LMFDB - Embedded newform 3525.2.a.bf.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.a (trivial)

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:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.563403$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.563403 q^{2} +1.00000 q^{3} -1.68258 q^{4} +0.563403 q^{6} -1.09545 q^{7} -2.07478 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.563403 q^{2} +1.00000 q^{3} -1.68258 q^{4} +0.563403 q^{6} -1.09545 q^{7} -2.07478 q^{8} +1.00000 q^{9} +0.827260 q^{11} -1.68258 q^{12} -2.66383 q^{13} -0.617178 q^{14} +2.19622 q^{16} +4.16840 q^{17} +0.563403 q^{18} -5.48002 q^{19} -1.09545 q^{21} +0.466081 q^{22} +5.61254 q^{23} -2.07478 q^{24} -1.50081 q^{26} +1.00000 q^{27} +1.84317 q^{28} +9.79508 q^{29} -9.33410 q^{31} +5.38691 q^{32} +0.827260 q^{33} +2.34849 q^{34} -1.68258 q^{36} -11.5659 q^{37} -3.08746 q^{38} -2.66383 q^{39} +2.92305 q^{41} -0.617178 q^{42} +4.68831 q^{43} -1.39193 q^{44} +3.16212 q^{46} -1.00000 q^{47} +2.19622 q^{48} -5.80000 q^{49} +4.16840 q^{51} +4.48211 q^{52} -14.1000 q^{53} +0.563403 q^{54} +2.27281 q^{56} -5.48002 q^{57} +5.51858 q^{58} -9.17901 q^{59} -4.17349 q^{61} -5.25886 q^{62} -1.09545 q^{63} -1.35744 q^{64} +0.466081 q^{66} -7.79626 q^{67} -7.01365 q^{68} +5.61254 q^{69} -8.28687 q^{71} -2.07478 q^{72} -4.51755 q^{73} -6.51627 q^{74} +9.22056 q^{76} -0.906219 q^{77} -1.50081 q^{78} +3.96364 q^{79} +1.00000 q^{81} +1.64686 q^{82} -9.53997 q^{83} +1.84317 q^{84} +2.64141 q^{86} +9.79508 q^{87} -1.71638 q^{88} +4.86438 q^{89} +2.91809 q^{91} -9.44353 q^{92} -9.33410 q^{93} -0.563403 q^{94} +5.38691 q^{96} -11.0089 q^{97} -3.26774 q^{98} +0.827260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.563403	0.398386	0.199193	−	0.979960i	$-0.436168\pi$
$2$	0.563403	0.398386	0.199193	+	0.979960i	$0.436168\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.68258	−0.841288
$5$	0	0
$5$	0	0
$6$	0.563403	0.230008
$7$	−1.09545	−0.414040	−0.207020	−	0.978337i	$-0.566377\pi$
$7$	−1.09545	−0.414040	−0.207020	+	0.978337i	$0.566377\pi$
$8$	−2.07478	−0.733544
$9$	1.00000	0.333333
$10$	0	0
$11$	0.827260	0.249428	0.124714	−	0.992193i	$-0.460199\pi$
$11$	0.827260	0.249428	0.124714	+	0.992193i	$0.460199\pi$
$12$	−1.68258	−0.485718
$13$	−2.66383	−0.738815	−0.369407	−	0.929268i	$-0.620439\pi$
$13$	−2.66383	−0.738815	−0.369407	+	0.929268i	$0.620439\pi$
$14$	−0.617178	−0.164948
$15$	0	0
$16$	2.19622	0.549055
$17$	4.16840	1.01098	0.505492	−	0.862831i	$-0.331311\pi$
$17$	4.16840	1.01098	0.505492	+	0.862831i	$0.331311\pi$
$18$	0.563403	0.132795
$19$	−5.48002	−1.25720	−0.628602	−	0.777728i	$-0.716372\pi$
$19$	−5.48002	−1.25720	−0.628602	+	0.777728i	$0.716372\pi$
$20$	0	0
$21$	−1.09545	−0.239046
$22$	0.466081	0.0993687
$23$	5.61254	1.17029	0.585147	−	0.810927i	$-0.301037\pi$
$23$	5.61254	1.17029	0.585147	+	0.810927i	$0.301037\pi$
$24$	−2.07478	−0.423512
$25$	0	0
$26$	−1.50081	−0.294334
$27$	1.00000	0.192450
$28$	1.84317	0.348327
$29$	9.79508	1.81890	0.909450	−	0.415813i	$-0.136503\pi$
$29$	9.79508	1.81890	0.909450	+	0.415813i	$0.136503\pi$
$30$	0	0
$31$	−9.33410	−1.67645	−0.838227	−	0.545322i	$-0.816407\pi$
$31$	−9.33410	−1.67645	−0.838227	+	0.545322i	$0.816407\pi$
$32$	5.38691	0.952280
$33$	0.827260	0.144007
$34$	2.34849	0.402762
$35$	0	0
$36$	−1.68258	−0.280429
$37$	−11.5659	−1.90142	−0.950712	−	0.310077i	$-0.899645\pi$
$37$	−11.5659	−1.90142	−0.950712	+	0.310077i	$0.899645\pi$
$38$	−3.08746	−0.500852
$39$	−2.66383	−0.426555
$40$	0	0
$41$	2.92305	0.456504	0.228252	−	0.973602i	$-0.426699\pi$
$41$	2.92305	0.456504	0.228252	+	0.973602i	$0.426699\pi$
$42$	−0.617178	−0.0952327
$43$	4.68831	0.714960	0.357480	−	0.933921i	$-0.383636\pi$
$43$	4.68831	0.714960	0.357480	+	0.933921i	$0.383636\pi$
$44$	−1.39193	−0.209841
$45$	0	0
$46$	3.16212	0.466229
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	2.19622	0.316997
$49$	−5.80000	−0.828571
$50$	0	0
$51$	4.16840	0.583692
$52$	4.48211	0.621556
$53$	−14.1000	−1.93679	−0.968394	−	0.249426i	$-0.919758\pi$
$53$	−14.1000	−1.93679	−0.968394	+	0.249426i	$0.919758\pi$
$54$	0.563403	0.0766695
$55$	0	0
$56$	2.27281	0.303717
$57$	−5.48002	−0.725847
$58$	5.51858	0.724625
$59$	−9.17901	−1.19500	−0.597502	−	0.801867i	$-0.703840\pi$
$59$	−9.17901	−1.19500	−0.597502	+	0.801867i	$0.703840\pi$
$60$	0	0
$61$	−4.17349	−0.534361	−0.267180	−	0.963647i	$-0.586092\pi$
$61$	−4.17349	−0.534361	−0.267180	+	0.963647i	$0.586092\pi$
$62$	−5.25886	−0.667876
$63$	−1.09545	−0.138013
$64$	−1.35744	−0.169680
$65$	0	0
$66$	0.466081	0.0573706
$67$	−7.79626	−0.952465	−0.476232	−	0.879319i	$-0.657998\pi$
$67$	−7.79626	−0.952465	−0.476232	+	0.879319i	$0.657998\pi$
$68$	−7.01365	−0.850530
$69$	5.61254	0.675670
$70$	0	0
$71$	−8.28687	−0.983470	−0.491735	−	0.870745i	$-0.663637\pi$
$71$	−8.28687	−0.983470	−0.491735	+	0.870745i	$0.663637\pi$
$72$	−2.07478	−0.244515
$73$	−4.51755	−0.528739	−0.264369	−	0.964421i	$-0.585164\pi$
$73$	−4.51755	−0.528739	−0.264369	+	0.964421i	$0.585164\pi$
$74$	−6.51627	−0.757501
$75$	0	0
$76$	9.22056	1.05767
$77$	−0.906219	−0.103273
$78$	−1.50081	−0.169934
$79$	3.96364	0.445944	0.222972	−	0.974825i	$-0.428424\pi$
$79$	3.96364	0.445944	0.222972	+	0.974825i	$0.428424\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.64686	0.181865
$83$	−9.53997	−1.04715	−0.523574	−	0.851980i	$-0.675402\pi$
$83$	−9.53997	−1.04715	−0.523574	+	0.851980i	$0.675402\pi$
$84$	1.84317	0.201107
$85$	0	0
$86$	2.64141	0.284830
$87$	9.79508	1.05014
$88$	−1.71638	−0.182966
$89$	4.86438	0.515623	0.257811	−	0.966195i	$-0.416999\pi$
$89$	4.86438	0.515623	0.257811	+	0.966195i	$0.416999\pi$
$90$	0	0
$91$	2.91809	0.305899
$92$	−9.44353	−0.984556
$93$	−9.33410	−0.967901
$94$	−0.563403	−0.0581106
$95$	0	0
$96$	5.38691	0.549799
$97$	−11.0089	−1.11779	−0.558895	−	0.829239i	$-0.688774\pi$
$97$	−11.0089	−1.11779	−0.558895	+	0.829239i	$0.688774\pi$
$98$	−3.26774	−0.330091
$99$	0.827260	0.0831427
$100$	0	0
$101$	−14.1722	−1.41019	−0.705095	−	0.709113i	$-0.749096\pi$
$101$	−14.1722	−1.41019	−0.705095	+	0.709113i	$0.749096\pi$
$102$	2.34849	0.232535
$103$	3.58397	0.353139	0.176569	−	0.984288i	$-0.443500\pi$
$103$	3.58397	0.353139	0.176569	+	0.984288i	$0.443500\pi$
$104$	5.52686	0.541953
$105$	0	0
$106$	−7.94400	−0.771589
$107$	5.74250	0.555149	0.277574	−	0.960704i	$-0.410470\pi$
$107$	5.74250	0.555149	0.277574	+	0.960704i	$0.410470\pi$
$108$	−1.68258	−0.161906
$109$	4.40964	0.422367	0.211183	−	0.977446i	$-0.432268\pi$
$109$	4.40964	0.422367	0.211183	+	0.977446i	$0.432268\pi$
$110$	0	0
$111$	−11.5659	−1.09779
$112$	−2.40584	−0.227331
$113$	10.0821	0.948446	0.474223	−	0.880405i	$-0.342729\pi$
$113$	10.0821	0.948446	0.474223	+	0.880405i	$0.342729\pi$
$114$	−3.08746	−0.289167
$115$	0	0
$116$	−16.4810	−1.53022
$117$	−2.66383	−0.246272
$118$	−5.17148	−0.476073
$119$	−4.56626	−0.418588
$120$	0	0
$121$	−10.3156	−0.937786
$122$	−2.35136	−0.212882
$123$	2.92305	0.263563
$124$	15.7053	1.41038
$125$	0	0
$126$	−0.617178	−0.0549826
$127$	9.00334	0.798918	0.399459	−	0.916751i	$-0.369198\pi$
$127$	9.00334	0.798918	0.399459	+	0.916751i	$0.369198\pi$
$128$	−11.5386	−1.01988
$129$	4.68831	0.412782
$130$	0	0
$131$	−10.3496	−0.904250	−0.452125	−	0.891954i	$-0.649334\pi$
$131$	−10.3496	−0.904250	−0.452125	+	0.891954i	$0.649334\pi$
$132$	−1.39193	−0.121152
$133$	6.00307	0.520532
$134$	−4.39244	−0.379449
$135$	0	0
$136$	−8.64849	−0.741602
$137$	12.2363	1.04542	0.522709	−	0.852511i	$-0.324922\pi$
$137$	12.2363	1.04542	0.522709	+	0.852511i	$0.324922\pi$
$138$	3.16212	0.269178
$139$	−19.5561	−1.65873	−0.829364	−	0.558709i	$-0.811297\pi$
$139$	−19.5561	−1.65873	−0.829364	+	0.558709i	$0.811297\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−4.66885	−0.391801
$143$	−2.20368	−0.184281
$144$	2.19622	0.183018
$145$	0	0
$146$	−2.54520	−0.210642
$147$	−5.80000	−0.478376
$148$	19.4605	1.59965
$149$	18.7965	1.53987	0.769935	−	0.638122i	$-0.220289\pi$
$149$	18.7965	1.53987	0.769935	+	0.638122i	$0.220289\pi$
$150$	0	0
$151$	−0.966201	−0.0786284	−0.0393142	−	0.999227i	$-0.512517\pi$
$151$	−0.966201	−0.0786284	−0.0393142	+	0.999227i	$0.512517\pi$
$152$	11.3698	0.922214
$153$	4.16840	0.336995
$154$	−0.510567	−0.0411426
$155$	0	0
$156$	4.48211	0.358856
$157$	16.1830	1.29154	0.645772	−	0.763530i	$-0.276536\pi$
$157$	16.1830	1.29154	0.645772	+	0.763530i	$0.276536\pi$
$158$	2.23313	0.177658
$159$	−14.1000	−1.11820
$160$	0	0
$161$	−6.14824	−0.484549
$162$	0.563403	0.0442651
$163$	−21.9173	−1.71669	−0.858346	−	0.513072i	$-0.828508\pi$
$163$	−21.9173	−1.71669	−0.858346	+	0.513072i	$0.828508\pi$
$164$	−4.91826	−0.384052
$165$	0	0
$166$	−5.37485	−0.417169
$167$	6.21850	0.481202	0.240601	−	0.970624i	$-0.422655\pi$
$167$	6.21850	0.481202	0.240601	+	0.970624i	$0.422655\pi$
$168$	2.27281	0.175351
$169$	−5.90399	−0.454153
$170$	0	0
$171$	−5.48002	−0.419068
$172$	−7.88844	−0.601488
$173$	21.5574	1.63898	0.819489	−	0.573094i	$-0.194257\pi$
$173$	21.5574	1.63898	0.819489	+	0.573094i	$0.194257\pi$
$174$	5.51858	0.418362
$175$	0	0
$176$	1.81684	0.136950
$177$	−9.17901	−0.689936
$178$	2.74060	0.205417
$179$	6.83254	0.510688	0.255344	−	0.966850i	$-0.417811\pi$
$179$	6.83254	0.510688	0.255344	+	0.966850i	$0.417811\pi$
$180$	0	0
$181$	−17.9374	−1.33327	−0.666637	−	0.745382i	$-0.732267\pi$
$181$	−17.9374	−1.33327	−0.666637	+	0.745382i	$0.732267\pi$
$182$	1.64406	0.121866
$183$	−4.17349	−0.308513
$184$	−11.6448	−0.858463
$185$	0	0
$186$	−5.25886	−0.385598
$187$	3.44835	0.252168
$188$	1.68258	0.122715
$189$	−1.09545	−0.0796821
$190$	0	0
$191$	5.55123	0.401673	0.200836	−	0.979625i	$-0.435634\pi$
$191$	5.55123	0.401673	0.200836	+	0.979625i	$0.435634\pi$
$192$	−1.35744	−0.0979646
$193$	15.1011	1.08700	0.543499	−	0.839410i	$-0.317099\pi$
$193$	15.1011	1.08700	0.543499	+	0.839410i	$0.317099\pi$
$194$	−6.20248	−0.445312
$195$	0	0
$196$	9.75894	0.697067
$197$	−3.61872	−0.257823	−0.128912	−	0.991656i	$-0.541148\pi$
$197$	−3.61872	−0.257823	−0.128912	+	0.991656i	$0.541148\pi$
$198$	0.466081	0.0331229
$199$	−22.2128	−1.57462	−0.787310	−	0.616557i	$-0.788527\pi$
$199$	−22.2128	−1.57462	−0.787310	+	0.616557i	$0.788527\pi$
$200$	0	0
$201$	−7.79626	−0.549906
$202$	−7.98468	−0.561800
$203$	−10.7300	−0.753098
$204$	−7.01365	−0.491054
$205$	0	0
$206$	2.01922	0.140686
$207$	5.61254	0.390098
$208$	−5.85036	−0.405650
$209$	−4.53340	−0.313582
$210$	0	0
$211$	−11.9468	−0.822450	−0.411225	−	0.911534i	$-0.634899\pi$
$211$	−11.9468	−0.822450	−0.411225	+	0.911534i	$0.634899\pi$
$212$	23.7244	1.62940
$213$	−8.28687	−0.567807
$214$	3.23534	0.221164
$215$	0	0
$216$	−2.07478	−0.141171
$217$	10.2250	0.694119
$218$	2.48440	0.168265
$219$	−4.51755	−0.305268
$220$	0	0
$221$	−11.1039	−0.746930
$222$	−6.51627	−0.437343
$223$	24.5415	1.64342	0.821709	−	0.569907i	$-0.193021\pi$
$223$	24.5415	1.64342	0.821709	+	0.569907i	$0.193021\pi$
$224$	−5.90107	−0.394282
$225$	0	0
$226$	5.68030	0.377848
$227$	−25.7309	−1.70782	−0.853909	−	0.520422i	$-0.825775\pi$
$227$	−25.7309	−1.70782	−0.853909	+	0.520422i	$0.825775\pi$
$228$	9.22056	0.610646
$229$	21.3252	1.40921	0.704605	−	0.709600i	$-0.251124\pi$
$229$	21.3252	1.40921	0.704605	+	0.709600i	$0.251124\pi$
$230$	0	0
$231$	−0.906219	−0.0596248
$232$	−20.3226	−1.33424
$233$	−24.7402	−1.62078	−0.810392	−	0.585889i	$-0.800746\pi$
$233$	−24.7402	−1.62078	−0.810392	+	0.585889i	$0.800746\pi$
$234$	−1.50081	−0.0981112
$235$	0	0
$236$	15.4444	1.00534
$237$	3.96364	0.257466
$238$	−2.57264	−0.166760
$239$	−2.16083	−0.139773	−0.0698864	−	0.997555i	$-0.522264\pi$
$239$	−2.16083	−0.139773	−0.0698864	+	0.997555i	$0.522264\pi$
$240$	0	0
$241$	−20.4436	−1.31689	−0.658443	−	0.752631i	$-0.728785\pi$
$241$	−20.4436	−1.31689	−0.658443	+	0.752631i	$0.728785\pi$
$242$	−5.81186	−0.373601
$243$	1.00000	0.0641500
$244$	7.02222	0.449552
$245$	0	0
$246$	1.64686	0.105000
$247$	14.5979	0.928840
$248$	19.3662	1.22975
$249$	−9.53997	−0.604571
$250$	0	0
$251$	−0.390156	−0.0246264	−0.0123132	−	0.999924i	$-0.503920\pi$
$251$	−0.390156	−0.0246264	−0.0123132	+	0.999924i	$0.503920\pi$
$252$	1.84317	0.116109
$253$	4.64303	0.291905
$254$	5.07251	0.318278
$255$	0	0
$256$	−3.78601	−0.236625
$257$	−1.89331	−0.118102	−0.0590508	−	0.998255i	$-0.518807\pi$
$257$	−1.89331	−0.118102	−0.0590508	+	0.998255i	$0.518807\pi$
$258$	2.64141	0.164447
$259$	12.6698	0.787265
$260$	0	0
$261$	9.79508	0.606300
$262$	−5.83101	−0.360241
$263$	7.07178	0.436065	0.218032	−	0.975942i	$-0.430036\pi$
$263$	7.07178	0.436065	0.218032	+	0.975942i	$0.430036\pi$
$264$	−1.71638	−0.105636
$265$	0	0
$266$	3.38215	0.207373
$267$	4.86438	0.297695
$268$	13.1178	0.801298
$269$	−17.7243	−1.08067	−0.540336	−	0.841449i	$-0.681703\pi$
$269$	−17.7243	−1.08067	−0.540336	+	0.841449i	$0.681703\pi$
$270$	0	0
$271$	6.65328	0.404158	0.202079	−	0.979369i	$-0.435230\pi$
$271$	6.65328	0.404158	0.202079	+	0.979369i	$0.435230\pi$
$272$	9.15471	0.555086
$273$	2.91809	0.176611
$274$	6.89397	0.416480
$275$	0	0
$276$	−9.44353	−0.568433
$277$	23.9253	1.43753	0.718766	−	0.695252i	$-0.244707\pi$
$277$	23.9253	1.43753	0.718766	+	0.695252i	$0.244707\pi$
$278$	−11.0180	−0.660814
$279$	−9.33410	−0.558818
$280$	0	0
$281$	17.8703	1.06605	0.533027	−	0.846098i	$-0.321055\pi$
$281$	17.8703	1.06605	0.533027	+	0.846098i	$0.321055\pi$
$282$	−0.563403	−0.0335502
$283$	−3.41975	−0.203283	−0.101641	−	0.994821i	$-0.532409\pi$
$283$	−3.41975	−0.203283	−0.101641	+	0.994821i	$0.532409\pi$
$284$	13.9433	0.827382
$285$	0	0
$286$	−1.24156	−0.0734151
$287$	−3.20205	−0.189011
$288$	5.38691	0.317427
$289$	0.375527	0.0220898
$290$	0	0
$291$	−11.0089	−0.645356
$292$	7.60112	0.444822
$293$	5.38265	0.314458	0.157229	−	0.987562i	$-0.449744\pi$
$293$	5.38265	0.314458	0.157229	+	0.987562i	$0.449744\pi$
$294$	−3.26774	−0.190578
$295$	0	0
$296$	23.9967	1.39478
$297$	0.827260	0.0480025
$298$	10.5900	0.613463
$299$	−14.9509	−0.864631
$300$	0	0
$301$	−5.13579	−0.296022
$302$	−0.544361	−0.0313244
$303$	−14.1722	−0.814174
$304$	−12.0353	−0.690273
$305$	0	0
$306$	2.34849	0.134254
$307$	3.55149	0.202694	0.101347	−	0.994851i	$-0.467685\pi$
$307$	3.55149	0.202694	0.101347	+	0.994851i	$0.467685\pi$
$308$	1.52478	0.0868826
$309$	3.58397	0.203885
$310$	0	0
$311$	−4.50283	−0.255332	−0.127666	−	0.991817i	$-0.540749\pi$
$311$	−4.50283	−0.255332	−0.127666	+	0.991817i	$0.540749\pi$
$312$	5.52686	0.312897
$313$	−3.69868	−0.209062	−0.104531	−	0.994522i	$-0.533334\pi$
$313$	−3.69868	−0.209062	−0.104531	+	0.994522i	$0.533334\pi$
$314$	9.11755	0.514533
$315$	0	0
$316$	−6.66913	−0.375168
$317$	−3.28048	−0.184250	−0.0921249	−	0.995747i	$-0.529366\pi$
$317$	−3.28048	−0.184250	−0.0921249	+	0.995747i	$0.529366\pi$
$318$	−7.94400	−0.445477
$319$	8.10307	0.453685
$320$	0	0
$321$	5.74250	0.320515
$322$	−3.46394	−0.193038
$323$	−22.8429	−1.27101
$324$	−1.68258	−0.0934765
$325$	0	0
$326$	−12.3482	−0.683906
$327$	4.40964	0.243854
$328$	−6.06468	−0.334866
$329$	1.09545	0.0603940
$330$	0	0
$331$	8.39325	0.461335	0.230667	−	0.973033i	$-0.425909\pi$
$331$	8.39325	0.461335	0.230667	+	0.973033i	$0.425909\pi$
$332$	16.0517	0.880954
$333$	−11.5659	−0.633808
$334$	3.50352	0.191704
$335$	0	0
$336$	−2.40584	−0.131249
$337$	18.5994	1.01318	0.506588	−	0.862189i	$-0.330907\pi$
$337$	18.5994	1.01318	0.506588	+	0.862189i	$0.330907\pi$
$338$	−3.32632	−0.180928
$339$	10.0821	0.547586
$340$	0	0
$341$	−7.72172	−0.418155
$342$	−3.08746	−0.166951
$343$	14.0217	0.757102
$344$	−9.72718	−0.524455
$345$	0	0
$346$	12.1455	0.652946
$347$	3.53217	0.189617	0.0948085	−	0.995496i	$-0.469776\pi$
$347$	3.53217	0.189617	0.0948085	+	0.995496i	$0.469776\pi$
$348$	−16.4810	−0.883473
$349$	−24.4677	−1.30973	−0.654863	−	0.755748i	$-0.727274\pi$
$349$	−24.4677	−1.30973	−0.654863	+	0.755748i	$0.727274\pi$
$350$	0	0
$351$	−2.66383	−0.142185
$352$	4.45637	0.237525
$353$	−21.5934	−1.14930	−0.574651	−	0.818399i	$-0.694862\pi$
$353$	−21.5934	−1.14930	−0.574651	+	0.818399i	$0.694862\pi$
$354$	−5.17148	−0.274861
$355$	0	0
$356$	−8.18469	−0.433788
$357$	−4.56626	−0.241672
$358$	3.84947	0.203451
$359$	10.0517	0.530506	0.265253	−	0.964179i	$-0.414544\pi$
$359$	10.0517	0.530506	0.265253	+	0.964179i	$0.414544\pi$
$360$	0	0
$361$	11.0306	0.580559
$362$	−10.1060	−0.531158
$363$	−10.3156	−0.541431
$364$	−4.90991	−0.257349
$365$	0	0
$366$	−2.35136	−0.122907
$367$	−7.85205	−0.409874	−0.204937	−	0.978775i	$-0.565699\pi$
$367$	−7.85205	−0.409874	−0.204937	+	0.978775i	$0.565699\pi$
$368$	12.3264	0.642556
$369$	2.92305	0.152168
$370$	0	0
$371$	15.4458	0.801908
$372$	15.7053	0.814284
$373$	8.79747	0.455516	0.227758	−	0.973718i	$-0.426861\pi$
$373$	8.79747	0.455516	0.227758	+	0.973718i	$0.426861\pi$
$374$	1.94281	0.100460
$375$	0	0
$376$	2.07478	0.106998
$377$	−26.0925	−1.34383
$378$	−0.617178	−0.0317442
$379$	−9.17566	−0.471322	−0.235661	−	0.971835i	$-0.575725\pi$
$379$	−9.17566	−0.471322	−0.235661	+	0.971835i	$0.575725\pi$
$380$	0	0
$381$	9.00334	0.461255
$382$	3.12758	0.160021
$383$	21.1797	1.08223	0.541116	−	0.840948i	$-0.318002\pi$
$383$	21.1797	1.08223	0.541116	+	0.840948i	$0.318002\pi$
$384$	−11.5386	−0.588827
$385$	0	0
$386$	8.50799	0.433045
$387$	4.68831	0.238320
$388$	18.5234	0.940383
$389$	−8.53664	−0.432825	−0.216413	−	0.976302i	$-0.569436\pi$
$389$	−8.53664	−0.432825	−0.216413	+	0.976302i	$0.569436\pi$
$390$	0	0
$391$	23.3953	1.18315
$392$	12.0337	0.607793
$393$	−10.3496	−0.522069
$394$	−2.03880	−0.102713
$395$	0	0
$396$	−1.39193	−0.0699470
$397$	14.8481	0.745206	0.372603	−	0.927991i	$-0.378465\pi$
$397$	14.8481	0.745206	0.372603	+	0.927991i	$0.378465\pi$
$398$	−12.5147	−0.627307
$399$	6.00307	0.300530
$400$	0	0
$401$	−21.0795	−1.05266	−0.526331	−	0.850280i	$-0.676433\pi$
$401$	−21.0795	−1.05266	−0.526331	+	0.850280i	$0.676433\pi$
$402$	−4.39244	−0.219075
$403$	24.8645	1.23859
$404$	23.8459	1.18638
$405$	0	0
$406$	−6.04531	−0.300024
$407$	−9.56801	−0.474268
$408$	−8.64849	−0.428164
$409$	−34.9063	−1.72601	−0.863003	−	0.505199i	$-0.831419\pi$
$409$	−34.9063	−1.72601	−0.863003	+	0.505199i	$0.831419\pi$
$410$	0	0
$411$	12.2363	0.603572
$412$	−6.03030	−0.297092
$413$	10.0551	0.494780
$414$	3.16212	0.155410
$415$	0	0
$416$	−14.3498	−0.703558
$417$	−19.5561	−0.957667
$418$	−2.55413	−0.124927
$419$	−6.33914	−0.309687	−0.154844	−	0.987939i	$-0.549487\pi$
$419$	−6.33914	−0.309687	−0.154844	+	0.987939i	$0.549487\pi$
$420$	0	0
$421$	−7.68154	−0.374375	−0.187188	−	0.982324i	$-0.559937\pi$
$421$	−7.68154	−0.374375	−0.187188	+	0.982324i	$0.559937\pi$
$422$	−6.73085	−0.327653
$423$	−1.00000	−0.0486217
$424$	29.2544	1.42072
$425$	0	0
$426$	−4.66885	−0.226206
$427$	4.57184	0.221247
$428$	−9.66220	−0.467040
$429$	−2.20368	−0.106395
$430$	0	0
$431$	33.1824	1.59834	0.799171	−	0.601104i	$-0.205272\pi$
$431$	33.1824	1.59834	0.799171	+	0.601104i	$0.205272\pi$
$432$	2.19622	0.105666
$433$	36.0585	1.73286	0.866430	−	0.499299i	$-0.166409\pi$
$433$	36.0585	1.73286	0.866430	+	0.499299i	$0.166409\pi$
$434$	5.76080	0.276527
$435$	0	0
$436$	−7.41955	−0.355332
$437$	−30.7568	−1.47130
$438$	−2.54520	−0.121614
$439$	−10.3370	−0.493359	−0.246680	−	0.969097i	$-0.579340\pi$
$439$	−10.3370	−0.493359	−0.246680	+	0.969097i	$0.579340\pi$
$440$	0	0
$441$	−5.80000	−0.276190
$442$	−6.25598	−0.297567
$443$	14.0196	0.666092	0.333046	−	0.942911i	$-0.391924\pi$
$443$	14.0196	0.666092	0.333046	+	0.942911i	$0.391924\pi$
$444$	19.4605	0.923556
$445$	0	0
$446$	13.8267	0.654715
$447$	18.7965	0.889044
$448$	1.48700	0.0702542
$449$	32.8025	1.54804	0.774022	−	0.633159i	$-0.218242\pi$
$449$	32.8025	1.54804	0.774022	+	0.633159i	$0.218242\pi$
$450$	0	0
$451$	2.41812	0.113865
$452$	−16.9639	−0.797917
$453$	−0.966201	−0.0453961
$454$	−14.4969	−0.680371
$455$	0	0
$456$	11.3698	0.532440
$457$	30.0426	1.40534	0.702668	−	0.711518i	$-0.251992\pi$
$457$	30.0426	1.40534	0.702668	+	0.711518i	$0.251992\pi$
$458$	12.0147	0.561410
$459$	4.16840	0.194564
$460$	0	0
$461$	16.2562	0.757128	0.378564	−	0.925575i	$-0.376418\pi$
$461$	16.2562	0.757128	0.378564	+	0.925575i	$0.376418\pi$
$462$	−0.510567	−0.0237537
$463$	−42.3387	−1.96764	−0.983822	−	0.179148i	$-0.942666\pi$
$463$	−42.3387	−1.96764	−0.983822	+	0.179148i	$0.942666\pi$
$464$	21.5121	0.998676
$465$	0	0
$466$	−13.9387	−0.645698
$467$	−25.9990	−1.20309	−0.601544	−	0.798839i	$-0.705448\pi$
$467$	−25.9990	−1.20309	−0.601544	+	0.798839i	$0.705448\pi$
$468$	4.48211	0.207185
$469$	8.54039	0.394359
$470$	0	0
$471$	16.1830	0.745673
$472$	19.0444	0.876588
$473$	3.87845	0.178331
$474$	2.23313	0.102571
$475$	0	0
$476$	7.68308	0.352153
$477$	−14.1000	−0.645596
$478$	−1.21742	−0.0556835
$479$	−26.6776	−1.21893	−0.609465	−	0.792813i	$-0.708616\pi$
$479$	−26.6776	−1.21893	−0.609465	+	0.792813i	$0.708616\pi$
$480$	0	0
$481$	30.8097	1.40480
$482$	−11.5180	−0.524629
$483$	−6.14824	−0.279755
$484$	17.3569	0.788948
$485$	0	0
$486$	0.563403	0.0255565
$487$	31.4219	1.42386	0.711931	−	0.702250i	$-0.247821\pi$
$487$	31.4219	1.42386	0.711931	+	0.702250i	$0.247821\pi$
$488$	8.65906	0.391977
$489$	−21.9173	−0.991132
$490$	0	0
$491$	17.2112	0.776729	0.388364	−	0.921506i	$-0.373040\pi$
$491$	17.2112	0.776729	0.388364	+	0.921506i	$0.373040\pi$
$492$	−4.91826	−0.221732
$493$	40.8298	1.83888
$494$	8.22448	0.370037
$495$	0	0
$496$	−20.4997	−0.920464
$497$	9.07783	0.407196
$498$	−5.37485	−0.240853
$499$	1.65982	0.0743038	0.0371519	−	0.999310i	$-0.488171\pi$
$499$	1.65982	0.0743038	0.0371519	+	0.999310i	$0.488171\pi$
$500$	0	0
$501$	6.21850	0.277822
$502$	−0.219815	−0.00981082
$503$	42.7711	1.90707	0.953535	−	0.301281i	$-0.0974143\pi$
$503$	42.7711	1.90707	0.953535	+	0.301281i	$0.0974143\pi$
$504$	2.27281	0.101239
$505$	0	0
$506$	2.61590	0.116291
$507$	−5.90399	−0.262205
$508$	−15.1488	−0.672120
$509$	−25.4205	−1.12675	−0.563373	−	0.826203i	$-0.690497\pi$
$509$	−25.4205	−1.12675	−0.563373	+	0.826203i	$0.690497\pi$
$510$	0	0
$511$	4.94873	0.218919
$512$	20.9441	0.925609
$513$	−5.48002	−0.241949
$514$	−1.06670	−0.0470501
$515$	0	0
$516$	−7.88844	−0.347269
$517$	−0.827260	−0.0363828
$518$	7.13823	0.313636
$519$	21.5574	0.946265
$520$	0	0
$521$	−5.18070	−0.226971	−0.113485	−	0.993540i	$-0.536201\pi$
$521$	−5.18070	−0.226971	−0.113485	+	0.993540i	$0.536201\pi$
$522$	5.51858	0.241542
$523$	−27.8382	−1.21728	−0.608640	−	0.793446i	$-0.708285\pi$
$523$	−27.8382	−1.21728	−0.608640	+	0.793446i	$0.708285\pi$
$524$	17.4140	0.760735
$525$	0	0
$526$	3.98426	0.173722
$527$	−38.9082	−1.69487
$528$	1.81684	0.0790680
$529$	8.50058	0.369590
$530$	0	0
$531$	−9.17901	−0.398335
$532$	−10.1006	−0.437918
$533$	−7.78653	−0.337272
$534$	2.74060	0.118598
$535$	0	0
$536$	16.1755	0.698675
$537$	6.83254	0.294846
$538$	−9.98595	−0.430525
$539$	−4.79810	−0.206669
$540$	0	0
$541$	29.8864	1.28492	0.642459	−	0.766320i	$-0.277914\pi$
$541$	29.8864	1.28492	0.642459	+	0.766320i	$0.277914\pi$
$542$	3.74848	0.161011
$543$	−17.9374	−0.769767
$544$	22.4548	0.962740
$545$	0	0
$546$	1.64406	0.0703593
$547$	−23.8418	−1.01940	−0.509702	−	0.860351i	$-0.670244\pi$
$547$	−23.8418	−1.01940	−0.509702	+	0.860351i	$0.670244\pi$
$548$	−20.5885	−0.879497
$549$	−4.17349	−0.178120
$550$	0	0
$551$	−53.6772	−2.28673
$552$	−11.6448	−0.495634
$553$	−4.34196	−0.184639
$554$	13.4796	0.572693
$555$	0	0
$556$	32.9047	1.39547
$557$	−6.69961	−0.283872	−0.141936	−	0.989876i	$-0.545333\pi$
$557$	−6.69961	−0.283872	−0.141936	+	0.989876i	$0.545333\pi$
$558$	−5.25886	−0.222625
$559$	−12.4889	−0.528223
$560$	0	0
$561$	3.44835	0.145589
$562$	10.0682	0.424701
$563$	10.0985	0.425602	0.212801	−	0.977096i	$-0.431741\pi$
$563$	10.0985	0.425602	0.212801	+	0.977096i	$0.431741\pi$
$564$	1.68258	0.0708493
$565$	0	0
$566$	−1.92670	−0.0809851
$567$	−1.09545	−0.0460045
$568$	17.1934	0.721419
$569$	6.61412	0.277278	0.138639	−	0.990343i	$-0.455727\pi$
$569$	6.61412	0.277278	0.138639	+	0.990343i	$0.455727\pi$
$570$	0	0
$571$	10.3604	0.433570	0.216785	−	0.976219i	$-0.430443\pi$
$571$	10.3604	0.433570	0.216785	+	0.976219i	$0.430443\pi$
$572$	3.70787	0.155034
$573$	5.55123	0.231906
$574$	−1.80404	−0.0752993
$575$	0	0
$576$	−1.35744	−0.0565599
$577$	−15.8028	−0.657878	−0.328939	−	0.944351i	$-0.606691\pi$
$577$	−15.8028	−0.657878	−0.328939	+	0.944351i	$0.606691\pi$
$578$	0.211573	0.00880028
$579$	15.1011	0.627579
$580$	0	0
$581$	10.4505	0.433561
$582$	−6.20248	−0.257101
$583$	−11.6644	−0.483089
$584$	9.37290	0.387853
$585$	0	0
$586$	3.03260	0.125276
$587$	−15.4746	−0.638706	−0.319353	−	0.947636i	$-0.603466\pi$
$587$	−15.4746	−0.638706	−0.319353	+	0.947636i	$0.603466\pi$
$588$	9.75894	0.402452
$589$	51.1510	2.10764
$590$	0	0
$591$	−3.61872	−0.148854
$592$	−25.4013	−1.04399
$593$	2.73740	0.112412	0.0562058	−	0.998419i	$-0.482100\pi$
$593$	2.73740	0.112412	0.0562058	+	0.998419i	$0.482100\pi$
$594$	0.466081	0.0191235
$595$	0	0
$596$	−31.6266	−1.29547
$597$	−22.2128	−0.909108
$598$	−8.42337	−0.344457
$599$	−17.8399	−0.728919	−0.364459	−	0.931219i	$-0.618746\pi$
$599$	−17.8399	−0.728919	−0.364459	+	0.931219i	$0.618746\pi$
$600$	0	0
$601$	−3.28995	−0.134200	−0.0670999	−	0.997746i	$-0.521375\pi$
$601$	−3.28995	−0.134200	−0.0670999	+	0.997746i	$0.521375\pi$
$602$	−2.89352	−0.117931
$603$	−7.79626	−0.317488
$604$	1.62571	0.0661491
$605$	0	0
$606$	−7.98468	−0.324355
$607$	11.8466	0.480839	0.240420	−	0.970669i	$-0.422715\pi$
$607$	11.8466	0.480839	0.240420	+	0.970669i	$0.422715\pi$
$608$	−29.5204	−1.19721
$609$	−10.7300	−0.434801
$610$	0	0
$611$	2.66383	0.107767
$612$	−7.01365	−0.283510
$613$	5.75653	0.232504	0.116252	−	0.993220i	$-0.462912\pi$
$613$	5.75653	0.232504	0.116252	+	0.993220i	$0.462912\pi$
$614$	2.00092	0.0807506
$615$	0	0
$616$	1.88020	0.0757555
$617$	−12.8509	−0.517357	−0.258678	−	0.965963i	$-0.583287\pi$
$617$	−12.8509	−0.517357	−0.258678	+	0.965963i	$0.583287\pi$
$618$	2.01922	0.0812249
$619$	19.5444	0.785556	0.392778	−	0.919633i	$-0.371514\pi$
$619$	19.5444	0.785556	0.392778	+	0.919633i	$0.371514\pi$
$620$	0	0
$621$	5.61254	0.225223
$622$	−2.53691	−0.101721
$623$	−5.32867	−0.213489
$624$	−5.85036	−0.234202
$625$	0	0
$626$	−2.08385	−0.0832873
$627$	−4.53340	−0.181047
$628$	−27.2291	−1.08656
$629$	−48.2113	−1.92231
$630$	0	0
$631$	−12.7472	−0.507458	−0.253729	−	0.967275i	$-0.581657\pi$
$631$	−12.7472	−0.507458	−0.253729	+	0.967275i	$0.581657\pi$
$632$	−8.22366	−0.327120
$633$	−11.9468	−0.474842
$634$	−1.84823	−0.0734026
$635$	0	0
$636$	23.7244	0.940733
$637$	15.4502	0.612160
$638$	4.56530	0.180742
$639$	−8.28687	−0.327823
$640$	0	0
$641$	0.803805	0.0317484	0.0158742	−	0.999874i	$-0.494947\pi$
$641$	0.803805	0.0317484	0.0158742	+	0.999874i	$0.494947\pi$
$642$	3.23534	0.127689
$643$	8.33857	0.328841	0.164421	−	0.986390i	$-0.447425\pi$
$643$	8.33857	0.328841	0.164421	+	0.986390i	$0.447425\pi$
$644$	10.3449	0.407646
$645$	0	0
$646$	−12.8698	−0.506354
$647$	28.4338	1.11785	0.558924	−	0.829219i	$-0.311214\pi$
$647$	28.4338	1.11785	0.558924	+	0.829219i	$0.311214\pi$
$648$	−2.07478	−0.0815049
$649$	−7.59342	−0.298068
$650$	0	0
$651$	10.2250	0.400750
$652$	36.8775	1.44423
$653$	−11.2194	−0.439049	−0.219524	−	0.975607i	$-0.570451\pi$
$653$	−11.2194	−0.439049	−0.219524	+	0.975607i	$0.570451\pi$
$654$	2.48440	0.0971479
$655$	0	0
$656$	6.41966	0.250646
$657$	−4.51755	−0.176246
$658$	0.617178	0.0240601
$659$	−34.8950	−1.35932	−0.679658	−	0.733529i	$-0.737872\pi$
$659$	−34.8950	−1.35932	−0.679658	+	0.733529i	$0.737872\pi$
$660$	0	0
$661$	−14.4847	−0.563391	−0.281696	−	0.959504i	$-0.590897\pi$
$661$	−14.4847	−0.563391	−0.281696	+	0.959504i	$0.590897\pi$
$662$	4.72878	0.183789
$663$	−11.1039	−0.431240
$664$	19.7933	0.768129
$665$	0	0
$666$	−6.51627	−0.252500
$667$	54.9752	2.12865
$668$	−10.4631	−0.404830
$669$	24.5415	0.948828
$670$	0	0
$671$	−3.45256	−0.133285
$672$	−5.90107	−0.227639
$673$	26.7669	1.03179	0.515895	−	0.856652i	$-0.327460\pi$
$673$	26.7669	1.03179	0.515895	+	0.856652i	$0.327460\pi$
$674$	10.4790	0.403635
$675$	0	0
$676$	9.93391	0.382073
$677$	−2.03471	−0.0782001	−0.0391001	−	0.999235i	$-0.512449\pi$
$677$	−2.03471	−0.0782001	−0.0391001	+	0.999235i	$0.512449\pi$
$678$	5.68030	0.218151
$679$	12.0597	0.462810
$680$	0	0
$681$	−25.7309	−0.986009
$682$	−4.35044	−0.166587
$683$	45.2365	1.73093	0.865463	−	0.500973i	$-0.167024\pi$
$683$	45.2365	1.73093	0.865463	+	0.500973i	$0.167024\pi$
$684$	9.22056	0.352557
$685$	0	0
$686$	7.89988	0.301619
$687$	21.3252	0.813608
$688$	10.2965	0.392552
$689$	37.5601	1.43093
$690$	0	0
$691$	21.5811	0.820985	0.410493	−	0.911864i	$-0.365357\pi$
$691$	21.5811	0.820985	0.410493	+	0.911864i	$0.365357\pi$
$692$	−36.2720	−1.37885
$693$	−0.906219	−0.0344244
$694$	1.99004	0.0755408
$695$	0	0
$696$	−20.3226	−0.770326
$697$	12.1844	0.461518
$698$	−13.7852	−0.521776
$699$	−24.7402	−0.935760
$700$	0	0
$701$	8.67792	0.327761	0.163880	−	0.986480i	$-0.447599\pi$
$701$	8.67792	0.327761	0.163880	+	0.986480i	$0.447599\pi$
$702$	−1.50081	−0.0566445
$703$	63.3814	2.39047
$704$	−1.12295	−0.0423229
$705$	0	0
$706$	−12.1658	−0.457866
$707$	15.5249	0.583875
$708$	15.4444	0.580435
$709$	−23.0562	−0.865894	−0.432947	−	0.901419i	$-0.642526\pi$
$709$	−23.0562	−0.865894	−0.432947	+	0.901419i	$0.642526\pi$
$710$	0	0
$711$	3.96364	0.148648
$712$	−10.0925	−0.378232
$713$	−52.3880	−1.96194
$714$	−2.57264	−0.0962788
$715$	0	0
$716$	−11.4963	−0.429636
$717$	−2.16083	−0.0806978
$718$	5.66314	0.211346
$719$	32.5449	1.21372	0.606860	−	0.794808i	$-0.292429\pi$
$719$	32.5449	1.21372	0.606860	+	0.794808i	$0.292429\pi$
$720$	0	0
$721$	−3.92605	−0.146214
$722$	6.21469	0.231287
$723$	−20.4436	−0.760304
$724$	30.1810	1.12167
$725$	0	0
$726$	−5.81186	−0.215699
$727$	8.28803	0.307386	0.153693	−	0.988119i	$-0.450883\pi$
$727$	8.28803	0.307386	0.153693	+	0.988119i	$0.450883\pi$
$728$	−6.05438	−0.224390
$729$	1.00000	0.0370370
$730$	0	0
$731$	19.5427	0.722814
$732$	7.02222	0.259549
$733$	−18.0925	−0.668261	−0.334130	−	0.942527i	$-0.608443\pi$
$733$	−18.0925	−0.668261	−0.334130	+	0.942527i	$0.608443\pi$
$734$	−4.42387	−0.163288
$735$	0	0
$736$	30.2342	1.11445
$737$	−6.44953	−0.237572
$738$	1.64686	0.0606216
$739$	−28.6295	−1.05315	−0.526577	−	0.850127i	$-0.676525\pi$
$739$	−28.6295	−1.05315	−0.526577	+	0.850127i	$0.676525\pi$
$740$	0	0
$741$	14.5979	0.536266
$742$	8.70223	0.319469
$743$	−5.07215	−0.186079	−0.0930396	−	0.995662i	$-0.529658\pi$
$743$	−5.07215	−0.186079	−0.0930396	+	0.995662i	$0.529658\pi$
$744$	19.3662	0.709998
$745$	0	0
$746$	4.95652	0.181471
$747$	−9.53997	−0.349049
$748$	−5.80211	−0.212146
$749$	−6.29061	−0.229854
$750$	0	0
$751$	−45.8043	−1.67142	−0.835711	−	0.549169i	$-0.814944\pi$
$751$	−45.8043	−1.67142	−0.835711	+	0.549169i	$0.814944\pi$
$752$	−2.19622	−0.0800879
$753$	−0.390156	−0.0142181
$754$	−14.7006	−0.535363
$755$	0	0
$756$	1.84317	0.0670356
$757$	−15.3439	−0.557682	−0.278841	−	0.960337i	$-0.589950\pi$
$757$	−15.3439	−0.557682	−0.278841	+	0.960337i	$0.589950\pi$
$758$	−5.16959	−0.187768
$759$	4.64303	0.168531
$760$	0	0
$761$	−12.2071	−0.442507	−0.221253	−	0.975216i	$-0.571015\pi$
$761$	−12.2071	−0.442507	−0.221253	+	0.975216i	$0.571015\pi$
$762$	5.07251	0.183758
$763$	−4.83052	−0.174877
$764$	−9.34037	−0.337923
$765$	0	0
$766$	11.9327	0.431146
$767$	24.4513	0.882887
$768$	−3.78601	−0.136616
$769$	15.1932	0.547881	0.273941	−	0.961747i	$-0.411673\pi$
$769$	15.1932	0.547881	0.273941	+	0.961747i	$0.411673\pi$
$770$	0	0
$771$	−1.89331	−0.0681860
$772$	−25.4087	−0.914480
$773$	−0.293600	−0.0105601	−0.00528003	−	0.999986i	$-0.501681\pi$
$773$	−0.293600	−0.0105601	−0.00528003	+	0.999986i	$0.501681\pi$
$774$	2.64141	0.0949434
$775$	0	0
$776$	22.8411	0.819948
$777$	12.6698	0.454528
$778$	−4.80957	−0.172431
$779$	−16.0184	−0.573918
$780$	0	0
$781$	−6.85539	−0.245305
$782$	13.1810	0.471351
$783$	9.79508	0.350047
$784$	−12.7381	−0.454931
$785$	0	0
$786$	−5.83101	−0.207985
$787$	−10.4754	−0.373406	−0.186703	−	0.982416i	$-0.559780\pi$
$787$	−10.4754	−0.373406	−0.186703	+	0.982416i	$0.559780\pi$
$788$	6.08878	0.216904
$789$	7.07178	0.251762
$790$	0	0
$791$	−11.0444	−0.392695
$792$	−1.71638	−0.0609888
$793$	11.1175	0.394794
$794$	8.36548	0.296880
$795$	0	0
$796$	37.3747	1.32471
$797$	−1.34051	−0.0474834	−0.0237417	−	0.999718i	$-0.507558\pi$
$797$	−1.34051	−0.0474834	−0.0237417	+	0.999718i	$0.507558\pi$
$798$	3.38215	0.119727
$799$	−4.16840	−0.147467
$800$	0	0
$801$	4.86438	0.171874
$802$	−11.8763	−0.419366
$803$	−3.73718	−0.131882
$804$	13.1178	0.462629
$805$	0	0
$806$	14.0087	0.493436
$807$	−17.7243	−0.623926
$808$	29.4042	1.03444
$809$	17.6060	0.618995	0.309497	−	0.950900i	$-0.399839\pi$
$809$	17.6060	0.618995	0.309497	+	0.950900i	$0.399839\pi$
$810$	0	0
$811$	−4.49647	−0.157892	−0.0789462	−	0.996879i	$-0.525156\pi$
$811$	−4.49647	−0.157892	−0.0789462	+	0.996879i	$0.525156\pi$
$812$	18.0540	0.633572
$813$	6.65328	0.233341
$814$	−5.39064	−0.188942
$815$	0	0
$816$	9.15471	0.320479
$817$	−25.6920	−0.898850
$818$	−19.6663	−0.687617
$819$	2.91809	0.101966
$820$	0	0
$821$	3.11503	0.108715	0.0543577	−	0.998522i	$-0.482689\pi$
$821$	3.11503	0.108715	0.0543577	+	0.998522i	$0.482689\pi$
$822$	6.89397	0.240455
$823$	3.47107	0.120994	0.0604969	−	0.998168i	$-0.480731\pi$
$823$	3.47107	0.120994	0.0604969	+	0.998168i	$0.480731\pi$
$824$	−7.43593	−0.259043
$825$	0	0
$826$	5.66508	0.197113
$827$	29.3453	1.02044	0.510218	−	0.860045i	$-0.329565\pi$
$827$	29.3453	1.02044	0.510218	+	0.860045i	$0.329565\pi$
$828$	−9.44353	−0.328185
$829$	−36.2932	−1.26051	−0.630257	−	0.776387i	$-0.717051\pi$
$829$	−36.2932	−1.26051	−0.630257	+	0.776387i	$0.717051\pi$
$830$	0	0
$831$	23.9253	0.829960
$832$	3.61599	0.125362
$833$	−24.1767	−0.837672
$834$	−11.0180	−0.381521
$835$	0	0
$836$	7.62779	0.263813
$837$	−9.33410	−0.322634
$838$	−3.57149	−0.123375
$839$	49.6379	1.71369	0.856845	−	0.515573i	$-0.172421\pi$
$839$	49.6379	1.71369	0.856845	+	0.515573i	$0.172421\pi$
$840$	0	0
$841$	66.9435	2.30840
$842$	−4.32780	−0.149146
$843$	17.8703	0.615486
$844$	20.1014	0.691918
$845$	0	0
$846$	−0.563403	−0.0193702
$847$	11.3002	0.388281
$848$	−30.9667	−1.06340
$849$	−3.41975	−0.117365
$850$	0	0
$851$	−64.9141	−2.22523
$852$	13.9433	0.477689
$853$	−19.4164	−0.664806	−0.332403	−	0.943137i	$-0.607859\pi$
$853$	−19.4164	−0.664806	−0.332403	+	0.943137i	$0.607859\pi$
$854$	2.57579	0.0881417
$855$	0	0
$856$	−11.9144	−0.407226
$857$	−17.3396	−0.592309	−0.296155	−	0.955140i	$-0.595704\pi$
$857$	−17.3396	−0.592309	−0.296155	+	0.955140i	$0.595704\pi$
$858$	−1.24156	−0.0423862
$859$	21.6547	0.738849	0.369424	−	0.929261i	$-0.379555\pi$
$859$	21.6547	0.738849	0.369424	+	0.929261i	$0.379555\pi$
$860$	0	0
$861$	−3.20205	−0.109126
$862$	18.6951	0.636757
$863$	−31.9883	−1.08890	−0.544448	−	0.838795i	$-0.683261\pi$
$863$	−31.9883	−1.08890	−0.544448	+	0.838795i	$0.683261\pi$
$864$	5.38691	0.183266
$865$	0	0
$866$	20.3155	0.690347
$867$	0.375527	0.0127536
$868$	−17.2044	−0.583954
$869$	3.27896	0.111231
$870$	0	0
$871$	20.7679	0.703695
$872$	−9.14901	−0.309824
$873$	−11.0089	−0.372596
$874$	−17.3285	−0.586145
$875$	0	0
$876$	7.60112	0.256818
$877$	36.2859	1.22529	0.612644	−	0.790359i	$-0.290106\pi$
$877$	36.2859	1.22529	0.612644	+	0.790359i	$0.290106\pi$
$878$	−5.82391	−0.196547
$879$	5.38265	0.181552
$880$	0	0
$881$	28.0052	0.943521	0.471760	−	0.881727i	$-0.343619\pi$
$881$	28.0052	0.943521	0.471760	+	0.881727i	$0.343619\pi$
$882$	−3.26774	−0.110030
$883$	25.8366	0.869470	0.434735	−	0.900559i	$-0.356842\pi$
$883$	25.8366	0.869470	0.434735	+	0.900559i	$0.356842\pi$
$884$	18.6832	0.628384
$885$	0	0
$886$	7.89870	0.265362
$887$	−16.9851	−0.570302	−0.285151	−	0.958483i	$-0.592044\pi$
$887$	−16.9851	−0.570302	−0.285151	+	0.958483i	$0.592044\pi$
$888$	23.9967	0.805275
$889$	−9.86269	−0.330784
$890$	0	0
$891$	0.827260	0.0277142
$892$	−41.2929	−1.38259
$893$	5.48002	0.183382
$894$	10.5900	0.354183
$895$	0	0
$896$	12.6399	0.422270
$897$	−14.9509	−0.499195
$898$	18.4810	0.616719
$899$	−91.4282	−3.04930
$900$	0	0
$901$	−58.7745	−1.95806
$902$	1.36238	0.0453622
$903$	−5.13579	−0.170908
$904$	−20.9181	−0.695727
$905$	0	0
$906$	−0.544361	−0.0180852
$907$	−22.4397	−0.745098	−0.372549	−	0.928013i	$-0.621516\pi$
$907$	−22.4397	−0.745098	−0.372549	+	0.928013i	$0.621516\pi$
$908$	43.2942	1.43677
$909$	−14.1722	−0.470063
$910$	0	0
$911$	10.7645	0.356643	0.178322	−	0.983972i	$-0.442933\pi$
$911$	10.7645	0.356643	0.178322	+	0.983972i	$0.442933\pi$
$912$	−12.0353	−0.398529
$913$	−7.89204	−0.261188
$914$	16.9261	0.559866
$915$	0	0
$916$	−35.8813	−1.18555
$917$	11.3375	0.374396
$918$	2.34849	0.0775116
$919$	−35.5614	−1.17306	−0.586531	−	0.809927i	$-0.699507\pi$
$919$	−35.5614	−1.17306	−0.586531	+	0.809927i	$0.699507\pi$
$920$	0	0
$921$	3.55149	0.117026
$922$	9.15881	0.301629
$923$	22.0748	0.726602
$924$	1.52478	0.0501617
$925$	0	0
$926$	−23.8537	−0.783882
$927$	3.58397	0.117713
$928$	52.7652	1.73210
$929$	−21.3940	−0.701914	−0.350957	−	0.936392i	$-0.614144\pi$
$929$	−21.3940	−0.701914	−0.350957	+	0.936392i	$0.614144\pi$
$930$	0	0
$931$	31.7841	1.04168
$932$	41.6273	1.36355
$933$	−4.50283	−0.147416
$934$	−14.6479	−0.479294
$935$	0	0
$936$	5.52686	0.180651
$937$	−48.9582	−1.59939	−0.799697	−	0.600403i	$-0.795007\pi$
$937$	−48.9582	−1.59939	−0.799697	+	0.600403i	$0.795007\pi$
$938$	4.81168	0.157107
$939$	−3.69868	−0.120702
$940$	0	0
$941$	31.1716	1.01616	0.508082	−	0.861308i	$-0.330355\pi$
$941$	31.1716	1.01616	0.508082	+	0.861308i	$0.330355\pi$
$942$	9.11755	0.297066
$943$	16.4057	0.534244
$944$	−20.1591	−0.656123
$945$	0	0
$946$	2.18513	0.0710447
$947$	−50.5561	−1.64285	−0.821426	−	0.570315i	$-0.806821\pi$
$947$	−50.5561	−1.64285	−0.821426	+	0.570315i	$0.806821\pi$
$948$	−6.66913	−0.216603
$949$	12.0340	0.390640
$950$	0	0
$951$	−3.28048	−0.106377
$952$	9.47396	0.307053
$953$	−4.40600	−0.142724	−0.0713622	−	0.997450i	$-0.522735\pi$
$953$	−4.40600	−0.142724	−0.0713622	+	0.997450i	$0.522735\pi$
$954$	−7.94400	−0.257196
$955$	0	0
$956$	3.63577	0.117589
$957$	8.10307	0.261935
$958$	−15.0302	−0.485605
$959$	−13.4042	−0.432845
$960$	0	0
$961$	56.1253	1.81049
$962$	17.3583	0.559653
$963$	5.74250	0.185050
$964$	34.3979	1.10788
$965$	0	0
$966$	−3.46394	−0.111450
$967$	−26.3386	−0.846991	−0.423496	−	0.905898i	$-0.639197\pi$
$967$	−26.3386	−0.846991	−0.423496	+	0.905898i	$0.639197\pi$
$968$	21.4026	0.687907
$969$	−22.8429	−0.733820
$970$	0	0
$971$	−8.23271	−0.264200	−0.132100	−	0.991236i	$-0.542172\pi$
$971$	−8.23271	−0.264200	−0.132100	+	0.991236i	$0.542172\pi$
$972$	−1.68258	−0.0539687
$973$	21.4227	0.686780
$974$	17.7032	0.567247
$975$	0	0
$976$	−9.16590	−0.293393
$977$	58.7794	1.88052	0.940260	−	0.340457i	$-0.110582\pi$
$977$	58.7794	1.88052	0.940260	+	0.340457i	$0.110582\pi$
$978$	−12.3482	−0.394853
$979$	4.02410	0.128611
$980$	0	0
$981$	4.40964	0.140789
$982$	9.69682	0.309438
$983$	−31.6109	−1.00823	−0.504115	−	0.863637i	$-0.668181\pi$
$983$	−31.6109	−1.00823	−0.504115	+	0.863637i	$0.668181\pi$
$984$	−6.06468	−0.193335
$985$	0	0
$986$	23.0036	0.732584
$987$	1.09545	0.0348685
$988$	−24.5620	−0.781422
$989$	26.3133	0.836714
$990$	0	0
$991$	−11.0823	−0.352040	−0.176020	−	0.984387i	$-0.556322\pi$
$991$	−11.0823	−0.352040	−0.176020	+	0.984387i	$0.556322\pi$
$992$	−50.2819	−1.59645
$993$	8.39325	0.266352
$994$	5.11448	0.162221
$995$	0	0
$996$	16.0517	0.508619
$997$	0.0286076	0.000906010 0	0.000453005	−	1.00000i	$-0.499856\pi$
$997$	0.0286076	0.000906010 0	0.000453005		1.00000i	$0.499856\pi$
$998$	0.935149	0.0296016
$999$	−11.5659	−0.365929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.7		10
5.2	odd	4		705.2.c.b.424.12	yes	20
5.3	odd	4		705.2.c.b.424.9	✓	20
5.4	even	2		3525.2.a.bg.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.9	✓	20	5.3	odd	4
705.2.c.b.424.12	yes	20	5.2	odd	4
3525.2.a.bf.1.7		10	1.1	even	1	trivial
3525.2.a.bg.1.4		10	5.4	even	2

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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.563403 q^{2} +1.00000 q^{3} -1.68258 q^{4} +0.563403 q^{6} -1.09545 q^{7} -2.07478 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.563403 q^{2} +1.00000 q^{3} -1.68258 q^{4} +0.563403 q^{6} -1.09545 q^{7} -2.07478 q^{8} +1.00000 q^{9} +0.827260 q^{11} -1.68258 q^{12} -2.66383 q^{13} -0.617178 q^{14} +2.19622 q^{16} +4.16840 q^{17} +0.563403 q^{18} -5.48002 q^{19} -1.09545 q^{21} +0.466081 q^{22} +5.61254 q^{23} -2.07478 q^{24} -1.50081 q^{26} +1.00000 q^{27} +1.84317 q^{28} +9.79508 q^{29} -9.33410 q^{31} +5.38691 q^{32} +0.827260 q^{33} +2.34849 q^{34} -1.68258 q^{36} -11.5659 q^{37} -3.08746 q^{38} -2.66383 q^{39} +2.92305 q^{41} -0.617178 q^{42} +4.68831 q^{43} -1.39193 q^{44} +3.16212 q^{46} -1.00000 q^{47} +2.19622 q^{48} -5.80000 q^{49} +4.16840 q^{51} +4.48211 q^{52} -14.1000 q^{53} +0.563403 q^{54} +2.27281 q^{56} -5.48002 q^{57} +5.51858 q^{58} -9.17901 q^{59} -4.17349 q^{61} -5.25886 q^{62} -1.09545 q^{63} -1.35744 q^{64} +0.466081 q^{66} -7.79626 q^{67} -7.01365 q^{68} +5.61254 q^{69} -8.28687 q^{71} -2.07478 q^{72} -4.51755 q^{73} -6.51627 q^{74} +9.22056 q^{76} -0.906219 q^{77} -1.50081 q^{78} +3.96364 q^{79} +1.00000 q^{81} +1.64686 q^{82} -9.53997 q^{83} +1.84317 q^{84} +2.64141 q^{86} +9.79508 q^{87} -1.71638 q^{88} +4.86438 q^{89} +2.91809 q^{91} -9.44353 q^{92} -9.33410 q^{93} -0.563403 q^{94} +5.38691 q^{96} -11.0089 q^{97} -3.26774 q^{98} +0.827260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

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