LMFDB - Embedded newform 684.5.y.d.145.3

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:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2826 x^{12} + 21668 x^{11} + 6144398 x^{10} + 32400228 x^{9} + 4476099452 x^{8} + \cdots + 21\!\cdots\!16 $ x^14 - 2x^13 + 2826x^12 + 21668x^11 + 6144398x^10 + 32400228x^9 + 4476099452x^8 + 1249545344x^7 + 2308151528484x^6 - 2140142598776x^5 + 625358881541536x^4 - 2569874136887808x^3 + 115090576468624800x^2 - 159892348486261824*x + 219826226298839616
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$-10.7603 - 18.6373i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.d.217.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.7603 - 20.3694i) q^{5} -65.4503 q^{7} +O(q^{10})$	$q+(-11.7603 - 20.3694i) q^{5} -65.4503 q^{7} -235.758 q^{11} +(-173.596 - 100.226i) q^{13} +(-251.933 - 436.360i) q^{17} +(-97.9251 + 347.465i) q^{19} +(253.553 - 439.166i) q^{23} +(35.8930 - 62.1685i) q^{25} +(-273.846 - 158.105i) q^{29} +1058.76i q^{31} +(769.712 + 1333.18i) q^{35} +700.999i q^{37} +(-826.431 + 477.140i) q^{41} +(209.869 + 363.503i) q^{43} +(1204.42 - 2086.12i) q^{47} +1882.75 q^{49} +(-3715.82 - 2145.33i) q^{53} +(2772.58 + 4802.25i) q^{55} +(1413.61 - 816.147i) q^{59} +(-939.800 + 1627.78i) q^{61} +4714.71i q^{65} +(-391.195 - 225.857i) q^{67} +(1069.19 - 617.298i) q^{71} +(-3193.55 - 5531.39i) q^{73} +15430.5 q^{77} +(9445.55 - 5453.39i) q^{79} +635.960 q^{83} +(-5925.58 + 10263.4i) q^{85} +(-6254.44 - 3611.00i) q^{89} +(11361.9 + 6559.80i) q^{91} +(8229.25 - 2091.60i) q^{95} +(4793.05 - 2767.27i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) $ 14 * q - 12 * q^5 - 110 * q^7	$ 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) $ 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * 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
$5$	−11.7603	−	20.3694i	−0.470410	−	0.814774i	0.529017	−	0.848611i	$-0.322561\pi$
$5$	−11.7603	−	20.3694i	−0.470410	−	0.814774i	−0.999427	+	0.0338370i	$0.989227\pi$
$6$		0			0
$7$	−65.4503			−1.33572			−0.667861	−	0.744286i	$-0.732790\pi$
$7$	−65.4503			−1.33572			−0.667861	+	0.744286i	$0.732790\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−235.758			−1.94842			−0.974209	−	0.225649i	$-0.927550\pi$
$11$	−235.758			−1.94842			−0.974209	+	0.225649i	$0.927550\pi$
$12$		0			0
$13$	−173.596	−	100.226i	−1.02719	−	0.593051i	−0.111015	−	0.993819i	$-0.535410\pi$
$13$	−173.596	−	100.226i	−1.02719	−	0.593051i	−0.916180	+	0.400768i	$0.868743\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−251.933	−	436.360i	−0.871739	−	1.50990i	−0.860196	−	0.509964i	$-0.829659\pi$
$17$	−251.933	−	436.360i	−0.871739	−	1.50990i	−0.0115435	−	0.999933i	$-0.503674\pi$
$18$		0			0
$19$	−97.9251	+	347.465i	−0.271261	+	0.962506i
$19$	−97.9251	+	347.465i	−0.271261	+	0.962506i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	253.553	−	439.166i	0.479306	−	0.830182i	−0.520413	−	0.853915i	$-0.674222\pi$
$23$	253.553	−	439.166i	0.479306	−	0.830182i	0.999718	+	0.0237331i	$0.00755518\pi$
$24$		0			0
$25$	35.8930	−	62.1685i	0.0574288	−	0.0994697i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−273.846	−	158.105i	−0.325620	−	0.187997i	0.328275	−	0.944582i	$-0.393533\pi$
$29$	−273.846	−	158.105i	−0.325620	−	0.187997i	−0.653895	+	0.756586i	$0.726866\pi$
$30$		0			0
$31$			1058.76i			1.10172i	0.834597	+	0.550861i	$0.185701\pi$
$31$			1058.76i			1.10172i	−0.834597	+	0.550861i	$0.814299\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	769.712	+	1333.18i	0.628337	+	1.08831i
$36$		0			0
$37$			700.999i			0.512052i	0.966670	+	0.256026i	$0.0824133\pi$
$37$			700.999i			0.512052i	−0.966670	+	0.256026i	$0.917587\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−826.431	+	477.140i	−0.491631	+	0.283843i	−0.725251	−	0.688485i	$-0.758276\pi$
$41$	−826.431	+	477.140i	−0.491631	+	0.283843i	0.233620	+	0.972328i	$0.424943\pi$
$42$		0			0
$43$	209.869	+	363.503i	0.113504	+	0.196594i	0.917181	−	0.398472i	$-0.130459\pi$
$43$	209.869	+	363.503i	0.113504	+	0.196594i	−0.803677	+	0.595066i	$0.797126\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1204.42	−	2086.12i	0.545234	−	0.944373i	−0.453358	−	0.891329i	$-0.649774\pi$
$47$	1204.42	−	2086.12i	0.545234	−	0.944373i	0.998592	−	0.0530448i	$-0.0168926\pi$
$48$		0			0
$49$	1882.75			0.784151
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3715.82	−	2145.33i	−1.32283	−	0.763735i	−0.338649	−	0.940913i	$-0.609970\pi$
$53$	−3715.82	−	2145.33i	−1.32283	−	0.763735i	−0.984179	+	0.177178i	$0.943303\pi$
$54$		0			0
$55$	2772.58	+	4802.25i	0.916555	+	1.58752i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1413.61	−	816.147i	0.406093	−	0.234458i	−0.283017	−	0.959115i	$-0.591335\pi$
$59$	1413.61	−	816.147i	0.406093	−	0.234458i	0.689109	+	0.724657i	$0.258002\pi$
$60$		0			0
$61$	−939.800	+	1627.78i	−0.252566	+	0.437458i	−0.964232	−	0.265061i	$-0.914608\pi$
$61$	−939.800	+	1627.78i	−0.252566	+	0.437458i	0.711665	+	0.702519i	$0.247941\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			4714.71i			1.11591i
$66$		0			0
$67$	−391.195	−	225.857i	−0.0871452	−	0.0503133i	0.455794	−	0.890085i	$-0.349355\pi$
$67$	−391.195	−	225.857i	−0.0871452	−	0.0503133i	−0.542939	+	0.839772i	$0.682689\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1069.19	−	617.298i	0.212099	−	0.122455i	−0.390188	−	0.920735i	$-0.627590\pi$
$71$	1069.19	−	617.298i	0.212099	−	0.122455i	0.602287	+	0.798280i	$0.294256\pi$
$72$		0			0
$73$	−3193.55	−	5531.39i	−0.599277	−	1.03798i	−0.992928	−	0.118719i	$-0.962121\pi$
$73$	−3193.55	−	5531.39i	−0.599277	−	1.03798i	0.393651	−	0.919260i	$-0.371212\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15430.5			2.60254
$78$		0			0
$79$	9445.55	−	5453.39i	1.51347	−	0.873801i	0.513592	−	0.858035i	$-0.328315\pi$
$79$	9445.55	−	5453.39i	1.51347	−	0.873801i	0.999876	−	0.0157663i	$-0.00501879\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	635.960			0.0923153			0.0461577	−	0.998934i	$-0.485302\pi$
$83$	635.960			0.0923153			0.0461577	+	0.998934i	$0.485302\pi$
$84$		0			0
$85$	−5925.58	+	10263.4i	−0.820150	+	1.42054i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6254.44	−	3611.00i	−0.789602	−	0.455877i	0.0502202	−	0.998738i	$-0.484008\pi$
$89$	−6254.44	−	3611.00i	−0.789602	−	0.455877i	−0.839823	+	0.542861i	$0.817341\pi$
$90$		0			0
$91$	11361.9	+	6559.80i	1.37205	+	0.792151i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8229.25	−	2091.60i	0.911829	−	0.231756i
$96$		0			0
$97$	4793.05	−	2767.27i	0.509412	−	0.294109i	−0.223180	−	0.974777i	$-0.571644\pi$
$97$	4793.05	−	2767.27i	0.509412	−	0.294109i	0.732592	+	0.680668i	$0.238310\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2230.19	+	3862.80i	−0.218625	+	0.378669i	−0.954388	−	0.298570i	$-0.903490\pi$
$101$	−2230.19	+	3862.80i	−0.218625	+	0.378669i	0.735763	+	0.677239i	$0.236824\pi$
$102$		0			0
$103$		−	4247.13i		−	0.400333i	−0.979762	−	0.200166i	$-0.935852\pi$
$103$		−	4247.13i		−	0.400333i	0.979762	−	0.200166i	$-0.0641483\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	77.6703i		−	0.00678402i	−0.999994	−	0.00339201i	$-0.998920\pi$
$107$		−	77.6703i		−	0.00678402i	0.999994	−	0.00339201i	$-0.00107971\pi$
$108$		0			0
$109$	−8744.18	+	5048.45i	−0.735980	+	0.424918i	−0.820606	−	0.571495i	$-0.806364\pi$
$109$	−8744.18	+	5048.45i	−0.735980	+	0.424918i	0.0846259	+	0.996413i	$0.473030\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			14654.4i			1.14766i	0.818976	+	0.573828i	$0.194542\pi$
$113$			14654.4i			1.14766i	−0.818976	+	0.573828i	$0.805458\pi$
$114$		0			0
$115$	−11927.4			−0.901881
$116$		0			0
$117$		0			0
$118$		0			0
$119$	16489.1	+	28559.9i	1.16440	+	2.01680i
$120$		0			0
$121$	40941.1			2.79633
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−16388.8			−1.04888
$126$		0			0
$127$	−25422.2	−	14677.5i	−1.57618	−	0.910006i	−0.995386	−	0.0959538i	$-0.969410\pi$
$127$	−25422.2	−	14677.5i	−1.57618	−	0.910006i	−0.580791	−	0.814052i	$-0.697257\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1039.31	+	1800.14i	0.0605624	+	0.104897i	0.894717	−	0.446634i	$-0.147377\pi$
$131$	1039.31	+	1800.14i	0.0605624	+	0.104897i	−0.834155	+	0.551531i	$0.814044\pi$
$132$		0			0
$133$	6409.23	−	22741.7i	0.362329	−	1.28564i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1961.29	+	3397.05i	−0.104496	+	0.180993i	−0.913532	−	0.406766i	$-0.866656\pi$
$137$	−1961.29	+	3397.05i	−0.104496	+	0.180993i	0.809036	+	0.587759i	$0.199990\pi$
$138$		0			0
$139$	−12883.2	+	22314.3i	−0.666795	+	1.15492i	0.312000	+	0.950082i	$0.399001\pi$
$139$	−12883.2	+	22314.3i	−0.666795	+	1.15492i	−0.978795	+	0.204841i	$0.934332\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	40926.7	+	23629.0i	2.00140	+	1.15551i
$144$		0			0
$145$			7437.43i			0.353742i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9338.95	+	16175.5i	0.420654	+	0.728595i	0.996004	−	0.0893132i	$-0.0284672\pi$
$149$	9338.95	+	16175.5i	0.420654	+	0.728595i	−0.575349	+	0.817908i	$0.695134\pi$
$150$		0			0
$151$		−	26660.1i		−	1.16925i	−0.811303	−	0.584627i	$-0.801241\pi$
$151$		−	26660.1i		−	1.16925i	0.811303	−	0.584627i	$-0.198759\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	21566.2	−	12451.2i	0.897655	−	0.518261i
$156$		0			0
$157$	−14041.1	−	24320.0i	−0.569644	−	0.986652i	−0.996601	−	0.0823800i	$-0.973748\pi$
$157$	−14041.1	−	24320.0i	−0.569644	−	0.986652i	0.426957	−	0.904272i	$-0.359585\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−16595.1	+	28743.6i	−0.640219	+	1.10889i
$162$		0			0
$163$	−52021.7			−1.95799			−0.978993	−	0.203893i	$-0.934640\pi$
$163$	−52021.7			−1.95799			−0.978993	+	0.203893i	$0.934640\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10934.1	+	6312.79i	0.392057	+	0.226354i	0.683051	−	0.730371i	$-0.260653\pi$
$167$	10934.1	+	6312.79i	0.392057	+	0.226354i	−0.290994	+	0.956725i	$0.593986\pi$
$168$		0			0
$169$	5809.86	+	10063.0i	0.203419	+	0.352332i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	44192.3	−	25514.5i	1.47657	−	0.852500i	0.476922	−	0.878945i	$-0.341752\pi$
$173$	44192.3	−	25514.5i	1.47657	−	0.852500i	0.999650	+	0.0264457i	$0.00841892\pi$
$174$		0			0
$175$	−2349.21	+	4068.95i	−0.0767089	+	0.132864i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			57297.5i			1.78826i	0.447811	+	0.894128i	$0.352204\pi$
$179$			57297.5i			1.78826i	−0.447811	+	0.894128i	$0.647796\pi$
$180$		0			0
$181$	55108.6	+	31817.0i	1.68214	+	0.971185i	0.960235	+	0.279194i	$0.0900673\pi$
$181$	55108.6	+	31817.0i	1.68214	+	0.971185i	0.721906	+	0.691991i	$0.243266\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14278.9	−	8243.93i	0.417207	−	0.240874i
$186$		0			0
$187$	59395.3	+	102876.i	1.69851	+	2.94191i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10670.2			−0.292487			−0.146244	−	0.989249i	$-0.546718\pi$
$191$	−10670.2			−0.292487			−0.146244	+	0.989249i	$0.546718\pi$
$192$		0			0
$193$	15309.9	−	8839.19i	0.411016	−	0.237300i	−0.280210	−	0.959939i	$-0.590404\pi$
$193$	15309.9	−	8839.19i	0.411016	−	0.237300i	0.691226	+	0.722639i	$0.257071\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−30688.6			−0.790759			−0.395379	−	0.918518i	$-0.629387\pi$
$197$	−30688.6			−0.790759			−0.395379	+	0.918518i	$0.629387\pi$
$198$		0			0
$199$	−12473.5	+	21604.7i	−0.314978	+	0.545558i	−0.979433	−	0.201770i	$-0.935331\pi$
$199$	−12473.5	+	21604.7i	−0.314978	+	0.545558i	0.664455	+	0.747329i	$0.268664\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	17923.3	+	10348.0i	0.434937	+	0.251111i
$204$		0			0
$205$	19438.1	+	11222.6i	0.462536	+	0.267045i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	23086.7	−	81917.7i	0.528529	−	1.87536i
$210$		0			0
$211$	52610.1	−	30374.5i	1.18169	−	0.682250i	0.225287	−	0.974292i	$-0.427668\pi$
$211$	52610.1	−	30374.5i	1.18169	−	0.682250i	0.956406	+	0.292042i	$0.0943347\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4936.22	−	8549.78i	0.106787	−	0.184960i
$216$		0			0
$217$		−	69295.9i		−	1.47159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			101000.i			2.06794i
$222$		0			0
$223$	−28897.5	+	16684.0i	−0.581100	+	0.335498i	−0.761570	−	0.648082i	$-0.775571\pi$
$223$	−28897.5	+	16684.0i	−0.581100	+	0.335498i	0.180471	+	0.983580i	$0.442238\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	35889.8i		−	0.696497i	−0.937402	−	0.348249i	$-0.886776\pi$
$227$		−	35889.8i		−	0.696497i	0.937402	−	0.348249i	$-0.113224\pi$
$228$		0			0
$229$	55230.7			1.05320			0.526598	−	0.850114i	$-0.323467\pi$
$229$	55230.7			1.05320			0.526598	+	0.850114i	$0.323467\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14889.5	−	25789.4i	−0.274263	−	0.475038i	0.695686	−	0.718346i	$-0.255101\pi$
$233$	−14889.5	−	25789.4i	−0.274263	−	0.475038i	−0.969949	+	0.243308i	$0.921767\pi$
$234$		0			0
$235$	−56657.2			−1.02593
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9102.99			0.159363			0.0796817	−	0.996820i	$-0.474610\pi$
$239$	9102.99			0.159363			0.0796817	+	0.996820i	$0.474610\pi$
$240$		0			0
$241$	−11714.1	−	6763.17i	−0.201686	−	0.116444i	0.395755	−	0.918356i	$-0.370483\pi$
$241$	−11714.1	−	6763.17i	−0.201686	−	0.116444i	−0.597442	+	0.801912i	$0.703816\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−22141.6	−	38350.3i	−0.368873	−	0.638906i
$246$		0			0
$247$	51824.3	−	50503.8i	0.849453	−	0.827809i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	39277.4	−	68030.5i	0.623441	−	1.07983i	−0.365399	−	0.930851i	$-0.619067\pi$
$251$	39277.4	−	68030.5i	0.623441	−	1.07983i	0.988840	−	0.148981i	$-0.0475992\pi$
$252$		0			0
$253$	−59777.2	+	103537.i	−0.933888	+	1.61754i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−93485.1	−	53973.7i	−1.41539	−	0.817176i	−0.419501	−	0.907755i	$-0.637795\pi$
$257$	−93485.1	−	53973.7i	−1.41539	−	0.817176i	−0.995889	+	0.0905788i	$0.971128\pi$
$258$		0			0
$259$		−	45880.6i		−	0.683959i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−33136.9	−	57394.8i	−0.479072	−	0.829777i	0.520640	−	0.853776i	$-0.325693\pi$
$263$	−33136.9	−	57394.8i	−0.479072	−	0.829777i	−0.999712	+	0.0239994i	$0.992360\pi$
$264$		0			0
$265$			100919.i			1.43707i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−21975.6	+	12687.6i	−0.303694	+	0.175338i	−0.644101	−	0.764940i	$-0.722768\pi$
$269$	−21975.6	+	12687.6i	−0.303694	+	0.175338i	0.340407	+	0.940278i	$0.389435\pi$
$270$		0			0
$271$	−6201.76	−	10741.8i	−0.0844455	−	0.146264i	0.820709	−	0.571346i	$-0.193579\pi$
$271$	−6201.76	−	10741.8i	−0.0844455	−	0.146264i	−0.905155	+	0.425082i	$0.860245\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8462.08	+	14656.8i	−0.111895	+	0.193808i
$276$		0			0
$277$	63188.2			0.823524			0.411762	−	0.911291i	$-0.364913\pi$
$277$	63188.2			0.823524			0.411762	+	0.911291i	$0.364913\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9125.33	−	5268.51i	−0.115568	−	0.0667230i	0.441102	−	0.897457i	$-0.354588\pi$
$281$	−9125.33	−	5268.51i	−0.115568	−	0.0667230i	−0.556670	+	0.830734i	$0.687921\pi$
$282$		0			0
$283$	−56557.5	−	97960.5i	−0.706183	−	1.22315i	−0.966263	−	0.257558i	$-0.917082\pi$
$283$	−56557.5	−	97960.5i	−0.706183	−	1.22315i	0.260080	−	0.965587i	$-0.416251\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	54090.2	−	31229.0i	0.656682	−	0.379135i
$288$		0			0
$289$	−85179.7	+	147536.i	−1.01986	+	1.76645i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			109752.i			1.27843i	0.769026	+	0.639217i	$0.220742\pi$
$293$			109752.i			1.27843i	−0.769026	+	0.639217i	$0.779258\pi$
$294$		0			0
$295$	−33248.8	−	19196.2i	−0.382060	−	0.220582i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−88031.4	+	50825.0i	−0.984681	+	0.568506i
$300$		0			0
$301$	−13736.0	−	23791.4i	−0.151610	−	0.262595i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	44209.1			0.475239
$306$		0			0
$307$	122622.	−	70795.6i	1.30104	−	0.751155i	0.320457	−	0.947263i	$-0.396164\pi$
$307$	122622.	−	70795.6i	1.30104	−	0.751155i	0.980582	+	0.196108i	$0.0628303\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4681.90			0.0484062			0.0242031	−	0.999707i	$-0.492295\pi$
$311$	4681.90			0.0484062			0.0242031	+	0.999707i	$0.492295\pi$
$312$		0			0
$313$	12801.9	−	22173.6i	0.130673	−	0.226333i	−0.793263	−	0.608879i	$-0.791619\pi$
$313$	12801.9	−	22173.6i	0.130673	−	0.226333i	0.923936	+	0.382546i	$0.124953\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18817.4	+	10864.2i	0.187258	+	0.108113i	0.590698	−	0.806893i	$-0.298852\pi$
$317$	18817.4	+	10864.2i	0.187258	+	0.108113i	−0.403440	+	0.915006i	$0.632186\pi$
$318$		0			0
$319$	64561.6	+	37274.6i	0.634443	+	0.366296i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	176290.	−	44807.1i	1.68975	−	0.429479i
$324$		0			0
$325$	−12461.8	+	7194.80i	−0.117981	+	0.0681165i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−78829.8	+	136537.i	−0.728281	+	1.26142i
$330$		0			0
$331$			96306.8i			0.879024i	0.898237	+	0.439512i	$0.144849\pi$
$331$			96306.8i			0.879024i	−0.898237	+	0.439512i	$0.855151\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			10624.5i			0.0946716i
$336$		0			0
$337$	72022.4	−	41582.1i	0.634173	−	0.366140i	−0.148194	−	0.988958i	$-0.547346\pi$
$337$	72022.4	−	41582.1i	0.634173	−	0.366140i	0.782366	+	0.622819i	$0.214013\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	249611.i		−	2.14662i
$342$		0			0
$343$	33919.9			0.288314
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−114154.	−	197720.i	−0.948048	−	1.64207i	−0.749529	−	0.661971i	$-0.769720\pi$
$347$	−114154.	−	197720.i	−0.948048	−	1.64207i	−0.198519	−	0.980097i	$-0.563613\pi$
$348$		0			0
$349$	−211316.			−1.73493			−0.867465	−	0.497499i	$-0.834252\pi$
$349$	−211316.			−1.73493			−0.867465	+	0.497499i	$0.834252\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−243806.			−1.95657			−0.978284	−	0.207269i	$-0.933542\pi$
$353$	−243806.			−1.95657			−0.978284	+	0.207269i	$0.933542\pi$
$354$		0			0
$355$	−25147.9	−	14519.2i	−0.199547	−	0.115209i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	60221.1	+	104306.i	0.467261	+	0.809320i	0.999300	−	0.0373997i	$-0.0119075\pi$
$359$	60221.1	+	104306.i	0.467261	+	0.809320i	−0.532039	+	0.846720i	$0.678574\pi$
$360$		0			0
$361$	−111142.	−	68051.0i	−0.852835	−	0.522180i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−75113.9	+	130101.i	−0.563812	+	0.976551i
$366$		0			0
$367$	−67916.2	+	117634.i	−0.504245	+	0.873377i	0.495743	+	0.868469i	$0.334896\pi$
$367$	−67916.2	+	117634.i	−0.504245	+	0.873377i	−0.999988	+	0.00490827i	$0.998438\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	243202.	+	140413.i	1.76693	+	1.02014i
$372$		0			0
$373$			90500.5i			0.650479i	0.945632	+	0.325239i	$0.105445\pi$
$373$			90500.5i			0.650479i	−0.945632	+	0.325239i	$0.894555\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	31692.4	+	54892.8i	0.222983	+	0.386218i
$378$		0			0
$379$		−	156567.i		−	1.08999i	−0.838440	−	0.544994i	$-0.816532\pi$
$379$		−	156567.i		−	1.08999i	0.838440	−	0.544994i	$-0.183468\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−65338.3	+	37723.1i	−0.445421	+	0.257164i	−0.705894	−	0.708317i	$-0.749455\pi$
$383$	−65338.3	+	37723.1i	−0.445421	+	0.257164i	0.260474	+	0.965481i	$0.416121\pi$
$384$		0			0
$385$	−181466.	−	314309.i	−1.22426	−	2.12048i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15844.1	−	27442.8i	0.104705	−	0.181355i	−0.808913	−	0.587929i	$-0.799943\pi$
$389$	15844.1	−	27442.8i	0.104705	−	0.181355i	0.913618	+	0.406574i	$0.133277\pi$
$390$		0			0
$391$	−255513.			−1.67132
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−222164.	−	128267.i	−1.42390	−	0.822089i
$396$		0			0
$397$	−16931.4	−	29326.1i	−0.107427	−	0.186069i	0.807300	−	0.590141i	$-0.200928\pi$
$397$	−16931.4	−	29326.1i	−0.107427	−	0.186069i	−0.914727	+	0.404072i	$0.867594\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−159758.	+	92236.5i	−0.993516	+	0.573607i	−0.906323	−	0.422585i	$-0.861123\pi$
$401$	−159758.	+	92236.5i	−0.993516	+	0.573607i	−0.0871925	+	0.996191i	$0.527790\pi$
$402$		0			0
$403$	106114.	−	183796.i	0.653378	−	1.13168i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	165267.i		−	0.997691i
$408$		0			0
$409$	−194740.	−	112433.i	−1.16415	−	0.672121i	−0.211853	−	0.977302i	$-0.567950\pi$
$409$	−194740.	−	112433.i	−1.16415	−	0.672121i	−0.952294	+	0.305181i	$0.901283\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−92521.1	+	53417.1i	−0.542426	+	0.313170i
$414$		0			0
$415$	−7479.05	−	12954.1i	−0.0434261	−	0.0752161i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−51251.6			−0.291930			−0.145965	−	0.989290i	$-0.546629\pi$
$419$	−51251.6			−0.291930			−0.145965	+	0.989290i	$0.546629\pi$
$420$		0			0
$421$	259550.	−	149851.i	1.46439	−	0.845465i	0.465179	−	0.885216i	$-0.345990\pi$
$421$	259550.	−	149851.i	1.46439	−	0.845465i	0.999210	+	0.0397512i	$0.0126565\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−36170.5			−0.200252
$426$		0			0
$427$	61510.2	−	106539.i	0.337358	−	0.584322i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−97465.8	−	56271.9i	−0.524684	−	0.302926i	0.214165	−	0.976797i	$-0.431297\pi$
$431$	−97465.8	−	56271.9i	−0.524684	−	0.302926i	−0.738849	+	0.673871i	$0.764630\pi$
$432$		0			0
$433$	−90585.7	−	52299.7i	−0.483152	−	0.278948i	0.238577	−	0.971124i	$-0.423319\pi$
$433$	−90585.7	−	52299.7i	−0.483152	−	0.278948i	−0.721729	+	0.692176i	$0.756652\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	127766.	+	131106.i	0.669038	+	0.686530i
$438$		0			0
$439$	174691.	−	100858.i	0.906447	−	0.523337i	0.0271607	−	0.999631i	$-0.491353\pi$
$439$	174691.	−	100858.i	0.906447	−	0.523337i	0.879286	+	0.476294i	$0.158020\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−875.560	+	1516.51i	−0.00446147	+	0.00772750i	−0.868248	−	0.496131i	$-0.834753\pi$
$443$	−875.560	+	1516.51i	−0.00446147	+	0.00772750i	0.863786	+	0.503859i	$0.168087\pi$
$444$		0			0
$445$			169865.i			0.857797i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	257162.i		−	1.27560i	−0.770203	−	0.637799i	$-0.779845\pi$
$449$		−	257162.i		−	1.27560i	0.770203	−	0.637799i	$-0.220155\pi$
$450$		0			0
$451$	194838.	−	112490.i	0.957902	−	0.553045i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	308580.i		−	1.49054i
$456$		0			0
$457$	50950.4			0.243958			0.121979	−	0.992533i	$-0.461076\pi$
$457$	50950.4			0.243958			0.121979	+	0.992533i	$0.461076\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−67175.7	−	116352.i	−0.316090	−	0.547484i	0.663579	−	0.748106i	$-0.269037\pi$
$461$	−67175.7	−	116352.i	−0.316090	−	0.547484i	−0.979669	+	0.200623i	$0.935703\pi$
$462$		0			0
$463$	−205084.			−0.956689			−0.478344	−	0.878172i	$-0.658763\pi$
$463$	−205084.			−0.956689			−0.478344	+	0.878172i	$0.658763\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	356976.			1.63684			0.818419	−	0.574622i	$-0.194851\pi$
$467$	356976.			1.63684			0.818419	+	0.574622i	$0.194851\pi$
$468$		0			0
$469$	25603.8	+	14782.4i	0.116402	+	0.0672046i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−49478.3	−	85699.0i	−0.221153	−	0.383048i
$474$		0			0
$475$	18086.5	+	18559.4i	0.0801620	+	0.0822578i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−130587.	+	226183.i	−0.569153	+	0.985802i	0.427497	+	0.904017i	$0.359395\pi$
$479$	−130587.	+	226183.i	−0.569153	+	0.985802i	−0.996650	+	0.0817849i	$0.973938\pi$
$480$		0			0
$481$	70258.1	−	121691.i	0.303673	−	0.525977i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−112735.	−	65087.6i	−0.479265	−	0.276704i
$486$		0			0
$487$			396512.i			1.67185i	0.548840	+	0.835927i	$0.315070\pi$
$487$			396512.i			1.67185i	−0.548840	+	0.835927i	$0.684930\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−71555.9	−	123938.i	−0.296812	−	0.514094i	0.678592	−	0.734515i	$-0.262590\pi$
$491$	−71555.9	−	123938.i	−0.296812	−	0.514094i	−0.975405	+	0.220421i	$0.929257\pi$
$492$		0			0
$493$			159327.i			0.655536i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−69978.9	+	40402.3i	−0.283305	+	0.163566i
$498$		0			0
$499$	−19958.4	−	34569.0i	−0.0801539	−	0.138831i	0.823162	−	0.567807i	$-0.192208\pi$
$499$	−19958.4	−	34569.0i	−0.0801539	−	0.138831i	−0.903316	+	0.428976i	$0.858875\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17438.6	+	30204.5i	−0.0689247	+	0.119381i	−0.898428	−	0.439120i	$-0.855290\pi$
$503$	−17438.6	+	30204.5i	−0.0689247	+	0.119381i	0.829504	+	0.558501i	$0.188623\pi$
$504$		0			0
$505$	104910.			0.411373
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−50233.3	−	29002.2i	−0.193890	−	0.111943i	0.399912	−	0.916553i	$-0.369041\pi$
$509$	−50233.3	−	29002.2i	−0.193890	−	0.111943i	−0.593803	+	0.804611i	$0.702374\pi$
$510$		0			0
$511$	209019.	+	362031.i	0.800468	+	1.38645i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−86511.3	+	49947.3i	−0.326181	+	0.188321i
$516$		0			0
$517$	−283953.	+	491821.i	−1.06234	+	1.84003i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			214679.i			0.790887i	0.918490	+	0.395444i	$0.129409\pi$
$521$			214679.i			0.790887i	−0.918490	+	0.395444i	$0.870591\pi$
$522$		0			0
$523$	48503.0	+	28003.2i	0.177323	+	0.102378i	0.586034	−	0.810286i	$-0.300688\pi$
$523$	48503.0	+	28003.2i	0.177323	+	0.102378i	−0.408711	+	0.912664i	$0.634022\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	461999.	−	266735.i	1.66349	−	0.960415i
$528$		0			0
$529$	11342.5	+	19645.8i	0.0405321	+	0.0702036i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	191287.			0.673334
$534$		0			0
$535$	−1582.09	+	913.422i	−0.00552745	+	0.00319127i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−443874.			−1.52785
$540$		0			0
$541$	81891.0	−	141839.i	0.279796	−	0.484621i	−0.691538	−	0.722340i	$-0.743067\pi$
$541$	81891.0	−	141839.i	0.279796	−	0.484621i	0.971334	+	0.237719i	$0.0763999\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	205667.	+	118742.i	0.692425	+	0.399772i
$546$		0			0
$547$	−343054.	−	198062.i	−1.14654	−	0.661952i	−0.198495	−	0.980102i	$-0.563605\pi$
$547$	−343054.	−	198062.i	−1.14654	−	0.661952i	−0.948041	+	0.318149i	$0.896939\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	81752.4	−	79669.4i	0.269276	−	0.262415i
$552$		0			0
$553$	−618215.	+	356926.i	−2.02157	+	1.16715i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−296738.	+	513965.i	−0.956450	+	1.65662i	−0.225436	+	0.974258i	$0.572381\pi$
$557$	−296738.	+	513965.i	−0.956450	+	1.65662i	−0.731014	+	0.682362i	$0.760953\pi$
$558$		0			0
$559$		−	84136.9i		−	0.269254i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	510299.i		−	1.60993i	−0.593320	−	0.804966i	$-0.702183\pi$
$563$		−	510299.i		−	1.60993i	0.593320	−	0.804966i	$-0.297817\pi$
$564$		0			0
$565$	298501.	−	172340.i	0.935080	−	0.539869i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	474137.i		−	1.46447i	−0.681054	−	0.732233i	$-0.738478\pi$
$569$		−	474137.i		−	1.46447i	0.681054	−	0.732233i	$-0.261522\pi$
$570$		0			0
$571$	403714.			1.23823			0.619116	−	0.785300i	$-0.287491\pi$
$571$	403714.			1.23823			0.619116	+	0.785300i	$0.287491\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−18201.5	−	31526.0i	−0.0550519	−	0.0953528i
$576$		0			0
$577$	−199280.			−0.598566			−0.299283	−	0.954164i	$-0.596747\pi$
$577$	−199280.			−0.598566			−0.299283	+	0.954164i	$0.596747\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−41623.8			−0.123308
$582$		0			0
$583$	876037.	+	505780.i	2.57742	+	1.48807i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	274321.	+	475138.i	0.796128	+	1.37893i	0.922120	+	0.386903i	$0.126455\pi$
$587$	274321.	+	475138.i	0.796128	+	1.37893i	−0.125992	+	0.992031i	$0.540211\pi$
$588$		0			0
$589$	−367880.	−	103679.i	−1.06041	−	0.298854i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16938.2	+	29337.9i	−0.0481680	+	0.0834295i	−0.889104	−	0.457705i	$-0.848672\pi$
$593$	−16938.2	+	29337.9i	−0.0481680	+	0.0834295i	0.840936	+	0.541134i	$0.182005\pi$
$594$		0			0
$595$	387831.	−	671744.i	1.09549	−	1.89745i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14875.4	−	8588.32i	−0.0414586	−	0.0239362i	0.479127	−	0.877745i	$-0.340953\pi$
$599$	−14875.4	−	8588.32i	−0.0414586	−	0.0239362i	−0.520586	+	0.853809i	$0.674287\pi$
$600$		0			0
$601$			159959.i			0.442852i	0.975177	+	0.221426i	$0.0710711\pi$
$601$			159959.i			0.442852i	−0.975177	+	0.221426i	$0.928929\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−481477.	−	833943.i	−1.31542	−	2.27838i
$606$		0			0
$607$		−	327100.i		−	0.887776i	−0.896082	−	0.443888i	$-0.853599\pi$
$607$		−	327100.i		−	0.887776i	0.896082	−	0.443888i	$-0.146401\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−418166.	+	241428.i	−1.12012	+	0.646703i
$612$		0			0
$613$	−61903.0	−	107219.i	−0.164737	−	0.285332i	0.771825	−	0.635835i	$-0.219344\pi$
$613$	−61903.0	−	107219.i	−0.164737	−	0.285332i	−0.936562	+	0.350503i	$0.886011\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	146270.	−	253348.i	0.384225	−	0.665497i	−0.607436	−	0.794368i	$-0.707802\pi$
$617$	146270.	−	253348.i	0.384225	−	0.665497i	0.991661	+	0.128871i	$0.0411353\pi$
$618$		0			0
$619$	−435433.			−1.13642			−0.568211	−	0.822883i	$-0.692364\pi$
$619$	−435433.			−1.13642			−0.568211	+	0.822883i	$0.692364\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	409355.	+	236341.i	1.05469	+	0.608925i
$624$		0			0
$625$	170303.	+	294973.i	0.435975	+	0.755131i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	305888.	−	176605.i	0.773146	−	0.446376i
$630$		0			0
$631$	−308271.	+	533941.i	−0.774237	+	1.34102i	0.160985	+	0.986957i	$0.448533\pi$
$631$	−308271.	+	533941.i	−0.774237	+	1.34102i	−0.935222	+	0.354061i	$0.884801\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$			690444.i			1.71230i
$636$		0			0
$637$	−326837.	−	188699.i	−0.805476	−	0.465042i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−88221.4	+	50934.7i	−0.214713	+	0.123965i	−0.603500	−	0.797363i	$-0.706228\pi$
$641$	−88221.4	+	50934.7i	−0.214713	+	0.123965i	0.388787	+	0.921328i	$0.372894\pi$
$642$		0			0
$643$	367887.	+	637199.i	0.889801	+	1.54118i	0.840111	+	0.542415i	$0.182490\pi$
$643$	367887.	+	637199.i	0.889801	+	1.54118i	0.0496900	+	0.998765i	$0.484177\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−116804.			−0.279030			−0.139515	−	0.990220i	$-0.544554\pi$
$647$	−116804.			−0.279030			−0.139515	+	0.990220i	$0.544554\pi$
$648$		0			0
$649$	−333270.	+	192414.i	−0.791238	+	0.456821i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	159338.			0.373673			0.186837	−	0.982391i	$-0.440176\pi$
$653$	159338.			0.373673			0.186837	+	0.982391i	$0.440176\pi$
$654$		0			0
$655$	24445.1	−	42340.2i	0.0569783	−	0.0986893i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−221810.	−	128062.i	−0.510753	−	0.294883i	0.222390	−	0.974958i	$-0.428614\pi$
$659$	−221810.	−	128062.i	−0.510753	−	0.294883i	−0.733143	+	0.680074i	$0.761947\pi$
$660$		0			0
$661$	−243433.	−	140546.i	−0.557155	−	0.321673i	0.194848	−	0.980833i	$-0.437579\pi$
$661$	−243433.	−	140546.i	−0.557155	−	0.321673i	−0.752003	+	0.659160i	$0.770912\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−538607.	+	136896.i	−1.21795	+	0.309562i
$666$		0			0
$667$	−138869.	+	80176.0i	−0.312143	+	0.180216i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	221566.	−	383763.i	0.492105	−	0.852350i
$672$		0			0
$673$		−	706406.i		−	1.55964i	−0.626004	−	0.779819i	$-0.715311\pi$
$673$		−	706406.i		−	1.55964i	0.626004	−	0.779819i	$-0.284689\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			668885.i			1.45940i	0.683768	+	0.729699i	$0.260340\pi$
$677$			668885.i			1.45940i	−0.683768	+	0.729699i	$0.739660\pi$
$678$		0			0
$679$	−313707.	+	181119.i	−0.680432	+	0.392848i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	198199.i		−	0.424874i	−0.977175	−	0.212437i	$-0.931860\pi$
$683$		−	198199.i		−	0.424874i	0.977175	−	0.212437i	$-0.0681401\pi$
$684$		0			0
$685$	92261.0			0.196624
$686$		0			0
$687$		0			0
$688$		0			0
$689$	430034.	+	744841.i	0.905867	+	1.56901i
$690$		0			0
$691$	862033.			1.80538			0.902689	−	0.430294i	$-0.141590\pi$
$691$	862033.			1.80538			0.902689	+	0.430294i	$0.141590\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	606036.			1.25467
$696$		0			0
$697$	416410.	+	240415.i	0.857148	+	0.494875i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	341360.	+	591253.i	0.694668	+	1.20320i	0.970293	+	0.241934i	$0.0777818\pi$
$701$	341360.	+	591253.i	0.694668	+	1.20320i	−0.275625	+	0.961265i	$0.588885\pi$
$702$		0			0
$703$	−243572.	−	68645.4i	−0.492853	−	0.138900i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	145967.	−	252822.i	0.292022	−	0.505797i
$708$		0			0
$709$	313492.	−	542985.i	0.623641	−	1.08018i	−0.365161	−	0.930944i	$-0.618986\pi$
$709$	313492.	−	542985.i	0.623641	−	1.08018i	0.988802	−	0.149233i	$-0.0476805\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	464970.	+	268450.i	0.914630	+	0.528062i
$714$		0			0
$715$		−	1.11153e6i		−	2.17426i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	462065.	+	800321.i	0.893811	+	1.54813i	0.835269	+	0.549841i	$0.185312\pi$
$719$	462065.	+	800321.i	0.893811	+	1.54813i	0.0585415	+	0.998285i	$0.481355\pi$
$720$		0			0
$721$			277976.i			0.534733i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19658.3	+	11349.7i	−0.0373999	+	0.0215929i
$726$		0			0
$727$	294731.	+	510490.i	0.557645	+	0.965869i	0.997692	+	0.0678947i	$0.0216282\pi$
$727$	294731.	+	510490.i	0.557645	+	0.965869i	−0.440048	+	0.897974i	$0.645038\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	105746.	−	183157.i	0.197892	−	0.342758i
$732$		0			0
$733$	−362914.			−0.675455			−0.337727	−	0.941244i	$-0.609658\pi$
$733$	−362914.			−0.675455			−0.337727	+	0.941244i	$0.609658\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	92227.5	+	53247.6i	0.169795	+	0.0980313i
$738$		0			0
$739$	263089.	+	455683.i	0.481740	+	0.834399i	0.999780	−	0.0209576i	$-0.00667149\pi$
$739$	263089.	+	455683.i	0.481740	+	0.834399i	−0.518040	+	0.855356i	$0.673338\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	734764.	−	424216.i	1.33098	−	0.768439i	0.345527	−	0.938409i	$-0.387700\pi$
$743$	734764.	−	424216.i	1.33098	−	0.768439i	0.985449	+	0.169970i	$0.0543669\pi$
$744$		0			0
$745$	219657.	−	380457.i	0.395760	−	0.685476i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			5083.55i			0.00906156i
$750$		0			0
$751$	566439.	+	327034.i	1.00432	+	0.579846i	0.909525	−	0.415650i	$-0.136446\pi$
$751$	566439.	+	327034.i	1.00432	+	0.579846i	0.0947986	+	0.995496i	$0.469779\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−543050.	+	313530.i	−0.952677	+	0.550028i
$756$		0			0
$757$	357054.	+	618436.i	0.623078	+	1.07920i	0.988909	+	0.148522i	$0.0474515\pi$
$757$	357054.	+	618436.i	0.623078	+	1.07920i	−0.365831	+	0.930681i	$0.619215\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	491467.			0.848643			0.424322	−	0.905512i	$-0.360513\pi$
$761$	491467.			0.848643			0.424322	+	0.905512i	$0.360513\pi$
$762$		0			0
$763$	572309.	−	330423.i	0.983064	−	0.567572i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−327195.			−0.556181
$768$		0			0
$769$	151680.	−	262717.i	0.256493	−	0.444258i	−0.708807	−	0.705402i	$-0.750766\pi$
$769$	151680.	−	262717.i	0.256493	−	0.444258i	0.965300	+	0.261144i	$0.0840997\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	699519.	+	403868.i	1.17069	+	0.675896i	0.953842	−	0.300310i	$-0.0970900\pi$
$773$	699519.	+	403868.i	1.17069	+	0.675896i	0.216845	+	0.976206i	$0.430423\pi$
$774$		0			0
$775$	65821.3	+	38001.9i	0.109588	+	0.0632706i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−84861.0	−	333880.i	−0.139841	−	0.550193i
$780$		0			0
$781$	−252071.	+	145533.i	−0.413257	+	0.238594i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−330255.	+	572018.i	−0.535932	+	0.928262i
$786$		0			0
$787$		−	168832.i		−	0.272587i	−0.990668	−	0.136294i	$-0.956481\pi$
$787$		−	168832.i		−	0.272587i	0.990668	−	0.136294i	$-0.0435191\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	959137.i		−	1.53295i
$792$		0			0
$793$	326291.	−	188384.i	0.518870	−	0.299570i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	115316.i		−	0.181541i	−0.995872	−	0.0907703i	$-0.971067\pi$
$797$		−	115316.i		−	0.181541i	0.995872	−	0.0907703i	$-0.0289329\pi$
$798$		0			0
$799$	−1.21373e6			−1.90121
$800$		0			0
$801$		0			0
$802$		0			0
$803$	752906.	+	1.30407e6i	1.16764	+	2.02242i
$804$		0			0
$805$	780651.			1.20466
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.15686e6			1.76760			0.883801	−	0.467863i	$-0.154976\pi$
$809$	1.15686e6			1.76760			0.883801	+	0.467863i	$0.154976\pi$
$810$		0			0
$811$	−315438.	−	182118.i	−0.479592	−	0.276893i	0.240654	−	0.970611i	$-0.422638\pi$
$811$	−315438.	−	182118.i	−0.479592	−	0.276893i	−0.720247	+	0.693718i	$0.755971\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	611789.	+	1.05965e6i	0.921056	+	1.59532i
$816$		0			0
$817$	−146856.	+	37325.8i	−0.220012	+	0.0559198i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−414504.	+	717943.i	−0.614954	+	1.06513i	0.375438	+	0.926847i	$0.377492\pi$
$821$	−414504.	+	717943.i	−0.614954	+	1.06513i	−0.990393	+	0.138285i	$0.955841\pi$
$822$		0			0
$823$	535759.	−	927962.i	0.790988	−	1.37003i	−0.134368	−	0.990932i	$-0.542900\pi$
$823$	535759.	−	927962.i	0.790988	−	1.37003i	0.925356	−	0.379100i	$-0.123766\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	563832.	+	325528.i	0.824401	+	0.475968i	0.851932	−	0.523653i	$-0.175431\pi$
$827$	563832.	+	325528.i	0.824401	+	0.475968i	−0.0275310	+	0.999621i	$0.508764\pi$
$828$		0			0
$829$		−	258132.i		−	0.375606i	−0.982207	−	0.187803i	$-0.939863\pi$
$829$		−	258132.i		−	0.375606i	0.982207	−	0.187803i	$-0.0601367\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−474325.	−	821556.i	−0.683575	−	1.18399i
$834$		0			0
$835$		−	296960.i		−	0.425917i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−386606.	+	223207.i	−0.549218	+	0.317091i	−0.748806	−	0.662789i	$-0.769373\pi$
$839$	−386606.	+	223207.i	−0.549218	+	0.317091i	0.199589	+	0.979880i	$0.436039\pi$
$840$		0			0
$841$	−303646.	−	525930.i	−0.429315	−	0.743595i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	136651.	−	236686.i	0.191381	−	0.331481i
$846$		0			0
$847$	−2.67961e6			−3.73512
$848$		0			0
$849$		0			0
$850$		0			0
$851$	307855.	+	177740.i	0.425096	+	0.245429i
$852$		0			0
$853$	331994.	+	575030.i	0.456280	+	0.790301i	0.998761	−	0.0497677i	$-0.0158481\pi$
$853$	331994.	+	575030.i	0.456280	+	0.790301i	−0.542480	+	0.840068i	$0.682515\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−627468.	+	362269.i	−0.854339	+	0.493253i	−0.862112	−	0.506717i	$-0.830859\pi$
$857$	−627468.	+	362269.i	−0.854339	+	0.493253i	0.00777362	+	0.999970i	$0.497526\pi$
$858$		0			0
$859$	−312334.	+	540979.i	−0.423286	+	0.733152i	−0.996259	−	0.0864219i	$-0.972457\pi$
$859$	−312334.	+	540979.i	−0.423286	+	0.733152i	0.572973	+	0.819574i	$0.305790\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	338390.i		−	0.454355i	−0.973853	−	0.227178i	$-0.927050\pi$
$863$		−	338390.i		−	0.454355i	0.973853	−	0.227178i	$-0.0729498\pi$
$864$		0			0
$865$	−1.03943e6	−	600113.i	−1.38919	−	0.802049i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.22687e6	+	1.28568e6i	−2.94887	+	1.70253i
$870$		0			0
$871$	45273.2	+	78415.5i	0.0596767	+	0.103363i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.07265e6			1.40101
$876$		0			0
$877$	176036.	−	101634.i	0.228877	−	0.132142i	−0.381177	−	0.924502i	$-0.624481\pi$
$877$	176036.	−	101634.i	0.228877	−	0.132142i	0.610054	+	0.792360i	$0.291148\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−586337.			−0.755433			−0.377716	−	0.925921i	$-0.623291\pi$
$881$	−586337.			−0.755433			−0.377716	+	0.925921i	$0.623291\pi$
$882$		0			0
$883$	−428782.	+	742673.i	−0.549940	+	0.952524i	0.448338	+	0.893864i	$0.352016\pi$
$883$	−428782.	+	742673.i	−0.549940	+	0.952524i	−0.998278	+	0.0586601i	$0.981317\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−902069.	−	520810.i	−1.14655	−	0.661960i	−0.198505	−	0.980100i	$-0.563609\pi$
$887$	−902069.	−	520810.i	−1.14655	−	0.661960i	−0.948044	+	0.318140i	$0.896942\pi$
$888$		0			0
$889$	1.66389e6	+	960647.i	2.10533	+	1.21551i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	606910.	+	622778.i	0.761064	+	0.780962i
$894$		0			0
$895$	1.16711e6	−	673833.i	1.45703	−	0.841214i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	167395.	−	289936.i	0.207120	−	0.358743i
$900$		0			0
$901$			2.16192e6i			2.66311i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	1.49670e6i		−	1.82742i
$906$		0			0
$907$	1.09406e6	−	631656.i	1.32992	−	0.767831i	0.344635	−	0.938737i	$-0.388003\pi$
$907$	1.09406e6	−	631656.i	1.32992	−	0.767831i	0.985287	+	0.170905i	$0.0546692\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	480561.i		−	0.579044i	−0.957171	−	0.289522i	$-0.906504\pi$
$911$		−	480561.i		−	0.579044i	0.957171	−	0.289522i	$-0.0934964\pi$
$912$		0			0
$913$	−149933.			−0.179869
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−68023.2	−	117820.i	−0.0808944	−	0.140113i
$918$		0			0
$919$	−541806.			−0.641524			−0.320762	−	0.947160i	$-0.603939\pi$
$919$	−541806.			−0.641524			−0.320762	+	0.947160i	$0.603939\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−247476.			−0.290489
$924$		0			0
$925$	43580.1	+	25161.0i	0.0509336	+	0.0294066i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−381424.	−	660645.i	−0.441953	−	0.765486i	0.555881	−	0.831262i	$-0.312381\pi$
$929$	−381424.	−	660645.i	−0.441953	−	0.765486i	−0.997834	+	0.0657762i	$0.979048\pi$
$930$		0			0
$931$	−184368.	+	654188.i	−0.212709	+	0.754750i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.39701e6	−	2.41969e6i	1.59799	−	2.76781i
$936$		0			0
$937$	−402682.	+	697465.i	−0.458651	+	0.794408i	−0.998890	−	0.0471044i	$-0.985001\pi$
$937$	−402682.	+	697465.i	−0.458651	+	0.794408i	0.540239	+	0.841512i	$0.318334\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.44735e6	−	835625.i	−1.63453	−	0.943696i	−0.982672	−	0.185355i	$-0.940656\pi$
$941$	−1.44735e6	−	835625.i	−1.63453	−	0.943696i	−0.651858	−	0.758341i	$-0.726010\pi$
$942$		0			0
$943$			483921.i			0.544191i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	363298.	+	629250.i	0.405101	+	0.701655i	0.994333	−	0.106309i	$-0.0339032\pi$
$947$	363298.	+	629250.i	0.405101	+	0.701655i	−0.589233	+	0.807963i	$0.700570\pi$
$948$		0			0
$949$			1.28030e6i			1.42161i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	118884.	−	68637.8i	0.130900	−	0.0755749i	−0.433120	−	0.901336i	$-0.642587\pi$
$953$	118884.	−	68637.8i	0.130900	−	0.0755749i	0.564020	+	0.825761i	$0.309254\pi$
$954$		0			0
$955$	125485.	+	217346.i	0.137589	+	0.238311i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	128367.	−	222338.i	0.139578	−	0.241756i
$960$		0			0
$961$	−197442.			−0.213793
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−360097.	−	207902.i	−0.386692	−	0.223257i
$966$		0			0
$967$	−624204.	−	1.08115e6i	−0.667534	−	1.15620i	−0.978592	−	0.205812i	$-0.934017\pi$
$967$	−624204.	−	1.08115e6i	−0.667534	−	1.15620i	0.311058	−	0.950391i	$-0.399317\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.46265e6	+	844459.i	−1.55132	+	0.895654i	−0.553283	+	0.832993i	$0.686625\pi$
$971$	−1.46265e6	+	844459.i	−1.55132	+	0.895654i	−0.998035	+	0.0626603i	$0.980042\pi$
$972$		0			0
$973$	843207.	−	1.46048e6i	0.890653	−	1.54266i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			67912.5i			0.0711477i	0.999367	+	0.0355738i	$0.0113259\pi$
$977$			67912.5i			0.0711477i	−0.999367	+	0.0355738i	$0.988674\pi$
$978$		0			0
$979$	1.47454e6	+	851325.i	1.53847	+	0.888239i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	221789.	−	128050.i	0.229527	−	0.132518i	−0.380827	−	0.924646i	$-0.624361\pi$
$983$	221789.	−	128050.i	0.229527	−	0.132518i	0.610354	+	0.792129i	$0.291027\pi$
$984$		0			0
$985$	360905.	+	625106.i	0.371981	+	0.644290i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	212851.			0.217612
$990$		0			0
$991$	1.21160e6	−	699516.i	1.23370	−	0.712279i	0.265904	−	0.964000i	$-0.414330\pi$
$991$	1.21160e6	−	699516.i	1.23370	−	0.712279i	0.967800	+	0.251720i	$0.0809963\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	586764.			0.592676
$996$		0			0
$997$	540384.	−	935973.i	0.543641	−	0.941614i	−0.455050	−	0.890466i	$-0.650379\pi$
$997$	540384.	−	935973.i	0.543641	−	0.941614i	0.998691	−	0.0511482i	$-0.0162881\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.5.y.d.145.3		14
3.2	odd	2		228.5.l.b.145.5	✓	14
19.8	odd	6	inner	684.5.y.d.217.3		14
57.8	even	6		228.5.l.b.217.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.5.l.b.145.5	✓	14	3.2	odd	2
228.5.l.b.217.5	yes	14	57.8	even	6
684.5.y.d.145.3		14	1.1	even	1	trivial
684.5.y.d.217.3		14	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)

\(f(q)\)	\(=\)	\(q+(-11.7603 - 20.3694i) q^{5} -65.4503 q^{7} +O(q^{10})\)	\(q+(-11.7603 - 20.3694i) q^{5} -65.4503 q^{7} -235.758 q^{11} +(-173.596 - 100.226i) q^{13} +(-251.933 - 436.360i) q^{17} +(-97.9251 + 347.465i) q^{19} +(253.553 - 439.166i) q^{23} +(35.8930 - 62.1685i) q^{25} +(-273.846 - 158.105i) q^{29} +1058.76i q^{31} +(769.712 + 1333.18i) q^{35} +700.999i q^{37} +(-826.431 + 477.140i) q^{41} +(209.869 + 363.503i) q^{43} +(1204.42 - 2086.12i) q^{47} +1882.75 q^{49} +(-3715.82 - 2145.33i) q^{53} +(2772.58 + 4802.25i) q^{55} +(1413.61 - 816.147i) q^{59} +(-939.800 + 1627.78i) q^{61} +4714.71i q^{65} +(-391.195 - 225.857i) q^{67} +(1069.19 - 617.298i) q^{71} +(-3193.55 - 5531.39i) q^{73} +15430.5 q^{77} +(9445.55 - 5453.39i) q^{79} +635.960 q^{83} +(-5925.58 + 10263.4i) q^{85} +(-6254.44 - 3611.00i) q^{89} +(11361.9 + 6559.80i) q^{91} +(8229.25 - 2091.60i) q^{95} +(4793.05 - 2767.27i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) \) 14 * q - 12 * q^5 - 110 * q^7	\( 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) \) 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

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