LMFDB - Embedded newform 45.12.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,12,Mod(1,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("45.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	45.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:	$34.5754431252$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{151}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 151 $ x^2 - 151
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$12.2882$ of defining polynomial
Character	$\chi$	$=$	45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+83.7292 q^{2} +4962.58 q^{4} +3125.00 q^{5} +15973.7 q^{7} +244036. q^{8} +O(q^{10})$	\(q+83.7292 q^{2} +4962.58 q^{4} +3125.00 q^{5} +15973.7 q^{7} +244036. q^{8} +261654. q^{10} -339729. q^{11} +2.02328e6 q^{13} +1.33746e6 q^{14} +1.02696e7 q^{16} +2.45063e6 q^{17} -4.08504e6 q^{19} +1.55081e7 q^{20} -2.84453e7 q^{22} -2.86497e7 q^{23} +9.76562e6 q^{25} +1.69408e8 q^{26} +7.92706e7 q^{28} +9.41230e6 q^{29} +2.99399e8 q^{31} +3.60078e8 q^{32} +2.05190e8 q^{34} +4.99177e7 q^{35} -4.57279e8 q^{37} -3.42037e8 q^{38} +7.62612e8 q^{40} -1.83814e8 q^{41} +6.56811e8 q^{43} -1.68594e9 q^{44} -2.39882e9 q^{46} +1.97090e8 q^{47} -1.72217e9 q^{49} +8.17668e8 q^{50} +1.00407e10 q^{52} -5.15890e9 q^{53} -1.06165e9 q^{55} +3.89815e9 q^{56} +7.88085e8 q^{58} +6.62200e8 q^{59} +5.58296e8 q^{61} +2.50684e10 q^{62} +9.11694e9 q^{64} +6.32275e9 q^{65} +1.01206e10 q^{67} +1.21615e10 q^{68} +4.17957e9 q^{70} -1.78161e10 q^{71} -2.33380e10 q^{73} -3.82876e10 q^{74} -2.02724e10 q^{76} -5.42672e9 q^{77} +1.24957e10 q^{79} +3.20924e10 q^{80} -1.53906e10 q^{82} -3.37037e10 q^{83} +7.65823e9 q^{85} +5.49943e10 q^{86} -8.29062e10 q^{88} -2.94282e10 q^{89} +3.23192e10 q^{91} -1.42177e11 q^{92} +1.65022e10 q^{94} -1.27657e10 q^{95} -1.13262e11 q^{97} -1.44196e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 20 q^{2} + 6976 q^{4} + 6250 q^{5} + 57900 q^{7} + 246240 q^{8}+O(q^{10}) $ 2 * q + 20 * q^2 + 6976 * q^4 + 6250 * q^5 + 57900 * q^7 + 246240 * q^8	\( 2 q + 20 q^{2} + 6976 q^{4} + 6250 q^{5} + 57900 q^{7} + 246240 q^{8} + 62500 q^{10} + 618176 q^{11} + 3414260 q^{13} - 1334472 q^{14} + 6005632 q^{16} - 1317940 q^{17} + 5325320 q^{19} + 21800000 q^{20} - 89491840 q^{22} - 58943940 q^{23} + 19531250 q^{25} + 80761736 q^{26} + 163685760 q^{28} - 94140380 q^{29} + 244543464 q^{31} + 627301120 q^{32} + 445358072 q^{34} + 180937500 q^{35} + 21003220 q^{37} - 941752240 q^{38} + 769500000 q^{40} + 745743316 q^{41} + 629950100 q^{43} + 242725888 q^{44} - 468194856 q^{46} + 1402061540 q^{47} - 1941677414 q^{49} + 195312500 q^{50} + 12841321600 q^{52} - 1138320580 q^{53} + 1931800000 q^{55} + 3990553920 q^{56} + 7387417960 q^{58} - 7317515560 q^{59} - 1516425676 q^{61} + 28564327440 q^{62} + 819531776 q^{64} + 10669562500 q^{65} + 15734290140 q^{67} + 4573774720 q^{68} - 4170225000 q^{70} - 32938471544 q^{71} - 29982848860 q^{73} - 68768198072 q^{74} - 1325392640 q^{76} + 34734748800 q^{77} - 3302823120 q^{79} + 18767600000 q^{80} - 74630515640 q^{82} - 13299102420 q^{83} - 4118562500 q^{85} + 56706093896 q^{86} - 80794874880 q^{88} + 12674770860 q^{89} + 90637859064 q^{91} - 203171571840 q^{92} - 60289765528 q^{94} + 16641625000 q^{95} - 3080703740 q^{97} - 130206802940 q^{98}+O(q^{100}) \) 2 * q + 20 * q^2 + 6976 * q^4 + 6250 * q^5 + 57900 * q^7 + 246240 * q^8 + 62500 * q^10 + 618176 * q^11 + 3414260 * q^13 - 1334472 * q^14 + 6005632 * q^16 - 1317940 * q^17 + 5325320 * q^19 + 21800000 * q^20 - 89491840 * q^22 - 58943940 * q^23 + 19531250 * q^25 + 80761736 * q^26 + 163685760 * q^28 - 94140380 * q^29 + 244543464 * q^31 + 627301120 * q^32 + 445358072 * q^34 + 180937500 * q^35 + 21003220 * q^37 - 941752240 * q^38 + 769500000 * q^40 + 745743316 * q^41 + 629950100 * q^43 + 242725888 * q^44 - 468194856 * q^46 + 1402061540 * q^47 - 1941677414 * q^49 + 195312500 * q^50 + 12841321600 * q^52 - 1138320580 * q^53 + 1931800000 * q^55 + 3990553920 * q^56 + 7387417960 * q^58 - 7317515560 * q^59 - 1516425676 * q^61 + 28564327440 * q^62 + 819531776 * q^64 + 10669562500 * q^65 + 15734290140 * q^67 + 4573774720 * q^68 - 4170225000 * q^70 - 32938471544 * q^71 - 29982848860 * q^73 - 68768198072 * q^74 - 1325392640 * q^76 + 34734748800 * q^77 - 3302823120 * q^79 + 18767600000 * q^80 - 74630515640 * q^82 - 13299102420 * q^83 - 4118562500 * q^85 + 56706093896 * q^86 - 80794874880 * q^88 + 12674770860 * q^89 + 90637859064 * q^91 - 203171571840 * q^92 - 60289765528 * q^94 + 16641625000 * q^95 - 3080703740 * q^97 - 130206802940 * q^98

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 $

$2$	83.7292	1.85017	0.925086	−	0.379757i	$-0.123993\pi$
$2$	83.7292	1.85017	0.925086	+	0.379757i	$0.123993\pi$
$3$	0	0
$3$	0	0
$4$	4962.58	2.42314
$5$	3125.00	0.447214
$5$	3125.00	0.447214
$6$	0	0
$7$	15973.7	0.359224	0.179612	−	0.983738i	$-0.442516\pi$
$7$	15973.7	0.359224	0.179612	+	0.983738i	$0.442516\pi$
$8$	244036.	2.63305
$9$	0	0
$10$	261654.	0.827422
$11$	−339729.	−0.636024	−0.318012	−	0.948087i	$-0.603015\pi$
$11$	−339729.	−0.636024	−0.318012	+	0.948087i	$0.603015\pi$
$12$	0	0
$13$	2.02328e6	1.51136	0.755680	−	0.654941i	$-0.227307\pi$
$13$	2.02328e6	1.51136	0.755680	+	0.654941i	$0.227307\pi$
$14$	1.33746e6	0.664626
$15$	0	0
$16$	1.02696e7	2.44846
$17$	2.45063e6	0.418610	0.209305	−	0.977850i	$-0.432880\pi$
$17$	2.45063e6	0.418610	0.209305	+	0.977850i	$0.432880\pi$
$18$	0	0
$19$	−4.08504e6	−0.378487	−0.189244	−	0.981930i	$-0.560604\pi$
$19$	−4.08504e6	−0.378487	−0.189244	+	0.981930i	$0.560604\pi$
$20$	1.55081e7	1.08366
$21$	0	0
$22$	−2.84453e7	−1.17675
$23$	−2.86497e7	−0.928149	−0.464074	−	0.885796i	$-0.653613\pi$
$23$	−2.86497e7	−0.928149	−0.464074	+	0.885796i	$0.653613\pi$
$24$	0	0
$25$	9.76562e6	0.200000
$26$	1.69408e8	2.79628
$27$	0	0
$28$	7.92706e7	0.870448
$29$	9.41230e6	0.0852132	0.0426066	−	0.999092i	$-0.486434\pi$
$29$	9.41230e6	0.0852132	0.0426066	+	0.999092i	$0.486434\pi$
$30$	0	0
$31$	2.99399e8	1.87828	0.939141	−	0.343532i	$-0.111623\pi$
$31$	2.99399e8	1.87828	0.939141	+	0.343532i	$0.111623\pi$
$32$	3.60078e8	1.89702
$33$	0	0
$34$	2.05190e8	0.774500
$35$	4.99177e7	0.160650
$36$	0	0
$37$	−4.57279e8	−1.08411	−0.542053	−	0.840344i	$-0.682353\pi$
$37$	−4.57279e8	−1.08411	−0.542053	+	0.840344i	$0.682353\pi$
$38$	−3.42037e8	−0.700267
$39$	0	0
$40$	7.62612e8	1.17754
$41$	−1.83814e8	−0.247780	−0.123890	−	0.992296i	$-0.539537\pi$
$41$	−1.83814e8	−0.247780	−0.123890	+	0.992296i	$0.539537\pi$
$42$	0	0
$43$	6.56811e8	0.681340	0.340670	−	0.940183i	$-0.389346\pi$
$43$	6.56811e8	0.681340	0.340670	+	0.940183i	$0.389346\pi$
$44$	−1.68594e9	−1.54117
$45$	0	0
$46$	−2.39882e9	−1.71724
$47$	1.97090e8	0.125350	0.0626752	−	0.998034i	$-0.480037\pi$
$47$	1.97090e8	0.125350	0.0626752	+	0.998034i	$0.480037\pi$
$48$	0	0
$49$	−1.72217e9	−0.870958
$50$	8.17668e8	0.370034
$51$	0	0
$52$	1.00407e10	3.66223
$53$	−5.15890e9	−1.69449	−0.847247	−	0.531199i	$-0.821742\pi$
$53$	−5.15890e9	−1.69449	−0.847247	+	0.531199i	$0.821742\pi$
$54$	0	0
$55$	−1.06165e9	−0.284438
$56$	3.89815e9	0.945854
$57$	0	0
$58$	7.88085e8	0.157659
$59$	6.62200e8	0.120588	0.0602939	−	0.998181i	$-0.480796\pi$
$59$	6.62200e8	0.120588	0.0602939	+	0.998181i	$0.480796\pi$
$60$	0	0
$61$	5.58296e8	0.0846351	0.0423176	−	0.999104i	$-0.486526\pi$
$61$	5.58296e8	0.0846351	0.0423176	+	0.999104i	$0.486526\pi$
$62$	2.50684e10	3.47515
$63$	0	0
$64$	9.11694e9	1.06135
$65$	6.32275e9	0.675900
$66$	0	0
$67$	1.01206e10	0.915787	0.457894	−	0.889007i	$-0.348604\pi$
$67$	1.01206e10	0.915787	0.457894	+	0.889007i	$0.348604\pi$
$68$	1.21615e10	1.01435
$69$	0	0
$70$	4.17957e9	0.297230
$71$	−1.78161e10	−1.17190	−0.585952	−	0.810346i	$-0.699279\pi$
$71$	−1.78161e10	−1.17190	−0.585952	+	0.810346i	$0.699279\pi$
$72$	0	0
$73$	−2.33380e10	−1.31761	−0.658807	−	0.752312i	$-0.728939\pi$
$73$	−2.33380e10	−1.31761	−0.658807	+	0.752312i	$0.728939\pi$
$74$	−3.82876e10	−2.00578
$75$	0	0
$76$	−2.02724e10	−0.917127
$77$	−5.42672e9	−0.228475
$78$	0	0
$79$	1.24957e10	0.456888	0.228444	−	0.973557i	$-0.426636\pi$
$79$	1.24957e10	0.456888	0.228444	+	0.973557i	$0.426636\pi$
$80$	3.20924e10	1.09498
$81$	0	0
$82$	−1.53906e10	−0.458436
$83$	−3.37037e10	−0.939179	−0.469589	−	0.882885i	$-0.655598\pi$
$83$	−3.37037e10	−0.939179	−0.469589	+	0.882885i	$0.655598\pi$
$84$	0	0
$85$	7.65823e9	0.187208
$86$	5.49943e10	1.26060
$87$	0	0
$88$	−8.29062e10	−1.67468
$89$	−2.94282e10	−0.558623	−0.279311	−	0.960201i	$-0.590106\pi$
$89$	−2.94282e10	−0.558623	−0.279311	+	0.960201i	$0.590106\pi$
$90$	0	0
$91$	3.23192e10	0.542916
$92$	−1.42177e11	−2.24903
$93$	0	0
$94$	1.65022e10	0.231920
$95$	−1.27657e10	−0.169265
$96$	0	0
$97$	−1.13262e11	−1.33918	−0.669588	−	0.742732i	$-0.733529\pi$
$97$	−1.13262e11	−1.33918	−0.669588	+	0.742732i	$0.733529\pi$
$98$	−1.44196e11	−1.61142
$99$	0	0
$100$	4.84627e10	0.484627
$101$	−1.19564e11	−1.13196	−0.565982	−	0.824417i	$-0.691503\pi$
$101$	−1.19564e11	−1.13196	−0.565982	+	0.824417i	$0.691503\pi$
$102$	0	0
$103$	−9.46874e10	−0.804799	−0.402399	−	0.915464i	$-0.631824\pi$
$103$	−9.46874e10	−0.804799	−0.402399	+	0.915464i	$0.631824\pi$
$104$	4.93753e11	3.97948
$105$	0	0
$106$	−4.31951e11	−3.13511
$107$	−1.52769e11	−1.05299	−0.526497	−	0.850177i	$-0.676495\pi$
$107$	−1.52769e11	−1.05299	−0.526497	+	0.850177i	$0.676495\pi$
$108$	0	0
$109$	2.85078e11	1.77467	0.887337	−	0.461122i	$-0.152553\pi$
$109$	2.85078e11	1.77467	0.887337	+	0.461122i	$0.152553\pi$
$110$	−8.88915e10	−0.526260
$111$	0	0
$112$	1.64043e11	0.879544
$113$	2.35563e11	1.20275	0.601374	−	0.798968i	$-0.294620\pi$
$113$	2.35563e11	1.20275	0.601374	+	0.798968i	$0.294620\pi$
$114$	0	0
$115$	−8.95304e10	−0.415081
$116$	4.67093e10	0.206483
$117$	0	0
$118$	5.54455e10	0.223108
$119$	3.91456e10	0.150375
$120$	0	0
$121$	−1.69896e11	−0.595474
$122$	4.67457e10	0.156590
$123$	0	0
$124$	1.48579e12	4.55133
$125$	3.05176e10	0.0894427
$126$	0	0
$127$	−1.25786e11	−0.337840	−0.168920	−	0.985630i	$-0.554028\pi$
$127$	−1.25786e11	−0.337840	−0.168920	+	0.985630i	$0.554028\pi$
$128$	2.59156e10	0.0666664
$129$	0	0
$130$	5.29399e11	1.25053
$131$	2.97347e11	0.673397	0.336698	−	0.941613i	$-0.390690\pi$
$131$	2.97347e11	0.673397	0.336698	+	0.941613i	$0.390690\pi$
$132$	0	0
$133$	−6.52530e10	−0.135962
$134$	8.47389e11	1.69436
$135$	0	0
$136$	5.98043e11	1.10222
$137$	6.29203e10	0.111385	0.0556926	−	0.998448i	$-0.482263\pi$
$137$	6.29203e10	0.111385	0.0556926	+	0.998448i	$0.482263\pi$
$138$	0	0
$139$	−5.11416e11	−0.835974	−0.417987	−	0.908453i	$-0.637264\pi$
$139$	−5.11416e11	−0.835974	−0.417987	+	0.908453i	$0.637264\pi$
$140$	2.47721e11	0.389276
$141$	0	0
$142$	−1.49173e12	−2.16823
$143$	−6.87368e11	−0.961260
$144$	0	0
$145$	2.94134e10	0.0381085
$146$	−1.95407e12	−2.43781
$147$	0	0
$148$	−2.26929e12	−2.62694
$149$	−7.94154e11	−0.885891	−0.442945	−	0.896549i	$-0.646066\pi$
$149$	−7.94154e11	−0.885891	−0.442945	+	0.896549i	$0.646066\pi$
$150$	0	0
$151$	1.24629e12	1.29195	0.645974	−	0.763360i	$-0.276452\pi$
$151$	1.24629e12	1.29195	0.645974	+	0.763360i	$0.276452\pi$
$152$	−9.96896e11	−0.996576
$153$	0	0
$154$	−4.54375e11	−0.422718
$155$	9.35621e11	0.839993
$156$	0	0
$157$	9.73519e11	0.814510	0.407255	−	0.913315i	$-0.366486\pi$
$157$	9.73519e11	0.814510	0.407255	+	0.913315i	$0.366486\pi$
$158$	1.04625e12	0.845322
$159$	0	0
$160$	1.12524e12	0.848372
$161$	−4.57641e11	−0.333413
$162$	0	0
$163$	1.26084e12	0.858281	0.429140	−	0.903238i	$-0.358817\pi$
$163$	1.26084e12	0.858281	0.429140	+	0.903238i	$0.358817\pi$
$164$	−9.12190e11	−0.600405
$165$	0	0
$166$	−2.82199e12	−1.73764
$167$	3.01398e12	1.79556	0.897780	−	0.440443i	$-0.145179\pi$
$167$	3.01398e12	1.79556	0.897780	+	0.440443i	$0.145179\pi$
$168$	0	0
$169$	2.30151e12	1.28421
$170$	6.41218e11	0.346367
$171$	0	0
$172$	3.25948e12	1.65098
$173$	3.07482e11	0.150857	0.0754285	−	0.997151i	$-0.475968\pi$
$173$	3.07482e11	0.150857	0.0754285	+	0.997151i	$0.475968\pi$
$174$	0	0
$175$	1.55993e11	0.0718448
$176$	−3.48887e12	−1.55728
$177$	0	0
$178$	−2.46400e12	−1.03355
$179$	1.91470e12	0.778769	0.389384	−	0.921075i	$-0.372688\pi$
$179$	1.91470e12	0.778769	0.389384	+	0.921075i	$0.372688\pi$
$180$	0	0
$181$	1.10300e11	0.0422032	0.0211016	−	0.999777i	$-0.493283\pi$
$181$	1.10300e11	0.0422032	0.0211016	+	0.999777i	$0.493283\pi$
$182$	2.70606e12	1.00449
$183$	0	0
$184$	−6.99157e12	−2.44386
$185$	−1.42900e12	−0.484827
$186$	0	0
$187$	−8.32552e11	−0.266246
$188$	9.78074e11	0.303741
$189$	0	0
$190$	−1.06887e12	−0.313169
$191$	4.43991e12	1.26384	0.631918	−	0.775035i	$-0.282268\pi$
$191$	4.43991e12	1.26384	0.631918	+	0.775035i	$0.282268\pi$
$192$	0	0
$193$	3.15713e12	0.848647	0.424324	−	0.905511i	$-0.360512\pi$
$193$	3.15713e12	0.848647	0.424324	+	0.905511i	$0.360512\pi$
$194$	−9.48330e12	−2.47771
$195$	0	0
$196$	−8.54641e12	−2.11045
$197$	3.58626e12	0.861147	0.430574	−	0.902555i	$-0.358311\pi$
$197$	3.58626e12	0.861147	0.430574	+	0.902555i	$0.358311\pi$
$198$	0	0
$199$	4.14823e12	0.942260	0.471130	−	0.882064i	$-0.343846\pi$
$199$	4.14823e12	0.942260	0.471130	+	0.882064i	$0.343846\pi$
$200$	2.38316e12	0.526610
$201$	0	0
$202$	−1.00110e13	−2.09433
$203$	1.50349e11	0.0306106
$204$	0	0
$205$	−5.74417e11	−0.110811
$206$	−7.92810e12	−1.48902
$207$	0	0
$208$	2.07782e13	3.70050
$209$	1.38781e12	0.240727
$210$	0	0
$211$	1.14275e12	0.188104	0.0940519	−	0.995567i	$-0.470018\pi$
$211$	1.14275e12	0.188104	0.0940519	+	0.995567i	$0.470018\pi$
$212$	−2.56015e13	−4.10599
$213$	0	0
$214$	−1.27913e13	−1.94822
$215$	2.05253e12	0.304704
$216$	0	0
$217$	4.78249e12	0.674724
$218$	2.38694e13	3.28345
$219$	0	0
$220$	−5.26855e12	−0.689233
$221$	4.95832e12	0.632670
$222$	0	0
$223$	3.54889e12	0.430939	0.215469	−	0.976511i	$-0.430872\pi$
$223$	3.54889e12	0.430939	0.215469	+	0.976511i	$0.430872\pi$
$224$	5.75175e12	0.681454
$225$	0	0
$226$	1.97235e13	2.22529
$227$	−3.90543e12	−0.430058	−0.215029	−	0.976608i	$-0.568985\pi$
$227$	−3.90543e12	−0.430058	−0.215029	+	0.976608i	$0.568985\pi$
$228$	0	0
$229$	−4.85126e12	−0.509048	−0.254524	−	0.967066i	$-0.581919\pi$
$229$	−4.85126e12	−0.509048	−0.254524	+	0.967066i	$0.581919\pi$
$230$	−7.49632e12	−0.767971
$231$	0	0
$232$	2.29694e12	0.224370
$233$	−1.03473e13	−0.987115	−0.493557	−	0.869713i	$-0.664304\pi$
$233$	−1.03473e13	−0.987115	−0.493557	+	0.869713i	$0.664304\pi$
$234$	0	0
$235$	6.15905e11	0.0560584
$236$	3.28622e12	0.292201
$237$	0	0
$238$	3.27763e12	0.278219
$239$	−1.85140e12	−0.153572	−0.0767859	−	0.997048i	$-0.524466\pi$
$239$	−1.85140e12	−0.153572	−0.0767859	+	0.997048i	$0.524466\pi$
$240$	0	0
$241$	2.73018e12	0.216321	0.108160	−	0.994133i	$-0.465504\pi$
$241$	2.73018e12	0.216321	0.108160	+	0.994133i	$0.465504\pi$
$242$	−1.42252e13	−1.10173
$243$	0	0
$244$	2.77059e12	0.205083
$245$	−5.38178e12	−0.389504
$246$	0	0
$247$	−8.26518e12	−0.572031
$248$	7.30641e13	4.94561
$249$	0	0
$250$	2.55521e12	0.165484
$251$	−1.18976e13	−0.753796	−0.376898	−	0.926255i	$-0.623009\pi$
$251$	−1.18976e13	−0.753796	−0.376898	+	0.926255i	$0.623009\pi$
$252$	0	0
$253$	9.73316e12	0.590324
$254$	−1.05319e13	−0.625062
$255$	0	0
$256$	−1.65016e13	−0.938007
$257$	−3.53878e10	−0.00196889	−0.000984443	−	1.00000i	$-0.500313\pi$
$257$	−3.53878e10	−0.00196889	−0.000984443		1.00000i	$0.500313\pi$
$258$	0	0
$259$	−7.30442e12	−0.389437
$260$	3.13772e13	1.63780
$261$	0	0
$262$	2.48966e13	1.24590
$263$	1.19904e13	0.587592	0.293796	−	0.955868i	$-0.405081\pi$
$263$	1.19904e13	0.587592	0.293796	+	0.955868i	$0.405081\pi$
$264$	0	0
$265$	−1.61216e13	−0.757801
$266$	−5.46358e12	−0.251553
$267$	0	0
$268$	5.02243e13	2.21908
$269$	3.81149e13	1.64990	0.824948	−	0.565208i	$-0.191204\pi$
$269$	3.81149e13	1.64990	0.824948	+	0.565208i	$0.191204\pi$
$270$	0	0
$271$	−1.13510e13	−0.471740	−0.235870	−	0.971785i	$-0.575794\pi$
$271$	−1.13510e13	−0.471740	−0.235870	+	0.971785i	$0.575794\pi$
$272$	2.51670e13	1.02495
$273$	0	0
$274$	5.26827e12	0.206082
$275$	−3.31767e12	−0.127205
$276$	0	0
$277$	3.02533e13	1.11464	0.557320	−	0.830298i	$-0.311830\pi$
$277$	3.02533e13	1.11464	0.557320	+	0.830298i	$0.311830\pi$
$278$	−4.28205e13	−1.54670
$279$	0	0
$280$	1.21817e13	0.422999
$281$	−4.72047e13	−1.60731	−0.803657	−	0.595093i	$-0.797115\pi$
$281$	−4.72047e13	−1.60731	−0.803657	+	0.595093i	$0.797115\pi$
$282$	0	0
$283$	−8.68805e12	−0.284510	−0.142255	−	0.989830i	$-0.545435\pi$
$283$	−8.68805e12	−0.284510	−0.142255	+	0.989830i	$0.545435\pi$
$284$	−8.84140e13	−2.83969
$285$	0	0
$286$	−5.75528e13	−1.77850
$287$	−2.93617e12	−0.0890085
$288$	0	0
$289$	−2.82663e13	−0.824766
$290$	2.46277e12	0.0705073
$291$	0	0
$292$	−1.15817e14	−3.19276
$293$	−2.17869e13	−0.589417	−0.294709	−	0.955587i	$-0.595223\pi$
$293$	−2.17869e13	−0.589417	−0.294709	+	0.955587i	$0.595223\pi$
$294$	0	0
$295$	2.06938e12	0.0539285
$296$	−1.11593e14	−2.85450
$297$	0	0
$298$	−6.64939e13	−1.63905
$299$	−5.79665e13	−1.40277
$300$	0	0
$301$	1.04917e13	0.244754
$302$	1.04351e14	2.39033
$303$	0	0
$304$	−4.19516e13	−0.926710
$305$	1.74468e12	0.0378500
$306$	0	0
$307$	2.05380e13	0.429829	0.214915	−	0.976633i	$-0.431053\pi$
$307$	2.05380e13	0.429829	0.214915	+	0.976633i	$0.431053\pi$
$308$	−2.69305e13	−0.553626
$309$	0	0
$310$	7.83389e13	1.55413
$311$	7.37156e13	1.43674	0.718369	−	0.695663i	$-0.244889\pi$
$311$	7.37156e13	1.43674	0.718369	+	0.695663i	$0.244889\pi$
$312$	0	0
$313$	−2.82026e13	−0.530634	−0.265317	−	0.964161i	$-0.585477\pi$
$313$	−2.82026e13	−0.530634	−0.265317	+	0.964161i	$0.585477\pi$
$314$	8.15120e13	1.50698
$315$	0	0
$316$	6.20108e13	1.10710
$317$	−2.56938e13	−0.450819	−0.225410	−	0.974264i	$-0.572372\pi$
$317$	−2.56938e13	−0.450819	−0.225410	+	0.974264i	$0.572372\pi$
$318$	0	0
$319$	−3.19763e12	−0.0541976
$320$	2.84904e13	0.474651
$321$	0	0
$322$	−3.83179e13	−0.616872
$323$	−1.00109e13	−0.158439
$324$	0	0
$325$	1.97586e13	0.302272
$326$	1.05569e14	1.58797
$327$	0	0
$328$	−4.48571e13	−0.652417
$329$	3.14824e12	0.0450288
$330$	0	0
$331$	−6.14309e13	−0.849831	−0.424916	−	0.905233i	$-0.639696\pi$
$331$	−6.14309e13	−0.849831	−0.424916	+	0.905233i	$0.639696\pi$
$332$	−1.67258e14	−2.27576
$333$	0	0
$334$	2.52358e14	3.32210
$335$	3.16269e13	0.409552
$336$	0	0
$337$	1.35566e14	1.69898	0.849488	−	0.527608i	$-0.176911\pi$
$337$	1.35566e14	1.69898	0.849488	+	0.527608i	$0.176911\pi$
$338$	1.92703e14	2.37600
$339$	0	0
$340$	3.80046e13	0.453631
$341$	−1.01715e14	−1.19463
$342$	0	0
$343$	−5.90945e13	−0.672093
$344$	1.60285e14	1.79400
$345$	0	0
$346$	2.57452e13	0.279111
$347$	2.88020e13	0.307334	0.153667	−	0.988123i	$-0.450892\pi$
$347$	2.88020e13	0.307334	0.153667	+	0.988123i	$0.450892\pi$
$348$	0	0
$349$	3.70742e13	0.383294	0.191647	−	0.981464i	$-0.438617\pi$
$349$	3.70742e13	0.383294	0.191647	+	0.981464i	$0.438617\pi$
$350$	1.30612e13	0.132925
$351$	0	0
$352$	−1.22329e14	−1.20655
$353$	5.64627e13	0.548278	0.274139	−	0.961690i	$-0.411607\pi$
$353$	5.64627e13	0.548278	0.274139	+	0.961690i	$0.411607\pi$
$354$	0	0
$355$	−5.56754e13	−0.524092
$356$	−1.46040e14	−1.35362
$357$	0	0
$358$	1.60316e14	1.44086
$359$	1.96868e14	1.74243	0.871217	−	0.490899i	$-0.163332\pi$
$359$	1.96868e14	1.74243	0.871217	+	0.490899i	$0.163332\pi$
$360$	0	0
$361$	−9.98027e13	−0.856747
$362$	9.23537e12	0.0780831
$363$	0	0
$364$	1.60387e14	1.31556
$365$	−7.29313e13	−0.589255
$366$	0	0
$367$	−1.00444e14	−0.787514	−0.393757	−	0.919214i	$-0.628825\pi$
$367$	−1.00444e14	−0.787514	−0.393757	+	0.919214i	$0.628825\pi$
$368$	−2.94221e14	−2.27253
$369$	0	0
$370$	−1.19649e14	−0.897014
$371$	−8.24065e13	−0.608703
$372$	0	0
$373$	−7.09849e13	−0.509058	−0.254529	−	0.967065i	$-0.581921\pi$
$373$	−7.09849e13	−0.509058	−0.254529	+	0.967065i	$0.581921\pi$
$374$	−6.97090e13	−0.492600
$375$	0	0
$376$	4.80970e13	0.330054
$377$	1.90437e13	0.128788
$378$	0	0
$379$	6.79976e13	0.446661	0.223330	−	0.974743i	$-0.428307\pi$
$379$	6.79976e13	0.446661	0.223330	+	0.974743i	$0.428307\pi$
$380$	−6.33511e13	−0.410152
$381$	0	0
$382$	3.71750e14	2.33831
$383$	−1.89007e14	−1.17188	−0.585942	−	0.810353i	$-0.699275\pi$
$383$	−1.89007e14	−1.17188	−0.585942	+	0.810353i	$0.699275\pi$
$384$	0	0
$385$	−1.69585e13	−0.102177
$386$	2.64344e14	1.57014
$387$	0	0
$388$	−5.62070e14	−3.24501
$389$	2.90163e14	1.65165	0.825826	−	0.563924i	$-0.190709\pi$
$389$	2.90163e14	1.65165	0.825826	+	0.563924i	$0.190709\pi$
$390$	0	0
$391$	−7.02100e13	−0.388532
$392$	−4.20271e14	−2.29328
$393$	0	0
$394$	3.00275e14	1.59327
$395$	3.90489e13	0.204327
$396$	0	0
$397$	−5.15115e13	−0.262154	−0.131077	−	0.991372i	$-0.541843\pi$
$397$	−5.15115e13	−0.262154	−0.131077	+	0.991372i	$0.541843\pi$
$398$	3.47328e14	1.74334
$399$	0	0
$400$	1.00289e14	0.489691
$401$	1.11012e14	0.534657	0.267329	−	0.963605i	$-0.413859\pi$
$401$	1.11012e14	0.534657	0.267329	+	0.963605i	$0.413859\pi$
$402$	0	0
$403$	6.05768e14	2.83876
$404$	−5.93346e14	−2.74291
$405$	0	0
$406$	1.25886e13	0.0566349
$407$	1.55351e14	0.689517
$408$	0	0
$409$	−1.92951e14	−0.833623	−0.416811	−	0.908993i	$-0.636852\pi$
$409$	−1.92951e14	−0.833623	−0.416811	+	0.908993i	$0.636852\pi$
$410$	−4.80955e13	−0.205019
$411$	0	0
$412$	−4.69894e14	−1.95014
$413$	1.05778e13	0.0433180
$414$	0	0
$415$	−1.05324e14	−0.420013
$416$	7.28538e14	2.86707
$417$	0	0
$418$	1.16200e14	0.445386
$419$	−2.28750e14	−0.865336	−0.432668	−	0.901553i	$-0.642428\pi$
$419$	−2.28750e14	−0.865336	−0.432668	+	0.901553i	$0.642428\pi$
$420$	0	0
$421$	−4.00332e14	−1.47526	−0.737630	−	0.675205i	$-0.764055\pi$
$421$	−4.00332e14	−1.47526	−0.737630	+	0.675205i	$0.764055\pi$
$422$	9.56816e13	0.348024
$423$	0	0
$424$	−1.25896e15	−4.46169
$425$	2.39320e13	0.0837220
$426$	0	0
$427$	8.91803e12	0.0304030
$428$	−7.58132e14	−2.55155
$429$	0	0
$430$	1.71857e14	0.563756
$431$	−1.29757e14	−0.420250	−0.210125	−	0.977675i	$-0.567387\pi$
$431$	−1.29757e14	−0.420250	−0.210125	+	0.977675i	$0.567387\pi$
$432$	0	0
$433$	−3.09354e14	−0.976725	−0.488363	−	0.872641i	$-0.662406\pi$
$433$	−3.09354e14	−0.976725	−0.488363	+	0.872641i	$0.662406\pi$
$434$	4.00435e14	1.24835
$435$	0	0
$436$	1.41473e15	4.30028
$437$	1.17035e14	0.351293
$438$	0	0
$439$	−6.15652e13	−0.180211	−0.0901054	−	0.995932i	$-0.528720\pi$
$439$	−6.15652e13	−0.180211	−0.0901054	+	0.995932i	$0.528720\pi$
$440$	−2.59082e14	−0.748940
$441$	0	0
$442$	4.15156e14	1.17055
$443$	2.42894e13	0.0676389	0.0338194	−	0.999428i	$-0.489233\pi$
$443$	2.42894e13	0.0676389	0.0338194	+	0.999428i	$0.489233\pi$
$444$	0	0
$445$	−9.19631e13	−0.249824
$446$	2.97146e14	0.797311
$447$	0	0
$448$	1.45631e14	0.381263
$449$	−6.65728e14	−1.72164	−0.860820	−	0.508910i	$-0.830049\pi$
$449$	−6.65728e14	−1.72164	−0.860820	+	0.508910i	$0.830049\pi$
$450$	0	0
$451$	6.24468e13	0.157594
$452$	1.16900e15	2.91442
$453$	0	0
$454$	−3.26999e14	−0.795681
$455$	1.00997e14	0.242800
$456$	0	0
$457$	6.99716e14	1.64204	0.821018	−	0.570902i	$-0.193406\pi$
$457$	6.99716e14	1.64204	0.821018	+	0.570902i	$0.193406\pi$
$458$	−4.06192e14	−0.941827
$459$	0	0
$460$	−4.44302e14	−1.00580
$461$	−3.43320e14	−0.767971	−0.383985	−	0.923339i	$-0.625449\pi$
$461$	−3.43320e14	−0.767971	−0.383985	+	0.923339i	$0.625449\pi$
$462$	0	0
$463$	3.77708e14	0.825012	0.412506	−	0.910955i	$-0.364654\pi$
$463$	3.77708e14	0.825012	0.412506	+	0.910955i	$0.364654\pi$
$464$	9.66603e13	0.208641
$465$	0	0
$466$	−8.66368e14	−1.82633
$467$	5.01733e14	1.04527	0.522637	−	0.852555i	$-0.324948\pi$
$467$	5.01733e14	1.04527	0.522637	+	0.852555i	$0.324948\pi$
$468$	0	0
$469$	1.61663e14	0.328972
$470$	5.15693e13	0.103718
$471$	0	0
$472$	1.61601e14	0.317513
$473$	−2.23138e14	−0.433348
$474$	0	0
$475$	−3.98930e13	−0.0756975
$476$	1.94263e14	0.364378
$477$	0	0
$478$	−1.55016e14	−0.284134
$479$	−9.56649e14	−1.73343	−0.866717	−	0.498800i	$-0.833774\pi$
$479$	−9.56649e14	−1.73343	−0.866717	+	0.498800i	$0.833774\pi$
$480$	0	0
$481$	−9.25204e14	−1.63847
$482$	2.28596e14	0.400231
$483$	0	0
$484$	−8.43122e14	−1.44292
$485$	−3.53942e14	−0.598898
$486$	0	0
$487$	1.81856e14	0.300828	0.150414	−	0.988623i	$-0.451939\pi$
$487$	1.81856e14	0.300828	0.150414	+	0.988623i	$0.451939\pi$
$488$	1.36244e14	0.222848
$489$	0	0
$490$	−4.50612e14	−0.720650
$491$	−9.28536e14	−1.46842	−0.734210	−	0.678922i	$-0.762447\pi$
$491$	−9.28536e14	−1.46842	−0.734210	+	0.678922i	$0.762447\pi$
$492$	0	0
$493$	2.30661e13	0.0356711
$494$	−6.92037e14	−1.05835
$495$	0	0
$496$	3.07470e15	4.59889
$497$	−2.84589e14	−0.420976
$498$	0	0
$499$	1.10604e15	1.60036	0.800178	−	0.599763i	$-0.204739\pi$
$499$	1.10604e15	1.60036	0.800178	+	0.599763i	$0.204739\pi$
$500$	1.51446e14	0.216732
$501$	0	0
$502$	−9.96177e14	−1.39465
$503$	1.07467e15	1.48816	0.744081	−	0.668089i	$-0.232888\pi$
$503$	1.07467e15	1.48816	0.744081	+	0.668089i	$0.232888\pi$
$504$	0	0
$505$	−3.73637e14	−0.506230
$506$	8.14950e14	1.09220
$507$	0	0
$508$	−6.24222e14	−0.818632
$509$	1.50116e15	1.94750	0.973752	−	0.227610i	$-0.0730910\pi$
$509$	1.50116e15	1.94750	0.973752	+	0.227610i	$0.0730910\pi$
$510$	0	0
$511$	−3.72793e14	−0.473318
$512$	−1.43474e15	−1.80214
$513$	0	0
$514$	−2.96299e12	−0.00364278
$515$	−2.95898e14	−0.359917
$516$	0	0
$517$	−6.69571e13	−0.0797258
$518$	−6.11593e14	−0.720525
$519$	0	0
$520$	1.54298e15	1.77968
$521$	8.31060e13	0.0948473	0.0474237	−	0.998875i	$-0.484899\pi$
$521$	8.31060e13	0.0948473	0.0474237	+	0.998875i	$0.484899\pi$
$522$	0	0
$523$	−9.42223e14	−1.05292	−0.526459	−	0.850201i	$-0.676481\pi$
$523$	−9.42223e14	−1.05292	−0.526459	+	0.850201i	$0.676481\pi$
$524$	1.47561e15	1.63173
$525$	0	0
$526$	1.00394e15	1.08715
$527$	7.33717e14	0.786267
$528$	0	0
$529$	−1.32002e14	−0.138540
$530$	−1.34985e15	−1.40206
$531$	0	0
$532$	−3.23824e14	−0.329454
$533$	−3.71906e14	−0.374485
$534$	0	0
$535$	−4.77405e14	−0.470913
$536$	2.46979e15	2.41131
$537$	0	0
$538$	3.19133e15	3.05259
$539$	5.85071e14	0.553950
$540$	0	0
$541$	1.18229e15	1.09683	0.548416	−	0.836206i	$-0.315231\pi$
$541$	1.18229e15	1.09683	0.548416	+	0.836206i	$0.315231\pi$
$542$	−9.50410e14	−0.872800
$543$	0	0
$544$	8.82418e14	0.794110
$545$	8.90870e14	0.793658
$546$	0	0
$547$	1.57701e15	1.37691	0.688453	−	0.725281i	$-0.258290\pi$
$547$	1.57701e15	1.37691	0.688453	+	0.725281i	$0.258290\pi$
$548$	3.12247e14	0.269902
$549$	0	0
$550$	−2.77786e14	−0.235351
$551$	−3.84496e13	−0.0322521
$552$	0	0
$553$	1.99601e14	0.164125
$554$	2.53309e15	2.06228
$555$	0	0
$556$	−2.53795e15	−2.02568
$557$	−4.53070e14	−0.358065	−0.179033	−	0.983843i	$-0.557297\pi$
$557$	−4.53070e14	−0.358065	−0.179033	+	0.983843i	$0.557297\pi$
$558$	0	0
$559$	1.32891e15	1.02975
$560$	5.12633e14	0.393344
$561$	0	0
$562$	−3.95241e15	−2.97381
$563$	−4.23450e13	−0.0315505	−0.0157752	−	0.999876i	$-0.505022\pi$
$563$	−4.23450e13	−0.0315505	−0.0157752	+	0.999876i	$0.505022\pi$
$564$	0	0
$565$	7.36133e14	0.537885
$566$	−7.27444e14	−0.526392
$567$	0	0
$568$	−4.34777e15	−3.08568
$569$	9.72594e14	0.683619	0.341810	−	0.939769i	$-0.388960\pi$
$569$	9.72594e14	0.683619	0.341810	+	0.939769i	$0.388960\pi$
$570$	0	0
$571$	−2.07663e15	−1.43173	−0.715863	−	0.698241i	$-0.753966\pi$
$571$	−2.07663e15	−1.43173	−0.715863	+	0.698241i	$0.753966\pi$
$572$	−3.41112e15	−2.32927
$573$	0	0
$574$	−2.45844e14	−0.164681
$575$	−2.79783e14	−0.185630
$576$	0	0
$577$	2.62999e15	1.71194	0.855968	−	0.517028i	$-0.172962\pi$
$577$	2.62999e15	1.71194	0.855968	+	0.517028i	$0.172962\pi$
$578$	−2.36671e15	−1.52596
$579$	0	0
$580$	1.45967e14	0.0923421
$581$	−5.38371e14	−0.337375
$582$	0	0
$583$	1.75263e15	1.07774
$584$	−5.69531e15	−3.46934
$585$	0	0
$586$	−1.82420e15	−1.09052
$587$	2.89275e15	1.71317	0.856587	−	0.516003i	$-0.172581\pi$
$587$	2.89275e15	1.71317	0.856587	+	0.516003i	$0.172581\pi$
$588$	0	0
$589$	−1.22306e15	−0.710906
$590$	1.73267e14	0.0997770
$591$	0	0
$592$	−4.69606e15	−2.65439
$593$	1.15734e15	0.648125	0.324063	−	0.946036i	$-0.394951\pi$
$593$	1.15734e15	0.648125	0.324063	+	0.946036i	$0.394951\pi$
$594$	0	0
$595$	1.22330e14	0.0672496
$596$	−3.94106e15	−2.14663
$597$	0	0
$598$	−4.85349e15	−2.59536
$599$	−2.42056e14	−0.128253	−0.0641265	−	0.997942i	$-0.520426\pi$
$599$	−2.42056e14	−0.128253	−0.0641265	+	0.997942i	$0.520426\pi$
$600$	0	0
$601$	−3.08465e15	−1.60471	−0.802354	−	0.596848i	$-0.796419\pi$
$601$	−3.08465e15	−1.60471	−0.802354	+	0.596848i	$0.796419\pi$
$602$	8.78460e14	0.452836
$603$	0	0
$604$	6.18480e15	3.13057
$605$	−5.30924e14	−0.266304
$606$	0	0
$607$	2.71223e15	1.33595	0.667973	−	0.744186i	$-0.267162\pi$
$607$	2.71223e15	1.33595	0.667973	+	0.744186i	$0.267162\pi$
$608$	−1.47093e15	−0.717997
$609$	0	0
$610$	1.46080e14	0.0700290
$611$	3.98768e14	0.189449
$612$	0	0
$613$	−1.80466e15	−0.842097	−0.421049	−	0.907038i	$-0.638338\pi$
$613$	−1.80466e15	−0.842097	−0.421049	+	0.907038i	$0.638338\pi$
$614$	1.71963e15	0.795258
$615$	0	0
$616$	−1.32431e15	−0.601585
$617$	−4.28183e14	−0.192780	−0.0963898	−	0.995344i	$-0.530730\pi$
$617$	−4.28183e14	−0.192780	−0.0963898	+	0.995344i	$0.530730\pi$
$618$	0	0
$619$	2.39110e15	1.05754	0.528772	−	0.848764i	$-0.322653\pi$
$619$	2.39110e15	1.05754	0.528772	+	0.848764i	$0.322653\pi$
$620$	4.64310e15	2.03542
$621$	0	0
$622$	6.17215e15	2.65821
$623$	−4.70076e14	−0.200671
$624$	0	0
$625$	9.53674e13	0.0400000
$626$	−2.36138e15	−0.981763
$627$	0	0
$628$	4.83117e15	1.97367
$629$	−1.12062e15	−0.453818
$630$	0	0
$631$	3.26028e15	1.29746	0.648730	−	0.761019i	$-0.275301\pi$
$631$	3.26028e15	1.29746	0.648730	+	0.761019i	$0.275301\pi$
$632$	3.04939e15	1.20301
$633$	0	0
$634$	−2.15132e15	−0.834093
$635$	−3.93080e14	−0.151087
$636$	0	0
$637$	−3.48443e15	−1.31633
$638$	−2.67735e14	−0.100275
$639$	0	0
$640$	8.09863e13	0.0298141
$641$	2.32104e15	0.847157	0.423579	−	0.905859i	$-0.360774\pi$
$641$	2.32104e15	0.847157	0.423579	+	0.905859i	$0.360774\pi$
$642$	0	0
$643$	−2.55397e15	−0.916336	−0.458168	−	0.888866i	$-0.651494\pi$
$643$	−2.55397e15	−0.916336	−0.458168	+	0.888866i	$0.651494\pi$
$644$	−2.27108e15	−0.807906
$645$	0	0
$646$	−8.38208e14	−0.293139
$647$	1.70408e15	0.590902	0.295451	−	0.955358i	$-0.404530\pi$
$647$	1.70408e15	0.590902	0.295451	+	0.955358i	$0.404530\pi$
$648$	0	0
$649$	−2.24969e14	−0.0766966
$650$	1.65437e15	0.559255
$651$	0	0
$652$	6.25704e15	2.07973
$653$	2.20439e15	0.726552	0.363276	−	0.931682i	$-0.381658\pi$
$653$	2.20439e15	0.726552	0.363276	+	0.931682i	$0.381658\pi$
$654$	0	0
$655$	9.29208e14	0.301152
$656$	−1.88769e15	−0.606679
$657$	0	0
$658$	2.63600e14	0.0833111
$659$	−1.97759e14	−0.0619821	−0.0309910	−	0.999520i	$-0.509866\pi$
$659$	−1.97759e14	−0.0619821	−0.0309910	+	0.999520i	$0.509866\pi$
$660$	0	0
$661$	−3.43414e15	−1.05855	−0.529274	−	0.848451i	$-0.677536\pi$
$661$	−3.43414e15	−1.05855	−0.529274	+	0.848451i	$0.677536\pi$
$662$	−5.14356e15	−1.57233
$663$	0	0
$664$	−8.22492e15	−2.47290
$665$	−2.03916e14	−0.0608039
$666$	0	0
$667$	−2.69660e14	−0.0790905
$668$	1.49571e16	4.35089
$669$	0	0
$670$	2.64809e15	0.757743
$671$	−1.89670e14	−0.0538299
$672$	0	0
$673$	2.01250e15	0.561892	0.280946	−	0.959724i	$-0.409352\pi$
$673$	2.01250e15	0.561892	0.280946	+	0.959724i	$0.409352\pi$
$674$	1.13509e16	3.14340
$675$	0	0
$676$	1.14214e16	3.11181
$677$	1.01903e15	0.275392	0.137696	−	0.990475i	$-0.456030\pi$
$677$	1.01903e15	0.275392	0.137696	+	0.990475i	$0.456030\pi$
$678$	0	0
$679$	−1.80920e15	−0.481064
$680$	1.86888e15	0.492928
$681$	0	0
$682$	−8.51648e15	−2.21027
$683$	−2.86885e15	−0.738575	−0.369287	−	0.929315i	$-0.620398\pi$
$683$	−2.86885e15	−0.738575	−0.369287	+	0.929315i	$0.620398\pi$
$684$	0	0
$685$	1.96626e14	0.0498130
$686$	−4.94793e15	−1.24349
$687$	0	0
$688$	6.74517e15	1.66823
$689$	−1.04379e16	−2.56099
$690$	0	0
$691$	−1.79931e15	−0.434487	−0.217243	−	0.976117i	$-0.569707\pi$
$691$	−1.79931e15	−0.434487	−0.217243	+	0.976117i	$0.569707\pi$
$692$	1.52590e15	0.365547
$693$	0	0
$694$	2.41157e15	0.568621
$695$	−1.59817e15	−0.373859
$696$	0	0
$697$	−4.50460e14	−0.103723
$698$	3.10420e15	0.709160
$699$	0	0
$700$	7.74127e14	0.174090
$701$	−2.99337e15	−0.667899	−0.333949	−	0.942591i	$-0.608381\pi$
$701$	−2.99337e15	−0.667899	−0.333949	+	0.942591i	$0.608381\pi$
$702$	0	0
$703$	1.86800e15	0.410321
$704$	−3.09729e15	−0.675045
$705$	0	0
$706$	4.72758e15	1.01441
$707$	−1.90987e15	−0.406629
$708$	0	0
$709$	2.74187e15	0.574769	0.287384	−	0.957815i	$-0.407214\pi$
$709$	2.74187e15	0.574769	0.287384	+	0.957815i	$0.407214\pi$
$710$	−4.66166e15	−0.969660
$711$	0	0
$712$	−7.18154e15	−1.47088
$713$	−8.57770e15	−1.74333
$714$	0	0
$715$	−2.14802e15	−0.429889
$716$	9.50185e15	1.88706
$717$	0	0
$718$	1.64836e16	3.22380
$719$	4.38021e15	0.850131	0.425065	−	0.905163i	$-0.360251\pi$
$719$	4.38021e15	0.850131	0.425065	+	0.905163i	$0.360251\pi$
$720$	0	0
$721$	−1.51250e15	−0.289103
$722$	−8.35640e15	−1.58513
$723$	0	0
$724$	5.47375e14	0.102264
$725$	9.19170e13	0.0170426
$726$	0	0
$727$	6.60205e15	1.20570	0.602851	−	0.797854i	$-0.294031\pi$
$727$	6.60205e15	1.20570	0.602851	+	0.797854i	$0.294031\pi$
$728$	7.88704e15	1.42952
$729$	0	0
$730$	−6.10648e15	−1.09022
$731$	1.60960e15	0.285216
$732$	0	0
$733$	−8.22795e15	−1.43622	−0.718108	−	0.695932i	$-0.754992\pi$
$733$	−8.22795e15	−1.43622	−0.718108	+	0.695932i	$0.754992\pi$
$734$	−8.41006e15	−1.45704
$735$	0	0
$736$	−1.03161e16	−1.76071
$737$	−3.43826e15	−0.582462
$738$	0	0
$739$	−1.10770e16	−1.84875	−0.924376	−	0.381483i	$-0.875414\pi$
$739$	−1.10770e16	−1.84875	−0.924376	+	0.381483i	$0.875414\pi$
$740$	−7.09152e15	−1.17480
$741$	0	0
$742$	−6.89984e15	−1.12620
$743$	3.86160e15	0.625646	0.312823	−	0.949811i	$-0.398725\pi$
$743$	3.86160e15	0.625646	0.312823	+	0.949811i	$0.398725\pi$
$744$	0	0
$745$	−2.48173e15	−0.396182
$746$	−5.94352e15	−0.941846
$747$	0	0
$748$	−4.13161e15	−0.645150
$749$	−2.44029e15	−0.378260
$750$	0	0
$751$	1.05947e15	0.161834	0.0809168	−	0.996721i	$-0.474215\pi$
$751$	1.05947e15	0.161834	0.0809168	+	0.996721i	$0.474215\pi$
$752$	2.02403e15	0.306915
$753$	0	0
$754$	1.59452e15	0.238280
$755$	3.89465e15	0.577776
$756$	0	0
$757$	−7.04375e15	−1.02986	−0.514928	−	0.857233i	$-0.672182\pi$
$757$	−7.04375e15	−1.02986	−0.514928	+	0.857233i	$0.672182\pi$
$758$	5.69339e15	0.826400
$759$	0	0
$760$	−3.11530e15	−0.445682
$761$	−3.63598e15	−0.516424	−0.258212	−	0.966088i	$-0.583133\pi$
$761$	−3.63598e15	−0.516424	−0.258212	+	0.966088i	$0.583133\pi$
$762$	0	0
$763$	4.55374e15	0.637505
$764$	2.20334e16	3.06245
$765$	0	0
$766$	−1.58254e16	−2.16819
$767$	1.33982e15	0.182251
$768$	0	0
$769$	−5.34829e15	−0.717167	−0.358583	−	0.933498i	$-0.616740\pi$
$769$	−5.34829e15	−0.717167	−0.358583	+	0.933498i	$0.616740\pi$
$770$	−1.41992e15	−0.189045
$771$	0	0
$772$	1.56675e16	2.05639
$773$	−8.06669e15	−1.05126	−0.525628	−	0.850715i	$-0.676169\pi$
$773$	−8.06669e15	−1.05126	−0.525628	+	0.850715i	$0.676169\pi$
$774$	0	0
$775$	2.92382e15	0.375656
$776$	−2.76399e16	−3.52612
$777$	0	0
$778$	2.42951e16	3.05584
$779$	7.50886e14	0.0937816
$780$	0	0
$781$	6.05266e15	0.745359
$782$	−5.87863e15	−0.718851
$783$	0	0
$784$	−1.76859e16	−2.13250
$785$	3.04225e15	0.364260
$786$	0	0
$787$	−8.56068e15	−1.01076	−0.505379	−	0.862897i	$-0.668647\pi$
$787$	−8.56068e15	−1.01076	−0.505379	+	0.862897i	$0.668647\pi$
$788$	1.77971e16	2.08668
$789$	0	0
$790$	3.26954e15	0.378040
$791$	3.76279e15	0.432056
$792$	0	0
$793$	1.12959e15	0.127914
$794$	−4.31302e15	−0.485030
$795$	0	0
$796$	2.05859e16	2.28323
$797$	1.47001e16	1.61919	0.809596	−	0.586987i	$-0.199686\pi$
$797$	1.47001e16	1.61919	0.809596	+	0.586987i	$0.199686\pi$
$798$	0	0
$799$	4.82995e14	0.0524729
$800$	3.51638e15	0.379403
$801$	0	0
$802$	9.29494e15	0.989208
$803$	7.92861e15	0.838033
$804$	0	0
$805$	−1.43013e15	−0.149107
$806$	5.07205e16	5.25219
$807$	0	0
$808$	−2.91779e16	−2.98052
$809$	−5.20792e15	−0.528382	−0.264191	−	0.964470i	$-0.585105\pi$
$809$	−5.20792e15	−0.528382	−0.264191	+	0.964470i	$0.585105\pi$
$810$	0	0
$811$	1.95571e16	1.95745	0.978724	−	0.205183i	$-0.0657789\pi$
$811$	1.95571e16	1.95745	0.978724	+	0.205183i	$0.0657789\pi$
$812$	7.46119e14	0.0741737
$813$	0	0
$814$	1.30074e16	1.27573
$815$	3.94014e15	0.383835
$816$	0	0
$817$	−2.68310e15	−0.257879
$818$	−1.61557e16	−1.54235
$819$	0	0
$820$	−2.85059e15	−0.268509
$821$	−1.02440e16	−0.958476	−0.479238	−	0.877685i	$-0.659087\pi$
$821$	−1.02440e16	−0.958476	−0.479238	+	0.877685i	$0.659087\pi$
$822$	0	0
$823$	−1.40372e16	−1.29593	−0.647964	−	0.761671i	$-0.724379\pi$
$823$	−1.40372e16	−1.29593	−0.647964	+	0.761671i	$0.724379\pi$
$824$	−2.31071e16	−2.11907
$825$	0	0
$826$	8.85667e14	0.0801457
$827$	−8.80160e14	−0.0791191	−0.0395596	−	0.999217i	$-0.512595\pi$
$827$	−8.80160e14	−0.0791191	−0.0395596	+	0.999217i	$0.512595\pi$
$828$	0	0
$829$	4.54642e14	0.0403292	0.0201646	−	0.999797i	$-0.493581\pi$
$829$	4.54642e14	0.0403292	0.0201646	+	0.999797i	$0.493581\pi$
$830$	−8.81871e15	−0.777097
$831$	0	0
$832$	1.84461e16	1.60408
$833$	−4.22041e15	−0.364592
$834$	0	0
$835$	9.41870e15	0.802999
$836$	6.88711e15	0.583314
$837$	0	0
$838$	−1.91531e16	−1.60102
$839$	−1.32346e16	−1.09906	−0.549529	−	0.835474i	$-0.685193\pi$
$839$	−1.32346e16	−1.09906	−0.549529	+	0.835474i	$0.685193\pi$
$840$	0	0
$841$	−1.21119e16	−0.992739
$842$	−3.35195e16	−2.72949
$843$	0	0
$844$	5.67099e15	0.455801
$845$	7.19220e15	0.574315
$846$	0	0
$847$	−2.71386e15	−0.213908
$848$	−5.29797e16	−4.14889
$849$	0	0
$850$	2.00381e15	0.154900
$851$	1.31009e16	1.00621
$852$	0	0
$853$	−2.60074e15	−0.197186	−0.0985932	−	0.995128i	$-0.531434\pi$
$853$	−2.60074e15	−0.197186	−0.0985932	+	0.995128i	$0.531434\pi$
$854$	7.46700e14	0.0562507
$855$	0	0
$856$	−3.72812e16	−2.77258
$857$	1.68895e16	1.24802	0.624011	−	0.781415i	$-0.285502\pi$
$857$	1.68895e16	1.24802	0.624011	+	0.781415i	$0.285502\pi$
$858$	0	0
$859$	8.98241e15	0.655285	0.327643	−	0.944802i	$-0.393746\pi$
$859$	8.98241e15	0.655285	0.327643	+	0.944802i	$0.393746\pi$
$860$	1.01859e16	0.738341
$861$	0	0
$862$	−1.08645e16	−0.777534
$863$	1.16178e16	0.826164	0.413082	−	0.910694i	$-0.364452\pi$
$863$	1.16178e16	0.826164	0.413082	+	0.910694i	$0.364452\pi$
$864$	0	0
$865$	9.60880e14	0.0674653
$866$	−2.59020e16	−1.80711
$867$	0	0
$868$	2.37335e16	1.63495
$869$	−4.24514e15	−0.290592
$870$	0	0
$871$	2.04768e16	1.38408
$872$	6.95694e16	4.67280
$873$	0	0
$874$	9.79928e15	0.649952
$875$	4.87477e14	0.0321300
$876$	0	0
$877$	4.73202e15	0.307999	0.153999	−	0.988071i	$-0.450785\pi$
$877$	4.73202e15	0.307999	0.153999	+	0.988071i	$0.450785\pi$
$878$	−5.15481e15	−0.333421
$879$	0	0
$880$	−1.09027e16	−0.696435
$881$	−2.81982e15	−0.179000	−0.0895002	−	0.995987i	$-0.528527\pi$
$881$	−2.81982e15	−0.179000	−0.0895002	+	0.995987i	$0.528527\pi$
$882$	0	0
$883$	1.91741e16	1.20208	0.601038	−	0.799221i	$-0.294754\pi$
$883$	1.91741e16	1.20208	0.601038	+	0.799221i	$0.294754\pi$
$884$	2.46061e16	1.53305
$885$	0	0
$886$	2.03373e15	0.125144
$887$	−2.08389e15	−0.127437	−0.0637183	−	0.997968i	$-0.520296\pi$
$887$	−2.08389e15	−0.127437	−0.0637183	+	0.997968i	$0.520296\pi$
$888$	0	0
$889$	−2.00926e15	−0.121360
$890$	−7.70000e15	−0.462217
$891$	0	0
$892$	1.76117e16	1.04422
$893$	−8.05119e14	−0.0474435
$894$	0	0
$895$	5.98343e15	0.348276
$896$	4.13967e14	0.0239481
$897$	0	0
$898$	−5.57409e16	−3.18533
$899$	2.81803e15	0.160054
$900$	0	0
$901$	−1.26426e16	−0.709332
$902$	5.22863e15	0.291576
$903$	0	0
$904$	5.74857e16	3.16689
$905$	3.44689e14	0.0188738
$906$	0	0
$907$	3.20443e16	1.73345	0.866723	−	0.498791i	$-0.166222\pi$
$907$	3.20443e16	1.73345	0.866723	+	0.498791i	$0.166222\pi$
$908$	−1.93810e16	−1.04209
$909$	0	0
$910$	8.45644e15	0.449221
$911$	8.44282e15	0.445797	0.222898	−	0.974842i	$-0.428448\pi$
$911$	8.44282e15	0.445797	0.222898	+	0.974842i	$0.428448\pi$
$912$	0	0
$913$	1.14501e16	0.597340
$914$	5.85867e16	3.03805
$915$	0	0
$916$	−2.40748e16	−1.23349
$917$	4.74971e15	0.241900
$918$	0	0
$919$	−1.08277e16	−0.544880	−0.272440	−	0.962173i	$-0.587831\pi$
$919$	−1.08277e16	−0.544880	−0.272440	+	0.962173i	$0.587831\pi$
$920$	−2.18486e16	−1.09293
$921$	0	0
$922$	−2.87460e16	−1.42088
$923$	−3.60470e16	−1.77117
$924$	0	0
$925$	−4.46562e15	−0.216821
$926$	3.16252e16	1.52641
$927$	0	0
$928$	3.38916e15	0.161651
$929$	1.30338e16	0.617994	0.308997	−	0.951063i	$-0.400007\pi$
$929$	1.30338e16	0.617994	0.308997	+	0.951063i	$0.400007\pi$
$930$	0	0
$931$	7.03513e15	0.329647
$932$	−5.13491e16	−2.39191
$933$	0	0
$934$	4.20098e16	1.93394
$935$	−2.60173e15	−0.119069
$936$	0	0
$937$	−2.06679e16	−0.934819	−0.467410	−	0.884041i	$-0.654813\pi$
$937$	−2.06679e16	−0.934819	−0.467410	+	0.884041i	$0.654813\pi$
$938$	1.35359e16	0.608656
$939$	0	0
$940$	3.05648e15	0.135837
$941$	3.48692e16	1.54063	0.770317	−	0.637661i	$-0.220098\pi$
$941$	3.48692e16	1.54063	0.770317	+	0.637661i	$0.220098\pi$
$942$	0	0
$943$	5.26621e15	0.229977
$944$	6.80051e15	0.295254
$945$	0	0
$946$	−1.86832e16	−0.801769
$947$	2.53080e15	0.107977	0.0539887	−	0.998542i	$-0.482807\pi$
$947$	2.53080e15	0.107977	0.0539887	+	0.998542i	$0.482807\pi$
$948$	0	0
$949$	−4.72194e16	−1.99139
$950$	−3.34021e15	−0.140053
$951$	0	0
$952$	9.55293e15	0.395944
$953$	1.68411e16	0.693999	0.347000	−	0.937865i	$-0.387201\pi$
$953$	1.68411e16	0.693999	0.347000	+	0.937865i	$0.387201\pi$
$954$	0	0
$955$	1.38747e16	0.565205
$956$	−9.18773e15	−0.372126
$957$	0	0
$958$	−8.00995e16	−3.20715
$959$	1.00507e15	0.0400122
$960$	0	0
$961$	6.42312e16	2.52794
$962$	−7.74666e16	−3.03146
$963$	0	0
$964$	1.35488e16	0.524175
$965$	9.86603e15	0.379527
$966$	0	0
$967$	−2.82761e16	−1.07541	−0.537705	−	0.843133i	$-0.680708\pi$
$967$	−2.82761e16	−1.07541	−0.537705	+	0.843133i	$0.680708\pi$
$968$	−4.14607e16	−1.56791
$969$	0	0
$970$	−2.96353e16	−1.10806
$971$	−2.55089e16	−0.948386	−0.474193	−	0.880421i	$-0.657260\pi$
$971$	−2.55089e16	−0.948386	−0.474193	+	0.880421i	$0.657260\pi$
$972$	0	0
$973$	−8.16918e15	−0.300302
$974$	1.52266e16	0.556583
$975$	0	0
$976$	5.73346e15	0.207225
$977$	−5.16659e16	−1.85688	−0.928441	−	0.371480i	$-0.878850\pi$
$977$	−5.16659e16	−1.85688	−0.928441	+	0.371480i	$0.878850\pi$
$978$	0	0
$979$	9.99762e15	0.355297
$980$	−2.67075e16	−0.943823
$981$	0	0
$982$	−7.77456e16	−2.71683
$983$	−1.06975e15	−0.0371740	−0.0185870	−	0.999827i	$-0.505917\pi$
$983$	−1.06975e15	−0.0371740	−0.0185870	+	0.999827i	$0.505917\pi$
$984$	0	0
$985$	1.12071e16	0.385117
$986$	1.93131e15	0.0659976
$987$	0	0
$988$	−4.10167e16	−1.38611
$989$	−1.88175e16	−0.632385
$990$	0	0
$991$	2.05333e16	0.682423	0.341211	−	0.939987i	$-0.389163\pi$
$991$	2.05333e16	0.682423	0.341211	+	0.939987i	$0.389163\pi$
$992$	1.07807e17	3.56313
$993$	0	0
$994$	−2.38284e16	−0.778878
$995$	1.29632e16	0.421391
$996$	0	0
$997$	−1.61931e16	−0.520603	−0.260301	−	0.965527i	$-0.583822\pi$
$997$	−1.61931e16	−0.520603	−0.260301	+	0.965527i	$0.583822\pi$
$998$	9.26076e16	2.96093
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.12.a.d.1.2		2
3.2	odd	2		5.12.a.b.1.1	✓	2
5.2	odd	4		225.12.b.f.199.4		4
5.3	odd	4		225.12.b.f.199.1		4
5.4	even	2		225.12.a.h.1.1		2
12.11	even	2		80.12.a.j.1.2		2
15.2	even	4		25.12.b.c.24.1		4
15.8	even	4		25.12.b.c.24.4		4
15.14	odd	2		25.12.a.c.1.2		2
21.20	even	2		245.12.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.12.a.b.1.1	✓	2	3.2	odd	2
25.12.a.c.1.2		2	15.14	odd	2
25.12.b.c.24.1		4	15.2	even	4
25.12.b.c.24.4		4	15.8	even	4
45.12.a.d.1.2		2	1.1	even	1	trivial
80.12.a.j.1.2		2	12.11	even	2
225.12.a.h.1.1		2	5.4	even	2
225.12.b.f.199.1		4	5.3	odd	4
225.12.b.f.199.4		4	5.2	odd	4
245.12.a.b.1.1		2	21.20	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	45.a (trivial)

\(f(q)\)	\(=\)	\(q+83.7292 q^{2} +4962.58 q^{4} +3125.00 q^{5} +15973.7 q^{7} +244036. q^{8} +O(q^{10})\)	\(q+83.7292 q^{2} +4962.58 q^{4} +3125.00 q^{5} +15973.7 q^{7} +244036. q^{8} +261654. q^{10} -339729. q^{11} +2.02328e6 q^{13} +1.33746e6 q^{14} +1.02696e7 q^{16} +2.45063e6 q^{17} -4.08504e6 q^{19} +1.55081e7 q^{20} -2.84453e7 q^{22} -2.86497e7 q^{23} +9.76562e6 q^{25} +1.69408e8 q^{26} +7.92706e7 q^{28} +9.41230e6 q^{29} +2.99399e8 q^{31} +3.60078e8 q^{32} +2.05190e8 q^{34} +4.99177e7 q^{35} -4.57279e8 q^{37} -3.42037e8 q^{38} +7.62612e8 q^{40} -1.83814e8 q^{41} +6.56811e8 q^{43} -1.68594e9 q^{44} -2.39882e9 q^{46} +1.97090e8 q^{47} -1.72217e9 q^{49} +8.17668e8 q^{50} +1.00407e10 q^{52} -5.15890e9 q^{53} -1.06165e9 q^{55} +3.89815e9 q^{56} +7.88085e8 q^{58} +6.62200e8 q^{59} +5.58296e8 q^{61} +2.50684e10 q^{62} +9.11694e9 q^{64} +6.32275e9 q^{65} +1.01206e10 q^{67} +1.21615e10 q^{68} +4.17957e9 q^{70} -1.78161e10 q^{71} -2.33380e10 q^{73} -3.82876e10 q^{74} -2.02724e10 q^{76} -5.42672e9 q^{77} +1.24957e10 q^{79} +3.20924e10 q^{80} -1.53906e10 q^{82} -3.37037e10 q^{83} +7.65823e9 q^{85} +5.49943e10 q^{86} -8.29062e10 q^{88} -2.94282e10 q^{89} +3.23192e10 q^{91} -1.42177e11 q^{92} +1.65022e10 q^{94} -1.27657e10 q^{95} -1.13262e11 q^{97} -1.44196e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 20 q^{2} + 6976 q^{4} + 6250 q^{5} + 57900 q^{7} + 246240 q^{8}+O(q^{10}) \) 2 * q + 20 * q^2 + 6976 * q^4 + 6250 * q^5 + 57900 * q^7 + 246240 * q^8	\( 2 q + 20 q^{2} + 6976 q^{4} + 6250 q^{5} + 57900 q^{7} + 246240 q^{8} + 62500 q^{10} + 618176 q^{11} + 3414260 q^{13} - 1334472 q^{14} + 6005632 q^{16} - 1317940 q^{17} + 5325320 q^{19} + 21800000 q^{20} - 89491840 q^{22} - 58943940 q^{23} + 19531250 q^{25} + 80761736 q^{26} + 163685760 q^{28} - 94140380 q^{29} + 244543464 q^{31} + 627301120 q^{32} + 445358072 q^{34} + 180937500 q^{35} + 21003220 q^{37} - 941752240 q^{38} + 769500000 q^{40} + 745743316 q^{41} + 629950100 q^{43} + 242725888 q^{44} - 468194856 q^{46} + 1402061540 q^{47} - 1941677414 q^{49} + 195312500 q^{50} + 12841321600 q^{52} - 1138320580 q^{53} + 1931800000 q^{55} + 3990553920 q^{56} + 7387417960 q^{58} - 7317515560 q^{59} - 1516425676 q^{61} + 28564327440 q^{62} + 819531776 q^{64} + 10669562500 q^{65} + 15734290140 q^{67} + 4573774720 q^{68} - 4170225000 q^{70} - 32938471544 q^{71} - 29982848860 q^{73} - 68768198072 q^{74} - 1325392640 q^{76} + 34734748800 q^{77} - 3302823120 q^{79} + 18767600000 q^{80} - 74630515640 q^{82} - 13299102420 q^{83} - 4118562500 q^{85} + 56706093896 q^{86} - 80794874880 q^{88} + 12674770860 q^{89} + 90637859064 q^{91} - 203171571840 q^{92} - 60289765528 q^{94} + 16641625000 q^{95} - 3080703740 q^{97} - 130206802940 q^{98}+O(q^{100}) \) 2 * q + 20 * q^2 + 6976 * q^4 + 6250 * q^5 + 57900 * q^7 + 246240 * q^8 + 62500 * q^10 + 618176 * q^11 + 3414260 * q^13 - 1334472 * q^14 + 6005632 * q^16 - 1317940 * q^17 + 5325320 * q^19 + 21800000 * q^20 - 89491840 * q^22 - 58943940 * q^23 + 19531250 * q^25 + 80761736 * q^26 + 163685760 * q^28 - 94140380 * q^29 + 244543464 * q^31 + 627301120 * q^32 + 445358072 * q^34 + 180937500 * q^35 + 21003220 * q^37 - 941752240 * q^38 + 769500000 * q^40 + 745743316 * q^41 + 629950100 * q^43 + 242725888 * q^44 - 468194856 * q^46 + 1402061540 * q^47 - 1941677414 * q^49 + 195312500 * q^50 + 12841321600 * q^52 - 1138320580 * q^53 + 1931800000 * q^55 + 3990553920 * q^56 + 7387417960 * q^58 - 7317515560 * q^59 - 1516425676 * q^61 + 28564327440 * q^62 + 819531776 * q^64 + 10669562500 * q^65 + 15734290140 * q^67 + 4573774720 * q^68 - 4170225000 * q^70 - 32938471544 * q^71 - 29982848860 * q^73 - 68768198072 * q^74 - 1325392640 * q^76 + 34734748800 * q^77 - 3302823120 * q^79 + 18767600000 * q^80 - 74630515640 * q^82 - 13299102420 * q^83 - 4118562500 * q^85 + 56706093896 * q^86 - 80794874880 * q^88 + 12674770860 * q^89 + 90637859064 * q^91 - 203171571840 * q^92 - 60289765528 * q^94 + 16641625000 * q^95 - 3080703740 * q^97 - 130206802940 * q^98

Introduction

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