LMFDB - Embedded newform 99.3.k.c.73.1

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			73.1
Root			$-1.43448 + 2.82504i$ of defining polynomial
Character	$\chi$	$=$	99.73
Dual form			99.3.k.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69557 + 2.33376i) q^{2} +(-1.33538 - 4.10989i) q^{4} +(-0.356879 + 0.259287i) q^{5} +(-10.0641 + 3.27002i) q^{7} +(0.881730 + 0.286491i) q^{8} +O(q^{10})$	\(q+(-1.69557 + 2.33376i) q^{2} +(-1.33538 - 4.10989i) q^{4} +(-0.356879 + 0.259287i) q^{5} +(-10.0641 + 3.27002i) q^{7} +(0.881730 + 0.286491i) q^{8} -1.27251i q^{10} +(-9.39298 - 5.72468i) q^{11} +(3.78967 - 5.21603i) q^{13} +(9.43297 - 29.0317i) q^{14} +(11.8207 - 8.58822i) q^{16} +(11.1080 + 15.2889i) q^{17} +(-26.1968 - 8.51187i) q^{19} +(1.54221 + 1.12048i) q^{20} +(29.2865 - 12.2143i) q^{22} -6.29263 q^{23} +(-7.66529 + 23.5913i) q^{25} +(5.74728 + 17.6883i) q^{26} +(26.8788 + 36.9955i) q^{28} +(-42.0059 + 13.6485i) q^{29} +(21.9270 + 15.9309i) q^{31} +45.8569i q^{32} -54.5151 q^{34} +(2.74378 - 3.77649i) q^{35} +(-0.263636 - 0.811388i) q^{37} +(64.2833 - 46.7045i) q^{38} +(-0.388954 + 0.126379i) q^{40} +(12.5843 + 4.08890i) q^{41} +68.8186i q^{43} +(-10.9845 + 46.2487i) q^{44} +(10.6696 - 14.6855i) q^{46} +(4.98694 - 15.3482i) q^{47} +(50.9510 - 37.0181i) q^{49} +(-42.0594 - 57.8898i) q^{50} +(-26.4979 - 8.60970i) q^{52} +(31.2946 + 22.7368i) q^{53} +(4.83649 - 0.392468i) q^{55} -9.81064 q^{56} +(39.3717 - 121.174i) q^{58} +(-23.7669 - 73.1470i) q^{59} +(-16.8490 - 23.1906i) q^{61} +(-74.3578 + 24.1603i) q^{62} +(-59.7363 - 43.4009i) q^{64} +2.84410i q^{65} -78.0944 q^{67} +(48.0022 - 66.0693i) q^{68} +(4.16113 + 12.8066i) q^{70} +(-21.9400 + 15.9403i) q^{71} +(-12.3454 + 4.01127i) q^{73} +(2.34060 + 0.760506i) q^{74} +119.033i q^{76} +(113.252 + 26.8984i) q^{77} +(55.4014 - 76.2534i) q^{79} +(-1.99173 + 6.12990i) q^{80} +(-30.8801 + 22.4357i) q^{82} +(68.1685 + 93.8258i) q^{83} +(-7.92844 - 2.57611i) q^{85} +(-160.606 - 116.687i) q^{86} +(-6.64200 - 7.73862i) q^{88} -65.2779 q^{89} +(-21.0830 + 64.8868i) q^{91} +(8.40307 + 25.8620i) q^{92} +(27.3633 + 37.6623i) q^{94} +(11.5561 - 3.75481i) q^{95} +(56.8734 + 41.3209i) q^{97} +181.674i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−1.69557	+	2.33376i	−0.847787	+	1.16688i	0.136559	+	0.990632i	$0.456396\pi$
$2$	−1.69557	+	2.33376i	−0.847787	+	1.16688i	−0.984346	+	0.176246i	$0.943604\pi$
$3$		0			0
$3$		0			0
$4$	−1.33538	−	4.10989i	−0.333846	−	1.02747i
$5$	−0.356879	+	0.259287i	−0.0713757	+	0.0518575i	−0.622901	−	0.782301i	$-0.714046\pi$
$5$	−0.356879	+	0.259287i	−0.0713757	+	0.0518575i	0.551525	+	0.834158i	$0.314046\pi$
$6$		0			0
$7$	−10.0641	+	3.27002i	−1.43773	+	0.467146i	−0.921188	−	0.389118i	$-0.872780\pi$
$7$	−10.0641	+	3.27002i	−1.43773	+	0.467146i	−0.516539	+	0.856264i	$0.672780\pi$
$8$	0.881730	+	0.286491i	0.110216	+	0.0358114i
$9$		0			0
$10$		−	1.27251i		−	0.127251i
$11$	−9.39298	−	5.72468i	−0.853907	−	0.520425i
$11$	−9.39298	−	5.72468i	−0.853907	−	0.520425i
$12$		0			0
$13$	3.78967	−	5.21603i	0.291513	−	0.401233i	−0.637992	−	0.770043i	$-0.720235\pi$
$13$	3.78967	−	5.21603i	0.291513	−	0.401233i	0.929505	+	0.368810i	$0.120235\pi$
$14$	9.43297	−	29.0317i	0.673784	−	2.07369i
$15$		0			0
$16$	11.8207	−	8.58822i	0.738792	−	0.536764i
$17$	11.1080	+	15.2889i	0.653414	+	0.899347i	0.999241	−	0.0389508i	$-0.0124016\pi$
$17$	11.1080	+	15.2889i	0.653414	+	0.899347i	−0.345827	+	0.938298i	$0.612402\pi$
$18$		0			0
$19$	−26.1968	−	8.51187i	−1.37878	−	0.447993i	−0.476512	−	0.879168i	$-0.658099\pi$
$19$	−26.1968	−	8.51187i	−1.37878	−	0.447993i	−0.902268	+	0.431175i	$0.858099\pi$
$20$	1.54221	+	1.12048i	0.0771106	+	0.0560241i
$21$		0			0
$22$	29.2865	−	12.2143i	1.33120	−	0.555197i
$23$	−6.29263			−0.273593			−0.136796	−	0.990599i	$-0.543681\pi$
$23$	−6.29263			−0.273593			−0.136796	+	0.990599i	$0.543681\pi$
$24$		0			0
$25$	−7.66529	+	23.5913i	−0.306612	+	0.943654i
$26$	5.74728	+	17.6883i	0.221049	+	0.680320i
$27$		0			0
$28$	26.8788	+	36.9955i	0.959958	+	1.32127i
$29$	−42.0059	+	13.6485i	−1.44848	+	0.470639i	−0.924529	−	0.381111i	$-0.875542\pi$
$29$	−42.0059	+	13.6485i	−1.44848	+	0.470639i	−0.523949	+	0.851750i	$0.675542\pi$
$30$		0			0
$31$	21.9270	+	15.9309i	0.707323	+	0.513900i	0.882309	−	0.470671i	$-0.155988\pi$
$31$	21.9270	+	15.9309i	0.707323	+	0.513900i	−0.174986	+	0.984571i	$0.555988\pi$
$32$			45.8569i			1.43303i
$33$		0			0
$34$	−54.5151			−1.60338
$35$	2.74378	−	3.77649i	0.0783938	−	0.107900i
$36$		0			0
$37$	−0.263636	−	0.811388i	−0.00712529	−	0.0219294i	0.947431	−	0.319961i	$-0.103670\pi$
$37$	−0.263636	−	0.811388i	−0.00712529	−	0.0219294i	−0.954556	+	0.298032i	$0.903670\pi$
$38$	64.2833	−	46.7045i	1.69166	−	1.22907i
$39$		0			0
$40$	−0.388954	+	0.126379i	−0.00972385	+	0.00315947i
$41$	12.5843	+	4.08890i	0.306935	+	0.0997292i	0.458435	−	0.888728i	$-0.348410\pi$
$41$	12.5843	+	4.08890i	0.306935	+	0.0997292i	−0.151500	+	0.988457i	$0.548410\pi$
$42$		0			0
$43$			68.8186i			1.60043i	0.599712	+	0.800216i	$0.295282\pi$
$43$			68.8186i			1.60043i	−0.599712	+	0.800216i	$0.704718\pi$
$44$	−10.9845	+	46.2487i	−0.249649	+	1.05111i
$45$		0			0
$46$	10.6696	−	14.6855i	0.231948	−	0.319249i
$47$	4.98694	−	15.3482i	0.106105	−	0.326558i	−0.883883	−	0.467708i	$-0.845080\pi$
$47$	4.98694	−	15.3482i	0.106105	−	0.326558i	0.989988	+	0.141150i	$0.0450800\pi$
$48$		0			0
$49$	50.9510	−	37.0181i	1.03982	−	0.755471i
$50$	−42.0594	−	57.8898i	−0.841188	−	1.15780i
$51$		0			0
$52$	−26.4979	−	8.60970i	−0.509576	−	0.165571i
$53$	31.2946	+	22.7368i	0.590463	+	0.428997i	0.842481	−	0.538726i	$-0.181094\pi$
$53$	31.2946	+	22.7368i	0.590463	+	0.428997i	−0.252018	+	0.967723i	$0.581094\pi$
$54$		0			0
$55$	4.83649	−	0.392468i	0.0879362	−	0.00713579i
$56$	−9.81064			−0.175190
$57$		0			0
$58$	39.3717	−	121.174i	0.678822	−	2.08920i
$59$	−23.7669	−	73.1470i	−0.402829	−	1.23978i	−0.922694	−	0.385532i	$-0.874018\pi$
$59$	−23.7669	−	73.1470i	−0.402829	−	1.23978i	0.519866	−	0.854248i	$-0.325982\pi$
$60$		0			0
$61$	−16.8490	−	23.1906i	−0.276213	−	0.380174i	0.648262	−	0.761417i	$-0.275496\pi$
$61$	−16.8490	−	23.1906i	−0.276213	−	0.380174i	−0.924475	+	0.381243i	$0.875496\pi$
$62$	−74.3578	+	24.1603i	−1.19932	+	0.389682i
$63$		0			0
$64$	−59.7363	−	43.4009i	−0.933379	−	0.678140i
$65$			2.84410i			0.0437554i
$66$		0			0
$67$	−78.0944			−1.16559			−0.582794	−	0.812620i	$-0.698041\pi$
$67$	−78.0944			−1.16559			−0.582794	+	0.812620i	$0.698041\pi$
$68$	48.0022	−	66.0693i	0.705914	−	0.971608i
$69$		0			0
$70$	4.16113	+	12.8066i	0.0594447	+	0.182952i
$71$	−21.9400	+	15.9403i	−0.309014	+	0.224512i	−0.731473	−	0.681870i	$-0.761167\pi$
$71$	−21.9400	+	15.9403i	−0.309014	+	0.224512i	0.422459	+	0.906382i	$0.361167\pi$
$72$		0			0
$73$	−12.3454	+	4.01127i	−0.169115	+	0.0549489i	−0.392351	−	0.919816i	$-0.628338\pi$
$73$	−12.3454	+	4.01127i	−0.169115	+	0.0549489i	0.223236	+	0.974765i	$0.428338\pi$
$74$	2.34060	+	0.760506i	0.0316297	+	0.0102771i
$75$		0			0
$76$			119.033i			1.56622i
$77$	113.252	+	26.8984i	1.47080	+	0.349330i
$78$		0			0
$79$	55.4014	−	76.2534i	0.701283	−	0.965233i	−0.298658	−	0.954360i	$-0.596539\pi$
$79$	55.4014	−	76.2534i	0.701283	−	0.965233i	0.999941	−	0.0108729i	$-0.00346103\pi$
$80$	−1.99173	+	6.12990i	−0.0248966	+	0.0766238i
$81$		0			0
$82$	−30.8801	+	22.4357i	−0.376587	+	0.273606i
$83$	68.1685	+	93.8258i	0.821307	+	1.13043i	0.989479	+	0.144674i	$0.0462134\pi$
$83$	68.1685	+	93.8258i	0.821307	+	1.13043i	−0.168173	+	0.985758i	$0.553787\pi$
$84$		0			0
$85$	−7.92844	−	2.57611i	−0.0932758	−	0.0303071i
$86$	−160.606	−	116.687i	−1.86751	−	1.35683i
$87$		0			0
$88$	−6.64200	−	7.73862i	−0.0754773	−	0.0879389i
$89$	−65.2779			−0.733460			−0.366730	−	0.930327i	$-0.619523\pi$
$89$	−65.2779			−0.733460			−0.366730	+	0.930327i	$0.619523\pi$
$90$		0			0
$91$	−21.0830	+	64.8868i	−0.231681	+	0.713042i
$92$	8.40307	+	25.8620i	0.0913377	+	0.281109i
$93$		0			0
$94$	27.3633	+	37.6623i	0.291099	+	0.400663i
$95$	11.5561	−	3.75481i	0.121643	−	0.0395243i
$96$		0			0
$97$	56.8734	+	41.3209i	0.586323	+	0.425989i	0.840998	−	0.541038i	$-0.181968\pi$
$97$	56.8734	+	41.3209i	0.586323	+	0.425989i	−0.254675	+	0.967027i	$0.581968\pi$
$98$			181.674i			1.85382i
$99$		0			0
$100$	107.194			1.07194
$101$	27.8677	−	38.3567i	0.275918	−	0.379769i	−0.648458	−	0.761250i	$-0.724586\pi$
$101$	27.8677	−	38.3567i	0.275918	−	0.379769i	0.924377	+	0.381481i	$0.124586\pi$
$102$		0			0
$103$	−29.3497	−	90.3290i	−0.284948	−	0.876980i	−0.986414	−	0.164277i	$-0.947471\pi$
$103$	−29.3497	−	90.3290i	−0.284948	−	0.876980i	0.701466	−	0.712703i	$-0.252529\pi$
$104$	4.83581	−	3.51342i	0.0464981	−	0.0337829i
$105$		0			0
$106$	−106.124	+	34.4819i	−1.00117	+	0.325301i
$107$	29.2513	+	9.50434i	0.273377	+	0.0888256i	0.442497	−	0.896770i	$-0.354093\pi$
$107$	29.2513	+	9.50434i	0.273377	+	0.0888256i	−0.169120	+	0.985595i	$0.554093\pi$
$108$		0			0
$109$		−	79.2234i		−	0.726820i	−0.931629	−	0.363410i	$-0.881612\pi$
$109$		−	79.2234i		−	0.726820i	0.931629	−	0.363410i	$-0.118388\pi$
$110$	−7.28470	+	11.9526i	−0.0662245	+	0.108660i
$111$		0			0
$112$	−90.8806	+	125.086i	−0.811434	+	1.11684i
$113$	8.17981	−	25.1749i	0.0723877	−	0.222786i	−0.908317	−	0.418283i	$-0.862632\pi$
$113$	8.17981	−	25.1749i	0.0723877	−	0.222786i	0.980704	+	0.195497i	$0.0626319\pi$
$114$		0			0
$115$	2.24571	−	1.63160i	0.0195279	−	0.0141878i
$116$	112.188	+	154.413i	0.967136	+	1.33115i
$117$		0			0
$118$	211.006	+	68.5600i	1.78819	+	0.581017i
$119$	−161.787	−	117.545i	−1.35956	−	0.987776i
$120$		0			0
$121$	55.4562	+	107.544i	0.458316	+	0.888790i
$122$	82.6900			0.677787
$123$		0			0
$124$	36.1933	−	111.391i	0.291881	−	0.898318i
$125$	−6.78925	−	20.8952i	−0.0543140	−	0.167161i
$126$		0			0
$127$	−83.3148	−	114.673i	−0.656022	−	0.902937i	0.343320	−	0.939219i	$-0.388449\pi$
$127$	−83.3148	−	114.673i	−0.656022	−	0.902937i	−0.999342	+	0.0362819i	$0.988449\pi$
$128$	28.1243	−	9.13813i	0.219721	−	0.0713916i
$129$		0			0
$130$	−6.63744	−	4.82238i	−0.0510572	−	0.0370952i
$131$		−	92.6286i		−	0.707088i	−0.935418	−	0.353544i	$-0.884976\pi$
$131$		−	92.6286i		−	0.707088i	0.935418	−	0.353544i	$-0.115024\pi$
$132$		0			0
$133$	291.481			2.19159
$134$	132.415	−	182.253i	0.988170	−	1.36010i
$135$		0			0
$136$	5.41415	+	16.6630i	0.0398099	+	0.122522i
$137$	−17.7382	+	12.8875i	−0.129476	+	0.0940696i	−0.650638	−	0.759388i	$-0.725499\pi$
$137$	−17.7382	+	12.8875i	−0.129476	+	0.0940696i	0.521163	+	0.853457i	$0.325499\pi$
$138$		0			0
$139$	−180.373	+	58.6066i	−1.29764	+	0.421630i	−0.874761	−	0.484554i	$-0.838982\pi$
$139$	−180.373	+	58.6066i	−1.29764	+	0.421630i	−0.422883	+	0.906184i	$0.638982\pi$
$140$	−19.1849	−	6.23357i	−0.137035	−	0.0445255i
$141$		0			0
$142$		−	78.2307i		−	0.550920i
$143$	−65.4563	+	27.2994i	−0.457737	+	0.190905i
$144$		0			0
$145$	11.4521	−	15.7625i	0.0789800	−	0.108707i
$146$	11.5712	−	35.6126i	0.0792551	−	0.243922i
$147$		0			0
$148$	−2.98266	+	2.16703i	−0.0201531	+	0.0146421i
$149$	7.82372	+	10.7684i	0.0525082	+	0.0722713i	0.834464	−	0.551063i	$-0.185778\pi$
$149$	7.82372	+	10.7684i	0.0525082	+	0.0722713i	−0.781955	+	0.623334i	$0.785778\pi$
$150$		0			0
$151$	78.3247	+	25.4492i	0.518706	+	0.168538i	0.556658	−	0.830742i	$-0.312083\pi$
$151$	78.3247	+	25.4492i	0.518706	+	0.168538i	−0.0379518	+	0.999280i	$0.512083\pi$
$152$	−20.6599	−	15.0103i	−0.135921	−	0.0987522i
$153$		0			0
$154$	−254.801	+	218.693i	−1.65455	+	1.42009i
$155$	−11.9560			−0.0771353
$156$		0			0
$157$	−28.5644	+	87.9122i	−0.181939	+	0.559950i	−0.999882	−	0.0153485i	$-0.995114\pi$
$157$	−28.5644	+	87.9122i	−0.181939	+	0.559950i	0.817943	+	0.575299i	$0.195114\pi$
$158$	84.0199	+	258.587i	0.531771	+	1.63662i
$159$		0			0
$160$	−11.8901	−	16.3654i	−0.0743133	−	0.102284i
$161$	63.3296	−	20.5770i	0.393352	−	0.127808i
$162$		0			0
$163$	−188.999	−	137.316i	−1.15950	−	0.842428i	−0.169788	−	0.985481i	$-0.554308\pi$
$163$	−188.999	−	137.316i	−1.15950	−	0.842428i	−0.989715	+	0.143052i	$0.954308\pi$
$164$		−	57.1804i		−	0.348661i
$165$		0			0
$166$	−334.551			−2.01537
$167$	−113.435	+	156.130i	−0.679250	+	0.934907i	−0.999925	−	0.0122820i	$-0.996090\pi$
$167$	−113.435	+	156.130i	−0.679250	+	0.934907i	0.320675	+	0.947189i	$0.396090\pi$
$168$		0			0
$169$	39.3785	+	121.195i	0.233009	+	0.717128i
$170$	19.4553	−	14.1351i	0.114443	−	0.0831475i
$171$		0			0
$172$	282.837	−	91.8992i	1.64440	−	0.534297i
$173$	−83.7953	−	27.2267i	−0.484366	−	0.157380i	0.0566472	−	0.998394i	$-0.481959\pi$
$173$	−83.7953	−	27.2267i	−0.484366	−	0.157380i	−0.541013	+	0.841014i	$0.681959\pi$
$174$		0			0
$175$		−	262.491i		−	1.49995i
$176$	−160.196	+	12.9995i	−0.910205	+	0.0738607i
$177$		0			0
$178$	110.684	−	152.343i	0.621818	−	0.855859i
$179$	−98.0477	+	301.760i	−0.547752	+	1.68581i	0.166602	+	0.986024i	$0.446720\pi$
$179$	−98.0477	+	301.760i	−0.547752	+	1.68581i	−0.714355	+	0.699784i	$0.753280\pi$
$180$		0			0
$181$	12.3615	−	8.98115i	0.0682955	−	0.0496196i	−0.553114	−	0.833106i	$-0.686560\pi$
$181$	12.3615	−	8.98115i	0.0682955	−	0.0496196i	0.621409	+	0.783486i	$0.286560\pi$
$182$	−115.682	−	159.223i	−0.635617	−	0.874852i
$183$		0			0
$184$	−5.54840	−	1.80278i	−0.0301544	−	0.00979774i
$185$	0.304469	+	0.221209i	0.00164578	+	0.00119573i
$186$		0			0
$187$	−16.8136	−	207.198i	−0.0899123	−	1.10801i
$188$	−69.7389			−0.370952
$189$		0			0
$190$	−10.8314	+	33.3357i	−0.0570075	+	0.175451i
$191$	−6.32586	−	19.4690i	−0.0331197	−	0.101932i	0.933130	−	0.359539i	$-0.117066\pi$
$191$	−6.32586	−	19.4690i	−0.0331197	−	0.101932i	−0.966250	+	0.257607i	$0.917066\pi$
$192$		0			0
$193$	111.231	+	153.097i	0.576328	+	0.793248i	0.993287	−	0.115678i	$-0.0369040\pi$
$193$	111.231	+	153.097i	0.576328	+	0.793248i	−0.416959	+	0.908925i	$0.636904\pi$
$194$	−192.866	+	62.6660i	−0.994154	+	0.323020i
$195$		0			0
$196$	−220.179	−	159.970i	−1.12336	−	0.816171i
$197$		−	380.855i		−	1.93327i	−0.256150	−	0.966637i	$-0.582454\pi$
$197$		−	380.855i		−	1.93327i	0.256150	−	0.966637i	$-0.417546\pi$
$198$		0			0
$199$	291.989			1.46728			0.733642	−	0.679537i	$-0.237819\pi$
$199$	291.989			1.46728			0.733642	+	0.679537i	$0.237819\pi$
$200$	−13.5174	+	18.6051i	−0.0675872	+	0.0930257i
$201$		0			0
$202$	42.2633	+	130.073i	0.209224	+	0.643926i
$203$	378.120	−	274.720i	1.86266	−	1.35330i
$204$		0			0
$205$	−5.55128	+	1.80372i	−0.0270794	+	0.00879863i
$206$	260.570	+	84.6644i	1.26490	+	0.410992i
$207$		0			0
$208$		−	94.2034i		−	0.452901i
$209$	197.339	+	229.920i	0.944204	+	1.10010i
$210$		0			0
$211$	−19.6293	+	27.0174i	−0.0930299	+	0.128045i	−0.852995	−	0.521920i	$-0.825216\pi$
$211$	−19.6293	+	27.0174i	−0.0930299	+	0.128045i	0.759965	+	0.649964i	$0.225216\pi$
$212$	51.6555	−	158.979i	0.243658	−	0.749903i
$213$		0			0
$214$	−71.7786	+	52.1502i	−0.335414	+	0.243693i
$215$	−17.8438	−	24.5599i	−0.0829944	−	0.114232i
$216$		0			0
$217$	−272.770	−	88.6283i	−1.25700	−	0.408425i
$218$	184.888	+	134.329i	0.848110	+	0.616188i
$219$		0			0
$220$	−8.07156	−	19.3533i	−0.0366889	−	0.0879697i
$221$	121.843			0.551326
$222$		0			0
$223$	−114.637	+	352.817i	−0.514068	+	1.58214i	0.270904	+	0.962606i	$0.412677\pi$
$223$	−114.637	+	352.817i	−0.514068	+	1.58214i	−0.784972	+	0.619531i	$0.787323\pi$
$224$	−149.953	−	461.508i	−0.669434	−	2.06031i
$225$		0			0
$226$	44.8825	+	61.7755i	0.198595	+	0.273343i
$227$	−108.568	+	35.2758i	−0.478273	+	0.155400i	−0.538225	−	0.842801i	$-0.680905\pi$
$227$	−108.568	+	35.2758i	−0.478273	+	0.155400i	0.0599526	+	0.998201i	$0.480905\pi$
$228$		0			0
$229$	43.4024	+	31.5337i	0.189530	+	0.137702i	0.678504	−	0.734597i	$-0.262629\pi$
$229$	43.4024	+	31.5337i	0.189530	+	0.137702i	−0.488974	+	0.872299i	$0.662629\pi$
$230$			8.00743i			0.0348149i
$231$		0			0
$232$	−40.9480			−0.176500
$233$	114.007	−	156.917i	0.489299	−	0.673463i	−0.490959	−	0.871183i	$-0.663354\pi$
$233$	114.007	−	156.917i	0.489299	−	0.673463i	0.980259	+	0.197720i	$0.0633536\pi$
$234$		0			0
$235$	2.19987	+	6.77050i	0.00936115	+	0.0288106i
$236$	−268.888	+	195.359i	−1.13936	+	0.827790i
$237$		0			0
$238$	548.645	−	178.265i	2.30523	−	0.749015i
$239$	−142.797	−	46.3976i	−0.597478	−	0.194132i	−0.00536244	−	0.999986i	$-0.501707\pi$
$239$	−142.797	−	46.3976i	−0.597478	−	0.194132i	−0.592115	+	0.805853i	$0.701707\pi$
$240$		0			0
$241$			135.128i			0.560696i	0.959898	+	0.280348i	$0.0904499\pi$
$241$			135.128i			0.560696i	−0.959898	+	0.280348i	$0.909550\pi$
$242$	−345.010	−	52.9267i	−1.42566	−	0.218705i
$243$		0			0
$244$	−72.8110	+	100.216i	−0.298406	+	0.410720i
$245$	−8.58500	+	26.4219i	−0.0350408	+	0.107845i
$246$		0			0
$247$	−143.675	+	104.386i	−0.581682	+	0.422616i
$248$	14.7696	+	20.3287i	0.0595550	+	0.0819704i
$249$		0			0
$250$	60.2759	+	19.5848i	0.241104	+	0.0783393i
$251$	190.283	+	138.249i	0.758099	+	0.550791i	0.898327	−	0.439328i	$-0.144783\pi$
$251$	190.283	+	138.249i	0.758099	+	0.550791i	−0.140228	+	0.990119i	$0.544783\pi$
$252$		0			0
$253$	59.1066	+	36.0233i	0.233623	+	0.142384i
$254$	408.885			1.60978
$255$		0			0
$256$	64.9083	−	199.767i	0.253548	−	0.780341i
$257$	123.361	+	379.665i	0.480002	+	1.47729i	0.839091	+	0.543991i	$0.183087\pi$
$257$	123.361	+	379.665i	0.480002	+	1.47729i	−0.359089	+	0.933303i	$0.616913\pi$
$258$		0			0
$259$	5.30651	+	7.30378i	0.0204885	+	0.0281999i
$260$	11.6889	−	3.79796i	0.0449574	−	0.0146076i
$261$		0			0
$262$	216.173	+	157.059i	0.825086	+	0.599460i
$263$			281.116i			1.06888i	0.845206	+	0.534441i	$0.179478\pi$
$263$			281.116i			1.06888i	−0.845206	+	0.534441i	$0.820522\pi$
$264$		0			0
$265$	−17.0637			−0.0643914
$266$	−494.228	+	680.246i	−1.85800	+	2.55732i
$267$		0			0
$268$	104.286	+	320.959i	0.389126	+	1.19761i
$269$	−360.002	+	261.557i	−1.33830	+	0.972331i	−0.338794	+	0.940861i	$0.610019\pi$
$269$	−360.002	+	261.557i	−1.33830	+	0.972331i	−0.999505	+	0.0314699i	$0.989981\pi$
$270$		0			0
$271$	−203.606	+	66.1557i	−0.751315	+	0.244117i	−0.659547	−	0.751663i	$-0.729252\pi$
$271$	−203.606	+	66.1557i	−0.751315	+	0.244117i	−0.0917680	+	0.995780i	$0.529252\pi$
$272$	262.609	+	85.3268i	0.965474	+	0.313702i
$273$		0			0
$274$		−	63.2483i		−	0.230833i
$275$	207.053	−	177.712i	0.752919	−	0.646225i
$276$		0			0
$277$	10.6030	−	14.5938i	0.0382781	−	0.0526853i	−0.789449	−	0.613816i	$-0.789634\pi$
$277$	10.6030	−	14.5938i	0.0382781	−	0.0526853i	0.827727	+	0.561131i	$0.189634\pi$
$278$	169.061	−	520.318i	0.608135	−	1.87165i
$279$		0			0
$280$	3.50121	−	2.54378i	0.0125043	−	0.00908491i
$281$	−117.975	−	162.378i	−0.419839	−	0.577858i	0.545745	−	0.837951i	$-0.316247\pi$
$281$	−117.975	−	162.378i	−0.419839	−	0.577858i	−0.965584	+	0.260093i	$0.916247\pi$
$282$		0			0
$283$	179.648	+	58.3712i	0.634799	+	0.206259i	0.608700	−	0.793401i	$-0.291691\pi$
$283$	179.648	+	58.3712i	0.634799	+	0.206259i	0.0260990	+	0.999659i	$0.491691\pi$
$284$	94.8113	+	68.8844i	0.333843	+	0.242551i
$285$		0			0
$286$	47.2757	−	199.047i	0.165300	−	0.695970i
$287$	−140.021			−0.487876
$288$		0			0
$289$	−21.0562	+	64.8043i	−0.0728588	+	0.224236i
$290$	17.3679	+	53.4528i	0.0598892	+	0.184320i
$291$		0			0
$292$	32.9717	+	45.3817i	0.112917	+	0.155417i
$293$	186.202	−	60.5007i	0.635502	−	0.206487i	0.0264910	−	0.999649i	$-0.491567\pi$
$293$	186.202	−	60.5007i	0.635502	−	0.206487i	0.609011	+	0.793162i	$0.291567\pi$
$294$		0			0
$295$	27.4480	+	19.9421i	0.0930441	+	0.0676005i
$296$		−	0.790954i		−	0.00267214i
$297$		0			0
$298$	−38.3966			−0.128848
$299$	−23.8470	+	32.8225i	−0.0797558	+	0.109774i
$300$		0			0
$301$	−225.038	−	692.597i	−0.747635	−	2.30099i
$302$	−192.198	+	139.640i	−0.636416	+	0.462383i
$303$		0			0
$304$	−382.766	+	124.368i	−1.25910	+	0.409106i
$305$	12.0261	+	3.90751i	0.0394298	+	0.0128115i
$306$		0			0
$307$			115.995i			0.377832i	0.981993	+	0.188916i	$0.0604974\pi$
$307$			115.995i			0.377832i	−0.981993	+	0.188916i	$0.939503\pi$
$308$	−40.6849	−	501.371i	−0.132094	−	1.62783i
$309$		0			0
$310$	20.2722	−	27.9023i	0.0653943	−	0.0900075i
$311$	−84.6472	+	260.517i	−0.272177	+	0.837676i	0.717775	+	0.696275i	$0.245161\pi$
$311$	−84.6472	+	260.517i	−0.272177	+	0.837676i	−0.989952	+	0.141401i	$0.954839\pi$
$312$		0			0
$313$	−7.30849	+	5.30993i	−0.0233498	+	0.0169646i	−0.599399	−	0.800450i	$-0.704594\pi$
$313$	−7.30849	+	5.30993i	−0.0233498	+	0.0169646i	0.576049	+	0.817415i	$0.304594\pi$
$314$	−156.733	−	215.724i	−0.499149	−	0.687019i
$315$		0			0
$316$	−387.375	−	125.866i	−1.22587	−	0.398309i
$317$	−131.514	−	95.5504i	−0.414870	−	0.301421i	0.360700	−	0.932682i	$-0.382538\pi$
$317$	−131.514	−	95.5504i	−0.414870	−	0.301421i	−0.775570	+	0.631261i	$0.782538\pi$
$318$		0			0
$319$	472.694	+	112.270i	1.48180	+	0.351942i
$320$	32.5719			0.101787
$321$		0			0
$322$	−59.3582	+	182.686i	−0.184342	+	0.567347i
$323$	−160.858	−	495.071i	−0.498013	−	1.53273i
$324$		0			0
$325$	94.0042	+	129.386i	0.289244	+	0.398110i
$326$	640.923	−	208.249i	1.96602	−	0.638800i
$327$		0			0
$328$	9.92454	+	7.21060i	0.0302577	+	0.0219835i
$329$			170.773i			0.519068i
$330$		0			0
$331$	−448.559			−1.35516			−0.677581	−	0.735448i	$-0.736972\pi$
$331$	−448.559			−1.35516			−0.677581	+	0.735448i	$0.736972\pi$
$332$	294.582	−	405.458i	0.887297	−	1.22126i
$333$		0			0
$334$	−172.031	−	529.458i	−0.515064	−	1.58520i
$335$	27.8702	−	20.2489i	0.0831947	−	0.0604445i
$336$		0			0
$337$	40.4589	−	13.1459i	0.120056	−	0.0390086i	−0.248373	−	0.968665i	$-0.579896\pi$
$337$	40.4589	−	13.1459i	0.120056	−	0.0390086i	0.368429	+	0.929656i	$0.379896\pi$
$338$	−349.608	−	113.594i	−1.03434	−	0.336078i
$339$		0			0
$340$			36.0251i			0.105956i
$341$	−114.761	−	275.164i	−0.336542	−	0.806932i
$342$		0			0
$343$	−86.9482	+	119.674i	−0.253493	+	0.348904i
$344$	−19.7159	+	60.6794i	−0.0573138	+	0.176394i
$345$		0			0
$346$	205.622	−	149.393i	0.594282	−	0.431771i
$347$	−99.5136	−	136.969i	−0.286783	−	0.394722i	0.641183	−	0.767388i	$-0.278444\pi$
$347$	−99.5136	−	136.969i	−0.286783	−	0.394722i	−0.927966	+	0.372665i	$0.878444\pi$
$348$		0			0
$349$	−282.504	−	91.7910i	−0.809466	−	0.263012i	−0.125095	−	0.992145i	$-0.539923\pi$
$349$	−282.504	−	91.7910i	−0.809466	−	0.263012i	−0.684372	+	0.729133i	$0.739923\pi$
$350$	612.590	+	445.073i	1.75026	+	1.27164i
$351$		0			0
$352$	262.516	−	430.733i	0.745784	−	1.22367i
$353$	−639.289			−1.81102			−0.905509	−	0.424327i	$-0.860511\pi$
$353$	−639.289			−1.81102			−0.905509	+	0.424327i	$0.860511\pi$
$354$		0			0
$355$	3.69679	−	11.3775i	0.0104135	−	0.0320494i
$356$	87.1710	+	268.285i	0.244862	+	0.753609i
$357$		0			0
$358$	−537.987	−	740.475i	−1.50276	−	2.06837i
$359$	364.478	−	118.426i	1.01526	−	0.329877i	0.246312	−	0.969191i	$-0.420781\pi$
$359$	364.478	−	118.426i	1.01526	−	0.329877i	0.768946	+	0.639313i	$0.220781\pi$
$360$		0			0
$361$	321.767	+	233.777i	0.891321	+	0.647582i
$362$			44.0769i			0.121759i
$363$		0			0
$364$	294.831			0.809976
$365$	3.36574	−	4.63255i	0.00922122	−	0.0126919i
$366$		0			0
$367$	109.464	+	336.895i	0.298267	+	0.917971i	0.982105	+	0.188337i	$0.0603096\pi$
$367$	109.464	+	336.895i	0.298267	+	0.917971i	−0.683838	+	0.729634i	$0.739690\pi$
$368$	−74.3831	+	54.0425i	−0.202128	+	0.146855i
$369$		0			0
$370$	−1.03250	+	0.335479i	−0.00279054	+	0.000906700i
$371$	−389.301	−	126.492i	−1.04933	−	0.340948i
$372$		0			0
$373$		−	185.060i		−	0.496140i	−0.968742	−	0.248070i	$-0.920204\pi$
$373$		−	185.060i		−	0.496140i	0.968742	−	0.248070i	$-0.0797962\pi$
$374$	512.059	+	312.081i	1.36914	+	0.834442i
$375$		0			0
$376$	8.79427	−	12.1043i	0.0233890	−	0.0321922i
$377$	−87.9970	+	270.827i	−0.233414	+	0.718374i
$378$		0			0
$379$	204.346	−	148.466i	0.539171	−	0.391730i	−0.284606	−	0.958644i	$-0.591863\pi$
$379$	204.346	−	148.466i	0.539171	−	0.391730i	0.823777	+	0.566914i	$0.191863\pi$
$380$	−30.8636	−	42.4802i	−0.0812201	−	0.111790i
$381$		0			0
$382$	56.1619	+	18.2481i	0.147021	+	0.0477699i
$383$	−203.119	−	147.575i	−0.530337	−	0.385312i	0.290147	−	0.956982i	$-0.406296\pi$
$383$	−203.119	−	147.575i	−0.530337	−	0.385312i	−0.820484	+	0.571670i	$0.806296\pi$
$384$		0			0
$385$	−47.3915	+	19.7653i	−0.123095	+	0.0513383i
$386$	−545.891			−1.41423
$387$		0			0
$388$	93.8765	−	288.922i	0.241950	−	0.744645i
$389$	46.4217	+	142.871i	0.119336	+	0.367279i	0.992827	−	0.119562i	$-0.0381491\pi$
$389$	46.4217	+	142.871i	0.119336	+	0.367279i	−0.873491	+	0.486841i	$0.838149\pi$
$390$		0			0
$391$	−69.8988	−	96.2075i	−0.178769	−	0.246055i
$392$	55.5304	−	18.0429i	0.141659	−	0.0460279i
$393$		0			0
$394$	888.823	+	645.768i	2.25590	+	1.63900i
$395$			41.5781i			0.105261i
$396$		0			0
$397$	−516.245			−1.30036			−0.650182	−	0.759778i	$-0.725307\pi$
$397$	−516.245			−1.30036			−0.650182	+	0.759778i	$0.725307\pi$
$398$	−495.089	+	681.432i	−1.24394	+	1.71214i
$399$		0			0
$400$	111.999	+	344.697i	0.279997	+	0.861742i
$401$	−13.4444	+	9.76791i	−0.0335271	+	0.0243589i	−0.604423	−	0.796664i	$-0.706596\pi$
$401$	−13.4444	+	9.76791i	−0.0335271	+	0.0243589i	0.570896	+	0.821023i	$0.306596\pi$
$402$		0			0
$403$	166.192	−	53.9991i	0.412388	−	0.133993i
$404$	−194.856	−	63.3124i	−0.482316	−	0.156714i
$405$		0			0
$406$			1348.25i			3.32081i
$407$	−2.16861	+	9.13058i	−0.00532827	+	0.0224339i
$408$		0			0
$409$	−238.507	+	328.277i	−0.583147	+	0.802633i	−0.994036	−	0.109052i	$-0.965218\pi$
$409$	−238.507	+	328.277i	−0.583147	+	0.802633i	0.410889	+	0.911685i	$0.365218\pi$
$410$	5.20315	−	16.0137i	0.0126906	−	0.0390577i
$411$		0			0
$412$	−332.049	+	241.247i	−0.805943	+	0.585552i
$413$	478.385	+	658.440i	1.15832	+	1.59429i
$414$		0			0
$415$	−48.6557	−	15.8092i	−0.117243	−	0.0380945i
$416$	239.191	+	173.783i	0.574979	+	0.417746i
$417$		0			0
$418$	−871.180	+	70.6939i	−2.08416	+	0.169124i
$419$	628.759			1.50062			0.750309	−	0.661087i	$-0.229905\pi$
$419$	628.759			1.50062			0.750309	+	0.661087i	$0.229905\pi$
$420$		0			0
$421$	186.966	−	575.421i	0.444099	−	1.36680i	−0.439370	−	0.898306i	$-0.644798\pi$
$421$	186.966	−	575.421i	0.444099	−	1.36680i	0.883469	−	0.468490i	$-0.155202\pi$
$422$	−29.7692	−	91.6200i	−0.0705430	−	0.217109i
$423$		0			0
$424$	21.0794	+	29.0134i	0.0497157	+	0.0684277i
$425$	−445.832	+	144.860i	−1.04902	+	0.340846i
$426$		0			0
$427$	245.403	+	178.296i	0.574715	+	0.417555i
$428$		−	132.912i		−	0.310541i
$429$		0			0
$430$	87.5723			0.203656
$431$	426.829	−	587.479i	0.990322	−	1.36306i	0.0592423	−	0.998244i	$-0.481132\pi$
$431$	426.829	−	587.479i	0.990322	−	1.36306i	0.931079	−	0.364817i	$-0.118868\pi$
$432$		0			0
$433$	−72.5855	−	223.395i	−0.167634	−	0.515925i	0.831587	−	0.555395i	$-0.187433\pi$
$433$	−72.5855	−	223.395i	−0.167634	−	0.515925i	−0.999221	+	0.0394704i	$0.987433\pi$
$434$	669.338	−	486.303i	1.54225	−	1.12051i
$435$		0			0
$436$	−325.599	+	105.794i	−0.746787	+	0.242646i
$437$	164.847	+	53.5620i	0.377224	+	0.122568i
$438$		0			0
$439$		−	142.495i		−	0.324589i	−0.986742	−	0.162295i	$-0.948111\pi$
$439$		−	142.495i		−	0.324589i	0.986742	−	0.162295i	$-0.0518895\pi$
$440$	4.37692	+	1.03956i	0.00994754	+	0.00236264i
$441$		0			0
$442$	−206.594	+	284.352i	−0.467407	+	0.643331i
$443$	−120.643	+	371.301i	−0.272332	+	0.838152i	0.717581	+	0.696475i	$0.245249\pi$
$443$	−120.643	+	371.301i	−0.272332	+	0.838152i	−0.989913	+	0.141677i	$0.954751\pi$
$444$		0			0
$445$	23.2963	−	16.9258i	0.0523512	−	0.0380354i
$446$	−629.013	−	865.762i	−1.41034	−	1.94117i
$447$		0			0
$448$	743.113	+	241.452i	1.65873	+	0.538956i
$449$	579.861	+	421.294i	1.29145	+	0.938294i	0.999834	−	0.0182417i	$-0.00580683\pi$
$449$	579.861	+	421.294i	1.29145	+	0.938294i	0.291617	+	0.956535i	$0.405807\pi$
$450$		0			0
$451$	−94.7967	−	110.448i	−0.210192	−	0.244896i
$452$	−114.389			−0.253073
$453$		0			0
$454$	101.760	−	313.184i	0.224140	−	0.689832i
$455$	−9.30027	−	28.6233i	−0.0204402	−	0.0629083i
$456$		0			0
$457$	111.947	+	154.082i	0.244960	+	0.337159i	0.913738	−	0.406303i	$-0.133182\pi$
$457$	111.947	+	154.082i	0.244960	+	0.337159i	−0.668778	+	0.743462i	$0.733182\pi$
$458$	−147.184	+	47.8230i	−0.321363	+	0.104417i
$459$		0			0
$460$	−9.70457	−	7.05078i	−0.0210969	−	0.0153278i
$461$		−	857.726i		−	1.86058i	−0.366828	−	0.930289i	$-0.619556\pi$
$461$		−	857.726i		−	1.86058i	0.366828	−	0.930289i	$-0.380444\pi$
$462$		0			0
$463$	−33.4807			−0.0723126			−0.0361563	−	0.999346i	$-0.511511\pi$
$463$	−33.4807			−0.0723126			−0.0361563	+	0.999346i	$0.511511\pi$
$464$	−379.321	+	522.090i	−0.817502	+	1.12519i
$465$		0			0
$466$	172.899	+	532.128i	0.371028	+	1.14191i
$467$	−213.054	+	154.793i	−0.456218	+	0.331461i	−0.792046	−	0.610462i	$-0.790984\pi$
$467$	−213.054	+	154.793i	−0.456218	+	0.331461i	0.335828	+	0.941923i	$0.390984\pi$
$468$		0			0
$469$	785.949	−	255.370i	1.67580	−	0.544500i
$470$	−19.5307	−	6.34592i	−0.0415548	−	0.0135020i
$471$		0			0
$472$		−	71.3049i		−	0.151070i
$473$	393.964	−	646.412i	0.832905	−	1.36662i
$474$		0			0
$475$	401.613	−	552.772i	0.845500	−	1.16373i
$476$	−267.050	+	821.896i	−0.561030	+	1.72667i
$477$		0			0
$478$	350.404	−	254.583i	0.733062	−	0.532601i
$479$	361.564	+	497.651i	0.754832	+	1.03894i	0.997626	+	0.0688591i	$0.0219359\pi$
$479$	361.564	+	497.651i	0.754832	+	1.03894i	−0.242795	+	0.970078i	$0.578064\pi$
$480$		0			0
$481$	−5.23131	−	1.69976i	−0.0108759	−	0.00353380i
$482$	−315.355	−	229.119i	−0.654264	−	0.475351i
$483$		0			0
$484$	367.936	−	371.530i	0.760199	−	0.767625i
$485$	−31.0109			−0.0639400
$486$		0			0
$487$	92.2075	−	283.786i	0.189338	−	0.582722i	−0.810658	−	0.585520i	$-0.800891\pi$
$487$	92.2075	−	283.786i	0.189338	−	0.582722i	0.999996	+	0.00279765i	$0.000890521\pi$
$488$	−8.21233	−	25.2750i	−0.0168285	−	0.0517929i
$489$		0			0
$490$	−47.1058	−	64.8356i	−0.0961343	−	0.132318i
$491$	442.951	−	143.924i	0.902141	−	0.293123i	0.179021	−	0.983845i	$-0.442707\pi$
$491$	442.951	−	143.924i	0.902141	−	0.293123i	0.723120	+	0.690722i	$0.242707\pi$
$492$		0			0
$493$	−675.274	−	490.615i	−1.36972	−	0.995163i
$494$		−	512.298i		−	1.03704i
$495$		0			0
$496$	396.010			0.798408
$497$	168.681	−	232.169i	0.339398	−	0.467142i
$498$		0			0
$499$	168.684	+	519.155i	0.338043	+	1.04039i	0.965203	+	0.261500i	$0.0842171\pi$
$499$	168.684	+	519.155i	0.338043	+	1.04039i	−0.627160	+	0.778890i	$0.715783\pi$
$500$	−76.8105	+	55.8061i	−0.153621	+	0.111612i
$501$		0			0
$502$	−645.277	+	209.663i	−1.28541	+	0.417656i
$503$	−595.104	−	193.361i	−1.18311	−	0.384415i	−0.349588	−	0.936904i	$-0.613678\pi$
$503$	−595.104	−	193.361i	−1.18311	−	0.384415i	−0.833521	+	0.552488i	$0.813678\pi$
$504$		0			0
$505$			20.9144i			0.0414147i
$506$	−184.289	+	76.8602i	−0.364208	+	0.151898i
$507$		0			0
$508$	−360.036	+	495.546i	−0.708731	+	0.975485i
$509$	64.3048	−	197.910i	0.126335	−	0.388821i	−0.867807	−	0.496902i	$-0.834471\pi$
$509$	64.3048	−	197.910i	0.126335	−	0.388821i	0.994142	+	0.108082i	$0.0344708\pi$
$510$		0			0
$511$	111.129	−	80.7396i	0.217473	−	0.158003i
$512$	425.678	+	585.896i	0.831403	+	1.14433i
$513$		0			0
$514$	−1095.21	−	355.856i	−2.13076	−	0.692326i
$515$	33.8954	+	24.6265i	0.0658164	+	0.0478184i
$516$		0			0
$517$	−134.706	+	115.617i	−0.260553	+	0.223630i
$518$	−26.0428			−0.0502757
$519$		0			0
$520$	−0.814810	+	2.50773i	−0.00156694	+	0.00482255i
$521$	−97.3922	−	299.742i	−0.186933	−	0.575321i	0.813043	−	0.582204i	$-0.197809\pi$
$521$	−97.3922	−	299.742i	−0.186933	−	0.575321i	−0.999976	+	0.00688211i	$0.997809\pi$
$522$		0			0
$523$	277.921	+	382.525i	0.531397	+	0.731406i	0.987343	−	0.158602i	$-0.0506987\pi$
$523$	277.921	+	382.525i	0.531397	+	0.731406i	−0.455945	+	0.890008i	$0.650699\pi$
$524$	−380.693	+	123.695i	−0.726513	+	0.236058i
$525$		0			0
$526$	−656.056	−	476.653i	−1.24726	−	0.906184i
$527$			512.201i			0.971919i
$528$		0			0
$529$	−489.403			−0.925147
$530$	28.9328	−	39.8226i	0.0545902	−	0.0751370i
$531$		0			0
$532$	−389.239	−	1197.95i	−0.731652	−	2.25179i
$533$	69.0182	−	50.1446i	0.129490	−	0.0940800i
$534$		0			0
$535$	−12.9035	+	4.19261i	−0.0241188	+	0.00783666i
$536$	−68.8581	−	22.3734i	−0.128467	−	0.0417414i
$537$		0			0
$538$		−	1283.65i		−	2.38596i
$539$	−690.498	+	56.0321i	−1.28107	+	0.103956i
$540$		0			0
$541$	8.33162	−	11.4675i	0.0154004	−	0.0211969i	−0.801247	−	0.598333i	$-0.795830\pi$
$541$	8.33162	−	11.4675i	0.0154004	−	0.0211969i	0.816648	+	0.577136i	$0.195830\pi$
$542$	190.838	−	587.339i	0.352100	−	1.08365i
$543$		0			0
$544$	−701.103	+	509.381i	−1.28879	+	0.936362i
$545$	20.5416	+	28.2731i	0.0376911	+	0.0518773i
$546$		0			0
$547$	608.751	+	197.795i	1.11289	+	0.361600i	0.807050	−	0.590483i	$-0.201063\pi$
$547$	608.751	+	197.795i	1.11289	+	0.361600i	0.305840	+	0.952083i	$0.401063\pi$
$548$	76.6535	+	55.6920i	0.139879	+	0.101628i
$549$		0			0
$550$	63.6628	+	784.534i	0.115751	+	1.42643i
$551$	1216.59			2.20798
$552$		0			0
$553$	−308.214	+	948.585i	−0.557349	+	1.71534i
$554$	16.0802	+	49.4898i	0.0290256	+	0.0893317i
$555$		0			0
$556$	481.733	+	663.048i	0.866426	+	1.19253i
$557$	−542.238	+	176.184i	−0.973498	+	0.316309i	−0.752227	−	0.658904i	$-0.771020\pi$
$557$	−542.238	+	176.184i	−0.973498	+	0.316309i	−0.221271	+	0.975212i	$0.571020\pi$
$558$		0			0
$559$	358.960	+	260.799i	0.642146	+	0.466546i
$560$		−	68.2049i		−	0.121794i
$561$		0			0
$562$	578.986			1.03022
$563$	−138.672	+	190.865i	−0.246309	+	0.339015i	−0.914214	−	0.405231i	$-0.867191\pi$
$563$	−138.672	+	190.865i	−0.246309	+	0.339015i	0.667905	+	0.744246i	$0.267191\pi$
$564$		0			0
$565$	3.60833	+	11.1053i	0.00638642	+	0.0196554i
$566$	−440.831	+	320.282i	−0.778853	+	0.565869i
$567$		0			0
$568$	−23.9119	+	7.76946i	−0.0420985	+	0.0136786i
$569$	−376.660	−	122.384i	−0.661969	−	0.215087i	−0.0412847	−	0.999147i	$-0.513145\pi$
$569$	−376.660	−	122.384i	−0.661969	−	0.215087i	−0.620684	+	0.784061i	$0.713145\pi$
$570$		0			0
$571$		−	67.0903i		−	0.117496i	−0.998273	−	0.0587481i	$-0.981289\pi$
$571$		−	67.0903i		−	0.117496i	0.998273	−	0.0587481i	$-0.0187109\pi$
$572$	199.607	+	232.563i	0.348963	+	0.406578i
$573$		0			0
$574$	237.415	−	326.774i	0.413615	−	0.569292i
$575$	48.2349	−	148.452i	0.0838867	−	0.258177i
$576$		0			0
$577$	130.247	−	94.6302i	0.225732	−	0.164004i	−0.469171	−	0.883107i	$-0.655447\pi$
$577$	130.247	−	94.6302i	0.225732	−	0.164004i	0.694903	+	0.719103i	$0.255447\pi$
$578$	−115.535	−	159.020i	−0.199888	−	0.275122i
$579$		0			0
$580$	−80.0748	−	26.0179i	−0.138060	−	0.0448584i
$581$	−992.866	−	721.359i	−1.70889	−	1.24158i
$582$		0			0
$583$	−163.788	−	392.718i	−0.280940	−	0.673615i
$584$	−12.0345			−0.0206071
$585$		0			0
$586$	−174.525	+	537.133i	−0.297825	+	0.916610i
$587$	187.759	+	577.862i	0.319861	+	0.984432i	0.973707	+	0.227804i	$0.0731546\pi$
$587$	187.759	+	577.862i	0.319861	+	0.984432i	−0.653845	+	0.756628i	$0.726845\pi$
$588$		0			0
$589$	−438.817	−	603.979i	−0.745020	−	1.02543i
$590$	−93.0802	+	30.2436i	−0.157763	+	0.0512603i
$591$		0			0
$592$	−10.0847	−	7.32699i	−0.0170350	−	0.0123767i
$593$			691.234i			1.16566i	0.812596	+	0.582828i	$0.198054\pi$
$593$			691.234i			1.16566i	−0.812596	+	0.582828i	$0.801946\pi$
$594$		0			0
$595$	88.2165			0.148263
$596$	33.8094	−	46.5346i	0.0567271	−	0.0780782i
$597$		0			0
$598$	−36.1655	−	111.306i	−0.0604775	−	0.186131i
$599$	195.721	−	142.199i	0.326746	−	0.237395i	−0.412303	−	0.911047i	$-0.635275\pi$
$599$	195.721	−	142.199i	0.326746	−	0.237395i	0.739048	+	0.673652i	$0.235275\pi$
$600$		0			0
$601$	60.4959	−	19.6563i	0.100659	−	0.0327060i	−0.258255	−	0.966077i	$-0.583147\pi$
$601$	60.4959	−	19.6563i	0.100659	−	0.0327060i	0.358913	+	0.933371i	$0.383147\pi$
$602$	1997.92	+	649.164i	3.31880	+	1.07835i
$603$		0			0
$604$		−	355.890i		−	0.589222i
$605$	−47.6758	−	24.0009i	−0.0788030	−	0.0396709i
$606$		0			0
$607$	302.894	−	416.898i	0.499002	−	0.686818i	−0.483014	−	0.875612i	$-0.660458\pi$
$607$	302.894	−	416.898i	0.499002	−	0.686818i	0.982017	+	0.188795i	$0.0604581\pi$
$608$	390.328	−	1201.31i	0.641987	−	1.97583i
$609$		0			0
$610$	−29.5103	+	21.4405i	−0.0483775	+	0.0351483i
$611$	−61.1579	−	84.1766i	−0.100095	−	0.137769i
$612$		0			0
$613$	36.9296	+	11.9992i	0.0602440	+	0.0195745i	0.338984	−	0.940792i	$-0.389917\pi$
$613$	36.9296	+	11.9992i	0.0602440	+	0.0195745i	−0.278740	+	0.960367i	$0.589917\pi$
$614$	−270.703	−	196.677i	−0.440884	−	0.320321i
$615$		0			0
$616$	92.1511	+	56.1627i	0.149596	+	0.0911733i
$617$	−636.272			−1.03124			−0.515618	−	0.856819i	$-0.672438\pi$
$617$	−636.272			−1.03124			−0.515618	+	0.856819i	$0.672438\pi$
$618$		0			0
$619$	−13.2021	+	40.6319i	−0.0213281	+	0.0656413i	−0.961154	−	0.276012i	$-0.910987\pi$
$619$	−13.2021	+	40.6319i	−0.0213281	+	0.0656413i	0.939826	+	0.341654i	$0.110987\pi$
$620$	15.9658	+	49.1377i	0.0257513	+	0.0792543i
$621$		0			0
$622$	−464.458	−	639.272i	−0.746718	−	1.02777i
$623$	656.963	−	213.460i	1.05452	−	0.342633i
$624$		0			0
$625$	−493.859	−	358.810i	−0.790175	−	0.574095i
$626$		−	26.0596i		−	0.0416287i
$627$		0			0
$628$	399.454			0.636072
$629$	9.47676	−	13.0436i	0.0150664	−	0.0207371i
$630$		0			0
$631$	180.738	+	556.254i	0.286431	+	0.881544i	0.985966	+	0.166946i	$0.0533904\pi$
$631$	180.738	+	556.254i	0.286431	+	0.881544i	−0.699535	+	0.714598i	$0.746610\pi$
$632$	70.6950	−	51.3629i	0.111859	−	0.0812704i
$633$		0			0
$634$	445.983	−	144.909i	0.703443	−	0.228562i
$635$	59.4665	+	19.3218i	0.0936481	+	0.0304281i
$636$		0			0
$637$		−	406.048i		−	0.637438i
$638$	−1063.50	+	912.791i	−1.66692	+	1.43071i
$639$		0			0
$640$	−7.66755	+	10.5535i	−0.0119805	+	0.0164898i
$641$	63.5221	−	195.501i	0.0990984	−	0.304994i	−0.889202	−	0.457515i	$-0.848739\pi$
$641$	63.5221	−	195.501i	0.0990984	−	0.304994i	0.988300	+	0.152522i	$0.0487395\pi$
$642$		0			0
$643$	−97.3386	+	70.7206i	−0.151382	+	0.109985i	−0.660898	−	0.750476i	$-0.729824\pi$
$643$	−97.3386	+	70.7206i	−0.151382	+	0.109985i	0.509516	+	0.860461i	$0.329824\pi$
$644$	−169.139	−	232.799i	−0.262637	−	0.361489i
$645$		0			0
$646$	1428.12	+	464.025i	2.21072	+	0.718305i
$647$	−472.072	−	342.980i	−0.729632	−	0.530108i	0.159815	−	0.987147i	$-0.448910\pi$
$647$	−472.072	−	342.980i	−0.729632	−	0.530108i	−0.889447	+	0.457039i	$0.848910\pi$
$648$		0			0
$649$	−195.501	+	823.126i	−0.301234	+	1.26830i
$650$	−461.346			−0.709763
$651$		0			0
$652$	−311.966	+	960.133i	−0.478476	+	1.47260i
$653$	135.579	+	417.270i	0.207625	+	0.639005i	0.999595	+	0.0284450i	$0.00905555\pi$
$653$	135.579	+	417.270i	0.207625	+	0.639005i	−0.791970	+	0.610560i	$0.790944\pi$
$654$		0			0
$655$	24.0174	+	33.0572i	0.0366678	+	0.0504689i
$656$	183.872	−	59.7435i	0.280292	−	0.0910724i
$657$		0			0
$658$	−398.543	−	289.559i	−0.605689	−	0.440059i
$659$			598.225i			0.907777i	0.891058	+	0.453888i	$0.149964\pi$
$659$			598.225i			0.907777i	−0.891058	+	0.453888i	$0.850036\pi$
$660$		0			0
$661$	811.159			1.22717			0.613585	−	0.789629i	$-0.289727\pi$
$661$	811.159			1.22717			0.613585	+	0.789629i	$0.289727\pi$
$662$	760.564	−	1046.83i	1.14889	−	1.58131i
$663$		0			0
$664$	33.2259	+	102.259i	0.0500390	+	0.154004i
$665$	−104.023	+	75.5774i	−0.156426	+	0.113650i
$666$		0			0
$667$	264.327	−	85.8852i	0.396293	−	0.128763i
$668$	793.153	+	257.711i	1.18736	+	0.385795i
$669$		0			0
$670$			99.3758i			0.148322i
$671$	25.5033	+	314.284i	0.0380079	+	0.468382i
$672$		0			0
$673$	−548.703	+	755.226i	−0.815310	+	1.12218i	0.175173	+	0.984538i	$0.443952\pi$
$673$	−548.703	+	755.226i	−0.815310	+	1.12218i	−0.990482	+	0.137640i	$0.956048\pi$
$674$	−37.9217	+	116.711i	−0.0562636	+	0.173162i
$675$		0			0
$676$	445.510	−	323.682i	0.659039	−	0.478820i
$677$	−467.307	−	643.193i	−0.690261	−	0.950063i	0.309739	−	0.950822i	$-0.399758\pi$
$677$	−467.307	−	643.193i	−0.690261	−	0.950063i	−1.00000		0.000758765i	$0.999758\pi$
$678$		0			0
$679$	−707.499	−	229.880i	−1.04197	−	0.338557i
$680$	−6.25271	−	4.54286i	−0.00919516	−	0.00668068i
$681$		0			0
$682$	836.751	+	198.737i	1.22691	+	0.291403i
$683$	−364.827			−0.534154			−0.267077	−	0.963675i	$-0.586058\pi$
$683$	−364.827			−0.534154			−0.267077	+	0.963675i	$0.586058\pi$
$684$		0			0
$685$	2.98880	−	9.19857i	0.00436321	−	0.0134286i
$686$	−131.863	−	405.832i	−0.192220	−	0.591592i
$687$		0			0
$688$	591.029	+	813.482i	0.859054	+	1.18239i
$689$	237.192	−	77.0683i	0.344255	−	0.111855i
$690$		0			0
$691$	−714.337	−	518.997i	−1.03377	−	0.751080i	−0.0647130	−	0.997904i	$-0.520613\pi$
$691$	−714.337	−	518.997i	−1.03377	−	0.751080i	−0.969060	+	0.246824i	$0.920613\pi$
$692$			380.747i			0.550212i
$693$		0			0
$694$	488.384			0.703724
$695$	49.1751	−	67.6838i	0.0707556	−	0.0973867i
$696$		0			0
$697$	77.2725	+	237.820i	0.110864	+	0.341205i
$698$	693.224	−	503.657i	0.993157	−	0.721571i
$699$		0			0
$700$	−1078.81	+	350.526i	−1.54115	+	0.500751i
$701$	1046.64	+	340.075i	1.49307	+	0.485129i	0.937989	−	0.346666i	$-0.112686\pi$
$701$	1046.64	+	340.075i	1.49307	+	0.485129i	0.555084	+	0.831795i	$0.312686\pi$
$702$		0			0
$703$			23.4998i			0.0334279i
$704$	312.645	+	749.635i	0.444099	+	1.06482i
$705$		0			0
$706$	1083.96	−	1491.95i	1.53536	−	2.11324i
$707$	−155.036	+	477.153i	−0.219288	+	0.674898i
$708$		0			0
$709$	−1124.68	+	817.130i	−1.58630	+	1.15251i	−0.677298	+	0.735708i	$0.736849\pi$
$709$	−1124.68	+	817.130i	−1.58630	+	1.15251i	−0.908997	+	0.416803i	$0.863151\pi$
$710$	20.2842	+	27.9188i	0.0285693	+	0.0393223i
$711$		0			0
$712$	−57.5575	−	18.7016i	−0.0808392	−	0.0262662i
$713$	−137.979	−	100.247i	−0.193518	−	0.140599i
$714$		0			0
$715$	16.2816	−	26.7146i	0.0227714	−	0.0373631i
$716$	1371.13			1.91498
$717$		0			0
$718$	−341.621	+	1051.40i	−0.475796	+	1.46435i
$719$	18.4769	+	56.8661i	0.0256981	+	0.0790906i	0.963083	−	0.269204i	$-0.0867607\pi$
$719$	18.4769	+	56.8661i	0.0256981	+	0.0790906i	−0.937385	+	0.348295i	$0.886761\pi$
$720$		0			0
$721$	590.755	+	813.105i	0.819355	+	1.12775i
$722$	−1091.16	+	354.539i	−1.51130	+	0.491051i
$723$		0			0
$724$	−53.4188	−	38.8110i	−0.0737829	−	0.0536064i
$725$		−	1095.59i		−	1.51116i
$726$		0			0
$727$	−1173.95			−1.61479			−0.807396	−	0.590010i	$-0.799124\pi$
$727$	−1173.95			−1.61479			−0.807396	+	0.590010i	$0.799124\pi$
$728$	−37.1790	+	51.1726i	−0.0510701	+	0.0702920i
$729$		0			0
$730$	5.10438	+	15.7097i	0.00699230	+	0.0215201i
$731$	−1052.16	+	764.440i	−1.43934	+	1.04575i
$732$		0			0
$733$	548.402	−	178.187i	0.748161	−	0.243092i	0.0899712	−	0.995944i	$-0.471323\pi$
$733$	548.402	−	178.187i	0.748161	−	0.243092i	0.658190	+	0.752852i	$0.271323\pi$
$734$	−971.835	−	315.768i	−1.32403	−	0.430202i
$735$		0			0
$736$		−	288.561i		−	0.392066i
$737$	733.539	+	447.065i	0.995304	+	0.606601i
$738$		0			0
$739$	100.875	−	138.843i	0.136502	−	0.187879i	−0.735293	−	0.677749i	$-0.762956\pi$
$739$	100.875	−	138.843i	0.136502	−	0.187879i	0.871796	+	0.489870i	$0.162956\pi$
$740$	0.502563	−	1.54673i	0.000679140	−	0.00209018i
$741$		0			0
$742$	955.289	−	694.058i	1.28745	−	0.935389i
$743$	−147.567	−	203.109i	−0.198610	−	0.273363i	0.698082	−	0.716018i	$-0.254037\pi$
$743$	−147.567	−	203.109i	−0.198610	−	0.273363i	−0.896692	+	0.442654i	$0.854037\pi$
$744$		0			0
$745$	−5.58424	−	1.81443i	−0.00749562	−	0.00243547i
$746$	431.885	+	313.783i	0.578935	+	0.420621i
$747$		0			0
$748$	−829.109	+	345.791i	−1.10843	+	0.462287i
$749$	−325.468			−0.434536
$750$		0			0
$751$	124.755	−	383.957i	0.166119	−	0.511261i	−0.832998	−	0.553275i	$-0.813378\pi$
$751$	124.755	−	383.957i	0.166119	−	0.511261i	0.999117	+	0.0420149i	$0.0133777\pi$
$752$	−72.8649	−	224.255i	−0.0968949	−	0.298212i
$753$		0			0
$754$	−482.839	−	664.571i	−0.640370	−	0.881394i
$755$	−34.5511	+	11.2263i	−0.0457630	+	0.0148693i
$756$		0			0
$757$	−873.924	−	634.943i	−1.15446	−	0.838762i	−0.165390	−	0.986228i	$-0.552888\pi$
$757$	−873.924	−	634.943i	−1.15446	−	0.838762i	−0.989067	+	0.147466i	$0.952888\pi$
$758$			728.628i			0.961250i
$759$		0			0
$760$	11.2651			0.0148225
$761$	−799.255	+	1100.08i	−1.05027	+	1.44557i	−0.161693	+	0.986841i	$0.551695\pi$
$761$	−799.255	+	1100.08i	−1.05027	+	1.44557i	−0.888576	+	0.458730i	$0.848305\pi$
$762$		0			0
$763$	259.062	+	797.311i	0.339531	+	1.04497i
$764$	−71.5679	+	51.9972i	−0.0936753	+	0.0680591i
$765$		0			0
$766$	688.806	−	223.807i	0.899225	−	0.292176i
$767$	−471.606	−	153.234i	−0.614870	−	0.199783i
$768$		0			0
$769$			925.077i			1.20296i	0.798888	+	0.601480i	$0.205422\pi$
$769$			925.077i			1.20296i	−0.798888	+	0.601480i	$0.794578\pi$
$770$	34.2284	−	144.114i	0.0444525	−	0.187161i
$771$		0			0
$772$	480.674	−	661.591i	0.622634	−	0.856983i
$773$	−112.314	+	345.665i	−0.145296	+	0.447174i	−0.997049	−	0.0767692i	$-0.975540\pi$
$773$	−112.314	+	345.665i	−0.145296	+	0.447174i	0.851753	+	0.523943i	$0.175540\pi$
$774$		0			0
$775$	−543.909	+	395.173i	−0.701818	+	0.509900i
$776$	38.3089	+	52.7276i	0.0493671	+	0.0679480i
$777$		0			0
$778$	−412.138	−	133.912i	−0.529741	−	0.172123i
$779$	−294.865	−	214.232i	−0.378518	−	0.275009i
$780$		0			0
$781$	297.335	−	24.1280i	0.380711	−	0.0308937i
$782$	343.043			0.438674
$783$		0			0
$784$	284.356	−	875.157i	0.362699	−	1.11627i
$785$	−12.6005	−	38.7804i	−0.0160516	−	0.0494018i
$786$		0			0
$787$	65.9383	+	90.7563i	0.0837844	+	0.115319i	0.848852	−	0.528631i	$-0.177294\pi$
$787$	65.9383	+	90.7563i	0.0837844	+	0.115319i	−0.765067	+	0.643950i	$0.777294\pi$
$788$	−1565.27	+	508.587i	−1.98638	+	0.645415i
$789$		0			0
$790$	−97.0331	−	70.4987i	−0.122827	−	0.0892389i
$791$			280.110i			0.354122i
$792$		0			0
$793$	−184.815			−0.233058
$794$	875.331	−	1204.79i	1.10243	−	1.51737i
$795$		0			0
$796$	−389.918	−	1200.04i	−0.489846	−	1.50759i
$797$	1168.51	−	848.970i	1.46613	−	1.06521i	0.484420	−	0.874835i	$-0.339031\pi$
$797$	1168.51	−	848.970i	1.46613	−	1.06521i	0.981712	−	0.190372i	$-0.0609695\pi$
$798$		0			0
$799$	290.053	−	94.2438i	0.363020	−	0.117952i
$800$	−1081.83	−	351.507i	−1.35228	−	0.439384i
$801$		0			0
$802$		−	47.9381i		−	0.0597732i
$803$	138.924	+	32.9957i	0.173006	+	0.0410906i
$804$		0			0
$805$	−17.2656	+	23.7641i	−0.0214480	+	0.0295206i
$806$	−155.770	+	479.412i	−0.193263	+	0.594803i
$807$		0			0
$808$	35.5607	−	25.8363i	0.0440107	−	0.0319757i
$809$	348.569	+	479.764i	0.430864	+	0.593033i	0.968151	−	0.250366i	$-0.0805510\pi$
$809$	348.569	+	479.764i	0.430864	+	0.593033i	−0.537287	+	0.843399i	$0.680551\pi$
$810$		0			0
$811$	411.277	+	133.632i	0.507124	+	0.164775i	0.551394	−	0.834245i	$-0.314096\pi$
$811$	411.277	+	133.632i	0.507124	+	0.164775i	−0.0442700	+	0.999020i	$0.514096\pi$
$812$	−1634.00	−	1187.17i	−2.01232	−	1.46203i
$813$		0			0
$814$	−17.6315	−	20.5426i	−0.0216603	−	0.0252366i
$815$	103.054			0.126447
$816$		0			0
$817$	585.775	−	1802.83i	0.716982	−	2.20665i
$818$	−361.712	−	1113.24i	−0.442191	−	1.36092i
$819$		0			0
$820$	14.8262	+	20.4065i	0.0180807	+	0.0248859i
$821$	555.042	−	180.344i	0.676056	−	0.219664i	0.0491884	−	0.998790i	$-0.484337\pi$
$821$	555.042	−	180.344i	0.676056	−	0.219664i	0.626868	+	0.779125i	$0.284337\pi$
$822$		0			0
$823$	−0.221929	−	0.161241i	−0.000269659	−	0.000195918i	0.587650	−	0.809115i	$-0.300053\pi$
$823$	−0.221929	−	0.161241i	−0.000269659	−	0.000195918i	−0.587920	+	0.808919i	$0.700053\pi$
$824$		−	88.0541i		−	0.106862i
$825$		0			0
$826$	−2347.77			−2.84234
$827$	870.734	−	1198.46i	1.05288	−	1.44917i	0.166599	−	0.986025i	$-0.446721\pi$
$827$	870.734	−	1198.46i	1.05288	−	1.44917i	0.886283	−	0.463144i	$-0.153279\pi$
$828$		0			0
$829$	−218.705	−	673.104i	−0.263818	−	0.811947i	−0.991963	−	0.126525i	$-0.959618\pi$
$829$	−218.705	−	673.104i	−0.263818	−	0.811947i	0.728146	−	0.685422i	$-0.240382\pi$
$830$	119.394	−	86.7450i	0.143848	−	0.104512i
$831$		0			0
$832$	−452.761	+	147.111i	−0.544184	+	0.176816i
$833$	1131.93	+	367.787i	1.35886	+	0.441521i
$834$		0			0
$835$		−	85.1315i		−	0.101954i
$836$	681.423	−	1118.07i	0.815099	−	1.33740i
$837$		0			0
$838$	−1066.11	+	1467.37i	−1.27220	+	1.75104i
$839$	417.229	−	1284.10i	0.497293	−	1.53051i	−0.316060	−	0.948739i	$-0.602360\pi$
$839$	417.229	−	1284.10i	0.497293	−	1.53051i	0.813353	−	0.581770i	$-0.197640\pi$
$840$		0			0
$841$	897.826	−	652.309i	1.06757	−	0.775635i
$842$	1025.88	+	1412.00i	1.21838	+	1.67696i
$843$		0			0
$844$	137.251	+	44.5956i	0.162620	+	0.0528384i
$845$	−45.4776	−	33.0414i	−0.0538196	−	0.0391022i
$846$		0			0
$847$	−909.786	−	900.985i	−1.07413	−	1.06374i
$848$	565.192			0.666499
$849$		0			0
$850$	417.874	−	1286.08i	0.491617	−	1.51304i
$851$	1.65896	+	5.10577i	0.00194943	+	0.00599972i
$852$		0			0
$853$	251.385	+	346.002i	0.294707	+	0.405630i	0.930536	−	0.366200i	$-0.119341\pi$
$853$	251.385	+	346.002i	0.294707	+	0.405630i	−0.635829	+	0.771830i	$0.719341\pi$
$854$	−832.199	+	270.398i	−0.974472	+	0.316625i
$855$		0			0
$856$	23.0689	+	16.7605i	0.0269496	+	0.0195800i
$857$		−	281.918i		−	0.328959i	−0.986380	−	0.164480i	$-0.947405\pi$
$857$		−	281.918i		−	0.328959i	0.986380	−	0.164480i	$-0.0525945\pi$
$858$		0			0
$859$	1367.66			1.59215			0.796075	−	0.605198i	$-0.206906\pi$
$859$	1367.66			1.59215			0.796075	+	0.605198i	$0.206906\pi$
$860$	−77.1100	+	106.133i	−0.0896628	+	0.123410i
$861$		0			0
$862$	647.314	+	1992.23i	0.750944	+	2.31117i
$863$	925.535	−	672.440i	1.07246	−	0.779189i	0.0961090	−	0.995371i	$-0.469360\pi$
$863$	925.535	−	672.440i	1.07246	−	0.779189i	0.976353	+	0.216181i	$0.0693603\pi$
$864$		0			0
$865$	36.9643	−	12.0104i	0.0427333	−	0.0138849i
$866$	644.424	+	209.386i	0.744139	+	0.241785i
$867$		0			0
$868$			1239.41i			1.42789i
$869$	−956.910	+	399.092i	−1.10116	+	0.459255i
$870$		0			0
$871$	−295.952	+	407.342i	−0.339784	+	0.467672i
$872$	22.6968	−	69.8536i	0.0260285	−	0.0801073i
$873$		0			0
$874$	−404.511	+	293.894i	−0.462827	+	0.336264i
$875$	136.655	+	188.090i	0.156177	+	0.214960i
$876$		0			0
$877$	423.966	+	137.755i	0.483427	+	0.157075i	0.540584	−	0.841290i	$-0.318203\pi$
$877$	423.966	+	137.755i	0.483427	+	0.157075i	−0.0571564	+	0.998365i	$0.518203\pi$
$878$	332.548	+	241.610i	0.378756	+	0.275182i
$879$		0			0
$880$	53.8000	−	46.1761i	0.0611363	−	0.0524728i
$881$	−1122.27			−1.27386			−0.636931	−	0.770921i	$-0.719796\pi$
$881$	−1122.27			−1.27386			−0.636931	+	0.770921i	$0.719796\pi$
$882$		0			0
$883$	−2.59782	+	7.99526i	−0.00294204	+	0.00905465i	−0.952517	−	0.304486i	$-0.901515\pi$
$883$	−2.59782	+	7.99526i	−0.00294204	+	0.00905465i	0.949575	+	0.313541i	$0.101515\pi$
$884$	−162.707	−	500.761i	−0.184058	−	0.566472i
$885$		0			0
$886$	−661.968	−	911.120i	−0.747142	−	1.02835i
$887$	−1265.50	+	411.187i	−1.42672	+	0.463570i	−0.917731	−	0.397201i	$-0.869981\pi$
$887$	−1265.50	+	411.187i	−1.42672	+	0.463570i	−0.508991	+	0.860772i	$0.669981\pi$
$888$		0			0
$889$	1213.47	+	881.638i	1.36498	+	0.991719i
$890$			83.0667i			0.0933334i
$891$		0			0
$892$	1603.12			1.79722
$893$	−261.284	+	359.627i	−0.292591	+	0.402717i
$894$		0			0
$895$	−43.2514	−	133.114i	−0.0483256	−	0.148731i
$896$	−253.163	+	183.934i	−0.282548	+	0.205283i
$897$		0			0
$898$	−1966.39	+	638.920i	−2.18975	+	0.711493i
$899$	−1138.50	−	369.920i	−1.26640	−	0.411479i
$900$		0			0
$901$			731.021i			0.811344i
$902$	418.494	−	33.9597i	0.463962	−	0.0376493i
$903$		0			0
$904$	14.4248	−	19.8540i	0.0159566	−	0.0219624i
$905$	−2.08285	+	6.41036i	−0.00230149	+	0.00708327i
$906$		0			0
$907$	−29.1817	+	21.2018i	−0.0321739	+	0.0233757i	−0.603756	−	0.797169i	$-0.706330\pi$
$907$	−29.1817	+	21.2018i	−0.0321739	+	0.0233757i	0.571582	+	0.820545i	$0.306330\pi$
$908$	289.959	+	399.095i	0.319338	+	0.439532i
$909$		0			0
$910$	82.5691	+	26.8283i	0.0907352	+	0.0294817i
$911$	1219.04	+	885.686i	1.33814	+	0.972213i	0.999510	+	0.0312916i	$0.00996207\pi$
$911$	1219.04	+	885.686i	1.33814	+	0.972213i	0.338626	+	0.940921i	$0.390038\pi$
$912$		0			0
$913$	−103.183	−	1271.55i	−0.113015	−	1.39271i
$914$	−549.403			−0.601098
$915$		0			0
$916$	71.6411	−	220.489i	0.0782108	−	0.240708i
$917$	302.897	+	932.222i	0.330313	+	1.01660i
$918$		0			0
$919$	264.444	+	363.976i	0.287752	+	0.396056i	0.928282	−	0.371876i	$-0.121285\pi$
$919$	264.444	+	363.976i	0.287752	+	0.396056i	−0.640530	+	0.767933i	$0.721285\pi$
$920$	2.44754	−	0.795255i	0.00266037	−	0.000864408i
$921$		0			0
$922$	2001.72	+	1454.34i	2.17107	+	1.57737i
$923$			174.848i			0.189435i
$924$		0			0
$925$	21.1626			0.0228785
$926$	56.7691	−	78.1359i	0.0613057	−	0.0843800i
$927$		0			0
$928$	−625.880	−	1926.26i	−0.674440	−	2.07571i
$929$	−148.944	+	108.214i	−0.160327	+	0.116484i	−0.665056	−	0.746794i	$-0.731592\pi$
$929$	−148.944	+	108.214i	−0.160327	+	0.116484i	0.504729	+	0.863278i	$0.331592\pi$
$930$		0			0
$931$	−1649.85	+	536.068i	−1.77212	+	0.575798i
$932$	−797.153	−	259.011i	−0.855314	−	0.277908i
$933$		0			0
$934$		−	759.677i		−	0.813359i
$935$	59.7243	+	69.5851i	0.0638763	+	0.0744226i
$936$		0			0
$937$	−233.446	+	321.311i	−0.249142	+	0.342914i	−0.915211	−	0.402976i	$-0.867976\pi$
$937$	−233.446	+	321.311i	−0.249142	+	0.342914i	0.666069	+	0.745890i	$0.267976\pi$
$938$	−736.662	+	2267.21i	−0.785354	+	2.41707i
$939$		0			0
$940$	24.8883	−	18.0824i	0.0264769	−	0.0192366i
$941$	566.846	+	780.197i	0.602387	+	0.829115i	0.995924	−	0.0901939i	$-0.0287487\pi$
$941$	566.846	+	780.197i	0.602387	+	0.829115i	−0.393537	+	0.919309i	$0.628749\pi$
$942$		0			0
$943$	−79.1885	−	25.7299i	−0.0839751	−	0.0272852i
$944$	−909.143	−	660.531i	−0.963076	−	0.699715i
$945$		0			0
$946$	840.573	+	2015.46i	0.888555	+	2.13050i
$947$	−154.326			−0.162963			−0.0814815	−	0.996675i	$-0.525965\pi$
$947$	−154.326			−0.162963			−0.0814815	+	0.996675i	$0.525965\pi$
$948$		0			0
$949$	−25.8621	+	79.5954i	−0.0272520	+	0.0838730i
$950$	609.073	+	1874.53i	0.641129	+	1.97319i
$951$		0			0
$952$	−108.977	−	149.994i	−0.114472	−	0.157557i
$953$	663.494	−	215.582i	0.696216	−	0.226214i	0.0605349	−	0.998166i	$-0.480719\pi$
$953$	663.494	−	215.582i	0.696216	−	0.226214i	0.635681	+	0.771952i	$0.280719\pi$
$954$		0			0
$955$	7.30564	+	5.30785i	0.00764988	+	0.00555796i
$956$			648.838i			0.678701i
$957$		0			0
$958$	−1774.45			−1.85225
$959$	136.376	−	187.705i	0.142206	−	0.195730i
$960$		0			0
$961$	−69.9651	−	215.330i	−0.0728044	−	0.224069i
$962$	12.8369	−	9.32655i	0.0133440	−	0.00969496i
$963$		0			0
$964$	555.360	−	180.447i	0.576099	−	0.187186i
$965$	−79.3921	−	25.7961i	−0.0822717	−	0.0267317i
$966$		0			0
$967$			1569.06i			1.62260i	0.584627	+	0.811302i	$0.301241\pi$
$967$			1569.06i			1.62260i	−0.584627	+	0.811302i	$0.698759\pi$
$968$	18.0871	+	110.712i	0.0186850	+	0.114372i
$969$		0			0
$970$	52.5812	−	72.3719i	0.0542075	−	0.0746102i
$971$	382.910	−	1178.48i	0.394346	−	1.21367i	−0.535123	−	0.844774i	$-0.679735\pi$
$971$	382.910	−	1178.48i	0.394346	−	1.21367i	0.929469	−	0.368899i	$-0.120265\pi$
$972$		0			0
$973$	1623.64	−	1179.64i	1.66870	−	1.21238i
$974$	505.942	+	696.369i	0.519447	+	0.714958i
$975$		0			0
$976$	−398.332	−	129.426i	−0.408127	−	0.132609i
$977$	57.7334	+	41.9457i	0.0590925	+	0.0429332i	0.616939	−	0.787011i	$-0.288372\pi$
$977$	57.7334	+	41.9457i	0.0590925	+	0.0429332i	−0.557847	+	0.829944i	$0.688372\pi$
$978$		0			0
$979$	613.154	+	373.695i	0.626307	+	0.381711i
$980$	120.055			0.122505
$981$		0			0
$982$	−415.174	+	1277.77i	−0.422784	+	1.30119i
$983$	90.9553	+	279.932i	0.0925283	+	0.284773i	0.986602	−	0.163148i	$-0.0521647\pi$
$983$	90.9553	+	279.932i	0.0925283	+	0.284773i	−0.894073	+	0.447921i	$0.852165\pi$
$984$		0			0
$985$	98.7509	+	135.919i	0.100255	+	0.137989i
$986$	2289.95	−	744.051i	2.32247	−	0.754615i
$987$		0			0
$988$	620.877	+	451.094i	0.628418	+	0.456572i
$989$		−	433.050i		−	0.437867i
$990$		0			0
$991$	1230.78			1.24195			0.620977	−	0.783829i	$-0.286736\pi$
$991$	1230.78			1.24195			0.620977	+	0.783829i	$0.286736\pi$
$992$	−730.543	+	1005.51i	−0.736435	+	1.01362i
$993$		0			0
$994$	255.816	+	787.320i	0.257360	+	0.792073i
$995$	−104.205	+	75.7092i	−0.104728	+	0.0760896i
$996$		0			0
$997$	153.358	−	49.8292i	0.153820	−	0.0499791i	−0.231095	−	0.972931i	$-0.574231\pi$
$997$	153.358	−	49.8292i	0.153820	−	0.0499791i	0.384915	+	0.922952i	$0.374231\pi$
$998$	−1497.60	−	486.598i	−1.50060	−	0.487574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.c.73.1		16
3.2	odd	2		33.3.g.a.7.4	✓	16
11.5	even	5		1089.3.c.m.604.2		16
11.6	odd	10		1089.3.c.m.604.15		16
11.8	odd	10	inner	99.3.k.c.19.1		16
12.11	even	2		528.3.bf.b.337.4		16
33.2	even	10		363.3.g.g.94.4		16
33.5	odd	10		363.3.c.e.241.15		16
33.8	even	10		33.3.g.a.19.4	yes	16
33.14	odd	10		363.3.g.f.118.1		16
33.17	even	10		363.3.c.e.241.2		16
33.20	odd	10		363.3.g.a.94.1		16
33.26	odd	10		363.3.g.g.112.4		16
33.29	even	10		363.3.g.a.112.1		16
33.32	even	2		363.3.g.f.40.1		16
132.107	odd	10		528.3.bf.b.481.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.7.4	✓	16	3.2	odd	2
33.3.g.a.19.4	yes	16	33.8	even	10
99.3.k.c.19.1		16	11.8	odd	10	inner
99.3.k.c.73.1		16	1.1	even	1	trivial
363.3.c.e.241.2		16	33.17	even	10
363.3.c.e.241.15		16	33.5	odd	10
363.3.g.a.94.1		16	33.20	odd	10
363.3.g.a.112.1		16	33.29	even	10
363.3.g.f.40.1		16	33.32	even	2
363.3.g.f.118.1		16	33.14	odd	10
363.3.g.g.94.4		16	33.2	even	10
363.3.g.g.112.4		16	33.26	odd	10
528.3.bf.b.337.4		16	12.11	even	2
528.3.bf.b.481.4		16	132.107	odd	10
1089.3.c.m.604.2		16	11.5	even	5
1089.3.c.m.604.15		16	11.6	odd	10

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)

\(f(q)\)	\(=\)	\(q+(-1.69557 + 2.33376i) q^{2} +(-1.33538 - 4.10989i) q^{4} +(-0.356879 + 0.259287i) q^{5} +(-10.0641 + 3.27002i) q^{7} +(0.881730 + 0.286491i) q^{8} +O(q^{10})\)	\(q+(-1.69557 + 2.33376i) q^{2} +(-1.33538 - 4.10989i) q^{4} +(-0.356879 + 0.259287i) q^{5} +(-10.0641 + 3.27002i) q^{7} +(0.881730 + 0.286491i) q^{8} -1.27251i q^{10} +(-9.39298 - 5.72468i) q^{11} +(3.78967 - 5.21603i) q^{13} +(9.43297 - 29.0317i) q^{14} +(11.8207 - 8.58822i) q^{16} +(11.1080 + 15.2889i) q^{17} +(-26.1968 - 8.51187i) q^{19} +(1.54221 + 1.12048i) q^{20} +(29.2865 - 12.2143i) q^{22} -6.29263 q^{23} +(-7.66529 + 23.5913i) q^{25} +(5.74728 + 17.6883i) q^{26} +(26.8788 + 36.9955i) q^{28} +(-42.0059 + 13.6485i) q^{29} +(21.9270 + 15.9309i) q^{31} +45.8569i q^{32} -54.5151 q^{34} +(2.74378 - 3.77649i) q^{35} +(-0.263636 - 0.811388i) q^{37} +(64.2833 - 46.7045i) q^{38} +(-0.388954 + 0.126379i) q^{40} +(12.5843 + 4.08890i) q^{41} +68.8186i q^{43} +(-10.9845 + 46.2487i) q^{44} +(10.6696 - 14.6855i) q^{46} +(4.98694 - 15.3482i) q^{47} +(50.9510 - 37.0181i) q^{49} +(-42.0594 - 57.8898i) q^{50} +(-26.4979 - 8.60970i) q^{52} +(31.2946 + 22.7368i) q^{53} +(4.83649 - 0.392468i) q^{55} -9.81064 q^{56} +(39.3717 - 121.174i) q^{58} +(-23.7669 - 73.1470i) q^{59} +(-16.8490 - 23.1906i) q^{61} +(-74.3578 + 24.1603i) q^{62} +(-59.7363 - 43.4009i) q^{64} +2.84410i q^{65} -78.0944 q^{67} +(48.0022 - 66.0693i) q^{68} +(4.16113 + 12.8066i) q^{70} +(-21.9400 + 15.9403i) q^{71} +(-12.3454 + 4.01127i) q^{73} +(2.34060 + 0.760506i) q^{74} +119.033i q^{76} +(113.252 + 26.8984i) q^{77} +(55.4014 - 76.2534i) q^{79} +(-1.99173 + 6.12990i) q^{80} +(-30.8801 + 22.4357i) q^{82} +(68.1685 + 93.8258i) q^{83} +(-7.92844 - 2.57611i) q^{85} +(-160.606 - 116.687i) q^{86} +(-6.64200 - 7.73862i) q^{88} -65.2779 q^{89} +(-21.0830 + 64.8868i) q^{91} +(8.40307 + 25.8620i) q^{92} +(27.3633 + 37.6623i) q^{94} +(11.5561 - 3.75481i) q^{95} +(56.8734 + 41.3209i) q^{97} +181.674i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) 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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