LMFDB - Embedded newform 525.4.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.78066700.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 18x^{3} + 7x^{2} + 30x - 10 $ x^5 - x^4 - 18x^3 + 7x^2 + 30*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 5 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.329739$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.428319 q^{2} +3.00000 q^{3} -7.81654 q^{4} +1.28496 q^{6} -7.00000 q^{7} -6.77452 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.428319 q^{2} +3.00000 q^{3} -7.81654 q^{4} +1.28496 q^{6} -7.00000 q^{7} -6.77452 q^{8} +9.00000 q^{9} -27.4721 q^{11} -23.4496 q^{12} +46.5524 q^{13} -2.99823 q^{14} +59.6307 q^{16} -5.20546 q^{17} +3.85487 q^{18} -91.0007 q^{19} -21.0000 q^{21} -11.7668 q^{22} +111.563 q^{23} -20.3236 q^{24} +19.9393 q^{26} +27.0000 q^{27} +54.7158 q^{28} +0.0763413 q^{29} +201.784 q^{31} +79.7371 q^{32} -82.4163 q^{33} -2.22960 q^{34} -70.3489 q^{36} +312.859 q^{37} -38.9773 q^{38} +139.657 q^{39} +102.432 q^{41} -8.99470 q^{42} -257.280 q^{43} +214.737 q^{44} +47.7847 q^{46} +350.994 q^{47} +178.892 q^{48} +49.0000 q^{49} -15.6164 q^{51} -363.879 q^{52} -196.260 q^{53} +11.5646 q^{54} +47.4217 q^{56} -273.002 q^{57} +0.0326984 q^{58} +881.060 q^{59} +737.897 q^{61} +86.4280 q^{62} -63.0000 q^{63} -442.893 q^{64} -35.3004 q^{66} -365.021 q^{67} +40.6887 q^{68} +334.690 q^{69} +1112.53 q^{71} -60.9707 q^{72} -261.995 q^{73} +134.004 q^{74} +711.311 q^{76} +192.305 q^{77} +59.8179 q^{78} +273.829 q^{79} +81.0000 q^{81} +43.8735 q^{82} +87.1353 q^{83} +164.147 q^{84} -110.198 q^{86} +0.229024 q^{87} +186.110 q^{88} -1090.99 q^{89} -325.867 q^{91} -872.039 q^{92} +605.353 q^{93} +150.337 q^{94} +239.211 q^{96} -228.830 q^{97} +20.9876 q^{98} -247.249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9	$ 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9} + 66 q^{11} + 81 q^{12} + 2 q^{13} + 7 q^{14} + 155 q^{16} - 108 q^{17} - 9 q^{18} + 174 q^{19} - 105 q^{21} + 506 q^{22} + 116 q^{23} - 99 q^{24} + 446 q^{26} + 135 q^{27} - 189 q^{28} + 370 q^{29} + 342 q^{31} + 55 q^{32} + 198 q^{33} + 112 q^{34} + 243 q^{36} + 408 q^{37} + 34 q^{38} + 6 q^{39} + 802 q^{41} + 21 q^{42} + 584 q^{43} + 290 q^{44} + 640 q^{46} - 716 q^{47} + 465 q^{48} + 245 q^{49} - 324 q^{51} - 338 q^{52} - 98 q^{53} - 27 q^{54} + 231 q^{56} + 522 q^{57} - 482 q^{58} + 704 q^{59} + 650 q^{61} - 2070 q^{62} - 315 q^{63} + 75 q^{64} + 1518 q^{66} - 180 q^{67} - 4520 q^{68} + 348 q^{69} + 1470 q^{71} - 297 q^{72} + 534 q^{73} - 1312 q^{74} + 4370 q^{76} - 462 q^{77} + 1338 q^{78} - 820 q^{79} + 405 q^{81} + 1338 q^{82} - 1520 q^{83} - 567 q^{84} + 832 q^{86} + 1110 q^{87} + 3258 q^{88} + 286 q^{89} - 14 q^{91} - 1288 q^{92} + 1026 q^{93} + 2540 q^{94} + 165 q^{96} - 278 q^{97} - 49 q^{98} + 594 q^{99}+O(q^{100}) $ 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9 + 66 * q^11 + 81 * q^12 + 2 * q^13 + 7 * q^14 + 155 * q^16 - 108 * q^17 - 9 * q^18 + 174 * q^19 - 105 * q^21 + 506 * q^22 + 116 * q^23 - 99 * q^24 + 446 * q^26 + 135 * q^27 - 189 * q^28 + 370 * q^29 + 342 * q^31 + 55 * q^32 + 198 * q^33 + 112 * q^34 + 243 * q^36 + 408 * q^37 + 34 * q^38 + 6 * q^39 + 802 * q^41 + 21 * q^42 + 584 * q^43 + 290 * q^44 + 640 * q^46 - 716 * q^47 + 465 * q^48 + 245 * q^49 - 324 * q^51 - 338 * q^52 - 98 * q^53 - 27 * q^54 + 231 * q^56 + 522 * q^57 - 482 * q^58 + 704 * q^59 + 650 * q^61 - 2070 * q^62 - 315 * q^63 + 75 * q^64 + 1518 * q^66 - 180 * q^67 - 4520 * q^68 + 348 * q^69 + 1470 * q^71 - 297 * q^72 + 534 * q^73 - 1312 * q^74 + 4370 * q^76 - 462 * q^77 + 1338 * q^78 - 820 * q^79 + 405 * q^81 + 1338 * q^82 - 1520 * q^83 - 567 * q^84 + 832 * q^86 + 1110 * q^87 + 3258 * q^88 + 286 * q^89 - 14 * q^91 - 1288 * q^92 + 1026 * q^93 + 2540 * q^94 + 165 * q^96 - 278 * q^97 - 49 * q^98 + 594 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.428319	0.151434	0.0757168	−	0.997129i	$-0.475876\pi$
$2$	0.428319	0.151434	0.0757168	+	0.997129i	$0.475876\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.81654	−0.977068
$5$	0	0
$5$	0	0
$6$	1.28496	0.0874302
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−6.77452	−0.299394
$9$	9.00000	0.333333
$10$	0	0
$11$	−27.4721	−0.753013	−0.376507	−	0.926414i	$-0.622875\pi$
$11$	−27.4721	−0.753013	−0.376507	+	0.926414i	$0.622875\pi$
$12$	−23.4496	−0.564110
$13$	46.5524	0.993179	0.496589	−	0.867986i	$-0.334586\pi$
$13$	46.5524	0.993179	0.496589	+	0.867986i	$0.334586\pi$
$14$	−2.99823	−0.0572365
$15$	0	0
$16$	59.6307	0.931729
$17$	−5.20546	−0.0742653	−0.0371326	−	0.999310i	$-0.511822\pi$
$17$	−5.20546	−0.0742653	−0.0371326	+	0.999310i	$0.511822\pi$
$18$	3.85487	0.0504779
$19$	−91.0007	−1.09879	−0.549395	−	0.835563i	$-0.685142\pi$
$19$	−91.0007	−1.09879	−0.549395	+	0.835563i	$0.685142\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	−11.7668	−0.114032
$23$	111.563	1.01142	0.505708	−	0.862705i	$-0.331231\pi$
$23$	111.563	1.01142	0.505708	+	0.862705i	$0.331231\pi$
$24$	−20.3236	−0.172855
$25$	0	0
$26$	19.9393	0.150401
$27$	27.0000	0.192450
$28$	54.7158	0.369297
$29$	0.0763413	0.000488835 0	0.000244418	−	1.00000i	$-0.499922\pi$
$29$	0.0763413	0.000488835 0	0.000244418		1.00000i	$0.499922\pi$
$30$	0	0
$31$	201.784	1.16908	0.584541	−	0.811364i	$-0.301275\pi$
$31$	201.784	1.16908	0.584541	+	0.811364i	$0.301275\pi$
$32$	79.7371	0.440490
$33$	−82.4163	−0.434752
$34$	−2.22960	−0.0112463
$35$	0	0
$36$	−70.3489	−0.325689
$37$	312.859	1.39010	0.695051	−	0.718960i	$-0.255382\pi$
$37$	312.859	1.39010	0.695051	+	0.718960i	$0.255382\pi$
$38$	−38.9773	−0.166394
$39$	139.657	0.573412
$40$	0	0
$41$	102.432	0.390175	0.195087	−	0.980786i	$-0.437501\pi$
$41$	102.432	0.390175	0.195087	+	0.980786i	$0.437501\pi$
$42$	−8.99470	−0.0330455
$43$	−257.280	−0.912439	−0.456219	−	0.889867i	$-0.650797\pi$
$43$	−257.280	−0.912439	−0.456219	+	0.889867i	$0.650797\pi$
$44$	214.737	0.735745
$45$	0	0
$46$	47.7847	0.153162
$47$	350.994	1.08931	0.544657	−	0.838659i	$-0.316660\pi$
$47$	350.994	1.08931	0.544657	+	0.838659i	$0.316660\pi$
$48$	178.892	0.537934
$49$	49.0000	0.142857
$50$	0	0
$51$	−15.6164	−0.0428771
$52$	−363.879	−0.970403
$53$	−196.260	−0.508649	−0.254324	−	0.967119i	$-0.581853\pi$
$53$	−196.260	−0.508649	−0.254324	+	0.967119i	$0.581853\pi$
$54$	11.5646	0.0291434
$55$	0	0
$56$	47.4217	0.113160
$57$	−273.002	−0.634386
$58$	0.0326984	7.40261e−5 0
$59$	881.060	1.94414	0.972070	−	0.234692i	$-0.0754082\pi$
$59$	881.060	1.94414	0.972070	+	0.234692i	$0.0754082\pi$
$60$	0	0
$61$	737.897	1.54882	0.774410	−	0.632684i	$-0.218047\pi$
$61$	737.897	1.54882	0.774410	+	0.632684i	$0.218047\pi$
$62$	86.4280	0.177038
$63$	−63.0000	−0.125988
$64$	−442.893	−0.865025
$65$	0	0
$66$	−35.3004	−0.0658361
$67$	−365.021	−0.665589	−0.332794	−	0.942999i	$-0.607991\pi$
$67$	−365.021	−0.665589	−0.332794	+	0.942999i	$0.607991\pi$
$68$	40.6887	0.0725622
$69$	334.690	0.583941
$70$	0	0
$71$	1112.53	1.85962	0.929809	−	0.368042i	$-0.119972\pi$
$71$	1112.53	1.85962	0.929809	+	0.368042i	$0.119972\pi$
$72$	−60.9707	−0.0997982
$73$	−261.995	−0.420057	−0.210029	−	0.977695i	$-0.567356\pi$
$73$	−261.995	−0.420057	−0.210029	+	0.977695i	$0.567356\pi$
$74$	134.004	0.210508
$75$	0	0
$76$	711.311	1.07359
$77$	192.305	0.284612
$78$	59.8179	0.0868338
$79$	273.829	0.389977	0.194988	−	0.980806i	$-0.437533\pi$
$79$	273.829	0.389977	0.194988	+	0.980806i	$0.437533\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	43.8735	0.0590856
$83$	87.1353	0.115233	0.0576165	−	0.998339i	$-0.481650\pi$
$83$	87.1353	0.115233	0.0576165	+	0.998339i	$0.481650\pi$
$84$	164.147	0.213214
$85$	0	0
$86$	−110.198	−0.138174
$87$	0.229024	0.000282229 0
$88$	186.110	0.225448
$89$	−1090.99	−1.29938	−0.649690	−	0.760199i	$-0.725101\pi$
$89$	−1090.99	−1.29938	−0.649690	+	0.760199i	$0.725101\pi$
$90$	0	0
$91$	−325.867	−0.375386
$92$	−872.039	−0.988221
$93$	605.353	0.674969
$94$	150.337	0.164959
$95$	0	0
$96$	239.211	0.254317
$97$	−228.830	−0.239527	−0.119764	−	0.992802i	$-0.538214\pi$
$97$	−228.830	−0.239527	−0.119764	+	0.992802i	$0.538214\pi$
$98$	20.9876	0.0216334
$99$	−247.249	−0.251004
$100$	0	0
$101$	−590.728	−0.581976	−0.290988	−	0.956727i	$-0.593984\pi$
$101$	−590.728	−0.581976	−0.290988	+	0.956727i	$0.593984\pi$
$102$	−6.68879	−0.00649303
$103$	1471.06	1.40726	0.703629	−	0.710568i	$-0.251562\pi$
$103$	1471.06	1.40726	0.703629	+	0.710568i	$0.251562\pi$
$104$	−315.371	−0.297352
$105$	0	0
$106$	−84.0619	−0.0770265
$107$	−1223.29	−1.10523	−0.552617	−	0.833435i	$-0.686371\pi$
$107$	−1223.29	−1.10523	−0.552617	+	0.833435i	$0.686371\pi$
$108$	−211.047	−0.188037
$109$	1280.64	1.12535	0.562674	−	0.826679i	$-0.309773\pi$
$109$	1280.64	1.12535	0.562674	+	0.826679i	$0.309773\pi$
$110$	0	0
$111$	938.578	0.802576
$112$	−417.415	−0.352161
$113$	−1805.38	−1.50297	−0.751487	−	0.659748i	$-0.770663\pi$
$113$	−1805.38	−1.50297	−0.751487	+	0.659748i	$0.770663\pi$
$114$	−116.932	−0.0960674
$115$	0	0
$116$	−0.596725	−0.000477625 0
$117$	418.972	0.331060
$118$	377.375	0.294408
$119$	36.4382	0.0280696
$120$	0	0
$121$	−576.284	−0.432971
$122$	316.055	0.234543
$123$	307.296	0.225268
$124$	−1577.26	−1.14227
$125$	0	0
$126$	−26.9841	−0.0190788
$127$	1642.42	1.14757	0.573786	−	0.819005i	$-0.305474\pi$
$127$	1642.42	1.14757	0.573786	+	0.819005i	$0.305474\pi$
$128$	−827.596	−0.571483
$129$	−771.841	−0.526797
$130$	0	0
$131$	2371.85	1.58190	0.790951	−	0.611879i	$-0.209586\pi$
$131$	2371.85	1.58190	0.790951	+	0.611879i	$0.209586\pi$
$132$	644.210	0.424783
$133$	637.005	0.415303
$134$	−156.345	−0.100792
$135$	0	0
$136$	35.2645	0.0222346
$137$	762.828	0.475714	0.237857	−	0.971300i	$-0.423555\pi$
$137$	762.828	0.475714	0.237857	+	0.971300i	$0.423555\pi$
$138$	143.354	0.0884283
$139$	2025.84	1.23618	0.618092	−	0.786105i	$-0.287906\pi$
$139$	2025.84	1.23618	0.618092	+	0.786105i	$0.287906\pi$
$140$	0	0
$141$	1052.98	0.628916
$142$	476.517	0.281609
$143$	−1278.89	−0.747877
$144$	536.676	0.310576
$145$	0	0
$146$	−112.217	−0.0636108
$147$	147.000	0.0824786
$148$	−2445.48	−1.35822
$149$	−10.7903	−0.00593272	−0.00296636	−	0.999996i	$-0.500944\pi$
$149$	−10.7903	−0.00593272	−0.00296636	+	0.999996i	$0.500944\pi$
$150$	0	0
$151$	−2404.48	−1.29585	−0.647925	−	0.761704i	$-0.724363\pi$
$151$	−2404.48	−1.29585	−0.647925	+	0.761704i	$0.724363\pi$
$152$	616.487	0.328972
$153$	−46.8491	−0.0247551
$154$	82.3677	0.0430999
$155$	0	0
$156$	−1091.64	−0.560262
$157$	396.624	0.201618	0.100809	−	0.994906i	$-0.467857\pi$
$157$	396.624	0.201618	0.100809	+	0.994906i	$0.467857\pi$
$158$	117.286	0.0590556
$159$	−588.780	−0.293669
$160$	0	0
$161$	−780.943	−0.382279
$162$	34.6938	0.0168260
$163$	2751.69	1.32226	0.661132	−	0.750270i	$-0.270077\pi$
$163$	2751.69	1.32226	0.661132	+	0.750270i	$0.270077\pi$
$164$	−800.663	−0.381227
$165$	0	0
$166$	37.3217	0.0174501
$167$	−2079.43	−0.963541	−0.481771	−	0.876297i	$-0.660006\pi$
$167$	−2079.43	−0.963541	−0.481771	+	0.876297i	$0.660006\pi$
$168$	142.265	0.0653332
$169$	−29.8706	−0.0135961
$170$	0	0
$171$	−819.007	−0.366263
$172$	2011.04	0.891515
$173$	−1929.59	−0.848000	−0.424000	−	0.905662i	$-0.639374\pi$
$173$	−1929.59	−0.848000	−0.424000	+	0.905662i	$0.639374\pi$
$174$	0.0980953	4.27390e−5 0
$175$	0	0
$176$	−1638.18	−0.701605
$177$	2643.18	1.12245
$178$	−467.292	−0.196770
$179$	1638.15	0.684027	0.342014	−	0.939695i	$-0.388891\pi$
$179$	1638.15	0.684027	0.342014	+	0.939695i	$0.388891\pi$
$180$	0	0
$181$	−36.6604	−0.0150550	−0.00752749	−	0.999972i	$-0.502396\pi$
$181$	−36.6604	−0.0150550	−0.00752749	+	0.999972i	$0.502396\pi$
$182$	−139.575	−0.0568461
$183$	2213.69	0.894212
$184$	−755.788	−0.302812
$185$	0	0
$186$	259.284	0.102213
$187$	143.005	0.0559227
$188$	−2743.56	−1.06433
$189$	−189.000	−0.0727393
$190$	0	0
$191$	1054.82	0.399603	0.199801	−	0.979836i	$-0.435970\pi$
$191$	1054.82	0.399603	0.199801	+	0.979836i	$0.435970\pi$
$192$	−1328.68	−0.499422
$193$	−213.661	−0.0796873	−0.0398436	−	0.999206i	$-0.512686\pi$
$193$	−213.661	−0.0796873	−0.0398436	+	0.999206i	$0.512686\pi$
$194$	−98.0121	−0.0362725
$195$	0	0
$196$	−383.011	−0.139581
$197$	−3953.62	−1.42987	−0.714933	−	0.699193i	$-0.753543\pi$
$197$	−3953.62	−1.42987	−0.714933	+	0.699193i	$0.753543\pi$
$198$	−105.901	−0.0380105
$199$	929.168	0.330990	0.165495	−	0.986211i	$-0.447078\pi$
$199$	929.168	0.330990	0.165495	+	0.986211i	$0.447078\pi$
$200$	0	0
$201$	−1095.06	−0.384278
$202$	−253.020	−0.0881308
$203$	−0.534389	−0.000184762 0
$204$	122.066	0.0418938
$205$	0	0
$206$	630.081	0.213106
$207$	1004.07	0.337138
$208$	2775.95	0.925374
$209$	2499.98	0.827403
$210$	0	0
$211$	−926.806	−0.302388	−0.151194	−	0.988504i	$-0.548312\pi$
$211$	−926.806	−0.302388	−0.151194	+	0.988504i	$0.548312\pi$
$212$	1534.07	0.496984
$213$	3337.59	1.07365
$214$	−523.959	−0.167370
$215$	0	0
$216$	−182.912	−0.0576185
$217$	−1412.49	−0.441871
$218$	548.521	0.170415
$219$	−785.985	−0.242520
$220$	0	0
$221$	−242.327	−0.0737587
$222$	402.011	0.121537
$223$	5351.73	1.60708	0.803538	−	0.595253i	$-0.202948\pi$
$223$	5351.73	1.60708	0.803538	+	0.595253i	$0.202948\pi$
$224$	−558.160	−0.166489
$225$	0	0
$226$	−773.279	−0.227601
$227$	−6016.48	−1.75915	−0.879576	−	0.475758i	$-0.842174\pi$
$227$	−6016.48	−1.75915	−0.879576	+	0.475758i	$0.842174\pi$
$228$	2133.93	0.619839
$229$	1210.84	0.349408	0.174704	−	0.984621i	$-0.444103\pi$
$229$	1210.84	0.349408	0.174704	+	0.984621i	$0.444103\pi$
$230$	0	0
$231$	576.914	0.164321
$232$	−0.517176	−0.000146355 0
$233$	−3517.31	−0.988957	−0.494478	−	0.869190i	$-0.664641\pi$
$233$	−3517.31	−0.988957	−0.494478	+	0.869190i	$0.664641\pi$
$234$	179.454	0.0501335
$235$	0	0
$236$	−6886.84	−1.89956
$237$	821.487	0.225153
$238$	15.6072	0.00425068
$239$	−6715.89	−1.81764	−0.908818	−	0.417194i	$-0.863014\pi$
$239$	−6715.89	−1.81764	−0.908818	+	0.417194i	$0.863014\pi$
$240$	0	0
$241$	−1715.70	−0.458582	−0.229291	−	0.973358i	$-0.573641\pi$
$241$	−1715.70	−0.458582	−0.229291	+	0.973358i	$0.573641\pi$
$242$	−246.833	−0.0655663
$243$	243.000	0.0641500
$244$	−5767.80	−1.51330
$245$	0	0
$246$	131.620	0.0341131
$247$	−4236.31	−1.09129
$248$	−1366.99	−0.350017
$249$	261.406	0.0665298
$250$	0	0
$251$	−2464.48	−0.619748	−0.309874	−	0.950778i	$-0.600287\pi$
$251$	−2464.48	−0.619748	−0.309874	+	0.950778i	$0.600287\pi$
$252$	492.442	0.123099
$253$	−3064.88	−0.761609
$254$	703.482	0.173781
$255$	0	0
$256$	3188.67	0.778483
$257$	1873.99	0.454850	0.227425	−	0.973796i	$-0.426969\pi$
$257$	1873.99	0.454850	0.227425	+	0.973796i	$0.426969\pi$
$258$	−330.594	−0.0797747
$259$	−2190.02	−0.525409
$260$	0	0
$261$	0.687072	0.000162945 0
$262$	1015.91	0.239553
$263$	−2064.39	−0.484013	−0.242007	−	0.970275i	$-0.577806\pi$
$263$	−2064.39	−0.484013	−0.242007	+	0.970275i	$0.577806\pi$
$264$	558.331	0.130162
$265$	0	0
$266$	272.841	0.0628909
$267$	−3272.97	−0.750197
$268$	2853.20	0.650325
$269$	5649.86	1.28059	0.640294	−	0.768130i	$-0.278812\pi$
$269$	5649.86	1.28059	0.640294	+	0.768130i	$0.278812\pi$
$270$	0	0
$271$	−3094.93	−0.693739	−0.346870	−	0.937913i	$-0.612755\pi$
$271$	−3094.93	−0.693739	−0.346870	+	0.937913i	$0.612755\pi$
$272$	−310.405	−0.0691951
$273$	−977.601	−0.216729
$274$	326.734	0.0720391
$275$	0	0
$276$	−2616.12	−0.570550
$277$	8962.93	1.94415	0.972076	−	0.234665i	$-0.0753995\pi$
$277$	8962.93	1.94415	0.972076	+	0.234665i	$0.0753995\pi$
$278$	867.706	0.187200
$279$	1816.06	0.389694
$280$	0	0
$281$	−5858.94	−1.24383	−0.621913	−	0.783086i	$-0.713644\pi$
$281$	−5858.94	−1.24383	−0.621913	+	0.783086i	$0.713644\pi$
$282$	451.012	0.0952390
$283$	−5819.46	−1.22237	−0.611186	−	0.791487i	$-0.709307\pi$
$283$	−5819.46	−1.22237	−0.611186	+	0.791487i	$0.709307\pi$
$284$	−8696.13	−1.81697
$285$	0	0
$286$	−547.774	−0.113254
$287$	−717.023	−0.147472
$288$	717.634	0.146830
$289$	−4885.90	−0.994485
$290$	0	0
$291$	−686.489	−0.138291
$292$	2047.90	0.410425
$293$	−5678.78	−1.13228	−0.566139	−	0.824310i	$-0.691564\pi$
$293$	−5678.78	−1.13228	−0.566139	+	0.824310i	$0.691564\pi$
$294$	62.9629	0.0124900
$295$	0	0
$296$	−2119.47	−0.416189
$297$	−741.746	−0.144917
$298$	−4.62169	−0.000898413 0
$299$	5193.54	1.00452
$300$	0	0
$301$	1800.96	0.344869
$302$	−1029.88	−0.196235
$303$	−1772.18	−0.336004
$304$	−5426.44	−1.02377
$305$	0	0
$306$	−20.0664	−0.00374875
$307$	−9184.53	−1.70745	−0.853727	−	0.520720i	$-0.825663\pi$
$307$	−9184.53	−1.70745	−0.853727	+	0.520720i	$0.825663\pi$
$308$	−1503.16	−0.278086
$309$	4413.17	0.812480
$310$	0	0
$311$	4410.22	0.804119	0.402059	−	0.915614i	$-0.368295\pi$
$311$	4410.22	0.804119	0.402059	+	0.915614i	$0.368295\pi$
$312$	−946.112	−0.171676
$313$	4405.28	0.795530	0.397765	−	0.917487i	$-0.369786\pi$
$313$	4405.28	0.795530	0.397765	+	0.917487i	$0.369786\pi$
$314$	169.882	0.0305318
$315$	0	0
$316$	−2140.40	−0.381034
$317$	7486.86	1.32651	0.663256	−	0.748393i	$-0.269174\pi$
$317$	7486.86	1.32651	0.663256	+	0.748393i	$0.269174\pi$
$318$	−252.186	−0.0444713
$319$	−2.09726	−0.000368100 0
$320$	0	0
$321$	−3669.87	−0.638107
$322$	−334.493	−0.0578899
$323$	473.701	0.0816019
$324$	−633.140	−0.108563
$325$	0	0
$326$	1178.60	0.200235
$327$	3841.91	0.649719
$328$	−693.927	−0.116816
$329$	−2456.96	−0.411722
$330$	0	0
$331$	8860.56	1.47136	0.735680	−	0.677329i	$-0.236863\pi$
$331$	8860.56	1.47136	0.735680	+	0.677329i	$0.236863\pi$
$332$	−681.097	−0.112590
$333$	2815.74	0.463367
$334$	−890.660	−0.145912
$335$	0	0
$336$	−1252.24	−0.203320
$337$	8742.01	1.41308	0.706539	−	0.707674i	$-0.250255\pi$
$337$	8742.01	1.41308	0.706539	+	0.707674i	$0.250255\pi$
$338$	−12.7942	−0.00205891
$339$	−5416.15	−0.867742
$340$	0	0
$341$	−5543.44	−0.880334
$342$	−350.796	−0.0554646
$343$	−343.000	−0.0539949
$344$	1742.95	0.273179
$345$	0	0
$346$	−826.480	−0.128416
$347$	7285.82	1.12716	0.563579	−	0.826063i	$-0.309424\pi$
$347$	7285.82	1.12716	0.563579	+	0.826063i	$0.309424\pi$
$348$	−1.79018	−0.000275757 0
$349$	12610.9	1.93423	0.967117	−	0.254330i	$-0.0818550\pi$
$349$	12610.9	1.93423	0.967117	+	0.254330i	$0.0818550\pi$
$350$	0	0
$351$	1256.92	0.191137
$352$	−2190.55	−0.331695
$353$	1202.59	0.181325	0.0906623	−	0.995882i	$-0.471102\pi$
$353$	1202.59	0.181325	0.0906623	+	0.995882i	$0.471102\pi$
$354$	1132.12	0.169977
$355$	0	0
$356$	8527.78	1.26958
$357$	109.315	0.0162060
$358$	701.649	0.103585
$359$	3216.35	0.472848	0.236424	−	0.971650i	$-0.424025\pi$
$359$	3216.35	0.472848	0.236424	+	0.971650i	$0.424025\pi$
$360$	0	0
$361$	1422.14	0.207339
$362$	−15.7024	−0.00227983
$363$	−1728.85	−0.249976
$364$	2547.15	0.366778
$365$	0	0
$366$	948.166	0.135414
$367$	1259.66	0.179165	0.0895824	−	0.995979i	$-0.471447\pi$
$367$	1259.66	0.179165	0.0895824	+	0.995979i	$0.471447\pi$
$368$	6652.59	0.942365
$369$	921.887	0.130058
$370$	0	0
$371$	1373.82	0.192251
$372$	−4731.77	−0.659491
$373$	386.230	0.0536145	0.0268073	−	0.999641i	$-0.491466\pi$
$373$	386.230	0.0536145	0.0268073	+	0.999641i	$0.491466\pi$
$374$	61.2517	0.00846858
$375$	0	0
$376$	−2377.82	−0.326135
$377$	3.55387	0.000485501 0
$378$	−80.9523	−0.0110152
$379$	14246.0	1.93079	0.965395	−	0.260794i	$-0.0839842\pi$
$379$	14246.0	1.93079	0.965395	+	0.260794i	$0.0839842\pi$
$380$	0	0
$381$	4927.27	0.662551
$382$	451.800	0.0605133
$383$	−9298.85	−1.24060	−0.620299	−	0.784365i	$-0.712989\pi$
$383$	−9298.85	−1.24060	−0.620299	+	0.784365i	$0.712989\pi$
$384$	−2482.79	−0.329946
$385$	0	0
$386$	−91.5150	−0.0120673
$387$	−2315.52	−0.304146
$388$	1788.66	0.234034
$389$	−1043.80	−0.136049	−0.0680244	−	0.997684i	$-0.521670\pi$
$389$	−1043.80	−0.136049	−0.0680244	+	0.997684i	$0.521670\pi$
$390$	0	0
$391$	−580.738	−0.0751130
$392$	−331.952	−0.0427706
$393$	7115.54	0.913312
$394$	−1693.41	−0.216530
$395$	0	0
$396$	1932.63	0.245248
$397$	−4482.04	−0.566617	−0.283309	−	0.959029i	$-0.591432\pi$
$397$	−4482.04	−0.566617	−0.283309	+	0.959029i	$0.591432\pi$
$398$	397.980	0.0501230
$399$	1911.02	0.239776
$400$	0	0
$401$	12686.2	1.57984	0.789921	−	0.613209i	$-0.210122\pi$
$401$	12686.2	1.57984	0.789921	+	0.613209i	$0.210122\pi$
$402$	−469.036	−0.0581926
$403$	9393.55	1.16111
$404$	4617.45	0.568630
$405$	0	0
$406$	−0.228889	−2.79792e−5 0
$407$	−8594.90	−1.04677
$408$	105.794	0.0128372
$409$	−6836.54	−0.826516	−0.413258	−	0.910614i	$-0.635609\pi$
$409$	−6836.54	−0.826516	−0.413258	+	0.910614i	$0.635609\pi$
$410$	0	0
$411$	2288.48	0.274654
$412$	−11498.6	−1.37499
$413$	−6167.42	−0.734816
$414$	430.062	0.0510541
$415$	0	0
$416$	3711.96	0.437485
$417$	6077.53	0.713712
$418$	1070.79	0.125297
$419$	−5091.64	−0.593659	−0.296829	−	0.954930i	$-0.595929\pi$
$419$	−5091.64	−0.593659	−0.296829	+	0.954930i	$0.595929\pi$
$420$	0	0
$421$	8373.48	0.969355	0.484677	−	0.874693i	$-0.338937\pi$
$421$	8373.48	0.969355	0.484677	+	0.874693i	$0.338937\pi$
$422$	−396.968	−0.0457918
$423$	3158.95	0.363105
$424$	1329.57	0.152287
$425$	0	0
$426$	1429.55	0.162587
$427$	−5165.28	−0.585399
$428$	9561.91	1.07989
$429$	−3836.68	−0.431787
$430$	0	0
$431$	6027.75	0.673657	0.336829	−	0.941566i	$-0.390646\pi$
$431$	6027.75	0.673657	0.336829	+	0.941566i	$0.390646\pi$
$432$	1610.03	0.179311
$433$	−11927.5	−1.32379	−0.661894	−	0.749597i	$-0.730247\pi$
$433$	−11927.5	−1.32379	−0.661894	+	0.749597i	$0.730247\pi$
$434$	−604.996	−0.0669141
$435$	0	0
$436$	−10010.2	−1.09954
$437$	−10152.3	−1.11133
$438$	−336.652	−0.0367257
$439$	7914.93	0.860499	0.430250	−	0.902710i	$-0.358426\pi$
$439$	7914.93	0.860499	0.430250	+	0.902710i	$0.358426\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−103.793	−0.0111695
$443$	2522.71	0.270559	0.135279	−	0.990807i	$-0.456807\pi$
$443$	2522.71	0.270559	0.135279	+	0.990807i	$0.456807\pi$
$444$	−7336.44	−0.784171
$445$	0	0
$446$	2292.24	0.243365
$447$	−32.3709	−0.00342526
$448$	3100.25	0.326949
$449$	−5339.89	−0.561258	−0.280629	−	0.959816i	$-0.590543\pi$
$449$	−5339.89	−0.561258	−0.280629	+	0.959816i	$0.590543\pi$
$450$	0	0
$451$	−2814.02	−0.293807
$452$	14111.8	1.46851
$453$	−7213.43	−0.748160
$454$	−2576.97	−0.266395
$455$	0	0
$456$	1849.46	0.189932
$457$	13765.8	1.40905	0.704526	−	0.709679i	$-0.251160\pi$
$457$	13765.8	1.40905	0.704526	+	0.709679i	$0.251160\pi$
$458$	518.625	0.0529122
$459$	−140.547	−0.0142924
$460$	0	0
$461$	−12501.1	−1.26298	−0.631489	−	0.775384i	$-0.717556\pi$
$461$	−12501.1	−1.26298	−0.631489	+	0.775384i	$0.717556\pi$
$462$	247.103	0.0248837
$463$	−3566.32	−0.357972	−0.178986	−	0.983852i	$-0.557282\pi$
$463$	−3566.32	−0.357972	−0.178986	+	0.983852i	$0.557282\pi$
$464$	4.55229	0.000455462 0
$465$	0	0
$466$	−1506.53	−0.149761
$467$	4078.17	0.404101	0.202050	−	0.979375i	$-0.435240\pi$
$467$	4078.17	0.404101	0.202050	+	0.979375i	$0.435240\pi$
$468$	−3274.91	−0.323468
$469$	2555.15	0.251569
$470$	0	0
$471$	1189.87	0.116404
$472$	−5968.76	−0.582065
$473$	7068.03	0.687079
$474$	351.858	0.0340958
$475$	0	0
$476$	−284.821	−0.0274259
$477$	−1766.34	−0.169550
$478$	−2876.54	−0.275251
$479$	19078.0	1.81982	0.909911	−	0.414803i	$-0.136150\pi$
$479$	19078.0	1.81982	0.909911	+	0.414803i	$0.136150\pi$
$480$	0	0
$481$	14564.4	1.38062
$482$	−734.868	−0.0694447
$483$	−2342.83	−0.220709
$484$	4504.55	0.423042
$485$	0	0
$486$	104.081	0.00971447
$487$	15616.4	1.45307	0.726537	−	0.687128i	$-0.241129\pi$
$487$	15616.4	1.45307	0.726537	+	0.687128i	$0.241129\pi$
$488$	−4998.90	−0.463708
$489$	8255.07	0.763409
$490$	0	0
$491$	7547.46	0.693711	0.346856	−	0.937919i	$-0.387249\pi$
$491$	7547.46	0.693711	0.346856	+	0.937919i	$0.387249\pi$
$492$	−2401.99	−0.220102
$493$	−0.397392	−3.63035e−5 0
$494$	−1814.49	−0.165259
$495$	0	0
$496$	12032.5	1.08927
$497$	−7787.70	−0.702870
$498$	111.965	0.0100748
$499$	3288.10	0.294982	0.147491	−	0.989063i	$-0.452880\pi$
$499$	3288.10	0.294982	0.147491	+	0.989063i	$0.452880\pi$
$500$	0	0
$501$	−6238.30	−0.556301
$502$	−1055.58	−0.0938506
$503$	−1044.67	−0.0926032	−0.0463016	−	0.998928i	$-0.514744\pi$
$503$	−1044.67	−0.0926032	−0.0463016	+	0.998928i	$0.514744\pi$
$504$	426.795	0.0377202
$505$	0	0
$506$	−1312.74	−0.115333
$507$	−89.6119	−0.00784972
$508$	−12838.1	−1.12126
$509$	−8783.91	−0.764912	−0.382456	−	0.923974i	$-0.624922\pi$
$509$	−8783.91	−0.764912	−0.382456	+	0.923974i	$0.624922\pi$
$510$	0	0
$511$	1833.97	0.158767
$512$	7986.54	0.689372
$513$	−2457.02	−0.211462
$514$	802.666	0.0688796
$515$	0	0
$516$	6033.13	0.514716
$517$	−9642.54	−0.820268
$518$	−938.025	−0.0795646
$519$	−5788.77	−0.489593
$520$	0	0
$521$	9983.79	0.839535	0.419767	−	0.907632i	$-0.362112\pi$
$521$	9983.79	0.839535	0.419767	+	0.907632i	$0.362112\pi$
$522$	0.294286	2.46754e−5 0
$523$	8177.52	0.683706	0.341853	−	0.939754i	$-0.388946\pi$
$523$	8177.52	0.683706	0.341853	+	0.939754i	$0.388946\pi$
$524$	−18539.6	−1.54563
$525$	0	0
$526$	−884.215	−0.0732958
$527$	−1050.38	−0.0868221
$528$	−4914.54	−0.405072
$529$	279.364	0.0229608
$530$	0	0
$531$	7929.54	0.648046
$532$	−4979.18	−0.405780
$533$	4768.45	0.387513
$534$	−1401.88	−0.113605
$535$	0	0
$536$	2472.85	0.199274
$537$	4914.44	0.394923
$538$	2419.94	0.193924
$539$	−1346.13	−0.107573
$540$	0	0
$541$	−3425.16	−0.272198	−0.136099	−	0.990695i	$-0.543457\pi$
$541$	−3425.16	−0.272198	−0.136099	+	0.990695i	$0.543457\pi$
$542$	−1325.61	−0.105055
$543$	−109.981	−0.00869199
$544$	−415.068	−0.0327131
$545$	0	0
$546$	−418.725	−0.0328201
$547$	5955.72	0.465536	0.232768	−	0.972532i	$-0.425222\pi$
$547$	5955.72	0.465536	0.232768	+	0.972532i	$0.425222\pi$
$548$	−5962.68	−0.464805
$549$	6641.07	0.516273
$550$	0	0
$551$	−6.94712	−0.000537127 0
$552$	−2267.36	−0.174829
$553$	−1916.80	−0.147397
$554$	3838.99	0.294410
$555$	0	0
$556$	−15835.1	−1.20784
$557$	2506.35	0.190660	0.0953298	−	0.995446i	$-0.469609\pi$
$557$	2506.35	0.190660	0.0953298	+	0.995446i	$0.469609\pi$
$558$	777.852	0.0590127
$559$	−11977.0	−0.906215
$560$	0	0
$561$	429.015	0.0322870
$562$	−2509.50	−0.188357
$563$	−3460.79	−0.259068	−0.129534	−	0.991575i	$-0.541348\pi$
$563$	−3460.79	−0.259068	−0.129534	+	0.991575i	$0.541348\pi$
$564$	−8230.68	−0.614493
$565$	0	0
$566$	−2492.59	−0.185108
$567$	−567.000	−0.0419961
$568$	−7536.86	−0.556760
$569$	22561.2	1.66224	0.831119	−	0.556095i	$-0.187701\pi$
$569$	22561.2	1.66224	0.831119	+	0.556095i	$0.187701\pi$
$570$	0	0
$571$	−992.585	−0.0727467	−0.0363734	−	0.999338i	$-0.511581\pi$
$571$	−992.585	−0.0727467	−0.0363734	+	0.999338i	$0.511581\pi$
$572$	9996.52	0.730726
$573$	3164.46	0.230711
$574$	−307.114	−0.0223322
$575$	0	0
$576$	−3986.03	−0.288342
$577$	−9202.70	−0.663975	−0.331987	−	0.943284i	$-0.607719\pi$
$577$	−9202.70	−0.663975	−0.331987	+	0.943284i	$0.607719\pi$
$578$	−2092.72	−0.150598
$579$	−640.983	−0.0460075
$580$	0	0
$581$	−609.947	−0.0435540
$582$	−294.036	−0.0209419
$583$	5391.67	0.383019
$584$	1774.89	0.125763
$585$	0	0
$586$	−2432.33	−0.171465
$587$	−27046.3	−1.90174	−0.950869	−	0.309593i	$-0.899807\pi$
$587$	−27046.3	−1.90174	−0.950869	+	0.309593i	$0.899807\pi$
$588$	−1149.03	−0.0805872
$589$	−18362.5	−1.28457
$590$	0	0
$591$	−11860.9	−0.825534
$592$	18656.0	1.29520
$593$	26364.0	1.82570	0.912849	−	0.408298i	$-0.133877\pi$
$593$	26364.0	1.82570	0.912849	+	0.408298i	$0.133877\pi$
$594$	−317.704	−0.0219454
$595$	0	0
$596$	84.3428	0.00579667
$597$	2787.50	0.191097
$598$	2224.49	0.152117
$599$	6624.09	0.451841	0.225921	−	0.974146i	$-0.427461\pi$
$599$	6624.09	0.451841	0.225921	+	0.974146i	$0.427461\pi$
$600$	0	0
$601$	−3984.03	−0.270403	−0.135201	−	0.990818i	$-0.543168\pi$
$601$	−3984.03	−0.270403	−0.135201	+	0.990818i	$0.543168\pi$
$602$	771.386	0.0522248
$603$	−3285.19	−0.221863
$604$	18794.7	1.26613
$605$	0	0
$606$	−759.060	−0.0508823
$607$	8605.79	0.575450	0.287725	−	0.957713i	$-0.407101\pi$
$607$	8605.79	0.575450	0.287725	+	0.957713i	$0.407101\pi$
$608$	−7256.14	−0.484005
$609$	−1.60317	−0.000106673 0
$610$	0	0
$611$	16339.6	1.08188
$612$	366.198	0.0241874
$613$	22070.4	1.45418	0.727091	−	0.686541i	$-0.240872\pi$
$613$	22070.4	1.45418	0.727091	+	0.686541i	$0.240872\pi$
$614$	−3933.91	−0.258566
$615$	0	0
$616$	−1302.77	−0.0852114
$617$	−17328.8	−1.13068	−0.565340	−	0.824858i	$-0.691255\pi$
$617$	−17328.8	−1.13068	−0.565340	+	0.824858i	$0.691255\pi$
$618$	1890.24	0.123037
$619$	1240.99	0.0805808	0.0402904	−	0.999188i	$-0.487172\pi$
$619$	1240.99	0.0805808	0.0402904	+	0.999188i	$0.487172\pi$
$620$	0	0
$621$	3012.21	0.194647
$622$	1888.98	0.121771
$623$	7636.94	0.491119
$624$	8327.86	0.534265
$625$	0	0
$626$	1886.86	0.120470
$627$	7499.94	0.477701
$628$	−3100.23	−0.196995
$629$	−1628.58	−0.103236
$630$	0	0
$631$	10004.0	0.631143	0.315572	−	0.948902i	$-0.397804\pi$
$631$	10004.0	0.631143	0.315572	+	0.948902i	$0.397804\pi$
$632$	−1855.06	−0.116757
$633$	−2780.42	−0.174584
$634$	3206.76	0.200878
$635$	0	0
$636$	4602.22	0.286934
$637$	2281.07	0.141883
$638$	−0.898294	−5.57426e−5 0
$639$	10012.8	0.619873
$640$	0	0
$641$	−23107.3	−1.42384	−0.711921	−	0.702260i	$-0.752174\pi$
$641$	−23107.3	−1.42384	−0.711921	+	0.702260i	$0.752174\pi$
$642$	−1571.88	−0.0966308
$643$	−11629.9	−0.713281	−0.356641	−	0.934242i	$-0.616078\pi$
$643$	−11629.9	−0.713281	−0.356641	+	0.934242i	$0.616078\pi$
$644$	6104.27	0.373513
$645$	0	0
$646$	202.895	0.0123573
$647$	−6371.50	−0.387156	−0.193578	−	0.981085i	$-0.562009\pi$
$647$	−6371.50	−0.387156	−0.193578	+	0.981085i	$0.562009\pi$
$648$	−548.736	−0.0332661
$649$	−24204.6	−1.46396
$650$	0	0
$651$	−4237.47	−0.255114
$652$	−21508.7	−1.29194
$653$	20264.5	1.21441	0.607207	−	0.794544i	$-0.292290\pi$
$653$	20264.5	1.21441	0.607207	+	0.794544i	$0.292290\pi$
$654$	1645.56	0.0983893
$655$	0	0
$656$	6108.08	0.363537
$657$	−2357.96	−0.140019
$658$	−1052.36	−0.0623485
$659$	−7132.74	−0.421627	−0.210813	−	0.977526i	$-0.567611\pi$
$659$	−7132.74	−0.421627	−0.210813	+	0.977526i	$0.567611\pi$
$660$	0	0
$661$	10555.8	0.621140	0.310570	−	0.950550i	$-0.399480\pi$
$661$	10555.8	0.621140	0.310570	+	0.950550i	$0.399480\pi$
$662$	3795.14	0.222813
$663$	−726.980	−0.0425846
$664$	−590.300	−0.0345001
$665$	0	0
$666$	1206.03	0.0701694
$667$	8.51689	0.000494416 0
$668$	16254.0	0.941445
$669$	16055.2	0.927846
$670$	0	0
$671$	−20271.6	−1.16628
$672$	−1674.48	−0.0961227
$673$	−3828.08	−0.219259	−0.109630	−	0.993973i	$-0.534966\pi$
$673$	−3828.08	−0.219259	−0.109630	+	0.993973i	$0.534966\pi$
$674$	3744.37	0.213988
$675$	0	0
$676$	233.485	0.0132843
$677$	24660.6	1.39998	0.699989	−	0.714154i	$-0.253188\pi$
$677$	24660.6	1.39998	0.699989	+	0.714154i	$0.253188\pi$
$678$	−2319.84	−0.131405
$679$	1601.81	0.0905328
$680$	0	0
$681$	−18049.4	−1.01565
$682$	−2374.36	−0.133312
$683$	18562.2	1.03992	0.519958	−	0.854192i	$-0.325948\pi$
$683$	18562.2	1.03992	0.519958	+	0.854192i	$0.325948\pi$
$684$	6401.80	0.357864
$685$	0	0
$686$	−146.913	−0.00817665
$687$	3632.52	0.201731
$688$	−15341.8	−0.850146
$689$	−9136.38	−0.505179
$690$	0	0
$691$	27335.9	1.50493	0.752465	−	0.658632i	$-0.228865\pi$
$691$	27335.9	1.50493	0.752465	+	0.658632i	$0.228865\pi$
$692$	15082.7	0.828554
$693$	1730.74	0.0948708
$694$	3120.66	0.170689
$695$	0	0
$696$	−1.55153	−8.44979e−5 0
$697$	−533.205	−0.0289764
$698$	5401.50	0.292908
$699$	−10551.9	−0.570974
$700$	0	0
$701$	−30924.1	−1.66617	−0.833087	−	0.553142i	$-0.813429\pi$
$701$	−30924.1	−1.66617	−0.833087	+	0.553142i	$0.813429\pi$
$702$	538.361	0.0289446
$703$	−28470.4	−1.52743
$704$	12167.2	0.651375
$705$	0	0
$706$	515.093	0.0274586
$707$	4135.09	0.219966
$708$	−20660.5	−1.09671
$709$	−28329.0	−1.50059	−0.750295	−	0.661103i	$-0.770088\pi$
$709$	−28329.0	−1.50059	−0.750295	+	0.661103i	$0.770088\pi$
$710$	0	0
$711$	2464.46	0.129992
$712$	7390.95	0.389027
$713$	22511.7	1.18243
$714$	46.8215	0.00245413
$715$	0	0
$716$	−12804.6	−0.668341
$717$	−20147.7	−1.04941
$718$	1377.62	0.0716051
$719$	−12563.4	−0.651651	−0.325825	−	0.945430i	$-0.605642\pi$
$719$	−12563.4	−0.651651	−0.325825	+	0.945430i	$0.605642\pi$
$720$	0	0
$721$	−10297.4	−0.531893
$722$	609.127	0.0313980
$723$	−5147.11	−0.264762
$724$	286.558	0.0147097
$725$	0	0
$726$	−740.500	−0.0378547
$727$	13523.2	0.689888	0.344944	−	0.938623i	$-0.387898\pi$
$727$	13523.2	0.689888	0.344944	+	0.938623i	$0.387898\pi$
$728$	2207.59	0.112389
$729$	729.000	0.0370370
$730$	0	0
$731$	1339.26	0.0677625
$732$	−17303.4	−0.873706
$733$	−21325.0	−1.07457	−0.537284	−	0.843402i	$-0.680550\pi$
$733$	−21325.0	−1.07457	−0.537284	+	0.843402i	$0.680550\pi$
$734$	539.534	0.0271316
$735$	0	0
$736$	8895.74	0.445518
$737$	10027.9	0.501197
$738$	394.861	0.0196952
$739$	−7403.75	−0.368540	−0.184270	−	0.982876i	$-0.558992\pi$
$739$	−7403.75	−0.368540	−0.184270	+	0.982876i	$0.558992\pi$
$740$	0	0
$741$	−12708.9	−0.630059
$742$	588.433	0.0291133
$743$	−27131.6	−1.33965	−0.669825	−	0.742519i	$-0.733631\pi$
$743$	−27131.6	−1.33965	−0.669825	+	0.742519i	$0.733631\pi$
$744$	−4100.98	−0.202082
$745$	0	0
$746$	165.430	0.00811904
$747$	784.217	0.0384110
$748$	−1117.80	−0.0546403
$749$	8563.04	0.417739
$750$	0	0
$751$	−29393.3	−1.42820	−0.714098	−	0.700046i	$-0.753163\pi$
$751$	−29393.3	−1.42820	−0.714098	+	0.700046i	$0.753163\pi$
$752$	20930.0	1.01495
$753$	−7393.44	−0.357811
$754$	1.52219	7.35211e−5 0
$755$	0	0
$756$	1477.33	0.0710712
$757$	−37648.5	−1.80761	−0.903804	−	0.427946i	$-0.859237\pi$
$757$	−37648.5	−1.80761	−0.903804	+	0.427946i	$0.859237\pi$
$758$	6101.84	0.292386
$759$	−9194.63	−0.439715
$760$	0	0
$761$	−35633.2	−1.69738	−0.848688	−	0.528894i	$-0.822607\pi$
$761$	−35633.2	−1.69738	−0.848688	+	0.528894i	$0.822607\pi$
$762$	2110.44	0.100332
$763$	−8964.46	−0.425341
$764$	−8245.05	−0.390439
$765$	0	0
$766$	−3982.87	−0.187868
$767$	41015.5	1.93088
$768$	9566.00	0.449457
$769$	−3571.28	−0.167469	−0.0837345	−	0.996488i	$-0.526685\pi$
$769$	−3571.28	−0.167469	−0.0837345	+	0.996488i	$0.526685\pi$
$770$	0	0
$771$	5621.98	0.262608
$772$	1670.09	0.0778599
$773$	−16250.3	−0.756122	−0.378061	−	0.925781i	$-0.623409\pi$
$773$	−16250.3	−0.756122	−0.378061	+	0.925781i	$0.623409\pi$
$774$	−991.782	−0.0460580
$775$	0	0
$776$	1550.21	0.0717131
$777$	−6570.05	−0.303345
$778$	−447.081	−0.0206024
$779$	−9321.37	−0.428720
$780$	0	0
$781$	−30563.5	−1.40032
$782$	−248.741	−0.0113746
$783$	2.06122	9.40764e−5 0
$784$	2921.90	0.133104
$785$	0	0
$786$	3047.72	0.138306
$787$	−13156.5	−0.595906	−0.297953	−	0.954581i	$-0.596304\pi$
$787$	−13156.5	−0.595906	−0.297953	+	0.954581i	$0.596304\pi$
$788$	30903.6	1.39708
$789$	−6193.16	−0.279445
$790$	0	0
$791$	12637.7	0.568071
$792$	1674.99	0.0751494
$793$	34350.9	1.53826
$794$	−1919.74	−0.0858049
$795$	0	0
$796$	−7262.88	−0.323399
$797$	−13868.8	−0.616385	−0.308192	−	0.951324i	$-0.599724\pi$
$797$	−13868.8	−0.616385	−0.308192	+	0.951324i	$0.599724\pi$
$798$	818.524	0.0363101
$799$	−1827.09	−0.0808982
$800$	0	0
$801$	−9818.92	−0.433127
$802$	5433.72	0.239241
$803$	7197.55	0.316309
$804$	8559.61	0.375465
$805$	0	0
$806$	4023.43	0.175831
$807$	16949.6	0.739348
$808$	4001.90	0.174240
$809$	−7042.67	−0.306066	−0.153033	−	0.988221i	$-0.548904\pi$
$809$	−7042.67	−0.306066	−0.153033	+	0.988221i	$0.548904\pi$
$810$	0	0
$811$	−8985.64	−0.389061	−0.194531	−	0.980896i	$-0.562318\pi$
$811$	−8985.64	−0.389061	−0.194531	+	0.980896i	$0.562318\pi$
$812$	4.17708	0.000180525 0
$813$	−9284.78	−0.400530
$814$	−3681.36	−0.158515
$815$	0	0
$816$	−931.215	−0.0399498
$817$	23412.7	1.00258
$818$	−2928.22	−0.125162
$819$	−2932.80	−0.125129
$820$	0	0
$821$	−1293.90	−0.0550031	−0.0275016	−	0.999622i	$-0.508755\pi$
$821$	−1293.90	−0.0550031	−0.0275016	+	0.999622i	$0.508755\pi$
$822$	980.201	0.0415918
$823$	−28480.7	−1.20629	−0.603144	−	0.797632i	$-0.706086\pi$
$823$	−28480.7	−1.20629	−0.603144	+	0.797632i	$0.706086\pi$
$824$	−9965.71	−0.421325
$825$	0	0
$826$	−2641.62	−0.111276
$827$	8825.09	0.371074	0.185537	−	0.982637i	$-0.440597\pi$
$827$	8825.09	0.371074	0.185537	+	0.982637i	$0.440597\pi$
$828$	−7848.35	−0.329407
$829$	−6673.08	−0.279572	−0.139786	−	0.990182i	$-0.544642\pi$
$829$	−6673.08	−0.279572	−0.139786	+	0.990182i	$0.544642\pi$
$830$	0	0
$831$	26888.8	1.12246
$832$	−20617.7	−0.859124
$833$	−255.068	−0.0106093
$834$	2603.12	0.108080
$835$	0	0
$836$	−19541.2	−0.808429
$837$	5448.18	0.224990
$838$	−2180.85	−0.0898999
$839$	−7026.24	−0.289121	−0.144561	−	0.989496i	$-0.546177\pi$
$839$	−7026.24	−0.289121	−0.144561	+	0.989496i	$0.546177\pi$
$840$	0	0
$841$	−24389.0	−1.00000
$842$	3586.52	0.146793
$843$	−17576.8	−0.718123
$844$	7244.42	0.295454
$845$	0	0
$846$	1353.04	0.0549862
$847$	4033.99	0.163648
$848$	−11703.1	−0.473923
$849$	−17458.4	−0.705736
$850$	0	0
$851$	34903.6	1.40597
$852$	−26088.4	−1.04903
$853$	−7181.30	−0.288257	−0.144128	−	0.989559i	$-0.546038\pi$
$853$	−7181.30	−0.288257	−0.144128	+	0.989559i	$0.546038\pi$
$854$	−2212.39	−0.0886491
$855$	0	0
$856$	8287.21	0.330901
$857$	−23061.9	−0.919228	−0.459614	−	0.888119i	$-0.652012\pi$
$857$	−23061.9	−0.919228	−0.459614	+	0.888119i	$0.652012\pi$
$858$	−1643.32	−0.0653870
$859$	32264.0	1.28153	0.640764	−	0.767738i	$-0.278618\pi$
$859$	32264.0	1.28153	0.640764	+	0.767738i	$0.278618\pi$
$860$	0	0
$861$	−2151.07	−0.0851431
$862$	2581.80	0.102014
$863$	−2831.11	−0.111671	−0.0558354	−	0.998440i	$-0.517782\pi$
$863$	−2831.11	−0.111671	−0.0558354	+	0.998440i	$0.517782\pi$
$864$	2152.90	0.0847723
$865$	0	0
$866$	−5108.79	−0.200466
$867$	−14657.7	−0.574166
$868$	11040.8	0.431738
$869$	−7522.66	−0.293658
$870$	0	0
$871$	−16992.6	−0.661048
$872$	−8675.71	−0.336923
$873$	−2059.47	−0.0798424
$874$	−4348.44	−0.168293
$875$	0	0
$876$	6143.69	0.236959
$877$	17952.1	0.691218	0.345609	−	0.938379i	$-0.387672\pi$
$877$	17952.1	0.691218	0.345609	+	0.938379i	$0.387672\pi$
$878$	3390.12	0.130309
$879$	−17036.3	−0.653721
$880$	0	0
$881$	25983.2	0.993641	0.496821	−	0.867853i	$-0.334501\pi$
$881$	25983.2	0.993641	0.496821	+	0.867853i	$0.334501\pi$
$882$	188.889	0.00721112
$883$	10296.7	0.392424	0.196212	−	0.980562i	$-0.437136\pi$
$883$	10296.7	0.392424	0.196212	+	0.980562i	$0.437136\pi$
$884$	1894.16	0.0720672
$885$	0	0
$886$	1080.52	0.0409717
$887$	−14925.6	−0.564996	−0.282498	−	0.959268i	$-0.591163\pi$
$887$	−14925.6	−0.564996	−0.282498	+	0.959268i	$0.591163\pi$
$888$	−6358.42	−0.240287
$889$	−11497.0	−0.433741
$890$	0	0
$891$	−2225.24	−0.0836682
$892$	−41832.0	−1.57022
$893$	−31940.7	−1.19693
$894$	−13.8651	−0.000518699 0
$895$	0	0
$896$	5793.17	0.216000
$897$	15580.6	0.579958
$898$	−2287.17	−0.0849933
$899$	15.4045	0.000571488 0
$900$	0	0
$901$	1021.62	0.0377749
$902$	−1205.30	−0.0444922
$903$	5402.89	0.199110
$904$	12230.6	0.449982
$905$	0	0
$906$	−3089.65	−0.113297
$907$	−24744.9	−0.905889	−0.452944	−	0.891539i	$-0.649626\pi$
$907$	−24744.9	−0.905889	−0.452944	+	0.891539i	$0.649626\pi$
$908$	47028.0	1.71881
$909$	−5316.55	−0.193992
$910$	0	0
$911$	4378.72	0.159246	0.0796232	−	0.996825i	$-0.474628\pi$
$911$	4378.72	0.159246	0.0796232	+	0.996825i	$0.474628\pi$
$912$	−16279.3	−0.591077
$913$	−2393.79	−0.0867720
$914$	5896.15	0.213378
$915$	0	0
$916$	−9464.58	−0.341396
$917$	−16602.9	−0.597903
$918$	−60.1991	−0.00216434
$919$	26026.1	0.934192	0.467096	−	0.884207i	$-0.345300\pi$
$919$	26026.1	0.934192	0.467096	+	0.884207i	$0.345300\pi$
$920$	0	0
$921$	−27553.6	−0.985799
$922$	−5354.45	−0.191257
$923$	51790.9	1.84693
$924$	−4509.47	−0.160553
$925$	0	0
$926$	−1527.52	−0.0542090
$927$	13239.5	0.469086
$928$	6.08724	0.000215327 0
$929$	4240.78	0.149769	0.0748846	−	0.997192i	$-0.476141\pi$
$929$	4240.78	0.149769	0.0748846	+	0.997192i	$0.476141\pi$
$930$	0	0
$931$	−4459.04	−0.156970
$932$	27493.2	0.966278
$933$	13230.7	0.464258
$934$	1746.76	0.0611944
$935$	0	0
$936$	−2838.34	−0.0991174
$937$	664.833	0.0231794	0.0115897	−	0.999933i	$-0.496311\pi$
$937$	664.833	0.0231794	0.0115897	+	0.999933i	$0.496311\pi$
$938$	1094.42	0.0380960
$939$	13215.8	0.459299
$940$	0	0
$941$	9520.60	0.329822	0.164911	−	0.986308i	$-0.447266\pi$
$941$	9520.60	0.329822	0.164911	+	0.986308i	$0.447266\pi$
$942$	509.645	0.0176275
$943$	11427.6	0.394629
$944$	52538.2	1.81141
$945$	0	0
$946$	3027.37	0.104047
$947$	−17066.3	−0.585618	−0.292809	−	0.956171i	$-0.594590\pi$
$947$	−17066.3	−0.585618	−0.292809	+	0.956171i	$0.594590\pi$
$948$	−6421.19	−0.219990
$949$	−12196.5	−0.417192
$950$	0	0
$951$	22460.6	0.765862
$952$	−246.852	−0.00840389
$953$	−6991.85	−0.237658	−0.118829	−	0.992915i	$-0.537914\pi$
$953$	−6991.85	−0.237658	−0.118829	+	0.992915i	$0.537914\pi$
$954$	−756.557	−0.0256755
$955$	0	0
$956$	52495.0	1.77595
$957$	−6.29177	−0.000212522 0
$958$	8171.46	0.275582
$959$	−5339.80	−0.179803
$960$	0	0
$961$	10925.9	0.366751
$962$	6238.20	0.209072
$963$	−11009.6	−0.368411
$964$	13410.9	0.448065
$965$	0	0
$966$	−1003.48	−0.0334227
$967$	−18731.2	−0.622911	−0.311455	−	0.950261i	$-0.600816\pi$
$967$	−18731.2	−0.622911	−0.311455	+	0.950261i	$0.600816\pi$
$968$	3904.05	0.129629
$969$	1421.10	0.0471129
$970$	0	0
$971$	−45780.2	−1.51303	−0.756517	−	0.653974i	$-0.773100\pi$
$971$	−45780.2	−1.51303	−0.756517	+	0.653974i	$0.773100\pi$
$972$	−1899.42	−0.0626789
$973$	−14180.9	−0.467234
$974$	6688.80	0.220044
$975$	0	0
$976$	44001.3	1.44308
$977$	20137.9	0.659436	0.329718	−	0.944080i	$-0.393046\pi$
$977$	20137.9	0.659436	0.329718	+	0.944080i	$0.393046\pi$
$978$	3535.80	0.115606
$979$	29971.8	0.978451
$980$	0	0
$981$	11525.7	0.375116
$982$	3232.72	0.105051
$983$	6220.73	0.201842	0.100921	−	0.994894i	$-0.467821\pi$
$983$	6220.73	0.201842	0.100921	+	0.994894i	$0.467821\pi$
$984$	−2081.78	−0.0674439
$985$	0	0
$986$	−0.170210	−5.49757e−6 0
$987$	−7370.88	−0.237708
$988$	33113.3	1.06627
$989$	−28703.0	−0.922855
$990$	0	0
$991$	−10296.5	−0.330049	−0.165025	−	0.986289i	$-0.552770\pi$
$991$	−10296.5	−0.330049	−0.165025	+	0.986289i	$0.552770\pi$
$992$	16089.7	0.514968
$993$	26581.7	0.849490
$994$	−3335.62	−0.106438
$995$	0	0
$996$	−2043.29	−0.0650041
$997$	27392.6	0.870144	0.435072	−	0.900396i	$-0.356723\pi$
$997$	27392.6	0.870144	0.435072	+	0.900396i	$0.356723\pi$
$998$	1408.36	0.0446701
$999$	8447.21	0.267525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.w.1.3		5
3.2	odd	2		1575.4.a.bp.1.3		5
5.2	odd	4		105.4.d.b.64.6	yes	10
5.3	odd	4		105.4.d.b.64.5	✓	10
5.4	even	2		525.4.a.x.1.3		5
15.2	even	4		315.4.d.b.64.5		10
15.8	even	4		315.4.d.b.64.6		10
15.14	odd	2		1575.4.a.bo.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.5	✓	10	5.3	odd	4
105.4.d.b.64.6	yes	10	5.2	odd	4
315.4.d.b.64.5		10	15.2	even	4
315.4.d.b.64.6		10	15.8	even	4
525.4.a.w.1.3		5	1.1	even	1	trivial
525.4.a.x.1.3		5	5.4	even	2
1575.4.a.bo.1.3		5	15.14	odd	2
1575.4.a.bp.1.3		5	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.428319 q^{2} +3.00000 q^{3} -7.81654 q^{4} +1.28496 q^{6} -7.00000 q^{7} -6.77452 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.428319 q^{2} +3.00000 q^{3} -7.81654 q^{4} +1.28496 q^{6} -7.00000 q^{7} -6.77452 q^{8} +9.00000 q^{9} -27.4721 q^{11} -23.4496 q^{12} +46.5524 q^{13} -2.99823 q^{14} +59.6307 q^{16} -5.20546 q^{17} +3.85487 q^{18} -91.0007 q^{19} -21.0000 q^{21} -11.7668 q^{22} +111.563 q^{23} -20.3236 q^{24} +19.9393 q^{26} +27.0000 q^{27} +54.7158 q^{28} +0.0763413 q^{29} +201.784 q^{31} +79.7371 q^{32} -82.4163 q^{33} -2.22960 q^{34} -70.3489 q^{36} +312.859 q^{37} -38.9773 q^{38} +139.657 q^{39} +102.432 q^{41} -8.99470 q^{42} -257.280 q^{43} +214.737 q^{44} +47.7847 q^{46} +350.994 q^{47} +178.892 q^{48} +49.0000 q^{49} -15.6164 q^{51} -363.879 q^{52} -196.260 q^{53} +11.5646 q^{54} +47.4217 q^{56} -273.002 q^{57} +0.0326984 q^{58} +881.060 q^{59} +737.897 q^{61} +86.4280 q^{62} -63.0000 q^{63} -442.893 q^{64} -35.3004 q^{66} -365.021 q^{67} +40.6887 q^{68} +334.690 q^{69} +1112.53 q^{71} -60.9707 q^{72} -261.995 q^{73} +134.004 q^{74} +711.311 q^{76} +192.305 q^{77} +59.8179 q^{78} +273.829 q^{79} +81.0000 q^{81} +43.8735 q^{82} +87.1353 q^{83} +164.147 q^{84} -110.198 q^{86} +0.229024 q^{87} +186.110 q^{88} -1090.99 q^{89} -325.867 q^{91} -872.039 q^{92} +605.353 q^{93} +150.337 q^{94} +239.211 q^{96} -228.830 q^{97} +20.9876 q^{98} -247.249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9	\( 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9} + 66 q^{11} + 81 q^{12} + 2 q^{13} + 7 q^{14} + 155 q^{16} - 108 q^{17} - 9 q^{18} + 174 q^{19} - 105 q^{21} + 506 q^{22} + 116 q^{23} - 99 q^{24} + 446 q^{26} + 135 q^{27} - 189 q^{28} + 370 q^{29} + 342 q^{31} + 55 q^{32} + 198 q^{33} + 112 q^{34} + 243 q^{36} + 408 q^{37} + 34 q^{38} + 6 q^{39} + 802 q^{41} + 21 q^{42} + 584 q^{43} + 290 q^{44} + 640 q^{46} - 716 q^{47} + 465 q^{48} + 245 q^{49} - 324 q^{51} - 338 q^{52} - 98 q^{53} - 27 q^{54} + 231 q^{56} + 522 q^{57} - 482 q^{58} + 704 q^{59} + 650 q^{61} - 2070 q^{62} - 315 q^{63} + 75 q^{64} + 1518 q^{66} - 180 q^{67} - 4520 q^{68} + 348 q^{69} + 1470 q^{71} - 297 q^{72} + 534 q^{73} - 1312 q^{74} + 4370 q^{76} - 462 q^{77} + 1338 q^{78} - 820 q^{79} + 405 q^{81} + 1338 q^{82} - 1520 q^{83} - 567 q^{84} + 832 q^{86} + 1110 q^{87} + 3258 q^{88} + 286 q^{89} - 14 q^{91} - 1288 q^{92} + 1026 q^{93} + 2540 q^{94} + 165 q^{96} - 278 q^{97} - 49 q^{98} + 594 q^{99}+O(q^{100}) \) 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9 + 66 * q^11 + 81 * q^12 + 2 * q^13 + 7 * q^14 + 155 * q^16 - 108 * q^17 - 9 * q^18 + 174 * q^19 - 105 * q^21 + 506 * q^22 + 116 * q^23 - 99 * q^24 + 446 * q^26 + 135 * q^27 - 189 * q^28 + 370 * q^29 + 342 * q^31 + 55 * q^32 + 198 * q^33 + 112 * q^34 + 243 * q^36 + 408 * q^37 + 34 * q^38 + 6 * q^39 + 802 * q^41 + 21 * q^42 + 584 * q^43 + 290 * q^44 + 640 * q^46 - 716 * q^47 + 465 * q^48 + 245 * q^49 - 324 * q^51 - 338 * q^52 - 98 * q^53 - 27 * q^54 + 231 * q^56 + 522 * q^57 - 482 * q^58 + 704 * q^59 + 650 * q^61 - 2070 * q^62 - 315 * q^63 + 75 * q^64 + 1518 * q^66 - 180 * q^67 - 4520 * q^68 + 348 * q^69 + 1470 * q^71 - 297 * q^72 + 534 * q^73 - 1312 * q^74 + 4370 * q^76 - 462 * q^77 + 1338 * q^78 - 820 * q^79 + 405 * q^81 + 1338 * q^82 - 1520 * q^83 - 567 * q^84 + 832 * q^86 + 1110 * q^87 + 3258 * q^88 + 286 * q^89 - 14 * q^91 - 1288 * q^92 + 1026 * q^93 + 2540 * q^94 + 165 * q^96 - 278 * q^97 - 49 * q^98 + 594 * q^99

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