$565$	0	0
$566$	8.31272e11	0.340462
$567$	5.15564e12	2.09488
$568$	3.32488e11	0.134032
$569$	6.91496e11	0.276557	0.138278	−	0.990393i	$-0.455843\pi$
$569$	6.91496e11	0.276557	0.138278	+	0.990393i	$0.455843\pi$
$570$	0	0
$571$	−2.70238e11	−0.106386	−0.0531930	−	0.998584i	$-0.516940\pi$
$571$	−2.70238e11	−0.106386	−0.0531930	+	0.998584i	$0.516940\pi$
$572$	1.08220e11	0.0422695
$573$	2.17341e12	0.842259
$574$	1.12233e12	0.431537
$575$	0	0
$576$	6.41978e12	2.43007
$577$	3.66686e12	1.37722	0.688610	−	0.725132i	$-0.258221\pi$
$577$	3.66686e12	1.37722	0.688610	+	0.725132i	$0.258221\pi$
$578$	−5.67395e12	−2.11451
$579$	−5.84891e12	−2.16283
$580$	0	0
$581$	−4.55321e12	−1.65777
$582$	−4.93347e11	−0.178238
$583$	7.46864e11	0.267752
$584$	−3.04169e12	−1.08207
$585$	0	0
$586$	1.91949e12	0.672431
$587$	−1.16732e12	−0.405806	−0.202903	−	0.979199i	$-0.565038\pi$
$587$	−1.16732e12	−0.405806	−0.202903	+	0.979199i	$0.565038\pi$
$588$	8.95811e11	0.309043
$589$	−2.99812e11	−0.102643
$590$	0	0
$591$	−6.57085e11	−0.221553
$592$	2.24664e12	0.751773
$593$	−3.14463e12	−1.04430	−0.522148	−	0.852855i	$-0.674869\pi$
$593$	−3.14463e12	−1.04430	−0.522148	+	0.852855i	$0.674869\pi$
$594$	3.54990e12	1.16998
$595$	0	0
$596$	8.48508e11	0.275453
$597$	−2.09594e12	−0.675297
$598$	2.87867e11	0.0920527
$599$	2.09251e12	0.664120	0.332060	−	0.943258i	$-0.392256\pi$
$599$	2.09251e12	0.664120	0.332060	+	0.943258i	$0.392256\pi$
$600$	0	0
$601$	4.34608e12	1.35882	0.679410	−	0.733758i	$-0.262236\pi$
$601$	4.34608e12	1.35882	0.679410	+	0.733758i	$0.262236\pi$
$602$	6.31742e12	1.96045
$603$	3.11243e12	0.958675
$604$	−4.94177e11	−0.151083
$605$	0	0
$606$	−3.33942e12	−1.00588
$607$	−1.73690e12	−0.519310	−0.259655	−	0.965701i	$-0.583609\pi$
$607$	−1.73690e12	−0.519310	−0.259655	+	0.965701i	$0.583609\pi$
$608$	−2.94982e11	−0.0875447
$609$	−1.63124e12	−0.480552
$610$	0	0
$611$	−3.72441e11	−0.108112
$612$	−3.38189e12	−0.974492
$613$	−4.02259e12	−1.15062	−0.575312	−	0.817934i	$-0.695119\pi$
$613$	−4.02259e12	−1.15062	−0.575312	+	0.817934i	$0.695119\pi$
$614$	−3.20744e12	−0.910752
$615$	0	0
$616$	3.20815e12	0.897722
$617$	5.03083e12	1.39752	0.698758	−	0.715358i	$-0.253737\pi$
$617$	5.03083e12	1.39752	0.698758	+	0.715358i	$0.253737\pi$
$618$	8.55736e11	0.235989
$619$	−4.77626e12	−1.30761	−0.653807	−	0.756661i	$-0.726829\pi$
$619$	−4.77626e12	−1.30761	−0.653807	+	0.756661i	$0.726829\pi$
$620$	0	0
$621$	−2.99269e12	−0.807513
$622$	−3.55510e12	−0.952348
$623$	3.04582e12	0.810044
$624$	−1.31542e12	−0.347324
$625$	0	0
$626$	−1.20066e12	−0.312489
$627$	−8.15198e11	−0.210649
$628$	1.15813e12	0.297125
$629$	−7.78864e12	−1.98396
$630$	0	0
$631$	−3.04417e12	−0.764428	−0.382214	−	0.924074i	$-0.624838\pi$
$631$	−3.04417e12	−0.764428	−0.382214	+	0.924074i	$0.624838\pi$
$632$	−5.81521e12	−1.44990
$633$	−9.17549e12	−2.27150
$634$	9.36884e11	0.230295
$635$	0	0
$636$	7.49579e11	0.181660
$637$	−8.28989e11	−0.199490
$638$	−4.74081e11	−0.113282
$639$	1.14298e12	0.271198
$640$	0	0
$641$	−1.53417e12	−0.358932	−0.179466	−	0.983764i	$-0.557437\pi$
$641$	−1.53417e12	−0.358932	−0.179466	+	0.983764i	$0.557437\pi$
$642$	−6.10854e12	−1.41915
$643$	−3.17074e12	−0.731494	−0.365747	−	0.930714i	$-0.619186\pi$
$643$	−3.17074e12	−0.731494	−0.365747	+	0.930714i	$0.619186\pi$
$644$	−5.24624e11	−0.120188
$645$	0	0
$646$	−1.33024e12	−0.300527
$647$	6.75140e12	1.51469	0.757347	−	0.653013i	$-0.226495\pi$
$647$	6.75140e12	1.51469	0.757347	+	0.653013i	$0.226495\pi$
$648$	7.75255e12	1.72726
$649$	5.03517e12	1.11407
$650$	0	0
$651$	5.91027e12	1.28971
$652$	4.58544e11	0.0993726
$653$	3.96591e12	0.853559	0.426780	−	0.904356i	$-0.359648\pi$
$653$	3.96591e12	0.853559	0.426780	+	0.904356i	$0.359648\pi$
$654$	−5.16016e12	−1.10297
$655$	0	0
$656$	1.25654e12	0.264916
$657$	−1.04563e13	−2.18945
$658$	−2.14166e12	−0.445384
$659$	−1.08932e12	−0.224993	−0.112497	−	0.993652i	$-0.535885\pi$
$659$	−1.08932e12	−0.224993	−0.112497	+	0.993652i	$0.535885\pi$
$660$	0	0
$661$	−9.01775e12	−1.83735	−0.918674	−	0.395017i	$-0.870739\pi$
$661$	−9.01775e12	−1.83735	−0.918674	+	0.395017i	$0.870739\pi$
$662$	1.76716e12	0.357615
$663$	4.56030e12	0.916606
$664$	−6.84667e12	−1.36686
$665$	0	0
$666$	1.03730e13	2.04302
$667$	3.99667e11	0.0781865
$668$	−5.52759e11	−0.107409
$669$	1.55894e13	3.00893
$670$	0	0
$671$	5.86587e11	0.111707
$672$	5.81506e12	1.10000
$673$	−6.77812e12	−1.27362	−0.636812	−	0.771019i	$-0.719747\pi$
$673$	−6.77812e12	−1.27362	−0.636812	+	0.771019i	$0.719747\pi$
$674$	4.05683e12	0.757211
$675$	0	0
$676$	−1.00512e11	−0.0185122
$677$	9.77011e12	1.78752	0.893759	−	0.448548i	$-0.148059\pi$
$677$	9.77011e12	1.78752	0.893759	+	0.448548i	$0.148059\pi$
$678$	5.80274e12	1.05463
$679$	−8.32035e11	−0.150220
$680$	0	0
$681$	1.00325e13	1.78750
$682$	1.71768e12	0.304027
$683$	−7.99180e12	−1.40524	−0.702621	−	0.711564i	$-0.747987\pi$
$683$	−7.99180e12	−1.40524	−0.702621	+	0.711564i	$0.747987\pi$
$684$	−5.61483e11	−0.0980809
$685$	0	0
$686$	1.86053e12	0.320758
$687$	−1.15626e13	−1.98040
$688$	7.07285e12	1.20350
$689$	−6.93664e11	−0.117264
$690$	0	0
$691$	−7.13265e12	−1.19014	−0.595072	−	0.803672i	$-0.702877\pi$
$691$	−7.13265e12	−1.19014	−0.595072	+	0.803672i	$0.702877\pi$
$692$	−2.08589e12	−0.345791
$693$	1.10286e13	1.81643
$694$	6.72982e12	1.10125
$695$	0	0
$696$	−2.45290e12	−0.396222
$697$	−4.35616e12	−0.699127
$698$	8.18974e12	1.30593
$699$	−7.06456e12	−1.11928
$700$	0	0
$701$	1.19764e13	1.87325	0.936626	−	0.350330i	$-0.113931\pi$
$701$	1.19764e13	1.87325	0.936626	+	0.350330i	$0.113931\pi$
$702$	−3.29704e12	−0.512398
$703$	−1.29312e12	−0.199683
$704$	4.58507e12	0.703507
$705$	0	0
$706$	−1.97767e12	−0.299594
$707$	−5.63196e12	−0.847759
$708$	5.05347e12	0.755858
$709$	−6.13692e12	−0.912099	−0.456050	−	0.889954i	$-0.650736\pi$
$709$	−6.13692e12	−0.912099	−0.456050	+	0.889954i	$0.650736\pi$
$710$	0	0
$711$	−1.99908e13	−2.93371
$712$	4.58002e12	0.667893
$713$	−1.44806e12	−0.209838
$714$	2.62233e13	3.77612
$715$	0	0
$716$	−1.51713e12	−0.215733
$717$	−1.98861e12	−0.281004
$718$	6.62226e12	0.929922
$719$	4.74258e12	0.661812	0.330906	−	0.943664i	$-0.392646\pi$
$719$	4.74258e12	0.661812	0.330906	+	0.943664i	$0.392646\pi$
$720$	0	0
$721$	1.44321e12	0.198893
$722$	6.14177e12	0.841155
$723$	1.08475e13	1.47641
$724$	3.00339e12	0.406245
$725$	0	0
$726$	−6.97510e12	−0.931827
$727$	9.67795e12	1.28493	0.642464	−	0.766316i	$-0.277912\pi$
$727$	9.67795e12	1.28493	0.642464	+	0.766316i	$0.277912\pi$
$728$	−2.97963e12	−0.393162
$729$	−2.21347e12	−0.290268
$730$	0	0
$731$	−2.45201e13	−3.17610
$732$	5.88719e11	0.0757894
$733$	−1.50341e13	−1.92357	−0.961787	−	0.273798i	$-0.911720\pi$
$733$	−1.50341e13	−1.92357	−0.961787	+	0.273798i	$0.911720\pi$
$734$	6.76810e12	0.860666
$735$	0	0
$736$	−1.42474e12	−0.178972
$737$	2.22293e12	0.277537
$738$	5.80160e12	0.719937
$739$	−2.14842e12	−0.264983	−0.132492	−	0.991184i	$-0.542298\pi$
$739$	−2.14842e12	−0.264983	−0.132492	+	0.991184i	$0.542298\pi$
$740$	0	0
$741$	7.57131e11	0.0922548
$742$	−3.98881e12	−0.483087
$743$	−5.22310e12	−0.628751	−0.314376	−	0.949299i	$-0.601795\pi$
$743$	−5.22310e12	−0.628751	−0.314376	+	0.949299i	$0.601795\pi$
$744$	8.88730e12	1.06339
$745$	0	0
$746$	−6.32035e12	−0.747165
$747$	−2.35366e13	−2.76567
$748$	−2.41538e12	−0.282116
$749$	−1.03021e13	−1.19607
$750$	0	0
$751$	1.65523e13	1.89880	0.949399	−	0.314071i	$-0.101693\pi$
$751$	1.65523e13	1.89880	0.949399	+	0.314071i	$0.101693\pi$
$752$	−2.39776e12	−0.273417
$753$	−8.72786e12	−0.989305
$754$	4.40312e11	0.0496123
$755$	0	0
$756$	6.00870e12	0.669010
$757$	−1.59809e13	−1.76877	−0.884384	−	0.466761i	$-0.845421\pi$
$757$	−1.59809e13	−1.76877	−0.884384	+	0.466761i	$0.845421\pi$
$758$	−1.10247e13	−1.21298
$759$	−3.93733e12	−0.430639
$760$	0	0
$761$	3.31655e12	0.358473	0.179236	−	0.983806i	$-0.442637\pi$
$761$	3.31655e12	0.358473	0.179236	+	0.983806i	$0.442637\pi$
$762$	−3.13597e12	−0.336957
$763$	−8.70266e12	−0.929591
$764$	1.06916e12	0.113533
$765$	0	0
$766$	−2.25092e12	−0.236227
$767$	−4.67651e12	−0.487914
$768$	1.16497e13	1.20834
$769$	−2.26842e12	−0.233913	−0.116956	−	0.993137i	$-0.537314\pi$
$769$	−2.26842e12	−0.233913	−0.116956	+	0.993137i	$0.537314\pi$
$770$	0	0
$771$	1.54583e13	1.57549
$772$	−2.87723e12	−0.291539
$773$	−1.45998e13	−1.47075	−0.735375	−	0.677661i	$-0.762994\pi$
$773$	−1.45998e13	−1.47075	−0.735375	+	0.677661i	$0.762994\pi$
$774$	3.26563e13	3.27064
$775$	0	0
$776$	−1.25113e12	−0.123859
$777$	2.54916e13	2.50901
$778$	2.18634e12	0.213949
$779$	−7.23237e11	−0.0703659
$780$	0	0
$781$	8.16330e11	0.0785120
$782$	−6.42492e12	−0.614380
$783$	−4.57752e12	−0.435214
$784$	−5.33700e12	−0.504516
$785$	0	0
$786$	−2.80828e13	−2.62445
$787$	1.26923e13	1.17938	0.589692	−	0.807628i	$-0.299249\pi$
$787$	1.26923e13	1.17938	0.589692	+	0.807628i	$0.299249\pi$
$788$	−3.23237e11	−0.0298643
$789$	−4.47249e12	−0.410869
$790$	0	0
$791$	9.78638e12	0.888849
$792$	1.65837e13	1.49768
$793$	−5.44804e11	−0.0489228
$794$	4.56831e12	0.407909
$795$	0	0
$796$	−1.03105e12	−0.0910270
$797$	1.22392e13	1.07446	0.537230	−	0.843436i	$-0.319471\pi$
$797$	1.22392e13	1.07446	0.537230	+	0.843436i	$0.319471\pi$
$798$	4.35376e12	0.380059
$799$	8.31254e12	0.721561
$800$	0	0
$801$	1.57446e13	1.35140
$802$	−1.07358e12	−0.0916328
$803$	−7.46801e12	−0.633847
$804$	2.23101e12	0.188299
$805$	0	0
$806$	−1.59533e12	−0.133150
$807$	1.31351e13	1.09019
$808$	−8.46880e12	−0.698990
$809$	−4.89425e12	−0.401714	−0.200857	−	0.979621i	$-0.564373\pi$
$809$	−4.89425e12	−0.401714	−0.200857	+	0.979621i	$0.564373\pi$
$810$	0	0
$811$	−3.11178e12	−0.252590	−0.126295	−	0.991993i	$-0.540309\pi$
$811$	−3.11178e12	−0.252590	−0.126295	+	0.991993i	$0.540309\pi$
$812$	−8.02449e11	−0.0647761
$813$	1.26238e13	1.01341
$814$	7.40853e12	0.591456
$815$	0	0
$816$	2.93590e13	2.31812
$817$	−4.07098e12	−0.319669
$818$	−4.64926e12	−0.363073
$819$	−1.02430e13	−0.795517
$820$	0	0
$821$	3.48502e12	0.267708	0.133854	−	0.991001i	$-0.457265\pi$
$821$	3.48502e12	0.267708	0.133854	+	0.991001i	$0.457265\pi$
$822$	−2.20846e13	−1.68720
$823$	4.38954e12	0.333518	0.166759	−	0.985998i	$-0.446670\pi$
$823$	4.38954e12	0.333518	0.166759	+	0.985998i	$0.446670\pi$
$824$	2.17016e12	0.163990
$825$	0	0
$826$	−2.68916e13	−2.01004
$827$	1.21660e13	0.904424	0.452212	−	0.891910i	$-0.350635\pi$
$827$	1.21660e13	0.904424	0.452212	+	0.891910i	$0.350635\pi$
$828$	−2.71191e12	−0.200511
$829$	−1.35524e12	−0.0996600	−0.0498300	−	0.998758i	$-0.515868\pi$
$829$	−1.35524e12	−0.0996600	−0.0498300	+	0.998758i	$0.515868\pi$
$830$	0	0
$831$	−3.97453e13	−2.89122
$832$	−4.25847e12	−0.308105
$833$	1.85023e13	1.33144
$834$	−4.26362e13	−3.05163
$835$	0	0
$836$	−4.01017e11	−0.0283945
$837$	1.65852e13	1.16803
$838$	−1.07192e13	−0.750872
$839$	−1.12215e13	−0.781847	−0.390924	−	0.920423i	$-0.627844\pi$
$839$	−1.12215e13	−0.781847	−0.390924	+	0.920423i	$0.627844\pi$
$840$	0	0
$841$	−1.38958e13	−0.957861
$842$	−5.33601e12	−0.365858
$843$	−7.62799e12	−0.520219
$844$	−4.51366e12	−0.306188
$845$	0	0
$846$	−1.10708e13	−0.743038
$847$	−1.17636e13	−0.785351
$848$	−4.46578e12	−0.296563
$849$	1.05599e13	0.697551
$850$	0	0
$851$	−6.24564e12	−0.408220
$852$	8.19297e11	0.0532676
$853$	−7.91778e11	−0.0512074	−0.0256037	−	0.999672i	$-0.508151\pi$
$853$	−7.91778e11	−0.0512074	−0.0256037	+	0.999672i	$0.508151\pi$
$854$	−3.13281e12	−0.201546
$855$	0	0
$856$	−1.54913e13	−0.986180
$857$	−1.76782e13	−1.11950	−0.559751	−	0.828661i	$-0.689103\pi$
$857$	−1.76782e13	−1.11950	−0.559751	+	0.828661i	$0.689103\pi$
$858$	−4.33774e12	−0.273257
$859$	4.03561e12	0.252895	0.126448	−	0.991973i	$-0.459642\pi$
$859$	4.03561e12	0.252895	0.126448	+	0.991973i	$0.459642\pi$
$860$	0	0
$861$	1.42573e13	0.884147
$862$	2.12068e13	1.30826
$863$	7.74540e11	0.0475330	0.0237665	−	0.999718i	$-0.492434\pi$
$863$	7.74540e11	0.0475330	0.0237665	+	0.999718i	$0.492434\pi$
$864$	1.63180e13	0.996219
$865$	0	0
$866$	−5.18739e12	−0.313414
$867$	−7.20780e13	−4.33228
$868$	2.90741e12	0.173847
$869$	−1.42776e13	−0.849311
$870$	0	0
$871$	−2.06459e12	−0.121549
$872$	−1.30862e13	−0.766461
$873$	−4.30099e12	−0.250613
$874$	−1.06671e12	−0.0618363
$875$	0	0
$876$	−7.49515e12	−0.430043
$877$	2.57530e13	1.47004	0.735020	−	0.678046i	$-0.237173\pi$
$877$	2.57530e13	1.47004	0.735020	+	0.678046i	$0.237173\pi$
$878$	1.61693e13	0.918261
$879$	2.43839e13	1.37770
$880$	0	0
$881$	1.93336e12	0.108124	0.0540620	−	0.998538i	$-0.482783\pi$
$881$	1.93336e12	0.108124	0.0540620	+	0.998538i	$0.482783\pi$
$882$	−2.46416e13	−1.37107
$883$	−2.94334e13	−1.62936	−0.814681	−	0.579910i	$-0.803088\pi$
$883$	−2.94334e13	−1.62936	−0.814681	+	0.579910i	$0.803088\pi$
$884$	2.24333e12	0.123554
$885$	0	0
$886$	−3.50928e11	−0.0191323
$887$	−4.07138e12	−0.220844	−0.110422	−	0.993885i	$-0.535220\pi$
$887$	−4.07138e12	−0.220844	−0.110422	+	0.993885i	$0.535220\pi$
$888$	3.83318e13	2.06872
$889$	−5.28884e12	−0.283990
$890$	0	0
$891$	1.90342e13	1.01178
$892$	7.66881e12	0.405589
$893$	1.38010e12	0.0726238
$894$	−3.40103e13	−1.78070
$895$	0	0
$896$	−1.26012e13	−0.653168
$897$	3.65687e12	0.188601
$898$	−2.28473e13	−1.17244
$899$	−2.21491e12	−0.113094
$900$	0	0
$901$	1.54819e13	0.782643
$902$	4.14356e12	0.208422
$903$	8.02523e13	4.01664
$904$	1.47158e13	0.732869
$905$	0	0
$906$	1.98078e13	0.976698
$907$	5.11710e12	0.251068	0.125534	−	0.992089i	$-0.459936\pi$
$907$	5.11710e12	0.251068	0.125534	+	0.992089i	$0.459936\pi$
$908$	4.93522e12	0.240946
$909$	−2.91130e13	−1.41432
$910$	0	0
$911$	−1.65675e13	−0.796937	−0.398468	−	0.917182i	$-0.630458\pi$
$911$	−1.65675e13	−0.796937	−0.398468	+	0.917182i	$0.630458\pi$
$912$	4.87438e12	0.233315
$913$	−1.68101e13	−0.800665
$914$	−1.82108e13	−0.863121
$915$	0	0
$916$	−5.68796e12	−0.266948
$917$	−4.73618e13	−2.21191
$918$	7.35868e13	3.41986
$919$	2.46210e13	1.13864	0.569319	−	0.822117i	$-0.307207\pi$
$919$	2.46210e13	1.13864	0.569319	+	0.822117i	$0.307207\pi$
$920$	0	0
$921$	−4.07451e13	−1.86598
$922$	−1.24757e13	−0.568558
$923$	−7.58182e11	−0.0343848
$924$	7.90534e12	0.356777
$925$	0	0
$926$	4.23153e12	0.189125
$927$	7.46028e12	0.331815
$928$	−2.17923e12	−0.0964577
$929$	2.10967e13	0.929272	0.464636	−	0.885502i	$-0.346185\pi$
$929$	2.10967e13	0.929272	0.464636	+	0.885502i	$0.346185\pi$
$930$	0	0
$931$	3.07186e12	0.134007
$932$	−3.47524e12	−0.150873
$933$	−4.51616e13	−1.95120
$934$	1.08431e13	0.466223
$935$	0	0
$936$	−1.54024e13	−0.655915
$937$	3.29230e13	1.39531	0.697656	−	0.716433i	$-0.254226\pi$
$937$	3.29230e13	1.39531	0.697656	+	0.716433i	$0.254226\pi$
$938$	−1.18721e13	−0.500742
$939$	−1.52523e13	−0.640238
$940$	0	0
$941$	3.85496e13	1.60275	0.801376	−	0.598161i	$-0.204102\pi$
$941$	3.85496e13	1.60275	0.801376	+	0.598161i	$0.204102\pi$
$942$	−4.64208e13	−1.92080
$943$	−3.49316e12	−0.143852
$944$	−3.01072e13	−1.23395
$945$	0	0
$946$	2.33234e13	0.946852
$947$	−1.22394e13	−0.494521	−0.247261	−	0.968949i	$-0.579530\pi$
$947$	−1.22394e13	−0.494521	−0.247261	+	0.968949i	$0.579530\pi$
$948$	−1.43295e13	−0.576227
$949$	6.93605e12	0.277597
$950$	0	0
$951$	1.19015e13	0.471836
$952$	6.65026e13	2.62405
$953$	−3.26425e13	−1.28194	−0.640968	−	0.767568i	$-0.721467\pi$
$953$	−3.26425e13	−1.28194	−0.640968	+	0.767568i	$0.721467\pi$
$954$	−2.06191e13	−0.805939
$955$	0	0
$956$	−9.78247e11	−0.0378781
$957$	−6.02241e12	−0.232095
$958$	−3.17143e13	−1.21649
$959$	−3.72459e13	−1.42198
$960$	0	0
$961$	−1.84146e13	−0.696478
$962$	−6.88081e12	−0.259031
$963$	−5.32540e13	−1.99542
$964$	5.33614e12	0.199013
$965$	0	0
$966$	2.10282e13	0.776973
$967$	1.28552e13	0.472780	0.236390	−	0.971658i	$-0.424036\pi$
$967$	1.28552e13	0.472780	0.236390	+	0.971658i	$0.424036\pi$
$968$	−1.76889e13	−0.647533
$969$	−1.68984e13	−0.615729
$970$	0	0
$971$	−4.30846e13	−1.55538	−0.777689	−	0.628650i	$-0.783608\pi$
$971$	−4.30846e13	−1.55538	−0.777689	+	0.628650i	$0.783608\pi$
$972$	4.90435e12	0.176231
$973$	−7.19064e13	−2.57193
$974$	−2.76105e13	−0.983012
$975$	0	0
$976$	−3.50743e12	−0.123727
$977$	−3.58870e13	−1.26012	−0.630059	−	0.776547i	$-0.716969\pi$
$977$	−3.58870e13	−1.26012	−0.630059	+	0.776547i	$0.716969\pi$
$978$	−1.83796e13	−0.642407
$979$	1.12449e13	0.391233
$980$	0	0
$981$	−4.49861e13	−1.55084
$982$	−2.58840e13	−0.888239
$983$	−4.49637e12	−0.153593	−0.0767964	−	0.997047i	$-0.524469\pi$
$983$	−4.49637e12	−0.153593	−0.0767964	+	0.997047i	$0.524469\pi$
$984$	2.14388e13	0.728992
$985$	0	0
$986$	−9.82735e12	−0.331124
$987$	−2.72062e13	−0.912518
$988$	3.72452e11	0.0124355
$989$	−1.96624e13	−0.653513
$990$	0	0
$991$	1.56221e13	0.514526	0.257263	−	0.966341i	$-0.417179\pi$
$991$	1.56221e13	0.514526	0.257263	+	0.966341i	$0.417179\pi$
$992$	7.89573e12	0.258875
$993$	2.24488e13	0.732693
$994$	−4.35981e12	−0.141654
$995$	0	0
$996$	−1.68712e13	−0.543223
$997$	3.76783e13	1.20771	0.603856	−	0.797094i	$-0.293630\pi$
$997$	3.76783e13	1.20771	0.603856	+	0.797094i	$0.293630\pi$
$998$	6.90603e12	0.220364
$999$	7.15335e13	2.27230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.b.1.2		5
5.4	even	2		13.10.a.b.1.4	✓	5
15.14	odd	2		117.10.a.e.1.2		5
20.19	odd	2		208.10.a.h.1.1		5
65.64	even	2		169.10.a.b.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.4	✓	5	5.4	even	2
117.10.a.e.1.2		5	15.14	odd	2
169.10.a.b.1.2		5	65.64	even	2
208.10.a.h.1.1		5	20.19	odd	2
325.10.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-19.7176 q^{2} -250.479 q^{3} -123.217 q^{4} +4938.84 q^{6} +8329.39 q^{7} +12524.9 q^{8} +43056.6 q^{9} +O(q^{10})\)	\(q-19.7176 q^{2} -250.479 q^{3} -123.217 q^{4} +4938.84 q^{6} +8329.39 q^{7} +12524.9 q^{8} +43056.6 q^{9} +30751.5 q^{11} +30863.2 q^{12} -28561.0 q^{13} -164236. q^{14} -183875. q^{16} +637455. q^{17} -848973. q^{18} +105834. q^{19} -2.08634e6 q^{21} -606345. q^{22} +511169. q^{23} -3.13723e6 q^{24} +563154. q^{26} -5.85460e6 q^{27} -1.02632e6 q^{28} +781868. q^{29} -2.83285e6 q^{31} -2.78721e6 q^{32} -7.70259e6 q^{33} -1.25691e7 q^{34} -5.30530e6 q^{36} -1.22183e7 q^{37} -2.08680e6 q^{38} +7.15392e6 q^{39} -6.83367e6 q^{41} +4.11375e7 q^{42} -3.84656e7 q^{43} -3.78910e6 q^{44} -1.00790e7 q^{46} +1.30402e7 q^{47} +4.60567e7 q^{48} +2.90252e7 q^{49} -1.59669e8 q^{51} +3.51920e6 q^{52} +2.42871e7 q^{53} +1.15439e8 q^{54} +1.04325e8 q^{56} -2.65092e7 q^{57} -1.54166e7 q^{58} +1.63738e8 q^{59} +1.90751e7 q^{61} +5.58569e7 q^{62} +3.58636e8 q^{63} +1.49101e8 q^{64} +1.51876e8 q^{66} +7.22869e7 q^{67} -7.85452e7 q^{68} -1.28037e8 q^{69} +2.65461e7 q^{71} +5.39282e8 q^{72} -2.42850e8 q^{73} +2.40916e8 q^{74} -1.30406e7 q^{76} +2.56141e8 q^{77} -1.41058e8 q^{78} -4.64290e8 q^{79} +6.18969e8 q^{81} +1.34744e8 q^{82} -5.46643e8 q^{83} +2.57072e8 q^{84} +7.58449e8 q^{86} -1.95841e8 q^{87} +3.85160e8 q^{88} +3.65672e8 q^{89} -2.37896e8 q^{91} -6.29847e7 q^{92} +7.09568e8 q^{93} -2.57121e8 q^{94} +6.98137e8 q^{96} -9.98914e7 q^{97} -5.72307e8 q^{98} +1.32405e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} - 161 q^{3} + 361 q^{4} + 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9}+O(q^{10}) \) 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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