LMFDB - Embedded newform 200.3.l.e.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,3,Mod(57,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("200.57");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.l (of order $4$, 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:	$5.44960528721$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.1
Root			$2.70156i$ of defining polynomial
Character	$\chi$	$=$	200.57
Dual form			200.3.l.e.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70156 + 2.70156i) q^{3} +(-6.70156 - 6.70156i) q^{7} -5.59688i q^{9} +O(q^{10})$	$q+(-2.70156 + 2.70156i) q^{3} +(-6.70156 - 6.70156i) q^{7} -5.59688i q^{9} -1.40312 q^{11} +(14.4031 - 14.4031i) q^{13} +(2.40312 + 2.40312i) q^{17} -22.8062i q^{19} +36.2094 q^{21} +(0.104686 - 0.104686i) q^{23} +(-9.19375 - 9.19375i) q^{27} -45.6125i q^{29} -2.59688 q^{31} +(3.79063 - 3.79063i) q^{33} +(-10.6125 - 10.6125i) q^{37} +77.8219i q^{39} -44.6281 q^{41} +(-26.7016 + 26.7016i) q^{43} +(10.4922 + 10.4922i) q^{47} +40.8219i q^{49} -12.9844 q^{51} +(3.00000 - 3.00000i) q^{53} +(61.6125 + 61.6125i) q^{57} +41.1938i q^{59} -57.4031 q^{61} +(-37.5078 + 37.5078i) q^{63} +(-34.7016 - 34.7016i) q^{67} +0.565633i q^{69} +45.4031 q^{71} +(-11.3875 + 11.3875i) q^{73} +(9.40312 + 9.40312i) q^{77} -86.4500i q^{79} +100.047 q^{81} +(81.7172 - 81.7172i) q^{83} +(123.225 + 123.225i) q^{87} +91.2250i q^{89} -193.047 q^{91} +(7.01562 - 7.01562i) q^{93} +(-49.0000 - 49.0000i) q^{97} +7.85311i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 14 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 14 * q^7	$ 4 q + 2 q^{3} - 14 q^{7} + 20 q^{11} + 32 q^{13} - 16 q^{17} + 68 q^{21} - 38 q^{23} - 88 q^{27} - 36 q^{31} + 92 q^{33} + 60 q^{37} + 52 q^{41} - 94 q^{43} + 106 q^{47} - 180 q^{51} + 12 q^{53} + 144 q^{57} - 204 q^{61} - 86 q^{63} - 126 q^{67} + 156 q^{71} - 148 q^{73} + 12 q^{77} + 16 q^{81} + 186 q^{83} + 288 q^{87} - 388 q^{91} - 100 q^{93} - 196 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 - 14 * q^7 + 20 * q^11 + 32 * q^13 - 16 * q^17 + 68 * q^21 - 38 * q^23 - 88 * q^27 - 36 * q^31 + 92 * q^33 + 60 * q^37 + 52 * q^41 - 94 * q^43 + 106 * q^47 - 180 * q^51 + 12 * q^53 + 144 * q^57 - 204 * q^61 - 86 * q^63 - 126 * q^67 + 156 * q^71 - 148 * q^73 + 12 * q^77 + 16 * q^81 + 186 * q^83 + 288 * q^87 - 388 * q^91 - 100 * q^93 - 196 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.70156	+	2.70156i	−0.900521	+	0.900521i	−0.995481	−	0.0949603i	$-0.969728\pi$
$3$	−2.70156	+	2.70156i	−0.900521	+	0.900521i	0.0949603	+	0.995481i	$0.469728\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−6.70156	−	6.70156i	−0.957366	−	0.957366i	0.0417616	−	0.999128i	$-0.486703\pi$
$7$	−6.70156	−	6.70156i	−0.957366	−	0.957366i	−0.999128	+	0.0417616i	$0.986703\pi$
$8$		0			0
$9$		−	5.59688i		−	0.621875i
$10$		0			0
$11$	−1.40312			−0.127557			−0.0637784	−	0.997964i	$-0.520315\pi$
$11$	−1.40312			−0.127557			−0.0637784	+	0.997964i	$0.520315\pi$
$12$		0			0
$13$	14.4031	−	14.4031i	1.10793	−	1.10793i	0.114511	−	0.993422i	$-0.463470\pi$
$13$	14.4031	−	14.4031i	1.10793	−	1.10793i	0.993422	−	0.114511i	$-0.0365300\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.40312	+	2.40312i	0.141360	+	0.141360i	0.774246	−	0.632885i	$-0.218130\pi$
$17$	2.40312	+	2.40312i	0.141360	+	0.141360i	−0.632885	+	0.774246i	$0.718130\pi$
$18$		0			0
$19$		−	22.8062i		−	1.20033i	−0.799877	−	0.600164i	$-0.795102\pi$
$19$		−	22.8062i		−	1.20033i	0.799877	−	0.600164i	$-0.204898\pi$
$20$		0			0
$21$	36.2094			1.72426
$22$		0			0
$23$	0.104686	−	0.104686i	0.00455158	−	0.00455158i	−0.704827	−	0.709379i	$-0.748976\pi$
$23$	0.104686	−	0.104686i	0.00455158	−	0.00455158i	0.709379	+	0.704827i	$0.248976\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−9.19375	−	9.19375i	−0.340509	−	0.340509i
$28$		0			0
$29$		−	45.6125i		−	1.57284i	−0.617689	−	0.786422i	$-0.711931\pi$
$29$		−	45.6125i		−	1.57284i	0.617689	−	0.786422i	$-0.288069\pi$
$30$		0			0
$31$	−2.59688			−0.0837702			−0.0418851	−	0.999122i	$-0.513336\pi$
$31$	−2.59688			−0.0837702			−0.0418851	+	0.999122i	$0.513336\pi$
$32$		0			0
$33$	3.79063	−	3.79063i	0.114867	−	0.114867i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−10.6125	−	10.6125i	−0.286824	−	0.286824i	0.548999	−	0.835823i	$-0.315009\pi$
$37$	−10.6125	−	10.6125i	−0.286824	−	0.286824i	−0.835823	+	0.548999i	$0.815009\pi$
$38$		0			0
$39$			77.8219i			1.99543i
$40$		0			0
$41$	−44.6281			−1.08849			−0.544245	−	0.838926i	$-0.683184\pi$
$41$	−44.6281			−1.08849			−0.544245	+	0.838926i	$0.683184\pi$
$42$		0			0
$43$	−26.7016	+	26.7016i	−0.620967	+	0.620967i	−0.945779	−	0.324812i	$-0.894699\pi$
$43$	−26.7016	+	26.7016i	−0.620967	+	0.620967i	0.324812	+	0.945779i	$0.394699\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.4922	+	10.4922i	0.223238	+	0.223238i	0.809861	−	0.586622i	$-0.199543\pi$
$47$	10.4922	+	10.4922i	0.223238	+	0.223238i	−0.586622	+	0.809861i	$0.699543\pi$
$48$		0			0
$49$			40.8219i			0.833099i
$50$		0			0
$51$	−12.9844			−0.254596
$52$		0			0
$53$	3.00000	−	3.00000i	0.0566038	−	0.0566038i	−0.678238	−	0.734842i	$-0.737256\pi$
$53$	3.00000	−	3.00000i	0.0566038	−	0.0566038i	0.734842	+	0.678238i	$0.237256\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	61.6125	+	61.6125i	1.08092	+	1.08092i
$58$		0			0
$59$			41.1938i			0.698199i	0.937086	+	0.349100i	$0.113513\pi$
$59$			41.1938i			0.698199i	−0.937086	+	0.349100i	$0.886487\pi$
$60$		0			0
$61$	−57.4031			−0.941035			−0.470517	−	0.882391i	$-0.655933\pi$
$61$	−57.4031			−0.941035			−0.470517	+	0.882391i	$0.655933\pi$
$62$		0			0
$63$	−37.5078	+	37.5078i	−0.595362	+	0.595362i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−34.7016	−	34.7016i	−0.517934	−	0.517934i	0.399012	−	0.916946i	$-0.369353\pi$
$67$	−34.7016	−	34.7016i	−0.517934	−	0.517934i	−0.916946	+	0.399012i	$0.869353\pi$
$68$		0			0
$69$			0.565633i			0.00819759i
$70$		0			0
$71$	45.4031			0.639481			0.319740	−	0.947505i	$-0.396404\pi$
$71$	45.4031			0.639481			0.319740	+	0.947505i	$0.396404\pi$
$72$		0			0
$73$	−11.3875	+	11.3875i	−0.155993	+	0.155993i	−0.780789	−	0.624795i	$-0.785182\pi$
$73$	−11.3875	+	11.3875i	−0.155993	+	0.155993i	0.624795	+	0.780789i	$0.285182\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.40312	+	9.40312i	0.122118	+	0.122118i
$78$		0			0
$79$		−	86.4500i		−	1.09430i	−0.837033	−	0.547152i	$-0.815712\pi$
$79$		−	86.4500i		−	1.09430i	0.837033	−	0.547152i	$-0.184288\pi$
$80$		0			0
$81$	100.047			1.23515
$82$		0			0
$83$	81.7172	−	81.7172i	0.984544	−	0.984544i	−0.0153380	−	0.999882i	$-0.504882\pi$
$83$	81.7172	−	81.7172i	0.984544	−	0.984544i	0.999882	+	0.0153380i	$0.00488242\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	123.225	+	123.225i	1.41638	+	1.41638i
$88$		0			0
$89$			91.2250i			1.02500i	0.858687	+	0.512500i	$0.171281\pi$
$89$			91.2250i			1.02500i	−0.858687	+	0.512500i	$0.828719\pi$
$90$		0			0
$91$	−193.047			−2.12139
$92$		0			0
$93$	7.01562	−	7.01562i	0.0754368	−	0.0754368i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−49.0000	−	49.0000i	−0.505155	−	0.505155i	0.407881	−	0.913035i	$-0.366268\pi$
$97$	−49.0000	−	49.0000i	−0.505155	−	0.505155i	−0.913035	+	0.407881i	$0.866268\pi$
$98$		0			0
$99$			7.85311i			0.0793244i
$100$		0			0
$101$	60.0312			0.594369			0.297184	−	0.954820i	$-0.403952\pi$
$101$	60.0312			0.594369			0.297184	+	0.954820i	$0.403952\pi$
$102$		0			0
$103$	−61.5078	+	61.5078i	−0.597163	+	0.597163i	−0.939557	−	0.342393i	$-0.888762\pi$
$103$	−61.5078	+	61.5078i	−0.597163	+	0.597163i	0.342393	+	0.939557i	$0.388762\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−67.5391	−	67.5391i	−0.631206	−	0.631206i	0.317164	−	0.948371i	$-0.397269\pi$
$107$	−67.5391	−	67.5391i	−0.631206	−	0.631206i	−0.948371	+	0.317164i	$0.897269\pi$
$108$		0			0
$109$			19.0469i			0.174742i	0.996176	+	0.0873709i	$0.0278465\pi$
$109$			19.0469i			0.174742i	−0.996176	+	0.0873709i	$0.972153\pi$
$110$		0			0
$111$	57.3406			0.516582
$112$		0			0
$113$	−8.82187	+	8.82187i	−0.0780696	+	0.0780696i	−0.745063	−	0.666994i	$-0.767581\pi$
$113$	−8.82187	+	8.82187i	−0.0780696	+	0.0780696i	0.666994	+	0.745063i	$0.267581\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−80.6125	−	80.6125i	−0.688996	−	0.688996i
$118$		0			0
$119$		−	32.2094i		−	0.270667i
$120$		0			0
$121$	−119.031			−0.983729
$122$		0			0
$123$	120.566	−	120.566i	0.980208	−	0.980208i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−14.7016	−	14.7016i	−0.115760	−	0.115760i	0.646854	−	0.762614i	$-0.276084\pi$
$127$	−14.7016	−	14.7016i	−0.115760	−	0.115760i	−0.762614	+	0.646854i	$0.776084\pi$
$128$		0			0
$129$		−	144.272i		−	1.11839i
$130$		0			0
$131$	237.884			1.81591			0.907956	−	0.419066i	$-0.137643\pi$
$131$	237.884			1.81591			0.907956	+	0.419066i	$0.137643\pi$
$132$		0			0
$133$	−152.837	+	152.837i	−1.14915	+	1.14915i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−86.6125	−	86.6125i	−0.632208	−	0.632208i	0.316413	−	0.948621i	$-0.397521\pi$
$137$	−86.6125	−	86.6125i	−0.632208	−	0.632208i	−0.948621	+	0.316413i	$0.897521\pi$
$138$		0			0
$139$		−	246.806i		−	1.77558i	−0.460244	−	0.887792i	$-0.652238\pi$
$139$		−	246.806i		−	1.77558i	0.460244	−	0.887792i	$-0.347762\pi$
$140$		0			0
$141$	−56.6906			−0.402061
$142$		0			0
$143$	−20.2094	+	20.2094i	−0.141324	+	0.141324i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−110.283	−	110.283i	−0.750223	−	0.750223i
$148$		0			0
$149$			121.853i			0.817806i	0.912578	+	0.408903i	$0.134089\pi$
$149$			121.853i			0.817806i	−0.912578	+	0.408903i	$0.865911\pi$
$150$		0			0
$151$	245.528			1.62601			0.813007	−	0.582254i	$-0.197829\pi$
$151$	245.528			1.62601			0.813007	+	0.582254i	$0.197829\pi$
$152$		0			0
$153$	13.4500	−	13.4500i	0.0879084	−	0.0879084i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	146.466	+	146.466i	0.932902	+	0.932902i	0.997886	−	0.0649843i	$-0.0206997\pi$
$157$	146.466	+	146.466i	0.932902	+	0.932902i	−0.0649843	+	0.997886i	$0.520700\pi$
$158$		0			0
$159$			16.2094i			0.101946i
$160$		0			0
$161$	−1.40312			−0.00871506
$162$		0			0
$163$	174.973	−	174.973i	1.07346	−	1.07346i	0.0763776	−	0.997079i	$-0.475665\pi$
$163$	174.973	−	174.973i	1.07346	−	1.07346i	0.997079	−	0.0763776i	$-0.0243354\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	203.330	+	203.330i	1.21754	+	1.21754i	0.968490	+	0.249053i	$0.0801194\pi$
$167$	203.330	+	203.330i	1.21754	+	1.21754i	0.249053	+	0.968490i	$0.419881\pi$
$168$		0			0
$169$		−	245.900i		−	1.45503i
$170$		0			0
$171$	−127.644			−0.746455
$172$		0			0
$173$	168.612	−	168.612i	0.974639	−	0.974639i	−0.0250476	−	0.999686i	$-0.507974\pi$
$173$	168.612	−	168.612i	0.974639	−	0.974639i	0.999686	+	0.0250476i	$0.00797372\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−111.287	−	111.287i	−0.628743	−	0.628743i
$178$		0			0
$179$			27.5813i			0.154085i	0.997028	+	0.0770426i	$0.0245477\pi$
$179$			27.5813i			0.154085i	−0.997028	+	0.0770426i	$0.975452\pi$
$180$		0			0
$181$	−88.3875			−0.488329			−0.244164	−	0.969734i	$-0.578514\pi$
$181$	−88.3875			−0.488329			−0.244164	+	0.969734i	$0.578514\pi$
$182$		0			0
$183$	155.078	−	155.078i	0.847421	−	0.847421i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.37188	−	3.37188i	−0.0180315	−	0.0180315i
$188$		0			0
$189$			123.225i			0.651984i
$190$		0			0
$191$	−79.4969			−0.416214			−0.208107	−	0.978106i	$-0.566730\pi$
$191$	−79.4969			−0.416214			−0.208107	+	0.978106i	$0.566730\pi$
$192$		0			0
$193$	−104.822	+	104.822i	−0.543118	+	0.543118i	−0.924442	−	0.381323i	$-0.875468\pi$
$193$	−104.822	+	104.822i	−0.543118	+	0.543118i	0.381323	+	0.924442i	$0.375468\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−68.1625	−	68.1625i	−0.346003	−	0.346003i	0.512616	−	0.858618i	$-0.328677\pi$
$197$	−68.1625	−	68.1625i	−0.346003	−	0.346003i	−0.858618	+	0.512616i	$0.828677\pi$
$198$		0			0
$199$			250.512i			1.25886i	0.777059	+	0.629428i	$0.216711\pi$
$199$			250.512i			1.25886i	−0.777059	+	0.629428i	$0.783289\pi$
$200$		0			0
$201$	187.497			0.932820
$202$		0			0
$203$	−305.675	+	305.675i	−1.50579	+	1.50579i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.585917	−	0.585917i	−0.00283051	−	0.00283051i
$208$		0			0
$209$			32.0000i			0.153110i
$210$		0			0
$211$	−332.628			−1.57644			−0.788218	−	0.615396i	$-0.788996\pi$
$211$	−332.628			−1.57644			−0.788218	+	0.615396i	$0.788996\pi$
$212$		0			0
$213$	−122.659	+	122.659i	−0.575866	+	0.575866i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	17.4031	+	17.4031i	0.0801987	+	0.0801987i
$218$		0			0
$219$		−	61.5281i		−	0.280950i
$220$		0			0
$221$	69.2250			0.313235
$222$		0			0
$223$	−187.602	+	187.602i	−0.841263	+	0.841263i	−0.989023	−	0.147761i	$-0.952793\pi$
$223$	−187.602	+	187.602i	−0.841263	+	0.841263i	0.147761	+	0.989023i	$0.452793\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	152.167	+	152.167i	0.670340	+	0.670340i	0.957794	−	0.287454i	$-0.0928090\pi$
$227$	152.167	+	152.167i	0.670340	+	0.670340i	−0.287454	+	0.957794i	$0.592809\pi$
$228$		0			0
$229$			196.062i			0.856168i	0.903739	+	0.428084i	$0.140811\pi$
$229$			196.062i			0.856168i	−0.903739	+	0.428084i	$0.859189\pi$
$230$		0			0
$231$	−50.8062			−0.219940
$232$		0			0
$233$	60.7906	−	60.7906i	0.260904	−	0.260904i	−0.564517	−	0.825421i	$-0.690938\pi$
$233$	60.7906	−	60.7906i	0.260904	−	0.260904i	0.825421	+	0.564517i	$0.190938\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	233.550	+	233.550i	0.985443	+	0.985443i
$238$		0			0
$239$			178.388i			0.746391i	0.927753	+	0.373196i	$0.121738\pi$
$239$			178.388i			0.746391i	−0.927753	+	0.373196i	$0.878262\pi$
$240$		0			0
$241$	89.8219			0.372705			0.186352	−	0.982483i	$-0.440333\pi$
$241$	89.8219			0.372705			0.186352	+	0.982483i	$0.440333\pi$
$242$		0			0
$243$	−187.539	+	187.539i	−0.771766	+	0.771766i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−328.481	−	328.481i	−1.32988	−	1.32988i
$248$		0			0
$249$			441.528i			1.77321i
$250$		0			0
$251$	−5.46561			−0.0217753			−0.0108877	−	0.999941i	$-0.503466\pi$
$251$	−5.46561			−0.0217753			−0.0108877	+	0.999941i	$0.503466\pi$
$252$		0			0
$253$	−0.146888	+	0.146888i	−0.000580585	+	0.000580585i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	340.078	+	340.078i	1.32326	+	1.32326i	0.911120	+	0.412141i	$0.135219\pi$
$257$	340.078	+	340.078i	1.32326	+	1.32326i	0.412141	+	0.911120i	$0.364781\pi$
$258$		0			0
$259$			142.241i			0.549192i
$260$		0			0
$261$	−255.287			−0.978113
$262$		0			0
$263$	29.3609	−	29.3609i	0.111638	−	0.111638i	−0.649081	−	0.760719i	$-0.724846\pi$
$263$	29.3609	−	29.3609i	0.111638	−	0.111638i	0.760719	+	0.649081i	$0.224846\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−246.450	−	246.450i	−0.923034	−	0.923034i
$268$		0			0
$269$		−	403.047i		−	1.49832i	−0.662392	−	0.749158i	$-0.730458\pi$
$269$		−	403.047i		−	1.49832i	0.662392	−	0.749158i	$-0.269542\pi$
$270$		0			0
$271$	−308.984			−1.14016			−0.570082	−	0.821588i	$-0.693089\pi$
$271$	−308.984			−1.14016			−0.570082	+	0.821588i	$0.693089\pi$
$272$		0			0
$273$	521.528	−	521.528i	1.91036	−	1.91036i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.59688	−	9.59688i	−0.0346458	−	0.0346458i	0.689572	−	0.724217i	$-0.257799\pi$
$277$	−9.59688	−	9.59688i	−0.0346458	−	0.0346458i	−0.724217	+	0.689572i	$0.757799\pi$
$278$		0			0
$279$			14.5344i			0.0520946i
$280$		0			0
$281$	−268.628			−0.955972			−0.477986	−	0.878367i	$-0.658633\pi$
$281$	−268.628			−0.955972			−0.477986	+	0.878367i	$0.658633\pi$
$282$		0			0
$283$	116.942	−	116.942i	0.413223	−	0.413223i	−0.469637	−	0.882860i	$-0.655615\pi$
$283$	116.942	−	116.942i	0.413223	−	0.413223i	0.882860	+	0.469637i	$0.155615\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	299.078	+	299.078i	1.04208	+	1.04208i
$288$		0			0
$289$		−	277.450i		−	0.960035i
$290$		0			0
$291$	264.753			0.909804
$292$		0			0
$293$	133.691	−	133.691i	0.456282	−	0.456282i	−0.441151	−	0.897433i	$-0.645430\pi$
$293$	133.691	−	133.691i	0.456282	−	0.456282i	0.897433	+	0.441151i	$0.145430\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	12.9000	+	12.9000i	0.0434343	+	0.0434343i
$298$		0			0
$299$		−	3.01562i		−	0.0100857i
$300$		0			0
$301$	357.884			1.18898
$302$		0			0
$303$	−162.178	+	162.178i	−0.535241	+	0.535241i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	109.298	+	109.298i	0.356021	+	0.356021i	0.862344	−	0.506323i	$-0.168996\pi$
$307$	109.298	+	109.298i	0.356021	+	0.356021i	−0.506323	+	0.862344i	$0.668996\pi$
$308$		0			0
$309$		−	332.334i		−	1.07552i
$310$		0			0
$311$	428.691			1.37843			0.689213	−	0.724559i	$-0.257956\pi$
$311$	428.691			1.37843			0.689213	+	0.724559i	$0.257956\pi$
$312$		0			0
$313$	−299.334	+	299.334i	−0.956340	+	0.956340i	−0.999086	−	0.0427462i	$-0.986389\pi$
$313$	−299.334	+	299.334i	−0.956340	+	0.956340i	0.0427462	+	0.999086i	$0.486389\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−412.109	−	412.109i	−1.30003	−	1.30003i	−0.928369	−	0.371661i	$-0.878788\pi$
$317$	−412.109	−	412.109i	−1.30003	−	1.30003i	−0.371661	−	0.928369i	$-0.621212\pi$
$318$		0			0
$319$			64.0000i			0.200627i
$320$		0			0
$321$	364.922			1.13683
$322$		0			0
$323$	54.8062	−	54.8062i	0.169679	−	0.169679i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−51.4563	−	51.4563i	−0.157359	−	0.157359i
$328$		0			0
$329$		−	140.628i		−	0.427441i
$330$		0			0
$331$	12.9219			0.0390390			0.0195195	−	0.999809i	$-0.493786\pi$
$331$	12.9219			0.0390390			0.0195195	+	0.999809i	$0.493786\pi$
$332$		0			0
$333$	−59.3968	+	59.3968i	−0.178369	+	0.178369i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	61.3250	+	61.3250i	0.181973	+	0.181973i	0.792215	−	0.610242i	$-0.208928\pi$
$337$	61.3250	+	61.3250i	0.181973	+	0.181973i	−0.610242	+	0.792215i	$0.708928\pi$
$338$		0			0
$339$		−	47.6657i		−	0.140607i
$340$		0			0
$341$	3.64374			0.0106855
$342$		0			0
$343$	−54.8062	+	54.8062i	−0.159785	+	0.159785i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−179.183	−	179.183i	−0.516377	−	0.516377i	0.400096	−	0.916473i	$-0.368977\pi$
$347$	−179.183	−	179.183i	−0.516377	−	0.516377i	−0.916473	+	0.400096i	$0.868977\pi$
$348$		0			0
$349$		−	240.962i		−	0.690437i	−0.938522	−	0.345218i	$-0.887805\pi$
$349$		−	240.962i		−	0.690437i	0.938522	−	0.345218i	$-0.112195\pi$
$350$		0			0
$351$	−264.837			−0.754523
$352$		0			0
$353$	−141.900	+	141.900i	−0.401983	+	0.401983i	−0.878931	−	0.476948i	$-0.841743\pi$
$353$	−141.900	+	141.900i	−0.401983	+	0.401983i	0.476948	+	0.878931i	$0.341743\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	87.0156	+	87.0156i	0.243741	+	0.243741i
$358$		0			0
$359$		−	238.325i		−	0.663858i	−0.943304	−	0.331929i	$-0.892301\pi$
$359$		−	238.325i		−	0.663858i	0.943304	−	0.331929i	$-0.107699\pi$
$360$		0			0
$361$	−159.125			−0.440789
$362$		0			0
$363$	321.570	−	321.570i	0.885869	−	0.885869i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−259.477	−	259.477i	−0.707021	−	0.707021i	0.258887	−	0.965908i	$-0.416644\pi$
$367$	−259.477	−	259.477i	−0.707021	−	0.707021i	−0.965908	+	0.258887i	$0.916644\pi$
$368$		0			0
$369$			249.778i			0.676905i
$370$		0			0
$371$	−40.2094			−0.108381
$372$		0			0
$373$	310.350	−	310.350i	0.832037	−	0.832037i	−0.155758	−	0.987795i	$-0.549782\pi$
$373$	310.350	−	310.350i	0.832037	−	0.832037i	0.987795	+	0.155758i	$0.0497819\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−656.962	−	656.962i	−1.74261	−	1.74261i
$378$		0			0
$379$			90.1562i			0.237879i	0.992901	+	0.118940i	$0.0379495\pi$
$379$			90.1562i			0.237879i	−0.992901	+	0.118940i	$0.962051\pi$
$380$		0			0
$381$	79.4344			0.208489
$382$		0			0
$383$	209.298	−	209.298i	0.546471	−	0.546471i	−0.378947	−	0.925418i	$-0.623714\pi$
$383$	209.298	−	209.298i	0.546471	−	0.546471i	0.925418	+	0.378947i	$0.123714\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	149.445	+	149.445i	0.386164	+	0.386164i
$388$		0			0
$389$			193.372i			0.497100i	0.968619	+	0.248550i	$0.0799540\pi$
$389$			193.372i			0.497100i	−0.968619	+	0.248550i	$0.920046\pi$
$390$		0			0
$391$	0.503149			0.00128683
$392$		0			0
$393$	−642.659	+	642.659i	−1.63527	+	1.63527i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−80.2250	−	80.2250i	−0.202078	−	0.202078i	0.598812	−	0.800890i	$-0.295640\pi$
$397$	−80.2250	−	80.2250i	−0.202078	−	0.202078i	−0.800890	+	0.598812i	$0.795640\pi$
$398$		0			0
$399$		−	825.800i		−	2.06967i
$400$		0			0
$401$	−727.800			−1.81496			−0.907481	−	0.420093i	$-0.861998\pi$
$401$	−727.800			−1.81496			−0.907481	+	0.420093i	$0.861998\pi$
$402$		0			0
$403$	−37.4031	+	37.4031i	−0.0928117	+	0.0928117i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	14.8907	+	14.8907i	0.0365864	+	0.0365864i
$408$		0			0
$409$			355.403i			0.868956i	0.900682	+	0.434478i	$0.143067\pi$
$409$			355.403i			0.868956i	−0.900682	+	0.434478i	$0.856933\pi$
$410$		0			0
$411$	467.978			1.13863
$412$		0			0
$413$	276.062	−	276.062i	0.668432	−	0.668432i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	666.762	+	666.762i	1.59895	+	1.59895i
$418$		0			0
$419$			767.644i			1.83209i	0.401081	+	0.916043i	$0.368635\pi$
$419$			767.644i			1.83209i	−0.401081	+	0.916043i	$0.631365\pi$
$420$		0			0
$421$	446.722			1.06110			0.530549	−	0.847655i	$-0.321986\pi$
$421$	446.722			1.06110			0.530549	+	0.847655i	$0.321986\pi$
$422$		0			0
$423$	58.7235	−	58.7235i	0.138826	−	0.138826i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	384.691	+	384.691i	0.900915	+	0.900915i
$428$		0			0
$429$		−	109.194i		−	0.254531i
$430$		0			0
$431$	303.791			0.704851			0.352425	−	0.935840i	$-0.385357\pi$
$431$	303.791			0.704851			0.352425	+	0.935840i	$0.385357\pi$
$432$		0			0
$433$	610.350	−	610.350i	1.40958	−	1.40958i	0.647625	−	0.761959i	$-0.275762\pi$
$433$	610.350	−	610.350i	1.40958	−	1.40958i	0.761959	−	0.647625i	$-0.224238\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.38750	−	2.38750i	−0.00546339	−	0.00546339i
$438$		0			0
$439$		−	737.925i		−	1.68092i	−0.541872	−	0.840461i	$-0.682284\pi$
$439$		−	737.925i		−	1.68092i	0.541872	−	0.840461i	$-0.317716\pi$
$440$		0			0
$441$	228.475			0.518084
$442$		0			0
$443$	−481.508	+	481.508i	−1.08693	+	1.08693i	−0.0910817	+	0.995843i	$0.529032\pi$
$443$	−481.508	+	481.508i	−1.08693	+	1.08693i	−0.995843	+	0.0910817i	$0.970968\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−329.194	−	329.194i	−0.736451	−	0.736451i
$448$		0			0
$449$		−	568.428i		−	1.26599i	−0.774157	−	0.632993i	$-0.781826\pi$
$449$		−	568.428i		−	1.26599i	0.774157	−	0.632993i	$-0.218174\pi$
$450$		0			0
$451$	62.6188			0.138844
$452$		0			0
$453$	−663.309	+	663.309i	−1.46426	+	1.46426i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	108.791	+	108.791i	0.238054	+	0.238054i	0.816044	−	0.577990i	$-0.196163\pi$
$457$	108.791	+	108.791i	0.238054	+	0.238054i	−0.577990	+	0.816044i	$0.696163\pi$
$458$		0			0
$459$		−	44.1875i		−	0.0962690i
$460$		0			0
$461$	348.281			0.755491			0.377745	−	0.925910i	$-0.376699\pi$
$461$	348.281			0.755491			0.377745	+	0.925910i	$0.376699\pi$
$462$		0			0
$463$	307.330	−	307.330i	0.663779	−	0.663779i	−0.292490	−	0.956269i	$-0.594484\pi$
$463$	307.330	−	307.330i	0.663779	−	0.663779i	0.956269	+	0.292490i	$0.0944837\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−50.3453	−	50.3453i	−0.107806	−	0.107806i	0.651146	−	0.758952i	$-0.274288\pi$
$467$	−50.3453	−	50.3453i	−0.107806	−	0.107806i	−0.758952	+	0.651146i	$0.774288\pi$
$468$		0			0
$469$			465.109i			0.991704i
$470$		0			0
$471$	−791.372			−1.68020
$472$		0			0
$473$	37.4656	−	37.4656i	0.0792085	−	0.0792085i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−16.7906	−	16.7906i	−0.0352005	−	0.0352005i
$478$		0			0
$479$			445.862i			0.930819i	0.885095	+	0.465410i	$0.154093\pi$
$479$			445.862i			0.930819i	−0.885095	+	0.465410i	$0.845907\pi$
$480$		0			0
$481$	−305.706			−0.635564
$482$		0			0
$483$	3.79063	−	3.79063i	0.00784809	−	0.00784809i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	322.136	+	322.136i	0.661470	+	0.661470i	0.955727	−	0.294256i	$-0.0950720\pi$
$487$	322.136	+	322.136i	0.661470	+	0.661470i	−0.294256	+	0.955727i	$0.595072\pi$
$488$		0			0
$489$			945.403i			1.93334i
$490$		0			0
$491$	−362.953			−0.739212			−0.369606	−	0.929189i	$-0.620507\pi$
$491$	−362.953			−0.739212			−0.369606	+	0.929189i	$0.620507\pi$
$492$		0			0
$493$	109.612	−	109.612i	0.222338	−	0.222338i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−304.272	−	304.272i	−0.612217	−	0.612217i
$498$		0			0
$499$		−	555.831i		−	1.11389i	−0.830549	−	0.556945i	$-0.811973\pi$
$499$		−	555.831i		−	1.11389i	0.830549	−	0.556945i	$-0.188027\pi$
$500$		0			0
$501$	−1098.62			−2.19285
$502$		0			0
$503$	173.717	−	173.717i	0.345362	−	0.345362i	−0.513017	−	0.858379i	$-0.671472\pi$
$503$	173.717	−	173.717i	0.345362	−	0.345362i	0.858379	+	0.513017i	$0.171472\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	664.314	+	664.314i	1.31028	+	1.31028i
$508$		0			0
$509$			213.737i			0.419916i	0.977710	+	0.209958i	$0.0673328\pi$
$509$			213.737i			0.419916i	−0.977710	+	0.209958i	$0.932667\pi$
$510$		0			0
$511$	152.628			0.298685
$512$		0			0
$513$	−209.675	+	209.675i	−0.408723	+	0.408723i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−14.7218	−	14.7218i	−0.0284755	−	0.0284755i
$518$		0			0
$519$			911.034i			1.75536i
$520$		0			0
$521$	312.094			0.599028			0.299514	−	0.954092i	$-0.403175\pi$
$521$	312.094			0.599028			0.299514	+	0.954092i	$0.403175\pi$
$522$		0			0
$523$	197.655	−	197.655i	0.377925	−	0.377925i	−0.492428	−	0.870353i	$-0.663891\pi$
$523$	197.655	−	197.655i	0.377925	−	0.377925i	0.870353	+	0.492428i	$0.163891\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.24062	−	6.24062i	−0.0118418	−	0.0118418i
$528$		0			0
$529$			528.978i			0.999959i
$530$		0			0
$531$	230.556			0.434193
$532$		0			0
$533$	−642.784	+	642.784i	−1.20597	+	1.20597i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−74.5125	−	74.5125i	−0.138757	−	0.138757i
$538$		0			0
$539$		−	57.2782i		−	0.106267i
$540$		0			0
$541$	172.031			0.317988			0.158994	−	0.987280i	$-0.449175\pi$
$541$	172.031			0.317988			0.158994	+	0.987280i	$0.449175\pi$
$542$		0			0
$543$	238.784	−	238.784i	0.439750	−	0.439750i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	60.9422	+	60.9422i	0.111412	+	0.111412i	0.760615	−	0.649203i	$-0.224898\pi$
$547$	60.9422	+	60.9422i	0.111412	+	0.111412i	−0.649203	+	0.760615i	$0.724898\pi$
$548$		0			0
$549$			321.278i			0.585206i
$550$		0			0
$551$	−1040.25			−1.88793
$552$		0			0
$553$	−579.350	+	579.350i	−1.04765	+	1.04765i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	441.575	+	441.575i	0.792774	+	0.792774i	0.981944	−	0.189171i	$-0.0605799\pi$
$557$	441.575	+	441.575i	0.792774	+	0.792774i	−0.189171	+	0.981944i	$0.560580\pi$
$558$		0			0
$559$			769.172i			1.37598i
$560$		0			0
$561$	18.2187			0.0324754
$562$		0			0
$563$	−502.764	+	502.764i	−0.893009	+	0.893009i	−0.994805	−	0.101796i	$-0.967541\pi$
$563$	−502.764	+	502.764i	−0.893009	+	0.893009i	0.101796	+	0.994805i	$0.467541\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−670.470	−	670.470i	−1.18249	−	1.18249i
$568$		0			0
$569$		−	518.753i		−	0.911693i	−0.890059	−	0.455846i	$-0.849337\pi$
$569$		−	518.753i		−	0.911693i	0.890059	−	0.455846i	$-0.150663\pi$
$570$		0			0
$571$	1034.07			1.81098			0.905492	−	0.424363i	$-0.139502\pi$
$571$	1034.07			1.81098			0.905492	+	0.424363i	$0.139502\pi$
$572$		0			0
$573$	214.766	−	214.766i	0.374809	−	0.374809i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−220.172	−	220.172i	−0.381580	−	0.381580i	0.490091	−	0.871671i	$-0.336964\pi$
$577$	−220.172	−	220.172i	−0.381580	−	0.381580i	−0.871671	+	0.490091i	$0.836964\pi$
$578$		0			0
$579$		−	566.366i		−	0.978179i
$580$		0			0
$581$	−1095.27			−1.88514
$582$		0			0
$583$	−4.20937	+	4.20937i	−0.00722019	+	0.00722019i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	547.517	+	547.517i	0.932738	+	0.932738i	0.997876	−	0.0651384i	$-0.0207489\pi$
$587$	547.517	+	547.517i	0.932738	+	0.932738i	−0.0651384	+	0.997876i	$0.520749\pi$
$588$		0			0
$589$			59.2250i			0.100552i
$590$		0			0
$591$	368.291			0.623165
$592$		0			0
$593$	165.450	−	165.450i	0.279005	−	0.279005i	−0.553707	−	0.832712i	$-0.686787\pi$
$593$	165.450	−	165.450i	0.279005	−	0.279005i	0.832712	+	0.553707i	$0.186787\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−676.775	−	676.775i	−1.13363	−	1.13363i
$598$		0			0
$599$		−	997.987i		−	1.66609i	−0.553206	−	0.833045i	$-0.686596\pi$
$599$		−	997.987i		−	1.66609i	0.553206	−	0.833045i	$-0.313404\pi$
$600$		0			0
$601$	691.372			1.15037			0.575185	−	0.818024i	$-0.304930\pi$
$601$	691.372			1.15037			0.575185	+	0.818024i	$0.304930\pi$
$602$		0			0
$603$	−194.220	+	194.220i	−0.322090	+	0.322090i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−115.833	−	115.833i	−0.190828	−	0.190828i	0.605226	−	0.796054i	$-0.293083\pi$
$607$	−115.833	−	115.833i	−0.190828	−	0.190828i	−0.796054	+	0.605226i	$0.793083\pi$
$608$		0			0
$609$		−	1651.60i		−	2.71199i
$610$		0			0
$611$	302.241			0.494665
$612$		0			0
$613$	72.7906	−	72.7906i	0.118745	−	0.118745i	−0.645237	−	0.763982i	$-0.723242\pi$
$613$	72.7906	−	72.7906i	0.118745	−	0.118745i	0.763982	+	0.645237i	$0.223242\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.5344	−	17.5344i	−0.0284188	−	0.0284188i	0.692755	−	0.721173i	$-0.256397\pi$
$617$	−17.5344	−	17.5344i	−0.0284188	−	0.0284188i	−0.721173	+	0.692755i	$0.756397\pi$
$618$		0			0
$619$			1026.99i			1.65912i	0.558419	+	0.829559i	$0.311408\pi$
$619$			1026.99i			1.65912i	−0.558419	+	0.829559i	$0.688592\pi$
$620$		0			0
$621$	−1.92492			−0.00309971
$622$		0			0
$623$	611.350	−	611.350i	0.981300	−	0.981300i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−86.4500	−	86.4500i	−0.137879	−	0.137879i
$628$		0			0
$629$		−	51.0063i		−	0.0810911i
$630$		0			0
$631$	246.241			0.390239			0.195119	−	0.980780i	$-0.437491\pi$
$631$	246.241			0.390239			0.195119	+	0.980780i	$0.437491\pi$
$632$		0			0
$633$	898.616	−	898.616i	1.41961	−	1.41961i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	587.962	+	587.962i	0.923018	+	0.923018i
$638$		0			0
$639$		−	254.116i		−	0.397677i
$640$		0			0
$641$	825.822			1.28833			0.644167	−	0.764885i	$-0.277204\pi$
$641$	825.822			1.28833			0.644167	+	0.764885i	$0.277204\pi$
$642$		0			0
$643$	−15.2453	+	15.2453i	−0.0237096	+	0.0237096i	−0.718862	−	0.695153i	$-0.755337\pi$
$643$	−15.2453	+	15.2453i	−0.0237096	+	0.0237096i	0.695153	+	0.718862i	$0.255337\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−359.414	−	359.414i	−0.555509	−	0.555509i	0.372517	−	0.928025i	$-0.378495\pi$
$647$	−359.414	−	359.414i	−0.555509	−	0.555509i	−0.928025	+	0.372517i	$0.878495\pi$
$648$		0			0
$649$		−	57.8000i		−	0.0890600i
$650$		0			0
$651$	−94.0312			−0.144441
$652$		0			0
$653$	247.187	−	247.187i	0.378541	−	0.378541i	−0.492034	−	0.870576i	$-0.663747\pi$
$653$	247.187	−	247.187i	0.378541	−	0.378541i	0.870576	+	0.492034i	$0.163747\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	63.7344	+	63.7344i	0.0970083	+	0.0970083i
$658$		0			0
$659$		−	400.606i		−	0.607900i	−0.952688	−	0.303950i	$-0.901694\pi$
$659$		−	400.606i		−	0.607900i	0.952688	−	0.303950i	$-0.0983056\pi$
$660$		0			0
$661$	121.947			0.184488			0.0922442	−	0.995736i	$-0.470596\pi$
$661$	121.947			0.184488			0.0922442	+	0.995736i	$0.470596\pi$
$662$		0			0
$663$	−187.016	+	187.016i	−0.282075	+	0.282075i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.77501	−	4.77501i	−0.00715893	−	0.00715893i
$668$		0			0
$669$		−	1013.63i		−	1.51515i
$670$		0			0
$671$	80.5437			0.120035
$672$		0			0
$673$	645.450	−	645.450i	0.959064	−	0.959064i	−0.0401306	−	0.999194i	$-0.512777\pi$
$673$	645.450	−	645.450i	0.959064	−	0.959064i	0.999194	+	0.0401306i	$0.0127774\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	684.087	+	684.087i	1.01047	+	1.01047i	0.999945	+	0.0105243i	$0.00335004\pi$
$677$	684.087	+	684.087i	1.01047	+	1.01047i	0.0105243	+	0.999945i	$0.496650\pi$
$678$		0			0
$679$			656.753i			0.967236i
$680$		0			0
$681$	−822.178			−1.20731
$682$		0			0
$683$	−164.252	+	164.252i	−0.240485	+	0.240485i	−0.817051	−	0.576565i	$-0.804393\pi$
$683$	−164.252	+	164.252i	−0.240485	+	0.240485i	0.576565	+	0.817051i	$0.304393\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−529.675	−	529.675i	−0.770997	−	0.770997i
$688$		0			0
$689$		−	86.4187i		−	0.125426i
$690$		0			0
$691$	−241.403			−0.349353			−0.174677	−	0.984626i	$-0.555888\pi$
$691$	−241.403			−0.349353			−0.174677	+	0.984626i	$0.555888\pi$
$692$		0			0
$693$	52.6281	−	52.6281i	0.0759425	−	0.0759425i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−107.247	−	107.247i	−0.153869	−	0.153869i
$698$		0			0
$699$			328.459i			0.469899i
$700$		0			0
$701$	353.822			0.504739			0.252369	−	0.967631i	$-0.418790\pi$
$701$	353.822			0.504739			0.252369	+	0.967631i	$0.418790\pi$
$702$		0			0
$703$	−242.031	+	242.031i	−0.344283	+	0.344283i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−402.303	−	402.303i	−0.569028	−	0.569028i
$708$		0			0
$709$			362.762i			0.511654i	0.966723	+	0.255827i	$0.0823477\pi$
$709$			362.762i			0.511654i	−0.966723	+	0.255827i	$0.917652\pi$
$710$		0			0
$711$	−483.850			−0.680520
$712$		0			0
$713$	−0.271857	+	0.271857i	−0.000381287	+	0.000381287i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−481.925	−	481.925i	−0.672141	−	0.672141i
$718$		0			0
$719$		−	1191.41i		−	1.65704i	−0.559959	−	0.828520i	$-0.689183\pi$
$719$		−	1191.41i		−	1.65704i	0.559959	−	0.828520i	$-0.310817\pi$
$720$		0			0
$721$	824.397			1.14341
$722$		0			0
$723$	−242.659	+	242.659i	−0.335628	+	0.335628i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−304.502	−	304.502i	−0.418847	−	0.418847i	0.465959	−	0.884806i	$-0.345709\pi$
$727$	−304.502	−	304.502i	−0.418847	−	0.418847i	−0.884806	+	0.465959i	$0.845709\pi$
$728$		0			0
$729$		−	112.875i		−	0.154835i
$730$		0			0
$731$	−128.334			−0.175560
$732$		0			0
$733$	117.263	−	117.263i	0.159976	−	0.159976i	−0.622580	−	0.782556i	$-0.713915\pi$
$733$	117.263	−	117.263i	0.159976	−	0.159976i	0.782556	+	0.622580i	$0.213915\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	48.6906	+	48.6906i	0.0660659	+	0.0660659i
$738$		0			0
$739$		−	692.669i		−	0.937305i	−0.883383	−	0.468653i	$-0.844740\pi$
$739$		−	692.669i		−	0.937305i	0.883383	−	0.468653i	$-0.155260\pi$
$740$		0			0
$741$	1774.82			2.39518
$742$		0			0
$743$	−826.301	+	826.301i	−1.11212	+	1.11212i	−0.119251	+	0.992864i	$0.538049\pi$
$743$	−826.301	+	826.301i	−1.11212	+	1.11212i	−0.992864	+	0.119251i	$0.961951\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−457.361	−	457.361i	−0.612264	−	0.612264i
$748$		0			0
$749$			905.234i			1.20859i
$750$		0			0
$751$	61.4031			0.0817618			0.0408809	−	0.999164i	$-0.486984\pi$
$751$	61.4031			0.0817618			0.0408809	+	0.999164i	$0.486984\pi$
$752$		0			0
$753$	14.7657	−	14.7657i	0.0196091	−	0.0196091i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−366.372	−	366.372i	−0.483979	−	0.483979i	0.422421	−	0.906400i	$-0.361180\pi$
$757$	−366.372	−	366.372i	−0.483979	−	0.483979i	−0.906400	+	0.422421i	$0.861180\pi$
$758$		0			0
$759$		−	0.793654i		−	0.00104566i
$760$		0			0
$761$	−895.675			−1.17697			−0.588486	−	0.808508i	$-0.700276\pi$
$761$	−895.675			−1.17697			−0.588486	+	0.808508i	$0.700276\pi$
$762$		0			0
$763$	127.644	−	127.644i	0.167292	−	0.167292i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	593.319	+	593.319i	0.773558	+	0.773558i
$768$		0			0
$769$		−	241.675i		−	0.314272i	−0.987577	−	0.157136i	$-0.949774\pi$
$769$		−	241.675i		−	0.314272i	0.987577	−	0.157136i	$-0.0502261\pi$
$770$		0			0
$771$	−1837.48			−2.38325
$772$		0			0
$773$	−359.459	+	359.459i	−0.465019	+	0.465019i	−0.900296	−	0.435278i	$-0.856650\pi$
$773$	−359.459	+	359.459i	−0.465019	+	0.465019i	0.435278	+	0.900296i	$0.356650\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−384.272	−	384.272i	−0.494558	−	0.494558i
$778$		0			0
$779$			1017.80i			1.30655i
$780$		0			0
$781$	−63.7062			−0.0815701
$782$		0			0
$783$	−419.350	+	419.350i	−0.535568	+	0.535568i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−171.789	−	171.789i	−0.218283	−	0.218283i	0.589491	−	0.807775i	$-0.299328\pi$
$787$	−171.789	−	171.789i	−0.218283	−	0.218283i	−0.807775	+	0.589491i	$0.799328\pi$
$788$		0			0
$789$			158.641i			0.201066i
$790$		0			0
$791$	118.241			0.149482
$792$		0			0
$793$	−826.784	+	826.784i	−1.04260	+	1.04260i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	547.891	+	547.891i	0.687441	+	0.687441i	0.961666	−	0.274224i	$-0.0884211\pi$
$797$	547.891	+	547.891i	0.687441	+	0.687441i	−0.274224	+	0.961666i	$0.588421\pi$
$798$		0			0
$799$			50.4281i			0.0631140i
$800$		0			0
$801$	510.575			0.637422
$802$		0			0
$803$	15.9781	−	15.9781i	0.0198980	−	0.0198980i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1088.86	+	1088.86i	1.34926	+	1.34926i
$808$		0			0
$809$			225.925i			0.279264i	0.990203	+	0.139632i	$0.0445920\pi$
$809$			225.925i			0.279264i	−0.990203	+	0.139632i	$0.955408\pi$
$810$		0			0
$811$	1083.03			1.33543			0.667715	−	0.744417i	$-0.267272\pi$
$811$	1083.03			1.33543			0.667715	+	0.744417i	$0.267272\pi$
$812$		0			0
$813$	834.740	−	834.740i	1.02674	−	1.02674i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	608.962	+	608.962i	0.745364	+	0.745364i
$818$		0			0
$819$			1080.46i			1.31924i
$820$		0			0
$821$	125.297			0.152615			0.0763074	−	0.997084i	$-0.475687\pi$
$821$	125.297			0.152615			0.0763074	+	0.997084i	$0.475687\pi$
$822$		0			0
$823$	408.480	−	408.480i	0.496330	−	0.496330i	−0.413963	−	0.910293i	$-0.635856\pi$
$823$	408.480	−	408.480i	0.496330	−	0.496330i	0.910293	+	0.413963i	$0.135856\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−705.508	−	705.508i	−0.853093	−	0.853093i	0.137420	−	0.990513i	$-0.456119\pi$
$827$	−705.508	−	705.508i	−0.853093	−	0.853093i	−0.990513	+	0.137420i	$0.956119\pi$
$828$		0			0
$829$		−	1040.20i		−	1.25476i	−0.778713	−	0.627380i	$-0.784127\pi$
$829$		−	1040.20i		−	1.25476i	0.778713	−	0.627380i	$-0.215873\pi$
$830$		0			0
$831$	51.8531			0.0623985
$832$		0			0
$833$	−98.1000	+	98.1000i	−0.117767	+	0.117767i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	23.8750	+	23.8750i	0.0285245	+	0.0285245i
$838$		0			0
$839$			154.512i			0.184163i	0.995751	+	0.0920813i	$0.0293520\pi$
$839$			154.512i			0.184163i	−0.995751	+	0.0920813i	$0.970648\pi$
$840$		0			0
$841$	−1239.50			−1.47384
$842$		0			0
$843$	725.716	−	725.716i	0.860873	−	0.860873i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	797.695	+	797.695i	0.941789	+	0.941789i
$848$		0			0
$849$			631.853i			0.744232i
$850$		0			0
$851$	−2.22197			−0.00261101
$852$		0			0
$853$	572.141	−	572.141i	0.670739	−	0.670739i	−0.287147	−	0.957886i	$-0.592707\pi$
$853$	572.141	−	572.141i	0.670739	−	0.670739i	0.957886	+	0.287147i	$0.0927069\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	81.2625	+	81.2625i	0.0948221	+	0.0948221i	0.752927	−	0.658105i	$-0.228642\pi$
$857$	81.2625	+	81.2625i	0.0948221	+	0.0948221i	−0.658105	+	0.752927i	$0.728642\pi$
$858$		0			0
$859$			214.094i			0.249236i	0.992205	+	0.124618i	$0.0397705\pi$
$859$			214.094i			0.249236i	−0.992205	+	0.124618i	$0.960229\pi$
$860$		0			0
$861$	−1615.96			−1.87684
$862$		0			0
$863$	72.8172	−	72.8172i	0.0843768	−	0.0843768i	−0.663659	−	0.748036i	$-0.730997\pi$
$863$	72.8172	−	72.8172i	0.0843768	−	0.0843768i	0.748036	+	0.663659i	$0.230997\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	749.548	+	749.548i	0.864531	+	0.864531i
$868$		0			0
$869$			121.300i			0.139586i
$870$		0			0
$871$	−999.622			−1.14767
$872$		0			0
$873$	−274.247	+	274.247i	−0.314143	+	0.314143i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	922.841	+	922.841i	1.05227	+	1.05227i	0.998556	+	0.0537133i	$0.0171057\pi$
$877$	922.841	+	922.841i	1.05227	+	1.05227i	0.0537133	+	0.998556i	$0.482894\pi$
$878$		0			0
$879$			722.347i			0.821783i
$880$		0			0
$881$	364.922			0.414213			0.207107	−	0.978318i	$-0.433595\pi$
$881$	364.922			0.414213			0.207107	+	0.978318i	$0.433595\pi$
$882$		0			0
$883$	274.786	−	274.786i	0.311196	−	0.311196i	−0.534177	−	0.845373i	$-0.679378\pi$
$883$	274.786	−	274.786i	0.311196	−	0.311196i	0.845373	+	0.534177i	$0.179378\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−609.464	−	609.464i	−0.687107	−	0.687107i	0.274484	−	0.961592i	$-0.411493\pi$
$887$	−609.464	−	609.464i	−0.687107	−	0.687107i	−0.961592	+	0.274484i	$0.911493\pi$
$888$		0			0
$889$			197.047i			0.221650i
$890$		0			0
$891$	−140.378			−0.157551
$892$		0			0
$893$	239.287	−	239.287i	0.267959	−	0.267959i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	8.14689	+	8.14689i	0.00908237	+	0.00908237i
$898$		0			0
$899$			118.450i			0.131757i
$900$		0			0
$901$	14.4187			0.0160030
$902$		0			0
$903$	−966.847	+	966.847i	−1.07071	+	1.07071i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−112.439	−	112.439i	−0.123968	−	0.123968i	0.642401	−	0.766369i	$-0.277938\pi$
$907$	−112.439	−	112.439i	−0.123968	−	0.123968i	−0.766369	+	0.642401i	$0.777938\pi$
$908$		0			0
$909$		−	335.987i		−	0.369623i
$910$		0			0
$911$	1469.90			1.61350			0.806752	−	0.590890i	$-0.201223\pi$
$911$	1469.90			1.61350			0.806752	+	0.590890i	$0.201223\pi$
$912$		0			0
$913$	−114.659	+	114.659i	−0.125585	+	0.125585i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1594.20	−	1594.20i	−1.73849	−	1.73849i
$918$		0			0
$919$		−	503.662i		−	0.548055i	−0.961722	−	0.274027i	$-0.911644\pi$
$919$		−	503.662i		−	0.548055i	0.961722	−	0.274027i	$-0.0883559\pi$
$920$		0			0
$921$	−590.553			−0.641209
$922$		0			0
$923$	653.947	−	653.947i	0.708501	−	0.708501i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	344.252	+	344.252i	0.371361	+	0.371361i
$928$		0			0
$929$			1016.43i			1.09411i	0.837097	+	0.547055i	$0.184251\pi$
$929$			1016.43i			1.09411i	−0.837097	+	0.547055i	$0.815749\pi$
$930$		0			0
$931$	930.994			0.999993
$932$		0			0
$933$	−1158.13	+	1158.13i	−1.24130	+	1.24130i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	678.841	+	678.841i	0.724483	+	0.724483i	0.969515	−	0.245032i	$-0.0787985\pi$
$937$	678.841	+	678.841i	0.724483	+	0.724483i	−0.245032	+	0.969515i	$0.578798\pi$
$938$		0			0
$939$		−	1617.34i		−	1.72241i
$940$		0			0
$941$	−603.987			−0.641857			−0.320928	−	0.947103i	$-0.603995\pi$
$941$	−603.987			−0.641857			−0.320928	+	0.947103i	$0.603995\pi$
$942$		0			0
$943$	−4.67196	+	4.67196i	−0.00495435	+	0.00495435i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.02658	−	1.02658i	−0.00108403	−	0.00108403i	0.706565	−	0.707649i	$-0.250244\pi$
$947$	−1.02658	−	1.02658i	−0.00108403	−	0.00108403i	−0.707649	+	0.706565i	$0.750244\pi$
$948$		0			0
$949$			328.031i			0.345660i
$950$		0			0
$951$	2226.68			2.34141
$952$		0			0
$953$	−531.459	+	531.459i	−0.557670	+	0.557670i	−0.928643	−	0.370974i	$-0.879024\pi$
$953$	−531.459	+	531.459i	−0.557670	+	0.557670i	0.370974	+	0.928643i	$0.379024\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−172.900	−	172.900i	−0.180669	−	0.180669i
$958$		0			0
$959$			1160.88i			1.21051i
$960$		0			0
$961$	−954.256			−0.992983
$962$		0			0
$963$	−378.008	+	378.008i	−0.392531	+	0.392531i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	303.392	+	303.392i	0.313746	+	0.313746i	0.846359	−	0.532613i	$-0.178790\pi$
$967$	303.392	+	303.392i	0.313746	+	0.313746i	−0.532613	+	0.846359i	$0.678790\pi$
$968$		0			0
$969$			296.125i			0.305599i
$970$		0			0
$971$	−1156.04			−1.19057			−0.595284	−	0.803516i	$-0.702960\pi$
$971$	−1156.04			−1.19057			−0.595284	+	0.803516i	$0.702960\pi$
$972$		0			0
$973$	−1653.99	+	1653.99i	−1.69988	+	1.69988i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	287.000	+	287.000i	0.293756	+	0.293756i	0.838562	−	0.544806i	$-0.183397\pi$
$977$	287.000	+	287.000i	0.293756	+	0.293756i	−0.544806	+	0.838562i	$0.683397\pi$
$978$		0			0
$979$		−	128.000i		−	0.130746i
$980$		0			0
$981$	106.603			0.108668
$982$		0			0
$983$	868.523	−	868.523i	0.883544	−	0.883544i	−0.110349	−	0.993893i	$-0.535197\pi$
$983$	868.523	−	868.523i	0.883544	−	0.883544i	0.993893	+	0.110349i	$0.0351969\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	379.916	+	379.916i	0.384920	+	0.384920i
$988$		0			0
$989$			5.59058i			0.00565276i
$990$		0			0
$991$	−1263.28			−1.27476			−0.637379	−	0.770551i	$-0.719981\pi$
$991$	−1263.28			−1.27476			−0.637379	+	0.770551i	$0.719981\pi$
$992$		0			0
$993$	−34.9093	+	34.9093i	−0.0351554	+	0.0351554i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−992.547	−	992.547i	−0.995533	−	0.995533i	0.00445673	−	0.999990i	$-0.498581\pi$
$997$	−992.547	−	992.547i	−0.995533	−	0.995533i	−0.999990	+	0.00445673i	$0.998581\pi$
$998$		0			0
$999$			195.137i			0.195333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.3.l.e.57.1		4
3.2	odd	2		1800.3.v.k.1657.1		4
4.3	odd	2		400.3.p.i.257.2		4
5.2	odd	4		40.3.l.b.33.2	yes	4
5.3	odd	4	inner	200.3.l.e.193.1		4
5.4	even	2		40.3.l.b.17.2	✓	4
15.2	even	4		360.3.v.c.73.2		4
15.8	even	4		1800.3.v.k.793.1		4
15.14	odd	2		360.3.v.c.217.2		4
20.3	even	4		400.3.p.i.193.2		4
20.7	even	4		80.3.p.d.33.1		4
20.19	odd	2		80.3.p.d.17.1		4
40.19	odd	2		320.3.p.i.257.2		4
40.27	even	4		320.3.p.i.193.2		4
40.29	even	2		320.3.p.l.257.1		4
40.37	odd	4		320.3.p.l.193.1		4
60.47	odd	4		720.3.bh.l.433.2		4
60.59	even	2		720.3.bh.l.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.l.b.17.2	✓	4	5.4	even	2
40.3.l.b.33.2	yes	4	5.2	odd	4
80.3.p.d.17.1		4	20.19	odd	2
80.3.p.d.33.1		4	20.7	even	4
200.3.l.e.57.1		4	1.1	even	1	trivial
200.3.l.e.193.1		4	5.3	odd	4	inner
320.3.p.i.193.2		4	40.27	even	4
320.3.p.i.257.2		4	40.19	odd	2
320.3.p.l.193.1		4	40.37	odd	4
320.3.p.l.257.1		4	40.29	even	2
360.3.v.c.73.2		4	15.2	even	4
360.3.v.c.217.2		4	15.14	odd	2
400.3.p.i.193.2		4	20.3	even	4
400.3.p.i.257.2		4	4.3	odd	2
720.3.bh.l.433.2		4	60.47	odd	4
720.3.bh.l.577.2		4	60.59	even	2
1800.3.v.k.793.1		4	15.8	even	4
1800.3.v.k.1657.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70156 + 2.70156i) q^{3} +(-6.70156 - 6.70156i) q^{7} -5.59688i q^{9} +O(q^{10})\)	\(q+(-2.70156 + 2.70156i) q^{3} +(-6.70156 - 6.70156i) q^{7} -5.59688i q^{9} -1.40312 q^{11} +(14.4031 - 14.4031i) q^{13} +(2.40312 + 2.40312i) q^{17} -22.8062i q^{19} +36.2094 q^{21} +(0.104686 - 0.104686i) q^{23} +(-9.19375 - 9.19375i) q^{27} -45.6125i q^{29} -2.59688 q^{31} +(3.79063 - 3.79063i) q^{33} +(-10.6125 - 10.6125i) q^{37} +77.8219i q^{39} -44.6281 q^{41} +(-26.7016 + 26.7016i) q^{43} +(10.4922 + 10.4922i) q^{47} +40.8219i q^{49} -12.9844 q^{51} +(3.00000 - 3.00000i) q^{53} +(61.6125 + 61.6125i) q^{57} +41.1938i q^{59} -57.4031 q^{61} +(-37.5078 + 37.5078i) q^{63} +(-34.7016 - 34.7016i) q^{67} +0.565633i q^{69} +45.4031 q^{71} +(-11.3875 + 11.3875i) q^{73} +(9.40312 + 9.40312i) q^{77} -86.4500i q^{79} +100.047 q^{81} +(81.7172 - 81.7172i) q^{83} +(123.225 + 123.225i) q^{87} +91.2250i q^{89} -193.047 q^{91} +(7.01562 - 7.01562i) q^{93} +(-49.0000 - 49.0000i) q^{97} +7.85311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 14 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 14 * q^7	\( 4 q + 2 q^{3} - 14 q^{7} + 20 q^{11} + 32 q^{13} - 16 q^{17} + 68 q^{21} - 38 q^{23} - 88 q^{27} - 36 q^{31} + 92 q^{33} + 60 q^{37} + 52 q^{41} - 94 q^{43} + 106 q^{47} - 180 q^{51} + 12 q^{53} + 144 q^{57} - 204 q^{61} - 86 q^{63} - 126 q^{67} + 156 q^{71} - 148 q^{73} + 12 q^{77} + 16 q^{81} + 186 q^{83} + 288 q^{87} - 388 q^{91} - 100 q^{93} - 196 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 - 14 * q^7 + 20 * q^11 + 32 * q^13 - 16 * q^17 + 68 * q^21 - 38 * q^23 - 88 * q^27 - 36 * q^31 + 92 * q^33 + 60 * q^37 + 52 * q^41 - 94 * q^43 + 106 * q^47 - 180 * q^51 + 12 * q^53 + 144 * q^57 - 204 * q^61 - 86 * q^63 - 126 * q^67 + 156 * q^71 - 148 * q^73 + 12 * q^77 + 16 * q^81 + 186 * q^83 + 288 * q^87 - 388 * q^91 - 100 * q^93 - 196 * q^97

Introduction

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