LMFDB - Embedded newform 75.22.a.m.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,22,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	75.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:	$209.608008215$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 15486550 x^{8} - 930225020 x^{7} + 80619202368510 x^{6} + \cdots + 47\!\cdots\!18 $ x^10 - 5x^9 - 15486550x^8 - 930225020x^7 + 80619202368510x^6 + 14206919536731394x^5 - 159833300365521427920x^4 - 53427455410418539963580x^3 + 93639331506281672292832825x^2 + 44269185428005803484908321595*x + 4729332062567824907768533377518
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{14}\cdot 5^{24}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-173.651$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-238.651 q^{2} +59049.0 q^{3} -2.04020e6 q^{4} -1.40921e7 q^{6} -6.18210e8 q^{7} +9.87381e8 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q-238.651 q^{2} +59049.0 q^{3} -2.04020e6 q^{4} -1.40921e7 q^{6} -6.18210e8 q^{7} +9.87381e8 q^{8} +3.48678e9 q^{9} -1.54555e11 q^{11} -1.20472e11 q^{12} +3.64291e11 q^{13} +1.47536e11 q^{14} +4.04297e12 q^{16} -2.70949e12 q^{17} -8.32123e11 q^{18} -5.88717e12 q^{19} -3.65047e13 q^{21} +3.68846e13 q^{22} +3.03993e14 q^{23} +5.83039e13 q^{24} -8.69382e13 q^{26} +2.05891e14 q^{27} +1.26127e15 q^{28} +1.45010e15 q^{29} +1.69163e15 q^{31} -3.03554e15 q^{32} -9.12632e15 q^{33} +6.46622e14 q^{34} -7.11373e15 q^{36} -1.82754e16 q^{37} +1.40498e15 q^{38} +2.15110e16 q^{39} -4.21105e16 q^{41} +8.71186e15 q^{42} +1.70731e17 q^{43} +3.15323e17 q^{44} -7.25480e16 q^{46} +1.64776e17 q^{47} +2.38733e17 q^{48} -1.76363e17 q^{49} -1.59993e17 q^{51} -7.43225e17 q^{52} +2.18231e18 q^{53} -4.91360e16 q^{54} -6.10409e17 q^{56} -3.47631e17 q^{57} -3.46068e17 q^{58} +1.67554e18 q^{59} -8.99964e18 q^{61} -4.03708e17 q^{62} -2.15556e18 q^{63} -7.75428e18 q^{64} +2.17800e18 q^{66} +2.10743e19 q^{67} +5.52790e18 q^{68} +1.79505e19 q^{69} +3.20418e18 q^{71} +3.44278e18 q^{72} +2.93900e19 q^{73} +4.36143e18 q^{74} +1.20110e19 q^{76} +9.55474e19 q^{77} -5.13361e18 q^{78} -1.30349e20 q^{79} +1.21577e19 q^{81} +1.00497e19 q^{82} -1.91067e20 q^{83} +7.44767e19 q^{84} -4.07450e19 q^{86} +8.56272e19 q^{87} -1.52605e20 q^{88} -1.00721e20 q^{89} -2.25208e20 q^{91} -6.20205e20 q^{92} +9.98890e19 q^{93} -3.93240e19 q^{94} -1.79246e20 q^{96} -1.27757e19 q^{97} +4.20890e19 q^{98} -5.38900e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9}+O(q^{10}) $ 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9	$ 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9} + 5976221790 q^{11} + 593041212045 q^{12} - 842570747430 q^{13} + 1605059874570 q^{14} + 6061861547825 q^{16} - 12910340404230 q^{17} - 2248975938645 q^{18} - 76155422176280 q^{19} - 6811732617210 q^{21} - 461780887241010 q^{22} - 82640920915920 q^{23} - 18549814359015 q^{24} + 286555331159670 q^{26} + 20\!\cdots\!90 q^{27}+ \cdots + 20\!\cdots\!90 q^{99}+O(q^{100}) $ 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9 + 5976221790 * q^11 + 593041212045 * q^12 - 842570747430 * q^13 + 1605059874570 * q^14 + 6061861547825 * q^16 - 12910340404230 * q^17 - 2248975938645 * q^18 - 76155422176280 * q^19 - 6811732617210 * q^21 - 461780887241010 * q^22 - 82640920915920 * q^23 - 18549814359015 * q^24 + 286555331159670 * q^26 + 2058911320946490 * q^27 - 1520428218531930 * q^28 - 2553653160731010 * q^29 - 5579671364724940 * q^31 - 29255856594217815 * q^32 + 352889920477710 * q^33 + 36285968426431010 * q^34 + 35018490530045205 * q^36 - 1797908431222890 * q^37 - 10684960744876320 * q^38 - 49752960064994070 * q^39 - 157319729506021440 * q^41 + 94777180533483930 * q^42 + 148924853700743400 * q^43 + 49118820773767290 * q^44 - 238453286038259540 * q^46 + 43171138083158100 * q^47 + 357946862537518425 * q^48 + 453692886452454950 * q^49 - 762342690529377270 * q^51 - 5077473324432504030 * q^52 - 1835165786666252970 * q^53 - 132799780201048605 * q^54 - 5146515624013530450 * q^56 - 4496901524087157720 * q^57 - 3684042125074285440 * q^58 + 4936135121536323630 * q^59 - 4443080871007408300 * q^61 - 39366851097921260280 * q^62 - 402225999313633290 * q^63 - 14877283608188093455 * q^64 - 27267699610694399490 * q^66 - 33664559574358232580 * q^67 - 44791395195934111290 * q^68 - 4879863739164160080 * q^69 - 74662724971386630180 * q^71 - 1095347988085476735 * q^72 - 16062862692682477620 * q^73 - 130249023546610518030 * q^74 - 258736483662380220720 * q^76 - 56216747719240740180 * q^77 + 16920805749647353830 * q^78 - 49130708010799643300 * q^79 + 121576654590569288010 * q^81 - 117185080045656261930 * q^82 - 118408383608453695560 * q^83 - 89779765876091934570 * q^84 - 1007271272794707382260 * q^86 - 150790665488005409490 * q^87 - 41803519849182967710 * q^88 - 572103976713991581780 * q^89 - 1669810835257196575140 * q^91 + 1206545757146297440260 * q^92 - 329474014415642982060 * q^93 - 1671319720124696594920 * q^94 - 1727529076031967757935 * q^96 + 1299275526640742173920 * q^97 + 2683959884079093505455 * q^98 + 20837796914288297790 * 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 $

$2$	−238.651	−0.164796	−0.0823982	−	0.996599i	$-0.526258\pi$
$2$	−238.651	−0.164796	−0.0823982	+	0.996599i	$0.526258\pi$
$3$	59049.0	0.577350
$3$	59049.0	0.577350
$4$	−2.04020e6	−0.972842
$5$	0	0
$5$	0	0
$6$	−1.40921e7	−0.0951452
$7$	−6.18210e8	−0.827192	−0.413596	−	0.910460i	$-0.635727\pi$
$7$	−6.18210e8	−0.827192	−0.413596	+	0.910460i	$0.635727\pi$
$8$	9.87381e8	0.325117
$9$	3.48678e9	0.333333
$10$	0	0
$11$	−1.54555e11	−1.79663	−0.898317	−	0.439347i	$-0.855210\pi$
$11$	−1.54555e11	−1.79663	−0.898317	+	0.439347i	$0.855210\pi$
$12$	−1.20472e11	−0.561671
$13$	3.64291e11	0.732897	0.366449	−	0.930438i	$-0.380574\pi$
$13$	3.64291e11	0.732897	0.366449	+	0.930438i	$0.380574\pi$
$14$	1.47536e11	0.136318
$15$	0	0
$16$	4.04297e12	0.919264
$17$	−2.70949e12	−0.325968	−0.162984	−	0.986629i	$-0.552112\pi$
$17$	−2.70949e12	−0.325968	−0.162984	+	0.986629i	$0.552112\pi$
$18$	−8.32123e11	−0.0549321
$19$	−5.88717e12	−0.220289	−0.110145	−	0.993916i	$-0.535131\pi$
$19$	−5.88717e12	−0.220289	−0.110145	+	0.993916i	$0.535131\pi$
$20$	0	0
$21$	−3.65047e13	−0.477580
$22$	3.68846e13	0.296079
$23$	3.03993e14	1.53010	0.765052	−	0.643969i	$-0.222713\pi$
$23$	3.03993e14	1.53010	0.765052	+	0.643969i	$0.222713\pi$
$24$	5.83039e13	0.187706
$25$	0	0
$26$	−8.69382e13	−0.120779
$27$	2.05891e14	0.192450
$28$	1.26127e15	0.804727
$29$	1.45010e15	0.640059	0.320030	−	0.947408i	$-0.396307\pi$
$29$	1.45010e15	0.640059	0.320030	+	0.947408i	$0.396307\pi$
$30$	0	0
$31$	1.69163e15	0.370687	0.185343	−	0.982674i	$-0.440660\pi$
$31$	1.69163e15	0.370687	0.185343	+	0.982674i	$0.440660\pi$
$32$	−3.03554e15	−0.476608
$33$	−9.12632e15	−1.03729
$34$	6.46622e14	0.0537183
$35$	0	0
$36$	−7.11373e15	−0.324281
$37$	−1.82754e16	−0.624811	−0.312405	−	0.949949i	$-0.601135\pi$
$37$	−1.82754e16	−0.624811	−0.312405	+	0.949949i	$0.601135\pi$
$38$	1.40498e15	0.0363029
$39$	2.15110e16	0.423138
$40$	0	0
$41$	−4.21105e16	−0.489959	−0.244979	−	0.969528i	$-0.578781\pi$
$41$	−4.21105e16	−0.489959	−0.244979	+	0.969528i	$0.578781\pi$
$42$	8.71186e15	0.0787034
$43$	1.70731e17	1.20474	0.602369	−	0.798217i	$-0.294223\pi$
$43$	1.70731e17	1.20474	0.602369	+	0.798217i	$0.294223\pi$
$44$	3.15323e17	1.74784
$45$	0	0
$46$	−7.25480e16	−0.252155
$47$	1.64776e17	0.456949	0.228474	−	0.973550i	$-0.426626\pi$
$47$	1.64776e17	0.456949	0.228474	+	0.973550i	$0.426626\pi$
$48$	2.38733e17	0.530737
$49$	−1.76363e17	−0.315753
$50$	0	0
$51$	−1.59993e17	−0.188197
$52$	−7.43225e17	−0.712993
$53$	2.18231e18	1.71404	0.857019	−	0.515284i	$-0.172314\pi$
$53$	2.18231e18	1.71404	0.857019	+	0.515284i	$0.172314\pi$
$54$	−4.91360e16	−0.0317151
$55$	0	0
$56$	−6.10409e17	−0.268934
$57$	−3.47631e17	−0.127184
$58$	−3.46068e17	−0.105479
$59$	1.67554e18	0.426784	0.213392	−	0.976967i	$-0.431549\pi$
$59$	1.67554e18	0.426784	0.213392	+	0.976967i	$0.431549\pi$
$60$	0	0
$61$	−8.99964e18	−1.61533	−0.807666	−	0.589640i	$-0.799270\pi$
$61$	−8.99964e18	−1.61533	−0.807666	+	0.589640i	$0.799270\pi$
$62$	−4.03708e17	−0.0610878
$63$	−2.15556e18	−0.275731
$64$	−7.75428e18	−0.840721
$65$	0	0
$66$	2.17800e18	0.170941
$67$	2.10743e19	1.41243	0.706217	−	0.707995i	$-0.250400\pi$
$67$	2.10743e19	1.41243	0.706217	+	0.707995i	$0.250400\pi$
$68$	5.52790e18	0.317115
$69$	1.79505e19	0.883406
$70$	0	0
$71$	3.20418e18	0.116816	0.0584082	−	0.998293i	$-0.481398\pi$
$71$	3.20418e18	0.116816	0.0584082	+	0.998293i	$0.481398\pi$
$72$	3.44278e18	0.108372
$73$	2.93900e19	0.800404	0.400202	−	0.916427i	$-0.368940\pi$
$73$	2.93900e19	0.800404	0.400202	+	0.916427i	$0.368940\pi$
$74$	4.36143e18	0.102967
$75$	0	0
$76$	1.20110e19	0.214307
$77$	9.55474e19	1.48616
$78$	−5.13361e18	−0.0697316
$79$	−1.30349e20	−1.54890	−0.774450	−	0.632635i	$-0.781973\pi$
$79$	−1.30349e20	−1.54890	−0.774450	+	0.632635i	$0.781973\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	1.00497e19	0.0807434
$83$	−1.91067e20	−1.35166	−0.675829	−	0.737059i	$-0.736214\pi$
$83$	−1.91067e20	−1.35166	−0.675829	+	0.737059i	$0.736214\pi$
$84$	7.44767e19	0.464610
$85$	0	0
$86$	−4.07450e19	−0.198537
$87$	8.56272e19	0.369538
$88$	−1.52605e20	−0.584117
$89$	−1.00721e20	−0.342393	−0.171196	−	0.985237i	$-0.554763\pi$
$89$	−1.00721e20	−0.342393	−0.171196	+	0.985237i	$0.554763\pi$
$90$	0	0
$91$	−2.25208e20	−0.606247
$92$	−6.20205e20	−1.48855
$93$	9.98890e19	0.214016
$94$	−3.93240e19	−0.0753034
$95$	0	0
$96$	−1.79246e20	−0.275170
$97$	−1.27757e19	−0.0175907	−0.00879533	−	0.999961i	$-0.502800\pi$
$97$	−1.27757e19	−0.0175907	−0.00879533	+	0.999961i	$0.502800\pi$
$98$	4.20890e19	0.0520349
$99$	−5.38900e20	−0.598878
$100$	0	0
$101$	−6.44776e20	−0.580811	−0.290405	−	0.956904i	$-0.593790\pi$
$101$	−6.44776e20	−0.580811	−0.290405	+	0.956904i	$0.593790\pi$
$102$	3.81824e19	0.0310142
$103$	1.96314e21	1.43933	0.719666	−	0.694321i	$-0.244295\pi$
$103$	1.96314e21	1.43933	0.719666	+	0.694321i	$0.244295\pi$
$104$	3.59694e20	0.238277
$105$	0	0
$106$	−5.20810e20	−0.282467
$107$	−2.47787e21	−1.21773	−0.608863	−	0.793275i	$-0.708374\pi$
$107$	−2.47787e21	−1.21773	−0.608863	+	0.793275i	$0.708374\pi$
$108$	−4.20059e20	−0.187224
$109$	3.30325e21	1.33648	0.668241	−	0.743945i	$-0.267047\pi$
$109$	3.30325e21	1.33648	0.668241	+	0.743945i	$0.267047\pi$
$110$	0	0
$111$	−1.07914e21	−0.360735
$112$	−2.49940e21	−0.760408
$113$	−2.76645e21	−0.766653	−0.383326	−	0.923613i	$-0.625222\pi$
$113$	−2.76645e21	−0.766653	−0.383326	+	0.923613i	$0.625222\pi$
$114$	8.29624e19	0.0209595
$115$	0	0
$116$	−2.95850e21	−0.622677
$117$	1.27020e21	0.244299
$118$	−3.99868e20	−0.0703325
$119$	1.67504e21	0.269638
$120$	0	0
$121$	1.64870e22	2.22790
$122$	2.14777e21	0.266201
$123$	−2.48658e21	−0.282878
$124$	−3.45126e21	−0.360620
$125$	0	0
$126$	5.14427e20	0.0454394
$127$	1.00090e22	0.813678	0.406839	−	0.913500i	$-0.366631\pi$
$127$	1.00090e22	0.813678	0.406839	+	0.913500i	$0.366631\pi$
$128$	8.21656e21	0.615156
$129$	1.00815e22	0.695556
$130$	0	0
$131$	4.52685e21	0.265734	0.132867	−	0.991134i	$-0.457582\pi$
$131$	4.52685e21	0.265734	0.132867	+	0.991134i	$0.457582\pi$
$132$	1.86195e22	1.00912
$133$	3.63950e21	0.182222
$134$	−5.02940e21	−0.232764
$135$	0	0
$136$	−2.67530e21	−0.105978
$137$	1.95786e22	0.718152	0.359076	−	0.933308i	$-0.383092\pi$
$137$	1.95786e22	0.718152	0.359076	+	0.933308i	$0.383092\pi$
$138$	−4.28389e21	−0.145582
$139$	−5.05073e22	−1.59110	−0.795552	−	0.605885i	$-0.792819\pi$
$139$	−5.05073e22	−1.59110	−0.795552	+	0.605885i	$0.792819\pi$
$140$	0	0
$141$	9.72988e21	0.263819
$142$	−7.64679e20	−0.0192509
$143$	−5.63029e22	−1.31675
$144$	1.40970e22	0.306421
$145$	0	0
$146$	−7.01393e21	−0.131904
$147$	−1.04140e22	−0.182300
$148$	3.72854e22	0.607842
$149$	9.33439e22	1.41785	0.708924	−	0.705284i	$-0.249181\pi$
$149$	9.33439e22	1.41785	0.708924	+	0.705284i	$0.249181\pi$
$150$	0	0
$151$	9.83621e22	1.29888	0.649441	−	0.760412i	$-0.275003\pi$
$151$	9.83621e22	1.29888	0.649441	+	0.760412i	$0.275003\pi$
$152$	−5.81288e21	−0.0716198
$153$	−9.44742e21	−0.108656
$154$	−2.28024e22	−0.244914
$155$	0	0
$156$	−4.38867e22	−0.411647
$157$	−2.23677e23	−1.96189	−0.980947	−	0.194276i	$-0.937764\pi$
$157$	−2.23677e23	−1.96189	−0.980947	+	0.194276i	$0.937764\pi$
$158$	3.11079e22	0.255253
$159$	1.28863e23	0.989601
$160$	0	0
$161$	−1.87931e23	−1.26569
$162$	−2.90143e21	−0.0183107
$163$	4.52230e22	0.267541	0.133770	−	0.991012i	$-0.457292\pi$
$163$	4.52230e22	0.267541	0.133770	+	0.991012i	$0.457292\pi$
$164$	8.59137e22	0.476653
$165$	0	0
$166$	4.55984e22	0.222748
$167$	5.26177e22	0.241329	0.120664	−	0.992693i	$-0.461498\pi$
$167$	5.26177e22	0.241329	0.120664	+	0.992693i	$0.461498\pi$
$168$	−3.60440e22	−0.155269
$169$	−1.14357e23	−0.462862
$170$	0	0
$171$	−2.05273e22	−0.0734298
$172$	−3.48324e23	−1.17202
$173$	−1.50105e23	−0.475238	−0.237619	−	0.971358i	$-0.576367\pi$
$173$	−1.50105e23	−0.475238	−0.237619	+	0.971358i	$0.576367\pi$
$174$	−2.04350e22	−0.0608986
$175$	0	0
$176$	−6.24861e23	−1.65158
$177$	9.89389e22	0.246404
$178$	2.40371e22	0.0564251
$179$	−8.39340e23	−1.85772	−0.928861	−	0.370428i	$-0.879211\pi$
$179$	−8.39340e23	−1.85772	−0.928861	+	0.370428i	$0.879211\pi$
$180$	0	0
$181$	6.73386e23	1.32629	0.663146	−	0.748490i	$-0.269221\pi$
$181$	6.73386e23	1.32629	0.663146	+	0.748490i	$0.269221\pi$
$182$	5.37460e22	0.0999072
$183$	−5.31420e23	−0.932613
$184$	3.00157e23	0.497463
$185$	0	0
$186$	−2.38386e22	−0.0352691
$187$	4.18766e23	0.585645
$188$	−3.36176e23	−0.444539
$189$	−1.27284e23	−0.159193
$190$	0	0
$191$	−5.16905e23	−0.578843	−0.289421	−	0.957202i	$-0.593463\pi$
$191$	−5.16905e23	−0.578843	−0.289421	+	0.957202i	$0.593463\pi$
$192$	−4.57882e23	−0.485390
$193$	−1.02137e24	−1.02525	−0.512625	−	0.858613i	$-0.671327\pi$
$193$	−1.02137e24	−1.02525	−0.512625	+	0.858613i	$0.671327\pi$
$194$	3.04893e21	0.00289888
$195$	0	0
$196$	3.59814e23	0.307178
$197$	1.84469e24	1.49289	0.746444	−	0.665448i	$-0.231759\pi$
$197$	1.84469e24	1.49289	0.746444	+	0.665448i	$0.231759\pi$
$198$	1.28609e23	0.0986929
$199$	−7.85318e23	−0.571595	−0.285797	−	0.958290i	$-0.592258\pi$
$199$	−7.85318e23	−0.571595	−0.285797	+	0.958290i	$0.592258\pi$
$200$	0	0
$201$	1.24442e24	0.815469
$202$	1.53876e23	0.0957155
$203$	−8.96468e23	−0.529452
$204$	3.26417e23	0.183086
$205$	0	0
$206$	−4.68505e23	−0.237196
$207$	1.05996e24	0.510035
$208$	1.47282e24	0.673726
$209$	9.09891e23	0.395779
$210$	0	0
$211$	−4.06508e23	−0.159994	−0.0799969	−	0.996795i	$-0.525491\pi$
$211$	−4.06508e23	−0.159994	−0.0799969	+	0.996795i	$0.525491\pi$
$212$	−4.45235e24	−1.66749
$213$	1.89203e23	0.0674440
$214$	5.91346e23	0.200677
$215$	0	0
$216$	2.03293e23	0.0625688
$217$	−1.04578e24	−0.306629
$218$	−7.88323e23	−0.220247
$219$	1.73545e24	0.462113
$220$	0	0
$221$	−9.87043e23	−0.238901
$222$	2.57538e23	0.0594477
$223$	−8.43437e24	−1.85717	−0.928585	−	0.371120i	$-0.878974\pi$
$223$	−8.43437e24	−1.85717	−0.928585	+	0.371120i	$0.878974\pi$
$224$	1.87660e24	0.394247
$225$	0	0
$226$	6.60214e23	0.126342
$227$	−7.73212e24	−1.41263	−0.706313	−	0.707900i	$-0.749643\pi$
$227$	−7.73212e24	−1.41263	−0.706313	+	0.707900i	$0.749643\pi$
$228$	7.09237e23	0.123730
$229$	−4.54284e23	−0.0756929	−0.0378464	−	0.999284i	$-0.512050\pi$
$229$	−4.54284e23	−0.0756929	−0.0378464	+	0.999284i	$0.512050\pi$
$230$	0	0
$231$	5.64198e24	0.858036
$232$	1.43180e24	0.208094
$233$	−1.11888e25	−1.55434	−0.777171	−	0.629289i	$-0.783346\pi$
$233$	−1.11888e25	−1.55434	−0.777171	+	0.629289i	$0.783346\pi$
$234$	−3.03135e23	−0.0402596
$235$	0	0
$236$	−3.41843e24	−0.415194
$237$	−7.69698e24	−0.894258
$238$	−3.99748e23	−0.0444353
$239$	−1.59625e25	−1.69794	−0.848971	−	0.528440i	$-0.822777\pi$
$239$	−1.59625e25	−1.69794	−0.848971	+	0.528440i	$0.822777\pi$
$240$	0	0
$241$	−1.12567e25	−1.09706	−0.548532	−	0.836130i	$-0.684813\pi$
$241$	−1.12567e25	−1.09706	−0.548532	+	0.836130i	$0.684813\pi$
$242$	−3.93463e24	−0.367149
$243$	7.17898e23	0.0641500
$244$	1.83611e25	1.57146
$245$	0	0
$246$	5.93424e23	0.0466172
$247$	−2.14464e24	−0.161449
$248$	1.67028e24	0.120517
$249$	−1.12823e25	−0.780380
$250$	0	0
$251$	1.51746e25	0.965037	0.482519	−	0.875886i	$-0.339722\pi$
$251$	1.51746e25	0.965037	0.482519	+	0.875886i	$0.339722\pi$
$252$	4.39778e24	0.268242
$253$	−4.69836e25	−2.74904
$254$	−2.38866e24	−0.134091
$255$	0	0
$256$	1.43010e25	0.739345
$257$	5.90512e24	0.293043	0.146521	−	0.989207i	$-0.453192\pi$
$257$	5.90512e24	0.293043	0.146521	+	0.989207i	$0.453192\pi$
$258$	−2.40595e24	−0.114625
$259$	1.12980e25	0.516839
$260$	0	0
$261$	5.05620e24	0.213353
$262$	−1.08034e24	−0.0437921
$263$	−3.44551e25	−1.34189	−0.670947	−	0.741505i	$-0.734112\pi$
$263$	−3.44551e25	−1.34189	−0.670947	+	0.741505i	$0.734112\pi$
$264$	−9.01115e24	−0.337240
$265$	0	0
$266$	−8.68570e23	−0.0300295
$267$	−5.94747e24	−0.197681
$268$	−4.29958e25	−1.37408
$269$	1.94334e25	0.597241	0.298620	−	0.954372i	$-0.403474\pi$
$269$	1.94334e25	0.597241	0.298620	+	0.954372i	$0.403474\pi$
$270$	0	0
$271$	−3.68343e25	−1.04731	−0.523654	−	0.851931i	$-0.675432\pi$
$271$	−3.68343e25	−1.04731	−0.523654	+	0.851931i	$0.675432\pi$
$272$	−1.09544e25	−0.299650
$273$	−1.32983e25	−0.350017
$274$	−4.67245e24	−0.118349
$275$	0	0
$276$	−3.66225e25	−0.859414
$277$	−4.57582e24	−0.103379	−0.0516894	−	0.998663i	$-0.516461\pi$
$277$	−4.57582e24	−0.103379	−0.0516894	+	0.998663i	$0.516461\pi$
$278$	1.20536e25	0.262208
$279$	5.89834e24	0.123562
$280$	0	0
$281$	1.24301e24	0.0241579	0.0120790	−	0.999927i	$-0.496155\pi$
$281$	1.24301e24	0.0241579	0.0120790	+	0.999927i	$0.496155\pi$
$282$	−2.32204e24	−0.0434765
$283$	5.91462e25	1.06701	0.533506	−	0.845797i	$-0.320874\pi$
$283$	5.91462e25	1.06701	0.533506	+	0.845797i	$0.320874\pi$
$284$	−6.53715e24	−0.113644
$285$	0	0
$286$	1.34367e25	0.216995
$287$	2.60331e25	0.405290
$288$	−1.05843e25	−0.158869
$289$	−6.17506e25	−0.893745
$290$	0	0
$291$	−7.54394e23	−0.0101560
$292$	−5.99614e25	−0.778667
$293$	−6.18392e25	−0.774736	−0.387368	−	0.921925i	$-0.626616\pi$
$293$	−6.18392e25	−0.774736	−0.387368	+	0.921925i	$0.626616\pi$
$294$	2.48531e24	0.0300424
$295$	0	0
$296$	−1.80448e25	−0.203137
$297$	−3.18215e25	−0.345763
$298$	−2.22766e25	−0.233656
$299$	1.10742e26	1.12141
$300$	0	0
$301$	−1.05547e26	−0.996551
$302$	−2.34742e25	−0.214051
$303$	−3.80734e25	−0.335331
$304$	−2.38016e25	−0.202504
$305$	0	0
$306$	2.25463e24	0.0179061
$307$	−1.45164e26	−1.11405	−0.557026	−	0.830495i	$-0.688058\pi$
$307$	−1.45164e26	−1.11405	−0.557026	+	0.830495i	$0.688058\pi$
$308$	−1.94936e26	−1.44580
$309$	1.15922e26	0.830998
$310$	0	0
$311$	2.62778e26	1.76037	0.880186	−	0.474628i	$-0.157418\pi$
$311$	2.62778e26	1.76037	0.880186	+	0.474628i	$0.157418\pi$
$312$	2.12396e25	0.137570
$313$	−1.65162e26	−1.03441	−0.517206	−	0.855861i	$-0.673028\pi$
$313$	−1.65162e26	−1.03441	−0.517206	+	0.855861i	$0.673028\pi$
$314$	5.33807e25	0.323313
$315$	0	0
$316$	2.65938e26	1.50684
$317$	−1.58885e26	−0.870884	−0.435442	−	0.900217i	$-0.643408\pi$
$317$	−1.58885e26	−0.870884	−0.435442	+	0.900217i	$0.643408\pi$
$318$	−3.07533e25	−0.163083
$319$	−2.24121e26	−1.14995
$320$	0	0
$321$	−1.46316e26	−0.703054
$322$	4.48499e25	0.208581
$323$	1.59512e25	0.0718072
$324$	−2.48040e25	−0.108094
$325$	0	0
$326$	−1.07925e25	−0.0440897
$327$	1.95054e26	0.771619
$328$	−4.15791e25	−0.159294
$329$	−1.01866e26	−0.377984
$330$	0	0
$331$	1.34319e26	0.467676	0.233838	−	0.972276i	$-0.424871\pi$
$331$	1.34319e26	0.467676	0.233838	+	0.972276i	$0.424871\pi$
$332$	3.89815e26	1.31495
$333$	−6.37223e25	−0.208270
$334$	−1.25572e25	−0.0397701
$335$	0	0
$336$	−1.47587e26	−0.439022
$337$	−3.55145e26	−1.02398	−0.511990	−	0.858991i	$-0.671092\pi$
$337$	−3.55145e26	−1.02398	−0.511990	+	0.858991i	$0.671092\pi$
$338$	2.72913e25	0.0762780
$339$	−1.63356e26	−0.442627
$340$	0	0
$341$	−2.61450e26	−0.665989
$342$	4.89885e24	0.0121010
$343$	4.54328e26	1.08838
$344$	1.68576e26	0.391681
$345$	0	0
$346$	3.58227e25	0.0783175
$347$	−2.39692e26	−0.508387	−0.254194	−	0.967153i	$-0.581810\pi$
$347$	−2.39692e26	−0.508387	−0.254194	+	0.967153i	$0.581810\pi$
$348$	−1.74696e26	−0.359502
$349$	9.09176e25	0.181544	0.0907719	−	0.995872i	$-0.471067\pi$
$349$	9.09176e25	0.181544	0.0907719	+	0.995872i	$0.471067\pi$
$350$	0	0
$351$	7.50042e25	0.141046
$352$	4.69158e26	0.856291
$353$	−2.48587e26	−0.440397	−0.220198	−	0.975455i	$-0.570670\pi$
$353$	−2.48587e26	−0.440397	−0.220198	+	0.975455i	$0.570670\pi$
$354$	−2.36118e25	−0.0406065
$355$	0	0
$356$	2.05491e26	0.333094
$357$	9.89091e25	0.155675
$358$	2.00309e26	0.306146
$359$	−3.60579e26	−0.535190	−0.267595	−	0.963531i	$-0.586229\pi$
$359$	−3.60579e26	−0.535190	−0.267595	+	0.963531i	$0.586229\pi$
$360$	0	0
$361$	−6.79551e26	−0.951473
$362$	−1.60704e26	−0.218568
$363$	9.73540e26	1.28628
$364$	4.59469e26	0.589782
$365$	0	0
$366$	1.26824e26	0.153691
$367$	2.92218e26	0.344123	0.172061	−	0.985086i	$-0.444957\pi$
$367$	2.92218e26	0.344123	0.172061	+	0.985086i	$0.444957\pi$
$368$	1.22903e27	1.40657
$369$	−1.46830e26	−0.163320
$370$	0	0
$371$	−1.34913e27	−1.41784
$372$	−2.03793e26	−0.208204
$373$	1.53329e26	0.152294	0.0761468	−	0.997097i	$-0.475738\pi$
$373$	1.53329e26	0.152294	0.0761468	+	0.997097i	$0.475738\pi$
$374$	−9.99387e25	−0.0965121
$375$	0	0
$376$	1.62697e26	0.148562
$377$	5.28259e26	0.469097
$378$	3.03764e25	0.0262345
$379$	7.82323e26	0.657165	0.328583	−	0.944475i	$-0.393429\pi$
$379$	7.82323e26	0.657165	0.328583	+	0.944475i	$0.393429\pi$
$380$	0	0
$381$	5.91023e26	0.469777
$382$	1.23360e26	0.0953911
$383$	1.92100e27	1.44524	0.722619	−	0.691247i	$-0.242938\pi$
$383$	1.92100e27	1.44524	0.722619	+	0.691247i	$0.242938\pi$
$384$	4.85180e26	0.355161
$385$	0	0
$386$	2.43750e26	0.168957
$387$	5.95301e26	0.401580
$388$	2.60650e25	0.0171129
$389$	−6.13581e26	−0.392104	−0.196052	−	0.980593i	$-0.562812\pi$
$389$	−6.13581e26	−0.392104	−0.196052	+	0.980593i	$0.562812\pi$
$390$	0	0
$391$	−8.23666e26	−0.498764
$392$	−1.74137e26	−0.102657
$393$	2.67306e26	0.153422
$394$	−4.40236e26	−0.246023
$395$	0	0
$396$	1.09946e27	0.582614
$397$	1.77249e27	0.914711	0.457356	−	0.889284i	$-0.348797\pi$
$397$	1.77249e27	0.914711	0.457356	+	0.889284i	$0.348797\pi$
$398$	1.87417e26	0.0941967
$399$	2.14909e26	0.105206
$400$	0	0
$401$	1.10075e27	0.511296	0.255648	−	0.966770i	$-0.417711\pi$
$401$	1.10075e27	0.511296	0.255648	+	0.966770i	$0.417711\pi$
$402$	−2.96981e26	−0.134386
$403$	6.16245e26	0.271675
$404$	1.31547e27	0.565037
$405$	0	0
$406$	2.13943e26	0.0872517
$407$	2.82455e27	1.12256
$408$	−1.57974e26	−0.0611862
$409$	−1.93550e27	−0.730632	−0.365316	−	0.930884i	$-0.619039\pi$
$409$	−1.93550e27	−0.730632	−0.365316	+	0.930884i	$0.619039\pi$
$410$	0	0
$411$	1.15610e27	0.414625
$412$	−4.00520e27	−1.40024
$413$	−1.03583e27	−0.353033
$414$	−2.52959e26	−0.0840518
$415$	0	0
$416$	−1.10582e27	−0.349305
$417$	−2.98240e27	−0.918624
$418$	−2.17146e26	−0.0652230
$419$	−2.12269e27	−0.621785	−0.310892	−	0.950445i	$-0.600628\pi$
$419$	−2.12269e27	−0.621785	−0.310892	+	0.950445i	$0.600628\pi$
$420$	0	0
$421$	3.84770e27	1.07211	0.536054	−	0.844184i	$-0.319914\pi$
$421$	3.84770e27	1.07211	0.536054	+	0.844184i	$0.319914\pi$
$422$	9.70133e25	0.0263664
$423$	5.74539e26	0.152316
$424$	2.15477e27	0.557263
$425$	0	0
$426$	−4.51535e25	−0.0111145
$427$	5.56367e27	1.33619
$428$	5.05535e27	1.18466
$429$	−3.32463e27	−0.760225
$430$	0	0
$431$	3.98462e26	0.0867711	0.0433856	−	0.999058i	$-0.486186\pi$
$431$	3.98462e26	0.0867711	0.0433856	+	0.999058i	$0.486186\pi$
$432$	8.32411e26	0.176912
$433$	3.37662e27	0.700421	0.350210	−	0.936671i	$-0.386110\pi$
$433$	3.37662e27	0.700421	0.350210	+	0.936671i	$0.386110\pi$
$434$	2.49576e26	0.0505314
$435$	0	0
$436$	−6.73929e27	−1.30019
$437$	−1.78966e27	−0.337066
$438$	−4.14166e26	−0.0761546
$439$	8.54517e27	1.53406	0.767032	−	0.641609i	$-0.221733\pi$
$439$	8.54517e27	1.53406	0.767032	+	0.641609i	$0.221733\pi$
$440$	0	0
$441$	−6.14938e26	−0.105251
$442$	2.35558e26	0.0393699
$443$	8.30162e27	1.35495	0.677476	−	0.735545i	$-0.263074\pi$
$443$	8.30162e27	1.35495	0.677476	+	0.735545i	$0.263074\pi$
$444$	2.20167e27	0.350938
$445$	0	0
$446$	2.01287e27	0.306055
$447$	5.51186e27	0.818595
$448$	4.79377e27	0.695438
$449$	−2.06284e26	−0.0292333	−0.0146167	−	0.999893i	$-0.504653\pi$
$449$	−2.06284e26	−0.0292333	−0.0146167	+	0.999893i	$0.504653\pi$
$450$	0	0
$451$	6.50838e27	0.880277
$452$	5.64410e27	0.745832
$453$	5.80818e27	0.749910
$454$	1.84528e27	0.232796
$455$	0	0
$456$	−3.43244e26	−0.0413497
$457$	−6.71470e27	−0.790509	−0.395254	−	0.918572i	$-0.629344\pi$
$457$	−6.71470e27	−0.790509	−0.395254	+	0.918572i	$0.629344\pi$
$458$	1.08415e26	0.0124739
$459$	−5.57861e26	−0.0627325
$460$	0	0
$461$	−6.39024e27	−0.686526	−0.343263	−	0.939239i	$-0.611532\pi$
$461$	−6.39024e27	−0.686526	−0.343263	+	0.939239i	$0.611532\pi$
$462$	−1.34646e27	−0.141401
$463$	−9.84656e26	−0.101084	−0.0505422	−	0.998722i	$-0.516095\pi$
$463$	−9.84656e26	−0.101084	−0.0505422	+	0.998722i	$0.516095\pi$
$464$	5.86272e27	0.588383
$465$	0	0
$466$	2.67022e27	0.256150
$467$	−5.49320e27	−0.515226	−0.257613	−	0.966248i	$-0.582936\pi$
$467$	−5.49320e27	−0.515226	−0.257613	+	0.966248i	$0.582936\pi$
$468$	−2.59147e27	−0.237664
$469$	−1.30284e28	−1.16835
$470$	0	0
$471$	−1.32079e28	−1.13270
$472$	1.65440e27	0.138755
$473$	−2.63873e28	−2.16448
$474$	1.83689e27	0.147370
$475$	0	0
$476$	−3.41740e27	−0.262315
$477$	7.60926e27	0.571346
$478$	3.80946e27	0.279815
$479$	3.00436e27	0.215888	0.107944	−	0.994157i	$-0.465573\pi$
$479$	3.00436e27	0.215888	0.107944	+	0.994157i	$0.465573\pi$
$480$	0	0
$481$	−6.65755e27	−0.457922
$482$	2.68642e27	0.180792
$483$	−1.10972e28	−0.730746
$484$	−3.36367e28	−2.16739
$485$	0	0
$486$	−1.71327e26	−0.0105717
$487$	−6.19460e27	−0.374075	−0.187038	−	0.982353i	$-0.559889\pi$
$487$	−6.19460e27	−0.374075	−0.187038	+	0.982353i	$0.559889\pi$
$488$	−8.88608e27	−0.525172
$489$	2.67038e27	0.154465
$490$	0	0
$491$	1.93704e28	1.07345	0.536725	−	0.843757i	$-0.319661\pi$
$491$	1.93704e28	1.07345	0.536725	+	0.843757i	$0.319661\pi$
$492$	5.07312e27	0.275195
$493$	−3.92905e27	−0.208639
$494$	5.11820e26	0.0266063
$495$	0	0
$496$	6.83920e27	0.340759
$497$	−1.98085e27	−0.0966296
$498$	2.69254e27	0.128604
$499$	−1.61660e28	−0.756044	−0.378022	−	0.925797i	$-0.623396\pi$
$499$	−1.61660e28	−0.756044	−0.378022	+	0.925797i	$0.623396\pi$
$500$	0	0
$501$	3.10702e27	0.139331
$502$	−3.62143e27	−0.159035
$503$	2.77615e27	0.119393	0.0596965	−	0.998217i	$-0.480987\pi$
$503$	2.77615e27	0.119393	0.0596965	+	0.998217i	$0.480987\pi$
$504$	−2.12836e27	−0.0896448
$505$	0	0
$506$	1.12127e28	0.453031
$507$	−6.75265e27	−0.267233
$508$	−2.04204e28	−0.791580
$509$	4.11106e28	1.56105	0.780526	−	0.625123i	$-0.214951\pi$
$509$	4.11106e28	1.56105	0.780526	+	0.625123i	$0.214951\pi$
$510$	0	0
$511$	−1.81692e28	−0.662088
$512$	−2.06443e28	−0.736998
$513$	−1.21212e27	−0.0423947
$514$	−1.40926e27	−0.0482924
$515$	0	0
$516$	−2.05682e28	−0.676666
$517$	−2.54670e28	−0.820970
$518$	−2.69628e27	−0.0851731
$519$	−8.86356e27	−0.274379
$520$	0	0
$521$	7.72777e27	0.229751	0.114876	−	0.993380i	$-0.463353\pi$
$521$	7.72777e27	0.229751	0.114876	+	0.993380i	$0.463353\pi$
$522$	−1.20666e27	−0.0351598
$523$	−5.81807e28	−1.66154	−0.830771	−	0.556615i	$-0.812100\pi$
$523$	−5.81807e28	−1.66154	−0.830771	+	0.556615i	$0.812100\pi$
$524$	−9.23568e27	−0.258518
$525$	0	0
$526$	8.22273e27	0.221139
$527$	−4.58346e27	−0.120832
$528$	−3.68974e28	−0.953541
$529$	5.29400e28	1.34122
$530$	0	0
$531$	5.84225e27	0.142261
$532$	−7.42531e27	−0.177273
$533$	−1.53405e28	−0.359089
$534$	1.41937e27	0.0325770
$535$	0	0
$536$	2.08084e28	0.459207
$537$	−4.95622e28	−1.07256
$538$	−4.63779e27	−0.0984231
$539$	2.72577e28	0.567293
$540$	0	0
$541$	−5.75030e28	−1.15112	−0.575558	−	0.817761i	$-0.695215\pi$
$541$	−5.75030e28	−1.15112	−0.575558	+	0.817761i	$0.695215\pi$
$542$	8.79052e27	0.172592
$543$	3.97628e28	0.765735
$544$	8.22479e27	0.155359
$545$	0	0
$546$	3.17365e27	0.0576815
$547$	2.64165e27	0.0470986	0.0235493	−	0.999723i	$-0.492503\pi$
$547$	2.64165e27	0.0470986	0.0235493	+	0.999723i	$0.492503\pi$
$548$	−3.99443e28	−0.698648
$549$	−3.13798e28	−0.538444
$550$	0	0
$551$	−8.53700e27	−0.140998
$552$	1.77239e28	0.287210
$553$	8.05830e28	1.28124
$554$	1.09202e27	0.0170365
$555$	0	0
$556$	1.03045e29	1.54789
$557$	−1.61986e28	−0.238780	−0.119390	−	0.992847i	$-0.538094\pi$
$557$	−1.61986e28	−0.238780	−0.119390	+	0.992847i	$0.538094\pi$
$558$	−1.40764e27	−0.0203626
$559$	6.21956e28	0.882949
$560$	0	0
$561$	2.47277e28	0.338122
$562$	−2.96646e26	−0.00398113
$563$	−3.13287e28	−0.412671	−0.206336	−	0.978481i	$-0.566154\pi$
$563$	−3.13287e28	−0.412671	−0.206336	+	0.978481i	$0.566154\pi$
$564$	−1.98509e28	−0.256655
$565$	0	0
$566$	−1.41153e28	−0.175840
$567$	−7.51599e27	−0.0919102
$568$	3.16374e27	0.0379790
$569$	−9.30168e28	−1.09618	−0.548091	−	0.836419i	$-0.684645\pi$
$569$	−9.30168e28	−1.09618	−0.548091	+	0.836419i	$0.684645\pi$
$570$	0	0
$571$	−5.88338e28	−0.668264	−0.334132	−	0.942526i	$-0.608443\pi$
$571$	−5.88338e28	−0.668264	−0.334132	+	0.942526i	$0.608443\pi$
$572$	1.14869e29	1.28099
$573$	−3.05227e28	−0.334195
$574$	−6.21281e27	−0.0667903
$575$	0	0
$576$	−2.70375e28	−0.280240
$577$	1.87651e29	1.90988	0.954939	−	0.296801i	$-0.0959198\pi$
$577$	1.87651e29	1.90988	0.954939	+	0.296801i	$0.0959198\pi$
$578$	1.47368e28	0.147286
$579$	−6.03106e28	−0.591928
$580$	0	0
$581$	1.18120e29	1.11808
$582$	1.80036e26	0.00167367
$583$	−3.37287e29	−3.07950
$584$	2.90191e28	0.260225
$585$	0	0
$586$	1.47580e28	0.127674
$587$	−1.87717e29	−1.59516	−0.797579	−	0.603215i	$-0.793886\pi$
$587$	−1.87717e29	−1.59516	−0.797579	+	0.603215i	$0.793886\pi$
$588$	2.12467e28	0.177349
$589$	−9.95890e27	−0.0816584
$590$	0	0
$591$	1.08927e29	0.861920
$592$	−7.38868e28	−0.574366
$593$	3.20214e28	0.244549	0.122274	−	0.992496i	$-0.460981\pi$
$593$	3.20214e28	0.244549	0.122274	+	0.992496i	$0.460981\pi$
$594$	7.59422e27	0.0569804
$595$	0	0
$596$	−1.90440e29	−1.37934
$597$	−4.63722e28	−0.330010
$598$	−2.64286e28	−0.184804
$599$	1.98807e29	1.36600	0.683000	−	0.730418i	$-0.260675\pi$
$599$	1.98807e29	1.36600	0.683000	+	0.730418i	$0.260675\pi$
$600$	0	0
$601$	−2.40143e29	−1.59327	−0.796633	−	0.604463i	$-0.793388\pi$
$601$	−2.40143e29	−1.59327	−0.796633	+	0.604463i	$0.793388\pi$
$602$	2.51889e28	0.164228
$603$	7.34816e28	0.470812
$604$	−2.00678e29	−1.26361
$605$	0	0
$606$	9.08624e27	0.0552614
$607$	4.94536e28	0.295609	0.147804	−	0.989017i	$-0.452779\pi$
$607$	4.94536e28	0.295609	0.147804	+	0.989017i	$0.452779\pi$
$608$	1.78708e28	0.104992
$609$	−5.29356e28	−0.305679
$610$	0	0
$611$	6.00265e28	0.334896
$612$	1.92746e28	0.105705
$613$	2.16838e29	1.16896	0.584480	−	0.811408i	$-0.301298\pi$
$613$	2.16838e29	1.16896	0.584480	+	0.811408i	$0.301298\pi$
$614$	3.46434e28	0.183592
$615$	0	0
$616$	9.43417e28	0.483177
$617$	−1.37822e29	−0.693946	−0.346973	−	0.937875i	$-0.612790\pi$
$617$	−1.37822e29	−0.693946	−0.346973	+	0.937875i	$0.612790\pi$
$618$	−2.76647e28	−0.136945
$619$	−8.43470e28	−0.410504	−0.205252	−	0.978709i	$-0.565801\pi$
$619$	−8.43470e28	−0.410504	−0.205252	+	0.978709i	$0.565801\pi$
$620$	0	0
$621$	6.25894e28	0.294469
$622$	−6.27121e28	−0.290103
$623$	6.22667e28	0.283225
$624$	8.69683e28	0.388976
$625$	0	0
$626$	3.94159e28	0.170467
$627$	5.37281e28	0.228503
$628$	4.56346e29	1.90861
$629$	4.95170e28	0.203668
$630$	0	0
$631$	9.90368e28	0.393993	0.196996	−	0.980404i	$-0.436881\pi$
$631$	9.90368e28	0.393993	0.196996	+	0.980404i	$0.436881\pi$
$632$	−1.28704e29	−0.503574
$633$	−2.40039e28	−0.0923724
$634$	3.79180e28	0.143518
$635$	0	0
$636$	−2.62907e29	−0.962725
$637$	−6.42472e28	−0.231414
$638$	5.34865e28	0.189508
$639$	1.11723e28	0.0389388
$640$	0	0
$641$	−4.20469e29	−1.41816	−0.709080	−	0.705128i	$-0.750889\pi$
$641$	−4.20469e29	−1.41816	−0.709080	+	0.705128i	$0.750889\pi$
$642$	3.49184e28	0.115861
$643$	1.51418e29	0.494268	0.247134	−	0.968981i	$-0.420511\pi$
$643$	1.51418e29	0.494268	0.247134	+	0.968981i	$0.420511\pi$
$644$	3.83417e29	1.23132
$645$	0	0
$646$	−3.80677e27	−0.0118336
$647$	4.12001e29	1.26009	0.630047	−	0.776557i	$-0.283035\pi$
$647$	4.12001e29	1.26009	0.630047	+	0.776557i	$0.283035\pi$
$648$	1.20042e28	0.0361241
$649$	−2.58963e29	−0.766776
$650$	0	0
$651$	−6.17523e28	−0.177033
$652$	−9.22639e28	−0.260275
$653$	4.42347e29	1.22793	0.613967	−	0.789332i	$-0.289573\pi$
$653$	4.42347e29	1.22793	0.613967	+	0.789332i	$0.289573\pi$
$654$	−4.65497e28	−0.127160
$655$	0	0
$656$	−1.70251e29	−0.450402
$657$	1.02477e29	0.266801
$658$	2.43105e28	0.0622904
$659$	−3.37292e28	−0.0850568	−0.0425284	−	0.999095i	$-0.513541\pi$
$659$	−3.37292e28	−0.0850568	−0.0425284	+	0.999095i	$0.513541\pi$
$660$	0	0
$661$	2.88358e29	0.704396	0.352198	−	0.935926i	$-0.385434\pi$
$661$	2.88358e29	0.704396	0.352198	+	0.935926i	$0.385434\pi$
$662$	−3.20554e28	−0.0770713
$663$	−5.82839e28	−0.137929
$664$	−1.88656e29	−0.439447
$665$	0	0
$666$	1.52074e28	0.0343222
$667$	4.40821e29	0.979357
$668$	−1.07351e29	−0.234775
$669$	−4.98041e29	−1.07224
$670$	0	0
$671$	1.39094e30	2.90216
$672$	1.10812e29	0.227619
$673$	2.34456e29	0.474137	0.237068	−	0.971493i	$-0.423813\pi$
$673$	2.34456e29	0.474137	0.237068	+	0.971493i	$0.423813\pi$
$674$	8.47555e28	0.168748
$675$	0	0
$676$	2.33310e29	0.450292
$677$	6.20076e29	1.17832	0.589161	−	0.808016i	$-0.299458\pi$
$677$	6.20076e29	1.17832	0.589161	+	0.808016i	$0.299458\pi$
$678$	3.89850e28	0.0729433
$679$	7.89808e27	0.0145509
$680$	0	0
$681$	−4.56574e29	−0.815580
$682$	6.23951e28	0.109753
$683$	−2.25018e28	−0.0389762	−0.0194881	−	0.999810i	$-0.506204\pi$
$683$	−2.25018e28	−0.0389762	−0.0194881	+	0.999810i	$0.506204\pi$
$684$	4.18797e28	0.0714356
$685$	0	0
$686$	−1.08426e29	−0.179361
$687$	−2.68250e28	−0.0437013
$688$	6.90259e29	1.10747
$689$	7.94997e29	1.25621
$690$	0	0
$691$	−1.32668e29	−0.203351	−0.101675	−	0.994818i	$-0.532420\pi$
$691$	−1.32668e29	−0.203351	−0.101675	+	0.994818i	$0.532420\pi$
$692$	3.06244e29	0.462332
$693$	3.33153e29	0.495387
$694$	5.72027e28	0.0837804
$695$	0	0
$696$	8.45466e28	0.120143
$697$	1.14098e29	0.159711
$698$	−2.16975e28	−0.0299177
$699$	−6.60688e29	−0.897400
$700$	0	0
$701$	−8.60200e27	−0.0113386	−0.00566931	−	0.999984i	$-0.501805\pi$
$701$	−8.60200e27	−0.0113386	−0.00566931	+	0.999984i	$0.501805\pi$
$702$	−1.78998e28	−0.0232439
$703$	1.07590e29	0.137639
$704$	1.19846e30	1.51047
$705$	0	0
$706$	5.93254e28	0.0725757
$707$	3.98607e29	0.480442
$708$	−2.01855e29	−0.239712
$709$	−8.59402e29	−1.00557	−0.502784	−	0.864412i	$-0.667691\pi$
$709$	−8.59402e29	−1.00557	−0.502784	+	0.864412i	$0.667691\pi$
$710$	0	0
$711$	−4.54499e29	−0.516300
$712$	−9.94499e28	−0.111318
$713$	5.14243e29	0.567189
$714$	−2.36047e28	−0.0256547
$715$	0	0
$716$	1.71242e30	1.80727
$717$	−9.42569e29	−0.980307
$718$	8.60523e28	0.0881974
$719$	1.26833e30	1.28109	0.640544	−	0.767922i	$-0.278709\pi$
$719$	1.26833e30	1.28109	0.640544	+	0.767922i	$0.278709\pi$
$720$	0	0
$721$	−1.21363e30	−1.19060
$722$	1.62175e29	0.156799
$723$	−6.64697e29	−0.633390
$724$	−1.37384e30	−1.29027
$725$	0	0
$726$	−2.32336e29	−0.211974
$727$	−1.13357e30	−1.01939	−0.509693	−	0.860356i	$-0.670241\pi$
$727$	−1.13357e30	−1.01939	−0.509693	+	0.860356i	$0.670241\pi$
$728$	−2.22366e29	−0.197101
$729$	4.23912e28	0.0370370
$730$	0	0
$731$	−4.62594e29	−0.392706
$732$	1.08420e30	0.907285
$733$	−9.73600e29	−0.803136	−0.401568	−	0.915829i	$-0.631535\pi$
$733$	−9.73600e29	−0.803136	−0.401568	+	0.915829i	$0.631535\pi$
$734$	−6.97380e28	−0.0567101
$735$	0	0
$736$	−9.22783e29	−0.729260
$737$	−3.25714e30	−2.53763
$738$	3.50411e28	0.0269145
$739$	−2.04462e29	−0.154827	−0.0774133	−	0.996999i	$-0.524666\pi$
$739$	−2.04462e29	−0.154827	−0.0774133	+	0.996999i	$0.524666\pi$
$740$	0	0
$741$	−1.26639e29	−0.0932128
$742$	3.21970e29	0.233655
$743$	1.27839e30	0.914703	0.457352	−	0.889286i	$-0.348798\pi$
$743$	1.27839e30	0.914703	0.457352	+	0.889286i	$0.348798\pi$
$744$	9.86285e28	0.0695803
$745$	0	0
$746$	−3.65921e28	−0.0250974
$747$	−6.66211e29	−0.450553
$748$	−8.54365e29	−0.569740
$749$	1.53185e30	1.00729
$750$	0	0
$751$	−1.86607e30	−1.19319	−0.596594	−	0.802543i	$-0.703480\pi$
$751$	−1.86607e30	−1.19319	−0.596594	+	0.802543i	$0.703480\pi$
$752$	6.66185e29	0.420056
$753$	8.96047e29	0.557164
$754$	−1.26069e29	−0.0773055
$755$	0	0
$756$	2.59684e29	0.154870
$757$	−1.30211e30	−0.765846	−0.382923	−	0.923780i	$-0.625083\pi$
$757$	−1.30211e30	−0.765846	−0.382923	+	0.923780i	$0.625083\pi$
$758$	−1.86702e29	−0.108298
$759$	−2.77433e30	−1.58716
$760$	0	0
$761$	1.62377e30	0.903620	0.451810	−	0.892114i	$-0.350779\pi$
$761$	1.62377e30	0.903620	0.451810	+	0.892114i	$0.350779\pi$
$762$	−1.41048e29	−0.0774175
$763$	−2.04210e30	−1.10553
$764$	1.05459e30	0.563122
$765$	0	0
$766$	−4.58447e29	−0.238170
$767$	6.10384e29	0.312789
$768$	8.44461e29	0.426861
$769$	2.16647e30	1.08026	0.540128	−	0.841583i	$-0.318376\pi$
$769$	2.16647e30	1.08026	0.540128	+	0.841583i	$0.318376\pi$
$770$	0	0
$771$	3.48692e29	0.169188
$772$	2.08379e30	0.997406
$773$	−7.62722e29	−0.360148	−0.180074	−	0.983653i	$-0.557634\pi$
$773$	−7.62722e29	−0.360148	−0.180074	+	0.983653i	$0.557634\pi$
$774$	−1.42069e29	−0.0661788
$775$	0	0
$776$	−1.26145e28	−0.00571903
$777$	6.67137e29	0.298397
$778$	1.46432e29	0.0646173
$779$	2.47911e29	0.107933
$780$	0	0
$781$	−4.95221e29	−0.209876
$782$	1.96568e29	0.0821945
$783$	2.98563e29	0.123179
$784$	−7.13028e29	−0.290260
$785$	0	0
$786$	−6.37928e28	−0.0252834
$787$	2.64705e30	1.03521	0.517605	−	0.855620i	$-0.326824\pi$
$787$	2.64705e30	1.03521	0.517605	+	0.855620i	$0.326824\pi$
$788$	−3.76353e30	−1.45234
$789$	−2.03454e30	−0.774743
$790$	0	0
$791$	1.71024e30	0.634169
$792$	−5.32099e29	−0.194706
$793$	−3.27849e30	−1.18387
$794$	−4.23006e29	−0.150741
$795$	0	0
$796$	1.60220e30	0.556071
$797$	−2.95211e30	−1.01116	−0.505580	−	0.862780i	$-0.668721\pi$
$797$	−2.95211e30	−1.01116	−0.505580	+	0.862780i	$0.668721\pi$
$798$	−5.12882e28	−0.0173375
$799$	−4.46460e29	−0.148950
$800$	0	0
$801$	−3.51192e29	−0.114131
$802$	−2.62694e29	−0.0842596
$803$	−4.54237e30	−1.43803
$804$	−2.53886e30	−0.793323
$805$	0	0
$806$	−1.47067e29	−0.0447711
$807$	1.14752e30	0.344817
$808$	−6.36640e29	−0.188832
$809$	4.85270e30	1.42077	0.710386	−	0.703813i	$-0.248521\pi$
$809$	4.85270e30	1.42077	0.710386	+	0.703813i	$0.248521\pi$
$810$	0	0
$811$	3.89435e30	1.11100	0.555502	−	0.831515i	$-0.312526\pi$
$811$	3.89435e30	1.11100	0.555502	+	0.831515i	$0.312526\pi$
$812$	1.82897e30	0.515073
$813$	−2.17503e30	−0.604663
$814$	−6.74081e29	−0.184993
$815$	0	0
$816$	−6.46846e29	−0.173003
$817$	−1.00512e30	−0.265391
$818$	4.61908e29	0.120405
$819$	−7.85252e29	−0.202082
$820$	0	0
$821$	1.50546e30	0.377630	0.188815	−	0.982013i	$-0.439535\pi$
$821$	1.50546e30	0.377630	0.188815	+	0.982013i	$0.439535\pi$
$822$	−2.75903e29	−0.0683287
$823$	1.55269e30	0.379652	0.189826	−	0.981818i	$-0.439208\pi$
$823$	1.55269e30	0.379652	0.189826	+	0.981818i	$0.439208\pi$
$824$	1.93837e30	0.467951
$825$	0	0
$826$	2.47203e29	0.0581785
$827$	1.06632e30	0.247787	0.123894	−	0.992295i	$-0.460462\pi$
$827$	1.06632e30	0.247787	0.123894	+	0.992295i	$0.460462\pi$
$828$	−2.16252e30	−0.496183
$829$	−4.91687e30	−1.11395	−0.556976	−	0.830529i	$-0.688038\pi$
$829$	−4.91687e30	−1.11395	−0.556976	+	0.830529i	$0.688038\pi$
$830$	0	0
$831$	−2.70198e29	−0.0596858
$832$	−2.82481e30	−0.616162
$833$	4.77853e29	0.102925
$834$	7.11753e29	0.151386
$835$	0	0
$836$	−1.85636e30	−0.385031
$837$	3.48291e29	0.0713387
$838$	5.06582e29	0.102468
$839$	2.83508e30	0.566324	0.283162	−	0.959072i	$-0.408617\pi$
$839$	2.83508e30	0.566324	0.283162	+	0.959072i	$0.408617\pi$
$840$	0	0
$841$	−3.03004e30	−0.590324
$842$	−9.18255e29	−0.176680
$843$	7.33987e28	0.0139476
$844$	8.29356e29	0.155649
$845$	0	0
$846$	−1.37114e29	−0.0251011
$847$	−1.01924e31	−1.84290
$848$	8.82302e30	1.57565
$849$	3.49252e30	0.616039
$850$	0	0
$851$	−5.55558e30	−0.956025
$852$	−3.86012e29	−0.0656123
$853$	−2.51586e30	−0.422398	−0.211199	−	0.977443i	$-0.567737\pi$
$853$	−2.51586e30	−0.422398	−0.211199	+	0.977443i	$0.567737\pi$
$854$	−1.32777e30	−0.220199
$855$	0	0
$856$	−2.44661e30	−0.395904
$857$	−4.65739e30	−0.744465	−0.372233	−	0.928139i	$-0.621408\pi$
$857$	−4.65739e30	−0.744465	−0.372233	+	0.928139i	$0.621408\pi$
$858$	7.93426e29	0.125282
$859$	−1.19789e31	−1.86848	−0.934242	−	0.356639i	$-0.883923\pi$
$859$	−1.19789e31	−1.86848	−0.934242	+	0.356639i	$0.883923\pi$
$860$	0	0
$861$	1.53723e30	0.233994
$862$	−9.50931e28	−0.0142996
$863$	−1.01034e31	−1.50090	−0.750452	−	0.660925i	$-0.770164\pi$
$863$	−1.01034e31	−1.50090	−0.750452	+	0.660925i	$0.770164\pi$
$864$	−6.24992e29	−0.0917233
$865$	0	0
$866$	−8.05832e29	−0.115427
$867$	−3.64631e30	−0.516004
$868$	2.13360e30	0.298302
$869$	2.01461e31	2.78281
$870$	0	0
$871$	7.67718e30	1.03517
$872$	3.26157e30	0.434513
$873$	−4.45462e28	−0.00586355
$874$	4.27102e29	0.0555472
$875$	0	0
$876$	−3.54066e30	−0.449563
$877$	−1.24814e31	−1.56592	−0.782958	−	0.622074i	$-0.786290\pi$
$877$	−1.24814e31	−1.56592	−0.782958	+	0.622074i	$0.786290\pi$
$878$	−2.03931e30	−0.252808
$879$	−3.65154e30	−0.447294
$880$	0	0
$881$	4.57704e30	0.547442	0.273721	−	0.961809i	$-0.411746\pi$
$881$	4.57704e30	0.547442	0.273721	+	0.961809i	$0.411746\pi$
$882$	1.46755e29	0.0173450
$883$	−2.28608e30	−0.266996	−0.133498	−	0.991049i	$-0.542621\pi$
$883$	−2.28608e30	−0.266996	−0.133498	+	0.991049i	$0.542621\pi$
$884$	2.01376e30	0.232413
$885$	0	0
$886$	−1.98119e30	−0.223291
$887$	1.09577e31	1.22045	0.610225	−	0.792228i	$-0.291079\pi$
$887$	1.09577e31	1.22045	0.610225	+	0.792228i	$0.291079\pi$
$888$	−1.06553e30	−0.117281
$889$	−6.18767e30	−0.673068
$890$	0	0
$891$	−1.87903e30	−0.199626
$892$	1.72078e31	1.80673
$893$	−9.70065e29	−0.100661
$894$	−1.31541e30	−0.134902
$895$	0	0
$896$	−5.07956e30	−0.508852
$897$	6.53919e30	0.647445
$898$	4.92297e28	0.00481754
$899$	2.45304e30	0.237262
$900$	0	0
$901$	−5.91296e30	−0.558721
$902$	−1.55323e30	−0.145066
$903$	−6.23247e30	−0.575359
$904$	−2.73154e30	−0.249252
$905$	0	0
$906$	−1.38613e30	−0.123582
$907$	1.08448e31	0.955748	0.477874	−	0.878428i	$-0.341407\pi$
$907$	1.08448e31	0.955748	0.477874	+	0.878428i	$0.341407\pi$
$908$	1.57751e31	1.37426
$909$	−2.24820e30	−0.193604
$910$	0	0
$911$	2.32383e31	1.95551	0.977757	−	0.209741i	$-0.0672621\pi$
$911$	2.32383e31	1.95551	0.977757	+	0.209741i	$0.0672621\pi$
$912$	−1.40546e30	−0.116916
$913$	2.95304e31	2.42844
$914$	1.60247e30	0.130273
$915$	0	0
$916$	9.26830e29	0.0736372
$917$	−2.79854e30	−0.219813
$918$	1.33134e29	0.0103381
$919$	−6.13649e30	−0.471093	−0.235547	−	0.971863i	$-0.575688\pi$
$919$	−6.13649e30	−0.471093	−0.235547	+	0.971863i	$0.575688\pi$
$920$	0	0
$921$	−8.57177e30	−0.643198
$922$	1.52503e30	0.113137
$923$	1.16725e30	0.0856144
$924$	−1.15108e31	−0.834734
$925$	0	0
$926$	2.34989e29	0.0166583
$927$	6.84505e30	0.479777
$928$	−4.40185e30	−0.305058
$929$	5.98770e30	0.410294	0.205147	−	0.978731i	$-0.434233\pi$
$929$	5.98770e30	0.410294	0.205147	+	0.978731i	$0.434233\pi$
$930$	0	0
$931$	1.03828e30	0.0695570
$932$	2.28274e31	1.51213
$933$	1.55168e31	1.01635
$934$	1.31095e30	0.0849074
$935$	0	0
$936$	1.25417e30	0.0794258
$937$	1.79715e30	0.112543	0.0562716	−	0.998416i	$-0.482079\pi$
$937$	1.79715e30	0.112543	0.0562716	+	0.998416i	$0.482079\pi$
$938$	3.10922e30	0.192541
$939$	−9.75262e30	−0.597218
$940$	0	0
$941$	−1.27143e31	−0.761380	−0.380690	−	0.924703i	$-0.624313\pi$
$941$	−1.27143e31	−0.761380	−0.380690	+	0.924703i	$0.624313\pi$
$942$	3.15208e30	0.186665
$943$	−1.28013e31	−0.749688
$944$	6.77415e30	0.392328
$945$	0	0
$946$	6.29734e30	0.356698
$947$	−2.25956e31	−1.26576	−0.632878	−	0.774252i	$-0.718127\pi$
$947$	−2.25956e31	−1.26576	−0.632878	+	0.774252i	$0.718127\pi$
$948$	1.57034e31	0.869972
$949$	1.07065e31	0.586614
$950$	0	0
$951$	−9.38199e30	−0.502805
$952$	1.65390e30	0.0876639
$953$	1.64499e30	0.0862359	0.0431179	−	0.999070i	$-0.486271\pi$
$953$	1.64499e30	0.0862359	0.0431179	+	0.999070i	$0.486271\pi$
$954$	−1.81595e30	−0.0941557
$955$	0	0
$956$	3.25666e31	1.65183
$957$	−1.32341e31	−0.663925
$958$	−7.16992e29	−0.0355776
$959$	−1.21037e31	−0.594049
$960$	0	0
$961$	−1.79639e31	−0.862591
$962$	1.58883e30	0.0754639
$963$	−8.63981e30	−0.405909
$964$	2.29659e31	1.06727
$965$	0	0
$966$	2.64834e30	0.120424
$967$	2.22265e31	0.999752	0.499876	−	0.866097i	$-0.333379\pi$
$967$	2.22265e31	0.999752	0.499876	+	0.866097i	$0.333379\pi$
$968$	1.62789e31	0.724327
$969$	9.41904e29	0.0414579
$970$	0	0
$971$	6.28485e30	0.270703	0.135352	−	0.990798i	$-0.456784\pi$
$971$	6.28485e30	0.270703	0.135352	+	0.990798i	$0.456784\pi$
$972$	−1.46465e30	−0.0624079
$973$	3.12241e31	1.31615
$974$	1.47834e30	0.0616463
$975$	0	0
$976$	−3.63853e31	−1.48492
$977$	−2.11622e31	−0.854414	−0.427207	−	0.904154i	$-0.640502\pi$
$977$	−2.11622e31	−0.854414	−0.427207	+	0.904154i	$0.640502\pi$
$978$	−6.37287e29	−0.0254552
$979$	1.55669e31	0.615155
$980$	0	0
$981$	1.15177e31	0.445494
$982$	−4.62275e30	−0.176901
$983$	2.87227e31	1.08746	0.543730	−	0.839260i	$-0.317011\pi$
$983$	2.87227e31	1.08746	0.543730	+	0.839260i	$0.317011\pi$
$984$	−2.45520e30	−0.0919684
$985$	0	0
$986$	9.37669e29	0.0343829
$987$	−6.01510e30	−0.218229
$988$	4.37549e30	0.157065
$989$	5.19009e31	1.84338
$990$	0	0
$991$	−7.43052e30	−0.258372	−0.129186	−	0.991620i	$-0.541236\pi$
$991$	−7.43052e30	−0.258372	−0.129186	+	0.991620i	$0.541236\pi$
$992$	−5.13501e30	−0.176673
$993$	7.93143e30	0.270013
$994$	4.72732e29	0.0159242
$995$	0	0
$996$	2.30182e31	0.759186
$997$	−3.26030e31	−1.06404	−0.532020	−	0.846732i	$-0.678567\pi$
$997$	−3.26030e31	−1.06404	−0.532020	+	0.846732i	$0.678567\pi$
$998$	3.85803e30	0.124593
$999$	−3.76274e30	−0.120245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.a.m.1.6		10
5.2	odd	4		15.22.b.a.4.10	✓	20
5.3	odd	4		15.22.b.a.4.11	yes	20
5.4	even	2		75.22.a.n.1.5		10
15.2	even	4		45.22.b.d.19.11		20
15.8	even	4		45.22.b.d.19.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.22.b.a.4.10	✓	20	5.2	odd	4
15.22.b.a.4.11	yes	20	5.3	odd	4
45.22.b.d.19.10		20	15.8	even	4
45.22.b.d.19.11		20	15.2	even	4
75.22.a.m.1.6		10	1.1	even	1	trivial
75.22.a.n.1.5		10	5.4	even	2

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q-238.651 q^{2} +59049.0 q^{3} -2.04020e6 q^{4} -1.40921e7 q^{6} -6.18210e8 q^{7} +9.87381e8 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q-238.651 q^{2} +59049.0 q^{3} -2.04020e6 q^{4} -1.40921e7 q^{6} -6.18210e8 q^{7} +9.87381e8 q^{8} +3.48678e9 q^{9} -1.54555e11 q^{11} -1.20472e11 q^{12} +3.64291e11 q^{13} +1.47536e11 q^{14} +4.04297e12 q^{16} -2.70949e12 q^{17} -8.32123e11 q^{18} -5.88717e12 q^{19} -3.65047e13 q^{21} +3.68846e13 q^{22} +3.03993e14 q^{23} +5.83039e13 q^{24} -8.69382e13 q^{26} +2.05891e14 q^{27} +1.26127e15 q^{28} +1.45010e15 q^{29} +1.69163e15 q^{31} -3.03554e15 q^{32} -9.12632e15 q^{33} +6.46622e14 q^{34} -7.11373e15 q^{36} -1.82754e16 q^{37} +1.40498e15 q^{38} +2.15110e16 q^{39} -4.21105e16 q^{41} +8.71186e15 q^{42} +1.70731e17 q^{43} +3.15323e17 q^{44} -7.25480e16 q^{46} +1.64776e17 q^{47} +2.38733e17 q^{48} -1.76363e17 q^{49} -1.59993e17 q^{51} -7.43225e17 q^{52} +2.18231e18 q^{53} -4.91360e16 q^{54} -6.10409e17 q^{56} -3.47631e17 q^{57} -3.46068e17 q^{58} +1.67554e18 q^{59} -8.99964e18 q^{61} -4.03708e17 q^{62} -2.15556e18 q^{63} -7.75428e18 q^{64} +2.17800e18 q^{66} +2.10743e19 q^{67} +5.52790e18 q^{68} +1.79505e19 q^{69} +3.20418e18 q^{71} +3.44278e18 q^{72} +2.93900e19 q^{73} +4.36143e18 q^{74} +1.20110e19 q^{76} +9.55474e19 q^{77} -5.13361e18 q^{78} -1.30349e20 q^{79} +1.21577e19 q^{81} +1.00497e19 q^{82} -1.91067e20 q^{83} +7.44767e19 q^{84} -4.07450e19 q^{86} +8.56272e19 q^{87} -1.52605e20 q^{88} -1.00721e20 q^{89} -2.25208e20 q^{91} -6.20205e20 q^{92} +9.98890e19 q^{93} -3.93240e19 q^{94} -1.79246e20 q^{96} -1.27757e19 q^{97} +4.20890e19 q^{98} -5.38900e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9}+O(q^{10}) \) 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9	\( 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9} + 5976221790 q^{11} + 593041212045 q^{12} - 842570747430 q^{13} + 1605059874570 q^{14} + 6061861547825 q^{16} - 12910340404230 q^{17} - 2248975938645 q^{18} - 76155422176280 q^{19} - 6811732617210 q^{21} - 461780887241010 q^{22} - 82640920915920 q^{23} - 18549814359015 q^{24} + 286555331159670 q^{26} + 20\!\cdots\!90 q^{27}+ \cdots + 20\!\cdots\!90 q^{99}+O(q^{100}) \) 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9 + 5976221790 * q^11 + 593041212045 * q^12 - 842570747430 * q^13 + 1605059874570 * q^14 + 6061861547825 * q^16 - 12910340404230 * q^17 - 2248975938645 * q^18 - 76155422176280 * q^19 - 6811732617210 * q^21 - 461780887241010 * q^22 - 82640920915920 * q^23 - 18549814359015 * q^24 + 286555331159670 * q^26 + 2058911320946490 * q^27 - 1520428218531930 * q^28 - 2553653160731010 * q^29 - 5579671364724940 * q^31 - 29255856594217815 * q^32 + 352889920477710 * q^33 + 36285968426431010 * q^34 + 35018490530045205 * q^36 - 1797908431222890 * q^37 - 10684960744876320 * q^38 - 49752960064994070 * q^39 - 157319729506021440 * q^41 + 94777180533483930 * q^42 + 148924853700743400 * q^43 + 49118820773767290 * q^44 - 238453286038259540 * q^46 + 43171138083158100 * q^47 + 357946862537518425 * q^48 + 453692886452454950 * q^49 - 762342690529377270 * q^51 - 5077473324432504030 * q^52 - 1835165786666252970 * q^53 - 132799780201048605 * q^54 - 5146515624013530450 * q^56 - 4496901524087157720 * q^57 - 3684042125074285440 * q^58 + 4936135121536323630 * q^59 - 4443080871007408300 * q^61 - 39366851097921260280 * q^62 - 402225999313633290 * q^63 - 14877283608188093455 * q^64 - 27267699610694399490 * q^66 - 33664559574358232580 * q^67 - 44791395195934111290 * q^68 - 4879863739164160080 * q^69 - 74662724971386630180 * q^71 - 1095347988085476735 * q^72 - 16062862692682477620 * q^73 - 130249023546610518030 * q^74 - 258736483662380220720 * q^76 - 56216747719240740180 * q^77 + 16920805749647353830 * q^78 - 49130708010799643300 * q^79 + 121576654590569288010 * q^81 - 117185080045656261930 * q^82 - 118408383608453695560 * q^83 - 89779765876091934570 * q^84 - 1007271272794707382260 * q^86 - 150790665488005409490 * q^87 - 41803519849182967710 * q^88 - 572103976713991581780 * q^89 - 1669810835257196575140 * q^91 + 1206545757146297440260 * q^92 - 329474014415642982060 * q^93 - 1671319720124696594920 * q^94 - 1727529076031967757935 * q^96 + 1299275526640742173920 * q^97 + 2683959884079093505455 * q^98 + 20837796914288297790 * q^99

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