LMFDB - Embedded newform 684.5.y.c.145.1

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			145.1
Root			$0.500000 - 14.3199i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.c.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.9265 - 34.5138i) q^{5} -53.3663 q^{7} +O(q^{10})$	$q+(-19.9265 - 34.5138i) q^{5} -53.3663 q^{7} -9.01156 q^{11} +(-5.39539 - 3.11503i) q^{13} +(261.609 + 453.120i) q^{17} +(-329.612 + 147.231i) q^{19} +(-204.027 + 353.386i) q^{23} +(-481.633 + 834.213i) q^{25} +(-1176.08 - 679.011i) q^{29} -214.814i q^{31} +(1063.41 + 1841.87i) q^{35} +1223.68i q^{37} +(666.384 - 384.737i) q^{41} +(-1147.74 - 1987.94i) q^{43} +(1740.86 - 3015.26i) q^{47} +446.963 q^{49} +(4815.71 + 2780.35i) q^{53} +(179.569 + 311.023i) q^{55} +(2130.74 - 1230.18i) q^{59} +(-1471.38 + 2548.51i) q^{61} +248.287i q^{65} +(1474.24 + 851.150i) q^{67} +(2989.25 - 1725.84i) q^{71} +(-4122.11 - 7139.70i) q^{73} +480.914 q^{77} +(7356.86 - 4247.48i) q^{79} +2757.20 q^{83} +(10425.9 - 18058.2i) q^{85} +(-5987.69 - 3457.00i) q^{89} +(287.932 + 166.238i) q^{91} +(11649.5 + 8442.33i) q^{95} +(-10519.1 + 6073.22i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−19.9265	−	34.5138i	−0.797061	−	1.38055i	−0.921522	−	0.388326i	$-0.873053\pi$
$5$	−19.9265	−	34.5138i	−0.797061	−	1.38055i	0.124461	−	0.992225i	$-0.460280\pi$
$6$		0			0
$7$	−53.3663			−1.08911			−0.544554	−	0.838726i	$-0.683301\pi$
$7$	−53.3663			−1.08911			−0.544554	+	0.838726i	$0.683301\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−9.01156			−0.0744757			−0.0372379	−	0.999306i	$-0.511856\pi$
$11$	−9.01156			−0.0744757			−0.0372379	+	0.999306i	$0.511856\pi$
$12$		0			0
$13$	−5.39539	−	3.11503i	−0.0319254	−	0.0184321i	0.483952	−	0.875094i	$-0.339201\pi$
$13$	−5.39539	−	3.11503i	−0.0319254	−	0.0184321i	−0.515878	+	0.856662i	$0.672534\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	261.609	+	453.120i	0.905222	+	1.56789i	0.820619	+	0.571476i	$0.193629\pi$
$17$	261.609	+	453.120i	0.905222	+	1.56789i	0.0846030	+	0.996415i	$0.473038\pi$
$18$		0			0
$19$	−329.612	+	147.231i	−0.913052	+	0.407843i
$19$	−329.612	+	147.231i	−0.913052	+	0.407843i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−204.027	+	353.386i	−0.385685	+	0.668026i	−0.991864	−	0.127302i	$-0.959368\pi$
$23$	−204.027	+	353.386i	−0.385685	+	0.668026i	0.606179	+	0.795328i	$0.292701\pi$
$24$		0			0
$25$	−481.633	+	834.213i	−0.770613	+	1.33474i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1176.08	−	679.011i	−1.39843	−	0.807385i	−0.404204	−	0.914669i	$-0.632451\pi$
$29$	−1176.08	−	679.011i	−1.39843	−	0.807385i	−0.994228	+	0.107283i	$0.965785\pi$
$30$		0			0
$31$		−	214.814i		−	0.223532i	−0.993735	−	0.111766i	$-0.964349\pi$
$31$		−	214.814i		−	0.223532i	0.993735	−	0.111766i	$-0.0356506\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1063.41	+	1841.87i	0.868086	+	1.50357i
$36$		0			0
$37$			1223.68i			0.893851i	0.894571	+	0.446925i	$0.147481\pi$
$37$			1223.68i			0.893851i	−0.894571	+	0.446925i	$0.852519\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	666.384	−	384.737i	0.396421	−	0.228874i	−0.288517	−	0.957475i	$-0.593162\pi$
$41$	666.384	−	384.737i	0.396421	−	0.228874i	0.684939	+	0.728601i	$0.259829\pi$
$42$		0			0
$43$	−1147.74	−	1987.94i	−0.620733	−	1.07514i	−0.989349	−	0.145560i	$-0.953502\pi$
$43$	−1147.74	−	1987.94i	−0.620733	−	1.07514i	0.368616	−	0.929582i	$-0.379832\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1740.86	−	3015.26i	0.788076	−	1.36499i	−0.139067	−	0.990283i	$-0.544410\pi$
$47$	1740.86	−	3015.26i	0.788076	−	1.36499i	0.927144	−	0.374706i	$-0.122256\pi$
$48$		0			0
$49$	446.963			0.186157
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4815.71	+	2780.35i	1.71438	+	0.989801i	0.928422	+	0.371527i	$0.121166\pi$
$53$	4815.71	+	2780.35i	1.71438	+	0.989801i	0.785963	+	0.618274i	$0.212168\pi$
$54$		0			0
$55$	179.569	+	311.023i	0.0593617	+	0.102817i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2130.74	−	1230.18i	0.612105	−	0.353399i	−0.161684	−	0.986843i	$-0.551693\pi$
$59$	2130.74	−	1230.18i	0.612105	−	0.353399i	0.773789	+	0.633444i	$0.218359\pi$
$60$		0			0
$61$	−1471.38	+	2548.51i	−0.395427	+	0.684900i	−0.993156	−	0.116799i	$-0.962737\pi$
$61$	−1471.38	+	2548.51i	−0.395427	+	0.684900i	0.597728	+	0.801699i	$0.296070\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			248.287i			0.0587661i
$66$		0			0
$67$	1474.24	+	851.150i	0.328411	+	0.189608i	0.655135	−	0.755512i	$-0.272612\pi$
$67$	1474.24	+	851.150i	0.328411	+	0.189608i	−0.326725	+	0.945120i	$0.605945\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2989.25	−	1725.84i	0.592988	−	0.342361i	−0.173290	−	0.984871i	$-0.555440\pi$
$71$	2989.25	−	1725.84i	0.592988	−	0.342361i	0.766278	+	0.642509i	$0.222107\pi$
$72$		0			0
$73$	−4122.11	−	7139.70i	−0.773524	−	1.33978i	−0.935620	−	0.353008i	$-0.885159\pi$
$73$	−4122.11	−	7139.70i	−0.773524	−	1.33978i	0.162097	−	0.986775i	$-0.448174\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	480.914			0.0811121
$78$		0			0
$79$	7356.86	−	4247.48i	1.17879	−	0.680577i	0.223059	−	0.974805i	$-0.428396\pi$
$79$	7356.86	−	4247.48i	1.17879	−	0.680577i	0.955735	+	0.294227i	$0.0950623\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2757.20			0.400233			0.200116	−	0.979772i	$-0.435868\pi$
$83$	2757.20			0.400233			0.200116	+	0.979772i	$0.435868\pi$
$84$		0			0
$85$	10425.9	−	18058.2i	1.44303	−	2.49941i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5987.69	−	3457.00i	−0.755926	−	0.436434i	0.0719049	−	0.997411i	$-0.477092\pi$
$89$	−5987.69	−	3457.00i	−0.755926	−	0.436434i	−0.827831	+	0.560977i	$0.810426\pi$
$90$		0			0
$91$	287.932	+	166.238i	0.0347702	+	0.0200746i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11649.5	+	8442.33i	1.29081	+	0.935438i
$96$		0			0
$97$	−10519.1	+	6073.22i	−1.11798	+	0.645469i	−0.940886	−	0.338724i	$-0.890005\pi$
$97$	−10519.1	+	6073.22i	−1.11798	+	0.645469i	−0.177099	+	0.984193i	$0.556671\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4704.98	−	8149.27i	0.461228	−	0.798870i	−0.537795	−	0.843076i	$-0.680743\pi$
$101$	4704.98	−	8149.27i	0.461228	−	0.798870i	0.999022	+	0.0442061i	$0.0140758\pi$
$102$		0			0
$103$			15630.0i			1.47328i	0.676284	+	0.736641i	$0.263589\pi$
$103$			15630.0i			1.47328i	−0.676284	+	0.736641i	$0.736411\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1064.07i		−	0.0929398i	−0.998920	−	0.0464699i	$-0.985203\pi$
$107$		−	1064.07i		−	0.0929398i	0.998920	−	0.0464699i	$-0.0147972\pi$
$108$		0			0
$109$	2702.69	−	1560.40i	0.227480	−	0.131336i	−0.381929	−	0.924192i	$-0.624740\pi$
$109$	2702.69	−	1560.40i	0.227480	−	0.131336i	0.609409	+	0.792856i	$0.291407\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	4559.56i		−	0.357081i	−0.983933	−	0.178540i	$-0.942863\pi$
$113$		−	4559.56i		−	0.357081i	0.983933	−	0.178540i	$-0.0571375\pi$
$114$		0			0
$115$	16262.2			1.22966
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−13961.1	−	24181.4i	−0.985885	−	1.70760i
$120$		0			0
$121$	−14559.8			−0.994453
$122$		0			0
$123$		0			0
$124$		0			0
$125$	13480.9			0.862781
$126$		0			0
$127$	16901.8	+	9758.24i	1.04791	+	0.605012i	0.922064	−	0.387038i	$-0.126502\pi$
$127$	16901.8	+	9758.24i	1.04791	+	0.605012i	0.125848	+	0.992050i	$0.459835\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9199.29	+	15933.6i	0.536058	+	0.928479i	0.999111	+	0.0421489i	$0.0134204\pi$
$131$	9199.29	+	15933.6i	0.536058	+	0.928479i	−0.463054	+	0.886330i	$0.653246\pi$
$132$		0			0
$133$	17590.2	−	7857.20i	0.994413	−	0.444186i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9527.92	+	16502.8i	−0.507642	+	0.879261i	0.492319	+	0.870415i	$0.336149\pi$
$137$	−9527.92	+	16502.8i	−0.507642	+	0.879261i	−0.999961	+	0.00884630i	$0.997184\pi$
$138$		0			0
$139$	7531.70	−	13045.3i	0.389819	−	0.675187i	−0.602606	−	0.798039i	$-0.705871\pi$
$139$	7531.70	−	13045.3i	0.389819	−	0.675187i	0.992425	+	0.122852i	$0.0392041\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	48.6209	+	28.0713i	0.00237766	+	0.00137274i
$144$		0			0
$145$			54121.3i			2.57414i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6317.79	+	10942.7i	0.284572	+	0.492894i	0.972505	−	0.232880i	$-0.0748151\pi$
$149$	6317.79	+	10942.7i	0.284572	+	0.492894i	−0.687933	+	0.725774i	$0.741482\pi$
$150$		0			0
$151$			14119.5i			0.619248i	0.950859	+	0.309624i	$0.100203\pi$
$151$			14119.5i			0.619248i	−0.950859	+	0.309624i	$0.899797\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7414.03	+	4280.49i	−0.308597	+	0.178168i
$156$		0			0
$157$	6248.53	+	10822.8i	0.253500	+	0.439075i	0.964487	−	0.264130i	$-0.0850848\pi$
$157$	6248.53	+	10822.8i	0.253500	+	0.439075i	−0.710987	+	0.703205i	$0.751751\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10888.2	−	18858.9i	0.420053	−	0.727553i
$162$		0			0
$163$	29683.1			1.11721			0.558604	−	0.829434i	$-0.311337\pi$
$163$	29683.1			1.11721			0.558604	+	0.829434i	$0.311337\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	20882.9	+	12056.8i	0.748788	+	0.432313i	0.825256	−	0.564759i	$-0.191031\pi$
$167$	20882.9	+	12056.8i	0.748788	+	0.432313i	−0.0764680	+	0.997072i	$0.524364\pi$
$168$		0			0
$169$	−14261.1	−	24700.9i	−0.499321	−	0.864848i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	26503.6	−	15301.9i	0.885550	−	0.511273i	0.0130660	−	0.999915i	$-0.495841\pi$
$173$	26503.6	−	15301.9i	0.885550	−	0.511273i	0.872484	+	0.488642i	$0.162508\pi$
$174$		0			0
$175$	25703.0	−	44518.9i	0.839281	−	1.45368i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	31622.5i		−	0.986940i	−0.869763	−	0.493470i	$-0.835728\pi$
$179$		−	31622.5i		−	0.986940i	0.869763	−	0.493470i	$-0.164272\pi$
$180$		0			0
$181$	−2932.84	−	1693.28i	−0.0895223	−	0.0516857i	0.454571	−	0.890711i	$-0.349793\pi$
$181$	−2932.84	−	1693.28i	−0.0895223	−	0.0516857i	−0.544093	+	0.839025i	$0.683126\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	42233.9	−	24383.7i	1.23401	−	0.712454i
$186$		0			0
$187$	−2357.51	−	4083.32i	−0.0674170	−	0.116770i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7140.61			0.195735			0.0978675	−	0.995199i	$-0.468798\pi$
$191$	7140.61			0.195735			0.0978675	+	0.995199i	$0.468798\pi$
$192$		0			0
$193$	−13922.0	+	8037.86i	−0.373754	+	0.215787i	−0.675097	−	0.737729i	$-0.735898\pi$
$193$	−13922.0	+	8037.86i	−0.373754	+	0.215787i	0.301343	+	0.953516i	$0.402565\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	26545.9			0.684013			0.342007	−	0.939698i	$-0.388893\pi$
$197$	26545.9			0.684013			0.342007	+	0.939698i	$0.388893\pi$
$198$		0			0
$199$	−2357.02	+	4082.47i	−0.0595191	+	0.103090i	−0.894250	−	0.447569i	$-0.852290\pi$
$199$	−2357.02	+	4082.47i	−0.0595191	+	0.103090i	0.834731	+	0.550659i	$0.185623\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	62763.1	+	36236.3i	1.52304	+	0.879330i
$204$		0			0
$205$	−26557.4	−	15332.9i	−0.631944	−	0.364853i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2970.32	−	1326.78i	0.0680002	−	0.0303744i
$210$		0			0
$211$	−7586.62	+	4380.14i	−0.170405	+	0.0983836i	−0.582777	−	0.812632i	$-0.698034\pi$
$211$	−7586.62	+	4380.14i	−0.170405	+	0.0983836i	0.412372	+	0.911016i	$0.364701\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−45740.8	+	79225.3i	−0.989524	+	1.71391i
$216$		0			0
$217$			11463.8i			0.243450i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	3259.68i		−	0.0667406i
$222$		0			0
$223$	74100.7	−	42782.0i	1.49009	−	0.860304i	0.490154	−	0.871636i	$-0.336941\pi$
$223$	74100.7	−	42782.0i	1.49009	−	0.860304i	0.999936	+	0.0113323i	$0.00360726\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	52738.6i		−	1.02347i	−0.859142	−	0.511737i	$-0.829002\pi$
$227$		−	52738.6i		−	1.02347i	0.859142	−	0.511737i	$-0.170998\pi$
$228$		0			0
$229$	27552.9			0.525407			0.262704	−	0.964877i	$-0.415386\pi$
$229$	27552.9			0.525407			0.262704	+	0.964877i	$0.415386\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−29960.8	−	51893.6i	−0.551876	−	0.955877i	−0.998139	−	0.0609754i	$-0.980579\pi$
$233$	−29960.8	−	51893.6i	−0.551876	−	0.955877i	0.446263	−	0.894902i	$-0.352754\pi$
$234$		0			0
$235$	−138757.			−2.51258
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−18546.4			−0.324686			−0.162343	−	0.986734i	$-0.551905\pi$
$239$	−18546.4			−0.324686			−0.162343	+	0.986734i	$0.551905\pi$
$240$		0			0
$241$	51352.4	+	29648.3i	0.884152	+	0.510465i	0.872025	−	0.489461i	$-0.162807\pi$
$241$	51352.4	+	29648.3i	0.884152	+	0.510465i	0.0121266	+	0.999926i	$0.496140\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8906.43	−	15426.4i	−0.148379	−	0.256999i
$246$		0			0
$247$	2237.01	+	232.379i	0.0366669	+	0.00380893i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13531.1	−	23436.6i	0.214776	−	0.372003i	−0.738427	−	0.674333i	$-0.764431\pi$
$251$	13531.1	−	23436.6i	0.214776	−	0.372003i	0.953203	+	0.302330i	$0.0977645\pi$
$252$		0			0
$253$	1838.60	−	3184.56i	0.0287242	−	0.0497517i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	43689.8	+	25224.3i	0.661475	+	0.381903i	0.792839	−	0.609431i	$-0.208602\pi$
$257$	43689.8	+	25224.3i	0.661475	+	0.381903i	−0.131364	+	0.991334i	$0.541936\pi$
$258$		0			0
$259$		−	65303.4i		−	0.973500i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1642.93	+	2845.63i	0.0237523	+	0.0411403i	0.877657	−	0.479289i	$-0.159105\pi$
$263$	1642.93	+	2845.63i	0.0237523	+	0.0411403i	−0.853905	+	0.520429i	$0.825772\pi$
$264$		0			0
$265$		−	221611.i		−	3.15573i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14796.8	−	8542.92i	0.204486	−	0.118060i	−0.394260	−	0.918999i	$-0.628999\pi$
$269$	14796.8	−	8542.92i	0.204486	−	0.118060i	0.598746	+	0.800939i	$0.295666\pi$
$270$		0			0
$271$	−10303.0	−	17845.4i	−0.140290	−	0.242989i	0.787316	−	0.616550i	$-0.211470\pi$
$271$	−10303.0	−	17845.4i	−0.140290	−	0.242989i	−0.927606	+	0.373561i	$0.878137\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4340.27	−	7517.56i	0.0573919	−	0.0994058i
$276$		0			0
$277$	−24421.2			−0.318278			−0.159139	−	0.987256i	$-0.550872\pi$
$277$	−24421.2			−0.318278			−0.159139	+	0.987256i	$0.550872\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6075.51	+	3507.70i	0.0769431	+	0.0444231i	0.537978	−	0.842959i	$-0.319188\pi$
$281$	6075.51	+	3507.70i	0.0769431	+	0.0444231i	−0.461035	+	0.887382i	$0.652522\pi$
$282$		0			0
$283$	47805.3	+	82801.3i	0.596903	+	1.03387i	0.993275	+	0.115776i	$0.0369354\pi$
$283$	47805.3	+	82801.3i	0.596903	+	1.03387i	−0.396373	+	0.918090i	$0.629731\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−35562.5	+	20532.0i	−0.431746	+	0.249269i
$288$		0			0
$289$	−95118.2	+	164750.i	−1.13885	+	1.97255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			110120.i			1.28272i	0.767239	+	0.641361i	$0.221630\pi$
$293$			110120.i			1.28272i	−0.767239	+	0.641361i	$0.778370\pi$
$294$		0			0
$295$	−84916.4	−	49026.5i	−0.975770	−	0.563361i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2201.61	−	1271.10i	0.0246263	−	0.0142180i
$300$		0			0
$301$	61250.4	+	106089.i	0.676046	+	1.17095i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	117278.			1.26072
$306$		0			0
$307$	37032.8	−	21380.9i	0.392925	−	0.226855i	−0.290502	−	0.956874i	$-0.593822\pi$
$307$	37032.8	−	21380.9i	0.392925	−	0.226855i	0.683427	+	0.730019i	$0.260489\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	62672.8			0.647976			0.323988	−	0.946061i	$-0.394976\pi$
$311$	62672.8			0.647976			0.323988	+	0.946061i	$0.394976\pi$
$312$		0			0
$313$	−87372.5	+	151334.i	−0.891838	+	1.54471i	−0.0541679	+	0.998532i	$0.517251\pi$
$313$	−87372.5	+	151334.i	−0.891838	+	1.54471i	−0.837670	+	0.546177i	$0.816083\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−26126.0	−	15083.9i	−0.259989	−	0.150105i	0.364341	−	0.931266i	$-0.381294\pi$
$317$	−26126.0	−	15083.9i	−0.259989	−	0.150105i	−0.624329	+	0.781161i	$0.714628\pi$
$318$		0			0
$319$	10598.3	+	6118.95i	0.104149	+	0.0601306i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−152943.	−	110837.i	−1.46597	−	1.06238i
$324$		0			0
$325$	5197.19	−	3000.60i	0.0492042	−	0.0284081i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−92903.3	+	160913.i	−0.858301	+	1.48662i
$330$		0			0
$331$			63185.8i			0.576718i	0.957522	+	0.288359i	$0.0931096\pi$
$331$			63185.8i			0.576718i	−0.957522	+	0.288359i	$0.906890\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	67841.9i		−	0.604517i
$336$		0			0
$337$	−125600.	+	72515.1i	−1.10593	+	0.638511i	−0.937773	−	0.347249i	$-0.887116\pi$
$337$	−125600.	+	72515.1i	−1.10593	+	0.638511i	−0.168160	+	0.985760i	$0.553783\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			1935.81i			0.0166477i
$342$		0			0
$343$	104280.			0.886363
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1089.43	−	1886.95i	−0.00904776	−	0.0156712i	0.861466	−	0.507815i	$-0.169547\pi$
$347$	−1089.43	−	1886.95i	−0.00904776	−	0.0156712i	−0.870514	+	0.492144i	$0.836213\pi$
$348$		0			0
$349$	88628.2			0.727647			0.363824	−	0.931468i	$-0.381471\pi$
$349$	88628.2			0.727647			0.363824	+	0.931468i	$0.381471\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−197267.			−1.58309			−0.791545	−	0.611111i	$-0.790723\pi$
$353$	−197267.			−1.58309			−0.791545	+	0.611111i	$0.790723\pi$
$354$		0			0
$355$	−119131.	−	68780.2i	−0.945295	−	0.545766i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	69978.8	+	121207.i	0.542972	+	0.940455i	0.998732	+	0.0503521i	$0.0160344\pi$
$359$	69978.8	+	121207.i	0.542972	+	0.940455i	−0.455760	+	0.890103i	$0.650632\pi$
$360$		0			0
$361$	86966.8	−	97058.4i	0.667328	−	0.744764i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−164279.	+	284539.i	−1.23309	+	2.13578i
$366$		0			0
$367$	16609.2	−	28768.0i	0.123315	−	0.213588i	−0.797758	−	0.602978i	$-0.793981\pi$
$367$	16609.2	−	28768.0i	0.123315	−	0.213588i	0.921073	+	0.389390i	$0.127314\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−256997.	−	148377.i	−1.86715	−	1.07800i
$372$		0			0
$373$			23103.2i			0.166056i	0.996547	+	0.0830281i	$0.0264591\pi$
$373$			23103.2i			0.166056i	−0.996547	+	0.0830281i	$0.973541\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4230.28	+	7327.06i	0.0297636	+	0.0515521i
$378$		0			0
$379$		−	32221.6i		−	0.224321i	−0.993690	−	0.112160i	$-0.964223\pi$
$379$		−	32221.6i		−	0.224321i	0.993690	−	0.112160i	$-0.0357770\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	195003.	−	112585.i	1.32936	−	0.767509i	0.344163	−	0.938910i	$-0.388163\pi$
$383$	195003.	−	112585.i	1.32936	−	0.767509i	0.985201	+	0.171401i	$0.0548294\pi$
$384$		0			0
$385$	−9582.94	−	16598.1i	−0.0646513	−	0.111979i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14122.8	+	24461.4i	−0.0933302	+	0.161653i	−0.908910	−	0.416991i	$-0.863085\pi$
$389$	−14122.8	+	24461.4i	−0.0933302	+	0.161653i	0.815580	+	0.578644i	$0.196418\pi$
$390$		0			0
$391$	−213502.			−1.39652
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−293193.	−	169275.i	−1.87914	−	1.08492i
$396$		0			0
$397$	97341.9	+	168601.i	0.617616	+	1.06974i	0.989919	+	0.141632i	$0.0452349\pi$
$397$	97341.9	+	168601.i	0.617616	+	1.06974i	−0.372303	+	0.928111i	$0.621432\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	20526.9	−	11851.2i	0.127654	−	0.0737012i	−0.434813	−	0.900521i	$-0.643186\pi$
$401$	20526.9	−	11851.2i	0.127654	−	0.0737012i	0.562467	+	0.826820i	$0.309852\pi$
$402$		0			0
$403$	−669.151	+	1159.00i	−0.00412016	+	0.00713633i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	11027.3i		−	0.0665702i
$408$		0			0
$409$	142037.	+	82004.9i	0.849090	+	0.490222i	0.860344	−	0.509715i	$-0.170249\pi$
$409$	142037.	+	82004.9i	0.849090	+	0.490222i	−0.0112539	+	0.999937i	$0.503582\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−113710.	+	65650.3i	−0.666649	+	0.384890i
$414$		0			0
$415$	−54941.5	−	95161.5i	−0.319010	−	0.552542i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−60552.8			−0.344910			−0.172455	−	0.985017i	$-0.555170\pi$
$419$	−60552.8			−0.344910			−0.172455	+	0.985017i	$0.555170\pi$
$420$		0			0
$421$	116808.	−	67439.2i	0.659036	−	0.380494i	−0.132874	−	0.991133i	$-0.542420\pi$
$421$	116808.	−	67439.2i	0.659036	−	0.380494i	0.791909	+	0.610638i	$0.209087\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−503999.			−2.79030
$426$		0			0
$427$	78522.4	−	136005.i	0.430663	−	0.745931i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	93228.7	+	53825.6i	0.501874	+	0.289757i	0.729487	−	0.683994i	$-0.239759\pi$
$431$	93228.7	+	53825.6i	0.501874	+	0.289757i	−0.227613	+	0.973752i	$0.573092\pi$
$432$		0			0
$433$	82985.3	+	47911.6i	0.442614	+	0.255543i	0.704706	−	0.709500i	$-0.251079\pi$
$433$	82985.3	+	47911.6i	0.442614	+	0.255543i	−0.262092	+	0.965043i	$0.584412\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15220.3	−	146519.i	0.0797005	−	0.767241i
$438$		0			0
$439$	−220263.	+	127169.i	−1.14291	+	0.659859i	−0.947149	−	0.320793i	$-0.896051\pi$
$439$	−220263.	+	127169.i	−1.14291	+	0.659859i	−0.195760	+	0.980652i	$0.562717\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	146103.	−	253058.i	0.744479	−	1.28947i	−0.205959	−	0.978561i	$-0.566031\pi$
$443$	146103.	−	253058.i	0.744479	−	1.28947i	0.950438	−	0.310914i	$-0.100635\pi$
$444$		0			0
$445$			275544.i			1.39146i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			123714.i			0.613657i	0.951765	+	0.306828i	$0.0992677\pi$
$449$			123714.i			0.613657i	−0.951765	+	0.306828i	$0.900732\pi$
$450$		0			0
$451$	−6005.16	+	3467.08i	−0.0295238	+	0.0170455i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	13250.2i		−	0.0640027i
$456$		0			0
$457$	−249320.			−1.19378			−0.596890	−	0.802323i	$-0.703597\pi$
$457$	−249320.			−1.19378			−0.596890	+	0.802323i	$0.703597\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−63180.9	−	109432.i	−0.297292	−	0.514925i	0.678223	−	0.734856i	$-0.262750\pi$
$461$	−63180.9	−	109432.i	−0.297292	−	0.514925i	−0.975516	+	0.219931i	$0.929417\pi$
$462$		0			0
$463$	−86701.1			−0.404448			−0.202224	−	0.979339i	$-0.564817\pi$
$463$	−86701.1			−0.404448			−0.202224	+	0.979339i	$0.564817\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−226847.			−1.04016			−0.520078	−	0.854119i	$-0.674097\pi$
$467$	−226847.			−1.04016			−0.520078	+	0.854119i	$0.674097\pi$
$468$		0			0
$469$	−78674.5	−	45422.7i	−0.357675	−	0.206504i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10342.9	+	17914.4i	0.0462295	+	0.0800719i
$474$		0			0
$475$	35929.6	−	345878.i	0.159245	−	1.53298i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−130496.	+	226026.i	−0.568757	+	0.985117i	0.427932	+	0.903811i	$0.359242\pi$
$479$	−130496.	+	226026.i	−0.568757	+	0.985117i	−0.996689	+	0.0813056i	$0.974091\pi$
$480$		0			0
$481$	3811.80	−	6602.24i	0.0164756	−	0.0285365i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	419219.	+	242036.i	1.78220	+	1.02896i
$486$		0			0
$487$		−	402444.i		−	1.69687i	−0.529303	−	0.848433i	$-0.677547\pi$
$487$		−	402444.i		−	1.69687i	0.529303	−	0.848433i	$-0.322453\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8446.75	−	14630.2i	−0.0350370	−	0.0606858i	0.847975	−	0.530036i	$-0.177822\pi$
$491$	−8446.75	−	14630.2i	−0.0350370	−	0.0606858i	−0.883012	+	0.469350i	$0.844488\pi$
$492$		0			0
$493$		−	710542.i		−	2.92345i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−159525.	+	92101.9i	−0.645828	+	0.372869i
$498$		0			0
$499$	96752.2	+	167580.i	0.388562	+	0.673009i	0.992256	−	0.124207i	$-0.0396387\pi$
$499$	96752.2	+	167580.i	0.388562	+	0.673009i	−0.603695	+	0.797216i	$0.706305\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7000.74	−	12125.6i	0.0276699	−	0.0479257i	−0.851859	−	0.523771i	$-0.824525\pi$
$503$	7000.74	−	12125.6i	0.0276699	−	0.0479257i	0.879529	+	0.475846i	$0.157858\pi$
$504$		0			0
$505$	−375016.			−1.47051
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−68947.5	−	39806.9i	−0.266123	−	0.153646i	0.361001	−	0.932565i	$-0.382435\pi$
$509$	−68947.5	−	39806.9i	−0.266123	−	0.153646i	−0.627125	+	0.778919i	$0.715768\pi$
$510$		0			0
$511$	219982.	+	381020.i	0.842451	+	1.45917i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	539451.	−	311452.i	2.03394	−	1.17430i
$516$		0			0
$517$	−15687.9	+	27172.2i	−0.0586925	+	0.101658i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			358410.i			1.32040i	0.751090	+	0.660200i	$0.229528\pi$
$521$			358410.i			1.32040i	−0.751090	+	0.660200i	$0.770472\pi$
$522$		0			0
$523$	194918.	+	112536.i	0.712606	+	0.411423i	0.812025	−	0.583622i	$-0.198365\pi$
$523$	194918.	+	112536.i	0.712606	+	0.411423i	−0.0994192	+	0.995046i	$0.531698\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	97336.5	−	56197.3i	0.350473	−	0.202346i
$528$		0			0
$529$	56666.2	+	98148.8i	0.202494	+	0.350731i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4793.87			−0.0168745
$534$		0			0
$535$	−36725.0	+	21203.2i	−0.128308	+	0.0740787i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4027.84			−0.0138642
$540$		0			0
$541$	122595.	−	212341.i	0.418870	−	0.725504i	−0.576956	−	0.816775i	$-0.695760\pi$
$541$	122595.	−	212341.i	0.418870	−	0.725504i	0.995826	+	0.0912713i	$0.0290930\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−107711.	−	62186.8i	−0.362631	−	0.209365i
$546$		0			0
$547$	381981.	+	220537.i	1.27664	+	0.737067i	0.976229	−	0.216744i	$-0.0695436\pi$
$547$	381981.	+	220537.i	1.27664	+	0.737067i	0.300409	+	0.953811i	$0.402877\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	487622.	+	50653.8i	1.60613	+	0.166843i
$552$		0			0
$553$	−392608.	+	226673.i	−1.28384	+	0.741223i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	161284.	−	279353.i	0.519855	−	0.900415i	−0.479879	−	0.877335i	$-0.659319\pi$
$557$	161284.	−	279353.i	0.519855	−	0.900415i	0.999734	−	0.0230804i	$-0.00734736\pi$
$558$		0			0
$559$			14300.9i			0.0457657i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			35055.3i			0.110595i	0.998470	+	0.0552977i	$0.0176108\pi$
$563$			35055.3i			0.110595i	−0.998470	+	0.0552977i	$0.982389\pi$
$564$		0			0
$565$	−157368.	+	90856.2i	−0.492968	+	0.284615i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			510214.i			1.57590i	0.615742	+	0.787948i	$0.288856\pi$
$569$			510214.i			1.57590i	−0.615742	+	0.787948i	$0.711144\pi$
$570$		0			0
$571$	−191075.			−0.586047			−0.293023	−	0.956105i	$-0.594661\pi$
$571$	−191075.			−0.586047			−0.293023	+	0.956105i	$0.594661\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−196533.	−	340404.i	−0.594428	−	1.02958i
$576$		0			0
$577$	−397878.			−1.19508			−0.597542	−	0.801838i	$-0.703856\pi$
$577$	−397878.			−1.19508			−0.597542	+	0.801838i	$0.703856\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−147142.			−0.435897
$582$		0			0
$583$	−43397.0	−	25055.3i	−0.127680	−	0.0737161i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	294687.	+	510414.i	0.855235	+	1.48131i	0.876427	+	0.481535i	$0.159921\pi$
$587$	294687.	+	510414.i	0.855235	+	1.48131i	−0.0211920	+	0.999775i	$0.506746\pi$
$588$		0			0
$589$	31627.3	+	70805.2i	0.0911658	+	0.204096i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	153979.	−	266700.i	0.437878	−	0.758426i	−0.559648	−	0.828730i	$-0.689064\pi$
$593$	153979.	−	266700.i	0.437878	−	0.758426i	0.997526	+	0.0703041i	$0.0223970\pi$
$594$		0			0
$595$	−556393.	+	963701.i	−1.57162	+	2.72213i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−529620.	−	305776.i	−1.47608	−	0.852217i	−0.476447	−	0.879203i	$-0.658076\pi$
$599$	−529620.	−	305776.i	−1.47608	−	0.852217i	−0.999636	+	0.0269863i	$0.991409\pi$
$600$		0			0
$601$		−	374521.i		−	1.03688i	−0.855115	−	0.518439i	$-0.826513\pi$
$601$		−	374521.i		−	1.03688i	0.855115	−	0.518439i	$-0.173487\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	290126.	+	502513.i	0.792640	+	1.37289i
$606$		0			0
$607$		−	66013.3i		−	0.179165i	−0.995979	−	0.0895827i	$-0.971447\pi$
$607$		−	66013.3i		−	0.179165i	0.995979	−	0.0895827i	$-0.0285533\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−18785.2	+	10845.7i	−0.0503193	+	0.0290518i
$612$		0			0
$613$	18704.7	+	32397.6i	0.0497772	+	0.0862167i	0.889840	−	0.456272i	$-0.150816\pi$
$613$	18704.7	+	32397.6i	0.0497772	+	0.0862167i	−0.840063	+	0.542489i	$0.817482\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−56603.6	+	98040.4i	−0.148687	+	0.257534i	−0.930743	−	0.365675i	$-0.880838\pi$
$617$	−56603.6	+	98040.4i	−0.148687	+	0.257534i	0.782055	+	0.623209i	$0.214171\pi$
$618$		0			0
$619$	313267.			0.817586			0.408793	−	0.912627i	$-0.365950\pi$
$619$	313267.			0.817586			0.408793	+	0.912627i	$0.365950\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	319541.	+	184487.i	0.823286	+	0.475324i
$624$		0			0
$625$	32392.2	+	56105.0i	0.0829241	+	0.143629i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−554475.	+	320126.i	−1.40146	+	0.809133i
$630$		0			0
$631$	−246290.	+	426586.i	−0.618568	+	1.07139i	0.371180	+	0.928561i	$0.378953\pi$
$631$	−246290.	+	426586.i	−0.618568	+	1.07139i	−0.989747	+	0.142830i	$0.954380\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		−	777791.i		−	1.92893i
$636$		0			0
$637$	−2411.54	−	1392.30i	−0.00594314	−	0.00343127i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	168128.	−	97068.9i	0.409190	−	0.236246i	−0.281252	−	0.959634i	$-0.590750\pi$
$641$	168128.	−	97068.9i	0.409190	−	0.236246i	0.690441	+	0.723388i	$0.257416\pi$
$642$		0			0
$643$	−43796.5	−	75857.7i	−0.105930	−	0.183475i	0.808188	−	0.588925i	$-0.200448\pi$
$643$	−43796.5	−	75857.7i	−0.105930	−	0.183475i	−0.914118	+	0.405449i	$0.867115\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	636027.			1.51938			0.759690	−	0.650285i	$-0.225350\pi$
$647$	636027.			1.51938			0.759690	+	0.650285i	$0.225350\pi$
$648$		0			0
$649$	−19201.3	+	11085.9i	−0.0455869	+	0.0263196i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−46609.6			−0.109307			−0.0546536	−	0.998505i	$-0.517405\pi$
$653$	−46609.6			−0.109307			−0.0546536	+	0.998505i	$0.517405\pi$
$654$		0			0
$655$	366620.	−	635004.i	0.854542	−	1.48011i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	577704.	+	333537.i	1.33025	+	0.768022i	0.985338	−	0.170612i	$-0.0545744\pi$
$659$	577704.	+	333537.i	1.33025	+	0.768022i	0.344915	+	0.938634i	$0.387908\pi$
$660$		0			0
$661$	387846.	+	223923.i	0.887681	+	0.512503i	0.873183	−	0.487392i	$-0.162052\pi$
$661$	387846.	+	223923.i	0.887681	+	0.512503i	0.0144975	+	0.999895i	$0.495385\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−621692.	−	450536.i	−1.40583	−	1.01879i
$666$		0			0
$667$	479906.	−	277074.i	1.07871	−	0.622793i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	13259.5	−	22966.1i	0.0294497	−	0.0510084i
$672$		0			0
$673$		−	146080.i		−	0.322522i	−0.986912	−	0.161261i	$-0.948444\pi$
$673$		−	146080.i		−	0.322522i	0.986912	−	0.161261i	$-0.0515561\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			383372.i			0.836456i	0.908342	+	0.418228i	$0.137349\pi$
$677$			383372.i			0.836456i	−0.908342	+	0.418228i	$0.862651\pi$
$678$		0			0
$679$	561367.	−	324105.i	1.21761	−	0.702986i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	828560.i		−	1.77616i	−0.459687	−	0.888081i	$-0.652038\pi$
$683$		−	828560.i		−	1.77616i	0.459687	−	0.888081i	$-0.347962\pi$
$684$		0			0
$685$	759434.			1.61849
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17321.7	−	30002.1i	−0.0364882	−	0.0631995i
$690$		0			0
$691$	−734197.			−1.53765			−0.768824	−	0.639461i	$-0.779158\pi$
$691$	−734197.			−1.53765			−0.768824	+	0.639461i	$0.779158\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−600322.			−1.24284
$696$		0			0
$697$	348664.	+	201301.i	0.717699	+	0.414363i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	86328.7	+	149526.i	0.175679	+	0.304284i	0.940396	−	0.340082i	$-0.110455\pi$
$701$	86328.7	+	149526.i	0.175679	+	0.304284i	−0.764717	+	0.644366i	$0.777121\pi$
$702$		0			0
$703$	−180164.	−	403340.i	−0.364551	−	0.816132i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−251088.	+	434896.i	−0.502327	+	0.870056i
$708$		0			0
$709$	81982.8	−	141998.i	0.163091	−	0.282482i	−0.772885	−	0.634547i	$-0.781187\pi$
$709$	81982.8	−	141998.i	0.163091	−	0.282482i	0.935976	+	0.352064i	$0.114520\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	75912.1	+	43827.9i	0.149325	+	0.0862127i
$714$		0			0
$715$		−	2237.45i		−	0.00437665i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	309781.	+	536556.i	0.599234	+	1.03790i	0.992934	+	0.118665i	$0.0378616\pi$
$719$	309781.	+	536556.i	0.599234	+	1.03790i	−0.393700	+	0.919239i	$0.628805\pi$
$720$		0			0
$721$		−	834118.i		−	1.60456i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.13288e6	−	654069.i	2.15530	−	1.24436i
$726$		0			0
$727$	−95900.8	−	166105.i	−0.181449	−	0.314278i	0.760925	−	0.648839i	$-0.224745\pi$
$727$	−95900.8	−	166105.i	−0.181449	−	0.314278i	−0.942374	+	0.334561i	$0.891412\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	600516.	−	1.04012e6i	1.12380	−	1.94648i
$732$		0			0
$733$	589533.			1.09724			0.548618	−	0.836073i	$-0.315154\pi$
$733$	589533.			1.09724			0.548618	+	0.836073i	$0.315154\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13285.2	−	7670.19i	−0.0244586	−	0.0141212i
$738$		0			0
$739$	415929.	+	720409.i	0.761605	+	1.31914i	0.942023	+	0.335549i	$0.108922\pi$
$739$	415929.	+	720409.i	0.761605	+	1.31914i	−0.180418	+	0.983590i	$0.557745\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−79675.6	+	46000.7i	−0.144327	+	0.0833273i	−0.570425	−	0.821350i	$-0.693221\pi$
$743$	−79675.6	+	46000.7i	−0.144327	+	0.0833273i	0.426098	+	0.904677i	$0.359888\pi$
$744$		0			0
$745$	251783.	−	436101.i	0.453643	−	0.785733i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			56785.4i			0.101221i
$750$		0			0
$751$	−807256.	−	466069.i	−1.43130	−	0.826362i	−0.434082	−	0.900874i	$-0.642927\pi$
$751$	−807256.	−	466069.i	−1.43130	−	0.826362i	−0.997220	+	0.0745111i	$0.976260\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	487316.	−	281352.i	0.854904	−	0.493579i
$756$		0			0
$757$	286555.	+	496329.i	0.500054	+	0.866119i	1.00000		6.22515e-5i	$1.98153e-5\pi$
$757$	286555.	+	496329.i	0.500054	+	0.866119i	−0.499946	+	0.866057i	$0.666647\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−250379.			−0.432342			−0.216171	−	0.976355i	$-0.569357\pi$
$761$	−250379.			−0.432342			−0.216171	+	0.976355i	$0.569357\pi$
$762$		0			0
$763$	−144233.	+	83272.8i	−0.247751	+	0.143039i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15328.2			−0.0260556
$768$		0			0
$769$	−330979.	+	573272.i	−0.559690	+	0.969411i	0.437832	+	0.899057i	$0.355746\pi$
$769$	−330979.	+	573272.i	−0.559690	+	0.969411i	−0.997522	+	0.0703546i	$0.977587\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	519862.	+	300143.i	0.870020	+	0.502306i	0.867355	−	0.497690i	$-0.165818\pi$
$773$	519862.	+	300143.i	0.870020	+	0.502306i	0.00266520	+	0.999996i	$0.499152\pi$
$774$		0			0
$775$	179201.	+	103461.i	0.298357	+	0.172256i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−163003.	+	224927.i	−0.268609	+	0.370652i
$780$		0			0
$781$	−26937.8	+	15552.5i	−0.0441632	+	0.0254976i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	249023.	−	431320.i	0.404110	−	0.699940i
$786$		0			0
$787$		−	51876.0i		−	0.0837563i	−0.999123	−	0.0418781i	$-0.986666\pi$
$787$		−	51876.0i		−	0.0837563i	0.999123	−	0.0418781i	$-0.0133341\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			243327.i			0.388899i
$792$		0			0
$793$	15877.4	−	9166.81i	0.0252483	−	0.0145771i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	532921.i		−	0.838969i	−0.907762	−	0.419485i	$-0.862211\pi$
$797$		−	532921.i		−	0.838969i	0.907762	−	0.419485i	$-0.137789\pi$
$798$		0			0
$799$	1.82170e6			2.85354
$800$		0			0
$801$		0			0
$802$		0			0
$803$	37146.6	+	64339.8i	0.0576087	+	0.0997812i
$804$		0			0
$805$	−867855.			−1.33923
$806$		0			0
$807$		0			0
$808$		0			0
$809$	253863.			0.387884			0.193942	−	0.981013i	$-0.437873\pi$
$809$	253863.			0.387884			0.193942	+	0.981013i	$0.437873\pi$
$810$		0			0
$811$	45687.4	+	26377.7i	0.0694632	+	0.0401046i	0.534329	−	0.845276i	$-0.320564\pi$
$811$	45687.4	+	26377.7i	0.0694632	+	0.0401046i	−0.464866	+	0.885381i	$0.653898\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−591481.	−	1.02448e6i	−0.890483	−	1.54236i
$816$		0			0
$817$	670994.	+	486264.i	1.00525	+	0.728498i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	432787.	−	749609.i	0.642078	−	1.11211i	−0.342890	−	0.939376i	$-0.611406\pi$
$821$	432787.	−	749609.i	0.642078	−	1.11211i	0.984968	−	0.172737i	$-0.0552609\pi$
$822$		0			0
$823$	564220.	−	977258.i	0.833008	−	1.44281i	−0.0626344	−	0.998037i	$-0.519950\pi$
$823$	564220.	−	977258.i	0.833008	−	1.44281i	0.895642	−	0.444775i	$-0.146716\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	878302.	+	507088.i	1.28420	+	0.741434i	0.977614	−	0.210409i	$-0.0674795\pi$
$827$	878302.	+	507088.i	1.28420	+	0.741434i	0.306587	+	0.951843i	$0.400813\pi$
$828$		0			0
$829$			561580.i			0.817152i	0.912724	+	0.408576i	$0.133975\pi$
$829$			561580.i			0.817152i	−0.912724	+	0.408576i	$0.866025\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	116930.	+	202528.i	0.168514	+	0.291874i
$834$		0			0
$835$		−	960998.i		−	1.37832i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	647385.	−	373768.i	0.919685	−	0.530980i	0.0361502	−	0.999346i	$-0.488491\pi$
$839$	647385.	−	373768.i	0.919685	−	0.530980i	0.883534	+	0.468366i	$0.155157\pi$
$840$		0			0
$841$	568472.	+	984622.i	0.803742	+	1.39212i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−568348.	+	984408.i	−0.795978	+	1.37867i
$846$		0			0
$847$	777002.			1.08307
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−432432.	−	249664.i	−0.597115	−	0.344745i
$852$		0			0
$853$	−190927.	−	330696.i	−0.262404	−	0.454496i	0.704477	−	0.709727i	$-0.251182\pi$
$853$	−190927.	−	330696.i	−0.262404	−	0.454496i	−0.966880	+	0.255231i	$0.917849\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.10306e6	+	636854.i	−1.50189	+	0.867119i	−0.501896	+	0.864928i	$0.667364\pi$
$857$	−1.10306e6	+	636854.i	−1.50189	+	0.867119i	−0.999998	+	0.00219068i	$0.999303\pi$
$858$		0			0
$859$	235569.	−	408017.i	0.319250	−	0.552957i	−0.661082	−	0.750314i	$-0.729902\pi$
$859$	235569.	−	408017.i	0.319250	−	0.552957i	0.980332	+	0.197357i	$0.0632357\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			25220.7i			0.0338638i	0.999857	+	0.0169319i	$0.00538985\pi$
$863$			25220.7i			0.0338638i	−0.999857	+	0.0169319i	$0.994610\pi$
$864$		0			0
$865$	−1.05625e6	−	609827.i	−1.41168	−	0.815031i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−66296.8	+	38276.5i	−0.0877916	+	0.0506865i
$870$		0			0
$871$	−5302.71	−	9184.57i	−0.00698975	−	0.0121066i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−719428.			−0.939662
$876$		0			0
$877$	883407.	−	510035.i	1.14858	−	0.663134i	0.200040	−	0.979788i	$-0.435893\pi$
$877$	883407.	−	510035.i	1.14858	−	0.663134i	0.948541	+	0.316654i	$0.102559\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.23116e6			1.58621			0.793107	−	0.609082i	$-0.208462\pi$
$881$	1.23116e6			1.58621			0.793107	+	0.609082i	$0.208462\pi$
$882$		0			0
$883$	−225170.	+	390006.i	−0.288794	+	0.500207i	−0.973522	−	0.228592i	$-0.926588\pi$
$883$	−225170.	+	390006.i	−0.288794	+	0.500207i	0.684728	+	0.728799i	$0.259921\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−82480.8	−	47620.3i	−0.104835	−	0.0605264i	0.446666	−	0.894701i	$-0.352611\pi$
$887$	−82480.8	−	47620.3i	−0.104835	−	0.0605264i	−0.551501	+	0.834174i	$0.685945\pi$
$888$		0			0
$889$	−901985.	−	520761.i	−1.14129	−	0.658924i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−129867.	+	1.25017e6i	−0.162853	+	1.56772i
$894$		0			0
$895$	−1.09141e6	+	630128.i	−1.36252	+	0.786652i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−145861.	+	252639.i	−0.180476	+	0.312594i
$900$		0			0
$901$			2.90946e6i			3.58396i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			134964.i			0.164787i
$906$		0			0
$907$	−780267.	+	450487.i	−0.948481	+	0.547606i	−0.892609	−	0.450832i	$-0.851127\pi$
$907$	−780267.	+	450487.i	−0.948481	+	0.547606i	−0.0558723	+	0.998438i	$0.517794\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			317691.i			0.382797i	0.981512	+	0.191398i	$0.0613022\pi$
$911$			317691.i			0.382797i	−0.981512	+	0.191398i	$0.938698\pi$
$912$		0			0
$913$	−24846.7			−0.0298076
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−490932.	−	850319.i	−0.583825	−	1.01121i
$918$		0			0
$919$	−371224.			−0.439547			−0.219774	−	0.975551i	$-0.570532\pi$
$919$	−371224.			−0.439547			−0.219774	+	0.975551i	$0.570532\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21504.2			−0.0252418
$924$		0			0
$925$	−1.02081e6	−	589366.i	−1.19306	−	0.688813i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	31626.7	+	54779.0i	0.0366456	+	0.0634721i	0.883767	−	0.467928i	$-0.154999\pi$
$929$	31626.7	+	54779.0i	0.0366456	+	0.0634721i	−0.847121	+	0.531400i	$0.821666\pi$
$930$		0			0
$931$	−147324.	+	65807.1i	−0.169971	+	0.0759230i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−93953.8	+	162733.i	−0.107471	+	0.186145i
$936$		0			0
$937$	−578958.	+	1.00279e6i	−0.659429	+	1.14216i	0.321335	+	0.946966i	$0.395869\pi$
$937$	−578958.	+	1.00279e6i	−0.659429	+	1.14216i	−0.980764	+	0.195199i	$0.937465\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	295283.	+	170482.i	0.333472	+	0.192530i	0.657381	−	0.753558i	$-0.271664\pi$
$941$	295283.	+	170482.i	0.333472	+	0.192530i	−0.323910	+	0.946088i	$0.604997\pi$
$942$		0			0
$943$			313987.i			0.353093i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	236902.	+	410326.i	0.264161	+	0.457541i	0.967344	−	0.253469i	$-0.0815716\pi$
$947$	236902.	+	410326.i	0.264161	+	0.457541i	−0.703182	+	0.711010i	$0.748238\pi$
$948$		0			0
$949$			51361.9i			0.0570307i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−305054.	+	176123.i	−0.335885	+	0.193923i	−0.658451	−	0.752624i	$-0.728788\pi$
$953$	−305054.	+	176123.i	−0.335885	+	0.193923i	0.322566	+	0.946547i	$0.395455\pi$
$954$		0			0
$955$	−142288.	−	246449.i	−0.156013	−	0.270222i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	508470.	−	880696.i	0.552877	−	0.957611i
$960$		0			0
$961$	877376.			0.950034
$962$		0			0
$963$		0			0
$964$		0			0
$965$	554833.	+	320333.i	0.595810	+	0.343991i
$966$		0			0
$967$	−342618.	−	593431.i	−0.366401	−	0.634626i	0.622599	−	0.782541i	$-0.286077\pi$
$967$	−342618.	−	593431.i	−0.366401	−	0.634626i	−0.989000	+	0.147916i	$0.952744\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	114126.	−	65890.5i	0.121045	−	0.0698851i	−0.438255	−	0.898851i	$-0.644403\pi$
$971$	114126.	−	65890.5i	0.121045	−	0.0698851i	0.559300	+	0.828965i	$0.311070\pi$
$972$		0			0
$973$	−401939.	+	696179.i	−0.424555	+	0.735352i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			853791.i			0.894463i	0.894418	+	0.447231i	$0.147590\pi$
$977$			853791.i			0.894463i	−0.894418	+	0.447231i	$0.852410\pi$
$978$		0			0
$979$	53958.5	+	31152.9i	0.0562981	+	0.0325038i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	63978.8	−	36938.2i	0.0662108	−	0.0382268i	−0.466529	−	0.884506i	$-0.654496\pi$
$983$	63978.8	−	36938.2i	0.0662108	−	0.0382268i	0.532740	+	0.846279i	$0.321162\pi$
$984$		0			0
$985$	−528967.	−	916198.i	−0.545201	−	0.944315i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	936677.			0.957629
$990$		0			0
$991$	−1.57948e6	+	911914.i	−1.60830	+	0.928553i	−0.618550	+	0.785745i	$0.712280\pi$
$991$	−1.57948e6	+	911914.i	−1.60830	+	0.928553i	−0.989750	+	0.142808i	$0.954387\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	187869.			0.189762
$996$		0			0
$997$	639728.	−	1.10804e6i	0.643583	−	1.11472i	−0.341043	−	0.940048i	$-0.610780\pi$
$997$	639728.	−	1.10804e6i	0.643583	−	1.11472i	0.984627	−	0.174672i	$-0.0558864\pi$
$998$		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.145.1		12
3.2	odd	2		76.5.h.a.69.1	yes	12
12.11	even	2		304.5.r.b.145.6		12
19.8	odd	6	inner	684.5.y.c.217.1		12
57.8	even	6		76.5.h.a.65.1	✓	12
228.179	odd	6		304.5.r.b.65.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.1	✓	12	57.8	even	6
76.5.h.a.69.1	yes	12	3.2	odd	2
304.5.r.b.65.6		12	228.179	odd	6
304.5.r.b.145.6		12	12.11	even	2
684.5.y.c.145.1		12	1.1	even	1	trivial
684.5.y.c.217.1		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)

\(f(q)\)	\(=\)	\(q+(-19.9265 - 34.5138i) q^{5} -53.3663 q^{7} +O(q^{10})\)	\(q+(-19.9265 - 34.5138i) q^{5} -53.3663 q^{7} -9.01156 q^{11} +(-5.39539 - 3.11503i) q^{13} +(261.609 + 453.120i) q^{17} +(-329.612 + 147.231i) q^{19} +(-204.027 + 353.386i) q^{23} +(-481.633 + 834.213i) q^{25} +(-1176.08 - 679.011i) q^{29} -214.814i q^{31} +(1063.41 + 1841.87i) q^{35} +1223.68i q^{37} +(666.384 - 384.737i) q^{41} +(-1147.74 - 1987.94i) q^{43} +(1740.86 - 3015.26i) q^{47} +446.963 q^{49} +(4815.71 + 2780.35i) q^{53} +(179.569 + 311.023i) q^{55} +(2130.74 - 1230.18i) q^{59} +(-1471.38 + 2548.51i) q^{61} +248.287i q^{65} +(1474.24 + 851.150i) q^{67} +(2989.25 - 1725.84i) q^{71} +(-4122.11 - 7139.70i) q^{73} +480.914 q^{77} +(7356.86 - 4247.48i) q^{79} +2757.20 q^{83} +(10425.9 - 18058.2i) q^{85} +(-5987.69 - 3457.00i) q^{89} +(287.932 + 166.238i) q^{91} +(11649.5 + 8442.33i) q^{95} +(-10519.1 + 6073.22i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{5} - 52 q^{7}+O(q^{10}) \) 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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