LMFDB - Embedded newform 684.5.y.c.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,5,Mod(145,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("684.145");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	684.y (of order $6$, degree $2$, 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:	$70.7050547493$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} + \cdots + 90728724573 $ x^12 - 6x^11 + 631x^10 - 3100x^9 + 142264x^8 - 550522x^7 + 14083117x^6 - 40335478x^5 + 638031136x^4 - 1209472584x^3 + 12784623475x^2 - 12186518934*x + 90728724573
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$0.500000 + 4.96177i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.c.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.5891 - 27.0012i) q^{5} -2.67956 q^{7} +O(q^{10})$	$q+(-15.5891 - 27.0012i) q^{5} -2.67956 q^{7} -42.3332 q^{11} +(113.779 + 65.6905i) q^{13} +(-143.163 - 247.965i) q^{17} +(326.580 - 153.840i) q^{19} +(158.172 - 273.962i) q^{23} +(-173.542 + 300.584i) q^{25} +(188.788 + 108.997i) q^{29} -475.836i q^{31} +(41.7721 + 72.3514i) q^{35} -1740.18i q^{37} +(104.869 - 60.5462i) q^{41} +(-1237.98 - 2144.24i) q^{43} +(-168.749 + 292.282i) q^{47} -2393.82 q^{49} +(3656.19 + 2110.90i) q^{53} +(659.938 + 1143.05i) q^{55} +(-4911.88 + 2835.87i) q^{59} +(-1945.85 + 3370.31i) q^{61} -4096.23i q^{65} +(2805.03 + 1619.49i) q^{67} +(-4050.68 + 2338.66i) q^{71} +(803.586 + 1391.85i) q^{73} +113.435 q^{77} +(-2909.85 + 1680.00i) q^{79} -6545.45 q^{83} +(-4463.57 + 7731.13i) q^{85} +(-3179.74 - 1835.82i) q^{89} +(-304.879 - 176.022i) q^{91} +(-9244.95 - 6419.80i) q^{95} +(4872.79 - 2813.31i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{5} - 52 q^{7}+O(q^{10}) $ 12 * q - 9 * q^5 - 52 * q^7	$ 12 q - 9 q^{5} - 52 q^{7} - 6 q^{11} - 93 q^{13} + 483 q^{17} - 533 q^{19} - 531 q^{23} - 217 q^{25} - 2025 q^{29} + 1128 q^{35} + 1692 q^{41} - 63 q^{43} + 3471 q^{47} + 420 q^{49} + 3771 q^{53} - 2014 q^{55} + 9594 q^{59} + 1229 q^{61} + 7590 q^{67} - 963 q^{71} - 2838 q^{73} + 15408 q^{77} + 11073 q^{79} + 14202 q^{83} + 9455 q^{85} - 6525 q^{89} - 7686 q^{91} - 1521 q^{95} - 34110 q^{97}+O(q^{100}) $ 12 * q - 9 * q^5 - 52 * q^7 - 6 * q^11 - 93 * q^13 + 483 * q^17 - 533 * q^19 - 531 * q^23 - 217 * q^25 - 2025 * q^29 + 1128 * q^35 + 1692 * q^41 - 63 * q^43 + 3471 * q^47 + 420 * q^49 + 3771 * q^53 - 2014 * q^55 + 9594 * q^59 + 1229 * q^61 + 7590 * q^67 - 963 * q^71 - 2838 * q^73 + 15408 * q^77 + 11073 * q^79 + 14202 * q^83 + 9455 * q^85 - 6525 * q^89 - 7686 * q^91 - 1521 * q^95 - 34110 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−15.5891	−	27.0012i	−0.623566	−	1.08005i	−0.988816	−	0.149138i	$-0.952350\pi$
$5$	−15.5891	−	27.0012i	−0.623566	−	1.08005i	0.365251	−	0.930909i	$-0.380983\pi$
$6$		0			0
$7$	−2.67956			−0.0546850			−0.0273425	−	0.999626i	$-0.508704\pi$
$7$	−2.67956			−0.0546850			−0.0273425	+	0.999626i	$0.508704\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−42.3332			−0.349861			−0.174931	−	0.984581i	$-0.555970\pi$
$11$	−42.3332			−0.349861			−0.174931	+	0.984581i	$0.555970\pi$
$12$		0			0
$13$	113.779	+	65.6905i	0.673250	+	0.388701i	0.797307	−	0.603574i	$-0.206257\pi$
$13$	113.779	+	65.6905i	0.673250	+	0.388701i	−0.124057	+	0.992275i	$0.539591\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−143.163	−	247.965i	−0.495373	−	0.858011i	0.504613	−	0.863346i	$-0.331635\pi$
$17$	−143.163	−	247.965i	−0.495373	−	0.858011i	−0.999986	+	0.00533450i	$0.998302\pi$
$18$		0			0
$19$	326.580	−	153.840i	0.904653	−	0.426149i
$19$	326.580	−	153.840i	0.904653	−	0.426149i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	158.172	−	273.962i	0.299002	−	0.517887i	−0.676906	−	0.736070i	$-0.736679\pi$
$23$	158.172	−	273.962i	0.299002	−	0.517887i	0.975908	+	0.218183i	$0.0700128\pi$
$24$		0			0
$25$	−173.542	+	300.584i	−0.277668	+	0.480935i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	188.788	+	108.997i	0.224481	+	0.129604i	0.608023	−	0.793919i	$-0.291963\pi$
$29$	188.788	+	108.997i	0.224481	+	0.129604i	−0.383542	+	0.923523i	$0.625296\pi$
$30$		0			0
$31$		−	475.836i		−	0.495147i	−0.968869	−	0.247573i	$-0.920367\pi$
$31$		−	475.836i		−	0.495147i	0.968869	−	0.247573i	$-0.0796331\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	41.7721	+	72.3514i	0.0340997	+	0.0590623i
$36$		0			0
$37$		−	1740.18i		−	1.27114i	−0.772045	−	0.635568i	$-0.780766\pi$
$37$		−	1740.18i		−	1.27114i	0.772045	−	0.635568i	$-0.219234\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	104.869	−	60.5462i	0.0623849	−	0.0360180i	−0.468483	−	0.883472i	$-0.655199\pi$
$41$	104.869	−	60.5462i	0.0623849	−	0.0360180i	0.530868	+	0.847454i	$0.321866\pi$
$42$		0			0
$43$	−1237.98	−	2144.24i	−0.669540	−	1.15968i	−0.978033	−	0.208451i	$-0.933158\pi$
$43$	−1237.98	−	2144.24i	−0.669540	−	1.15968i	0.308493	−	0.951227i	$-0.400175\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−168.749	+	292.282i	−0.0763917	+	0.132314i	−0.901691	−	0.432382i	$-0.857673\pi$
$47$	−168.749	+	292.282i	−0.0763917	+	0.132314i	0.825299	+	0.564696i	$0.191007\pi$
$48$		0			0
$49$	−2393.82			−0.997010
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3656.19	+	2110.90i	1.30160	+	0.751477i	0.980678	−	0.195630i	$-0.0626750\pi$
$53$	3656.19	+	2110.90i	1.30160	+	0.751477i	0.320919	+	0.947107i	$0.396008\pi$
$54$		0			0
$55$	659.938	+	1143.05i	0.218161	+	0.377867i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4911.88	+	2835.87i	−1.41105	+	0.814672i	−0.995488	−	0.0948915i	$-0.969750\pi$
$59$	−4911.88	+	2835.87i	−1.41105	+	0.814672i	−0.415565	+	0.909563i	$0.636416\pi$
$60$		0			0
$61$	−1945.85	+	3370.31i	−0.522937	+	0.905754i	0.476706	+	0.879063i	$0.341831\pi$
$61$	−1945.85	+	3370.31i	−0.522937	+	0.905754i	−0.999644	+	0.0266915i	$0.991503\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	4096.23i		−	0.969522i
$66$		0			0
$67$	2805.03	+	1619.49i	0.624868	+	0.360768i	0.778762	−	0.627320i	$-0.215848\pi$
$67$	2805.03	+	1619.49i	0.624868	+	0.360768i	−0.153894	+	0.988087i	$0.549181\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4050.68	+	2338.66i	−0.803546	+	0.463928i	−0.844710	−	0.535225i	$-0.820227\pi$
$71$	−4050.68	+	2338.66i	−0.803546	+	0.463928i	0.0411635	+	0.999152i	$0.486894\pi$
$72$		0			0
$73$	803.586	+	1391.85i	0.150795	+	0.261184i	0.931520	−	0.363690i	$-0.118483\pi$
$73$	803.586	+	1391.85i	0.150795	+	0.261184i	−0.780725	+	0.624875i	$0.785150\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	113.435			0.0191322
$78$		0			0
$79$	−2909.85	+	1680.00i	−0.466247	+	0.269188i	−0.714667	−	0.699464i	$-0.753422\pi$
$79$	−2909.85	+	1680.00i	−0.466247	+	0.269188i	0.248420	+	0.968652i	$0.420089\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6545.45			−0.950131			−0.475065	−	0.879950i	$-0.657576\pi$
$83$	−6545.45			−0.950131			−0.475065	+	0.879950i	$0.657576\pi$
$84$		0			0
$85$	−4463.57	+	7731.13i	−0.617795	+	1.07005i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3179.74	−	1835.82i	−0.401431	−	0.231766i	0.285670	−	0.958328i	$-0.407784\pi$
$89$	−3179.74	−	1835.82i	−0.401431	−	0.231766i	−0.687101	+	0.726562i	$0.741117\pi$
$90$		0			0
$91$	−304.879	−	176.022i	−0.0368166	−	0.0212561i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9244.95	−	6419.80i	−1.02437	−	0.711336i
$96$		0			0
$97$	4872.79	−	2813.31i	0.517886	−	0.299002i	−0.218183	−	0.975908i	$-0.570013\pi$
$97$	4872.79	−	2813.31i	0.517886	−	0.299002i	0.736069	+	0.676906i	$0.236680\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2277.54	+	3944.81i	−0.223266	+	0.386708i	−0.955798	−	0.294025i	$-0.905005\pi$
$101$	−2277.54	+	3944.81i	−0.223266	+	0.386708i	0.732532	+	0.680733i	$0.238339\pi$
$102$		0			0
$103$			3792.04i			0.357436i	0.983900	+	0.178718i	$0.0571950\pi$
$103$			3792.04i			0.357436i	−0.983900	+	0.178718i	$0.942805\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			973.573i			0.0850357i	0.999096	+	0.0425178i	$0.0135379\pi$
$107$			973.573i			0.0850357i	−0.999096	+	0.0425178i	$0.986462\pi$
$108$		0			0
$109$	947.163	−	546.845i	0.0797208	−	0.0460268i	−0.459610	−	0.888121i	$-0.652011\pi$
$109$	947.163	−	546.845i	0.0797208	−	0.0460268i	0.539331	+	0.842094i	$0.318677\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8095.59i			0.634003i	0.948425	+	0.317002i	$0.102676\pi$
$113$			8095.59i			0.634003i	−0.948425	+	0.317002i	$0.897324\pi$
$114$		0			0
$115$	−9863.08			−0.745790
$116$		0			0
$117$		0			0
$118$		0			0
$119$	383.614	+	664.439i	0.0270895	+	0.0469203i
$120$		0			0
$121$	−12848.9			−0.877597
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8664.91			−0.554555
$126$		0			0
$127$	−16925.5	−	9771.95i	−1.04938	−	0.605862i	−0.126907	−	0.991915i	$-0.540505\pi$
$127$	−16925.5	−	9771.95i	−1.04938	−	0.605862i	−0.922477	+	0.386053i	$0.873838\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4157.45	+	7200.92i	0.242262	+	0.419610i	0.961358	−	0.275301i	$-0.0887774\pi$
$131$	4157.45	+	7200.92i	0.242262	+	0.419610i	−0.719096	+	0.694910i	$0.755444\pi$
$132$		0			0
$133$	−875.091	+	412.224i	−0.0494709	+	0.0233040i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15897.5	+	27535.3i	−0.847008	+	1.46706i	0.0368587	+	0.999320i	$0.488265\pi$
$137$	−15897.5	+	27535.3i	−0.847008	+	1.46706i	−0.883866	+	0.467740i	$0.845068\pi$
$138$		0			0
$139$	14915.2	−	25833.8i	0.771967	−	1.33709i	−0.164516	−	0.986374i	$-0.552606\pi$
$139$	14915.2	−	25833.8i	0.771967	−	1.33709i	0.936483	−	0.350712i	$-0.114060\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4816.64	−	2780.89i	−0.235544	−	0.135991i
$144$		0			0
$145$		−	6796.68i		−	0.323267i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17689.6	−	30639.3i	−0.796793	−	1.38009i	−0.921694	−	0.387917i	$-0.873195\pi$
$149$	−17689.6	−	30639.3i	−0.796793	−	1.38009i	0.124901	−	0.992169i	$-0.460139\pi$
$150$		0			0
$151$		−	13999.5i		−	0.613987i	−0.951712	−	0.306994i	$-0.900677\pi$
$151$		−	13999.5i		−	0.613987i	0.951712	−	0.306994i	$-0.0993230\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12848.1	+	7417.87i	−0.534782	+	0.308756i
$156$		0			0
$157$	17868.1	+	30948.5i	0.724902	+	1.25557i	0.959014	+	0.283358i	$0.0914485\pi$
$157$	17868.1	+	30948.5i	0.724902	+	1.25557i	−0.234112	+	0.972210i	$0.575218\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−423.833	+	734.099i	−0.0163509	+	0.0283206i
$162$		0			0
$163$	−30641.7			−1.15329			−0.576644	−	0.816995i	$-0.695638\pi$
$163$	−30641.7			−1.15329			−0.576644	+	0.816995i	$0.695638\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−35977.1	−	20771.4i	−1.29001	−	0.744788i	−0.311355	−	0.950294i	$-0.600783\pi$
$167$	−35977.1	−	20771.4i	−1.29001	−	0.744788i	−0.978656	+	0.205506i	$0.934116\pi$
$168$		0			0
$169$	−5650.02	−	9786.13i	−0.197823	−	0.342640i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	27433.2	−	15838.6i	0.916611	−	0.529205i	0.0340586	−	0.999420i	$-0.489157\pi$
$173$	27433.2	−	15838.6i	0.916611	−	0.529205i	0.882552	+	0.470214i	$0.155823\pi$
$174$		0			0
$175$	465.018	−	805.434i	0.0151843	−	0.0262999i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	28590.1i		−	0.892298i	−0.894959	−	0.446149i	$-0.852795\pi$
$179$		−	28590.1i		−	0.892298i	0.894959	−	0.446149i	$-0.147205\pi$
$180$		0			0
$181$	32286.9	+	18640.9i	0.985529	+	0.568996i	0.903935	−	0.427670i	$-0.140665\pi$
$181$	32286.9	+	18640.9i	0.985529	+	0.568996i	0.0815944	+	0.996666i	$0.473999\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−46987.0	+	27128.0i	−1.37289	+	0.792636i
$186$		0			0
$187$	6060.54	+	10497.2i	0.173312	+	0.300185i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8555.08			0.234508			0.117254	−	0.993102i	$-0.462591\pi$
$191$	8555.08			0.234508			0.117254	+	0.993102i	$0.462591\pi$
$192$		0			0
$193$	20694.2	−	11947.8i	0.555563	−	0.320754i	−0.195800	−	0.980644i	$-0.562730\pi$
$193$	20694.2	−	11947.8i	0.555563	−	0.320754i	0.751363	+	0.659890i	$0.229397\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19842.4			−0.511284			−0.255642	−	0.966772i	$-0.582287\pi$
$197$	−19842.4			−0.511284			−0.255642	+	0.966772i	$0.582287\pi$
$198$		0			0
$199$	−14300.1	+	24768.5i	−0.361104	+	0.625451i	−0.988143	−	0.153537i	$-0.950933\pi$
$199$	−14300.1	+	24768.5i	−0.361104	+	0.625451i	0.627039	+	0.778988i	$0.284267\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−505.870	−	292.064i	−0.0122757	−	0.00708739i
$204$		0			0
$205$	−3269.64	−	1887.73i	−0.0778022	−	0.0449191i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13825.2	+	6512.54i	−0.316503	+	0.149093i
$210$		0			0
$211$	−74772.9	+	43170.2i	−1.67950	+	0.969659i	−0.717517	+	0.696541i	$0.754722\pi$
$211$	−74772.9	+	43170.2i	−1.67950	+	0.969659i	−0.961981	+	0.273118i	$0.911945\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−38598.1	+	66853.8i	−0.835004	+	1.44627i
$216$		0			0
$217$			1275.03i			0.0270771i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	37617.7i		−	0.770208i
$222$		0			0
$223$	−16078.0	+	9282.64i	−0.323313	+	0.186665i	−0.652868	−	0.757472i	$-0.726434\pi$
$223$	−16078.0	+	9282.64i	−0.323313	+	0.186665i	0.329556	+	0.944136i	$0.393101\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			43957.1i			0.853055i	0.904474	+	0.426528i	$0.140263\pi$
$227$			43957.1i			0.853055i	−0.904474	+	0.426528i	$0.859737\pi$
$228$		0			0
$229$	−93023.8			−1.77387			−0.886937	−	0.461890i	$-0.847172\pi$
$229$	−93023.8			−1.77387			−0.886937	+	0.461890i	$0.847172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12284.1	−	21276.6i	−0.226272	−	0.391914i	0.730429	−	0.682989i	$-0.239320\pi$
$233$	−12284.1	−	21276.6i	−0.226272	−	0.391914i	−0.956700	+	0.291075i	$0.905987\pi$
$234$		0			0
$235$	10522.6			0.190541
$236$		0			0
$237$		0			0
$238$		0			0
$239$	61076.4			1.06925			0.534623	−	0.845091i	$-0.320454\pi$
$239$	61076.4			1.06925			0.534623	+	0.845091i	$0.320454\pi$
$240$		0			0
$241$	24641.4	+	14226.7i	0.424260	+	0.244947i	0.696898	−	0.717170i	$-0.254563\pi$
$241$	24641.4	+	14226.7i	0.424260	+	0.244947i	−0.272638	+	0.962117i	$0.587896\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	37317.6	+	64636.0i	0.621701	+	1.07682i
$246$		0			0
$247$	47263.8	+	3949.38i	0.774702	+	0.0647344i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−33418.7	+	57882.9i	−0.530447	+	0.918762i	0.468922	+	0.883240i	$0.344643\pi$
$251$	−33418.7	+	57882.9i	−0.530447	+	0.918762i	−0.999369	+	0.0355218i	$0.988691\pi$
$252$		0			0
$253$	−6695.94	+	11597.7i	−0.104609	+	0.181189i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−100520.	−	58035.5i	−1.52191	−	0.878673i	−0.999665	−	0.0258749i	$-0.991763\pi$
$257$	−100520.	−	58035.5i	−1.52191	−	0.878673i	−0.522241	−	0.852798i	$-0.674904\pi$
$258$		0			0
$259$			4662.93i			0.0695120i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	43974.4	+	76165.9i	0.635753	+	1.10116i	0.986355	+	0.164633i	$0.0526438\pi$
$263$	43974.4	+	76165.9i	0.635753	+	1.10116i	−0.350602	+	0.936525i	$0.614023\pi$
$264$		0			0
$265$		−	131628.i		−	1.87438i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	106194.	−	61311.2i	1.46756	−	0.847296i	0.468219	−	0.883613i	$-0.344896\pi$
$269$	106194.	−	61311.2i	1.46756	−	0.847296i	0.999340	+	0.0363169i	$0.0115626\pi$
$270$		0			0
$271$	−22643.2	−	39219.1i	−0.308318	−	0.534022i	0.669677	−	0.742653i	$-0.266433\pi$
$271$	−22643.2	−	39219.1i	−0.308318	−	0.534022i	−0.977995	+	0.208631i	$0.933099\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7346.61	−	12724.7i	0.0971453	−	0.168261i
$276$		0			0
$277$	−90121.7			−1.17454			−0.587272	−	0.809389i	$-0.699798\pi$
$277$	−90121.7			−1.17454			−0.587272	+	0.809389i	$0.699798\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	87904.2	+	50751.5i	1.11326	+	0.642742i	0.939672	−	0.342077i	$-0.111130\pi$
$281$	87904.2	+	50751.5i	1.11326	+	0.642742i	0.173589	+	0.984818i	$0.444464\pi$
$282$		0			0
$283$	−959.420	−	1661.76i	−0.0119794	−	0.0207490i	0.859974	−	0.510339i	$-0.170480\pi$
$283$	−959.420	−	1661.76i	−0.0119794	−	0.0207490i	−0.871953	+	0.489590i	$0.837147\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−281.003	+	162.237i	−0.00341152	+	0.00196964i
$288$		0			0
$289$	769.316	−	1332.49i	0.00921104	−	0.0159540i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	111146.i		−	1.29466i	−0.762208	−	0.647332i	$-0.775885\pi$
$293$		−	111146.i		−	1.29466i	0.762208	−	0.647332i	$-0.224115\pi$
$294$		0			0
$295$	153144.	+	88417.6i	1.75977	+	1.01600i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	35993.4	−	20780.8i	0.402607	−	0.232445i
$300$		0			0
$301$	3317.24	+	5745.64i	0.0366138	+	0.0634169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	121337.			1.30434
$306$		0			0
$307$	94905.2	−	54793.5i	1.00696	−	0.581370i	0.0966613	−	0.995317i	$-0.469184\pi$
$307$	94905.2	−	54793.5i	1.00696	−	0.581370i	0.910301	+	0.413948i	$0.135850\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−94945.0			−0.981637			−0.490819	−	0.871262i	$-0.663302\pi$
$311$	−94945.0			−0.981637			−0.490819	+	0.871262i	$0.663302\pi$
$312$		0			0
$313$	10819.3	−	18739.5i	0.110436	−	0.191280i	−0.805510	−	0.592582i	$-0.798109\pi$
$313$	10819.3	−	18739.5i	0.110436	−	0.191280i	0.915946	+	0.401302i	$0.131442\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−118433.	−	68377.5i	−1.17857	−	0.680448i	−0.222887	−	0.974844i	$-0.571548\pi$
$317$	−118433.	−	68377.5i	−1.17857	−	0.680448i	−0.955683	+	0.294396i	$0.904881\pi$
$318$		0			0
$319$	−7992.02	−	4614.20i	−0.0785372	−	0.0453435i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−84901.0	−	58956.3i	−0.813782	−	0.565099i
$324$		0			0
$325$	−39491.0	+	22800.2i	−0.373880	+	0.215860i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	452.174	−	783.189i	0.00417748	−	0.00723561i
$330$		0			0
$331$			201597.i			1.84004i	0.391869	+	0.920021i	$0.371829\pi$
$331$			201597.i			1.84004i	−0.391869	+	0.920021i	$0.628171\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	100986.i		−	0.899850i
$336$		0			0
$337$	178761.	−	103208.i	1.57403	−	0.908766i	0.578361	−	0.815781i	$-0.303693\pi$
$337$	178761.	−	103208.i	1.57403	−	0.908766i	0.995668	−	0.0929845i	$-0.0296407\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			20143.7i			0.173233i
$342$		0			0
$343$	12848.0			0.109206
$344$		0			0
$345$		0			0
$346$		0			0
$347$	610.820	+	1057.97i	0.00507288	+	0.00878648i	0.868551	−	0.495600i	$-0.165052\pi$
$347$	610.820	+	1057.97i	0.00507288	+	0.00878648i	−0.863478	+	0.504387i	$0.831719\pi$
$348$		0			0
$349$	−205690.			−1.68874			−0.844368	−	0.535763i	$-0.820024\pi$
$349$	−205690.			−1.68874			−0.844368	+	0.535763i	$0.820024\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	236605.			1.89878			0.949389	−	0.314101i	$-0.101703\pi$
$353$	236605.			1.89878			0.949389	+	0.314101i	$0.101703\pi$
$354$		0			0
$355$	126293.	+	72915.4i	1.00213	+	0.578578i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	54382.0	+	94192.4i	0.421955	+	0.730848i	0.996131	−	0.0878842i	$-0.0280106\pi$
$359$	54382.0	+	94192.4i	0.421955	+	0.730848i	−0.574175	+	0.818732i	$0.694677\pi$
$360$		0			0
$361$	82987.6	−	100482.i	0.636793	−	0.771034i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	25054.4	−	43395.5i	0.188061	−	0.325731i
$366$		0			0
$367$	93469.1	−	161893.i	0.693962	−	1.20198i	−0.276567	−	0.960995i	$-0.589197\pi$
$367$	93469.1	−	161893.i	0.693962	−	1.20198i	0.970529	−	0.240983i	$-0.0774699\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9796.98	−	5656.29i	−0.0711778	−	0.0410945i
$372$		0			0
$373$			53955.4i			0.387808i	0.981020	+	0.193904i	$0.0621151\pi$
$373$			53955.4i			0.387808i	−0.981020	+	0.193904i	$0.937885\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14320.1	+	24803.2i	0.100754	+	0.174512i
$378$		0			0
$379$		−	222631.i		−	1.54991i	−0.632014	−	0.774957i	$-0.717771\pi$
$379$		−	222631.i		−	1.54991i	0.632014	−	0.774957i	$-0.282229\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−28982.0	+	16732.7i	−0.197574	+	0.114070i	−0.595524	−	0.803338i	$-0.703055\pi$
$383$	−28982.0	+	16732.7i	−0.197574	+	0.114070i	0.397949	+	0.917407i	$0.369722\pi$
$384$		0			0
$385$	−1768.35	−	3062.87i	−0.0119301	−	0.0206636i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	41708.6	−	72241.3i	0.275630	−	0.477405i	−0.694664	−	0.719334i	$-0.744447\pi$
$389$	41708.6	−	72241.3i	0.275630	−	0.477405i	0.970294	+	0.241930i	$0.0777803\pi$
$390$		0			0
$391$	−90577.5			−0.592471
$392$		0			0
$393$		0			0
$394$		0			0
$395$	90724.1	+	52379.6i	0.581471	+	0.335713i
$396$		0			0
$397$	2130.79	+	3690.63i	0.0135194	+	0.0234164i	0.872706	−	0.488246i	$-0.162363\pi$
$397$	2130.79	+	3690.63i	0.0135194	+	0.0234164i	−0.859187	+	0.511662i	$0.829030\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	81965.1	−	47322.6i	0.509730	−	0.294293i	−0.222993	−	0.974820i	$-0.571583\pi$
$401$	81965.1	−	47322.6i	0.509730	−	0.294293i	0.732723	+	0.680527i	$0.238249\pi$
$402$		0			0
$403$	31257.9	−	54140.2i	0.192464	−	0.333357i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			73667.6i			0.444721i
$408$		0			0
$409$	−3842.38	−	2218.40i	−0.0229696	−	0.0132615i	0.488471	−	0.872580i	$-0.337555\pi$
$409$	−3842.38	−	2218.40i	−0.0229696	−	0.0132615i	−0.511441	+	0.859318i	$0.670888\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13161.7	−	7598.90i	0.0771634	−	0.0445503i
$414$		0			0
$415$	102038.	+	176735.i	0.592469	+	1.02619i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	316042.			1.80019			0.900093	−	0.435698i	$-0.143498\pi$
$419$	316042.			1.80019			0.900093	+	0.435698i	$0.143498\pi$
$420$		0			0
$421$	76625.6	−	44239.8i	0.432324	−	0.249603i	−0.268012	−	0.963416i	$-0.586367\pi$
$421$	76625.6	−	44239.8i	0.432324	−	0.249603i	0.700336	+	0.713813i	$0.253033\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	99379.3			0.550197
$426$		0			0
$427$	5214.03	−	9030.96i	0.0285968	−	0.0495311i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	279779.	+	161530.i	1.50612	+	0.869560i	0.999975	+	0.00711255i	$0.00226402\pi$
$431$	279779.	+	161530.i	1.50612	+	0.869560i	0.506147	+	0.862447i	$0.331069\pi$
$432$		0			0
$433$	77804.0	+	44920.2i	0.414979	+	0.239588i	0.692927	−	0.721008i	$-0.256321\pi$
$433$	77804.0	+	44920.2i	0.414979	+	0.239588i	−0.277948	+	0.960596i	$0.589654\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9509.49	−	113804.i	0.0497960	−	0.595928i
$438$		0			0
$439$	−314840.	+	181773.i	−1.63366	+	0.943192i	−0.650705	+	0.759331i	$0.725527\pi$
$439$	−314840.	+	181773.i	−1.63366	+	0.943192i	−0.982952	+	0.183862i	$0.941140\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−102342.	+	177262.i	−0.521492	+	0.903250i	0.478196	+	0.878253i	$0.341291\pi$
$443$	−102342.	+	177262.i	−0.521492	+	0.903250i	−0.999688	+	0.0249967i	$0.992042\pi$
$444$		0			0
$445$			114476.i			0.578086i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	14073.0i		−	0.0698063i	−0.999391	−	0.0349031i	$-0.988888\pi$
$449$		−	14073.0i		−	0.0698063i	0.999391	−	0.0349031i	$-0.0111123\pi$
$450$		0			0
$451$	−4439.45	+	2563.12i	−0.0218261	+	0.0126013i
$452$		0			0
$453$		0			0
$454$		0			0
$455$			10976.1i			0.0530183i
$456$		0			0
$457$	209656.			1.00387			0.501933	−	0.864906i	$-0.332622\pi$
$457$	209656.			1.00387			0.501933	+	0.864906i	$0.332622\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−91669.7	−	158777.i	−0.431344	−	0.747110i	0.565645	−	0.824649i	$-0.308627\pi$
$461$	−91669.7	−	158777.i	−0.431344	−	0.747110i	−0.996989	+	0.0775385i	$0.975294\pi$
$462$		0			0
$463$	−129586.			−0.604501			−0.302250	−	0.953229i	$-0.597738\pi$
$463$	−129586.			−0.604501			−0.302250	+	0.953229i	$0.597738\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−180073.			−0.825686			−0.412843	−	0.910802i	$-0.635464\pi$
$467$	−180073.			−0.825686			−0.412843	+	0.910802i	$0.635464\pi$
$468$		0			0
$469$	−7516.26	−	4339.52i	−0.0341709	−	0.0197286i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	52407.7	+	90772.7i	0.234246	+	0.405726i
$474$		0			0
$475$	−10433.6	+	124862.i	−0.0462429	+	0.553407i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−98408.8	+	170449.i	−0.428907	+	0.742889i	−0.996776	−	0.0802301i	$-0.974434\pi$
$479$	−98408.8	+	170449.i	−0.428907	+	0.742889i	0.567869	+	0.823119i	$0.307768\pi$
$480$		0			0
$481$	114314.	−	197997.i	0.494092	−	0.855792i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−151925.	−	87714.1i	−0.645872	−	0.372894i
$486$		0			0
$487$			170934.i			0.720728i	0.932812	+	0.360364i	$0.117348\pi$
$487$			170934.i			0.720728i	−0.932812	+	0.360364i	$0.882652\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−69546.2	−	120458.i	−0.288476	−	0.499656i	0.684970	−	0.728571i	$-0.259815\pi$
$491$	−69546.2	−	120458.i	−0.288476	−	0.499656i	−0.973446	+	0.228916i	$0.926482\pi$
$492$		0			0
$493$		−	62417.3i		−	0.256809i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10854.0	−	6266.58i	0.0439419	−	0.0253699i
$498$		0			0
$499$	131082.	+	227041.i	0.526432	+	0.911807i	0.999526	+	0.0307946i	$0.00980377\pi$
$499$	131082.	+	227041.i	0.526432	+	0.911807i	−0.473094	+	0.881012i	$0.656863\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	165915.	−	287373.i	0.655767	−	1.13582i	−0.325933	−	0.945393i	$-0.605678\pi$
$503$	165915.	−	287373.i	0.655767	−	1.13582i	0.981701	−	0.190430i	$-0.0609882\pi$
$504$		0			0
$505$	142019.			0.556884
$506$		0			0
$507$		0			0
$508$		0			0
$509$	84260.9	+	48648.0i	0.325230	+	0.187772i	0.653721	−	0.756735i	$-0.273207\pi$
$509$	84260.9	+	48648.0i	0.325230	+	0.187772i	−0.328491	+	0.944507i	$0.606540\pi$
$510$		0			0
$511$	−2153.26	−	3729.55i	−0.00824621	−	0.0142829i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	102390.	−	59114.6i	0.386048	−	0.222885i
$516$		0			0
$517$	7143.70	−	12373.3i	0.0267265	−	0.0462917i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	147455.i		−	0.543231i	−0.962406	−	0.271615i	$-0.912442\pi$
$521$		−	147455.i		−	0.543231i	0.962406	−	0.271615i	$-0.0875578\pi$
$522$		0			0
$523$	−304145.	−	175598.i	−1.11193	−	0.641973i	−0.172601	−	0.984992i	$-0.555217\pi$
$523$	−304145.	−	175598.i	−1.11193	−	0.641973i	−0.939329	+	0.343019i	$0.888551\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−117991.	+	68122.0i	−0.424841	+	0.245282i
$528$		0			0
$529$	89883.6	+	155683.i	0.321195	+	0.556326i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	15909.2			0.0560009
$534$		0			0
$535$	26287.6	−	15177.2i	0.0918425	−	0.0530253i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	101338.			0.348815
$540$		0			0
$541$	41571.0	−	72003.1i	0.142035	−	0.246012i	−0.786228	−	0.617937i	$-0.787969\pi$
$541$	41571.0	−	72003.1i	0.142035	−	0.246012i	0.928263	+	0.371925i	$0.121302\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−29530.9	−	17049.7i	−0.0994223	−	0.0574015i
$546$		0			0
$547$	260352.	+	150314.i	0.870135	+	0.502373i	0.867393	−	0.497624i	$-0.165794\pi$
$547$	260352.	+	150314.i	0.870135	+	0.502373i	0.00274192	+	0.999996i	$0.499127\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	78422.5	+	6553.02i	0.258308	+	0.0215843i
$552$		0			0
$553$	7797.12	−	4501.67i	0.0254967	−	0.0147205i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−79597.5	+	137867.i	−0.256560	+	0.444375i	−0.965318	−	0.261077i	$-0.915923\pi$
$557$	−79597.5	+	137867.i	−0.256560	+	0.444375i	0.708758	+	0.705452i	$0.249256\pi$
$558$		0			0
$559$		−	325294.i		−	1.04100i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			325284.i			1.02623i	0.858319	+	0.513117i	$0.171509\pi$
$563$			325284.i			1.02623i	−0.858319	+	0.513117i	$0.828491\pi$
$564$		0			0
$565$	218590.	−	126203.i	0.684753	−	0.395343i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	489736.i		−	1.51265i	−0.654199	−	0.756323i	$-0.726994\pi$
$569$		−	489736.i		−	1.51265i	0.654199	−	0.756323i	$-0.273006\pi$
$570$		0			0
$571$	−307676.			−0.943672			−0.471836	−	0.881686i	$-0.656409\pi$
$571$	−307676.			−0.943672			−0.471836	+	0.881686i	$0.656409\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	54899.2	+	95088.2i	0.166047	+	0.287601i
$576$		0			0
$577$	−20529.7			−0.0616638			−0.0308319	−	0.999525i	$-0.509816\pi$
$577$	−20529.7			−0.0616638			−0.0308319	+	0.999525i	$0.509816\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	17538.9			0.0519579
$582$		0			0
$583$	−154778.	−	89361.2i	−0.455378	−	0.262913i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18925.0	+	32779.0i	0.0549236	+	0.0951305i	0.892180	−	0.451680i	$-0.149175\pi$
$587$	18925.0	+	32779.0i	0.0549236	+	0.0951305i	−0.837256	+	0.546811i	$0.815842\pi$
$588$		0			0
$589$	−73202.6	−	155398.i	−0.211006	−	0.447936i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	153015.	−	265029.i	0.435134	−	0.753675i	−0.562172	−	0.827020i	$-0.690034\pi$
$593$	153015.	−	265029.i	0.435134	−	0.753675i	0.997307	+	0.0733454i	$0.0233675\pi$
$594$		0			0
$595$	11960.4	−	20716.0i	0.0337841	−	0.0585158i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	121787.	+	70313.5i	0.339427	+	0.195968i	0.660018	−	0.751249i	$-0.270548\pi$
$599$	121787.	+	70313.5i	0.339427	+	0.195968i	−0.320592	+	0.947217i	$0.603882\pi$
$600$		0			0
$601$		−	210748.i		−	0.583464i	−0.956500	−	0.291732i	$-0.905768\pi$
$601$		−	210748.i		−	0.583464i	0.956500	−	0.291732i	$-0.0942315\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	200303.	+	346935.i	0.547239	+	0.947846i
$606$		0			0
$607$		−	432873.i		−	1.17485i	−0.809278	−	0.587426i	$-0.800141\pi$
$607$		−	432873.i		−	1.17485i	0.809278	−	0.587426i	$-0.199859\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−38400.3	+	22170.4i	−0.102861	+	0.0593871i
$612$		0			0
$613$	−358892.	−	621619.i	−0.955087	−	1.65426i	−0.734169	−	0.678967i	$-0.762428\pi$
$613$	−358892.	−	621619.i	−0.955087	−	1.65426i	−0.220918	−	0.975292i	$-0.570905\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	83115.0	−	143959.i	0.218328	−	0.378155i	−0.735969	−	0.677015i	$-0.763273\pi$
$617$	83115.0	−	143959.i	0.218328	−	0.378155i	0.954297	+	0.298860i	$0.0966065\pi$
$618$		0			0
$619$	−475284.			−1.24043			−0.620214	−	0.784433i	$-0.712954\pi$
$619$	−475284.			−1.24043			−0.620214	+	0.784433i	$0.712954\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8520.30	+	4919.20i	0.0219523	+	0.0126741i
$624$		0			0
$625$	243543.	+	421828.i	0.623469	+	1.07988i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−431505.	+	249130.i	−1.09065	+	0.629686i
$630$		0			0
$631$	−235600.	+	408071.i	−0.591720	+	1.02489i	0.402281	+	0.915516i	$0.368217\pi$
$631$	−235600.	+	408071.i	−0.591720	+	1.02489i	−0.994001	+	0.109372i	$0.965116\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$			609345.i			1.51118i
$636$		0			0
$637$	−272367.	−	157251.i	−0.671237	−	0.387539i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	172675.	−	99693.7i	0.420254	−	0.242634i	−0.274932	−	0.961464i	$-0.588655\pi$
$641$	172675.	−	99693.7i	0.420254	−	0.242634i	0.695186	+	0.718830i	$0.255322\pi$
$642$		0			0
$643$	205975.	+	356759.i	0.498187	+	0.862885i	0.999998	−	0.00209261i	$-0.000666100\pi$
$643$	205975.	+	356759.i	0.498187	+	0.862885i	−0.501811	+	0.864977i	$0.667333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−438545.			−1.04762			−0.523812	−	0.851834i	$-0.675491\pi$
$647$	−438545.			−1.04762			−0.523812	+	0.851834i	$0.675491\pi$
$648$		0			0
$649$	207936.	−	120052.i	0.493673	−	0.285022i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−282897.			−0.663440			−0.331720	−	0.943378i	$-0.607629\pi$
$653$	−282897.			−0.663440			−0.331720	+	0.943378i	$0.607629\pi$
$654$		0			0
$655$	129622.	−	224512.i	0.302132	−	0.523308i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−612072.	−	353380.i	−1.40939	−	0.813712i	−0.414061	−	0.910249i	$-0.635890\pi$
$659$	−612072.	−	353380.i	−1.40939	−	0.813712i	−0.995329	+	0.0965371i	$0.969223\pi$
$660$		0			0
$661$	−213537.	−	123285.i	−0.488730	−	0.282169i	0.235317	−	0.971919i	$-0.424387\pi$
$661$	−213537.	−	123285.i	−0.488730	−	0.282169i	−0.724048	+	0.689750i	$0.757720\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	24772.4	+	17202.3i	0.0560177	+	0.0388994i
$666$		0			0
$667$	59722.2	−	34480.6i	0.134241	−	0.0775039i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	82374.1	−	142676.i	0.182956	−	0.316888i
$672$		0			0
$673$			717726.i			1.58463i	0.610110	+	0.792316i	$0.291125\pi$
$673$			717726.i			1.58463i	−0.610110	+	0.792316i	$0.708875\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			3440.63i			0.00750690i	0.999993	+	0.00375345i	$0.00119476\pi$
$677$			3440.63i			0.00750690i	−0.999993	+	0.00375345i	$0.998805\pi$
$678$		0			0
$679$	−13057.0	+	7538.43i	−0.0283206	+	0.0163509i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	399217.i		−	0.855792i	−0.903828	−	0.427896i	$-0.859255\pi$
$683$		−	399217.i		−	0.855792i	0.903828	−	0.427896i	$-0.140745\pi$
$684$		0			0
$685$	991312.			2.11266
$686$		0			0
$687$		0			0
$688$		0			0
$689$	277332.	+	480353.i	0.584200	+	1.01186i
$690$		0			0
$691$	−523284.			−1.09593			−0.547963	−	0.836503i	$-0.684596\pi$
$691$	−523284.			−1.09593			−0.547963	+	0.836503i	$0.684596\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−930059.			−1.92549
$696$		0			0
$697$	−30026.7	−	17335.9i	−0.0618076	−	0.0356847i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−188003.	−	325630.i	−0.382585	−	0.662657i	0.608846	−	0.793289i	$-0.291633\pi$
$701$	−188003.	−	325630.i	−0.382585	−	0.662657i	−0.991431	+	0.130632i	$0.958299\pi$
$702$		0			0
$703$	−267710.	−	568309.i	−0.541694	−	1.14994i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6102.81	−	10570.4i	0.0122093	−	0.0211471i
$708$		0			0
$709$	−443869.	+	768803.i	−0.883003	+	1.52941i	−0.0350172	+	0.999387i	$0.511149\pi$
$709$	−443869.	+	768803.i	−0.883003	+	1.52941i	−0.847986	+	0.530019i	$0.822185\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−130361.	−	75264.0i	−0.256430	−	0.148050i
$714$		0			0
$715$			173407.i			0.339198i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3549.67	+	6148.21i	0.00686642	+	0.0118930i	0.869438	−	0.494042i	$-0.164481\pi$
$719$	3549.67	+	6148.21i	0.00686642	+	0.0118930i	−0.862572	+	0.505935i	$0.831148\pi$
$720$		0			0
$721$		−	10161.0i		−	0.0195464i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−65525.6	+	37831.2i	−0.124662	+	0.0719738i
$726$		0			0
$727$	401282.	+	695041.i	0.759243	+	1.31505i	0.943237	+	0.332120i	$0.107764\pi$
$727$	401282.	+	695041.i	0.759243	+	1.31505i	−0.183994	+	0.982927i	$0.558903\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−354465.	+	613952.i	−0.663344	+	1.14895i
$732$		0			0
$733$	−407403.			−0.758257			−0.379128	−	0.925344i	$-0.623776\pi$
$733$	−407403.			−0.758257			−0.379128	+	0.925344i	$0.623776\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−118746.	−	68558.1i	−0.218617	−	0.126219i
$738$		0			0
$739$	417909.	+	723839.i	0.765231	+	1.32542i	0.940125	+	0.340831i	$0.110708\pi$
$739$	417909.	+	723839.i	0.765231	+	1.32542i	−0.174894	+	0.984587i	$0.555958\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−615115.	+	355137.i	−1.11424	+	0.643307i	−0.939924	−	0.341383i	$-0.889105\pi$
$743$	−615115.	+	355137.i	−1.11424	+	0.643307i	−0.174316	+	0.984690i	$0.555771\pi$
$744$		0			0
$745$	−551531.	+	955280.i	−0.993706	+	1.72115i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	2608.75i		−	0.00465017i
$750$		0			0
$751$	−49411.3	−	28527.6i	−0.0876085	−	0.0505808i	0.455556	−	0.890207i	$-0.349441\pi$
$751$	−49411.3	−	28527.6i	−0.0876085	−	0.0505808i	−0.543164	+	0.839626i	$0.682774\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−378004.	+	218241.i	−0.663135	+	0.382861i
$756$		0			0
$757$	−184006.	−	318708.i	−0.321100	−	0.556162i	0.659615	−	0.751604i	$-0.270719\pi$
$757$	−184006.	−	318708.i	−0.321100	−	0.556162i	−0.980715	+	0.195441i	$0.937386\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−216648.			−0.374097			−0.187049	−	0.982351i	$-0.559892\pi$
$761$	−216648.			−0.374097			−0.187049	+	0.982351i	$0.559892\pi$
$762$		0			0
$763$	−2537.98	+	1465.31i	−0.00435953	+	0.00251698i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−745159.			−1.26666
$768$		0			0
$769$	72005.9	−	124718.i	0.121763	−	0.210900i	−0.798700	−	0.601729i	$-0.794479\pi$
$769$	72005.9	−	124718.i	0.121763	−	0.210900i	0.920463	+	0.390830i	$0.127812\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−386420.	−	223100.i	−0.646697	−	0.373371i	0.140492	−	0.990082i	$-0.455131\pi$
$773$	−386420.	−	223100.i	−0.646697	−	0.373371i	−0.787190	+	0.616711i	$0.788465\pi$
$774$		0			0
$775$	143029.	+	82577.7i	0.238133	+	0.137486i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24933.7	−	35906.2i	0.0410877	−	0.0591691i
$780$		0			0
$781$	171478.	−	99003.0i	0.281130	−	0.162310i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	557097.	−	964921.i	0.904048	−	1.56586i
$786$		0			0
$787$		−	766710.i		−	1.23789i	−0.785435	−	0.618944i	$-0.787561\pi$
$787$		−	766710.i		−	1.23789i	0.785435	−	0.618944i	$-0.212439\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	21692.6i		−	0.0346704i
$792$		0			0
$793$	−442795.	+	255648.i	−0.704135	+	0.406533i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	367354.i		−	0.578320i	−0.957281	−	0.289160i	$-0.906624\pi$
$797$		−	367354.i		−	0.578320i	0.957281	−	0.289160i	$-0.0933760\pi$
$798$		0			0
$799$	96634.5			0.151370
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−34018.4	−	58921.6i	−0.0527573	−	0.0913783i
$804$		0			0
$805$	26428.7			0.0407835
$806$		0			0
$807$		0			0
$808$		0			0
$809$	76993.0			0.117640			0.0588199	−	0.998269i	$-0.481266\pi$
$809$	76993.0			0.117640			0.0588199	+	0.998269i	$0.481266\pi$
$810$		0			0
$811$	32488.6	+	18757.3i	0.0493958	+	0.0285187i	0.524495	−	0.851414i	$-0.324254\pi$
$811$	32488.6	+	18757.3i	0.0493958	+	0.0285187i	−0.475099	+	0.879932i	$0.657588\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	477678.	+	827363.i	0.719151	+	1.24561i
$816$		0			0
$817$	−734169.	−	509816.i	−1.09990	−	0.763781i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	193430.	−	335030.i	0.286970	−	0.497047i	−0.686115	−	0.727493i	$-0.740685\pi$
$821$	193430.	−	335030.i	0.286970	−	0.497047i	0.973085	+	0.230446i	$0.0740185\pi$
$822$		0			0
$823$	−32063.3	+	55535.3i	−0.0473379	+	0.0819916i	−0.888723	−	0.458444i	$-0.848407\pi$
$823$	−32063.3	+	55535.3i	−0.0473379	+	0.0819916i	0.841386	+	0.540435i	$0.181740\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	733365.	+	423408.i	1.07228	+	0.619082i	0.928804	−	0.370571i	$-0.120838\pi$
$827$	733365.	+	423408.i	1.07228	+	0.619082i	0.143478	+	0.989653i	$0.454171\pi$
$828$		0			0
$829$		−	1.00726e6i		−	1.46566i	−0.680413	−	0.732829i	$-0.738200\pi$
$829$		−	1.00726e6i		−	1.46566i	0.680413	−	0.732829i	$-0.261800\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	342706.	+	593584.i	0.493892	+	0.855445i
$834$		0			0
$835$			1.29523e6i			1.85770i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−453943.	+	262084.i	−0.644878	+	0.372321i	−0.786491	−	0.617602i	$-0.788104\pi$
$839$	−453943.	+	262084.i	−0.644878	+	0.372321i	0.141613	+	0.989922i	$0.454771\pi$
$840$		0			0
$841$	−329880.	−	571369.i	−0.466406	−	0.807838i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−176158.	+	305115.i	−0.246711	+	0.427316i
$846$		0			0
$847$	34429.4			0.0479914
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−476745.	−	275249.i	−0.658305	−	0.380073i
$852$		0			0
$853$	124659.	+	215915.i	0.171327	+	0.296747i	0.938884	−	0.344234i	$-0.111861\pi$
$853$	124659.	+	215915.i	0.171327	+	0.296747i	−0.767557	+	0.640980i	$0.778528\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−364453.	+	210417.i	−0.496227	+	0.286497i	−0.727154	−	0.686474i	$-0.759157\pi$
$857$	−364453.	+	210417.i	−0.496227	+	0.286497i	0.230927	+	0.972971i	$0.425824\pi$
$858$		0			0
$859$	668834.	−	1.15845e6i	0.906426	−	1.56998i	0.0874335	−	0.996170i	$-0.472133\pi$
$859$	668834.	−	1.15845e6i	0.906426	−	1.56998i	0.818992	−	0.573805i	$-0.194533\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1.05678e6i			1.41894i	0.704734	+	0.709472i	$0.251066\pi$
$863$			1.05678e6i			1.41894i	−0.704734	+	0.709472i	$0.748934\pi$
$864$		0			0
$865$	−855321.	−	493820.i	−1.14313	−	0.659989i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	123183.	−	71119.9i	0.163122	−	0.0941785i
$870$		0			0
$871$	212770.	+	368528.i	0.280462	+	0.485774i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23218.2			0.0303258
$876$		0			0
$877$	443505.	−	256058.i	0.576633	−	0.332919i	−0.183161	−	0.983083i	$-0.558633\pi$
$877$	443505.	−	256058.i	0.576633	−	0.332919i	0.759794	+	0.650164i	$0.225300\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−692838.			−0.892647			−0.446323	−	0.894872i	$-0.647267\pi$
$881$	−692838.			−0.892647			−0.446323	+	0.894872i	$0.647267\pi$
$882$		0			0
$883$	437281.	−	757394.i	0.560841	−	0.971405i	−0.436583	−	0.899664i	$-0.643811\pi$
$883$	437281.	−	757394.i	0.560841	−	0.971405i	0.997423	−	0.0717406i	$-0.0228554\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.16648e6	+	673468.i	1.48262	+	0.855992i	0.999805	−	0.0197298i	$-0.00628059\pi$
$887$	1.16648e6	+	673468.i	1.48262	+	0.855992i	0.482816	+	0.875722i	$0.339614\pi$
$888$		0			0
$889$	45353.0	+	26184.6i	0.0573855	+	0.0331315i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−10145.4	+	121414.i	−0.0127223	+	0.152253i
$894$		0			0
$895$	−771967.	+	445695.i	−0.963723	+	0.556406i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	51864.7	−	89832.3i	0.0641730	−	0.111151i
$900$		0			0
$901$		−	1.20881e6i		−	1.48905i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	1.16238e6i		−	1.41922i
$906$		0			0
$907$	−1.04154e6	+	601332.i	−1.26608	+	0.730971i	−0.974244	−	0.225498i	$-0.927599\pi$
$907$	−1.04154e6	+	601332.i	−1.26608	+	0.730971i	−0.291835	+	0.956469i	$0.594266\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	1.13879e6i		−	1.37216i	−0.727526	−	0.686080i	$-0.759330\pi$
$911$		−	1.13879e6i		−	1.37216i	0.727526	−	0.686080i	$-0.240670\pi$
$912$		0			0
$913$	277090.			0.332414
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11140.2	−	19295.3i	−0.0132481	−	0.0229463i
$918$		0			0
$919$	558543.			0.661341			0.330671	−	0.943746i	$-0.392725\pi$
$919$	558543.			0.661341			0.330671	+	0.943746i	$0.392725\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−614510.			−0.721317
$924$		0			0
$925$	523072.	+	301996.i	0.611334	+	0.352954i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−329379.	−	570502.i	−0.381650	−	0.661036i	0.609649	−	0.792672i	$-0.291311\pi$
$929$	−329379.	−	570502.i	−0.381650	−	0.661036i	−0.991298	+	0.131635i	$0.957977\pi$
$930$		0			0
$931$	−781773.	+	368265.i	−0.901947	+	0.424875i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	188957.	−	327284.i	0.216143	−	0.374370i
$936$		0			0
$937$	−117517.	+	203546.i	−0.133851	+	0.231837i	−0.925158	−	0.379582i	$-0.876068\pi$
$937$	−117517.	+	203546.i	−0.133851	+	0.231837i	0.791307	+	0.611419i	$0.209401\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	503887.	+	290919.i	0.569055	+	0.328544i	0.756772	−	0.653679i	$-0.226775\pi$
$941$	503887.	+	290919.i	0.569055	+	0.328544i	−0.187717	+	0.982223i	$0.560109\pi$
$942$		0			0
$943$		−	38306.9i		−	0.0430778i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−468017.	−	810629.i	−0.521869	−	0.903904i	−0.999676	−	0.0254391i	$-0.991902\pi$
$947$	−468017.	−	810629.i	−0.521869	−	0.903904i	0.477807	−	0.878465i	$-0.341432\pi$
$948$		0			0
$949$			211152.i			0.234457i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	26206.7	−	15130.5i	0.0288554	−	0.0166597i	−0.485503	−	0.874235i	$-0.661363\pi$
$953$	26206.7	−	15130.5i	0.0288554	−	0.0166597i	0.514358	+	0.857575i	$0.328030\pi$
$954$		0			0
$955$	−133366.	−	230997.i	−0.146231	−	0.253280i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	42598.3	−	73782.4i	0.0463186	−	0.0802261i
$960$		0			0
$961$	697101.			0.754830
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−645208.	−	372511.i	−0.692859	−	0.400023i
$966$		0			0
$967$	163335.	+	282905.i	0.174673	+	0.302543i	0.940048	−	0.341042i	$-0.110780\pi$
$967$	163335.	+	282905.i	0.174673	+	0.302543i	−0.765375	+	0.643585i	$0.777446\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	882382.	−	509444.i	0.935876	−	0.540328i	0.0472107	−	0.998885i	$-0.484967\pi$
$971$	882382.	−	509444.i	0.935876	−	0.540328i	0.888665	+	0.458557i	$0.151633\pi$
$972$		0			0
$973$	−39966.2	+	69223.4i	−0.0422150	+	0.0731185i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			411302.i			0.430895i	0.976515	+	0.215448i	$0.0691210\pi$
$977$			411302.i			0.430895i	−0.976515	+	0.215448i	$0.930879\pi$
$978$		0			0
$979$	134609.	+	77716.3i	0.140445	+	0.0810861i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−195401.	+	112815.i	−0.202218	+	0.116751i	−0.597690	−	0.801728i	$-0.703915\pi$
$983$	−195401.	+	112815.i	−0.202218	+	0.116751i	0.395472	+	0.918478i	$0.370581\pi$
$984$		0			0
$985$	309326.	+	535769.i	0.318819	+	0.552211i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−783256.			−0.800776
$990$		0			0
$991$	464516.	−	268188.i	0.472991	−	0.273082i	−0.244500	−	0.969649i	$-0.578624\pi$
$991$	464516.	−	268188.i	0.472991	−	0.273082i	0.717491	+	0.696568i	$0.245290\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	891704.			0.900689
$996$		0			0
$997$	−270086.	+	467803.i	−0.271714	+	0.470623i	−0.969301	−	0.245878i	$-0.920924\pi$
$997$	−270086.	+	467803.i	−0.271714	+	0.470623i	0.697587	+	0.716500i	$0.254257\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.5.y.c.145.2		12
3.2	odd	2		76.5.h.a.69.4	yes	12
12.11	even	2		304.5.r.b.145.3		12
19.8	odd	6	inner	684.5.y.c.217.2		12
57.8	even	6		76.5.h.a.65.4	✓	12
228.179	odd	6		304.5.r.b.65.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.4	✓	12	57.8	even	6
76.5.h.a.69.4	yes	12	3.2	odd	2
304.5.r.b.65.3		12	228.179	odd	6
304.5.r.b.145.3		12	12.11	even	2
684.5.y.c.145.2		12	1.1	even	1	trivial
684.5.y.c.217.2		12	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	684.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.5891 - 27.0012i) q^{5} -2.67956 q^{7} +O(q^{10})\)	\(q+(-15.5891 - 27.0012i) q^{5} -2.67956 q^{7} -42.3332 q^{11} +(113.779 + 65.6905i) q^{13} +(-143.163 - 247.965i) q^{17} +(326.580 - 153.840i) q^{19} +(158.172 - 273.962i) q^{23} +(-173.542 + 300.584i) q^{25} +(188.788 + 108.997i) q^{29} -475.836i q^{31} +(41.7721 + 72.3514i) q^{35} -1740.18i q^{37} +(104.869 - 60.5462i) q^{41} +(-1237.98 - 2144.24i) q^{43} +(-168.749 + 292.282i) q^{47} -2393.82 q^{49} +(3656.19 + 2110.90i) q^{53} +(659.938 + 1143.05i) q^{55} +(-4911.88 + 2835.87i) q^{59} +(-1945.85 + 3370.31i) q^{61} -4096.23i q^{65} +(2805.03 + 1619.49i) q^{67} +(-4050.68 + 2338.66i) q^{71} +(803.586 + 1391.85i) q^{73} +113.435 q^{77} +(-2909.85 + 1680.00i) q^{79} -6545.45 q^{83} +(-4463.57 + 7731.13i) q^{85} +(-3179.74 - 1835.82i) q^{89} +(-304.879 - 176.022i) q^{91} +(-9244.95 - 6419.80i) q^{95} +(4872.79 - 2813.31i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{5} - 52 q^{7}+O(q^{10}) \) 12 * q - 9 * q^5 - 52 * q^7	\( 12 q - 9 q^{5} - 52 q^{7} - 6 q^{11} - 93 q^{13} + 483 q^{17} - 533 q^{19} - 531 q^{23} - 217 q^{25} - 2025 q^{29} + 1128 q^{35} + 1692 q^{41} - 63 q^{43} + 3471 q^{47} + 420 q^{49} + 3771 q^{53} - 2014 q^{55} + 9594 q^{59} + 1229 q^{61} + 7590 q^{67} - 963 q^{71} - 2838 q^{73} + 15408 q^{77} + 11073 q^{79} + 14202 q^{83} + 9455 q^{85} - 6525 q^{89} - 7686 q^{91} - 1521 q^{95} - 34110 q^{97}+O(q^{100}) \) 12 * q - 9 * q^5 - 52 * q^7 - 6 * q^11 - 93 * q^13 + 483 * q^17 - 533 * q^19 - 531 * q^23 - 217 * q^25 - 2025 * q^29 + 1128 * q^35 + 1692 * q^41 - 63 * q^43 + 3471 * q^47 + 420 * q^49 + 3771 * q^53 - 2014 * q^55 + 9594 * q^59 + 1229 * q^61 + 7590 * q^67 - 963 * q^71 - 2838 * q^73 + 15408 * q^77 + 11073 * q^79 + 14202 * q^83 + 9455 * q^85 - 6525 * q^89 - 7686 * q^91 - 1521 * q^95 - 34110 * q^97

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