LMFDB - Embedded newform 99.3.k.c.28.2

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			28.2
Root			$0.988132 - 0.846795i$ of defining polynomial
Character	$\chi$	$=$	99.28
Dual form			99.3.k.c.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28981 + 0.419086i) q^{2} +(-1.74808 + 1.27006i) q^{4} +(-0.708979 + 2.18201i) q^{5} +(-5.74346 - 7.90520i) q^{7} +(4.91103 - 6.75946i) q^{8} +O(q^{10})$	\(q+(-1.28981 + 0.419086i) q^{2} +(-1.74808 + 1.27006i) q^{4} +(-0.708979 + 2.18201i) q^{5} +(-5.74346 - 7.90520i) q^{7} +(4.91103 - 6.75946i) q^{8} -3.11151i q^{10} +(-10.3340 - 3.76954i) q^{11} +(-14.6363 + 4.75561i) q^{13} +(10.7210 + 7.78923i) q^{14} +(-0.830695 + 2.55662i) q^{16} +(-11.2386 - 3.65165i) q^{17} +(7.10329 - 9.77683i) q^{19} +(-1.53192 - 4.71477i) q^{20} +(14.9086 + 0.531195i) q^{22} -16.6610 q^{23} +(15.9669 + 11.6006i) q^{25} +(16.8850 - 12.2677i) q^{26} +(20.0801 + 6.52441i) q^{28} +(15.6013 + 21.4734i) q^{29} +(1.28594 + 3.95770i) q^{31} +29.7749i q^{32} +16.0261 q^{34} +(21.3212 - 6.92769i) q^{35} +(-54.4646 + 39.5709i) q^{37} +(-5.06458 + 15.5872i) q^{38} +(11.2674 + 15.5082i) q^{40} +(10.6080 - 14.6006i) q^{41} -46.3735i q^{43} +(22.8521 - 6.53522i) q^{44} +(21.4896 - 6.98238i) q^{46} +(49.2812 + 35.8049i) q^{47} +(-14.3630 + 44.2047i) q^{49} +(-25.4560 - 8.27115i) q^{50} +(19.5455 - 26.9020i) q^{52} +(-31.2773 - 96.2616i) q^{53} +(15.5517 - 19.8763i) q^{55} -81.6412 q^{56} +(-29.1220 - 21.1584i) q^{58} +(-78.7122 + 57.1878i) q^{59} +(1.19706 + 0.388949i) q^{61} +(-3.31724 - 4.56578i) q^{62} +(-15.8010 - 48.6305i) q^{64} -35.3081i q^{65} -55.1168 q^{67} +(24.2838 - 7.89030i) q^{68} +(-24.5971 + 17.8709i) q^{70} +(4.62167 - 14.2240i) q^{71} +(-44.6021 - 61.3895i) q^{73} +(53.6656 - 73.8644i) q^{74} +26.1123i q^{76} +(29.5537 + 103.342i) q^{77} +(27.7900 - 9.02950i) q^{79} +(-4.98962 - 3.62517i) q^{80} +(-7.56341 + 23.2778i) q^{82} +(6.06044 + 1.96915i) q^{83} +(15.9359 - 21.9339i) q^{85} +(19.4345 + 59.8133i) q^{86} +(-76.2304 + 51.3395i) q^{88} +3.95503 q^{89} +(121.657 + 88.3889i) q^{91} +(29.1247 - 21.1604i) q^{92} +(-78.5689 - 25.5286i) q^{94} +(16.2971 + 22.4310i) q^{95} +(-10.2392 - 31.5131i) q^{97} -63.0352i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.28981	+	0.419086i	−0.644907	+	0.209543i	−0.613167	−	0.789953i	$-0.710105\pi$
$2$	−1.28981	+	0.419086i	−0.644907	+	0.209543i	−0.0317398	+	0.999496i	$0.510105\pi$
$3$		0			0
$3$		0			0
$4$	−1.74808	+	1.27006i	−0.437020	+	0.317514i
$5$	−0.708979	+	2.18201i	−0.141796	+	0.436402i	−0.996585	−	0.0825729i	$-0.973686\pi$
$5$	−0.708979	+	2.18201i	−0.141796	+	0.436402i	0.854789	+	0.518975i	$0.173686\pi$
$6$		0			0
$7$	−5.74346	−	7.90520i	−0.820495	−	1.12931i	−0.989618	−	0.143720i	$-0.954094\pi$
$7$	−5.74346	−	7.90520i	−0.820495	−	1.12931i	0.169123	−	0.985595i	$-0.445906\pi$
$8$	4.91103	−	6.75946i	0.613879	−	0.844932i
$9$		0			0
$10$		−	3.11151i		−	0.311151i
$11$	−10.3340	−	3.76954i	−0.939450	−	0.342686i
$11$	−10.3340	−	3.76954i	−0.939450	−	0.342686i
$12$		0			0
$13$	−14.6363	+	4.75561i	−1.12587	+	0.365816i	−0.812004	−	0.583652i	$-0.801623\pi$
$13$	−14.6363	+	4.75561i	−1.12587	+	0.365816i	−0.313862	+	0.949468i	$0.601623\pi$
$14$	10.7210	+	7.78923i	0.765783	+	0.556374i
$15$		0			0
$16$	−0.830695	+	2.55662i	−0.0519184	+	0.159789i
$17$	−11.2386	−	3.65165i	−0.661096	−	0.214803i	−0.0407956	−	0.999168i	$-0.512989\pi$
$17$	−11.2386	−	3.65165i	−0.661096	−	0.214803i	−0.620300	+	0.784364i	$0.712989\pi$
$18$		0			0
$19$	7.10329	−	9.77683i	0.373857	−	0.514570i	−0.580087	−	0.814555i	$-0.696981\pi$
$19$	7.10329	−	9.77683i	0.373857	−	0.514570i	0.953944	+	0.299984i	$0.0969814\pi$
$20$	−1.53192	−	4.71477i	−0.0765962	−	0.235739i
$21$		0			0
$22$	14.9086	+	0.531195i	0.677665	+	0.0241452i
$23$	−16.6610			−0.724390			−0.362195	−	0.932102i	$-0.617973\pi$
$23$	−16.6610			−0.724390			−0.362195	+	0.932102i	$0.617973\pi$
$24$		0			0
$25$	15.9669	+	11.6006i	0.638676	+	0.464025i
$26$	16.8850	−	12.2677i	0.649425	−	0.471835i
$27$		0			0
$28$	20.0801	+	6.52441i	0.717146	+	0.233015i
$29$	15.6013	+	21.4734i	0.537977	+	0.740462i	0.988320	−	0.152394i	$-0.0486981\pi$
$29$	15.6013	+	21.4734i	0.537977	+	0.740462i	−0.450343	+	0.892856i	$0.648698\pi$
$30$		0			0
$31$	1.28594	+	3.95770i	0.0414818	+	0.127668i	0.969653	−	0.244486i	$-0.0786193\pi$
$31$	1.28594	+	3.95770i	0.0414818	+	0.127668i	−0.928171	+	0.372154i	$0.878619\pi$
$32$			29.7749i			0.930466i
$33$		0			0
$34$	16.0261			0.471356
$35$	21.3212	−	6.92769i	0.609178	−	0.197934i
$36$		0			0
$37$	−54.4646	+	39.5709i	−1.47202	+	1.06948i	−0.491994	+	0.870599i	$0.663732\pi$
$37$	−54.4646	+	39.5709i	−1.47202	+	1.06948i	−0.980023	+	0.198884i	$0.936268\pi$
$38$	−5.06458	+	15.5872i	−0.133279	+	0.410189i
$39$		0			0
$40$	11.2674	+	15.5082i	0.281685	+	0.387706i
$41$	10.6080	−	14.6006i	0.258731	−	0.356113i	−0.659814	−	0.751429i	$-0.729365\pi$
$41$	10.6080	−	14.6006i	0.258731	−	0.356113i	0.918545	+	0.395316i	$0.129365\pi$
$42$		0			0
$43$		−	46.3735i		−	1.07845i	−0.842160	−	0.539227i	$-0.818716\pi$
$43$		−	46.3735i		−	1.07845i	0.842160	−	0.539227i	$-0.181284\pi$
$44$	22.8521	−	6.53522i	0.519366	−	0.148528i
$45$		0			0
$46$	21.4896	−	6.98238i	0.467164	−	0.151791i
$47$	49.2812	+	35.8049i	1.04854	+	0.761806i	0.971934	−	0.235255i	$-0.0755926\pi$
$47$	49.2812	+	35.8049i	1.04854	+	0.761806i	0.0766030	+	0.997062i	$0.475593\pi$
$48$		0			0
$49$	−14.3630	+	44.2047i	−0.293122	+	0.902137i
$50$	−25.4560	−	8.27115i	−0.509120	−	0.165423i
$51$		0			0
$52$	19.5455	−	26.9020i	0.375875	−	0.517347i
$53$	−31.2773	−	96.2616i	−0.590138	−	1.81626i	−0.577578	−	0.816335i	$-0.696002\pi$
$53$	−31.2773	−	96.2616i	−0.590138	−	1.81626i	−0.0125594	−	0.999921i	$-0.503998\pi$
$54$		0			0
$55$	15.5517	−	19.8763i	0.282759	−	0.361387i
$56$	−81.6412			−1.45788
$57$		0			0
$58$	−29.1220	−	21.1584i	−0.502104	−	0.364800i
$59$	−78.7122	+	57.1878i	−1.33411	+	0.969284i	−0.334467	+	0.942408i	$0.608556\pi$
$59$	−78.7122	+	57.1878i	−1.33411	+	0.969284i	−0.999639	+	0.0268769i	$0.991444\pi$
$60$		0			0
$61$	1.19706	+	0.388949i	0.0196240	+	0.00637621i	0.318813	−	0.947818i	$-0.396716\pi$
$61$	1.19706	+	0.388949i	0.0196240	+	0.00637621i	−0.299189	+	0.954194i	$0.596716\pi$
$62$	−3.31724	−	4.56578i	−0.0535038	−	0.0736416i
$63$		0			0
$64$	−15.8010	−	48.6305i	−0.246891	−	0.759852i
$65$		−	35.3081i		−	0.543202i
$66$		0			0
$67$	−55.1168			−0.822638			−0.411319	−	0.911491i	$-0.634932\pi$
$67$	−55.1168			−0.822638			−0.411319	+	0.911491i	$0.634932\pi$
$68$	24.2838	−	7.89030i	0.357115	−	0.116034i
$69$		0			0
$70$	−24.5971	+	17.8709i	−0.351388	+	0.255298i
$71$	4.62167	−	14.2240i	0.0650939	−	0.200338i	−0.913220	−	0.407467i	$-0.866412\pi$
$71$	4.62167	−	14.2240i	0.0650939	−	0.200338i	0.978314	+	0.207129i	$0.0664120\pi$
$72$		0			0
$73$	−44.6021	−	61.3895i	−0.610987	−	0.840952i	0.385671	−	0.922636i	$-0.373970\pi$
$73$	−44.6021	−	61.3895i	−0.610987	−	0.840952i	−0.996658	+	0.0816847i	$0.973970\pi$
$74$	53.6656	−	73.8644i	0.725211	−	0.998168i
$75$		0			0
$76$			26.1123i			0.343582i
$77$	29.5537	+	103.342i	0.383814	+	1.34211i
$78$		0			0
$79$	27.7900	−	9.02950i	0.351772	−	0.114298i	−0.127801	−	0.991800i	$-0.540792\pi$
$79$	27.7900	−	9.02950i	0.351772	−	0.114298i	0.479572	+	0.877502i	$0.340792\pi$
$80$	−4.98962	−	3.62517i	−0.0623703	−	0.0453147i
$81$		0			0
$82$	−7.56341	+	23.2778i	−0.0922367	+	0.283875i
$83$	6.06044	+	1.96915i	0.0730173	+	0.0237248i	0.345298	−	0.938493i	$-0.387778\pi$
$83$	6.06044	+	1.96915i	0.0730173	+	0.0237248i	−0.272281	+	0.962218i	$0.587778\pi$
$84$		0			0
$85$	15.9359	−	21.9339i	0.187481	−	0.258046i
$86$	19.4345	+	59.8133i	0.225983	+	0.695503i
$87$		0			0
$88$	−76.2304	+	51.3395i	−0.866255	+	0.583404i
$89$	3.95503			0.0444385			0.0222193	−	0.999753i	$-0.492927\pi$
$89$	3.95503			0.0444385			0.0222193	+	0.999753i	$0.492927\pi$
$90$		0			0
$91$	121.657	+	88.3889i	1.33689	+	0.971306i
$92$	29.1247	−	21.1604i	0.316573	−	0.230004i
$93$		0			0
$94$	−78.5689	−	25.5286i	−0.835840	−	0.271581i
$95$	16.2971	+	22.4310i	0.171548	+	0.236116i
$96$		0			0
$97$	−10.2392	−	31.5131i	−0.105559	−	0.324877i	0.884302	−	0.466915i	$-0.154635\pi$
$97$	−10.2392	−	31.5131i	−0.105559	−	0.324877i	−0.989861	+	0.142038i	$0.954635\pi$
$98$		−	63.0352i		−	0.643216i
$99$		0			0
$100$	−42.6449			−0.426449
$101$	−92.3279	+	29.9992i	−0.914138	+	0.297021i	−0.728060	−	0.685514i	$-0.759578\pi$
$101$	−92.3279	+	29.9992i	−0.914138	+	0.297021i	−0.186078	+	0.982535i	$0.559578\pi$
$102$		0			0
$103$	150.522	−	109.361i	1.46138	−	1.06175i	0.478380	−	0.878153i	$-0.341224\pi$
$103$	150.522	−	109.361i	1.46138	−	1.06175i	0.983001	−	0.183602i	$-0.0587757\pi$
$104$	−39.7338	+	122.288i	−0.382056	+	1.17585i
$105$		0			0
$106$	80.6838	+	111.052i	0.761168	+	1.04766i
$107$	112.786	−	155.236i	1.05407	−	1.45081i	0.168849	−	0.985642i	$-0.445995\pi$
$107$	112.786	−	155.236i	1.05407	−	1.45081i	0.885224	−	0.465165i	$-0.154005\pi$
$108$		0			0
$109$			113.760i			1.04367i	0.853047	+	0.521834i	$0.174752\pi$
$109$			113.760i			1.04367i	−0.853047	+	0.521834i	$0.825248\pi$
$110$	−11.7290	+	32.1542i	−0.106627	+	0.292311i
$111$		0			0
$112$	24.9816	−	8.11703i	0.223050	−	0.0724734i
$113$	13.2504	+	9.62696i	0.117260	+	0.0851944i	0.644870	−	0.764293i	$-0.276912\pi$
$113$	13.2504	+	9.62696i	0.117260	+	0.0851944i	−0.527610	+	0.849487i	$0.676912\pi$
$114$		0			0
$115$	11.8123	−	36.3544i	0.102715	−	0.316125i
$116$	−54.5448	−	17.7227i	−0.470214	−	0.152782i
$117$		0			0
$118$	77.5575	−	106.749i	0.657267	−	0.904651i
$119$	35.6816	+	109.817i	0.299846	+	0.922830i
$120$		0			0
$121$	92.5811	+	77.9085i	0.765133	+	0.643872i
$122$	−1.70699			−0.0139917
$123$		0			0
$124$	−7.27442	−	5.28518i	−0.0586647	−	0.0426224i
$125$	−83.0361	+	60.3293i	−0.664289	+	0.482634i
$126$		0			0
$127$	5.31423	+	1.72670i	0.0418443	+	0.0135960i	0.329864	−	0.944028i	$-0.392997\pi$
$127$	5.31423	+	1.72670i	0.0418443	+	0.0135960i	−0.288020	+	0.957624i	$0.592997\pi$
$128$	−29.2442	−	40.2512i	−0.228471	−	0.314463i
$129$		0			0
$130$	14.7971	+	45.5409i	0.113824	+	0.350315i
$131$		−	225.713i		−	1.72300i	−0.507758	−	0.861500i	$-0.669526\pi$
$131$		−	225.713i		−	1.72300i	0.507758	−	0.861500i	$-0.330474\pi$
$132$		0			0
$133$	−118.085			−0.887860
$134$	71.0904	−	23.0987i	0.530525	−	0.172378i
$135$		0			0
$136$	−79.8765	+	58.0336i	−0.587327	+	0.426718i
$137$	−16.1770	+	49.7877i	−0.118080	+	0.363414i	−0.992577	−	0.121618i	$-0.961192\pi$
$137$	−16.1770	+	49.7877i	−0.118080	+	0.363414i	0.874497	+	0.485031i	$0.161192\pi$
$138$		0			0
$139$	16.4968	+	22.7058i	0.118682	+	0.163351i	0.864224	−	0.503106i	$-0.167810\pi$
$139$	16.4968	+	22.7058i	0.118682	+	0.163351i	−0.745543	+	0.666458i	$0.767810\pi$
$140$	−28.4727	+	39.1893i	−0.203376	+	0.279924i
$141$		0			0
$142$			20.2832i			0.142840i
$143$	169.177	+	6.02777i	1.18305	+	0.0421523i
$144$		0			0
$145$	−57.9162	+	18.8181i	−0.399422	+	0.129780i
$146$	83.2558	+	60.4889i	0.570245	+	0.414308i
$147$		0			0
$148$	44.9514	−	138.346i	0.303726	−	0.934771i
$149$	−10.6920	−	3.47406i	−0.0717587	−	0.0233158i	0.272918	−	0.962037i	$-0.412011\pi$
$149$	−10.6920	−	3.47406i	−0.0717587	−	0.0233158i	−0.344676	+	0.938722i	$0.612011\pi$
$150$		0			0
$151$	−59.4636	+	81.8446i	−0.393799	+	0.542018i	−0.959174	−	0.282816i	$-0.908731\pi$
$151$	−59.4636	+	81.8446i	−0.393799	+	0.542018i	0.565375	+	0.824834i	$0.308731\pi$
$152$	−31.2016	−	96.0287i	−0.205274	−	0.631768i
$153$		0			0
$154$	−81.4280	−	120.907i	−0.528753	−	0.785108i
$155$	−9.54745			−0.0615965
$156$		0			0
$157$	−15.4295	−	11.2102i	−0.0982772	−	0.0714025i	0.537561	−	0.843225i	$-0.319346\pi$
$157$	−15.4295	−	11.2102i	−0.0982772	−	0.0714025i	−0.635839	+	0.771822i	$0.719346\pi$
$158$	−32.0597	+	23.2928i	−0.202910	+	0.147423i
$159$		0			0
$160$	−64.9692	−	21.1098i	−0.406057	−	0.131936i
$161$	95.6917	+	131.708i	0.594358	+	0.818064i
$162$		0			0
$163$	−4.46584	−	13.7444i	−0.0273978	−	0.0843217i	0.936423	−	0.350874i	$-0.114115\pi$
$163$	−4.46584	−	13.7444i	−0.0273978	−	0.0843217i	−0.963820	+	0.266552i	$0.914115\pi$
$164$			38.9958i			0.237779i
$165$		0			0
$166$	−8.64208			−0.0520607
$167$	−125.427	+	40.7538i	−0.751062	+	0.244035i	−0.659438	−	0.751759i	$-0.729206\pi$
$167$	−125.427	+	40.7538i	−0.751062	+	0.244035i	−0.0916237	+	0.995794i	$0.529206\pi$
$168$		0			0
$169$	54.8803	−	39.8729i	0.324736	−	0.235934i
$170$	−11.3622	+	34.9691i	−0.0668362	+	0.205701i
$171$		0			0
$172$	58.8970	+	81.0647i	0.342424	+	0.471306i
$173$	20.6503	−	28.4227i	0.119366	−	0.164293i	−0.745153	−	0.666894i	$-0.767623\pi$
$173$	20.6503	−	28.4227i	0.119366	−	0.164293i	0.864519	+	0.502601i	$0.167623\pi$
$174$		0			0
$175$		−	192.849i		−	1.10200i
$176$	18.2216	−	23.2886i	0.103532	−	0.132322i
$177$		0			0
$178$	−5.10125	+	1.65750i	−0.0286587	+	0.00931178i
$179$	−146.405	−	106.370i	−0.817907	−	0.594244i	0.0982054	−	0.995166i	$-0.468690\pi$
$179$	−146.405	−	106.370i	−0.817907	−	0.594244i	−0.916112	+	0.400922i	$0.868690\pi$
$180$		0			0
$181$	6.29265	−	19.3668i	0.0347660	−	0.106999i	−0.932168	−	0.362027i	$-0.882085\pi$
$181$	6.29265	−	19.3668i	0.0347660	−	0.106999i	0.966934	+	0.255028i	$0.0820848\pi$
$182$	−193.957	−	63.0205i	−1.06570	−	0.346267i
$183$		0			0
$184$	−81.8226	+	112.619i	−0.444688	+	0.612060i
$185$	−47.7298	−	146.897i	−0.257999	−	0.794040i
$186$		0			0
$187$	102.374	+	80.1005i	0.547457	+	0.428345i
$188$	−131.622			−0.700116
$189$		0			0
$190$	−30.4207	−	22.1020i	−0.160109	−	0.116326i
$191$	48.1778	−	35.0032i	0.252240	−	0.183263i	−0.454479	−	0.890757i	$-0.650175\pi$
$191$	48.1778	−	35.0032i	0.252240	−	0.183263i	0.706719	+	0.707495i	$0.250175\pi$
$192$		0			0
$193$	−235.929	−	76.6578i	−1.22243	−	0.397191i	−0.374462	−	0.927242i	$-0.622173\pi$
$193$	−235.929	−	76.6578i	−1.22243	−	0.397191i	−0.847965	+	0.530051i	$0.822173\pi$
$194$	26.4134	+	36.3549i	0.136151	+	0.187396i
$195$		0			0
$196$	−31.0348	−	95.5152i	−0.158341	−	0.487323i
$197$			166.342i			0.844374i	0.906509	+	0.422187i	$0.138737\pi$
$197$			166.342i			0.844374i	−0.906509	+	0.422187i	$0.861263\pi$
$198$		0			0
$199$	97.9933			0.492429			0.246214	−	0.969215i	$-0.420813\pi$
$199$	97.9933			0.492429			0.246214	+	0.969215i	$0.420813\pi$
$200$	156.828	−	50.9565i	0.784140	−	0.254782i
$201$		0			0
$202$	106.514	−	77.3866i	0.527295	−	0.383102i
$203$	80.1458	−	246.664i	0.394807	−	1.21509i
$204$		0			0
$205$	24.3379	+	33.4983i	0.118722	+	0.163406i
$206$	−148.314	+	204.137i	−0.719971	+	0.990955i
$207$		0			0
$208$		−	41.3698i		−	0.198893i
$209$	−110.259	+	74.2572i	−0.527556	+	0.355298i
$210$		0			0
$211$	−11.0358	+	3.58574i	−0.0523023	+	0.0169940i	−0.335051	−	0.942200i	$-0.608754\pi$
$211$	−11.0358	+	3.58574i	−0.0523023	+	0.0169940i	0.282749	+	0.959194i	$0.408754\pi$
$212$	176.933	+	128.549i	0.834589	+	0.606364i
$213$		0			0
$214$	−80.4153	+	247.493i	−0.375773	+	1.15651i
$215$	101.188	+	32.8778i	0.470640	+	0.152920i
$216$		0			0
$217$	23.9007	−	32.8965i	0.110142	−	0.151597i
$218$	−47.6751	−	146.729i	−0.218693	−	0.673069i
$219$		0			0
$220$	−1.94172	+	54.4969i	−0.00882602	+	0.247713i
$221$	181.857			0.822884
$222$		0			0
$223$	−252.345	−	183.339i	−1.13159	−	0.822149i	−0.145666	−	0.989334i	$-0.546532\pi$
$223$	−252.345	−	183.339i	−1.13159	−	0.822149i	−0.985926	+	0.167185i	$0.946532\pi$
$224$	235.377	−	171.011i	1.05079	−	0.763442i
$225$		0			0
$226$	−21.1251	−	6.86395i	−0.0934737	−	0.0303714i
$227$	5.60519	+	7.71488i	0.0246925	+	0.0339863i	0.821185	−	0.570662i	$-0.193314\pi$
$227$	5.60519	+	7.71488i	0.0246925	+	0.0339863i	−0.796492	+	0.604649i	$0.793314\pi$
$228$		0			0
$229$	62.0564	+	190.990i	0.270989	+	0.834017i	0.990253	+	0.139281i	$0.0444791\pi$
$229$	62.0564	+	190.990i	0.270989	+	0.834017i	−0.719264	+	0.694737i	$0.755521\pi$
$230$			51.8408i			0.225395i
$231$		0			0
$232$	221.767			0.955893
$233$	−228.533	+	74.2548i	−0.980827	+	0.318690i	−0.755179	−	0.655519i	$-0.772450\pi$
$233$	−228.533	+	74.2548i	−0.980827	+	0.318690i	−0.225648	+	0.974209i	$0.572450\pi$
$234$		0			0
$235$	−113.066	+	82.1473i	−0.481132	+	0.349563i
$236$	64.9637	−	199.938i	0.275270	−	0.847194i
$237$		0			0
$238$	−92.0453	−	126.690i	−0.386745	−	0.532309i
$239$	−47.4322	+	65.2848i	−0.198461	+	0.273158i	−0.896636	−	0.442769i	$-0.853996\pi$
$239$	−47.4322	+	65.2848i	−0.198461	+	0.273158i	0.698174	+	0.715928i	$0.253996\pi$
$240$		0			0
$241$		−	153.259i		−	0.635928i	−0.948103	−	0.317964i	$-0.897001\pi$
$241$		−	153.259i		−	0.635928i	0.948103	−	0.317964i	$-0.102999\pi$
$242$	−152.063	−	61.6881i	−0.628359	−	0.254909i
$243$		0			0
$244$	−2.58655	+	0.840420i	−0.0106006	+	0.00344435i
$245$	−86.2722	−	62.6804i	−0.352131	−	0.255838i
$246$		0			0
$247$	−57.4707	+	176.877i	−0.232675	+	0.716100i
$248$	33.0672	+	10.7442i	0.133335	+	0.0433233i
$249$		0			0
$250$	81.8180	−	112.613i	0.327272	−	0.450451i
$251$	108.893	+	335.138i	0.433836	+	1.33521i	0.894275	+	0.447518i	$0.147692\pi$
$251$	108.893	+	335.138i	0.433836	+	1.33521i	−0.460439	+	0.887691i	$0.652308\pi$
$252$		0			0
$253$	172.174	+	62.8042i	0.680528	+	0.248238i
$254$	−7.57800			−0.0298347
$255$		0			0
$256$	220.059	+	159.882i	0.859605	+	0.624539i
$257$	104.897	−	76.2121i	0.408159	−	0.296545i	−0.364697	−	0.931126i	$-0.618827\pi$
$257$	104.897	−	76.2121i	0.408159	−	0.296545i	0.772856	+	0.634581i	$0.218827\pi$
$258$		0			0
$259$	625.631	+	203.280i	2.41557	+	0.784865i
$260$	44.8432	+	61.7214i	0.172474	+	0.237390i
$261$		0			0
$262$	94.5931	+	291.128i	0.361042	+	1.11117i
$263$			180.174i			0.685072i	0.939505	+	0.342536i	$0.111286\pi$
$263$			180.174i			0.685072i	−0.939505	+	0.342536i	$0.888714\pi$
$264$		0			0
$265$	232.219			0.876297
$266$	152.308	−	49.4879i	0.572587	−	0.186045i
$267$		0			0
$268$	96.3485	−	70.0013i	0.359509	−	0.261199i
$269$	−103.985	+	320.033i	−0.386561	+	1.18971i	0.548781	+	0.835966i	$0.315092\pi$
$269$	−103.985	+	320.033i	−0.386561	+	1.18971i	−0.935342	+	0.353746i	$0.884908\pi$
$270$		0			0
$271$	−129.003	−	177.557i	−0.476026	−	0.655193i	0.501709	−	0.865036i	$-0.332705\pi$
$271$	−129.003	−	177.557i	−0.476026	−	0.655193i	−0.977735	+	0.209843i	$0.932705\pi$
$272$	18.6717	−	25.6995i	0.0686461	−	0.0944833i
$273$		0			0
$274$		−	70.9964i		−	0.259111i
$275$	−121.272	−	180.068i	−0.440989	−	0.654794i
$276$		0			0
$277$	−232.844	+	75.6555i	−0.840591	+	0.273125i	−0.697500	−	0.716585i	$-0.745704\pi$
$277$	−232.844	+	75.6555i	−0.840591	+	0.273125i	−0.143091	+	0.989709i	$0.545704\pi$
$278$	−30.7934	−	22.3727i	−0.110768	−	0.0804775i
$279$		0			0
$280$	57.8819	−	178.142i	0.206721	−	0.636222i
$281$	328.343	+	106.685i	1.16848	+	0.379662i	0.828075	−	0.560617i	$-0.189436\pi$
$281$	328.343	+	106.685i	1.16848	+	0.379662i	0.340404	+	0.940279i	$0.389436\pi$
$282$		0			0
$283$	−136.711	+	188.166i	−0.483077	+	0.664898i	−0.979093	−	0.203415i	$-0.934796\pi$
$283$	−136.711	+	188.166i	−0.483077	+	0.664898i	0.496016	+	0.868313i	$0.334796\pi$
$284$	9.98625	+	30.7345i	0.0351629	+	0.108220i
$285$		0			0
$286$	−220.733	+	63.1249i	−0.771793	+	0.220717i
$287$	−176.348			−0.614452
$288$		0			0
$289$	−120.834	−	87.7908i	−0.418110	−	0.303774i
$290$	66.8148	−	48.5438i	0.230396	−	0.167392i
$291$		0			0
$292$	155.936	+	50.6667i	0.534027	+	0.173516i
$293$	−313.718	−	431.796i	−1.07071	−	1.47371i	−0.869355	−	0.494188i	$-0.835465\pi$
$293$	−313.718	−	431.796i	−1.07071	−	1.47371i	−0.201355	−	0.979518i	$-0.564535\pi$
$294$		0			0
$295$	−68.9791	−	212.296i	−0.233828	−	0.719647i
$296$			562.485i			1.90029i
$297$		0			0
$298$	15.2467			0.0511633
$299$	243.854	−	79.2331i	0.815566	−	0.264993i
$300$		0			0
$301$	−366.592	+	266.345i	−1.21791	+	0.884867i
$302$	42.3971	−	130.485i	0.140388	−	0.432069i
$303$		0			0
$304$	19.0950	+	26.2819i	0.0628123	+	0.0864538i
$305$	−1.69738	+	2.33625i	−0.00556519	+	0.00765982i
$306$		0			0
$307$			142.846i			0.465296i	0.972561	+	0.232648i	$0.0747389\pi$
$307$			142.846i			0.465296i	−0.972561	+	0.232648i	$0.925261\pi$
$308$	−182.913	−	143.116i	−0.593872	−	0.464661i
$309$		0			0
$310$	12.3144	−	4.00120i	0.0397240	−	0.0129071i
$311$	−37.1343	−	26.9797i	−0.119403	−	0.0867514i	0.526481	−	0.850187i	$-0.323511\pi$
$311$	−37.1343	−	26.9797i	−0.119403	−	0.0867514i	−0.645884	+	0.763435i	$0.723511\pi$
$312$		0			0
$313$	110.168	−	339.062i	0.351975	−	1.08327i	−0.605768	−	0.795641i	$-0.707134\pi$
$313$	110.168	−	339.062i	0.351975	−	1.08327i	0.957743	−	0.287625i	$-0.0928658\pi$
$314$	24.5992	+	7.99278i	0.0783415	+	0.0254547i
$315$		0			0
$316$	−37.1111	+	51.0791i	−0.117440	+	0.161643i
$317$	19.1154	+	58.8312i	0.0603010	+	0.185587i	0.976669	−	0.214749i	$-0.0688933\pi$
$317$	19.1154	+	58.8312i	0.0603010	+	0.185587i	−0.916368	+	0.400336i	$0.868893\pi$
$318$		0			0
$319$	−80.2786	−	280.715i	−0.251657	−	0.879985i
$320$	117.315			0.366609
$321$		0			0
$322$	−178.622	−	129.776i	−0.554726	−	0.403032i
$323$	−115.533	+	83.9395i	−0.357687	+	0.259875i
$324$		0			0
$325$	−288.864	−	93.8575i	−0.888812	−	0.288792i
$326$	11.5202	+	15.8562i	0.0353380	+	0.0486386i
$327$		0			0
$328$	−46.5962	−	143.408i	−0.142062	−	0.437221i
$329$		−	595.222i		−	1.80919i
$330$		0			0
$331$	−339.961			−1.02707			−0.513536	−	0.858068i	$-0.671665\pi$
$331$	−339.961			−1.02707			−0.513536	+	0.858068i	$0.671665\pi$
$332$	−13.0951	+	4.25485i	−0.0394430	+	0.0128158i
$333$		0			0
$334$	144.699	−	105.130i	0.433229	−	0.314759i
$335$	39.0766	−	120.265i	0.116647	−	0.359001i
$336$		0			0
$337$	−175.877	−	242.074i	−0.521890	−	0.718320i	0.463977	−	0.885847i	$-0.346422\pi$
$337$	−175.877	−	242.074i	−0.521890	−	0.718320i	−0.985868	+	0.167527i	$0.946422\pi$
$338$	−54.0753	+	74.4282i	−0.159986	+	0.220202i
$339$		0			0
$340$			58.5817i			0.172299i
$341$	1.62993	−	45.7461i	0.00477986	−	0.134153i
$342$		0			0
$343$	−23.4224	+	7.61041i	−0.0682870	+	0.0221878i
$344$	−313.460	−	227.742i	−0.911221	−	0.662041i
$345$		0			0
$346$	−14.7235	+	45.3143i	−0.0425535	+	0.130966i
$347$	−202.617	−	65.8344i	−0.583912	−	0.189724i	0.00214053	−	0.999998i	$-0.499319\pi$
$347$	−202.617	−	65.8344i	−0.583912	−	0.189724i	−0.586052	+	0.810273i	$0.699319\pi$
$348$		0			0
$349$	−44.0593	+	60.6425i	−0.126245	+	0.173761i	−0.867461	−	0.497506i	$-0.834249\pi$
$349$	−44.0593	+	60.6425i	−0.126245	+	0.173761i	0.741216	+	0.671266i	$0.234249\pi$
$350$	80.8205	+	248.740i	0.230916	+	0.710685i
$351$		0			0
$352$	112.238	−	307.692i	0.318857	−	0.874126i
$353$	372.860			1.05626			0.528130	−	0.849164i	$-0.322893\pi$
$353$	372.860			1.05626			0.528130	+	0.849164i	$0.322893\pi$
$354$		0			0
$355$	27.7603	+	20.1691i	0.0781981	+	0.0568142i
$356$	−6.91371	+	5.02310i	−0.0194205	+	0.0141098i
$357$		0			0
$358$	233.414	+	75.8407i	0.651993	+	0.211846i
$359$	−156.070	−	214.812i	−0.434736	−	0.598363i	0.534296	−	0.845297i	$-0.320577\pi$
$359$	−156.070	−	214.812i	−0.434736	−	0.598363i	−0.969032	+	0.246934i	$0.920577\pi$
$360$		0			0
$361$	66.4253	+	204.436i	0.184004	+	0.566305i
$362$			27.6167i			0.0762892i
$363$		0			0
$364$	−324.925			−0.892651
$365$	165.574	−	53.7984i	0.453629	−	0.147393i
$366$		0			0
$367$	−80.4998	+	58.4866i	−0.219346	+	0.159364i	−0.692032	−	0.721867i	$-0.743284\pi$
$367$	−80.4998	+	58.4866i	−0.219346	+	0.159364i	0.472686	+	0.881231i	$0.343284\pi$
$368$	13.8402	−	42.5957i	0.0376092	−	0.115749i
$369$		0			0
$370$	123.125	+	169.467i	0.332771	+	0.458020i
$371$	−581.327	+	800.128i	−1.56692	+	2.15668i
$372$		0			0
$373$			469.949i			1.25992i	0.776629	+	0.629959i	$0.216928\pi$
$373$			469.949i			1.25992i	−0.776629	+	0.629959i	$0.783072\pi$
$374$	−165.613	−	60.4111i	−0.442815	−	0.161527i
$375$		0			0
$376$	484.043	−	157.275i	1.28735	−	0.418285i
$377$	−330.464	−	240.096i	−0.876563	−	0.636861i
$378$		0			0
$379$	89.1943	−	274.512i	0.235341	−	0.724305i	−0.761735	−	0.647889i	$-0.775652\pi$
$379$	89.1943	−	274.512i	0.235341	−	0.724305i	0.997076	−	0.0764166i	$-0.0243479\pi$
$380$	−56.9773	−	18.5130i	−0.149940	−	0.0487185i
$381$		0			0
$382$	−47.4710	+	65.3382i	−0.124270	+	0.171042i
$383$	60.7882	+	187.087i	0.158716	+	0.488477i	0.998518	−	0.0544147i	$-0.0173293\pi$
$383$	60.7882	+	187.087i	0.158716	+	0.488477i	−0.839803	+	0.542892i	$0.817329\pi$
$384$		0			0
$385$	−246.447	−	8.78090i	−0.640122	−	0.0228075i
$386$	336.430			0.871581
$387$		0			0
$388$	57.9223	+	42.0830i	0.149284	+	0.108461i
$389$	−363.076	+	263.790i	−0.933358	+	0.678124i	−0.946813	−	0.321785i	$-0.895717\pi$
$389$	−363.076	+	263.790i	−0.933358	+	0.678124i	0.0134546	+	0.999909i	$0.495717\pi$
$390$		0			0
$391$	187.247	+	60.8401i	0.478891	+	0.155601i
$392$	228.263	+	314.177i	0.582303	+	0.801471i
$393$		0			0
$394$	−69.7115	−	214.550i	−0.176933	−	0.544543i
$395$			67.0397i			0.169721i
$396$		0			0
$397$	608.594			1.53298			0.766491	−	0.642255i	$-0.222001\pi$
$397$	608.594			1.53298			0.766491	+	0.642255i	$0.222001\pi$
$398$	−126.393	+	41.0676i	−0.317571	+	0.103185i
$399$		0			0
$400$	−42.9220	+	31.1847i	−0.107305	+	0.0779616i
$401$	80.0898	−	246.491i	0.199725	−	0.614691i	−0.800164	−	0.599782i	$-0.795254\pi$
$401$	80.0898	−	246.491i	0.199725	−	0.614691i	0.999889	−	0.0149093i	$-0.00474596\pi$
$402$		0			0
$403$	−37.6426	−	51.8105i	−0.0934059	−	0.128562i
$404$	123.296	−	169.702i	0.305188	−	0.420056i
$405$		0			0
$406$			351.738i			0.866350i
$407$	711.999	−	203.617i	1.74938	−	0.500287i
$408$		0			0
$409$	249.341	−	81.0159i	0.609637	−	0.198083i	0.0121029	−	0.999927i	$-0.496147\pi$
$409$	249.341	−	81.0159i	0.609637	−	0.198083i	0.597534	+	0.801844i	$0.296147\pi$
$410$	−45.4301	−	33.0069i	−0.110805	−	0.0805046i
$411$		0			0
$412$	−124.231	+	382.343i	−0.301531	+	0.928017i
$413$	904.162	+	293.780i	2.18925	+	0.711332i
$414$		0			0
$415$	−8.59344	+	11.8279i	−0.0207071	+	0.0285008i
$416$	−141.598	−	435.793i	−0.340379	−	1.04758i
$417$		0			0
$418$	111.094	−	141.986i	0.265774	−	0.339680i
$419$	650.465			1.55242			0.776211	−	0.630473i	$-0.217139\pi$
$419$	650.465			1.55242			0.776211	+	0.630473i	$0.217139\pi$
$420$		0			0
$421$	508.799	+	369.664i	1.20855	+	0.878062i	0.995098	−	0.0988920i	$-0.0315298\pi$
$421$	508.799	+	369.664i	1.20855	+	0.878062i	0.213450	+	0.976954i	$0.431530\pi$
$422$	12.7314	−	9.24988i	0.0301691	−	0.0219191i
$423$		0			0
$424$	−804.280	−	261.326i	−1.89689	−	0.616336i
$425$	−137.085	−	188.681i	−0.322552	−	0.443955i
$426$		0			0
$427$	−3.80056	−	11.6969i	−0.00890062	−	0.0273933i
$428$			414.610i			0.968715i
$429$		0			0
$430$	−144.292			−0.335562
$431$	−560.194	+	182.018i	−1.29975	+	0.422316i	−0.875496	−	0.483225i	$-0.839465\pi$
$431$	−560.194	+	182.018i	−1.29975	+	0.422316i	−0.424258	+	0.905541i	$0.639465\pi$
$432$		0			0
$433$	126.292	−	91.7565i	0.291668	−	0.211909i	−0.432323	−	0.901719i	$-0.642306\pi$
$433$	126.292	−	91.7565i	0.291668	−	0.211909i	0.723990	+	0.689810i	$0.242306\pi$
$434$	−17.0410	+	52.4468i	−0.0392650	+	0.120845i
$435$		0			0
$436$	−144.481	−	198.861i	−0.331379	−	0.456104i
$437$	−118.348	+	162.892i	−0.270818	+	0.372750i
$438$		0			0
$439$		−	209.017i		−	0.476121i	−0.971250	−	0.238060i	$-0.923488\pi$
$439$		−	209.017i		−	0.476121i	0.971250	−	0.238060i	$-0.0765116\pi$
$440$	−57.9777	−	202.734i	−0.131768	−	0.460760i
$441$		0			0
$442$	−234.562	+	76.2138i	−0.530683	+	0.172430i
$443$	276.987	+	201.242i	0.625252	+	0.454272i	0.854752	−	0.519037i	$-0.173709\pi$
$443$	276.987	+	201.242i	0.625252	+	0.454272i	−0.229500	+	0.973309i	$0.573709\pi$
$444$		0			0
$445$	−2.80403	+	8.62992i	−0.00630119	+	0.0193931i
$446$	402.313	+	130.719i	0.902047	+	0.293093i
$447$		0			0
$448$	−293.682	+	404.218i	−0.655539	+	0.902273i
$449$	−17.7730	−	54.6996i	−0.0395835	−	0.121825i	0.929312	−	0.369295i	$-0.120401\pi$
$449$	−17.7730	−	54.6996i	−0.0395835	−	0.121825i	−0.968896	+	0.247470i	$0.920401\pi$
$450$		0			0
$451$	−164.660	+	110.895i	−0.365100	+	0.245887i
$452$	−35.3895			−0.0782954
$453$		0			0
$454$	−10.4629	−	7.60171i	−0.0230459	−	0.0167438i
$455$	−279.118	+	202.791i	−0.613445	+	0.445694i
$456$		0			0
$457$	608.260	+	197.636i	1.33098	+	0.432463i	0.886253	−	0.463201i	$-0.153299\pi$
$457$	608.260	+	197.636i	1.33098	+	0.432463i	0.444731	+	0.895664i	$0.353299\pi$
$458$	−160.082	−	220.335i	−0.349525	−	0.481080i
$459$		0			0
$460$	25.5233	+	78.5527i	0.0554855	+	0.170767i
$461$		−	492.084i		−	1.06743i	−0.845666	−	0.533713i	$-0.820796\pi$
$461$		−	492.084i		−	1.06743i	0.845666	−	0.533713i	$-0.179204\pi$
$462$		0			0
$463$	366.054			0.790614			0.395307	−	0.918549i	$-0.370638\pi$
$463$	366.054			0.790614			0.395307	+	0.918549i	$0.370638\pi$
$464$	−67.8592	+	22.0488i	−0.146248	+	0.0475190i
$465$		0			0
$466$	263.646	−	191.550i	0.565763	−	0.411051i
$467$	−100.584	+	309.566i	−0.215383	+	0.662882i	0.783743	+	0.621086i	$0.213308\pi$
$467$	−100.584	+	309.566i	−0.215383	+	0.662882i	−0.999126	+	0.0417963i	$0.986692\pi$
$468$		0			0
$469$	316.561	+	435.709i	0.674970	+	0.929017i
$470$	111.407	−	153.339i	0.237037	−	0.326253i
$471$		0			0
$472$			812.903i			1.72225i
$473$	−174.807	+	479.222i	−0.369571	+	1.01315i
$474$		0			0
$475$	226.835	−	73.7031i	0.477547	−	0.155165i
$476$	−201.848	−	146.651i	−0.424050	−	0.308090i
$477$		0			0
$478$	33.8188	−	104.083i	0.0707506	−	0.217748i
$479$	−312.398	−	101.504i	−0.652187	−	0.211908i	−0.0358087	−	0.999359i	$-0.511401\pi$
$479$	−312.398	−	101.504i	−0.652187	−	0.211908i	−0.616378	+	0.787450i	$0.711401\pi$
$480$		0			0
$481$	608.975	−	838.182i	1.26606	−	1.74258i
$482$	64.2285	+	197.675i	0.133254	+	0.410114i
$483$		0			0
$484$	−260.787	−	18.6073i	−0.538817	−	0.0384449i
$485$	76.0213			0.156745
$486$		0			0
$487$	−260.740	−	189.439i	−0.535400	−	0.388991i	0.286974	−	0.957938i	$-0.407351\pi$
$487$	−260.740	−	189.439i	−0.535400	−	0.388991i	−0.822374	+	0.568947i	$0.807351\pi$
$488$	8.50789	−	6.18135i	0.0174342	−	0.0126667i
$489$		0			0
$490$	137.544	+	44.6906i	0.280701	+	0.0912053i
$491$	−454.813	−	625.997i	−0.926300	−	1.27494i	−0.961286	−	0.275554i	$-0.911139\pi$
$491$	−454.813	−	625.997i	−0.926300	−	1.27494i	0.0349859	−	0.999388i	$-0.488861\pi$
$492$		0			0
$493$	−96.9243	−	298.302i	−0.196601	−	0.605076i
$494$		−	252.223i		−	0.510573i
$495$		0			0
$496$	−11.1865			−0.0225535
$497$	−138.988	+	45.1600i	−0.279654	+	0.0908652i
$498$		0			0
$499$	41.3425	−	30.0371i	0.0828507	−	0.0601946i	−0.545589	−	0.838053i	$-0.683694\pi$
$499$	41.3425	−	30.0371i	0.0828507	−	0.0601946i	0.628440	+	0.777858i	$0.283694\pi$
$500$	68.5324	−	210.921i	0.137065	−	0.421842i
$501$		0			0
$502$	−280.903	−	386.630i	−0.559568	−	0.770179i
$503$	244.325	−	336.284i	0.485735	−	0.668557i	−0.493859	−	0.869542i	$-0.664414\pi$
$503$	244.325	−	336.284i	0.485735	−	0.668557i	0.979594	+	0.200985i	$0.0644141\pi$
$504$		0			0
$505$		−	222.729i		−	0.441048i
$506$	−248.392	−	8.85022i	−0.490894	−	0.0174906i
$507$		0			0
$508$	−11.4827	+	3.73096i	−0.0226038	+	0.00734441i
$509$	270.522	+	196.546i	0.531478	+	0.386141i	0.820910	−	0.571057i	$-0.193467\pi$
$509$	270.522	+	196.546i	0.531478	+	0.386141i	−0.289433	+	0.957198i	$0.593467\pi$
$510$		0			0
$511$	−229.126	+	705.177i	−0.448387	+	1.37999i
$512$	−161.567	−	52.4962i	−0.315560	−	0.102532i
$513$		0			0
$514$	−103.358	+	142.260i	−0.201086	+	0.276771i
$515$	131.909	+	405.976i	0.256135	+	0.788302i
$516$		0			0
$517$	−374.302	−	555.774i	−0.723988	−	1.07500i
$518$	−892.140			−1.72228
$519$		0			0
$520$	−238.664	−	173.399i	−0.458968	−	0.333460i
$521$	700.990	−	509.299i	1.34547	−	0.977541i	0.346246	−	0.938144i	$-0.387456\pi$
$521$	700.990	−	509.299i	1.34547	−	0.977541i	0.999224	−	0.0393970i	$-0.0125437\pi$
$522$		0			0
$523$	−415.392	−	134.969i	−0.794248	−	0.258067i	−0.116336	−	0.993210i	$-0.537115\pi$
$523$	−415.392	−	134.969i	−0.794248	−	0.258067i	−0.677912	+	0.735143i	$0.737115\pi$
$524$	286.668	+	394.564i	0.547076	+	0.752986i
$525$		0			0
$526$	−75.5083	−	232.391i	−0.143552	−	0.441808i
$527$		−	49.1749i		−	0.0933111i
$528$		0			0
$529$	−251.412			−0.475259
$530$	−299.519	+	97.3197i	−0.565130	+	0.183622i
$531$		0			0
$532$	206.423	−	149.975i	0.388013	−	0.281908i
$533$	−85.8263	+	264.146i	−0.161025	+	0.495584i
$534$		0			0
$535$	258.765	+	356.159i	0.483672	+	0.665718i
$536$	−270.680	+	372.559i	−0.505000	+	0.695073i
$537$		0			0
$538$		−	456.361i		−	0.848255i
$539$	315.058	−	402.668i	0.584523	−	0.747064i
$540$		0			0
$541$	−738.226	+	239.864i	−1.36456	+	0.443372i	−0.897562	−	0.440888i	$-0.854664\pi$
$541$	−738.226	+	239.864i	−1.36456	+	0.443372i	−0.466996	+	0.884259i	$0.654664\pi$
$542$	240.802	+	174.953i	0.444283	+	0.322791i
$543$		0			0
$544$	108.728	−	334.629i	0.199867	−	0.615127i
$545$	−248.225	−	80.6533i	−0.455459	−	0.147988i
$546$		0			0
$547$	−466.258	+	641.749i	−0.852391	+	1.17322i	0.130940	+	0.991390i	$0.458200\pi$
$547$	−466.258	+	641.749i	−0.852391	+	1.17322i	−0.983331	+	0.181825i	$0.941800\pi$
$548$	−34.9544	−	107.579i	−0.0637854	−	0.196311i
$549$		0			0
$550$	231.883	+	181.431i	0.421605	+	0.329875i
$551$	320.763			0.582147
$552$		0			0
$553$	−230.991	−	167.825i	−0.417705	−	0.303480i
$554$	268.619	−	195.163i	0.484872	−	0.352280i
$555$		0			0
$556$	−57.6753	−	18.7399i	−0.103733	−	0.0337048i
$557$	390.960	+	538.111i	0.701904	+	0.966088i	0.999934	+	0.0115312i	$0.00367058\pi$
$557$	390.960	+	538.111i	0.701904	+	0.966088i	−0.298030	+	0.954557i	$0.596329\pi$
$558$		0			0
$559$	220.534	+	678.735i	0.394516	+	1.21420i
$560$			60.2650i			0.107616i
$561$		0			0
$562$	−468.211			−0.833116
$563$	375.847	−	122.120i	0.667579	−	0.216910i	0.0444299	−	0.999013i	$-0.485853\pi$
$563$	375.847	−	122.120i	0.667579	−	0.216910i	0.623149	+	0.782103i	$0.285853\pi$
$564$		0			0
$565$	−30.4004	+	22.0872i	−0.0538060	+	0.0390923i
$566$	97.4736	−	299.993i	0.172215	−	0.530023i
$567$		0			0
$568$	−73.4495	−	101.095i	−0.129313	−	0.177983i
$569$	31.1806	−	42.9165i	0.0547990	−	0.0754244i	−0.780738	−	0.624858i	$-0.785157\pi$
$569$	31.1806	−	42.9165i	0.0547990	−	0.0754244i	0.835537	+	0.549434i	$0.185157\pi$
$570$		0			0
$571$		−	878.429i		−	1.53840i	−0.639005	−	0.769202i	$-0.720654\pi$
$571$		−	878.429i		−	1.53840i	0.639005	−	0.769202i	$-0.279346\pi$
$572$	−303.390	+	204.327i	−0.530403	+	0.357215i
$573$		0			0
$574$	227.456	−	73.9048i	0.396264	−	0.128754i
$575$	−266.024	−	193.278i	−0.462651	−	0.336135i
$576$		0			0
$577$	334.518	−	1029.54i	0.579755	−	1.78430i	−0.0396306	−	0.999214i	$-0.512618\pi$
$577$	334.518	−	1029.54i	0.579755	−	1.78430i	0.619385	−	0.785087i	$-0.287382\pi$
$578$	192.645	+	62.5941i	0.333296	+	0.108294i
$579$		0			0
$580$	77.3422	−	106.452i	0.133349	−	0.183539i
$581$	−19.2413	−	59.2187i	−0.0331176	−	0.101926i
$582$		0			0
$583$	−39.6442	+	1112.66i	−0.0680004	+	1.90851i
$584$	−634.002			−1.08562
$585$		0			0
$586$	585.598	+	425.462i	0.999313	+	0.726044i
$587$	12.3428	−	8.96760i	0.0210270	−	0.0152770i	−0.577222	−	0.816587i	$-0.695863\pi$
$587$	12.3428	−	8.96760i	0.0210270	−	0.0152770i	0.598249	+	0.801310i	$0.295863\pi$
$588$		0			0
$589$	47.8282	+	15.5403i	0.0812023	+	0.0263842i
$590$	177.940	+	244.914i	0.301594	+	0.415109i
$591$		0			0
$592$	−55.9240	−	172.116i	−0.0944663	−	0.290737i
$593$		−	214.000i		−	0.360877i	−0.983586	−	0.180439i	$-0.942248\pi$
$593$		−	214.000i		−	0.360877i	0.983586	−	0.180439i	$-0.0577517\pi$
$594$		0			0
$595$	−264.919			−0.445242
$596$	23.1028	−	7.50655i	0.0387631	−	0.0125949i
$597$		0			0
$598$	−281.321	+	204.392i	−0.470437	+	0.341792i
$599$	−192.777	+	593.308i	−0.321832	+	0.990498i	0.651018	+	0.759062i	$0.274342\pi$
$599$	−192.777	+	593.308i	−0.321832	+	0.990498i	−0.972850	+	0.231435i	$0.925658\pi$
$600$		0			0
$601$	237.449	+	326.821i	0.395090	+	0.543795i	0.959503	−	0.281698i	$-0.0908975\pi$
$601$	237.449	+	326.821i	0.395090	+	0.543795i	−0.564413	+	0.825493i	$0.690897\pi$
$602$	361.214	−	497.169i	0.600024	−	0.825862i
$603$		0			0
$604$		−	218.593i		−	0.361909i
$605$	−235.635	+	146.778i	−0.389480	+	0.242607i
$606$		0			0
$607$	−349.561	+	113.579i	−0.575882	+	0.187115i	−0.582455	−	0.812863i	$-0.697908\pi$
$607$	−349.561	+	113.579i	−0.575882	+	0.187115i	0.00657281	+	0.999978i	$0.497908\pi$
$608$	291.104	+	211.500i	0.478790	+	0.347861i
$609$		0			0
$610$	1.21022	−	3.72467i	0.00198397	−	0.00610602i
$611$	−891.567	−	289.688i	−1.45919	−	0.474120i
$612$		0			0
$613$	286.364	−	394.147i	0.467152	−	0.642980i	−0.508820	−	0.860873i	$-0.669918\pi$
$613$	286.364	−	394.147i	0.467152	−	0.642980i	0.975973	+	0.217893i	$0.0699183\pi$
$614$	−59.8646	−	184.244i	−0.0974994	−	0.300072i
$615$		0			0
$616$	843.676	+	307.750i	1.36960	+	0.499594i
$617$	−455.862			−0.738836			−0.369418	−	0.929263i	$-0.620443\pi$
$617$	−455.862			−0.738836			−0.369418	+	0.929263i	$0.620443\pi$
$618$		0			0
$619$	−463.020	−	336.404i	−0.748013	−	0.543463i	0.147197	−	0.989107i	$-0.452975\pi$
$619$	−463.020	−	336.404i	−0.748013	−	0.543463i	−0.895210	+	0.445644i	$0.852975\pi$
$620$	16.6897	−	12.1258i	0.0269189	−	0.0195577i
$621$		0			0
$622$	59.2032	+	19.2363i	0.0951820	+	0.0309265i
$623$	−22.7156	−	31.2653i	−0.0364616	−	0.0501851i
$624$		0			0
$625$	79.7020	+	245.297i	0.127523	+	0.392476i
$626$			483.497i			0.772360i
$627$		0			0
$628$	41.2096			0.0656204
$629$	756.607	−	245.836i	1.20287	−	0.390837i
$630$		0			0
$631$	−181.250	+	131.686i	−0.287243	+	0.208694i	−0.722070	−	0.691820i	$-0.756809\pi$
$631$	−181.250	+	131.686i	−0.287243	+	0.208694i	0.434828	+	0.900514i	$0.356809\pi$
$632$	75.4428	−	232.189i	0.119372	−	0.367388i
$633$		0			0
$634$	−49.3106	−	67.8703i	−0.0777770	−	0.107051i
$635$	−7.53535	+	10.3715i	−0.0118667	+	0.0163331i
$636$		0			0
$637$		−	715.296i		−	1.12291i
$638$	221.188	+	328.427i	0.346690	+	0.514775i
$639$		0			0
$640$	108.562	−	35.2740i	0.169628	−	0.0551156i
$641$	−383.601	−	278.702i	−0.598441	−	0.434793i	0.246884	−	0.969045i	$-0.420593\pi$
$641$	−383.601	−	278.702i	−0.598441	−	0.434793i	−0.845325	+	0.534252i	$0.820593\pi$
$642$		0			0
$643$	−255.732	+	787.063i	−0.397717	+	1.22405i	0.529108	+	0.848554i	$0.322527\pi$
$643$	−255.732	+	787.063i	−0.397717	+	1.22405i	−0.926825	+	0.375493i	$0.877473\pi$
$644$	−334.554	−	108.703i	−0.519493	−	0.168794i
$645$		0			0
$646$	113.838	−	156.685i	0.176220	−	0.242546i
$647$	−153.080	−	471.133i	−0.236600	−	0.728181i	−0.996905	−	0.0786144i	$-0.974950\pi$
$647$	−153.080	−	471.133i	−0.236600	−	0.728181i	0.760305	−	0.649567i	$-0.225050\pi$
$648$		0			0
$649$	1028.98	−	294.267i	1.58549	−	0.453415i
$650$	411.915			0.633715
$651$		0			0
$652$	25.2628	+	18.3545i	0.0387467	+	0.0281511i
$653$	−543.344	+	394.762i	−0.832073	+	0.604536i	−0.920145	−	0.391578i	$-0.871929\pi$
$653$	−543.344	+	394.762i	−0.832073	+	0.604536i	0.0880721	+	0.996114i	$0.471929\pi$
$654$		0			0
$655$	492.508	+	160.026i	0.751921	+	0.244314i
$656$	28.5162	+	39.2492i	0.0434699	+	0.0598312i
$657$		0			0
$658$	249.449	+	767.726i	0.379102	+	1.16676i
$659$			59.3106i			0.0900009i	0.998987	+	0.0450004i	$0.0143289\pi$
$659$			59.3106i			0.0900009i	−0.998987	+	0.0450004i	$0.985671\pi$
$660$		0			0
$661$	604.118			0.913946			0.456973	−	0.889481i	$-0.348934\pi$
$661$	604.118			0.913946			0.456973	+	0.889481i	$0.348934\pi$
$662$	438.486	−	142.473i	0.662366	−	0.215216i
$663$		0			0
$664$	43.0734	−	31.2947i	0.0648696	−	0.0471305i
$665$	83.7200	−	257.664i	0.125895	−	0.387464i
$666$		0			0
$667$	−259.934	−	357.768i	−0.389705	−	0.536384i
$668$	167.498	−	230.541i	0.250745	−	0.345121i
$669$		0			0
$670$			171.496i			0.255965i
$671$	−10.9042	−	8.53176i	−0.0162507	−	0.0127150i
$672$		0			0
$673$	96.0114	−	31.1960i	0.142662	−	0.0463536i	−0.236816	−	0.971555i	$-0.576104\pi$
$673$	96.0114	−	31.1960i	0.142662	−	0.0463536i	0.379477	+	0.925201i	$0.376104\pi$
$674$	328.298	+	238.523i	0.487090	+	0.353891i
$675$		0			0
$676$	−45.2945	+	139.402i	−0.0670037	+	0.206216i
$677$	−191.488	−	62.2184i	−0.282849	−	0.0919031i	0.164157	−	0.986434i	$-0.447510\pi$
$677$	−191.488	−	62.2184i	−0.282849	−	0.0919031i	−0.447006	+	0.894531i	$0.647510\pi$
$678$		0			0
$679$	−190.309	+	261.937i	−0.280278	+	0.385769i
$680$	−69.9994	−	215.436i	−0.102940	−	0.316818i
$681$		0			0
$682$	17.0692	+	59.6870i	0.0250282	+	0.0875176i
$683$	−381.312			−0.558290			−0.279145	−	0.960249i	$-0.590051\pi$
$683$	−381.312			−0.558290			−0.279145	+	0.960249i	$0.590051\pi$
$684$		0			0
$685$	−97.1682	−	70.5968i	−0.141851	−	0.103061i
$686$	27.0212	−	19.6320i	0.0393895	−	0.0286181i
$687$		0			0
$688$	118.559	+	38.5223i	0.172325	+	0.0559917i
$689$	915.565	+	1260.17i	1.32883	+	1.82898i
$690$		0			0
$691$	−353.424	−	1087.73i	−0.511468	−	1.57414i	−0.789618	−	0.613598i	$-0.789721\pi$
$691$	−353.424	−	1087.73i	−0.511468	−	1.57414i	0.278150	−	0.960538i	$-0.410279\pi$
$692$			75.9123i			0.109700i
$693$		0			0
$694$	288.929			0.416324
$695$	−61.2403	+	19.8982i	−0.0881155	+	0.0286305i
$696$		0			0
$697$	−172.536	+	125.355i	−0.247541	+	0.179849i
$698$	31.4139	−	96.6822i	0.0450056	−	0.138513i
$699$		0			0
$700$	244.929	+	337.116i	0.349899	+	0.481595i
$701$	302.844	−	416.829i	0.432017	−	0.594620i	−0.536398	−	0.843965i	$-0.680215\pi$
$701$	302.844	−	416.829i	0.432017	−	0.594620i	0.968415	+	0.249345i	$0.0802153\pi$
$702$		0			0
$703$			813.575i			1.15729i
$704$	−20.0279	+	562.108i	−0.0284488	+	0.798449i
$705$		0			0
$706$	−480.920	+	156.260i	−0.681189	+	0.221332i
$707$	767.431	+	557.572i	1.08548	+	0.788644i
$708$		0			0
$709$	−276.488	+	850.942i	−0.389969	+	1.20020i	0.542842	+	0.839835i	$0.317348\pi$
$709$	−276.488	+	850.942i	−0.389969	+	1.20020i	−0.932811	+	0.360366i	$0.882652\pi$
$710$	−44.2582	−	14.3804i	−0.0623355	−	0.0202540i
$711$		0			0
$712$	19.4233	−	26.7338i	0.0272799	−	0.0375475i
$713$	−21.4249	−	65.9392i	−0.0300490	−	0.0924813i
$714$		0			0
$715$	−133.095	+	364.872i	−0.186147	+	0.510311i
$716$	391.024			0.546122
$717$		0			0
$718$	291.326	+	211.661i	0.405747	+	0.294793i
$719$	126.704	−	92.0559i	0.176223	−	0.128033i	−0.496177	−	0.868221i	$-0.665263\pi$
$719$	126.704	−	92.0559i	0.176223	−	0.128033i	0.672400	+	0.740188i	$0.265263\pi$
$720$		0			0
$721$	−1729.04	−	561.798i	−2.39811	−	0.779193i
$722$	−171.353	−	235.847i	−0.237330	−	0.326657i
$723$		0			0
$724$	13.5968	+	41.8467i	0.0187801	+	0.0577993i
$725$			523.849i			0.722551i
$726$		0			0
$727$	28.5853			0.0393195			0.0196598	−	0.999807i	$-0.493742\pi$
$727$	28.5853			0.0393195			0.0196598	+	0.999807i	$0.493742\pi$
$728$	1194.92	−	388.254i	1.64138	−	0.533315i
$729$		0			0
$730$	−191.014	+	138.780i	−0.261663	+	0.190109i
$731$	−169.340	+	521.175i	−0.231655	+	0.712962i
$732$		0			0
$733$	317.269	+	436.684i	0.432837	+	0.595749i	0.968601	−	0.248619i	$-0.0799766\pi$
$733$	317.269	+	436.684i	0.432837	+	0.595749i	−0.535765	+	0.844367i	$0.679977\pi$
$734$	79.3189	−	109.173i	0.108064	−	0.148737i
$735$		0			0
$736$		−	496.079i		−	0.674020i
$737$	569.574	+	207.765i	0.772827	+	0.281906i
$738$		0			0
$739$	337.414	−	109.632i	0.456582	−	0.148352i	−0.0716913	−	0.997427i	$-0.522840\pi$
$739$	337.414	−	109.632i	0.456582	−	0.148352i	0.528273	+	0.849074i	$0.322840\pi$
$740$	270.003	+	196.169i	0.364869	+	0.265093i
$741$		0			0
$742$	414.481	−	1275.64i	0.558600	−	1.71920i
$743$	−820.225	−	266.507i	−1.10394	−	0.358691i	−0.300321	−	0.953838i	$-0.597094\pi$
$743$	−820.225	−	266.507i	−1.10394	−	0.358691i	−0.803617	+	0.595147i	$0.797094\pi$
$744$		0			0
$745$	15.1609	−	20.8671i	0.0203501	−	0.0280096i
$746$	−196.949	−	606.147i	−0.264007	−	0.812529i
$747$		0			0
$748$	−280.691	−	10.0010i	−0.375255	−	0.0133703i
$749$	−1874.96			−2.50328
$750$		0			0
$751$	−15.0547	−	10.9379i	−0.0200462	−	0.0145644i	0.577717	−	0.816237i	$-0.303944\pi$
$751$	−15.0547	−	10.9379i	−0.0200462	−	0.0145644i	−0.597763	+	0.801673i	$0.703944\pi$
$752$	−132.477	+	96.2502i	−0.176166	+	0.127992i
$753$		0			0
$754$	526.859	+	171.187i	0.698752	+	0.227038i
$755$	−136.428	−	187.776i	−0.180699	−	0.248710i
$756$		0			0
$757$	194.396	+	598.290i	0.256798	+	0.790343i	0.993470	+	0.114093i	$0.0363962\pi$
$757$	194.396	+	598.290i	0.256798	+	0.790343i	−0.736672	+	0.676250i	$0.763604\pi$
$758$			391.449i			0.516424i
$759$		0			0
$760$	231.657			0.304812
$761$	−897.680	+	291.674i	−1.17961	+	0.383277i	−0.832220	−	0.554445i	$-0.812930\pi$
$761$	−897.680	+	291.674i	−1.17961	+	0.383277i	−0.347385	+	0.937722i	$0.612930\pi$
$762$		0			0
$763$	899.294	−	653.376i	1.17863	−	0.856324i
$764$	−39.7626	+	122.377i	−0.0520453	+	0.160179i
$765$		0			0
$766$	−156.811	−	215.832i	−0.204714	−	0.281765i
$767$	880.090	−	1211.34i	1.14744	−	1.57932i
$768$		0			0
$769$		−	332.508i		−	0.432390i	−0.976350	−	0.216195i	$-0.930635\pi$
$769$		−	332.508i		−	0.432390i	0.976350	−	0.216195i	$-0.0693646\pi$
$770$	321.550	−	91.9567i	0.417598	−	0.119424i
$771$		0			0
$772$	509.782	−	165.638i	0.660339	−	0.214557i
$773$	−747.482	−	543.077i	−0.966988	−	0.702558i	−0.0122246	−	0.999925i	$-0.503891\pi$
$773$	−747.482	−	543.077i	−0.966988	−	0.702558i	−0.954763	+	0.297368i	$0.903891\pi$
$774$		0			0
$775$	−25.3794	+	78.1099i	−0.0327477	+	0.100787i
$776$	−263.296	−	85.5502i	−0.339300	−	0.110245i
$777$		0			0
$778$	357.750	−	492.401i	0.459833	−	0.632906i
$779$	−67.3965	−	207.425i	−0.0865167	−	0.266271i
$780$		0			0
$781$	−101.378	+	129.569i	−0.129806	+	0.165901i
$782$	−267.010			−0.341445
$783$		0			0
$784$	−101.083	−	73.4413i	−0.128933	−	0.0936751i
$785$	35.4000	−	25.7196i	0.0450955	−	0.0327638i
$786$		0			0
$787$	−1224.73	−	397.937i	−1.55619	−	0.505638i	−0.600407	−	0.799695i	$-0.704995\pi$
$787$	−1224.73	−	397.937i	−1.55619	−	0.505638i	−0.955788	+	0.294057i	$0.904995\pi$
$788$	−211.263	−	290.779i	−0.268100	−	0.369009i
$789$		0			0
$790$	−28.0954	−	86.4688i	−0.0355638	−	0.109454i
$791$		−	160.039i		−	0.202325i
$792$		0			0
$793$	−19.3702			−0.0244265
$794$	−784.973	+	255.053i	−0.988630	+	0.321225i
$795$		0			0
$796$	−171.300	+	124.457i	−0.215201	+	0.156353i
$797$	67.4452	−	207.575i	0.0846239	−	0.260445i	−0.899787	−	0.436329i	$-0.856278\pi$
$797$	67.4452	−	207.575i	0.0846239	−	0.260445i	0.984411	+	0.175884i	$0.0562783\pi$
$798$		0			0
$799$	−423.106	−	582.356i	−0.529545	−	0.728856i
$800$	−345.408	+	475.413i	−0.431760	+	0.594266i
$801$		0			0
$802$			351.492i			0.438270i
$803$	229.505	+	802.525i	0.285810	+	0.999409i
$804$		0			0
$805$	−355.232	+	115.422i	−0.441283	+	0.143381i
$806$	70.2650	+	51.0505i	0.0871774	+	0.0633381i
$807$		0			0
$808$	−250.647	+	771.413i	−0.310207	+	0.954719i
$809$	733.095	+	238.197i	0.906174	+	0.294434i	0.724783	−	0.688977i	$-0.241940\pi$
$809$	733.095	+	238.197i	0.906174	+	0.294434i	0.181391	+	0.983411i	$0.441940\pi$
$810$		0			0
$811$	929.155	−	1278.87i	1.14569	−	1.57691i	0.391602	−	0.920135i	$-0.371921\pi$
$811$	929.155	−	1278.87i	1.14569	−	1.57691i	0.754088	−	0.656773i	$-0.228079\pi$
$812$	173.175	+	532.977i	0.213270	+	0.656376i
$813$		0			0
$814$	−833.013	+	561.016i	−1.02336	+	0.689209i
$815$	33.1567			0.0406831
$816$		0			0
$817$	−453.387	−	329.405i	−0.554941	−	0.403188i
$818$	−287.651	+	208.991i	−0.351652	+	0.255490i
$819$		0			0
$820$	−85.0894	−	27.6472i	−0.103768	−	0.0337161i
$821$	−116.880	−	160.872i	−0.142364	−	0.195947i	0.731881	−	0.681433i	$-0.238643\pi$
$821$	−116.880	−	160.872i	−0.142364	−	0.195947i	−0.874245	+	0.485486i	$0.838643\pi$
$822$		0			0
$823$	41.5286	+	127.812i	0.0504600	+	0.155300i	0.973111	−	0.230335i	$-0.0739823\pi$
$823$	41.5286	+	127.812i	0.0504600	+	0.155300i	−0.922651	+	0.385635i	$0.873982\pi$
$824$		−	1554.52i		−	1.88656i
$825$		0			0
$826$	−1289.32			−1.56092
$827$	−1136.57	+	369.292i	−1.37432	+	0.446545i	−0.900799	−	0.434236i	$-0.857018\pi$
$827$	−1136.57	+	369.292i	−1.37432	+	0.446545i	−0.473524	+	0.880781i	$0.657018\pi$
$828$		0			0
$829$	−1155.60	+	839.591i	−1.39397	+	1.01278i	−0.398549	+	0.917147i	$0.630486\pi$
$829$	−1155.60	+	839.591i	−1.39397	+	1.01278i	−0.995417	+	0.0956281i	$0.969514\pi$
$830$	6.12705	−	18.8571i	0.00738199	−	0.0227194i
$831$		0			0
$832$	462.536	+	636.626i	0.555932	+	0.765175i
$833$	322.841	−	444.352i	0.387564	−	0.533436i
$834$		0			0
$835$		−	302.577i		−	0.362368i
$836$	98.4313	−	269.843i	0.117741	−	0.322779i
$837$		0			0
$838$	−838.979	+	272.601i	−1.00117	+	0.325299i
$839$	771.245	+	560.342i	0.919243	+	0.667869i	0.943335	−	0.331841i	$-0.107670\pi$
$839$	771.245	+	560.342i	0.919243	+	0.667869i	−0.0240928	+	0.999710i	$0.507670\pi$
$840$		0			0
$841$	42.1780	−	129.810i	0.0501522	−	0.154353i
$842$	−811.177	−	263.567i	−0.963393	−	0.313025i
$843$		0			0
$844$	14.7373	−	20.2842i	0.0174613	−	0.0240334i
$845$	48.0941	+	148.019i	0.0569162	+	0.175170i
$846$		0			0
$847$	84.1464	−	1179.34i	0.0993464	−	1.39237i
$848$	272.086			0.320856
$849$		0			0
$850$	255.887	+	185.913i	0.301044	+	0.218721i
$851$	907.434	−	659.289i	1.06631	−	0.774723i
$852$		0			0
$853$	926.904	+	301.170i	1.08664	+	0.353071i	0.796947	−	0.604049i	$-0.206447\pi$
$853$	926.904	+	301.170i	1.08664	+	0.353071i	0.289693	+	0.957120i	$0.406447\pi$
$854$	9.80404	+	13.4941i	0.0114801	+	0.0158011i
$855$		0			0
$856$	−495.419	−	1524.74i	−0.578760	−	1.78124i
$857$		−	1571.80i		−	1.83407i	−0.398805	−	0.917036i	$-0.630575\pi$
$857$		−	1571.80i		−	1.83407i	0.398805	−	0.917036i	$-0.369425\pi$
$858$		0			0
$859$	−740.779			−0.862373			−0.431187	−	0.902263i	$-0.641905\pi$
$859$	−740.779			−0.862373			−0.431187	+	0.902263i	$0.641905\pi$
$860$	−218.641	+	71.0407i	−0.254234	+	0.0826055i
$861$		0			0
$862$	646.265	−	469.539i	0.749727	−	0.544709i
$863$	−105.378	+	324.320i	−0.122106	+	0.375805i	−0.993363	−	0.115023i	$-0.963306\pi$
$863$	−105.378	+	324.320i	−0.122106	+	0.375805i	0.871256	+	0.490828i	$0.163306\pi$
$864$		0			0
$865$	47.3781	+	65.2103i	0.0547723	+	0.0753877i
$866$	−124.439	+	171.276i	−0.143694	+	0.197778i
$867$		0			0
$868$			87.8610i			0.101222i
$869$	−321.217	−	11.4450i	−0.369640	−	0.0131703i
$870$		0			0
$871$	806.703	−	262.114i	0.926180	−	0.300934i
$872$	768.955	+	558.678i	0.881829	+	0.640686i
$873$		0			0
$874$	84.3809	−	259.698i	0.0965456	−	0.297137i
$875$	953.830	+	309.918i	1.09009	+	0.354192i
$876$		0			0
$877$	−601.554	+	827.969i	−0.685923	+	0.944092i	−0.999986	−	0.00531028i	$-0.998310\pi$
$877$	−601.554	+	827.969i	−0.685923	+	0.944092i	0.314063	+	0.949402i	$0.398310\pi$
$878$	87.5961	+	269.593i	0.0997678	+	0.307054i
$879$		0			0
$880$	37.8973	+	56.2709i	0.0430651	+	0.0639443i
$881$	1023.93			1.16224			0.581121	−	0.813817i	$-0.302614\pi$
$881$	1023.93			1.16224			0.581121	+	0.813817i	$0.302614\pi$
$882$		0			0
$883$	1348.73	+	979.908i	1.52744	+	1.10975i	0.957642	+	0.287961i	$0.0929775\pi$
$883$	1348.73	+	979.908i	1.52744	+	1.10975i	0.569795	+	0.821787i	$0.307022\pi$
$884$	−317.901	+	230.969i	−0.359617	+	0.261277i
$885$		0			0
$886$	−441.599	−	143.484i	−0.498419	−	0.161946i
$887$	−408.038	−	561.617i	−0.460021	−	0.633164i	0.514492	−	0.857495i	$-0.327980\pi$
$887$	−408.038	−	561.617i	−0.460021	−	0.633164i	−0.974513	+	0.224331i	$0.927980\pi$
$888$		0			0
$889$	−16.8722	−	51.9273i	−0.0189789	−	0.0584109i
$890$		−	12.3061i		−	0.0138271i
$891$		0			0
$892$	673.970			0.755572
$893$	700.117	−	227.482i	0.784006	−	0.254739i
$894$		0			0
$895$	335.898	−	244.044i	0.375305	−	0.272675i
$896$	−150.231	+	462.363i	−0.167668	+	0.516030i
$897$		0			0
$898$	45.8477	+	63.1039i	0.0510553	+	0.0702717i
$899$	−64.9230	+	89.3589i	−0.0722169	+	0.0993981i
$900$		0			0
$901$			1196.06i			1.32748i
$902$	165.906	−	212.041i	0.183932	−	0.235078i
$903$		0			0
$904$	130.146	−	42.2870i	0.143967	−	0.0467777i
$905$	37.7972	+	27.4613i	0.0417648	+	0.0303439i
$906$		0			0
$907$	−249.523	+	767.953i	−0.275108	+	0.846696i	0.714083	+	0.700062i	$0.246844\pi$
$907$	−249.523	+	767.953i	−0.275108	+	0.846696i	−0.989191	+	0.146635i	$0.953156\pi$
$908$	−19.5967	−	6.36734i	−0.0215822	−	0.00701249i
$909$		0			0
$910$	275.023	−	378.537i	0.302223	−	0.415974i
$911$	282.696	+	870.047i	0.310313	+	0.955046i	0.977641	+	0.210282i	$0.0674382\pi$
$911$	282.696	+	870.047i	0.310313	+	0.955046i	−0.667327	+	0.744765i	$0.732562\pi$
$912$		0			0
$913$	−55.2054	−	43.1942i	−0.0604660	−	0.0473102i
$914$	−867.368			−0.948981
$915$		0			0
$916$	−351.047	−	255.051i	−0.383240	−	0.278440i
$917$	−1784.31	+	1296.37i	−1.94581	+	1.41371i
$918$		0			0
$919$	960.986	+	312.243i	1.04569	+	0.339764i	0.780974	−	0.624563i	$-0.214723\pi$
$919$	960.986	+	312.243i	1.04569	+	0.339764i	0.264712	+	0.964327i	$0.414723\pi$
$920$	−187.726	−	258.382i	−0.204050	−	0.280850i
$921$		0			0
$922$	206.225	+	634.696i	0.223672	+	0.688391i
$923$			230.165i			0.249367i
$924$		0			0
$925$	−1328.68			−1.43641
$926$	−472.142	+	153.408i	−0.509872	+	0.165668i
$927$		0			0
$928$	−639.369	+	464.528i	−0.688975	+	0.500569i
$929$	76.5132	−	235.483i	0.0823608	−	0.253480i	−0.901393	−	0.433001i	$-0.857455\pi$
$929$	76.5132	−	235.483i	0.0823608	−	0.253480i	0.983754	+	0.179521i	$0.0574547\pi$
$930$		0			0
$931$	330.158	+	454.423i	0.354627	+	0.488102i
$932$	305.186	−	420.053i	0.327453	−	0.450700i
$933$		0			0
$934$		−	441.436i		−	0.472629i
$935$	−247.361	+	166.593i	−0.264558	+	0.178174i
$936$		0			0
$937$	1221.51	−	396.891i	1.30363	−	0.423576i	0.426790	−	0.904351i	$-0.359644\pi$
$937$	1221.51	−	396.891i	1.30363	−	0.423576i	0.876844	+	0.480774i	$0.159644\pi$
$938$	−590.904	−	429.317i	−0.629962	−	0.457694i
$939$		0			0
$940$	93.3170	−	287.200i	0.0992734	−	0.305532i
$941$	1665.76	+	541.238i	1.77020	+	0.575173i	0.998173	−	0.0604169i	$-0.0192430\pi$
$941$	1665.76	+	541.238i	1.77020	+	0.575173i	0.772027	+	0.635590i	$0.219243\pi$
$942$		0			0
$943$	−176.739	+	243.261i	−0.187422	+	0.257965i
$944$	−80.8214	−	248.743i	−0.0856159	−	0.263498i
$945$		0			0
$946$	24.6334	−	691.366i	0.0260395	−	0.730831i
$947$	87.2570			0.0921405			0.0460702	−	0.998938i	$-0.485330\pi$
$947$	87.2570			0.0921405			0.0460702	+	0.998938i	$0.485330\pi$
$948$		0			0
$949$	944.752	+	686.402i	0.995523	+	0.723290i
$950$	−261.687	+	190.127i	−0.275460	+	0.200133i
$951$		0			0
$952$	917.535	+	298.125i	0.963798	+	0.313157i
$953$	758.674	+	1044.23i	0.796090	+	1.09572i	0.993323	+	0.115368i	$0.0368046\pi$
$953$	758.674	+	1044.23i	0.796090	+	1.09572i	−0.197233	+	0.980357i	$0.563195\pi$
$954$		0			0
$955$	42.2204	+	129.941i	0.0442098	+	0.136064i
$956$		−	174.365i		−	0.182390i
$957$		0			0
$958$	445.474			0.465004
$959$	486.494	−	158.071i	0.507293	−	0.164829i
$960$		0			0
$961$	763.456	−	554.683i	0.794439	−	0.577193i
$962$	−434.194	+	1336.31i	−0.451345	+	1.38910i
$963$		0			0
$964$	194.647	+	267.908i	0.201916	+	0.277913i
$965$	334.536	−	460.450i	0.346670	−	0.477150i
$966$		0			0
$967$			321.693i			0.332671i	0.986069	+	0.166336i	$0.0531935\pi$
$967$			321.693i			0.332671i	−0.986069	+	0.166336i	$0.946806\pi$
$968$	981.288	−	243.187i	1.01373	−	0.251226i
$969$		0			0
$970$	−98.0533	+	31.8595i	−0.101086	+	0.0328448i
$971$	101.171	+	73.5048i	0.104192	+	0.0757001i	0.638661	−	0.769488i	$-0.279488\pi$
$971$	101.171	+	73.5048i	0.104192	+	0.0757001i	−0.534469	+	0.845188i	$0.679488\pi$
$972$		0			0
$973$	84.7457	−	260.820i	0.0870973	−	0.268058i
$974$	415.697	+	135.068i	0.426794	+	0.138674i
$975$		0			0
$976$	−1.98879	+	2.73733i	−0.00203769	+	0.00280464i
$977$	−435.482	−	1340.28i	−0.445734	−	1.37183i	−0.881677	−	0.471854i	$-0.843585\pi$
$977$	−435.482	−	1340.28i	−0.445734	−	1.37183i	0.435943	−	0.899974i	$-0.356415\pi$
$978$		0			0
$979$	−40.8711	−	14.9086i	−0.0417478	−	0.0152284i
$980$	230.418			0.235121
$981$		0			0
$982$	848.971	+	616.813i	0.864532	+	0.628119i
$983$	14.9478	−	10.8602i	0.0152063	−	0.0110480i	−0.580156	−	0.814505i	$-0.697008\pi$
$983$	14.9478	−	10.8602i	0.0152063	−	0.0110480i	0.595362	+	0.803457i	$0.297008\pi$
$984$		0			0
$985$	−362.960	−	117.933i	−0.368487	−	0.119729i
$986$	250.029	+	344.135i	0.253579	+	0.349021i
$987$		0			0
$988$	−124.180	−	382.186i	−0.125688	−	0.386828i
$989$			772.628i			0.781222i
$990$		0			0
$991$	−212.736			−0.214668			−0.107334	−	0.994223i	$-0.534231\pi$
$991$	−212.736			−0.214668			−0.107334	+	0.994223i	$0.534231\pi$
$992$	−117.840	+	38.2886i	−0.118791	+	0.0385974i
$993$		0			0
$994$	160.343	−	116.496i	0.161311	−	0.117199i
$995$	−69.4751	+	213.822i	−0.0698242	+	0.214897i
$996$		0			0
$997$	−206.481	−	284.197i	−0.207103	−	0.285052i	0.692812	−	0.721118i	$-0.256372\pi$
$997$	−206.481	−	284.197i	−0.207103	−	0.285052i	−0.899915	+	0.436066i	$0.856372\pi$
$998$	−40.7360	+	56.0683i	−0.0408177	+	0.0561807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.c.28.2		16
3.2	odd	2		33.3.g.a.28.3	yes	16
11.2	odd	10	inner	99.3.k.c.46.2		16
11.3	even	5		1089.3.c.m.604.11		16
11.8	odd	10		1089.3.c.m.604.6		16
12.11	even	2		528.3.bf.b.193.2		16
33.2	even	10		33.3.g.a.13.3	✓	16
33.5	odd	10		363.3.g.g.40.2		16
33.8	even	10		363.3.c.e.241.11		16
33.14	odd	10		363.3.c.e.241.6		16
33.17	even	10		363.3.g.a.40.3		16
33.20	odd	10		363.3.g.f.112.2		16
33.26	odd	10		363.3.g.a.118.3		16
33.29	even	10		363.3.g.g.118.2		16
33.32	even	2		363.3.g.f.94.2		16
132.35	odd	10		528.3.bf.b.145.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.13.3	✓	16	33.2	even	10
33.3.g.a.28.3	yes	16	3.2	odd	2
99.3.k.c.28.2		16	1.1	even	1	trivial
99.3.k.c.46.2		16	11.2	odd	10	inner
363.3.c.e.241.6		16	33.14	odd	10
363.3.c.e.241.11		16	33.8	even	10
363.3.g.a.40.3		16	33.17	even	10
363.3.g.a.118.3		16	33.26	odd	10
363.3.g.f.94.2		16	33.32	even	2
363.3.g.f.112.2		16	33.20	odd	10
363.3.g.g.40.2		16	33.5	odd	10
363.3.g.g.118.2		16	33.29	even	10
528.3.bf.b.145.2		16	132.35	odd	10
528.3.bf.b.193.2		16	12.11	even	2
1089.3.c.m.604.6		16	11.8	odd	10
1089.3.c.m.604.11		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)

\(f(q)\)	\(=\)	\(q+(-1.28981 + 0.419086i) q^{2} +(-1.74808 + 1.27006i) q^{4} +(-0.708979 + 2.18201i) q^{5} +(-5.74346 - 7.90520i) q^{7} +(4.91103 - 6.75946i) q^{8} +O(q^{10})\)	\(q+(-1.28981 + 0.419086i) q^{2} +(-1.74808 + 1.27006i) q^{4} +(-0.708979 + 2.18201i) q^{5} +(-5.74346 - 7.90520i) q^{7} +(4.91103 - 6.75946i) q^{8} -3.11151i q^{10} +(-10.3340 - 3.76954i) q^{11} +(-14.6363 + 4.75561i) q^{13} +(10.7210 + 7.78923i) q^{14} +(-0.830695 + 2.55662i) q^{16} +(-11.2386 - 3.65165i) q^{17} +(7.10329 - 9.77683i) q^{19} +(-1.53192 - 4.71477i) q^{20} +(14.9086 + 0.531195i) q^{22} -16.6610 q^{23} +(15.9669 + 11.6006i) q^{25} +(16.8850 - 12.2677i) q^{26} +(20.0801 + 6.52441i) q^{28} +(15.6013 + 21.4734i) q^{29} +(1.28594 + 3.95770i) q^{31} +29.7749i q^{32} +16.0261 q^{34} +(21.3212 - 6.92769i) q^{35} +(-54.4646 + 39.5709i) q^{37} +(-5.06458 + 15.5872i) q^{38} +(11.2674 + 15.5082i) q^{40} +(10.6080 - 14.6006i) q^{41} -46.3735i q^{43} +(22.8521 - 6.53522i) q^{44} +(21.4896 - 6.98238i) q^{46} +(49.2812 + 35.8049i) q^{47} +(-14.3630 + 44.2047i) q^{49} +(-25.4560 - 8.27115i) q^{50} +(19.5455 - 26.9020i) q^{52} +(-31.2773 - 96.2616i) q^{53} +(15.5517 - 19.8763i) q^{55} -81.6412 q^{56} +(-29.1220 - 21.1584i) q^{58} +(-78.7122 + 57.1878i) q^{59} +(1.19706 + 0.388949i) q^{61} +(-3.31724 - 4.56578i) q^{62} +(-15.8010 - 48.6305i) q^{64} -35.3081i q^{65} -55.1168 q^{67} +(24.2838 - 7.89030i) q^{68} +(-24.5971 + 17.8709i) q^{70} +(4.62167 - 14.2240i) q^{71} +(-44.6021 - 61.3895i) q^{73} +(53.6656 - 73.8644i) q^{74} +26.1123i q^{76} +(29.5537 + 103.342i) q^{77} +(27.7900 - 9.02950i) q^{79} +(-4.98962 - 3.62517i) q^{80} +(-7.56341 + 23.2778i) q^{82} +(6.06044 + 1.96915i) q^{83} +(15.9359 - 21.9339i) q^{85} +(19.4345 + 59.8133i) q^{86} +(-76.2304 + 51.3395i) q^{88} +3.95503 q^{89} +(121.657 + 88.3889i) q^{91} +(29.1247 - 21.1604i) q^{92} +(-78.5689 - 25.5286i) q^{94} +(16.2971 + 22.4310i) q^{95} +(-10.2392 - 31.5131i) q^{97} -63.0352i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) 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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