LMFDB - Embedded newform 325.10.a.b.1.5

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			1.5
Root			$-27.7188$ 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)

$f(q)$	$=$	$q+24.7188 q^{2} -194.269 q^{3} +99.0182 q^{4} -4802.09 q^{6} -5359.02 q^{7} -10208.4 q^{8} +18057.4 q^{9} +O(q^{10})$	\(q+24.7188 q^{2} -194.269 q^{3} +99.0182 q^{4} -4802.09 q^{6} -5359.02 q^{7} -10208.4 q^{8} +18057.4 q^{9} +79284.0 q^{11} -19236.2 q^{12} -28561.0 q^{13} -132468. q^{14} -303037. q^{16} -452068. q^{17} +446357. q^{18} +212533. q^{19} +1.04109e6 q^{21} +1.95980e6 q^{22} +759566. q^{23} +1.98318e6 q^{24} -705993. q^{26} +315803. q^{27} -530640. q^{28} -900101. q^{29} +2.27141e6 q^{31} -2.26400e6 q^{32} -1.54024e7 q^{33} -1.11746e7 q^{34} +1.78801e6 q^{36} +4.70433e6 q^{37} +5.25355e6 q^{38} +5.54851e6 q^{39} +3.39775e7 q^{41} +2.57345e7 q^{42} +2.33244e7 q^{43} +7.85057e6 q^{44} +1.87755e7 q^{46} +5.14121e7 q^{47} +5.88706e7 q^{48} -1.16346e7 q^{49} +8.78228e7 q^{51} -2.82806e6 q^{52} -1.01005e8 q^{53} +7.80627e6 q^{54} +5.47070e7 q^{56} -4.12885e7 q^{57} -2.22494e7 q^{58} +1.32234e8 q^{59} -1.23648e8 q^{61} +5.61465e7 q^{62} -9.67699e7 q^{63} +9.91916e7 q^{64} -3.80729e8 q^{66} +2.15282e8 q^{67} -4.47630e7 q^{68} -1.47560e8 q^{69} -2.06198e8 q^{71} -1.84337e8 q^{72} -3.44444e8 q^{73} +1.16285e8 q^{74} +2.10446e7 q^{76} -4.24884e8 q^{77} +1.37153e8 q^{78} +5.03324e7 q^{79} -4.16775e8 q^{81} +8.39883e8 q^{82} -8.20266e7 q^{83} +1.03087e8 q^{84} +5.76552e8 q^{86} +1.74862e8 q^{87} -8.09364e8 q^{88} -6.17891e8 q^{89} +1.53059e8 q^{91} +7.52109e7 q^{92} -4.41265e8 q^{93} +1.27084e9 q^{94} +4.39824e8 q^{96} +9.91253e8 q^{97} -2.87592e8 q^{98} +1.43166e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	24.7188	1.09243	0.546213	−	0.837646i	$-0.316069\pi$
$2$	24.7188	1.09243	0.546213	+	0.837646i	$0.316069\pi$
$3$	−194.269	−1.38471	−0.692353	−	0.721559i	$-0.743426\pi$
$3$	−194.269	−1.38471	−0.692353	+	0.721559i	$0.743426\pi$
$4$	99.0182	0.193395
$5$	0	0
$5$	0	0
$6$	−4802.09	−1.51269
$7$	−5359.02	−0.843614	−0.421807	−	0.906686i	$-0.638604\pi$
$7$	−5359.02	−0.843614	−0.421807	+	0.906686i	$0.638604\pi$
$8$	−10208.4	−0.881156
$9$	18057.4	0.917411
$10$	0	0
$11$	79284.0	1.63275	0.816373	−	0.577525i	$-0.195981\pi$
$11$	79284.0	1.63275	0.816373	+	0.577525i	$0.195981\pi$
$12$	−19236.2	−0.267795
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−132468.	−0.921586
$15$	0	0
$16$	−303037.	−1.15599
$17$	−452068.	−1.31276	−0.656378	−	0.754432i	$-0.727912\pi$
$17$	−452068.	−1.31276	−0.656378	+	0.754432i	$0.727912\pi$
$18$	446357.	1.00220
$19$	212533.	0.374141	0.187070	−	0.982347i	$-0.440101\pi$
$19$	212533.	0.374141	0.187070	+	0.982347i	$0.440101\pi$
$20$	0	0
$21$	1.04109e6	1.16816
$22$	1.95980e6	1.78365
$23$	759566.	0.565966	0.282983	−	0.959125i	$-0.408676\pi$
$23$	759566.	0.565966	0.282983	+	0.959125i	$0.408676\pi$
$24$	1.98318e6	1.22014
$25$	0	0
$26$	−705993.	−0.302985
$27$	315803.	0.114361
$28$	−530640.	−0.163151
$29$	−900101.	−0.236320	−0.118160	−	0.992995i	$-0.537700\pi$
$29$	−900101.	−0.236320	−0.118160	+	0.992995i	$0.537700\pi$
$30$	0	0
$31$	2.27141e6	0.441742	0.220871	−	0.975303i	$-0.429110\pi$
$31$	2.27141e6	0.441742	0.220871	+	0.975303i	$0.429110\pi$
$32$	−2.26400e6	−0.381681
$33$	−1.54024e7	−2.26087
$34$	−1.11746e7	−1.43409
$35$	0	0
$36$	1.78801e6	0.177423
$37$	4.70433e6	0.412658	0.206329	−	0.978483i	$-0.433848\pi$
$37$	4.70433e6	0.412658	0.206329	+	0.978483i	$0.433848\pi$
$38$	5.25355e6	0.408721
$39$	5.54851e6	0.384048
$40$	0	0
$41$	3.39775e7	1.87786	0.938932	−	0.344102i	$-0.111817\pi$
$41$	3.39775e7	1.87786	0.938932	+	0.344102i	$0.111817\pi$
$42$	2.57345e7	1.27613
$43$	2.33244e7	1.04041	0.520203	−	0.854042i	$-0.325856\pi$
$43$	2.33244e7	1.04041	0.520203	+	0.854042i	$0.325856\pi$
$44$	7.85057e6	0.315765
$45$	0	0
$46$	1.87755e7	0.618276
$47$	5.14121e7	1.53683	0.768413	−	0.639954i	$-0.221046\pi$
$47$	5.14121e7	1.53683	0.768413	+	0.639954i	$0.221046\pi$
$48$	5.88706e7	1.60071
$49$	−1.16346e7	−0.288315
$50$	0	0
$51$	8.78228e7	1.81778
$52$	−2.82806e6	−0.0536381
$53$	−1.01005e8	−1.75834	−0.879170	−	0.476509i	$-0.841902\pi$
$53$	−1.01005e8	−1.75834	−0.879170	+	0.476509i	$0.841902\pi$
$54$	7.80627e6	0.124931
$55$	0	0
$56$	5.47070e7	0.743356
$57$	−4.12885e7	−0.518075
$58$	−2.22494e7	−0.258162
$59$	1.32234e8	1.42073	0.710363	−	0.703836i	$-0.248531\pi$
$59$	1.32234e8	1.42073	0.710363	+	0.703836i	$0.248531\pi$
$60$	0	0
$61$	−1.23648e8	−1.14341	−0.571706	−	0.820459i	$-0.693718\pi$
$61$	−1.23648e8	−1.14341	−0.571706	+	0.820459i	$0.693718\pi$
$62$	5.61465e7	0.482570
$63$	−9.67699e7	−0.773941
$64$	9.91916e7	0.739035
$65$	0	0
$66$	−3.80729e8	−2.46984
$67$	2.15282e8	1.30518	0.652592	−	0.757710i	$-0.273682\pi$
$67$	2.15282e8	1.30518	0.652592	+	0.757710i	$0.273682\pi$
$68$	−4.47630e7	−0.253880
$69$	−1.47560e8	−0.783696
$70$	0	0
$71$	−2.06198e8	−0.962992	−0.481496	−	0.876448i	$-0.659906\pi$
$71$	−2.06198e8	−0.962992	−0.481496	+	0.876448i	$0.659906\pi$
$72$	−1.84337e8	−0.808383
$73$	−3.44444e8	−1.41960	−0.709800	−	0.704403i	$-0.751215\pi$
$73$	−3.44444e8	−1.41960	−0.709800	+	0.704403i	$0.751215\pi$
$74$	1.16285e8	0.450799
$75$	0	0
$76$	2.10446e7	0.0723569
$77$	−4.24884e8	−1.37741
$78$	1.37153e8	0.419545
$79$	5.03324e7	0.145387	0.0726935	−	0.997354i	$-0.476841\pi$
$79$	5.03324e7	0.145387	0.0726935	+	0.997354i	$0.476841\pi$
$80$	0	0
$81$	−4.16775e8	−1.07577
$82$	8.39883e8	2.05143
$83$	−8.20266e7	−0.189716	−0.0948579	−	0.995491i	$-0.530240\pi$
$83$	−8.20266e7	−0.189716	−0.0948579	+	0.995491i	$0.530240\pi$
$84$	1.03087e8	0.225916
$85$	0	0
$86$	5.76552e8	1.13657
$87$	1.74862e8	0.327233
$88$	−8.09364e8	−1.43870
$89$	−6.17891e8	−1.04390	−0.521948	−	0.852977i	$-0.674794\pi$
$89$	−6.17891e8	−1.04390	−0.521948	+	0.852977i	$0.674794\pi$
$90$	0	0
$91$	1.53059e8	0.233976
$92$	7.52109e7	0.109455
$93$	−4.41265e8	−0.611682
$94$	1.27084e9	1.67887
$95$	0	0
$96$	4.39824e8	0.528516
$97$	9.91253e8	1.13687	0.568436	−	0.822727i	$-0.307549\pi$
$97$	9.91253e8	1.13687	0.568436	+	0.822727i	$0.307549\pi$
$98$	−2.87592e8	−0.314963
$99$	1.43166e9	1.49790
$100$	0	0
$101$	−1.15157e9	−1.10115	−0.550573	−	0.834787i	$-0.685591\pi$
$101$	−1.15157e9	−1.10115	−0.550573	+	0.834787i	$0.685591\pi$
$102$	2.17087e9	1.98579
$103$	−1.28814e9	−1.12770	−0.563852	−	0.825876i	$-0.690681\pi$
$103$	−1.28814e9	−1.12770	−0.563852	+	0.825876i	$0.690681\pi$
$104$	2.91562e8	0.244389
$105$	0	0
$106$	−2.49673e9	−1.92086
$107$	−7.90577e8	−0.583065	−0.291533	−	0.956561i	$-0.594165\pi$
$107$	−7.90577e8	−0.583065	−0.291533	+	0.956561i	$0.594165\pi$
$108$	3.12703e7	0.0221169
$109$	−4.40070e8	−0.298609	−0.149304	−	0.988791i	$-0.547703\pi$
$109$	−4.40070e8	−0.298609	−0.149304	+	0.988791i	$0.547703\pi$
$110$	0	0
$111$	−9.13906e8	−0.571410
$112$	1.62398e9	0.975212
$113$	8.28687e8	0.478121	0.239060	−	0.971005i	$-0.423161\pi$
$113$	8.28687e8	0.478121	0.239060	+	0.971005i	$0.423161\pi$
$114$	−1.02060e9	−0.565958
$115$	0	0
$116$	−8.91264e7	−0.0457031
$117$	−5.15737e8	−0.254444
$118$	3.26867e9	1.55204
$119$	2.42264e9	1.10746
$120$	0	0
$121$	3.92801e9	1.66586
$122$	−3.05643e9	−1.24909
$123$	−6.60077e9	−2.60029
$124$	2.24911e8	0.0854306
$125$	0	0
$126$	−2.39203e9	−0.845473
$127$	2.09036e9	0.713025	0.356513	−	0.934291i	$-0.383966\pi$
$127$	2.09036e9	0.713025	0.356513	+	0.934291i	$0.383966\pi$
$128$	3.61106e9	1.18902
$129$	−4.53121e9	−1.44066
$130$	0	0
$131$	1.23787e8	0.0367243	0.0183621	−	0.999831i	$-0.494155\pi$
$131$	1.23787e8	0.0367243	0.0183621	+	0.999831i	$0.494155\pi$
$132$	−1.52512e9	−0.437242
$133$	−1.13897e9	−0.315630
$134$	5.32152e9	1.42582
$135$	0	0
$136$	4.61490e9	1.15674
$137$	1.31278e9	0.318383	0.159192	−	0.987248i	$-0.449111\pi$
$137$	1.31278e9	0.318383	0.159192	+	0.987248i	$0.449111\pi$
$138$	−3.64750e9	−0.856130
$139$	−4.82994e9	−1.09743	−0.548713	−	0.836011i	$-0.684882\pi$
$139$	−4.82994e9	−1.09743	−0.548713	+	0.836011i	$0.684882\pi$
$140$	0	0
$141$	−9.98777e9	−2.12805
$142$	−5.09697e9	−1.05200
$143$	−2.26443e9	−0.452842
$144$	−5.47206e9	−1.06052
$145$	0	0
$146$	−8.51424e9	−1.55081
$147$	2.26023e9	0.399232
$148$	4.65815e8	0.0798060
$149$	−4.39244e9	−0.730075	−0.365037	−	0.930993i	$-0.618944\pi$
$149$	−4.39244e9	−0.730075	−0.365037	+	0.930993i	$0.618944\pi$
$150$	0	0
$151$	−4.70301e9	−0.736172	−0.368086	−	0.929792i	$-0.619987\pi$
$151$	−4.70301e9	−0.736172	−0.368086	+	0.929792i	$0.619987\pi$
$152$	−2.16962e9	−0.329676
$153$	−8.16318e9	−1.20434
$154$	−1.05026e10	−1.50472
$155$	0	0
$156$	5.49404e8	0.0742730
$157$	5.28793e9	0.694605	0.347302	−	0.937753i	$-0.387098\pi$
$157$	5.28793e9	0.694605	0.347302	+	0.937753i	$0.387098\pi$
$158$	1.24416e9	0.158825
$159$	1.96222e10	2.43478
$160$	0	0
$161$	−4.07052e9	−0.477457
$162$	−1.03022e10	−1.17520
$163$	−6.72980e9	−0.746721	−0.373360	−	0.927686i	$-0.621794\pi$
$163$	−6.72980e9	−0.746721	−0.373360	+	0.927686i	$0.621794\pi$
$164$	3.36439e9	0.363170
$165$	0	0
$166$	−2.02760e9	−0.207251
$167$	−5.87782e9	−0.584780	−0.292390	−	0.956299i	$-0.594450\pi$
$167$	−5.87782e9	−0.584780	−0.292390	+	0.956299i	$0.594450\pi$
$168$	−1.06279e10	−1.02933
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	3.83779e9	0.343241
$172$	2.30954e9	0.201209
$173$	1.40328e10	1.19107	0.595534	−	0.803330i	$-0.296941\pi$
$173$	1.40328e10	1.19107	0.595534	+	0.803330i	$0.296941\pi$
$174$	4.32236e9	0.357478
$175$	0	0
$176$	−2.40260e10	−1.88744
$177$	−2.56890e10	−1.96729
$178$	−1.52735e10	−1.14038
$179$	−2.48592e10	−1.80987	−0.904936	−	0.425548i	$-0.860081\pi$
$179$	−2.48592e10	−1.80987	−0.904936	+	0.425548i	$0.860081\pi$
$180$	0	0
$181$	1.35989e10	0.941784	0.470892	−	0.882191i	$-0.343932\pi$
$181$	1.35989e10	0.941784	0.470892	+	0.882191i	$0.343932\pi$
$182$	3.78343e9	0.255602
$183$	2.40209e10	1.58329
$184$	−7.75396e9	−0.498704
$185$	0	0
$186$	−1.09075e10	−0.668218
$187$	−3.58418e10	−2.14340
$188$	5.09074e9	0.297215
$189$	−1.69240e9	−0.0964770
$190$	0	0
$191$	−1.65985e9	−0.0902440	−0.0451220	−	0.998981i	$-0.514368\pi$
$191$	−1.65985e9	−0.0902440	−0.0451220	+	0.998981i	$0.514368\pi$
$192$	−1.92698e10	−1.02335
$193$	−3.09499e10	−1.60565	−0.802827	−	0.596212i	$-0.796672\pi$
$193$	−3.09499e10	−1.60565	−0.802827	+	0.596212i	$0.796672\pi$
$194$	2.45026e10	1.24195
$195$	0	0
$196$	−1.15203e9	−0.0557587
$197$	3.04341e10	1.43967	0.719835	−	0.694145i	$-0.244217\pi$
$197$	3.04341e10	1.43967	0.719835	+	0.694145i	$0.244217\pi$
$198$	3.53890e10	1.63634
$199$	4.44812e8	0.0201066	0.0100533	−	0.999949i	$-0.496800\pi$
$199$	4.44812e8	0.0201066	0.0100533	+	0.999949i	$0.496800\pi$
$200$	0	0
$201$	−4.18227e10	−1.80730
$202$	−2.84655e10	−1.20292
$203$	4.82365e9	0.199363
$204$	8.69606e9	0.351550
$205$	0	0
$206$	−3.18412e10	−1.23193
$207$	1.37158e10	0.519223
$208$	8.65503e9	0.320615
$209$	1.68505e10	0.610877
$210$	0	0
$211$	4.88078e9	0.169519	0.0847595	−	0.996401i	$-0.472988\pi$
$211$	4.88078e9	0.169519	0.0847595	+	0.996401i	$0.472988\pi$
$212$	−1.00014e10	−0.340054
$213$	4.00579e10	1.33346
$214$	−1.95421e10	−0.636956
$215$	0	0
$216$	−3.22385e9	−0.100770
$217$	−1.21725e10	−0.372660
$218$	−1.08780e10	−0.326208
$219$	6.69148e10	1.96573
$220$	0	0
$221$	1.29115e10	0.364093
$222$	−2.25906e10	−0.624223
$223$	−2.47486e10	−0.670162	−0.335081	−	0.942189i	$-0.608764\pi$
$223$	−2.47486e10	−0.670162	−0.335081	+	0.942189i	$0.608764\pi$
$224$	1.21328e10	0.321992
$225$	0	0
$226$	2.04841e10	0.522312
$227$	−2.62443e10	−0.656022	−0.328011	−	0.944674i	$-0.606378\pi$
$227$	−2.62443e10	−0.656022	−0.328011	+	0.944674i	$0.606378\pi$
$228$	−4.08832e9	−0.100193
$229$	−4.15262e10	−0.997844	−0.498922	−	0.866647i	$-0.666271\pi$
$229$	−4.15262e10	−0.997844	−0.498922	+	0.866647i	$0.666271\pi$
$230$	0	0
$231$	8.25418e10	1.90731
$232$	9.18859e9	0.208235
$233$	−3.67402e10	−0.816657	−0.408329	−	0.912835i	$-0.633888\pi$
$233$	−3.67402e10	−0.816657	−0.408329	+	0.912835i	$0.633888\pi$
$234$	−1.27484e10	−0.277961
$235$	0	0
$236$	1.30936e10	0.274761
$237$	−9.77802e9	−0.201318
$238$	5.98847e10	1.20982
$239$	−4.35921e10	−0.864206	−0.432103	−	0.901824i	$-0.642228\pi$
$239$	−4.35921e10	−0.864206	−0.432103	+	0.901824i	$0.642228\pi$
$240$	0	0
$241$	−1.04473e10	−0.199493	−0.0997464	−	0.995013i	$-0.531803\pi$
$241$	−1.04473e10	−0.199493	−0.0997464	+	0.995013i	$0.531803\pi$
$242$	9.70956e10	1.81983
$243$	7.47504e10	1.37526
$244$	−1.22434e10	−0.221130
$245$	0	0
$246$	−1.63163e11	−2.84063
$247$	−6.07015e9	−0.103768
$248$	−2.31875e10	−0.389243
$249$	1.59352e10	0.262701
$250$	0	0
$251$	8.69402e10	1.38258	0.691288	−	0.722580i	$-0.257044\pi$
$251$	8.69402e10	1.38258	0.691288	+	0.722580i	$0.257044\pi$
$252$	−9.58199e9	−0.149676
$253$	6.02214e10	0.924078
$254$	5.16712e10	0.778927
$255$	0	0
$256$	3.84749e10	0.559884
$257$	−4.05492e10	−0.579807	−0.289903	−	0.957056i	$-0.593623\pi$
$257$	−4.05492e10	−0.579807	−0.289903	+	0.957056i	$0.593623\pi$
$258$	−1.12006e11	−1.57381
$259$	−2.52106e10	−0.348124
$260$	0	0
$261$	−1.62535e10	−0.216802
$262$	3.05986e9	0.0401185
$263$	−1.55920e10	−0.200956	−0.100478	−	0.994939i	$-0.532037\pi$
$263$	−1.55920e10	−0.200956	−0.100478	+	0.994939i	$0.532037\pi$
$264$	1.57234e11	1.99218
$265$	0	0
$266$	−2.81539e10	−0.344803
$267$	1.20037e11	1.44549
$268$	2.13169e10	0.252416
$269$	1.34814e11	1.56982	0.784911	−	0.619608i	$-0.212708\pi$
$269$	1.34814e11	1.56982	0.784911	+	0.619608i	$0.212708\pi$
$270$	0	0
$271$	1.08155e10	0.121810	0.0609052	−	0.998144i	$-0.480601\pi$
$271$	1.08155e10	0.121810	0.0609052	+	0.998144i	$0.480601\pi$
$272$	1.36993e11	1.51754
$273$	−2.97346e10	−0.323989
$274$	3.24504e10	0.347810
$275$	0	0
$276$	−1.46111e10	−0.151563
$277$	−1.05265e11	−1.07429	−0.537147	−	0.843488i	$-0.680498\pi$
$277$	−1.05265e11	−1.07429	−0.537147	+	0.843488i	$0.680498\pi$
$278$	−1.19390e11	−1.19886
$279$	4.10158e10	0.405259
$280$	0	0
$281$	5.90656e10	0.565140	0.282570	−	0.959247i	$-0.408813\pi$
$281$	5.90656e10	0.565140	0.282570	+	0.959247i	$0.408813\pi$
$282$	−2.46886e11	−2.32474
$283$	1.45893e11	1.35206	0.676030	−	0.736875i	$-0.263699\pi$
$283$	1.45893e11	1.35206	0.676030	+	0.736875i	$0.263699\pi$
$284$	−2.04174e10	−0.186238
$285$	0	0
$286$	−5.59740e10	−0.494697
$287$	−1.82086e11	−1.58419
$288$	−4.08819e10	−0.350158
$289$	8.57779e10	0.723328
$290$	0	0
$291$	−1.92570e11	−1.57423
$292$	−3.41063e10	−0.274544
$293$	7.69633e9	0.0610070	0.0305035	−	0.999535i	$-0.490289\pi$
$293$	7.69633e9	0.0610070	0.0305035	+	0.999535i	$0.490289\pi$
$294$	5.58702e10	0.436131
$295$	0	0
$296$	−4.80238e10	−0.363616
$297$	2.50382e10	0.186723
$298$	−1.08576e11	−0.797553
$299$	−2.16940e10	−0.156971
$300$	0	0
$301$	−1.24996e11	−0.877702
$302$	−1.16253e11	−0.804214
$303$	2.23715e11	1.52476
$304$	−6.44053e10	−0.432504
$305$	0	0
$306$	−2.01784e11	−1.31565
$307$	−7.83929e10	−0.503679	−0.251839	−	0.967769i	$-0.581035\pi$
$307$	−7.83929e10	−0.503679	−0.251839	+	0.967769i	$0.581035\pi$
$308$	−4.20713e10	−0.266384
$309$	2.50245e11	1.56154
$310$	0	0
$311$	−2.02455e11	−1.22717	−0.613587	−	0.789627i	$-0.710274\pi$
$311$	−2.02455e11	−1.22717	−0.613587	+	0.789627i	$0.710274\pi$
$312$	−5.66415e10	−0.338407
$313$	−4.65893e10	−0.274370	−0.137185	−	0.990545i	$-0.543805\pi$
$313$	−4.65893e10	−0.274370	−0.137185	+	0.990545i	$0.543805\pi$
$314$	1.30711e11	0.758804
$315$	0	0
$316$	4.98383e9	0.0281171
$317$	1.19232e10	0.0663170	0.0331585	−	0.999450i	$-0.489443\pi$
$317$	1.19232e10	0.0663170	0.0331585	+	0.999450i	$0.489443\pi$
$318$	4.85036e11	2.65982
$319$	−7.13636e10	−0.385850
$320$	0	0
$321$	1.53585e11	0.807374
$322$	−1.00618e11	−0.521586
$323$	−9.60794e10	−0.491155
$324$	−4.12683e10	−0.208048
$325$	0	0
$326$	−1.66353e11	−0.815737
$327$	8.54918e10	0.413485
$328$	−3.46856e11	−1.65469
$329$	−2.75518e11	−1.29649
$330$	0	0
$331$	1.99404e11	0.913076	0.456538	−	0.889704i	$-0.349089\pi$
$331$	1.99404e11	0.913076	0.456538	+	0.889704i	$0.349089\pi$
$332$	−8.12213e9	−0.0366901
$333$	8.49480e10	0.378577
$334$	−1.45293e11	−0.638829
$335$	0	0
$336$	−3.15489e11	−1.35038
$337$	−3.29370e11	−1.39107	−0.695536	−	0.718491i	$-0.744833\pi$
$337$	−3.29370e11	−1.39107	−0.695536	+	0.718491i	$0.744833\pi$
$338$	2.01639e10	0.0840328
$339$	−1.60988e11	−0.662057
$340$	0	0
$341$	1.80087e11	0.721252
$342$	9.48655e10	0.374965
$343$	2.78605e11	1.08684
$344$	−2.38105e11	−0.916761
$345$	0	0
$346$	3.46873e11	1.30115
$347$	2.16834e10	0.0802868	0.0401434	−	0.999194i	$-0.487219\pi$
$347$	2.16834e10	0.0802868	0.0401434	+	0.999194i	$0.487219\pi$
$348$	1.73145e10	0.0632853
$349$	1.43336e11	0.517178	0.258589	−	0.965987i	$-0.416742\pi$
$349$	1.43336e11	0.517178	0.258589	+	0.965987i	$0.416742\pi$
$350$	0	0
$351$	−9.01966e9	−0.0317182
$352$	−1.79499e11	−0.623188
$353$	8.38423e10	0.287393	0.143697	−	0.989622i	$-0.454101\pi$
$353$	8.38423e10	0.287393	0.143697	+	0.989622i	$0.454101\pi$
$354$	−6.35001e11	−2.14912
$355$	0	0
$356$	−6.11825e10	−0.201884
$357$	−4.70644e11	−1.53351
$358$	−6.14488e11	−1.97715
$359$	1.26213e11	0.401033	0.200516	−	0.979690i	$-0.435738\pi$
$359$	1.26213e11	0.401033	0.200516	+	0.979690i	$0.435738\pi$
$360$	0	0
$361$	−2.77517e11	−0.860019
$362$	3.36149e11	1.02883
$363$	−7.63090e11	−2.30673
$364$	1.51556e10	0.0452499
$365$	0	0
$366$	5.93768e11	1.72963
$367$	6.56218e11	1.88821	0.944106	−	0.329642i	$-0.106928\pi$
$367$	6.56218e11	1.88821	0.944106	+	0.329642i	$0.106928\pi$
$368$	−2.30176e11	−0.654253
$369$	6.13546e11	1.72277
$370$	0	0
$371$	5.41289e11	1.48336
$372$	−4.36933e10	−0.118296
$373$	5.52730e11	1.47851	0.739253	−	0.673428i	$-0.235179\pi$
$373$	5.52730e11	1.47851	0.739253	+	0.673428i	$0.235179\pi$
$374$	−8.85966e11	−2.34150
$375$	0	0
$376$	−5.24836e11	−1.35418
$377$	2.57078e10	0.0655433
$378$	−4.18340e10	−0.105394
$379$	−3.07664e11	−0.765950	−0.382975	−	0.923759i	$-0.625100\pi$
$379$	−3.07664e11	−0.765950	−0.382975	+	0.923759i	$0.625100\pi$
$380$	0	0
$381$	−4.06092e11	−0.987330
$382$	−4.10295e10	−0.0985849
$383$	−1.31812e11	−0.313012	−0.156506	−	0.987677i	$-0.550023\pi$
$383$	−1.31812e11	−0.313012	−0.156506	+	0.987677i	$0.550023\pi$
$384$	−7.01517e11	−1.64645
$385$	0	0
$386$	−7.65045e11	−1.75406
$387$	4.21179e11	0.954480
$388$	9.81521e10	0.219865
$389$	1.31742e11	0.291709	0.145855	−	0.989306i	$-0.453407\pi$
$389$	1.31742e11	0.291709	0.145855	+	0.989306i	$0.453407\pi$
$390$	0	0
$391$	−3.43376e11	−0.742975
$392$	1.18770e11	0.254051
$393$	−2.40479e10	−0.0508523
$394$	7.52295e11	1.57273
$395$	0	0
$396$	1.41761e11	0.289686
$397$	−4.44767e11	−0.898619	−0.449309	−	0.893376i	$-0.648330\pi$
$397$	−4.44767e11	−0.898619	−0.449309	+	0.893376i	$0.648330\pi$
$398$	1.09952e10	0.0219649
$399$	2.21266e11	0.437055
$400$	0	0
$401$	−8.36539e11	−1.61561	−0.807805	−	0.589450i	$-0.799345\pi$
$401$	−8.36539e11	−1.61561	−0.807805	+	0.589450i	$0.799345\pi$
$402$	−1.03381e12	−1.97434
$403$	−6.48738e10	−0.122517
$404$	−1.14027e11	−0.212956
$405$	0	0
$406$	1.19235e11	0.217789
$407$	3.72979e11	0.673766
$408$	−8.96531e11	−1.60175
$409$	2.11826e11	0.374304	0.187152	−	0.982331i	$-0.440074\pi$
$409$	2.11826e11	0.374304	0.187152	+	0.982331i	$0.440074\pi$
$410$	0	0
$411$	−2.55033e11	−0.440867
$412$	−1.27549e11	−0.218092
$413$	−7.08646e11	−1.19854
$414$	3.39037e11	0.567213
$415$	0	0
$416$	6.46620e10	0.105859
$417$	9.38307e11	1.51961
$418$	4.16523e11	0.667338
$419$	5.30153e11	0.840308	0.420154	−	0.907453i	$-0.361976\pi$
$419$	5.30153e11	0.840308	0.420154	+	0.907453i	$0.361976\pi$
$420$	0	0
$421$	3.41563e10	0.0529909	0.0264955	−	0.999649i	$-0.491565\pi$
$421$	3.41563e10	0.0529909	0.0264955	+	0.999649i	$0.491565\pi$
$422$	1.20647e11	0.185187
$423$	9.28369e11	1.40990
$424$	1.03110e12	1.54937
$425$	0	0
$426$	9.90183e11	1.45671
$427$	6.62631e11	0.964598
$428$	−7.82815e10	−0.112762
$429$	4.39909e11	0.627054
$430$	0	0
$431$	8.63019e11	1.20468	0.602342	−	0.798238i	$-0.294235\pi$
$431$	8.63019e11	1.20468	0.602342	+	0.798238i	$0.294235\pi$
$432$	−9.57000e10	−0.132201
$433$	3.23681e11	0.442509	0.221254	−	0.975216i	$-0.428985\pi$
$433$	3.23681e11	0.442509	0.221254	+	0.975216i	$0.428985\pi$
$434$	−3.00890e11	−0.407103
$435$	0	0
$436$	−4.35749e10	−0.0577494
$437$	1.61433e11	0.211751
$438$	1.65405e12	2.14741
$439$	−1.45809e12	−1.87368	−0.936838	−	0.349763i	$-0.886262\pi$
$439$	−1.45809e12	−1.87368	−0.936838	+	0.349763i	$0.886262\pi$
$440$	0	0
$441$	−2.10090e11	−0.264503
$442$	3.19157e11	0.397745
$443$	−1.49027e12	−1.83844	−0.919219	−	0.393748i	$-0.871178\pi$
$443$	−1.49027e12	−1.83844	−0.919219	+	0.393748i	$0.871178\pi$
$444$	−9.04933e10	−0.110508
$445$	0	0
$446$	−6.11756e11	−0.732102
$447$	8.53314e11	1.01094
$448$	−5.31569e11	−0.623460
$449$	3.04750e11	0.353862	0.176931	−	0.984223i	$-0.443383\pi$
$449$	3.04750e11	0.353862	0.176931	+	0.984223i	$0.443383\pi$
$450$	0	0
$451$	2.69387e12	3.06608
$452$	8.20551e10	0.0924661
$453$	9.13648e11	1.01938
$454$	−6.48727e11	−0.716656
$455$	0	0
$456$	4.21490e11	0.456505
$457$	1.23809e11	0.132779	0.0663896	−	0.997794i	$-0.478852\pi$
$457$	1.23809e11	0.132779	0.0663896	+	0.997794i	$0.478852\pi$
$458$	−1.02648e12	−1.09007
$459$	−1.42765e11	−0.150129
$460$	0	0
$461$	3.16152e11	0.326018	0.163009	−	0.986625i	$-0.447880\pi$
$461$	3.16152e11	0.326018	0.163009	+	0.986625i	$0.447880\pi$
$462$	2.04033e12	2.08359
$463$	−1.73371e12	−1.75332	−0.876659	−	0.481112i	$-0.840233\pi$
$463$	−1.73371e12	−1.75332	−0.876659	+	0.481112i	$0.840233\pi$
$464$	2.72764e11	0.273184
$465$	0	0
$466$	−9.08173e11	−0.892138
$467$	5.67889e11	0.552506	0.276253	−	0.961085i	$-0.410907\pi$
$467$	5.67889e11	0.552506	0.276253	+	0.961085i	$0.410907\pi$
$468$	−5.10674e10	−0.0492082
$469$	−1.15370e12	−1.10107
$470$	0	0
$471$	−1.02728e12	−0.961823
$472$	−1.34990e12	−1.25188
$473$	1.84926e12	1.69872
$474$	−2.41701e11	−0.219925
$475$	0	0
$476$	2.39886e11	0.214177
$477$	−1.82389e12	−1.61312
$478$	−1.07754e12	−0.944081
$479$	9.31010e11	0.808062	0.404031	−	0.914745i	$-0.367609\pi$
$479$	9.31010e11	0.808062	0.404031	+	0.914745i	$0.367609\pi$
$480$	0	0
$481$	−1.34360e11	−0.114451
$482$	−2.58244e11	−0.217931
$483$	7.90776e11	0.661137
$484$	3.88945e11	0.322169
$485$	0	0
$486$	1.84774e12	1.50237
$487$	4.49592e10	0.0362192	0.0181096	−	0.999836i	$-0.494235\pi$
$487$	4.49592e10	0.0362192	0.0181096	+	0.999836i	$0.494235\pi$
$488$	1.26225e12	1.00752
$489$	1.30739e12	1.03399
$490$	0	0
$491$	4.47956e11	0.347831	0.173916	−	0.984761i	$-0.444358\pi$
$491$	4.47956e11	0.347831	0.173916	+	0.984761i	$0.444358\pi$
$492$	−6.53597e11	−0.502883
$493$	4.06907e11	0.310230
$494$	−1.50047e11	−0.113359
$495$	0	0
$496$	−6.88321e11	−0.510650
$497$	1.10502e12	0.812394
$498$	3.93899e11	0.286981
$499$	7.27774e11	0.525465	0.262733	−	0.964869i	$-0.415376\pi$
$499$	7.27774e11	0.525465	0.262733	+	0.964869i	$0.415376\pi$
$500$	0	0
$501$	1.14188e12	0.809748
$502$	2.14906e12	1.51036
$503$	−6.23613e11	−0.434369	−0.217185	−	0.976131i	$-0.569687\pi$
$503$	−6.23613e11	−0.434369	−0.217185	+	0.976131i	$0.569687\pi$
$504$	9.87866e11	0.681963
$505$	0	0
$506$	1.48860e12	1.00949
$507$	−1.58471e11	−0.106516
$508$	2.06984e11	0.137896
$509$	1.18958e12	0.785534	0.392767	−	0.919638i	$-0.371518\pi$
$509$	1.18958e12	0.785534	0.392767	+	0.919638i	$0.371518\pi$
$510$	0	0
$511$	1.84588e12	1.19760
$512$	−8.97810e11	−0.577390
$513$	6.71186e10	0.0427873
$514$	−1.00233e12	−0.633396
$515$	0	0
$516$	−4.48673e11	−0.278616
$517$	4.07616e12	2.50925
$518$	−6.23175e11	−0.380300
$519$	−2.72613e12	−1.64928
$520$	0	0
$521$	2.26245e12	1.34527	0.672635	−	0.739974i	$-0.265162\pi$
$521$	2.26245e12	1.34527	0.672635	+	0.739974i	$0.265162\pi$
$522$	−4.01766e11	−0.236841
$523$	−1.15246e12	−0.673549	−0.336775	−	0.941585i	$-0.609336\pi$
$523$	−1.15246e12	−0.673549	−0.336775	+	0.941585i	$0.609336\pi$
$524$	1.22571e10	0.00710229
$525$	0	0
$526$	−3.85415e11	−0.219530
$527$	−1.02683e12	−0.579899
$528$	4.66750e12	2.61355
$529$	−1.22421e12	−0.679683
$530$	0	0
$531$	2.38781e12	1.30339
$532$	−1.12778e11	−0.0610413
$533$	−9.70432e11	−0.520826
$534$	2.96717e12	1.57909
$535$	0	0
$536$	−2.19769e12	−1.15007
$537$	4.82936e12	2.50614
$538$	3.33244e12	1.71492
$539$	−9.22434e11	−0.470745
$540$	0	0
$541$	1.31455e12	0.659766	0.329883	−	0.944022i	$-0.392991\pi$
$541$	1.31455e12	0.659766	0.329883	+	0.944022i	$0.392991\pi$
$542$	2.67346e11	0.133069
$543$	−2.64185e12	−1.30409
$544$	1.02348e12	0.501054
$545$	0	0
$546$	−7.35002e11	−0.353934
$547$	−1.63148e12	−0.779182	−0.389591	−	0.920988i	$-0.627384\pi$
$547$	−1.63148e12	−0.779182	−0.389591	+	0.920988i	$0.627384\pi$
$548$	1.29989e11	0.0615738
$549$	−2.23276e12	−1.04898
$550$	0	0
$551$	−1.91301e11	−0.0884168
$552$	1.50635e12	0.690559
$553$	−2.69732e11	−0.122651
$554$	−2.60201e12	−1.17359
$555$	0	0
$556$	−4.78252e11	−0.212237
$557$	2.20811e12	0.972013	0.486007	−	0.873955i	$-0.338453\pi$
$557$	2.20811e12	0.972013	0.486007	+	0.873955i	$0.338453\pi$
$558$	1.01386e12	0.442715
$559$	−6.66169e11	−0.288557
$560$	0	0
$561$	6.96295e12	2.96797
$562$	1.46003e12	0.617374
$563$	1.16602e12	0.489125	0.244563	−	0.969634i	$-0.421356\pi$
$563$	1.16602e12	0.489125	0.244563	+	0.969634i	$0.421356\pi$
$564$	−9.88972e11	−0.411555
$565$	0	0
$566$	3.60630e12	1.47702
$567$	2.23350e12	0.907533
$568$	2.10496e12	0.848547
$569$	−2.63455e12	−1.05366	−0.526831	−	0.849970i	$-0.676620\pi$
$569$	−2.63455e12	−1.05366	−0.526831	+	0.849970i	$0.676620\pi$
$570$	0	0
$571$	−1.65379e12	−0.651055	−0.325527	−	0.945533i	$-0.605542\pi$
$571$	−1.65379e12	−0.651055	−0.325527	+	0.945533i	$0.605542\pi$
$572$	−2.24220e11	−0.0875774
$573$	3.22457e11	0.124961
$574$	−4.50094e12	−1.73061
$575$	0	0
$576$	1.79114e12	0.677999
$577$	−1.77685e12	−0.667358	−0.333679	−	0.942687i	$-0.608290\pi$
$577$	−1.77685e12	−0.667358	−0.333679	+	0.942687i	$0.608290\pi$
$578$	2.12033e12	0.790182
$579$	6.01261e12	2.22336
$580$	0	0
$581$	4.39582e11	0.160047
$582$	−4.76009e12	−1.71973
$583$	−8.00811e12	−2.87092
$584$	3.51623e12	1.25089
$585$	0	0
$586$	1.90244e11	0.0666456
$587$	−4.61417e12	−1.60406	−0.802032	−	0.597281i	$-0.796248\pi$
$587$	−4.61417e12	−1.60406	−0.802032	+	0.597281i	$0.796248\pi$
$588$	2.23804e11	0.0772094
$589$	4.82750e11	0.165273
$590$	0	0
$591$	−5.91241e12	−1.99352
$592$	−1.42559e12	−0.477030
$593$	1.60396e12	0.532655	0.266328	−	0.963883i	$-0.414190\pi$
$593$	1.60396e12	0.532655	0.266328	+	0.963883i	$0.414190\pi$
$594$	6.18913e11	0.203981
$595$	0	0
$596$	−4.34931e11	−0.141193
$597$	−8.64132e10	−0.0278417
$598$	−5.36248e11	−0.171479
$599$	−3.56445e12	−1.13128	−0.565642	−	0.824651i	$-0.691372\pi$
$599$	−3.56445e12	−1.13128	−0.565642	+	0.824651i	$0.691372\pi$
$600$	0	0
$601$	−4.23106e12	−1.32286	−0.661431	−	0.750006i	$-0.730051\pi$
$601$	−4.23106e12	−1.32286	−0.661431	+	0.750006i	$0.730051\pi$
$602$	−3.08975e12	−0.958824
$603$	3.88744e12	1.19739
$604$	−4.65683e11	−0.142372
$605$	0	0
$606$	5.52995e12	1.66569
$607$	−2.69700e12	−0.806366	−0.403183	−	0.915119i	$-0.632096\pi$
$607$	−2.69700e12	−0.806366	−0.403183	+	0.915119i	$0.632096\pi$
$608$	−4.81173e11	−0.142802
$609$	−9.37086e11	−0.276059
$610$	0	0
$611$	−1.46838e12	−0.426239
$612$	−8.08304e11	−0.232913
$613$	4.29368e12	1.22817	0.614084	−	0.789240i	$-0.289525\pi$
$613$	4.29368e12	1.22817	0.614084	+	0.789240i	$0.289525\pi$
$614$	−1.93778e12	−0.550232
$615$	0	0
$616$	4.33739e12	1.21371
$617$	−2.63888e12	−0.733054	−0.366527	−	0.930407i	$-0.619453\pi$
$617$	−2.63888e12	−0.733054	−0.366527	+	0.930407i	$0.619453\pi$
$618$	6.18576e12	1.70587
$619$	−2.36449e12	−0.647335	−0.323667	−	0.946171i	$-0.604916\pi$
$619$	−2.36449e12	−0.647335	−0.323667	+	0.946171i	$0.604916\pi$
$620$	0	0
$621$	2.39873e11	0.0647247
$622$	−5.00444e12	−1.34060
$623$	3.31129e12	0.880645
$624$	−1.68140e12	−0.443957
$625$	0	0
$626$	−1.15163e12	−0.299729
$627$	−3.27352e12	−0.845885
$628$	5.23602e11	0.134333
$629$	−2.12668e12	−0.541719
$630$	0	0
$631$	−4.08896e12	−1.02679	−0.513393	−	0.858153i	$-0.671612\pi$
$631$	−4.08896e12	−1.02679	−0.513393	+	0.858153i	$0.671612\pi$
$632$	−5.13814e11	−0.128109
$633$	−9.48184e11	−0.234734
$634$	2.94726e11	0.0724464
$635$	0	0
$636$	1.94295e12	0.470875
$637$	3.32295e11	0.0799642
$638$	−1.76402e12	−0.421513
$639$	−3.72341e12	−0.883459
$640$	0	0
$641$	−3.55153e12	−0.830911	−0.415456	−	0.909613i	$-0.636378\pi$
$641$	−3.55153e12	−0.830911	−0.415456	+	0.909613i	$0.636378\pi$
$642$	3.79642e12	0.881997
$643$	−6.85000e12	−1.58031	−0.790153	−	0.612910i	$-0.789999\pi$
$643$	−6.85000e12	−1.58031	−0.790153	+	0.612910i	$0.789999\pi$
$644$	−4.03056e11	−0.0923377
$645$	0	0
$646$	−2.37496e12	−0.536551
$647$	4.28931e12	0.962317	0.481159	−	0.876634i	$-0.340216\pi$
$647$	4.28931e12	0.962317	0.481159	+	0.876634i	$0.340216\pi$
$648$	4.25460e12	0.947920
$649$	1.04841e13	2.31968
$650$	0	0
$651$	2.36474e12	0.516024
$652$	−6.66373e11	−0.144412
$653$	−8.81913e12	−1.89809	−0.949045	−	0.315142i	$-0.897948\pi$
$653$	−8.81913e12	−1.89809	−0.949045	+	0.315142i	$0.897948\pi$
$654$	2.11325e12	0.451702
$655$	0	0
$656$	−1.02964e13	−2.17080
$657$	−6.21977e12	−1.30236
$658$	−6.81048e12	−1.41632
$659$	5.76538e12	1.19081	0.595406	−	0.803425i	$-0.296991\pi$
$659$	5.76538e12	1.19081	0.595406	+	0.803425i	$0.296991\pi$
$660$	0	0
$661$	−4.77184e12	−0.972254	−0.486127	−	0.873888i	$-0.661591\pi$
$661$	−4.77184e12	−0.972254	−0.486127	+	0.873888i	$0.661591\pi$
$662$	4.92901e12	0.997468
$663$	−2.50831e12	−0.504162
$664$	8.37361e11	0.167169
$665$	0	0
$666$	2.09981e12	0.413568
$667$	−6.83686e11	−0.133749
$668$	−5.82012e11	−0.113093
$669$	4.80789e12	0.927977
$670$	0	0
$671$	−9.80330e12	−1.86690
$672$	−2.35702e12	−0.445864
$673$	−1.38206e10	−0.00259692	−0.00129846	−	0.999999i	$-0.500413\pi$
$673$	−1.38206e10	−0.00259692	−0.00129846	+	0.999999i	$0.500413\pi$
$674$	−8.14163e12	−1.51964
$675$	0	0
$676$	8.07722e10	0.0148765
$677$	2.70699e12	0.495265	0.247633	−	0.968854i	$-0.420347\pi$
$677$	2.70699e12	0.495265	0.247633	+	0.968854i	$0.420347\pi$
$678$	−3.97943e12	−0.723248
$679$	−5.31214e12	−0.959082
$680$	0	0
$681$	5.09845e12	0.908398
$682$	4.45152e12	0.787915
$683$	3.77305e12	0.663436	0.331718	−	0.943379i	$-0.392372\pi$
$683$	3.77305e12	0.663436	0.331718	+	0.943379i	$0.392372\pi$
$684$	3.80011e11	0.0663810
$685$	0	0
$686$	6.88679e12	1.18729
$687$	8.06725e12	1.38172
$688$	−7.06816e12	−1.20270
$689$	2.88481e12	0.487676
$690$	0	0
$691$	−1.42326e12	−0.237484	−0.118742	−	0.992925i	$-0.537886\pi$
$691$	−1.42326e12	−0.237484	−0.118742	+	0.992925i	$0.537886\pi$
$692$	1.38950e12	0.230346
$693$	−7.67231e12	−1.26365
$694$	5.35986e11	0.0877074
$695$	0	0
$696$	−1.78506e12	−0.288344
$697$	−1.53602e13	−2.46518
$698$	3.54309e12	0.564979
$699$	7.13748e12	1.13083
$700$	0	0
$701$	−4.18953e12	−0.655291	−0.327645	−	0.944801i	$-0.606255\pi$
$701$	−4.18953e12	−0.655291	−0.327645	+	0.944801i	$0.606255\pi$
$702$	−2.22955e11	−0.0346498
$703$	9.99825e11	0.154392
$704$	7.86431e12	1.20666
$705$	0	0
$706$	2.07248e12	0.313956
$707$	6.17129e12	0.928942
$708$	−2.54368e12	−0.380463
$709$	−5.30584e12	−0.788580	−0.394290	−	0.918986i	$-0.629009\pi$
$709$	−5.30584e12	−0.788580	−0.394290	+	0.918986i	$0.629009\pi$
$710$	0	0
$711$	9.08872e11	0.133380
$712$	6.30769e12	0.919836
$713$	1.72529e12	0.250011
$714$	−1.16337e13	−1.67524
$715$	0	0
$716$	−2.46151e12	−0.350020
$717$	8.46859e12	1.19667
$718$	3.11984e12	0.438099
$719$	2.67496e12	0.373282	0.186641	−	0.982428i	$-0.440240\pi$
$719$	2.67496e12	0.373282	0.186641	+	0.982428i	$0.440240\pi$
$720$	0	0
$721$	6.90316e12	0.951347
$722$	−6.85989e12	−0.939507
$723$	2.02958e12	0.276239
$724$	1.34654e12	0.182136
$725$	0	0
$726$	−1.88627e13	−2.51993
$727$	8.33355e12	1.10643	0.553217	−	0.833037i	$-0.313400\pi$
$727$	8.33355e12	1.10643	0.553217	+	0.833037i	$0.313400\pi$
$728$	−1.56249e12	−0.206170
$729$	−6.31830e12	−0.828564
$730$	0	0
$731$	−1.05442e13	−1.36580
$732$	2.37851e12	0.306200
$733$	−1.11038e11	−0.0142071	−0.00710355	−	0.999975i	$-0.502261\pi$
$733$	−1.11038e11	−0.0142071	−0.00710355	+	0.999975i	$0.502261\pi$
$734$	1.62209e13	2.06273
$735$	0	0
$736$	−1.71965e12	−0.216018
$737$	1.70684e13	2.13103
$738$	1.51661e13	1.88200
$739$	1.02565e13	1.26502	0.632511	−	0.774551i	$-0.282024\pi$
$739$	1.02565e13	1.26502	0.632511	+	0.774551i	$0.282024\pi$
$740$	0	0
$741$	1.17924e12	0.143688
$742$	1.33800e13	1.62046
$743$	−3.90792e12	−0.470431	−0.235215	−	0.971943i	$-0.575580\pi$
$743$	−3.90792e12	−0.470431	−0.235215	+	0.971943i	$0.575580\pi$
$744$	4.50461e12	0.538988
$745$	0	0
$746$	1.36628e13	1.61516
$747$	−1.48119e12	−0.174047
$748$	−3.54899e12	−0.414522
$749$	4.23671e12	0.491882
$750$	0	0
$751$	−2.63552e12	−0.302333	−0.151167	−	0.988508i	$-0.548303\pi$
$751$	−2.63552e12	−0.302333	−0.151167	+	0.988508i	$0.548303\pi$
$752$	−1.55798e13	−1.77656
$753$	−1.68898e13	−1.91446
$754$	6.35465e11	0.0716012
$755$	0	0
$756$	−1.67578e11	−0.0186582
$757$	1.02796e13	1.13774	0.568870	−	0.822428i	$-0.307381\pi$
$757$	1.02796e13	1.13774	0.568870	+	0.822428i	$0.307381\pi$
$758$	−7.60508e12	−0.836744
$759$	−1.16992e13	−1.27958
$760$	0	0
$761$	1.47695e12	0.159638	0.0798190	−	0.996809i	$-0.474566\pi$
$761$	1.47695e12	0.159638	0.0798190	+	0.996809i	$0.474566\pi$
$762$	−1.00381e13	−1.07859
$763$	2.35834e12	0.251910
$764$	−1.64355e11	−0.0174527
$765$	0	0
$766$	−3.25823e12	−0.341942
$767$	−3.77674e12	−0.394038
$768$	−7.47448e12	−0.775275
$769$	−3.06990e12	−0.316560	−0.158280	−	0.987394i	$-0.550595\pi$
$769$	−3.06990e12	−0.316560	−0.158280	+	0.987394i	$0.550595\pi$
$770$	0	0
$771$	7.87745e12	0.802862
$772$	−3.06461e12	−0.310526
$773$	−1.22536e13	−1.23440	−0.617200	−	0.786807i	$-0.711733\pi$
$773$	−1.22536e13	−1.23440	−0.617200	+	0.786807i	$0.711733\pi$
$774$	1.04110e13	1.04270
$775$	0	0
$776$	−1.01191e13	−1.00176
$777$	4.89764e12	0.482050
$778$	3.25650e12	0.318671
$779$	7.22134e12	0.702585
$780$	0	0
$781$	−1.63482e13	−1.57232
$782$	−8.48783e12	−0.811645
$783$	−2.84255e11	−0.0270259
$784$	3.52570e12	0.333290
$785$	0	0
$786$	−5.94435e11	−0.0555524
$787$	−1.16840e13	−1.08569	−0.542847	−	0.839832i	$-0.682653\pi$
$787$	−1.16840e13	−1.08569	−0.542847	+	0.839832i	$0.682653\pi$
$788$	3.01353e12	0.278425
$789$	3.02904e12	0.278265
$790$	0	0
$791$	−4.44095e12	−0.403349
$792$	−1.46150e13	−1.31988
$793$	3.53151e12	0.317125
$794$	−1.09941e13	−0.981675
$795$	0	0
$796$	4.40445e10	0.00388851
$797$	1.05711e13	0.928024	0.464012	−	0.885829i	$-0.346410\pi$
$797$	1.05711e13	0.928024	0.464012	+	0.885829i	$0.346410\pi$
$798$	5.46942e12	0.477451
$799$	−2.32418e13	−2.01748
$800$	0	0
$801$	−1.11575e13	−0.957682
$802$	−2.06782e13	−1.76494
$803$	−2.73089e13	−2.31785
$804$	−4.14121e12	−0.349522
$805$	0	0
$806$	−1.60360e12	−0.133841
$807$	−2.61902e13	−2.17374
$808$	1.17557e13	0.970282
$809$	−9.18043e12	−0.753520	−0.376760	−	0.926311i	$-0.622962\pi$
$809$	−9.18043e12	−0.753520	−0.376760	+	0.926311i	$0.622962\pi$
$810$	0	0
$811$	−1.38738e12	−0.112616	−0.0563081	−	0.998413i	$-0.517933\pi$
$811$	−1.38738e12	−0.112616	−0.0563081	+	0.998413i	$0.517933\pi$
$812$	4.77630e11	0.0385558
$813$	−2.10111e12	−0.168672
$814$	9.21958e12	0.736040
$815$	0	0
$816$	−2.66135e13	−2.10134
$817$	4.95721e12	0.389258
$818$	5.23609e12	0.408900
$819$	2.76385e12	0.214653
$820$	0	0
$821$	1.09862e12	0.0843924	0.0421962	−	0.999109i	$-0.486565\pi$
$821$	1.09862e12	0.0843924	0.0421962	+	0.999109i	$0.486565\pi$
$822$	−6.30410e12	−0.481615
$823$	1.94330e13	1.47653	0.738263	−	0.674513i	$-0.235646\pi$
$823$	1.94330e13	1.47653	0.738263	+	0.674513i	$0.235646\pi$
$824$	1.31498e13	0.993684
$825$	0	0
$826$	−1.75169e13	−1.30932
$827$	2.56778e12	0.190890	0.0954448	−	0.995435i	$-0.469573\pi$
$827$	2.56778e12	0.190890	0.0954448	+	0.995435i	$0.469573\pi$
$828$	1.35811e12	0.100415
$829$	1.15684e13	0.850703	0.425352	−	0.905028i	$-0.360150\pi$
$829$	1.15684e13	0.850703	0.425352	+	0.905028i	$0.360150\pi$
$830$	0	0
$831$	2.04496e13	1.48758
$832$	−2.83301e12	−0.204971
$833$	5.25961e12	0.378487
$834$	2.31938e13	1.66006
$835$	0	0
$836$	1.66850e12	0.118140
$837$	7.17320e11	0.0505182
$838$	1.31047e13	0.917974
$839$	−1.07035e13	−0.745754	−0.372877	−	0.927881i	$-0.621629\pi$
$839$	−1.07035e13	−0.745754	−0.372877	+	0.927881i	$0.621629\pi$
$840$	0	0
$841$	−1.36970e13	−0.944153
$842$	8.44302e11	0.0578887
$843$	−1.14746e13	−0.782553
$844$	4.83287e11	0.0327841
$845$	0	0
$846$	2.29481e13	1.54021
$847$	−2.10503e13	−1.40534
$848$	3.06083e13	2.03263
$849$	−2.83425e13	−1.87220
$850$	0	0
$851$	3.57325e12	0.233550
$852$	3.96647e12	0.257885
$853$	−1.85417e13	−1.19917	−0.599583	−	0.800313i	$-0.704667\pi$
$853$	−1.85417e13	−1.19917	−0.599583	+	0.800313i	$0.704667\pi$
$854$	1.63794e13	1.05375
$855$	0	0
$856$	8.07053e12	0.513772
$857$	−8.38633e12	−0.531078	−0.265539	−	0.964100i	$-0.585550\pi$
$857$	−8.38633e12	−0.531078	−0.265539	+	0.964100i	$0.585550\pi$
$858$	1.08740e13	0.685010
$859$	2.49383e12	0.156278	0.0781390	−	0.996942i	$-0.475102\pi$
$859$	2.49383e12	0.156278	0.0781390	+	0.996942i	$0.475102\pi$
$860$	0	0
$861$	3.53736e13	2.19364
$862$	2.13328e13	1.31603
$863$	1.05758e12	0.0649029	0.0324515	−	0.999473i	$-0.489669\pi$
$863$	1.05758e12	0.0649029	0.0324515	+	0.999473i	$0.489669\pi$
$864$	−7.14977e11	−0.0436496
$865$	0	0
$866$	8.00101e12	0.483408
$867$	−1.66640e13	−1.00160
$868$	−1.20530e12	−0.0720705
$869$	3.99056e12	0.237380
$870$	0	0
$871$	−6.14868e12	−0.361993
$872$	4.49241e12	0.263121
$873$	1.78995e13	1.04298
$874$	3.99042e12	0.231322
$875$	0	0
$876$	6.62579e12	0.380162
$877$	−2.46623e13	−1.40778	−0.703891	−	0.710308i	$-0.748556\pi$
$877$	−2.46623e13	−1.40778	−0.703891	+	0.710308i	$0.748556\pi$
$878$	−3.60423e13	−2.04685
$879$	−1.49516e12	−0.0844767
$880$	0	0
$881$	−7.21428e12	−0.403461	−0.201731	−	0.979441i	$-0.564657\pi$
$881$	−7.21428e12	−0.403461	−0.201731	+	0.979441i	$0.564657\pi$
$882$	−5.19316e12	−0.288951
$883$	5.65890e12	0.313263	0.156631	−	0.987657i	$-0.449937\pi$
$883$	5.65890e12	0.313263	0.156631	+	0.987657i	$0.449937\pi$
$884$	1.27848e12	0.0704138
$885$	0	0
$886$	−3.68377e13	−2.00836
$887$	−1.70857e13	−0.926778	−0.463389	−	0.886155i	$-0.653367\pi$
$887$	−1.70857e13	−0.926778	−0.463389	+	0.886155i	$0.653367\pi$
$888$	9.32952e12	0.503502
$889$	−1.12023e13	−0.601518
$890$	0	0
$891$	−3.30436e13	−1.75646
$892$	−2.45057e12	−0.129606
$893$	1.09268e13	0.574989
$894$	2.10929e13	1.10438
$895$	0	0
$896$	−1.93517e13	−1.00308
$897$	4.21446e12	0.217358
$898$	7.53304e12	0.386569
$899$	−2.04450e12	−0.104392
$900$	0	0
$901$	4.56613e13	2.30827
$902$	6.65893e13	3.34946
$903$	2.42828e13	1.21536
$904$	−8.45957e12	−0.421299
$905$	0	0
$906$	2.25843e13	1.11360
$907$	−4.31310e12	−0.211620	−0.105810	−	0.994386i	$-0.533744\pi$
$907$	−4.31310e12	−0.211620	−0.105810	+	0.994386i	$0.533744\pi$
$908$	−2.59866e12	−0.126871
$909$	−2.07944e13	−1.01020
$910$	0	0
$911$	3.59972e13	1.73155	0.865777	−	0.500430i	$-0.166825\pi$
$911$	3.59972e13	1.73155	0.865777	+	0.500430i	$0.166825\pi$
$912$	1.25119e13	0.598891
$913$	−6.50340e12	−0.309758
$914$	3.06041e12	0.145051
$915$	0	0
$916$	−4.11185e12	−0.192978
$917$	−6.63375e11	−0.0309811
$918$	−3.52897e12	−0.164005
$919$	−1.78486e13	−0.825437	−0.412719	−	0.910859i	$-0.635421\pi$
$919$	−1.78486e13	−0.825437	−0.412719	+	0.910859i	$0.635421\pi$
$920$	0	0
$921$	1.52293e13	0.697447
$922$	7.81490e12	0.356151
$923$	5.88923e12	0.267086
$924$	8.17315e12	0.368863
$925$	0	0
$926$	−4.28551e13	−1.91537
$927$	−2.32604e13	−1.03457
$928$	2.03782e12	0.0901988
$929$	−2.28123e13	−1.00484	−0.502422	−	0.864622i	$-0.667558\pi$
$929$	−2.28123e13	−1.00484	−0.502422	+	0.864622i	$0.667558\pi$
$930$	0	0
$931$	−2.47272e12	−0.107870
$932$	−3.63795e12	−0.157937
$933$	3.93307e13	1.69928
$934$	1.40375e13	0.603572
$935$	0	0
$936$	5.26486e12	0.224205
$937$	−9.14211e12	−0.387452	−0.193726	−	0.981056i	$-0.562057\pi$
$937$	−9.14211e12	−0.387452	−0.193726	+	0.981056i	$0.562057\pi$
$938$	−2.85181e13	−1.20284
$939$	9.05084e12	0.379922
$940$	0	0
$941$	2.42073e13	1.00645	0.503225	−	0.864155i	$-0.332147\pi$
$941$	2.42073e13	1.00645	0.503225	+	0.864155i	$0.332147\pi$
$942$	−2.53931e13	−1.05072
$943$	2.58082e13	1.06281
$944$	−4.00719e13	−1.64235
$945$	0	0
$946$	4.57113e13	1.85573
$947$	−1.63239e13	−0.659550	−0.329775	−	0.944060i	$-0.606973\pi$
$947$	−1.63239e13	−0.659550	−0.329775	+	0.944060i	$0.606973\pi$
$948$	−9.68202e11	−0.0389340
$949$	9.83767e12	0.393726
$950$	0	0
$951$	−2.31630e12	−0.0918295
$952$	−2.47313e13	−0.975845
$953$	−2.42382e13	−0.951880	−0.475940	−	0.879478i	$-0.657892\pi$
$953$	−2.42382e13	−0.951880	−0.475940	+	0.879478i	$0.657892\pi$
$954$	−4.50844e13	−1.76221
$955$	0	0
$956$	−4.31641e12	−0.167133
$957$	1.38637e13	0.534289
$958$	2.30134e13	0.882748
$959$	−7.03523e12	−0.268593
$960$	0	0
$961$	−2.12803e13	−0.804864
$962$	−3.32123e12	−0.125029
$963$	−1.42758e13	−0.534910
$964$	−1.03447e12	−0.0385809
$965$	0	0
$966$	1.95470e13	0.722244
$967$	1.11387e13	0.409654	0.204827	−	0.978798i	$-0.434337\pi$
$967$	1.11387e13	0.409654	0.204827	+	0.978798i	$0.434337\pi$
$968$	−4.00987e13	−1.46788
$969$	1.86652e13	0.680106
$970$	0	0
$971$	−3.10112e13	−1.11952	−0.559760	−	0.828655i	$-0.689107\pi$
$971$	−3.10112e13	−1.11952	−0.559760	+	0.828655i	$0.689107\pi$
$972$	7.40165e12	0.265969
$973$	2.58837e13	0.925804
$974$	1.11134e12	0.0395668
$975$	0	0
$976$	3.74699e13	1.32178
$977$	−1.16626e13	−0.409516	−0.204758	−	0.978813i	$-0.565641\pi$
$977$	−1.16626e13	−0.409516	−0.204758	+	0.978813i	$0.565641\pi$
$978$	3.23171e13	1.12956
$979$	−4.89889e13	−1.70442
$980$	0	0
$981$	−7.94651e12	−0.273947
$982$	1.10729e13	0.379980
$983$	1.20376e13	0.411198	0.205599	−	0.978636i	$-0.434086\pi$
$983$	1.20376e13	0.411198	0.205599	+	0.978636i	$0.434086\pi$
$984$	6.73834e13	2.29126
$985$	0	0
$986$	1.00582e13	0.338904
$987$	5.35246e13	1.79526
$988$	−6.01056e11	−0.0200682
$989$	1.77164e13	0.588834
$990$	0	0
$991$	4.45908e13	1.46863	0.734317	−	0.678806i	$-0.237502\pi$
$991$	4.45908e13	1.46863	0.734317	+	0.678806i	$0.237502\pi$
$992$	−5.14247e12	−0.168604
$993$	−3.87379e13	−1.26434
$994$	2.73148e13	0.887480
$995$	0	0
$996$	1.57788e12	0.0508050
$997$	−5.03829e13	−1.61493	−0.807467	−	0.589912i	$-0.799162\pi$
$997$	−5.03829e13	−1.61493	−0.807467	+	0.589912i	$0.799162\pi$
$998$	1.79897e13	0.574032
$999$	1.48564e12	0.0471922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.b.1.5		5
5.4	even	2		13.10.a.b.1.1	✓	5
15.14	odd	2		117.10.a.e.1.5		5
20.19	odd	2		208.10.a.h.1.2		5
65.64	even	2		169.10.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.1	✓	5	5.4	even	2
117.10.a.e.1.5		5	15.14	odd	2
169.10.a.b.1.5		5	65.64	even	2
208.10.a.h.1.2		5	20.19	odd	2
325.10.a.b.1.5		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)

\(f(q)\)	\(=\)	\(q+24.7188 q^{2} -194.269 q^{3} +99.0182 q^{4} -4802.09 q^{6} -5359.02 q^{7} -10208.4 q^{8} +18057.4 q^{9} +O(q^{10})\)	\(q+24.7188 q^{2} -194.269 q^{3} +99.0182 q^{4} -4802.09 q^{6} -5359.02 q^{7} -10208.4 q^{8} +18057.4 q^{9} +79284.0 q^{11} -19236.2 q^{12} -28561.0 q^{13} -132468. q^{14} -303037. q^{16} -452068. q^{17} +446357. q^{18} +212533. q^{19} +1.04109e6 q^{21} +1.95980e6 q^{22} +759566. q^{23} +1.98318e6 q^{24} -705993. q^{26} +315803. q^{27} -530640. q^{28} -900101. q^{29} +2.27141e6 q^{31} -2.26400e6 q^{32} -1.54024e7 q^{33} -1.11746e7 q^{34} +1.78801e6 q^{36} +4.70433e6 q^{37} +5.25355e6 q^{38} +5.54851e6 q^{39} +3.39775e7 q^{41} +2.57345e7 q^{42} +2.33244e7 q^{43} +7.85057e6 q^{44} +1.87755e7 q^{46} +5.14121e7 q^{47} +5.88706e7 q^{48} -1.16346e7 q^{49} +8.78228e7 q^{51} -2.82806e6 q^{52} -1.01005e8 q^{53} +7.80627e6 q^{54} +5.47070e7 q^{56} -4.12885e7 q^{57} -2.22494e7 q^{58} +1.32234e8 q^{59} -1.23648e8 q^{61} +5.61465e7 q^{62} -9.67699e7 q^{63} +9.91916e7 q^{64} -3.80729e8 q^{66} +2.15282e8 q^{67} -4.47630e7 q^{68} -1.47560e8 q^{69} -2.06198e8 q^{71} -1.84337e8 q^{72} -3.44444e8 q^{73} +1.16285e8 q^{74} +2.10446e7 q^{76} -4.24884e8 q^{77} +1.37153e8 q^{78} +5.03324e7 q^{79} -4.16775e8 q^{81} +8.39883e8 q^{82} -8.20266e7 q^{83} +1.03087e8 q^{84} +5.76552e8 q^{86} +1.74862e8 q^{87} -8.09364e8 q^{88} -6.17891e8 q^{89} +1.53059e8 q^{91} +7.52109e7 q^{92} -4.41265e8 q^{93} +1.27084e9 q^{94} +4.39824e8 q^{96} +9.91253e8 q^{97} -2.87592e8 q^{98} +1.43166e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} - 161 q^{3} + 361 q^{4} + 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9}+O(q^{10}) \) 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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