LMFDB - Embedded newform 825.4.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.23612.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 20x + 26 $ x^3 - x^2 - 20*x + 26
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.32906$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.32906 q^{2} +3.00000 q^{3} -2.57547 q^{4} +6.98719 q^{6} -22.4672 q^{7} -24.6309 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.32906 q^{2} +3.00000 q^{3} -2.57547 q^{4} +6.98719 q^{6} -22.4672 q^{7} -24.6309 q^{8} +9.00000 q^{9} +11.0000 q^{11} -7.72640 q^{12} +9.86030 q^{13} -52.3275 q^{14} -36.7633 q^{16} +128.137 q^{17} +20.9616 q^{18} +7.04001 q^{19} -67.4015 q^{21} +25.6197 q^{22} -0.654969 q^{23} -73.8928 q^{24} +22.9653 q^{26} +27.0000 q^{27} +57.8635 q^{28} -229.279 q^{29} +155.789 q^{31} +111.423 q^{32} +33.0000 q^{33} +298.438 q^{34} -23.1792 q^{36} +110.279 q^{37} +16.3966 q^{38} +29.5809 q^{39} +154.749 q^{41} -156.982 q^{42} +401.014 q^{43} -28.3301 q^{44} -1.52546 q^{46} +277.532 q^{47} -110.290 q^{48} +161.774 q^{49} +384.410 q^{51} -25.3949 q^{52} +651.566 q^{53} +62.8847 q^{54} +553.388 q^{56} +21.1200 q^{57} -534.005 q^{58} -423.869 q^{59} +681.851 q^{61} +362.842 q^{62} -202.205 q^{63} +553.618 q^{64} +76.8591 q^{66} -374.028 q^{67} -330.011 q^{68} -1.96491 q^{69} +96.6950 q^{71} -221.678 q^{72} +19.9460 q^{73} +256.848 q^{74} -18.1313 q^{76} -247.139 q^{77} +68.8958 q^{78} +24.4286 q^{79} +81.0000 q^{81} +360.419 q^{82} +1127.35 q^{83} +173.590 q^{84} +933.987 q^{86} -687.836 q^{87} -270.940 q^{88} -639.624 q^{89} -221.533 q^{91} +1.68685 q^{92} +467.366 q^{93} +646.389 q^{94} +334.270 q^{96} +730.865 q^{97} +376.783 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} + 9 q^{3} + 22 q^{4} + 12 q^{6} + 4 q^{7} + 48 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 4 * q^2 + 9 * q^3 + 22 * q^4 + 12 * q^6 + 4 * q^7 + 48 * q^8 + 27 * q^9	$ 3 q + 4 q^{2} + 9 q^{3} + 22 q^{4} + 12 q^{6} + 4 q^{7} + 48 q^{8} + 27 q^{9} + 33 q^{11} + 66 q^{12} - 56 q^{14} + 50 q^{16} + 218 q^{17} + 36 q^{18} + 146 q^{19} + 12 q^{21} + 44 q^{22} + 200 q^{23} + 144 q^{24} - 508 q^{26} + 81 q^{27} + 340 q^{28} + 68 q^{29} - 68 q^{31} + 688 q^{32} + 99 q^{33} - 176 q^{34} + 198 q^{36} + 390 q^{37} + 316 q^{38} - 196 q^{41} - 168 q^{42} + 524 q^{43} + 242 q^{44} + 1160 q^{46} + 60 q^{47} + 150 q^{48} - 157 q^{49} + 654 q^{51} - 1020 q^{52} + 158 q^{53} + 108 q^{54} + 1368 q^{56} + 438 q^{57} - 1092 q^{58} - 1044 q^{59} + 642 q^{61} - 88 q^{62} + 36 q^{63} + 1166 q^{64} + 132 q^{66} + 236 q^{67} - 144 q^{68} + 600 q^{69} - 544 q^{71} + 432 q^{72} - 900 q^{73} + 1536 q^{74} + 1996 q^{76} + 44 q^{77} - 1524 q^{78} - 1586 q^{79} + 243 q^{81} - 380 q^{82} + 1582 q^{83} + 1020 q^{84} + 3568 q^{86} + 204 q^{87} + 528 q^{88} - 2122 q^{89} - 8 q^{91} + 4128 q^{92} - 204 q^{93} - 2152 q^{94} + 2064 q^{96} - 618 q^{97} - 572 q^{98} + 297 q^{99}+O(q^{100}) $ 3 * q + 4 * q^2 + 9 * q^3 + 22 * q^4 + 12 * q^6 + 4 * q^7 + 48 * q^8 + 27 * q^9 + 33 * q^11 + 66 * q^12 - 56 * q^14 + 50 * q^16 + 218 * q^17 + 36 * q^18 + 146 * q^19 + 12 * q^21 + 44 * q^22 + 200 * q^23 + 144 * q^24 - 508 * q^26 + 81 * q^27 + 340 * q^28 + 68 * q^29 - 68 * q^31 + 688 * q^32 + 99 * q^33 - 176 * q^34 + 198 * q^36 + 390 * q^37 + 316 * q^38 - 196 * q^41 - 168 * q^42 + 524 * q^43 + 242 * q^44 + 1160 * q^46 + 60 * q^47 + 150 * q^48 - 157 * q^49 + 654 * q^51 - 1020 * q^52 + 158 * q^53 + 108 * q^54 + 1368 * q^56 + 438 * q^57 - 1092 * q^58 - 1044 * q^59 + 642 * q^61 - 88 * q^62 + 36 * q^63 + 1166 * q^64 + 132 * q^66 + 236 * q^67 - 144 * q^68 + 600 * q^69 - 544 * q^71 + 432 * q^72 - 900 * q^73 + 1536 * q^74 + 1996 * q^76 + 44 * q^77 - 1524 * q^78 - 1586 * q^79 + 243 * q^81 - 380 * q^82 + 1582 * q^83 + 1020 * q^84 + 3568 * q^86 + 204 * q^87 + 528 * q^88 - 2122 * q^89 - 8 * q^91 + 4128 * q^92 - 204 * q^93 - 2152 * q^94 + 2064 * q^96 - 618 * q^97 - 572 * q^98 + 297 * 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 $

$2$	2.32906	0.823448	0.411724	−	0.911309i	$-0.364927\pi$
$2$	2.32906	0.823448	0.411724	+	0.911309i	$0.364927\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.57547	−0.321933
$5$	0	0
$5$	0	0
$6$	6.98719	0.475418
$7$	−22.4672	−1.21311	−0.606557	−	0.795040i	$-0.707450\pi$
$7$	−22.4672	−1.21311	−0.606557	+	0.795040i	$0.707450\pi$
$8$	−24.6309	−1.08854
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−7.72640	−0.185868
$13$	9.86030	0.210366	0.105183	−	0.994453i	$-0.466457\pi$
$13$	9.86030	0.210366	0.105183	+	0.994453i	$0.466457\pi$
$14$	−52.3275	−0.998936
$15$	0	0
$16$	−36.7633	−0.574426
$17$	128.137	1.82810	0.914049	−	0.405603i	$-0.132938\pi$
$17$	128.137	1.82810	0.914049	+	0.405603i	$0.132938\pi$
$18$	20.9616	0.274483
$19$	7.04001	0.0850047	0.0425024	−	0.999096i	$-0.486467\pi$
$19$	7.04001	0.0850047	0.0425024	+	0.999096i	$0.486467\pi$
$20$	0	0
$21$	−67.4015	−0.700392
$22$	25.6197	0.248279
$23$	−0.654969	−0.00593785	−0.00296892	−	0.999996i	$-0.500945\pi$
$23$	−0.654969	−0.00593785	−0.00296892	+	0.999996i	$0.500945\pi$
$24$	−73.8928	−0.628471
$25$	0	0
$26$	22.9653	0.173225
$27$	27.0000	0.192450
$28$	57.8635	0.390542
$29$	−229.279	−1.46814	−0.734069	−	0.679075i	$-0.762381\pi$
$29$	−229.279	−1.46814	−0.734069	+	0.679075i	$0.762381\pi$
$30$	0	0
$31$	155.789	0.902596	0.451298	−	0.892373i	$-0.350961\pi$
$31$	155.789	0.902596	0.451298	+	0.892373i	$0.350961\pi$
$32$	111.423	0.615534
$33$	33.0000	0.174078
$34$	298.438	1.50534
$35$	0	0
$36$	−23.1792	−0.107311
$37$	110.279	0.489995	0.244998	−	0.969524i	$-0.421213\pi$
$37$	110.279	0.489995	0.244998	+	0.969524i	$0.421213\pi$
$38$	16.3966	0.0699970
$39$	29.5809	0.121455
$40$	0	0
$41$	154.749	0.589456	0.294728	−	0.955581i	$-0.404771\pi$
$41$	154.749	0.589456	0.294728	+	0.955581i	$0.404771\pi$
$42$	−156.982	−0.576736
$43$	401.014	1.42219	0.711094	−	0.703097i	$-0.248200\pi$
$43$	401.014	1.42219	0.711094	+	0.703097i	$0.248200\pi$
$44$	−28.3301	−0.0970665
$45$	0	0
$46$	−1.52546	−0.00488951
$47$	277.532	0.861323	0.430661	−	0.902514i	$-0.358280\pi$
$47$	277.532	0.861323	0.430661	+	0.902514i	$0.358280\pi$
$48$	−110.290	−0.331645
$49$	161.774	0.471645
$50$	0	0
$51$	384.410	1.05545
$52$	−25.3949	−0.0677237
$53$	651.566	1.68867	0.844334	−	0.535817i	$-0.179996\pi$
$53$	651.566	1.68867	0.844334	+	0.535817i	$0.179996\pi$
$54$	62.8847	0.158473
$55$	0	0
$56$	553.388	1.32053
$57$	21.1200	0.0490775
$58$	−534.005	−1.20894
$59$	−423.869	−0.935307	−0.467653	−	0.883912i	$-0.654900\pi$
$59$	−423.869	−0.935307	−0.467653	+	0.883912i	$0.654900\pi$
$60$	0	0
$61$	681.851	1.43118	0.715590	−	0.698520i	$-0.246158\pi$
$61$	681.851	1.43118	0.715590	+	0.698520i	$0.246158\pi$
$62$	362.842	0.743241
$63$	−202.205	−0.404371
$64$	553.618	1.08129
$65$	0	0
$66$	76.8591	0.143344
$67$	−374.028	−0.682012	−0.341006	−	0.940061i	$-0.610768\pi$
$67$	−374.028	−0.682012	−0.341006	+	0.940061i	$0.610768\pi$
$68$	−330.011	−0.588526
$69$	−1.96491	−0.00342822
$70$	0	0
$71$	96.6950	0.161628	0.0808140	−	0.996729i	$-0.474248\pi$
$71$	96.6950	0.161628	0.0808140	+	0.996729i	$0.474248\pi$
$72$	−221.678	−0.362848
$73$	19.9460	0.0319795	0.0159897	−	0.999872i	$-0.494910\pi$
$73$	19.9460	0.0319795	0.0159897	+	0.999872i	$0.494910\pi$
$74$	256.848	0.403486
$75$	0	0
$76$	−18.1313	−0.0273658
$77$	−247.139	−0.365768
$78$	68.8958	0.100012
$79$	24.4286	0.0347903	0.0173951	−	0.999849i	$-0.494463\pi$
$79$	24.4286	0.0347903	0.0173951	+	0.999849i	$0.494463\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	360.419	0.485386
$83$	1127.35	1.49088	0.745439	−	0.666574i	$-0.232240\pi$
$83$	1127.35	1.49088	0.745439	+	0.666574i	$0.232240\pi$
$84$	173.590	0.225479
$85$	0	0
$86$	933.987	1.17110
$87$	−687.836	−0.847630
$88$	−270.940	−0.328208
$89$	−639.624	−0.761798	−0.380899	−	0.924617i	$-0.624385\pi$
$89$	−639.624	−0.761798	−0.380899	+	0.924617i	$0.624385\pi$
$90$	0	0
$91$	−221.533	−0.255198
$92$	1.68685	0.00191159
$93$	467.366	0.521114
$94$	646.389	0.709255
$95$	0	0
$96$	334.270	0.355378
$97$	730.865	0.765032	0.382516	−	0.923949i	$-0.375058\pi$
$97$	730.865	0.765032	0.382516	+	0.923949i	$0.375058\pi$
$98$	376.783	0.388375
$99$	99.0000	0.100504
$100$	0	0
$101$	−810.342	−0.798337	−0.399168	−	0.916878i	$-0.630701\pi$
$101$	−810.342	−0.798337	−0.399168	+	0.916878i	$0.630701\pi$
$102$	895.314	0.869111
$103$	1461.89	1.39849	0.699245	−	0.714882i	$-0.253520\pi$
$103$	1461.89	1.39849	0.699245	+	0.714882i	$0.253520\pi$
$104$	−242.868	−0.228992
$105$	0	0
$106$	1517.54	1.39053
$107$	−1690.40	−1.52726	−0.763630	−	0.645654i	$-0.776585\pi$
$107$	−1690.40	−1.52726	−0.763630	+	0.645654i	$0.776585\pi$
$108$	−69.5376	−0.0619561
$109$	−1409.41	−1.23851	−0.619254	−	0.785190i	$-0.712565\pi$
$109$	−1409.41	−1.23851	−0.619254	+	0.785190i	$0.712565\pi$
$110$	0	0
$111$	330.838	0.282899
$112$	825.967	0.696844
$113$	−2185.67	−1.81956	−0.909780	−	0.415090i	$-0.863750\pi$
$113$	−2185.67	−1.81956	−0.909780	+	0.415090i	$0.863750\pi$
$114$	49.1899	0.0404128
$115$	0	0
$116$	590.499	0.472642
$117$	88.7427	0.0701219
$118$	−987.219	−0.770177
$119$	−2878.87	−2.21769
$120$	0	0
$121$	121.000	0.0909091
$122$	1588.07	1.17850
$123$	464.246	0.340322
$124$	−401.228	−0.290576
$125$	0	0
$126$	−470.947	−0.332979
$127$	1918.85	1.34071	0.670357	−	0.742038i	$-0.266141\pi$
$127$	1918.85	1.34071	0.670357	+	0.742038i	$0.266141\pi$
$128$	398.024	0.274849
$129$	1203.04	0.821100
$130$	0	0
$131$	1339.41	0.893320	0.446660	−	0.894704i	$-0.352613\pi$
$131$	1339.41	0.893320	0.446660	+	0.894704i	$0.352613\pi$
$132$	−84.9904	−0.0560414
$133$	−158.169	−0.103120
$134$	−871.135	−0.561602
$135$	0	0
$136$	−3156.12	−1.98996
$137$	1100.56	0.686330	0.343165	−	0.939275i	$-0.388501\pi$
$137$	1100.56	0.686330	0.343165	+	0.939275i	$0.388501\pi$
$138$	−4.57639	−0.00282296
$139$	−1284.51	−0.783819	−0.391910	−	0.920004i	$-0.628185\pi$
$139$	−1284.51	−0.783819	−0.391910	+	0.920004i	$0.628185\pi$
$140$	0	0
$141$	832.595	0.497285
$142$	225.209	0.133092
$143$	108.463	0.0634277
$144$	−330.869	−0.191475
$145$	0	0
$146$	46.4554	0.0263334
$147$	485.323	0.272305
$148$	−284.021	−0.157746
$149$	1277.21	0.702236	0.351118	−	0.936331i	$-0.385802\pi$
$149$	1277.21	0.702236	0.351118	+	0.936331i	$0.385802\pi$
$150$	0	0
$151$	886.317	0.477665	0.238833	−	0.971061i	$-0.423235\pi$
$151$	886.317	0.477665	0.238833	+	0.971061i	$0.423235\pi$
$152$	−173.402	−0.0925313
$153$	1153.23	0.609366
$154$	−575.602	−0.301191
$155$	0	0
$156$	−76.1846	−0.0391003
$157$	1681.12	0.854575	0.427288	−	0.904116i	$-0.359469\pi$
$157$	1681.12	0.854575	0.427288	+	0.904116i	$0.359469\pi$
$158$	56.8958	0.0286480
$159$	1954.70	0.974953
$160$	0	0
$161$	14.7153	0.00720329
$162$	188.654	0.0914942
$163$	622.100	0.298937	0.149468	−	0.988767i	$-0.452244\pi$
$163$	622.100	0.298937	0.149468	+	0.988767i	$0.452244\pi$
$164$	−398.550	−0.189765
$165$	0	0
$166$	2625.67	1.22766
$167$	2611.82	1.21023	0.605115	−	0.796138i	$-0.293127\pi$
$167$	2611.82	1.21023	0.605115	+	0.796138i	$0.293127\pi$
$168$	1660.16	0.762407
$169$	−2099.77	−0.955746
$170$	0	0
$171$	63.3601	0.0283349
$172$	−1032.80	−0.457849
$173$	−2342.97	−1.02967	−0.514835	−	0.857290i	$-0.672147\pi$
$173$	−2342.97	−1.02967	−0.514835	+	0.857290i	$0.672147\pi$
$174$	−1602.01	−0.697979
$175$	0	0
$176$	−404.396	−0.173196
$177$	−1271.61	−0.540000
$178$	−1489.72	−0.627301
$179$	1314.75	0.548991	0.274495	−	0.961588i	$-0.411489\pi$
$179$	1314.75	0.548991	0.274495	+	0.961588i	$0.411489\pi$
$180$	0	0
$181$	8.69006	0.00356866	0.00178433	−	0.999998i	$-0.499432\pi$
$181$	8.69006	0.00356866	0.00178433	+	0.999998i	$0.499432\pi$
$182$	−515.965	−0.210142
$183$	2045.55	0.826292
$184$	16.1325	0.00646361
$185$	0	0
$186$	1088.53	0.429110
$187$	1409.50	0.551192
$188$	−714.774	−0.277288
$189$	−606.614	−0.233464
$190$	0	0
$191$	644.102	0.244008	0.122004	−	0.992530i	$-0.461068\pi$
$191$	644.102	0.244008	0.122004	+	0.992530i	$0.461068\pi$
$192$	1660.85	0.624281
$193$	−3970.76	−1.48094	−0.740470	−	0.672089i	$-0.765397\pi$
$193$	−3970.76	−1.48094	−0.740470	+	0.672089i	$0.765397\pi$
$194$	1702.23	0.629964
$195$	0	0
$196$	−416.644	−0.151838
$197$	−3756.34	−1.35852	−0.679260	−	0.733898i	$-0.737699\pi$
$197$	−3756.34	−1.35852	−0.679260	+	0.733898i	$0.737699\pi$
$198$	230.577	0.0827596
$199$	4825.48	1.71894	0.859470	−	0.511186i	$-0.170794\pi$
$199$	4825.48	1.71894	0.859470	+	0.511186i	$0.170794\pi$
$200$	0	0
$201$	−1122.08	−0.393760
$202$	−1887.34	−0.657389
$203$	5151.25	1.78102
$204$	−990.034	−0.339785
$205$	0	0
$206$	3404.84	1.15158
$207$	−5.89472	−0.00197928
$208$	−362.497	−0.120840
$209$	77.4401	0.0256299
$210$	0	0
$211$	−4394.02	−1.43363	−0.716817	−	0.697261i	$-0.754402\pi$
$211$	−4394.02	−1.43363	−0.716817	+	0.697261i	$0.754402\pi$
$212$	−1678.08	−0.543638
$213$	290.085	0.0933160
$214$	−3937.04	−1.25762
$215$	0	0
$216$	−665.035	−0.209490
$217$	−3500.13	−1.09495
$218$	−3282.62	−1.01985
$219$	59.8379	0.0184633
$220$	0	0
$221$	1263.46	0.384569
$222$	770.543	0.232953
$223$	−2189.67	−0.657538	−0.328769	−	0.944410i	$-0.606634\pi$
$223$	−2189.67	−0.657538	−0.328769	+	0.944410i	$0.606634\pi$
$224$	−2503.37	−0.746712
$225$	0	0
$226$	−5090.56	−1.49831
$227$	1139.27	0.333110	0.166555	−	0.986032i	$-0.446736\pi$
$227$	1139.27	0.333110	0.166555	+	0.986032i	$0.446736\pi$
$228$	−54.3939	−0.0157997
$229$	3416.10	0.985773	0.492886	−	0.870094i	$-0.335942\pi$
$229$	3416.10	0.985773	0.492886	+	0.870094i	$0.335942\pi$
$230$	0	0
$231$	−741.417	−0.211176
$232$	5647.35	1.59813
$233$	−6147.08	−1.72836	−0.864181	−	0.503181i	$-0.832163\pi$
$233$	−6147.08	−1.72836	−0.864181	+	0.503181i	$0.832163\pi$
$234$	206.687	0.0577418
$235$	0	0
$236$	1091.66	0.301106
$237$	73.2858	0.0200862
$238$	−6705.06	−1.82615
$239$	−2080.03	−0.562954	−0.281477	−	0.959568i	$-0.590824\pi$
$239$	−2080.03	−0.562954	−0.281477	+	0.959568i	$0.590824\pi$
$240$	0	0
$241$	1846.28	0.493484	0.246742	−	0.969081i	$-0.420640\pi$
$241$	1846.28	0.493484	0.246742	+	0.969081i	$0.420640\pi$
$242$	281.817	0.0748589
$243$	243.000	0.0641500
$244$	−1756.08	−0.460745
$245$	0	0
$246$	1081.26	0.280238
$247$	69.4166	0.0178821
$248$	−3837.22	−0.982515
$249$	3382.05	0.860758
$250$	0	0
$251$	−2555.32	−0.642592	−0.321296	−	0.946979i	$-0.604118\pi$
$251$	−2555.32	−0.642592	−0.321296	+	0.946979i	$0.604118\pi$
$252$	520.771	0.130181
$253$	−7.20466	−0.00179033
$254$	4469.13	1.10401
$255$	0	0
$256$	−3501.92	−0.854962
$257$	1819.39	0.441598	0.220799	−	0.975319i	$-0.429134\pi$
$257$	1819.39	0.441598	0.220799	+	0.975319i	$0.429134\pi$
$258$	2801.96	0.676134
$259$	−2477.67	−0.594420
$260$	0	0
$261$	−2063.51	−0.489379
$262$	3119.57	0.735603
$263$	6023.03	1.41215	0.706076	−	0.708136i	$-0.250464\pi$
$263$	6023.03	1.41215	0.706076	+	0.708136i	$0.250464\pi$
$264$	−812.821	−0.189491
$265$	0	0
$266$	−368.386	−0.0849143
$267$	−1918.87	−0.439824
$268$	963.297	0.219562
$269$	−2978.38	−0.675075	−0.337537	−	0.941312i	$-0.609594\pi$
$269$	−2978.38	−0.675075	−0.337537	+	0.941312i	$0.609594\pi$
$270$	0	0
$271$	−524.969	−0.117674	−0.0588369	−	0.998268i	$-0.518739\pi$
$271$	−524.969	−0.117674	−0.0588369	+	0.998268i	$0.518739\pi$
$272$	−4710.72	−1.05011
$273$	−664.600	−0.147338
$274$	2563.28	0.565157
$275$	0	0
$276$	5.06055	0.00110366
$277$	1693.07	0.367245	0.183623	−	0.982997i	$-0.441218\pi$
$277$	1693.07	0.367245	0.183623	+	0.982997i	$0.441218\pi$
$278$	−2991.71	−0.645435
$279$	1402.10	0.300865
$280$	0	0
$281$	7346.60	1.55965	0.779824	−	0.625998i	$-0.215308\pi$
$281$	7346.60	1.55965	0.779824	+	0.625998i	$0.215308\pi$
$282$	1939.17	0.409488
$283$	1501.69	0.315429	0.157714	−	0.987485i	$-0.449587\pi$
$283$	1501.69	0.315429	0.157714	+	0.987485i	$0.449587\pi$
$284$	−249.035	−0.0520334
$285$	0	0
$286$	252.618	0.0522294
$287$	−3476.77	−0.715077
$288$	1002.81	0.205178
$289$	11506.0	2.34194
$290$	0	0
$291$	2192.59	0.441691
$292$	−51.3702	−0.0102952
$293$	4481.03	0.893462	0.446731	−	0.894668i	$-0.352588\pi$
$293$	4481.03	0.893462	0.446731	+	0.894668i	$0.352588\pi$
$294$	1130.35	0.224229
$295$	0	0
$296$	−2716.28	−0.533381
$297$	297.000	0.0580259
$298$	2974.71	0.578255
$299$	−6.45819	−0.00124912
$300$	0	0
$301$	−9009.66	−1.72528
$302$	2064.29	0.393333
$303$	−2431.02	−0.460920
$304$	−258.814	−0.0488289
$305$	0	0
$306$	2685.94	0.501781
$307$	−3052.17	−0.567416	−0.283708	−	0.958911i	$-0.591565\pi$
$307$	−3052.17	−0.567416	−0.283708	+	0.958911i	$0.591565\pi$
$308$	636.498	0.117753
$309$	4385.67	0.807418
$310$	0	0
$311$	10255.1	1.86983	0.934913	−	0.354878i	$-0.115477\pi$
$311$	10255.1	1.86983	0.934913	+	0.354878i	$0.115477\pi$
$312$	−728.605	−0.132209
$313$	6190.18	1.11786	0.558929	−	0.829215i	$-0.311212\pi$
$313$	6190.18	1.11786	0.558929	+	0.829215i	$0.311212\pi$
$314$	3915.44	0.703698
$315$	0	0
$316$	−62.9150	−0.0112001
$317$	6735.38	1.19337	0.596683	−	0.802477i	$-0.296485\pi$
$317$	6735.38	1.19337	0.596683	+	0.802477i	$0.296485\pi$
$318$	4552.61	0.802823
$319$	−2522.07	−0.442660
$320$	0	0
$321$	−5071.19	−0.881764
$322$	34.2729	0.00593153
$323$	902.083	0.155397
$324$	−208.613	−0.0357704
$325$	0	0
$326$	1448.91	0.246159
$327$	−4228.24	−0.715053
$328$	−3811.60	−0.641648
$329$	−6235.36	−1.04488
$330$	0	0
$331$	−4780.83	−0.793891	−0.396946	−	0.917842i	$-0.629930\pi$
$331$	−4780.83	−0.793891	−0.396946	+	0.917842i	$0.629930\pi$
$332$	−2903.45	−0.479963
$333$	992.515	0.163332
$334$	6083.09	0.996562
$335$	0	0
$336$	2477.90	0.402323
$337$	−11890.3	−1.92197	−0.960984	−	0.276604i	$-0.910791\pi$
$337$	−11890.3	−1.92197	−0.960984	+	0.276604i	$0.910791\pi$
$338$	−4890.51	−0.787007
$339$	−6557.00	−1.05052
$340$	0	0
$341$	1713.68	0.272143
$342$	147.570	0.0233323
$343$	4071.63	0.640954
$344$	−9877.35	−1.54811
$345$	0	0
$346$	−5456.93	−0.847879
$347$	−8462.47	−1.30919	−0.654595	−	0.755979i	$-0.727161\pi$
$347$	−8462.47	−1.30919	−0.654595	+	0.755979i	$0.727161\pi$
$348$	1771.50	0.272880
$349$	−3291.90	−0.504903	−0.252452	−	0.967610i	$-0.581237\pi$
$349$	−3291.90	−0.504903	−0.252452	+	0.967610i	$0.581237\pi$
$350$	0	0
$351$	266.228	0.0404849
$352$	1225.66	0.185590
$353$	8193.52	1.23540	0.617701	−	0.786413i	$-0.288064\pi$
$353$	8193.52	1.23540	0.617701	+	0.786413i	$0.288064\pi$
$354$	−2961.66	−0.444662
$355$	0	0
$356$	1647.33	0.245248
$357$	−8636.60	−1.28038
$358$	3062.15	0.452066
$359$	12817.6	1.88437	0.942185	−	0.335093i	$-0.108768\pi$
$359$	12817.6	1.88437	0.942185	+	0.335093i	$0.108768\pi$
$360$	0	0
$361$	−6809.44	−0.992774
$362$	20.2397	0.00293861
$363$	363.000	0.0524864
$364$	570.551	0.0821566
$365$	0	0
$366$	4764.22	0.680409
$367$	2801.22	0.398427	0.199213	−	0.979956i	$-0.436161\pi$
$367$	2801.22	0.398427	0.199213	+	0.979956i	$0.436161\pi$
$368$	24.0788	0.00341085
$369$	1392.74	0.196485
$370$	0	0
$371$	−14638.8	−2.04855
$372$	−1203.69	−0.167764
$373$	−6838.03	−0.949222	−0.474611	−	0.880196i	$-0.657411\pi$
$373$	−6838.03	−0.949222	−0.474611	+	0.880196i	$0.657411\pi$
$374$	3282.82	0.453878
$375$	0	0
$376$	−6835.86	−0.937587
$377$	−2260.76	−0.308846
$378$	−1412.84	−0.192245
$379$	−7465.79	−1.01185	−0.505926	−	0.862577i	$-0.668849\pi$
$379$	−7465.79	−1.01185	−0.505926	+	0.862577i	$0.668849\pi$
$380$	0	0
$381$	5756.56	0.774062
$382$	1500.16	0.200928
$383$	8646.55	1.15357	0.576786	−	0.816895i	$-0.304307\pi$
$383$	8646.55	1.15357	0.576786	+	0.816895i	$0.304307\pi$
$384$	1194.07	0.158684
$385$	0	0
$386$	−9248.15	−1.21948
$387$	3609.13	0.474063
$388$	−1882.32	−0.246289
$389$	4382.78	0.571248	0.285624	−	0.958342i	$-0.407799\pi$
$389$	4382.78	0.571248	0.285624	+	0.958342i	$0.407799\pi$
$390$	0	0
$391$	−83.9255	−0.0108550
$392$	−3984.65	−0.513406
$393$	4018.24	0.515759
$394$	−8748.76	−1.11867
$395$	0	0
$396$	−254.971	−0.0323555
$397$	4432.58	0.560365	0.280182	−	0.959947i	$-0.409605\pi$
$397$	4432.58	0.560365	0.280182	+	0.959947i	$0.409605\pi$
$398$	11238.8	1.41546
$399$	−474.508	−0.0595366
$400$	0	0
$401$	−5034.93	−0.627013	−0.313507	−	0.949586i	$-0.601504\pi$
$401$	−5034.93	−0.627013	−0.313507	+	0.949586i	$0.601504\pi$
$402$	−2613.41	−0.324241
$403$	1536.12	0.189875
$404$	2087.01	0.257011
$405$	0	0
$406$	11997.6	1.46658
$407$	1213.07	0.147739
$408$	−9468.36	−1.14891
$409$	6474.64	0.782764	0.391382	−	0.920228i	$-0.371997\pi$
$409$	6474.64	0.782764	0.391382	+	0.920228i	$0.371997\pi$
$410$	0	0
$411$	3301.68	0.396253
$412$	−3765.05	−0.450220
$413$	9523.15	1.13463
$414$	−13.7292	−0.00162984
$415$	0	0
$416$	1098.67	0.129487
$417$	−3853.54	−0.452538
$418$	180.363	0.0211049
$419$	−8257.80	−0.962816	−0.481408	−	0.876497i	$-0.659874\pi$
$419$	−8257.80	−0.962816	−0.481408	+	0.876497i	$0.659874\pi$
$420$	0	0
$421$	−3429.36	−0.397000	−0.198500	−	0.980101i	$-0.563607\pi$
$421$	−3429.36	−0.397000	−0.198500	+	0.980101i	$0.563607\pi$
$422$	−10233.9	−1.18052
$423$	2497.79	0.287108
$424$	−16048.7	−1.83819
$425$	0	0
$426$	675.626	0.0768408
$427$	−15319.3	−1.73618
$428$	4353.56	0.491676
$429$	325.390	0.0366200
$430$	0	0
$431$	−11260.4	−1.25846	−0.629230	−	0.777219i	$-0.716630\pi$
$431$	−11260.4	−1.25846	−0.629230	+	0.777219i	$0.716630\pi$
$432$	−992.608	−0.110548
$433$	−12598.5	−1.39826	−0.699128	−	0.714996i	$-0.746428\pi$
$433$	−12598.5	−1.39826	−0.699128	+	0.714996i	$0.746428\pi$
$434$	−8152.03	−0.901636
$435$	0	0
$436$	3629.90	0.398717
$437$	−4.61099	−0.000504745 0
$438$	139.366	0.0152036
$439$	4176.90	0.454106	0.227053	−	0.973882i	$-0.427091\pi$
$439$	4176.90	0.454106	0.227053	+	0.973882i	$0.427091\pi$
$440$	0	0
$441$	1455.97	0.157215
$442$	2942.69	0.316673
$443$	−2354.16	−0.252482	−0.126241	−	0.992000i	$-0.540291\pi$
$443$	−2354.16	−0.252482	−0.126241	+	0.992000i	$0.540291\pi$
$444$	−852.062	−0.0910745
$445$	0	0
$446$	−5099.88	−0.541449
$447$	3831.63	0.405436
$448$	−12438.2	−1.31172
$449$	9286.18	0.976040	0.488020	−	0.872832i	$-0.337719\pi$
$449$	9286.18	0.976040	0.488020	+	0.872832i	$0.337719\pi$
$450$	0	0
$451$	1702.24	0.177728
$452$	5629.11	0.585777
$453$	2658.95	0.275780
$454$	2653.43	0.274299
$455$	0	0
$456$	−520.206	−0.0534230
$457$	−14378.4	−1.47176	−0.735878	−	0.677115i	$-0.763230\pi$
$457$	−14378.4	−1.47176	−0.735878	+	0.677115i	$0.763230\pi$
$458$	7956.30	0.811733
$459$	3459.69	0.351818
$460$	0	0
$461$	−5383.19	−0.543861	−0.271931	−	0.962317i	$-0.587662\pi$
$461$	−5383.19	−0.543861	−0.271931	+	0.962317i	$0.587662\pi$
$462$	−1726.81	−0.173892
$463$	−18360.5	−1.84294	−0.921471	−	0.388446i	$-0.873012\pi$
$463$	−18360.5	−1.84294	−0.921471	+	0.388446i	$0.873012\pi$
$464$	8429.03	0.843336
$465$	0	0
$466$	−14316.9	−1.42322
$467$	−9063.65	−0.898106	−0.449053	−	0.893505i	$-0.648239\pi$
$467$	−9063.65	−0.898106	−0.449053	+	0.893505i	$0.648239\pi$
$468$	−228.554	−0.0225746
$469$	8403.36	0.827358
$470$	0	0
$471$	5043.37	0.493389
$472$	10440.3	1.01812
$473$	4411.15	0.428806
$474$	170.687	0.0165399
$475$	0	0
$476$	7414.42	0.713949
$477$	5864.09	0.562889
$478$	−4844.53	−0.463564
$479$	12608.2	1.20268	0.601341	−	0.798992i	$-0.294633\pi$
$479$	12608.2	1.20268	0.601341	+	0.798992i	$0.294633\pi$
$480$	0	0
$481$	1087.39	0.103078
$482$	4300.11	0.406358
$483$	44.1459	0.00415882
$484$	−311.631	−0.0292667
$485$	0	0
$486$	565.962	0.0528242
$487$	13214.2	1.22955	0.614775	−	0.788703i	$-0.289247\pi$
$487$	13214.2	1.22955	0.614775	+	0.788703i	$0.289247\pi$
$488$	−16794.6	−1.55790
$489$	1866.30	0.172591
$490$	0	0
$491$	6553.27	0.602332	0.301166	−	0.953572i	$-0.402624\pi$
$491$	6553.27	0.602332	0.301166	+	0.953572i	$0.402624\pi$
$492$	−1195.65	−0.109561
$493$	−29379.0	−2.68390
$494$	161.676	0.0147250
$495$	0	0
$496$	−5727.30	−0.518474
$497$	−2172.46	−0.196073
$498$	7877.01	0.708790
$499$	−2596.63	−0.232948	−0.116474	−	0.993194i	$-0.537159\pi$
$499$	−2596.63	−0.232948	−0.116474	+	0.993194i	$0.537159\pi$
$500$	0	0
$501$	7835.45	0.698727
$502$	−5951.51	−0.529141
$503$	659.714	0.0584795	0.0292398	−	0.999572i	$-0.490691\pi$
$503$	659.714	0.0584795	0.0292398	+	0.999572i	$0.490691\pi$
$504$	4980.49	0.440176
$505$	0	0
$506$	−16.7801	−0.00147424
$507$	−6299.32	−0.551800
$508$	−4941.94	−0.431621
$509$	4825.41	0.420201	0.210101	−	0.977680i	$-0.432621\pi$
$509$	4825.41	0.420201	0.210101	+	0.977680i	$0.432621\pi$
$510$	0	0
$511$	−448.130	−0.0387947
$512$	−11340.4	−0.978866
$513$	190.080	0.0163592
$514$	4237.48	0.363633
$515$	0	0
$516$	−3098.39	−0.264339
$517$	3052.85	0.259699
$518$	−5770.64	−0.489474
$519$	−7028.91	−0.594480
$520$	0	0
$521$	−2329.24	−0.195866	−0.0979328	−	0.995193i	$-0.531223\pi$
$521$	−2329.24	−0.195866	−0.0979328	+	0.995193i	$0.531223\pi$
$522$	−4806.04	−0.402978
$523$	15104.6	1.26287	0.631434	−	0.775429i	$-0.282467\pi$
$523$	15104.6	1.26287	0.631434	+	0.775429i	$0.282467\pi$
$524$	−3449.61	−0.287589
$525$	0	0
$526$	14028.0	1.16283
$527$	19962.2	1.65003
$528$	−1213.19	−0.0999947
$529$	−12166.6	−0.999965
$530$	0	0
$531$	−3814.82	−0.311769
$532$	407.359	0.0331979
$533$	1525.87	0.124001
$534$	−4469.17	−0.362172
$535$	0	0
$536$	9212.66	0.742400
$537$	3944.26	0.316960
$538$	−6936.84	−0.555889
$539$	1779.52	0.142206
$540$	0	0
$541$	10712.1	0.851293	0.425647	−	0.904889i	$-0.360047\pi$
$541$	10712.1	0.851293	0.425647	+	0.904889i	$0.360047\pi$
$542$	−1222.69	−0.0968983
$543$	26.0702	0.00206037
$544$	14277.4	1.12526
$545$	0	0
$546$	−1547.89	−0.121326
$547$	17251.6	1.34849	0.674245	−	0.738508i	$-0.264469\pi$
$547$	17251.6	1.34849	0.674245	+	0.738508i	$0.264469\pi$
$548$	−2834.46	−0.220953
$549$	6136.65	0.477060
$550$	0	0
$551$	−1614.12	−0.124799
$552$	48.3975	0.00373177
$553$	−548.842	−0.0422046
$554$	3943.27	0.302407
$555$	0	0
$556$	3308.22	0.252337
$557$	8179.34	0.622208	0.311104	−	0.950376i	$-0.399301\pi$
$557$	8179.34	0.622208	0.311104	+	0.950376i	$0.399301\pi$
$558$	3265.58	0.247747
$559$	3954.12	0.299180
$560$	0	0
$561$	4228.51	0.318231
$562$	17110.7	1.28429
$563$	−4939.38	−0.369752	−0.184876	−	0.982762i	$-0.559188\pi$
$563$	−4939.38	−0.369752	−0.184876	+	0.982762i	$0.559188\pi$
$564$	−2144.32	−0.160093
$565$	0	0
$566$	3497.54	0.259739
$567$	−1819.84	−0.134790
$568$	−2381.69	−0.175939
$569$	−7658.76	−0.564274	−0.282137	−	0.959374i	$-0.591043\pi$
$569$	−7658.76	−0.564274	−0.282137	+	0.959374i	$0.591043\pi$
$570$	0	0
$571$	−1744.16	−0.127830	−0.0639149	−	0.997955i	$-0.520359\pi$
$571$	−1744.16	−0.127830	−0.0639149	+	0.997955i	$0.520359\pi$
$572$	−279.344	−0.0204195
$573$	1932.31	0.140878
$574$	−8097.61	−0.588829
$575$	0	0
$576$	4982.56	0.360429
$577$	−1264.61	−0.0912414	−0.0456207	−	0.998959i	$-0.514527\pi$
$577$	−1264.61	−0.0912414	−0.0456207	+	0.998959i	$0.514527\pi$
$578$	26798.1	1.92847
$579$	−11912.3	−0.855022
$580$	0	0
$581$	−25328.4	−1.80860
$582$	5106.69	0.363710
$583$	7167.22	0.509153
$584$	−491.288	−0.0348110
$585$	0	0
$586$	10436.6	0.735720
$587$	17167.4	1.20711	0.603557	−	0.797320i	$-0.293750\pi$
$587$	17167.4	1.20711	0.603557	+	0.797320i	$0.293750\pi$
$588$	−1249.93	−0.0876639
$589$	1096.75	0.0767249
$590$	0	0
$591$	−11269.0	−0.784342
$592$	−4054.23	−0.281466
$593$	21429.5	1.48399	0.741995	−	0.670406i	$-0.233880\pi$
$593$	21429.5	1.48399	0.741995	+	0.670406i	$0.233880\pi$
$594$	691.732	0.0477813
$595$	0	0
$596$	−3289.41	−0.226073
$597$	14476.4	0.992431
$598$	−15.0415	−0.00102859
$599$	−7994.61	−0.545327	−0.272664	−	0.962109i	$-0.587905\pi$
$599$	−7994.61	−0.545327	−0.272664	+	0.962109i	$0.587905\pi$
$600$	0	0
$601$	−24313.4	−1.65019	−0.825094	−	0.564996i	$-0.808878\pi$
$601$	−24313.4	−1.65019	−0.825094	+	0.564996i	$0.808878\pi$
$602$	−20984.1	−1.42067
$603$	−3366.25	−0.227337
$604$	−2282.68	−0.153776
$605$	0	0
$606$	−5662.01	−0.379544
$607$	−24569.7	−1.64292	−0.821460	−	0.570266i	$-0.806840\pi$
$607$	−24569.7	−1.64292	−0.821460	+	0.570266i	$0.806840\pi$
$608$	784.423	0.0523232
$609$	15453.7	1.02827
$610$	0	0
$611$	2736.55	0.181193
$612$	−2970.10	−0.196175
$613$	12746.7	0.839859	0.419929	−	0.907557i	$-0.362055\pi$
$613$	12746.7	0.839859	0.419929	+	0.907557i	$0.362055\pi$
$614$	−7108.70	−0.467237
$615$	0	0
$616$	6087.26	0.398154
$617$	15607.4	1.01837	0.509183	−	0.860658i	$-0.329948\pi$
$617$	15607.4	1.01837	0.509183	+	0.860658i	$0.329948\pi$
$618$	10214.5	0.664867
$619$	−11909.7	−0.773329	−0.386665	−	0.922220i	$-0.626373\pi$
$619$	−11909.7	−0.773329	−0.386665	+	0.922220i	$0.626373\pi$
$620$	0	0
$621$	−17.6842	−0.00114274
$622$	23884.9	1.53970
$623$	14370.5	0.924147
$624$	−1087.49	−0.0697667
$625$	0	0
$626$	14417.3	0.920499
$627$	232.320	0.0147974
$628$	−4329.68	−0.275116
$629$	14130.8	0.895759
$630$	0	0
$631$	−19304.2	−1.21789	−0.608946	−	0.793212i	$-0.708407\pi$
$631$	−19304.2	−1.21789	−0.608946	+	0.793212i	$0.708407\pi$
$632$	−601.699	−0.0378707
$633$	−13182.1	−0.827709
$634$	15687.1	0.982674
$635$	0	0
$636$	−5034.25	−0.313870
$637$	1595.14	0.0992180
$638$	−5874.05	−0.364508
$639$	870.255	0.0538760
$640$	0	0
$641$	26678.6	1.64390	0.821950	−	0.569560i	$-0.192886\pi$
$641$	26678.6	1.64390	0.821950	+	0.569560i	$0.192886\pi$
$642$	−11811.1	−0.726087
$643$	26456.2	1.62260	0.811299	−	0.584631i	$-0.198761\pi$
$643$	26456.2	1.62260	0.811299	+	0.584631i	$0.198761\pi$
$644$	−37.8988	−0.00231898
$645$	0	0
$646$	2101.01	0.127961
$647$	23523.7	1.42939	0.714694	−	0.699438i	$-0.246566\pi$
$647$	23523.7	1.42939	0.714694	+	0.699438i	$0.246566\pi$
$648$	−1995.10	−0.120949
$649$	−4662.56	−0.282006
$650$	0	0
$651$	−10500.4	−0.632171
$652$	−1602.20	−0.0962376
$653$	−18071.1	−1.08296	−0.541482	−	0.840712i	$-0.682137\pi$
$653$	−18071.1	−1.08296	−0.541482	+	0.840712i	$0.682137\pi$
$654$	−9847.85	−0.588809
$655$	0	0
$656$	−5689.07	−0.338599
$657$	179.514	0.0106598
$658$	−14522.5	−0.860407
$659$	17023.1	1.00626	0.503130	−	0.864210i	$-0.332182\pi$
$659$	17023.1	1.00626	0.503130	+	0.864210i	$0.332182\pi$
$660$	0	0
$661$	2137.74	0.125792	0.0628959	−	0.998020i	$-0.479966\pi$
$661$	2137.74	0.125792	0.0628959	+	0.998020i	$0.479966\pi$
$662$	−11134.8	−0.653728
$663$	3790.39	0.222031
$664$	−27767.7	−1.62288
$665$	0	0
$666$	2311.63	0.134495
$667$	150.171	0.00871758
$668$	−6726.65	−0.389614
$669$	−6569.01	−0.379630
$670$	0	0
$671$	7500.36	0.431517
$672$	−7510.11	−0.431115
$673$	−31790.1	−1.82083	−0.910414	−	0.413698i	$-0.864237\pi$
$673$	−31790.1	−1.82083	−0.910414	+	0.413698i	$0.864237\pi$
$674$	−27693.1	−1.58264
$675$	0	0
$676$	5407.90	0.307686
$677$	10225.1	0.580476	0.290238	−	0.956955i	$-0.406266\pi$
$677$	10225.1	0.580476	0.290238	+	0.956955i	$0.406266\pi$
$678$	−15271.7	−0.865052
$679$	−16420.5	−0.928071
$680$	0	0
$681$	3417.81	0.192321
$682$	3991.26	0.224096
$683$	−21274.0	−1.19184	−0.595919	−	0.803044i	$-0.703212\pi$
$683$	−21274.0	−1.19184	−0.595919	+	0.803044i	$0.703212\pi$
$684$	−163.182	−0.00912195
$685$	0	0
$686$	9483.08	0.527793
$687$	10248.3	0.569136
$688$	−14742.6	−0.816941
$689$	6424.63	0.355238
$690$	0	0
$691$	−22568.1	−1.24245	−0.621224	−	0.783633i	$-0.713364\pi$
$691$	−22568.1	−1.24245	−0.621224	+	0.783633i	$0.713364\pi$
$692$	6034.24	0.331485
$693$	−2224.25	−0.121923
$694$	−19709.6	−1.07805
$695$	0	0
$696$	16942.0	0.922682
$697$	19829.0	1.07758
$698$	−7667.03	−0.415761
$699$	−18441.2	−0.997870
$700$	0	0
$701$	−7735.03	−0.416759	−0.208380	−	0.978048i	$-0.566819\pi$
$701$	−7735.03	−0.416759	−0.208380	+	0.978048i	$0.566819\pi$
$702$	620.062	0.0333372
$703$	776.368	0.0416519
$704$	6089.80	0.326020
$705$	0	0
$706$	19083.2	1.01729
$707$	18206.1	0.968473
$708$	3274.98	0.173844
$709$	35115.1	1.86005	0.930025	−	0.367497i	$-0.119785\pi$
$709$	35115.1	1.86005	0.930025	+	0.367497i	$0.119785\pi$
$710$	0	0
$711$	219.857	0.0115968
$712$	15754.5	0.829250
$713$	−102.037	−0.00535948
$714$	−20115.2	−1.05433
$715$	0	0
$716$	−3386.11	−0.176738
$717$	−6240.10	−0.325022
$718$	29853.1	1.55168
$719$	15334.3	0.795370	0.397685	−	0.917522i	$-0.369814\pi$
$719$	15334.3	0.795370	0.397685	+	0.917522i	$0.369814\pi$
$720$	0	0
$721$	−32844.6	−1.69653
$722$	−15859.6	−0.817498
$723$	5538.85	0.284913
$724$	−22.3810	−0.00114887
$725$	0	0
$726$	845.450	0.0432198
$727$	12360.4	0.630567	0.315284	−	0.948997i	$-0.397900\pi$
$727$	12360.4	0.630567	0.315284	+	0.948997i	$0.397900\pi$
$728$	5456.57	0.277794
$729$	729.000	0.0370370
$730$	0	0
$731$	51384.6	2.59990
$732$	−5268.25	−0.266011
$733$	15097.6	0.760769	0.380384	−	0.924828i	$-0.375792\pi$
$733$	15097.6	0.760769	0.380384	+	0.924828i	$0.375792\pi$
$734$	6524.23	0.328084
$735$	0	0
$736$	−72.9790	−0.00365495
$737$	−4114.31	−0.205634
$738$	3243.78	0.161795
$739$	−3667.49	−0.182559	−0.0912793	−	0.995825i	$-0.529096\pi$
$739$	−3667.49	−0.182559	−0.0912793	+	0.995825i	$0.529096\pi$
$740$	0	0
$741$	208.250	0.0103242
$742$	−34094.8	−1.68687
$743$	−10172.1	−0.502257	−0.251128	−	0.967954i	$-0.580802\pi$
$743$	−10172.1	−0.502257	−0.251128	+	0.967954i	$0.580802\pi$
$744$	−11511.7	−0.567255
$745$	0	0
$746$	−15926.2	−0.781635
$747$	10146.2	0.496959
$748$	−3630.12	−0.177447
$749$	37978.5	1.85274
$750$	0	0
$751$	31430.3	1.52718	0.763588	−	0.645704i	$-0.223436\pi$
$751$	31430.3	1.52718	0.763588	+	0.645704i	$0.223436\pi$
$752$	−10203.0	−0.494766
$753$	−7665.97	−0.371000
$754$	−5265.45	−0.254319
$755$	0	0
$756$	1562.31	0.0751598
$757$	28362.0	1.36174	0.680868	−	0.732406i	$-0.261603\pi$
$757$	28362.0	1.36174	0.680868	+	0.732406i	$0.261603\pi$
$758$	−17388.3	−0.833207
$759$	−21.6140	−0.00103365
$760$	0	0
$761$	30722.6	1.46346	0.731731	−	0.681594i	$-0.238713\pi$
$761$	30722.6	1.46346	0.731731	+	0.681594i	$0.238713\pi$
$762$	13407.4	0.637400
$763$	31665.6	1.50245
$764$	−1658.86	−0.0785544
$765$	0	0
$766$	20138.4	0.949906
$767$	−4179.48	−0.196757
$768$	−10505.8	−0.493612
$769$	−18443.1	−0.864855	−0.432427	−	0.901669i	$-0.642343\pi$
$769$	−18443.1	−0.864855	−0.432427	+	0.901669i	$0.642343\pi$
$770$	0	0
$771$	5458.18	0.254956
$772$	10226.6	0.476764
$773$	545.742	0.0253932	0.0126966	−	0.999919i	$-0.495958\pi$
$773$	545.742	0.0253932	0.0126966	+	0.999919i	$0.495958\pi$
$774$	8405.88	0.390366
$775$	0	0
$776$	−18001.9	−0.832770
$777$	−7433.00	−0.343189
$778$	10207.8	0.470393
$779$	1089.43	0.0501065
$780$	0	0
$781$	1063.65	0.0487327
$782$	−195.468	−0.00893851
$783$	−6190.53	−0.282543
$784$	−5947.35	−0.270925
$785$	0	0
$786$	9358.72	0.424701
$787$	−17365.2	−0.786536	−0.393268	−	0.919424i	$-0.628655\pi$
$787$	−17365.2	−0.786536	−0.393268	+	0.919424i	$0.628655\pi$
$788$	9674.33	0.437352
$789$	18069.1	0.815306
$790$	0	0
$791$	49105.8	2.20733
$792$	−2438.46	−0.109403
$793$	6723.25	0.301071
$794$	10323.8	0.461431
$795$	0	0
$796$	−12427.9	−0.553384
$797$	−7055.12	−0.313557	−0.156779	−	0.987634i	$-0.550111\pi$
$797$	−7055.12	−0.313557	−0.156779	+	0.987634i	$0.550111\pi$
$798$	−1105.16	−0.0490253
$799$	35562.0	1.57458
$800$	0	0
$801$	−5756.61	−0.253933
$802$	−11726.7	−0.516313
$803$	219.406	0.00964217
$804$	2889.89	0.126764
$805$	0	0
$806$	3577.73	0.156353
$807$	−8935.14	−0.389755
$808$	19959.5	0.869024
$809$	−6937.17	−0.301481	−0.150740	−	0.988573i	$-0.548166\pi$
$809$	−6937.17	−0.301481	−0.150740	+	0.988573i	$0.548166\pi$
$810$	0	0
$811$	5610.44	0.242921	0.121461	−	0.992596i	$-0.461242\pi$
$811$	5610.44	0.242921	0.121461	+	0.992596i	$0.461242\pi$
$812$	−13266.9	−0.573369
$813$	−1574.91	−0.0679390
$814$	2825.32	0.121655
$815$	0	0
$816$	−14132.1	−0.606280
$817$	2823.14	0.120893
$818$	15079.8	0.644565
$819$	−1993.80	−0.0850659
$820$	0	0
$821$	−17001.8	−0.722735	−0.361368	−	0.932423i	$-0.617690\pi$
$821$	−17001.8	−0.722735	−0.361368	+	0.932423i	$0.617690\pi$
$822$	7689.83	0.326294
$823$	−14567.3	−0.616991	−0.308496	−	0.951226i	$-0.599825\pi$
$823$	−14567.3	−0.616991	−0.308496	+	0.951226i	$0.599825\pi$
$824$	−36007.7	−1.52232
$825$	0	0
$826$	22180.0	0.934312
$827$	7345.87	0.308877	0.154438	−	0.988002i	$-0.450643\pi$
$827$	7345.87	0.308877	0.154438	+	0.988002i	$0.450643\pi$
$828$	15.1817	0.000637197 0
$829$	−13903.2	−0.582482	−0.291241	−	0.956650i	$-0.594068\pi$
$829$	−13903.2	−0.582482	−0.291241	+	0.956650i	$0.594068\pi$
$830$	0	0
$831$	5079.22	0.212029
$832$	5458.84	0.227466
$833$	20729.2	0.862214
$834$	−8975.13	−0.372642
$835$	0	0
$836$	−199.444	−0.00825111
$837$	4206.30	0.173705
$838$	−19232.9	−0.792829
$839$	−25111.9	−1.03332	−0.516662	−	0.856190i	$-0.672825\pi$
$839$	−25111.9	−1.03332	−0.516662	+	0.856190i	$0.672825\pi$
$840$	0	0
$841$	28179.7	1.15543
$842$	−7987.20	−0.326909
$843$	22039.8	0.900464
$844$	11316.6	0.461534
$845$	0	0
$846$	5817.50	0.236418
$847$	−2718.53	−0.110283
$848$	−23953.7	−0.970014
$849$	4505.08	0.182113
$850$	0	0
$851$	−72.2296	−0.00290952
$852$	−747.104	−0.0300415
$853$	27545.3	1.10567	0.552833	−	0.833292i	$-0.313547\pi$
$853$	27545.3	1.10567	0.552833	+	0.833292i	$0.313547\pi$
$854$	−35679.5	−1.42966
$855$	0	0
$856$	41636.1	1.66249
$857$	−1808.04	−0.0720669	−0.0360334	−	0.999351i	$-0.511472\pi$
$857$	−1808.04	−0.0720669	−0.0360334	+	0.999351i	$0.511472\pi$
$858$	757.854	0.0301547
$859$	32160.8	1.27743	0.638716	−	0.769443i	$-0.279466\pi$
$859$	32160.8	1.27743	0.638716	+	0.769443i	$0.279466\pi$
$860$	0	0
$861$	−10430.3	−0.412850
$862$	−26226.3	−1.03628
$863$	−33734.8	−1.33064	−0.665321	−	0.746557i	$-0.731706\pi$
$863$	−33734.8	−1.33064	−0.665321	+	0.746557i	$0.731706\pi$
$864$	3008.43	0.118459
$865$	0	0
$866$	−29342.7	−1.15139
$867$	34517.9	1.35212
$868$	9014.47	0.352501
$869$	268.715	0.0104897
$870$	0	0
$871$	−3688.03	−0.143472
$872$	34715.2	1.34817
$873$	6577.78	0.255011
$874$	−10.7393	−0.000415631 0
$875$	0	0
$876$	−154.111	−0.00594397
$877$	−46573.5	−1.79325	−0.896623	−	0.442795i	$-0.853987\pi$
$877$	−46573.5	−1.79325	−0.896623	+	0.442795i	$0.853987\pi$
$878$	9728.26	0.373933
$879$	13443.1	0.515841
$880$	0	0
$881$	−9949.72	−0.380493	−0.190247	−	0.981736i	$-0.560929\pi$
$881$	−9949.72	−0.380493	−0.190247	+	0.981736i	$0.560929\pi$
$882$	3391.04	0.129458
$883$	49269.1	1.87773	0.938866	−	0.344282i	$-0.111878\pi$
$883$	49269.1	1.87773	0.938866	+	0.344282i	$0.111878\pi$
$884$	−3254.01	−0.123806
$885$	0	0
$886$	−5483.00	−0.207906
$887$	−27347.5	−1.03522	−0.517609	−	0.855617i	$-0.673178\pi$
$887$	−27347.5	−1.03522	−0.517609	+	0.855617i	$0.673178\pi$
$888$	−8148.85	−0.307948
$889$	−43111.2	−1.62644
$890$	0	0
$891$	891.000	0.0335013
$892$	5639.42	0.211683
$893$	1953.83	0.0732165
$894$	8924.12	0.333856
$895$	0	0
$896$	−8942.48	−0.333423
$897$	−19.3746	−0.000721180 0
$898$	21628.1	0.803718
$899$	−35719.0	−1.32514
$900$	0	0
$901$	83489.4	3.08705
$902$	3964.61	0.146349
$903$	−27029.0	−0.996088
$904$	53835.0	1.98067
$905$	0	0
$906$	6192.86	0.227091
$907$	25516.6	0.934141	0.467071	−	0.884220i	$-0.345309\pi$
$907$	25516.6	0.934141	0.467071	+	0.884220i	$0.345309\pi$
$908$	−2934.15	−0.107239
$909$	−7293.07	−0.266112
$910$	0	0
$911$	22379.0	0.813885	0.406942	−	0.913454i	$-0.366595\pi$
$911$	22379.0	0.813885	0.406942	+	0.913454i	$0.366595\pi$
$912$	−776.441	−0.0281914
$913$	12400.9	0.449516
$914$	−33488.1	−1.21191
$915$	0	0
$916$	−8798.04	−0.317353
$917$	−30092.8	−1.08370
$918$	8057.83	0.289704
$919$	−6244.97	−0.224159	−0.112080	−	0.993699i	$-0.535751\pi$
$919$	−6244.97	−0.224159	−0.112080	+	0.993699i	$0.535751\pi$
$920$	0	0
$921$	−9156.52	−0.327598
$922$	−12537.8	−0.447841
$923$	953.442	0.0340010
$924$	1909.49	0.0679846
$925$	0	0
$926$	−42762.6	−1.51757
$927$	13157.0	0.466163
$928$	−25547.0	−0.903688
$929$	16122.2	0.569378	0.284689	−	0.958620i	$-0.408110\pi$
$929$	16122.2	0.569378	0.284689	+	0.958620i	$0.408110\pi$
$930$	0	0
$931$	1138.89	0.0400921
$932$	15831.6	0.556417
$933$	30765.4	1.07954
$934$	−21109.8	−0.739544
$935$	0	0
$936$	−2185.82	−0.0763308
$937$	−56379.6	−1.96568	−0.982839	−	0.184466i	$-0.940945\pi$
$937$	−56379.6	−1.96568	−0.982839	+	0.184466i	$0.940945\pi$
$938$	19572.0	0.681287
$939$	18570.5	0.645396
$940$	0	0
$941$	25527.0	0.884332	0.442166	−	0.896933i	$-0.354210\pi$
$941$	25527.0	0.884332	0.442166	+	0.896933i	$0.354210\pi$
$942$	11746.3	0.406280
$943$	−101.356	−0.00350010
$944$	15582.8	0.537264
$945$	0	0
$946$	10273.9	0.353099
$947$	−46411.3	−1.59257	−0.796285	−	0.604921i	$-0.793205\pi$
$947$	−46411.3	−1.59257	−0.796285	+	0.604921i	$0.793205\pi$
$948$	−188.745	−0.00646641
$949$	196.673	0.00672738
$950$	0	0
$951$	20206.1	0.688990
$952$	70909.2	2.41405
$953$	21266.1	0.722850	0.361425	−	0.932401i	$-0.382290\pi$
$953$	21266.1	0.722850	0.361425	+	0.932401i	$0.382290\pi$
$954$	13657.8	0.463510
$955$	0	0
$956$	5357.05	0.181234
$957$	−7566.20	−0.255570
$958$	29365.4	0.990347
$959$	−24726.5	−0.832597
$960$	0	0
$961$	−5520.88	−0.185320
$962$	2532.60	0.0848796
$963$	−15213.6	−0.509087
$964$	−4755.04	−0.158869
$965$	0	0
$966$	102.819	0.00342457
$967$	−20035.9	−0.666300	−0.333150	−	0.942874i	$-0.608112\pi$
$967$	−20035.9	−0.666300	−0.333150	+	0.942874i	$0.608112\pi$
$968$	−2980.34	−0.0989585
$969$	2706.25	0.0897185
$970$	0	0
$971$	21354.1	0.705751	0.352876	−	0.935670i	$-0.385204\pi$
$971$	21354.1	0.705751	0.352876	+	0.935670i	$0.385204\pi$
$972$	−625.838	−0.0206520
$973$	28859.4	0.950862
$974$	30776.6	1.01247
$975$	0	0
$976$	−25067.0	−0.822107
$977$	34057.7	1.11525	0.557626	−	0.830092i	$-0.311712\pi$
$977$	34057.7	1.11525	0.557626	+	0.830092i	$0.311712\pi$
$978$	4346.73	0.142120
$979$	−7035.86	−0.229691
$980$	0	0
$981$	−12684.7	−0.412836
$982$	15263.0	0.495989
$983$	−31846.5	−1.03331	−0.516657	−	0.856193i	$-0.672824\pi$
$983$	−31846.5	−1.03331	−0.516657	+	0.856193i	$0.672824\pi$
$984$	−11434.8	−0.370456
$985$	0	0
$986$	−68425.5	−2.21005
$987$	−18706.1	−0.603263
$988$	−178.780	−0.00575684
$989$	−262.652	−0.00844474
$990$	0	0
$991$	−20462.5	−0.655915	−0.327957	−	0.944693i	$-0.606360\pi$
$991$	−20462.5	−0.655915	−0.327957	+	0.944693i	$0.606360\pi$
$992$	17358.5	0.555578
$993$	−14342.5	−0.458353
$994$	−5059.81	−0.161456
$995$	0	0
$996$	−8710.36	−0.277107
$997$	−35227.4	−1.11902	−0.559510	−	0.828824i	$-0.689011\pi$
$997$	−35227.4	−1.11902	−0.559510	+	0.828824i	$0.689011\pi$
$998$	−6047.71	−0.191820
$999$	2977.54	0.0942996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.s.1.2		3
3.2	odd	2		2475.4.a.s.1.2		3
5.2	odd	4		825.4.c.l.199.4		6
5.3	odd	4		825.4.c.l.199.3		6
5.4	even	2		165.4.a.d.1.2	✓	3
15.14	odd	2		495.4.a.l.1.2		3
55.54	odd	2		1815.4.a.s.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.d.1.2	✓	3	5.4	even	2
495.4.a.l.1.2		3	15.14	odd	2
825.4.a.s.1.2		3	1.1	even	1	trivial
825.4.c.l.199.3		6	5.3	odd	4
825.4.c.l.199.4		6	5.2	odd	4
1815.4.a.s.1.2		3	55.54	odd	2
2475.4.a.s.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+2.32906 q^{2} +3.00000 q^{3} -2.57547 q^{4} +6.98719 q^{6} -22.4672 q^{7} -24.6309 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.32906 q^{2} +3.00000 q^{3} -2.57547 q^{4} +6.98719 q^{6} -22.4672 q^{7} -24.6309 q^{8} +9.00000 q^{9} +11.0000 q^{11} -7.72640 q^{12} +9.86030 q^{13} -52.3275 q^{14} -36.7633 q^{16} +128.137 q^{17} +20.9616 q^{18} +7.04001 q^{19} -67.4015 q^{21} +25.6197 q^{22} -0.654969 q^{23} -73.8928 q^{24} +22.9653 q^{26} +27.0000 q^{27} +57.8635 q^{28} -229.279 q^{29} +155.789 q^{31} +111.423 q^{32} +33.0000 q^{33} +298.438 q^{34} -23.1792 q^{36} +110.279 q^{37} +16.3966 q^{38} +29.5809 q^{39} +154.749 q^{41} -156.982 q^{42} +401.014 q^{43} -28.3301 q^{44} -1.52546 q^{46} +277.532 q^{47} -110.290 q^{48} +161.774 q^{49} +384.410 q^{51} -25.3949 q^{52} +651.566 q^{53} +62.8847 q^{54} +553.388 q^{56} +21.1200 q^{57} -534.005 q^{58} -423.869 q^{59} +681.851 q^{61} +362.842 q^{62} -202.205 q^{63} +553.618 q^{64} +76.8591 q^{66} -374.028 q^{67} -330.011 q^{68} -1.96491 q^{69} +96.6950 q^{71} -221.678 q^{72} +19.9460 q^{73} +256.848 q^{74} -18.1313 q^{76} -247.139 q^{77} +68.8958 q^{78} +24.4286 q^{79} +81.0000 q^{81} +360.419 q^{82} +1127.35 q^{83} +173.590 q^{84} +933.987 q^{86} -687.836 q^{87} -270.940 q^{88} -639.624 q^{89} -221.533 q^{91} +1.68685 q^{92} +467.366 q^{93} +646.389 q^{94} +334.270 q^{96} +730.865 q^{97} +376.783 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} + 9 q^{3} + 22 q^{4} + 12 q^{6} + 4 q^{7} + 48 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 4 * q^2 + 9 * q^3 + 22 * q^4 + 12 * q^6 + 4 * q^7 + 48 * q^8 + 27 * q^9	\( 3 q + 4 q^{2} + 9 q^{3} + 22 q^{4} + 12 q^{6} + 4 q^{7} + 48 q^{8} + 27 q^{9} + 33 q^{11} + 66 q^{12} - 56 q^{14} + 50 q^{16} + 218 q^{17} + 36 q^{18} + 146 q^{19} + 12 q^{21} + 44 q^{22} + 200 q^{23} + 144 q^{24} - 508 q^{26} + 81 q^{27} + 340 q^{28} + 68 q^{29} - 68 q^{31} + 688 q^{32} + 99 q^{33} - 176 q^{34} + 198 q^{36} + 390 q^{37} + 316 q^{38} - 196 q^{41} - 168 q^{42} + 524 q^{43} + 242 q^{44} + 1160 q^{46} + 60 q^{47} + 150 q^{48} - 157 q^{49} + 654 q^{51} - 1020 q^{52} + 158 q^{53} + 108 q^{54} + 1368 q^{56} + 438 q^{57} - 1092 q^{58} - 1044 q^{59} + 642 q^{61} - 88 q^{62} + 36 q^{63} + 1166 q^{64} + 132 q^{66} + 236 q^{67} - 144 q^{68} + 600 q^{69} - 544 q^{71} + 432 q^{72} - 900 q^{73} + 1536 q^{74} + 1996 q^{76} + 44 q^{77} - 1524 q^{78} - 1586 q^{79} + 243 q^{81} - 380 q^{82} + 1582 q^{83} + 1020 q^{84} + 3568 q^{86} + 204 q^{87} + 528 q^{88} - 2122 q^{89} - 8 q^{91} + 4128 q^{92} - 204 q^{93} - 2152 q^{94} + 2064 q^{96} - 618 q^{97} - 572 q^{98} + 297 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 + 9 * q^3 + 22 * q^4 + 12 * q^6 + 4 * q^7 + 48 * q^8 + 27 * q^9 + 33 * q^11 + 66 * q^12 - 56 * q^14 + 50 * q^16 + 218 * q^17 + 36 * q^18 + 146 * q^19 + 12 * q^21 + 44 * q^22 + 200 * q^23 + 144 * q^24 - 508 * q^26 + 81 * q^27 + 340 * q^28 + 68 * q^29 - 68 * q^31 + 688 * q^32 + 99 * q^33 - 176 * q^34 + 198 * q^36 + 390 * q^37 + 316 * q^38 - 196 * q^41 - 168 * q^42 + 524 * q^43 + 242 * q^44 + 1160 * q^46 + 60 * q^47 + 150 * q^48 - 157 * q^49 + 654 * q^51 - 1020 * q^52 + 158 * q^53 + 108 * q^54 + 1368 * q^56 + 438 * q^57 - 1092 * q^58 - 1044 * q^59 + 642 * q^61 - 88 * q^62 + 36 * q^63 + 1166 * q^64 + 132 * q^66 + 236 * q^67 - 144 * q^68 + 600 * q^69 - 544 * q^71 + 432 * q^72 - 900 * q^73 + 1536 * q^74 + 1996 * q^76 + 44 * q^77 - 1524 * q^78 - 1586 * q^79 + 243 * q^81 - 380 * q^82 + 1582 * q^83 + 1020 * q^84 + 3568 * q^86 + 204 * q^87 + 528 * q^88 - 2122 * q^89 - 8 * q^91 + 4128 * q^92 - 204 * q^93 - 2152 * q^94 + 2064 * q^96 - 618 * q^97 - 572 * q^98 + 297 * q^99

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