LMFDB - Embedded newform 1127.4.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1127,4,Mod(1,1127)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1127, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1127.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1127 = 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1127.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:	$66.4951525765$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.334189.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 16x^{2} - 5x + 4 $ x^4 - 2x^3 - 16x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.22031$ of defining polynomial
Character	$\chi$	$=$	1127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0323756 q^{2} -6.42170 q^{3} -7.99895 q^{4} -14.1026 q^{5} +0.207906 q^{6} +0.517976 q^{8} +14.2382 q^{9} +O(q^{10})$	\(q-0.0323756 q^{2} -6.42170 q^{3} -7.99895 q^{4} -14.1026 q^{5} +0.207906 q^{6} +0.517976 q^{8} +14.2382 q^{9} +0.456580 q^{10} -55.5140 q^{11} +51.3668 q^{12} +18.3149 q^{13} +90.5626 q^{15} +63.9748 q^{16} -10.0273 q^{17} -0.460970 q^{18} -161.106 q^{19} +112.806 q^{20} +1.79730 q^{22} -23.0000 q^{23} -3.32628 q^{24} +73.8833 q^{25} -0.592956 q^{26} +81.9525 q^{27} +183.185 q^{29} -2.93202 q^{30} +144.762 q^{31} -6.21503 q^{32} +356.494 q^{33} +0.324640 q^{34} -113.891 q^{36} +181.411 q^{37} +5.21591 q^{38} -117.613 q^{39} -7.30481 q^{40} -77.7996 q^{41} +315.335 q^{43} +444.054 q^{44} -200.795 q^{45} +0.744639 q^{46} +524.190 q^{47} -410.827 q^{48} -2.39202 q^{50} +64.3923 q^{51} -146.500 q^{52} +73.7334 q^{53} -2.65326 q^{54} +782.892 q^{55} +1034.57 q^{57} -5.93071 q^{58} +132.892 q^{59} -724.406 q^{60} -236.683 q^{61} -4.68676 q^{62} -511.598 q^{64} -258.288 q^{65} -11.5417 q^{66} +493.624 q^{67} +80.2079 q^{68} +147.699 q^{69} -806.060 q^{71} +7.37504 q^{72} -1011.91 q^{73} -5.87328 q^{74} -474.456 q^{75} +1288.68 q^{76} +3.80779 q^{78} -599.386 q^{79} -902.212 q^{80} -910.705 q^{81} +2.51881 q^{82} +642.245 q^{83} +141.411 q^{85} -10.2092 q^{86} -1176.36 q^{87} -28.7549 q^{88} -883.399 q^{89} +6.50088 q^{90} +183.976 q^{92} -929.617 q^{93} -16.9710 q^{94} +2272.02 q^{95} +39.9111 q^{96} +71.2938 q^{97} -790.419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 7 q^{3} + 20 q^{4} - 14 q^{5} + 17 q^{6} - 63 q^{8} - 33 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 7 * q^3 + 20 * q^4 - 14 * q^5 + 17 * q^6 - 63 * q^8 - 33 * q^9	\( 4 q + 2 q^{2} - 7 q^{3} + 20 q^{4} - 14 q^{5} + 17 q^{6} - 63 q^{8} - 33 q^{9} + 70 q^{10} + 8 q^{11} + 67 q^{12} - 111 q^{13} + 10 q^{15} + 64 q^{16} - 98 q^{17} + 49 q^{18} - 96 q^{19} - 140 q^{20} + 220 q^{22} - 92 q^{23} + 188 q^{24} + 184 q^{25} + 229 q^{26} + 155 q^{27} + 21 q^{29} - 406 q^{30} + 193 q^{31} - 432 q^{32} + 418 q^{33} - 666 q^{34} - 629 q^{36} + 170 q^{37} - 748 q^{38} - 291 q^{39} + 26 q^{40} + 125 q^{41} + 2 q^{43} + 830 q^{44} - 168 q^{45} - 46 q^{46} + 677 q^{47} - 551 q^{48} + 414 q^{50} - 340 q^{51} - 2247 q^{52} - 230 q^{53} - 641 q^{54} + 972 q^{55} + 1322 q^{57} - 1835 q^{58} + 1140 q^{59} - 804 q^{60} - 754 q^{61} - 443 q^{62} - 805 q^{64} + 1318 q^{65} + 398 q^{66} + 488 q^{67} - 284 q^{68} + 161 q^{69} - 401 q^{71} + 1503 q^{72} - 1509 q^{73} + 1366 q^{74} - 1401 q^{75} + 3832 q^{76} - 1907 q^{78} - 838 q^{79} - 2846 q^{80} - 932 q^{81} + 949 q^{82} - 142 q^{83} + 112 q^{85} + 918 q^{86} - 2223 q^{87} - 404 q^{88} - 2342 q^{89} - 1784 q^{90} - 460 q^{92} - 509 q^{93} - 1567 q^{94} - 956 q^{95} - 799 q^{96} - 1062 q^{97} - 1498 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 7 * q^3 + 20 * q^4 - 14 * q^5 + 17 * q^6 - 63 * q^8 - 33 * q^9 + 70 * q^10 + 8 * q^11 + 67 * q^12 - 111 * q^13 + 10 * q^15 + 64 * q^16 - 98 * q^17 + 49 * q^18 - 96 * q^19 - 140 * q^20 + 220 * q^22 - 92 * q^23 + 188 * q^24 + 184 * q^25 + 229 * q^26 + 155 * q^27 + 21 * q^29 - 406 * q^30 + 193 * q^31 - 432 * q^32 + 418 * q^33 - 666 * q^34 - 629 * q^36 + 170 * q^37 - 748 * q^38 - 291 * q^39 + 26 * q^40 + 125 * q^41 + 2 * q^43 + 830 * q^44 - 168 * q^45 - 46 * q^46 + 677 * q^47 - 551 * q^48 + 414 * q^50 - 340 * q^51 - 2247 * q^52 - 230 * q^53 - 641 * q^54 + 972 * q^55 + 1322 * q^57 - 1835 * q^58 + 1140 * q^59 - 804 * q^60 - 754 * q^61 - 443 * q^62 - 805 * q^64 + 1318 * q^65 + 398 * q^66 + 488 * q^67 - 284 * q^68 + 161 * q^69 - 401 * q^71 + 1503 * q^72 - 1509 * q^73 + 1366 * q^74 - 1401 * q^75 + 3832 * q^76 - 1907 * q^78 - 838 * q^79 - 2846 * q^80 - 932 * q^81 + 949 * q^82 - 142 * q^83 + 112 * q^85 + 918 * q^86 - 2223 * q^87 - 404 * q^88 - 2342 * q^89 - 1784 * q^90 - 460 * q^92 - 509 * q^93 - 1567 * q^94 - 956 * q^95 - 799 * q^96 - 1062 * q^97 - 1498 * 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 $

$2$	−0.0323756	−0.0114465	−0.00572325	−	0.999984i	$-0.501822\pi$
$2$	−0.0323756	−0.0114465	−0.00572325	+	0.999984i	$0.501822\pi$
$3$	−6.42170	−1.23586	−0.617928	−	0.786235i	$-0.712028\pi$
$3$	−6.42170	−1.23586	−0.617928	+	0.786235i	$0.712028\pi$
$4$	−7.99895	−0.999869
$5$	−14.1026	−1.26137	−0.630687	−	0.776037i	$-0.717227\pi$
$5$	−14.1026	−1.26137	−0.630687	+	0.776037i	$0.717227\pi$
$6$	0.207906	0.0141462
$7$	0	0
$7$	0	0
$8$	0.517976	0.0228915
$9$	14.2382	0.527340
$10$	0.456580	0.0144383
$11$	−55.5140	−1.52165	−0.760823	−	0.648959i	$-0.775204\pi$
$11$	−55.5140	−1.52165	−0.760823	+	0.648959i	$0.775204\pi$
$12$	51.3668	1.23569
$13$	18.3149	0.390742	0.195371	−	0.980729i	$-0.437409\pi$
$13$	18.3149	0.390742	0.195371	+	0.980729i	$0.437409\pi$
$14$	0	0
$15$	90.5626	1.55888
$16$	63.9748	0.999607
$17$	−10.0273	−0.143058	−0.0715288	−	0.997439i	$-0.522788\pi$
$17$	−10.0273	−0.143058	−0.0715288	+	0.997439i	$0.522788\pi$
$18$	−0.460970	−0.00603620
$19$	−161.106	−1.94528	−0.972639	−	0.232321i	$-0.925368\pi$
$19$	−161.106	−1.94528	−0.972639	+	0.232321i	$0.925368\pi$
$20$	112.806	1.26121
$21$	0	0
$22$	1.79730	0.0174175
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−3.32628	−0.0282906
$25$	73.8833	0.591066
$26$	−0.592956	−0.00447263
$27$	81.9525	0.584139
$28$	0	0
$29$	183.185	1.17298	0.586492	−	0.809955i	$-0.300509\pi$
$29$	183.185	1.17298	0.586492	+	0.809955i	$0.300509\pi$
$30$	−2.93202	−0.0178437
$31$	144.762	0.838710	0.419355	−	0.907822i	$-0.362256\pi$
$31$	144.762	0.838710	0.419355	+	0.907822i	$0.362256\pi$
$32$	−6.21503	−0.0343335
$33$	356.494	1.88054
$34$	0.324640	0.00163751
$35$	0	0
$36$	−113.891	−0.527271
$37$	181.411	0.806047	0.403023	−	0.915190i	$-0.367959\pi$
$37$	181.411	0.806047	0.403023	+	0.915190i	$0.367959\pi$
$38$	5.21591	0.0222666
$39$	−117.613	−0.482900
$40$	−7.30481	−0.0288748
$41$	−77.7996	−0.296348	−0.148174	−	0.988961i	$-0.547340\pi$
$41$	−77.7996	−0.296348	−0.148174	+	0.988961i	$0.547340\pi$
$42$	0	0
$43$	315.335	1.11833	0.559164	−	0.829057i	$-0.311122\pi$
$43$	315.335	1.11833	0.559164	+	0.829057i	$0.311122\pi$
$44$	444.054	1.52145
$45$	−200.795	−0.665174
$46$	0.744639	0.00238676
$47$	524.190	1.62683	0.813414	−	0.581685i	$-0.197607\pi$
$47$	524.190	1.62683	0.813414	+	0.581685i	$0.197607\pi$
$48$	−410.827	−1.23537
$49$	0	0
$50$	−2.39202	−0.00676565
$51$	64.3923	0.176799
$52$	−146.500	−0.390690
$53$	73.7334	0.191095	0.0955477	−	0.995425i	$-0.469540\pi$
$53$	73.7334	0.191095	0.0955477	+	0.995425i	$0.469540\pi$
$54$	−2.65326	−0.00668636
$55$	782.892	1.91937
$56$	0	0
$57$	1034.57	2.40408
$58$	−5.93071	−0.0134266
$59$	132.892	0.293239	0.146619	−	0.989193i	$-0.453161\pi$
$59$	132.892	0.293239	0.146619	+	0.989193i	$0.453161\pi$
$60$	−724.406	−1.55867
$61$	−236.683	−0.496789	−0.248394	−	0.968659i	$-0.579903\pi$
$61$	−236.683	−0.496789	−0.248394	+	0.968659i	$0.579903\pi$
$62$	−4.68676	−0.00960030
$63$	0	0
$64$	−511.598	−0.999214
$65$	−258.288	−0.492872
$66$	−11.5417	−0.0215256
$67$	493.624	0.900086	0.450043	−	0.893007i	$-0.351409\pi$
$67$	493.624	0.900086	0.450043	+	0.893007i	$0.351409\pi$
$68$	80.2079	0.143039
$69$	147.699	0.257694
$70$	0	0
$71$	−806.060	−1.34735	−0.673674	−	0.739029i	$-0.735285\pi$
$71$	−806.060	−1.34735	−0.673674	+	0.739029i	$0.735285\pi$
$72$	7.37504	0.0120716
$73$	−1011.91	−1.62241	−0.811203	−	0.584764i	$-0.801187\pi$
$73$	−1011.91	−1.62241	−0.811203	+	0.584764i	$0.801187\pi$
$74$	−5.87328	−0.00922642
$75$	−474.456	−0.730473
$76$	1288.68	1.94502
$77$	0	0
$78$	3.80779	0.00552752
$79$	−599.386	−0.853623	−0.426811	−	0.904341i	$-0.640363\pi$
$79$	−599.386	−0.853623	−0.426811	+	0.904341i	$0.640363\pi$
$80$	−902.212	−1.26088
$81$	−910.705	−1.24925
$82$	2.51881	0.00339215
$83$	642.245	0.849344	0.424672	−	0.905347i	$-0.360390\pi$
$83$	642.245	0.849344	0.424672	+	0.905347i	$0.360390\pi$
$84$	0	0
$85$	141.411	0.180449
$86$	−10.2092	−0.0128009
$87$	−1176.36	−1.44964
$88$	−28.7549	−0.0348328
$89$	−883.399	−1.05214	−0.526068	−	0.850442i	$-0.676334\pi$
$89$	−883.399	−1.05214	−0.526068	+	0.850442i	$0.676334\pi$
$90$	6.50088	0.00761392
$91$	0	0
$92$	183.976	0.208487
$93$	−929.617	−1.03652
$94$	−16.9710	−0.0186215
$95$	2272.02	2.45373
$96$	39.9111	0.0424313
$97$	71.2938	0.0746266	0.0373133	−	0.999304i	$-0.488120\pi$
$97$	71.2938	0.0746266	0.0373133	+	0.999304i	$0.488120\pi$
$98$	0	0
$99$	−790.419	−0.802425
$100$	−590.989	−0.590989
$101$	942.689	0.928723	0.464361	−	0.885646i	$-0.346284\pi$
$101$	942.689	0.928723	0.464361	+	0.885646i	$0.346284\pi$
$102$	−2.08474	−0.00202373
$103$	556.624	0.532484	0.266242	−	0.963906i	$-0.414218\pi$
$103$	556.624	0.532484	0.266242	+	0.963906i	$0.414218\pi$
$104$	9.48668	0.00894467
$105$	0	0
$106$	−2.38716	−0.00218738
$107$	647.477	0.584990	0.292495	−	0.956267i	$-0.405514\pi$
$107$	647.477	0.584990	0.292495	+	0.956267i	$0.405514\pi$
$108$	−655.534	−0.584063
$109$	−1349.13	−1.18554	−0.592768	−	0.805373i	$-0.701965\pi$
$109$	−1349.13	−1.18554	−0.592768	+	0.805373i	$0.701965\pi$
$110$	−25.3466	−0.0219700
$111$	−1164.96	−0.996158
$112$	0	0
$113$	−284.549	−0.236886	−0.118443	−	0.992961i	$-0.537790\pi$
$113$	−284.549	−0.236886	−0.118443	+	0.992961i	$0.537790\pi$
$114$	−33.4950	−0.0275184
$115$	324.360	0.263015
$116$	−1465.28	−1.17283
$117$	260.771	0.206054
$118$	−4.30247	−0.00335656
$119$	0	0
$120$	46.9093	0.0356851
$121$	1750.81	1.31541
$122$	7.66275	0.00568650
$123$	499.605	0.366243
$124$	−1157.94	−0.838600
$125$	720.878	0.515819
$126$	0	0
$127$	−753.553	−0.526512	−0.263256	−	0.964726i	$-0.584796\pi$
$127$	−753.553	−0.526512	−0.263256	+	0.964726i	$0.584796\pi$
$128$	66.2835	0.0457710
$129$	−2024.98	−1.38209
$130$	8.36223	0.00564166
$131$	769.226	0.513035	0.256518	−	0.966540i	$-0.417425\pi$
$131$	769.226	0.513035	0.256518	+	0.966540i	$0.417425\pi$
$132$	−2851.58	−1.88029
$133$	0	0
$134$	−15.9814	−0.0103028
$135$	−1155.74	−0.736819
$136$	−5.19390	−0.00327481
$137$	−211.638	−0.131982	−0.0659908	−	0.997820i	$-0.521021\pi$
$137$	−211.638	−0.131982	−0.0659908	+	0.997820i	$0.521021\pi$
$138$	−4.78185	−0.00294969
$139$	−1998.54	−1.21953	−0.609763	−	0.792584i	$-0.708735\pi$
$139$	−1998.54	−1.21953	−0.609763	+	0.792584i	$0.708735\pi$
$140$	0	0
$141$	−3366.19	−2.01052
$142$	26.0967	0.0154224
$143$	−1016.73	−0.594570
$144$	910.886	0.527133
$145$	−2583.38	−1.47957
$146$	32.7614	0.0185709
$147$	0	0
$148$	−1451.10	−0.805941
$149$	499.968	0.274893	0.137446	−	0.990509i	$-0.456111\pi$
$149$	499.968	0.274893	0.137446	+	0.990509i	$0.456111\pi$
$150$	15.3608	0.00836136
$151$	501.652	0.270357	0.135178	−	0.990821i	$-0.456839\pi$
$151$	501.652	0.270357	0.135178	+	0.990821i	$0.456839\pi$
$152$	−83.4491	−0.0445304
$153$	−142.771	−0.0754400
$154$	0	0
$155$	−2041.52	−1.05793
$156$	940.779	0.482837
$157$	−1686.36	−0.857237	−0.428619	−	0.903485i	$-0.641000\pi$
$157$	−1686.36	−0.857237	−0.428619	+	0.903485i	$0.641000\pi$
$158$	19.4055	0.00977100
$159$	−473.493	−0.236166
$160$	87.6481	0.0433074
$161$	0	0
$162$	29.4846	0.0142996
$163$	3183.54	1.52978	0.764890	−	0.644161i	$-0.222793\pi$
$163$	3183.54	1.52978	0.764890	+	0.644161i	$0.222793\pi$
$164$	622.315	0.296309
$165$	−5027.49	−2.37206
$166$	−20.7931	−0.00972202
$167$	3771.37	1.74753	0.873764	−	0.486350i	$-0.161672\pi$
$167$	3771.37	1.74753	0.873764	+	0.486350i	$0.161672\pi$
$168$	0	0
$169$	−1861.56	−0.847321
$170$	−4.57827	−0.00206551
$171$	−2293.86	−1.02582
$172$	−2522.35	−1.11818
$173$	−129.941	−0.0571052	−0.0285526	−	0.999592i	$-0.509090\pi$
$173$	−129.941	−0.0571052	−0.0285526	+	0.999592i	$0.509090\pi$
$174$	38.0852	0.0165933
$175$	0	0
$176$	−3551.50	−1.52105
$177$	−853.393	−0.362401
$178$	28.6006	0.0120433
$179$	810.182	0.338301	0.169150	−	0.985590i	$-0.445898\pi$
$179$	810.182	0.338301	0.169150	+	0.985590i	$0.445898\pi$
$180$	1606.15	0.665086
$181$	−2430.33	−0.998039	−0.499019	−	0.866591i	$-0.666306\pi$
$181$	−2430.33	−0.998039	−0.499019	+	0.866591i	$0.666306\pi$
$182$	0	0
$183$	1519.90	0.613960
$184$	−11.9134	−0.00477321
$185$	−2558.36	−1.01673
$186$	30.0969	0.0118646
$187$	556.656	0.217683
$188$	−4192.97	−1.62661
$189$	0	0
$190$	−73.5579	−0.0280866
$191$	2462.87	0.933022	0.466511	−	0.884515i	$-0.345511\pi$
$191$	2462.87	0.933022	0.466511	+	0.884515i	$0.345511\pi$
$192$	3285.32	1.23488
$193$	4021.66	1.49992	0.749962	−	0.661481i	$-0.230072\pi$
$193$	4021.66	1.49992	0.749962	+	0.661481i	$0.230072\pi$
$194$	−2.30818	−0.000854214 0
$195$	1658.65	0.609118
$196$	0	0
$197$	1811.60	0.655182	0.327591	−	0.944820i	$-0.393763\pi$
$197$	1811.60	0.655182	0.327591	+	0.944820i	$0.393763\pi$
$198$	25.5903	0.00918497
$199$	−723.923	−0.257877	−0.128939	−	0.991653i	$-0.541157\pi$
$199$	−723.923	−0.257877	−0.128939	+	0.991653i	$0.541157\pi$
$200$	38.2698	0.0135304
$201$	−3169.90	−1.11238
$202$	−30.5201	−0.0106306
$203$	0	0
$204$	−515.071	−0.176775
$205$	1097.18	0.373805
$206$	−18.0211	−0.00609508
$207$	−327.478	−0.109958
$208$	1171.69	0.390588
$209$	8943.65	2.96003
$210$	0	0
$211$	−583.883	−0.190503	−0.0952515	−	0.995453i	$-0.530366\pi$
$211$	−583.883	−0.190503	−0.0952515	+	0.995453i	$0.530366\pi$
$212$	−589.790	−0.191070
$213$	5176.27	1.66513
$214$	−20.9625	−0.00669610
$215$	−4447.04	−1.41063
$216$	42.4494	0.0133718
$217$	0	0
$218$	43.6790	0.0135703
$219$	6498.21	2.00506
$220$	−6262.31	−1.91911
$221$	−183.649	−0.0558985
$222$	37.7164	0.0114025
$223$	−3157.57	−0.948191	−0.474096	−	0.880473i	$-0.657225\pi$
$223$	−3157.57	−0.948191	−0.474096	+	0.880473i	$0.657225\pi$
$224$	0	0
$225$	1051.96	0.311693
$226$	9.21245	0.00271152
$227$	2219.80	0.649044	0.324522	−	0.945878i	$-0.394797\pi$
$227$	2219.80	0.649044	0.324522	+	0.945878i	$0.394797\pi$
$228$	−8275.52	−2.40377
$229$	4398.24	1.26919	0.634593	−	0.772846i	$-0.281168\pi$
$229$	4398.24	1.26919	0.634593	+	0.772846i	$0.281168\pi$
$230$	−10.5013	−0.00301060
$231$	0	0
$232$	94.8852	0.0268514
$233$	2112.84	0.594065	0.297032	−	0.954867i	$-0.404003\pi$
$233$	2112.84	0.594065	0.297032	+	0.954867i	$0.404003\pi$
$234$	−8.44262	−0.00235860
$235$	−7392.43	−2.05204
$236$	−1063.00	−0.293200
$237$	3849.08	1.05496
$238$	0	0
$239$	−1548.69	−0.419147	−0.209574	−	0.977793i	$-0.567208\pi$
$239$	−1548.69	−0.419147	−0.209574	+	0.977793i	$0.567208\pi$
$240$	5793.73	1.55826
$241$	2516.92	0.672734	0.336367	−	0.941731i	$-0.390802\pi$
$241$	2516.92	0.672734	0.336367	+	0.941731i	$0.390802\pi$
$242$	−56.6834	−0.0150568
$243$	3635.55	0.959757
$244$	1893.21	0.496724
$245$	0	0
$246$	−16.1750	−0.00419220
$247$	−2950.64	−0.760101
$248$	74.9832	0.0191993
$249$	−4124.30	−1.04967
$250$	−23.3389	−0.00590432
$251$	−386.310	−0.0971461	−0.0485731	−	0.998820i	$-0.515467\pi$
$251$	−386.310	−0.0971461	−0.0485731	+	0.998820i	$0.515467\pi$
$252$	0	0
$253$	1276.82	0.317285
$254$	24.3967	0.00602672
$255$	−908.099	−0.223009
$256$	4090.63	0.998690
$257$	−3816.61	−0.926357	−0.463178	−	0.886265i	$-0.653291\pi$
$257$	−3816.61	−0.926357	−0.463178	+	0.886265i	$0.653291\pi$
$258$	65.5601	0.0158201
$259$	0	0
$260$	2066.03	0.492807
$261$	2608.22	0.618561
$262$	−24.9042	−0.00587246
$263$	4510.11	1.05744	0.528718	−	0.848798i	$-0.322673\pi$
$263$	4510.11	1.05744	0.528718	+	0.848798i	$0.322673\pi$
$264$	184.655	0.0430483
$265$	−1039.83	−0.241043
$266$	0	0
$267$	5672.92	1.30029
$268$	−3948.47	−0.899968
$269$	550.730	0.124827	0.0624137	−	0.998050i	$-0.480120\pi$
$269$	550.730	0.124827	0.0624137	+	0.998050i	$0.480120\pi$
$270$	37.4179	0.00843400
$271$	897.873	0.201262	0.100631	−	0.994924i	$-0.467914\pi$
$271$	897.873	0.201262	0.100631	+	0.994924i	$0.467914\pi$
$272$	−641.495	−0.143001
$273$	0	0
$274$	6.85192	0.00151073
$275$	−4101.56	−0.899394
$276$	−1181.44	−0.257660
$277$	2288.67	0.496437	0.248219	−	0.968704i	$-0.420155\pi$
$277$	2288.67	0.496437	0.248219	+	0.968704i	$0.420155\pi$
$278$	64.7040	0.0139593
$279$	2061.15	0.442285
$280$	0	0
$281$	−2587.28	−0.549268	−0.274634	−	0.961549i	$-0.588557\pi$
$281$	−2587.28	−0.549268	−0.274634	+	0.961549i	$0.588557\pi$
$282$	108.982	0.0230135
$283$	−1488.48	−0.312653	−0.156326	−	0.987705i	$-0.549965\pi$
$283$	−1488.48	−0.312653	−0.156326	+	0.987705i	$0.549965\pi$
$284$	6447.63	1.34717
$285$	−14590.2	−3.03245
$286$	32.9174	0.00680576
$287$	0	0
$288$	−88.4908	−0.0181055
$289$	−4812.45	−0.979535
$290$	83.6384	0.0169359
$291$	−457.827	−0.0922278
$292$	8094.26	1.62219
$293$	2821.24	0.562522	0.281261	−	0.959631i	$-0.409247\pi$
$293$	2821.24	0.562522	0.281261	+	0.959631i	$0.409247\pi$
$294$	0	0
$295$	−1874.12	−0.369884
$296$	93.9664	0.0184516
$297$	−4549.51	−0.888853
$298$	−16.1868	−0.00314656
$299$	−421.243	−0.0814753
$300$	3795.15	0.730377
$301$	0	0
$302$	−16.2413	−0.00309464
$303$	−6053.66	−1.14777
$304$	−10306.7	−1.94451
$305$	3337.84	0.626637
$306$	4.62229	0.000863525 0
$307$	4085.72	0.759558	0.379779	−	0.925077i	$-0.376000\pi$
$307$	4085.72	0.759558	0.379779	+	0.925077i	$0.376000\pi$
$308$	0	0
$309$	−3574.47	−0.658073
$310$	66.0954	0.0121096
$311$	−4044.84	−0.737498	−0.368749	−	0.929529i	$-0.620214\pi$
$311$	−4044.84	−0.737498	−0.368749	+	0.929529i	$0.620214\pi$
$312$	−60.9206	−0.0110543
$313$	−5111.54	−0.923072	−0.461536	−	0.887122i	$-0.652701\pi$
$313$	−5111.54	−0.923072	−0.461536	+	0.887122i	$0.652701\pi$
$314$	54.5970	0.00981238
$315$	0	0
$316$	4794.46	0.853511
$317$	−7017.95	−1.24343	−0.621715	−	0.783244i	$-0.713564\pi$
$317$	−7017.95	−1.24343	−0.621715	+	0.783244i	$0.713564\pi$
$318$	15.3296	0.00270328
$319$	−10169.3	−1.78487
$320$	7214.85	1.26038
$321$	−4157.90	−0.722964
$322$	0	0
$323$	1615.46	0.278287
$324$	7284.69	1.24909
$325$	1353.17	0.230954
$326$	−103.069	−0.0175106
$327$	8663.72	1.46515
$328$	−40.2983	−0.00678385
$329$	0	0
$330$	162.768	0.0271518
$331$	−6537.02	−1.08552	−0.542760	−	0.839888i	$-0.682621\pi$
$331$	−6537.02	−1.08552	−0.542760	+	0.839888i	$0.682621\pi$
$332$	−5137.28	−0.849232
$333$	2582.96	0.425061
$334$	−122.100	−0.0200031
$335$	−6961.38	−1.13535
$336$	0	0
$337$	−838.254	−0.135497	−0.0677486	−	0.997702i	$-0.521582\pi$
$337$	−838.254	−0.135497	−0.0677486	+	0.997702i	$0.521582\pi$
$338$	60.2693	0.00969887
$339$	1827.29	0.292757
$340$	−1131.14	−0.180426
$341$	−8036.32	−1.27622
$342$	74.2651	0.0117421
$343$	0	0
$344$	163.336	0.0256002
$345$	−2082.94	−0.325048
$346$	4.20691	0.000653655 0
$347$	7101.86	1.09870	0.549348	−	0.835593i	$-0.314876\pi$
$347$	7101.86	1.09870	0.549348	+	0.835593i	$0.314876\pi$
$348$	9409.61	1.44945
$349$	2675.10	0.410300	0.205150	−	0.978731i	$-0.434232\pi$
$349$	2675.10	0.410300	0.205150	+	0.978731i	$0.434232\pi$
$350$	0	0
$351$	1500.95	0.228248
$352$	345.021	0.0522435
$353$	8032.84	1.21118	0.605588	−	0.795778i	$-0.292938\pi$
$353$	8032.84	1.21118	0.605588	+	0.795778i	$0.292938\pi$
$354$	27.6291	0.00414823
$355$	11367.5	1.69951
$356$	7066.27	1.05200
$357$	0	0
$358$	−26.2301	−0.00387236
$359$	4828.72	0.709889	0.354944	−	0.934887i	$-0.384500\pi$
$359$	4828.72	0.709889	0.354944	+	0.934887i	$0.384500\pi$
$360$	−104.007	−0.0152268
$361$	19096.2	2.78411
$362$	78.6834	0.0114241
$363$	−11243.1	−1.62565
$364$	0	0
$365$	14270.6	2.04646
$366$	−49.2079	−0.00702769
$367$	−89.8597	−0.0127810	−0.00639052	−	0.999980i	$-0.502034\pi$
$367$	−89.8597	−0.0127810	−0.00639052	+	0.999980i	$0.502034\pi$
$368$	−1471.42	−0.208432
$369$	−1107.72	−0.156276
$370$	82.8285	0.0116380
$371$	0	0
$372$	7435.96	1.03639
$373$	5196.16	0.721306	0.360653	−	0.932700i	$-0.382554\pi$
$373$	5196.16	0.721306	0.360653	+	0.932700i	$0.382554\pi$
$374$	−18.0221	−0.00249171
$375$	−4629.26	−0.637478
$376$	271.518	0.0372406
$377$	3355.01	0.458333
$378$	0	0
$379$	4900.54	0.664179	0.332090	−	0.943248i	$-0.392246\pi$
$379$	4900.54	0.664179	0.332090	+	0.943248i	$0.392246\pi$
$380$	−18173.7	−2.45340
$381$	4839.09	0.650693
$382$	−79.7370	−0.0106798
$383$	−9973.73	−1.33064	−0.665318	−	0.746560i	$-0.731704\pi$
$383$	−9973.73	−1.33064	−0.665318	+	0.746560i	$0.731704\pi$
$384$	−425.653	−0.0565664
$385$	0	0
$386$	−130.204	−0.0171689
$387$	4489.79	0.589739
$388$	−570.275	−0.0746169
$389$	−6277.96	−0.818266	−0.409133	−	0.912475i	$-0.634169\pi$
$389$	−6277.96	−0.818266	−0.409133	+	0.912475i	$0.634169\pi$
$390$	−53.6997	−0.00697228
$391$	230.628	0.0298296
$392$	0	0
$393$	−4939.74	−0.634038
$394$	−58.6515	−0.00749955
$395$	8452.90	1.07674
$396$	6322.52	0.802320
$397$	11309.9	1.42979	0.714895	−	0.699232i	$-0.246474\pi$
$397$	11309.9	1.42979	0.714895	+	0.699232i	$0.246474\pi$
$398$	23.4375	0.00295179
$399$	0	0
$400$	4726.67	0.590834
$401$	−14306.5	−1.78163	−0.890813	−	0.454371i	$-0.849864\pi$
$401$	−14306.5	−1.78163	−0.890813	+	0.454371i	$0.849864\pi$
$402$	102.628	0.0127328
$403$	2651.30	0.327719
$404$	−7540.52	−0.928601
$405$	12843.3	1.57578
$406$	0	0
$407$	−10070.8	−1.22652
$408$	33.3537	0.00404719
$409$	−4363.34	−0.527514	−0.263757	−	0.964589i	$-0.584962\pi$
$409$	−4363.34	−0.527514	−0.263757	+	0.964589i	$0.584962\pi$
$410$	−35.5218	−0.00427877
$411$	1359.08	0.163110
$412$	−4452.41	−0.532414
$413$	0	0
$414$	10.6023	0.00125864
$415$	−9057.32	−1.07134
$416$	−113.828	−0.0134155
$417$	12834.0	1.50716
$418$	−289.556	−0.0338820
$419$	−12304.9	−1.43468	−0.717341	−	0.696722i	$-0.754641\pi$
$419$	−12304.9	−1.43468	−0.717341	+	0.696722i	$0.754641\pi$
$420$	0	0
$421$	−8353.05	−0.966990	−0.483495	−	0.875347i	$-0.660633\pi$
$421$	−8353.05	−0.966990	−0.483495	+	0.875347i	$0.660633\pi$
$422$	18.9036	0.00218059
$423$	7463.51	0.857892
$424$	38.1921	0.00437446
$425$	−740.850	−0.0845565
$426$	−167.585	−0.0190599
$427$	0	0
$428$	−5179.14	−0.584914
$429$	6529.16	0.734803
$430$	143.976	0.0161468
$431$	−15959.9	−1.78367	−0.891835	−	0.452361i	$-0.850582\pi$
$431$	−15959.9	−1.78367	−0.891835	+	0.452361i	$0.850582\pi$
$432$	5242.90	0.583910
$433$	−5779.60	−0.641454	−0.320727	−	0.947172i	$-0.603927\pi$
$433$	−5779.60	−0.641454	−0.320727	+	0.947172i	$0.603927\pi$
$434$	0	0
$435$	16589.7	1.82854
$436$	10791.6	1.18538
$437$	3705.44	0.405619
$438$	−210.384	−0.0229509
$439$	−795.488	−0.0864842	−0.0432421	−	0.999065i	$-0.513769\pi$
$439$	−795.488	−0.0864842	−0.0432421	+	0.999065i	$0.513769\pi$
$440$	405.519	0.0439372
$441$	0	0
$442$	5.94575	0.000639843 0
$443$	7357.81	0.789120	0.394560	−	0.918870i	$-0.370897\pi$
$443$	7357.81	0.789120	0.394560	+	0.918870i	$0.370897\pi$
$444$	9318.49	0.996027
$445$	12458.2	1.32714
$446$	102.228	0.0108535
$447$	−3210.65	−0.339728
$448$	0	0
$449$	−6672.34	−0.701308	−0.350654	−	0.936505i	$-0.614041\pi$
$449$	−6672.34	−0.701308	−0.350654	+	0.936505i	$0.614041\pi$
$450$	−34.0580	−0.00356780
$451$	4318.97	0.450936
$452$	2276.09	0.236855
$453$	−3221.46	−0.334122
$454$	−71.8673	−0.00742929
$455$	0	0
$456$	535.885	0.0550331
$457$	−6324.72	−0.647392	−0.323696	−	0.946161i	$-0.604925\pi$
$457$	−6324.72	−0.647392	−0.323696	+	0.946161i	$0.604925\pi$
$458$	−142.396	−0.0145278
$459$	−821.763	−0.0835656
$460$	−2594.54	−0.262980
$461$	641.556	0.0648162	0.0324081	−	0.999475i	$-0.489682\pi$
$461$	641.556	0.0648162	0.0324081	+	0.999475i	$0.489682\pi$
$462$	0	0
$463$	714.350	0.0717034	0.0358517	−	0.999357i	$-0.488586\pi$
$463$	714.350	0.0717034	0.0358517	+	0.999357i	$0.488586\pi$
$464$	11719.2	1.17252
$465$	13110.0	1.30745
$466$	−68.4047	−0.00679997
$467$	−3937.64	−0.390176	−0.195088	−	0.980786i	$-0.562499\pi$
$467$	−3937.64	−0.390176	−0.195088	+	0.980786i	$0.562499\pi$
$468$	−2085.89	−0.206027
$469$	0	0
$470$	239.335	0.0234887
$471$	10829.3	1.05942
$472$	68.8349	0.00671268
$473$	−17505.5	−1.70170
$474$	−124.616	−0.0120756
$475$	−11903.1	−1.14979
$476$	0	0
$477$	1049.83	0.100772
$478$	50.1397	0.00479777
$479$	2252.09	0.214824	0.107412	−	0.994215i	$-0.465744\pi$
$479$	2252.09	0.214824	0.107412	+	0.994215i	$0.465744\pi$
$480$	−562.850	−0.0535218
$481$	3322.52	0.314956
$482$	−81.4868	−0.00770046
$483$	0	0
$484$	−14004.6	−1.31523
$485$	−1005.43	−0.0941322
$486$	−117.703	−0.0109859
$487$	11821.8	1.09999	0.549995	−	0.835168i	$-0.314630\pi$
$487$	11821.8	1.09999	0.549995	+	0.835168i	$0.314630\pi$
$488$	−122.596	−0.0113723
$489$	−20443.7	−1.89059
$490$	0	0
$491$	20198.1	1.85647	0.928235	−	0.371993i	$-0.121326\pi$
$491$	20198.1	1.85647	0.928235	+	0.371993i	$0.121326\pi$
$492$	−3996.32	−0.366195
$493$	−1836.85	−0.167804
$494$	95.5289	0.00870051
$495$	11147.0	1.01216
$496$	9261.12	0.838380
$497$	0	0
$498$	133.527	0.0120150
$499$	−633.684	−0.0568488	−0.0284244	−	0.999596i	$-0.509049\pi$
$499$	−633.684	−0.0568488	−0.0284244	+	0.999596i	$0.509049\pi$
$500$	−5766.27	−0.515751
$501$	−24218.6	−2.15969
$502$	12.5070	0.00111198
$503$	−10068.6	−0.892518	−0.446259	−	0.894904i	$-0.647244\pi$
$503$	−10068.6	−0.892518	−0.446259	+	0.894904i	$0.647244\pi$
$504$	0	0
$505$	−13294.4	−1.17147
$506$	−41.3379	−0.00363181
$507$	11954.4	1.04717
$508$	6027.63	0.526443
$509$	4287.40	0.373351	0.186675	−	0.982422i	$-0.440229\pi$
$509$	4287.40	0.373351	0.186675	+	0.982422i	$0.440229\pi$
$510$	29.4003	0.00255268
$511$	0	0
$512$	−662.705	−0.0572026
$513$	−13203.1	−1.13631
$514$	123.565	0.0106035
$515$	−7849.85	−0.671662
$516$	16197.7	1.38191
$517$	−29099.9	−2.47546
$518$	0	0
$519$	834.439	0.0705738
$520$	−133.787	−0.0112826
$521$	19842.9	1.66858	0.834291	−	0.551324i	$-0.185877\pi$
$521$	19842.9	1.66858	0.834291	+	0.551324i	$0.185877\pi$
$522$	−84.4426	−0.00708037
$523$	10894.9	0.910897	0.455448	−	0.890262i	$-0.349479\pi$
$523$	10894.9	0.910897	0.455448	+	0.890262i	$0.349479\pi$
$524$	−6153.00	−0.512968
$525$	0	0
$526$	−146.018	−0.0121039
$527$	−1451.57	−0.119984
$528$	22806.7	1.87980
$529$	529.000	0.0434783
$530$	33.6652	0.00275910
$531$	1892.14	0.154637
$532$	0	0
$533$	−1424.89	−0.115795
$534$	−183.664	−0.0148838
$535$	−9131.11	−0.737892
$536$	255.685	0.0206043
$537$	−5202.74	−0.418091
$538$	−17.8302	−0.00142884
$539$	0	0
$540$	9244.73	0.736722
$541$	4405.04	0.350069	0.175035	−	0.984562i	$-0.443996\pi$
$541$	4405.04	0.350069	0.175035	+	0.984562i	$0.443996\pi$
$542$	−29.0692	−0.00230374
$543$	15606.8	1.23343
$544$	62.3200	0.00491167
$545$	19026.3	1.49541
$546$	0	0
$547$	10031.2	0.784099	0.392050	−	0.919944i	$-0.371766\pi$
$547$	10031.2	0.784099	0.392050	+	0.919944i	$0.371766\pi$
$548$	1692.88	0.131964
$549$	−3369.93	−0.261977
$550$	132.790	0.0102949
$551$	−29512.2	−2.28178
$552$	76.5045	0.00589900
$553$	0	0
$554$	−74.0972	−0.00568247
$555$	16429.0	1.25653
$556$	15986.2	1.21937
$557$	23278.3	1.77079	0.885396	−	0.464837i	$-0.153887\pi$
$557$	23278.3	1.77079	0.885396	+	0.464837i	$0.153887\pi$
$558$	−66.7309	−0.00506262
$559$	5775.32	0.436977
$560$	0	0
$561$	−3574.68	−0.269025
$562$	83.7648	0.00628720
$563$	20989.8	1.57125	0.785625	−	0.618702i	$-0.212341\pi$
$563$	20989.8	1.57125	0.785625	+	0.618702i	$0.212341\pi$
$564$	26926.0	2.01026
$565$	4012.88	0.298802
$566$	48.1904	0.00357878
$567$	0	0
$568$	−417.520	−0.0308428
$569$	−11942.2	−0.879868	−0.439934	−	0.898030i	$-0.644998\pi$
$569$	−11942.2	−0.879868	−0.439934	+	0.898030i	$0.644998\pi$
$570$	472.367	0.0347110
$571$	−13981.9	−1.02473	−0.512367	−	0.858767i	$-0.671231\pi$
$571$	−13981.9	−1.02473	−0.512367	+	0.858767i	$0.671231\pi$
$572$	8132.81	0.594492
$573$	−15815.8	−1.15308
$574$	0	0
$575$	−1699.32	−0.123246
$576$	−7284.22	−0.526926
$577$	5024.27	0.362501	0.181251	−	0.983437i	$-0.441985\pi$
$577$	5024.27	0.362501	0.181251	+	0.983437i	$0.441985\pi$
$578$	155.806	0.0112123
$579$	−25825.9	−1.85369
$580$	20664.3	1.47938
$581$	0	0
$582$	14.8224	0.00105569
$583$	−4093.24	−0.290780
$584$	−524.148	−0.0371393
$585$	−3677.55	−0.259911
$586$	−91.3395	−0.00643891
$587$	22464.4	1.57957	0.789784	−	0.613385i	$-0.210193\pi$
$587$	22464.4	1.57957	0.789784	+	0.613385i	$0.210193\pi$
$588$	0	0
$589$	−23322.0	−1.63152
$590$	60.6760	0.00423388
$591$	−11633.5	−0.809710
$592$	11605.7	0.805730
$593$	−14073.1	−0.974561	−0.487281	−	0.873245i	$-0.662011\pi$
$593$	−14073.1	−0.974561	−0.487281	+	0.873245i	$0.662011\pi$
$594$	147.293	0.0101743
$595$	0	0
$596$	−3999.22	−0.274857
$597$	4648.82	0.318699
$598$	13.6380	0.000932607 0
$599$	−8952.63	−0.610675	−0.305338	−	0.952244i	$-0.598769\pi$
$599$	−8952.63	−0.610675	−0.305338	+	0.952244i	$0.598769\pi$
$600$	−245.757	−0.0167216
$601$	20522.5	1.39290	0.696449	−	0.717607i	$-0.254762\pi$
$601$	20522.5	1.39290	0.696449	+	0.717607i	$0.254762\pi$
$602$	0	0
$603$	7028.31	0.474651
$604$	−4012.69	−0.270321
$605$	−24690.9	−1.65922
$606$	195.991	0.0131379
$607$	−23022.8	−1.53949	−0.769743	−	0.638353i	$-0.779616\pi$
$607$	−23022.8	−1.53949	−0.769743	+	0.638353i	$0.779616\pi$
$608$	1001.28	0.0667883
$609$	0	0
$610$	−108.065	−0.00717281
$611$	9600.48	0.635669
$612$	1142.02	0.0754301
$613$	−6159.74	−0.405856	−0.202928	−	0.979194i	$-0.565046\pi$
$613$	−6159.74	−0.405856	−0.202928	+	0.979194i	$0.565046\pi$
$614$	−132.278	−0.00869429
$615$	−7045.73	−0.461970
$616$	0	0
$617$	26889.1	1.75448	0.877241	−	0.480050i	$-0.159381\pi$
$617$	26889.1	1.75448	0.877241	+	0.480050i	$0.159381\pi$
$618$	115.726	0.00753264
$619$	6478.47	0.420665	0.210333	−	0.977630i	$-0.432545\pi$
$619$	6478.47	0.420665	0.210333	+	0.977630i	$0.432545\pi$
$620$	16330.0	1.05779
$621$	−1884.91	−0.121801
$622$	130.954	0.00844178
$623$	0	0
$624$	−7524.26	−0.482711
$625$	−19401.7	−1.24171
$626$	165.489	0.0105659
$627$	−57433.4	−3.65817
$628$	13489.1	0.857125
$629$	−1819.06	−0.115311
$630$	0	0
$631$	2956.54	0.186526	0.0932630	−	0.995642i	$-0.470270\pi$
$631$	2956.54	0.186526	0.0932630	+	0.995642i	$0.470270\pi$
$632$	−310.468	−0.0195407
$633$	3749.52	0.235434
$634$	227.210	0.0142329
$635$	10627.1	0.664129
$636$	3787.45	0.236135
$637$	0	0
$638$	329.238	0.0204305
$639$	−11476.8	−0.710511
$640$	−934.770	−0.0577344
$641$	20604.4	1.26961	0.634807	−	0.772670i	$-0.281079\pi$
$641$	20604.4	1.26961	0.634807	+	0.772670i	$0.281079\pi$
$642$	134.615	0.00827541
$643$	23773.4	1.45806	0.729030	−	0.684482i	$-0.239972\pi$
$643$	23773.4	1.45806	0.729030	+	0.684482i	$0.239972\pi$
$644$	0	0
$645$	28557.5	1.74334
$646$	−52.3015	−0.00318541
$647$	24907.8	1.51349	0.756744	−	0.653712i	$-0.226789\pi$
$647$	24907.8	1.51349	0.756744	+	0.653712i	$0.226789\pi$
$648$	−471.723	−0.0285973
$649$	−7377.38	−0.446206
$650$	−43.8096	−0.00264362
$651$	0	0
$652$	−25465.0	−1.52958
$653$	−18523.9	−1.11010	−0.555050	−	0.831817i	$-0.687301\pi$
$653$	−18523.9	−1.11010	−0.555050	+	0.831817i	$0.687301\pi$
$654$	−280.493	−0.0167709
$655$	−10848.1	−0.647130
$656$	−4977.22	−0.296231
$657$	−14407.8	−0.855560
$658$	0	0
$659$	24408.5	1.44282	0.721411	−	0.692507i	$-0.243494\pi$
$659$	24408.5	1.44282	0.721411	+	0.692507i	$0.243494\pi$
$660$	40214.7	2.37175
$661$	−20341.7	−1.19697	−0.598487	−	0.801133i	$-0.704231\pi$
$661$	−20341.7	−1.19697	−0.598487	+	0.801133i	$0.704231\pi$
$662$	211.640	0.0124254
$663$	1179.34	0.0690826
$664$	332.667	0.0194428
$665$	0	0
$666$	−83.6249	−0.00486546
$667$	−4213.24	−0.244584
$668$	−30167.0	−1.74730
$669$	20277.0	1.17183
$670$	225.379	0.0129957
$671$	13139.2	0.755937
$672$	0	0
$673$	12282.3	0.703490	0.351745	−	0.936096i	$-0.385588\pi$
$673$	12282.3	0.703490	0.351745	+	0.936096i	$0.385588\pi$
$674$	27.1390	0.00155097
$675$	6054.92	0.345265
$676$	14890.6	0.847210
$677$	−21868.0	−1.24144	−0.620721	−	0.784031i	$-0.713160\pi$
$677$	−21868.0	−1.24144	−0.620721	+	0.784031i	$0.713160\pi$
$678$	−59.1596	−0.00335105
$679$	0	0
$680$	73.2475	0.00413076
$681$	−14254.9	−0.802125
$682$	260.181	0.0146083
$683$	−22877.0	−1.28165	−0.640823	−	0.767688i	$-0.721407\pi$
$683$	−22877.0	−1.28165	−0.640823	+	0.767688i	$0.721407\pi$
$684$	18348.5	1.02569
$685$	2984.65	0.166478
$686$	0	0
$687$	−28244.2	−1.56853
$688$	20173.5	1.11789
$689$	1350.42	0.0746689
$690$	67.4365	0.00372067
$691$	−24499.1	−1.34875	−0.674376	−	0.738388i	$-0.735587\pi$
$691$	−24499.1	−1.34875	−0.674376	+	0.738388i	$0.735587\pi$
$692$	1039.39	0.0570977
$693$	0	0
$694$	−229.927	−0.0125762
$695$	28184.6	1.53828
$696$	−609.324	−0.0331844
$697$	780.120	0.0423948
$698$	−86.6080	−0.00469650
$699$	−13568.0	−0.734178
$700$	0	0
$701$	−25020.5	−1.34809	−0.674044	−	0.738691i	$-0.735444\pi$
$701$	−25020.5	−1.34809	−0.674044	+	0.738691i	$0.735444\pi$
$702$	−48.5943	−0.00261264
$703$	−29226.4	−1.56799
$704$	28400.8	1.52045
$705$	47472.0	2.53603
$706$	−260.068	−0.0138637
$707$	0	0
$708$	6826.25	0.362353
$709$	−15069.4	−0.798225	−0.399112	−	0.916902i	$-0.630682\pi$
$709$	−15069.4	−0.798225	−0.399112	+	0.916902i	$0.630682\pi$
$710$	−368.031	−0.0194535
$711$	−8534.17	−0.450150
$712$	−457.579	−0.0240850
$713$	−3329.52	−0.174883
$714$	0	0
$715$	14338.6	0.749976
$716$	−6480.61	−0.338256
$717$	9945.19	0.518006
$718$	−156.333	−0.00812575
$719$	23894.6	1.23938	0.619692	−	0.784845i	$-0.287257\pi$
$719$	23894.6	1.23938	0.619692	+	0.784845i	$0.287257\pi$
$720$	−12845.9	−0.664912
$721$	0	0
$722$	−618.251	−0.0318683
$723$	−16162.9	−0.831403
$724$	19440.1	0.997908
$725$	13534.3	0.693311
$726$	364.004	0.0186081
$727$	−32641.3	−1.66520	−0.832598	−	0.553877i	$-0.813148\pi$
$727$	−32641.3	−1.66520	−0.832598	+	0.553877i	$0.813148\pi$
$728$	0	0
$729$	1242.61	0.0631312
$730$	−462.020	−0.0234249
$731$	−3161.96	−0.159985
$732$	−12157.6	−0.613879
$733$	628.010	0.0316454	0.0158227	−	0.999875i	$-0.494963\pi$
$733$	628.010	0.0316454	0.0158227	+	0.999875i	$0.494963\pi$
$734$	2.90926	0.000146298 0
$735$	0	0
$736$	142.946	0.00715904
$737$	−27403.0	−1.36961
$738$	35.8633	0.00178881
$739$	−20111.4	−1.00109	−0.500547	−	0.865709i	$-0.666868\pi$
$739$	−20111.4	−1.00109	−0.500547	+	0.865709i	$0.666868\pi$
$740$	20464.2	1.01659
$741$	18948.1	0.939376
$742$	0	0
$743$	19508.4	0.963251	0.481625	−	0.876377i	$-0.340047\pi$
$743$	19508.4	0.963251	0.481625	+	0.876377i	$0.340047\pi$
$744$	−481.519	−0.0237276
$745$	−7050.85	−0.346743
$746$	−168.229	−0.00825643
$747$	9144.40	0.447893
$748$	−4452.66	−0.217654
$749$	0	0
$750$	149.875	0.00729689
$751$	5494.75	0.266986	0.133493	−	0.991050i	$-0.457381\pi$
$751$	5494.75	0.266986	0.133493	+	0.991050i	$0.457381\pi$
$752$	33534.9	1.62619
$753$	2480.77	0.120059
$754$	−108.620	−0.00524632
$755$	−7074.60	−0.341021
$756$	0	0
$757$	−3411.29	−0.163785	−0.0818926	−	0.996641i	$-0.526096\pi$
$757$	−3411.29	−0.163785	−0.0818926	+	0.996641i	$0.526096\pi$
$758$	−158.658	−0.00760253
$759$	−8199.37	−0.392119
$760$	1176.85	0.0561695
$761$	15927.5	0.758700	0.379350	−	0.925253i	$-0.376148\pi$
$761$	15927.5	0.758700	0.379350	+	0.925253i	$0.376148\pi$
$762$	−156.668	−0.00744816
$763$	0	0
$764$	−19700.4	−0.932899
$765$	2013.44	0.0951581
$766$	322.906	0.0152311
$767$	2433.91	0.114581
$768$	−26268.8	−1.23424
$769$	−20621.3	−0.967000	−0.483500	−	0.875344i	$-0.660635\pi$
$769$	−20621.3	−0.967000	−0.483500	+	0.875344i	$0.660635\pi$
$770$	0	0
$771$	24509.1	1.14484
$772$	−32169.1	−1.49973
$773$	−18163.8	−0.845156	−0.422578	−	0.906326i	$-0.638875\pi$
$773$	−18163.8	−0.845156	−0.422578	+	0.906326i	$0.638875\pi$
$774$	−145.360	−0.00675045
$775$	10695.5	0.495733
$776$	36.9284	0.00170832
$777$	0	0
$778$	203.253	0.00936628
$779$	12534.0	0.576479
$780$	−13267.4	−0.609039
$781$	44747.6	2.05019
$782$	−7.46672	−0.000341444 0
$783$	15012.4	0.685186
$784$	0	0
$785$	23782.1	1.08130
$786$	159.927	0.00725752
$787$	30750.8	1.39282	0.696408	−	0.717646i	$-0.254780\pi$
$787$	30750.8	1.39282	0.696408	+	0.717646i	$0.254780\pi$
$788$	−14490.9	−0.655096
$789$	−28962.6	−1.30684
$790$	−273.668	−0.0123249
$791$	0	0
$792$	−409.418	−0.0183687
$793$	−4334.82	−0.194116
$794$	−366.164	−0.0163661
$795$	6677.49	0.297894
$796$	5790.63	0.257843
$797$	32871.8	1.46095	0.730475	−	0.682939i	$-0.239299\pi$
$797$	32871.8	1.46095	0.730475	+	0.682939i	$0.239299\pi$
$798$	0	0
$799$	−5256.21	−0.232730
$800$	−459.187	−0.0202934
$801$	−12578.0	−0.554834
$802$	463.181	0.0203934
$803$	56175.5	2.46873
$804$	25355.9	1.11223
$805$	0	0
$806$	−85.8375	−0.00375124
$807$	−3536.62	−0.154269
$808$	488.290	0.0212599
$809$	−2591.22	−0.112611	−0.0563055	−	0.998414i	$-0.517932\pi$
$809$	−2591.22	−0.112611	−0.0563055	+	0.998414i	$0.517932\pi$
$810$	−415.810	−0.0180371
$811$	−37339.5	−1.61673	−0.808364	−	0.588683i	$-0.799647\pi$
$811$	−37339.5	−1.61673	−0.808364	+	0.588683i	$0.799647\pi$
$812$	0	0
$813$	−5765.87	−0.248730
$814$	326.050	0.0140393
$815$	−44896.2	−1.92963
$816$	4119.49	0.176729
$817$	−50802.4	−2.17546
$818$	141.266	0.00603819
$819$	0	0
$820$	−8776.26	−0.373756
$821$	20494.9	0.871226	0.435613	−	0.900134i	$-0.356532\pi$
$821$	20494.9	0.871226	0.435613	+	0.900134i	$0.356532\pi$
$822$	−44.0009	−0.00186704
$823$	−13568.2	−0.574675	−0.287338	−	0.957829i	$-0.592770\pi$
$823$	−13568.2	−0.574675	−0.287338	+	0.957829i	$0.592770\pi$
$824$	288.318	0.0121894
$825$	26339.0	1.11152
$826$	0	0
$827$	−39430.4	−1.65796	−0.828978	−	0.559281i	$-0.811077\pi$
$827$	−39430.4	−1.65796	−0.828978	+	0.559281i	$0.811077\pi$
$828$	2619.48	0.109944
$829$	−14439.0	−0.604931	−0.302465	−	0.953160i	$-0.597810\pi$
$829$	−14439.0	−0.604931	−0.302465	+	0.953160i	$0.597810\pi$
$830$	293.236	0.0122631
$831$	−14697.2	−0.613525
$832$	−9369.86	−0.390434
$833$	0	0
$834$	−415.510	−0.0172517
$835$	−53186.1	−2.20429
$836$	−71539.8	−2.95964
$837$	11863.6	0.489924
$838$	398.378	0.0164221
$839$	−33140.6	−1.36369	−0.681847	−	0.731495i	$-0.738823\pi$
$839$	−33140.6	−1.36369	−0.681847	+	0.731495i	$0.738823\pi$
$840$	0	0
$841$	9167.56	0.375889
$842$	270.435	0.0110687
$843$	16614.7	0.678816
$844$	4670.45	0.190478
$845$	26252.9	1.06879
$846$	−241.636	−0.00981986
$847$	0	0
$848$	4717.08	0.191020
$849$	9558.55	0.386394
$850$	23.9855	0.000967877 0
$851$	−4172.45	−0.168072
$852$	−41404.7	−1.66491
$853$	−27379.7	−1.09902	−0.549510	−	0.835487i	$-0.685185\pi$
$853$	−27379.7	−1.09902	−0.549510	+	0.835487i	$0.685185\pi$
$854$	0	0
$855$	32349.4	1.29395
$856$	335.378	0.0133913
$857$	−20497.8	−0.817025	−0.408513	−	0.912753i	$-0.633952\pi$
$857$	−20497.8	−0.817025	−0.408513	+	0.912753i	$0.633952\pi$
$858$	−211.385	−0.00841093
$859$	26376.7	1.04768	0.523842	−	0.851816i	$-0.324498\pi$
$859$	26376.7	1.04768	0.523842	+	0.851816i	$0.324498\pi$
$860$	35571.6	1.41045
$861$	0	0
$862$	516.712	0.0204168
$863$	−32543.2	−1.28364	−0.641821	−	0.766854i	$-0.721821\pi$
$863$	−32543.2	−1.28364	−0.641821	+	0.766854i	$0.721821\pi$
$864$	−509.337	−0.0200556
$865$	1832.50	0.0720311
$866$	187.118	0.00734241
$867$	30904.1	1.21056
$868$	0	0
$869$	33274.3	1.29891
$870$	−537.101	−0.0209304
$871$	9040.67	0.351701
$872$	−698.818	−0.0271387
$873$	1015.09	0.0393536
$874$	−119.966	−0.00464292
$875$	0	0
$876$	−51978.9	−2.00480
$877$	6671.86	0.256890	0.128445	−	0.991717i	$-0.459001\pi$
$877$	6671.86	0.256890	0.128445	+	0.991717i	$0.459001\pi$
$878$	25.7544	0.000989942 0
$879$	−18117.2	−0.695196
$880$	50085.4	1.91861
$881$	25432.9	0.972595	0.486298	−	0.873793i	$-0.338347\pi$
$881$	25432.9	0.972595	0.486298	+	0.873793i	$0.338347\pi$
$882$	0	0
$883$	16292.4	0.620933	0.310467	−	0.950584i	$-0.399515\pi$
$883$	16292.4	0.620933	0.310467	+	0.950584i	$0.399515\pi$
$884$	1469.00	0.0558912
$885$	12035.1	0.457123
$886$	−238.214	−0.00903267
$887$	−8139.80	−0.308126	−0.154063	−	0.988061i	$-0.549236\pi$
$887$	−8139.80	−0.308126	−0.154063	+	0.988061i	$0.549236\pi$
$888$	−603.423	−0.0228036
$889$	0	0
$890$	−403.343	−0.0151911
$891$	50556.9	1.90092
$892$	25257.3	0.948067
$893$	−84450.2	−3.16463
$894$	103.947	0.00388870
$895$	−11425.7	−0.426724
$896$	0	0
$897$	2705.09	0.100692
$898$	216.021	0.00802753
$899$	26518.1	0.983793
$900$	−8414.61	−0.311652
$901$	−739.347	−0.0273376
$902$	−139.829	−0.00516164
$903$	0	0
$904$	−147.390	−0.00542268
$905$	34274.0	1.25890
$906$	104.297	0.00382453
$907$	16087.6	0.588954	0.294477	−	0.955659i	$-0.404855\pi$
$907$	16087.6	0.588954	0.294477	+	0.955659i	$0.404855\pi$
$908$	−17756.0	−0.648959
$909$	13422.2	0.489753
$910$	0	0
$911$	−36379.0	−1.32304	−0.661521	−	0.749927i	$-0.730089\pi$
$911$	−36379.0	−1.32304	−0.661521	+	0.749927i	$0.730089\pi$
$912$	66186.8	2.40314
$913$	−35653.6	−1.29240
$914$	204.767	0.00741037
$915$	−21434.6	−0.774433
$916$	−35181.3	−1.26902
$917$	0	0
$918$	26.6051	0.000956534 0
$919$	−10077.9	−0.361739	−0.180869	−	0.983507i	$-0.557891\pi$
$919$	−10077.9	−0.361739	−0.180869	+	0.983507i	$0.557891\pi$
$920$	168.011	0.00602081
$921$	−26237.2	−0.938704
$922$	−20.7708	−0.000741919 0
$923$	−14762.9	−0.526465
$924$	0	0
$925$	13403.2	0.476427
$926$	−23.1275	−0.000820753 0
$927$	7925.32	0.280800
$928$	−1138.50	−0.0402726
$929$	7768.50	0.274355	0.137178	−	0.990546i	$-0.456197\pi$
$929$	7768.50	0.274355	0.137178	+	0.990546i	$0.456197\pi$
$930$	−424.445	−0.0149657
$931$	0	0
$932$	−16900.5	−0.593987
$933$	25974.8	0.911442
$934$	127.484	0.00446615
$935$	−7850.30	−0.274580
$936$	135.073	0.00471688
$937$	1611.36	0.0561804	0.0280902	−	0.999605i	$-0.491057\pi$
$937$	1611.36	0.0561804	0.0280902	+	0.999605i	$0.491057\pi$
$938$	0	0
$939$	32824.8	1.14078
$940$	59131.7	2.05177
$941$	1974.16	0.0683909	0.0341954	−	0.999415i	$-0.489113\pi$
$941$	1974.16	0.0683909	0.0341954	+	0.999415i	$0.489113\pi$
$942$	−350.605	−0.0121267
$943$	1789.39	0.0617927
$944$	8501.76	0.293124
$945$	0	0
$946$	566.751	0.0194785
$947$	57242.2	1.96422	0.982112	−	0.188297i	$-0.0602969\pi$
$947$	57242.2	1.96422	0.982112	+	0.188297i	$0.0602969\pi$
$948$	−30788.6	−1.05482
$949$	−18533.1	−0.633942
$950$	385.369	0.0131611
$951$	45067.1	1.53670
$952$	0	0
$953$	−14723.4	−0.500458	−0.250229	−	0.968187i	$-0.580506\pi$
$953$	−14723.4	−0.500458	−0.250229	+	0.968187i	$0.580506\pi$
$954$	−33.9889	−0.00115349
$955$	−34732.9	−1.17689
$956$	12387.9	0.419092
$957$	65304.2	2.20584
$958$	−72.9128	−0.00245898
$959$	0	0
$960$	−46331.6	−1.55765
$961$	−8834.99	−0.296566
$962$	−107.569	−0.00360515
$963$	9218.90	0.308489
$964$	−20132.7	−0.672646
$965$	−56715.9	−1.89197
$966$	0	0
$967$	−46140.9	−1.53443	−0.767214	−	0.641391i	$-0.778358\pi$
$967$	−46140.9	−1.53443	−0.767214	+	0.641391i	$0.778358\pi$
$968$	906.875	0.0301117
$969$	−10374.0	−0.343922
$970$	32.5513	0.00107748
$971$	−15349.8	−0.507310	−0.253655	−	0.967295i	$-0.581633\pi$
$971$	−15349.8	−0.507310	−0.253655	+	0.967295i	$0.581633\pi$
$972$	−29080.6	−0.959631
$973$	0	0
$974$	−382.737	−0.0125910
$975$	−8689.62	−0.285426
$976$	−15141.7	−0.496594
$977$	−1517.18	−0.0496815	−0.0248407	−	0.999691i	$-0.507908\pi$
$977$	−1517.18	−0.0496815	−0.0248407	+	0.999691i	$0.507908\pi$
$978$	661.879	0.0216406
$979$	49041.0	1.60098
$980$	0	0
$981$	−19209.2	−0.625181
$982$	−653.926	−0.0212501
$983$	−22648.4	−0.734866	−0.367433	−	0.930050i	$-0.619763\pi$
$983$	−22648.4	−0.734866	−0.367433	+	0.930050i	$0.619763\pi$
$984$	258.783	0.00838386
$985$	−25548.2	−0.826430
$986$	59.4691	0.00192077
$987$	0	0
$988$	23602.1	0.760002
$989$	−7252.70	−0.233187
$990$	−360.890	−0.0115857
$991$	12346.4	0.395760	0.197880	−	0.980226i	$-0.436594\pi$
$991$	12346.4	0.395760	0.197880	+	0.980226i	$0.436594\pi$
$992$	−899.700	−0.0287959
$993$	41978.8	1.34155
$994$	0	0
$995$	10209.2	0.325280
$996$	32990.1	1.04953
$997$	43566.0	1.38390	0.691950	−	0.721945i	$-0.256752\pi$
$997$	43566.0	1.38390	0.691950	+	0.721945i	$0.256752\pi$
$998$	20.5159	0.000650721 0
$999$	14867.1	0.470844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1127.4.a.c.1.2		4
7.6	odd	2		23.4.a.b.1.2	✓	4
21.20	even	2		207.4.a.e.1.3		4
28.27	even	2		368.4.a.l.1.1		4
35.13	even	4		575.4.b.g.24.5		8
35.27	even	4		575.4.b.g.24.4		8
35.34	odd	2		575.4.a.i.1.3		4
56.13	odd	2		1472.4.a.y.1.1		4
56.27	even	2		1472.4.a.bf.1.4		4
161.160	even	2		529.4.a.g.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.a.b.1.2	✓	4	7.6	odd	2
207.4.a.e.1.3		4	21.20	even	2
368.4.a.l.1.1		4	28.27	even	2
529.4.a.g.1.2		4	161.160	even	2
575.4.a.i.1.3		4	35.34	odd	2
575.4.b.g.24.4		8	35.27	even	4
575.4.b.g.24.5		8	35.13	even	4
1127.4.a.c.1.2		4	1.1	even	1	trivial
1472.4.a.y.1.1		4	56.13	odd	2
1472.4.a.bf.1.4		4	56.27	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:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1127.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0323756 q^{2} -6.42170 q^{3} -7.99895 q^{4} -14.1026 q^{5} +0.207906 q^{6} +0.517976 q^{8} +14.2382 q^{9} +O(q^{10})\)	\(q-0.0323756 q^{2} -6.42170 q^{3} -7.99895 q^{4} -14.1026 q^{5} +0.207906 q^{6} +0.517976 q^{8} +14.2382 q^{9} +0.456580 q^{10} -55.5140 q^{11} +51.3668 q^{12} +18.3149 q^{13} +90.5626 q^{15} +63.9748 q^{16} -10.0273 q^{17} -0.460970 q^{18} -161.106 q^{19} +112.806 q^{20} +1.79730 q^{22} -23.0000 q^{23} -3.32628 q^{24} +73.8833 q^{25} -0.592956 q^{26} +81.9525 q^{27} +183.185 q^{29} -2.93202 q^{30} +144.762 q^{31} -6.21503 q^{32} +356.494 q^{33} +0.324640 q^{34} -113.891 q^{36} +181.411 q^{37} +5.21591 q^{38} -117.613 q^{39} -7.30481 q^{40} -77.7996 q^{41} +315.335 q^{43} +444.054 q^{44} -200.795 q^{45} +0.744639 q^{46} +524.190 q^{47} -410.827 q^{48} -2.39202 q^{50} +64.3923 q^{51} -146.500 q^{52} +73.7334 q^{53} -2.65326 q^{54} +782.892 q^{55} +1034.57 q^{57} -5.93071 q^{58} +132.892 q^{59} -724.406 q^{60} -236.683 q^{61} -4.68676 q^{62} -511.598 q^{64} -258.288 q^{65} -11.5417 q^{66} +493.624 q^{67} +80.2079 q^{68} +147.699 q^{69} -806.060 q^{71} +7.37504 q^{72} -1011.91 q^{73} -5.87328 q^{74} -474.456 q^{75} +1288.68 q^{76} +3.80779 q^{78} -599.386 q^{79} -902.212 q^{80} -910.705 q^{81} +2.51881 q^{82} +642.245 q^{83} +141.411 q^{85} -10.2092 q^{86} -1176.36 q^{87} -28.7549 q^{88} -883.399 q^{89} +6.50088 q^{90} +183.976 q^{92} -929.617 q^{93} -16.9710 q^{94} +2272.02 q^{95} +39.9111 q^{96} +71.2938 q^{97} -790.419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 7 q^{3} + 20 q^{4} - 14 q^{5} + 17 q^{6} - 63 q^{8} - 33 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 7 * q^3 + 20 * q^4 - 14 * q^5 + 17 * q^6 - 63 * q^8 - 33 * q^9	\( 4 q + 2 q^{2} - 7 q^{3} + 20 q^{4} - 14 q^{5} + 17 q^{6} - 63 q^{8} - 33 q^{9} + 70 q^{10} + 8 q^{11} + 67 q^{12} - 111 q^{13} + 10 q^{15} + 64 q^{16} - 98 q^{17} + 49 q^{18} - 96 q^{19} - 140 q^{20} + 220 q^{22} - 92 q^{23} + 188 q^{24} + 184 q^{25} + 229 q^{26} + 155 q^{27} + 21 q^{29} - 406 q^{30} + 193 q^{31} - 432 q^{32} + 418 q^{33} - 666 q^{34} - 629 q^{36} + 170 q^{37} - 748 q^{38} - 291 q^{39} + 26 q^{40} + 125 q^{41} + 2 q^{43} + 830 q^{44} - 168 q^{45} - 46 q^{46} + 677 q^{47} - 551 q^{48} + 414 q^{50} - 340 q^{51} - 2247 q^{52} - 230 q^{53} - 641 q^{54} + 972 q^{55} + 1322 q^{57} - 1835 q^{58} + 1140 q^{59} - 804 q^{60} - 754 q^{61} - 443 q^{62} - 805 q^{64} + 1318 q^{65} + 398 q^{66} + 488 q^{67} - 284 q^{68} + 161 q^{69} - 401 q^{71} + 1503 q^{72} - 1509 q^{73} + 1366 q^{74} - 1401 q^{75} + 3832 q^{76} - 1907 q^{78} - 838 q^{79} - 2846 q^{80} - 932 q^{81} + 949 q^{82} - 142 q^{83} + 112 q^{85} + 918 q^{86} - 2223 q^{87} - 404 q^{88} - 2342 q^{89} - 1784 q^{90} - 460 q^{92} - 509 q^{93} - 1567 q^{94} - 956 q^{95} - 799 q^{96} - 1062 q^{97} - 1498 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 7 * q^3 + 20 * q^4 - 14 * q^5 + 17 * q^6 - 63 * q^8 - 33 * q^9 + 70 * q^10 + 8 * q^11 + 67 * q^12 - 111 * q^13 + 10 * q^15 + 64 * q^16 - 98 * q^17 + 49 * q^18 - 96 * q^19 - 140 * q^20 + 220 * q^22 - 92 * q^23 + 188 * q^24 + 184 * q^25 + 229 * q^26 + 155 * q^27 + 21 * q^29 - 406 * q^30 + 193 * q^31 - 432 * q^32 + 418 * q^33 - 666 * q^34 - 629 * q^36 + 170 * q^37 - 748 * q^38 - 291 * q^39 + 26 * q^40 + 125 * q^41 + 2 * q^43 + 830 * q^44 - 168 * q^45 - 46 * q^46 + 677 * q^47 - 551 * q^48 + 414 * q^50 - 340 * q^51 - 2247 * q^52 - 230 * q^53 - 641 * q^54 + 972 * q^55 + 1322 * q^57 - 1835 * q^58 + 1140 * q^59 - 804 * q^60 - 754 * q^61 - 443 * q^62 - 805 * q^64 + 1318 * q^65 + 398 * q^66 + 488 * q^67 - 284 * q^68 + 161 * q^69 - 401 * q^71 + 1503 * q^72 - 1509 * q^73 + 1366 * q^74 - 1401 * q^75 + 3832 * q^76 - 1907 * q^78 - 838 * q^79 - 2846 * q^80 - 932 * q^81 + 949 * q^82 - 142 * q^83 + 112 * q^85 + 918 * q^86 - 2223 * q^87 - 404 * q^88 - 2342 * q^89 - 1784 * q^90 - 460 * q^92 - 509 * q^93 - 1567 * q^94 - 956 * q^95 - 799 * q^96 - 1062 * q^97 - 1498 * q^99

Introduction

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