LMFDB - Embedded newform 288.2.w.a.35.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			35.7
Character	$\chi$	$=$	288.35
Dual form			288.2.w.a.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16775 + 0.797726i) q^{2} +(0.727265 + 1.86308i) q^{4} +(1.65625 - 0.686041i) q^{5} +(-0.456585 - 0.456585i) q^{7} +(-0.636970 + 2.75577i) q^{8} +O(q^{10})$	\(q+(1.16775 + 0.797726i) q^{2} +(0.727265 + 1.86308i) q^{4} +(1.65625 - 0.686041i) q^{5} +(-0.456585 - 0.456585i) q^{7} +(-0.636970 + 2.75577i) q^{8} +(2.48135 + 0.520112i) q^{10} +(2.79166 - 1.15634i) q^{11} +(-1.29543 + 3.12746i) q^{13} +(-0.168946 - 0.897406i) q^{14} +(-2.94217 + 2.70991i) q^{16} +3.55642 q^{17} +(-5.61657 - 2.32646i) q^{19} +(2.48269 + 2.58680i) q^{20} +(4.18240 + 0.876665i) q^{22} +(-4.10130 - 4.10130i) q^{23} +(-1.26302 + 1.26302i) q^{25} +(-4.00759 + 2.61867i) q^{26} +(0.518598 - 1.18272i) q^{28} +(1.87699 - 4.53146i) q^{29} -0.580857i q^{31} +(-5.59748 + 0.817447i) q^{32} +(4.15300 + 2.83705i) q^{34} +(-1.06946 - 0.442983i) q^{35} +(2.58037 + 6.22957i) q^{37} +(-4.70285 - 7.19720i) q^{38} +(0.835590 + 5.00123i) q^{40} +(2.98306 - 2.98306i) q^{41} +(-2.78658 - 6.72741i) q^{43} +(4.18465 + 4.36013i) q^{44} +(-1.51756 - 8.06099i) q^{46} +8.67935i q^{47} -6.58306i q^{49} +(-2.48244 + 0.467344i) q^{50} +(-6.76884 - 0.139014i) q^{52} +(-3.70833 - 8.95270i) q^{53} +(3.83039 - 3.83039i) q^{55} +(1.54907 - 0.967413i) q^{56} +(5.80671 - 3.79427i) q^{58} +(-1.77297 - 4.28032i) q^{59} +(-9.49421 - 3.93263i) q^{61} +(0.463365 - 0.678294i) q^{62} +(-7.18854 - 3.51069i) q^{64} +6.06857i q^{65} +(3.50440 - 8.46037i) q^{67} +(2.58646 + 6.62592i) q^{68} +(-0.895474 - 1.37042i) q^{70} +(-7.84134 + 7.84134i) q^{71} +(10.7396 + 10.7396i) q^{73} +(-1.95627 + 9.33299i) q^{74} +(0.249655 - 12.1561i) q^{76} +(-1.80260 - 0.746662i) q^{77} -5.27177 q^{79} +(-3.01386 + 6.50675i) q^{80} +(5.86313 - 1.10379i) q^{82} +(-1.80609 + 4.36028i) q^{83} +(5.89033 - 2.43985i) q^{85} +(2.11261 - 10.0788i) q^{86} +(1.40841 + 8.42973i) q^{88} +(12.4990 + 12.4990i) q^{89} +(2.01943 - 0.836474i) q^{91} +(4.65833 - 10.6238i) q^{92} +(-6.92374 + 10.1353i) q^{94} -10.8985 q^{95} +9.99452 q^{97} +(5.25148 - 7.68735i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 - 4 * q^8	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	1.16775	+	0.797726i	0.825722	+	0.564078i
$2$	1.16775	+	0.797726i	0.825722	+	0.564078i
$3$		0			0
$3$		0			0
$4$	0.727265	+	1.86308i	0.363633	+	0.931542i
$5$	1.65625	−	0.686041i	0.740698	−	0.306807i	0.0197579	−	0.999805i	$-0.493710\pi$
$5$	1.65625	−	0.686041i	0.740698	−	0.306807i	0.720940	+	0.692998i	$0.243710\pi$
$6$		0			0
$7$	−0.456585	−	0.456585i	−0.172573	−	0.172573i	0.615536	−	0.788109i	$-0.288940\pi$
$7$	−0.456585	−	0.456585i	−0.172573	−	0.172573i	−0.788109	+	0.615536i	$0.788940\pi$
$8$	−0.636970	+	2.75577i	−0.225203	+	0.974312i
$9$		0			0
$10$	2.48135	+	0.520112i	0.784673	+	0.164474i
$11$	2.79166	−	1.15634i	0.841718	−	0.348651i	0.0801871	−	0.996780i	$-0.474448\pi$
$11$	2.79166	−	1.15634i	0.841718	−	0.348651i	0.761531	+	0.648129i	$0.224448\pi$
$12$		0			0
$13$	−1.29543	+	3.12746i	−0.359289	+	0.867400i	0.636111	+	0.771597i	$0.280542\pi$
$13$	−1.29543	+	3.12746i	−0.359289	+	0.867400i	−0.995400	+	0.0958031i	$0.969458\pi$
$14$	−0.168946	−	0.897406i	−0.0451527	−	0.239842i
$15$		0			0
$16$	−2.94217	+	2.70991i	−0.735543	+	0.677479i
$17$	3.55642			0.862560			0.431280	−	0.902218i	$-0.358062\pi$
$17$	3.55642			0.862560			0.431280	+	0.902218i	$0.358062\pi$
$18$		0			0
$19$	−5.61657	−	2.32646i	−1.28853	−	0.533726i	−0.369982	−	0.929039i	$-0.620636\pi$
$19$	−5.61657	−	2.32646i	−1.28853	−	0.533726i	−0.918547	+	0.395313i	$0.870636\pi$
$20$	2.48269	+	2.58680i	0.555146	+	0.578426i
$21$		0			0
$22$	4.18240	+	0.876665i	0.891691	+	0.186906i
$23$	−4.10130	−	4.10130i	−0.855180	−	0.855180i	0.135586	−	0.990766i	$-0.456708\pi$
$23$	−4.10130	−	4.10130i	−0.855180	−	0.855180i	−0.990766	+	0.135586i	$0.956708\pi$
$24$		0			0
$25$	−1.26302	+	1.26302i	−0.252604	+	0.252604i
$26$	−4.00759	+	2.61867i	−0.785954	+	0.513564i
$27$		0			0
$28$	0.518598	−	1.18272i	0.0980059	−	0.223512i
$29$	1.87699	−	4.53146i	0.348548	−	0.841470i	−0.648243	−	0.761433i	$-0.724496\pi$
$29$	1.87699	−	4.53146i	0.348548	−	0.841470i	0.996792	−	0.0800372i	$-0.0255039\pi$
$30$		0			0
$31$		−	0.580857i		−	0.104325i	−0.998639	−	0.0521625i	$-0.983389\pi$
$31$		−	0.580857i		−	0.104325i	0.998639	−	0.0521625i	$-0.0166114\pi$
$32$	−5.59748	+	0.817447i	−0.989504	+	0.144506i
$33$		0			0
$34$	4.15300	+	2.83705i	0.712234	+	0.486551i
$35$	−1.06946	−	0.442983i	−0.180771	−	0.0748778i
$36$		0			0
$37$	2.58037	+	6.22957i	0.424210	+	1.02413i	0.981092	+	0.193543i	$0.0619978\pi$
$37$	2.58037	+	6.22957i	0.424210	+	1.02413i	−0.556881	+	0.830592i	$0.688002\pi$
$38$	−4.70285	−	7.19720i	−0.762903	−	1.16754i
$39$		0			0
$40$	0.835590	+	5.00123i	0.132118	+	0.790764i
$41$	2.98306	−	2.98306i	0.465876	−	0.465876i	−0.434699	−	0.900576i	$-0.643145\pi$
$41$	2.98306	−	2.98306i	0.465876	−	0.465876i	0.900576	+	0.434699i	$0.143145\pi$
$42$		0			0
$43$	−2.78658	−	6.72741i	−0.424950	−	1.02592i	−0.980866	−	0.194682i	$-0.937633\pi$
$43$	−2.78658	−	6.72741i	−0.424950	−	1.02592i	0.555917	−	0.831238i	$-0.312367\pi$
$44$	4.18465	+	4.36013i	0.630859	+	0.657315i
$45$		0			0
$46$	−1.51756	−	8.06099i	−0.223753	−	1.18853i
$47$			8.67935i			1.26601i	0.774147	+	0.633006i	$0.218179\pi$
$47$			8.67935i			1.26601i	−0.774147	+	0.633006i	$0.781821\pi$
$48$		0			0
$49$		−	6.58306i		−	0.940437i
$50$	−2.48244	+	0.467344i	−0.351069	+	0.0660924i
$51$		0			0
$52$	−6.76884	−	0.139014i	−0.938669	−	0.0192778i
$53$	−3.70833	−	8.95270i	−0.509378	−	1.22975i	−0.944242	−	0.329252i	$-0.893203\pi$
$53$	−3.70833	−	8.95270i	−0.509378	−	1.22975i	0.434864	−	0.900496i	$-0.356797\pi$
$54$		0			0
$55$	3.83039	−	3.83039i	0.516490	−	0.516490i
$56$	1.54907	−	0.967413i	0.207004	−	0.129276i
$57$		0			0
$58$	5.80671	−	3.79427i	0.762459	−	0.498212i
$59$	−1.77297	−	4.28032i	−0.230820	−	0.557250i	0.765454	−	0.643491i	$-0.222515\pi$
$59$	−1.77297	−	4.28032i	−0.230820	−	0.557250i	−0.996274	+	0.0862410i	$0.972515\pi$
$60$		0			0
$61$	−9.49421	−	3.93263i	−1.21561	−	0.503522i	−0.319598	−	0.947553i	$-0.603548\pi$
$61$	−9.49421	−	3.93263i	−1.21561	−	0.503522i	−0.896011	+	0.444031i	$0.853548\pi$
$62$	0.463365	−	0.678294i	0.0588474	−	0.0861434i
$63$		0			0
$64$	−7.18854	−	3.51069i	−0.898567	−	0.438836i
$65$			6.06857i			0.752714i
$66$		0			0
$67$	3.50440	−	8.46037i	0.428131	−	1.03360i	−0.551749	−	0.834010i	$-0.686039\pi$
$67$	3.50440	−	8.46037i	0.428131	−	1.03360i	0.979880	−	0.199589i	$-0.0639607\pi$
$68$	2.58646	+	6.62592i	0.313655	+	0.803511i
$69$		0			0
$70$	−0.895474	−	1.37042i	−0.107030	−	0.163797i
$71$	−7.84134	+	7.84134i	−0.930596	+	0.930596i	−0.997743	−	0.0671471i	$-0.978610\pi$
$71$	−7.84134	+	7.84134i	−0.930596	+	0.930596i	0.0671471	+	0.997743i	$0.478610\pi$
$72$		0			0
$73$	10.7396	+	10.7396i	1.25698	+	1.25698i	0.952527	+	0.304453i	$0.0984738\pi$
$73$	10.7396	+	10.7396i	1.25698	+	1.25698i	0.304453	+	0.952527i	$0.401526\pi$
$74$	−1.95627	+	9.33299i	−0.227412	+	1.08494i
$75$		0			0
$76$	0.249655	−	12.1561i	0.0286373	−	1.39440i
$77$	−1.80260	−	0.746662i	−0.205425	−	0.0850900i
$78$		0			0
$79$	−5.27177			−0.593121			−0.296560	−	0.955014i	$-0.595840\pi$
$79$	−5.27177			−0.593121			−0.296560	+	0.955014i	$0.595840\pi$
$80$	−3.01386	+	6.50675i	−0.336959	+	0.727476i
$81$		0			0
$82$	5.86313	−	1.10379i	0.647475	−	0.121894i
$83$	−1.80609	+	4.36028i	−0.198244	+	0.478603i	−0.991472	−	0.130322i	$-0.958399\pi$
$83$	−1.80609	+	4.36028i	−0.198244	+	0.478603i	0.793228	+	0.608925i	$0.208399\pi$
$84$		0			0
$85$	5.89033	−	2.43985i	0.638896	−	0.264639i
$86$	2.11261	−	10.0788i	0.227808	−	1.08683i
$87$		0			0
$88$	1.40841	+	8.42973i	0.150137	+	0.898613i
$89$	12.4990	+	12.4990i	1.32489	+	1.32489i	0.909764	+	0.415125i	$0.136262\pi$
$89$	12.4990	+	12.4990i	1.32489	+	1.32489i	0.415125	+	0.909764i	$0.363738\pi$
$90$		0			0
$91$	2.01943	−	0.836474i	0.211693	−	0.0876863i
$92$	4.65833	−	10.6238i	0.485665	−	1.10761i
$93$		0			0
$94$	−6.92374	+	10.1353i	−0.714130	+	1.04537i
$95$	−10.8985			−1.11816
$96$		0			0
$97$	9.99452			1.01479			0.507395	−	0.861714i	$-0.330608\pi$
$97$	9.99452			1.01479			0.507395	+	0.861714i	$0.330608\pi$
$98$	5.25148	−	7.68735i	0.530480	−	0.776539i
$99$		0			0
$100$	−3.27167	−	1.43456i	−0.327167	−	0.143456i
$101$	−3.85763	+	1.59788i	−0.383849	+	0.158995i	−0.566259	−	0.824227i	$-0.691610\pi$
$101$	−3.85763	+	1.59788i	−0.383849	+	0.158995i	0.182411	+	0.983222i	$0.441610\pi$
$102$		0			0
$103$	1.59155	+	1.59155i	0.156820	+	0.156820i	0.781156	−	0.624336i	$-0.214630\pi$
$103$	1.59155	+	1.59155i	0.156820	+	0.156820i	−0.624336	+	0.781156i	$0.714630\pi$
$104$	−7.79340	−	5.56202i	−0.764206	−	0.545401i
$105$		0			0
$106$	2.81141	−	13.4127i	0.273069	−	1.30276i
$107$	16.1209	−	6.67752i	1.55847	−	0.645540i	0.573648	−	0.819102i	$-0.305528\pi$
$107$	16.1209	−	6.67752i	1.55847	−	0.645540i	0.984823	+	0.173562i	$0.0555277\pi$
$108$		0			0
$109$	−4.94159	+	11.9301i	−0.473318	+	1.14269i	0.489369	+	0.872077i	$0.337227\pi$
$109$	−4.94159	+	11.9301i	−0.473318	+	1.14269i	−0.962688	+	0.270615i	$0.912773\pi$
$110$	7.52853	−	1.41732i	0.717817	−	0.135136i
$111$		0			0
$112$	2.58066	+	0.106045i	0.243849	+	0.0100203i
$113$	−5.30221			−0.498790			−0.249395	−	0.968402i	$-0.580232\pi$
$113$	−5.30221			−0.498790			−0.249395	+	0.968402i	$0.580232\pi$
$114$		0			0
$115$	−9.60644	−	3.97912i	−0.895805	−	0.371054i
$116$	9.80756	+	0.201422i	0.910609	+	0.0187015i
$117$		0			0
$118$	1.34415	−	6.41267i	0.123739	−	0.590334i
$119$	−1.62381	−	1.62381i	−0.148855	−	0.148855i
$120$		0			0
$121$	−1.32193	+	1.32193i	−0.120176	+	0.120176i
$122$	−7.94967	−	12.1661i	−0.719729	−	1.10147i
$123$		0			0
$124$	1.08219	−	0.422437i	0.0971831	−	0.0379360i
$125$	−4.65560	+	11.2396i	−0.416410	+	1.00530i
$126$		0			0
$127$			22.3469i			1.98297i	0.130223	+	0.991485i	$0.458431\pi$
$127$			22.3469i			1.98297i	−0.130223	+	0.991485i	$0.541569\pi$
$128$	−5.59383	−	9.83408i	−0.494429	−	0.869218i
$129$		0			0
$130$	−4.84106	+	7.08656i	−0.424589	+	0.621532i
$131$	−1.42416	−	0.589906i	−0.124429	−	0.0515403i	0.319600	−	0.947553i	$-0.396451\pi$
$131$	−1.42416	−	0.589906i	−0.124429	−	0.0515403i	−0.444029	+	0.896012i	$0.646451\pi$
$132$		0			0
$133$	1.50221	+	3.62667i	0.130259	+	0.314472i
$134$	10.8413	−	7.08402i	0.936547	−	0.611966i
$135$		0			0
$136$	−2.26534	+	9.80069i	−0.194251	+	0.840402i
$137$	−0.460816	+	0.460816i	−0.0393702	+	0.0393702i	−0.726518	−	0.687148i	$-0.758863\pi$
$137$	−0.460816	+	0.460816i	−0.0393702	+	0.0393702i	0.687148	+	0.726518i	$0.258863\pi$
$138$		0			0
$139$	8.10753	+	19.5733i	0.687672	+	1.66019i	0.749420	+	0.662095i	$0.230333\pi$
$139$	8.10753	+	19.5733i	0.687672	+	1.66019i	−0.0617480	+	0.998092i	$0.519667\pi$
$140$	0.0475370	−	2.31465i	0.00401761	−	0.195624i
$141$		0			0
$142$	−15.4119	+	2.90146i	−1.29334	+	0.243485i
$143$			10.2288i			0.855373i
$144$		0			0
$145$		−	8.79292i		−	0.730212i
$146$	3.97389	+	21.1085i	0.328881	+	1.74695i
$147$		0			0
$148$	−9.72960	+	9.33800i	−0.799768	+	0.767579i
$149$	−4.69000	−	11.3227i	−0.384220	−	0.927589i	−0.991139	−	0.132826i	$-0.957595\pi$
$149$	−4.69000	−	11.3227i	−0.384220	−	0.927589i	0.606919	−	0.794764i	$-0.292405\pi$
$150$		0			0
$151$	7.98867	−	7.98867i	0.650109	−	0.650109i	−0.302910	−	0.953019i	$-0.597958\pi$
$151$	7.98867	−	7.98867i	0.650109	−	0.650109i	0.953019	+	0.302910i	$0.0979582\pi$
$152$	9.98877	−	13.9961i	0.810196	−	1.13523i
$153$		0			0
$154$	−1.50935	−	2.30989i	−0.121627	−	0.186137i
$155$	−0.398492	−	0.962044i	−0.0320076	−	0.0772732i
$156$		0			0
$157$	−3.47084	−	1.43767i	−0.277003	−	0.114739i	0.239857	−	0.970808i	$-0.422899\pi$
$157$	−3.47084	−	1.43767i	−0.277003	−	0.114739i	−0.516860	+	0.856070i	$0.672899\pi$
$158$	−6.15609	−	4.20543i	−0.489753	−	0.334566i
$159$		0			0
$160$	−8.71003	+	5.19400i	−0.688588	+	0.410622i
$161$			3.74518i			0.295162i
$162$		0			0
$163$	0.897968	−	2.16789i	0.0703343	−	0.169802i	−0.884803	−	0.465965i	$-0.845707\pi$
$163$	0.897968	−	2.16789i	0.0703343	−	0.169802i	0.955137	+	0.296163i	$0.0957072\pi$
$164$	7.72718	+	3.38822i	0.603391	+	0.264576i
$165$		0			0
$166$	−5.58736	+	3.65094i	−0.433663	+	0.283368i
$167$	−4.17718	+	4.17718i	−0.323240	+	0.323240i	−0.850009	−	0.526769i	$-0.823403\pi$
$167$	−4.17718	+	4.17718i	−0.323240	+	0.323240i	0.526769	+	0.850009i	$0.323403\pi$
$168$		0			0
$169$	1.08956	+	1.08956i	0.0838119	+	0.0838119i
$170$	8.82475	+	1.84974i	0.676827	+	0.141868i
$171$		0			0
$172$	10.5071	−	10.0843i	0.801162	−	0.768917i
$173$	−5.46721	−	2.26459i	−0.415664	−	0.172174i	0.165043	−	0.986286i	$-0.447224\pi$
$173$	−5.46721	−	2.26459i	−0.415664	−	0.172174i	−0.580707	+	0.814113i	$0.697224\pi$
$174$		0			0
$175$	1.15335			0.0871854
$176$	−5.07995	+	10.9673i	−0.382916	+	0.826693i
$177$		0			0
$178$	4.62488	+	24.5664i	0.346649	+	1.84133i
$179$	2.19833	−	5.30724i	0.164311	−	0.396681i	−0.820183	−	0.572101i	$-0.806128\pi$
$179$	2.19833	−	5.30724i	0.164311	−	0.396681i	0.984494	+	0.175420i	$0.0561283\pi$
$180$		0			0
$181$	0.557980	−	0.231123i	0.0414743	−	0.0171792i	−0.361850	−	0.932236i	$-0.617855\pi$
$181$	0.557980	−	0.231123i	0.0414743	−	0.0171792i	0.403324	+	0.915057i	$0.367855\pi$
$182$	3.02546	+	0.634160i	0.224262	+	0.0470071i
$183$		0			0
$184$	13.9146	−	8.68983i	1.02580	−	0.640623i
$185$	8.54748	+	8.54748i	0.628423	+	0.628423i
$186$		0			0
$187$	9.92834	−	4.11245i	0.726032	−	0.300732i
$188$	−16.1704	+	6.31219i	−1.17934	+	0.460364i
$189$		0			0
$190$	−12.7267	−	8.69401i	−0.923290	−	0.630730i
$191$	23.5071			1.70091			0.850457	−	0.526044i	$-0.176325\pi$
$191$	23.5071			1.70091			0.850457	+	0.526044i	$0.176325\pi$
$192$		0			0
$193$	−9.17175			−0.660197			−0.330098	−	0.943946i	$-0.607082\pi$
$193$	−9.17175			−0.660197			−0.330098	+	0.943946i	$0.607082\pi$
$194$	11.6711	+	7.97290i	0.837934	+	0.572421i
$195$		0			0
$196$	12.2648	−	4.78763i	0.876057	−	0.341974i
$197$	8.13281	−	3.36872i	0.579439	−	0.240011i	−0.0736610	−	0.997283i	$-0.523468\pi$
$197$	8.13281	−	3.36872i	0.579439	−	0.240011i	0.653100	+	0.757272i	$0.273468\pi$
$198$		0			0
$199$	13.2257	+	13.2257i	0.937548	+	0.937548i	0.998161	−	0.0606129i	$-0.0193055\pi$
$199$	13.2257	+	13.2257i	0.937548	+	0.937548i	−0.0606129	+	0.998161i	$0.519306\pi$
$200$	−2.67609	−	4.28510i	−0.189228	−	0.303003i
$201$		0			0
$202$	−5.77941	−	1.21141i	−0.406638	−	0.0852346i
$203$	−2.92600	+	1.21199i	−0.205365	+	0.0850650i
$204$		0			0
$205$	2.89419	−	6.98720i	0.202139	−	0.488008i
$206$	0.588905	+	3.12814i	0.0410310	+	0.217948i
$207$		0			0
$208$	−4.66375	−	12.7120i	−0.323373	−	0.881420i
$209$	−18.3697			−1.27066
$210$		0			0
$211$	−19.9447	−	8.26135i	−1.37305	−	0.568735i	−0.430434	−	0.902622i	$-0.641640\pi$
$211$	−19.9447	−	8.26135i	−1.37305	−	0.568735i	−0.942613	+	0.333887i	$0.891640\pi$
$212$	13.9827	−	13.4199i	0.960336	−	0.921684i
$213$		0			0
$214$	24.1520	+	5.06246i	1.65100	+	0.346062i
$215$	−9.23056	−	9.23056i	−0.629519	−	0.629519i
$216$		0			0
$217$	−0.265211	+	0.265211i	−0.0180037	+	0.0180037i
$218$	−15.2874	+	9.98925i	−1.03540	+	0.676557i
$219$		0			0
$220$	9.92205	+	4.35063i	0.668945	+	0.293320i
$221$	−4.60712	+	11.1226i	−0.309908	+	0.748185i
$222$		0			0
$223$			13.8784i			0.929363i	0.885478	+	0.464682i	$0.153831\pi$
$223$			13.8784i			0.929363i	−0.885478	+	0.464682i	$0.846169\pi$
$224$	2.92896	+	2.18249i	0.195699	+	0.145824i
$225$		0			0
$226$	−6.19164	−	4.22971i	−0.411862	−	0.281356i
$227$	17.3888	+	7.20270i	1.15414	+	0.478060i	0.875919	−	0.482458i	$-0.160256\pi$
$227$	17.3888	+	7.20270i	1.15414	+	0.478060i	0.278219	+	0.960518i	$0.410256\pi$
$228$		0			0
$229$	−3.50393	−	8.45924i	−0.231546	−	0.559002i	0.764813	−	0.644252i	$-0.222831\pi$
$229$	−3.50393	−	8.45924i	−0.231546	−	0.559002i	−0.996360	+	0.0852496i	$0.972831\pi$
$230$	−8.04364	−	12.3099i	−0.530382	−	0.811691i
$231$		0			0
$232$	11.2921	+	8.05896i	0.741360	+	0.529097i
$233$	5.85253	−	5.85253i	0.383412	−	0.383412i	−0.488918	−	0.872330i	$-0.662608\pi$
$233$	5.85253	−	5.85253i	0.383412	−	0.383412i	0.872330	+	0.488918i	$0.162608\pi$
$234$		0			0
$235$	5.95439	+	14.3752i	0.388422	+	0.937733i
$236$	6.68518	−	6.41611i	0.435168	−	0.417653i
$237$		0			0
$238$	−0.600843	−	3.19156i	−0.0389469	−	0.206878i
$239$		−	7.83888i		−	0.507055i	−0.967328	−	0.253527i	$-0.918409\pi$
$239$		−	7.83888i		−	0.507055i	0.967328	−	0.253527i	$-0.0815908\pi$
$240$		0			0
$241$		−	29.7873i		−	1.91877i	−0.282104	−	0.959384i	$-0.591032\pi$
$241$		−	29.7873i		−	1.91877i	0.282104	−	0.959384i	$-0.408968\pi$
$242$	−2.59822	+	0.489142i	−0.167020	+	0.0314432i
$243$		0			0
$244$	0.422015	−	20.5486i	0.0270167	−	1.31549i
$245$	−4.51625	−	10.9032i	−0.288533	−	0.696580i
$246$		0			0
$247$	14.5518	−	14.5518i	0.925908	−	0.925908i
$248$	1.60071	+	0.369988i	0.101645	+	0.0234943i
$249$		0			0
$250$	−14.4027	+	9.41113i	−0.910907	+	0.595212i
$251$	0.558412	+	1.34813i	0.0352466	+	0.0850929i	0.940523	−	0.339731i	$-0.110336\pi$
$251$	0.558412	+	1.34813i	0.0352466	+	0.0850929i	−0.905276	+	0.424824i	$0.860336\pi$
$252$		0			0
$253$	−16.1919	−	6.70692i	−1.01798	−	0.421661i
$254$	−17.8267	+	26.0956i	−1.11855	+	1.63738i
$255$		0			0
$256$	1.31273	−	15.9461i	0.0820457	−	0.996629i
$257$			4.05507i			0.252948i	0.991970	+	0.126474i	$0.0403661\pi$
$257$			4.05507i			0.252948i	−0.991970	+	0.126474i	$0.959634\pi$
$258$		0			0
$259$	1.66617	−	4.02249i	0.103531	−	0.249945i
$260$	−11.3063	+	4.41346i	−0.701185	+	0.273711i
$261$		0			0
$262$	−1.19247	−	1.82495i	−0.0736712	−	0.112746i
$263$	8.79592	−	8.79592i	0.542380	−	0.542380i	−0.381846	−	0.924226i	$-0.624712\pi$
$263$	8.79592	−	8.79592i	0.542380	−	0.542380i	0.924226	+	0.381846i	$0.124712\pi$
$264$		0			0
$265$	−12.2838	−	12.2838i	−0.754591	−	0.754591i
$266$	−1.13888	+	5.43338i	−0.0698293	+	0.333142i
$267$		0			0
$268$	18.3110	+	0.376061i	1.11852	+	0.0229716i
$269$	1.15796	+	0.479643i	0.0706021	+	0.0292443i	0.417705	−	0.908583i	$-0.362835\pi$
$269$	1.15796	+	0.479643i	0.0706021	+	0.0292443i	−0.347103	+	0.937827i	$0.612835\pi$
$270$		0			0
$271$	−25.5808			−1.55392			−0.776961	−	0.629549i	$-0.783240\pi$
$271$	−25.5808			−1.55392			−0.776961	+	0.629549i	$0.783240\pi$
$272$	−10.4636	+	9.63761i	−0.634449	+	0.584366i
$273$		0			0
$274$	−0.905722	+	0.170511i	−0.0547167	+	0.0103010i
$275$	−2.06544	+	4.98642i	−0.124551	+	0.300692i
$276$		0			0
$277$	7.32573	−	3.03442i	0.440161	−	0.182320i	−0.151587	−	0.988444i	$-0.548438\pi$
$277$	7.32573	−	3.03442i	0.440161	−	0.182320i	0.591747	+	0.806123i	$0.298438\pi$
$278$	−6.14660	+	29.3243i	−0.368649	+	1.75875i
$279$		0			0
$280$	1.90197	−	2.66501i	0.113664	−	0.159265i
$281$	−15.2794	−	15.2794i	−0.911490	−	0.911490i	0.0848997	−	0.996390i	$-0.472943\pi$
$281$	−15.2794	−	15.2794i	−0.911490	−	0.911490i	−0.996390	+	0.0848997i	$0.972943\pi$
$282$		0			0
$283$	−10.6335	+	4.40456i	−0.632098	+	0.261824i	−0.675644	−	0.737228i	$-0.736134\pi$
$283$	−10.6335	+	4.40456i	−0.632098	+	0.261824i	0.0435461	+	0.999051i	$0.486134\pi$
$284$	−20.3118	−	8.90635i	−1.20528	−	0.528495i
$285$		0			0
$286$	−8.15976	+	11.9446i	−0.482497	+	0.706300i
$287$	−2.72405			−0.160795
$288$		0			0
$289$	−4.35184			−0.255991
$290$	7.01434	−	10.2679i	0.411896	−	0.602952i
$291$		0			0
$292$	−12.1983	+	27.8194i	−0.713852	+	1.62801i
$293$	8.77403	−	3.63432i	0.512584	−	0.212319i	−0.111372	−	0.993779i	$-0.535524\pi$
$293$	8.77403	−	3.63432i	0.512584	−	0.212319i	0.623956	+	0.781460i	$0.285524\pi$
$294$		0			0
$295$	−5.87295	−	5.87295i	−0.341936	−	0.341936i
$296$	−18.8109	+	3.14286i	−1.09336	+	0.182675i
$297$		0			0
$298$	3.55566	−	16.9634i	0.205974	−	0.982661i
$299$	18.1396	−	7.51367i	1.04904	−	0.434527i
$300$		0			0
$301$	−1.79932	+	4.34395i	−0.103711	+	0.250381i
$302$	15.7015	−	2.95597i	0.903521	−	0.170097i
$303$		0			0
$304$	22.8294	−	8.37558i	1.30936	−	0.480372i
$305$	−18.4227			−1.05488
$306$		0			0
$307$	10.2808	+	4.25844i	0.586755	+	0.243042i	0.656254	−	0.754540i	$-0.272140\pi$
$307$	10.2808	+	4.25844i	0.586755	+	0.243042i	−0.0694988	+	0.997582i	$0.522140\pi$
$308$	0.0801250	−	3.90142i	0.00456555	−	0.222304i
$309$		0			0
$310$	0.302111	−	1.44131i	0.0171587	−	0.0818610i
$311$	−1.40680	−	1.40680i	−0.0797723	−	0.0797723i	0.666095	−	0.745867i	$-0.267965\pi$
$311$	−1.40680	−	1.40680i	−0.0797723	−	0.0797723i	−0.745867	+	0.666095i	$0.767965\pi$
$312$		0			0
$313$	−6.25438	+	6.25438i	−0.353518	+	0.353518i	−0.861417	−	0.507899i	$-0.830422\pi$
$313$	−6.25438	+	6.25438i	−0.353518	+	0.353518i	0.507899	+	0.861417i	$0.330422\pi$
$314$	−2.90620	−	4.44762i	−0.164006	−	0.250994i
$315$		0			0
$316$	−3.83398	−	9.82176i	−0.215678	−	0.552517i
$317$	−2.54838	+	6.15234i	−0.143131	+	0.345550i	−0.979146	−	0.203157i	$-0.934880\pi$
$317$	−2.54838	+	6.15234i	−0.143131	+	0.345550i	0.836015	+	0.548707i	$0.184880\pi$
$318$		0			0
$319$		−	14.8207i		−	0.829802i
$320$	−14.3145	−	0.882941i	−0.800205	−	0.0493579i
$321$		0			0
$322$	−2.98763	+	4.37343i	−0.166494	+	0.243722i
$323$	−19.9749	−	8.27387i	−1.11143	−	0.460371i
$324$		0			0
$325$	−2.31388	−	5.58621i	−0.128351	−	0.309867i
$326$	2.77798	−	1.81521i	0.153858	−	0.100535i
$327$		0			0
$328$	6.32052	+	10.1208i	0.348992	+	0.558825i
$329$	3.96286	−	3.96286i	0.218480	−	0.218480i
$330$		0			0
$331$	2.67191	+	6.45057i	0.146862	+	0.354555i	0.980142	−	0.198295i	$-0.0635403\pi$
$331$	2.67191	+	6.45057i	0.146862	+	0.354555i	−0.833281	+	0.552850i	$0.813540\pi$
$332$	−9.43707	−	0.193813i	−0.517927	−	0.0106369i
$333$		0			0
$334$	−8.21013	+	1.54564i	−0.449239	+	0.0845738i
$335$		−	16.4167i		−	0.896938i
$336$		0			0
$337$		−	5.72840i		−	0.312046i	−0.987753	−	0.156023i	$-0.950133\pi$
$337$		−	5.72840i		−	0.312046i	0.987753	−	0.156023i	$-0.0498674\pi$
$338$	0.403158	+	2.14149i	0.0219289	+	0.116482i
$339$		0			0
$340$	8.82949	+	9.19976i	0.478846	+	0.498927i
$341$	−0.671670	−	1.62156i	−0.0363730	−	0.0878122i
$342$		0			0
$343$	−6.20182	+	6.20182i	−0.334867	+	0.334867i
$344$	20.3142	−	3.39403i	1.09527	−	0.182994i
$345$		0			0
$346$	−4.57779	−	7.00581i	−0.246104	−	0.376635i
$347$	−8.72462	−	21.0631i	−0.468362	−	1.13073i	−0.964878	−	0.262699i	$-0.915387\pi$
$347$	−8.72462	−	21.0631i	−0.468362	−	1.13073i	0.496515	−	0.868028i	$-0.334613\pi$
$348$		0			0
$349$	−23.6969	−	9.81557i	−1.26847	−	0.525415i	−0.355968	−	0.934498i	$-0.615849\pi$
$349$	−23.6969	−	9.81557i	−1.26847	−	0.525415i	−0.912497	+	0.409083i	$0.865849\pi$
$350$	1.34683	+	0.920061i	0.0719909	+	0.0491793i
$351$		0			0
$352$	−14.6810	+	8.75465i	−0.782501	+	0.466624i
$353$		−	19.1720i		−	1.02042i	−0.860049	−	0.510211i	$-0.829567\pi$
$353$		−	19.1720i		−	1.02042i	0.860049	−	0.510211i	$-0.170433\pi$
$354$		0			0
$355$	−7.60774	+	18.3667i	−0.403777	+	0.974804i
$356$	−14.1966	+	32.3767i	−0.752418	+	1.71596i
$357$		0			0
$358$	6.80081	−	4.44384i	0.359434	−	0.234864i
$359$	19.4520	−	19.4520i	1.02664	−	1.02664i	0.0270016	−	0.999635i	$-0.491404\pi$
$359$	19.4520	−	19.4520i	1.02664	−	1.02664i	0.999635	−	0.0270016i	$-0.00859591\pi$
$360$		0			0
$361$	12.6984	+	12.6984i	0.668336	+	0.668336i
$362$	0.835952	+	0.175222i	0.0439367	+	0.00920948i
$363$		0			0
$364$	3.02708	+	3.15402i	0.158662	+	0.165316i
$365$	25.1554	+	10.4197i	1.31669	+	0.545392i
$366$		0			0
$367$	19.4899			1.01737			0.508683	−	0.860954i	$-0.330133\pi$
$367$	19.4899			1.01737			0.508683	+	0.860954i	$0.330133\pi$
$368$	23.1809	+	0.952552i	1.20839	+	0.0496552i
$369$		0			0
$370$	3.16274	+	16.7998i	0.164423	+	0.873382i
$371$	−2.39450	+	5.78084i	−0.124316	+	0.300126i
$372$		0			0
$373$	32.4958	−	13.4602i	1.68257	−	0.696943i	0.683126	−	0.730300i	$-0.260620\pi$
$373$	32.4958	−	13.4602i	1.68257	−	0.696943i	0.999443	+	0.0333572i	$0.0106199\pi$
$374$	14.8744	+	3.11779i	0.769137	+	0.161217i
$375$		0			0
$376$	−23.9183	−	5.52848i	−1.23349	−	0.285110i
$377$	11.7404	+	11.7404i	0.604662	+	0.604662i
$378$		0			0
$379$	11.4703	−	4.75115i	0.589189	−	0.244050i	−0.0681125	−	0.997678i	$-0.521698\pi$
$379$	11.4703	−	4.75115i	0.589189	−	0.244050i	0.657302	+	0.753627i	$0.271698\pi$
$380$	−7.92609	−	20.3048i	−0.406600	−	1.04161i
$381$		0			0
$382$	27.4504	+	18.7522i	1.40448	+	0.959448i
$383$	21.4414			1.09560			0.547801	−	0.836609i	$-0.315465\pi$
$383$	21.4414			1.09560			0.547801	+	0.836609i	$0.315465\pi$
$384$		0			0
$385$	−3.49780			−0.178264
$386$	−10.7103	−	7.31655i	−0.545139	−	0.372402i
$387$		0			0
$388$	7.26867	+	18.6206i	0.369011	+	0.945320i
$389$	−22.8503	+	9.46489i	−1.15855	+	0.479889i	−0.877393	−	0.479772i	$-0.840719\pi$
$389$	−22.8503	+	9.46489i	−1.15855	+	0.479889i	−0.281161	+	0.959661i	$0.590719\pi$
$390$		0			0
$391$	−14.5860	−	14.5860i	−0.737644	−	0.737644i
$392$	18.1414	+	4.19321i	0.916279	+	0.211789i
$393$		0			0
$394$	12.1844	+	2.55394i	0.613840	+	0.128666i
$395$	−8.73137	+	3.61665i	−0.439323	+	0.181974i
$396$		0			0
$397$	2.00126	−	4.83148i	0.100441	−	0.242485i	−0.865669	−	0.500616i	$-0.833107\pi$
$397$	2.00126	−	4.83148i	0.100441	−	0.242485i	0.966110	+	0.258131i	$0.0831067\pi$
$398$	4.89380	+	25.9949i	0.245304	+	1.30300i
$399$		0			0
$400$	0.293345	−	7.13871i	0.0146672	−	0.356935i
$401$	16.4805			0.822996			0.411498	−	0.911411i	$-0.365006\pi$
$401$	16.4805			0.822996			0.411498	+	0.911411i	$0.365006\pi$
$402$		0			0
$403$	1.81660	+	0.752462i	0.0904915	+	0.0374828i
$404$	−5.78252	−	6.02501i	−0.287691	−	0.299756i
$405$		0			0
$406$	−4.38367	−	0.918852i	−0.217558	−	0.0456019i
$407$	14.4070	+	14.4070i	0.714131	+	0.714131i
$408$		0			0
$409$	−14.4679	+	14.4679i	−0.715393	+	0.715393i	−0.967658	−	0.252265i	$-0.918824\pi$
$409$	−14.4679	+	14.4679i	−0.715393	+	0.715393i	0.252265	+	0.967658i	$0.418824\pi$
$410$	8.95356	−	5.85051i	0.442185	−	0.288936i
$411$		0			0
$412$	−1.80771	+	4.12266i	−0.0890595	+	0.203109i
$413$	−1.14482	+	2.76384i	−0.0563329	+	0.136000i
$414$		0			0
$415$			8.46076i			0.415323i
$416$	4.69464	−	18.5648i	0.230174	−	0.910215i
$417$		0			0
$418$	−21.4512	−	14.6540i	−1.04921	−	0.716752i
$419$	−13.2299	−	5.48000i	−0.646322	−	0.267715i	0.0353481	−	0.999375i	$-0.488746\pi$
$419$	−13.2299	−	5.48000i	−0.646322	−	0.267715i	−0.681670	+	0.731660i	$0.738746\pi$
$420$		0			0
$421$	3.58725	+	8.66038i	0.174832	+	0.422081i	0.986869	−	0.161525i	$-0.0516412\pi$
$421$	3.58725	+	8.66038i	0.174832	+	0.422081i	−0.812037	+	0.583606i	$0.801641\pi$
$422$	−16.7000	−	25.5576i	−0.812944	−	1.24412i
$423$		0			0
$424$	27.0337	−	4.51670i	1.31287	−	0.219350i
$425$	−4.49184	+	4.49184i	−0.217886	+	0.217886i
$426$		0			0
$427$	2.53933	+	6.13050i	0.122887	+	0.296676i
$428$	24.1650	+	25.1784i	1.16806	+	1.21704i
$429$		0			0
$430$	−3.41550	−	18.1424i	−0.164710	−	0.874905i
$431$			29.9638i			1.44330i	0.692256	+	0.721652i	$0.256617\pi$
$431$			29.9638i			1.44330i	−0.692256	+	0.721652i	$0.743383\pi$
$432$		0			0
$433$			30.4045i			1.46115i	0.682834	+	0.730574i	$0.260747\pi$
$433$			30.4045i			1.46115i	−0.682834	+	0.730574i	$0.739253\pi$
$434$	−0.521264	+	0.0981334i	−0.0250215	+	0.00471055i
$435$		0			0
$436$	−25.8205	−	0.530287i	−1.23658	−	0.0253961i
$437$	13.4937	+	32.5767i	0.645492	+	1.55836i
$438$		0			0
$439$	−10.1550	+	10.1550i	−0.484670	+	0.484670i	−0.906619	−	0.421949i	$-0.861346\pi$
$439$	−10.1550	+	10.1550i	−0.484670	+	0.484670i	0.421949	+	0.906619i	$0.361346\pi$
$440$	8.11583	+	12.9955i	0.386907	+	0.619537i
$441$		0			0
$442$	−14.2527	+	9.31312i	−0.677932	+	0.442980i
$443$	12.0051	+	28.9828i	0.570379	+	1.37702i	0.901233	+	0.433335i	$0.142663\pi$
$443$	12.0051	+	28.9828i	0.570379	+	1.37702i	−0.330854	+	0.943682i	$0.607337\pi$
$444$		0			0
$445$	29.2763	+	12.1266i	1.38783	+	0.574857i
$446$	−11.0711	+	16.2064i	−0.524233	+	0.767395i
$447$		0			0
$448$	1.67925	+	4.88511i	0.0793372	+	0.230800i
$449$		−	22.5653i		−	1.06492i	−0.846454	−	0.532462i	$-0.821267\pi$
$449$		−	22.5653i		−	1.06492i	0.846454	−	0.532462i	$-0.178733\pi$
$450$		0			0
$451$	4.87826	−	11.7772i	0.229708	−	0.554564i
$452$	−3.85612	−	9.87847i	−0.181376	−	0.464644i
$453$		0			0
$454$	14.5600	+	22.2825i	0.683334	+	1.04577i
$455$	2.77082	−	2.77082i	0.129898	−	0.129898i
$456$		0			0
$457$	9.14050	+	9.14050i	0.427575	+	0.427575i	0.887801	−	0.460227i	$-0.152232\pi$
$457$	9.14050	+	9.14050i	0.427575	+	0.427575i	−0.460227	+	0.887801i	$0.652232\pi$
$458$	2.65645	−	12.6734i	0.124128	−	0.592191i
$459$		0			0
$460$	0.427003	−	20.7915i	0.0199091	−	0.969408i
$461$	2.78980	+	1.15557i	0.129934	+	0.0538203i	0.446703	−	0.894682i	$-0.352598\pi$
$461$	2.78980	+	1.15557i	0.129934	+	0.0538203i	−0.316769	+	0.948503i	$0.602598\pi$
$462$		0			0
$463$	−33.4593			−1.55499			−0.777494	−	0.628891i	$-0.783509\pi$
$463$	−33.4593			−1.55499			−0.777494	+	0.628891i	$0.783509\pi$
$464$	6.75743	+	18.4188i	0.313706	+	0.855071i
$465$		0			0
$466$	11.5030	−	2.16555i	0.532866	−	0.100317i
$467$	−14.0784	+	33.9882i	−0.651470	+	1.57279i	0.159175	+	0.987250i	$0.449117\pi$
$467$	−14.0784	+	33.9882i	−0.651470	+	1.57279i	−0.810645	+	0.585538i	$0.800883\pi$
$468$		0			0
$469$	−5.46294	+	2.26282i	−0.252255	+	0.104487i
$470$	−4.51423	+	21.5365i	−0.208226	+	0.993406i
$471$		0			0
$472$	12.9249	−	2.15945i	0.594917	−	0.0993968i
$473$	−15.5584	−	15.5584i	−0.715376	−	0.715376i
$474$		0			0
$475$	10.0322	−	4.15548i	0.460309	−	0.190666i
$476$	1.84436	−	4.20624i	0.0845359	−	0.192793i
$477$		0			0
$478$	6.25328	−	9.15383i	0.286018	−	0.418686i
$479$	−2.68362			−0.122618			−0.0613088	−	0.998119i	$-0.519527\pi$
$479$	−2.68362			−0.122618			−0.0613088	+	0.998119i	$0.519527\pi$
$480$		0			0
$481$	−22.8254			−1.04075
$482$	23.7621	−	34.7840i	1.08233	−	1.58437i
$483$		0			0
$484$	−3.42426	−	1.50148i	−0.155648	−	0.0682489i
$485$	16.5534	−	6.85666i	0.751653	−	0.311345i
$486$		0			0
$487$	2.23834	+	2.23834i	0.101429	+	0.101429i	0.756000	−	0.654571i	$-0.227151\pi$
$487$	2.23834	+	2.23834i	0.101429	+	0.101429i	−0.654571	+	0.756000i	$0.727151\pi$
$488$	16.8850	−	23.6589i	0.764346	−	1.07099i
$489$		0			0
$490$	3.42393	−	16.3349i	0.154677	−	0.737936i
$491$	−12.4388	+	5.15233i	−0.561356	+	0.232521i	−0.645274	−	0.763951i	$-0.723257\pi$
$491$	−12.4388	+	5.15233i	−0.561356	+	0.232521i	0.0839179	+	0.996473i	$0.473257\pi$
$492$		0			0
$493$	6.67538	−	16.1158i	0.300644	−	0.725818i
$494$	28.6012	−	5.38446i	1.28683	−	0.242258i
$495$		0			0
$496$	1.57407	+	1.70898i	0.0706779	+	0.0767354i
$497$	7.16048			0.321191
$498$		0			0
$499$	24.8865	+	10.3083i	1.11407	+	0.461464i	0.862338	−	0.506333i	$-0.168999\pi$
$499$	24.8865	+	10.3083i	1.11407	+	0.461464i	0.251734	+	0.967796i	$0.418999\pi$
$500$	−24.3262	−	0.499597i	−1.08790	−	0.0223427i
$501$		0			0
$502$	−0.423351	+	2.01973i	−0.0188951	+	0.0901449i
$503$	−22.4779	−	22.4779i	−1.00224	−	1.00224i	−0.999997	−	0.00224387i	$-0.999286\pi$
$503$	−22.4779	−	22.4779i	−1.00224	−	1.00224i	−0.00224387	−	0.999997i	$-0.500714\pi$
$504$		0			0
$505$	−5.29299	+	5.29299i	−0.235535	+	0.235535i
$506$	−13.5578	−	20.7487i	−0.602718	−	0.922394i
$507$		0			0
$508$	−41.6342	+	16.2521i	−1.84722	+	0.721072i
$509$	5.50936	−	13.3008i	0.244198	−	0.589546i	−0.753493	−	0.657455i	$-0.771633\pi$
$509$	5.50936	−	13.3008i	0.244198	−	0.589546i	0.997692	+	0.0679092i	$0.0216328\pi$
$510$		0			0
$511$		−	9.80713i		−	0.433842i
$512$	14.2535	−	17.5738i	0.629923	−	0.776658i
$513$		0			0
$514$	−3.23484	+	4.73530i	−0.142683	+	0.208865i
$515$	3.72787	+	1.54413i	0.164269	+	0.0680426i
$516$		0			0
$517$	10.0363	+	24.2298i	0.441396	+	1.06563i
$518$	5.15451	−	3.36810i	0.226476	−	0.147986i
$519$		0			0
$520$	−16.7236	−	3.86550i	−0.733378	−	0.169513i
$521$	5.57998	−	5.57998i	0.244463	−	0.244463i	−0.574230	−	0.818694i	$-0.694699\pi$
$521$	5.57998	−	5.57998i	0.244463	−	0.244463i	0.818694	+	0.574230i	$0.194699\pi$
$522$		0			0
$523$	−3.24273	−	7.82865i	−0.141795	−	0.342323i	0.836989	−	0.547220i	$-0.184314\pi$
$523$	−3.24273	−	7.82865i	−0.141795	−	0.342323i	−0.978783	+	0.204897i	$0.934314\pi$
$524$	0.0633034	−	3.08235i	0.00276542	−	0.134653i
$525$		0			0
$526$	17.2881	−	3.25467i	0.753799	−	0.141910i
$527$		−	2.06577i		−	0.0899865i
$528$		0			0
$529$			10.6413i			0.462665i
$530$	−4.54527	−	24.1436i	−0.197434	−	1.04873i
$531$		0			0
$532$	−5.66428	+	5.43630i	−0.245578	+	0.235694i
$533$	5.46504	+	13.1938i	0.236717	+	0.571485i
$534$		0			0
$535$	22.1193	−	22.1193i	0.956300	−	0.956300i
$536$	21.0826	+	15.0463i	0.910632	+	0.649903i
$537$		0			0
$538$	0.969581	+	1.48384i	0.0418016	+	0.0639728i
$539$	−7.61228	−	18.3777i	−0.327884	−	0.791583i
$540$		0			0
$541$	10.7796	+	4.46504i	0.463450	+	0.191967i	0.602176	−	0.798364i	$-0.294301\pi$
$541$	10.7796	+	4.46504i	0.463450	+	0.191967i	−0.138726	+	0.990331i	$0.544301\pi$
$542$	−29.8719	−	20.4065i	−1.28311	−	0.876532i
$543$		0			0
$544$	−19.9070	+	2.90719i	−0.853506	+	0.124645i
$545$			23.1493i			0.991607i
$546$		0			0
$547$	−2.24172	+	5.41200i	−0.0958492	+	0.231400i	−0.964531	−	0.263970i	$-0.914968\pi$
$547$	−2.24172	+	5.41200i	−0.0958492	+	0.231400i	0.868682	+	0.495371i	$0.164968\pi$
$548$	−1.19368	−	0.523404i	−0.0509913	−	0.0223587i
$549$		0			0
$550$	−6.38971	+	4.17522i	−0.272458	+	0.178032i
$551$	−21.0845	+	21.0845i	−0.898229	+	0.898229i
$552$		0			0
$553$	2.40701	+	2.40701i	0.102357	+	0.102357i
$554$	10.9752	+	2.30050i	0.466293	+	0.0977388i
$555$		0			0
$556$	−30.5704	+	29.3400i	−1.29647	+	1.24429i
$557$	−9.25052	−	3.83169i	−0.391957	−	0.162354i	0.177996	−	0.984031i	$-0.443039\pi$
$557$	−9.25052	−	3.83169i	−0.391957	−	0.162354i	−0.569953	+	0.821677i	$0.693039\pi$
$558$		0			0
$559$	24.6495			1.04256
$560$	4.34697	−	1.59480i	0.183693	−	0.0673927i
$561$		0			0
$562$	−5.65367	−	30.0312i	−0.238486	−	1.26679i
$563$	−7.82586	+	18.8933i	−0.329820	+	0.796257i	0.668785	+	0.743456i	$0.266815\pi$
$563$	−7.82586	+	18.8933i	−0.329820	+	0.796257i	−0.998605	+	0.0528009i	$0.983185\pi$
$564$		0			0
$565$	−8.78179	+	3.63754i	−0.369453	+	0.153032i
$566$	−15.9309	−	3.33925i	−0.669626	−	0.140359i
$567$		0			0
$568$	−16.6142	−	26.6036i	−0.697118	−	1.11626i
$569$	−31.2631	−	31.2631i	−1.31062	−	1.31062i	−0.920959	−	0.389659i	$-0.872593\pi$
$569$	−31.2631	−	31.2631i	−1.31062	−	1.31062i	−0.389659	−	0.920959i	$-0.627407\pi$
$570$		0			0
$571$	0.191448	−	0.0793005i	0.00801186	−	0.00331862i	−0.378674	−	0.925530i	$-0.623620\pi$
$571$	0.191448	−	0.0793005i	0.00801186	−	0.00331862i	0.386686	+	0.922212i	$0.373620\pi$
$572$	−19.0571	+	7.43903i	−0.796816	+	0.311041i
$573$		0			0
$574$	−3.18100	−	2.17304i	−0.132772	−	0.0907010i
$575$	10.3601			0.432044
$576$		0			0
$577$	38.6731			1.60998			0.804991	−	0.593287i	$-0.202170\pi$
$577$	38.6731			1.60998			0.804991	+	0.593287i	$0.202170\pi$
$578$	−5.08185	−	3.47158i	−0.211377	−	0.144399i
$579$		0			0
$580$	16.3820	−	6.39479i	0.680224	−	0.265529i
$581$	2.81547	−	1.16621i	0.116805	−	0.0483824i
$582$		0			0
$583$	−20.7048	−	20.7048i	−0.857506	−	0.857506i
$584$	−36.4368	+	22.7552i	−1.50777	+	0.941615i
$585$		0			0
$586$	13.1450	+	2.75531i	0.543016	+	0.113821i
$587$	−43.3422	+	17.9529i	−1.78892	+	0.740997i	−0.798662	+	0.601779i	$0.794459\pi$
$587$	−43.3422	+	17.9529i	−1.78892	+	0.740997i	−0.990262	+	0.139217i	$0.955541\pi$
$588$		0			0
$589$	−1.35134	+	3.26242i	−0.0556809	+	0.134426i
$590$	−2.17311	−	11.5431i	−0.0894656	−	0.475223i
$591$		0			0
$592$	−24.4735	−	11.3359i	−1.00585	−	0.465901i
$593$	−17.0532			−0.700290			−0.350145	−	0.936695i	$-0.613868\pi$
$593$	−17.0532			−0.700290			−0.350145	+	0.936695i	$0.613868\pi$
$594$		0			0
$595$	−3.80344	−	1.57544i	−0.155926	−	0.0645866i
$596$	17.6842	−	16.9725i	0.724374	−	0.695219i
$597$		0			0
$598$	27.1763	+	5.69637i	1.11132	+	0.232942i
$599$	−1.20304	−	1.20304i	−0.0491549	−	0.0491549i	0.682102	−	0.731257i	$-0.261066\pi$
$599$	−1.20304	−	1.20304i	−0.0491549	−	0.0491549i	−0.731257	+	0.682102i	$0.761066\pi$
$600$		0			0
$601$	−7.21057	+	7.21057i	−0.294125	+	0.294125i	−0.838707	−	0.544582i	$-0.816688\pi$
$601$	−7.21057	+	7.21057i	−0.294125	+	0.294125i	0.544582	+	0.838707i	$0.316688\pi$
$602$	−5.56643	+	3.63726i	−0.226871	+	0.148244i
$603$		0			0
$604$	20.6935	+	9.07369i	0.842005	+	0.369203i
$605$	−1.28255	+	3.09635i	−0.0521431	+	0.125884i
$606$		0			0
$607$		−	39.4020i		−	1.59928i	−0.600480	−	0.799640i	$-0.705024\pi$
$607$		−	39.4020i		−	1.59928i	0.600480	−	0.799640i	$-0.294976\pi$
$608$	33.3404	+	8.43106i	1.35213	+	0.341924i
$609$		0			0
$610$	−21.5131	−	14.6963i	−0.871040	−	0.595036i
$611$	−27.1443	−	11.2435i	−1.09814	−	0.454864i
$612$		0			0
$613$	−4.28364	−	10.3416i	−0.173015	−	0.417694i	0.813457	−	0.581625i	$-0.197583\pi$
$613$	−4.28364	−	10.3416i	−0.173015	−	0.417694i	−0.986472	+	0.163930i	$0.947583\pi$
$614$	8.60828	+	13.1740i	0.347402	+	0.531661i
$615$		0			0
$616$	3.20583	−	4.49195i	0.129167	−	0.180986i
$617$	−3.31416	+	3.31416i	−0.133423	+	0.133423i	−0.770664	−	0.637241i	$-0.780075\pi$
$617$	−3.31416	+	3.31416i	−0.133423	+	0.133423i	0.637241	+	0.770664i	$0.280075\pi$
$618$		0			0
$619$	−9.98010	−	24.0941i	−0.401134	−	0.968423i	−0.987391	−	0.158298i	$-0.949399\pi$
$619$	−9.98010	−	24.0941i	−0.401134	−	0.968423i	0.586257	−	0.810125i	$-0.300601\pi$
$620$	1.50256	−	1.44209i	0.0603443	−	0.0579155i
$621$		0			0
$622$	−0.520544	−	2.76503i	−0.0208719	−	0.110867i
$623$		−	11.4137i		−	0.457280i
$624$		0			0
$625$			12.8786i			0.515146i
$626$	−12.2928	+	2.31425i	−0.491320	+	0.0924959i
$627$		0			0
$628$	0.154278	−	7.51204i	0.00615635	−	0.299763i
$629$	9.17690	+	22.1550i	0.365907	+	0.883377i
$630$		0			0
$631$	−13.8296	+	13.8296i	−0.550550	+	0.550550i	−0.926599	−	0.376050i	$-0.877282\pi$
$631$	−13.8296	+	13.8296i	−0.550550	+	0.550550i	0.376050	+	0.926599i	$0.377282\pi$
$632$	3.35796	−	14.5278i	0.133572	−	0.577884i
$633$		0			0
$634$	−7.88375	+	5.15147i	−0.313104	+	0.204591i
$635$	15.3309	+	37.0121i	0.608389	+	1.46878i
$636$		0			0
$637$	20.5882	+	8.52793i	0.815736	+	0.337889i
$638$	11.8229	−	17.3069i	0.468073	−	0.685186i
$639$		0			0
$640$	−16.0114	−	12.4501i	−0.632905	−	0.492133i
$641$			4.78350i			0.188937i	0.995528	+	0.0944684i	$0.0301151\pi$
$641$			4.78350i			0.188937i	−0.995528	+	0.0944684i	$0.969885\pi$
$642$		0			0
$643$	−4.20578	+	10.1536i	−0.165860	+	0.400421i	−0.984855	−	0.173379i	$-0.944531\pi$
$643$	−4.20578	+	10.1536i	−0.165860	+	0.400421i	0.818995	+	0.573800i	$0.194531\pi$
$644$	−6.97759	+	2.72374i	−0.274956	+	0.107330i
$645$		0			0
$646$	−16.7253	−	25.5963i	−0.658049	−	1.00707i
$647$	11.3311	−	11.3311i	0.445473	−	0.445473i	−0.448373	−	0.893846i	$-0.647997\pi$
$647$	11.3311	−	11.3311i	0.445473	−	0.445473i	0.893846	+	0.448373i	$0.147997\pi$
$648$		0			0
$649$	−9.89904	−	9.89904i	−0.388571	−	0.388571i
$650$	1.75424	−	8.36912i	0.0688068	−	0.328264i
$651$		0			0
$652$	4.69202	+	0.0963619i	0.183754	+	0.00377382i
$653$	27.7945	+	11.5129i	1.08768	+	0.450533i	0.853198	−	0.521587i	$-0.174660\pi$
$653$	27.7945	+	11.5129i	1.08768	+	0.450533i	0.234485	+	0.972120i	$0.424660\pi$
$654$		0			0
$655$	−2.76346			−0.107977
$656$	−0.692835	+	16.8605i	−0.0270507	+	0.658293i
$657$		0			0
$658$	7.78890	−	1.46634i	0.303643	−	0.0571639i
$659$	7.68871	−	18.5622i	0.299510	−	0.723080i	−0.700446	−	0.713705i	$-0.747016\pi$
$659$	7.68871	−	18.5622i	0.299510	−	0.723080i	0.999956	−	0.00937514i	$-0.00298424\pi$
$660$		0			0
$661$	7.39058	−	3.06128i	0.287460	−	0.119070i	−0.234294	−	0.972166i	$-0.575278\pi$
$661$	7.39058	−	3.06128i	0.287460	−	0.119070i	0.521754	+	0.853096i	$0.325278\pi$
$662$	−2.02567	+	9.66409i	−0.0787299	+	0.375605i
$663$		0			0
$664$	−10.8655	−	7.75453i	−0.421663	−	0.300934i
$665$	4.97609	+	4.97609i	0.192964	+	0.192964i
$666$		0			0
$667$	−26.2830	+	10.8868i	−1.01768	+	0.421537i
$668$	−10.8204	−	4.74452i	−0.418652	−	0.183571i
$669$		0			0
$670$	13.0960	−	19.1705i	0.505943	−	0.740621i
$671$	−31.0521			−1.19875
$672$		0			0
$673$	13.4300			0.517690			0.258845	−	0.965919i	$-0.416658\pi$
$673$	13.4300			0.517690			0.258845	+	0.965919i	$0.416658\pi$
$674$	4.56970	−	6.68932i	0.176018	−	0.257663i
$675$		0			0
$676$	−1.23754	+	2.82233i	−0.0475976	+	0.108551i
$677$	−12.8609	+	5.32714i	−0.494283	+	0.204739i	−0.615879	−	0.787841i	$-0.711199\pi$
$677$	−12.8609	+	5.32714i	−0.494283	+	0.204739i	0.121596	+	0.992580i	$0.461199\pi$
$678$		0			0
$679$	−4.56335	−	4.56335i	−0.175125	−	0.175125i
$680$	2.97171	+	17.7865i	0.113960	+	0.682081i
$681$		0			0
$682$	0.509217	−	2.42938i	0.0194989	−	0.0930256i
$683$	0.117538	−	0.0486859i	0.00449748	−	0.00186292i	−0.380434	−	0.924808i	$-0.624225\pi$
$683$	0.117538	−	0.0486859i	0.00449748	−	0.00186292i	0.384931	+	0.922945i	$0.374225\pi$
$684$		0			0
$685$	−0.447088	+	1.07937i	−0.0170824	+	0.0412405i
$686$	−12.1895	+	2.29480i	−0.465398	+	0.0876159i
$687$		0			0
$688$	26.4293	+	12.2418i	1.00761	+	0.466713i
$689$	32.8031			1.24970
$690$		0			0
$691$	−9.94322	−	4.11862i	−0.378258	−	0.156680i	0.185450	−	0.982654i	$-0.440626\pi$
$691$	−9.94322	−	4.11862i	−0.378258	−	0.156680i	−0.563708	+	0.825974i	$0.690626\pi$
$692$	0.243016	−	11.8328i	0.00923807	−	0.449817i
$693$		0			0
$694$	6.61444	−	31.5562i	0.251081	−	1.19786i
$695$	26.8562	+	26.8562i	1.01871	+	1.01871i
$696$		0			0
$697$	10.6090	−	10.6090i	0.401846	−	0.401846i
$698$	−19.8418	−	30.3657i	−0.751024	−	1.14936i
$699$		0			0
$700$	0.838794	+	2.14880i	0.0317034	+	0.0812169i
$701$	−4.26297	+	10.2917i	−0.161010	+	0.388713i	−0.983710	−	0.179763i	$-0.942467\pi$
$701$	−4.26297	+	10.2917i	−0.161010	+	0.388713i	0.822700	+	0.568476i	$0.192467\pi$
$702$		0			0
$703$		−	40.9919i		−	1.54604i
$704$	−24.1275	−	1.48822i	−0.909340	−	0.0560896i
$705$		0			0
$706$	15.2940	−	22.3880i	0.575597	−	0.842584i
$707$	2.49091	+	1.03177i	0.0936803	+	0.0388036i
$708$		0			0
$709$	−4.70620	−	11.3618i	−0.176745	−	0.426700i	0.810535	−	0.585690i	$-0.199176\pi$
$709$	−4.70620	−	11.3618i	−0.176745	−	0.426700i	−0.987280	+	0.158990i	$0.949176\pi$
$710$	−23.5355	+	15.3788i	−0.883272	+	0.577155i
$711$		0			0
$712$	−42.4058	+	26.4828i	−1.58922	+	0.992487i
$713$	−2.38227	+	2.38227i	−0.0892166	+	0.0892166i
$714$		0			0
$715$	7.01736	+	16.9414i	0.262434	+	0.633573i
$716$	11.4866	+	0.235905i	0.429274	+	0.00881618i
$717$		0			0
$718$	38.2324	−	7.19764i	1.42682	−	0.268613i
$719$		−	31.7208i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$719$		−	31.7208i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$720$		0			0
$721$		−	1.45335i		−	0.0541257i
$722$	4.69866	+	24.9583i	0.174866	+	0.928852i
$723$		0			0
$724$	0.836401	+	0.871477i	0.0310846	+	0.0323882i
$725$	3.35265	+	8.09401i	0.124514	+	0.300604i
$726$		0			0
$727$	−19.1550	+	19.1550i	−0.710421	+	0.710421i	−0.966623	−	0.256202i	$-0.917529\pi$
$727$	−19.1550	+	19.1550i	−0.710421	+	0.710421i	0.256202	+	0.966623i	$0.417529\pi$
$728$	1.01882	+	6.09788i	0.0377598	+	0.226003i
$729$		0			0
$730$	21.0630	+	32.2347i	0.779578	+	1.19306i
$731$	−9.91027	−	23.9255i	−0.366545	−	0.884917i
$732$		0			0
$733$	40.7560	+	16.8817i	1.50536	+	0.623539i	0.974593	−	0.223981i	$-0.0719054\pi$
$733$	40.7560	+	16.8817i	1.50536	+	0.623539i	0.530763	+	0.847520i	$0.321905\pi$
$734$	22.7593	+	15.5476i	0.840060	+	0.573873i
$735$		0			0
$736$	26.3095	+	19.6043i	0.969782	+	0.722626i
$737$		−	27.6708i		−	1.01927i
$738$		0			0
$739$	8.11044	−	19.5803i	0.298348	−	0.720275i	−0.701623	−	0.712549i	$-0.747541\pi$
$739$	8.11044	−	19.5803i	0.298348	−	0.720275i	0.999970	−	0.00772594i	$-0.00245927\pi$
$740$	−9.70840	+	22.1410i	−0.356888	+	0.813918i
$741$		0			0
$742$	−7.40770	+	4.84040i	−0.271945	+	0.177697i
$743$	−0.927600	+	0.927600i	−0.0340303	+	0.0340303i	−0.723917	−	0.689887i	$-0.757660\pi$
$743$	−0.927600	+	0.927600i	−0.0340303	+	0.0340303i	0.689887	+	0.723917i	$0.257660\pi$
$744$		0			0
$745$	−15.5356	−	15.5356i	−0.569182	−	0.569182i
$746$	48.6845	+	10.2047i	1.78246	+	0.373619i
$747$		0			0
$748$	14.8824	+	15.5065i	0.544154	+	0.566973i
$749$	−10.4094	−	4.31173i	−0.380353	−	0.157547i
$750$		0			0
$751$	31.0488			1.13299			0.566493	−	0.824066i	$-0.308300\pi$
$751$	31.0488			1.13299			0.566493	+	0.824066i	$0.308300\pi$
$752$	−23.5203	−	25.5361i	−0.857696	−	0.931206i
$753$		0			0
$754$	4.34419	+	23.0755i	0.158206	+	0.840359i
$755$	7.75068	−	18.7118i	0.282076	−	0.680992i
$756$		0			0
$757$	−23.3806	+	9.68456i	−0.849782	+	0.351991i	−0.764703	−	0.644383i	$-0.777114\pi$
$757$	−23.3806	+	9.68456i	−0.849782	+	0.351991i	−0.0850792	+	0.996374i	$0.527114\pi$
$758$	17.1845	+	3.60201i	0.624170	+	0.130831i
$759$		0			0
$760$	6.94201	−	30.0337i	0.251813	−	1.08944i
$761$	7.78273	+	7.78273i	0.282124	+	0.282124i	0.833956	−	0.551832i	$-0.186071\pi$
$761$	7.78273	+	7.78273i	0.282124	+	0.282124i	−0.551832	+	0.833956i	$0.686071\pi$
$762$		0			0
$763$	7.70334	−	3.19083i	0.278880	−	0.115516i
$764$	17.0959	+	43.7957i	0.618508	+	1.58447i
$765$		0			0
$766$	25.0381	+	17.1043i	0.904663	+	0.618005i
$767$	15.6833			0.566290
$768$		0			0
$769$	−50.8529			−1.83380			−0.916902	−	0.399113i	$-0.869318\pi$
$769$	−50.8529			−1.83380			−0.916902	+	0.399113i	$0.869318\pi$
$770$	−4.08454	−	2.79029i	−0.147197	−	0.100555i
$771$		0			0
$772$	−6.67030	−	17.0877i	−0.240069	−	0.615001i
$773$	37.9455	−	15.7175i	1.36480	−	0.565320i	0.424429	−	0.905461i	$-0.360475\pi$
$773$	37.9455	−	15.7175i	1.36480	−	0.565320i	0.940374	+	0.340141i	$0.110475\pi$
$774$		0			0
$775$	0.733635	+	0.733635i	0.0263529	+	0.0263529i
$776$	−6.36621	+	27.5426i	−0.228534	+	0.988722i
$777$		0			0
$778$	−34.2337	−	7.17566i	−1.22734	−	0.257260i
$779$	−23.6945	+	9.81460i	−0.848945	+	0.351645i
$780$		0			0
$781$	−12.8231	+	30.9577i	−0.458846	+	1.10775i
$782$	−5.39710	−	28.6683i	−0.193000	−	1.02518i
$783$		0			0
$784$	17.8395	+	19.3685i	0.637126	+	0.691732i
$785$	−6.73488			−0.240378
$786$		0			0
$787$	21.7835	+	9.02304i	0.776499	+	0.321637i	0.735502	−	0.677523i	$-0.236946\pi$
$787$	21.7835	+	9.02304i	0.776499	+	0.321637i	0.0409975	+	0.999159i	$0.486946\pi$
$788$	12.1909	+	12.7022i	0.434284	+	0.452496i
$789$		0			0
$790$	−13.0811	−	2.74191i	−0.465406	−	0.0975528i
$791$	2.42091	+	2.42091i	0.0860777	+	0.0860777i
$792$		0			0
$793$	24.5983	−	24.5983i	0.873510	−	0.873510i
$794$	6.19117	−	4.04548i	0.219716	−	0.143569i
$795$		0			0
$796$	−15.0221	+	34.2593i	−0.532443	+	1.21429i
$797$	11.4401	−	27.6189i	0.405231	−	0.978313i	−0.581144	−	0.813800i	$-0.697395\pi$
$797$	11.4401	−	27.6189i	0.405231	−	0.978313i	0.986375	−	0.164513i	$-0.0526052\pi$
$798$		0			0
$799$			30.8674i			1.09201i
$800$	6.03729	−	8.10219i	0.213450	−	0.286456i
$801$		0			0
$802$	19.2450	+	13.1469i	0.679566	+	0.464234i
$803$	42.4002	+	17.5627i	1.49627	+	0.619775i
$804$		0			0
$805$	2.56935	+	6.20296i	0.0905577	+	0.218626i
$806$	1.52108	+	2.32784i	0.0535776	+	0.0819946i
$807$		0			0
$808$	−1.94620	−	11.6486i	−0.0684672	−	0.409795i
$809$	−5.79612	+	5.79612i	−0.203781	+	0.203781i	−0.801618	−	0.597837i	$-0.796027\pi$
$809$	−5.79612	+	5.79612i	−0.203781	+	0.203781i	0.597837	+	0.801618i	$0.296027\pi$
$810$		0			0
$811$	−19.2750	−	46.5341i	−0.676838	−	1.63403i	−0.769741	−	0.638356i	$-0.779615\pi$
$811$	−19.2750	−	46.5341i	−0.676838	−	1.63403i	0.0929028	−	0.995675i	$-0.470385\pi$
$812$	−4.38602	−	4.56995i	−0.153919	−	0.160374i
$813$		0			0
$814$	5.33090	+	28.3167i	0.186848	+	0.992499i
$815$		−	4.20661i		−	0.147351i
$816$		0			0
$817$			44.2678i			1.54873i
$818$	−28.4363	+	5.35343i	−0.994252	+	0.187178i
$819$		0			0
$820$	15.1226	+	0.310579i	0.528104	+	0.0108459i
$821$	−16.7271	−	40.3828i	−0.583779	−	1.40937i	−0.889363	−	0.457202i	$-0.848851\pi$
$821$	−16.7271	−	40.3828i	−0.583779	−	1.40937i	0.305583	−	0.952165i	$-0.401149\pi$
$822$		0			0
$823$	−8.13069	+	8.13069i	−0.283418	+	0.283418i	−0.834471	−	0.551053i	$-0.814226\pi$
$823$	−8.13069	+	8.13069i	−0.283418	+	0.283418i	0.551053	+	0.834471i	$0.314226\pi$
$824$	−5.39971	+	3.37217i	−0.188108	+	0.117475i
$825$		0			0
$826$	−3.54165	+	2.31421i	−0.123230	+	0.0805217i
$827$	15.6826	+	37.8612i	0.545339	+	1.31656i	0.920912	+	0.389771i	$0.127446\pi$
$827$	15.6826	+	37.8612i	0.545339	+	1.31656i	−0.375573	+	0.926793i	$0.622554\pi$
$828$		0			0
$829$	−15.7729	−	6.53333i	−0.547814	−	0.226912i	0.0915711	−	0.995799i	$-0.470811\pi$
$829$	−15.7729	−	6.53333i	−0.547814	−	0.226912i	−0.639385	+	0.768886i	$0.720811\pi$
$830$	−6.74937	+	9.88003i	−0.234274	+	0.342941i
$831$		0			0
$832$	20.2918	−	17.9340i	0.703492	−	0.621749i
$833$		−	23.4122i		−	0.811183i
$834$		0			0
$835$	−4.05274	+	9.78417i	−0.140251	+	0.338595i
$836$	−13.3597	−	34.2244i	−0.462054	−	1.18367i
$837$		0			0
$838$	−11.0776	−	16.9531i	−0.382670	−	0.585634i
$839$	8.63280	−	8.63280i	0.298037	−	0.298037i	−0.542207	−	0.840245i	$-0.682411\pi$
$839$	8.63280	−	8.63280i	0.298037	−	0.298037i	0.840245	+	0.542207i	$0.182411\pi$
$840$		0			0
$841$	3.49509	+	3.49509i	0.120520	+	0.120520i
$842$	−2.71962	+	12.9748i	−0.0937242	+	0.447140i
$843$		0			0
$844$	0.886534	−	43.1668i	0.0305158	−	1.48586i
$845$	2.55206	+	1.05710i	0.0877934	+	0.0363652i
$846$		0			0
$847$	1.20715			0.0414781
$848$	35.1716	+	16.2911i	1.20780	+	0.559439i
$849$		0			0
$850$	−8.82859	+	1.66207i	−0.302818	+	0.0570087i
$851$	14.9664	−	36.1322i	0.513043	−	1.23860i
$852$		0			0
$853$	−20.9586	+	8.68133i	−0.717608	+	0.297243i	−0.711449	−	0.702738i	$-0.751961\pi$
$853$	−20.9586	+	8.68133i	−0.717608	+	0.297243i	−0.00615957	+	0.999981i	$0.501961\pi$
$854$	−1.92516	+	9.18456i	−0.0658776	+	0.314289i
$855$		0			0
$856$	8.13314	+	48.6790i	0.277985	+	1.66381i
$857$	19.1816	+	19.1816i	0.655232	+	0.655232i	0.954248	−	0.299016i	$-0.0966584\pi$
$857$	19.1816	+	19.1816i	0.655232	+	0.655232i	−0.299016	+	0.954248i	$0.596658\pi$
$858$		0			0
$859$	−43.8743	+	18.1733i	−1.49697	+	0.620066i	−0.972821	−	0.231559i	$-0.925617\pi$
$859$	−43.8743	+	18.1733i	−1.49697	+	0.620066i	−0.524151	+	0.851625i	$0.675617\pi$
$860$	10.4842	−	23.9104i	0.357510	−	0.815337i
$861$		0			0
$862$	−23.9029	+	34.9901i	−0.814136	+	1.19177i
$863$	−41.7776			−1.42212			−0.711062	−	0.703129i	$-0.751786\pi$
$863$	−41.7776			−1.42212			−0.711062	+	0.703129i	$0.751786\pi$
$864$		0			0
$865$	−10.6087			−0.360706
$866$	−24.2545	+	35.5048i	−0.824201	+	1.20650i
$867$		0			0
$868$	−0.686988	−	0.301231i	−0.0233179	−	0.0102245i
$869$	−14.7170	+	6.09598i	−0.499240	+	0.206792i
$870$		0			0
$871$	21.9197	+	21.9197i	0.742722	+	0.742722i
$872$	−29.7288	−	21.2170i	−1.00675	−	0.718497i
$873$		0			0
$874$	−10.2301	+	48.8056i	−0.346037	+	1.65088i
$875$	7.25752	−	3.00616i	0.245349	−	0.101627i
$876$		0			0
$877$	20.1913	−	48.7461i	0.681811	−	1.64604i	−0.0788487	−	0.996887i	$-0.525124\pi$
$877$	20.1913	−	48.7461i	0.681811	−	1.64604i	0.760660	−	0.649151i	$-0.224876\pi$
$878$	−19.9593	+	3.75755i	−0.673594	+	0.126811i
$879$		0			0
$880$	−0.889632	+	21.6497i	−0.0299895	+	0.729811i
$881$	0.703923			0.0237158			0.0118579	−	0.999930i	$-0.496225\pi$
$881$	0.703923			0.0237158			0.0118579	+	0.999930i	$0.496225\pi$
$882$		0			0
$883$	0.756687	+	0.313430i	0.0254645	+	0.0105478i	0.395379	−	0.918518i	$-0.370613\pi$
$883$	0.756687	+	0.313430i	0.0254645	+	0.0105478i	−0.369915	+	0.929066i	$0.620613\pi$
$884$	−24.0729	−	0.494394i	−0.809659	−	0.0166283i
$885$		0			0
$886$	−9.10148	+	43.4214i	−0.305770	+	1.45877i
$887$	20.2480	+	20.2480i	0.679862	+	0.679862i	0.959969	−	0.280106i	$-0.0903698\pi$
$887$	20.2480	+	20.2480i	0.679862	+	0.679862i	−0.280106	+	0.959969i	$0.590370\pi$
$888$		0			0
$889$	10.2033	−	10.2033i	0.342207	−	0.342207i
$890$	24.5135	+	37.5153i	0.821696	+	1.25751i
$891$		0			0
$892$	−25.8565	+	10.0932i	−0.865741	+	0.337947i
$893$	20.1921	−	48.7481i	0.675704	−	1.63129i
$894$		0			0
$895$		−	10.2983i		−	0.344233i
$896$	−1.93604	+	7.04415i	−0.0646785	+	0.235329i
$897$		0			0
$898$	18.0010	−	26.3506i	0.600700	−	0.879330i
$899$	−2.63213	−	1.09026i	−0.0877864	−	0.0363623i
$900$		0			0
$901$	−13.1884	−	31.8396i	−0.439369	−	1.06073i
$902$	15.0915	−	9.86122i	0.502492	−	0.328343i
$903$		0			0
$904$	3.37735	−	14.6117i	0.112329	−	0.485977i
$905$	0.765595	−	0.765595i	0.0254492	−	0.0254492i
$906$		0			0
$907$	−2.52443	−	6.09451i	−0.0838223	−	0.202365i	0.876411	−	0.481564i	$-0.159931\pi$
$907$	−2.52443	−	6.09451i	−0.0838223	−	0.202365i	−0.960233	+	0.279199i	$0.909931\pi$
$908$	−0.772929	+	37.6352i	−0.0256505	+	1.24897i
$909$		0			0
$910$	5.44597	−	1.02526i	0.180532	−	0.0339870i
$911$		−	44.3943i		−	1.47085i	−0.677608	−	0.735424i	$-0.736983\pi$
$911$		−	44.3943i		−	1.47085i	0.677608	−	0.735424i	$-0.263017\pi$
$912$		0			0
$913$			14.2609i			0.471966i
$914$	3.38217	+	17.9654i	0.111872	+	0.594243i
$915$		0			0
$916$	13.2120	−	12.6802i	0.436537	−	0.418967i
$917$	0.380907	+	0.919592i	0.0125787	+	0.0303676i
$918$		0			0
$919$	−13.6702	+	13.6702i	−0.450938	+	0.450938i	−0.895666	−	0.444728i	$-0.853300\pi$
$919$	−13.6702	+	13.6702i	−0.450938	+	0.450938i	0.444728	+	0.895666i	$0.353300\pi$
$920$	17.0845	−	23.9385i	0.563261	−	0.789231i
$921$		0			0
$922$	2.33595	+	3.57491i	0.0769303	+	0.117733i
$923$	−14.3655	−	34.6814i	−0.472846	−	1.14155i
$924$		0			0
$925$	−11.1271	−	4.60901i	−0.365858	−	0.151543i
$926$	−39.0720	−	26.6914i	−1.28399	−	0.877134i
$927$		0			0
$928$	−6.80219	+	26.8991i	−0.223293	+	0.883006i
$929$			29.8610i			0.979709i	0.871804	+	0.489855i	$0.162950\pi$
$929$			29.8610i			0.979709i	−0.871804	+	0.489855i	$0.837050\pi$
$930$		0			0
$931$	−15.3152	+	36.9742i	−0.501936	+	1.21178i
$932$	15.1601	+	6.64741i	0.496585	+	0.217743i
$933$		0			0
$934$	−43.5533	+	28.4590i	−1.42511	+	0.931206i
$935$	13.6225	−	13.6225i	0.445503	−	0.445503i
$936$		0			0
$937$	−25.0276	−	25.0276i	−0.817617	−	0.817617i	0.168145	−	0.985762i	$-0.446222\pi$
$937$	−25.0276	−	25.0276i	−0.817617	−	0.817617i	−0.985762	+	0.168145i	$0.946222\pi$
$938$	−8.18444	−	1.71553i	−0.267232	−	0.0560139i
$939$		0			0
$940$	−22.4517	+	21.5481i	−0.732295	+	0.702821i
$941$	−39.6214	−	16.4117i	−1.29162	−	0.535007i	−0.372152	−	0.928172i	$-0.621380\pi$
$941$	−39.6214	−	16.4117i	−1.29162	−	0.535007i	−0.919468	+	0.393165i	$0.871380\pi$
$942$		0			0
$943$	−24.4689			−0.796816
$944$	16.8157	+	7.78884i	0.547303	+	0.253505i
$945$		0			0
$946$	−5.75692	−	30.5796i	−0.187174	−	0.994229i
$947$	17.0273	−	41.1075i	0.553312	−	1.33581i	−0.361665	−	0.932308i	$-0.617792\pi$
$947$	17.0273	−	41.1075i	0.553312	−	1.33581i	0.914977	−	0.403505i	$-0.132208\pi$
$948$		0			0
$949$	−47.5003	+	19.6753i	−1.54192	+	0.638686i
$950$	15.0300	+	3.15041i	0.487638	+	0.102213i
$951$		0			0
$952$	5.50917	−	3.44053i	0.178553	−	0.111508i
$953$	−12.7204	−	12.7204i	−0.412054	−	0.412054i	0.470400	−	0.882454i	$-0.344110\pi$
$953$	−12.7204	−	12.7204i	−0.412054	−	0.412054i	−0.882454	+	0.470400i	$0.844110\pi$
$954$		0			0
$955$	38.9337	−	16.1268i	1.25986	−	0.521853i
$956$	14.6045	−	5.70094i	0.472343	−	0.184382i
$957$		0			0
$958$	−3.13379	−	2.14079i	−0.101248	−	0.0691659i
$959$	0.420804			0.0135885
$960$		0			0
$961$	30.6626			0.989116
$962$	−26.6543	−	18.2084i	−0.859369	−	0.587063i
$963$		0			0
$964$	55.4962	−	21.6633i	1.78741	−	0.697727i
$965$	−15.1907	+	6.29220i	−0.489006	+	0.202553i
$966$		0			0
$967$	13.4994	+	13.4994i	0.434112	+	0.434112i	0.890025	−	0.455913i	$-0.150687\pi$
$967$	13.4994	+	13.4994i	0.434112	+	0.434112i	−0.455913	+	0.890025i	$0.650687\pi$
$968$	−2.80091	−	4.48497i	−0.0900246	−	0.144152i
$969$		0			0
$970$	24.8000	+	5.19827i	0.796279	+	0.166906i
$971$	28.1525	−	11.6611i	0.903457	−	0.374224i	0.117909	−	0.993024i	$-0.462381\pi$
$971$	28.1525	−	11.6611i	0.903457	−	0.374224i	0.785548	+	0.618800i	$0.212381\pi$
$972$		0			0
$973$	5.23511	−	12.6387i	0.167830	−	0.405177i
$974$	0.828231	+	4.39939i	0.0265382	+	0.140966i
$975$		0			0
$976$	38.5907	−	14.1580i	1.23526	−	0.453187i
$977$	30.5548			0.977534			0.488767	−	0.872414i	$-0.337447\pi$
$977$	30.5548			0.977534			0.488767	+	0.872414i	$0.337447\pi$
$978$		0			0
$979$	49.3461	+	20.4398i	1.57711	+	0.653259i
$980$	17.0291	−	16.3437i	0.543973	−	0.522080i
$981$		0			0
$982$	−18.6355	−	3.90616i	−0.594684	−	0.124651i
$983$	30.3548	+	30.3548i	0.968168	+	0.968168i	0.999509	−	0.0313409i	$-0.00997774\pi$
$983$	30.3548	+	30.3548i	0.968168	+	0.968168i	−0.0313409	+	0.999509i	$0.509978\pi$
$984$		0			0
$985$	11.1589	−	11.1589i	0.355552	−	0.355552i
$986$	20.6511	−	13.4940i	0.657666	−	0.429738i
$987$		0			0
$988$	37.6942	+	16.5282i	1.19921	+	0.525832i
$989$	−16.1625	+	39.0197i	−0.513937	+	1.24075i
$990$		0			0
$991$			45.5684i			1.44753i	0.690048	+	0.723764i	$0.257589\pi$
$991$			45.5684i			1.44753i	−0.690048	+	0.723764i	$0.742411\pi$
$992$	0.474819	+	3.25133i	0.0150755	+	0.103230i
$993$		0			0
$994$	8.36163	+	5.71210i	0.265215	+	0.181177i
$995$	30.9786	+	12.8317i	0.982086	+	0.406793i
$996$		0			0
$997$	−4.87805	−	11.7767i	−0.154490	−	0.372971i	0.827618	−	0.561292i	$-0.189695\pi$
$997$	−4.87805	−	11.7767i	−0.154490	−	0.372971i	−0.982108	+	0.188321i	$0.939695\pi$
$998$	20.8379	+	31.8901i	0.659612	+	1.00946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.35.7	✓	32
3.2	odd	2		288.2.w.b.35.2	yes	32
4.3	odd	2		1152.2.w.b.431.6		32
12.11	even	2		1152.2.w.a.431.3		32
32.11	odd	8		288.2.w.b.107.2	yes	32
32.21	even	8		1152.2.w.a.719.3		32
96.11	even	8	inner	288.2.w.a.107.7	yes	32
96.53	odd	8		1152.2.w.b.719.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.7	✓	32	1.1	even	1	trivial
288.2.w.a.107.7	yes	32	96.11	even	8	inner
288.2.w.b.35.2	yes	32	3.2	odd	2
288.2.w.b.107.2	yes	32	32.11	odd	8
1152.2.w.a.431.3		32	12.11	even	2
1152.2.w.a.719.3		32	32.21	even	8
1152.2.w.b.431.6		32	4.3	odd	2
1152.2.w.b.719.6		32	96.53	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16775 + 0.797726i) q^{2} +(0.727265 + 1.86308i) q^{4} +(1.65625 - 0.686041i) q^{5} +(-0.456585 - 0.456585i) q^{7} +(-0.636970 + 2.75577i) q^{8} +O(q^{10})\)	\(q+(1.16775 + 0.797726i) q^{2} +(0.727265 + 1.86308i) q^{4} +(1.65625 - 0.686041i) q^{5} +(-0.456585 - 0.456585i) q^{7} +(-0.636970 + 2.75577i) q^{8} +(2.48135 + 0.520112i) q^{10} +(2.79166 - 1.15634i) q^{11} +(-1.29543 + 3.12746i) q^{13} +(-0.168946 - 0.897406i) q^{14} +(-2.94217 + 2.70991i) q^{16} +3.55642 q^{17} +(-5.61657 - 2.32646i) q^{19} +(2.48269 + 2.58680i) q^{20} +(4.18240 + 0.876665i) q^{22} +(-4.10130 - 4.10130i) q^{23} +(-1.26302 + 1.26302i) q^{25} +(-4.00759 + 2.61867i) q^{26} +(0.518598 - 1.18272i) q^{28} +(1.87699 - 4.53146i) q^{29} -0.580857i q^{31} +(-5.59748 + 0.817447i) q^{32} +(4.15300 + 2.83705i) q^{34} +(-1.06946 - 0.442983i) q^{35} +(2.58037 + 6.22957i) q^{37} +(-4.70285 - 7.19720i) q^{38} +(0.835590 + 5.00123i) q^{40} +(2.98306 - 2.98306i) q^{41} +(-2.78658 - 6.72741i) q^{43} +(4.18465 + 4.36013i) q^{44} +(-1.51756 - 8.06099i) q^{46} +8.67935i q^{47} -6.58306i q^{49} +(-2.48244 + 0.467344i) q^{50} +(-6.76884 - 0.139014i) q^{52} +(-3.70833 - 8.95270i) q^{53} +(3.83039 - 3.83039i) q^{55} +(1.54907 - 0.967413i) q^{56} +(5.80671 - 3.79427i) q^{58} +(-1.77297 - 4.28032i) q^{59} +(-9.49421 - 3.93263i) q^{61} +(0.463365 - 0.678294i) q^{62} +(-7.18854 - 3.51069i) q^{64} +6.06857i q^{65} +(3.50440 - 8.46037i) q^{67} +(2.58646 + 6.62592i) q^{68} +(-0.895474 - 1.37042i) q^{70} +(-7.84134 + 7.84134i) q^{71} +(10.7396 + 10.7396i) q^{73} +(-1.95627 + 9.33299i) q^{74} +(0.249655 - 12.1561i) q^{76} +(-1.80260 - 0.746662i) q^{77} -5.27177 q^{79} +(-3.01386 + 6.50675i) q^{80} +(5.86313 - 1.10379i) q^{82} +(-1.80609 + 4.36028i) q^{83} +(5.89033 - 2.43985i) q^{85} +(2.11261 - 10.0788i) q^{86} +(1.40841 + 8.42973i) q^{88} +(12.4990 + 12.4990i) q^{89} +(2.01943 - 0.836474i) q^{91} +(4.65833 - 10.6238i) q^{92} +(-6.92374 + 10.1353i) q^{94} -10.8985 q^{95} +9.99452 q^{97} +(5.25148 - 7.68735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 - 4 * q^8	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

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