LMFDB - Embedded newform 1200.3.bg.d.1057.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,3,Mod(193,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))

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

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

chi := DirichletCharacter("1200.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1200.bg (of order $4$, 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:	$32.6976317232$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1200.1057
Dual form			1200.3.bg.d.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 1.22474i) q^{3} +(0.898979 + 0.898979i) q^{7} -3.00000i q^{9} +O(q^{10})$	$q+(1.22474 - 1.22474i) q^{3} +(0.898979 + 0.898979i) q^{7} -3.00000i q^{9} +13.7980 q^{11} +(-12.7980 + 12.7980i) q^{13} +(-15.8990 - 15.8990i) q^{17} -25.7980i q^{19} +2.20204 q^{21} +(10.6969 - 10.6969i) q^{23} +(-3.67423 - 3.67423i) q^{27} -25.7980i q^{29} +39.5959 q^{31} +(16.8990 - 16.8990i) q^{33} +(27.0000 + 27.0000i) q^{37} +31.3485i q^{39} +17.7980 q^{41} +(-12.4949 + 12.4949i) q^{43} +(9.30306 + 9.30306i) q^{47} -47.3837i q^{49} -38.9444 q^{51} +(19.0908 - 19.0908i) q^{53} +(-31.5959 - 31.5959i) q^{57} -20.0000i q^{59} +15.1918 q^{61} +(2.69694 - 2.69694i) q^{63} +(-48.0908 - 48.0908i) q^{67} -26.2020i q^{69} -6.20204 q^{71} +(37.2020 - 37.2020i) q^{73} +(12.4041 + 12.4041i) q^{77} -115.373i q^{79} -9.00000 q^{81} +(82.2929 - 82.2929i) q^{83} +(-31.5959 - 31.5959i) q^{87} +117.394i q^{89} -23.0102 q^{91} +(48.4949 - 48.4949i) q^{93} +(-81.9898 - 81.9898i) q^{97} -41.3939i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{7}+O(q^{10}) $ 4 * q - 16 * q^7	$ 4 q - 16 q^{7} + 16 q^{11} - 12 q^{13} - 44 q^{17} + 48 q^{21} - 16 q^{23} + 80 q^{31} + 48 q^{33} + 108 q^{37} + 32 q^{41} + 48 q^{43} + 96 q^{47} - 48 q^{51} - 100 q^{53} - 48 q^{57} - 96 q^{61} - 48 q^{63} - 16 q^{67} - 64 q^{71} + 188 q^{73} + 128 q^{77} - 36 q^{81} + 192 q^{83} - 48 q^{87} - 288 q^{91} + 96 q^{93} - 132 q^{97}+O(q^{100}) $ 4 * q - 16 * q^7 + 16 * q^11 - 12 * q^13 - 44 * q^17 + 48 * q^21 - 16 * q^23 + 80 * q^31 + 48 * q^33 + 108 * q^37 + 32 * q^41 + 48 * q^43 + 96 * q^47 - 48 * q^51 - 100 * q^53 - 48 * q^57 - 96 * q^61 - 48 * q^63 - 16 * q^67 - 64 * q^71 + 188 * q^73 + 128 * q^77 - 36 * q^81 + 192 * q^83 - 48 * q^87 - 288 * q^91 + 96 * q^93 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$.

$n$	$401$	$577$	$751$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.898979	+	0.898979i	0.128426	+	0.128426i	0.768398	−	0.639972i	$-0.221054\pi$
$7$	0.898979	+	0.898979i	0.128426	+	0.128426i	−0.639972	+	0.768398i	$0.721054\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	13.7980			1.25436			0.627180	−	0.778874i	$-0.284209\pi$
$11$	13.7980			1.25436			0.627180	+	0.778874i	$0.284209\pi$
$12$		0			0
$13$	−12.7980	+	12.7980i	−0.984458	+	0.984458i	−0.999881	−	0.0154227i	$-0.995091\pi$
$13$	−12.7980	+	12.7980i	−0.984458	+	0.984458i	0.0154227	+	0.999881i	$0.495091\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−15.8990	−	15.8990i	−0.935234	−	0.935234i	0.0627925	−	0.998027i	$-0.479999\pi$
$17$	−15.8990	−	15.8990i	−0.935234	−	0.935234i	−0.998027	+	0.0627925i	$0.979999\pi$
$18$		0			0
$19$		−	25.7980i		−	1.35779i	−0.734237	−	0.678894i	$-0.762460\pi$
$19$		−	25.7980i		−	1.35779i	0.734237	−	0.678894i	$-0.237540\pi$
$20$		0			0
$21$	2.20204			0.104859
$22$		0			0
$23$	10.6969	−	10.6969i	0.465084	−	0.465084i	−0.435233	−	0.900318i	$-0.643334\pi$
$23$	10.6969	−	10.6969i	0.465084	−	0.465084i	0.900318	+	0.435233i	$0.143334\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	25.7980i		−	0.889585i	−0.895634	−	0.444792i	$-0.853277\pi$
$29$		−	25.7980i		−	0.889585i	0.895634	−	0.444792i	$-0.146723\pi$
$30$		0			0
$31$	39.5959			1.27729			0.638644	−	0.769502i	$-0.279496\pi$
$31$	39.5959			1.27729			0.638644	+	0.769502i	$0.279496\pi$
$32$		0			0
$33$	16.8990	−	16.8990i	0.512090	−	0.512090i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	0.970566	−	0.240836i	$-0.0774216\pi$
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	−0.240836	+	0.970566i	$0.577422\pi$
$38$		0			0
$39$			31.3485i			0.803807i
$40$		0			0
$41$	17.7980			0.434097			0.217048	−	0.976161i	$-0.430357\pi$
$41$	17.7980			0.434097			0.217048	+	0.976161i	$0.430357\pi$
$42$		0			0
$43$	−12.4949	+	12.4949i	−0.290579	+	0.290579i	−0.837309	−	0.546730i	$-0.815872\pi$
$43$	−12.4949	+	12.4949i	−0.290579	+	0.290579i	0.546730	+	0.837309i	$0.315872\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.30306	+	9.30306i	0.197937	+	0.197937i	0.799115	−	0.601178i	$-0.205302\pi$
$47$	9.30306	+	9.30306i	0.197937	+	0.197937i	−0.601178	+	0.799115i	$0.705302\pi$
$48$		0			0
$49$		−	47.3837i		−	0.967014i
$50$		0			0
$51$	−38.9444			−0.763615
$52$		0			0
$53$	19.0908	−	19.0908i	0.360204	−	0.360204i	−0.503684	−	0.863888i	$-0.668022\pi$
$53$	19.0908	−	19.0908i	0.360204	−	0.360204i	0.863888	+	0.503684i	$0.168022\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−31.5959	−	31.5959i	−0.554314	−	0.554314i
$58$		0			0
$59$		−	20.0000i		−	0.338983i	−0.985532	−	0.169492i	$-0.945787\pi$
$59$		−	20.0000i		−	0.338983i	0.985532	−	0.169492i	$-0.0542125\pi$
$60$		0			0
$61$	15.1918			0.249046			0.124523	−	0.992217i	$-0.460260\pi$
$61$	15.1918			0.249046			0.124523	+	0.992217i	$0.460260\pi$
$62$		0			0
$63$	2.69694	−	2.69694i	0.0428085	−	0.0428085i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−48.0908	−	48.0908i	−0.717773	−	0.717773i	0.250375	−	0.968149i	$-0.419446\pi$
$67$	−48.0908	−	48.0908i	−0.717773	−	0.717773i	−0.968149	+	0.250375i	$0.919446\pi$
$68$		0			0
$69$		−	26.2020i		−	0.379740i
$70$		0			0
$71$	−6.20204			−0.0873527			−0.0436763	−	0.999046i	$-0.513907\pi$
$71$	−6.20204			−0.0873527			−0.0436763	+	0.999046i	$0.513907\pi$
$72$		0			0
$73$	37.2020	−	37.2020i	0.509617	−	0.509617i	−0.404792	−	0.914409i	$-0.632656\pi$
$73$	37.2020	−	37.2020i	0.509617	−	0.509617i	0.914409	+	0.404792i	$0.132656\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	12.4041	+	12.4041i	0.161092	+	0.161092i
$78$		0			0
$79$		−	115.373i		−	1.46042i	−0.683221	−	0.730212i	$-0.739421\pi$
$79$		−	115.373i		−	1.46042i	0.683221	−	0.730212i	$-0.260579\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	82.2929	−	82.2929i	0.991480	−	0.991480i	−0.00848381	−	0.999964i	$-0.502701\pi$
$83$	82.2929	−	82.2929i	0.991480	−	0.991480i	0.999964	+	0.00848381i	$0.00270051\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−31.5959	−	31.5959i	−0.363171	−	0.363171i
$88$		0			0
$89$			117.394i			1.31903i	0.751690	+	0.659516i	$0.229239\pi$
$89$			117.394i			1.31903i	−0.751690	+	0.659516i	$0.770761\pi$
$90$		0			0
$91$	−23.0102			−0.252859
$92$		0			0
$93$	48.4949	−	48.4949i	0.521451	−	0.521451i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−81.9898	−	81.9898i	−0.845256	−	0.845256i	0.144281	−	0.989537i	$-0.453913\pi$
$97$	−81.9898	−	81.9898i	−0.845256	−	0.845256i	−0.989537	+	0.144281i	$0.953913\pi$
$98$		0			0
$99$		−	41.3939i		−	0.418120i
$100$		0			0
$101$	28.3837			0.281026			0.140513	−	0.990079i	$-0.455125\pi$
$101$	28.3837			0.281026			0.140513	+	0.990079i	$0.455125\pi$
$102$		0			0
$103$	16.4949	−	16.4949i	0.160145	−	0.160145i	−0.622486	−	0.782631i	$-0.713877\pi$
$103$	16.4949	−	16.4949i	0.160145	−	0.160145i	0.782631	+	0.622486i	$0.213877\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.1010	+	15.1010i	0.141131	+	0.141131i	0.774142	−	0.633011i	$-0.218181\pi$
$107$	15.1010	+	15.1010i	0.141131	+	0.141131i	−0.633011	+	0.774142i	$0.718181\pi$
$108$		0			0
$109$		−	130.000i		−	1.19266i	−0.802739	−	0.596330i	$-0.796625\pi$
$109$		−	130.000i		−	1.19266i	0.802739	−	0.596330i	$-0.203375\pi$
$110$		0			0
$111$	66.1362			0.595822
$112$		0			0
$113$	−77.2929	+	77.2929i	−0.684008	+	0.684008i	−0.960901	−	0.276893i	$-0.910695\pi$
$113$	−77.2929	+	77.2929i	−0.684008	+	0.684008i	0.276893	+	0.960901i	$0.410695\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	38.3939	+	38.3939i	0.328153	+	0.328153i
$118$		0			0
$119$		−	28.5857i		−	0.240216i
$120$		0			0
$121$	69.3837			0.573419
$122$		0			0
$123$	21.7980	−	21.7980i	0.177219	−	0.177219i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	18.2929	+	18.2929i	0.144038	+	0.144038i	0.775449	−	0.631411i	$-0.217524\pi$
$127$	18.2929	+	18.2929i	0.144038	+	0.144038i	−0.631411	+	0.775449i	$0.717524\pi$
$128$		0			0
$129$			30.6061i			0.237257i
$130$		0			0
$131$	133.798			1.02136			0.510679	−	0.859771i	$-0.329394\pi$
$131$	133.798			1.02136			0.510679	+	0.859771i	$0.329394\pi$
$132$		0			0
$133$	23.1918	−	23.1918i	0.174375	−	0.174375i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−25.8990	−	25.8990i	−0.189044	−	0.189044i	0.606239	−	0.795283i	$-0.292678\pi$
$137$	−25.8990	−	25.8990i	−0.189044	−	0.189044i	−0.795283	+	0.606239i	$0.792678\pi$
$138$		0			0
$139$			54.2020i			0.389943i	0.980809	+	0.194971i	$0.0624614\pi$
$139$			54.2020i			0.389943i	−0.980809	+	0.194971i	$0.937539\pi$
$140$		0			0
$141$	22.7878			0.161615
$142$		0			0
$143$	−176.586	+	176.586i	−1.23487	+	1.23487i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−58.0329	−	58.0329i	−0.394782	−	0.394782i
$148$		0			0
$149$		−	42.7673i		−	0.287029i	−0.989648	−	0.143515i	$-0.954160\pi$
$149$		−	42.7673i		−	0.287029i	0.989648	−	0.143515i	$-0.0458404\pi$
$150$		0			0
$151$	−178.384			−1.18135			−0.590674	−	0.806910i	$-0.701138\pi$
$151$	−178.384			−1.18135			−0.590674	+	0.806910i	$0.701138\pi$
$152$		0			0
$153$	−47.6969	+	47.6969i	−0.311745	+	0.311745i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	0.196970	−	0.980410i	$-0.436890\pi$
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	−0.980410	+	0.196970i	$0.936890\pi$
$158$		0			0
$159$		−	46.7628i		−	0.294105i
$160$		0			0
$161$	19.2327			0.119457
$162$		0			0
$163$	−63.5051	+	63.5051i	−0.389602	+	0.389602i	−0.874545	−	0.484944i	$-0.838840\pi$
$163$	−63.5051	+	63.5051i	−0.389602	+	0.389602i	0.484944	+	0.874545i	$0.338840\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−48.6765	−	48.6765i	−0.291476	−	0.291476i	0.546187	−	0.837663i	$-0.316079\pi$
$167$	−48.6765	−	48.6765i	−0.291476	−	0.291476i	−0.837663	+	0.546187i	$0.816079\pi$
$168$		0			0
$169$		−	158.576i		−	0.938317i
$170$		0			0
$171$	−77.3939			−0.452596
$172$		0			0
$173$	−35.1112	+	35.1112i	−0.202955	+	0.202955i	−0.801265	−	0.598310i	$-0.795839\pi$
$173$	−35.1112	+	35.1112i	−0.202955	+	0.202955i	0.598310	+	0.801265i	$0.295839\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−24.4949	−	24.4949i	−0.138389	−	0.138389i
$178$		0			0
$179$		−	141.171i		−	0.788667i	−0.918967	−	0.394334i	$-0.870975\pi$
$179$		−	141.171i		−	0.788667i	0.918967	−	0.394334i	$-0.129025\pi$
$180$		0			0
$181$	58.8082			0.324907			0.162453	−	0.986716i	$-0.448059\pi$
$181$	58.8082			0.324907			0.162453	+	0.986716i	$0.448059\pi$
$182$		0			0
$183$	18.6061	−	18.6061i	0.101673	−	0.101673i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−219.373	−	219.373i	−1.17312	−	1.17312i
$188$		0			0
$189$		−	6.60612i		−	0.0349530i
$190$		0			0
$191$	325.394			1.70363			0.851816	−	0.523840i	$-0.175501\pi$
$191$	325.394			1.70363			0.851816	+	0.523840i	$0.175501\pi$
$192$		0			0
$193$	39.3837	−	39.3837i	0.204060	−	0.204060i	−0.597677	−	0.801737i	$-0.703909\pi$
$193$	39.3837	−	39.3837i	0.204060	−	0.204060i	0.801737	+	0.597677i	$0.203909\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	119.313	+	119.313i	0.605651	+	0.605651i	0.941807	−	0.336155i	$-0.109127\pi$
$197$	119.313	+	119.313i	0.605651	+	0.605651i	−0.336155	+	0.941807i	$0.609127\pi$
$198$		0			0
$199$			178.565i			0.897313i	0.893704	+	0.448657i	$0.148097\pi$
$199$			178.565i			0.897313i	−0.893704	+	0.448657i	$0.851903\pi$
$200$		0			0
$201$	−117.798			−0.586059
$202$		0			0
$203$	23.1918	−	23.1918i	0.114245	−	0.114245i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−32.0908	−	32.0908i	−0.155028	−	0.155028i
$208$		0			0
$209$		−	355.959i		−	1.70315i
$210$		0			0
$211$	318.747			1.51065			0.755324	−	0.655351i	$-0.227479\pi$
$211$	318.747			1.51065			0.755324	+	0.655351i	$0.227479\pi$
$212$		0			0
$213$	−7.59592	+	7.59592i	−0.0356616	+	0.0356616i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	35.5959	+	35.5959i	0.164036	+	0.164036i
$218$		0			0
$219$		−	91.1260i		−	0.416101i
$220$		0			0
$221$	406.949			1.84140
$222$		0			0
$223$	208.677	−	208.677i	0.935769	−	0.935769i	−0.0622890	−	0.998058i	$-0.519840\pi$
$223$	208.677	−	208.677i	0.935769	−	0.935769i	0.998058	+	0.0622890i	$0.0198400\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	242.070	+	242.070i	1.06639	+	1.06639i	0.997634	+	0.0687559i	$0.0219030\pi$
$227$	242.070	+	242.070i	1.06639	+	1.06639i	0.0687559	+	0.997634i	$0.478097\pi$
$228$		0			0
$229$			413.939i			1.80759i	0.427963	+	0.903796i	$0.359231\pi$
$229$			413.939i			1.80759i	−0.427963	+	0.903796i	$0.640769\pi$
$230$		0			0
$231$	30.3837			0.131531
$232$		0			0
$233$	−64.2622	+	64.2622i	−0.275804	+	0.275804i	−0.831431	−	0.555628i	$-0.812478\pi$
$233$	−64.2622	+	64.2622i	−0.275804	+	0.275804i	0.555628	+	0.831431i	$0.312478\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−141.303	−	141.303i	−0.596215	−	0.596215i
$238$		0			0
$239$			154.788i			0.647648i	0.946117	+	0.323824i	$0.104968\pi$
$239$			154.788i			0.647648i	−0.946117	+	0.323824i	$0.895032\pi$
$240$		0			0
$241$	−421.939			−1.75078			−0.875392	−	0.483414i	$-0.839396\pi$
$241$	−421.939			−1.75078			−0.875392	+	0.483414i	$0.839396\pi$
$242$		0			0
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	330.161	+	330.161i	1.33669	+	1.33669i
$248$		0			0
$249$		−	201.576i		−	0.809540i
$250$		0			0
$251$	−392.586			−1.56409			−0.782043	−	0.623224i	$-0.785822\pi$
$251$	−392.586			−1.56409			−0.782043	+	0.623224i	$0.785822\pi$
$252$		0			0
$253$	147.596	−	147.596i	0.583383	−	0.583383i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	123.515	+	123.515i	0.480604	+	0.480604i	0.905325	−	0.424720i	$-0.139628\pi$
$257$	123.515	+	123.515i	0.480604	+	0.480604i	−0.424720	+	0.905325i	$0.639628\pi$
$258$		0			0
$259$			48.5449i			0.187432i
$260$		0			0
$261$	−77.3939			−0.296528
$262$		0			0
$263$	30.6969	−	30.6969i	0.116718	−	0.116718i	−0.646335	−	0.763054i	$-0.723699\pi$
$263$	30.6969	−	30.6969i	0.116718	−	0.116718i	0.763054	+	0.646335i	$0.223699\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	143.778	+	143.778i	0.538493	+	0.538493i
$268$		0			0
$269$			429.151i			1.59536i	0.603083	+	0.797678i	$0.293939\pi$
$269$			429.151i			1.59536i	−0.603083	+	0.797678i	$0.706061\pi$
$270$		0			0
$271$	−220.727			−0.814489			−0.407245	−	0.913319i	$-0.633510\pi$
$271$	−220.727			−0.814489			−0.407245	+	0.913319i	$0.633510\pi$
$272$		0			0
$273$	−28.1816	+	28.1816i	−0.103229	+	0.103229i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	45.9898	+	45.9898i	0.166028	+	0.166028i	0.785231	−	0.619203i	$-0.212544\pi$
$277$	45.9898	+	45.9898i	0.166028	+	0.166028i	−0.619203	+	0.785231i	$0.712544\pi$
$278$		0			0
$279$		−	118.788i		−	0.425763i
$280$		0			0
$281$	−482.524			−1.71717			−0.858584	−	0.512672i	$-0.828656\pi$
$281$	−482.524			−1.71717			−0.858584	+	0.512672i	$0.828656\pi$
$282$		0			0
$283$	271.283	−	271.283i	0.958596	−	0.958596i	−0.0405803	−	0.999176i	$-0.512921\pi$
$283$	271.283	−	271.283i	0.958596	−	0.958596i	0.999176	+	0.0405803i	$0.0129207\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.0000	+	16.0000i	0.0557491	+	0.0557491i
$288$		0			0
$289$			216.555i			0.749326i
$290$		0			0
$291$	−200.833			−0.690148
$292$		0			0
$293$	149.091	−	149.091i	0.508842	−	0.508842i	−0.405329	−	0.914171i	$-0.632843\pi$
$293$	149.091	−	149.091i	0.508842	−	0.508842i	0.914171	+	0.405329i	$0.132843\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−50.6969	−	50.6969i	−0.170697	−	0.170697i
$298$		0			0
$299$			273.798i			0.915712i
$300$		0			0
$301$	−22.4653			−0.0746356
$302$		0			0
$303$	34.7628	−	34.7628i	0.114729	−	0.114729i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−230.697	−	230.697i	−0.751456	−	0.751456i	0.223295	−	0.974751i	$-0.428319\pi$
$307$	−230.697	−	230.697i	−0.751456	−	0.751456i	−0.974751	+	0.223295i	$0.928319\pi$
$308$		0			0
$309$		−	40.4041i		−	0.130758i
$310$		0			0
$311$	47.7367			0.153494			0.0767472	−	0.997051i	$-0.475547\pi$
$311$	47.7367			0.153494			0.0767472	+	0.997051i	$0.475547\pi$
$312$		0			0
$313$	−219.767	+	219.767i	−0.702132	+	0.702132i	−0.964868	−	0.262736i	$-0.915375\pi$
$313$	−219.767	+	219.767i	−0.702132	+	0.702132i	0.262736	+	0.964868i	$0.415375\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	332.828	+	332.828i	1.04993	+	1.04993i	0.998686	+	0.0512429i	$0.0163183\pi$
$317$	332.828	+	332.828i	1.04993	+	1.04993i	0.0512429	+	0.998686i	$0.483682\pi$
$318$		0			0
$319$		−	355.959i		−	1.11586i
$320$		0			0
$321$	36.9898			0.115233
$322$		0			0
$323$	−410.161	+	410.161i	−1.26985	+	1.26985i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−159.217	−	159.217i	−0.486902	−	0.486902i
$328$		0			0
$329$			16.7265i			0.0508405i
$330$		0			0
$331$	−209.980			−0.634379			−0.317190	−	0.948362i	$-0.602739\pi$
$331$	−209.980			−0.634379			−0.317190	+	0.948362i	$0.602739\pi$
$332$		0			0
$333$	81.0000	−	81.0000i	0.243243	−	0.243243i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−88.3735	−	88.3735i	−0.262236	−	0.262236i	0.563726	−	0.825962i	$-0.309367\pi$
$337$	−88.3735	−	88.3735i	−0.262236	−	0.262236i	−0.825962	+	0.563726i	$0.809367\pi$
$338$		0			0
$339$			189.328i			0.558490i
$340$		0			0
$341$	546.343			1.60218
$342$		0			0
$343$	86.6469	−	86.6469i	0.252615	−	0.252615i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	212.495	+	212.495i	0.612377	+	0.612377i	0.943565	−	0.331188i	$-0.107449\pi$
$347$	212.495	+	212.495i	0.612377	+	0.612377i	−0.331188	+	0.943565i	$0.607449\pi$
$348$		0			0
$349$			280.000i			0.802292i	0.916014	+	0.401146i	$0.131388\pi$
$349$			280.000i			0.802292i	−0.916014	+	0.401146i	$0.868612\pi$
$350$		0			0
$351$	94.0454			0.267936
$352$		0			0
$353$	−212.505	+	212.505i	−0.601997	+	0.601997i	−0.940842	−	0.338845i	$-0.889964\pi$
$353$	−212.505	+	212.505i	−0.601997	+	0.601997i	0.338845	+	0.940842i	$0.389964\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−35.0102	−	35.0102i	−0.0980678	−	0.0980678i
$358$		0			0
$359$			633.090i			1.76348i	0.471734	+	0.881741i	$0.343628\pi$
$359$			633.090i			1.76348i	−0.471734	+	0.881741i	$0.656372\pi$
$360$		0			0
$361$	−304.535			−0.843586
$362$		0			0
$363$	84.9773	−	84.9773i	0.234097	−	0.234097i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−267.505	−	267.505i	−0.728897	−	0.728897i	0.241503	−	0.970400i	$-0.422360\pi$
$367$	−267.505	−	267.505i	−0.728897	−	0.728897i	−0.970400	+	0.241503i	$0.922360\pi$
$368$		0			0
$369$		−	53.3939i		−	0.144699i
$370$		0			0
$371$	34.3245			0.0925189
$372$		0			0
$373$	376.939	−	376.939i	1.01056	−	1.01056i	0.0106161	−	0.999944i	$-0.496621\pi$
$373$	376.939	−	376.939i	1.01056	−	1.01056i	0.999944	−	0.0106161i	$-0.00337926\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	330.161	+	330.161i	0.875759	+	0.875759i
$378$		0			0
$379$		−	167.818i		−	0.442793i	−0.975184	−	0.221396i	$-0.928939\pi$
$379$		−	167.818i		−	0.442793i	0.975184	−	0.221396i	$-0.0710614\pi$
$380$		0			0
$381$	44.8082			0.117607
$382$		0			0
$383$	−478.293	+	478.293i	−1.24881	+	1.24881i	−0.292559	+	0.956248i	$0.594507\pi$
$383$	−478.293	+	478.293i	−1.24881	+	1.24881i	−0.956248	+	0.292559i	$0.905493\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	37.4847	+	37.4847i	0.0968597	+	0.0968597i
$388$		0			0
$389$			169.151i			0.434836i	0.976079	+	0.217418i	$0.0697634\pi$
$389$			169.151i			0.434836i	−0.976079	+	0.217418i	$0.930237\pi$
$390$		0			0
$391$	−340.141			−0.869925
$392$		0			0
$393$	163.868	−	163.868i	0.416968	−	0.416968i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	69.3429	+	69.3429i	0.174667	+	0.174667i	0.789026	−	0.614359i	$-0.210585\pi$
$397$	69.3429	+	69.3429i	0.174667	+	0.174667i	−0.614359	+	0.789026i	$0.710585\pi$
$398$		0			0
$399$		−	56.8082i		−	0.142376i
$400$		0			0
$401$	414.767			1.03433			0.517166	−	0.855885i	$-0.326987\pi$
$401$	414.767			1.03433			0.517166	+	0.855885i	$0.326987\pi$
$402$		0			0
$403$	−506.747	+	506.747i	−1.25744	+	1.25744i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	372.545	+	372.545i	0.915344	+	0.915344i
$408$		0			0
$409$		−	605.110i		−	1.47949i	−0.672889	−	0.739744i	$-0.734947\pi$
$409$		−	605.110i		−	1.47949i	0.672889	−	0.739744i	$-0.265053\pi$
$410$		0			0
$411$	−63.4393			−0.154353
$412$		0			0
$413$	17.9796	−	17.9796i	0.0435341	−	0.0435341i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	66.3837	+	66.3837i	0.159193	+	0.159193i
$418$		0			0
$419$			15.9592i			0.0380887i	0.999819	+	0.0190444i	$0.00606238\pi$
$419$			15.9592i			0.0380887i	−0.999819	+	0.0190444i	$0.993938\pi$
$420$		0			0
$421$	433.171			1.02891			0.514455	−	0.857517i	$-0.327994\pi$
$421$	433.171			1.02891			0.514455	+	0.857517i	$0.327994\pi$
$422$		0			0
$423$	27.9092	−	27.9092i	0.0659792	−	0.0659792i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	13.6571	+	13.6571i	0.0319840	+	0.0319840i
$428$		0			0
$429$			432.545i			1.00826i
$430$		0			0
$431$	−24.1816			−0.0561059			−0.0280529	−	0.999606i	$-0.508931\pi$
$431$	−24.1816			−0.0561059			−0.0280529	+	0.999606i	$0.508931\pi$
$432$		0			0
$433$	−528.918	+	528.918i	−1.22152	+	1.22152i	−0.254429	+	0.967091i	$0.581888\pi$
$433$	−528.918	+	528.918i	−1.22152	+	1.22152i	−0.967091	+	0.254429i	$0.918112\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−275.959	−	275.959i	−0.631486	−	0.631486i
$438$		0			0
$439$			44.6265i			0.101655i	0.998707	+	0.0508275i	$0.0161859\pi$
$439$			44.6265i			0.101655i	−0.998707	+	0.0508275i	$0.983814\pi$
$440$		0			0
$441$	−142.151			−0.322338
$442$		0			0
$443$	311.283	−	311.283i	0.702670	−	0.702670i	−0.262313	−	0.964983i	$-0.584485\pi$
$443$	311.283	−	311.283i	0.702670	−	0.702670i	0.964983	+	0.262313i	$0.0844853\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−52.3791	−	52.3791i	−0.117179	−	0.117179i
$448$		0			0
$449$			141.273i			0.314640i	0.987548	+	0.157320i	$0.0502855\pi$
$449$			141.273i			0.314640i	−0.987548	+	0.157320i	$0.949715\pi$
$450$		0			0
$451$	245.576			0.544513
$452$		0			0
$453$	−218.474	+	218.474i	−0.482284	+	0.482284i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−20.3939	−	20.3939i	−0.0446256	−	0.0446256i	0.684442	−	0.729067i	$-0.260046\pi$
$457$	−20.3939	−	20.3939i	−0.0446256	−	0.0446256i	−0.729067	+	0.684442i	$0.760046\pi$
$458$		0			0
$459$			116.833i			0.254538i
$460$		0			0
$461$	−626.727			−1.35949			−0.679747	−	0.733447i	$-0.737910\pi$
$461$	−626.727			−1.35949			−0.679747	+	0.733447i	$0.737910\pi$
$462$		0			0
$463$	−314.515	+	314.515i	−0.679299	+	0.679299i	−0.959842	−	0.280543i	$-0.909486\pi$
$463$	−314.515	+	314.515i	−0.679299	+	0.679299i	0.280543	+	0.959842i	$0.409486\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	46.6969	+	46.6969i	0.0999934	+	0.0999934i	0.755334	−	0.655340i	$-0.227475\pi$
$467$	46.6969	+	46.6969i	0.0999934	+	0.0999934i	−0.655340	+	0.755334i	$0.727475\pi$
$468$		0			0
$469$		−	86.4653i		−	0.184361i
$470$		0			0
$471$	−301.287			−0.639676
$472$		0			0
$473$	−172.404	+	172.404i	−0.364491	+	0.364491i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−57.2724	−	57.2724i	−0.120068	−	0.120068i
$478$		0			0
$479$			71.2735i			0.148796i	0.997229	+	0.0743982i	$0.0237036\pi$
$479$			71.2735i			0.148796i	−0.997229	+	0.0743982i	$0.976296\pi$
$480$		0			0
$481$	−691.090			−1.43678
$482$		0			0
$483$	23.5551	−	23.5551i	0.0487683	−	0.0487683i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	295.423	+	295.423i	0.606619	+	0.606619i	0.942061	−	0.335442i	$-0.108886\pi$
$487$	295.423	+	295.423i	0.606619	+	0.606619i	−0.335442	+	0.942061i	$0.608886\pi$
$488$		0			0
$489$			155.555i			0.318109i
$490$		0			0
$491$	910.080			1.85352			0.926761	−	0.375651i	$-0.122581\pi$
$491$	910.080			1.85352			0.926761	+	0.375651i	$0.122581\pi$
$492$		0			0
$493$	−410.161	+	410.161i	−0.831970	+	0.831970i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.57551	−	5.57551i	−0.0112183	−	0.0112183i
$498$		0			0
$499$			970.161i			1.94421i	0.234544	+	0.972105i	$0.424640\pi$
$499$			970.161i			1.94421i	−0.234544	+	0.972105i	$0.575360\pi$
$500$		0			0
$501$	−119.233			−0.237989
$502$		0			0
$503$	276.817	−	276.817i	0.550333	−	0.550333i	−0.376204	−	0.926537i	$-0.622771\pi$
$503$	276.817	−	276.817i	0.550333	−	0.550333i	0.926537	+	0.376204i	$0.122771\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−194.215	−	194.215i	−0.383066	−	0.383066i
$508$		0			0
$509$			900.059i			1.76829i	0.467213	+	0.884145i	$0.345258\pi$
$509$			900.059i			1.76829i	−0.467213	+	0.884145i	$0.654742\pi$
$510$		0			0
$511$	66.8877			0.130896
$512$		0			0
$513$	−94.7878	+	94.7878i	−0.184771	+	0.184771i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	128.363	+	128.363i	0.248285	+	0.248285i
$518$		0			0
$519$			86.0046i			0.165712i
$520$		0			0
$521$	−239.494			−0.459681			−0.229841	−	0.973228i	$-0.573820\pi$
$521$	−239.494			−0.459681			−0.229841	+	0.973228i	$0.573820\pi$
$522$		0			0
$523$	12.7173	−	12.7173i	0.0243162	−	0.0243162i	−0.694844	−	0.719160i	$-0.744527\pi$
$523$	12.7173	−	12.7173i	0.0243162	−	0.0243162i	0.719160	+	0.694844i	$0.244527\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−629.535	−	629.535i	−1.19456	−	1.19456i
$528$		0			0
$529$			300.151i			0.567393i
$530$		0			0
$531$	−60.0000			−0.112994
$532$		0			0
$533$	−227.778	+	227.778i	−0.427350	+	0.427350i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−172.899	−	172.899i	−0.321972	−	0.321972i
$538$		0			0
$539$		−	653.798i		−	1.21298i
$540$		0			0
$541$	477.110			0.881904			0.440952	−	0.897531i	$-0.354641\pi$
$541$	477.110			0.881904			0.440952	+	0.897531i	$0.354641\pi$
$542$		0			0
$543$	72.0250	−	72.0250i	0.132643	−	0.132643i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	720.372	+	720.372i	1.31695	+	1.31695i	0.916177	+	0.400775i	$0.131259\pi$
$547$	720.372	+	720.372i	1.31695	+	1.31695i	0.400775	+	0.916177i	$0.368741\pi$
$548$		0			0
$549$		−	45.5755i		−	0.0830155i
$550$		0			0
$551$	−665.535			−1.20787
$552$		0			0
$553$	103.718	−	103.718i	0.187556	−	0.187556i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	139.899	+	139.899i	0.251165	+	0.251165i	0.821448	−	0.570283i	$-0.193166\pi$
$557$	139.899	+	139.899i	0.251165	+	0.251165i	−0.570283	+	0.821448i	$0.693166\pi$
$558$		0			0
$559$		−	319.818i		−	0.572126i
$560$		0			0
$561$	−537.353			−0.957849
$562$		0			0
$563$	461.121	−	461.121i	0.819043	−	0.819043i	−0.166926	−	0.985969i	$-0.553384\pi$
$563$	461.121	−	461.121i	0.819043	−	0.819043i	0.985969	+	0.166926i	$0.0533841\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−8.09082	−	8.09082i	−0.0142695	−	0.0142695i
$568$		0			0
$569$		−	31.4939i		−	0.0553495i	−0.999617	−	0.0276748i	$-0.991190\pi$
$569$		−	31.4939i		−	0.0553495i	0.999617	−	0.0276748i	$-0.00881027\pi$
$570$		0			0
$571$	−139.233			−0.243840			−0.121920	−	0.992540i	$-0.538905\pi$
$571$	−139.233			−0.243840			−0.121920	+	0.992540i	$0.538905\pi$
$572$		0			0
$573$	398.524	−	398.524i	0.695505	−	0.695505i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−463.000	−	463.000i	−0.802426	−	0.802426i	0.181048	−	0.983474i	$-0.442051\pi$
$577$	−463.000	−	463.000i	−0.802426	−	0.802426i	−0.983474	+	0.181048i	$0.942051\pi$
$578$		0			0
$579$		−	96.4699i		−	0.166615i
$580$		0			0
$581$	147.959			0.254663
$582$		0			0
$583$	263.414	−	263.414i	0.451826	−	0.451826i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	464.091	+	464.091i	0.790615	+	0.790615i	0.981594	−	0.190979i	$-0.0611664\pi$
$587$	464.091	+	464.091i	0.790615	+	0.790615i	−0.190979	+	0.981594i	$0.561166\pi$
$588$		0			0
$589$		−	1021.49i		−	1.73429i
$590$		0			0
$591$	292.257			0.494512
$592$		0			0
$593$	−120.646	+	120.646i	−0.203450	+	0.203450i	−0.801476	−	0.598026i	$-0.795952\pi$
$593$	−120.646	+	120.646i	−0.203450	+	0.203450i	0.598026	+	0.801476i	$0.295952\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	218.697	+	218.697i	0.366327	+	0.366327i
$598$		0			0
$599$			157.131i			0.262322i	0.991361	+	0.131161i	$0.0418704\pi$
$599$			157.131i			0.262322i	−0.991361	+	0.131161i	$0.958130\pi$
$600$		0			0
$601$	550.302			0.915644			0.457822	−	0.889044i	$-0.348630\pi$
$601$	550.302			0.915644			0.457822	+	0.889044i	$0.348630\pi$
$602$		0			0
$603$	−144.272	+	144.272i	−0.239258	+	0.239258i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−182.030	−	182.030i	−0.299884	−	0.299884i	0.541084	−	0.840968i	$-0.318014\pi$
$607$	−182.030	−	182.030i	−0.299884	−	0.299884i	−0.840968	+	0.541084i	$0.818014\pi$
$608$		0			0
$609$		−	56.8082i		−	0.0932811i
$610$		0			0
$611$	−238.120			−0.389722
$612$		0			0
$613$	788.110	−	788.110i	1.28566	−	1.28566i	0.348265	−	0.937396i	$-0.386771\pi$
$613$	788.110	−	788.110i	1.28566	−	1.28566i	0.937396	−	0.348265i	$-0.113229\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−356.221	−	356.221i	−0.577344	−	0.577344i	0.356826	−	0.934171i	$-0.383859\pi$
$617$	−356.221	−	356.221i	−0.577344	−	0.577344i	−0.934171	+	0.356826i	$0.883859\pi$
$618$		0			0
$619$			73.8796i			0.119353i	0.998218	+	0.0596766i	$0.0190069\pi$
$619$			73.8796i			0.119353i	−0.998218	+	0.0596766i	$0.980993\pi$
$620$		0			0
$621$	−78.6061			−0.126580
$622$		0			0
$623$	−105.535	+	105.535i	−0.169398	+	0.169398i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−435.959	−	435.959i	−0.695310	−	0.695310i
$628$		0			0
$629$		−	858.545i		−	1.36494i
$630$		0			0
$631$	45.9796			0.0728678			0.0364339	−	0.999336i	$-0.488400\pi$
$631$	45.9796			0.0728678			0.0364339	+	0.999336i	$0.488400\pi$
$632$		0			0
$633$	390.384	−	390.384i	0.616720	−	0.616720i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	606.414	+	606.414i	0.951985	+	0.951985i
$638$		0			0
$639$			18.6061i			0.0291176i
$640$		0			0
$641$	−789.757			−1.23207			−0.616035	−	0.787719i	$-0.711262\pi$
$641$	−789.757			−1.23207			−0.616035	+	0.787719i	$0.711262\pi$
$642$		0			0
$643$	−530.474	+	530.474i	−0.824999	+	0.824999i	−0.986820	−	0.161821i	$-0.948263\pi$
$643$	−530.474	+	530.474i	−0.824999	+	0.824999i	0.161821	+	0.986820i	$0.448263\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−135.323	−	135.323i	−0.209155	−	0.209155i	0.594753	−	0.803908i	$-0.297250\pi$
$647$	−135.323	−	135.323i	−0.209155	−	0.209155i	−0.803908	+	0.594753i	$0.797250\pi$
$648$		0			0
$649$		−	275.959i		−	0.425207i
$650$		0			0
$651$	87.1918			0.133935
$652$		0			0
$653$	49.8377	−	49.8377i	0.0763212	−	0.0763212i	−0.667916	−	0.744237i	$-0.732813\pi$
$653$	49.8377	−	49.8377i	0.0763212	−	0.0763212i	0.744237	+	0.667916i	$0.232813\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−111.606	−	111.606i	−0.169872	−	0.169872i
$658$		0			0
$659$			209.576i			0.318020i	0.987277	+	0.159010i	$0.0508303\pi$
$659$			209.576i			0.318020i	−0.987277	+	0.159010i	$0.949170\pi$
$660$		0			0
$661$	−119.273			−0.180444			−0.0902220	−	0.995922i	$-0.528758\pi$
$661$	−119.273			−0.180444			−0.0902220	+	0.995922i	$0.528758\pi$
$662$		0			0
$663$	498.409	−	498.409i	0.751748	−	0.751748i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−275.959	−	275.959i	−0.413732	−	0.413732i
$668$		0			0
$669$		−	511.151i		−	0.764052i
$670$		0			0
$671$	209.616			0.312394
$672$		0			0
$673$	468.857	−	468.857i	0.696667	−	0.696667i	−0.267023	−	0.963690i	$-0.586040\pi$
$673$	468.857	−	468.857i	0.696667	−	0.696667i	0.963690	+	0.267023i	$0.0860399\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	654.160	+	654.160i	0.966263	+	0.966263i	0.999449	−	0.0331860i	$-0.0105654\pi$
$677$	654.160	+	654.160i	0.966263	+	0.966263i	−0.0331860	+	0.999449i	$0.510565\pi$
$678$		0			0
$679$		−	147.414i		−	0.217105i
$680$		0			0
$681$	592.949			0.870703
$682$		0			0
$683$	286.070	−	286.070i	0.418844	−	0.418844i	−0.465961	−	0.884805i	$-0.654291\pi$
$683$	286.070	−	286.070i	0.418844	−	0.418844i	0.884805	+	0.465961i	$0.154291\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	506.969	+	506.969i	0.737947	+	0.737947i
$688$		0			0
$689$			488.647i			0.709212i
$690$		0			0
$691$	−738.706			−1.06904			−0.534520	−	0.845156i	$-0.679507\pi$
$691$	−738.706			−1.06904			−0.534520	+	0.845156i	$0.679507\pi$
$692$		0			0
$693$	37.2122	−	37.2122i	0.0536973	−	0.0536973i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−282.969	−	282.969i	−0.405982	−	0.405982i
$698$		0			0
$699$			157.410i			0.225193i
$700$		0			0
$701$	475.778			0.678713			0.339356	−	0.940658i	$-0.389791\pi$
$701$	475.778			0.678713			0.339356	+	0.940658i	$0.389791\pi$
$702$		0			0
$703$	696.545	−	696.545i	0.990818	−	0.990818i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	25.5163	+	25.5163i	0.0360910	+	0.0360910i
$708$		0			0
$709$			504.363i			0.711373i	0.934605	+	0.355686i	$0.115753\pi$
$709$			504.363i			0.711373i	−0.934605	+	0.355686i	$0.884247\pi$
$710$		0			0
$711$	−346.120			−0.486808
$712$		0			0
$713$	423.555	−	423.555i	0.594046	−	0.594046i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	189.576	+	189.576i	0.264401	+	0.264401i
$718$		0			0
$719$		−	481.816i		−	0.670120i	−0.942197	−	0.335060i	$-0.891243\pi$
$719$		−	481.816i		−	0.670120i	0.942197	−	0.335060i	$-0.108757\pi$
$720$		0			0
$721$	29.6571			0.0411334
$722$		0			0
$723$	−516.767	+	516.767i	−0.714754	+	0.714754i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−782.352	−	782.352i	−1.07614	−	1.07614i	−0.996852	−	0.0792856i	$-0.974736\pi$
$727$	−782.352	−	782.352i	−1.07614	−	1.07614i	−0.0792856	−	0.996852i	$-0.525264\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	397.312			0.543519
$732$		0			0
$733$	−537.586	+	537.586i	−0.733405	+	0.733405i	−0.971293	−	0.237888i	$-0.923545\pi$
$733$	−537.586	+	537.586i	−0.733405	+	0.733405i	0.237888	+	0.971293i	$0.423545\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−663.555	−	663.555i	−0.900346	−	0.900346i
$738$		0			0
$739$		−	833.353i		−	1.12768i	−0.825885	−	0.563838i	$-0.809324\pi$
$739$		−	833.353i		−	1.12768i	0.825885	−	0.563838i	$-0.190676\pi$
$740$		0			0
$741$	808.727			1.09140
$742$		0			0
$743$	−991.383	+	991.383i	−1.33430	+	1.33430i	−0.432813	+	0.901484i	$0.642479\pi$
$743$	−991.383	+	991.383i	−1.33430	+	1.33430i	−0.901484	+	0.432813i	$0.857521\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−246.879	−	246.879i	−0.330493	−	0.330493i
$748$		0			0
$749$			27.1510i			0.0362497i
$750$		0			0
$751$	1276.73			1.70004			0.850018	−	0.526754i	$-0.176591\pi$
$751$	1276.73			1.70004			0.850018	+	0.526754i	$0.176591\pi$
$752$		0			0
$753$	−480.817	+	480.817i	−0.638536	+	0.638536i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	36.0918	+	36.0918i	0.0476775	+	0.0476775i	0.730544	−	0.682866i	$-0.239267\pi$
$757$	36.0918	+	36.0918i	0.0476775	+	0.0476775i	−0.682866	+	0.730544i	$0.739267\pi$
$758$		0			0
$759$		−	361.535i		−	0.476330i
$760$		0			0
$761$	716.261			0.941211			0.470605	−	0.882344i	$-0.344036\pi$
$761$	716.261			0.941211			0.470605	+	0.882344i	$0.344036\pi$
$762$		0			0
$763$	116.867	−	116.867i	0.153168	−	0.153168i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	255.959	+	255.959i	0.333715	+	0.333715i
$768$		0			0
$769$			389.576i			0.506600i	0.967388	+	0.253300i	$0.0815160\pi$
$769$			389.576i			0.506600i	−0.967388	+	0.253300i	$0.918484\pi$
$770$		0			0
$771$	302.549			0.392412
$772$		0			0
$773$	409.677	−	409.677i	0.529983	−	0.529983i	−0.390585	−	0.920567i	$-0.627727\pi$
$773$	409.677	−	409.677i	0.529983	−	0.529983i	0.920567	+	0.390585i	$0.127727\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	59.4551	+	59.4551i	0.0765188	+	0.0765188i
$778$		0			0
$779$		−	459.151i		−	0.589411i
$780$		0			0
$781$	−85.5755			−0.109572
$782$		0			0
$783$	−94.7878	+	94.7878i	−0.121057	+	0.121057i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−383.142	−	383.142i	−0.486838	−	0.486838i	0.420469	−	0.907307i	$-0.361866\pi$
$787$	−383.142	−	383.142i	−0.486838	−	0.486838i	−0.907307	+	0.420469i	$0.861866\pi$
$788$		0			0
$789$		−	75.1918i		−	0.0953002i
$790$		0			0
$791$	−138.969			−0.175688
$792$		0			0
$793$	−194.424	+	194.424i	−0.245176	+	0.245176i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−563.191	−	563.191i	−0.706638	−	0.706638i	0.259188	−	0.965827i	$-0.416545\pi$
$797$	−563.191	−	563.191i	−0.706638	−	0.706638i	−0.965827	+	0.259188i	$0.916545\pi$
$798$		0			0
$799$		−	295.818i		−	0.370236i
$800$		0			0
$801$	352.182			0.439677
$802$		0			0
$803$	513.312	−	513.312i	0.639243	−	0.639243i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	525.601	+	525.601i	0.651302	+	0.651302i
$808$		0			0
$809$		−	770.161i		−	0.951992i	−0.879448	−	0.475996i	$-0.842088\pi$
$809$		−	770.161i		−	0.951992i	0.879448	−	0.475996i	$-0.157912\pi$
$810$		0			0
$811$	−13.4939			−0.0166386			−0.00831928	−	0.999965i	$-0.502648\pi$
$811$	−13.4939			−0.0166386			−0.00831928	+	0.999965i	$0.502648\pi$
$812$		0			0
$813$	−270.334	+	270.334i	−0.332514	+	0.332514i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	322.343	+	322.343i	0.394544	+	0.394544i
$818$		0			0
$819$			69.0306i			0.0842865i
$820$		0			0
$821$	741.312			0.902938			0.451469	−	0.892287i	$-0.350900\pi$
$821$	741.312			0.902938			0.451469	+	0.892287i	$0.350900\pi$
$822$		0			0
$823$	−196.272	+	196.272i	−0.238484	+	0.238484i	−0.816222	−	0.577738i	$-0.803936\pi$
$823$	−196.272	+	196.272i	−0.238484	+	0.238484i	0.577738	+	0.816222i	$0.303936\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−20.5357	−	20.5357i	−0.0248316	−	0.0248316i	0.694582	−	0.719414i	$-0.255589\pi$
$827$	−20.5357	−	20.5357i	−0.0248316	−	0.0248316i	−0.719414	+	0.694582i	$0.755589\pi$
$828$		0			0
$829$			264.465i			0.319017i	0.987197	+	0.159509i	$0.0509910\pi$
$829$			264.465i			0.319017i	−0.987197	+	0.159509i	$0.949009\pi$
$830$		0			0
$831$	112.652			0.135561
$832$		0			0
$833$	−753.352	+	753.352i	−0.904384	+	0.904384i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−145.485	−	145.485i	−0.173817	−	0.173817i
$838$		0			0
$839$		−	353.090i		−	0.420846i	−0.977610	−	0.210423i	$-0.932516\pi$
$839$		−	353.090i		−	0.420846i	0.977610	−	0.210423i	$-0.0674841\pi$
$840$		0			0
$841$	175.465			0.208639
$842$		0			0
$843$	−590.969	+	590.969i	−0.701031	+	0.701031i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	62.3745	+	62.3745i	0.0736417	+	0.0736417i
$848$		0			0
$849$		−	664.504i		−	0.782690i
$850$		0			0
$851$	577.635			0.678772
$852$		0			0
$853$	−19.4449	+	19.4449i	−0.0227959	+	0.0227959i	−0.718413	−	0.695617i	$-0.755131\pi$
$853$	−19.4449	+	19.4449i	−0.0227959	+	0.0227959i	0.695617	+	0.718413i	$0.255131\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−602.444	−	602.444i	−0.702968	−	0.702968i	0.262078	−	0.965047i	$-0.415592\pi$
$857$	−602.444	−	602.444i	−0.702968	−	0.702968i	−0.965047	+	0.262078i	$0.915592\pi$
$858$		0			0
$859$		−	1099.53i		−	1.28001i	−0.768369	−	0.640007i	$-0.778931\pi$
$859$		−	1099.53i		−	1.28001i	0.768369	−	0.640007i	$-0.221069\pi$
$860$		0			0
$861$	39.1918			0.0455190
$862$		0			0
$863$	694.797	−	694.797i	0.805095	−	0.805095i	−0.178792	−	0.983887i	$-0.557219\pi$
$863$	694.797	−	694.797i	0.805095	−	0.805095i	0.983887	+	0.178792i	$0.0572189\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	265.225	+	265.225i	0.305911	+	0.305911i
$868$		0			0
$869$		−	1591.92i		−	1.83190i
$870$		0			0
$871$	1230.93			1.41324
$872$		0			0
$873$	−245.969	+	245.969i	−0.281752	+	0.281752i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1092.90	−	1092.90i	−1.24618	−	1.24618i	−0.957394	−	0.288783i	$-0.906749\pi$
$877$	−1092.90	−	1092.90i	−1.24618	−	1.24618i	−0.288783	−	0.957394i	$-0.593251\pi$
$878$		0			0
$879$		−	365.196i		−	0.415468i
$880$		0			0
$881$	138.443			0.157143			0.0785714	−	0.996908i	$-0.474964\pi$
$881$	138.443			0.157143			0.0785714	+	0.996908i	$0.474964\pi$
$882$		0			0
$883$	1008.41	−	1008.41i	1.14203	−	1.14203i	0.153953	−	0.988078i	$-0.450800\pi$
$883$	1008.41	−	1008.41i	1.14203	−	1.14203i	0.988078	−	0.153953i	$-0.0492003\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−639.687	−	639.687i	−0.721180	−	0.721180i	0.247666	−	0.968846i	$-0.420337\pi$
$887$	−639.687	−	639.687i	−0.721180	−	0.721180i	−0.968846	+	0.247666i	$0.920337\pi$
$888$		0			0
$889$			32.8898i			0.0369964i
$890$		0			0
$891$	−124.182			−0.139373
$892$		0			0
$893$	240.000	−	240.000i	0.268757	−	0.268757i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	335.333	+	335.333i	0.373838	+	0.373838i
$898$		0			0
$899$		−	1021.49i		−	1.13626i
$900$		0			0
$901$	−607.049			−0.673750
$902$		0			0
$903$	−27.5143	+	27.5143i	−0.0304699	+	0.0304699i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−893.303	−	893.303i	−0.984899	−	0.984899i	0.0149890	−	0.999888i	$-0.495229\pi$
$907$	−893.303	−	893.303i	−0.984899	−	0.984899i	−0.999888	+	0.0149890i	$0.995229\pi$
$908$		0			0
$909$		−	85.1510i		−	0.0936755i
$910$		0			0
$911$	−1045.03			−1.14712			−0.573562	−	0.819162i	$-0.694439\pi$
$911$	−1045.03			−1.14712			−0.573562	+	0.819162i	$0.694439\pi$
$912$		0			0
$913$	1135.47	−	1135.47i	1.24367	−	1.24367i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	120.282	+	120.282i	0.131169	+	0.131169i
$918$		0			0
$919$			803.573i			0.874400i	0.899364	+	0.437200i	$0.144030\pi$
$919$			803.573i			0.874400i	−0.899364	+	0.437200i	$0.855970\pi$
$920$		0			0
$921$	−565.090			−0.613561
$922$		0			0
$923$	79.3735	−	79.3735i	0.0859951	−	0.0859951i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−49.4847	−	49.4847i	−0.0533815	−	0.0533815i
$928$		0			0
$929$		−	1270.64i		−	1.36776i	−0.729597	−	0.683878i	$-0.760292\pi$
$929$		−	1270.64i		−	1.36776i	0.729597	−	0.683878i	$-0.239708\pi$
$930$		0			0
$931$	−1222.40			−1.31300
$932$		0			0
$933$	58.4653	−	58.4653i	0.0626638	−	0.0626638i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	970.616	+	970.616i	1.03588	+	1.03588i	0.999332	+	0.0365445i	$0.0116351\pi$
$937$	970.616	+	970.616i	1.03588	+	1.03588i	0.0365445	+	0.999332i	$0.488365\pi$
$938$		0			0
$939$			538.318i			0.573288i
$940$		0			0
$941$	−431.616			−0.458678			−0.229339	−	0.973347i	$-0.573656\pi$
$941$	−431.616			−0.458678			−0.229339	+	0.973347i	$0.573656\pi$
$942$		0			0
$943$	190.384	−	190.384i	0.201891	−	0.201891i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−721.121	−	721.121i	−0.761480	−	0.761480i	0.215110	−	0.976590i	$-0.430989\pi$
$947$	−721.121	−	721.121i	−0.761480	−	0.761480i	−0.976590	+	0.215110i	$0.930989\pi$
$948$		0			0
$949$			952.220i			1.00339i
$950$		0			0
$951$	815.258			0.857264
$952$		0			0
$953$	737.291	−	737.291i	0.773652	−	0.773652i	−0.205091	−	0.978743i	$-0.565749\pi$
$953$	737.291	−	737.291i	0.773652	−	0.773652i	0.978743	+	0.205091i	$0.0657489\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−435.959	−	435.959i	−0.455548	−	0.455548i
$958$		0			0
$959$		−	46.5653i		−	0.0485561i
$960$		0			0
$961$	606.837			0.631464
$962$		0			0
$963$	45.3031	−	45.3031i	0.0470437	−	0.0470437i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	958.879	+	958.879i	0.991601	+	0.991601i	0.999965	−	0.00836361i	$-0.00266225\pi$
$967$	958.879	+	958.879i	0.991601	+	0.991601i	−0.00836361	+	0.999965i	$0.502662\pi$
$968$		0			0
$969$			1004.69i			1.03683i
$970$		0			0
$971$	1507.86			1.55289			0.776444	−	0.630186i	$-0.217021\pi$
$971$	1507.86			1.55289			0.776444	+	0.630186i	$0.217021\pi$
$972$		0			0
$973$	−48.7265	+	48.7265i	−0.0500786	+	0.0500786i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	373.838	+	373.838i	0.382638	+	0.382638i	0.872052	−	0.489413i	$-0.162789\pi$
$977$	373.838	+	373.838i	0.382638	+	0.382638i	−0.489413	+	0.872052i	$0.662789\pi$
$978$		0			0
$979$			1619.80i			1.65454i
$980$		0			0
$981$	−390.000			−0.397554
$982$		0			0
$983$	−1319.46	+	1319.46i	−1.34228	+	1.34228i	−0.448501	+	0.893783i	$0.648042\pi$
$983$	−1319.46	+	1319.46i	−1.34228	+	1.34228i	−0.893783	+	0.448501i	$0.851958\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	20.4857	+	20.4857i	0.0207555	+	0.0207555i
$988$		0			0
$989$			267.314i			0.270287i
$990$		0			0
$991$	315.029			0.317890			0.158945	−	0.987287i	$-0.449191\pi$
$991$	315.029			0.317890			0.158945	+	0.987287i	$0.449191\pi$
$992$		0			0
$993$	−257.171	+	257.171i	−0.258984	+	0.258984i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1009.38	−	1009.38i	−1.01242	−	1.01242i	−0.999922	−	0.0124991i	$-0.996021\pi$
$997$	−1009.38	−	1009.38i	−1.01242	−	1.01242i	−0.0124991	−	0.999922i	$-0.503979\pi$
$998$		0			0
$999$		−	198.409i		−	0.198607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.3.bg.d.1057.2		4
4.3	odd	2		150.3.f.b.7.1		4
5.2	odd	4		240.3.bg.b.193.1		4
5.3	odd	4	inner	1200.3.bg.d.193.2		4
5.4	even	2		240.3.bg.b.97.1		4
12.11	even	2		450.3.g.j.307.1		4
15.2	even	4		720.3.bh.i.433.2		4
15.14	odd	2		720.3.bh.i.577.2		4
20.3	even	4		150.3.f.b.43.1		4
20.7	even	4		30.3.f.a.13.2	yes	4
20.19	odd	2		30.3.f.a.7.2	✓	4
40.19	odd	2		960.3.bg.e.577.1		4
40.27	even	4		960.3.bg.e.193.1		4
40.29	even	2		960.3.bg.g.577.2		4
40.37	odd	4		960.3.bg.g.193.2		4
60.23	odd	4		450.3.g.j.343.1		4
60.47	odd	4		90.3.g.d.73.2		4
60.59	even	2		90.3.g.d.37.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.2	✓	4	20.19	odd	2
30.3.f.a.13.2	yes	4	20.7	even	4
90.3.g.d.37.2		4	60.59	even	2
90.3.g.d.73.2		4	60.47	odd	4
150.3.f.b.7.1		4	4.3	odd	2
150.3.f.b.43.1		4	20.3	even	4
240.3.bg.b.97.1		4	5.4	even	2
240.3.bg.b.193.1		4	5.2	odd	4
450.3.g.j.307.1		4	12.11	even	2
450.3.g.j.343.1		4	60.23	odd	4
720.3.bh.i.433.2		4	15.2	even	4
720.3.bh.i.577.2		4	15.14	odd	2
960.3.bg.e.193.1		4	40.27	even	4
960.3.bg.e.577.1		4	40.19	odd	2
960.3.bg.g.193.2		4	40.37	odd	4
960.3.bg.g.577.2		4	40.29	even	2
1200.3.bg.d.193.2		4	5.3	odd	4	inner
1200.3.bg.d.1057.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 1.22474i) q^{3} +(0.898979 + 0.898979i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.22474 - 1.22474i) q^{3} +(0.898979 + 0.898979i) q^{7} -3.00000i q^{9} +13.7980 q^{11} +(-12.7980 + 12.7980i) q^{13} +(-15.8990 - 15.8990i) q^{17} -25.7980i q^{19} +2.20204 q^{21} +(10.6969 - 10.6969i) q^{23} +(-3.67423 - 3.67423i) q^{27} -25.7980i q^{29} +39.5959 q^{31} +(16.8990 - 16.8990i) q^{33} +(27.0000 + 27.0000i) q^{37} +31.3485i q^{39} +17.7980 q^{41} +(-12.4949 + 12.4949i) q^{43} +(9.30306 + 9.30306i) q^{47} -47.3837i q^{49} -38.9444 q^{51} +(19.0908 - 19.0908i) q^{53} +(-31.5959 - 31.5959i) q^{57} -20.0000i q^{59} +15.1918 q^{61} +(2.69694 - 2.69694i) q^{63} +(-48.0908 - 48.0908i) q^{67} -26.2020i q^{69} -6.20204 q^{71} +(37.2020 - 37.2020i) q^{73} +(12.4041 + 12.4041i) q^{77} -115.373i q^{79} -9.00000 q^{81} +(82.2929 - 82.2929i) q^{83} +(-31.5959 - 31.5959i) q^{87} +117.394i q^{89} -23.0102 q^{91} +(48.4949 - 48.4949i) q^{93} +(-81.9898 - 81.9898i) q^{97} -41.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{7}+O(q^{10}) \) 4 * q - 16 * q^7	\( 4 q - 16 q^{7} + 16 q^{11} - 12 q^{13} - 44 q^{17} + 48 q^{21} - 16 q^{23} + 80 q^{31} + 48 q^{33} + 108 q^{37} + 32 q^{41} + 48 q^{43} + 96 q^{47} - 48 q^{51} - 100 q^{53} - 48 q^{57} - 96 q^{61} - 48 q^{63} - 16 q^{67} - 64 q^{71} + 188 q^{73} + 128 q^{77} - 36 q^{81} + 192 q^{83} - 48 q^{87} - 288 q^{91} + 96 q^{93} - 132 q^{97}+O(q^{100}) \) 4 * q - 16 * q^7 + 16 * q^11 - 12 * q^13 - 44 * q^17 + 48 * q^21 - 16 * q^23 + 80 * q^31 + 48 * q^33 + 108 * q^37 + 32 * q^41 + 48 * q^43 + 96 * q^47 - 48 * q^51 - 100 * q^53 - 48 * q^57 - 96 * q^61 - 48 * q^63 - 16 * q^67 - 64 * q^71 + 188 * q^73 + 128 * q^77 - 36 * q^81 + 192 * q^83 - 48 * q^87 - 288 * q^91 + 96 * q^93 - 132 * q^97

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