LMFDB - Embedded newform 825.4.a.bd.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 31x^{5} + 50x^{4} + 272x^{3} - 322x^{2} - 704x + 512 $ x^7 - 2x^6 - 31x^5 + 50x^4 + 272x^3 - 322x^2 - 704x + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.647712$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.352288 q^{2} -3.00000 q^{3} -7.87589 q^{4} -1.05686 q^{6} +19.8486 q^{7} -5.59288 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.352288 q^{2} -3.00000 q^{3} -7.87589 q^{4} -1.05686 q^{6} +19.8486 q^{7} -5.59288 q^{8} +9.00000 q^{9} +11.0000 q^{11} +23.6277 q^{12} +25.5286 q^{13} +6.99242 q^{14} +61.0368 q^{16} -77.3644 q^{17} +3.17059 q^{18} +96.1609 q^{19} -59.5458 q^{21} +3.87517 q^{22} -173.860 q^{23} +16.7786 q^{24} +8.99340 q^{26} -27.0000 q^{27} -156.326 q^{28} -189.619 q^{29} -275.829 q^{31} +66.2456 q^{32} -33.0000 q^{33} -27.2545 q^{34} -70.8830 q^{36} +269.805 q^{37} +33.8763 q^{38} -76.5857 q^{39} +306.118 q^{41} -20.9773 q^{42} +477.907 q^{43} -86.6348 q^{44} -61.2487 q^{46} -257.405 q^{47} -183.111 q^{48} +50.9676 q^{49} +232.093 q^{51} -201.060 q^{52} +495.761 q^{53} -9.51177 q^{54} -111.011 q^{56} -288.483 q^{57} -66.8003 q^{58} +102.064 q^{59} -585.738 q^{61} -97.1710 q^{62} +178.638 q^{63} -464.957 q^{64} -11.6255 q^{66} +474.381 q^{67} +609.314 q^{68} +521.580 q^{69} +453.954 q^{71} -50.3359 q^{72} +655.838 q^{73} +95.0491 q^{74} -757.353 q^{76} +218.335 q^{77} -26.9802 q^{78} +482.235 q^{79} +81.0000 q^{81} +107.842 q^{82} +523.492 q^{83} +468.977 q^{84} +168.361 q^{86} +568.856 q^{87} -61.5217 q^{88} -750.979 q^{89} +506.707 q^{91} +1369.30 q^{92} +827.486 q^{93} -90.6806 q^{94} -198.737 q^{96} -572.084 q^{97} +17.9553 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9	\( 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9} + 77 q^{11} - 39 q^{12} + 80 q^{13} + 42 q^{14} - 43 q^{16} + 162 q^{17} + 45 q^{18} + 58 q^{19} - 102 q^{21} + 55 q^{22} + 324 q^{23} - 225 q^{24} - 200 q^{26} - 189 q^{27} - 168 q^{28} + 64 q^{29} - 348 q^{31} - 75 q^{32} - 231 q^{33} + 206 q^{34} + 117 q^{36} + 664 q^{37} + 334 q^{38} - 240 q^{39} - 332 q^{41} - 126 q^{42} + 774 q^{43} + 143 q^{44} - 328 q^{46} + 872 q^{47} + 129 q^{48} - 417 q^{49} - 486 q^{51} + 134 q^{52} + 1628 q^{53} - 135 q^{54} - 1618 q^{56} - 174 q^{57} + 1568 q^{58} - 332 q^{59} + 22 q^{61} - 260 q^{62} + 306 q^{63} + 561 q^{64} - 165 q^{66} + 1524 q^{67} + 2324 q^{68} - 972 q^{69} - 516 q^{71} + 675 q^{72} + 1700 q^{73} + 1628 q^{74} + 2794 q^{76} + 374 q^{77} + 600 q^{78} + 1746 q^{79} + 567 q^{81} + 364 q^{82} + 2344 q^{83} + 504 q^{84} + 1270 q^{86} - 192 q^{87} + 825 q^{88} - 2226 q^{89} + 1072 q^{91} + 4184 q^{92} + 1044 q^{93} + 4736 q^{94} + 225 q^{96} + 1048 q^{97} + 3057 q^{98} + 693 q^{99}+O(q^{100}) \) 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9 + 77 * q^11 - 39 * q^12 + 80 * q^13 + 42 * q^14 - 43 * q^16 + 162 * q^17 + 45 * q^18 + 58 * q^19 - 102 * q^21 + 55 * q^22 + 324 * q^23 - 225 * q^24 - 200 * q^26 - 189 * q^27 - 168 * q^28 + 64 * q^29 - 348 * q^31 - 75 * q^32 - 231 * q^33 + 206 * q^34 + 117 * q^36 + 664 * q^37 + 334 * q^38 - 240 * q^39 - 332 * q^41 - 126 * q^42 + 774 * q^43 + 143 * q^44 - 328 * q^46 + 872 * q^47 + 129 * q^48 - 417 * q^49 - 486 * q^51 + 134 * q^52 + 1628 * q^53 - 135 * q^54 - 1618 * q^56 - 174 * q^57 + 1568 * q^58 - 332 * q^59 + 22 * q^61 - 260 * q^62 + 306 * q^63 + 561 * q^64 - 165 * q^66 + 1524 * q^67 + 2324 * q^68 - 972 * q^69 - 516 * q^71 + 675 * q^72 + 1700 * q^73 + 1628 * q^74 + 2794 * q^76 + 374 * q^77 + 600 * q^78 + 1746 * q^79 + 567 * q^81 + 364 * q^82 + 2344 * q^83 + 504 * q^84 + 1270 * q^86 - 192 * q^87 + 825 * q^88 - 2226 * q^89 + 1072 * q^91 + 4184 * q^92 + 1044 * q^93 + 4736 * q^94 + 225 * q^96 + 1048 * q^97 + 3057 * q^98 + 693 * 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 $

$2$	0.352288	0.124553	0.0622763	−	0.998059i	$-0.480164\pi$
$2$	0.352288	0.124553	0.0622763	+	0.998059i	$0.480164\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.87589	−0.984487
$5$	0	0
$5$	0	0
$6$	−1.05686	−0.0719104
$7$	19.8486	1.07172	0.535862	−	0.844305i	$-0.319987\pi$
$7$	19.8486	1.07172	0.535862	+	0.844305i	$0.319987\pi$
$8$	−5.59288	−0.247173
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	23.6277	0.568394
$13$	25.5286	0.544643	0.272321	−	0.962206i	$-0.412209\pi$
$13$	25.5286	0.544643	0.272321	+	0.962206i	$0.412209\pi$
$14$	6.99242	0.133486
$15$	0	0
$16$	61.0368	0.953701
$17$	−77.3644	−1.10374	−0.551871	−	0.833929i	$-0.686086\pi$
$17$	−77.3644	−1.10374	−0.551871	+	0.833929i	$0.686086\pi$
$18$	3.17059	0.0415175
$19$	96.1609	1.16110	0.580548	−	0.814226i	$-0.302838\pi$
$19$	96.1609	1.16110	0.580548	+	0.814226i	$0.302838\pi$
$20$	0	0
$21$	−59.5458	−0.618760
$22$	3.87517	0.0375540
$23$	−173.860	−1.57619	−0.788094	−	0.615556i	$-0.788932\pi$
$23$	−173.860	−1.57619	−0.788094	+	0.615556i	$0.788932\pi$
$24$	16.7786	0.142705
$25$	0	0
$26$	8.99340	0.0678366
$27$	−27.0000	−0.192450
$28$	−156.326	−1.05510
$29$	−189.619	−1.21418	−0.607091	−	0.794632i	$-0.707664\pi$
$29$	−189.619	−1.21418	−0.607091	+	0.794632i	$0.707664\pi$
$30$	0	0
$31$	−275.829	−1.59807	−0.799037	−	0.601282i	$-0.794657\pi$
$31$	−275.829	−1.59807	−0.799037	+	0.601282i	$0.794657\pi$
$32$	66.2456	0.365959
$33$	−33.0000	−0.174078
$34$	−27.2545	−0.137474
$35$	0	0
$36$	−70.8830	−0.328162
$37$	269.805	1.19880	0.599401	−	0.800449i	$-0.295405\pi$
$37$	269.805	1.19880	0.599401	+	0.800449i	$0.295405\pi$
$38$	33.8763	0.144618
$39$	−76.5857	−0.314450
$40$	0	0
$41$	306.118	1.16604	0.583020	−	0.812458i	$-0.301871\pi$
$41$	306.118	1.16604	0.583020	+	0.812458i	$0.301871\pi$
$42$	−20.9773	−0.0770682
$43$	477.907	1.69489	0.847443	−	0.530887i	$-0.178141\pi$
$43$	477.907	1.69489	0.847443	+	0.530887i	$0.178141\pi$
$44$	−86.6348	−0.296834
$45$	0	0
$46$	−61.2487	−0.196318
$47$	−257.405	−0.798859	−0.399429	−	0.916764i	$-0.630792\pi$
$47$	−257.405	−0.798859	−0.399429	+	0.916764i	$0.630792\pi$
$48$	−183.111	−0.550619
$49$	50.9676	0.148594
$50$	0	0
$51$	232.093	0.637246
$52$	−201.060	−0.536193
$53$	495.761	1.28487	0.642434	−	0.766341i	$-0.277925\pi$
$53$	495.761	1.28487	0.642434	+	0.766341i	$0.277925\pi$
$54$	−9.51177	−0.0239701
$55$	0	0
$56$	−111.011	−0.264901
$57$	−288.483	−0.670359
$58$	−66.8003	−0.151229
$59$	102.064	0.225214	0.112607	−	0.993640i	$-0.464080\pi$
$59$	102.064	0.225214	0.112607	+	0.993640i	$0.464080\pi$
$60$	0	0
$61$	−585.738	−1.22944	−0.614721	−	0.788744i	$-0.710732\pi$
$61$	−585.738	−1.22944	−0.614721	+	0.788744i	$0.710732\pi$
$62$	−97.1710	−0.199044
$63$	178.638	0.357242
$64$	−464.957	−0.908120
$65$	0	0
$66$	−11.6255	−0.0216818
$67$	474.381	0.864997	0.432499	−	0.901635i	$-0.357632\pi$
$67$	474.381	0.864997	0.432499	+	0.901635i	$0.357632\pi$
$68$	609.314	1.08662
$69$	521.580	0.910012
$70$	0	0
$71$	453.954	0.758794	0.379397	−	0.925234i	$-0.376131\pi$
$71$	453.954	0.758794	0.379397	+	0.925234i	$0.376131\pi$
$72$	−50.3359	−0.0823909
$73$	655.838	1.05151	0.525753	−	0.850637i	$-0.323784\pi$
$73$	655.838	1.05151	0.525753	+	0.850637i	$0.323784\pi$
$74$	95.0491	0.149314
$75$	0	0
$76$	−757.353	−1.14308
$77$	218.335	0.323137
$78$	−26.9802	−0.0391655
$79$	482.235	0.686781	0.343390	−	0.939193i	$-0.388425\pi$
$79$	482.235	0.686781	0.343390	+	0.939193i	$0.388425\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	107.842	0.145233
$83$	523.492	0.692297	0.346149	−	0.938180i	$-0.387489\pi$
$83$	523.492	0.692297	0.346149	+	0.938180i	$0.387489\pi$
$84$	468.977	0.609161
$85$	0	0
$86$	168.361	0.211102
$87$	568.856	0.701008
$88$	−61.5217	−0.0745254
$89$	−750.979	−0.894423	−0.447211	−	0.894428i	$-0.647583\pi$
$89$	−750.979	−0.894423	−0.447211	+	0.894428i	$0.647583\pi$
$90$	0	0
$91$	506.707	0.583707
$92$	1369.30	1.55174
$93$	827.486	0.922648
$94$	−90.6806	−0.0994999
$95$	0	0
$96$	−198.737	−0.211286
$97$	−572.084	−0.598829	−0.299414	−	0.954123i	$-0.596791\pi$
$97$	−572.084	−0.598829	−0.299414	+	0.954123i	$0.596791\pi$
$98$	17.9553	0.0185077
$99$	99.0000	0.100504
$100$	0	0
$101$	79.5187	0.0783407	0.0391703	−	0.999233i	$-0.487529\pi$
$101$	79.5187	0.0783407	0.0391703	+	0.999233i	$0.487529\pi$
$102$	81.7636	0.0793706
$103$	1026.44	0.981925	0.490963	−	0.871181i	$-0.336645\pi$
$103$	1026.44	0.981925	0.490963	+	0.871181i	$0.336645\pi$
$104$	−142.778	−0.134621
$105$	0	0
$106$	174.650	0.160034
$107$	−1087.33	−0.982397	−0.491199	−	0.871048i	$-0.663441\pi$
$107$	−1087.33	−0.982397	−0.491199	+	0.871048i	$0.663441\pi$
$108$	212.649	0.189465
$109$	1330.39	1.16907	0.584534	−	0.811369i	$-0.301277\pi$
$109$	1330.39	1.16907	0.584534	+	0.811369i	$0.301277\pi$
$110$	0	0
$111$	−809.416	−0.692129
$112$	1211.50	1.02210
$113$	1460.20	1.21561	0.607805	−	0.794086i	$-0.292050\pi$
$113$	1460.20	1.21561	0.607805	+	0.794086i	$0.292050\pi$
$114$	−101.629	−0.0834950
$115$	0	0
$116$	1493.42	1.19535
$117$	229.757	0.181548
$118$	35.9560	0.0280510
$119$	−1535.58	−1.18291
$120$	0	0
$121$	121.000	0.0909091
$122$	−206.348	−0.153130
$123$	−918.354	−0.673213
$124$	2172.40	1.57328
$125$	0	0
$126$	62.9318	0.0444953
$127$	1022.85	0.714674	0.357337	−	0.933975i	$-0.383685\pi$
$127$	1022.85	0.714674	0.357337	+	0.933975i	$0.383685\pi$
$128$	−693.763	−0.479067
$129$	−1433.72	−0.978542
$130$	0	0
$131$	1308.85	0.872936	0.436468	−	0.899720i	$-0.356229\pi$
$131$	1308.85	0.872936	0.436468	+	0.899720i	$0.356229\pi$
$132$	259.904	0.171377
$133$	1908.66	1.24438
$134$	167.118	0.107738
$135$	0	0
$136$	432.690	0.272815
$137$	1405.87	0.876725	0.438363	−	0.898798i	$-0.355559\pi$
$137$	1405.87	0.876725	0.438363	+	0.898798i	$0.355559\pi$
$138$	183.746	0.113344
$139$	−725.138	−0.442485	−0.221242	−	0.975219i	$-0.571011\pi$
$139$	−725.138	−0.442485	−0.221242	+	0.975219i	$0.571011\pi$
$140$	0	0
$141$	772.215	0.461221
$142$	159.922	0.0945098
$143$	280.814	0.164216
$144$	549.332	0.317900
$145$	0	0
$146$	231.044	0.130968
$147$	−152.903	−0.0857905
$148$	−2124.96	−1.18021
$149$	2812.26	1.54624	0.773118	−	0.634262i	$-0.218696\pi$
$149$	2812.26	1.54624	0.773118	+	0.634262i	$0.218696\pi$
$150$	0	0
$151$	−469.633	−0.253100	−0.126550	−	0.991960i	$-0.540390\pi$
$151$	−469.633	−0.253100	−0.126550	+	0.991960i	$0.540390\pi$
$152$	−537.817	−0.286992
$153$	−696.279	−0.367914
$154$	76.9167	0.0402475
$155$	0	0
$156$	603.181	0.309571
$157$	276.945	0.140781	0.0703906	−	0.997520i	$-0.477575\pi$
$157$	276.945	0.140781	0.0703906	+	0.997520i	$0.477575\pi$
$158$	169.885	0.0855402
$159$	−1487.28	−0.741819
$160$	0	0
$161$	−3450.88	−1.68924
$162$	28.5353	0.0138392
$163$	−2654.73	−1.27567	−0.637836	−	0.770172i	$-0.720170\pi$
$163$	−2654.73	−1.27567	−0.637836	+	0.770172i	$0.720170\pi$
$164$	−2410.95	−1.14795
$165$	0	0
$166$	184.420	0.0862274
$167$	3219.81	1.49196	0.745978	−	0.665970i	$-0.231982\pi$
$167$	3219.81	1.49196	0.745978	+	0.665970i	$0.231982\pi$
$168$	333.033	0.152941
$169$	−1545.29	−0.703365
$170$	0	0
$171$	865.449	0.387032
$172$	−3763.94	−1.66859
$173$	2540.33	1.11640	0.558201	−	0.829706i	$-0.311492\pi$
$173$	2540.33	1.11640	0.558201	+	0.829706i	$0.311492\pi$
$174$	200.401	0.0873123
$175$	0	0
$176$	671.405	0.287552
$177$	−306.193	−0.130028
$178$	−264.561	−0.111403
$179$	−86.1324	−0.0359656	−0.0179828	−	0.999838i	$-0.505724\pi$
$179$	−86.1324	−0.0359656	−0.0179828	+	0.999838i	$0.505724\pi$
$180$	0	0
$181$	1745.36	0.716748	0.358374	−	0.933578i	$-0.383331\pi$
$181$	1745.36	0.716748	0.358374	+	0.933578i	$0.383331\pi$
$182$	178.507	0.0727021
$183$	1757.21	0.709819
$184$	972.378	0.389591
$185$	0	0
$186$	291.513	0.114918
$187$	−851.008	−0.332791
$188$	2027.29	0.786466
$189$	−535.913	−0.206253
$190$	0	0
$191$	−5019.02	−1.90138	−0.950690	−	0.310144i	$-0.899623\pi$
$191$	−5019.02	−1.90138	−0.950690	+	0.310144i	$0.899623\pi$
$192$	1394.87	0.524303
$193$	4275.03	1.59442	0.797211	−	0.603700i	$-0.206308\pi$
$193$	4275.03	1.59442	0.797211	+	0.603700i	$0.206308\pi$
$194$	−201.538	−0.0745856
$195$	0	0
$196$	−401.415	−0.146288
$197$	2006.68	0.725735	0.362867	−	0.931841i	$-0.381798\pi$
$197$	2006.68	0.725735	0.362867	+	0.931841i	$0.381798\pi$
$198$	34.8765	0.0125180
$199$	−3668.78	−1.30690	−0.653450	−	0.756970i	$-0.726679\pi$
$199$	−3668.78	−1.30690	−0.653450	+	0.756970i	$0.726679\pi$
$200$	0	0
$201$	−1423.14	−0.499406
$202$	28.0135	0.00975753
$203$	−3763.67	−1.30127
$204$	−1827.94	−0.627360
$205$	0	0
$206$	361.603	0.122301
$207$	−1564.74	−0.525396
$208$	1558.18	0.519426
$209$	1057.77	0.350084
$210$	0	0
$211$	1600.30	0.522129	0.261064	−	0.965321i	$-0.415927\pi$
$211$	1600.30	0.522129	0.261064	+	0.965321i	$0.415927\pi$
$212$	−3904.56	−1.26494
$213$	−1361.86	−0.438090
$214$	−383.054	−0.122360
$215$	0	0
$216$	151.008	0.0475684
$217$	−5474.81	−1.71269
$218$	468.681	0.145610
$219$	−1967.51	−0.607088
$220$	0	0
$221$	−1975.00	−0.601145
$222$	−285.147	−0.0862064
$223$	3904.42	1.17246	0.586232	−	0.810143i	$-0.300611\pi$
$223$	3904.42	1.17246	0.586232	+	0.810143i	$0.300611\pi$
$224$	1314.88	0.392207
$225$	0	0
$226$	514.410	0.151407
$227$	1364.98	0.399107	0.199553	−	0.979887i	$-0.436051\pi$
$227$	1364.98	0.399107	0.199553	+	0.979887i	$0.436051\pi$
$228$	2272.06	0.659960
$229$	5045.66	1.45601	0.728005	−	0.685571i	$-0.240448\pi$
$229$	5045.66	1.45601	0.728005	+	0.685571i	$0.240448\pi$
$230$	0	0
$231$	−655.004	−0.186563
$232$	1060.51	0.300113
$233$	−6083.69	−1.71054	−0.855270	−	0.518182i	$-0.826609\pi$
$233$	−6083.69	−1.71054	−0.855270	+	0.518182i	$0.826609\pi$
$234$	80.9406	0.0226122
$235$	0	0
$236$	−803.848	−0.221720
$237$	−1446.70	−0.396513
$238$	−540.965	−0.147334
$239$	3413.30	0.923799	0.461900	−	0.886932i	$-0.347168\pi$
$239$	3413.30	0.923799	0.461900	+	0.886932i	$0.347168\pi$
$240$	0	0
$241$	979.432	0.261787	0.130894	−	0.991396i	$-0.458215\pi$
$241$	979.432	0.261787	0.130894	+	0.991396i	$0.458215\pi$
$242$	42.6268	0.0113230
$243$	−243.000	−0.0641500
$244$	4613.21	1.21037
$245$	0	0
$246$	−323.525	−0.0838504
$247$	2454.85	0.632383
$248$	1542.68	0.395000
$249$	−1570.48	−0.399698
$250$	0	0
$251$	−2414.09	−0.607075	−0.303537	−	0.952820i	$-0.598168\pi$
$251$	−2414.09	−0.607075	−0.303537	+	0.952820i	$0.598168\pi$
$252$	−1406.93	−0.351700
$253$	−1912.46	−0.475238
$254$	360.339	0.0890145
$255$	0	0
$256$	3475.25	0.848451
$257$	−2888.26	−0.701029	−0.350514	−	0.936557i	$-0.613993\pi$
$257$	−2888.26	−0.701029	−0.350514	+	0.936557i	$0.613993\pi$
$258$	−505.082	−0.121880
$259$	5355.26	1.28479
$260$	0	0
$261$	−1706.57	−0.404727
$262$	461.091	0.108726
$263$	3916.08	0.918158	0.459079	−	0.888395i	$-0.348179\pi$
$263$	3916.08	0.918158	0.459079	+	0.888395i	$0.348179\pi$
$264$	184.565	0.0430273
$265$	0	0
$266$	672.398	0.154990
$267$	2252.94	0.516395
$268$	−3736.17	−0.851578
$269$	−3495.41	−0.792263	−0.396131	−	0.918194i	$-0.629647\pi$
$269$	−3495.41	−0.792263	−0.396131	+	0.918194i	$0.629647\pi$
$270$	0	0
$271$	774.974	0.173713	0.0868567	−	0.996221i	$-0.472318\pi$
$271$	774.974	0.173713	0.0868567	+	0.996221i	$0.472318\pi$
$272$	−4722.08	−1.05264
$273$	−1520.12	−0.337003
$274$	495.270	0.109198
$275$	0	0
$276$	−4107.91	−0.895895
$277$	7491.71	1.62503	0.812515	−	0.582940i	$-0.198098\pi$
$277$	7491.71	1.62503	0.812515	+	0.582940i	$0.198098\pi$
$278$	−255.457	−0.0551126
$279$	−2482.46	−0.532691
$280$	0	0
$281$	−125.514	−0.0266461	−0.0133230	−	0.999911i	$-0.504241\pi$
$281$	−125.514	−0.0266461	−0.0133230	+	0.999911i	$0.504241\pi$
$282$	272.042	0.0574463
$283$	8.28147	0.00173951	0.000869757	−	1.00000i	$-0.499723\pi$
$283$	8.28147	0.00173951	0.000869757		1.00000i	$0.499723\pi$
$284$	−3575.29	−0.747023
$285$	0	0
$286$	98.9274	0.0204535
$287$	6076.02	1.24967
$288$	596.210	0.121986
$289$	1072.25	0.218247
$290$	0	0
$291$	1716.25	0.345734
$292$	−5165.31	−1.03519
$293$	3055.93	0.609316	0.304658	−	0.952462i	$-0.401458\pi$
$293$	3055.93	0.609316	0.304658	+	0.952462i	$0.401458\pi$
$294$	−53.8658	−0.0106854
$295$	0	0
$296$	−1508.99	−0.296312
$297$	−297.000	−0.0580259
$298$	990.724	0.192588
$299$	−4438.40	−0.858458
$300$	0	0
$301$	9485.78	1.81645
$302$	−165.446	−0.0315243
$303$	−238.556	−0.0452300
$304$	5869.36	1.10734
$305$	0	0
$306$	−245.291	−0.0458246
$307$	8063.04	1.49896	0.749482	−	0.662024i	$-0.230302\pi$
$307$	8063.04	1.49896	0.749482	+	0.662024i	$0.230302\pi$
$308$	−1719.58	−0.318124
$309$	−3079.33	−0.566915
$310$	0	0
$311$	−6633.87	−1.20956	−0.604778	−	0.796394i	$-0.706738\pi$
$311$	−6633.87	−1.20956	−0.604778	+	0.796394i	$0.706738\pi$
$312$	428.335	0.0777234
$313$	−4751.78	−0.858104	−0.429052	−	0.903280i	$-0.641152\pi$
$313$	−4751.78	−0.858104	−0.429052	+	0.903280i	$0.641152\pi$
$314$	97.5644	0.0175346
$315$	0	0
$316$	−3798.03	−0.676126
$317$	−1207.20	−0.213890	−0.106945	−	0.994265i	$-0.534107\pi$
$317$	−1207.20	−0.213890	−0.106945	+	0.994265i	$0.534107\pi$
$318$	−523.951	−0.0923954
$319$	−2085.80	−0.366090
$320$	0	0
$321$	3262.00	0.567187
$322$	−1215.70	−0.210399
$323$	−7439.43	−1.28155
$324$	−637.947	−0.109387
$325$	0	0
$326$	−935.230	−0.158888
$327$	−3991.18	−0.674962
$328$	−1712.08	−0.288213
$329$	−5109.13	−0.856157
$330$	0	0
$331$	2437.37	0.404744	0.202372	−	0.979309i	$-0.435135\pi$
$331$	2437.37	0.404744	0.202372	+	0.979309i	$0.435135\pi$
$332$	−4122.97	−0.681558
$333$	2428.25	0.399601
$334$	1134.30	0.185827
$335$	0	0
$336$	−3634.49	−0.590112
$337$	−4057.48	−0.655861	−0.327930	−	0.944702i	$-0.606351\pi$
$337$	−4057.48	−0.655861	−0.327930	+	0.944702i	$0.606351\pi$
$338$	−544.387	−0.0876058
$339$	−4380.59	−0.701833
$340$	0	0
$341$	−3034.11	−0.481837
$342$	304.887	0.0482058
$343$	−5796.44	−0.912473
$344$	−2672.88	−0.418930
$345$	0	0
$346$	894.926	0.139051
$347$	7263.85	1.12376	0.561879	−	0.827219i	$-0.310079\pi$
$347$	7263.85	1.12376	0.561879	+	0.827219i	$0.310079\pi$
$348$	−4480.25	−0.690133
$349$	5331.58	0.817745	0.408872	−	0.912592i	$-0.365922\pi$
$349$	5331.58	0.817745	0.408872	+	0.912592i	$0.365922\pi$
$350$	0	0
$351$	−689.272	−0.104817
$352$	728.702	0.110341
$353$	−6448.09	−0.972231	−0.486115	−	0.873895i	$-0.661586\pi$
$353$	−6448.09	−0.972231	−0.486115	+	0.873895i	$0.661586\pi$
$354$	−107.868	−0.0161953
$355$	0	0
$356$	5914.63	0.880547
$357$	4606.73	0.682952
$358$	−30.3434	−0.00447960
$359$	−1845.68	−0.271341	−0.135670	−	0.990754i	$-0.543319\pi$
$359$	−1845.68	−0.271341	−0.135670	+	0.990754i	$0.543319\pi$
$360$	0	0
$361$	2387.93	0.348145
$362$	614.868	0.0892727
$363$	−363.000	−0.0524864
$364$	−3990.77	−0.574652
$365$	0	0
$366$	619.044	0.0884098
$367$	11384.6	1.61926	0.809632	−	0.586938i	$-0.199667\pi$
$367$	11384.6	1.61926	0.809632	+	0.586938i	$0.199667\pi$
$368$	−10611.9	−1.50321
$369$	2755.06	0.388680
$370$	0	0
$371$	9840.17	1.37702
$372$	−6517.19	−0.908335
$373$	−3543.87	−0.491943	−0.245972	−	0.969277i	$-0.579107\pi$
$373$	−3543.87	−0.491943	−0.245972	+	0.969277i	$0.579107\pi$
$374$	−299.800	−0.0414499
$375$	0	0
$376$	1439.64	0.197456
$377$	−4840.69	−0.661295
$378$	−188.795	−0.0256894
$379$	9256.66	1.25457	0.627286	−	0.778789i	$-0.284166\pi$
$379$	9256.66	1.25457	0.627286	+	0.778789i	$0.284166\pi$
$380$	0	0
$381$	−3068.56	−0.412617
$382$	−1768.14	−0.236822
$383$	−3260.36	−0.434978	−0.217489	−	0.976063i	$-0.569787\pi$
$383$	−3260.36	−0.434978	−0.217489	+	0.976063i	$0.569787\pi$
$384$	2081.29	0.276590
$385$	0	0
$386$	1506.04	0.198589
$387$	4301.16	0.564962
$388$	4505.68	0.589539
$389$	139.121	0.0181329	0.00906646	−	0.999959i	$-0.497114\pi$
$389$	139.121	0.0181329	0.00906646	+	0.999959i	$0.497114\pi$
$390$	0	0
$391$	13450.6	1.73970
$392$	−285.056	−0.0367283
$393$	−3926.54	−0.503990
$394$	706.927	0.0903921
$395$	0	0
$396$	−779.713	−0.0989446
$397$	−1324.39	−0.167428	−0.0837141	−	0.996490i	$-0.526678\pi$
$397$	−1324.39	−0.167428	−0.0837141	+	0.996490i	$0.526678\pi$
$398$	−1292.47	−0.162778
$399$	−5725.99	−0.718441
$400$	0	0
$401$	−638.767	−0.0795473	−0.0397737	−	0.999209i	$-0.512664\pi$
$401$	−638.767	−0.0795473	−0.0397737	+	0.999209i	$0.512664\pi$
$402$	−501.355	−0.0622023
$403$	−7041.51	−0.870379
$404$	−626.281	−0.0771253
$405$	0	0
$406$	−1325.89	−0.162076
$407$	2967.86	0.361453
$408$	−1298.07	−0.157510
$409$	7828.03	0.946384	0.473192	−	0.880959i	$-0.343102\pi$
$409$	7828.03	0.946384	0.473192	+	0.880959i	$0.343102\pi$
$410$	0	0
$411$	−4217.60	−0.506178
$412$	−8084.15	−0.966692
$413$	2025.84	0.241368
$414$	−551.238	−0.0654394
$415$	0	0
$416$	1691.16	0.199317
$417$	2175.41	0.255469
$418$	372.640	0.0436038
$419$	3829.62	0.446513	0.223257	−	0.974760i	$-0.428331\pi$
$419$	3829.62	0.446513	0.223257	+	0.974760i	$0.428331\pi$
$420$	0	0
$421$	−16051.8	−1.85824	−0.929120	−	0.369779i	$-0.879433\pi$
$421$	−16051.8	−1.85824	−0.929120	+	0.369779i	$0.879433\pi$
$422$	563.766	0.0650324
$423$	−2316.64	−0.266286
$424$	−2772.73	−0.317584
$425$	0	0
$426$	−479.767	−0.0545652
$427$	−11626.1	−1.31762
$428$	8563.72	0.967157
$429$	−842.443	−0.0948101
$430$	0	0
$431$	1613.07	0.180276	0.0901379	−	0.995929i	$-0.471269\pi$
$431$	1613.07	0.180276	0.0901379	+	0.995929i	$0.471269\pi$
$432$	−1647.99	−0.183540
$433$	1137.16	0.126209	0.0631044	−	0.998007i	$-0.479900\pi$
$433$	1137.16	0.126209	0.0631044	+	0.998007i	$0.479900\pi$
$434$	−1928.71	−0.213320
$435$	0	0
$436$	−10478.0	−1.15093
$437$	−16718.5	−1.83011
$438$	−693.131	−0.0756143
$439$	15605.6	1.69662	0.848309	−	0.529502i	$-0.177621\pi$
$439$	15605.6	1.69662	0.848309	+	0.529502i	$0.177621\pi$
$440$	0	0
$441$	458.708	0.0495312
$442$	−695.769	−0.0748741
$443$	−417.501	−0.0447767	−0.0223884	−	0.999749i	$-0.507127\pi$
$443$	−417.501	−0.0447767	−0.0223884	+	0.999749i	$0.507127\pi$
$444$	6374.87	0.681392
$445$	0	0
$446$	1375.48	0.146033
$447$	−8436.78	−0.892720
$448$	−9228.76	−0.973254
$449$	−2601.70	−0.273456	−0.136728	−	0.990609i	$-0.543659\pi$
$449$	−2601.70	−0.273456	−0.136728	+	0.990609i	$0.543659\pi$
$450$	0	0
$451$	3367.30	0.351574
$452$	−11500.4	−1.19675
$453$	1408.90	0.146128
$454$	480.867	0.0497097
$455$	0	0
$456$	1613.45	0.165695
$457$	−6957.44	−0.712156	−0.356078	−	0.934456i	$-0.615886\pi$
$457$	−6957.44	−0.712156	−0.356078	+	0.934456i	$0.615886\pi$
$458$	1777.52	0.181350
$459$	2088.84	0.212415
$460$	0	0
$461$	3120.45	0.315258	0.157629	−	0.987498i	$-0.449615\pi$
$461$	3120.45	0.315258	0.157629	+	0.987498i	$0.449615\pi$
$462$	−230.750	−0.0232369
$463$	76.4453	0.00767325	0.00383662	−	0.999993i	$-0.498779\pi$
$463$	76.4453	0.00767325	0.00383662	+	0.999993i	$0.498779\pi$
$464$	−11573.7	−1.15797
$465$	0	0
$466$	−2143.21	−0.213052
$467$	−9038.75	−0.895639	−0.447819	−	0.894124i	$-0.647799\pi$
$467$	−9038.75	−0.895639	−0.447819	+	0.894124i	$0.647799\pi$
$468$	−1809.54	−0.178731
$469$	9415.80	0.927039
$470$	0	0
$471$	−830.836	−0.0812800
$472$	−570.834	−0.0556668
$473$	5256.97	0.511027
$474$	−509.656	−0.0493867
$475$	0	0
$476$	12094.0	1.16456
$477$	4461.85	0.428289
$478$	1202.46	0.115062
$479$	−7767.93	−0.740972	−0.370486	−	0.928838i	$-0.620809\pi$
$479$	−7767.93	−0.740972	−0.370486	+	0.928838i	$0.620809\pi$
$480$	0	0
$481$	6887.74	0.652919
$482$	345.042	0.0326063
$483$	10352.6	0.975282
$484$	−952.983	−0.0894988
$485$	0	0
$486$	−85.6059	−0.00799005
$487$	311.944	0.0290258	0.0145129	−	0.999895i	$-0.495380\pi$
$487$	311.944	0.0290258	0.0145129	+	0.999895i	$0.495380\pi$
$488$	3275.96	0.303885
$489$	7964.20	0.736510
$490$	0	0
$491$	12908.1	1.18642	0.593211	−	0.805047i	$-0.297860\pi$
$491$	12908.1	1.18642	0.593211	+	0.805047i	$0.297860\pi$
$492$	7232.86	0.662769
$493$	14669.7	1.34014
$494$	864.814	0.0787648
$495$	0	0
$496$	−16835.7	−1.52408
$497$	9010.35	0.813219
$498$	−553.259	−0.0497834
$499$	−14175.0	−1.27166	−0.635831	−	0.771828i	$-0.719343\pi$
$499$	−14175.0	−1.27166	−0.635831	+	0.771828i	$0.719343\pi$
$500$	0	0
$501$	−9659.44	−0.861382
$502$	−850.453	−0.0756127
$503$	−7144.07	−0.633277	−0.316639	−	0.948546i	$-0.602554\pi$
$503$	−7144.07	−0.633277	−0.316639	+	0.948546i	$0.602554\pi$
$504$	−999.099	−0.0883004
$505$	0	0
$506$	−673.736	−0.0591921
$507$	4635.88	0.406088
$508$	−8055.89	−0.703587
$509$	8333.89	0.725724	0.362862	−	0.931843i	$-0.381800\pi$
$509$	8333.89	0.725724	0.362862	+	0.931843i	$0.381800\pi$
$510$	0	0
$511$	13017.5	1.12693
$512$	6774.40	0.584744
$513$	−2596.35	−0.223453
$514$	−1017.50	−0.0873149
$515$	0	0
$516$	11291.8	0.963362
$517$	−2831.45	−0.240865
$518$	1886.59	0.160023
$519$	−7620.98	−0.644555
$520$	0	0
$521$	−11728.3	−0.986232	−0.493116	−	0.869963i	$-0.664142\pi$
$521$	−11728.3	−0.986232	−0.493116	+	0.869963i	$0.664142\pi$
$522$	−601.203	−0.0504098
$523$	−15253.6	−1.27532	−0.637662	−	0.770316i	$-0.720099\pi$
$523$	−15253.6	−1.27532	−0.637662	+	0.770316i	$0.720099\pi$
$524$	−10308.3	−0.859393
$525$	0	0
$526$	1379.59	0.114359
$527$	21339.3	1.76386
$528$	−2014.22	−0.166018
$529$	18060.3	1.48437
$530$	0	0
$531$	918.579	0.0750714
$532$	−15032.4	−1.22507
$533$	7814.76	0.635075
$534$	793.682	0.0643183
$535$	0	0
$536$	−2653.15	−0.213804
$537$	258.397	0.0207647
$538$	−1231.39	−0.0986783
$539$	560.643	0.0448026
$540$	0	0
$541$	−22147.6	−1.76008	−0.880039	−	0.474902i	$-0.842483\pi$
$541$	−22147.6	−1.76008	−0.880039	+	0.474902i	$0.842483\pi$
$542$	273.014	0.0216364
$543$	−5236.07	−0.413814
$544$	−5125.05	−0.403924
$545$	0	0
$546$	−535.520	−0.0419746
$547$	2806.38	0.219364	0.109682	−	0.993967i	$-0.465017\pi$
$547$	2806.38	0.219364	0.109682	+	0.993967i	$0.465017\pi$
$548$	−11072.5	−0.863124
$549$	−5271.64	−0.409814
$550$	0	0
$551$	−18233.9	−1.40978
$552$	−2917.13	−0.224930
$553$	9571.69	0.736040
$554$	2639.24	0.202402
$555$	0	0
$556$	5711.11	0.435621
$557$	−8190.23	−0.623036	−0.311518	−	0.950240i	$-0.600837\pi$
$557$	−8190.23	−0.623036	−0.311518	+	0.950240i	$0.600837\pi$
$558$	−874.539	−0.0663480
$559$	12200.3	0.923107
$560$	0	0
$561$	2553.02	0.192137
$562$	−44.2171	−0.00331883
$563$	21508.4	1.61007	0.805036	−	0.593226i	$-0.202146\pi$
$563$	21508.4	1.61007	0.805036	+	0.593226i	$0.202146\pi$
$564$	−6081.88	−0.454066
$565$	0	0
$566$	2.91746	0.000216661 0
$567$	1607.74	0.119081
$568$	−2538.91	−0.187553
$569$	−7128.25	−0.525188	−0.262594	−	0.964906i	$-0.584578\pi$
$569$	−7128.25	−0.525188	−0.262594	+	0.964906i	$0.584578\pi$
$570$	0	0
$571$	14565.4	1.06750	0.533750	−	0.845642i	$-0.320782\pi$
$571$	14565.4	1.06750	0.533750	+	0.845642i	$0.320782\pi$
$572$	−2211.66	−0.161668
$573$	15057.1	1.09776
$574$	2140.51	0.155650
$575$	0	0
$576$	−4184.62	−0.302707
$577$	15188.8	1.09587	0.547937	−	0.836520i	$-0.315413\pi$
$577$	15188.8	1.09587	0.547937	+	0.836520i	$0.315413\pi$
$578$	377.739	0.0271832
$579$	−12825.1	−0.920540
$580$	0	0
$581$	10390.6	0.741952
$582$	604.615	0.0430620
$583$	5453.37	0.387402
$584$	−3668.02	−0.259904
$585$	0	0
$586$	1076.57	0.0758918
$587$	−10096.8	−0.709948	−0.354974	−	0.934876i	$-0.615510\pi$
$587$	−10096.8	−0.709948	−0.354974	+	0.934876i	$0.615510\pi$
$588$	1204.25	0.0844596
$589$	−26523.9	−1.85552
$590$	0	0
$591$	−6020.03	−0.419003
$592$	16468.1	1.14330
$593$	566.942	0.0392605	0.0196303	−	0.999807i	$-0.493751\pi$
$593$	566.942	0.0392605	0.0196303	+	0.999807i	$0.493751\pi$
$594$	−104.629	−0.00722727
$595$	0	0
$596$	−22149.0	−1.52225
$597$	11006.3	0.754539
$598$	−1563.59	−0.106923
$599$	3326.86	0.226931	0.113466	−	0.993542i	$-0.463805\pi$
$599$	3326.86	0.226931	0.113466	+	0.993542i	$0.463805\pi$
$600$	0	0
$601$	−27089.1	−1.83858	−0.919290	−	0.393581i	$-0.871236\pi$
$601$	−27089.1	−1.83858	−0.919290	+	0.393581i	$0.871236\pi$
$602$	3341.73	0.226243
$603$	4269.43	0.288332
$604$	3698.78	0.249174
$605$	0	0
$606$	−84.0404	−0.00563351
$607$	732.349	0.0489706	0.0244853	−	0.999700i	$-0.492205\pi$
$607$	732.349	0.0489706	0.0244853	+	0.999700i	$0.492205\pi$
$608$	6370.24	0.424913
$609$	11291.0	0.751288
$610$	0	0
$611$	−6571.18	−0.435092
$612$	5483.82	0.362206
$613$	7678.49	0.505924	0.252962	−	0.967476i	$-0.418595\pi$
$613$	7678.49	0.505924	0.252962	+	0.967476i	$0.418595\pi$
$614$	2840.51	0.186700
$615$	0	0
$616$	−1221.12	−0.0798707
$617$	21512.8	1.40368	0.701841	−	0.712334i	$-0.252362\pi$
$617$	21512.8	1.40368	0.701841	+	0.712334i	$0.252362\pi$
$618$	−1084.81	−0.0706107
$619$	−11921.8	−0.774112	−0.387056	−	0.922056i	$-0.626508\pi$
$619$	−11921.8	−0.774112	−0.387056	+	0.922056i	$0.626508\pi$
$620$	0	0
$621$	4694.22	0.303337
$622$	−2337.03	−0.150653
$623$	−14905.9	−0.958575
$624$	−4674.55	−0.299891
$625$	0	0
$626$	−1673.99	−0.106879
$627$	−3173.31	−0.202121
$628$	−2181.19	−0.138597
$629$	−20873.3	−1.32317
$630$	0	0
$631$	6522.97	0.411530	0.205765	−	0.978601i	$-0.434032\pi$
$631$	6522.97	0.411530	0.205765	+	0.978601i	$0.434032\pi$
$632$	−2697.08	−0.169753
$633$	−4800.90	−0.301451
$634$	−425.282	−0.0266405
$635$	0	0
$636$	11713.7	0.730311
$637$	1301.13	0.0809304
$638$	−734.803	−0.0455974
$639$	4085.58	0.252931
$640$	0	0
$641$	2973.80	0.183242	0.0916209	−	0.995794i	$-0.470795\pi$
$641$	2973.80	0.183242	0.0916209	+	0.995794i	$0.470795\pi$
$642$	1149.16	0.0706446
$643$	25884.2	1.58752	0.793758	−	0.608234i	$-0.208122\pi$
$643$	25884.2	1.58752	0.793758	+	0.608234i	$0.208122\pi$
$644$	27178.8	1.66303
$645$	0	0
$646$	−2620.82	−0.159620
$647$	13929.9	0.846433	0.423217	−	0.906028i	$-0.360901\pi$
$647$	13929.9	0.846433	0.423217	+	0.906028i	$0.360901\pi$
$648$	−453.023	−0.0274636
$649$	1122.71	0.0679047
$650$	0	0
$651$	16424.4	0.988824
$652$	20908.4	1.25588
$653$	−18254.9	−1.09398	−0.546989	−	0.837140i	$-0.684226\pi$
$653$	−18254.9	−1.09398	−0.546989	+	0.837140i	$0.684226\pi$
$654$	−1406.04	−0.0840682
$655$	0	0
$656$	18684.5	1.11205
$657$	5902.54	0.350502
$658$	−1799.88	−0.106636
$659$	24637.9	1.45638	0.728192	−	0.685373i	$-0.240361\pi$
$659$	24637.9	1.45638	0.728192	+	0.685373i	$0.240361\pi$
$660$	0	0
$661$	22721.6	1.33702	0.668508	−	0.743705i	$-0.266933\pi$
$661$	22721.6	1.33702	0.668508	+	0.743705i	$0.266933\pi$
$662$	858.657	0.0504118
$663$	5925.01	0.347071
$664$	−2927.83	−0.171117
$665$	0	0
$666$	855.442	0.0497713
$667$	32967.1	1.91378
$668$	−25358.9	−1.46881
$669$	−11713.3	−0.676923
$670$	0	0
$671$	−6443.11	−0.370691
$672$	−3944.65	−0.226441
$673$	−10281.6	−0.588898	−0.294449	−	0.955667i	$-0.595136\pi$
$673$	−10281.6	−0.588898	−0.294449	+	0.955667i	$0.595136\pi$
$674$	−1429.40	−0.0816891
$675$	0	0
$676$	12170.6	0.692453
$677$	18937.3	1.07507	0.537533	−	0.843243i	$-0.319356\pi$
$677$	18937.3	1.07507	0.537533	+	0.843243i	$0.319356\pi$
$678$	−1543.23	−0.0874150
$679$	−11355.1	−0.641779
$680$	0	0
$681$	−4094.95	−0.230424
$682$	−1068.88	−0.0600140
$683$	9590.55	0.537294	0.268647	−	0.963239i	$-0.413423\pi$
$683$	9590.55	0.537294	0.268647	+	0.963239i	$0.413423\pi$
$684$	−6816.18	−0.381028
$685$	0	0
$686$	−2042.01	−0.113651
$687$	−15137.0	−0.840628
$688$	29169.9	1.61641
$689$	12656.1	0.699794
$690$	0	0
$691$	−29379.5	−1.61744	−0.808718	−	0.588197i	$-0.799838\pi$
$691$	−29379.5	−1.61744	−0.808718	+	0.588197i	$0.799838\pi$
$692$	−20007.3	−1.09908
$693$	1965.01	0.107712
$694$	2558.97	0.139967
$695$	0	0
$696$	−3181.54	−0.173270
$697$	−23682.6	−1.28701
$698$	1878.25	0.101852
$699$	18251.1	0.987581
$700$	0	0
$701$	9839.37	0.530140	0.265070	−	0.964229i	$-0.414605\pi$
$701$	9839.37	0.530140	0.265070	+	0.964229i	$0.414605\pi$
$702$	−242.822	−0.0130552
$703$	25944.7	1.39193
$704$	−5114.53	−0.273808
$705$	0	0
$706$	−2271.58	−0.121094
$707$	1578.34	0.0839596
$708$	2411.54	0.128010
$709$	2732.03	0.144716	0.0723579	−	0.997379i	$-0.476948\pi$
$709$	2732.03	0.144716	0.0723579	+	0.997379i	$0.476948\pi$
$710$	0	0
$711$	4340.11	0.228927
$712$	4200.14	0.221077
$713$	47955.5	2.51886
$714$	1622.89	0.0850634
$715$	0	0
$716$	678.370	0.0354076
$717$	−10239.9	−0.533356
$718$	−650.211	−0.0337962
$719$	−12352.7	−0.640719	−0.320359	−	0.947296i	$-0.603804\pi$
$719$	−12352.7	−0.640719	−0.320359	+	0.947296i	$0.603804\pi$
$720$	0	0
$721$	20373.4	1.05235
$722$	841.238	0.0433624
$723$	−2938.30	−0.151143
$724$	−13746.2	−0.705628
$725$	0	0
$726$	−127.880	−0.00653731
$727$	4292.36	0.218975	0.109488	−	0.993988i	$-0.465079\pi$
$727$	4292.36	0.218975	0.109488	+	0.993988i	$0.465079\pi$
$728$	−2833.95	−0.144276
$729$	729.000	0.0370370
$730$	0	0
$731$	−36972.9	−1.87072
$732$	−13839.6	−0.698807
$733$	−28377.0	−1.42991	−0.714957	−	0.699168i	$-0.753554\pi$
$733$	−28377.0	−1.42991	−0.714957	+	0.699168i	$0.753554\pi$
$734$	4010.65	0.201683
$735$	0	0
$736$	−11517.5	−0.576819
$737$	5218.19	0.260806
$738$	970.575	0.0484110
$739$	15807.4	0.786853	0.393426	−	0.919356i	$-0.371290\pi$
$739$	15807.4	0.786853	0.393426	+	0.919356i	$0.371290\pi$
$740$	0	0
$741$	−7364.56	−0.365106
$742$	3466.57	0.171512
$743$	12809.5	0.632481	0.316241	−	0.948679i	$-0.397579\pi$
$743$	12809.5	0.632481	0.316241	+	0.948679i	$0.397579\pi$
$744$	−4628.03	−0.228053
$745$	0	0
$746$	−1248.46	−0.0612728
$747$	4711.43	0.230766
$748$	6702.45	0.327628
$749$	−21582.1	−1.05286
$750$	0	0
$751$	2792.75	0.135697	0.0678487	−	0.997696i	$-0.478386\pi$
$751$	2792.75	0.135697	0.0678487	+	0.997696i	$0.478386\pi$
$752$	−15711.2	−0.761872
$753$	7242.26	0.350495
$754$	−1705.32	−0.0823660
$755$	0	0
$756$	4220.79	0.203054
$757$	−19648.3	−0.943366	−0.471683	−	0.881768i	$-0.656353\pi$
$757$	−19648.3	−0.943366	−0.471683	+	0.881768i	$0.656353\pi$
$758$	3261.01	0.156260
$759$	5737.38	0.274379
$760$	0	0
$761$	3048.76	0.145226	0.0726132	−	0.997360i	$-0.476866\pi$
$761$	3048.76	0.145226	0.0726132	+	0.997360i	$0.476866\pi$
$762$	−1081.02	−0.0513925
$763$	26406.4	1.25292
$764$	39529.3	1.87188
$765$	0	0
$766$	−1148.59	−0.0541776
$767$	2605.56	0.122661
$768$	−10425.8	−0.489853
$769$	1792.84	0.0840722	0.0420361	−	0.999116i	$-0.486616\pi$
$769$	1792.84	0.0840722	0.0420361	+	0.999116i	$0.486616\pi$
$770$	0	0
$771$	8664.77	0.404739
$772$	−33669.7	−1.56969
$773$	17731.5	0.825044	0.412522	−	0.910948i	$-0.364648\pi$
$773$	17731.5	0.825044	0.412522	+	0.910948i	$0.364648\pi$
$774$	1515.25	0.0703674
$775$	0	0
$776$	3199.60	0.148014
$777$	−16065.8	−0.741772
$778$	49.0106	0.00225850
$779$	29436.6	1.35388
$780$	0	0
$781$	4993.49	0.228785
$782$	4738.47	0.216685
$783$	5119.70	0.233669
$784$	3110.90	0.141714
$785$	0	0
$786$	−1383.27	−0.0627732
$787$	7735.83	0.350385	0.175192	−	0.984534i	$-0.443945\pi$
$787$	7735.83	0.350385	0.175192	+	0.984534i	$0.443945\pi$
$788$	−15804.4	−0.714476
$789$	−11748.2	−0.530099
$790$	0	0
$791$	28982.9	1.30280
$792$	−553.695	−0.0248418
$793$	−14953.0	−0.669607
$794$	−466.565	−0.0208536
$795$	0	0
$796$	28894.9	1.28663
$797$	−25823.4	−1.14769	−0.573846	−	0.818963i	$-0.694549\pi$
$797$	−25823.4	−1.14769	−0.573846	+	0.818963i	$0.694549\pi$
$798$	−2017.19	−0.0894836
$799$	19914.0	0.881734
$800$	0	0
$801$	−6758.81	−0.298141
$802$	−225.030	−0.00990782
$803$	7214.21	0.317041
$804$	11208.5	0.491659
$805$	0	0
$806$	−2480.64	−0.108408
$807$	10486.2	0.457413
$808$	−444.739	−0.0193637
$809$	3169.71	0.137752	0.0688759	−	0.997625i	$-0.478059\pi$
$809$	3169.71	0.137752	0.0688759	+	0.997625i	$0.478059\pi$
$810$	0	0
$811$	23051.5	0.998085	0.499043	−	0.866577i	$-0.333685\pi$
$811$	23051.5	0.998085	0.499043	+	0.866577i	$0.333685\pi$
$812$	29642.2	1.28108
$813$	−2324.92	−0.100293
$814$	1045.54	0.0450198
$815$	0	0
$816$	14166.2	0.607742
$817$	45955.9	1.96793
$818$	2757.72	0.117875
$819$	4560.36	0.194569
$820$	0	0
$821$	6922.35	0.294265	0.147133	−	0.989117i	$-0.452996\pi$
$821$	6922.35	0.294265	0.147133	+	0.989117i	$0.452996\pi$
$822$	−1485.81	−0.0630457
$823$	6344.57	0.268722	0.134361	−	0.990932i	$-0.457102\pi$
$823$	6344.57	0.268722	0.134361	+	0.990932i	$0.457102\pi$
$824$	−5740.77	−0.242705
$825$	0	0
$826$	713.677	0.0300630
$827$	−40602.9	−1.70726	−0.853629	−	0.520882i	$-0.825603\pi$
$827$	−40602.9	−1.70726	−0.853629	+	0.520882i	$0.825603\pi$
$828$	12323.7	0.517245
$829$	−20652.2	−0.865238	−0.432619	−	0.901577i	$-0.642410\pi$
$829$	−20652.2	−0.865238	−0.432619	+	0.901577i	$0.642410\pi$
$830$	0	0
$831$	−22475.1	−0.938212
$832$	−11869.7	−0.494601
$833$	−3943.08	−0.164009
$834$	766.372	0.0318193
$835$	0	0
$836$	−8330.89	−0.344653
$837$	7447.37	0.307549
$838$	1349.13	0.0556143
$839$	−30274.0	−1.24574	−0.622870	−	0.782326i	$-0.714033\pi$
$839$	−30274.0	−1.24574	−0.622870	+	0.782326i	$0.714033\pi$
$840$	0	0
$841$	11566.2	0.474238
$842$	−5654.87	−0.231448
$843$	376.542	0.0153841
$844$	−12603.8	−0.514029
$845$	0	0
$846$	−816.125	−0.0331666
$847$	2401.68	0.0974295
$848$	30259.7	1.22538
$849$	−24.8444	−0.00100431
$850$	0	0
$851$	−46908.3	−1.88954
$852$	10725.9	0.431294
$853$	−19771.8	−0.793639	−0.396820	−	0.917897i	$-0.629886\pi$
$853$	−19771.8	−0.793639	−0.396820	+	0.917897i	$0.629886\pi$
$854$	−4095.73	−0.164113
$855$	0	0
$856$	6081.33	0.242822
$857$	−26489.4	−1.05585	−0.527923	−	0.849292i	$-0.677029\pi$
$857$	−26489.4	−1.05585	−0.527923	+	0.849292i	$0.677029\pi$
$858$	−296.782	−0.0118088
$859$	−24876.2	−0.988085	−0.494043	−	0.869438i	$-0.664481\pi$
$859$	−24876.2	−0.988085	−0.494043	+	0.869438i	$0.664481\pi$
$860$	0	0
$861$	−18228.1	−0.721499
$862$	568.265	0.0224538
$863$	13871.8	0.547162	0.273581	−	0.961849i	$-0.411792\pi$
$863$	13871.8	0.547162	0.273581	+	0.961849i	$0.411792\pi$
$864$	−1788.63	−0.0704288
$865$	0	0
$866$	400.608	0.0157196
$867$	−3216.74	−0.126005
$868$	43119.1	1.68612
$869$	5304.58	0.207072
$870$	0	0
$871$	12110.3	0.471114
$872$	−7440.72	−0.288962
$873$	−5148.76	−0.199610
$874$	−5889.74	−0.227944
$875$	0	0
$876$	15495.9	0.597670
$877$	34035.3	1.31048	0.655240	−	0.755421i	$-0.272568\pi$
$877$	34035.3	1.31048	0.655240	+	0.755421i	$0.272568\pi$
$878$	5497.66	0.211318
$879$	−9167.80	−0.351789
$880$	0	0
$881$	−642.501	−0.0245703	−0.0122851	−	0.999925i	$-0.503911\pi$
$881$	−642.501	−0.0245703	−0.0122851	+	0.999925i	$0.503911\pi$
$882$	161.597	0.00616923
$883$	37886.4	1.44392	0.721958	−	0.691937i	$-0.243242\pi$
$883$	37886.4	1.44392	0.721958	+	0.691937i	$0.243242\pi$
$884$	15554.9	0.591819
$885$	0	0
$886$	−147.081	−0.00557705
$887$	17674.7	0.669063	0.334532	−	0.942385i	$-0.391422\pi$
$887$	17674.7	0.669063	0.334532	+	0.942385i	$0.391422\pi$
$888$	4526.97	0.171076
$889$	20302.2	0.765934
$890$	0	0
$891$	891.000	0.0335013
$892$	−30750.8	−1.15428
$893$	−24752.3	−0.927552
$894$	−2972.17	−0.111191
$895$	0	0
$896$	−13770.2	−0.513428
$897$	13315.2	0.495631
$898$	−916.547	−0.0340597
$899$	52302.2	1.94035
$900$	0	0
$901$	−38354.2	−1.41816
$902$	1186.26	0.0437894
$903$	−28457.4	−1.04873
$904$	−8166.72	−0.300466
$905$	0	0
$906$	496.338	0.0182006
$907$	−46463.4	−1.70098	−0.850491	−	0.525989i	$-0.823695\pi$
$907$	−46463.4	−1.70098	−0.850491	+	0.525989i	$0.823695\pi$
$908$	−10750.5	−0.392915
$909$	715.668	0.0261136
$910$	0	0
$911$	15455.9	0.562103	0.281051	−	0.959693i	$-0.409317\pi$
$911$	15455.9	0.562103	0.281051	+	0.959693i	$0.409317\pi$
$912$	−17608.1	−0.639322
$913$	5758.41	0.208736
$914$	−2451.02	−0.0887008
$915$	0	0
$916$	−39739.1	−1.43342
$917$	25978.8	0.935546
$918$	735.872	0.0264569
$919$	−35769.7	−1.28393	−0.641965	−	0.766734i	$-0.721881\pi$
$919$	−35769.7	−1.28393	−0.641965	+	0.766734i	$0.721881\pi$
$920$	0	0
$921$	−24189.1	−0.865428
$922$	1099.30	0.0392661
$923$	11588.8	0.413272
$924$	5158.74	0.183669
$925$	0	0
$926$	26.9307	0.000955722 0
$927$	9237.98	0.327308
$928$	−12561.4	−0.444340
$929$	−50926.4	−1.79854	−0.899268	−	0.437398i	$-0.855900\pi$
$929$	−50926.4	−1.79854	−0.899268	+	0.437398i	$0.855900\pi$
$930$	0	0
$931$	4901.09	0.172531
$932$	47914.5	1.68400
$933$	19901.6	0.698338
$934$	−3184.24	−0.111554
$935$	0	0
$936$	−1285.00	−0.0448736
$937$	−15370.9	−0.535906	−0.267953	−	0.963432i	$-0.586347\pi$
$937$	−15370.9	−0.535906	−0.267953	+	0.963432i	$0.586347\pi$
$938$	3317.07	0.115465
$939$	14255.3	0.495426
$940$	0	0
$941$	35629.1	1.23430	0.617149	−	0.786846i	$-0.288287\pi$
$941$	35629.1	1.23430	0.617149	+	0.786846i	$0.288287\pi$
$942$	−292.693	−0.0101236
$943$	−53221.7	−1.83790
$944$	6229.68	0.214787
$945$	0	0
$946$	1851.97	0.0636497
$947$	−22204.2	−0.761920	−0.380960	−	0.924591i	$-0.624407\pi$
$947$	−22204.2	−0.761920	−0.380960	+	0.924591i	$0.624407\pi$
$948$	11394.1	0.390362
$949$	16742.6	0.572695
$950$	0	0
$951$	3621.60	0.123489
$952$	8588.30	0.292383
$953$	−50757.0	−1.72527	−0.862635	−	0.505827i	$-0.831187\pi$
$953$	−50757.0	−1.72527	−0.862635	+	0.505827i	$0.831187\pi$
$954$	1571.85	0.0533445
$955$	0	0
$956$	−26882.8	−0.909468
$957$	6257.41	0.211362
$958$	−2736.55	−0.0922900
$959$	27904.5	0.939608
$960$	0	0
$961$	46290.4	1.55384
$962$	2426.47	0.0813227
$963$	−9786.00	−0.327466
$964$	−7713.90	−0.257726
$965$	0	0
$966$	3647.11	0.121474
$967$	33405.1	1.11089	0.555447	−	0.831552i	$-0.312547\pi$
$967$	33405.1	1.11089	0.555447	+	0.831552i	$0.312547\pi$
$968$	−676.739	−0.0224703
$969$	22318.3	0.739904
$970$	0	0
$971$	48382.3	1.59903	0.799516	−	0.600644i	$-0.205089\pi$
$971$	48382.3	1.59903	0.799516	+	0.600644i	$0.205089\pi$
$972$	1913.84	0.0631548
$973$	−14393.0	−0.474222
$974$	109.894	0.00361523
$975$	0	0
$976$	−35751.6	−1.17252
$977$	14604.6	0.478241	0.239121	−	0.970990i	$-0.423141\pi$
$977$	14604.6	0.478241	0.239121	+	0.970990i	$0.423141\pi$
$978$	2805.69	0.0917342
$979$	−8260.77	−0.269679
$980$	0	0
$981$	11973.5	0.389689
$982$	4547.35	0.147772
$983$	−22492.6	−0.729809	−0.364904	−	0.931045i	$-0.618898\pi$
$983$	−22492.6	−0.729809	−0.364904	+	0.931045i	$0.618898\pi$
$984$	5136.25	0.166400
$985$	0	0
$986$	5167.96	0.166918
$987$	15327.4	0.494302
$988$	−19334.2	−0.622572
$989$	−83088.8	−2.67146
$990$	0	0
$991$	22276.1	0.714049	0.357025	−	0.934095i	$-0.383791\pi$
$991$	22276.1	0.714049	0.357025	+	0.934095i	$0.383791\pi$
$992$	−18272.4	−0.584829
$993$	−7312.12	−0.233679
$994$	3174.24	0.101288
$995$	0	0
$996$	12368.9	0.393497
$997$	−25955.4	−0.824490	−0.412245	−	0.911073i	$-0.635255\pi$
$997$	−25955.4	−0.824490	−0.412245	+	0.911073i	$0.635255\pi$
$998$	−4993.68	−0.158389
$999$	−7284.74	−0.230710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.bd.1.4		7
3.2	odd	2		2475.4.a.bo.1.4		7
5.2	odd	4		165.4.c.b.34.8	yes	14
5.3	odd	4		165.4.c.b.34.7	✓	14
5.4	even	2		825.4.a.ba.1.4		7
15.2	even	4		495.4.c.d.199.7		14
15.8	even	4		495.4.c.d.199.8		14
15.14	odd	2		2475.4.a.bs.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.7	✓	14	5.3	odd	4
165.4.c.b.34.8	yes	14	5.2	odd	4
495.4.c.d.199.7		14	15.2	even	4
495.4.c.d.199.8		14	15.8	even	4
825.4.a.ba.1.4		7	5.4	even	2
825.4.a.bd.1.4		7	1.1	even	1	trivial
2475.4.a.bo.1.4		7	3.2	odd	2
2475.4.a.bs.1.4		7	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+0.352288 q^{2} -3.00000 q^{3} -7.87589 q^{4} -1.05686 q^{6} +19.8486 q^{7} -5.59288 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.352288 q^{2} -3.00000 q^{3} -7.87589 q^{4} -1.05686 q^{6} +19.8486 q^{7} -5.59288 q^{8} +9.00000 q^{9} +11.0000 q^{11} +23.6277 q^{12} +25.5286 q^{13} +6.99242 q^{14} +61.0368 q^{16} -77.3644 q^{17} +3.17059 q^{18} +96.1609 q^{19} -59.5458 q^{21} +3.87517 q^{22} -173.860 q^{23} +16.7786 q^{24} +8.99340 q^{26} -27.0000 q^{27} -156.326 q^{28} -189.619 q^{29} -275.829 q^{31} +66.2456 q^{32} -33.0000 q^{33} -27.2545 q^{34} -70.8830 q^{36} +269.805 q^{37} +33.8763 q^{38} -76.5857 q^{39} +306.118 q^{41} -20.9773 q^{42} +477.907 q^{43} -86.6348 q^{44} -61.2487 q^{46} -257.405 q^{47} -183.111 q^{48} +50.9676 q^{49} +232.093 q^{51} -201.060 q^{52} +495.761 q^{53} -9.51177 q^{54} -111.011 q^{56} -288.483 q^{57} -66.8003 q^{58} +102.064 q^{59} -585.738 q^{61} -97.1710 q^{62} +178.638 q^{63} -464.957 q^{64} -11.6255 q^{66} +474.381 q^{67} +609.314 q^{68} +521.580 q^{69} +453.954 q^{71} -50.3359 q^{72} +655.838 q^{73} +95.0491 q^{74} -757.353 q^{76} +218.335 q^{77} -26.9802 q^{78} +482.235 q^{79} +81.0000 q^{81} +107.842 q^{82} +523.492 q^{83} +468.977 q^{84} +168.361 q^{86} +568.856 q^{87} -61.5217 q^{88} -750.979 q^{89} +506.707 q^{91} +1369.30 q^{92} +827.486 q^{93} -90.6806 q^{94} -198.737 q^{96} -572.084 q^{97} +17.9553 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9	\( 7 q + 5 q^{2} - 21 q^{3} + 13 q^{4} - 15 q^{6} + 34 q^{7} + 75 q^{8} + 63 q^{9} + 77 q^{11} - 39 q^{12} + 80 q^{13} + 42 q^{14} - 43 q^{16} + 162 q^{17} + 45 q^{18} + 58 q^{19} - 102 q^{21} + 55 q^{22} + 324 q^{23} - 225 q^{24} - 200 q^{26} - 189 q^{27} - 168 q^{28} + 64 q^{29} - 348 q^{31} - 75 q^{32} - 231 q^{33} + 206 q^{34} + 117 q^{36} + 664 q^{37} + 334 q^{38} - 240 q^{39} - 332 q^{41} - 126 q^{42} + 774 q^{43} + 143 q^{44} - 328 q^{46} + 872 q^{47} + 129 q^{48} - 417 q^{49} - 486 q^{51} + 134 q^{52} + 1628 q^{53} - 135 q^{54} - 1618 q^{56} - 174 q^{57} + 1568 q^{58} - 332 q^{59} + 22 q^{61} - 260 q^{62} + 306 q^{63} + 561 q^{64} - 165 q^{66} + 1524 q^{67} + 2324 q^{68} - 972 q^{69} - 516 q^{71} + 675 q^{72} + 1700 q^{73} + 1628 q^{74} + 2794 q^{76} + 374 q^{77} + 600 q^{78} + 1746 q^{79} + 567 q^{81} + 364 q^{82} + 2344 q^{83} + 504 q^{84} + 1270 q^{86} - 192 q^{87} + 825 q^{88} - 2226 q^{89} + 1072 q^{91} + 4184 q^{92} + 1044 q^{93} + 4736 q^{94} + 225 q^{96} + 1048 q^{97} + 3057 q^{98} + 693 q^{99}+O(q^{100}) \) 7 * q + 5 * q^2 - 21 * q^3 + 13 * q^4 - 15 * q^6 + 34 * q^7 + 75 * q^8 + 63 * q^9 + 77 * q^11 - 39 * q^12 + 80 * q^13 + 42 * q^14 - 43 * q^16 + 162 * q^17 + 45 * q^18 + 58 * q^19 - 102 * q^21 + 55 * q^22 + 324 * q^23 - 225 * q^24 - 200 * q^26 - 189 * q^27 - 168 * q^28 + 64 * q^29 - 348 * q^31 - 75 * q^32 - 231 * q^33 + 206 * q^34 + 117 * q^36 + 664 * q^37 + 334 * q^38 - 240 * q^39 - 332 * q^41 - 126 * q^42 + 774 * q^43 + 143 * q^44 - 328 * q^46 + 872 * q^47 + 129 * q^48 - 417 * q^49 - 486 * q^51 + 134 * q^52 + 1628 * q^53 - 135 * q^54 - 1618 * q^56 - 174 * q^57 + 1568 * q^58 - 332 * q^59 + 22 * q^61 - 260 * q^62 + 306 * q^63 + 561 * q^64 - 165 * q^66 + 1524 * q^67 + 2324 * q^68 - 972 * q^69 - 516 * q^71 + 675 * q^72 + 1700 * q^73 + 1628 * q^74 + 2794 * q^76 + 374 * q^77 + 600 * q^78 + 1746 * q^79 + 567 * q^81 + 364 * q^82 + 2344 * q^83 + 504 * q^84 + 1270 * q^86 - 192 * q^87 + 825 * q^88 - 2226 * q^89 + 1072 * q^91 + 4184 * q^92 + 1044 * q^93 + 4736 * q^94 + 225 * q^96 + 1048 * q^97 + 3057 * q^98 + 693 * q^99

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