LMFDB - Embedded newform 684.5.y.c.145.4

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			145.4
Root			$0.500000 + 15.2283i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.c.217.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.11411 + 5.39380i) q^{5} +49.9415 q^{7} +O(q^{10})$	$q+(3.11411 + 5.39380i) q^{5} +49.9415 q^{7} -1.88575 q^{11} +(-69.0003 - 39.8373i) q^{13} +(119.788 + 207.478i) q^{17} +(72.4707 + 353.651i) q^{19} +(-109.429 + 189.537i) q^{23} +(293.105 - 507.672i) q^{25} +(-340.159 - 196.391i) q^{29} +580.549i q^{31} +(155.523 + 269.374i) q^{35} +2478.77i q^{37} +(2840.91 - 1640.20i) q^{41} +(-162.917 - 282.181i) q^{43} +(969.593 - 1679.39i) q^{47} +93.1537 q^{49} +(-2087.49 - 1205.21i) q^{53} +(-5.87245 - 10.1714i) q^{55} +(-3046.44 + 1758.86i) q^{59} +(-1039.02 + 1799.64i) q^{61} -496.232i q^{65} +(-4389.01 - 2533.99i) q^{67} +(-2994.82 + 1729.06i) q^{71} +(4356.65 + 7545.94i) q^{73} -94.1773 q^{77} +(3640.40 - 2101.79i) q^{79} +11775.2 q^{83} +(-746.064 + 1292.22i) q^{85} +(8212.16 + 4741.29i) q^{89} +(-3445.98 - 1989.54i) q^{91} +(-1681.84 + 1492.20i) q^{95} +(5045.74 - 2913.16i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.11411	+	5.39380i	0.124564	+	0.215752i	0.921563	−	0.388230i	$-0.126913\pi$
$5$	3.11411	+	5.39380i	0.124564	+	0.215752i	−0.796998	+	0.603982i	$0.793580\pi$
$6$		0			0
$7$	49.9415			1.01921			0.509607	−	0.860407i	$-0.329791\pi$
$7$	49.9415			1.01921			0.509607	+	0.860407i	$0.329791\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.88575			−0.0155847			−0.00779237	−	0.999970i	$-0.502480\pi$
$11$	−1.88575			−0.0155847			−0.00779237	+	0.999970i	$0.502480\pi$
$12$		0			0
$13$	−69.0003	−	39.8373i	−0.408286	−	0.235724i	0.281767	−	0.959483i	$-0.409079\pi$
$13$	−69.0003	−	39.8373i	−0.408286	−	0.235724i	−0.690053	+	0.723759i	$0.742413\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	119.788	+	207.478i	0.414490	+	0.717918i	0.995375	−	0.0960680i	$-0.0306266\pi$
$17$	119.788	+	207.478i	0.414490	+	0.717918i	−0.580885	+	0.813986i	$0.697293\pi$
$18$		0			0
$19$	72.4707	+	353.651i	0.200750	+	0.979643i
$19$	72.4707	+	353.651i	0.200750	+	0.979643i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−109.429	+	189.537i	−0.206861	+	0.358294i	−0.950724	−	0.310038i	$-0.899658\pi$
$23$	−109.429	+	189.537i	−0.206861	+	0.358294i	0.743863	+	0.668332i	$0.232991\pi$
$24$		0			0
$25$	293.105	−	507.672i	0.468967	−	0.812275i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−340.159	−	196.391i	−0.404470	−	0.233521i	0.283941	−	0.958842i	$-0.408358\pi$
$29$	−340.159	−	196.391i	−0.404470	−	0.233521i	−0.688411	+	0.725321i	$0.741691\pi$
$30$		0			0
$31$			580.549i			0.604109i	0.953291	+	0.302055i	$0.0976725\pi$
$31$			580.549i			0.604109i	−0.953291	+	0.302055i	$0.902327\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	155.523	+	269.374i	0.126958	+	0.219898i
$36$		0			0
$37$			2478.77i			1.81064i	0.424727	+	0.905321i	$0.360370\pi$
$37$			2478.77i			1.81064i	−0.424727	+	0.905321i	$0.639630\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2840.91	−	1640.20i	1.69001	−	0.975729i	0.735516	−	0.677507i	$-0.236940\pi$
$41$	2840.91	−	1640.20i	1.69001	−	0.975729i	0.954497	−	0.298222i	$-0.0963936\pi$
$42$		0			0
$43$	−162.917	−	282.181i	−0.0881111	−	0.152613i	0.818602	−	0.574362i	$-0.194750\pi$
$43$	−162.917	−	282.181i	−0.0881111	−	0.152613i	−0.906713	+	0.421749i	$0.861416\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	969.593	−	1679.39i	0.438929	−	0.760247i	−0.558678	−	0.829384i	$-0.688691\pi$
$47$	969.593	−	1679.39i	0.438929	−	0.760247i	0.997607	+	0.0691376i	$0.0220247\pi$
$48$		0			0
$49$	93.1537			0.0387979
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2087.49	−	1205.21i	−0.743142	−	0.429053i	0.0800686	−	0.996789i	$-0.474486\pi$
$53$	−2087.49	−	1205.21i	−0.743142	−	0.429053i	−0.823211	+	0.567736i	$0.807819\pi$
$54$		0			0
$55$	−5.87245	−	10.1714i	−0.00194130	−	0.00336244i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3046.44	+	1758.86i	−0.875163	+	0.505275i	−0.869060	−	0.494706i	$-0.835276\pi$
$59$	−3046.44	+	1758.86i	−0.875163	+	0.505275i	−0.00610218	+	0.999981i	$0.501942\pi$
$60$		0			0
$61$	−1039.02	+	1799.64i	−0.279232	+	0.483644i	−0.971194	−	0.238290i	$-0.923413\pi$
$61$	−1039.02	+	1799.64i	−0.279232	+	0.483644i	0.691962	+	0.721934i	$0.256747\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	496.232i		−	0.117451i
$66$		0			0
$67$	−4389.01	−	2533.99i	−0.977725	−	0.564490i	−0.0761425	−	0.997097i	$-0.524260\pi$
$67$	−4389.01	−	2533.99i	−0.977725	−	0.564490i	−0.901583	+	0.432607i	$0.857594\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2994.82	+	1729.06i	−0.594092	+	0.342999i	−0.766714	−	0.641989i	$-0.778109\pi$
$71$	−2994.82	+	1729.06i	−0.594092	+	0.342999i	0.172622	+	0.984988i	$0.444776\pi$
$72$		0			0
$73$	4356.65	+	7545.94i	0.817536	+	1.41601i	0.907492	+	0.420069i	$0.137994\pi$
$73$	4356.65	+	7545.94i	0.817536	+	1.41601i	−0.0899558	+	0.995946i	$0.528673\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−94.1773			−0.0158842
$78$		0			0
$79$	3640.40	−	2101.79i	0.583304	−	0.336771i	−0.179141	−	0.983823i	$-0.557332\pi$
$79$	3640.40	−	2101.79i	0.583304	−	0.336771i	0.762445	+	0.647053i	$0.223999\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	11775.2			1.70927			0.854635	−	0.519229i	$-0.173781\pi$
$83$	11775.2			1.70927			0.854635	+	0.519229i	$0.173781\pi$
$84$		0			0
$85$	−746.064	+	1292.22i	−0.103261	+	0.178854i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8212.16	+	4741.29i	1.03676	+	0.598573i	0.918913	−	0.394460i	$-0.129068\pi$
$89$	8212.16	+	4741.29i	1.03676	+	0.598573i	0.117845	+	0.993032i	$0.462401\pi$
$90$		0			0
$91$	−3445.98	−	1989.54i	−0.416131	−	0.240253i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1681.84	+	1492.20i	−0.186354	+	0.165341i
$96$		0			0
$97$	5045.74	−	2913.16i	0.536267	−	0.309614i	−0.207297	−	0.978278i	$-0.566467\pi$
$97$	5045.74	−	2913.16i	0.536267	−	0.309614i	0.743565	+	0.668664i	$0.233133\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9167.14	+	15878.0i	−0.898651	+	1.55651i	−0.0694313	+	0.997587i	$0.522118\pi$
$101$	−9167.14	+	15878.0i	−0.898651	+	1.55651i	−0.829220	+	0.558923i	$0.811215\pi$
$102$		0			0
$103$			15685.2i			1.47848i	0.673443	+	0.739239i	$0.264815\pi$
$103$			15685.2i			1.47848i	−0.673443	+	0.739239i	$0.735185\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			15464.3i			1.35071i	0.737494	+	0.675354i	$0.236009\pi$
$107$			15464.3i			1.35071i	−0.737494	+	0.675354i	$0.763991\pi$
$108$		0			0
$109$	15286.3	−	8825.56i	1.28662	−	0.742830i	0.308569	−	0.951202i	$-0.400150\pi$
$109$	15286.3	−	8825.56i	1.28662	−	0.742830i	0.978050	+	0.208372i	$0.0668166\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			5351.37i			0.419090i	0.977799	+	0.209545i	$0.0671984\pi$
$113$			5351.37i			0.419090i	−0.977799	+	0.209545i	$0.932802\pi$
$114$		0			0
$115$	−1363.10			−0.103070
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5982.37	+	10361.8i	0.422454	+	0.731712i
$120$		0			0
$121$	−14637.4			−0.999757
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7543.68			0.482796
$126$		0			0
$127$	−5218.76	−	3013.05i	−0.323564	−	0.186810i	0.329416	−	0.944185i	$-0.393148\pi$
$127$	−5218.76	−	3013.05i	−0.323564	−	0.186810i	−0.652980	+	0.757375i	$0.726481\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5324.73	+	9222.71i	0.310281	+	0.537423i	0.978423	−	0.206611i	$-0.0662435\pi$
$131$	5324.73	+	9222.71i	0.310281	+	0.537423i	−0.668142	+	0.744034i	$0.732910\pi$
$132$		0			0
$133$	3619.30	+	17661.9i	0.204607	+	0.998466i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4402.76	−	7625.80i	0.234576	−	0.406298i	−0.724573	−	0.689198i	$-0.757963\pi$
$137$	4402.76	−	7625.80i	0.234576	−	0.406298i	0.959149	+	0.282900i	$0.0912965\pi$
$138$		0			0
$139$	3584.83	−	6209.10i	0.185540	−	0.321366i	−0.758218	−	0.652001i	$-0.773930\pi$
$139$	3584.83	−	6209.10i	0.185540	−	0.321366i	0.943759	+	0.330636i	$0.107263\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	130.117	+	75.1234i	0.00636302	+	0.00367369i
$144$		0			0
$145$		−	2446.33i		−	0.116354i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8324.08	+	14417.7i	0.374941	+	0.649418i	0.990318	−	0.138815i	$-0.0443295\pi$
$149$	8324.08	+	14417.7i	0.374941	+	0.649418i	−0.615377	+	0.788233i	$0.710996\pi$
$150$		0			0
$151$			1780.79i			0.0781013i	0.999237	+	0.0390506i	$0.0124334\pi$
$151$			1780.79i			0.0781013i	−0.999237	+	0.0390506i	$0.987567\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3131.37	+	1807.89i	−0.130338	+	0.0752506i
$156$		0			0
$157$	4609.89	+	7984.57i	0.187022	+	0.323931i	0.944256	−	0.329212i	$-0.106783\pi$
$157$	4609.89	+	7984.57i	0.187022	+	0.323931i	−0.757234	+	0.653143i	$0.773450\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5465.07	+	9465.78i	−0.210836	+	0.365178i
$162$		0			0
$163$	29276.2			1.10189			0.550947	−	0.834540i	$-0.314267\pi$
$163$	29276.2			1.10189			0.550947	+	0.834540i	$0.314267\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	37315.4	+	21544.1i	1.33800	+	0.772493i	0.986510	−	0.163700i	$-0.0523428\pi$
$167$	37315.4	+	21544.1i	1.33800	+	0.772493i	0.351487	+	0.936193i	$0.385676\pi$
$168$		0			0
$169$	−11106.5	−	19237.0i	−0.388869	−	0.673540i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−38605.2	+	22288.7i	−1.28989	+	0.744721i	−0.978635	−	0.205605i	$-0.934084\pi$
$173$	−38605.2	+	22288.7i	−1.28989	+	0.744721i	−0.311259	+	0.950325i	$0.600751\pi$
$174$		0			0
$175$	14638.1	−	25353.9i	0.477978	−	0.827883i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			18503.2i			0.577486i	0.957407	+	0.288743i	$0.0932373\pi$
$179$			18503.2i			0.577486i	−0.957407	+	0.288743i	$0.906763\pi$
$180$		0			0
$181$	27630.5	+	15952.4i	0.843395	+	0.486934i	0.858417	−	0.512953i	$-0.171448\pi$
$181$	27630.5	+	15952.4i	0.843395	+	0.486934i	−0.0150220	+	0.999887i	$0.504782\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−13370.0	+	7719.17i	−0.390650	+	0.225542i
$186$		0			0
$187$	−225.890	−	391.253i	−0.00645972	−	0.0111886i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	28246.4			0.774276			0.387138	−	0.922022i	$-0.373464\pi$
$191$	28246.4			0.774276			0.387138	+	0.922022i	$0.373464\pi$
$192$		0			0
$193$	−35466.8	+	20476.8i	−0.952154	+	0.549727i	−0.893750	−	0.448566i	$-0.851935\pi$
$193$	−35466.8	+	20476.8i	−0.952154	+	0.549727i	−0.0584049	+	0.998293i	$0.518601\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22359.6			0.576144			0.288072	−	0.957609i	$-0.406986\pi$
$197$	22359.6			0.576144			0.288072	+	0.957609i	$0.406986\pi$
$198$		0			0
$199$	−2166.66	+	3752.77i	−0.0547123	+	0.0947645i	−0.892084	−	0.451869i	$-0.850757\pi$
$199$	−2166.66	+	3752.77i	−0.0547123	+	0.0947645i	0.837372	+	0.546633i	$0.184091\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16988.1	−	9808.06i	−0.412241	−	0.238008i
$204$		0			0
$205$	17693.8	+	10215.5i	0.421031	+	0.243082i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−136.662	−	666.898i	−0.00312863	−	0.0152675i
$210$		0			0
$211$	−48243.9	+	27853.6i	−1.08362	+	0.625629i	−0.931871	−	0.362790i	$-0.881824\pi$
$211$	−48243.9	+	27853.6i	−1.08362	+	0.625629i	−0.151750	+	0.988419i	$0.548491\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1014.69	−	1757.49i	0.0219510	−	0.0380203i
$216$		0			0
$217$			28993.5i			0.615717i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	19088.1i		−	0.390821i
$222$		0			0
$223$	−23671.3	+	13666.6i	−0.476005	+	0.274822i	−0.718750	−	0.695268i	$-0.755285\pi$
$223$	−23671.3	+	13666.6i	−0.476005	+	0.274822i	0.242745	+	0.970090i	$0.421952\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			42099.3i			0.817003i	0.912758	+	0.408501i	$0.133949\pi$
$227$			42099.3i			0.817003i	−0.912758	+	0.408501i	$0.866051\pi$
$228$		0			0
$229$	12163.3			0.231942			0.115971	−	0.993253i	$-0.463002\pi$
$229$	12163.3			0.231942			0.115971	+	0.993253i	$0.463002\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12709.0	−	22012.6i	−0.234098	−	0.405470i	0.724912	−	0.688841i	$-0.241880\pi$
$233$	−12709.0	−	22012.6i	−0.234098	−	0.405470i	−0.959010	+	0.283372i	$0.908547\pi$
$234$		0			0
$235$	12077.7			0.218700
$236$		0			0
$237$		0			0
$238$		0			0
$239$	86525.4			1.51477			0.757387	−	0.652967i	$-0.226476\pi$
$239$	86525.4			1.51477			0.757387	+	0.652967i	$0.226476\pi$
$240$		0			0
$241$	45400.9	+	26212.2i	0.781682	+	0.451305i	0.837026	−	0.547163i	$-0.184292\pi$
$241$	45400.9	+	26212.2i	0.781682	+	0.451305i	−0.0553438	+	0.998467i	$0.517625\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	290.091	+	502.452i	0.00483284	+	0.00837072i
$246$		0			0
$247$	9088.01	−	27289.1i	0.148962	−	0.447296i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	19639.4	−	34016.4i	0.311732	−	0.539935i	−0.667006	−	0.745053i	$-0.732424\pi$
$251$	19639.4	−	34016.4i	0.311732	−	0.539935i	0.978737	+	0.205118i	$0.0657577\pi$
$252$		0			0
$253$	206.357	−	357.420i	0.00322387	−	0.00558391i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−64968.9	−	37509.8i	−0.983646	−	0.567908i	−0.0802773	−	0.996773i	$-0.525581\pi$
$257$	−64968.9	−	37509.8i	−0.983646	−	0.567908i	−0.903369	+	0.428864i	$0.858914\pi$
$258$		0			0
$259$			123793.i			1.84543i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14757.8	+	25561.3i	0.213359	+	0.369548i	0.952764	−	0.303713i	$-0.0982264\pi$
$263$	14757.8	+	25561.3i	0.213359	+	0.369548i	−0.739405	+	0.673261i	$0.764893\pi$
$264$		0			0
$265$		−	15012.6i		−	0.213779i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−87976.7	+	50793.4i	−1.21580	+	0.701944i	−0.964017	−	0.265839i	$-0.914351\pi$
$269$	−87976.7	+	50793.4i	−1.21580	+	0.701944i	−0.251785	+	0.967783i	$0.581018\pi$
$270$		0			0
$271$	11915.4	+	20638.0i	0.162244	+	0.281015i	0.935673	−	0.352868i	$-0.114793\pi$
$271$	11915.4	+	20638.0i	0.162244	+	0.281015i	−0.773429	+	0.633883i	$0.781460\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−552.723	+	957.344i	−0.00730873	+	0.0126591i
$276$		0			0
$277$	−109790.			−1.43088			−0.715438	−	0.698677i	$-0.753773\pi$
$277$	−109790.			−1.43088			−0.715438	+	0.698677i	$0.753773\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	52508.2	+	30315.6i	0.664989	+	0.383932i	0.794175	−	0.607689i	$-0.207903\pi$
$281$	52508.2	+	30315.6i	0.664989	+	0.383932i	−0.129186	+	0.991620i	$0.541236\pi$
$282$		0			0
$283$	−8384.27	−	14522.0i	−0.104687	−	0.181323i	0.808923	−	0.587914i	$-0.200051\pi$
$283$	−8384.27	−	14522.0i	−0.104687	−	0.181323i	−0.913610	+	0.406591i	$0.866717\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	141879.	−	81914.1i	1.72249	−	0.994477i
$288$		0			0
$289$	13062.3	−	22624.6i	0.156396	−	0.270886i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	127491.i		−	1.48506i	−0.669813	−	0.742530i	$-0.733626\pi$
$293$		−	127491.i		−	1.48506i	0.669813	−	0.742530i	$-0.266374\pi$
$294$		0			0
$295$	−18973.9	−	10954.6i	−0.218028	−	0.125879i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15101.3	−	8718.75i	0.168917	−	0.0975241i
$300$		0			0
$301$	−8136.34	−	14092.6i	−0.0898041	−	0.155545i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12942.5			−0.139130
$306$		0			0
$307$	94867.2	−	54771.6i	1.00656	−	0.581137i	0.0963769	−	0.995345i	$-0.469275\pi$
$307$	94867.2	−	54771.6i	1.00656	−	0.581137i	0.910182	+	0.414208i	$0.135941\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−150216.			−1.55309			−0.776544	−	0.630063i	$-0.783029\pi$
$311$	−150216.			−1.55309			−0.776544	+	0.630063i	$0.783029\pi$
$312$		0			0
$313$	20012.3	−	34662.3i	0.204272	−	0.353809i	−0.745629	−	0.666362i	$-0.767851\pi$
$313$	20012.3	−	34662.3i	0.204272	−	0.353809i	0.949900	+	0.312553i	$0.101184\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−143247.	−	82703.8i	−1.42550	−	0.823013i	−0.428739	−	0.903428i	$-0.641042\pi$
$317$	−143247.	−	82703.8i	−1.42550	−	0.823013i	−0.996761	+	0.0804148i	$0.974376\pi$
$318$		0			0
$319$	641.456	+	370.345i	0.00630356	+	0.00363936i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−64693.8	+	57399.1i	−0.620094	+	0.550174i
$324$		0			0
$325$	−40448.6	+	23353.0i	−0.382945	+	0.221094i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	48423.0	−	83871.0i	0.447362	−	0.774854i
$330$		0			0
$331$		−	188621.i		−	1.72161i	−0.508935	−	0.860805i	$-0.669961\pi$
$331$		−	188621.i		−	1.72161i	0.508935	−	0.860805i	$-0.330039\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	31564.6i		−	0.281262i
$336$		0			0
$337$	31324.9	−	18085.5i	0.275823	−	0.159246i	−0.355708	−	0.934597i	$-0.615760\pi$
$337$	31324.9	−	18085.5i	0.275823	−	0.159246i	0.631531	+	0.775351i	$0.282427\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	1094.77i		−	0.00941488i
$342$		0			0
$343$	−115257.			−0.979671
$344$		0			0
$345$		0			0
$346$		0			0
$347$	90478.1	+	156713.i	0.751423	+	1.30150i	0.947133	+	0.320841i	$0.103965\pi$
$347$	90478.1	+	156713.i	0.751423	+	1.30150i	−0.195710	+	0.980662i	$0.562701\pi$
$348$		0			0
$349$	128784.			1.05733			0.528666	−	0.848830i	$-0.322692\pi$
$349$	128784.			1.05733			0.528666	+	0.848830i	$0.322692\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−71514.4			−0.573910			−0.286955	−	0.957944i	$-0.592643\pi$
$353$	−71514.4			−0.573910			−0.286955	+	0.957944i	$0.592643\pi$
$354$		0			0
$355$	−18652.4	−	10769.0i	−0.148006	−	0.0854510i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−45696.9	−	79149.3i	−0.354566	−	0.614127i	0.632477	−	0.774579i	$-0.282038\pi$
$359$	−45696.9	−	79149.3i	−0.354566	−	0.614127i	−0.987044	+	0.160452i	$0.948705\pi$
$360$		0			0
$361$	−119817.	+	51258.7i	−0.919399	+	0.393326i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−27134.2	+	46997.8i	−0.203672	+	0.352770i
$366$		0			0
$367$	103142.	−	178648.i	0.765781	−	1.32637i	−0.174052	−	0.984736i	$-0.555686\pi$
$367$	103142.	−	178648.i	0.765781	−	1.32637i	0.939833	−	0.341634i	$-0.110980\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−104252.	−	60190.0i	−0.757421	−	0.437297i
$372$		0			0
$373$		−	63012.8i		−	0.452909i	−0.974022	−	0.226454i	$-0.927287\pi$
$373$		−	63012.8i		−	0.452909i	0.974022	−	0.226454i	$-0.0727134\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15647.4	+	27102.1i	0.110093	+	0.190686i
$378$		0			0
$379$			74224.9i			0.516739i	0.966046	+	0.258370i	$0.0831852\pi$
$379$			74224.9i			0.516739i	−0.966046	+	0.258370i	$0.916815\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	191250.	−	110418.i	1.30378	−	0.752738i	0.322731	−	0.946491i	$-0.395399\pi$
$383$	191250.	−	110418.i	1.30378	−	0.752738i	0.981050	+	0.193753i	$0.0620659\pi$
$384$		0			0
$385$	−293.279	−	507.974i	−0.00197861	−	0.00342704i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	119430.	−	206858.i	0.789248	−	1.36702i	−0.137181	−	0.990546i	$-0.543804\pi$
$389$	119430.	−	206858.i	0.789248	−	1.36702i	0.926428	−	0.376471i	$-0.122863\pi$
$390$		0			0
$391$	−52433.2			−0.342967
$392$		0			0
$393$		0			0
$394$		0			0
$395$	22673.2	+	13090.4i	0.145318	+	0.0838994i
$396$		0			0
$397$	−121860.	−	211069.i	−0.773182	−	1.33919i	−0.935810	−	0.352504i	$-0.885330\pi$
$397$	−121860.	−	211069.i	−0.773182	−	1.33919i	0.162628	−	0.986687i	$-0.448003\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−181404.	+	104733.i	−1.12812	+	0.651323i	−0.943463	−	0.331479i	$-0.892452\pi$
$401$	−181404.	+	104733.i	−1.12812	+	0.651323i	−0.184662	+	0.982802i	$0.559119\pi$
$402$		0			0
$403$	23127.5	−	40058.1i	0.142403	−	0.246649i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	4674.35i		−	0.0282184i
$408$		0			0
$409$	102139.	+	58969.8i	0.610581	+	0.352519i	0.773193	−	0.634171i	$-0.218658\pi$
$409$	102139.	+	58969.8i	0.610581	+	0.352519i	−0.162612	+	0.986690i	$0.551992\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−152144.	+	87840.3i	−0.891978	+	0.514984i
$414$		0			0
$415$	36669.2	+	63512.9i	0.212914	+	0.368779i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	59069.1			0.336459			0.168230	−	0.985748i	$-0.446195\pi$
$419$	59069.1			0.336459			0.168230	+	0.985748i	$0.446195\pi$
$420$		0			0
$421$	45326.1	−	26169.0i	0.255731	−	0.147647i	−0.366654	−	0.930357i	$-0.619497\pi$
$421$	45326.1	−	26169.0i	0.255731	−	0.147647i	0.622386	+	0.782711i	$0.286164\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	140441.			0.777529
$426$		0			0
$427$	−51890.4	+	89876.8i	−0.284597	+	0.492937i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−203718.	−	117616.i	−1.09667	−	0.633160i	−0.161322	−	0.986902i	$-0.551576\pi$
$431$	−203718.	−	117616.i	−1.09667	−	0.633160i	−0.935343	+	0.353742i	$0.884909\pi$
$432$		0			0
$433$	−127748.	−	73755.1i	−0.681360	−	0.393384i	0.119007	−	0.992893i	$-0.462029\pi$
$433$	−127748.	−	73755.1i	−0.681360	−	0.393384i	−0.800367	+	0.599510i	$0.795362\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−74960.5	−	24963.9i	−0.392527	−	0.130722i
$438$		0			0
$439$	−7033.58	+	4060.84i	−0.0364962	+	0.0210711i	−0.518137	−	0.855298i	$-0.673374\pi$
$439$	−7033.58	+	4060.84i	−0.0364962	+	0.0210711i	0.481641	+	0.876369i	$0.340041\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−102446.	+	177441.i	−0.522018	+	0.904162i	0.477654	+	0.878548i	$0.341487\pi$
$443$	−102446.	+	177441.i	−0.522018	+	0.904162i	−0.999672	+	0.0256140i	$0.991846\pi$
$444$		0			0
$445$			59059.7i			0.298244i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	114834.i		−	0.569611i	−0.958585	−	0.284806i	$-0.908071\pi$
$449$		−	114834.i		−	0.569611i	0.958585	−	0.284806i	$-0.0919291\pi$
$450$		0			0
$451$	−5357.26	+	3093.01i	−0.0263384	+	0.0152065i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	24782.6i		−	0.119708i
$456$		0			0
$457$	−230282.			−1.10262			−0.551312	−	0.834299i	$-0.685873\pi$
$457$	−230282.			−1.10262			−0.551312	+	0.834299i	$0.685873\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	52622.7	+	91145.2i	0.247612	+	0.428876i	0.962863	−	0.269992i	$-0.0870209\pi$
$461$	52622.7	+	91145.2i	0.247612	+	0.428876i	−0.715251	+	0.698868i	$0.753688\pi$
$462$		0			0
$463$	103267.			0.481724			0.240862	−	0.970559i	$-0.422570\pi$
$463$	103267.			0.481724			0.240862	+	0.970559i	$0.422570\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	203377.			0.932542			0.466271	−	0.884642i	$-0.345597\pi$
$467$	203377.			0.932542			0.466271	+	0.884642i	$0.345597\pi$
$468$		0			0
$469$	−219194.	−	126552.i	−0.996511	−	0.575336i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	307.222	+	532.124i	0.00137319	+	0.00237843i
$474$		0			0
$475$	200780.	+	66865.4i	0.889885	+	0.296356i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	221111.	−	382976.i	0.963697	−	1.66917i	0.250619	−	0.968086i	$-0.419366\pi$
$479$	221111.	−	382976.i	0.963697	−	1.66917i	0.713077	−	0.701086i	$-0.247301\pi$
$480$		0			0
$481$	98747.6	−	171036.i	0.426812	−	0.739260i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	31426.0	+	18143.8i	0.133600	+	0.0771339i
$486$		0			0
$487$		−	212627.i		−	0.896519i	−0.893903	−	0.448260i	$-0.852044\pi$
$487$		−	212627.i		−	0.896519i	0.893903	−	0.448260i	$-0.147956\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−216804.	−	375515.i	−0.899298	−	1.55763i	−0.828393	−	0.560147i	$-0.810745\pi$
$491$	−216804.	−	375515.i	−0.899298	−	1.55763i	−0.0709052	−	0.997483i	$-0.522589\pi$
$492$		0			0
$493$		−	94100.8i		−	0.387168i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−149566.	+	86351.8i	−0.605507	+	0.349590i
$498$		0			0
$499$	−80809.6	−	139966.i	−0.324535	−	0.562111i	0.656883	−	0.753992i	$-0.271875\pi$
$499$	−80809.6	−	139966.i	−0.324535	−	0.562111i	−0.981418	+	0.191881i	$0.938541\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27970.9	+	48446.9i	−0.110553	+	0.191483i	−0.915993	−	0.401194i	$-0.868595\pi$
$503$	−27970.9	+	48446.9i	−0.110553	+	0.191483i	0.805440	+	0.592677i	$0.201929\pi$
$504$		0			0
$505$	−114190.			−0.447760
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−180101.	−	103981.i	−0.695152	−	0.401346i	0.110387	−	0.993889i	$-0.464791\pi$
$509$	−180101.	−	103981.i	−0.695152	−	0.401346i	−0.805539	+	0.592542i	$0.798124\pi$
$510$		0			0
$511$	217578.	+	376856.i	0.833245	+	1.44322i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−84602.7	+	48845.4i	−0.318985	+	0.184166i
$516$		0			0
$517$	−1828.41	+	3166.91i	−0.00684059	+	0.0118482i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	207601.i		−	0.764810i	−0.923995	−	0.382405i	$-0.875096\pi$
$521$		−	207601.i		−	0.764810i	0.923995	−	0.382405i	$-0.124904\pi$
$522$		0			0
$523$	−35996.4	−	20782.5i	−0.131600	−	0.0759792i	0.432755	−	0.901512i	$-0.357542\pi$
$523$	−35996.4	−	20782.5i	−0.131600	−	0.0759792i	−0.564355	+	0.825532i	$0.690875\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−120451.	+	69542.6i	−0.433701	+	0.250397i
$528$		0			0
$529$	115971.	+	200868.i	0.414417	+	0.717792i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−261365.			−0.920011
$534$		0			0
$535$	−83411.1	+	48157.4i	−0.291418	+	0.168250i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−175.665			−0.000604654
$540$		0			0
$541$	−51917.0	+	89922.8i	−0.177384	+	0.307238i	−0.940984	−	0.338452i	$-0.890097\pi$
$541$	−51917.0	+	89922.8i	−0.177384	+	0.307238i	0.763600	+	0.645690i	$0.223430\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	95206.6	+	54967.6i	0.320534	+	0.185060i
$546$		0			0
$547$	142979.	+	82548.7i	0.477855	+	0.275890i	0.719522	−	0.694469i	$-0.244361\pi$
$547$	142979.	+	82548.7i	0.477855	+	0.275890i	−0.241667	+	0.970359i	$0.577694\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	44802.3	−	134530.i	0.147570	−	0.443115i
$552$		0			0
$553$	181807.	−	104966.i	0.594512	−	0.343242i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	30248.0	−	52391.2i	0.0974960	−	0.168868i	−0.813152	−	0.582052i	$-0.802250\pi$
$557$	30248.0	−	52391.2i	0.0974960	−	0.168868i	0.910648	+	0.413184i	$0.135583\pi$
$558$		0			0
$559$			25960.8i			0.0830796i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	248939.i		−	0.785374i	−0.919672	−	0.392687i	$-0.871546\pi$
$563$		−	248939.i		−	0.785374i	0.919672	−	0.392687i	$-0.128454\pi$
$564$		0			0
$565$	−28864.2	+	16664.8i	−0.0904196	+	0.0522038i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	87739.1i		−	0.270999i	−0.990777	−	0.135500i	$-0.956736\pi$
$569$		−	87739.1i		−	0.270999i	0.990777	−	0.135500i	$-0.0432640\pi$
$570$		0			0
$571$	130764.			0.401067			0.200533	−	0.979687i	$-0.435732\pi$
$571$	130764.			0.401067			0.200533	+	0.979687i	$0.435732\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	64148.5	+	111108.i	0.194022	+	0.336056i
$576$		0			0
$577$	−572106.			−1.71840			−0.859201	−	0.511639i	$-0.829039\pi$
$577$	−572106.			−1.71840			−0.859201	+	0.511639i	$0.829039\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	588069.			1.74211
$582$		0			0
$583$	3936.48	+	2272.73i	0.0115817	+	0.00668668i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17337.7	+	30029.7i	0.0503169	+	0.0871515i	0.890087	−	0.455791i	$-0.150644\pi$
$587$	17337.7	+	30029.7i	0.0503169	+	0.0871515i	−0.839770	+	0.542942i	$0.817310\pi$
$588$		0			0
$589$	−205312.	+	42072.8i	−0.591811	+	0.121275i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	200472.	−	347228.i	0.570092	−	0.987429i	−0.426463	−	0.904505i	$-0.640241\pi$
$593$	200472.	−	347228.i	0.570092	−	0.987429i	0.996556	−	0.0829242i	$-0.0264259\pi$
$594$		0			0
$595$	−37259.6	+	64535.5i	−0.105246	+	0.182291i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	461443.	+	266414.i	1.28607	+	0.742512i	0.977951	−	0.208836i	$-0.0669676\pi$
$599$	461443.	+	266414.i	1.28607	+	0.742512i	0.308118	+	0.951348i	$0.400301\pi$
$600$		0			0
$601$			169049.i			0.468019i	0.972234	+	0.234009i	$0.0751846\pi$
$601$			169049.i			0.468019i	−0.972234	+	0.234009i	$0.924815\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−45582.6	−	78951.4i	−0.124534	−	0.215700i
$606$		0			0
$607$			527599.i			1.43195i	0.698127	+	0.715974i	$0.254017\pi$
$607$			527599.i			1.43195i	−0.698127	+	0.715974i	$0.745983\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−133804.	+	77252.0i	−0.358417	+	0.206932i
$612$		0			0
$613$	144166.	+	249704.i	0.383657	+	0.664513i	0.991582	−	0.129481i	$-0.0413312\pi$
$613$	144166.	+	249704.i	0.383657	+	0.664513i	−0.607925	+	0.793995i	$0.707998\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−215208.	+	372751.i	−0.565311	+	0.979147i	0.431710	+	0.902013i	$0.357910\pi$
$617$	−215208.	+	372751.i	−0.565311	+	0.979147i	−0.997021	+	0.0771347i	$0.975423\pi$
$618$		0			0
$619$	490418.			1.27993			0.639963	−	0.768405i	$-0.278950\pi$
$619$	490418.			1.27993			0.639963	+	0.768405i	$0.278950\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	410128.	+	236787.i	1.05668	+	0.610074i
$624$		0			0
$625$	−159699.	−	276606.i	−0.408828	−	0.708111i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−514291.	+	296926.i	−1.29989	+	0.750493i
$630$		0			0
$631$	65005.3	−	112593.i	0.163264	−	0.282781i	−0.772774	−	0.634682i	$-0.781131\pi$
$631$	65005.3	−	112593.i	0.163264	−	0.282781i	0.936037	+	0.351901i	$0.114464\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		−	37531.9i		−	0.0930794i
$636$		0			0
$637$	−6427.63	−	3710.99i	−0.0158406	−	0.00914558i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−395283.	+	228217.i	−0.962037	+	0.555432i	−0.896799	−	0.442437i	$-0.854114\pi$
$641$	−395283.	+	228217.i	−0.962037	+	0.555432i	−0.0652376	+	0.997870i	$0.520781\pi$
$642$		0			0
$643$	194677.	+	337190.i	0.470860	+	0.815554i	0.999445	−	0.0333268i	$-0.0106102\pi$
$643$	194677.	+	337190.i	0.470860	+	0.815554i	−0.528584	+	0.848881i	$0.677277\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	656698.			1.56876			0.784381	−	0.620279i	$-0.212981\pi$
$647$	656698.			1.56876			0.784381	+	0.620279i	$0.212981\pi$
$648$		0			0
$649$	5744.83	−	3316.78i	0.0136392	−	0.00787458i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−280986.			−0.658959			−0.329480	−	0.944163i	$-0.606873\pi$
$653$	−280986.			−0.658959			−0.329480	+	0.944163i	$0.606873\pi$
$654$		0			0
$655$	−33163.6	+	57441.1i	−0.0773000	+	0.133888i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	331713.	+	191514.i	0.763820	+	0.440992i	0.830666	−	0.556772i	$-0.187960\pi$
$659$	331713.	+	191514.i	0.763820	+	0.440992i	−0.0668456	+	0.997763i	$0.521293\pi$
$660$		0			0
$661$	−314250.	−	181433.i	−0.719239	−	0.415253i	0.0952338	−	0.995455i	$-0.469640\pi$
$661$	−314250.	−	181433.i	−0.719239	−	0.415253i	−0.814472	+	0.580202i	$0.802973\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−83993.6	+	74522.8i	−0.189934	+	0.168518i
$666$		0			0
$667$	74446.8	−	42981.9i	0.167338	−	0.0966126i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1959.34	−	3393.68i	0.00435176	−	0.00753747i
$672$		0			0
$673$		−	191020.i		−	0.421744i	−0.977514	−	0.210872i	$-0.932370\pi$
$673$		−	191020.i		−	0.421744i	0.977514	−	0.210872i	$-0.0676304\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			336677.i			0.734575i	0.930107	+	0.367287i	$0.119713\pi$
$677$			336677.i			0.734575i	−0.930107	+	0.367287i	$0.880287\pi$
$678$		0			0
$679$	251992.	−	145488.i	0.546571	−	0.315563i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	313252.i		−	0.671509i	−0.941950	−	0.335755i	$-0.891009\pi$
$683$		−	313252.i		−	0.671509i	0.941950	−	0.335755i	$-0.108991\pi$
$684$		0			0
$685$	54842.7			0.116879
$686$		0			0
$687$		0			0
$688$		0			0
$689$	96024.8	+	166320.i	0.202276	+	0.350353i
$690$		0			0
$691$	803808.			1.68344			0.841718	−	0.539918i	$-0.181545\pi$
$691$	803808.			1.68344			0.841718	+	0.539918i	$0.181545\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	44654.2			0.0924470
$696$		0			0
$697$	680612.	+	392952.i	1.40099	+	0.808860i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	247655.	+	428950.i	0.503977	+	0.872913i	0.999989	+	0.00459793i	$0.00146357\pi$
$701$	247655.	+	428950.i	0.503977	+	0.872913i	−0.496013	+	0.868315i	$0.665203\pi$
$702$		0			0
$703$	−876619.	+	179638.i	−1.77378	+	0.363486i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−457821.	+	792969.i	−0.915918	+	1.58642i
$708$		0			0
$709$	−7754.66	+	13431.5i	−0.0154266	+	0.0267197i	−0.873636	−	0.486581i	$-0.838244\pi$
$709$	−7754.66	+	13431.5i	−0.0154266	+	0.0267197i	0.858209	+	0.513300i	$0.171577\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−110036.	−	63529.1i	−0.216448	−	0.124967i
$714$		0			0
$715$			935.770i			0.00183045i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	377951.	+	654630.i	0.731102	+	1.26631i	0.956413	+	0.292018i	$0.0943269\pi$
$719$	377951.	+	654630.i	0.731102	+	1.26631i	−0.225311	+	0.974287i	$0.572340\pi$
$720$		0			0
$721$			783342.i			1.50689i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−199404.	+	115126.i	−0.379366	+	0.219027i
$726$		0			0
$727$	−326273.	−	565122.i	−0.617323	−	1.06923i	−0.989972	−	0.141262i	$-0.954884\pi$
$727$	−326273.	−	565122.i	−0.617323	−	1.06923i	0.372649	−	0.927972i	$-0.378449\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	39031.0	−	67603.7i	0.0730424	−	0.126513i
$732$		0			0
$733$	−811947.			−1.51119			−0.755597	−	0.655037i	$-0.772653\pi$
$733$	−811947.			−1.51119			−0.755597	+	0.655037i	$0.772653\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8276.58	+	4778.49i	0.0152376	+	0.00879742i
$738$		0			0
$739$	−389853.	−	675246.i	−0.713859	−	1.23644i	−0.963398	−	0.268075i	$-0.913612\pi$
$739$	−389853.	−	675246.i	−0.713859	−	1.23644i	0.249539	−	0.968365i	$-0.419721\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	497760.	−	287382.i	0.901660	−	0.520574i	0.0239215	−	0.999714i	$-0.492385\pi$
$743$	497760.	−	287382.i	0.901660	−	0.520574i	0.877738	+	0.479140i	$0.159052\pi$
$744$		0			0
$745$	−51844.2	+	89796.8i	−0.0934088	+	0.161789i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			772308.i			1.37666i
$750$		0			0
$751$	168301.	+	97168.5i	0.298405	+	0.172284i	0.641726	−	0.766934i	$-0.278219\pi$
$751$	168301.	+	97168.5i	0.298405	+	0.172284i	−0.343321	+	0.939218i	$0.611552\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−9605.21	+	5545.57i	−0.0168505	+	0.00972864i
$756$		0			0
$757$	−144106.	−	249600.i	−0.251473	−	0.435564i	0.712458	−	0.701714i	$-0.247582\pi$
$757$	−144106.	−	249600.i	−0.251473	−	0.435564i	−0.963932	+	0.266150i	$0.914248\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−660814.			−1.14106			−0.570532	−	0.821275i	$-0.693263\pi$
$761$	−660814.			−1.14106			−0.570532	+	0.821275i	$0.693263\pi$
$762$		0			0
$763$	763422.	−	440762.i	1.31134	−	0.757103i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	280274.			0.476422
$768$		0			0
$769$	367592.	−	636688.i	0.621603	−	1.07665i	−0.367584	−	0.929990i	$-0.619815\pi$
$769$	367592.	−	636688.i	0.621603	−	1.07665i	0.989187	−	0.146658i	$-0.0468516\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−503015.	−	290416.i	−0.841824	−	0.486028i	0.0160595	−	0.999871i	$-0.494888\pi$
$773$	−503015.	−	290416.i	−0.841824	−	0.486028i	−0.857884	+	0.513843i	$0.828221\pi$
$774$		0			0
$775$	294729.	+	170162.i	0.490703	+	0.283308i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	785942.	+	885824.i	1.29514	+	1.45973i
$780$		0			0
$781$	5647.49	−	3260.58i	0.00925877	−	0.00534555i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−28711.5	+	49729.7i	−0.0465925	+	0.0807006i
$786$		0			0
$787$		−	209530.i		−	0.338296i	−0.985591	−	0.169148i	$-0.945898\pi$
$787$		−	209530.i		−	0.338296i	0.985591	−	0.169148i	$-0.0541015\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			267255.i			0.427143i
$792$		0			0
$793$	143386.	−	82783.8i	0.228013	−	0.131643i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	384377.i		−	0.605118i	−0.953131	−	0.302559i	$-0.902159\pi$
$797$		−	384377.i		−	0.605118i	0.953131	−	0.302559i	$-0.0978410\pi$
$798$		0			0
$799$	464581.			0.727726
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8215.57	−	14229.8i	−0.0127411	−	0.0220682i
$804$		0			0
$805$	−68075.3			−0.105050
$806$		0			0
$807$		0			0
$808$		0			0
$809$	133009.			0.203228			0.101614	−	0.994824i	$-0.467599\pi$
$809$	133009.			0.203228			0.101614	+	0.994824i	$0.467599\pi$
$810$		0			0
$811$	−71351.1	−	41194.6i	−0.108482	−	0.0626323i	0.444777	−	0.895641i	$-0.353283\pi$
$811$	−71351.1	−	41194.6i	−0.108482	−	0.0626323i	−0.553259	+	0.833009i	$0.686616\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	91169.4	+	157910.i	0.137257	+	0.237736i
$816$		0			0
$817$	87986.9	−	78065.8i	0.131818	−	0.116954i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	268164.	−	464473.i	0.397845	−	0.689087i	−0.595615	−	0.803270i	$-0.703092\pi$
$821$	268164.	−	464473.i	0.397845	−	0.689087i	0.993460	+	0.114183i	$0.0364250\pi$
$822$		0			0
$823$	−236126.	+	408982.i	−0.348613	+	0.603816i	−0.986003	−	0.166725i	$-0.946681\pi$
$823$	−236126.	+	408982.i	−0.348613	+	0.603816i	0.637390	+	0.770541i	$0.280014\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	189650.	+	109494.i	0.277294	+	0.160096i	0.632198	−	0.774807i	$-0.282153\pi$
$827$	189650.	+	109494.i	0.277294	+	0.160096i	−0.354903	+	0.934903i	$0.615486\pi$
$828$		0			0
$829$			1.15812e6i			1.68517i	0.538561	+	0.842586i	$0.318968\pi$
$829$			1.15812e6i			1.68517i	−0.538561	+	0.842586i	$0.681032\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	11158.7	+	19327.4i	0.0160813	+	0.0278537i
$834$		0			0
$835$			268362.i			0.384901i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−576430.	+	332802.i	−0.818885	+	0.472783i	−0.850032	−	0.526731i	$-0.823417\pi$
$839$	−576430.	+	332802.i	−0.818885	+	0.472783i	0.0311469	+	0.999515i	$0.490084\pi$
$840$		0			0
$841$	−276502.	−	478915.i	−0.390936	−	0.677121i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	69173.6	−	119812.i	0.0968784	−	0.167798i
$846$		0			0
$847$	−731016.			−1.01897
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−469819.	−	271250.i	−0.648742	−	0.374551i
$852$		0			0
$853$	441621.	+	764910.i	0.606949	+	1.05127i	0.991740	+	0.128262i	$0.0409399\pi$
$853$	441621.	+	764910.i	0.606949	+	1.05127i	−0.384792	+	0.923003i	$0.625727\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	680285.	−	392763.i	0.926252	−	0.534772i	0.0406278	−	0.999174i	$-0.487064\pi$
$857$	680285.	−	392763.i	0.926252	−	0.534772i	0.885624	+	0.464403i	$0.153731\pi$
$858$		0			0
$859$	−727091.	+	1.25936e6i	−0.985377	+	1.70672i	−0.345128	+	0.938556i	$0.612164\pi$
$859$	−727091.	+	1.25936e6i	−0.985377	+	1.70672i	−0.640249	+	0.768167i	$0.721169\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			899567.i			1.20785i	0.797042	+	0.603924i	$0.206397\pi$
$863$			899567.i			1.20785i	−0.797042	+	0.603924i	$0.793603\pi$
$864$		0			0
$865$	−240442.	−	138819.i	−0.321350	−	0.185531i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6864.90	+	3963.45i	−0.00909064	+	0.00524848i
$870$		0			0
$871$	201895.	+	349693.i	0.266127	+	0.460946i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	376743.			0.492072
$876$		0			0
$877$	279525.	−	161384.i	0.363431	−	0.209827i	−0.307154	−	0.951660i	$-0.599377\pi$
$877$	279525.	−	161384.i	0.363431	−	0.209827i	0.670585	+	0.741833i	$0.266043\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−547085.			−0.704860			−0.352430	−	0.935838i	$-0.614645\pi$
$881$	−547085.			−0.704860			−0.352430	+	0.935838i	$0.614645\pi$
$882$		0			0
$883$	524253.	−	908034.i	0.672388	−	1.16461i	−0.304837	−	0.952404i	$-0.598602\pi$
$883$	524253.	−	908034.i	0.672388	−	1.16461i	0.977225	−	0.212205i	$-0.0680646\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−318039.	−	183620.i	−0.404234	−	0.233385i	0.284075	−	0.958802i	$-0.408313\pi$
$887$	−318039.	−	183620.i	−0.404234	−	0.233385i	−0.688309	+	0.725417i	$0.741647\pi$
$888$		0			0
$889$	−260633.	−	150476.i	−0.329781	−	0.190399i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	664183.	+	221191.i	0.832885	+	0.277374i
$894$		0			0
$895$	−99802.7	+	57621.1i	−0.124594	+	0.0719342i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	114015.	−	197479.i	0.141072	−	0.244344i
$900$		0			0
$901$		−	577477.i		−	0.711353i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			198711.i			0.242619i
$906$		0			0
$907$	132002.	−	76211.4i	0.160460	−	0.0926415i	−0.417620	−	0.908622i	$-0.637136\pi$
$907$	132002.	−	76211.4i	0.160460	−	0.0926415i	0.578080	+	0.815980i	$0.303802\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	826053.i		−	0.995339i	−0.867367	−	0.497669i	$-0.834189\pi$
$911$		−	826053.i		−	0.995339i	0.867367	−	0.497669i	$-0.165811\pi$
$912$		0			0
$913$	−22205.0			−0.0266385
$914$		0			0
$915$		0			0
$916$		0			0
$917$	265925.	+	460596.i	0.316243	+	0.547749i
$918$		0			0
$919$	−139504.			−0.165180			−0.0825898	−	0.996584i	$-0.526319\pi$
$919$	−139504.			−0.165180			−0.0825898	+	0.996584i	$0.526319\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	275524.			0.323412
$924$		0			0
$925$	1.25840e6	+	726539.i	1.47074	+	0.849132i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−193588.	−	335304.i	−0.224309	−	0.388515i	0.731803	−	0.681516i	$-0.238679\pi$
$929$	−193588.	−	335304.i	−0.224309	−	0.388515i	−0.956112	+	0.293002i	$0.905346\pi$
$930$		0			0
$931$	6750.91	+	32943.9i	0.00778867	+	0.0380080i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1406.89	−	2436.81i	0.00160930	−	0.00278739i
$936$		0			0
$937$	31843.4	−	55154.4i	0.0362694	−	0.0628205i	−0.847321	−	0.531081i	$-0.821786\pi$
$937$	31843.4	−	55154.4i	0.0362694	−	0.0628205i	0.883590	+	0.468261i	$0.155119\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	783860.	+	452562.i	0.885237	+	0.511092i	0.872381	−	0.488826i	$-0.162575\pi$
$941$	783860.	+	452562.i	0.885237	+	0.511092i	0.0128552	+	0.999917i	$0.495908\pi$
$942$		0			0
$943$			717945.i			0.807361i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−86501.2	−	149824.i	−0.0964544	−	0.167064i	0.813760	−	0.581201i	$-0.197417\pi$
$947$	−86501.2	−	149824.i	−0.0964544	−	0.167064i	−0.910215	+	0.414137i	$0.864084\pi$
$948$		0			0
$949$		−	694230.i		−	0.770851i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−796366.	+	459782.i	−0.876853	+	0.506251i	−0.869620	−	0.493722i	$-0.835636\pi$
$953$	−796366.	+	459782.i	−0.876853	+	0.506251i	−0.00723358	+	0.999974i	$0.502303\pi$
$954$		0			0
$955$	87962.4	+	152355.i	0.0964473	+	0.167052i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	219880.	−	380844.i	0.239083	−	0.414104i
$960$		0			0
$961$	586484.			0.635052
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−220895.	−	127534.i	−0.237209	−	0.136953i
$966$		0			0
$967$	−51509.8	−	89217.7i	−0.0550855	−	0.0954109i	0.837168	−	0.546946i	$-0.184210\pi$
$967$	−51509.8	−	89217.7i	−0.0550855	−	0.0954109i	−0.892253	+	0.451535i	$0.850876\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	157988.	−	91214.6i	0.167566	−	0.0967445i	−0.413871	−	0.910335i	$-0.635824\pi$
$971$	157988.	−	91214.6i	0.167566	−	0.0967445i	0.581438	+	0.813591i	$0.302490\pi$
$972$		0			0
$973$	179032.	−	310092.i	0.189105	−	0.327540i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	436847.i		−	0.457657i	−0.973467	−	0.228828i	$-0.926511\pi$
$977$		−	436847.i		−	0.457657i	0.973467	−	0.228828i	$-0.0734895\pi$
$978$		0			0
$979$	−15486.1	−	8940.91i	−0.0161576	−	0.00932859i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−577269.	+	333286.i	−0.597408	+	0.344914i	−0.768021	−	0.640424i	$-0.778759\pi$
$983$	−577269.	+	333286.i	−0.597408	+	0.344914i	0.170613	+	0.985338i	$0.445425\pi$
$984$		0			0
$985$	69630.3	+	120603.i	0.0717671	+	0.124304i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	71311.8			0.0729070
$990$		0			0
$991$	−706100.	+	407667.i	−0.718984	+	0.415105i	−0.814378	−	0.580334i	$-0.802922\pi$
$991$	−706100.	+	407667.i	−0.718984	+	0.415105i	0.0953949	+	0.995440i	$0.469589\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−26988.9			−0.0272608
$996$		0			0
$997$	−720639.	+	1.24818e6i	−0.724983	+	1.25571i	0.233999	+	0.972237i	$0.424819\pi$
$997$	−720639.	+	1.24818e6i	−0.724983	+	1.25571i	−0.958981	+	0.283470i	$0.908514\pi$
$998$		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.145.4		12
3.2	odd	2		76.5.h.a.69.6	yes	12
12.11	even	2		304.5.r.b.145.1		12
19.8	odd	6	inner	684.5.y.c.217.4		12
57.8	even	6		76.5.h.a.65.6	✓	12
228.179	odd	6		304.5.r.b.65.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.6	✓	12	57.8	even	6
76.5.h.a.69.6	yes	12	3.2	odd	2
304.5.r.b.65.1		12	228.179	odd	6
304.5.r.b.145.1		12	12.11	even	2
684.5.y.c.145.4		12	1.1	even	1	trivial
684.5.y.c.217.4		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)

\(f(q)\)	\(=\)	\(q+(3.11411 + 5.39380i) q^{5} +49.9415 q^{7} +O(q^{10})\)	\(q+(3.11411 + 5.39380i) q^{5} +49.9415 q^{7} -1.88575 q^{11} +(-69.0003 - 39.8373i) q^{13} +(119.788 + 207.478i) q^{17} +(72.4707 + 353.651i) q^{19} +(-109.429 + 189.537i) q^{23} +(293.105 - 507.672i) q^{25} +(-340.159 - 196.391i) q^{29} +580.549i q^{31} +(155.523 + 269.374i) q^{35} +2478.77i q^{37} +(2840.91 - 1640.20i) q^{41} +(-162.917 - 282.181i) q^{43} +(969.593 - 1679.39i) q^{47} +93.1537 q^{49} +(-2087.49 - 1205.21i) q^{53} +(-5.87245 - 10.1714i) q^{55} +(-3046.44 + 1758.86i) q^{59} +(-1039.02 + 1799.64i) q^{61} -496.232i q^{65} +(-4389.01 - 2533.99i) q^{67} +(-2994.82 + 1729.06i) q^{71} +(4356.65 + 7545.94i) q^{73} -94.1773 q^{77} +(3640.40 - 2101.79i) q^{79} +11775.2 q^{83} +(-746.064 + 1292.22i) q^{85} +(8212.16 + 4741.29i) q^{89} +(-3445.98 - 1989.54i) q^{91} +(-1681.84 + 1492.20i) q^{95} +(5045.74 - 2913.16i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{5} - 52 q^{7}+O(q^{10}) \) 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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