LMFDB - Embedded newform 99.3.k.c.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 77x^12 + 88x^11 - 577x^10 + 578x^9 + 1520x^8 + 1868x^7 - 1619x^6 - 16804x^5 + 32427x^4 + 43316x^3 - 71672x^2 + 83521
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			28.1
Root			$1.64608 - 1.06057i$ of defining polynomial
Character	$\chi$	$=$	99.28
Dual form			99.3.k.c.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35440 + 0.764990i) q^{2} +(1.72190 - 1.25104i) q^{4} +(0.789076 - 2.42853i) q^{5} +(-0.100159 - 0.137856i) q^{7} +(2.72337 - 3.74840i) q^{8} +O(q^{10})$	\(q+(-2.35440 + 0.764990i) q^{2} +(1.72190 - 1.25104i) q^{4} +(0.789076 - 2.42853i) q^{5} +(-0.100159 - 0.137856i) q^{7} +(2.72337 - 3.74840i) q^{8} +6.32135i q^{10} +(7.69573 + 7.85976i) q^{11} +(18.3310 - 5.95611i) q^{13} +(0.341272 + 0.247948i) q^{14} +(-6.17525 + 19.0055i) q^{16} +(19.3014 + 6.27142i) q^{17} +(8.57343 - 11.8003i) q^{19} +(-1.67946 - 5.16886i) q^{20} +(-24.1314 - 12.6178i) q^{22} -7.74583 q^{23} +(14.9503 + 10.8620i) q^{25} +(-38.6022 + 28.0461i) q^{26} +(-0.344927 - 0.112074i) q^{28} +(-22.4904 - 30.9554i) q^{29} +(-13.0940 - 40.2993i) q^{31} -30.9373i q^{32} -50.2408 q^{34} +(-0.413821 + 0.134459i) q^{35} +(-41.7807 + 30.3554i) q^{37} +(-11.1581 + 34.3412i) q^{38} +(-6.95414 - 9.57156i) q^{40} +(27.1820 - 37.4128i) q^{41} +59.7836i q^{43} +(23.0842 + 3.90611i) q^{44} +(18.2367 - 5.92548i) q^{46} +(27.6137 + 20.0626i) q^{47} +(15.1329 - 46.5742i) q^{49} +(-43.5083 - 14.1367i) q^{50} +(24.1130 - 33.1887i) q^{52} +(4.70489 + 14.4801i) q^{53} +(25.1602 - 12.4873i) q^{55} -0.789510 q^{56} +(76.6320 + 55.6764i) q^{58} +(-21.3110 + 15.4833i) q^{59} +(60.2698 + 19.5828i) q^{61} +(61.6572 + 84.8638i) q^{62} +(-1.03430 - 3.18325i) q^{64} -49.2172i q^{65} -2.91469 q^{67} +(41.0810 - 13.3480i) q^{68} +(0.871439 - 0.633137i) q^{70} +(-29.9080 + 92.0473i) q^{71} +(-10.1852 - 14.0187i) q^{73} +(75.1467 - 103.431i) q^{74} -31.0447i q^{76} +(0.312725 - 1.84813i) q^{77} +(-50.1945 + 16.3092i) q^{79} +(41.2825 + 29.9935i) q^{80} +(-35.3768 + 108.879i) q^{82} +(-22.3267 - 7.25438i) q^{83} +(30.4606 - 41.9255i) q^{85} +(-45.7338 - 140.754i) q^{86} +(50.4198 - 7.44162i) q^{88} -97.1861 q^{89} +(-2.65710 - 1.93050i) q^{91} +(-13.3376 + 9.69032i) q^{92} +(-80.3613 - 26.1110i) q^{94} +(-21.8923 - 30.1321i) q^{95} +(-15.6408 - 48.1375i) q^{97} +121.230i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.35440	+	0.764990i	−1.17720	+	0.382495i	−0.831325	−	0.555786i	$-0.812417\pi$
$2$	−2.35440	+	0.764990i	−1.17720	+	0.382495i	−0.345873	+	0.938281i	$0.612417\pi$
$3$		0			0
$3$		0			0
$4$	1.72190	−	1.25104i	0.430476	−	0.312759i
$5$	0.789076	−	2.42853i	0.157815	−	0.485705i	−0.840620	−	0.541625i	$-0.817809\pi$
$5$	0.789076	−	2.42853i	0.157815	−	0.485705i	0.998435	+	0.0559199i	$0.0178092\pi$
$6$		0			0
$7$	−0.100159	−	0.137856i	−0.0143084	−	0.0196938i	0.801803	−	0.597589i	$-0.203874\pi$
$7$	−0.100159	−	0.137856i	−0.0143084	−	0.0196938i	−0.816111	+	0.577895i	$0.803874\pi$
$8$	2.72337	−	3.74840i	0.340422	−	0.468550i
$9$		0			0
$10$			6.32135i			0.632135i
$11$	7.69573	+	7.85976i	0.699612	+	0.714523i
$11$	7.69573	+	7.85976i	0.699612	+	0.714523i
$12$		0			0
$13$	18.3310	−	5.95611i	1.41008	−	0.458163i	0.497643	−	0.867382i	$-0.334199\pi$
$13$	18.3310	−	5.95611i	1.41008	−	0.458163i	0.912436	+	0.409219i	$0.134199\pi$
$14$	0.341272	+	0.247948i	0.0243766	+	0.0177106i
$15$		0			0
$16$	−6.17525	+	19.0055i	−0.385953	+	1.18784i
$17$	19.3014	+	6.27142i	1.13538	+	0.368907i	0.815618	−	0.578591i	$-0.196397\pi$
$17$	19.3014	+	6.27142i	1.13538	+	0.368907i	0.319761	+	0.947498i	$0.396397\pi$
$18$		0			0
$19$	8.57343	−	11.8003i	0.451233	−	0.621069i	−0.521429	−	0.853295i	$-0.674601\pi$
$19$	8.57343	−	11.8003i	0.451233	−	0.621069i	0.972662	+	0.232226i	$0.0746008\pi$
$20$	−1.67946	−	5.16886i	−0.0839732	−	0.258443i
$21$		0			0
$22$	−24.1314	−	12.6178i	−1.09688	−	0.573538i
$23$	−7.74583			−0.336775			−0.168388	−	0.985721i	$-0.553856\pi$
$23$	−7.74583			−0.336775			−0.168388	+	0.985721i	$0.553856\pi$
$24$		0			0
$25$	14.9503	+	10.8620i	0.598013	+	0.434482i
$26$	−38.6022	+	28.0461i	−1.48470	+	1.07870i
$27$		0			0
$28$	−0.344927	−	0.112074i	−0.0123188	−	0.00400263i
$29$	−22.4904	−	30.9554i	−0.775532	−	1.06743i	−0.995761	−	0.0919801i	$-0.970680\pi$
$29$	−22.4904	−	30.9554i	−0.775532	−	1.06743i	0.220229	−	0.975448i	$-0.429320\pi$
$30$		0			0
$31$	−13.0940	−	40.2993i	−0.422389	−	1.29998i	−0.905473	−	0.424405i	$-0.860483\pi$
$31$	−13.0940	−	40.2993i	−0.422389	−	1.29998i	0.483084	−	0.875574i	$-0.339517\pi$
$32$		−	30.9373i		−	0.966789i
$33$		0			0
$34$	−50.2408			−1.47767
$35$	−0.413821	+	0.134459i	−0.0118235	+	0.00384167i
$36$		0			0
$37$	−41.7807	+	30.3554i	−1.12921	+	0.820417i	−0.985579	−	0.169214i	$-0.945877\pi$
$37$	−41.7807	+	30.3554i	−1.12921	+	0.820417i	−0.143628	+	0.989632i	$0.545877\pi$
$38$	−11.1581	+	34.3412i	−0.293635	+	0.903716i
$39$		0			0
$40$	−6.95414	−	9.57156i	−0.173854	−	0.239289i
$41$	27.1820	−	37.4128i	0.662976	−	0.912508i	−0.336600	−	0.941648i	$-0.609277\pi$
$41$	27.1820	−	37.4128i	0.662976	−	0.912508i	0.999575	+	0.0291401i	$0.00927689\pi$
$42$		0			0
$43$			59.7836i			1.39032i	0.718857	+	0.695158i	$0.244666\pi$
$43$			59.7836i			1.39032i	−0.718857	+	0.695158i	$0.755334\pi$
$44$	23.0842	+	3.90611i	0.524640	+	0.0887753i
$45$		0			0
$46$	18.2367	−	5.92548i	0.396451	−	0.128815i
$47$	27.6137	+	20.0626i	0.587526	+	0.426863i	0.841430	−	0.540367i	$-0.181714\pi$
$47$	27.6137	+	20.0626i	0.587526	+	0.426863i	−0.253903	+	0.967230i	$0.581714\pi$
$48$		0			0
$49$	15.1329	−	46.5742i	0.308834	−	0.950493i
$50$	−43.5083	−	14.1367i	−0.870167	−	0.282734i
$51$		0			0
$52$	24.1130	−	33.1887i	0.463711	−	0.638244i
$53$	4.70489	+	14.4801i	0.0887714	+	0.273210i	0.985580	−	0.169208i	$-0.0541208\pi$
$53$	4.70489	+	14.4801i	0.0887714	+	0.273210i	−0.896809	+	0.442418i	$0.854121\pi$
$54$		0			0
$55$	25.1602	−	12.4873i	0.457457	−	0.227042i
$56$	−0.789510			−0.0140984
$57$		0			0
$58$	76.6320	+	55.6764i	1.32124	+	0.959938i
$59$	−21.3110	+	15.4833i	−0.361203	+	0.262430i	−0.753554	−	0.657386i	$-0.771662\pi$
$59$	−21.3110	+	15.4833i	−0.361203	+	0.262430i	0.392350	+	0.919816i	$0.371662\pi$
$60$		0			0
$61$	60.2698	+	19.5828i	0.988029	+	0.321030i	0.758072	−	0.652171i	$-0.226142\pi$
$61$	60.2698	+	19.5828i	0.988029	+	0.321030i	0.229957	+	0.973201i	$0.426142\pi$
$62$	61.6572	+	84.8638i	0.994470	+	1.36877i
$63$		0			0
$64$	−1.03430	−	3.18325i	−0.0161609	−	0.0497382i
$65$		−	49.2172i		−	0.757188i
$66$		0			0
$67$	−2.91469			−0.0435028			−0.0217514	−	0.999763i	$-0.506924\pi$
$67$	−2.91469			−0.0435028			−0.0217514	+	0.999763i	$0.506924\pi$
$68$	41.0810	−	13.3480i	0.604133	−	0.196295i
$69$		0			0
$70$	0.871439	−	0.633137i	0.0124491	−	0.00904482i
$71$	−29.9080	+	92.0473i	−0.421239	+	1.29644i	0.485311	+	0.874342i	$0.338707\pi$
$71$	−29.9080	+	92.0473i	−0.421239	+	1.29644i	−0.906550	+	0.422099i	$0.861293\pi$
$72$		0			0
$73$	−10.1852	−	14.0187i	−0.139523	−	0.192037i	0.733537	−	0.679649i	$-0.237868\pi$
$73$	−10.1852	−	14.0187i	−0.139523	−	0.192037i	−0.873060	+	0.487612i	$0.837868\pi$
$74$	75.1467	−	103.431i	1.01550	−	1.39771i
$75$		0			0
$76$		−	31.0447i		−	0.408483i
$77$	0.312725	−	1.84813i	0.00406136	−	0.0240017i
$78$		0			0
$79$	−50.1945	+	16.3092i	−0.635374	+	0.206445i	−0.608954	−	0.793205i	$-0.708411\pi$
$79$	−50.1945	+	16.3092i	−0.635374	+	0.206445i	−0.0264197	+	0.999651i	$0.508411\pi$
$80$	41.2825	+	29.9935i	0.516031	+	0.374919i
$81$		0			0
$82$	−35.3768	+	108.879i	−0.431424	+	1.32779i
$83$	−22.3267	−	7.25438i	−0.268996	−	0.0874021i	0.171413	−	0.985199i	$-0.445167\pi$
$83$	−22.3267	−	7.25438i	−0.268996	−	0.0874021i	−0.440409	+	0.897797i	$0.645167\pi$
$84$		0			0
$85$	30.4606	−	41.9255i	0.358360	−	0.493241i
$86$	−45.7338	−	140.754i	−0.531789	−	1.63668i
$87$		0			0
$88$	50.4198	−	7.44162i	0.572953	−	0.0845639i
$89$	−97.1861			−1.09198			−0.545989	−	0.837792i	$-0.683846\pi$
$89$	−97.1861			−1.09198			−0.545989	+	0.837792i	$0.683846\pi$
$90$		0			0
$91$	−2.65710	−	1.93050i	−0.0291989	−	0.0212142i
$92$	−13.3376	+	9.69032i	−0.144974	+	0.105330i
$93$		0			0
$94$	−80.3613	−	26.1110i	−0.854908	−	0.277776i
$95$	−21.8923	−	30.1321i	−0.230445	−	0.317180i
$96$		0			0
$97$	−15.6408	−	48.1375i	−0.161246	−	0.496263i	0.837494	−	0.546446i	$-0.184020\pi$
$97$	−15.6408	−	48.1375i	−0.161246	−	0.496263i	−0.998740	+	0.0501828i	$0.984020\pi$
$98$			121.230i			1.23705i
$99$		0			0
$100$	39.3318			0.393318
$101$	−62.5858	+	20.3354i	−0.619662	+	0.201340i	−0.601990	−	0.798504i	$-0.705625\pi$
$101$	−62.5858	+	20.3354i	−0.619662	+	0.201340i	−0.0176716	+	0.999844i	$0.505625\pi$
$102$		0			0
$103$	−112.599	+	81.8082i	−1.09320	+	0.794254i	−0.979936	−	0.199311i	$-0.936130\pi$
$103$	−112.599	+	81.8082i	−1.09320	+	0.794254i	−0.113261	+	0.993565i	$0.536130\pi$
$104$	27.5963	−	84.9328i	0.265349	−	0.816661i
$105$		0			0
$106$	−22.1543	−	30.4928i	−0.209003	−	0.287668i
$107$	7.57953	−	10.4323i	0.0708367	−	0.0974984i	−0.772129	−	0.635466i	$-0.780808\pi$
$107$	7.57953	−	10.4323i	0.0708367	−	0.0974984i	0.842965	+	0.537968i	$0.180808\pi$
$108$		0			0
$109$		−	117.681i		−	1.07964i	−0.841780	−	0.539821i	$-0.818492\pi$
$109$		−	117.681i		−	1.07964i	0.841780	−	0.539821i	$-0.181508\pi$
$110$	−49.6843	+	48.6474i	−0.451675	+	0.442249i
$111$		0			0
$112$	3.23853	−	1.05226i	0.0289154	−	0.00939519i
$113$	142.095	+	103.238i	1.25748	+	0.913614i	0.998631	−	0.0523039i	$-0.0166564\pi$
$113$	142.095	+	103.238i	1.25748	+	0.913614i	0.258850	+	0.965918i	$0.416656\pi$
$114$		0			0
$115$	−6.11205	+	18.8110i	−0.0531483	+	0.163574i
$116$	−77.4528	−	25.1659i	−0.667696	−	0.216948i
$117$		0			0
$118$	38.3299	−	52.7566i	0.324830	−	0.447090i
$119$	−1.06865	−	3.28896i	−0.00898025	−	0.0276384i
$120$		0			0
$121$	−2.55156	+	120.973i	−0.0210872	+	0.999778i
$122$	−156.880			−1.28590
$123$		0			0
$124$	−72.9627	−	53.0105i	−0.588408	−	0.427504i
$125$	89.8214	−	65.2591i	0.718571	−	0.522073i
$126$		0			0
$127$	−56.9179	−	18.4937i	−0.448172	−	0.145620i	0.0762307	−	0.997090i	$-0.475711\pi$
$127$	−56.9179	−	18.4937i	−0.448172	−	0.145620i	−0.524403	+	0.851470i	$0.675711\pi$
$128$	77.6082	+	106.818i	0.606314	+	0.834519i
$129$		0			0
$130$	37.6507	+	115.877i	0.289621	+	0.891361i
$131$		−	27.1623i		−	0.207346i	−0.994611	−	0.103673i	$-0.966940\pi$
$131$		−	27.1623i		−	0.207346i	0.994611	−	0.103673i	$-0.0330595\pi$
$132$		0			0
$133$	−2.48545			−0.0186876
$134$	6.86233	−	2.22971i	0.0512114	−	0.0166396i
$135$		0			0
$136$	76.0728	−	55.2701i	0.559359	−	0.406398i
$137$	25.0824	−	77.1956i	0.183083	−	0.563472i	−0.816827	−	0.576883i	$-0.804269\pi$
$137$	25.0824	−	77.1956i	0.183083	−	0.563472i	0.999910	+	0.0134110i	$0.00426898\pi$
$138$		0			0
$139$	114.273	+	157.283i	0.822108	+	1.13153i	0.989341	+	0.145617i	$0.0465167\pi$
$139$	114.273	+	157.283i	0.822108	+	1.13153i	−0.167233	+	0.985917i	$0.553483\pi$
$140$	−0.544347	+	0.749230i	−0.00388820	+	0.00535164i
$141$		0			0
$142$		−	239.595i		−	1.68729i
$143$	187.884	+	98.2408i	1.31388	+	0.686999i
$144$		0			0
$145$	−92.9228	+	30.1924i	−0.640847	+	0.208224i
$146$	34.7041	+	25.2140i	0.237699	+	0.172699i
$147$		0			0
$148$	−33.9666	+	104.538i	−0.229504	+	0.706340i
$149$	−115.358	−	37.4820i	−0.774212	−	0.251557i	−0.104845	−	0.994489i	$-0.533435\pi$
$149$	−115.358	−	37.4820i	−0.774212	−	0.251557i	−0.669367	+	0.742932i	$0.733435\pi$
$150$		0			0
$151$	−60.2816	+	82.9704i	−0.399216	+	0.549473i	−0.960547	−	0.278118i	$-0.910289\pi$
$151$	−60.2816	+	82.9704i	−0.399216	+	0.549473i	0.561331	+	0.827591i	$0.310289\pi$
$152$	−20.8837	−	64.2733i	−0.137392	−	0.422850i
$153$		0			0
$154$	0.677520	+	4.59046i	0.00439948	+	0.0298082i
$155$	−108.200			−0.698066
$156$		0			0
$157$	−143.464	−	104.232i	−0.913781	−	0.663901i	0.0281874	−	0.999603i	$-0.491026\pi$
$157$	−143.464	−	104.232i	−0.913781	−	0.663901i	−0.941968	+	0.335702i	$0.891026\pi$
$158$	105.701	−	76.7966i	0.668997	−	0.486054i
$159$		0			0
$160$	−75.1320	−	24.4119i	−0.469575	−	0.152574i
$161$	0.775811	+	1.06781i	0.00481870	+	0.00663237i
$162$		0			0
$163$	32.5033	+	100.035i	0.199407	+	0.613711i	0.999897	+	0.0143648i	$0.00457262\pi$
$163$	32.5033	+	100.035i	0.199407	+	0.613711i	−0.800490	+	0.599346i	$0.795427\pi$
$164$		−	98.4270i		−	0.600165i
$165$		0			0
$166$	58.1154			0.350093
$167$	123.073	−	39.9889i	0.736965	−	0.239454i	0.0836021	−	0.996499i	$-0.473358\pi$
$167$	123.073	−	39.9889i	0.736965	−	0.239454i	0.653363	+	0.757045i	$0.273358\pi$
$168$		0			0
$169$	163.828	−	119.028i	0.969394	−	0.704306i
$170$	−39.6438	+	122.011i	−0.233199	+	0.717713i
$171$		0			0
$172$	74.7915	+	102.942i	0.434834	+	0.598498i
$173$	−26.3311	+	36.2416i	−0.152203	+	0.209489i	−0.878309	−	0.478093i	$-0.841328\pi$
$173$	−26.3311	+	36.2416i	−0.152203	+	0.209489i	0.726106	+	0.687583i	$0.241328\pi$
$174$		0			0
$175$		−	3.14892i		−	0.0179939i
$176$	−196.901	+	97.7249i	−1.11876	+	0.555255i
$177$		0			0
$178$	228.815	−	74.3464i	1.28548	−	0.417676i
$179$	−257.046	−	186.755i	−1.43601	−	1.04332i	−0.988857	−	0.148867i	$-0.952437\pi$
$179$	−257.046	−	186.755i	−1.43601	−	1.04332i	−0.447155	−	0.894457i	$-0.647563\pi$
$180$		0			0
$181$	102.216	−	314.588i	0.564729	−	1.73806i	−0.104027	−	0.994574i	$-0.533173\pi$
$181$	102.216	−	314.588i	0.564729	−	1.73806i	0.668756	−	0.743482i	$-0.266827\pi$
$182$	7.73267	+	2.51250i	0.0424872	+	0.0138049i
$183$		0			0
$184$	−21.0948	+	29.0345i	−0.114646	+	0.157796i
$185$	40.7509	+	125.418i	0.220275	+	0.677937i
$186$		0			0
$187$	99.2468	+	199.968i	0.530732	+	1.06935i
$188$	72.6472			0.386421
$189$		0			0
$190$	74.5939	+	54.1956i	0.392599	+	0.285240i
$191$	−102.778	+	74.6723i	−0.538103	+	0.390955i	−0.823380	−	0.567490i	$-0.807914\pi$
$191$	−102.778	+	74.6723i	−0.538103	+	0.390955i	0.285277	+	0.958445i	$0.407914\pi$
$192$		0			0
$193$	201.049	+	65.3248i	1.04171	+	0.338471i	0.779408	−	0.626517i	$-0.215520\pi$
$193$	201.049	+	65.3248i	1.04171	+	0.338471i	0.262297	+	0.964987i	$0.415520\pi$
$194$	73.6494	+	101.370i	0.379636	+	0.522524i
$195$		0			0
$196$	−32.2086	−	99.1280i	−0.164330	−	0.505755i
$197$			2.87439i			0.0145908i	0.999973	+	0.00729541i	$0.00232222\pi$
$197$			2.87439i			0.0145908i	−0.999973	+	0.00729541i	$0.997678\pi$
$198$		0			0
$199$	−158.546			−0.796713			−0.398357	−	0.917231i	$-0.630419\pi$
$199$	−158.546			−0.796713			−0.398357	+	0.917231i	$0.630419\pi$
$200$	81.4306	−	26.4584i	0.407153	−	0.132292i
$201$		0			0
$202$	131.795	−	95.7550i	0.652453	−	0.474035i
$203$	−2.01479	+	6.20090i	−0.00992510	+	0.0305463i
$204$		0			0
$205$	−69.4094	−	95.5338i	−0.338582	−	0.466019i
$206$	202.521	−	278.746i	0.983112	−	1.35314i
$207$		0			0
$208$			385.170i			1.85178i
$209$	158.726	−	23.4269i	0.759456	−	0.112091i
$210$		0			0
$211$	−338.566	+	110.007i	−1.60458	+	0.521359i	−0.968234	−	0.250045i	$-0.919554\pi$
$211$	−338.566	+	110.007i	−1.60458	+	0.521359i	−0.636345	+	0.771405i	$0.719554\pi$
$212$	26.2166	+	19.0474i	0.123663	+	0.0898465i
$213$		0			0
$214$	−9.86459	+	30.3601i	−0.0460962	+	0.141870i
$215$	145.186	+	47.1738i	0.675284	+	0.219413i
$216$		0			0
$217$	−4.24404	+	5.84142i	−0.0195578	+	0.0269190i
$218$	90.0247	+	277.067i	0.412957	+	1.27095i
$219$		0			0
$220$	27.7013	−	52.9783i	0.125915	−	0.240810i
$221$	391.169			1.76999
$222$		0			0
$223$	172.623	+	125.418i	0.774092	+	0.562411i	0.903200	−	0.429219i	$-0.141211\pi$
$223$	172.623	+	125.418i	0.774092	+	0.562411i	−0.129108	+	0.991631i	$0.541211\pi$
$224$	−4.26490	+	3.09863i	−0.0190397	+	0.0138332i
$225$		0			0
$226$	−413.525	−	134.362i	−1.82976	−	0.594524i
$227$	−103.890	−	142.993i	−0.457666	−	0.629923i	0.516357	−	0.856374i	$-0.327288\pi$
$227$	−103.890	−	142.993i	−0.457666	−	0.629923i	−0.974023	+	0.226451i	$0.927288\pi$
$228$		0			0
$229$	−19.4570	−	59.8825i	−0.0849650	−	0.261495i	0.899544	−	0.436831i	$-0.143899\pi$
$229$	−19.4570	−	59.8825i	−0.0849650	−	0.261495i	−0.984509	+	0.175335i	$0.943899\pi$
$230$		−	48.9641i		−	0.212887i
$231$		0			0
$232$	−177.283			−0.764151
$233$	−292.304	+	94.9755i	−1.25453	+	0.407620i	−0.859541	−	0.511067i	$-0.829250\pi$
$233$	−292.304	+	94.9755i	−1.25453	+	0.407620i	−0.394985	+	0.918688i	$0.629250\pi$
$234$		0			0
$235$	70.5118	−	51.2298i	0.300050	−	0.217999i
$236$	−17.3253	+	53.3217i	−0.0734122	+	0.225939i
$237$		0			0
$238$	5.03205	+	6.92602i	0.0211431	+	0.0291009i
$239$	−219.365	+	301.930i	−0.917847	+	1.26331i	0.0465686	+	0.998915i	$0.485171\pi$
$239$	−219.365	+	301.930i	−0.917847	+	1.26331i	−0.964415	+	0.264392i	$0.914829\pi$
$240$		0			0
$241$			13.0743i			0.0542501i	0.999632	+	0.0271250i	$0.00863523\pi$
$241$			13.0743i			0.0542501i	−0.999632	+	0.0271250i	$0.991365\pi$
$242$	−86.5358	−	286.771i	−0.357586	−	1.18500i
$243$		0			0
$244$	128.278	−	41.6799i	0.525728	−	0.170819i
$245$	−101.166	−	73.5011i	−0.412921	−	0.300005i
$246$		0			0
$247$	86.8758	−	267.376i	0.351724	−	1.08249i
$248$	−186.718	−	60.6684i	−0.752895	−	0.244630i
$249$		0			0
$250$	−161.553	+	222.358i	−0.646211	+	0.889433i
$251$	−42.7719	−	131.638i	−0.170406	−	0.524456i	0.828988	−	0.559267i	$-0.188917\pi$
$251$	−42.7719	−	131.638i	−0.170406	−	0.524456i	−0.999394	+	0.0348107i	$0.988917\pi$
$252$		0			0
$253$	−59.6098	−	60.8803i	−0.235612	−	0.240634i
$254$	148.155			0.583286
$255$		0			0
$256$	−253.604	−	184.254i	−0.990641	−	0.719743i
$257$	−232.910	+	169.219i	−0.906264	+	0.658439i	−0.940067	−	0.340989i	$-0.889238\pi$
$257$	−232.910	+	169.219i	−0.906264	+	0.658439i	0.0338032	+	0.999429i	$0.489238\pi$
$258$		0			0
$259$	8.36939	+	2.71938i	0.0323142	+	0.0104995i
$260$	−61.5726	−	84.7474i	−0.236818	−	0.325952i
$261$		0			0
$262$	20.7789	+	63.9508i	0.0793087	+	0.244087i
$263$		−	338.296i		−	1.28629i	−0.765742	−	0.643147i	$-0.777628\pi$
$263$		−	338.296i		−	1.28629i	0.765742	−	0.643147i	$-0.222372\pi$
$264$		0			0
$265$	38.8779			0.146709
$266$	5.85174	−	1.90134i	0.0219990	−	0.00714791i
$267$		0			0
$268$	−5.01881	+	3.64638i	−0.0187269	+	0.0136059i
$269$	19.5161	−	60.0645i	0.0725507	−	0.223288i	−0.908206	−	0.418524i	$-0.862547\pi$
$269$	19.5161	−	60.0645i	0.0725507	−	0.223288i	0.980756	+	0.195236i	$0.0625474\pi$
$270$		0			0
$271$	−97.9877	−	134.868i	−0.361578	−	0.497670i	0.589009	−	0.808126i	$-0.299518\pi$
$271$	−97.9877	−	134.868i	−0.361578	−	0.497670i	−0.950588	+	0.310457i	$0.899518\pi$
$272$	−238.382	+	328.105i	−0.876406	+	1.20627i
$273$		0			0
$274$			200.937i			0.733346i
$275$	29.6806	+	201.097i	0.107929	+	0.731263i
$276$		0			0
$277$	40.3083	−	13.0970i	0.145517	−	0.0472815i	−0.235353	−	0.971910i	$-0.575625\pi$
$277$	40.3083	−	13.0970i	0.145517	−	0.0472815i	0.380870	+	0.924629i	$0.375625\pi$
$278$	−389.364	−	282.889i	−1.40059	−	1.01759i
$279$		0			0
$280$	−0.622984	+	1.91735i	−0.00222494	+	0.00684767i
$281$	135.807	+	44.1263i	0.483298	+	0.157033i	0.540525	−	0.841328i	$-0.318226\pi$
$281$	135.807	+	44.1263i	0.483298	+	0.157033i	−0.0572268	+	0.998361i	$0.518226\pi$
$282$		0			0
$283$	152.286	−	209.604i	0.538114	−	0.740650i	−0.450226	−	0.892915i	$-0.648657\pi$
$283$	152.286	−	209.604i	0.538114	−	0.740650i	0.988340	+	0.152264i	$0.0486565\pi$
$284$	63.6559	+	195.913i	0.224140	+	0.689833i
$285$		0			0
$286$	−517.507	−	87.5684i	−1.80947	−	0.306183i
$287$	−7.88011			−0.0274568
$288$		0			0
$289$	99.4092	+	72.2250i	0.343976	+	0.249914i
$290$	195.680	−	142.170i	0.674759	−	0.490241i
$291$		0			0
$292$	−35.0758	−	11.3968i	−0.120123	−	0.0390302i
$293$	−67.6072	−	93.0533i	−0.230741	−	0.317588i	0.677909	−	0.735146i	$-0.262886\pi$
$293$	−67.6072	−	93.0533i	−0.230741	−	0.317588i	−0.908651	+	0.417557i	$0.862886\pi$
$294$		0			0
$295$	20.7857	+	63.9719i	0.0704601	+	0.216854i
$296$			239.280i			0.808378i
$297$		0			0
$298$	300.271			1.00762
$299$	−141.989	+	46.1350i	−0.474880	+	0.154298i
$300$		0			0
$301$	8.24155	−	5.98784i	0.0273806	−	0.0198931i
$302$	78.4551	−	241.460i	0.259785	−	0.799537i
$303$		0			0
$304$	171.327	+	235.812i	0.563576	+	0.775696i
$305$	95.1149	−	130.914i	0.311852	−	0.429227i
$306$		0			0
$307$			22.9819i			0.0748596i	0.999299	+	0.0374298i	$0.0119171\pi$
$307$			22.9819i			0.0748596i	−0.999299	+	0.0374298i	$0.988083\pi$
$308$	−1.77359	−	3.57353i	−0.00575842	−	0.0116024i
$309$		0			0
$310$	254.746	−	82.7721i	0.821762	−	0.267007i
$311$	481.079	+	349.524i	1.54688	+	1.12387i	0.945831	+	0.324659i	$0.105250\pi$
$311$	481.079	+	349.524i	1.54688	+	1.12387i	0.601047	+	0.799214i	$0.294750\pi$
$312$		0			0
$313$	−161.264	+	496.318i	−0.515219	+	1.58568i	0.267664	+	0.963512i	$0.413748\pi$
$313$	−161.264	+	496.318i	−0.515219	+	1.58568i	−0.782883	+	0.622169i	$0.786252\pi$
$314$	417.507	+	135.656i	1.32964	+	0.432026i
$315$		0			0
$316$	−66.0268	+	90.8781i	−0.208946	+	0.287589i
$317$	−47.4779	−	146.122i	−0.149773	−	0.460953i	0.847821	−	0.530282i	$-0.177914\pi$
$317$	−47.4779	−	146.122i	−0.149773	−	0.460953i	−0.997594	+	0.0693294i	$0.977914\pi$
$318$		0			0
$319$	70.2219	−	414.994i	0.220131	−	1.30092i
$320$	−8.54675			−0.0267086
$321$		0			0
$322$	−2.64343	−	1.92057i	−0.00820942	−	0.00596449i
$323$	239.484	−	173.995i	0.741437	−	0.538686i
$324$		0			0
$325$	338.750	+	110.067i	1.04231	+	0.338667i
$326$	−153.051	−	210.657i	−0.469482	−	0.646187i
$327$		0			0
$328$	−66.2115	−	203.778i	−0.201864	−	0.621275i
$329$		−	5.81617i		−	0.0176783i
$330$		0			0
$331$	297.441			0.898613			0.449306	−	0.893378i	$-0.351671\pi$
$331$	297.441			0.898613			0.449306	+	0.893378i	$0.351671\pi$
$332$	−47.5199	+	15.4401i	−0.143132	+	0.0465065i
$333$		0			0
$334$	−259.172	+	188.299i	−0.775964	+	0.563771i
$335$	−2.29991	+	7.07840i	−0.00686540	+	0.0211295i
$336$		0			0
$337$	2.45661	+	3.38123i	0.00728964	+	0.0100333i	0.812646	−	0.582757i	$-0.198026\pi$
$337$	2.45661	+	3.38123i	0.00728964	+	0.0100333i	−0.805357	+	0.592791i	$0.798026\pi$
$338$	−294.660	+	405.565i	−0.871776	+	1.19990i
$339$		0			0
$340$		−	110.299i		−	0.324409i
$341$	215.975	−	413.049i	0.633357	−	1.21129i
$342$		0			0
$343$	−15.8772	+	5.15881i	−0.0462891	+	0.0150402i
$344$	224.093	+	162.813i	0.651433	+	0.473293i
$345$		0			0
$346$	34.2693	−	105.470i	0.0990443	−	0.304827i
$347$	557.200	+	181.045i	1.60576	+	0.521745i	0.968524	−	0.248920i	$-0.0800757\pi$
$347$	557.200	+	181.045i	1.60576	+	0.521745i	0.637241	+	0.770665i	$0.280076\pi$
$348$		0			0
$349$	−135.909	+	187.062i	−0.389424	+	0.535996i	−0.958050	−	0.286600i	$-0.907475\pi$
$349$	−135.909	+	187.062i	−0.389424	+	0.535996i	0.568627	+	0.822596i	$0.307475\pi$
$350$	2.40890	+	7.41382i	0.00688256	+	0.0211823i
$351$		0			0
$352$	243.159	−	238.085i	0.690794	−	0.676377i
$353$	416.133			1.17885			0.589423	−	0.807824i	$-0.299355\pi$
$353$	416.133			1.17885			0.589423	+	0.807824i	$0.299355\pi$
$354$		0			0
$355$	199.940	+	145.265i	0.563210	+	0.409196i
$356$	−167.345	+	121.583i	−0.470071	+	0.341526i
$357$		0			0
$358$	748.054	+	243.058i	2.08954	+	0.678932i
$359$	−22.2795	−	30.6650i	−0.0620598	−	0.0854179i	0.776859	−	0.629675i	$-0.216812\pi$
$359$	−22.2795	−	30.6650i	−0.0620598	−	0.0854179i	−0.838919	+	0.544257i	$0.816812\pi$
$360$		0			0
$361$	45.8115	+	140.993i	0.126902	+	0.390563i
$362$			818.859i			2.26204i
$363$		0			0
$364$	−6.99039			−0.0192044
$365$	−42.0817	+	13.6732i	−0.115292	+	0.0374607i
$366$		0			0
$367$	−177.269	+	128.793i	−0.483021	+	0.350935i	−0.802494	−	0.596660i	$-0.796494\pi$
$367$	−177.269	+	128.793i	−0.483021	+	0.350935i	0.319473	+	0.947595i	$0.396494\pi$
$368$	47.8324	−	147.213i	0.129979	−	0.400035i
$369$		0			0
$370$	−191.887	−	264.110i	−0.518615	−	0.713812i
$371$	1.52495	−	2.09891i	0.00411037	−	0.00565744i
$372$		0			0
$373$			17.9491i			0.0481209i	0.999711	+	0.0240605i	$0.00765942\pi$
$373$			17.9491i			0.0481209i	−0.999711	+	0.0240605i	$0.992341\pi$
$374$	−386.640	−	394.881i	−1.03380	−	1.05583i
$375$		0			0
$376$	150.405	−	48.8695i	0.400013	−	0.129972i
$377$	−596.647	−	433.489i	−1.58262	−	1.14984i
$378$		0			0
$379$	−14.1040	+	43.4075i	−0.0372136	+	0.114532i	−0.967938	−	0.251190i	$-0.919178\pi$
$379$	−14.1040	+	43.4075i	−0.0372136	+	0.114532i	0.930724	+	0.365722i	$0.119178\pi$
$380$	−75.3929	−	24.4966i	−0.198402	−	0.0644648i
$381$		0			0
$382$	184.856	−	254.432i	0.483916	−	0.666053i
$383$	8.70857	+	26.8022i	0.0227378	+	0.0699797i	0.961782	−	0.273818i	$-0.0882866\pi$
$383$	8.70857	+	26.8022i	0.0227378	+	0.0699797i	−0.939044	+	0.343798i	$0.888287\pi$
$384$		0			0
$385$	−4.24146	−	2.21778i	−0.0110168	−	0.00576045i
$386$	−523.322			−1.35576
$387$		0			0
$388$	−87.1538	−	63.3210i	−0.224623	−	0.163198i
$389$	−456.950	+	331.994i	−1.17468	+	0.853454i	−0.991562	−	0.129637i	$-0.958619\pi$
$389$	−456.950	+	331.994i	−1.17468	+	0.853454i	−0.183118	+	0.983091i	$0.558619\pi$
$390$		0			0
$391$	−149.506	−	48.5773i	−0.382367	−	0.124239i
$392$	−133.366	−	183.563i	−0.340220	−	0.468272i
$393$		0			0
$394$	−2.19888	−	6.76745i	−0.00558091	−	0.0171763i
$395$			134.768i			0.341185i
$396$		0			0
$397$	6.35093			0.0159973			0.00799866	−	0.999968i	$-0.497454\pi$
$397$	6.35093			0.0159973			0.00799866	+	0.999968i	$0.497454\pi$
$398$	373.280	−	121.286i	0.937889	−	0.304739i
$399$		0			0
$400$	−298.760	+	217.062i	−0.746900	+	0.542655i
$401$	51.2418	−	157.706i	0.127785	−	0.393282i	−0.866613	−	0.498981i	$-0.833708\pi$
$401$	51.2418	−	157.706i	0.127785	−	0.393282i	0.994398	+	0.105698i	$0.0337078\pi$
$402$		0			0
$403$	−480.055	−	660.739i	−1.19120	−	1.63955i
$404$	−82.3265	+	113.313i	−0.203779	+	0.280477i
$405$		0			0
$406$		−	16.1407i		−	0.0397554i
$407$	−560.119	−	94.7788i	−1.37621	−	0.232872i
$408$		0			0
$409$	36.1697	−	11.7523i	0.0884346	−	0.0287341i	−0.264466	−	0.964395i	$-0.585196\pi$
$409$	36.1697	−	11.7523i	0.0884346	−	0.0287341i	0.352900	+	0.935661i	$0.385196\pi$
$410$	236.500	+	171.827i	0.576828	+	0.419090i
$411$		0			0
$412$	−91.5402	+	281.732i	−0.222185	+	0.683815i
$413$	4.26896	+	1.38707i	0.0103365	+	0.00335852i
$414$		0			0
$415$	−35.2349	+	48.4967i	−0.0849034	+	0.116859i
$416$	−184.266	−	567.112i	−0.442947	−	1.36325i
$417$		0			0
$418$	−355.783	+	176.580i	−0.851156	+	0.422441i
$419$	254.746			0.607985			0.303993	−	0.952674i	$-0.401680\pi$
$419$	254.746			0.607985			0.303993	+	0.952674i	$0.401680\pi$
$420$		0			0
$421$	−448.793	−	326.067i	−1.06602	−	0.774507i	−0.0908248	−	0.995867i	$-0.528950\pi$
$421$	−448.793	−	326.067i	−1.06602	−	0.774507i	−0.975192	+	0.221360i	$0.928950\pi$
$422$	712.965	−	517.999i	1.68949	−	1.22749i
$423$		0			0
$424$	67.0905	+	21.7990i	0.158232	+	0.0514128i
$425$	220.442	+	303.413i	0.518688	+	0.713913i
$426$		0			0
$427$	−3.33691	−	10.2700i	−0.00781478	−	0.0240514i
$428$		−	27.4457i		−	0.0641256i
$429$		0			0
$430$	−377.913			−0.878867
$431$	−29.9493	+	9.73111i	−0.0694879	+	0.0225780i	−0.343555	−	0.939133i	$-0.611631\pi$
$431$	−29.9493	+	9.73111i	−0.0694879	+	0.0225780i	0.274067	+	0.961711i	$0.411631\pi$
$432$		0			0
$433$	−512.897	+	372.641i	−1.18452	+	0.860604i	−0.992674	−	0.120821i	$-0.961447\pi$
$433$	−512.897	+	372.641i	−1.18452	+	0.860604i	−0.191845	+	0.981425i	$0.561447\pi$
$434$	5.52353	−	16.9997i	0.0127270	−	0.0391697i
$435$		0			0
$436$	−147.223	−	202.635i	−0.337668	−	0.464760i
$437$	−66.4083	+	91.4032i	−0.151964	+	0.209161i
$438$		0			0
$439$		−	336.283i		−	0.766021i	−0.923744	−	0.383010i	$-0.874887\pi$
$439$		−	336.283i		−	0.766021i	0.923744	−	0.383010i	$-0.125113\pi$
$440$	21.7129	−	128.318i	0.0493475	−	0.291632i
$441$		0			0
$442$	−920.966	+	299.240i	−2.08363	+	0.677014i
$443$	−394.592	−	286.688i	−0.890728	−	0.647152i	0.0453398	−	0.998972i	$-0.485563\pi$
$443$	−394.592	−	286.688i	−0.890728	−	0.647152i	−0.936068	+	0.351820i	$0.885563\pi$
$444$		0			0
$445$	−76.6873	+	236.019i	−0.172331	+	0.530380i
$446$	−502.365	−	163.228i	−1.12638	−	0.365983i
$447$		0			0
$448$	−0.335237	+	0.461414i	−0.000748297	+	0.00102994i
$449$	206.541	+	635.666i	0.460001	+	1.41574i	0.865162	+	0.501493i	$0.167216\pi$
$449$	206.541	+	635.666i	0.460001	+	1.41574i	−0.405161	+	0.914245i	$0.632784\pi$
$450$		0			0
$451$	503.241	−	74.2749i	1.11583	−	0.164689i
$452$	373.830			0.827057
$453$		0			0
$454$	353.986	+	257.186i	0.779706	+	0.566489i
$455$	−6.78491	+	4.92953i	−0.0149119	+	0.0108341i
$456$		0			0
$457$	486.453	+	158.058i	1.06445	+	0.345860i	0.788323	−	0.615262i	$-0.210950\pi$
$457$	486.453	+	158.058i	1.06445	+	0.345860i	0.276125	+	0.961122i	$0.410950\pi$
$458$	91.6189	+	126.103i	0.200041	+	0.275333i
$459$		0			0
$460$	13.0088	+	40.0371i	0.0282801	+	0.0870371i
$461$		−	75.7082i		−	0.164226i	−0.996623	−	0.0821131i	$-0.973833\pi$
$461$		−	75.7082i		−	0.164226i	0.996623	−	0.0821131i	$-0.0261669\pi$
$462$		0			0
$463$	292.607			0.631980			0.315990	−	0.948763i	$-0.397663\pi$
$463$	292.607			0.631980			0.315990	+	0.948763i	$0.397663\pi$
$464$	727.206	−	236.283i	1.56725	−	0.509232i
$465$		0			0
$466$	615.545	−	447.220i	1.32091	−	0.959699i
$467$	−239.339	+	736.611i	−0.512504	+	1.57733i	0.275273	+	0.961366i	$0.411232\pi$
$467$	−239.339	+	736.611i	−0.512504	+	1.57733i	−0.787778	+	0.615960i	$0.788768\pi$
$468$		0			0
$469$	0.291931	+	0.401808i	0.000622454	+	0.000856734i
$470$	−126.822	+	174.556i	−0.269835	+	0.371396i
$471$		0			0
$472$			122.049i			0.258579i
$473$	−469.884	+	460.078i	−0.993413	+	0.972681i
$474$		0			0
$475$	256.351	−	83.2935i	0.539686	−	0.175355i
$476$	−5.95473	−	4.32636i	−0.0125099	−	0.00908900i
$477$		0			0
$478$	285.499	−	878.676i	0.597279	−	1.83823i
$479$	−62.4240	−	20.2828i	−0.130322	−	0.0423440i	0.243130	−	0.969994i	$-0.421826\pi$
$479$	−62.4240	−	20.2828i	−0.130322	−	0.0423440i	−0.373452	+	0.927650i	$0.621826\pi$
$480$		0			0
$481$	−585.083	+	805.297i	−1.21639	+	1.67421i
$482$	−10.0017	−	30.7820i	−0.0207504	−	0.0638631i
$483$		0			0
$484$	146.948	+	211.496i	0.303612	+	0.436976i
$485$	−129.245			−0.266485
$486$		0			0
$487$	14.6563	+	10.6484i	0.0300951	+	0.0218653i	0.602731	−	0.797944i	$-0.294079\pi$
$487$	14.6563	+	10.6484i	0.0300951	+	0.0218653i	−0.572636	+	0.819810i	$0.694079\pi$
$488$	237.541	−	172.584i	0.486765	−	0.353655i
$489$		0			0
$490$	294.412	+	95.6601i	0.600840	+	0.195225i
$491$	−250.927	−	345.371i	−0.511053	−	0.703404i	0.473043	−	0.881039i	$-0.343155\pi$
$491$	−250.927	−	345.371i	−0.511053	−	0.703404i	−0.984096	+	0.177635i	$0.943155\pi$
$492$		0			0
$493$	−239.963	−	738.531i	−0.486741	−	1.49804i
$494$			695.969i			1.40884i
$495$		0			0
$496$	846.766			1.70719
$497$	15.6849	−	5.09632i	0.0315591	−	0.0102542i
$498$		0			0
$499$	−230.872	+	167.738i	−0.462669	+	0.336149i	−0.794577	−	0.607163i	$-0.792307\pi$
$499$	−230.872	+	167.738i	−0.462669	+	0.336149i	0.331908	+	0.943312i	$0.392307\pi$
$500$	73.0224	−	224.740i	0.146045	−	0.449480i
$501$		0			0
$502$	201.404	+	277.209i	0.401203	+	0.552209i
$503$	319.511	−	439.769i	0.635210	−	0.874292i	−0.363139	−	0.931735i	$-0.618295\pi$
$503$	319.511	−	439.769i	0.635210	−	0.874292i	0.998349	+	0.0574435i	$0.0182949\pi$
$504$		0			0
$505$			168.038i			0.332748i
$506$	186.918	+	97.7355i	0.369403	+	0.193153i
$507$		0			0
$508$	−121.143	+	39.3619i	−0.238471	+	0.0774841i
$509$	158.973	+	115.501i	0.312324	+	0.226917i	0.732893	−	0.680344i	$-0.238170\pi$
$509$	158.973	+	115.501i	0.312324	+	0.226917i	−0.420569	+	0.907261i	$0.638170\pi$
$510$		0			0
$511$	−0.912435	+	2.80819i	−0.00178559	+	0.00549547i
$512$	235.746	+	76.5987i	0.460442	+	0.149607i
$513$		0			0
$514$	418.911	−	576.582i	0.815003	−	1.12175i
$515$	109.824	+	338.003i	0.213250	+	0.656317i
$516$		0			0
$517$	54.8210	+	371.433i	0.106037	+	0.718440i
$518$	−21.7851			−0.0420563
$519$		0			0
$520$	−184.486	−	134.037i	−0.354781	−	0.257763i
$521$	−463.782	+	336.958i	−0.890178	+	0.646752i	−0.935924	−	0.352201i	$-0.885433\pi$
$521$	−463.782	+	336.958i	−0.890178	+	0.646752i	0.0457468	+	0.998953i	$0.485433\pi$
$522$		0			0
$523$	−945.004	−	307.050i	−1.80689	−	0.587094i	−0.806897	−	0.590693i	$-0.798855\pi$
$523$	−945.004	−	307.050i	−1.80689	−	0.587094i	−0.999994	+	0.00359838i	$0.998855\pi$
$524$	−33.9811	−	46.7709i	−0.0648493	−	0.0892575i
$525$		0			0
$526$	258.793	+	796.482i	0.492001	+	1.51422i
$527$		−	859.954i		−	1.63179i
$528$		0			0
$529$	−469.002			−0.886583
$530$	−91.5341	+	29.7412i	−0.172706	+	0.0561155i
$531$		0			0
$532$	−4.27971	+	3.10939i	−0.00804457	+	0.00584472i
$533$	275.439	−	847.715i	0.516772	−	1.59046i
$534$		0			0
$535$	−19.3544	−	26.6390i	−0.0361764	−	0.0497925i
$536$	−7.93778	+	10.9254i	−0.0148093	+	0.0203832i
$537$		0			0
$538$			156.345i			0.290604i
$539$	482.520	−	239.481i	0.895213	−	0.444307i
$540$		0			0
$541$	215.044	−	69.8719i	0.397493	−	0.129153i	−0.103448	−	0.994635i	$-0.532987\pi$
$541$	215.044	−	69.8719i	0.397493	−	0.129153i	0.500941	+	0.865482i	$0.332987\pi$
$542$	333.875	+	242.574i	0.616005	+	0.447554i
$543$		0			0
$544$	194.021	−	597.134i	0.356655	−	1.09767i
$545$	−285.791	−	92.8592i	−0.524388	−	0.170384i
$546$		0			0
$547$	268.871	−	370.069i	0.491538	−	0.676543i	−0.489133	−	0.872209i	$-0.662687\pi$
$547$	268.871	−	370.069i	0.491538	−	0.676543i	0.980671	+	0.195666i	$0.0626868\pi$
$548$	−53.3851	−	164.302i	−0.0974181	−	0.299822i
$549$		0			0
$550$	−223.717	−	450.757i	−0.406758	−	0.819559i
$551$	−558.104			−1.01289
$552$		0			0
$553$	7.27574	+	5.28613i	0.0131569	+	0.00955901i
$554$	−84.8827	+	61.6709i	−0.153218	+	0.111319i
$555$		0			0
$556$	393.534	+	127.867i	0.707796	+	0.229977i
$557$	165.248	+	227.445i	0.296676	+	0.408339i	0.931168	−	0.364590i	$-0.118791\pi$
$557$	165.248	+	227.445i	0.296676	+	0.408339i	−0.634492	+	0.772929i	$0.718791\pi$
$558$		0			0
$559$	356.078	+	1095.89i	0.636991	+	1.96046i
$560$		−	8.69517i		−	0.0155271i
$561$		0			0
$562$	−353.499			−0.629002
$563$	−214.219	+	69.6039i	−0.380495	+	0.123630i	−0.493019	−	0.870019i	$-0.664107\pi$
$563$	−214.219	+	69.6039i	−0.380495	+	0.123630i	0.112524	+	0.993649i	$0.464107\pi$
$564$		0			0
$565$	362.841	−	263.620i	0.642197	−	0.466583i
$566$	−198.197	+	609.988i	−0.350172	+	1.07772i
$567$		0			0
$568$	263.580	+	362.786i	0.464049	+	0.638708i
$569$	87.1966	−	120.016i	0.153245	−	0.210924i	−0.725491	−	0.688232i	$-0.758387\pi$
$569$	87.1966	−	120.016i	0.153245	−	0.210924i	0.878736	+	0.477308i	$0.158387\pi$
$570$		0			0
$571$		−	111.405i		−	0.195106i	−0.995230	−	0.0975528i	$-0.968899\pi$
$571$		−	111.405i		−	0.195106i	0.995230	−	0.0975528i	$-0.0311015\pi$
$572$	446.422	−	65.8888i	0.780458	−	0.115190i
$573$		0			0
$574$	18.5529	−	6.02820i	0.0323221	−	0.0105021i
$575$	−115.803	−	84.1355i	−0.201396	−	0.146323i
$576$		0			0
$577$	−167.056	+	514.146i	−0.289526	+	0.891068i	0.695480	+	0.718545i	$0.255192\pi$
$577$	−167.056	+	514.146i	−0.289526	+	0.891068i	−0.985006	+	0.172523i	$0.944808\pi$
$578$	−289.300	−	93.9993i	−0.500519	−	0.162629i
$579$		0			0
$580$	−122.232	+	168.238i	−0.210745	+	0.290066i
$581$	1.23615	+	3.80446i	0.00212762	+	0.00654813i
$582$		0			0
$583$	−77.6029	+	148.415i	−0.133110	+	0.254570i
$584$	−80.2858			−0.137476
$585$		0			0
$586$	230.359	+	167.366i	0.393104	+	0.285607i
$587$	278.485	−	202.331i	0.474420	−	0.344687i	−0.324741	−	0.945803i	$-0.605277\pi$
$587$	278.485	−	202.331i	0.474420	−	0.344687i	0.799162	+	0.601116i	$0.205277\pi$
$588$		0			0
$589$	−587.805	−	190.990i	−0.997972	−	0.324261i
$590$	−97.8757	−	134.714i	−0.165891	−	0.228329i
$591$		0			0
$592$	−318.913	−	981.513i	−0.538704	−	1.65796i
$593$			723.311i			1.21975i	0.792498	+	0.609874i	$0.208780\pi$
$593$			723.311i			1.21975i	−0.792498	+	0.609874i	$0.791220\pi$
$594$		0			0
$595$	−8.83059			−0.0148413
$596$	−245.526	+	79.7763i	−0.411956	+	0.133853i
$597$		0			0
$598$	299.006	−	217.240i	0.500009	−	0.363278i
$599$	87.6892	−	269.880i	0.146393	−	0.450550i	−0.850795	−	0.525498i	$-0.823879\pi$
$599$	87.6892	−	269.880i	0.146393	−	0.450550i	0.997187	+	0.0749478i	$0.0238790\pi$
$600$		0			0
$601$	604.280	+	831.720i	1.00546	+	1.38389i	0.921916	+	0.387390i	$0.126623\pi$
$601$	604.280	+	831.720i	1.00546	+	1.38389i	0.0835420	+	0.996504i	$0.473377\pi$
$602$	−14.8232	+	20.4024i	−0.0246233	+	0.0338911i
$603$		0			0
$604$			218.282i			0.361393i
$605$	291.773	+	101.654i	0.482270	+	0.168022i
$606$		0			0
$607$	599.620	−	194.828i	0.987842	−	0.320969i	0.229845	−	0.973227i	$-0.426178\pi$
$607$	599.620	−	194.828i	0.987842	−	0.320969i	0.757997	+	0.652258i	$0.226178\pi$
$608$	−365.069	−	265.238i	−0.600443	−	0.436247i
$609$		0			0
$610$	−123.790	+	380.986i	−0.202934	+	0.624568i
$611$	625.683	+	203.297i	1.02403	+	0.332728i
$612$		0			0
$613$	330.524	−	454.927i	0.539190	−	0.742132i	−0.449306	−	0.893378i	$-0.648329\pi$
$613$	330.524	−	454.927i	0.539190	−	0.742132i	0.988496	+	0.151246i	$0.0483286\pi$
$614$	−17.5809	−	54.1085i	−0.0286334	−	0.0881246i
$615$		0			0
$616$	−6.07586	−	6.20536i	−0.00986340	−	0.0100736i
$617$	892.792			1.44699			0.723494	−	0.690331i	$-0.242535\pi$
$617$	892.792			1.44699			0.723494	+	0.690331i	$0.242535\pi$
$618$		0			0
$619$	−524.551	−	381.109i	−0.847417	−	0.615684i	0.0770159	−	0.997030i	$-0.475461\pi$
$619$	−524.551	−	381.109i	−0.847417	−	0.615684i	−0.924433	+	0.381346i	$0.875461\pi$
$620$	−186.310	+	135.362i	−0.300501	+	0.218327i
$621$		0			0
$622$	−1400.03	−	454.898i	−2.25086	−	0.731348i
$623$	9.73402	+	13.3977i	0.0156244	+	0.0215052i
$624$		0			0
$625$	55.1554	+	169.751i	0.0882486	+	0.271601i
$626$		−	1291.89i		−	2.06373i
$627$		0			0
$628$	−377.429			−0.601002
$629$	−996.799	+	323.880i	−1.58474	+	0.514912i
$630$		0			0
$631$	824.719	−	599.193i	1.30700	−	0.949593i	0.307005	−	0.951708i	$-0.400673\pi$
$631$	824.719	−	599.193i	1.30700	−	0.949593i	0.999998	+	0.00211458i	$0.000673092\pi$
$632$	−75.5650	+	232.565i	−0.119565	+	0.367983i
$633$		0			0
$634$	223.564	+	307.709i	0.352624	+	0.485346i
$635$	−89.8251	+	123.634i	−0.141457	+	0.194699i
$636$		0			0
$637$		−	943.885i		−	1.48177i
$638$	152.136	+	1030.78i	0.238458	+	1.61564i
$639$		0			0
$640$	320.650	−	104.186i	0.501016	−	0.162790i
$641$	353.056	+	256.510i	0.550789	+	0.400172i	0.828076	−	0.560615i	$-0.189435\pi$
$641$	353.056	+	256.510i	0.550789	+	0.400172i	−0.277287	+	0.960787i	$0.589435\pi$
$642$		0			0
$643$	−159.050	+	489.507i	−0.247357	+	0.761285i	0.747883	+	0.663830i	$0.231070\pi$
$643$	−159.050	+	489.507i	−0.247357	+	0.761285i	−0.995240	+	0.0974552i	$0.968930\pi$
$644$	2.67175	+	0.868103i	0.00414867	+	0.00134799i
$645$		0			0
$646$	−430.736	+	592.857i	−0.666774	+	0.917736i
$647$	−74.4847	−	229.240i	−0.115123	−	0.354313i	0.876849	−	0.480765i	$-0.159641\pi$
$647$	−74.4847	−	229.240i	−0.115123	−	0.354313i	−0.991973	+	0.126452i	$0.959641\pi$
$648$		0			0
$649$	−285.699	−	48.3437i	−0.440214	−	0.0744895i
$650$	−881.753			−1.35654
$651$		0			0
$652$	181.115	+	131.588i	0.277784	+	0.201822i
$653$	−131.498	+	95.5386i	−0.201374	+	0.146307i	−0.683903	−	0.729573i	$-0.739719\pi$
$653$	−131.498	+	95.5386i	−0.201374	+	0.146307i	0.482528	+	0.875881i	$0.339719\pi$
$654$		0			0
$655$	−65.9644	−	21.4331i	−0.100709	−	0.0327223i
$656$	543.192	+	747.640i	0.828037	+	1.13969i
$657$		0			0
$658$	4.44931	+	13.6936i	0.00676187	+	0.0208109i
$659$		−	1078.94i		−	1.63724i	−0.574332	−	0.818622i	$-0.694738\pi$
$659$		−	1078.94i		−	1.63724i	0.574332	−	0.818622i	$-0.305262\pi$
$660$		0			0
$661$	428.584			0.648387			0.324193	−	0.945991i	$-0.394907\pi$
$661$	428.584			0.648387			0.324193	+	0.945991i	$0.394907\pi$
$662$	−700.293	+	227.539i	−1.05785	+	0.343715i
$663$		0			0
$664$	−87.9961	+	63.9329i	−0.132524	+	0.0962845i
$665$	−1.96121	+	6.03599i	−0.00294919	+	0.00907667i
$666$		0			0
$667$	174.207	+	239.775i	0.261180	+	0.359483i
$668$	161.893	−	222.826i	0.242354	−	0.333572i
$669$		0			0
$670$		−	18.4248i		−	0.0274996i
$671$	309.903	+	624.410i	0.461853	+	0.930566i
$672$		0			0
$673$	−249.836	+	81.1765i	−0.371227	+	0.120619i	−0.488688	−	0.872459i	$-0.662524\pi$
$673$	−249.836	+	81.1765i	−0.371227	+	0.120619i	0.117461	+	0.993077i	$0.462524\pi$
$674$	−8.37044	−	6.08148i	−0.0124191	−	0.00902297i
$675$		0			0
$676$	133.187	−	409.909i	0.197023	−	0.606374i
$677$	−142.544	−	46.3152i	−0.210552	−	0.0684125i	0.201842	−	0.979418i	$-0.435307\pi$
$677$	−142.544	−	46.3152i	−0.210552	−	0.0684125i	−0.412394	+	0.911006i	$0.635307\pi$
$678$		0			0
$679$	−5.06950	+	6.97757i	−0.00746613	+	0.0102762i
$680$	−74.1978	−	228.357i	−0.109114	−	0.335819i
$681$		0			0
$682$	−192.512	+	1137.70i	−0.282276	+	1.66818i
$683$	52.4276			0.0767608			0.0383804	−	0.999263i	$-0.487780\pi$
$683$	52.4276			0.0767608			0.0383804	+	0.999263i	$0.487780\pi$
$684$		0			0
$685$	−167.680	−	121.826i	−0.244788	−	0.177849i
$686$	33.4347	−	24.2917i	0.0487387	−	0.0354107i
$687$		0			0
$688$	−1136.21	−	369.178i	−1.65147	−	0.536596i
$689$	172.491	+	237.413i	0.250350	+	0.344577i
$690$		0			0
$691$	−60.7905	−	187.094i	−0.0879747	−	0.270758i	0.897385	−	0.441249i	$-0.145465\pi$
$691$	−60.7905	−	187.094i	−0.0879747	−	0.270758i	−0.985359	+	0.170491i	$0.945465\pi$
$692$			95.3458i			0.137783i
$693$		0			0
$694$	−1450.37			−2.08987
$695$	472.137	−	153.407i	0.679334	−	0.220729i
$696$		0			0
$697$	759.283	−	551.652i	1.08936	−	0.791466i
$698$	176.882	−	544.388i	0.253413	−	0.779925i
$699$		0			0
$700$	−3.93942	−	5.42215i	−0.00562774	−	0.00774593i
$701$	521.017	−	717.119i	0.743248	−	1.02299i	−0.255177	−	0.966894i	$-0.582134\pi$
$701$	521.017	−	717.119i	0.743248	−	1.02299i	0.998425	−	0.0560992i	$-0.0178663\pi$
$702$		0			0
$703$			753.275i			1.07152i
$704$	17.0599	−	32.6268i	0.0242328	−	0.0463448i
$705$		0			0
$706$	−979.741	+	318.337i	−1.38774	+	0.450903i
$707$	9.07187	+	6.59110i	0.0128315	+	0.00932263i
$708$		0			0
$709$	95.8971	−	295.141i	0.135257	−	0.416278i	−0.860373	−	0.509665i	$-0.829769\pi$
$709$	95.8971	−	295.141i	0.135257	−	0.416278i	0.995630	+	0.0933872i	$0.0297694\pi$
$710$	−581.863	−	189.059i	−0.819526	−	0.266280i
$711$		0			0
$712$	−264.674	+	364.292i	−0.371733	+	0.511647i
$713$	101.424	+	312.152i	0.142250	+	0.437800i
$714$		0			0
$715$	386.836	−	378.763i	0.541029	−	0.529738i
$716$	−676.246			−0.944478
$717$		0			0
$718$	75.9131	+	55.1541i	0.105729	+	0.0768163i
$719$	364.996	−	265.185i	0.507644	−	0.368825i	−0.304285	−	0.952581i	$-0.598418\pi$
$719$	364.996	−	265.185i	0.507644	−	0.368825i	0.811929	+	0.583756i	$0.198418\pi$
$720$		0			0
$721$	22.5556	+	7.32875i	0.0312837	+	0.0101647i
$722$	−215.717	−	296.909i	−0.298777	−	0.411231i
$723$		0			0
$724$	−217.555	−	669.567i	−0.300491	−	0.924816i
$725$		−	707.086i		−	0.975290i
$726$		0			0
$727$	−89.6851			−0.123363			−0.0616817	−	0.998096i	$-0.519646\pi$
$727$	−89.6851			−0.123363			−0.0616817	+	0.998096i	$0.519646\pi$
$728$	−14.4725	+	4.70241i	−0.0198799	+	0.00645936i
$729$		0			0
$730$	88.6171	−	64.3841i	0.121393	−	0.0881974i
$731$	−374.928	+	1153.91i	−0.512897	+	1.57854i
$732$		0			0
$733$	−327.682	−	451.016i	−0.447042	−	0.615301i	0.524716	−	0.851277i	$-0.324171\pi$
$733$	−327.682	−	451.016i	−0.447042	−	0.615301i	−0.971759	+	0.235976i	$0.924171\pi$
$734$	318.835	−	438.839i	0.434381	−	0.597874i
$735$		0			0
$736$			239.635i			0.325591i
$737$	−22.4306	−	22.9087i	−0.0304351	−	0.0310838i
$738$		0			0
$739$	91.0451	−	29.5823i	0.123200	−	0.0400302i	−0.246768	−	0.969075i	$-0.579369\pi$
$739$	91.0451	−	29.5823i	0.123200	−	0.0400302i	0.369968	+	0.929044i	$0.379369\pi$
$740$	227.072	+	164.977i	0.306854	+	0.222943i
$741$		0			0
$742$	−1.98469	+	6.10823i	−0.00267478	+	0.00823212i
$743$	−1066.46	−	346.515i	−1.43535	−	0.466373i	−0.514904	−	0.857248i	$-0.672172\pi$
$743$	−1066.46	−	346.515i	−1.43535	−	0.466373i	−0.920444	+	0.390876i	$0.872172\pi$
$744$		0			0
$745$	−182.052	+	250.573i	−0.244365	+	0.336339i
$746$	−13.7309	−	42.2593i	−0.0184060	−	0.0566479i
$747$		0			0
$748$	421.061	+	220.164i	0.562915	+	0.294337i
$749$	−2.19732			−0.00293367
$750$		0			0
$751$	206.616	+	150.115i	0.275121	+	0.199887i	0.716786	−	0.697293i	$-0.245612\pi$
$751$	206.616	+	150.115i	0.275121	+	0.199887i	−0.441666	+	0.897180i	$0.645612\pi$
$752$	−551.820	+	400.920i	−0.733803	+	0.533139i
$753$		0			0
$754$	1736.36	+	564.177i	2.30286	+	0.748245i
$755$	153.929	+	211.865i	0.203880	+	0.280616i
$756$		0			0
$757$	38.2727	+	117.791i	0.0505584	+	0.155603i	0.973148	−	0.230180i	$-0.0739314\pi$
$757$	38.2727	+	117.791i	0.0505584	+	0.155603i	−0.922590	+	0.385783i	$0.873931\pi$
$758$		−	112.988i		−	0.149061i
$759$		0			0
$760$	−172.568			−0.227063
$761$	331.927	−	107.850i	0.436172	−	0.141721i	−0.0826967	−	0.996575i	$-0.526353\pi$
$761$	331.927	−	107.850i	0.436172	−	0.141721i	0.518869	+	0.854854i	$0.326353\pi$
$762$		0			0
$763$	−16.2231	+	11.7867i	−0.0212622	+	0.0154479i
$764$	−83.5555	+	257.157i	−0.109366	+	0.336593i
$765$		0			0
$766$	−41.0068	−	56.4411i	−0.0535337	−	0.0736829i
$767$	−298.432	+	410.757i	−0.389090	+	0.535537i
$768$		0			0
$769$		−	867.000i		−	1.12744i	−0.825966	−	0.563719i	$-0.809370\pi$
$769$		−	867.000i		−	1.12744i	0.825966	−	0.563719i	$-0.190630\pi$
$770$	11.6827	+	1.97684i	0.0151723	+	0.00256733i
$771$		0			0
$772$	427.911	−	139.037i	0.554289	−	0.180099i
$773$	−140.552	−	102.117i	−0.181827	−	0.132105i	0.493149	−	0.869945i	$-0.335846\pi$
$773$	−140.552	−	102.117i	−0.181827	−	0.132105i	−0.674976	+	0.737840i	$0.735846\pi$
$774$		0			0
$775$	241.973	−	744.716i	0.312223	−	0.960924i
$776$	−223.034	−	72.4683i	−0.287416	−	0.0933870i
$777$		0			0
$778$	821.870	−	1131.21i	1.05639	−	1.45399i
$779$	−208.440	−	641.512i	−0.267574	−	0.823507i
$780$		0			0
$781$	−953.633	+	473.302i	−1.22104	+	0.606020i
$782$	389.157			0.497643
$783$		0			0
$784$	791.714	+	575.214i	1.00984	+	0.733691i
$785$	−366.335	+	266.158i	−0.466669	+	0.339055i
$786$		0			0
$787$	43.0442	+	13.9859i	0.0546940	+	0.0177712i	0.336236	−	0.941778i	$-0.390846\pi$
$787$	43.0442	+	13.9859i	0.0546940	+	0.0177712i	−0.281542	+	0.959549i	$0.590846\pi$
$788$	3.59597	+	4.94943i	0.00456341	+	0.00628100i
$789$		0			0
$790$	−103.096	−	317.297i	−0.130501	−	0.401642i
$791$		−	29.9290i		−	0.0378369i
$792$		0			0
$793$	1221.44			1.54028
$794$	−14.9526	+	4.85840i	−0.0188320	+	0.00611889i
$795$		0			0
$796$	−273.001	+	198.347i	−0.342966	+	0.249179i
$797$	−291.551	+	897.301i	−0.365810	+	1.12585i	0.583662	+	0.811997i	$0.301619\pi$
$797$	−291.551	+	897.301i	−0.365810	+	1.12585i	−0.949472	+	0.313852i	$0.898381\pi$
$798$		0			0
$799$	407.164	+	560.414i	0.509593	+	0.701394i
$800$	336.042	−	462.522i	0.420052	−	0.578152i
$801$		0			0
$802$			410.502i			0.511848i
$803$	31.8012	−	187.937i	0.0396030	−	0.234044i
$804$		0			0
$805$	3.20539	−	1.04149i	0.00398185	−	0.00129378i
$806$	1635.70	+	1188.40i	2.02940	+	1.47445i
$807$		0			0
$808$	−94.2194	+	289.977i	−0.116608	+	0.358883i
$809$	−502.635	−	163.316i	−0.621304	−	0.201874i	−0.0185847	−	0.999827i	$-0.505916\pi$
$809$	−502.635	−	163.316i	−0.621304	−	0.201874i	−0.602719	+	0.797953i	$0.705916\pi$
$810$		0			0
$811$	430.074	−	591.946i	0.530301	−	0.729896i	−0.456876	−	0.889531i	$-0.651032\pi$
$811$	430.074	−	591.946i	0.530301	−	0.729896i	0.987176	+	0.159634i	$0.0510316\pi$
$812$	4.28827	+	13.1979i	0.00528112	+	0.0162536i
$813$		0			0
$814$	1391.25	−	205.339i	1.70915	−	0.252259i
$815$	268.585			0.329552
$816$		0			0
$817$	705.465	+	512.550i	0.863482	+	0.627356i
$818$	−76.1675	+	55.3390i	−0.0931143	+	0.0676515i
$819$		0			0
$820$	−239.033	−	77.6664i	−0.291503	−	0.0947151i
$821$	661.205	+	910.071i	0.805366	+	1.10849i	0.992022	+	0.126066i	$0.0402350\pi$
$821$	661.205	+	910.071i	0.805366	+	1.10849i	−0.186656	+	0.982425i	$0.559765\pi$
$822$		0			0
$823$	73.6727	+	226.741i	0.0895172	+	0.275506i	0.985786	−	0.168005i	$-0.0537326\pi$
$823$	73.6727	+	226.741i	0.0895172	+	0.275506i	−0.896269	+	0.443511i	$0.853733\pi$
$824$			644.861i			0.782599i
$825$		0			0
$826$	−11.1119			−0.0134527
$827$	1461.01	−	474.709i	1.76663	−	0.574014i	0.768780	−	0.639513i	$-0.220864\pi$
$827$	1461.01	−	474.709i	1.76663	−	0.574014i	0.997853	+	0.0654992i	$0.0208640\pi$
$828$		0			0
$829$	−1275.44	+	926.658i	−1.53852	+	1.11780i	−0.587269	+	0.809392i	$0.699797\pi$
$829$	−1275.44	+	926.658i	−1.53852	+	1.11780i	−0.951253	+	0.308410i	$0.900203\pi$
$830$	45.8575	−	141.135i	0.0552499	−	0.170042i
$831$		0			0
$832$	−37.9196	−	52.1918i	−0.0455764	−	0.0627306i
$833$	584.172	−	804.044i	0.701287	−	0.965239i
$834$		0			0
$835$		−	330.441i		−	0.395738i
$836$	244.004	−	238.911i	0.291870	−	0.285779i
$837$		0			0
$838$	−599.773	+	194.878i	−0.715719	+	0.232551i
$839$	−38.4075	−	27.9047i	−0.0457777	−	0.0332595i	0.564661	−	0.825323i	$-0.309007\pi$
$839$	−38.4075	−	27.9047i	−0.0457777	−	0.0332595i	−0.610439	+	0.792063i	$0.709007\pi$
$840$		0			0
$841$	−192.535	+	592.563i	−0.228936	+	0.704593i
$842$	1306.07	+	424.369i	1.55116	+	0.504002i
$843$		0			0
$844$	−445.356	+	612.980i	−0.527673	+	0.726280i
$845$	−159.790	−	491.782i	−0.189100	−	0.581990i
$846$		0			0
$847$	16.9325	−	11.7647i	0.0199911	−	0.0138899i
$848$	−304.256			−0.358792
$849$		0			0
$850$	−751.116	−	545.718i	−0.883666	−	0.642021i
$851$	323.626	−	235.128i	0.380289	−	0.276296i
$852$		0			0
$853$	706.895	+	229.684i	0.828716	+	0.269266i	0.692505	−	0.721413i	$-0.256507\pi$
$853$	706.895	+	229.684i	0.828716	+	0.269266i	0.136212	+	0.990680i	$0.456507\pi$
$854$	15.7128	+	21.6269i	0.0183991	+	0.0253242i
$855$		0			0
$856$	−18.4627	−	56.8222i	−0.0215685	−	0.0663811i
$857$			572.262i			0.667750i	0.942617	+	0.333875i	$0.108356\pi$
$857$			572.262i			0.667750i	−0.942617	+	0.333875i	$0.891644\pi$
$858$		0			0
$859$	−792.198			−0.922233			−0.461117	−	0.887340i	$-0.652551\pi$
$859$	−792.198			−0.922233			−0.461117	+	0.887340i	$0.652551\pi$
$860$	309.013	−	100.404i	0.359317	−	0.116749i
$861$		0			0
$862$	63.0682	−	45.8218i	0.0731650	−	0.0531575i
$863$	−325.355	+	1001.34i	−0.377005	+	1.16030i	0.565111	+	0.825015i	$0.308833\pi$
$863$	−325.355	+	1001.34i	−0.377005	+	1.16030i	−0.942116	+	0.335287i	$0.891167\pi$
$864$		0			0
$865$	67.2365	+	92.5432i	0.0777301	+	0.106986i
$866$	922.496	−	1269.71i	1.06524	−	1.46617i
$867$		0			0
$868$			15.3678i			0.0177049i
$869$	−514.470	−	269.006i	−0.592025	−	0.309558i
$870$		0			0
$871$	−53.4292	+	17.3602i	−0.0613424	+	0.0199314i
$872$	−441.115	−	320.489i	−0.505866	−	0.367533i
$873$		0			0
$874$	86.4290	−	266.001i	0.0988890	−	0.304349i
$875$	−17.9928	−	5.84621i	−0.0205632	−	0.00668138i
$876$		0			0
$877$	834.571	−	1148.69i	0.951621	−	1.30979i	0.000816940	−	1.00000i	$-0.499740\pi$
$877$	834.571	−	1148.69i	0.951621	−	1.30979i	0.950804	−	0.309794i	$-0.100260\pi$
$878$	257.253	+	791.744i	0.292999	+	0.901758i
$879$		0			0
$880$	81.9574	+	555.292i	0.0931334	+	0.631014i
$881$	−952.550			−1.08121			−0.540607	−	0.841275i	$-0.681805\pi$
$881$	−952.550			−1.08121			−0.540607	+	0.841275i	$0.681805\pi$
$882$		0			0
$883$	−287.851	−	209.136i	−0.325992	−	0.236847i	0.412736	−	0.910851i	$-0.364573\pi$
$883$	−287.851	−	209.136i	−0.325992	−	0.236847i	−0.738728	+	0.674004i	$0.764573\pi$
$884$	673.555	−	489.367i	0.761940	−	0.553582i
$885$		0			0
$886$	1148.34	+	373.118i	1.29610	+	0.421127i
$887$	−606.794	−	835.180i	−0.684097	−	0.941578i	0.315877	−	0.948800i	$-0.397701\pi$
$887$	−606.794	−	835.180i	−0.684097	−	0.941578i	−0.999974	+	0.00722178i	$0.997701\pi$
$888$		0			0
$889$	3.15133	+	9.69880i	0.00354480	+	0.0109098i
$890$		−	614.348i		−	0.690278i
$891$		0			0
$892$	454.142			0.509128
$893$	473.489	−	153.846i	0.530223	−	0.172280i
$894$		0			0
$895$	−656.368	+	476.880i	−0.733373	+	0.532826i
$896$	6.95249	−	21.3976i	0.00775948	−	0.0238812i
$897$		0			0
$898$	−972.557	−	1338.61i	−1.08303	−	1.49066i
$899$	−952.992	+	1311.68i	−1.06006	+	1.45904i
$900$		0			0
$901$			308.994i			0.342946i
$902$	−1128.01	+	559.847i	−1.25056	+	0.620673i
$903$		0			0
$904$	773.957	−	251.474i	0.856147	−	0.278179i
$905$	−683.330	−	496.468i	−0.755061	−	0.548584i
$906$		0			0
$907$	−335.921	+	1033.86i	−0.370365	+	1.13987i	0.576188	+	0.817317i	$0.304540\pi$
$907$	−335.921	+	1033.86i	−0.370365	+	1.13987i	−0.946553	+	0.322549i	$0.895460\pi$
$908$	−357.778	−	116.249i	−0.394028	−	0.128028i
$909$		0			0
$910$	12.2033	−	16.7965i	0.0134103	−	0.0184576i
$911$	−123.647	−	380.547i	−0.135727	−	0.417724i	0.859976	−	0.510335i	$-0.170479\pi$
$911$	−123.647	−	380.547i	−0.135727	−	0.417724i	−0.995702	+	0.0926112i	$0.970479\pi$
$912$		0			0
$913$	−114.802	−	231.310i	−0.125742	−	0.253351i
$914$	−1266.21			−1.38536
$915$		0			0
$916$	−108.418	−	78.7705i	−0.118361	−	0.0859940i
$917$	−3.74450	+	2.72054i	−0.00408342	+	0.00296678i
$918$		0			0
$919$	−1281.48	−	416.379i	−1.39443	−	0.453079i	−0.487047	−	0.873376i	$-0.661926\pi$
$919$	−1281.48	−	416.379i	−1.39443	−	0.453079i	−0.907387	+	0.420297i	$0.861926\pi$
$920$	53.8656	+	74.1396i	0.0585496	+	0.0805866i
$921$		0			0
$922$	57.9160	+	178.247i	0.0628156	+	0.193327i
$923$			1865.46i			2.02108i
$924$		0			0
$925$	−954.357			−1.03174
$926$	−688.912	+	223.841i	−0.743966	+	0.241729i
$927$		0			0
$928$	−957.676	+	695.792i	−1.03198	+	0.749776i
$929$	461.399	−	1420.04i	0.496662	−	1.52857i	−0.317689	−	0.948195i	$-0.602907\pi$
$929$	461.399	−	1420.04i	0.496662	−	1.52857i	0.814351	−	0.580373i	$-0.197093\pi$
$930$		0			0
$931$	−419.849	−	577.873i	−0.450966	−	0.620701i
$932$	−384.503	+	529.222i	−0.412556	+	0.567835i
$933$		0			0
$934$		−	1917.37i		−	2.05286i
$935$	563.941	−	83.2338i	0.603145	−	0.0890201i
$936$		0			0
$937$	−529.343	+	171.994i	−0.564934	+	0.183558i	−0.577540	−	0.816362i	$-0.695987\pi$
$937$	−529.343	+	171.994i	−0.564934	+	0.183558i	0.0126060	+	0.999921i	$0.495987\pi$
$938$	−0.994700	−	0.722692i	−0.00106045	−	0.000770461i
$939$		0			0
$940$	57.3242	−	176.426i	0.0609832	−	0.187687i
$941$	−801.454	−	260.408i	−0.851704	−	0.276735i	−0.149544	−	0.988755i	$-0.547781\pi$
$941$	−801.454	−	260.408i	−0.851704	−	0.276735i	−0.702160	+	0.712020i	$0.747781\pi$
$942$		0			0
$943$	−210.547	+	289.793i	−0.223274	+	0.307310i
$944$	−162.667	−	500.639i	−0.172317	−	0.530338i
$945$		0			0
$946$	754.339	−	1442.66i	0.797399	−	1.52501i
$947$	−789.960			−0.834171			−0.417085	−	0.908867i	$-0.636948\pi$
$947$	−789.960			−0.834171			−0.417085	+	0.908867i	$0.636948\pi$
$948$		0			0
$949$	−270.202	−	196.313i	−0.284723	−	0.206863i
$950$	−539.833	+	392.212i	−0.568245	+	0.412854i
$951$		0			0
$952$	−15.2387	−	4.95135i	−0.0160070	−	0.00520100i
$953$	−686.198	−	944.471i	−0.720040	−	0.991050i	−0.999522	−	0.0308995i	$-0.990163\pi$
$953$	−686.198	−	944.471i	−0.720040	−	0.991050i	0.279482	−	0.960151i	$-0.409837\pi$
$954$		0			0
$955$	100.244	+	308.520i	0.104968	+	0.323058i
$956$			794.330i			0.830889i
$957$		0			0
$958$	162.487			0.169611
$959$	−13.1541	+	4.27404i	−0.0137165	+	0.00445676i
$960$		0			0
$961$	−675.117	+	490.501i	−0.702515	+	0.510407i
$962$	761.472	−	2343.57i	0.791551	−	2.43614i
$963$		0			0
$964$	16.3564	+	22.5127i	0.0169672	+	0.0233534i
$965$	317.286	−	436.707i	0.328794	−	0.452546i
$966$		0			0
$967$			840.359i			0.869037i	0.900663	+	0.434518i	$0.143081\pi$
$967$			840.359i			0.869037i	−0.900663	+	0.434518i	$0.856919\pi$
$968$	446.507	+	339.019i	0.461267	+	0.350226i
$969$		0			0
$970$	304.294	−	98.8712i	0.313705	−	0.101929i
$971$	1011.70	+	735.040i	1.04191	+	0.756993i	0.970658	−	0.240465i	$-0.0773001\pi$
$971$	1011.70	+	735.040i	1.04191	+	0.756993i	0.0712535	+	0.997458i	$0.477300\pi$
$972$		0			0
$973$	10.2371	−	31.5065i	0.0105212	−	0.0323808i
$974$	−42.6527	−	13.8587i	−0.0437912	−	0.0142286i
$975$		0			0
$976$	−744.361	+	1024.53i	−0.762665	+	1.04972i
$977$	−35.4053	−	108.966i	−0.0362388	−	0.111532i	0.931301	−	0.364251i	$-0.118675\pi$
$977$	−35.4053	−	108.966i	−0.0362388	−	0.111532i	−0.967540	+	0.252720i	$0.918675\pi$
$978$		0			0
$979$	−747.918	−	763.859i	−0.763961	−	0.780244i
$980$	−266.150			−0.271582
$981$		0			0
$982$	854.987	+	621.185i	0.870659	+	0.632571i
$983$	−690.929	+	501.989i	−0.702878	+	0.510670i	−0.880868	−	0.473362i	$-0.843040\pi$
$983$	−690.929	+	501.989i	−0.702878	+	0.510670i	0.177991	+	0.984032i	$0.443040\pi$
$984$		0			0
$985$	6.98053	+	2.26811i	0.00708684	+	0.00230265i
$986$	1129.94	+	1555.23i	1.14598	+	1.57731i
$987$		0			0
$988$	−184.906	−	569.081i	−0.187151	−	0.575993i
$989$		−	463.073i		−	0.468224i
$990$		0			0
$991$	1236.21			1.24743			0.623716	−	0.781651i	$-0.285622\pi$
$991$	1236.21			1.24743			0.623716	+	0.781651i	$0.285622\pi$
$992$	−1246.75	+	405.094i	−1.25681	+	0.408361i
$993$		0			0
$994$	−33.0297	+	23.9975i	−0.0332291	+	0.0241424i
$995$	−125.105	+	385.033i	−0.125733	+	0.386968i
$996$		0			0
$997$	414.382	+	570.347i	0.415628	+	0.572063i	0.964580	−	0.263791i	$-0.0849729\pi$
$997$	414.382	+	570.347i	0.415628	+	0.572063i	−0.548952	+	0.835854i	$0.684973\pi$
$998$	415.246	−	571.537i	0.416078	−	0.572682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.c.28.1		16
3.2	odd	2		33.3.g.a.28.4	yes	16
11.2	odd	10	inner	99.3.k.c.46.1		16
11.3	even	5		1089.3.c.m.604.13		16
11.8	odd	10		1089.3.c.m.604.4		16
12.11	even	2		528.3.bf.b.193.3		16
33.2	even	10		33.3.g.a.13.4	✓	16
33.5	odd	10		363.3.g.g.40.1		16
33.8	even	10		363.3.c.e.241.13		16
33.14	odd	10		363.3.c.e.241.4		16
33.17	even	10		363.3.g.a.40.4		16
33.20	odd	10		363.3.g.f.112.1		16
33.26	odd	10		363.3.g.a.118.4		16
33.29	even	10		363.3.g.g.118.1		16
33.32	even	2		363.3.g.f.94.1		16
132.35	odd	10		528.3.bf.b.145.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.13.4	✓	16	33.2	even	10
33.3.g.a.28.4	yes	16	3.2	odd	2
99.3.k.c.28.1		16	1.1	even	1	trivial
99.3.k.c.46.1		16	11.2	odd	10	inner
363.3.c.e.241.4		16	33.14	odd	10
363.3.c.e.241.13		16	33.8	even	10
363.3.g.a.40.4		16	33.17	even	10
363.3.g.a.118.4		16	33.26	odd	10
363.3.g.f.94.1		16	33.32	even	2
363.3.g.f.112.1		16	33.20	odd	10
363.3.g.g.40.1		16	33.5	odd	10
363.3.g.g.118.1		16	33.29	even	10
528.3.bf.b.145.3		16	132.35	odd	10
528.3.bf.b.193.3		16	12.11	even	2
1089.3.c.m.604.4		16	11.8	odd	10
1089.3.c.m.604.13		16	11.3	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35440 + 0.764990i) q^{2} +(1.72190 - 1.25104i) q^{4} +(0.789076 - 2.42853i) q^{5} +(-0.100159 - 0.137856i) q^{7} +(2.72337 - 3.74840i) q^{8} +O(q^{10})\)	\(q+(-2.35440 + 0.764990i) q^{2} +(1.72190 - 1.25104i) q^{4} +(0.789076 - 2.42853i) q^{5} +(-0.100159 - 0.137856i) q^{7} +(2.72337 - 3.74840i) q^{8} +6.32135i q^{10} +(7.69573 + 7.85976i) q^{11} +(18.3310 - 5.95611i) q^{13} +(0.341272 + 0.247948i) q^{14} +(-6.17525 + 19.0055i) q^{16} +(19.3014 + 6.27142i) q^{17} +(8.57343 - 11.8003i) q^{19} +(-1.67946 - 5.16886i) q^{20} +(-24.1314 - 12.6178i) q^{22} -7.74583 q^{23} +(14.9503 + 10.8620i) q^{25} +(-38.6022 + 28.0461i) q^{26} +(-0.344927 - 0.112074i) q^{28} +(-22.4904 - 30.9554i) q^{29} +(-13.0940 - 40.2993i) q^{31} -30.9373i q^{32} -50.2408 q^{34} +(-0.413821 + 0.134459i) q^{35} +(-41.7807 + 30.3554i) q^{37} +(-11.1581 + 34.3412i) q^{38} +(-6.95414 - 9.57156i) q^{40} +(27.1820 - 37.4128i) q^{41} +59.7836i q^{43} +(23.0842 + 3.90611i) q^{44} +(18.2367 - 5.92548i) q^{46} +(27.6137 + 20.0626i) q^{47} +(15.1329 - 46.5742i) q^{49} +(-43.5083 - 14.1367i) q^{50} +(24.1130 - 33.1887i) q^{52} +(4.70489 + 14.4801i) q^{53} +(25.1602 - 12.4873i) q^{55} -0.789510 q^{56} +(76.6320 + 55.6764i) q^{58} +(-21.3110 + 15.4833i) q^{59} +(60.2698 + 19.5828i) q^{61} +(61.6572 + 84.8638i) q^{62} +(-1.03430 - 3.18325i) q^{64} -49.2172i q^{65} -2.91469 q^{67} +(41.0810 - 13.3480i) q^{68} +(0.871439 - 0.633137i) q^{70} +(-29.9080 + 92.0473i) q^{71} +(-10.1852 - 14.0187i) q^{73} +(75.1467 - 103.431i) q^{74} -31.0447i q^{76} +(0.312725 - 1.84813i) q^{77} +(-50.1945 + 16.3092i) q^{79} +(41.2825 + 29.9935i) q^{80} +(-35.3768 + 108.879i) q^{82} +(-22.3267 - 7.25438i) q^{83} +(30.4606 - 41.9255i) q^{85} +(-45.7338 - 140.754i) q^{86} +(50.4198 - 7.44162i) q^{88} -97.1861 q^{89} +(-2.65710 - 1.93050i) q^{91} +(-13.3376 + 9.69032i) q^{92} +(-80.3613 - 26.1110i) q^{94} +(-21.8923 - 30.1321i) q^{95} +(-15.6408 - 48.1375i) q^{97} +121.230i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

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