LMFDB - Embedded newform 1075.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,4,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1075.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1075.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:	$63.4270532562$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.15251$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -33.4879 q^{6} +23.3206 q^{7} -54.3507 q^{8} +15.2413 q^{9} +O(q^{10})$	\(q-5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -33.4879 q^{6} +23.3206 q^{7} -54.3507 q^{8} +15.2413 q^{9} -60.5580 q^{11} +120.552 q^{12} -10.9419 q^{13} -120.160 q^{14} +131.656 q^{16} +3.57473 q^{17} -78.5308 q^{18} +33.2403 q^{19} +151.568 q^{21} +312.026 q^{22} -63.7158 q^{23} -353.243 q^{24} +56.3783 q^{26} -76.4239 q^{27} +432.560 q^{28} -89.3510 q^{29} +222.839 q^{31} -243.552 q^{32} -393.586 q^{33} -18.4188 q^{34} +282.701 q^{36} +59.6535 q^{37} -171.271 q^{38} -71.1150 q^{39} -143.837 q^{41} -780.957 q^{42} +43.0000 q^{43} -1123.25 q^{44} +328.296 q^{46} -379.013 q^{47} +855.674 q^{48} +200.850 q^{49} +23.2334 q^{51} -202.955 q^{52} +150.129 q^{53} +393.775 q^{54} -1267.49 q^{56} +216.040 q^{57} +460.382 q^{58} +207.310 q^{59} -486.557 q^{61} -1148.18 q^{62} +355.435 q^{63} +201.659 q^{64} +2027.96 q^{66} -1019.41 q^{67} +66.3055 q^{68} -414.110 q^{69} +13.8437 q^{71} -828.374 q^{72} -411.158 q^{73} -307.365 q^{74} +616.555 q^{76} -1412.25 q^{77} +366.421 q^{78} -1315.13 q^{79} -908.218 q^{81} +741.120 q^{82} -813.425 q^{83} +2811.35 q^{84} -221.558 q^{86} -580.721 q^{87} +3291.37 q^{88} -350.573 q^{89} -255.171 q^{91} -1181.83 q^{92} +1448.30 q^{93} +1952.87 q^{94} -1582.92 q^{96} +1187.03 q^{97} -1034.88 q^{98} -922.981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * 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 $

$2$	−5.15251	−1.82169	−0.910844	−	0.412750i	$-0.864568\pi$
$2$	−5.15251	−1.82169	−0.910844	+	0.412750i	$0.864568\pi$
$3$	6.49933	1.25080	0.625398	−	0.780306i	$-0.284937\pi$
$3$	6.49933	1.25080	0.625398	+	0.780306i	$0.284937\pi$
$4$	18.5484	2.31855
$5$	0	0
$5$	0	0
$6$	−33.4879	−2.27856
$7$	23.3206	1.25919	0.629597	−	0.776922i	$-0.283220\pi$
$7$	23.3206	1.25919	0.629597	+	0.776922i	$0.283220\pi$
$8$	−54.3507	−2.40199
$9$	15.2413	0.564491
$10$	0	0
$11$	−60.5580	−1.65990	−0.829951	−	0.557836i	$-0.811632\pi$
$11$	−60.5580	−1.65990	−0.829951	+	0.557836i	$0.811632\pi$
$12$	120.552	2.90003
$13$	−10.9419	−0.233441	−0.116721	−	0.993165i	$-0.537238\pi$
$13$	−10.9419	−0.233441	−0.116721	+	0.993165i	$0.537238\pi$
$14$	−120.160	−2.29386
$15$	0	0
$16$	131.656	2.05712
$17$	3.57473	0.0510000	0.0255000	−	0.999675i	$-0.491882\pi$
$17$	3.57473	0.0510000	0.0255000	+	0.999675i	$0.491882\pi$
$18$	−78.5308	−1.02833
$19$	33.2403	0.401361	0.200680	−	0.979657i	$-0.435685\pi$
$19$	33.2403	0.401361	0.200680	+	0.979657i	$0.435685\pi$
$20$	0	0
$21$	151.568	1.57499
$22$	312.026	3.02383
$23$	−63.7158	−0.577637	−0.288819	−	0.957384i	$-0.593262\pi$
$23$	−63.7158	−0.577637	−0.288819	+	0.957384i	$0.593262\pi$
$24$	−353.243	−3.00440
$25$	0	0
$26$	56.3783	0.425257
$27$	−76.4239	−0.544733
$28$	432.560	2.91950
$29$	−89.3510	−0.572140	−0.286070	−	0.958209i	$-0.592349\pi$
$29$	−89.3510	−0.572140	−0.286070	+	0.958209i	$0.592349\pi$
$30$	0	0
$31$	222.839	1.29106	0.645532	−	0.763733i	$-0.276636\pi$
$31$	222.839	1.29106	0.645532	+	0.763733i	$0.276636\pi$
$32$	−243.552	−1.34545
$33$	−393.586	−2.07620
$34$	−18.4188	−0.0929061
$35$	0	0
$36$	282.701	1.30880
$37$	59.6535	0.265053	0.132527	−	0.991179i	$-0.457691\pi$
$37$	59.6535	0.265053	0.132527	+	0.991179i	$0.457691\pi$
$38$	−171.271	−0.731154
$39$	−71.1150	−0.291987
$40$	0	0
$41$	−143.837	−0.547890	−0.273945	−	0.961745i	$-0.588329\pi$
$41$	−143.837	−0.547890	−0.273945	+	0.961745i	$0.588329\pi$
$42$	−780.957	−2.86915
$43$	43.0000	0.152499
$43$	43.0000	0.152499
$44$	−1123.25	−3.84857
$45$	0	0
$46$	328.296	1.05228
$47$	−379.013	−1.17627	−0.588135	−	0.808763i	$-0.700138\pi$
$47$	−379.013	−1.17627	−0.588135	+	0.808763i	$0.700138\pi$
$48$	855.674	2.57304
$49$	200.850	0.585569
$50$	0	0
$51$	23.2334	0.0637906
$52$	−202.955	−0.541245
$53$	150.129	0.389090	0.194545	−	0.980894i	$-0.437677\pi$
$53$	150.129	0.389090	0.194545	+	0.980894i	$0.437677\pi$
$54$	393.775	0.992333
$55$	0	0
$56$	−1267.49	−3.02457
$57$	216.040	0.502021
$58$	460.382	1.04226
$59$	207.310	0.457448	0.228724	−	0.973491i	$-0.426545\pi$
$59$	207.310	0.457448	0.228724	+	0.973491i	$0.426545\pi$
$60$	0	0
$61$	−486.557	−1.02127	−0.510633	−	0.859799i	$-0.670589\pi$
$61$	−486.557	−1.02127	−0.510633	+	0.859799i	$0.670589\pi$
$62$	−1148.18	−2.35192
$63$	355.435	0.710804
$64$	201.659	0.393866
$65$	0	0
$66$	2027.96	3.78219
$67$	−1019.41	−1.85882	−0.929408	−	0.369054i	$-0.879682\pi$
$67$	−1019.41	−1.85882	−0.929408	+	0.369054i	$0.879682\pi$
$68$	66.3055	0.118246
$69$	−414.110	−0.722507
$70$	0	0
$71$	13.8437	0.0231400	0.0115700	−	0.999933i	$-0.496317\pi$
$71$	13.8437	0.0231400	0.0115700	+	0.999933i	$0.496317\pi$
$72$	−828.374	−1.35590
$73$	−411.158	−0.659211	−0.329605	−	0.944119i	$-0.606916\pi$
$73$	−411.158	−0.659211	−0.329605	+	0.944119i	$0.606916\pi$
$74$	−307.365	−0.482844
$75$	0	0
$76$	616.555	0.930575
$77$	−1412.25	−2.09014
$78$	366.421	0.531910
$79$	−1315.13	−1.87296	−0.936481	−	0.350718i	$-0.885938\pi$
$79$	−1315.13	−1.87296	−0.936481	+	0.350718i	$0.885938\pi$
$80$	0	0
$81$	−908.218	−1.24584
$82$	741.120	0.998085
$83$	−813.425	−1.07572	−0.537861	−	0.843033i	$-0.680768\pi$
$83$	−813.425	−1.07572	−0.537861	+	0.843033i	$0.680768\pi$
$84$	2811.35	3.65170
$85$	0	0
$86$	−221.558	−0.277805
$87$	−580.721	−0.715630
$88$	3291.37	3.98706
$89$	−350.573	−0.417535	−0.208768	−	0.977965i	$-0.566945\pi$
$89$	−350.573	−0.417535	−0.208768	+	0.977965i	$0.566945\pi$
$90$	0	0
$91$	−255.171	−0.293948
$92$	−1181.83	−1.33928
$93$	1448.30	1.61486
$94$	1952.87	2.14280
$95$	0	0
$96$	−1582.92	−1.68288
$97$	1187.03	1.24252	0.621262	−	0.783603i	$-0.286620\pi$
$97$	1187.03	1.24252	0.621262	+	0.783603i	$0.286620\pi$
$98$	−1034.88	−1.06672
$99$	−922.981	−0.937001
$100$	0	0
$101$	469.014	0.462066	0.231033	−	0.972946i	$-0.425790\pi$
$101$	469.014	0.462066	0.231033	+	0.972946i	$0.425790\pi$
$102$	−119.710	−0.116207
$103$	1299.82	1.24345	0.621725	−	0.783235i	$-0.286432\pi$
$103$	1299.82	1.24345	0.621725	+	0.783235i	$0.286432\pi$
$104$	594.700	0.560722
$105$	0	0
$106$	−773.541	−0.708801
$107$	1480.92	1.33800	0.669000	−	0.743263i	$-0.266723\pi$
$107$	1480.92	1.33800	0.669000	+	0.743263i	$0.266723\pi$
$108$	−1417.54	−1.26299
$109$	350.586	0.308073	0.154037	−	0.988065i	$-0.450773\pi$
$109$	350.586	0.308073	0.154037	+	0.988065i	$0.450773\pi$
$110$	0	0
$111$	387.707	0.331528
$112$	3070.29	2.59031
$113$	−785.106	−0.653598	−0.326799	−	0.945094i	$-0.605970\pi$
$113$	−785.106	−0.653598	−0.326799	+	0.945094i	$0.605970\pi$
$114$	−1113.15	−0.914525
$115$	0	0
$116$	−1657.32	−1.32653
$117$	−166.768	−0.131776
$118$	−1068.17	−0.833329
$119$	83.3649	0.0642189
$120$	0	0
$121$	2336.27	1.75528
$122$	2506.99	1.86043
$123$	−934.841	−0.685299
$124$	4133.30	2.99340
$125$	0	0
$126$	−1831.39	−1.29486
$127$	731.562	0.511147	0.255573	−	0.966790i	$-0.417736\pi$
$127$	731.562	0.511147	0.255573	+	0.966790i	$0.417736\pi$
$128$	909.364	0.627947
$129$	279.471	0.190745
$130$	0	0
$131$	2462.56	1.64240	0.821202	−	0.570638i	$-0.193304\pi$
$131$	2462.56	1.64240	0.821202	+	0.570638i	$0.193304\pi$
$132$	−7300.40	−4.81377
$133$	775.184	0.505391
$134$	5252.52	3.38618
$135$	0	0
$136$	−194.289	−0.122501
$137$	−2384.64	−1.48710	−0.743552	−	0.668678i	$-0.766861\pi$
$137$	−2384.64	−1.48710	−0.743552	+	0.668678i	$0.766861\pi$
$138$	2133.71	1.31618
$139$	−3086.87	−1.88363	−0.941816	−	0.336129i	$-0.890882\pi$
$139$	−3086.87	−1.88363	−0.941816	+	0.336129i	$0.890882\pi$
$140$	0	0
$141$	−2463.33	−1.47127
$142$	−71.3297	−0.0421539
$143$	662.619	0.387490
$144$	2006.60	1.16123
$145$	0	0
$146$	2118.50	1.20088
$147$	1305.39	0.732427
$148$	1106.48	0.614539
$149$	−1445.58	−0.794808	−0.397404	−	0.917644i	$-0.630089\pi$
$149$	−1445.58	−0.794808	−0.397404	+	0.917644i	$0.630089\pi$
$150$	0	0
$151$	−825.878	−0.445093	−0.222546	−	0.974922i	$-0.571437\pi$
$151$	−825.878	−0.445093	−0.222546	+	0.974922i	$0.571437\pi$
$152$	−1806.64	−0.964063
$153$	54.4834	0.0287891
$154$	7276.63	3.80758
$155$	0	0
$156$	−1319.07	−0.676987
$157$	−1187.82	−0.603809	−0.301904	−	0.953338i	$-0.597622\pi$
$157$	−1187.82	−0.603809	−0.301904	+	0.953338i	$0.597622\pi$
$158$	6776.24	3.41195
$159$	975.737	0.486673
$160$	0	0
$161$	−1485.89	−0.727357
$162$	4679.61	2.26953
$163$	−1514.60	−0.727809	−0.363904	−	0.931436i	$-0.618557\pi$
$163$	−1514.60	−0.727809	−0.363904	+	0.931436i	$0.618557\pi$
$164$	−2667.94	−1.27031
$165$	0	0
$166$	4191.18	1.95963
$167$	3354.48	1.55435	0.777177	−	0.629282i	$-0.216651\pi$
$167$	3354.48	1.55435	0.777177	+	0.629282i	$0.216651\pi$
$168$	−8237.84	−3.78312
$169$	−2077.27	−0.945505
$170$	0	0
$171$	506.625	0.226565
$172$	797.581	0.353575
$173$	−1654.64	−0.727166	−0.363583	−	0.931562i	$-0.618447\pi$
$173$	−1654.64	−0.727166	−0.363583	+	0.931562i	$0.618447\pi$
$174$	2992.17	1.30366
$175$	0	0
$176$	−7972.81	−3.41462
$177$	1347.38	0.572175
$178$	1806.33	0.760619
$179$	−1334.05	−0.557049	−0.278524	−	0.960429i	$-0.589845\pi$
$179$	−1334.05	−0.557049	−0.278524	+	0.960429i	$0.589845\pi$
$180$	0	0
$181$	2771.58	1.13817	0.569087	−	0.822277i	$-0.307297\pi$
$181$	2771.58	1.13817	0.569087	+	0.822277i	$0.307297\pi$
$182$	1314.77	0.535481
$183$	−3162.29	−1.27740
$184$	3463.00	1.38748
$185$	0	0
$186$	−7462.39	−2.94177
$187$	−216.479	−0.0846550
$188$	−7030.08	−2.72724
$189$	−1782.25	−0.685924
$190$	0	0
$191$	81.5135	0.0308802	0.0154401	−	0.999881i	$-0.495085\pi$
$191$	81.5135	0.0308802	0.0154401	+	0.999881i	$0.495085\pi$
$192$	1310.65	0.492646
$193$	−3305.29	−1.23275	−0.616373	−	0.787454i	$-0.711399\pi$
$193$	−3305.29	−1.23275	−0.616373	+	0.787454i	$0.711399\pi$
$194$	−6116.20	−2.26349
$195$	0	0
$196$	3725.45	1.35767
$197$	−2241.99	−0.810840	−0.405420	−	0.914131i	$-0.632875\pi$
$197$	−2241.99	−0.810840	−0.405420	+	0.914131i	$0.632875\pi$
$198$	4755.67	1.70692
$199$	−4074.29	−1.45135	−0.725675	−	0.688037i	$-0.758472\pi$
$199$	−4074.29	−1.45135	−0.725675	+	0.688037i	$0.758472\pi$
$200$	0	0
$201$	−6625.48	−2.32500
$202$	−2416.60	−0.841740
$203$	−2083.72	−0.720435
$204$	430.941	0.147902
$205$	0	0
$206$	−6697.36	−2.26518
$207$	−971.109	−0.326071
$208$	−1440.56	−0.480217
$209$	−2012.97	−0.666220
$210$	0	0
$211$	4267.62	1.39239	0.696196	−	0.717851i	$-0.254874\pi$
$211$	4267.62	1.39239	0.696196	+	0.717851i	$0.254874\pi$
$212$	2784.65	0.902125
$213$	89.9746	0.0289435
$214$	−7630.46	−2.43742
$215$	0	0
$216$	4153.69	1.30844
$217$	5196.73	1.62570
$218$	−1806.40	−0.561214
$219$	−2672.25	−0.824538
$220$	0	0
$221$	−39.1143	−0.0119055
$222$	−1997.67	−0.603940
$223$	889.370	0.267070	0.133535	−	0.991044i	$-0.457367\pi$
$223$	889.370	0.267070	0.133535	+	0.991044i	$0.457367\pi$
$224$	−5679.78	−1.69418
$225$	0	0
$226$	4045.27	1.19065
$227$	−232.389	−0.0679479	−0.0339739	−	0.999423i	$-0.510816\pi$
$227$	−232.389	−0.0679479	−0.0339739	+	0.999423i	$0.510816\pi$
$228$	4007.19	1.16396
$229$	851.806	0.245803	0.122902	−	0.992419i	$-0.460780\pi$
$229$	851.806	0.245803	0.122902	+	0.992419i	$0.460780\pi$
$230$	0	0
$231$	−9178.67	−2.61434
$232$	4856.29	1.37427
$233$	2083.62	0.585848	0.292924	−	0.956136i	$-0.405372\pi$
$233$	2083.62	0.585848	0.292924	+	0.956136i	$0.405372\pi$
$234$	859.276	0.240054
$235$	0	0
$236$	3845.27	1.06062
$237$	−8547.48	−2.34269
$238$	−429.539	−0.116987
$239$	986.983	0.267124	0.133562	−	0.991040i	$-0.457358\pi$
$239$	986.983	0.267124	0.133562	+	0.991040i	$0.457358\pi$
$240$	0	0
$241$	14.8772	0.00397644	0.00198822	−	0.999998i	$-0.499367\pi$
$241$	14.8772	0.00397644	0.00198822	+	0.999998i	$0.499367\pi$
$242$	−12037.7	−3.19757
$243$	−3839.36	−1.01356
$244$	−9024.85	−2.36786
$245$	0	0
$246$	4816.78	1.24840
$247$	−363.712	−0.0936942
$248$	−12111.4	−3.10112
$249$	−5286.72	−1.34551
$250$	0	0
$251$	−3027.27	−0.761274	−0.380637	−	0.924725i	$-0.624295\pi$
$251$	−3027.27	−0.761274	−0.380637	+	0.924725i	$0.624295\pi$
$252$	6592.76	1.64803
$253$	3858.50	0.958822
$254$	−3769.38	−0.931150
$255$	0	0
$256$	−6298.79	−1.53779
$257$	−5759.92	−1.39803	−0.699016	−	0.715106i	$-0.746378\pi$
$257$	−5759.92	−1.39803	−0.699016	+	0.715106i	$0.746378\pi$
$258$	−1439.98	−0.347477
$259$	1391.15	0.333753
$260$	0	0
$261$	−1361.82	−0.322968
$262$	−12688.4	−2.99195
$263$	−2545.09	−0.596719	−0.298359	−	0.954454i	$-0.596439\pi$
$263$	−2545.09	−0.596719	−0.298359	+	0.954454i	$0.596439\pi$
$264$	21391.7	4.98700
$265$	0	0
$266$	−3994.15	−0.920665
$267$	−2278.49	−0.522252
$268$	−18908.4	−4.30976
$269$	6757.89	1.53173	0.765866	−	0.643001i	$-0.222311\pi$
$269$	6757.89	1.53173	0.765866	+	0.643001i	$0.222311\pi$
$270$	0	0
$271$	2485.54	0.557143	0.278571	−	0.960415i	$-0.410139\pi$
$271$	2485.54	0.557143	0.278571	+	0.960415i	$0.410139\pi$
$272$	470.634	0.104913
$273$	−1658.44	−0.367669
$274$	12286.9	2.70904
$275$	0	0
$276$	−7681.07	−1.67517
$277$	2090.19	0.453385	0.226692	−	0.973966i	$-0.427209\pi$
$277$	2090.19	0.453385	0.226692	+	0.973966i	$0.427209\pi$
$278$	15905.1	3.43139
$279$	3396.34	0.728795
$280$	0	0
$281$	−6049.22	−1.28422	−0.642111	−	0.766612i	$-0.721941\pi$
$281$	−6049.22	−1.28422	−0.642111	+	0.766612i	$0.721941\pi$
$282$	12692.3	2.68020
$283$	650.183	0.136570	0.0682851	−	0.997666i	$-0.478247\pi$
$283$	650.183	0.136570	0.0682851	+	0.997666i	$0.478247\pi$
$284$	256.778	0.0536513
$285$	0	0
$286$	−3414.16	−0.705885
$287$	−3354.35	−0.689900
$288$	−3712.04	−0.759494
$289$	−4900.22	−0.997399
$290$	0	0
$291$	7714.92	1.55415
$292$	−7626.31	−1.52841
$293$	2172.20	0.433110	0.216555	−	0.976270i	$-0.430518\pi$
$293$	2172.20	0.433110	0.216555	+	0.976270i	$0.430518\pi$
$294$	−6726.04	−1.33425
$295$	0	0
$296$	−3242.21	−0.636654
$297$	4628.08	0.904203
$298$	7448.36	1.44789
$299$	697.171	0.134844
$300$	0	0
$301$	1002.79	0.192025
$302$	4255.35	0.810820
$303$	3048.28	0.577950
$304$	4376.28	0.825648
$305$	0	0
$306$	−280.727	−0.0524447
$307$	−1257.47	−0.233771	−0.116885	−	0.993145i	$-0.537291\pi$
$307$	−1257.47	−0.233771	−0.116885	+	0.993145i	$0.537291\pi$
$308$	−26194.9	−4.84609
$309$	8447.98	1.55530
$310$	0	0
$311$	−1316.02	−0.239950	−0.119975	−	0.992777i	$-0.538281\pi$
$311$	−1316.02	−0.239950	−0.119975	+	0.992777i	$0.538281\pi$
$312$	3865.15	0.701350
$313$	−3137.09	−0.566514	−0.283257	−	0.959044i	$-0.591415\pi$
$313$	−3137.09	−0.566514	−0.283257	+	0.959044i	$0.591415\pi$
$314$	6120.24	1.09995
$315$	0	0
$316$	−24393.6	−4.34256
$317$	−571.518	−0.101261	−0.0506303	−	0.998717i	$-0.516123\pi$
$317$	−571.518	−0.101261	−0.0506303	+	0.998717i	$0.516123\pi$
$318$	−5027.50	−0.886566
$319$	5410.92	0.949696
$320$	0	0
$321$	9624.99	1.67356
$322$	7656.07	1.32502
$323$	118.825	0.0204694
$324$	−16846.0	−2.88854
$325$	0	0
$326$	7804.01	1.32584
$327$	2278.57	0.385337
$328$	7817.62	1.31602
$329$	−8838.80	−1.48115
$330$	0	0
$331$	−2257.30	−0.374841	−0.187420	−	0.982280i	$-0.560013\pi$
$331$	−2257.30	−0.374841	−0.187420	+	0.982280i	$0.560013\pi$
$332$	−15087.7	−2.49412
$333$	909.194	0.149620
$334$	−17284.0	−2.83155
$335$	0	0
$336$	19954.8	3.23995
$337$	9222.66	1.49077	0.745386	−	0.666633i	$-0.232265\pi$
$337$	9222.66	1.49077	0.745386	+	0.666633i	$0.232265\pi$
$338$	10703.2	1.72242
$339$	−5102.66	−0.817517
$340$	0	0
$341$	−13494.7	−2.14304
$342$	−2610.39	−0.412730
$343$	−3315.02	−0.521849
$344$	−2337.08	−0.366299
$345$	0	0
$346$	8525.54	1.32467
$347$	−8840.48	−1.36767	−0.683835	−	0.729636i	$-0.739689\pi$
$347$	−8840.48	−1.36767	−0.683835	+	0.729636i	$0.739689\pi$
$348$	−10771.4	−1.65922
$349$	1431.64	0.219581	0.109791	−	0.993955i	$-0.464982\pi$
$349$	1431.64	0.219581	0.109791	+	0.993955i	$0.464982\pi$
$350$	0	0
$351$	836.222	0.127163
$352$	14749.0	2.23331
$353$	8308.06	1.25267	0.626336	−	0.779553i	$-0.284554\pi$
$353$	8308.06	1.25267	0.626336	+	0.779553i	$0.284554\pi$
$354$	−6942.37	−1.04232
$355$	0	0
$356$	−6502.56	−0.968076
$357$	541.816	0.0803247
$358$	6873.72	1.01477
$359$	11642.2	1.71157	0.855786	−	0.517330i	$-0.173074\pi$
$359$	11642.2	1.71157	0.855786	+	0.517330i	$0.173074\pi$
$360$	0	0
$361$	−5754.08	−0.838909
$362$	−14280.6	−2.07340
$363$	15184.2	2.19549
$364$	−4733.02	−0.681532
$365$	0	0
$366$	16293.8	2.32702
$367$	−4373.93	−0.622119	−0.311059	−	0.950391i	$-0.600684\pi$
$367$	−4373.93	−0.622119	−0.311059	+	0.950391i	$0.600684\pi$
$368$	−8388.55	−1.18827
$369$	−2192.25	−0.309279
$370$	0	0
$371$	3501.09	0.489940
$372$	26863.7	3.74413
$373$	−7970.63	−1.10644	−0.553222	−	0.833034i	$-0.686602\pi$
$373$	−7970.63	−1.10644	−0.553222	+	0.833034i	$0.686602\pi$
$374$	1115.41	0.154215
$375$	0	0
$376$	20599.6	2.82538
$377$	977.669	0.133561
$378$	9183.07	1.24954
$379$	−2020.56	−0.273850	−0.136925	−	0.990581i	$-0.543722\pi$
$379$	−2020.56	−0.273850	−0.136925	+	0.990581i	$0.543722\pi$
$380$	0	0
$381$	4754.66	0.639340
$382$	−420.000	−0.0562540
$383$	−11625.0	−1.55094	−0.775468	−	0.631386i	$-0.782486\pi$
$383$	−11625.0	−1.55094	−0.775468	+	0.631386i	$0.782486\pi$
$384$	5910.26	0.785434
$385$	0	0
$386$	17030.5	2.24568
$387$	655.375	0.0860841
$388$	22017.6	2.88086
$389$	6212.26	0.809702	0.404851	−	0.914383i	$-0.367323\pi$
$389$	6212.26	0.809702	0.404851	+	0.914383i	$0.367323\pi$
$390$	0	0
$391$	−227.767	−0.0294595
$392$	−10916.4	−1.40653
$393$	16005.0	2.05431
$394$	11551.9	1.47710
$395$	0	0
$396$	−17119.8	−2.17248
$397$	1647.75	0.208307	0.104154	−	0.994561i	$-0.466787\pi$
$397$	1647.75	0.208307	0.104154	+	0.994561i	$0.466787\pi$
$398$	20992.8	2.64391
$399$	5038.18	0.632141
$400$	0	0
$401$	6893.37	0.858450	0.429225	−	0.903198i	$-0.358787\pi$
$401$	6893.37	0.858450	0.429225	+	0.903198i	$0.358787\pi$
$402$	34137.8	4.23543
$403$	−2438.28	−0.301388
$404$	8699.46	1.07132
$405$	0	0
$406$	10736.4	1.31241
$407$	−3612.49	−0.439962
$408$	−1262.75	−0.153224
$409$	−2962.23	−0.358125	−0.179062	−	0.983838i	$-0.557306\pi$
$409$	−2962.23	−0.358125	−0.179062	+	0.983838i	$0.557306\pi$
$410$	0	0
$411$	−15498.5	−1.86006
$412$	24109.6	2.88300
$413$	4834.59	0.576016
$414$	5003.65	0.594000
$415$	0	0
$416$	2664.92	0.314083
$417$	−20062.6	−2.35604
$418$	10371.8	1.21365
$419$	−5520.25	−0.643633	−0.321816	−	0.946802i	$-0.604293\pi$
$419$	−5520.25	−0.643633	−0.321816	+	0.946802i	$0.604293\pi$
$420$	0	0
$421$	11017.9	1.27548	0.637742	−	0.770250i	$-0.279868\pi$
$421$	11017.9	1.27548	0.637742	+	0.770250i	$0.279868\pi$
$422$	−21989.0	−2.53651
$423$	−5776.63	−0.663994
$424$	−8159.61	−0.934589
$425$	0	0
$426$	−463.595	−0.0527260
$427$	−11346.8	−1.28597
$428$	27468.7	3.10222
$429$	4306.58	0.484671
$430$	0	0
$431$	8825.55	0.986338	0.493169	−	0.869934i	$-0.335838\pi$
$431$	8825.55	0.986338	0.493169	+	0.869934i	$0.335838\pi$
$432$	−10061.6	−1.12058
$433$	−4570.88	−0.507303	−0.253652	−	0.967296i	$-0.581632\pi$
$433$	−4570.88	−0.507303	−0.253652	+	0.967296i	$0.581632\pi$
$434$	−26776.2	−2.96152
$435$	0	0
$436$	6502.80	0.714283
$437$	−2117.93	−0.231841
$438$	13768.8	1.50205
$439$	−3059.73	−0.332649	−0.166325	−	0.986071i	$-0.553190\pi$
$439$	−3059.73	−0.332649	−0.166325	+	0.986071i	$0.553190\pi$
$440$	0	0
$441$	3061.21	0.330549
$442$	201.537	0.0216881
$443$	2764.55	0.296496	0.148248	−	0.988950i	$-0.452637\pi$
$443$	2764.55	0.296496	0.148248	+	0.988950i	$0.452637\pi$
$444$	7191.35	0.768663
$445$	0	0
$446$	−4582.49	−0.486518
$447$	−9395.29	−0.994143
$448$	4702.82	0.495954
$449$	7567.33	0.795377	0.397688	−	0.917521i	$-0.369812\pi$
$449$	7567.33	0.795377	0.397688	+	0.917521i	$0.369812\pi$
$450$	0	0
$451$	8710.46	0.909444
$452$	−14562.4	−1.51540
$453$	−5367.65	−0.556720
$454$	1197.38	0.123780
$455$	0	0
$456$	−11741.9	−1.20585
$457$	8079.05	0.826963	0.413482	−	0.910512i	$-0.364313\pi$
$457$	8079.05	0.826963	0.413482	+	0.910512i	$0.364313\pi$
$458$	−4388.94	−0.447777
$459$	−273.195	−0.0277813
$460$	0	0
$461$	14466.4	1.46154	0.730770	−	0.682624i	$-0.239161\pi$
$461$	14466.4	1.46154	0.730770	+	0.682624i	$0.239161\pi$
$462$	47293.2	4.76251
$463$	7966.79	0.799672	0.399836	−	0.916587i	$-0.369067\pi$
$463$	7966.79	0.799672	0.399836	+	0.916587i	$0.369067\pi$
$464$	−11763.6	−1.17696
$465$	0	0
$466$	−10735.9	−1.06723
$467$	−6737.29	−0.667590	−0.333795	−	0.942646i	$-0.608329\pi$
$467$	−6737.29	−0.667590	−0.333795	+	0.942646i	$0.608329\pi$
$468$	−3093.29	−0.305528
$469$	−23773.2	−2.34061
$470$	0	0
$471$	−7720.00	−0.755242
$472$	−11267.4	−1.09878
$473$	−2603.99	−0.253133
$474$	44041.0	4.26766
$475$	0	0
$476$	1546.28	0.148895
$477$	2288.15	0.219638
$478$	−5085.44	−0.486616
$479$	−18115.7	−1.72803	−0.864014	−	0.503468i	$-0.832057\pi$
$479$	−18115.7	−1.72803	−0.864014	+	0.503468i	$0.832057\pi$
$480$	0	0
$481$	−652.722	−0.0618743
$482$	−76.6548	−0.00724384
$483$	−9657.28	−0.909776
$484$	43334.1	4.06969
$485$	0	0
$486$	19782.4	1.84639
$487$	14966.4	1.39260	0.696298	−	0.717753i	$-0.254829\pi$
$487$	14966.4	1.39260	0.696298	+	0.717753i	$0.254829\pi$
$488$	26444.7	2.45307
$489$	−9843.90	−0.910341
$490$	0	0
$491$	−15713.8	−1.44430	−0.722151	−	0.691736i	$-0.756846\pi$
$491$	−15713.8	−1.44430	−0.722151	+	0.691736i	$0.756846\pi$
$492$	−17339.8	−1.58890
$493$	−319.406	−0.0291791
$494$	1874.03	0.170682
$495$	0	0
$496$	29338.0	2.65588
$497$	322.843	0.0291378
$498$	27239.9	2.45110
$499$	−15391.5	−1.38080	−0.690398	−	0.723430i	$-0.742565\pi$
$499$	−15391.5	−1.38080	−0.690398	+	0.723430i	$0.742565\pi$
$500$	0	0
$501$	21801.8	1.94418
$502$	15598.1	1.38680
$503$	12150.9	1.07710	0.538548	−	0.842595i	$-0.318973\pi$
$503$	12150.9	1.07710	0.538548	+	0.842595i	$0.318973\pi$
$504$	−19318.2	−1.70734
$505$	0	0
$506$	−19881.0	−1.74667
$507$	−13500.9	−1.18263
$508$	13569.3	1.18512
$509$	16646.6	1.44960	0.724799	−	0.688960i	$-0.241933\pi$
$509$	16646.6	1.44960	0.724799	+	0.688960i	$0.241933\pi$
$510$	0	0
$511$	−9588.44	−0.830074
$512$	25179.7	2.17343
$513$	−2540.35	−0.218634
$514$	29678.1	2.54678
$515$	0	0
$516$	5183.74	0.442251
$517$	22952.3	1.95249
$518$	−7167.94	−0.607995
$519$	−10754.0	−0.909536
$520$	0	0
$521$	16675.9	1.40227	0.701135	−	0.713028i	$-0.252677\pi$
$521$	16675.9	1.40227	0.701135	+	0.713028i	$0.252677\pi$
$522$	7016.81	0.588347
$523$	−14326.5	−1.19781	−0.598903	−	0.800821i	$-0.704397\pi$
$523$	−14326.5	−1.19781	−0.598903	+	0.800821i	$0.704397\pi$
$524$	45676.5	3.80799
$525$	0	0
$526$	13113.6	1.08704
$527$	796.588	0.0658443
$528$	−51817.9	−4.27099
$529$	−8107.30	−0.666335
$530$	0	0
$531$	3159.67	0.258226
$532$	14378.4	1.17177
$533$	1573.84	0.127900
$534$	11739.9	0.951380
$535$	0	0
$536$	55405.6	4.46485
$537$	−8670.44	−0.696754
$538$	−34820.1	−2.79034
$539$	−12163.1	−0.971987
$540$	0	0
$541$	−8159.73	−0.648455	−0.324228	−	0.945979i	$-0.605104\pi$
$541$	−8159.73	−0.648455	−0.324228	+	0.945979i	$0.605104\pi$
$542$	−12806.8	−1.01494
$543$	18013.4	1.42362
$544$	−870.633	−0.0686178
$545$	0	0
$546$	8545.15	0.669778
$547$	6089.67	0.476006	0.238003	−	0.971264i	$-0.423507\pi$
$547$	6089.67	0.476006	0.238003	+	0.971264i	$0.423507\pi$
$548$	−44231.2	−3.44793
$549$	−7415.74	−0.576496
$550$	0	0
$551$	−2970.06	−0.229635
$552$	22507.2	1.73545
$553$	−30669.7	−2.35842
$554$	−10769.8	−0.825926
$555$	0	0
$556$	−57256.5	−4.36729
$557$	−4160.66	−0.316504	−0.158252	−	0.987399i	$-0.550586\pi$
$557$	−4160.66	−0.316504	−0.158252	+	0.987399i	$0.550586\pi$
$558$	−17499.7	−1.32764
$559$	−470.501	−0.0355995
$560$	0	0
$561$	−1406.97	−0.105886
$562$	31168.7	2.33945
$563$	−7731.24	−0.578744	−0.289372	−	0.957217i	$-0.593446\pi$
$563$	−7731.24	−0.578744	−0.289372	+	0.957217i	$0.593446\pi$
$564$	−45690.8	−3.41122
$565$	0	0
$566$	−3350.08	−0.248788
$567$	−21180.2	−1.56875
$568$	−752.414	−0.0555820
$569$	9134.32	0.672989	0.336494	−	0.941685i	$-0.390759\pi$
$569$	9134.32	0.672989	0.336494	+	0.941685i	$0.390759\pi$
$570$	0	0
$571$	10421.5	0.763797	0.381898	−	0.924204i	$-0.375270\pi$
$571$	10421.5	0.763797	0.381898	+	0.924204i	$0.375270\pi$
$572$	12290.5	0.898414
$573$	529.783	0.0386248
$574$	17283.4	1.25678
$575$	0	0
$576$	3073.54	0.222334
$577$	−806.571	−0.0581941	−0.0290971	−	0.999577i	$-0.509263\pi$
$577$	−806.571	−0.0581941	−0.0290971	+	0.999577i	$0.509263\pi$
$578$	25248.5	1.81695
$579$	−21482.2	−1.54191
$580$	0	0
$581$	−18969.6	−1.35454
$582$	−39751.2	−2.83117
$583$	−9091.50	−0.645852
$584$	22346.7	1.58341
$585$	0	0
$586$	−11192.3	−0.788992
$587$	−11514.2	−0.809614	−0.404807	−	0.914402i	$-0.632661\pi$
$587$	−11514.2	−0.809614	−0.404807	+	0.914402i	$0.632661\pi$
$588$	24212.9	1.69817
$589$	7407.23	0.518183
$590$	0	0
$591$	−14571.5	−1.01420
$592$	7853.72	0.545246
$593$	−2702.41	−0.187141	−0.0935706	−	0.995613i	$-0.529828\pi$
$593$	−2702.41	−0.187141	−0.0935706	+	0.995613i	$0.529828\pi$
$594$	−23846.2	−1.64718
$595$	0	0
$596$	−26813.1	−1.84280
$597$	−26480.1	−1.81534
$598$	−3592.18	−0.245644
$599$	−27360.1	−1.86628	−0.933142	−	0.359507i	$-0.882945\pi$
$599$	−27360.1	−1.86628	−0.933142	+	0.359507i	$0.882945\pi$
$600$	0	0
$601$	−11506.8	−0.780985	−0.390492	−	0.920606i	$-0.627695\pi$
$601$	−11506.8	−0.780985	−0.390492	+	0.920606i	$0.627695\pi$
$602$	−5166.87	−0.349810
$603$	−15537.1	−1.04929
$604$	−15318.7	−1.03197
$605$	0	0
$606$	−15706.3	−1.05285
$607$	−8189.12	−0.547588	−0.273794	−	0.961788i	$-0.588279\pi$
$607$	−8189.12	−0.547588	−0.273794	+	0.961788i	$0.588279\pi$
$608$	−8095.75	−0.540010
$609$	−13542.8	−0.901117
$610$	0	0
$611$	4147.12	0.274590
$612$	1010.58	0.0667488
$613$	24210.1	1.59517	0.797583	−	0.603209i	$-0.206111\pi$
$613$	24210.1	1.59517	0.797583	+	0.603209i	$0.206111\pi$
$614$	6479.14	0.425858
$615$	0	0
$616$	76756.8	5.02048
$617$	8779.45	0.572848	0.286424	−	0.958103i	$-0.407533\pi$
$617$	8779.45	0.572848	0.286424	+	0.958103i	$0.407533\pi$
$618$	−43528.3	−2.83328
$619$	−6089.56	−0.395412	−0.197706	−	0.980261i	$-0.563349\pi$
$619$	−6089.56	−0.395412	−0.197706	+	0.980261i	$0.563349\pi$
$620$	0	0
$621$	4869.40	0.314658
$622$	6780.79	0.437114
$623$	−8175.57	−0.525758
$624$	−9362.69	−0.600653
$625$	0	0
$626$	16163.9	1.03201
$627$	−13082.9	−0.833305
$628$	−22032.1	−1.39996
$629$	213.245	0.0135177
$630$	0	0
$631$	13768.3	0.868634	0.434317	−	0.900760i	$-0.356990\pi$
$631$	13768.3	0.868634	0.434317	+	0.900760i	$0.356990\pi$
$632$	71478.5	4.49883
$633$	27736.6	1.74160
$634$	2944.75	0.184465
$635$	0	0
$636$	18098.3	1.12837
$637$	−2197.68	−0.136696
$638$	−27879.8	−1.73005
$639$	210.995	0.0130623
$640$	0	0
$641$	393.612	0.0242539	0.0121269	−	0.999926i	$-0.496140\pi$
$641$	393.612	0.0242539	0.0121269	+	0.999926i	$0.496140\pi$
$642$	−49592.9	−3.04871
$643$	29944.9	1.83656	0.918281	−	0.395929i	$-0.129577\pi$
$643$	29944.9	1.83656	0.918281	+	0.395929i	$0.129577\pi$
$644$	−27560.9	−1.68641
$645$	0	0
$646$	−612.249	−0.0372889
$647$	8372.05	0.508716	0.254358	−	0.967110i	$-0.418136\pi$
$647$	8372.05	0.508716	0.254358	+	0.967110i	$0.418136\pi$
$648$	49362.3	2.99249
$649$	−12554.3	−0.759320
$650$	0	0
$651$	33775.3	2.03342
$652$	−28093.4	−1.68746
$653$	−7203.34	−0.431682	−0.215841	−	0.976429i	$-0.569249\pi$
$653$	−7203.34	−0.431682	−0.215841	+	0.976429i	$0.569249\pi$
$654$	−11740.4	−0.701964
$655$	0	0
$656$	−18936.9	−1.12708
$657$	−6266.56	−0.372119
$658$	45542.0	2.69820
$659$	−28054.8	−1.65836	−0.829182	−	0.558979i	$-0.811193\pi$
$659$	−28054.8	−1.65836	−0.829182	+	0.558979i	$0.811193\pi$
$660$	0	0
$661$	−11582.1	−0.681531	−0.340766	−	0.940148i	$-0.610686\pi$
$661$	−11582.1	−0.681531	−0.340766	+	0.940148i	$0.610686\pi$
$662$	11630.8	0.682843
$663$	−254.217	−0.0148914
$664$	44210.2	2.58387
$665$	0	0
$666$	−4684.64	−0.272561
$667$	5693.07	0.330489
$668$	62220.1	3.60385
$669$	5780.31	0.334050
$670$	0	0
$671$	29464.9	1.69520
$672$	−36914.7	−2.11907
$673$	−9582.65	−0.548862	−0.274431	−	0.961607i	$-0.588489\pi$
$673$	−9582.65	−0.548862	−0.274431	+	0.961607i	$0.588489\pi$
$674$	−47519.9	−2.71572
$675$	0	0
$676$	−38530.1	−2.19220
$677$	−8247.63	−0.468216	−0.234108	−	0.972211i	$-0.575217\pi$
$677$	−8247.63	−0.468216	−0.234108	+	0.972211i	$0.575217\pi$
$678$	26291.5	1.48926
$679$	27682.3	1.56458
$680$	0	0
$681$	−1510.37	−0.0849890
$682$	69531.5	3.90395
$683$	−23171.1	−1.29812	−0.649061	−	0.760736i	$-0.724838\pi$
$683$	−23171.1	−1.29812	−0.649061	+	0.760736i	$0.724838\pi$
$684$	9397.08	0.525301
$685$	0	0
$686$	17080.7	0.950647
$687$	5536.16	0.307450
$688$	5661.20	0.313708
$689$	−1642.69	−0.0908297
$690$	0	0
$691$	24019.8	1.32237	0.661185	−	0.750223i	$-0.270054\pi$
$691$	24019.8	1.32237	0.661185	+	0.750223i	$0.270054\pi$
$692$	−30690.8	−1.68597
$693$	−21524.5	−1.17987
$694$	45550.7	2.49147
$695$	0	0
$696$	31562.6	1.71893
$697$	−514.177	−0.0279424
$698$	−7376.54	−0.400009
$699$	13542.1	0.732776
$700$	0	0
$701$	−756.339	−0.0407511	−0.0203755	−	0.999792i	$-0.506486\pi$
$701$	−756.339	−0.0407511	−0.0203755	+	0.999792i	$0.506486\pi$
$702$	−4308.64	−0.231651
$703$	1982.90	0.106382
$704$	−12212.1	−0.653779
$705$	0	0
$706$	−42807.4	−2.28198
$707$	10937.7	0.581830
$708$	24991.7	1.32662
$709$	−26580.1	−1.40795	−0.703975	−	0.710224i	$-0.748594\pi$
$709$	−26580.1	−1.40795	−0.703975	+	0.710224i	$0.748594\pi$
$710$	0	0
$711$	−20044.3	−1.05727
$712$	19053.9	1.00291
$713$	−14198.3	−0.745767
$714$	−2791.71	−0.146327
$715$	0	0
$716$	−24744.5	−1.29154
$717$	6414.72	0.334118
$718$	−59986.8	−3.11795
$719$	14125.2	0.732656	0.366328	−	0.930486i	$-0.380615\pi$
$719$	14125.2	0.732656	0.366328	+	0.930486i	$0.380615\pi$
$720$	0	0
$721$	30312.7	1.56575
$722$	29648.0	1.52823
$723$	96.6916	0.00497372
$724$	51408.3	2.63891
$725$	0	0
$726$	−78236.8	−3.99951
$727$	19206.2	0.979805	0.489903	−	0.871777i	$-0.337032\pi$
$727$	19206.2	0.979805	0.489903	+	0.871777i	$0.337032\pi$
$728$	13868.8	0.706058
$729$	−431.393	−0.0219170
$730$	0	0
$731$	153.713	0.00777742
$732$	−58655.5	−2.96170
$733$	29831.4	1.50320	0.751602	−	0.659617i	$-0.229282\pi$
$733$	29831.4	1.50320	0.751602	+	0.659617i	$0.229282\pi$
$734$	22536.8	1.13331
$735$	0	0
$736$	15518.1	0.777181
$737$	61733.4	3.08545
$738$	11295.6	0.563411
$739$	11720.8	0.583431	0.291715	−	0.956505i	$-0.405774\pi$
$739$	11720.8	0.583431	0.291715	+	0.956505i	$0.405774\pi$
$740$	0	0
$741$	−2363.89	−0.117192
$742$	−18039.4	−0.892518
$743$	−4257.57	−0.210222	−0.105111	−	0.994460i	$-0.533520\pi$
$743$	−4257.57	−0.210222	−0.105111	+	0.994460i	$0.533520\pi$
$744$	−78716.3	−3.87887
$745$	0	0
$746$	41068.8	2.01560
$747$	−12397.6	−0.607236
$748$	−4015.33	−0.196277
$749$	34535.9	1.68480
$750$	0	0
$751$	−16414.4	−0.797564	−0.398782	−	0.917046i	$-0.630567\pi$
$751$	−16414.4	−0.797564	−0.398782	+	0.917046i	$0.630567\pi$
$752$	−49899.2	−2.41973
$753$	−19675.2	−0.952199
$754$	−5037.45	−0.243307
$755$	0	0
$756$	−33057.9	−1.59035
$757$	22813.5	1.09534	0.547668	−	0.836696i	$-0.315516\pi$
$757$	22813.5	1.09534	0.547668	+	0.836696i	$0.315516\pi$
$758$	10410.9	0.498869
$759$	25077.7	1.19929
$760$	0	0
$761$	1695.44	0.0807617	0.0403808	−	0.999184i	$-0.487143\pi$
$761$	1695.44	0.0807617	0.0403808	+	0.999184i	$0.487143\pi$
$762$	−24498.5	−1.16468
$763$	8175.86	0.387924
$764$	1511.95	0.0715972
$765$	0	0
$766$	59897.9	2.82532
$767$	−2268.36	−0.106787
$768$	−40937.9	−1.92346
$769$	21604.9	1.01313	0.506563	−	0.862203i	$-0.330916\pi$
$769$	21604.9	1.01313	0.506563	+	0.862203i	$0.330916\pi$
$770$	0	0
$771$	−37435.6	−1.74865
$772$	−61307.8	−2.85818
$773$	−34435.4	−1.60227	−0.801136	−	0.598482i	$-0.795771\pi$
$773$	−34435.4	−1.60227	−0.801136	+	0.598482i	$0.795771\pi$
$774$	−3376.83	−0.156818
$775$	0	0
$776$	−64516.1	−2.98453
$777$	9041.57	0.417457
$778$	−32008.8	−1.47503
$779$	−4781.18	−0.219902
$780$	0	0
$781$	−838.345	−0.0384102
$782$	1173.57	0.0536660
$783$	6828.54	0.311663
$784$	26443.1	1.20459
$785$	0	0
$786$	−82465.9	−3.74232
$787$	12352.5	0.559490	0.279745	−	0.960074i	$-0.409750\pi$
$787$	12352.5	0.559490	0.279745	+	0.960074i	$0.409750\pi$
$788$	−41585.4	−1.87997
$789$	−16541.4	−0.746374
$790$	0	0
$791$	−18309.1	−0.823006
$792$	50164.7	2.25066
$793$	5323.85	0.238406
$794$	−8490.03	−0.379471
$795$	0	0
$796$	−75571.5	−3.36503
$797$	−29811.8	−1.32495	−0.662477	−	0.749083i	$-0.730495\pi$
$797$	−29811.8	−1.32495	−0.662477	+	0.749083i	$0.730495\pi$
$798$	−25959.3	−1.15156
$799$	−1354.87	−0.0599897
$800$	0	0
$801$	−5343.17	−0.235695
$802$	−35518.2	−1.56383
$803$	24898.9	1.09423
$804$	−122892.	−5.39063
$805$	0	0
$806$	12563.3	0.549035
$807$	43921.7	1.91588
$808$	−25491.3	−1.10988
$809$	−1273.45	−0.0553424	−0.0276712	−	0.999617i	$-0.508809\pi$
$809$	−1273.45	−0.0553424	−0.0276712	+	0.999617i	$0.508809\pi$
$810$	0	0
$811$	37825.5	1.63777	0.818886	−	0.573956i	$-0.194592\pi$
$811$	37825.5	1.63777	0.818886	+	0.573956i	$0.194592\pi$
$812$	−38649.6	−1.67036
$813$	16154.3	0.696872
$814$	18613.4	0.801475
$815$	0	0
$816$	3058.80	0.131225
$817$	1429.33	0.0612070
$818$	15262.9	0.652391
$819$	−3889.14	−0.165931
$820$	0	0
$821$	189.193	0.00804247	0.00402124	−	0.999992i	$-0.498720\pi$
$821$	189.193	0.00804247	0.00402124	+	0.999992i	$0.498720\pi$
$822$	79856.4	3.38846
$823$	−26388.5	−1.11767	−0.558837	−	0.829278i	$-0.688752\pi$
$823$	−26388.5	−1.11767	−0.558837	+	0.829278i	$0.688752\pi$
$824$	−70646.4	−2.98675
$825$	0	0
$826$	−24910.3	−1.04932
$827$	37247.2	1.56616	0.783079	−	0.621923i	$-0.213648\pi$
$827$	37247.2	1.56616	0.783079	+	0.621923i	$0.213648\pi$
$828$	−18012.5	−0.756012
$829$	−18429.8	−0.772128	−0.386064	−	0.922472i	$-0.626166\pi$
$829$	−18429.8	−0.772128	−0.386064	+	0.922472i	$0.626166\pi$
$830$	0	0
$831$	13584.9	0.567092
$832$	−2206.54	−0.0919445
$833$	717.985	0.0298640
$834$	103373.	4.29197
$835$	0	0
$836$	−37337.3	−1.54466
$837$	−17030.2	−0.703285
$838$	28443.2	1.17250
$839$	24344.3	1.00174	0.500870	−	0.865523i	$-0.333014\pi$
$839$	24344.3	1.00174	0.500870	+	0.865523i	$0.333014\pi$
$840$	0	0
$841$	−16405.4	−0.672656
$842$	−56769.8	−2.32354
$843$	−39315.9	−1.60630
$844$	79157.5	3.22833
$845$	0	0
$846$	29764.2	1.20959
$847$	54483.3	2.21023
$848$	19765.3	0.800406
$849$	4225.75	0.170822
$850$	0	0
$851$	−3800.87	−0.153105
$852$	1668.88	0.0671068
$853$	−14146.8	−0.567852	−0.283926	−	0.958846i	$-0.591637\pi$
$853$	−14146.8	−0.567852	−0.283926	+	0.958846i	$0.591637\pi$
$854$	58464.5	2.34264
$855$	0	0
$856$	−80489.1	−3.21386
$857$	−8682.05	−0.346060	−0.173030	−	0.984917i	$-0.555356\pi$
$857$	−8682.05	−0.346060	−0.173030	+	0.984917i	$0.555356\pi$
$858$	−22189.7	−0.882919
$859$	−25428.8	−1.01003	−0.505017	−	0.863110i	$-0.668514\pi$
$859$	−25428.8	−1.01003	−0.505017	+	0.863110i	$0.668514\pi$
$860$	0	0
$861$	−21801.0	−0.862924
$862$	−45473.7	−1.79680
$863$	39552.6	1.56012	0.780062	−	0.625703i	$-0.215188\pi$
$863$	39552.6	1.56012	0.780062	+	0.625703i	$0.215188\pi$
$864$	18613.2	0.732909
$865$	0	0
$866$	23551.5	0.924148
$867$	−31848.1	−1.24754
$868$	96391.0	3.76927
$869$	79641.9	3.10894
$870$	0	0
$871$	11154.3	0.433924
$872$	−19054.6	−0.739988
$873$	18091.9	0.701395
$874$	10912.7	0.422342
$875$	0	0
$876$	−49565.9	−1.91173
$877$	−1955.60	−0.0752975	−0.0376487	−	0.999291i	$-0.511987\pi$
$877$	−1955.60	−0.0752975	−0.0376487	+	0.999291i	$0.511987\pi$
$878$	15765.3	0.605983
$879$	14117.8	0.541733
$880$	0	0
$881$	3037.09	0.116143	0.0580716	−	0.998312i	$-0.481505\pi$
$881$	3037.09	0.116143	0.0580716	+	0.998312i	$0.481505\pi$
$882$	−15772.9	−0.602157
$883$	−15702.3	−0.598443	−0.299222	−	0.954184i	$-0.596727\pi$
$883$	−15702.3	−0.598443	−0.299222	+	0.954184i	$0.596727\pi$
$884$	−725.508	−0.0276035
$885$	0	0
$886$	−14244.4	−0.540123
$887$	−2964.83	−0.112231	−0.0561157	−	0.998424i	$-0.517872\pi$
$887$	−2964.83	−0.112231	−0.0561157	+	0.998424i	$0.517872\pi$
$888$	−21072.2	−0.796324
$889$	17060.5	0.643633
$890$	0	0
$891$	54999.9	2.06797
$892$	16496.4	0.619215
$893$	−12598.5	−0.472109
$894$	48409.3	1.81102
$895$	0	0
$896$	21206.9	0.790707
$897$	4531.14	0.168663
$898$	−38990.8	−1.44893
$899$	−19910.9	−0.738670
$900$	0	0
$901$	536.670	0.0198436
$902$	−44880.7	−1.65672
$903$	6517.43	0.240184
$904$	42671.1	1.56993
$905$	0	0
$906$	27656.9	1.01417
$907$	−47065.4	−1.72302	−0.861511	−	0.507738i	$-0.830482\pi$
$907$	−47065.4	−1.72302	−0.861511	+	0.507738i	$0.830482\pi$
$908$	−4310.43	−0.157540
$909$	7148.37	0.260832
$910$	0	0
$911$	−40218.3	−1.46267	−0.731335	−	0.682018i	$-0.761102\pi$
$911$	−40218.3	−1.46267	−0.731335	+	0.682018i	$0.761102\pi$
$912$	28442.9	1.03272
$913$	49259.4	1.78559
$914$	−41627.4	−1.50647
$915$	0	0
$916$	15799.6	0.569906
$917$	57428.4	2.06810
$918$	1407.64	0.0506090
$919$	−13015.3	−0.467175	−0.233587	−	0.972336i	$-0.575047\pi$
$919$	−13015.3	−0.467175	−0.233587	+	0.972336i	$0.575047\pi$
$920$	0	0
$921$	−8172.72	−0.292400
$922$	−74538.6	−2.66247
$923$	−151.476	−0.00540184
$924$	−170250.	−6.06147
$925$	0	0
$926$	−41049.0	−1.45675
$927$	19811.0	0.701917
$928$	21761.6	0.769784
$929$	−17365.8	−0.613298	−0.306649	−	0.951823i	$-0.599208\pi$
$929$	−17365.8	−0.613298	−0.306649	+	0.951823i	$0.599208\pi$
$930$	0	0
$931$	6676.32	0.235024
$932$	38647.8	1.35832
$933$	−8553.22	−0.300128
$934$	34714.0	1.21614
$935$	0	0
$936$	9063.98	0.316523
$937$	41655.6	1.45232	0.726162	−	0.687523i	$-0.241302\pi$
$937$	41655.6	1.45232	0.726162	+	0.687523i	$0.241302\pi$
$938$	122492.	4.26386
$939$	−20389.0	−0.708593
$940$	0	0
$941$	−11377.5	−0.394149	−0.197075	−	0.980388i	$-0.563144\pi$
$941$	−11377.5	−0.394149	−0.197075	+	0.980388i	$0.563144\pi$
$942$	39777.4	1.37582
$943$	9164.66	0.316482
$944$	27293.5	0.941027
$945$	0	0
$946$	13417.1	0.461129
$947$	−39835.0	−1.36691	−0.683455	−	0.729992i	$-0.739524\pi$
$947$	−39835.0	−1.36691	−0.683455	+	0.729992i	$0.739524\pi$
$948$	−158542.	−5.43165
$949$	4498.84	0.153887
$950$	0	0
$951$	−3714.48	−0.126656
$952$	−4530.94	−0.154253
$953$	−16468.3	−0.559769	−0.279885	−	0.960034i	$-0.590296\pi$
$953$	−16468.3	−0.559769	−0.279885	+	0.960034i	$0.590296\pi$
$954$	−11789.7	−0.400112
$955$	0	0
$956$	18306.9	0.619340
$957$	35167.3	1.18788
$958$	93341.2	3.14793
$959$	−55611.2	−1.87255
$960$	0	0
$961$	19866.1	0.666848
$962$	3363.16	0.112716
$963$	22571.1	0.755289
$964$	275.948	0.00921958
$965$	0	0
$966$	49759.3	1.65733
$967$	−55135.3	−1.83354	−0.916770	−	0.399416i	$-0.869213\pi$
$967$	−55135.3	−1.83354	−0.916770	+	0.399416i	$0.869213\pi$
$968$	−126978.	−4.21615
$969$	772.284	0.0256030
$970$	0	0
$971$	−13040.1	−0.430975	−0.215488	−	0.976507i	$-0.569134\pi$
$971$	−13040.1	−0.430975	−0.215488	+	0.976507i	$0.569134\pi$
$972$	−71214.0	−2.34999
$973$	−71987.6	−2.37186
$974$	−77114.7	−2.53687
$975$	0	0
$976$	−64058.0	−2.10087
$977$	45144.9	1.47831	0.739157	−	0.673534i	$-0.235224\pi$
$977$	45144.9	1.47831	0.739157	+	0.673534i	$0.235224\pi$
$978$	50720.8	1.65836
$979$	21230.0	0.693068
$980$	0	0
$981$	5343.37	0.173905
$982$	80965.4	2.63107
$983$	26573.6	0.862225	0.431113	−	0.902298i	$-0.358121\pi$
$983$	26573.6	0.862225	0.431113	+	0.902298i	$0.358121\pi$
$984$	50809.3	1.64608
$985$	0	0
$986$	1645.74	0.0531553
$987$	−57446.3	−1.85262
$988$	−6746.28	−0.217235
$989$	−2739.78	−0.0880889
$990$	0	0
$991$	20658.0	0.662183	0.331092	−	0.943599i	$-0.392583\pi$
$991$	20658.0	0.662183	0.331092	+	0.943599i	$0.392583\pi$
$992$	−54272.8	−1.73706
$993$	−14670.9	−0.468850
$994$	−1663.45	−0.0530800
$995$	0	0
$996$	−98060.1	−3.11963
$997$	27284.2	0.866701	0.433350	−	0.901226i	$-0.357331\pi$
$997$	27284.2	0.866701	0.433350	+	0.901226i	$0.357331\pi$
$998$	79304.8	2.51538
$999$	−4558.95	−0.144383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.4.a.b.1.1		6
5.4	even	2		43.4.a.b.1.6	✓	6
15.14	odd	2		387.4.a.h.1.1		6
20.19	odd	2		688.4.a.i.1.5		6
35.34	odd	2		2107.4.a.c.1.6		6
215.214	odd	2		1849.4.a.c.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.6	✓	6	5.4	even	2
387.4.a.h.1.1		6	15.14	odd	2
688.4.a.i.1.5		6	20.19	odd	2
1075.4.a.b.1.1		6	1.1	even	1	trivial
1849.4.a.c.1.1		6	215.214	odd	2
2107.4.a.c.1.6		6	35.34	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -33.4879 q^{6} +23.3206 q^{7} -54.3507 q^{8} +15.2413 q^{9} +O(q^{10})\)	\(q-5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -33.4879 q^{6} +23.3206 q^{7} -54.3507 q^{8} +15.2413 q^{9} -60.5580 q^{11} +120.552 q^{12} -10.9419 q^{13} -120.160 q^{14} +131.656 q^{16} +3.57473 q^{17} -78.5308 q^{18} +33.2403 q^{19} +151.568 q^{21} +312.026 q^{22} -63.7158 q^{23} -353.243 q^{24} +56.3783 q^{26} -76.4239 q^{27} +432.560 q^{28} -89.3510 q^{29} +222.839 q^{31} -243.552 q^{32} -393.586 q^{33} -18.4188 q^{34} +282.701 q^{36} +59.6535 q^{37} -171.271 q^{38} -71.1150 q^{39} -143.837 q^{41} -780.957 q^{42} +43.0000 q^{43} -1123.25 q^{44} +328.296 q^{46} -379.013 q^{47} +855.674 q^{48} +200.850 q^{49} +23.2334 q^{51} -202.955 q^{52} +150.129 q^{53} +393.775 q^{54} -1267.49 q^{56} +216.040 q^{57} +460.382 q^{58} +207.310 q^{59} -486.557 q^{61} -1148.18 q^{62} +355.435 q^{63} +201.659 q^{64} +2027.96 q^{66} -1019.41 q^{67} +66.3055 q^{68} -414.110 q^{69} +13.8437 q^{71} -828.374 q^{72} -411.158 q^{73} -307.365 q^{74} +616.555 q^{76} -1412.25 q^{77} +366.421 q^{78} -1315.13 q^{79} -908.218 q^{81} +741.120 q^{82} -813.425 q^{83} +2811.35 q^{84} -221.558 q^{86} -580.721 q^{87} +3291.37 q^{88} -350.573 q^{89} -255.171 q^{91} -1181.83 q^{92} +1448.30 q^{93} +1952.87 q^{94} -1582.92 q^{96} +1187.03 q^{97} -1034.88 q^{98} -922.981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * q^99

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