LMFDB - Embedded newform 252.4.k.f.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(37,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("252.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.k (of order $3$, degree $2$, minimal)

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:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$-3.22311 + 5.58259i$ of defining polynomial
Character	$\chi$	$=$	252.37
Dual form			252.4.k.f.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.22311 - 10.7787i) q^{5} +(15.3924 + 10.2992i) q^{7} +O(q^{10})$	$q+(6.22311 - 10.7787i) q^{5} +(15.3924 + 10.2992i) q^{7} +(-25.5618 - 44.2743i) q^{11} +37.2311 q^{13} +(11.1076 + 19.2389i) q^{17} +(-27.1693 + 47.0587i) q^{19} +(88.4622 - 153.221i) q^{23} +(-14.9542 - 25.9015i) q^{25} -61.0916 q^{29} +(-159.962 - 277.063i) q^{31} +(206.801 - 101.818i) q^{35} +(157.540 - 272.867i) q^{37} +206.032 q^{41} +339.661 q^{43} +(71.0320 - 123.031i) q^{47} +(130.855 + 317.058i) q^{49} +(155.008 + 268.482i) q^{53} -636.295 q^{55} +(-140.825 - 243.916i) q^{59} +(271.924 - 470.987i) q^{61} +(231.693 - 401.305i) q^{65} +(239.680 + 415.137i) q^{67} -1105.63 q^{71} +(-119.675 - 207.283i) q^{73} +(62.5298 - 944.754i) q^{77} +(-580.333 + 1005.17i) q^{79} +2.93158 q^{83} +276.494 q^{85} +(-639.371 + 1107.42i) q^{89} +(573.078 + 383.449i) q^{91} +(338.156 + 585.703i) q^{95} +79.0596 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 11 q^{5} + 6 q^{7}+O(q^{10}) $ 4 * q + 11 * q^5 + 6 * q^7	$ 4 q + 11 q^{5} + 6 q^{7} - 5 q^{11} + 10 q^{13} + 100 q^{17} - 67 q^{19} + 76 q^{23} + 93 q^{25} - 550 q^{29} - 362 q^{31} + 466 q^{35} + 5 q^{37} + 324 q^{41} + 1442 q^{43} - 216 q^{47} + 190 q^{49} + 495 q^{53} - 1406 q^{55} + 173 q^{59} + 532 q^{61} + 510 q^{65} - 111 q^{67} - 3200 q^{71} - 1215 q^{73} + 653 q^{77} - 1460 q^{79} + 2818 q^{83} + 328 q^{85} - 1974 q^{89} + 1945 q^{91} + 658 q^{95} + 1122 q^{97}+O(q^{100}) $ 4 * q + 11 * q^5 + 6 * q^7 - 5 * q^11 + 10 * q^13 + 100 * q^17 - 67 * q^19 + 76 * q^23 + 93 * q^25 - 550 * q^29 - 362 * q^31 + 466 * q^35 + 5 * q^37 + 324 * q^41 + 1442 * q^43 - 216 * q^47 + 190 * q^49 + 495 * q^53 - 1406 * q^55 + 173 * q^59 + 532 * q^61 + 510 * q^65 - 111 * q^67 - 3200 * q^71 - 1215 * q^73 + 653 * q^77 - 1460 * q^79 + 2818 * q^83 + 328 * q^85 - 1974 * q^89 + 1945 * q^91 + 658 * q^95 + 1122 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	6.22311	−	10.7787i	0.556612	−	0.964080i	−0.441164	−	0.897426i	$-0.645434\pi$
$5$	6.22311	−	10.7787i	0.556612	−	0.964080i	0.997776	−	0.0666538i	$-0.0212323\pi$
$6$		0			0
$7$	15.3924	+	10.2992i	0.831114	+	0.556102i
$7$	15.3924	+	10.2992i	0.831114	+	0.556102i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−25.5618	−	44.2743i	−0.700651	−	1.21356i	−0.968238	−	0.250030i	$-0.919559\pi$
$11$	−25.5618	−	44.2743i	−0.700651	−	1.21356i	0.267587	−	0.963534i	$-0.413774\pi$
$12$		0			0
$13$	37.2311			0.794312			0.397156	−	0.917751i	$-0.369997\pi$
$13$	37.2311			0.794312			0.397156	+	0.917751i	$0.369997\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	11.1076	+	19.2389i	0.158469	+	0.274477i	0.934317	−	0.356444i	$-0.116011\pi$
$17$	11.1076	+	19.2389i	0.158469	+	0.274477i	−0.775848	+	0.630920i	$0.782677\pi$
$18$		0			0
$19$	−27.1693	+	47.0587i	−0.328056	+	0.568210i	−0.982126	−	0.188224i	$-0.939727\pi$
$19$	−27.1693	+	47.0587i	−0.328056	+	0.568210i	0.654070	+	0.756434i	$0.273060\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	88.4622	−	153.221i	0.801985	−	1.38908i	−0.116323	−	0.993211i	$-0.537111\pi$
$23$	88.4622	−	153.221i	0.801985	−	1.38908i	0.918308	−	0.395867i	$-0.129556\pi$
$24$		0			0
$25$	−14.9542	−	25.9015i	−0.119634	−	0.207212i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−61.0916			−0.391187			−0.195593	−	0.980685i	$-0.562663\pi$
$29$	−61.0916			−0.391187			−0.195593	+	0.980685i	$0.562663\pi$
$30$		0			0
$31$	−159.962	−	277.063i	−0.926776	−	1.60522i	−0.788679	−	0.614805i	$-0.789235\pi$
$31$	−159.962	−	277.063i	−0.926776	−	1.60522i	−0.138097	−	0.990419i	$-0.544099\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	206.801	−	101.818i	0.998735	−	0.491727i
$36$		0			0
$37$	157.540	−	272.867i	0.699984	−	1.21241i	−0.268487	−	0.963283i	$-0.586524\pi$
$37$	157.540	−	272.867i	0.699984	−	1.21241i	0.968471	−	0.249125i	$-0.0801430\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	206.032			0.784800			0.392400	−	0.919795i	$-0.371645\pi$
$41$	206.032			0.784800			0.392400	+	0.919795i	$0.371645\pi$
$42$		0			0
$43$	339.661			1.20460			0.602301	−	0.798269i	$-0.294251\pi$
$43$	339.661			1.20460			0.602301	+	0.798269i	$0.294251\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	71.0320	−	123.031i	0.220449	−	0.381828i	−0.734496	−	0.678613i	$-0.762581\pi$
$47$	71.0320	−	123.031i	0.220449	−	0.381828i	0.954944	+	0.296785i	$0.0959146\pi$
$48$		0			0
$49$	130.855	+	317.058i	0.381500	+	0.924369i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	155.008	+	268.482i	0.401736	+	0.695826i	0.993936	−	0.109965i	$-0.0350738\pi$
$53$	155.008	+	268.482i	0.401736	+	0.695826i	−0.592200	+	0.805791i	$0.701740\pi$
$54$		0			0
$55$	−636.295			−1.55996
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−140.825	−	243.916i	−0.310743	−	0.538223i	0.667780	−	0.744358i	$-0.267245\pi$
$59$	−140.825	−	243.916i	−0.310743	−	0.538223i	−0.978523	+	0.206136i	$0.933911\pi$
$60$		0			0
$61$	271.924	−	470.987i	0.570760	−	0.988585i	−0.425728	−	0.904851i	$-0.639982\pi$
$61$	271.924	−	470.987i	0.570760	−	0.988585i	0.996488	−	0.0837341i	$-0.0266846\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	231.693	−	401.305i	0.442123	−	0.765780i
$66$		0			0
$67$	239.680	+	415.137i	0.437038	+	0.756971i	0.997459	−	0.0712360i	$-0.0226943\pi$
$67$	239.680	+	415.137i	0.437038	+	0.756971i	−0.560422	+	0.828207i	$0.689361\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1105.63			−1.84809			−0.924046	−	0.382280i	$-0.875139\pi$
$71$	−1105.63			−1.84809			−0.924046	+	0.382280i	$0.875139\pi$
$72$		0			0
$73$	−119.675	−	207.283i	−0.191876	−	0.332338i	0.753996	−	0.656879i	$-0.228124\pi$
$73$	−119.675	−	207.283i	−0.191876	−	0.332338i	−0.945872	+	0.324541i	$0.894790\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	62.5298	−	944.754i	0.0925445	−	1.39824i
$78$		0			0
$79$	−580.333	+	1005.17i	−0.826488	+	1.43152i	0.0742888	+	0.997237i	$0.476331\pi$
$79$	−580.333	+	1005.17i	−0.826488	+	1.43152i	−0.900777	+	0.434282i	$0.857002\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.93158			0.00387690			0.00193845	−	0.999998i	$-0.499383\pi$
$83$	2.93158			0.00387690			0.00193845	+	0.999998i	$0.499383\pi$
$84$		0			0
$85$	276.494			0.352824
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−639.371	+	1107.42i	−0.761496	+	1.31895i	0.180583	+	0.983560i	$0.442202\pi$
$89$	−639.371	+	1107.42i	−0.761496	+	1.31895i	−0.942079	+	0.335390i	$0.891132\pi$
$90$		0			0
$91$	573.078	+	383.449i	0.660163	+	0.441719i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	338.156	+	585.703i	0.365200	+	0.632545i
$96$		0			0
$97$	79.0596			0.0827555			0.0413777	−	0.999144i	$-0.486825\pi$
$97$	79.0596			0.0827555			0.0413777	+	0.999144i	$0.486825\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	686.052	+	1188.28i	0.675889	+	1.17067i	0.976208	+	0.216835i	$0.0695734\pi$
$101$	686.052	+	1188.28i	0.675889	+	1.17067i	−0.300319	+	0.953839i	$0.597093\pi$
$102$		0			0
$103$	−129.265	+	223.894i	−0.123659	+	0.214184i	−0.921208	−	0.389070i	$-0.872796\pi$
$103$	−129.265	+	223.894i	−0.123659	+	0.214184i	0.797549	+	0.603254i	$0.206130\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−631.184	+	1093.24i	−0.570270	+	0.987736i	0.426268	+	0.904597i	$0.359828\pi$
$107$	−631.184	+	1093.24i	−0.570270	+	0.987736i	−0.996538	+	0.0831393i	$0.973505\pi$
$108$		0			0
$109$	−138.416	−	239.744i	−0.121632	−	0.210673i	0.798779	−	0.601624i	$-0.205479\pi$
$109$	−138.416	−	239.744i	−0.121632	−	0.210673i	−0.920411	+	0.390951i	$0.872146\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−52.9156			−0.0440520			−0.0220260	−	0.999757i	$-0.507012\pi$
$113$	−52.9156			−0.0440520			−0.0220260	+	0.999757i	$0.507012\pi$
$114$		0			0
$115$	−1101.02	−	1907.02i	−0.892789	−	1.54636i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−27.1715	+	410.531i	−0.0209312	+	0.316247i
$120$		0			0
$121$	−641.309	+	1110.78i	−0.481825	+	0.834545i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1183.53			0.846866
$126$		0			0
$127$	443.700			0.310016			0.155008	−	0.987913i	$-0.450460\pi$
$127$	443.700			0.310016			0.155008	+	0.987913i	$0.450460\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1076.74	+	1864.97i	−0.718133	+	1.24384i	0.243606	+	0.969874i	$0.421670\pi$
$131$	−1076.74	+	1864.97i	−0.718133	+	1.24384i	−0.961739	+	0.273968i	$0.911664\pi$
$132$		0			0
$133$	−902.867	+	444.527i	−0.588635	+	0.289815i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	131.554	+	227.858i	0.0820394	+	0.142096i	0.904126	−	0.427266i	$-0.140523\pi$
$137$	131.554	+	227.858i	0.0820394	+	0.142096i	−0.822086	+	0.569363i	$0.807190\pi$
$138$		0			0
$139$	1165.77			0.711360			0.355680	−	0.934608i	$-0.384249\pi$
$139$	1165.77			0.711360			0.355680	+	0.934608i	$0.384249\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−951.693	−	1648.38i	−0.556536	−	0.963948i
$144$		0			0
$145$	−380.180	+	658.490i	−0.217739	+	0.377135i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−882.597	+	1528.70i	−0.485270	+	0.840512i	−0.999857	−	0.0169263i	$-0.994612\pi$
$149$	−882.597	+	1528.70i	−0.485270	+	0.840512i	0.514587	+	0.857438i	$0.327945\pi$
$150$		0			0
$151$	−1346.16	−	2331.61i	−0.725488	−	1.25658i	−0.958773	−	0.284173i	$-0.908281\pi$
$151$	−1346.16	−	2331.61i	−0.725488	−	1.25658i	0.233285	−	0.972408i	$-0.425052\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3981.85			−2.06342
$156$		0			0
$157$	970.691	+	1681.29i	0.493437	+	0.854657i	0.999971	−	0.00756226i	$-0.00240716\pi$
$157$	970.691	+	1681.29i	0.493437	+	0.854657i	−0.506535	+	0.862220i	$0.669074\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2939.70	−	1447.36i	1.43901	−	0.708497i
$162$		0			0
$163$	−1051.42	+	1821.11i	−0.505236	+	0.875094i	0.494746	+	0.869038i	$0.335261\pi$
$163$	−1051.42	+	1821.11i	−0.505236	+	0.875094i	−0.999982	+	0.00605658i	$0.998072\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2344.22			1.08623			0.543116	−	0.839658i	$-0.317244\pi$
$167$	2344.22			1.08623			0.543116	+	0.839658i	$0.317244\pi$
$168$		0			0
$169$	−810.844			−0.369069
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1735.32	−	3005.67i	0.762626	−	1.32091i	−0.178867	−	0.983873i	$-0.557243\pi$
$173$	1735.32	−	3005.67i	0.762626	−	1.32091i	0.941493	−	0.337033i	$-0.109424\pi$
$174$		0			0
$175$	36.5813	−	552.703i	0.0158017	−	0.238745i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−477.885	−	827.722i	−0.199547	−	0.345625i	0.748835	−	0.662757i	$-0.230614\pi$
$179$	−477.885	−	827.722i	−0.199547	−	0.345625i	−0.948381	+	0.317132i	$0.897280\pi$
$180$		0			0
$181$	4220.26			1.73309			0.866546	−	0.499098i	$-0.166335\pi$
$181$	4220.26			1.73309			0.866546	+	0.499098i	$0.166335\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1960.78	−	3396.17i	−0.779239	−	1.34968i
$186$		0			0
$187$	567.858	−	983.558i	0.222063	−	0.384625i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1759.02	+	3046.71i	−0.666377	+	1.15420i	0.312534	+	0.949907i	$0.398822\pi$
$191$	−1759.02	+	3046.71i	−0.666377	+	1.15420i	−0.978910	+	0.204291i	$0.934511\pi$
$192$		0			0
$193$	2508.84	+	4345.43i	0.935699	+	1.62068i	0.773382	+	0.633940i	$0.218563\pi$
$193$	2508.84	+	4345.43i	0.935699	+	1.62068i	0.162317	+	0.986739i	$0.448103\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2838.14			1.02644			0.513221	−	0.858257i	$-0.328452\pi$
$197$	2838.14			1.02644			0.513221	+	0.858257i	$0.328452\pi$
$198$		0			0
$199$	−177.451	−	307.354i	−0.0632118	−	0.109486i	0.832688	−	0.553743i	$-0.186801\pi$
$199$	−177.451	−	307.354i	−0.0632118	−	0.109486i	−0.895899	+	0.444257i	$0.853468\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−940.348	−	629.192i	−0.325121	−	0.217540i
$204$		0			0
$205$	1282.16	−	2220.77i	0.436829	−	0.756610i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2777.99			0.919413
$210$		0			0
$211$	752.672			0.245574			0.122787	−	0.992433i	$-0.460817\pi$
$211$	752.672			0.245574			0.122787	+	0.992433i	$0.460817\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2113.75	−	3661.12i	0.670496	−	1.16133i
$216$		0			0
$217$	391.303	−	5912.15i	0.122412	−	1.84951i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	413.547	+	716.284i	0.125874	+	0.218020i
$222$		0			0
$223$	−3077.75			−0.924221			−0.462111	−	0.886822i	$-0.652908\pi$
$223$	−3077.75			−0.924221			−0.462111	+	0.886822i	$0.652908\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3108.72	−	5384.46i	−0.908955	−	1.57436i	−0.815518	−	0.578731i	$-0.803548\pi$
$227$	−3108.72	−	5384.46i	−0.908955	−	1.57436i	−0.0934368	−	0.995625i	$-0.529785\pi$
$228$		0			0
$229$	−251.627	+	435.831i	−0.0726113	+	0.125766i	−0.900045	−	0.435797i	$-0.856467\pi$
$229$	−251.627	+	435.831i	−0.0726113	+	0.125766i	0.827434	+	0.561563i	$0.189800\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−134.170	+	232.389i	−0.0377243	+	0.0653404i	−0.884271	−	0.466974i	$-0.845344\pi$
$233$	−134.170	+	232.389i	−0.0377243	+	0.0653404i	0.846547	+	0.532314i	$0.178678\pi$
$234$		0			0
$235$	−884.080	−	1531.27i	−0.245409	−	0.425060i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5189.77			1.40459			0.702297	−	0.711884i	$-0.252158\pi$
$239$	5189.77			1.40459			0.702297	+	0.711884i	$0.252158\pi$
$240$		0			0
$241$	−3085.47	−	5344.19i	−0.824699	−	1.42842i	−0.902149	−	0.431425i	$-0.858011\pi$
$241$	−3085.47	−	5344.19i	−0.824699	−	1.42842i	0.0774495	−	0.996996i	$-0.475322\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4231.82	+	562.641i	1.10351	+	0.146718i
$246$		0			0
$247$	−1011.54	+	1752.05i	−0.260579	+	0.451336i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1891.91			−0.475763			−0.237882	−	0.971294i	$-0.576453\pi$
$251$	−1891.91			−0.475763			−0.237882	+	0.971294i	$0.576453\pi$
$252$		0			0
$253$	−9045.01			−2.24765
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3269.97	+	5663.75i	−0.793676	+	1.37469i	0.130000	+	0.991514i	$0.458502\pi$
$257$	−3269.97	+	5663.75i	−0.793676	+	1.37469i	−0.923676	+	0.383174i	$0.874831\pi$
$258$		0			0
$259$	5235.23	−	2577.56i	1.25599	−	0.618386i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2687.95	+	4655.67i	0.630214	+	1.09156i	0.987508	+	0.157570i	$0.0503661\pi$
$263$	2687.95	+	4655.67i	0.630214	+	1.09156i	−0.357294	+	0.933992i	$0.616301\pi$
$264$		0			0
$265$	3858.53			0.894443
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1619.44	−	2804.95i	−0.367060	−	0.635766i	0.622045	−	0.782982i	$-0.286302\pi$
$269$	−1619.44	−	2804.95i	−0.367060	−	0.635766i	−0.989104	+	0.147216i	$0.952969\pi$
$270$		0			0
$271$	−678.729	+	1175.59i	−0.152140	+	0.263514i	−0.932014	−	0.362423i	$-0.881950\pi$
$271$	−678.729	+	1175.59i	−0.152140	+	0.263514i	0.779874	+	0.625936i	$0.215283\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−764.513	+	1324.18i	−0.167643	+	0.290366i
$276$		0			0
$277$	1280.82	+	2218.44i	0.277823	+	0.481203i	0.970843	−	0.239715i	$-0.0770539\pi$
$277$	1280.82	+	2218.44i	0.277823	+	0.481203i	−0.693021	+	0.720918i	$0.743721\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1786.17			−0.379196			−0.189598	−	0.981862i	$-0.560718\pi$
$281$	−1786.17			−0.379196			−0.189598	+	0.981862i	$0.560718\pi$
$282$		0			0
$283$	3694.14	+	6398.44i	0.775950	+	1.34398i	0.934259	+	0.356595i	$0.116063\pi$
$283$	3694.14	+	6398.44i	0.775950	+	1.34398i	−0.158309	+	0.987390i	$0.550604\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3171.34	+	2121.96i	0.652258	+	0.436429i
$288$		0			0
$289$	2209.74	−	3827.39i	0.449775	−	0.779033i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−492.981			−0.0982945			−0.0491472	−	0.998792i	$-0.515650\pi$
$293$	−492.981			−0.0982945			−0.0491472	+	0.998792i	$0.515650\pi$
$294$		0			0
$295$	−3505.48			−0.691853
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3293.55	−	5704.59i	0.637026	−	1.10336i
$300$		0			0
$301$	5228.22	+	3498.23i	1.00116	+	0.669882i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3384.43	−	5862.01i	−0.635384	−	1.10052i
$306$		0			0
$307$	−988.810			−0.183825			−0.0919126	−	0.995767i	$-0.529298\pi$
$307$	−988.810			−0.183825			−0.0919126	+	0.995767i	$0.529298\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4798.28	−	8310.87i	−0.874874	−	1.51533i	−0.856897	−	0.515487i	$-0.827611\pi$
$311$	−4798.28	−	8310.87i	−0.874874	−	1.51533i	−0.0179763	−	0.999838i	$-0.505722\pi$
$312$		0			0
$313$	−482.856	+	836.332i	−0.0871970	+	0.151030i	−0.906325	−	0.422581i	$-0.861124\pi$
$313$	−482.856	+	836.332i	−0.0871970	+	0.151030i	0.819128	+	0.573610i	$0.194458\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4492.99	+	7782.08i	−0.796061	+	1.37882i	0.126103	+	0.992017i	$0.459753\pi$
$317$	−4492.99	+	7782.08i	−0.796061	+	1.37882i	−0.922163	+	0.386801i	$0.873580\pi$
$318$		0			0
$319$	1561.61	+	2704.79i	0.274086	+	0.474730i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1207.14			−0.207947
$324$		0			0
$325$	−556.762	−	964.340i	−0.0950265	−	0.164591i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2360.47	−	1162.18i	0.395553	−	0.194751i
$330$		0			0
$331$	1903.65	−	3297.22i	0.316115	−	0.547527i	−0.663559	−	0.748124i	$-0.730955\pi$
$331$	1903.65	−	3297.22i	0.316115	−	0.547527i	0.979674	+	0.200597i	$0.0642882\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5966.21			0.973041
$336$		0			0
$337$	−1649.82			−0.266681			−0.133340	−	0.991070i	$-0.542570\pi$
$337$	−1649.82			−0.266681			−0.133340	+	0.991070i	$0.542570\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8177.84	+	14164.4i	−1.29869	+	2.24940i
$342$		0			0
$343$	−1251.26	+	6228.00i	−0.196973	+	0.980409i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2855.00	+	4945.00i	0.441684	+	0.765019i	0.997815	−	0.0660760i	$-0.0210480\pi$
$347$	2855.00	+	4945.00i	0.441684	+	0.765019i	−0.556131	+	0.831095i	$0.687715\pi$
$348$		0			0
$349$	−447.244			−0.0685973			−0.0342986	−	0.999412i	$-0.510920\pi$
$349$	−447.244			−0.0685973			−0.0342986	+	0.999412i	$0.510920\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5322.85	−	9219.45i	−0.802569	−	1.39009i	−0.917920	−	0.396765i	$-0.870133\pi$
$353$	−5322.85	−	9219.45i	−0.802569	−	1.39009i	0.115352	−	0.993325i	$-0.463201\pi$
$354$		0			0
$355$	−6880.48	+	11917.3i	−1.02867	+	1.78171i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4548.73	+	7878.64i	−0.668727	+	1.15827i	0.309533	+	0.950889i	$0.399827\pi$
$359$	−4548.73	+	7878.64i	−0.668727	+	1.15827i	−0.978260	+	0.207381i	$0.933506\pi$
$360$		0			0
$361$	1953.15	+	3382.96i	0.284758	+	0.493215i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2979.01			−0.427201
$366$		0			0
$367$	−2643.91	−	4579.39i	−0.376052	−	0.651341i	0.614432	−	0.788970i	$-0.289385\pi$
$367$	−2643.91	−	4579.39i	−0.376052	−	0.651341i	−0.990484	+	0.137629i	$0.956052\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−379.184	+	5729.04i	−0.0530627	+	0.801717i
$372$		0			0
$373$	−2947.51	+	5105.23i	−0.409159	+	0.708683i	−0.994796	−	0.101890i	$-0.967511\pi$
$373$	−2947.51	+	5105.23i	−0.409159	+	0.708683i	0.585637	+	0.810573i	$0.300844\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2274.51			−0.310724
$378$		0			0
$379$	3842.41			0.520769			0.260384	−	0.965505i	$-0.416151\pi$
$379$	3842.41			0.520769			0.260384	+	0.965505i	$0.416151\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2506.87	−	4342.02i	0.334452	−	0.579287i	−0.648928	−	0.760850i	$-0.724782\pi$
$383$	2506.87	−	4342.02i	0.334452	−	0.579287i	0.983379	+	0.181563i	$0.0581156\pi$
$384$		0			0
$385$	−9794.14	−	6553.30i	−1.29651	−	0.867499i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5591.24	+	9684.31i	0.728758	+	1.26225i	0.957408	+	0.288738i	$0.0932355\pi$
$389$	5591.24	+	9684.31i	0.728758	+	1.26225i	−0.228650	+	0.973509i	$0.573431\pi$
$390$		0			0
$391$	3930.40			0.508360
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7222.95	+	12510.5i	0.920066	+	1.59360i
$396$		0			0
$397$	1703.40	−	2950.37i	0.215343	−	0.372985i	−0.738036	−	0.674762i	$-0.764246\pi$
$397$	1703.40	−	2950.37i	0.215343	−	0.372985i	0.953379	+	0.301777i	$0.0975798\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	41.5201	−	71.9149i	0.00517061	−	0.00895575i	−0.863429	−	0.504471i	$-0.831687\pi$
$401$	41.5201	−	71.9149i	0.00517061	−	0.00895575i	0.868599	+	0.495515i	$0.165021\pi$
$402$		0			0
$403$	−5955.57	−	10315.4i	−0.736149	−	1.27505i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16108.0			−1.96178
$408$		0			0
$409$	−1228.10	−	2127.13i	−0.148473	−	0.257164i	0.782190	−	0.623040i	$-0.214103\pi$
$409$	−1228.10	−	2127.13i	−0.148473	−	0.257164i	−0.930663	+	0.365876i	$0.880769\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	344.489	−	5204.84i	0.0410440	−	0.620129i
$414$		0			0
$415$	18.2435	−	31.5987i	0.00215793	−	0.00373764i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3437.96			0.400848			0.200424	−	0.979709i	$-0.435768\pi$
$419$	3437.96			0.400848			0.200424	+	0.979709i	$0.435768\pi$
$420$		0			0
$421$	−5347.62			−0.619067			−0.309533	−	0.950889i	$-0.600173\pi$
$421$	−5347.62			−0.619067			−0.309533	+	0.950889i	$0.600173\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	332.210	−	575.404i	0.0379166	−	0.0656734i
$426$		0			0
$427$	9036.35	−	4449.05i	1.02412	−	0.504226i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	425.821	+	737.544i	0.0475895	+	0.0824275i	0.888839	−	0.458220i	$-0.151513\pi$
$431$	425.821	+	737.544i	0.0475895	+	0.0824275i	−0.841249	+	0.540647i	$0.818179\pi$
$432$		0			0
$433$	−3433.42			−0.381061			−0.190531	−	0.981681i	$-0.561021\pi$
$433$	−3433.42			−0.381061			−0.190531	+	0.981681i	$0.561021\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4806.92	+	8325.83i	0.526192	+	0.911392i
$438$		0			0
$439$	4869.20	−	8433.70i	0.529371	−	0.916898i	−0.470042	−	0.882644i	$-0.655761\pi$
$439$	4869.20	−	8433.70i	0.529371	−	0.916898i	0.999413	−	0.0342540i	$-0.0109055\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4967.48	−	8603.93i	0.532759	−	0.922765i	−0.466509	−	0.884516i	$-0.654489\pi$
$443$	4967.48	−	8603.93i	0.532759	−	0.922765i	0.999268	−	0.0382491i	$-0.0121780\pi$
$444$		0			0
$445$	7957.75	+	13783.2i	0.847716	+	1.46829i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7557.33			0.794327			0.397163	−	0.917748i	$-0.369995\pi$
$449$	7557.33			0.794327			0.397163	+	0.917748i	$0.369995\pi$
$450$		0			0
$451$	−5266.54	−	9121.92i	−0.549871	−	0.952405i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7699.43	−	3790.81i	0.793307	−	0.390585i
$456$		0			0
$457$	−7005.92	+	12134.6i	−0.717118	+	1.24209i	0.245018	+	0.969518i	$0.421206\pi$
$457$	−7005.92	+	12134.6i	−0.717118	+	1.24209i	−0.962137	+	0.272567i	$0.912127\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1669.61			0.168680			0.0843399	−	0.996437i	$-0.473122\pi$
$461$	1669.61			0.168680			0.0843399	+	0.996437i	$0.473122\pi$
$462$		0			0
$463$	14785.4			1.48409			0.742046	−	0.670349i	$-0.233856\pi$
$463$	14785.4			1.48409			0.742046	+	0.670349i	$0.233856\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2301.58	−	3986.46i	0.228061	−	0.395014i	−0.729172	−	0.684330i	$-0.760095\pi$
$467$	2301.58	−	3986.46i	0.228061	−	0.395014i	0.957233	+	0.289317i	$0.0934280\pi$
$468$		0			0
$469$	−586.309	+	8858.47i	−0.0577255	+	0.872167i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8682.35	−	15038.3i	−0.844006	−	1.46186i
$474$		0			0
$475$	1625.18			0.156987
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1738.68	+	3011.47i	0.165850	+	0.287261i	0.936957	−	0.349445i	$-0.113630\pi$
$479$	1738.68	+	3011.47i	0.165850	+	0.287261i	−0.771107	+	0.636706i	$0.780297\pi$
$480$		0			0
$481$	5865.39	−	10159.2i	0.556006	−	0.963030i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	491.996	−	852.163i	0.0460627	−	0.0797829i
$486$		0			0
$487$	−2172.08	−	3762.16i	−0.202108	−	0.350061i	0.747100	−	0.664712i	$-0.231446\pi$
$487$	−2172.08	−	3762.16i	−0.202108	−	0.350061i	−0.949207	+	0.314651i	$0.898112\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4982.89			−0.457993			−0.228997	−	0.973427i	$-0.573544\pi$
$491$	−4982.89			−0.457993			−0.228997	+	0.973427i	$0.573544\pi$
$492$		0			0
$493$	−678.578	−	1175.33i	−0.0619911	−	0.107372i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17018.4	−	11387.1i	−1.53598	−	1.02773i
$498$		0			0
$499$	−7663.08	+	13272.8i	−0.687468	+	1.19073i	0.285187	+	0.958472i	$0.407944\pi$
$499$	−7663.08	+	13272.8i	−0.687468	+	1.19073i	−0.972654	+	0.232257i	$0.925389\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1516.04			0.134387			0.0671936	−	0.997740i	$-0.478595\pi$
$503$	1516.04			0.134387			0.0671936	+	0.997740i	$0.478595\pi$
$504$		0			0
$505$	17077.5			1.50483
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1326.82	−	2298.12i	0.115541	−	0.200122i	−0.802455	−	0.596713i	$-0.796473\pi$
$509$	1326.82	−	2298.12i	0.115541	−	0.200122i	0.917996	+	0.396590i	$0.129807\pi$
$510$		0			0
$511$	292.752	−	4423.15i	0.0253436	−	0.382913i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1608.86	+	2786.64i	0.137660	+	0.238435i
$516$		0			0
$517$	−7262.82			−0.617830
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6566.06	−	11372.8i	−0.552139	−	0.956333i	−0.998120	−	0.0612905i	$-0.980478\pi$
$521$	−6566.06	−	11372.8i	−0.552139	−	0.956333i	0.445981	−	0.895042i	$-0.352855\pi$
$522$		0			0
$523$	1543.17	−	2672.85i	0.129021	−	0.223471i	−0.794276	−	0.607557i	$-0.792150\pi$
$523$	1543.17	−	2672.85i	0.129021	−	0.223471i	0.923298	+	0.384085i	$0.125483\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3553.58	−	6154.98i	0.293731	−	0.508757i
$528$		0			0
$529$	−9567.63	−	16571.6i	−0.786359	−	1.36201i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7670.80			0.623376
$534$		0			0
$535$	7855.86	+	13606.7i	0.634838	+	1.09957i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10692.7	−	13898.1i	0.854482	−	1.11064i
$540$		0			0
$541$	−463.047	+	802.022i	−0.0367985	+	0.0637368i	−0.883838	−	0.467793i	$-0.845049\pi$
$541$	−463.047	+	802.022i	−0.0367985	+	0.0637368i	0.847040	+	0.531530i	$0.178383\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3445.52			−0.270807
$546$		0			0
$547$	592.871			0.0463425			0.0231712	−	0.999732i	$-0.492624\pi$
$547$	592.871			0.0463425			0.0231712	+	0.999732i	$0.492624\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1659.82	−	2874.89i	0.128331	−	0.222276i
$552$		0			0
$553$	−19285.1	+	9495.02i	−1.48298	+	0.730144i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6122.67	−	10604.8i	−0.465756	−	0.806713i	0.533480	−	0.845813i	$-0.320884\pi$
$557$	−6122.67	−	10604.8i	−0.465756	−	0.806713i	−0.999235	+	0.0391003i	$0.987551\pi$
$558$		0			0
$559$	12646.0			0.956829
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7297.31	+	12639.3i	0.546261	+	0.946152i	0.998526	+	0.0542682i	$0.0172826\pi$
$563$	7297.31	+	12639.3i	0.546261	+	0.946152i	−0.452266	+	0.891883i	$0.649384\pi$
$564$		0			0
$565$	−329.300	+	570.364i	−0.0245199	+	0.0424697i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11455.6	−	19841.7i	0.844015	−	1.46188i	−0.0424590	−	0.999098i	$-0.513519\pi$
$569$	11455.6	−	19841.7i	0.844015	−	1.46188i	0.886474	−	0.462779i	$-0.153147\pi$
$570$		0			0
$571$	−2952.32	−	5113.57i	−0.216376	−	0.374774i	0.737321	−	0.675542i	$-0.236090\pi$
$571$	−2952.32	−	5113.57i	−0.216376	−	0.374774i	−0.953697	+	0.300768i	$0.902757\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5291.53			−0.383778
$576$		0			0
$577$	−4756.61	−	8238.68i	−0.343189	−	0.594421i	0.641834	−	0.766844i	$-0.278174\pi$
$577$	−4756.61	−	8238.68i	−0.343189	−	0.594421i	−0.985023	+	0.172423i	$0.944840\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	45.1242	+	30.1928i	0.00322214	+	0.00215595i
$582$		0			0
$583$	7924.56	−	13725.7i	0.562953	−	0.975064i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22790.6			1.60250			0.801252	−	0.598327i	$-0.204167\pi$
$587$	22790.6			1.60250			0.801252	+	0.598327i	$0.204167\pi$
$588$		0			0
$589$	17384.3			1.21614
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9131.39	+	15816.0i	−0.632346	+	1.09526i	0.354724	+	0.934971i	$0.384575\pi$
$593$	−9131.39	+	15816.0i	−0.632346	+	1.09526i	−0.987071	+	0.160285i	$0.948759\pi$
$594$		0			0
$595$	4255.92	+	2847.66i	0.293237	+	0.196206i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3479.05	+	6025.88i	0.237312	+	0.411037i	0.959942	−	0.280198i	$-0.0904003\pi$
$599$	3479.05	+	6025.88i	0.237312	+	0.411037i	−0.722630	+	0.691235i	$0.757067\pi$
$600$		0			0
$601$	2305.39			0.156471			0.0782353	−	0.996935i	$-0.475071\pi$
$601$	2305.39			0.156471			0.0782353	+	0.996935i	$0.475071\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7981.87	+	13825.0i	0.536379	+	0.929036i
$606$		0			0
$607$	8089.62	−	14011.6i	0.540935	−	0.936927i	−0.457916	−	0.888996i	$-0.651404\pi$
$607$	8089.62	−	14011.6i	0.540935	−	0.936927i	0.998851	−	0.0479312i	$-0.0152628\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2644.60	−	4580.58i	0.175105	−	0.303291i
$612$		0			0
$613$	−10270.4	−	17788.8i	−0.676699	−	1.17208i	−0.975969	−	0.217908i	$-0.930077\pi$
$613$	−10270.4	−	17788.8i	−0.676699	−	1.17208i	0.299271	−	0.954168i	$-0.403257\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6918.19			−0.451403			−0.225702	−	0.974196i	$-0.572467\pi$
$617$	−6918.19			−0.451403			−0.225702	+	0.974196i	$0.572467\pi$
$618$		0			0
$619$	4040.81	+	6998.89i	0.262381	+	0.454457i	0.966874	−	0.255254i	$-0.0821589\pi$
$619$	4040.81	+	6998.89i	0.262381	+	0.454457i	−0.704493	+	0.709711i	$0.748826\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21247.0	+	10461.0i	−1.36636	+	0.672728i
$624$		0			0
$625$	9234.52	−	15994.7i	0.591009	−	1.02366i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6999.54			0.443704
$630$		0			0
$631$	−27293.3			−1.72191			−0.860957	−	0.508677i	$-0.830135\pi$
$631$	−27293.3			−1.72191			−0.860957	+	0.508677i	$0.830135\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2761.20	−	4782.53i	0.172559	−	0.298880i
$636$		0			0
$637$	4871.86	+	11804.4i	0.303030	+	0.734237i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9627.82	+	16675.9i	0.593254	+	1.02755i	0.993791	+	0.111266i	$0.0354905\pi$
$641$	9627.82	+	16675.9i	0.593254	+	1.02755i	−0.400536	+	0.916281i	$0.631176\pi$
$642$		0			0
$643$	−19996.4			−1.22641			−0.613204	−	0.789925i	$-0.710120\pi$
$643$	−19996.4			−1.22641			−0.613204	+	0.789925i	$0.710120\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3532.10	+	6117.77i	0.214623	+	0.371738i	0.953156	−	0.302479i	$-0.0978144\pi$
$647$	3532.10	+	6117.77i	0.214623	+	0.371738i	−0.738533	+	0.674218i	$0.764481\pi$
$648$		0			0
$649$	−7199.47	+	12469.8i	−0.435445	+	0.754213i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6910.53	+	11969.4i	−0.414134	+	0.717302i	−0.995337	−	0.0964570i	$-0.969249\pi$
$653$	−6910.53	+	11969.4i	−0.414134	+	0.717302i	0.581203	+	0.813759i	$0.302582\pi$
$654$		0			0
$655$	13401.4	+	23211.9i	0.799443	+	1.38468i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7802.80			0.461235			0.230617	−	0.973044i	$-0.425925\pi$
$659$	7802.80			0.461235			0.230617	+	0.973044i	$0.425925\pi$
$660$		0			0
$661$	−7908.65	−	13698.2i	−0.465372	−	0.806048i	0.533846	−	0.845581i	$-0.320746\pi$
$661$	−7908.65	−	13698.2i	−0.465372	−	0.806048i	−0.999218	+	0.0395338i	$0.987413\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−827.204	+	12498.1i	−0.0482370	+	0.728806i
$666$		0			0
$667$	−5404.29	+	9360.51i	−0.313726	+	0.543389i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−27803.5			−1.59962
$672$		0			0
$673$	2943.30			0.168582			0.0842911	−	0.996441i	$-0.473137\pi$
$673$	2943.30			0.168582			0.0842911	+	0.996441i	$0.473137\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1585.74	+	2746.58i	−0.0900220	+	0.155923i	−0.907520	−	0.420009i	$-0.862027\pi$
$677$	−1585.74	+	2746.58i	−0.0900220	+	0.155923i	0.817498	+	0.575931i	$0.195360\pi$
$678$		0			0
$679$	1216.92	+	814.247i	0.0687792	+	0.0460205i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12226.6	−	21177.1i	−0.684975	−	1.18641i	−0.973445	−	0.228923i	$-0.926480\pi$
$683$	−12226.6	−	21177.1i	−0.684975	−	1.18641i	0.288470	−	0.957489i	$-0.406854\pi$
$684$		0			0
$685$	3274.70			0.182656
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5771.12	+	9995.87i	0.319103	+	0.552703i
$690$		0			0
$691$	−4297.95	+	7444.26i	−0.236616	+	0.409831i	−0.959741	−	0.280886i	$-0.909372\pi$
$691$	−4297.95	+	7444.26i	−0.236616	+	0.409831i	0.723125	+	0.690717i	$0.242705\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7254.69	−	12565.5i	0.395951	−	0.685808i
$696$		0			0
$697$	2288.51	+	3963.82i	0.124367	+	0.215409i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	21476.1			1.15712			0.578561	−	0.815639i	$-0.303615\pi$
$701$	21476.1			1.15712			0.578561	+	0.815639i	$0.303615\pi$
$702$		0			0
$703$	8560.51	+	14827.2i	0.459269	+	0.795477i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1678.24	+	25356.3i	−0.0892738	+	1.34883i
$708$		0			0
$709$	6769.46	−	11725.0i	0.358579	−	0.621077i	−0.629145	−	0.777288i	$-0.716595\pi$
$709$	6769.46	−	11725.0i	0.358579	−	0.621077i	0.987724	+	0.156211i	$0.0499281\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−56602.5			−2.97304
$714$		0			0
$715$	−23690.0			−1.23910
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6941.84	−	12023.6i	0.360065	−	0.623652i	−0.627906	−	0.778289i	$-0.716088\pi$
$719$	6941.84	−	12023.6i	0.360065	−	0.623652i	0.987971	+	0.154638i	$0.0494210\pi$
$720$		0			0
$721$	−4295.63	+	2114.95i	−0.221883	+	0.109244i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	913.577	+	1582.36i	0.0467992	+	0.0810585i
$726$		0			0
$727$	−18292.9			−0.933215			−0.466607	−	0.884465i	$-0.654524\pi$
$727$	−18292.9			−0.933215			−0.466607	+	0.884465i	$0.654524\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3772.81	+	6534.69i	0.190892	+	0.330635i
$732$		0			0
$733$	−7122.92	+	12337.3i	−0.358924	+	0.621674i	−0.987781	−	0.155846i	$-0.950190\pi$
$733$	−7122.92	+	12337.3i	−0.358924	+	0.621674i	0.628857	+	0.777521i	$0.283523\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12253.3	−	21223.3i	0.612422	−	1.06075i
$738$		0			0
$739$	681.947	+	1181.17i	0.0339456	+	0.0587956i	0.882499	−	0.470314i	$-0.155859\pi$
$739$	681.947	+	1181.17i	0.0339456	+	0.0587956i	−0.848553	+	0.529110i	$0.822526\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21789.4			−1.07588			−0.537938	−	0.842984i	$-0.680797\pi$
$743$	−21789.4			−1.07588			−0.537938	+	0.842984i	$0.680797\pi$
$744$		0			0
$745$	10985.0	+	19026.6i	0.540214	+	0.935678i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−20974.9	+	10327.0i	−1.02324	+	0.503793i
$750$		0			0
$751$	1059.78	−	1835.59i	0.0514937	−	0.0891898i	−0.839130	−	0.543932i	$-0.816935\pi$
$751$	1059.78	−	1835.59i	0.0514937	−	0.0891898i	0.890623	+	0.454742i	$0.150268\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33509.1			−1.61526
$756$		0			0
$757$	28202.4			1.35408			0.677038	−	0.735948i	$-0.263263\pi$
$757$	28202.4			1.35408			0.677038	+	0.735948i	$0.263263\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5573.52	−	9653.62i	0.265493	−	0.459847i	−0.702200	−	0.711980i	$-0.747799\pi$
$761$	5573.52	−	9653.62i	0.265493	−	0.459847i	0.967693	+	0.252133i	$0.0811321\pi$
$762$		0			0
$763$	338.597	−	5115.82i	0.0160656	−	0.242733i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5243.07	−	9081.26i	−0.246827	−	0.427517i
$768$		0			0
$769$	−4109.29			−0.192698			−0.0963491	−	0.995348i	$-0.530717\pi$
$769$	−4109.29			−0.192698			−0.0963491	+	0.995348i	$0.530717\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6945.68	+	12030.3i	0.323181	+	0.559766i	0.981143	−	0.193286i	$-0.0619144\pi$
$773$	6945.68	+	12030.3i	0.323181	+	0.559766i	−0.657962	+	0.753052i	$0.728581\pi$
$774$		0			0
$775$	−4784.22	+	8286.51i	−0.221747	+	0.384078i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5597.75	+	9695.59i	−0.257459	+	0.445931i
$780$		0			0
$781$	28262.0	+	48951.2i	1.29487	+	2.24278i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	24162.9			1.09861
$786$		0			0
$787$	4671.18	+	8090.71i	0.211575	+	0.366458i	0.952208	−	0.305452i	$-0.0988074\pi$
$787$	4671.18	+	8090.71i	0.211575	+	0.366458i	−0.740633	+	0.671910i	$0.765474\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−814.500	−	544.986i	−0.0366123	−	0.0244974i
$792$		0			0
$793$	10124.0	−	17535.4i	0.453361	−	0.785245i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24324.3			1.08107			0.540534	−	0.841322i	$-0.318222\pi$
$797$	24324.3			1.08107			0.540534	+	0.841322i	$0.318222\pi$
$798$		0			0
$799$	3155.97			0.139737
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6118.22	+	10597.1i	−0.268876	+	0.465706i
$804$		0			0
$805$	2693.34	−	40693.3i	0.117923	−	1.78168i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	17227.5	+	29838.8i	0.748684	+	1.29676i	0.948454	+	0.316915i	$0.102647\pi$
$809$	17227.5	+	29838.8i	0.748684	+	1.29676i	−0.199770	+	0.979843i	$0.564020\pi$
$810$		0			0
$811$	−8350.13			−0.361545			−0.180772	−	0.983525i	$-0.557860\pi$
$811$	−8350.13			−0.361545			−0.180772	+	0.983525i	$0.557860\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13086.2	+	22665.9i	0.562441	+	0.974176i
$816$		0			0
$817$	−9228.37	+	15984.0i	−0.395177	+	0.684467i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9417.38	+	16311.4i	−0.400327	+	0.693387i	−0.993765	−	0.111492i	$-0.964437\pi$
$821$	−9417.38	+	16311.4i	−0.400327	+	0.693387i	0.593438	+	0.804880i	$0.297770\pi$
$822$		0			0
$823$	−4828.38	−	8363.00i	−0.204504	−	0.354211i	0.745471	−	0.666538i	$-0.232225\pi$
$823$	−4828.38	−	8363.00i	−0.204504	−	0.354211i	−0.949975	+	0.312327i	$0.898891\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	20759.6			0.872892			0.436446	−	0.899731i	$-0.356237\pi$
$827$	20759.6			0.872892			0.436446	+	0.899731i	$0.356237\pi$
$828$		0			0
$829$	7808.05	+	13523.9i	0.327123	+	0.566593i	0.981940	−	0.189194i	$-0.0605876\pi$
$829$	7808.05	+	13523.9i	0.327123	+	0.566593i	−0.654817	+	0.755787i	$0.727254\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4646.36	+	6039.24i	−0.193262	+	0.251197i
$834$		0			0
$835$	14588.3	−	25267.7i	0.604610	−	1.04722i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	417.027			0.0171601			0.00858007	−	0.999963i	$-0.497269\pi$
$839$	417.027			0.0171601			0.00858007	+	0.999963i	$0.497269\pi$
$840$		0			0
$841$	−20656.8			−0.846973
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5045.98	+	8739.89i	−0.205428	+	0.355812i
$846$		0			0
$847$	−21311.4	+	10492.7i	−0.864544	+	0.425658i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−27872.7	−	48276.9i	−1.12275	−	1.94467i
$852$		0			0
$853$	−24917.4			−1.00018			−0.500092	−	0.865972i	$-0.666700\pi$
$853$	−24917.4			−1.00018			−0.500092	+	0.865972i	$0.666700\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22261.9	−	38558.7i	−0.887342	−	1.53692i	−0.843006	−	0.537904i	$-0.819216\pi$
$857$	−22261.9	−	38558.7i	−0.887342	−	1.53692i	−0.0443361	−	0.999017i	$-0.514117\pi$
$858$		0			0
$859$	12073.2	−	20911.4i	0.479548	−	0.830602i	−0.520176	−	0.854059i	$-0.674134\pi$
$859$	12073.2	−	20911.4i	0.479548	−	0.830602i	0.999725	+	0.0234566i	$0.00746716\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−13221.3	+	22900.0i	−0.521505	+	0.903273i	0.478182	+	0.878261i	$0.341296\pi$
$863$	−13221.3	+	22900.0i	−0.521505	+	0.903273i	−0.999687	+	0.0250123i	$0.992037\pi$
$864$		0			0
$865$	−21598.2	−	37409.2i	−0.848973	−	1.47046i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	59337.4			2.31632
$870$		0			0
$871$	8923.54	+	15456.0i	0.347144	+	0.601271i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	18217.4	+	12189.4i	0.703842	+	0.470944i
$876$		0			0
$877$	11258.1	−	19499.5i	0.433475	−	0.750801i	−0.563695	−	0.825983i	$-0.690621\pi$
$877$	11258.1	−	19499.5i	0.433475	−	0.750801i	0.997170	+	0.0751826i	$0.0239540\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−10120.6			−0.387027			−0.193514	−	0.981098i	$-0.561988\pi$
$881$	−10120.6			−0.387027			−0.193514	+	0.981098i	$0.561988\pi$
$882$		0			0
$883$	−20748.5			−0.790761			−0.395380	−	0.918517i	$-0.629387\pi$
$883$	−20748.5			−0.790761			−0.395380	+	0.918517i	$0.629387\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12749.7	−	22083.1i	0.482630	−	0.835939i	−0.517172	−	0.855882i	$-0.673015\pi$
$887$	12749.7	−	22083.1i	0.482630	−	0.835939i	0.999801	+	0.0199428i	$0.00634841\pi$
$888$		0			0
$889$	6829.63	+	4569.74i	0.257659	+	0.172401i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3859.78	+	6685.34i	0.144639	+	0.250522i
$894$		0			0
$895$	−11895.7			−0.444280
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9772.34	+	16926.2i	0.362543	+	0.627942i
$900$		0			0
$901$	−3443.52	+	5964.35i	−0.127326	+	0.220534i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	26263.1	−	45489.1i	0.964659	−	1.67084i
$906$		0			0
$907$	−18903.5	−	32741.8i	−0.692040	−	1.19865i	−0.971168	−	0.238395i	$-0.923379\pi$
$907$	−18903.5	−	32741.8i	−0.692040	−	1.19865i	0.279128	−	0.960254i	$-0.409954\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3230.08			0.117472			0.0587362	−	0.998274i	$-0.481293\pi$
$911$	3230.08			0.117472			0.0587362	+	0.998274i	$0.481293\pi$
$912$		0			0
$913$	−74.9364	−	129.794i	−0.00271635	−	0.00470486i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−35781.3	+	17616.9i	−1.28855	+	0.634419i
$918$		0			0
$919$	17671.6	−	30608.0i	0.634310	−	1.09866i	−0.352351	−	0.935868i	$-0.614618\pi$
$919$	17671.6	−	30608.0i	0.634310	−	1.09866i	0.986661	−	0.162789i	$-0.0520490\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−41164.0			−1.46796
$924$		0			0
$925$	−9423.55			−0.334967
$926$		0			0
$927$		0			0
$928$		0			0
$929$	16515.1	−	28605.0i	0.583254	−	1.01023i	−0.411836	−	0.911258i	$-0.635112\pi$
$929$	16515.1	−	28605.0i	0.583254	−	1.01023i	0.995091	−	0.0989684i	$-0.0315543\pi$
$930$		0			0
$931$	−18475.6	−	2456.42i	−0.650390	−	0.0864725i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7067.68	−	12241.6i	−0.247206	−	0.428174i
$936$		0			0
$937$	54695.9			1.90698			0.953488	−	0.301430i	$-0.0974640\pi$
$937$	54695.9			1.90698			0.953488	+	0.301430i	$0.0974640\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9127.64	−	15809.5i	−0.316209	−	0.547690i	0.663485	−	0.748190i	$-0.269077\pi$
$941$	−9127.64	−	15809.5i	−0.316209	−	0.547690i	−0.979694	+	0.200500i	$0.935743\pi$
$942$		0			0
$943$	18226.0	−	31568.4i	0.629397	−	1.09015i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3107.88	−	5383.00i	0.106645	−	0.184714i	−0.807764	−	0.589506i	$-0.799323\pi$
$947$	3107.88	−	5383.00i	0.106645	−	0.184714i	0.914409	+	0.404792i	$0.132656\pi$
$948$		0			0
$949$	−4455.64	−	7717.39i	−0.152409	−	0.263980i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8594.53			−0.292135			−0.146067	−	0.989275i	$-0.546662\pi$
$953$	−8594.53			−0.292135			−0.146067	+	0.989275i	$0.546662\pi$
$954$		0			0
$955$	21893.1	+	37920.0i	0.741826	+	1.28488i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−321.810	+	4862.18i	−0.0108361	+	0.163721i
$960$		0			0
$961$	−36280.3	+	62839.4i	−1.21783	+	2.10934i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	62451.1			2.08329
$966$		0			0
$967$	−17168.1			−0.570929			−0.285464	−	0.958389i	$-0.592148\pi$
$967$	−17168.1			−0.570929			−0.285464	+	0.958389i	$0.592148\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5963.11	−	10328.4i	0.197081	−	0.341354i	−0.750500	−	0.660871i	$-0.770187\pi$
$971$	5963.11	−	10328.4i	0.197081	−	0.341354i	0.947581	+	0.319517i	$0.103521\pi$
$972$		0			0
$973$	17944.0	+	12006.4i	0.591221	+	0.395589i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7019.12	+	12157.5i	0.229848	+	0.398108i	0.957763	−	0.287559i	$-0.0928438\pi$
$977$	7019.12	+	12157.5i	0.229848	+	0.398108i	−0.727915	+	0.685667i	$0.759510\pi$
$978$		0			0
$979$	65373.8			2.13417
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10175.7	+	17624.8i	0.330167	+	0.571866i	0.982544	−	0.186028i	$-0.0595617\pi$
$983$	10175.7	+	17624.8i	0.330167	+	0.571866i	−0.652378	+	0.757894i	$0.726228\pi$
$984$		0			0
$985$	17662.0	−	30591.6i	0.571329	−	0.989571i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30047.2	−	52043.3i	0.966072	−	1.67329i
$990$		0			0
$991$	16252.9	+	28150.8i	0.520978	+	0.902360i	0.999702	+	0.0243951i	$0.00776598\pi$
$991$	16252.9	+	28150.8i	0.520978	+	0.902360i	−0.478724	+	0.877965i	$0.658901\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4417.18			−0.140738
$996$		0			0
$997$	12423.5	+	21518.2i	0.394641	+	0.683539i	0.993055	−	0.117648i	$-0.0375356\pi$
$997$	12423.5	+	21518.2i	0.394641	+	0.683539i	−0.598414	+	0.801187i	$0.704202\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.k.f.37.2		4
3.2	odd	2		84.4.i.a.37.1	yes	4
7.2	even	3		1764.4.a.o.1.1		2
7.3	odd	6		1764.4.k.q.361.1		4
7.4	even	3	inner	252.4.k.f.109.2		4
7.5	odd	6		1764.4.a.y.1.2		2
7.6	odd	2		1764.4.k.q.1549.1		4
12.11	even	2		336.4.q.i.289.1		4
21.2	odd	6		588.4.a.i.1.2		2
21.5	even	6		588.4.a.f.1.1		2
21.11	odd	6		84.4.i.a.25.1	✓	4
21.17	even	6		588.4.i.j.361.2		4
21.20	even	2		588.4.i.j.373.2		4
84.11	even	6		336.4.q.i.193.1		4
84.23	even	6		2352.4.a.bt.1.2		2
84.47	odd	6		2352.4.a.bx.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.a.25.1	✓	4	21.11	odd	6
84.4.i.a.37.1	yes	4	3.2	odd	2
252.4.k.f.37.2		4	1.1	even	1	trivial
252.4.k.f.109.2		4	7.4	even	3	inner
336.4.q.i.193.1		4	84.11	even	6
336.4.q.i.289.1		4	12.11	even	2
588.4.a.f.1.1		2	21.5	even	6
588.4.a.i.1.2		2	21.2	odd	6
588.4.i.j.361.2		4	21.17	even	6
588.4.i.j.373.2		4	21.20	even	2
1764.4.a.o.1.1		2	7.2	even	3
1764.4.a.y.1.2		2	7.5	odd	6
1764.4.k.q.361.1		4	7.3	odd	6
1764.4.k.q.1549.1		4	7.6	odd	2
2352.4.a.bt.1.2		2	84.23	even	6
2352.4.a.bx.1.1		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.22311 - 10.7787i) q^{5} +(15.3924 + 10.2992i) q^{7} +O(q^{10})\)	\(q+(6.22311 - 10.7787i) q^{5} +(15.3924 + 10.2992i) q^{7} +(-25.5618 - 44.2743i) q^{11} +37.2311 q^{13} +(11.1076 + 19.2389i) q^{17} +(-27.1693 + 47.0587i) q^{19} +(88.4622 - 153.221i) q^{23} +(-14.9542 - 25.9015i) q^{25} -61.0916 q^{29} +(-159.962 - 277.063i) q^{31} +(206.801 - 101.818i) q^{35} +(157.540 - 272.867i) q^{37} +206.032 q^{41} +339.661 q^{43} +(71.0320 - 123.031i) q^{47} +(130.855 + 317.058i) q^{49} +(155.008 + 268.482i) q^{53} -636.295 q^{55} +(-140.825 - 243.916i) q^{59} +(271.924 - 470.987i) q^{61} +(231.693 - 401.305i) q^{65} +(239.680 + 415.137i) q^{67} -1105.63 q^{71} +(-119.675 - 207.283i) q^{73} +(62.5298 - 944.754i) q^{77} +(-580.333 + 1005.17i) q^{79} +2.93158 q^{83} +276.494 q^{85} +(-639.371 + 1107.42i) q^{89} +(573.078 + 383.449i) q^{91} +(338.156 + 585.703i) q^{95} +79.0596 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 11 q^{5} + 6 q^{7}+O(q^{10}) \) 4 * q + 11 * q^5 + 6 * q^7	\( 4 q + 11 q^{5} + 6 q^{7} - 5 q^{11} + 10 q^{13} + 100 q^{17} - 67 q^{19} + 76 q^{23} + 93 q^{25} - 550 q^{29} - 362 q^{31} + 466 q^{35} + 5 q^{37} + 324 q^{41} + 1442 q^{43} - 216 q^{47} + 190 q^{49} + 495 q^{53} - 1406 q^{55} + 173 q^{59} + 532 q^{61} + 510 q^{65} - 111 q^{67} - 3200 q^{71} - 1215 q^{73} + 653 q^{77} - 1460 q^{79} + 2818 q^{83} + 328 q^{85} - 1974 q^{89} + 1945 q^{91} + 658 q^{95} + 1122 q^{97}+O(q^{100}) \) 4 * q + 11 * q^5 + 6 * q^7 - 5 * q^11 + 10 * q^13 + 100 * q^17 - 67 * q^19 + 76 * q^23 + 93 * q^25 - 550 * q^29 - 362 * q^31 + 466 * q^35 + 5 * q^37 + 324 * q^41 + 1442 * q^43 - 216 * q^47 + 190 * q^49 + 495 * q^53 - 1406 * q^55 + 173 * q^59 + 532 * q^61 + 510 * q^65 - 111 * q^67 - 3200 * q^71 - 1215 * q^73 + 653 * q^77 - 1460 * q^79 + 2818 * q^83 + 328 * q^85 - 1974 * q^89 + 1945 * q^91 + 658 * q^95 + 1122 * q^97

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