LMFDB - Embedded newform 2160.3.bs.c.881.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2160,3,Mod(881,2160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2160, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("2160.881");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2160.bs (of order $6$, degree $2$, not 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:	$58.8557371018$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.8
Root			$-2.82877i$ of defining polynomial
Character	$\chi$	$=$	2160.881
Dual form			2160.3.bs.c.1601.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93649 + 1.11803i) q^{5} +(3.97472 + 6.88441i) q^{7} +O(q^{10})$	$q+(1.93649 + 1.11803i) q^{5} +(3.97472 + 6.88441i) q^{7} +(-0.0594938 + 0.0343488i) q^{11} +(4.33957 - 7.51635i) q^{13} -26.5641i q^{17} -26.6131 q^{19} +(-25.6980 - 14.8368i) q^{23} +(2.50000 + 4.33013i) q^{25} +(0.650245 - 0.375419i) q^{29} +(-17.3205 + 30.0000i) q^{31} +17.7755i q^{35} -48.4411 q^{37} +(-52.4148 - 30.2617i) q^{41} +(16.6490 + 28.8369i) q^{43} +(-25.1252 + 14.5060i) q^{47} +(-7.09677 + 12.2920i) q^{49} -6.99851i q^{53} -0.153612 q^{55} +(-57.1733 - 33.0090i) q^{59} +(9.50414 + 16.4617i) q^{61} +(16.8071 - 9.70357i) q^{65} +(51.2260 - 88.7261i) q^{67} +11.3543i q^{71} +53.9568 q^{73} +(-0.472942 - 0.273053i) q^{77} +(26.7351 + 46.3066i) q^{79} +(30.5050 - 17.6121i) q^{83} +(29.6996 - 51.4412i) q^{85} -74.9349i q^{89} +68.9943 q^{91} +(-51.5361 - 29.7544i) q^{95} +(-34.4893 - 59.7373i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 18 q^{11} - 10 q^{13} + 52 q^{19} - 54 q^{23} + 40 q^{25} + 54 q^{29} - 32 q^{31} + 44 q^{37} - 144 q^{41} + 124 q^{43} - 216 q^{47} - 54 q^{49} - 486 q^{59} + 62 q^{61} + 90 q^{65} - 14 q^{67} - 268 q^{73} - 702 q^{77} + 40 q^{79} + 522 q^{83} + 30 q^{85} - 136 q^{91} + 180 q^{95} - 142 q^{97}+O(q^{100}) $ 16 * q - 2 * q^7 - 18 * q^11 - 10 * q^13 + 52 * q^19 - 54 * q^23 + 40 * q^25 + 54 * q^29 - 32 * q^31 + 44 * q^37 - 144 * q^41 + 124 * q^43 - 216 * q^47 - 54 * q^49 - 486 * q^59 + 62 * q^61 + 90 * q^65 - 14 * q^67 - 268 * q^73 - 702 * q^77 + 40 * q^79 + 522 * q^83 + 30 * q^85 - 136 * q^91 + 180 * q^95 - 142 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		0			0
$7$	3.97472	+	6.88441i	0.567817	+	0.983488i	0.996781	+	0.0801664i	$0.0255452\pi$
$7$	3.97472	+	6.88441i	0.567817	+	0.983488i	−0.428965	+	0.903321i	$0.641121\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.0594938	+	0.0343488i	−0.00540853	+	0.00312262i	−0.502702	−	0.864460i	$-0.667661\pi$
$11$	−0.0594938	+	0.0343488i	−0.00540853	+	0.00312262i	0.497293	+	0.867582i	$0.334327\pi$
$12$		0			0
$13$	4.33957	−	7.51635i	0.333813	−	0.578181i	−0.649443	−	0.760410i	$-0.724998\pi$
$13$	4.33957	−	7.51635i	0.333813	−	0.578181i	0.983256	+	0.182229i	$0.0583313\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	26.5641i		−	1.56260i	−0.624158	−	0.781298i	$-0.714558\pi$
$17$		−	26.5641i		−	1.56260i	0.624158	−	0.781298i	$-0.285442\pi$
$18$		0			0
$19$	−26.6131			−1.40069			−0.700345	−	0.713805i	$-0.746971\pi$
$19$	−26.6131			−1.40069			−0.700345	+	0.713805i	$0.746971\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−25.6980	−	14.8368i	−1.11731	−	0.645077i	−0.176594	−	0.984284i	$-0.556508\pi$
$23$	−25.6980	−	14.8368i	−1.11731	−	0.645077i	−0.940712	+	0.339207i	$0.889841\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.650245	−	0.375419i	0.0224222	−	0.0129455i	−0.488747	−	0.872426i	$-0.662546\pi$
$29$	0.650245	−	0.375419i	0.0224222	−	0.0129455i	0.511169	+	0.859480i	$0.329213\pi$
$30$		0			0
$31$	−17.3205	+	30.0000i	−0.558727	+	0.967743i	0.438877	+	0.898547i	$0.355377\pi$
$31$	−17.3205	+	30.0000i	−0.558727	+	0.967743i	−0.997603	+	0.0691954i	$0.977957\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			17.7755i			0.507871i
$36$		0			0
$37$	−48.4411			−1.30922			−0.654609	−	0.755967i	$-0.727167\pi$
$37$	−48.4411			−1.30922			−0.654609	+	0.755967i	$0.727167\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−52.4148	−	30.2617i	−1.27841	−	0.738091i	−0.301855	−	0.953354i	$-0.597606\pi$
$41$	−52.4148	−	30.2617i	−1.27841	−	0.738091i	−0.976556	+	0.215263i	$0.930939\pi$
$42$		0			0
$43$	16.6490	+	28.8369i	0.387186	+	0.670626i	0.992070	−	0.125688i	$-0.0401138\pi$
$43$	16.6490	+	28.8369i	0.387186	+	0.670626i	−0.604884	+	0.796314i	$0.706780\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−25.1252	+	14.5060i	−0.534578	+	0.308639i	−0.742879	−	0.669426i	$-0.766540\pi$
$47$	−25.1252	+	14.5060i	−0.534578	+	0.308639i	0.208301	+	0.978065i	$0.433207\pi$
$48$		0			0
$49$	−7.09677	+	12.2920i	−0.144832	+	0.250856i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	6.99851i		−	0.132047i	−0.997818	−	0.0660237i	$-0.978969\pi$
$53$		−	6.99851i		−	0.132047i	0.997818	−	0.0660237i	$-0.0210313\pi$
$54$		0			0
$55$	−0.153612			−0.00279295
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−57.1733	−	33.0090i	−0.969039	−	0.559475i	−0.0700958	−	0.997540i	$-0.522331\pi$
$59$	−57.1733	−	33.0090i	−0.969039	−	0.559475i	−0.898943	+	0.438065i	$0.855664\pi$
$60$		0			0
$61$	9.50414	+	16.4617i	0.155806	+	0.269863i	0.933352	−	0.358962i	$-0.116869\pi$
$61$	9.50414	+	16.4617i	0.155806	+	0.269863i	−0.777547	+	0.628825i	$0.783536\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	16.8071	−	9.70357i	0.258570	−	0.149286i
$66$		0			0
$67$	51.2260	−	88.7261i	0.764568	−	1.32427i	−0.175907	−	0.984407i	$-0.556286\pi$
$67$	51.2260	−	88.7261i	0.764568	−	1.32427i	0.940475	−	0.339864i	$-0.110381\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			11.3543i			0.159919i	0.996798	+	0.0799597i	$0.0254792\pi$
$71$			11.3543i			0.159919i	−0.996798	+	0.0799597i	$0.974521\pi$
$72$		0			0
$73$	53.9568			0.739134			0.369567	−	0.929204i	$-0.379506\pi$
$73$	53.9568			0.739134			0.369567	+	0.929204i	$0.379506\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.472942	−	0.273053i	−0.00614211	−	0.00354615i
$78$		0			0
$79$	26.7351	+	46.3066i	0.338419	+	0.586159i	0.984136	−	0.177418i	$-0.0567746\pi$
$79$	26.7351	+	46.3066i	0.338419	+	0.586159i	−0.645717	+	0.763577i	$0.723441\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	30.5050	−	17.6121i	0.367530	−	0.212194i	−0.304849	−	0.952401i	$-0.598606\pi$
$83$	30.5050	−	17.6121i	0.367530	−	0.212194i	0.672379	+	0.740207i	$0.265273\pi$
$84$		0			0
$85$	29.6996	−	51.4412i	0.349407	−	0.605191i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	74.9349i		−	0.841965i	−0.907069	−	0.420983i	$-0.861685\pi$
$89$		−	74.9349i		−	0.841965i	0.907069	−	0.420983i	$-0.138315\pi$
$90$		0			0
$91$	68.9943			0.758179
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−51.5361	−	29.7544i	−0.542485	−	0.313204i
$96$		0			0
$97$	−34.4893	−	59.7373i	−0.355560	−	0.615848i	0.631653	−	0.775251i	$-0.282377\pi$
$97$	−34.4893	−	59.7373i	−0.355560	−	0.615848i	−0.987214	+	0.159402i	$0.949043\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−15.7347	+	9.08446i	−0.155790	+	0.0899451i	−0.575868	−	0.817543i	$-0.695336\pi$
$101$	−15.7347	+	9.08446i	−0.155790	+	0.0899451i	0.420079	+	0.907488i	$0.362003\pi$
$102$		0			0
$103$	−23.8052	+	41.2318i	−0.231118	+	0.400309i	−0.958137	−	0.286309i	$-0.907572\pi$
$103$	−23.8052	+	41.2318i	−0.231118	+	0.400309i	0.727019	+	0.686617i	$0.240905\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	149.680i		−	1.39888i	−0.714693	−	0.699439i	$-0.753433\pi$
$107$		−	149.680i		−	1.39888i	0.714693	−	0.699439i	$-0.246567\pi$
$108$		0			0
$109$	−36.8532			−0.338103			−0.169051	−	0.985607i	$-0.554070\pi$
$109$	−36.8532			−0.338103			−0.169051	+	0.985607i	$0.554070\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	53.1170	+	30.6671i	0.470062	+	0.271390i	0.716266	−	0.697828i	$-0.245850\pi$
$113$	53.1170	+	30.6671i	0.470062	+	0.271390i	−0.246204	+	0.969218i	$0.579183\pi$
$114$		0			0
$115$	−33.1760	−	57.4626i	−0.288487	−	0.499674i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	182.879	−	105.585i	1.53679	−	0.887269i
$120$		0			0
$121$	−60.4976	+	104.785i	−0.499980	+	0.865992i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−190.745			−1.50193			−0.750965	−	0.660342i	$-0.770412\pi$
$127$	−190.745			−1.50193			−0.750965	+	0.660342i	$0.770412\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−24.8473	−	14.3456i	−0.189674	−	0.109508i	0.402156	−	0.915571i	$-0.368261\pi$
$131$	−24.8473	−	14.3456i	−0.189674	−	0.109508i	−0.591830	+	0.806063i	$0.701594\pi$
$132$		0			0
$133$	−105.780	−	183.216i	−0.795335	−	1.37756i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−101.630	+	58.6761i	−0.741825	+	0.428293i	−0.822732	−	0.568429i	$-0.807551\pi$
$137$	−101.630	+	58.6761i	−0.741825	+	0.428293i	0.0809076	+	0.996722i	$0.474218\pi$
$138$		0			0
$139$	15.7198	−	27.2275i	0.113092	−	0.195881i	−0.803923	−	0.594733i	$-0.797258\pi$
$139$	15.7198	−	27.2275i	0.113092	−	0.195881i	0.917015	+	0.398852i	$0.130591\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			0.596235i			0.00416948i
$144$		0			0
$145$	1.67893			0.0115788
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−23.0951	−	13.3340i	−0.155001	−	0.0894896i	0.420494	−	0.907296i	$-0.361857\pi$
$149$	−23.0951	−	13.3340i	−0.155001	−	0.0894896i	−0.575494	+	0.817806i	$0.695190\pi$
$150$		0			0
$151$	−50.6215	−	87.6791i	−0.335242	−	0.580656i	0.648289	−	0.761394i	$-0.275485\pi$
$151$	−50.6215	−	87.6791i	−0.335242	−	0.580656i	−0.983531	+	0.180738i	$0.942151\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−67.0821	+	38.7299i	−0.432788	+	0.249870i
$156$		0			0
$157$	−139.688	+	241.946i	−0.889731	+	1.54106i	−0.0495387	+	0.998772i	$0.515775\pi$
$157$	−139.688	+	241.946i	−0.889731	+	1.54106i	−0.840193	+	0.542288i	$0.817558\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	235.888i		−	1.46514i
$162$		0			0
$163$	−246.776			−1.51396			−0.756982	−	0.653436i	$-0.773327\pi$
$163$	−246.776			−1.51396			−0.756982	+	0.653436i	$0.773327\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	72.9485	+	42.1168i	0.436817	+	0.252197i	0.702247	−	0.711934i	$-0.252180\pi$
$167$	72.9485	+	42.1168i	0.436817	+	0.252197i	−0.265429	+	0.964130i	$0.585514\pi$
$168$		0			0
$169$	46.8363	+	81.1228i	0.277138	+	0.480017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	164.087	−	94.7357i	0.948480	−	0.547605i	0.0558715	−	0.998438i	$-0.482206\pi$
$173$	164.087	−	94.7357i	0.948480	−	0.547605i	0.892608	+	0.450833i	$0.148873\pi$
$174$		0			0
$175$	−19.8736	+	34.4221i	−0.113563	+	0.196698i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	111.227i		−	0.621378i	−0.950512	−	0.310689i	$-0.899440\pi$
$179$		−	111.227i		−	0.621378i	0.950512	−	0.310689i	$-0.100560\pi$
$180$		0			0
$181$	219.388			1.21209			0.606046	−	0.795430i	$-0.292755\pi$
$181$	219.388			1.21209			0.606046	+	0.795430i	$0.292755\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−93.8058	−	54.1588i	−0.507058	−	0.292750i
$186$		0			0
$187$	0.912445	+	1.58040i	0.00487939	+	0.00845135i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−31.7265	+	18.3173i	−0.166107	+	0.0959020i	−0.580749	−	0.814083i	$-0.697240\pi$
$191$	−31.7265	+	18.3173i	−0.166107	+	0.0959020i	0.414642	+	0.909985i	$0.363907\pi$
$192$		0			0
$193$	−76.2245	+	132.025i	−0.394946	+	0.684066i	−0.993094	−	0.117319i	$-0.962570\pi$
$193$	−76.2245	+	132.025i	−0.394946	+	0.684066i	0.598149	+	0.801385i	$0.295903\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			35.7863i			0.181657i	0.995867	+	0.0908283i	$0.0289514\pi$
$197$			35.7863i			0.181657i	−0.995867	+	0.0908283i	$0.971049\pi$
$198$		0			0
$199$	104.576			0.525509			0.262754	−	0.964863i	$-0.415369\pi$
$199$	104.576			0.525509			0.262754	+	0.964863i	$0.415369\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.16908	+	2.98437i	0.0254635	+	0.0147013i
$204$		0			0
$205$	−67.6673	−	117.203i	−0.330084	−	0.571723i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.58332	−	0.914128i	0.00757567	−	0.00437382i
$210$		0			0
$211$	−54.4388	+	94.2907i	−0.258004	+	0.446875i	−0.965707	−	0.259634i	$-0.916398\pi$
$211$	−54.4388	+	94.2907i	−0.258004	+	0.446875i	0.707703	+	0.706510i	$0.249731\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			74.4566i			0.346310i
$216$		0			0
$217$	−275.377			−1.26902
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−199.665	−	115.277i	−0.903464	−	0.521615i
$222$		0			0
$223$	−134.485	−	232.934i	−0.603070	−	1.04455i	−0.992353	−	0.123430i	$-0.960610\pi$
$223$	−134.485	−	232.934i	−0.603070	−	1.04455i	0.389283	−	0.921118i	$-0.372723\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−71.7385	+	41.4183i	−0.316029	+	0.182459i	−0.649621	−	0.760258i	$-0.725072\pi$
$227$	−71.7385	+	41.4183i	−0.316029	+	0.182459i	0.333592	+	0.942717i	$0.391739\pi$
$228$		0			0
$229$	94.5387	−	163.746i	0.412833	−	0.715047i	−0.582366	−	0.812927i	$-0.697873\pi$
$229$	94.5387	−	163.746i	0.412833	−	0.715047i	0.995198	+	0.0978799i	$0.0312061\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			273.780i			1.17502i	0.809216	+	0.587512i	$0.199892\pi$
$233$			273.780i			1.17502i	−0.809216	+	0.587512i	$0.800108\pi$
$234$		0			0
$235$	−64.8729			−0.276055
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−44.2330	−	25.5379i	−0.185075	−	0.106853i	0.404600	−	0.914494i	$-0.367411\pi$
$239$	−44.2330	−	25.5379i	−0.185075	−	0.106853i	−0.589675	+	0.807641i	$0.700744\pi$
$240$		0			0
$241$	−95.5289	−	165.461i	−0.396385	−	0.686560i	0.596892	−	0.802322i	$-0.296402\pi$
$241$	−95.5289	−	165.461i	−0.396385	−	0.686560i	−0.993277	+	0.115762i	$0.963069\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−27.4857	+	15.8689i	−0.112186	+	0.0647709i
$246$		0			0
$247$	−115.489	+	200.034i	−0.467569	+	0.809852i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	169.083i		−	0.673637i	−0.941570	−	0.336818i	$-0.890649\pi$
$251$		−	169.083i		−	0.673637i	0.941570	−	0.336818i	$-0.109351\pi$
$252$		0			0
$253$	2.03850			0.00805731
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−247.257	−	142.754i	−0.962090	−	0.555463i	−0.0652745	−	0.997867i	$-0.520792\pi$
$257$	−247.257	−	142.754i	−0.962090	−	0.555463i	−0.896816	+	0.442404i	$0.854126\pi$
$258$		0			0
$259$	−192.540	−	333.489i	−0.743396	−	1.28760i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	62.0090	−	35.8009i	0.235776	−	0.136125i	−0.377458	−	0.926027i	$-0.623202\pi$
$263$	62.0090	−	35.8009i	0.235776	−	0.136125i	0.613234	+	0.789902i	$0.289868\pi$
$264$		0			0
$265$	7.82457	−	13.5526i	0.0295267	−	0.0511417i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			39.6463i			0.147384i	0.997281	+	0.0736920i	$0.0234782\pi$
$269$			39.6463i			0.147384i	−0.997281	+	0.0736920i	$0.976522\pi$
$270$		0			0
$271$	−397.832			−1.46801			−0.734007	−	0.679142i	$-0.762352\pi$
$271$	−397.832			−1.46801			−0.734007	+	0.679142i	$0.762352\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.297469	−	0.171744i	−0.00108171	−	0.000624523i
$276$		0			0
$277$	−68.4595	−	118.575i	−0.247146	−	0.428070i	0.715587	−	0.698524i	$-0.246159\pi$
$277$	−68.4595	−	118.575i	−0.247146	−	0.428070i	−0.962733	+	0.270454i	$0.912826\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	381.758	−	220.408i	1.35857	−	0.784370i	0.369137	−	0.929375i	$-0.379653\pi$
$281$	381.758	−	220.408i	1.35857	−	0.784370i	0.989431	+	0.145005i	$0.0463198\pi$
$282$		0			0
$283$	84.1670	−	145.782i	0.297410	−	0.515129i	−0.678133	−	0.734939i	$-0.737211\pi$
$283$	84.1670	−	145.782i	0.297410	−	0.515129i	0.975543	+	0.219810i	$0.0705439\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	481.127i		−	1.67640i
$288$		0			0
$289$	−416.653			−1.44171
$290$		0			0
$291$		0			0
$292$		0			0
$293$	388.737	+	224.438i	1.32675	+	0.765999i	0.984795	−	0.173718i	$-0.0555782\pi$
$293$	388.737	+	224.438i	1.32675	+	0.765999i	0.341953	+	0.939717i	$0.388912\pi$
$294$		0			0
$295$	−73.8104	−	127.843i	−0.250205	−	0.433367i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−223.037	+	128.770i	−0.745943	+	0.430670i
$300$		0			0
$301$	−132.350	+	229.237i	−0.439702	+	0.761585i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			42.5038i			0.139357i
$306$		0			0
$307$	492.512			1.60427			0.802137	−	0.597140i	$-0.203696\pi$
$307$	492.512			1.60427			0.802137	+	0.597140i	$0.203696\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	71.5497	+	41.3092i	0.230063	+	0.132827i	0.610601	−	0.791938i	$-0.290928\pi$
$311$	71.5497	+	41.3092i	0.230063	+	0.132827i	−0.380538	+	0.924765i	$0.624261\pi$
$312$		0			0
$313$	−96.1876	−	166.602i	−0.307308	−	0.532274i	0.670464	−	0.741942i	$-0.266095\pi$
$313$	−96.1876	−	166.602i	−0.307308	−	0.532274i	−0.977773	+	0.209668i	$0.932762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	31.6063	−	18.2479i	0.0997043	−	0.0575643i	−0.449319	−	0.893372i	$-0.648333\pi$
$317$	31.6063	−	18.2479i	0.0997043	−	0.0575643i	0.549023	+	0.835807i	$0.315000\pi$
$318$		0			0
$319$	−0.0257904	+	0.0446702i	−8.08476e−5	+	0.000140032i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			706.954i			2.18871i
$324$		0			0
$325$	43.3957			0.133525
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−199.731	−	115.315i	−0.607085	−	0.350501i
$330$		0			0
$331$	142.388	+	246.624i	0.430176	+	0.745087i	0.996888	−	0.0788292i	$-0.0251182\pi$
$331$	142.388	+	246.624i	0.430176	+	0.745087i	−0.566712	+	0.823916i	$0.691785\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	198.398	−	114.545i	0.592232	−	0.341925i
$336$		0			0
$337$	122.391	−	211.988i	0.363178	−	0.629043i	−0.625304	−	0.780381i	$-0.715025\pi$
$337$	122.391	−	211.988i	0.363178	−	0.629043i	0.988482	+	0.151338i	$0.0483583\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	2.37975i		−	0.00697875i
$342$		0			0
$343$	276.692			0.806681
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−219.275	−	126.599i	−0.631918	−	0.364838i	0.149577	−	0.988750i	$-0.452209\pi$
$347$	−219.275	−	126.599i	−0.631918	−	0.364838i	−0.781494	+	0.623912i	$0.785542\pi$
$348$		0			0
$349$	−259.518	−	449.498i	−0.743603	−	1.28796i	−0.950845	−	0.309669i	$-0.899782\pi$
$349$	−259.518	−	449.498i	−0.743603	−	1.28796i	0.207241	−	0.978290i	$-0.433551\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−595.687	+	343.920i	−1.68750	+	0.974277i	−0.731072	+	0.682300i	$0.760980\pi$
$353$	−595.687	+	343.920i	−1.68750	+	0.974277i	−0.956425	+	0.291977i	$0.905687\pi$
$354$		0			0
$355$	−12.6945	+	21.9875i	−0.0357590	+	0.0619365i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	340.488i		−	0.948435i	−0.880408	−	0.474218i	$-0.842731\pi$
$359$		−	340.488i		−	0.948435i	0.880408	−	0.474218i	$-0.157269\pi$
$360$		0			0
$361$	347.258			0.961933
$362$		0			0
$363$		0			0
$364$		0			0
$365$	104.487	+	60.3256i	0.286266	+	0.165275i
$366$		0			0
$367$	−133.356	−	230.980i	−0.363368	−	0.629373i	0.625144	−	0.780509i	$-0.285040\pi$
$367$	−133.356	−	230.980i	−0.363368	−	0.629373i	−0.988513	+	0.151136i	$0.951707\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	48.1806	−	27.8171i	0.129867	−	0.0749787i
$372$		0			0
$373$	−140.463	+	243.288i	−0.376576	+	0.652248i	−0.990562	−	0.137069i	$-0.956232\pi$
$373$	−140.463	+	243.288i	−0.376576	+	0.652248i	0.613986	+	0.789317i	$0.289565\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	6.51663i		−	0.0172855i
$378$		0			0
$379$	532.151			1.40409			0.702046	−	0.712131i	$-0.252270\pi$
$379$	532.151			1.40409			0.702046	+	0.712131i	$0.252270\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	316.930	+	182.979i	0.827493	+	0.477753i	0.852993	−	0.521922i	$-0.174785\pi$
$383$	316.930	+	182.979i	0.827493	+	0.477753i	−0.0255008	+	0.999675i	$0.508118\pi$
$384$		0			0
$385$	−0.610566	−	1.05753i	−0.00158589	−	0.00274683i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	82.2932	−	47.5120i	0.211551	−	0.122139i	−0.390481	−	0.920611i	$-0.627691\pi$
$389$	82.2932	−	47.5120i	0.211551	−	0.122139i	0.602032	+	0.798472i	$0.294358\pi$
$390$		0			0
$391$	−394.126	+	682.646i	−1.00799	+	1.74590i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			119.563i			0.302691i
$396$		0			0
$397$	691.691			1.74229			0.871147	−	0.491023i	$-0.163377\pi$
$397$	691.691			1.74229			0.871147	+	0.491023i	$0.163377\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−57.8355	−	33.3913i	−0.144228	−	0.0832701i	0.426149	−	0.904653i	$-0.359870\pi$
$401$	−57.8355	−	33.3913i	−0.144228	−	0.0832701i	−0.570378	+	0.821383i	$0.693203\pi$
$402$		0			0
$403$	150.327	+	260.374i	0.373020	+	0.646090i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.88195	−	1.66389i	0.00708095	−	0.00408819i
$408$		0			0
$409$	−55.5485	+	96.2128i	−0.135815	+	0.235239i	−0.925909	−	0.377748i	$-0.876699\pi$
$409$	−55.5485	+	96.2128i	−0.135815	+	0.235239i	0.790093	+	0.612987i	$0.210032\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	524.806i		−	1.27072i
$414$		0			0
$415$	78.7635			0.189792
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−333.765	−	192.699i	−0.796576	−	0.459903i	0.0456967	−	0.998955i	$-0.485449\pi$
$419$	−333.765	−	192.699i	−0.796576	−	0.459903i	−0.842272	+	0.539052i	$0.818783\pi$
$420$		0			0
$421$	32.4176	+	56.1490i	0.0770015	+	0.133371i	0.901955	−	0.431830i	$-0.142132\pi$
$421$	32.4176	+	56.1490i	0.0770015	+	0.133371i	−0.824953	+	0.565201i	$0.808799\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	115.026	−	66.4103i	0.270650	−	0.156260i
$426$		0			0
$427$	−75.5525	+	130.861i	−0.176938	+	0.306466i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			205.696i			0.477253i	0.971111	+	0.238626i	$0.0766972\pi$
$431$			205.696i			0.477253i	−0.971111	+	0.238626i	$0.923303\pi$
$432$		0			0
$433$	−346.035			−0.799156			−0.399578	−	0.916699i	$-0.630843\pi$
$433$	−346.035			−0.799156			−0.399578	+	0.916699i	$0.630843\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	683.905	+	394.853i	1.56500	+	0.903553i
$438$		0			0
$439$	−276.226	−	478.437i	−0.629216	−	1.08983i	−0.987709	−	0.156301i	$-0.950043\pi$
$439$	−276.226	−	478.437i	−0.629216	−	1.08983i	0.358494	−	0.933532i	$-0.383290\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	37.5855	−	21.7000i	0.0848430	−	0.0489841i	−0.456978	−	0.889478i	$-0.651068\pi$
$443$	37.5855	−	21.7000i	0.0848430	−	0.0489841i	0.541821	+	0.840494i	$0.317735\pi$
$444$		0			0
$445$	83.7798	−	145.111i	0.188269	−	0.326092i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	651.887i		−	1.45186i	−0.687766	−	0.725932i	$-0.741409\pi$
$449$		−	651.887i		−	1.45186i	0.687766	−	0.725932i	$-0.258591\pi$
$450$		0			0
$451$	4.15781			0.00921909
$452$		0			0
$453$		0			0
$454$		0			0
$455$	133.607	+	77.1379i	0.293641	+	0.169534i
$456$		0			0
$457$	230.589	+	399.393i	0.504572	+	0.873945i	0.999986	+	0.00528755i	$0.00168309\pi$
$457$	230.589	+	399.393i	0.504572	+	0.873945i	−0.495414	+	0.868657i	$0.664984\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	632.194	−	364.998i	1.37135	−	0.791752i	0.380256	−	0.924881i	$-0.375836\pi$
$461$	632.194	−	364.998i	1.37135	−	0.791752i	0.991099	+	0.133129i	$0.0425026\pi$
$462$		0			0
$463$	−4.69689	+	8.13525i	−0.0101445	+	0.0175707i	−0.871053	−	0.491189i	$-0.836562\pi$
$463$	−4.69689	+	8.13525i	−0.0101445	+	0.0175707i	0.860909	+	0.508760i	$0.169896\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	56.2899i		−	0.120535i	−0.998182	−	0.0602676i	$-0.980805\pi$
$467$		−	56.2899i		−	0.120535i	0.998182	−	0.0602676i	$-0.0191954\pi$
$468$		0			0
$469$	814.436			1.73654
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.98102	−	1.14375i	−0.00418821	−	0.00241807i
$474$		0			0
$475$	−66.5328	−	115.238i	−0.140069	−	0.242607i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−649.023	+	374.714i	−1.35495	+	0.782283i	−0.988939	−	0.148325i	$-0.952612\pi$
$479$	−649.023	+	374.714i	−1.35495	+	0.782283i	−0.366016	+	0.930609i	$0.619278\pi$
$480$		0			0
$481$	−210.213	+	364.100i	−0.437034	+	0.756965i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	154.241i		−	0.318023i
$486$		0			0
$487$	440.830			0.905196			0.452598	−	0.891715i	$-0.350497\pi$
$487$	440.830			0.905196			0.452598	+	0.891715i	$0.350497\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−327.433	−	189.043i	−0.666869	−	0.385017i	0.128020	−	0.991772i	$-0.459138\pi$
$491$	−327.433	−	189.043i	−0.666869	−	0.385017i	−0.794889	+	0.606755i	$0.792471\pi$
$492$		0			0
$493$	−9.97268	−	17.2732i	−0.0202286	−	0.0350369i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−78.1675	+	45.1300i	−0.157279	+	0.0908049i
$498$		0			0
$499$	−286.566	+	496.347i	−0.574281	+	0.994684i	0.421838	+	0.906671i	$0.361385\pi$
$499$	−286.566	+	496.347i	−0.574281	+	0.994684i	−0.996119	+	0.0880128i	$0.971948\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	300.050i		−	0.596522i	−0.954484	−	0.298261i	$-0.903593\pi$
$503$		−	300.050i		−	0.596522i	0.954484	−	0.298261i	$-0.0964065\pi$
$504$		0			0
$505$	−40.6269			−0.0804494
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−643.429	−	371.484i	−1.26410	−	0.729831i	−0.290238	−	0.956954i	$-0.593735\pi$
$509$	−643.429	−	371.484i	−1.26410	−	0.729831i	−0.973866	+	0.227124i	$0.927068\pi$
$510$		0			0
$511$	214.463	+	371.461i	0.419693	+	0.726930i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−92.1971	+	53.2300i	−0.179023	+	0.103359i
$516$		0			0
$517$	0.996528	−	1.72604i	0.00192752	−	0.00333856i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			682.606i			1.31018i	0.755549	+	0.655092i	$0.227370\pi$
$521$			682.606i			1.31018i	−0.755549	+	0.655092i	$0.772630\pi$
$522$		0			0
$523$	−430.700			−0.823518			−0.411759	−	0.911293i	$-0.635085\pi$
$523$	−430.700			−0.823518			−0.411759	+	0.911293i	$0.635085\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	796.925	+	460.105i	1.51219	+	0.873064i
$528$		0			0
$529$	175.759	+	304.424i	0.332249	+	0.575471i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−454.916	+	262.646i	−0.853500	+	0.492769i
$534$		0			0
$535$	167.347	−	289.854i	0.312798	−	0.541783i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	0.975061i		−	0.00180902i
$540$		0			0
$541$	−297.028			−0.549034			−0.274517	−	0.961582i	$-0.588518\pi$
$541$	−297.028			−0.549034			−0.274517	+	0.961582i	$0.588518\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−71.3659	−	41.2031i	−0.130947	−	0.0756020i
$546$		0			0
$547$	425.338	+	736.708i	0.777584	+	1.34681i	0.933331	+	0.359018i	$0.116888\pi$
$547$	425.338	+	736.708i	0.777584	+	1.34681i	−0.155747	+	0.987797i	$0.549778\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−17.3050	+	9.99107i	−0.0314066	+	0.0181326i
$552$		0			0
$553$	−212.529	+	368.111i	−0.384320	+	0.665662i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	571.248i		−	1.02558i	−0.858514	−	0.512790i	$-0.828612\pi$
$557$		−	571.248i		−	1.02558i	0.858514	−	0.512790i	$-0.171388\pi$
$558$		0			0
$559$	288.998			0.516991
$560$		0			0
$561$		0			0
$562$		0			0
$563$	451.760	+	260.824i	0.802415	+	0.463275i	0.844315	−	0.535847i	$-0.180008\pi$
$563$	451.760	+	260.824i	0.802415	+	0.463275i	−0.0418998	+	0.999122i	$0.513341\pi$
$564$		0			0
$565$	68.5737	+	118.773i	0.121369	+	0.210218i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−912.977	+	527.108i	−1.60453	+	0.926376i	−0.613964	+	0.789334i	$0.710426\pi$
$569$	−912.977	+	527.108i	−1.60453	+	0.926376i	−0.990565	+	0.137042i	$0.956240\pi$
$570$		0			0
$571$	182.461	−	316.032i	0.319546	−	0.553470i	−0.660847	−	0.750521i	$-0.729803\pi$
$571$	182.461	−	316.032i	0.319546	−	0.553470i	0.980393	+	0.197050i	$0.0631362\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	148.368i		−	0.258031i
$576$		0			0
$577$	77.3098			0.133986			0.0669929	−	0.997753i	$-0.478660\pi$
$577$	77.3098			0.133986			0.0669929	+	0.997753i	$0.478660\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	242.497	+	140.006i	0.417379	+	0.240974i
$582$		0			0
$583$	0.240390	+	0.416368i	0.000412333	+	0.000714182i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−113.472	+	65.5132i	−0.193309	+	0.111607i	−0.593531	−	0.804811i	$-0.702266\pi$
$587$	−113.472	+	65.5132i	−0.193309	+	0.111607i	0.400222	+	0.916418i	$0.368933\pi$
$588$		0			0
$589$	460.953	−	798.394i	0.782603	−	1.35551i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			525.116i			0.885525i	0.896639	+	0.442762i	$0.146002\pi$
$593$			525.116i			0.885525i	−0.896639	+	0.442762i	$0.853998\pi$
$594$		0			0
$595$	472.190			0.793597
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−851.013	−	491.333i	−1.42072	−	0.820255i	−0.424363	−	0.905492i	$-0.639502\pi$
$599$	−851.013	−	491.333i	−1.42072	−	0.820255i	−0.996361	+	0.0852374i	$0.972835\pi$
$600$		0			0
$601$	415.553	+	719.759i	0.691436	+	1.19760i	0.971367	+	0.237582i	$0.0763549\pi$
$601$	415.553	+	719.759i	0.691436	+	1.19760i	−0.279932	+	0.960020i	$0.590312\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−234.306	+	135.277i	−0.387283	+	0.223598i
$606$		0			0
$607$	−83.8988	+	145.317i	−0.138219	+	0.239402i	−0.926822	−	0.375500i	$-0.877471\pi$
$607$	−83.8988	+	145.317i	−0.138219	+	0.239402i	0.788604	+	0.614902i	$0.210804\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			251.799i			0.412110i
$612$		0			0
$613$	833.750			1.36011			0.680057	−	0.733159i	$-0.261955\pi$
$613$	833.750			1.36011			0.680057	+	0.733159i	$0.261955\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	40.4387	+	23.3473i	0.0655408	+	0.0378400i	0.532412	−	0.846485i	$-0.321286\pi$
$617$	40.4387	+	23.3473i	0.0655408	+	0.0378400i	−0.466872	+	0.884325i	$0.654619\pi$
$618$		0			0
$619$	−499.429	−	865.037i	−0.806833	−	1.39748i	−0.915047	−	0.403347i	$-0.867847\pi$
$619$	−499.429	−	865.037i	−0.806833	−	1.39748i	0.108214	−	0.994128i	$-0.465487\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	515.883	−	297.845i	0.828063	−	0.478082i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1286.80i			2.04578i
$630$		0			0
$631$	676.922			1.07278			0.536388	−	0.843971i	$-0.319788\pi$
$631$	676.922			1.07278			0.536388	+	0.843971i	$0.319788\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−369.377	−	213.260i	−0.581695	−	0.335842i
$636$		0			0
$637$	61.5938	+	106.684i	0.0966936	+	0.167478i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−620.711	+	358.367i	−0.968347	+	0.559076i	−0.898732	−	0.438498i	$-0.855511\pi$
$641$	−620.711	+	358.367i	−0.968347	+	0.559076i	−0.0696153	+	0.997574i	$0.522177\pi$
$642$		0			0
$643$	−176.092	+	305.000i	−0.273860	+	0.474339i	−0.969847	−	0.243715i	$-0.921634\pi$
$643$	−176.092	+	305.000i	−0.273860	+	0.474339i	0.695987	+	0.718054i	$0.254967\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			719.658i			1.11230i	0.831082	+	0.556150i	$0.187722\pi$
$647$			719.658i			1.11230i	−0.831082	+	0.556150i	$0.812278\pi$
$648$		0			0
$649$	4.53528			0.00698810
$650$		0			0
$651$		0			0
$652$		0			0
$653$	925.220	+	534.176i	1.41688	+	0.818034i	0.996023	−	0.0890951i	$-0.0283975\pi$
$653$	925.220	+	534.176i	1.41688	+	0.818034i	0.420853	+	0.907129i	$0.361731\pi$
$654$		0			0
$655$	−32.0777	−	55.5602i	−0.0489736	−	0.0848248i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	896.771	−	517.751i	1.36081	−	0.785662i	0.371075	−	0.928603i	$-0.378989\pi$
$659$	896.771	−	517.751i	1.36081	−	0.785662i	0.989731	+	0.142941i	$0.0456560\pi$
$660$		0			0
$661$	559.316	−	968.764i	0.846166	−	1.46560i	−0.0384381	−	0.999261i	$-0.512238\pi$
$661$	559.316	−	968.764i	0.846166	−	1.46560i	0.884604	−	0.466342i	$-0.154428\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	473.061i		−	0.711370i
$666$		0			0
$667$	−22.2800			−0.0334033
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.13087	−	0.652911i	−0.00168536	−	0.000973042i
$672$		0			0
$673$	199.783	+	346.035i	0.296855	+	0.514168i	0.975415	−	0.220377i	$-0.0707289\pi$
$673$	199.783	+	346.035i	0.296855	+	0.514168i	−0.678560	+	0.734545i	$0.737396\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−43.7403	+	25.2535i	−0.0646091	+	0.0373021i	−0.531957	−	0.846772i	$-0.678543\pi$
$677$	−43.7403	+	25.2535i	−0.0646091	+	0.0373021i	0.467347	+	0.884074i	$0.345210\pi$
$678$		0			0
$679$	274.171	−	474.878i	0.403786	−	0.699378i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			857.907i			1.25609i	0.778179	+	0.628043i	$0.216144\pi$
$683$			857.907i			1.25609i	−0.778179	+	0.628043i	$0.783856\pi$
$684$		0			0
$685$	−262.408			−0.383077
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−52.6033	−	30.3705i	−0.0763473	−	0.0440791i
$690$		0			0
$691$	−106.360	−	184.220i	−0.153921	−	0.266599i	0.778744	−	0.627341i	$-0.215857\pi$
$691$	−106.360	−	184.220i	−0.153921	−	0.266599i	−0.932666	+	0.360742i	$0.882524\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	60.8824	−	35.1505i	0.0876006	−	0.0505763i
$696$		0			0
$697$	−803.877	+	1392.36i	−1.15334	+	1.99764i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			991.279i			1.41409i	0.707167	+	0.707046i	$0.249973\pi$
$701$			991.279i			1.41409i	−0.707167	+	0.707046i	$0.750027\pi$
$702$		0			0
$703$	1289.17			1.83381
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−125.082	−	72.2163i	−0.176920	−	0.102145i
$708$		0			0
$709$	−403.573	−	699.009i	−0.569215	−	0.985909i	−0.996644	−	0.0818599i	$-0.973914\pi$
$709$	−403.573	−	699.009i	−0.569215	−	0.985909i	0.427429	−	0.904049i	$-0.359419\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	890.207	−	513.961i	1.24854	−	0.720843i
$714$		0			0
$715$	−0.666611	+	1.15460i	−0.000932324	+	0.00161483i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			61.3194i			0.0852843i	0.999090	+	0.0426422i	$0.0135775\pi$
$719$			61.3194i			0.0852843i	−0.999090	+	0.0426422i	$0.986422\pi$
$720$		0			0
$721$	−378.476			−0.524931
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.25122	+	1.87710i	0.00448445	+	0.00258910i
$726$		0			0
$727$	−227.024	−	393.217i	−0.312275	−	0.540876i	0.666579	−	0.745434i	$-0.267758\pi$
$727$	−227.024	−	393.217i	−0.312275	−	0.540876i	−0.978855	+	0.204558i	$0.934424\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	766.028	−	442.266i	1.04792	−	0.605015i
$732$		0			0
$733$	−146.499	+	253.744i	−0.199863	+	0.346172i	−0.948484	−	0.316826i	$-0.897383\pi$
$733$	−146.499	+	253.744i	−0.199863	+	0.346172i	0.748621	+	0.662998i	$0.230716\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			7.03821i			0.00954981i
$738$		0			0
$739$	228.122			0.308690			0.154345	−	0.988017i	$-0.450673\pi$
$739$	228.122			0.308690			0.154345	+	0.988017i	$0.450673\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−177.764	−	102.632i	−0.239252	−	0.138132i	0.375581	−	0.926790i	$-0.377443\pi$
$743$	−177.764	−	102.632i	−0.239252	−	0.138132i	−0.614833	+	0.788657i	$0.710777\pi$
$744$		0			0
$745$	−29.8156	−	51.6422i	−0.0400210	−	0.0693184i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1030.46	−	594.935i	1.37578	−	0.794306i
$750$		0			0
$751$	96.3048	−	166.805i	0.128235	−	0.222110i	−0.794758	−	0.606927i	$-0.792402\pi$
$751$	96.3048	−	166.805i	0.128235	−	0.222110i	0.922993	+	0.384817i	$0.125735\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	226.386i		−	0.299850i
$756$		0			0
$757$	750.204			0.991023			0.495512	−	0.868601i	$-0.334981\pi$
$757$	750.204			0.991023			0.495512	+	0.868601i	$0.334981\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−897.102	−	517.942i	−1.17885	−	0.680607i	−0.223099	−	0.974796i	$-0.571617\pi$
$761$	−897.102	−	517.942i	−1.17885	−	0.680607i	−0.955747	+	0.294188i	$0.904951\pi$
$762$		0			0
$763$	−146.481	−	253.713i	−0.191980	−	0.332520i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−496.215	+	286.490i	−0.646956	+	0.373520i
$768$		0			0
$769$	92.5951	−	160.379i	0.120410	−	0.208556i	−0.799520	−	0.600640i	$-0.794912\pi$
$769$	92.5951	−	160.379i	0.120410	−	0.208556i	0.919929	+	0.392084i	$0.128246\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1178.69i			1.52482i	0.647093	+	0.762411i	$0.275985\pi$
$773$			1178.69i			1.52482i	−0.647093	+	0.762411i	$0.724015\pi$
$774$		0			0
$775$	−173.205			−0.223491
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1394.92	+	805.359i	1.79066	+	1.03384i
$780$		0			0
$781$	−0.390005	−	0.675509i	−0.000499367	−	0.000864928i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−541.009	+	312.351i	−0.689183	+	0.397900i
$786$		0			0
$787$	−57.1483	+	98.9837i	−0.0726153	+	0.125773i	−0.900047	−	0.435793i	$-0.856468\pi$
$787$	−57.1483	+	98.9837i	−0.0726153	+	0.125773i	0.827431	+	0.561567i	$0.189801\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			487.572i			0.616400i
$792$		0			0
$793$	164.975			0.208040
$794$		0			0
$795$		0			0
$796$		0			0
$797$	942.410	+	544.101i	1.18245	+	0.682686i	0.956579	−	0.291472i	$-0.0941449\pi$
$797$	942.410	+	544.101i	1.18245	+	0.682686i	0.225868	+	0.974158i	$0.427478\pi$
$798$		0			0
$799$	385.340	+	667.428i	0.482278	+	0.835330i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.21010	+	1.85335i	−0.00399763	+	0.00230803i
$804$		0			0
$805$	263.731	−	456.795i	0.327616	−	0.567447i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	1058.49i		−	1.30840i	−0.756322	−	0.654199i	$-0.773006\pi$
$809$		−	1058.49i		−	1.30840i	0.756322	−	0.654199i	$-0.226994\pi$
$810$		0			0
$811$	325.951			0.401913			0.200956	−	0.979600i	$-0.435595\pi$
$811$	325.951			0.401913			0.200956	+	0.979600i	$0.435595\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−477.880	−	275.904i	−0.586355	−	0.338532i
$816$		0			0
$817$	−443.082	−	767.440i	−0.542328	−	0.939339i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	494.193	−	285.323i	0.601941	−	0.347531i	−0.167864	−	0.985810i	$-0.553687\pi$
$821$	494.193	−	285.323i	0.601941	−	0.347531i	0.769805	+	0.638280i	$0.220354\pi$
$822$		0			0
$823$	−580.756	+	1005.90i	−0.705658	+	1.22223i	0.260796	+	0.965394i	$0.416015\pi$
$823$	−580.756	+	1005.90i	−0.705658	+	1.22223i	−0.966454	+	0.256841i	$0.917318\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	422.843i		−	0.511297i	−0.966770	−	0.255649i	$-0.917711\pi$
$827$		−	422.843i		−	0.511297i	0.966770	−	0.255649i	$-0.0822890\pi$
$828$		0			0
$829$	455.988			0.550046			0.275023	−	0.961438i	$-0.411315\pi$
$829$	455.988			0.550046			0.275023	+	0.961438i	$0.411315\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	326.525	+	188.520i	0.391987	+	0.226314i
$834$		0			0
$835$	94.1761	+	163.118i	0.112786	+	0.195351i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−900.311	+	519.795i	−1.07308	+	0.619541i	−0.929020	−	0.370029i	$-0.879348\pi$
$839$	−900.311	+	519.795i	−1.07308	+	0.619541i	−0.144056	+	0.989570i	$0.546015\pi$
$840$		0			0
$841$	−420.218	+	727.839i	−0.499665	+	0.865445i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			209.458i			0.247880i
$846$		0			0
$847$	−961.844			−1.13559
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1244.84	+	718.709i	1.46280	+	0.844547i
$852$		0			0
$853$	366.610	+	634.988i	0.429789	+	0.744417i	0.996854	−	0.0792562i	$-0.0252545\pi$
$853$	366.610	+	634.988i	0.429789	+	0.744417i	−0.567065	+	0.823673i	$0.691921\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−163.543	+	94.4217i	−0.190832	+	0.110177i	−0.592372	−	0.805665i	$-0.701808\pi$
$857$	−163.543	+	94.4217i	−0.190832	+	0.110177i	0.401540	+	0.915842i	$0.368475\pi$
$858$		0			0
$859$	626.637	−	1085.37i	0.729496	−	1.26352i	−0.227600	−	0.973755i	$-0.573088\pi$
$859$	626.637	−	1085.37i	0.729496	−	1.26352i	0.957096	−	0.289770i	$-0.0935788\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1407.42i			1.63085i	0.578865	+	0.815423i	$0.303496\pi$
$863$			1407.42i			1.63085i	−0.578865	+	0.815423i	$0.696504\pi$
$864$		0			0
$865$	423.671			0.489793
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.18115	−	1.83664i	−0.00366070	−	0.00211350i
$870$		0			0
$871$	−444.598	−	770.066i	−0.510445	−	0.884117i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−76.9701	+	44.4387i	−0.0879658	+	0.0507871i
$876$		0			0
$877$	387.079	−	670.440i	0.441367	−	0.764470i	−0.556424	−	0.830898i	$-0.687827\pi$
$877$	387.079	−	670.440i	0.441367	−	0.764470i	0.997791	+	0.0664286i	$0.0211605\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			1442.00i			1.63678i	0.574662	+	0.818391i	$0.305134\pi$
$881$			1442.00i			1.63678i	−0.574662	+	0.818391i	$0.694866\pi$
$882$		0			0
$883$	−1399.40			−1.58483			−0.792415	−	0.609983i	$-0.791176\pi$
$883$	−1399.40			−1.58483			−0.792415	+	0.609983i	$0.791176\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1215.08	+	701.524i	1.36987	+	0.790895i	0.990911	−	0.134518i	$-0.0429486\pi$
$887$	1215.08	+	701.524i	1.36987	+	0.790895i	0.378959	+	0.925413i	$0.376282\pi$
$888$		0			0
$889$	−758.158	−	1313.17i	−0.852822	−	1.47713i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	668.659	−	386.050i	0.748778	−	0.432307i
$894$		0			0
$895$	124.355	−	215.389i	0.138944	−	0.240659i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			26.0098i			0.0289319i
$900$		0			0
$901$	−185.909			−0.206337
$902$		0			0
$903$		0			0
$904$		0			0
$905$	424.844	+	245.284i	0.469441	+	0.271032i
$906$		0			0
$907$	−456.415	−	790.534i	−0.503214	−	0.871592i	−0.999993	−	0.00371472i	$-0.998818\pi$
$907$	−456.415	−	790.534i	−0.503214	−	0.871592i	0.496780	−	0.867877i	$-0.334516\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−757.008	+	437.059i	−0.830963	+	0.479757i	−0.854182	−	0.519973i	$-0.825942\pi$
$911$	−757.008	+	437.059i	−0.830963	+	0.479757i	0.0232190	+	0.999730i	$0.492609\pi$
$912$		0			0
$913$	−1.20991	+	2.09562i	−0.00132520	+	0.00229531i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	228.079i		−	0.248723i
$918$		0			0
$919$	234.165			0.254804			0.127402	−	0.991851i	$-0.459336\pi$
$919$	234.165			0.254804			0.127402	+	0.991851i	$0.459336\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	85.3427	+	49.2726i	0.0924623	+	0.0533831i
$924$		0			0
$925$	−121.103	−	209.756i	−0.130922	−	0.226763i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−200.544	+	115.784i	−0.215870	+	0.124633i	−0.604037	−	0.796957i	$-0.706442\pi$
$929$	−200.544	+	115.784i	−0.215870	+	0.124633i	0.388166	+	0.921589i	$0.373109\pi$
$930$		0			0
$931$	188.867	−	327.127i	0.202865	−	0.351372i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			4.08058i			0.00436426i
$936$		0			0
$937$	−140.899			−0.150372			−0.0751861	−	0.997170i	$-0.523955\pi$
$937$	−140.899			−0.150372			−0.0751861	+	0.997170i	$0.523955\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	442.126	+	255.262i	0.469847	+	0.271266i	0.716176	−	0.697920i	$-0.245891\pi$
$941$	442.126	+	255.262i	0.469847	+	0.271266i	−0.246329	+	0.969186i	$0.579224\pi$
$942$		0			0
$943$	897.972	+	1555.33i	0.952251	+	1.64935i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−724.176	+	418.103i	−0.764706	+	0.441503i	−0.830983	−	0.556298i	$-0.812221\pi$
$947$	−724.176	+	418.103i	−0.764706	+	0.441503i	0.0662770	+	0.997801i	$0.478888\pi$
$948$		0			0
$949$	234.149	−	405.559i	0.246733	−	0.427354i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	914.987i		−	0.960112i	−0.877238	−	0.480056i	$-0.840616\pi$
$953$		−	914.987i		−	0.960112i	0.877238	−	0.480056i	$-0.159384\pi$
$954$		0			0
$955$	−81.9174			−0.0857773
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−807.901	−	466.442i	−0.842441	−	0.486384i
$960$		0			0
$961$	−119.501	−	206.982i	−0.124351	−	0.215382i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−295.216	+	170.443i	−0.305924	+	0.176625i
$966$		0			0
$967$	−636.666	+	1102.74i	−0.658393	+	1.14037i	0.322639	+	0.946522i	$0.395430\pi$
$967$	−636.666	+	1102.74i	−0.658393	+	1.14037i	−0.981032	+	0.193848i	$0.937903\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1246.37i		−	1.28360i	−0.766872	−	0.641800i	$-0.778188\pi$
$971$		−	1246.37i		−	1.28360i	0.766872	−	0.641800i	$-0.221812\pi$
$972$		0			0
$973$	249.927			0.256862
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1011.30	−	583.875i	−1.03511	−	0.597620i	−0.116665	−	0.993171i	$-0.537220\pi$
$977$	−1011.30	−	583.875i	−1.03511	−	0.597620i	−0.918444	+	0.395551i	$0.870554\pi$
$978$		0			0
$979$	2.57392	+	4.45816i	0.00262913	+	0.00455379i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−82.9062	+	47.8659i	−0.0843400	+	0.0486937i	−0.541577	−	0.840651i	$-0.682172\pi$
$983$	−82.9062	+	47.8659i	−0.0843400	+	0.0486937i	0.457237	+	0.889345i	$0.348839\pi$
$984$		0			0
$985$	−40.0103	+	69.2999i	−0.0406196	+	0.0703553i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	988.069i		−	0.999059i
$990$		0			0
$991$	1725.68			1.74135			0.870674	−	0.491860i	$-0.163683\pi$
$991$	1725.68			1.74135			0.870674	+	0.491860i	$0.163683\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	202.511	+	116.920i	0.203529	+	0.117507i
$996$		0			0
$997$	−366.854	−	635.410i	−0.367958	−	0.637322i	0.621288	−	0.783582i	$-0.286610\pi$
$997$	−366.854	−	635.410i	−0.367958	−	0.637322i	−0.989246	+	0.146260i	$0.953276\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.3.bs.c.881.8		16
3.2	odd	2		720.3.bs.c.401.5		16
4.3	odd	2		135.3.i.a.71.2		16
9.2	odd	6	inner	2160.3.bs.c.1601.8		16
9.7	even	3		720.3.bs.c.641.5		16
12.11	even	2		45.3.i.a.41.7	yes	16
20.3	even	4		675.3.i.c.449.13		32
20.7	even	4		675.3.i.c.449.4		32
20.19	odd	2		675.3.j.b.476.7		16
36.7	odd	6		45.3.i.a.11.7	✓	16
36.11	even	6		135.3.i.a.116.2		16
36.23	even	6		405.3.c.a.161.13		16
36.31	odd	6		405.3.c.a.161.4		16
60.23	odd	4		225.3.i.b.149.4		32
60.47	odd	4		225.3.i.b.149.13		32
60.59	even	2		225.3.j.b.176.2		16
180.7	even	12		225.3.i.b.74.4		32
180.43	even	12		225.3.i.b.74.13		32
180.47	odd	12		675.3.i.c.224.13		32
180.79	odd	6		225.3.j.b.101.2		16
180.83	odd	12		675.3.i.c.224.4		32
180.119	even	6		675.3.j.b.251.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.7	✓	16	36.7	odd	6
45.3.i.a.41.7	yes	16	12.11	even	2
135.3.i.a.71.2		16	4.3	odd	2
135.3.i.a.116.2		16	36.11	even	6
225.3.i.b.74.4		32	180.7	even	12
225.3.i.b.74.13		32	180.43	even	12
225.3.i.b.149.4		32	60.23	odd	4
225.3.i.b.149.13		32	60.47	odd	4
225.3.j.b.101.2		16	180.79	odd	6
225.3.j.b.176.2		16	60.59	even	2
405.3.c.a.161.4		16	36.31	odd	6
405.3.c.a.161.13		16	36.23	even	6
675.3.i.c.224.4		32	180.83	odd	12
675.3.i.c.224.13		32	180.47	odd	12
675.3.i.c.449.4		32	20.7	even	4
675.3.i.c.449.13		32	20.3	even	4
675.3.j.b.251.7		16	180.119	even	6
675.3.j.b.476.7		16	20.19	odd	2
720.3.bs.c.401.5		16	3.2	odd	2
720.3.bs.c.641.5		16	9.7	even	3
2160.3.bs.c.881.8		16	1.1	even	1	trivial
2160.3.bs.c.1601.8		16	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2160.bs (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93649 + 1.11803i) q^{5} +(3.97472 + 6.88441i) q^{7} +O(q^{10})\)	\(q+(1.93649 + 1.11803i) q^{5} +(3.97472 + 6.88441i) q^{7} +(-0.0594938 + 0.0343488i) q^{11} +(4.33957 - 7.51635i) q^{13} -26.5641i q^{17} -26.6131 q^{19} +(-25.6980 - 14.8368i) q^{23} +(2.50000 + 4.33013i) q^{25} +(0.650245 - 0.375419i) q^{29} +(-17.3205 + 30.0000i) q^{31} +17.7755i q^{35} -48.4411 q^{37} +(-52.4148 - 30.2617i) q^{41} +(16.6490 + 28.8369i) q^{43} +(-25.1252 + 14.5060i) q^{47} +(-7.09677 + 12.2920i) q^{49} -6.99851i q^{53} -0.153612 q^{55} +(-57.1733 - 33.0090i) q^{59} +(9.50414 + 16.4617i) q^{61} +(16.8071 - 9.70357i) q^{65} +(51.2260 - 88.7261i) q^{67} +11.3543i q^{71} +53.9568 q^{73} +(-0.472942 - 0.273053i) q^{77} +(26.7351 + 46.3066i) q^{79} +(30.5050 - 17.6121i) q^{83} +(29.6996 - 51.4412i) q^{85} -74.9349i q^{89} +68.9943 q^{91} +(-51.5361 - 29.7544i) q^{95} +(-34.4893 - 59.7373i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 18 q^{11} - 10 q^{13} + 52 q^{19} - 54 q^{23} + 40 q^{25} + 54 q^{29} - 32 q^{31} + 44 q^{37} - 144 q^{41} + 124 q^{43} - 216 q^{47} - 54 q^{49} - 486 q^{59} + 62 q^{61} + 90 q^{65} - 14 q^{67} - 268 q^{73} - 702 q^{77} + 40 q^{79} + 522 q^{83} + 30 q^{85} - 136 q^{91} + 180 q^{95} - 142 q^{97}+O(q^{100}) \) 16 * q - 2 * q^7 - 18 * q^11 - 10 * q^13 + 52 * q^19 - 54 * q^23 + 40 * q^25 + 54 * q^29 - 32 * q^31 + 44 * q^37 - 144 * q^41 + 124 * q^43 - 216 * q^47 - 54 * q^49 - 486 * q^59 + 62 * q^61 + 90 * q^65 - 14 * q^67 - 268 * q^73 - 702 * q^77 + 40 * q^79 + 522 * q^83 + 30 * q^85 - 136 * q^91 + 180 * q^95 - 142 * q^97

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