LMFDB - Embedded newform 425.4.a.n.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,4,Mod(1,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("425.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.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:	$25.0758117524$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 64 x^{10} + 222 x^{9} + 1546 x^{8} - 4344 x^{7} - 17308 x^{6} + 36842 x^{5} + \cdots - 23104 $ x^12 - 4x^11 - 64x^10 + 222x^9 + 1546x^8 - 4344x^7 - 17308x^6 + 36842x^5 + 84161x^4 - 134636x^3 - 127824x^2 + 143552*x - 23104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-3.27583$ of defining polynomial
Character	$\chi$	$=$	425.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.27583 q^{2} +4.65510 q^{3} +2.73108 q^{4} +15.2493 q^{6} -34.5107 q^{7} -17.2601 q^{8} -5.33005 q^{9} +O(q^{10})$	\(q+3.27583 q^{2} +4.65510 q^{3} +2.73108 q^{4} +15.2493 q^{6} -34.5107 q^{7} -17.2601 q^{8} -5.33005 q^{9} +50.1040 q^{11} +12.7134 q^{12} -63.8218 q^{13} -113.051 q^{14} -78.3898 q^{16} -17.0000 q^{17} -17.4604 q^{18} +5.64888 q^{19} -160.651 q^{21} +164.132 q^{22} +29.9445 q^{23} -80.3475 q^{24} -209.070 q^{26} -150.500 q^{27} -94.2514 q^{28} +8.99822 q^{29} -65.9336 q^{31} -118.711 q^{32} +233.239 q^{33} -55.6892 q^{34} -14.5568 q^{36} -286.633 q^{37} +18.5048 q^{38} -297.097 q^{39} -264.000 q^{41} -526.264 q^{42} +234.414 q^{43} +136.838 q^{44} +98.0931 q^{46} +290.941 q^{47} -364.912 q^{48} +847.987 q^{49} -79.1367 q^{51} -174.302 q^{52} -378.284 q^{53} -493.011 q^{54} +595.658 q^{56} +26.2961 q^{57} +29.4766 q^{58} +665.556 q^{59} +299.597 q^{61} -215.988 q^{62} +183.944 q^{63} +238.241 q^{64} +764.053 q^{66} +389.295 q^{67} -46.4283 q^{68} +139.394 q^{69} -913.421 q^{71} +91.9973 q^{72} -438.323 q^{73} -938.960 q^{74} +15.4275 q^{76} -1729.12 q^{77} -973.240 q^{78} +423.708 q^{79} -556.679 q^{81} -864.821 q^{82} +272.141 q^{83} -438.749 q^{84} +767.902 q^{86} +41.8876 q^{87} -864.801 q^{88} -1456.29 q^{89} +2202.53 q^{91} +81.7807 q^{92} -306.928 q^{93} +953.073 q^{94} -552.612 q^{96} +749.861 q^{97} +2777.86 q^{98} -267.057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 12 q^{3} + 48 q^{4} + 8 q^{6} - 70 q^{7} - 102 q^{8} + 90 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 12 * q^3 + 48 * q^4 + 8 * q^6 - 70 * q^7 - 102 * q^8 + 90 * q^9	\( 12 q - 4 q^{2} - 12 q^{3} + 48 q^{4} + 8 q^{6} - 70 q^{7} - 102 q^{8} + 90 q^{9} + 30 q^{11} - 120 q^{12} - 112 q^{13} + 38 q^{14} + 120 q^{16} - 204 q^{17} - 166 q^{18} - 50 q^{19} - 64 q^{21} - 400 q^{22} - 262 q^{23} - 102 q^{24} - 50 q^{26} - 678 q^{27} - 428 q^{28} + 232 q^{29} + 18 q^{31} - 880 q^{32} - 168 q^{33} + 68 q^{34} + 302 q^{36} - 852 q^{37} + 200 q^{38} + 132 q^{39} + 408 q^{41} - 1794 q^{42} - 876 q^{43} + 52 q^{44} + 104 q^{46} - 1132 q^{47} + 494 q^{48} - 12 q^{49} + 204 q^{51} - 2790 q^{52} - 492 q^{53} - 150 q^{54} + 536 q^{56} - 1842 q^{57} - 866 q^{58} - 134 q^{59} + 712 q^{61} - 1648 q^{62} - 1246 q^{63} - 12 q^{64} - 2068 q^{66} - 2680 q^{67} - 816 q^{68} - 900 q^{69} + 98 q^{71} - 3992 q^{72} - 894 q^{73} - 1236 q^{74} - 1594 q^{76} - 1164 q^{77} - 40 q^{78} - 1134 q^{79} - 608 q^{81} - 5406 q^{82} - 2272 q^{83} + 560 q^{84} - 1932 q^{86} - 2320 q^{87} - 3238 q^{88} - 1622 q^{89} - 120 q^{91} - 2226 q^{92} - 5092 q^{93} + 1982 q^{94} - 1548 q^{96} - 2706 q^{97} + 2582 q^{98} + 614 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 12 * q^3 + 48 * q^4 + 8 * q^6 - 70 * q^7 - 102 * q^8 + 90 * q^9 + 30 * q^11 - 120 * q^12 - 112 * q^13 + 38 * q^14 + 120 * q^16 - 204 * q^17 - 166 * q^18 - 50 * q^19 - 64 * q^21 - 400 * q^22 - 262 * q^23 - 102 * q^24 - 50 * q^26 - 678 * q^27 - 428 * q^28 + 232 * q^29 + 18 * q^31 - 880 * q^32 - 168 * q^33 + 68 * q^34 + 302 * q^36 - 852 * q^37 + 200 * q^38 + 132 * q^39 + 408 * q^41 - 1794 * q^42 - 876 * q^43 + 52 * q^44 + 104 * q^46 - 1132 * q^47 + 494 * q^48 - 12 * q^49 + 204 * q^51 - 2790 * q^52 - 492 * q^53 - 150 * q^54 + 536 * q^56 - 1842 * q^57 - 866 * q^58 - 134 * q^59 + 712 * q^61 - 1648 * q^62 - 1246 * q^63 - 12 * q^64 - 2068 * q^66 - 2680 * q^67 - 816 * q^68 - 900 * q^69 + 98 * q^71 - 3992 * q^72 - 894 * q^73 - 1236 * q^74 - 1594 * q^76 - 1164 * q^77 - 40 * q^78 - 1134 * q^79 - 608 * q^81 - 5406 * q^82 - 2272 * q^83 + 560 * q^84 - 1932 * q^86 - 2320 * q^87 - 3238 * q^88 - 1622 * q^89 - 120 * q^91 - 2226 * q^92 - 5092 * q^93 + 1982 * q^94 - 1548 * q^96 - 2706 * q^97 + 2582 * q^98 + 614 * 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 $

$2$	3.27583	1.15818	0.579091	−	0.815263i	$-0.303408\pi$
$2$	3.27583	1.15818	0.579091	+	0.815263i	$0.303408\pi$
$3$	4.65510	0.895874	0.447937	−	0.894065i	$-0.352159\pi$
$3$	4.65510	0.895874	0.447937	+	0.894065i	$0.352159\pi$
$4$	2.73108	0.341385
$5$	0	0
$5$	0	0
$6$	15.2493	1.03759
$7$	−34.5107	−1.86340	−0.931701	−	0.363227i	$-0.881675\pi$
$7$	−34.5107	−1.86340	−0.931701	+	0.363227i	$0.881675\pi$
$8$	−17.2601	−0.762796
$9$	−5.33005	−0.197409
$10$	0	0
$11$	50.1040	1.37336	0.686679	−	0.726961i	$-0.259068\pi$
$11$	50.1040	1.37336	0.686679	+	0.726961i	$0.259068\pi$
$12$	12.7134	0.305838
$13$	−63.8218	−1.36161	−0.680807	−	0.732463i	$-0.738371\pi$
$13$	−63.8218	−1.36161	−0.680807	+	0.732463i	$0.738371\pi$
$14$	−113.051	−2.15816
$15$	0	0
$16$	−78.3898	−1.22484
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	−17.4604	−0.228636
$19$	5.64888	0.0682075	0.0341037	−	0.999418i	$-0.489142\pi$
$19$	5.64888	0.0682075	0.0341037	+	0.999418i	$0.489142\pi$
$20$	0	0
$21$	−160.651	−1.66937
$22$	164.132	1.59060
$23$	29.9445	0.271472	0.135736	−	0.990745i	$-0.456660\pi$
$23$	29.9445	0.271472	0.135736	+	0.990745i	$0.456660\pi$
$24$	−80.3475	−0.683369
$25$	0	0
$26$	−209.070	−1.57700
$27$	−150.500	−1.07273
$28$	−94.2514	−0.636137
$29$	8.99822	0.0576182	0.0288091	−	0.999585i	$-0.490829\pi$
$29$	8.99822	0.0576182	0.0288091	+	0.999585i	$0.490829\pi$
$30$	0	0
$31$	−65.9336	−0.382001	−0.191000	−	0.981590i	$-0.561173\pi$
$31$	−65.9336	−0.382001	−0.191000	+	0.981590i	$0.561173\pi$
$32$	−118.711	−0.655793
$33$	233.239	1.23036
$34$	−55.6892	−0.280900
$35$	0	0
$36$	−14.5568	−0.0673925
$37$	−286.633	−1.27357	−0.636785	−	0.771041i	$-0.719736\pi$
$37$	−286.633	−1.27357	−0.636785	+	0.771041i	$0.719736\pi$
$38$	18.5048	0.0789967
$39$	−297.097	−1.21984
$40$	0	0
$41$	−264.000	−1.00561	−0.502804	−	0.864400i	$-0.667698\pi$
$41$	−264.000	−1.00561	−0.502804	+	0.864400i	$0.667698\pi$
$42$	−526.264	−1.93344
$43$	234.414	0.831345	0.415673	−	0.909514i	$-0.363546\pi$
$43$	234.414	0.831345	0.415673	+	0.909514i	$0.363546\pi$
$44$	136.838	0.468843
$45$	0	0
$46$	98.0931	0.314414
$47$	290.941	0.902938	0.451469	−	0.892287i	$-0.350900\pi$
$47$	290.941	0.902938	0.451469	+	0.892287i	$0.350900\pi$
$48$	−364.912	−1.09730
$49$	847.987	2.47226
$50$	0	0
$51$	−79.1367	−0.217281
$52$	−174.302	−0.464834
$53$	−378.284	−0.980401	−0.490200	−	0.871610i	$-0.663076\pi$
$53$	−378.284	−0.980401	−0.490200	+	0.871610i	$0.663076\pi$
$54$	−493.011	−1.24241
$55$	0	0
$56$	595.658	1.42140
$57$	26.2961	0.0611053
$58$	29.4766	0.0667323
$59$	665.556	1.46861	0.734305	−	0.678820i	$-0.237508\pi$
$59$	665.556	1.46861	0.734305	+	0.678820i	$0.237508\pi$
$60$	0	0
$61$	299.597	0.628844	0.314422	−	0.949283i	$-0.398189\pi$
$61$	299.597	0.628844	0.314422	+	0.949283i	$0.398189\pi$
$62$	−215.988	−0.442427
$63$	183.944	0.367853
$64$	238.241	0.465314
$65$	0	0
$66$	764.053	1.42498
$67$	389.295	0.709849	0.354925	−	0.934895i	$-0.384507\pi$
$67$	389.295	0.709849	0.354925	+	0.934895i	$0.384507\pi$
$68$	−46.4283	−0.0827980
$69$	139.394	0.243205
$70$	0	0
$71$	−913.421	−1.52680	−0.763402	−	0.645923i	$-0.776473\pi$
$71$	−913.421	−1.52680	−0.763402	+	0.645923i	$0.776473\pi$
$72$	91.9973	0.150583
$73$	−438.323	−0.702765	−0.351382	−	0.936232i	$-0.614288\pi$
$73$	−438.323	−0.702765	−0.351382	+	0.936232i	$0.614288\pi$
$74$	−938.960	−1.47503
$75$	0	0
$76$	15.4275	0.0232850
$77$	−1729.12	−2.55912
$78$	−973.240	−1.41279
$79$	423.708	0.603428	0.301714	−	0.953398i	$-0.402441\pi$
$79$	423.708	0.603428	0.301714	+	0.953398i	$0.402441\pi$
$80$	0	0
$81$	−556.679	−0.763620
$82$	−864.821	−1.16468
$83$	272.141	0.359896	0.179948	−	0.983676i	$-0.442407\pi$
$83$	272.141	0.359896	0.179948	+	0.983676i	$0.442407\pi$
$84$	−438.749	−0.569899
$85$	0	0
$86$	767.902	0.962849
$87$	41.8876	0.0516186
$88$	−864.801	−1.04759
$89$	−1456.29	−1.73445	−0.867226	−	0.497914i	$-0.834099\pi$
$89$	−1456.29	−1.73445	−0.867226	+	0.497914i	$0.834099\pi$
$90$	0	0
$91$	2202.53	2.53723
$92$	81.7807	0.0926764
$93$	−306.928	−0.342225
$94$	953.073	1.04577
$95$	0	0
$96$	−552.612	−0.587508
$97$	749.861	0.784915	0.392458	−	0.919770i	$-0.371625\pi$
$97$	749.861	0.784915	0.392458	+	0.919770i	$0.371625\pi$
$98$	2777.86	2.86333
$99$	−267.057	−0.271114
$100$	0	0
$101$	833.706	0.821355	0.410677	−	0.911781i	$-0.365292\pi$
$101$	833.706	0.821355	0.410677	+	0.911781i	$0.365292\pi$
$102$	−259.239	−0.251651
$103$	−1181.34	−1.13011	−0.565054	−	0.825054i	$-0.691145\pi$
$103$	−1181.34	−1.13011	−0.565054	+	0.825054i	$0.691145\pi$
$104$	1101.57	1.03863
$105$	0	0
$106$	−1239.19	−1.13548
$107$	−570.147	−0.515123	−0.257562	−	0.966262i	$-0.582919\pi$
$107$	−570.147	−0.515123	−0.257562	+	0.966262i	$0.582919\pi$
$108$	−411.026	−0.366213
$109$	235.736	0.207150	0.103575	−	0.994622i	$-0.466972\pi$
$109$	235.736	0.207150	0.103575	+	0.994622i	$0.466972\pi$
$110$	0	0
$111$	−1334.30	−1.14096
$112$	2705.29	2.28237
$113$	61.1327	0.0508928	0.0254464	−	0.999676i	$-0.491899\pi$
$113$	61.1327	0.0508928	0.0254464	+	0.999676i	$0.491899\pi$
$114$	86.1416	0.0707711
$115$	0	0
$116$	24.5748	0.0196700
$117$	340.174	0.268795
$118$	2180.25	1.70092
$119$	586.681	0.451941
$120$	0	0
$121$	1179.41	0.886111
$122$	981.430	0.728316
$123$	−1228.95	−0.900898
$124$	−180.070	−0.130409
$125$	0	0
$126$	602.569	0.426040
$127$	−2236.90	−1.56293	−0.781466	−	0.623948i	$-0.785528\pi$
$127$	−2236.90	−1.56293	−0.781466	+	0.623948i	$0.785528\pi$
$128$	1730.13	1.19471
$129$	1091.22	0.744781
$130$	0	0
$131$	−317.265	−0.211600	−0.105800	−	0.994387i	$-0.533740\pi$
$131$	−317.265	−0.211600	−0.105800	+	0.994387i	$0.533740\pi$
$132$	636.995	0.420025
$133$	−194.947	−0.127098
$134$	1275.26	0.822135
$135$	0	0
$136$	293.422	0.185005
$137$	−2547.18	−1.58847	−0.794235	−	0.607611i	$-0.792128\pi$
$137$	−2547.18	−1.58847	−0.794235	+	0.607611i	$0.792128\pi$
$138$	456.633	0.281675
$139$	233.338	0.142384	0.0711922	−	0.997463i	$-0.477320\pi$
$139$	233.338	0.142384	0.0711922	+	0.997463i	$0.477320\pi$
$140$	0	0
$141$	1354.36	0.808919
$142$	−2992.21	−1.76832
$143$	−3197.73	−1.86998
$144$	417.822	0.241795
$145$	0	0
$146$	−1435.87	−0.813929
$147$	3947.46	2.21484
$148$	−782.816	−0.434778
$149$	−2245.84	−1.23481	−0.617404	−	0.786646i	$-0.711815\pi$
$149$	−2245.84	−1.23481	−0.617404	+	0.786646i	$0.711815\pi$
$150$	0	0
$151$	−614.709	−0.331287	−0.165644	−	0.986186i	$-0.552970\pi$
$151$	−614.709	−0.331287	−0.165644	+	0.986186i	$0.552970\pi$
$152$	−97.5003	−0.0520284
$153$	90.6109	0.0478788
$154$	−5664.32	−2.96392
$155$	0	0
$156$	−811.395	−0.416433
$157$	312.593	0.158902	0.0794511	−	0.996839i	$-0.474683\pi$
$157$	312.593	0.158902	0.0794511	+	0.996839i	$0.474683\pi$
$158$	1387.99	0.698879
$159$	−1760.95	−0.878316
$160$	0	0
$161$	−1033.40	−0.505861
$162$	−1823.59	−0.884411
$163$	961.947	0.462242	0.231121	−	0.972925i	$-0.425761\pi$
$163$	961.947	0.462242	0.231121	+	0.972925i	$0.425761\pi$
$164$	−721.006	−0.343299
$165$	0	0
$166$	891.489	0.416825
$167$	2471.88	1.14539	0.572694	−	0.819769i	$-0.305898\pi$
$167$	2471.88	1.14539	0.572694	+	0.819769i	$0.305898\pi$
$168$	2772.85	1.27339
$169$	1876.22	0.853994
$170$	0	0
$171$	−30.1088	−0.0134648
$172$	640.204	0.283809
$173$	1566.52	0.688440	0.344220	−	0.938889i	$-0.388143\pi$
$173$	1566.52	0.688440	0.344220	+	0.938889i	$0.388143\pi$
$174$	137.217	0.0597838
$175$	0	0
$176$	−3927.65	−1.68214
$177$	3098.23	1.31569
$178$	−4770.56	−2.00881
$179$	−2433.26	−1.01604	−0.508018	−	0.861346i	$-0.669622\pi$
$179$	−2433.26	−1.01604	−0.508018	+	0.861346i	$0.669622\pi$
$180$	0	0
$181$	−3659.79	−1.50293	−0.751464	−	0.659775i	$-0.770652\pi$
$181$	−3659.79	−1.50293	−0.751464	+	0.659775i	$0.770652\pi$
$182$	7215.13	2.93858
$183$	1394.65	0.563365
$184$	−516.845	−0.207078
$185$	0	0
$186$	−1005.44	−0.396359
$187$	−851.768	−0.333088
$188$	794.582	0.308249
$189$	5193.84	1.99892
$190$	0	0
$191$	2871.34	1.08776	0.543882	−	0.839162i	$-0.316954\pi$
$191$	2871.34	1.08776	0.543882	+	0.839162i	$0.316954\pi$
$192$	1109.03	0.416863
$193$	1814.28	0.676655	0.338327	−	0.941028i	$-0.390139\pi$
$193$	1814.28	0.676655	0.338327	+	0.941028i	$0.390139\pi$
$194$	2456.42	0.909075
$195$	0	0
$196$	2315.92	0.843993
$197$	1106.32	0.400112	0.200056	−	0.979784i	$-0.435888\pi$
$197$	1106.32	0.400112	0.200056	+	0.979784i	$0.435888\pi$
$198$	−874.834	−0.313999
$199$	924.956	0.329489	0.164745	−	0.986336i	$-0.447320\pi$
$199$	924.956	0.329489	0.164745	+	0.986336i	$0.447320\pi$
$200$	0	0
$201$	1812.21	0.635936
$202$	2731.08	0.951278
$203$	−310.535	−0.107366
$204$	−216.129	−0.0741766
$205$	0	0
$206$	−3869.88	−1.30887
$207$	−159.606	−0.0535911
$208$	5002.98	1.66776
$209$	283.032	0.0936733
$210$	0	0
$211$	1032.52	0.336881	0.168440	−	0.985712i	$-0.446127\pi$
$211$	1032.52	0.336881	0.168440	+	0.985712i	$0.446127\pi$
$212$	−1033.12	−0.334694
$213$	−4252.06	−1.36782
$214$	−1867.71	−0.596607
$215$	0	0
$216$	2597.64	0.818273
$217$	2275.41	0.711821
$218$	772.231	0.239918
$219$	−2040.44	−0.629589
$220$	0	0
$221$	1084.97	0.330240
$222$	−4370.95	−1.32144
$223$	−6265.36	−1.88143	−0.940717	−	0.339193i	$-0.889846\pi$
$223$	−6265.36	−1.88143	−0.940717	+	0.339193i	$0.889846\pi$
$224$	4096.80	1.22200
$225$	0	0
$226$	200.261	0.0589431
$227$	−1804.00	−0.527470	−0.263735	−	0.964595i	$-0.584954\pi$
$227$	−1804.00	−0.527470	−0.263735	+	0.964595i	$0.584954\pi$
$228$	71.8167	0.0208604
$229$	3195.06	0.921989	0.460995	−	0.887403i	$-0.347493\pi$
$229$	3195.06	0.921989	0.460995	+	0.887403i	$0.347493\pi$
$230$	0	0
$231$	−8049.24	−2.29265
$232$	−155.310	−0.0439509
$233$	−262.550	−0.0738208	−0.0369104	−	0.999319i	$-0.511752\pi$
$233$	−262.550	−0.0738208	−0.0369104	+	0.999319i	$0.511752\pi$
$234$	1114.35	0.311314
$235$	0	0
$236$	1817.69	0.501361
$237$	1972.40	0.540596
$238$	1921.87	0.523430
$239$	−1319.97	−0.357246	−0.178623	−	0.983918i	$-0.557164\pi$
$239$	−1319.97	−0.357246	−0.178623	+	0.983918i	$0.557164\pi$
$240$	0	0
$241$	5396.64	1.44244	0.721221	−	0.692705i	$-0.243581\pi$
$241$	5396.64	1.44244	0.721221	+	0.692705i	$0.243581\pi$
$242$	3863.56	1.02628
$243$	1472.09	0.388620
$244$	818.224	0.214678
$245$	0	0
$246$	−4025.83	−1.04340
$247$	−360.522	−0.0928723
$248$	1138.02	0.291389
$249$	1266.84	0.322422
$250$	0	0
$251$	−1304.31	−0.327997	−0.163999	−	0.986461i	$-0.552439\pi$
$251$	−1304.31	−0.327997	−0.163999	+	0.986461i	$0.552439\pi$
$252$	502.365	0.125579
$253$	1500.34	0.372828
$254$	−7327.69	−1.81016
$255$	0	0
$256$	3761.68	0.918378
$257$	−5987.20	−1.45320	−0.726598	−	0.687063i	$-0.758900\pi$
$257$	−5987.20	−1.45320	−0.726598	+	0.687063i	$0.758900\pi$
$258$	3574.66	0.862591
$259$	9891.88	2.37317
$260$	0	0
$261$	−47.9610	−0.0113744
$262$	−1039.31	−0.245071
$263$	−959.020	−0.224851	−0.112425	−	0.993660i	$-0.535862\pi$
$263$	−959.020	−0.224851	−0.112425	+	0.993660i	$0.535862\pi$
$264$	−4025.73	−0.938510
$265$	0	0
$266$	−638.613	−0.147202
$267$	−6779.17	−1.55385
$268$	1063.19	0.242332
$269$	−2252.18	−0.510475	−0.255237	−	0.966878i	$-0.582154\pi$
$269$	−2252.18	−0.510475	−0.255237	+	0.966878i	$0.582154\pi$
$270$	0	0
$271$	7886.49	1.76779	0.883894	−	0.467688i	$-0.154913\pi$
$271$	7886.49	1.76779	0.883894	+	0.467688i	$0.154913\pi$
$272$	1332.63	0.297068
$273$	10253.0	2.27304
$274$	−8344.14	−1.83974
$275$	0	0
$276$	380.697	0.0830264
$277$	−6724.54	−1.45862	−0.729312	−	0.684182i	$-0.760160\pi$
$277$	−6724.54	−1.45862	−0.729312	+	0.684182i	$0.760160\pi$
$278$	764.375	0.164907
$279$	351.430	0.0754106
$280$	0	0
$281$	2734.73	0.580572	0.290286	−	0.956940i	$-0.406250\pi$
$281$	2734.73	0.580572	0.290286	+	0.956940i	$0.406250\pi$
$282$	4436.65	0.936875
$283$	−5528.05	−1.16116	−0.580580	−	0.814203i	$-0.697174\pi$
$283$	−5528.05	−1.16116	−0.580580	+	0.814203i	$0.697174\pi$
$284$	−2494.62	−0.521228
$285$	0	0
$286$	−10475.2	−2.16578
$287$	9110.83	1.87385
$288$	632.737	0.129460
$289$	289.000	0.0588235
$290$	0	0
$291$	3490.67	0.703186
$292$	−1197.09	−0.239913
$293$	−7242.14	−1.44399	−0.721997	−	0.691896i	$-0.756775\pi$
$293$	−7242.14	−1.44399	−0.721997	+	0.691896i	$0.756775\pi$
$294$	12931.2	2.56518
$295$	0	0
$296$	4947.31	0.971475
$297$	−7540.64	−1.47324
$298$	−7356.99	−1.43013
$299$	−1911.11	−0.369640
$300$	0	0
$301$	−8089.80	−1.54913
$302$	−2013.68	−0.383691
$303$	3880.98	0.735831
$304$	−442.815	−0.0835433
$305$	0	0
$306$	296.826	0.0554523
$307$	750.891	0.139595	0.0697974	−	0.997561i	$-0.477765\pi$
$307$	750.891	0.139595	0.0697974	+	0.997561i	$0.477765\pi$
$308$	−4722.37	−0.873643
$309$	−5499.27	−1.01244
$310$	0	0
$311$	−1628.08	−0.296848	−0.148424	−	0.988924i	$-0.547420\pi$
$311$	−1628.08	−0.296848	−0.148424	+	0.988924i	$0.547420\pi$
$312$	5127.92	0.930486
$313$	244.772	0.0442023	0.0221011	−	0.999756i	$-0.492964\pi$
$313$	244.772	0.0442023	0.0221011	+	0.999756i	$0.492964\pi$
$314$	1024.00	0.184038
$315$	0	0
$316$	1157.18	0.206001
$317$	6650.27	1.17828	0.589142	−	0.808029i	$-0.299466\pi$
$317$	6650.27	1.17828	0.589142	+	0.808029i	$0.299466\pi$
$318$	−5768.57	−1.01725
$319$	450.847	0.0791303
$320$	0	0
$321$	−2654.09	−0.461486
$322$	−3385.26	−0.585879
$323$	−96.0310	−0.0165427
$324$	−1520.33	−0.260688
$325$	0	0
$326$	3151.18	0.535361
$327$	1097.37	0.185581
$328$	4556.67	0.767074
$329$	−10040.6	−1.68253
$330$	0	0
$331$	3304.63	0.548757	0.274379	−	0.961622i	$-0.411528\pi$
$331$	3304.63	0.548757	0.274379	+	0.961622i	$0.411528\pi$
$332$	743.239	0.122863
$333$	1527.77	0.251415
$334$	8097.46	1.32657
$335$	0	0
$336$	12593.4	2.04472
$337$	5694.42	0.920460	0.460230	−	0.887800i	$-0.347767\pi$
$337$	5694.42	0.920460	0.460230	+	0.887800i	$0.347767\pi$
$338$	6146.20	0.989080
$339$	284.579	0.0455935
$340$	0	0
$341$	−3303.54	−0.524624
$342$	−98.6315	−0.0155947
$343$	−17427.4	−2.74342
$344$	−4046.02	−0.634147
$345$	0	0
$346$	5131.65	0.797339
$347$	−8513.23	−1.31704	−0.658522	−	0.752562i	$-0.728818\pi$
$347$	−8513.23	−1.31704	−0.658522	+	0.752562i	$0.728818\pi$
$348$	114.398	0.0176218
$349$	−6744.53	−1.03446	−0.517230	−	0.855846i	$-0.673037\pi$
$349$	−6744.53	−1.03446	−0.517230	+	0.855846i	$0.673037\pi$
$350$	0	0
$351$	9605.16	1.46064
$352$	−5947.91	−0.900638
$353$	4419.33	0.666338	0.333169	−	0.942867i	$-0.391882\pi$
$353$	4419.33	0.666338	0.333169	+	0.942867i	$0.391882\pi$
$354$	10149.3	1.52381
$355$	0	0
$356$	−3977.24	−0.592116
$357$	2731.06	0.404882
$358$	−7970.96	−1.17675
$359$	−542.910	−0.0798153	−0.0399076	−	0.999203i	$-0.512706\pi$
$359$	−542.910	−0.0798153	−0.0399076	+	0.999203i	$0.512706\pi$
$360$	0	0
$361$	−6827.09	−0.995348
$362$	−11988.8	−1.74066
$363$	5490.29	0.793844
$364$	6015.29	0.866173
$365$	0	0
$366$	4568.66	0.652479
$367$	−10592.3	−1.50658	−0.753290	−	0.657688i	$-0.771534\pi$
$367$	−10592.3	−1.50658	−0.753290	+	0.657688i	$0.771534\pi$
$368$	−2347.34	−0.332510
$369$	1407.14	0.198516
$370$	0	0
$371$	13054.8	1.82688
$372$	−838.243	−0.116830
$373$	−2683.57	−0.372520	−0.186260	−	0.982500i	$-0.559637\pi$
$373$	−2683.57	−0.372520	−0.186260	+	0.982500i	$0.559637\pi$
$374$	−2790.25	−0.385777
$375$	0	0
$376$	−5021.67	−0.688757
$377$	−574.283	−0.0784537
$378$	17014.2	2.31512
$379$	−1773.15	−0.240318	−0.120159	−	0.992755i	$-0.538341\pi$
$379$	−1773.15	−0.240318	−0.120159	+	0.992755i	$0.538341\pi$
$380$	0	0
$381$	−10413.0	−1.40019
$382$	9406.03	1.25983
$383$	2712.79	0.361924	0.180962	−	0.983490i	$-0.442079\pi$
$383$	2712.79	0.361924	0.180962	+	0.983490i	$0.442079\pi$
$384$	8053.91	1.07031
$385$	0	0
$386$	5943.26	0.783689
$387$	−1249.44	−0.164115
$388$	2047.93	0.267958
$389$	−6666.89	−0.868958	−0.434479	−	0.900682i	$-0.643067\pi$
$389$	−6666.89	−0.868958	−0.434479	+	0.900682i	$0.643067\pi$
$390$	0	0
$391$	−509.056	−0.0658416
$392$	−14636.3	−1.88583
$393$	−1476.90	−0.189567
$394$	3624.12	0.463402
$395$	0	0
$396$	−729.354	−0.0925541
$397$	4658.21	0.588889	0.294445	−	0.955669i	$-0.404865\pi$
$397$	4658.21	0.588889	0.294445	+	0.955669i	$0.404865\pi$
$398$	3030.00	0.381609
$399$	−907.496	−0.113864
$400$	0	0
$401$	3325.75	0.414165	0.207082	−	0.978324i	$-0.433603\pi$
$401$	3325.75	0.414165	0.207082	+	0.978324i	$0.433603\pi$
$402$	5936.48	0.736529
$403$	4208.00	0.520138
$404$	2276.92	0.280398
$405$	0	0
$406$	−1017.26	−0.124349
$407$	−14361.4	−1.74907
$408$	1365.91	0.165741
$409$	9323.33	1.12716	0.563581	−	0.826061i	$-0.309423\pi$
$409$	9323.33	1.12716	0.563581	+	0.826061i	$0.309423\pi$
$410$	0	0
$411$	−11857.4	−1.42307
$412$	−3226.34	−0.385802
$413$	−22968.8	−2.73661
$414$	−522.841	−0.0620682
$415$	0	0
$416$	7576.36	0.892937
$417$	1086.21	0.127559
$418$	927.164	0.108491
$419$	−3581.15	−0.417544	−0.208772	−	0.977964i	$-0.566947\pi$
$419$	−3581.15	−0.417544	−0.208772	+	0.977964i	$0.566947\pi$
$420$	0	0
$421$	−14734.5	−1.70574	−0.852868	−	0.522126i	$-0.825139\pi$
$421$	−14734.5	−1.70574	−0.852868	+	0.522126i	$0.825139\pi$
$422$	3382.37	0.390169
$423$	−1550.73	−0.178248
$424$	6529.21	0.747846
$425$	0	0
$426$	−13929.1	−1.58419
$427$	−10339.3	−1.17179
$428$	−1557.12	−0.175855
$429$	−14885.8	−1.67527
$430$	0	0
$431$	543.650	0.0607580	0.0303790	−	0.999538i	$-0.490329\pi$
$431$	543.650	0.0607580	0.0303790	+	0.999538i	$0.490329\pi$
$432$	11797.6	1.31392
$433$	−3015.19	−0.334643	−0.167322	−	0.985902i	$-0.553512\pi$
$433$	−3015.19	−0.334643	−0.167322	+	0.985902i	$0.553512\pi$
$434$	7453.88	0.824418
$435$	0	0
$436$	643.813	0.0707180
$437$	169.153	0.0185164
$438$	−6684.13	−0.729178
$439$	13558.0	1.47401	0.737003	−	0.675890i	$-0.236241\pi$
$439$	13558.0	1.47401	0.737003	+	0.675890i	$0.236241\pi$
$440$	0	0
$441$	−4519.81	−0.488048
$442$	3554.18	0.382478
$443$	−4223.10	−0.452925	−0.226462	−	0.974020i	$-0.572716\pi$
$443$	−4223.10	−0.452925	−0.226462	+	0.974020i	$0.572716\pi$
$444$	−3644.09	−0.389506
$445$	0	0
$446$	−20524.3	−2.17904
$447$	−10454.6	−1.10623
$448$	−8221.85	−0.867067
$449$	4238.78	0.445525	0.222762	−	0.974873i	$-0.428493\pi$
$449$	4238.78	0.445525	0.222762	+	0.974873i	$0.428493\pi$
$450$	0	0
$451$	−13227.5	−1.38106
$452$	166.958	0.0173740
$453$	−2861.53	−0.296792
$454$	−5909.60	−0.610906
$455$	0	0
$456$	−453.873	−0.0466109
$457$	−8496.44	−0.869686	−0.434843	−	0.900506i	$-0.643196\pi$
$457$	−8496.44	−0.869686	−0.434843	+	0.900506i	$0.643196\pi$
$458$	10466.5	1.06783
$459$	2558.49	0.260175
$460$	0	0
$461$	−14111.4	−1.42567	−0.712835	−	0.701332i	$-0.752589\pi$
$461$	−14111.4	−1.42567	−0.712835	+	0.701332i	$0.752589\pi$
$462$	−26368.0	−2.65530
$463$	10313.2	1.03520	0.517598	−	0.855624i	$-0.326826\pi$
$463$	10313.2	1.03520	0.517598	+	0.855624i	$0.326826\pi$
$464$	−705.369	−0.0705731
$465$	0	0
$466$	−860.071	−0.0854979
$467$	8302.98	0.822733	0.411366	−	0.911470i	$-0.365052\pi$
$467$	8302.98	0.822733	0.411366	+	0.911470i	$0.365052\pi$
$468$	929.041	0.0917627
$469$	−13434.8	−1.32273
$470$	0	0
$471$	1455.15	0.142356
$472$	−11487.6	−1.12025
$473$	11745.1	1.14173
$474$	6461.25	0.626108
$475$	0	0
$476$	1602.27	0.154286
$477$	2016.27	0.193540
$478$	−4324.01	−0.413756
$479$	−20769.9	−1.98122	−0.990608	−	0.136729i	$-0.956341\pi$
$479$	−20769.9	−1.98122	−0.990608	+	0.136729i	$0.956341\pi$
$480$	0	0
$481$	18293.4	1.73411
$482$	17678.5	1.67061
$483$	−4810.60	−0.453188
$484$	3221.07	0.302505
$485$	0	0
$486$	4822.33	0.450093
$487$	14018.1	1.30436	0.652178	−	0.758066i	$-0.273856\pi$
$487$	14018.1	1.30436	0.652178	+	0.758066i	$0.273856\pi$
$488$	−5171.08	−0.479680
$489$	4477.96	0.414111
$490$	0	0
$491$	2789.89	0.256428	0.128214	−	0.991747i	$-0.459076\pi$
$491$	2789.89	0.256428	0.128214	+	0.991747i	$0.459076\pi$
$492$	−3356.35	−0.307553
$493$	−152.970	−0.0139745
$494$	−1181.01	−0.107563
$495$	0	0
$496$	5168.53	0.467891
$497$	31522.8	2.84505
$498$	4149.97	0.373423
$499$	11279.7	1.01192	0.505962	−	0.862556i	$-0.331137\pi$
$499$	11279.7	1.01192	0.505962	+	0.862556i	$0.331137\pi$
$500$	0	0
$501$	11506.8	1.02612
$502$	−4272.70	−0.379880
$503$	5305.23	0.470276	0.235138	−	0.971962i	$-0.424446\pi$
$503$	5305.23	0.470276	0.235138	+	0.971962i	$0.424446\pi$
$504$	−3174.89	−0.280597
$505$	0	0
$506$	4914.86	0.431803
$507$	8734.01	0.765071
$508$	−6109.14	−0.533561
$509$	−14665.4	−1.27708	−0.638539	−	0.769590i	$-0.720461\pi$
$509$	−14665.4	−1.27708	−0.638539	+	0.769590i	$0.720461\pi$
$510$	0	0
$511$	15126.8	1.30953
$512$	−1518.39	−0.131062
$513$	−850.154	−0.0731681
$514$	−19613.1	−1.68306
$515$	0	0
$516$	2980.21	0.254257
$517$	14577.3	1.24006
$518$	32404.2	2.74857
$519$	7292.29	0.616756
$520$	0	0
$521$	−6809.09	−0.572575	−0.286288	−	0.958144i	$-0.592421\pi$
$521$	−6809.09	−0.572575	−0.286288	+	0.958144i	$0.592421\pi$
$522$	−157.112	−0.0131736
$523$	14145.6	1.18268	0.591341	−	0.806421i	$-0.298599\pi$
$523$	14145.6	1.18268	0.591341	+	0.806421i	$0.298599\pi$
$524$	−866.475	−0.0722369
$525$	0	0
$526$	−3141.59	−0.260418
$527$	1120.87	0.0926488
$528$	−18283.6	−1.50699
$529$	−11270.3	−0.926303
$530$	0	0
$531$	−3547.45	−0.289917
$532$	−532.415	−0.0433893
$533$	16849.0	1.36925
$534$	−22207.4	−1.79964
$535$	0	0
$536$	−6719.27	−0.541470
$537$	−11327.1	−0.910241
$538$	−7377.76	−0.591223
$539$	42487.5	3.39530
$540$	0	0
$541$	12881.0	1.02366	0.511829	−	0.859087i	$-0.328968\pi$
$541$	12881.0	1.02366	0.511829	+	0.859087i	$0.328968\pi$
$542$	25834.8	2.04742
$543$	−17036.7	−1.34643
$544$	2018.09	0.159053
$545$	0	0
$546$	33587.2	2.63260
$547$	−14686.5	−1.14799	−0.573995	−	0.818859i	$-0.694607\pi$
$547$	−14686.5	−1.14799	−0.573995	+	0.818859i	$0.694607\pi$
$548$	−6956.55	−0.542279
$549$	−1596.87	−0.124140
$550$	0	0
$551$	50.8299	0.00392999
$552$	−2405.96	−0.185516
$553$	−14622.4	−1.12443
$554$	−22028.5	−1.68935
$555$	0	0
$556$	637.263	0.0486079
$557$	6020.07	0.457950	0.228975	−	0.973432i	$-0.426463\pi$
$557$	6020.07	0.457950	0.228975	+	0.973432i	$0.426463\pi$
$558$	1151.22	0.0873391
$559$	−14960.7	−1.13197
$560$	0	0
$561$	−3965.07	−0.298405
$562$	8958.53	0.672407
$563$	−11854.4	−0.887394	−0.443697	−	0.896177i	$-0.646333\pi$
$563$	−11854.4	−0.887394	−0.443697	+	0.896177i	$0.646333\pi$
$564$	3698.86	0.276152
$565$	0	0
$566$	−18109.0	−1.34483
$567$	19211.4	1.42293
$568$	15765.7	1.16464
$569$	3608.76	0.265882	0.132941	−	0.991124i	$-0.457558\pi$
$569$	3608.76	0.265882	0.132941	+	0.991124i	$0.457558\pi$
$570$	0	0
$571$	−998.841	−0.0732053	−0.0366026	−	0.999330i	$-0.511654\pi$
$571$	−998.841	−0.0732053	−0.0366026	+	0.999330i	$0.511654\pi$
$572$	−8733.25	−0.638384
$573$	13366.4	0.974499
$574$	29845.6	2.17026
$575$	0	0
$576$	−1269.84	−0.0918574
$577$	13833.0	0.998048	0.499024	−	0.866588i	$-0.333692\pi$
$577$	13833.0	0.998048	0.499024	+	0.866588i	$0.333692\pi$
$578$	946.716	0.0681283
$579$	8445.63	0.606198
$580$	0	0
$581$	−9391.77	−0.670631
$582$	11434.9	0.814417
$583$	−18953.5	−1.34644
$584$	7565.50	0.536066
$585$	0	0
$586$	−23724.0	−1.67241
$587$	−7803.65	−0.548707	−0.274354	−	0.961629i	$-0.588464\pi$
$587$	−7803.65	−0.548707	−0.274354	+	0.961629i	$0.588464\pi$
$588$	10780.8	0.756112
$589$	−372.451	−0.0260553
$590$	0	0
$591$	5150.03	0.358450
$592$	22469.1	1.55992
$593$	16488.1	1.14180	0.570900	−	0.821020i	$-0.306595\pi$
$593$	16488.1	1.14180	0.570900	+	0.821020i	$0.306595\pi$
$594$	−24701.9	−1.70628
$595$	0	0
$596$	−6133.56	−0.421545
$597$	4305.76	0.295181
$598$	−6260.48	−0.428110
$599$	−6832.25	−0.466040	−0.233020	−	0.972472i	$-0.574861\pi$
$599$	−6832.25	−0.466040	−0.233020	+	0.972472i	$0.574861\pi$
$600$	0	0
$601$	5903.31	0.400667	0.200334	−	0.979728i	$-0.435797\pi$
$601$	5903.31	0.400667	0.200334	+	0.979728i	$0.435797\pi$
$602$	−26500.8	−1.79417
$603$	−2074.96	−0.140131
$604$	−1678.82	−0.113096
$605$	0	0
$606$	12713.5	0.852226
$607$	−11613.0	−0.776538	−0.388269	−	0.921546i	$-0.626927\pi$
$607$	−11613.0	−0.776538	−0.388269	+	0.921546i	$0.626927\pi$
$608$	−670.585	−0.0447300
$609$	−1445.57	−0.0961862
$610$	0	0
$611$	−18568.4	−1.22945
$612$	247.465	0.0163451
$613$	374.068	0.0246467	0.0123234	−	0.999924i	$-0.496077\pi$
$613$	374.068	0.0246467	0.0123234	+	0.999924i	$0.496077\pi$
$614$	2459.79	0.161676
$615$	0	0
$616$	29844.9	1.95208
$617$	11209.6	0.731412	0.365706	−	0.930730i	$-0.380828\pi$
$617$	11209.6	0.731412	0.365706	+	0.930730i	$0.380828\pi$
$618$	−18014.7	−1.17258
$619$	−8904.95	−0.578223	−0.289112	−	0.957295i	$-0.593360\pi$
$619$	−8904.95	−0.578223	−0.289112	+	0.957295i	$0.593360\pi$
$620$	0	0
$621$	−4506.63	−0.291216
$622$	−5333.31	−0.343804
$623$	50257.5	3.23198
$624$	23289.4	1.49410
$625$	0	0
$626$	801.831	0.0511943
$627$	1317.54	0.0839195
$628$	853.716	0.0542468
$629$	4872.75	0.308886
$630$	0	0
$631$	−13667.4	−0.862268	−0.431134	−	0.902288i	$-0.641886\pi$
$631$	−13667.4	−0.862268	−0.431134	+	0.902288i	$0.641886\pi$
$632$	−7313.24	−0.460293
$633$	4806.50	0.301803
$634$	21785.2	1.36467
$635$	0	0
$636$	−4809.29	−0.299844
$637$	−54120.0	−3.36627
$638$	1476.90	0.0916473
$639$	4868.58	0.301405
$640$	0	0
$641$	28371.3	1.74820	0.874102	−	0.485742i	$-0.161450\pi$
$641$	28371.3	1.74820	0.874102	+	0.485742i	$0.161450\pi$
$642$	−8694.36	−0.534484
$643$	11905.6	0.730186	0.365093	−	0.930971i	$-0.381037\pi$
$643$	11905.6	0.730186	0.365093	+	0.930971i	$0.381037\pi$
$644$	−2822.31	−0.172693
$645$	0	0
$646$	−314.581	−0.0191595
$647$	20523.0	1.24705	0.623526	−	0.781802i	$-0.285699\pi$
$647$	20523.0	1.24705	0.623526	+	0.781802i	$0.285699\pi$
$648$	9608.34	0.582486
$649$	33347.0	2.01693
$650$	0	0
$651$	10592.3	0.637702
$652$	2627.15	0.157803
$653$	−11217.5	−0.672245	−0.336122	−	0.941818i	$-0.609116\pi$
$653$	−11217.5	−0.672245	−0.336122	+	0.941818i	$0.609116\pi$
$654$	3594.81	0.214936
$655$	0	0
$656$	20694.9	1.23171
$657$	2336.28	0.138732
$658$	−32891.2	−1.94868
$659$	27782.7	1.64227	0.821137	−	0.570731i	$-0.193340\pi$
$659$	27782.7	1.64227	0.821137	+	0.570731i	$0.193340\pi$
$660$	0	0
$661$	−10292.9	−0.605669	−0.302834	−	0.953043i	$-0.597933\pi$
$661$	−10292.9	−0.605669	−0.302834	+	0.953043i	$0.597933\pi$
$662$	10825.4	0.635561
$663$	5050.65	0.295854
$664$	−4697.18	−0.274527
$665$	0	0
$666$	5004.71	0.291184
$667$	269.447	0.0156417
$668$	6750.90	0.391018
$669$	−29165.9	−1.68553
$670$	0	0
$671$	15011.0	0.863628
$672$	19071.0	1.09476
$673$	−6149.53	−0.352225	−0.176112	−	0.984370i	$-0.556352\pi$
$673$	−6149.53	−0.352225	−0.176112	+	0.984370i	$0.556352\pi$
$674$	18654.0	1.06606
$675$	0	0
$676$	5124.12	0.291541
$677$	15234.9	0.864884	0.432442	−	0.901662i	$-0.357652\pi$
$677$	15234.9	0.864884	0.432442	+	0.901662i	$0.357652\pi$
$678$	932.233	0.0528056
$679$	−25878.2	−1.46261
$680$	0	0
$681$	−8397.80	−0.472547
$682$	−10821.8	−0.607610
$683$	7749.65	0.434161	0.217080	−	0.976154i	$-0.430347\pi$
$683$	7749.65	0.434161	0.217080	+	0.976154i	$0.430347\pi$
$684$	−82.2296	−0.00459668
$685$	0	0
$686$	−57089.3	−3.17738
$687$	14873.3	0.825986
$688$	−18375.7	−1.01827
$689$	24142.7	1.33493
$690$	0	0
$691$	−4725.56	−0.260157	−0.130079	−	0.991504i	$-0.541523\pi$
$691$	−4725.56	−0.260157	−0.130079	+	0.991504i	$0.541523\pi$
$692$	4278.28	0.235023
$693$	9216.32	0.505193
$694$	−27887.9	−1.52538
$695$	0	0
$696$	−722.984	−0.0393745
$697$	4488.01	0.243896
$698$	−22094.0	−1.19809
$699$	−1222.20	−0.0661341
$700$	0	0
$701$	35057.2	1.88886	0.944431	−	0.328710i	$-0.106614\pi$
$701$	35057.2	1.88886	0.944431	+	0.328710i	$0.106614\pi$
$702$	31464.9	1.69169
$703$	−1619.15	−0.0868670
$704$	11936.8	0.639043
$705$	0	0
$706$	14477.0	0.771741
$707$	−28771.8	−1.53051
$708$	8461.51	0.449157
$709$	−34719.8	−1.83911	−0.919557	−	0.392958i	$-0.871452\pi$
$709$	−34719.8	−1.83911	−0.919557	+	0.392958i	$0.871452\pi$
$710$	0	0
$711$	−2258.38	−0.119122
$712$	25135.7	1.32303
$713$	−1974.35	−0.103703
$714$	8946.50	0.468927
$715$	0	0
$716$	−6645.43	−0.346859
$717$	−6144.60	−0.320048
$718$	−1778.48	−0.0924406
$719$	15046.2	0.780429	0.390214	−	0.920724i	$-0.372401\pi$
$719$	15046.2	0.780429	0.390214	+	0.920724i	$0.372401\pi$
$720$	0	0
$721$	40769.0	2.10585
$722$	−22364.4	−1.15279
$723$	25121.9	1.29225
$724$	−9995.17	−0.513077
$725$	0	0
$726$	17985.3	0.919416
$727$	15632.9	0.797514	0.398757	−	0.917057i	$-0.369442\pi$
$727$	15632.9	0.797514	0.398757	+	0.917057i	$0.369442\pi$
$728$	−38016.0	−1.93539
$729$	21883.1	1.11178
$730$	0	0
$731$	−3985.04	−0.201631
$732$	3808.91	0.192324
$733$	26800.2	1.35046	0.675230	−	0.737607i	$-0.264044\pi$
$733$	26800.2	1.35046	0.675230	+	0.737607i	$0.264044\pi$
$734$	−34698.7	−1.74489
$735$	0	0
$736$	−3554.74	−0.178029
$737$	19505.2	0.974877
$738$	4609.54	0.229918
$739$	−12883.8	−0.641323	−0.320661	−	0.947194i	$-0.603905\pi$
$739$	−12883.8	−0.641323	−0.320661	+	0.947194i	$0.603905\pi$
$740$	0	0
$741$	−1678.26	−0.0832019
$742$	42765.4	2.11586
$743$	27419.8	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$743$	27419.8	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$744$	5297.60	0.261048
$745$	0	0
$746$	−8790.93	−0.431446
$747$	−1450.53	−0.0710468
$748$	−2326.25	−0.113711
$749$	19676.2	0.959882
$750$	0	0
$751$	−9936.68	−0.482816	−0.241408	−	0.970424i	$-0.577609\pi$
$751$	−9936.68	−0.482816	−0.241408	+	0.970424i	$0.577609\pi$
$752$	−22806.8	−1.10596
$753$	−6071.69	−0.293844
$754$	−1881.25	−0.0908637
$755$	0	0
$756$	14184.8	0.682402
$757$	8966.96	0.430528	0.215264	−	0.976556i	$-0.430939\pi$
$757$	8966.96	0.430528	0.215264	+	0.976556i	$0.430939\pi$
$758$	−5808.55	−0.278332
$759$	6984.23	0.334007
$760$	0	0
$761$	11727.8	0.558649	0.279324	−	0.960197i	$-0.409890\pi$
$761$	11727.8	0.558649	0.279324	+	0.960197i	$0.409890\pi$
$762$	−34111.1	−1.62167
$763$	−8135.40	−0.386004
$764$	7841.85	0.371346
$765$	0	0
$766$	8886.64	0.419174
$767$	−42477.0	−1.99968
$768$	17511.0	0.822751
$769$	22369.8	1.04899	0.524497	−	0.851412i	$-0.324253\pi$
$769$	22369.8	1.04899	0.524497	+	0.851412i	$0.324253\pi$
$770$	0	0
$771$	−27871.0	−1.30188
$772$	4954.93	0.231000
$773$	−11224.3	−0.522263	−0.261131	−	0.965303i	$-0.584096\pi$
$773$	−11224.3	−0.522263	−0.261131	+	0.965303i	$0.584096\pi$
$774$	−4092.96	−0.190075
$775$	0	0
$776$	−12942.7	−0.598730
$777$	46047.7	2.12606
$778$	−21839.6	−1.00641
$779$	−1491.31	−0.0685900
$780$	0	0
$781$	−45766.1	−2.09685
$782$	−1667.58	−0.0762565
$783$	−1354.23	−0.0618086
$784$	−66473.5	−3.02813
$785$	0	0
$786$	−4838.07	−0.219553
$787$	−39495.5	−1.78890	−0.894449	−	0.447169i	$-0.852432\pi$
$787$	−39495.5	−1.78890	−0.894449	+	0.447169i	$0.852432\pi$
$788$	3021.45	0.136592
$789$	−4464.33	−0.201438
$790$	0	0
$791$	−2109.73	−0.0948336
$792$	4609.43	0.206804
$793$	−19120.8	−0.856243
$794$	15259.5	0.682041
$795$	0	0
$796$	2526.13	0.112483
$797$	20207.8	0.898115	0.449057	−	0.893503i	$-0.351760\pi$
$797$	20207.8	0.898115	0.449057	+	0.893503i	$0.351760\pi$
$798$	−2972.81	−0.131875
$799$	−4945.99	−0.218995
$800$	0	0
$801$	7762.09	0.342397
$802$	10894.6	0.479678
$803$	−21961.7	−0.965147
$804$	4949.27	0.217099
$805$	0	0
$806$	13784.7	0.602414
$807$	−10484.1	−0.457321
$808$	−14389.9	−0.626526
$809$	−907.278	−0.0394291	−0.0197146	−	0.999806i	$-0.506276\pi$
$809$	−907.278	−0.0394291	−0.0197146	+	0.999806i	$0.506276\pi$
$810$	0	0
$811$	−16042.0	−0.694590	−0.347295	−	0.937756i	$-0.612900\pi$
$811$	−16042.0	−0.694590	−0.347295	+	0.937756i	$0.612900\pi$
$812$	−848.094	−0.0366530
$813$	36712.4	1.58372
$814$	−47045.7	−2.02574
$815$	0	0
$816$	6203.51	0.266135
$817$	1324.18	0.0567040
$818$	30541.7	1.30546
$819$	−11739.6	−0.500874
$820$	0	0
$821$	19313.4	0.821002	0.410501	−	0.911860i	$-0.365354\pi$
$821$	19313.4	0.821002	0.410501	+	0.911860i	$0.365354\pi$
$822$	−38842.8	−1.64817
$823$	−36587.3	−1.54964	−0.774820	−	0.632182i	$-0.782159\pi$
$823$	−36587.3	−1.54964	−0.774820	+	0.632182i	$0.782159\pi$
$824$	20390.1	0.862043
$825$	0	0
$826$	−75241.9	−3.16949
$827$	−27399.1	−1.15207	−0.576033	−	0.817426i	$-0.695400\pi$
$827$	−27399.1	−1.15207	−0.576033	+	0.817426i	$0.695400\pi$
$828$	−435.895	−0.0182952
$829$	18111.9	0.758807	0.379404	−	0.925231i	$-0.376129\pi$
$829$	18111.9	0.758807	0.379404	+	0.925231i	$0.376129\pi$
$830$	0	0
$831$	−31303.4	−1.30674
$832$	−15205.0	−0.633579
$833$	−14415.8	−0.599612
$834$	3558.24	0.147736
$835$	0	0
$836$	772.982	0.0319786
$837$	9922.99	0.409783
$838$	−11731.3	−0.483591
$839$	861.248	0.0354393	0.0177197	−	0.999843i	$-0.494359\pi$
$839$	861.248	0.0354393	0.0177197	+	0.999843i	$0.494359\pi$
$840$	0	0
$841$	−24308.0	−0.996680
$842$	−48267.7	−1.97555
$843$	12730.5	0.520119
$844$	2819.90	0.115006
$845$	0	0
$846$	−5079.93	−0.206444
$847$	−40702.4	−1.65118
$848$	29653.6	1.20084
$849$	−25733.6	−1.04025
$850$	0	0
$851$	−8583.06	−0.345739
$852$	−11612.7	−0.466955
$853$	42575.0	1.70896	0.854479	−	0.519486i	$-0.173876\pi$
$853$	42575.0	1.70896	0.854479	+	0.519486i	$0.173876\pi$
$854$	−33869.8	−1.35714
$855$	0	0
$856$	9840.80	0.392934
$857$	15280.9	0.609083	0.304542	−	0.952499i	$-0.401497\pi$
$857$	15280.9	0.609083	0.304542	+	0.952499i	$0.401497\pi$
$858$	−48763.2	−1.94027
$859$	5845.37	0.232179	0.116089	−	0.993239i	$-0.462964\pi$
$859$	5845.37	0.232179	0.116089	+	0.993239i	$0.462964\pi$
$860$	0	0
$861$	42411.8	1.67874
$862$	1780.91	0.0703688
$863$	−47529.7	−1.87477	−0.937387	−	0.348288i	$-0.886763\pi$
$863$	−47529.7	−1.87477	−0.937387	+	0.348288i	$0.886763\pi$
$864$	17866.0	0.703487
$865$	0	0
$866$	−9877.24	−0.387578
$867$	1345.32	0.0526985
$868$	6214.33	0.243005
$869$	21229.5	0.828723
$870$	0	0
$871$	−24845.5	−0.966541
$872$	−4068.82	−0.158014
$873$	−3996.80	−0.154950
$874$	554.116	0.0214454
$875$	0	0
$876$	−5572.59	−0.214932
$877$	11480.5	0.442040	0.221020	−	0.975269i	$-0.429061\pi$
$877$	11480.5	0.442040	0.221020	+	0.975269i	$0.429061\pi$
$878$	44413.7	1.70717
$879$	−33712.9	−1.29364
$880$	0	0
$881$	−4181.36	−0.159902	−0.0799510	−	0.996799i	$-0.525476\pi$
$881$	−4181.36	−0.159902	−0.0799510	+	0.996799i	$0.525476\pi$
$882$	−14806.1	−0.565248
$883$	−10063.6	−0.383541	−0.191770	−	0.981440i	$-0.561423\pi$
$883$	−10063.6	−0.383541	−0.191770	+	0.981440i	$0.561423\pi$
$884$	2963.14	0.112739
$885$	0	0
$886$	−13834.2	−0.524569
$887$	31064.4	1.17592	0.587959	−	0.808891i	$-0.299932\pi$
$887$	31064.4	1.17592	0.587959	+	0.808891i	$0.299932\pi$
$888$	23030.2	0.870319
$889$	77196.8	2.91237
$890$	0	0
$891$	−27891.9	−1.04872
$892$	−17111.2	−0.642293
$893$	1643.49	0.0615871
$894$	−34247.5	−1.28122
$895$	0	0
$896$	−59707.8	−2.22623
$897$	−8896.41	−0.331151
$898$	13885.5	0.515999
$899$	−593.285	−0.0220102
$900$	0	0
$901$	6430.82	0.237782
$902$	−43331.0	−1.59952
$903$	−37658.8	−1.38783
$904$	−1055.16	−0.0388208
$905$	0	0
$906$	−9373.90	−0.343738
$907$	−15326.0	−0.561071	−0.280536	−	0.959844i	$-0.590512\pi$
$907$	−15326.0	−0.561071	−0.280536	+	0.959844i	$0.590512\pi$
$908$	−4926.87	−0.180070
$909$	−4443.70	−0.162143
$910$	0	0
$911$	53173.5	1.93383	0.966913	−	0.255107i	$-0.0821107\pi$
$911$	53173.5	1.93383	0.966913	+	0.255107i	$0.0821107\pi$
$912$	−2061.35	−0.0748443
$913$	13635.4	0.494266
$914$	−27832.9	−1.00725
$915$	0	0
$916$	8725.96	0.314753
$917$	10949.0	0.394295
$918$	8381.19	0.301330
$919$	−50930.8	−1.82813	−0.914066	−	0.405566i	$-0.867075\pi$
$919$	−50930.8	−1.82813	−0.914066	+	0.405566i	$0.867075\pi$
$920$	0	0
$921$	3495.47	0.125059
$922$	−46226.6	−1.65119
$923$	58296.2	2.07892
$924$	−21983.1	−0.782675
$925$	0	0
$926$	33784.4	1.19895
$927$	6296.62	0.223094
$928$	−1068.19	−0.0377856
$929$	11885.0	0.419736	0.209868	−	0.977730i	$-0.432697\pi$
$929$	11885.0	0.419736	0.209868	+	0.977730i	$0.432697\pi$
$930$	0	0
$931$	4790.18	0.168627
$932$	−717.045	−0.0252013
$933$	−7578.86	−0.265939
$934$	27199.2	0.952874
$935$	0	0
$936$	−5871.43	−0.205036
$937$	1343.65	0.0468466	0.0234233	−	0.999726i	$-0.492543\pi$
$937$	1343.65	0.0468466	0.0234233	+	0.999726i	$0.492543\pi$
$938$	−44010.2	−1.53197
$939$	1139.44	0.0395997
$940$	0	0
$941$	34199.3	1.18477	0.592384	−	0.805656i	$-0.298187\pi$
$941$	34199.3	1.18477	0.592384	+	0.805656i	$0.298187\pi$
$942$	4766.83	0.164875
$943$	−7905.35	−0.272994
$944$	−52172.8	−1.79881
$945$	0	0
$946$	38475.0	1.32234
$947$	12727.3	0.436730	0.218365	−	0.975867i	$-0.429928\pi$
$947$	12727.3	0.436730	0.218365	+	0.975867i	$0.429928\pi$
$948$	5386.78	0.184551
$949$	27974.6	0.956895
$950$	0	0
$951$	30957.7	1.05559
$952$	−10126.2	−0.344739
$953$	−622.729	−0.0211670	−0.0105835	−	0.999944i	$-0.503369\pi$
$953$	−622.729	−0.0211670	−0.0105835	+	0.999944i	$0.503369\pi$
$954$	6604.97	0.224155
$955$	0	0
$956$	−3604.95	−0.121958
$957$	2098.74	0.0708908
$958$	−68038.9	−2.29461
$959$	87904.9	2.95996
$960$	0	0
$961$	−25443.8	−0.854075
$962$	59926.2	2.00842
$963$	3038.91	0.101690
$964$	14738.7	0.492428
$965$	0	0
$966$	−15758.7	−0.524874
$967$	−8784.53	−0.292132	−0.146066	−	0.989275i	$-0.546661\pi$
$967$	−8784.53	−0.292132	−0.146066	+	0.989275i	$0.546661\pi$
$968$	−20356.8	−0.675922
$969$	−447.034	−0.0148202
$970$	0	0
$971$	−1158.70	−0.0382949	−0.0191474	−	0.999817i	$-0.506095\pi$
$971$	−1158.70	−0.0382949	−0.0191474	+	0.999817i	$0.506095\pi$
$972$	4020.40	0.132669
$973$	−8052.64	−0.265319
$974$	45921.0	1.51068
$975$	0	0
$976$	−23485.4	−0.770234
$977$	−25678.4	−0.840864	−0.420432	−	0.907324i	$-0.638122\pi$
$977$	−25678.4	−0.840864	−0.420432	+	0.907324i	$0.638122\pi$
$978$	14669.0	0.479616
$979$	−72965.9	−2.38202
$980$	0	0
$981$	−1256.48	−0.0408934
$982$	9139.22	0.296990
$983$	−22023.4	−0.714585	−0.357293	−	0.933992i	$-0.616300\pi$
$983$	−22023.4	−0.714585	−0.357293	+	0.933992i	$0.616300\pi$
$984$	21211.8	0.687202
$985$	0	0
$986$	−501.103	−0.0161850
$987$	−46739.8	−1.50734
$988$	−984.613	−0.0317052
$989$	7019.41	0.225687
$990$	0	0
$991$	52307.2	1.67668	0.838342	−	0.545144i	$-0.183525\pi$
$991$	52307.2	1.67668	0.838342	+	0.545144i	$0.183525\pi$
$992$	7827.06	0.250513
$993$	15383.4	0.491618
$994$	103263.	3.29508
$995$	0	0
$996$	3459.85	0.110070
$997$	51748.8	1.64383	0.821916	−	0.569609i	$-0.192905\pi$
$997$	51748.8	1.64383	0.821916	+	0.569609i	$0.192905\pi$
$998$	36950.5	1.17199
$999$	43138.1	1.36619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.a.n.1.10		12
5.2	odd	4		85.4.b.a.69.19	yes	24
5.3	odd	4		85.4.b.a.69.6	✓	24
5.4	even	2		425.4.a.o.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.4.b.a.69.6	✓	24	5.3	odd	4
85.4.b.a.69.19	yes	24	5.2	odd	4
425.4.a.n.1.10		12	1.1	even	1	trivial
425.4.a.o.1.3		12	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.a (trivial)

\(f(q)\)	\(=\)	\(q+3.27583 q^{2} +4.65510 q^{3} +2.73108 q^{4} +15.2493 q^{6} -34.5107 q^{7} -17.2601 q^{8} -5.33005 q^{9} +O(q^{10})\)	\(q+3.27583 q^{2} +4.65510 q^{3} +2.73108 q^{4} +15.2493 q^{6} -34.5107 q^{7} -17.2601 q^{8} -5.33005 q^{9} +50.1040 q^{11} +12.7134 q^{12} -63.8218 q^{13} -113.051 q^{14} -78.3898 q^{16} -17.0000 q^{17} -17.4604 q^{18} +5.64888 q^{19} -160.651 q^{21} +164.132 q^{22} +29.9445 q^{23} -80.3475 q^{24} -209.070 q^{26} -150.500 q^{27} -94.2514 q^{28} +8.99822 q^{29} -65.9336 q^{31} -118.711 q^{32} +233.239 q^{33} -55.6892 q^{34} -14.5568 q^{36} -286.633 q^{37} +18.5048 q^{38} -297.097 q^{39} -264.000 q^{41} -526.264 q^{42} +234.414 q^{43} +136.838 q^{44} +98.0931 q^{46} +290.941 q^{47} -364.912 q^{48} +847.987 q^{49} -79.1367 q^{51} -174.302 q^{52} -378.284 q^{53} -493.011 q^{54} +595.658 q^{56} +26.2961 q^{57} +29.4766 q^{58} +665.556 q^{59} +299.597 q^{61} -215.988 q^{62} +183.944 q^{63} +238.241 q^{64} +764.053 q^{66} +389.295 q^{67} -46.4283 q^{68} +139.394 q^{69} -913.421 q^{71} +91.9973 q^{72} -438.323 q^{73} -938.960 q^{74} +15.4275 q^{76} -1729.12 q^{77} -973.240 q^{78} +423.708 q^{79} -556.679 q^{81} -864.821 q^{82} +272.141 q^{83} -438.749 q^{84} +767.902 q^{86} +41.8876 q^{87} -864.801 q^{88} -1456.29 q^{89} +2202.53 q^{91} +81.7807 q^{92} -306.928 q^{93} +953.073 q^{94} -552.612 q^{96} +749.861 q^{97} +2777.86 q^{98} -267.057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 12 q^{3} + 48 q^{4} + 8 q^{6} - 70 q^{7} - 102 q^{8} + 90 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 12 * q^3 + 48 * q^4 + 8 * q^6 - 70 * q^7 - 102 * q^8 + 90 * q^9	\( 12 q - 4 q^{2} - 12 q^{3} + 48 q^{4} + 8 q^{6} - 70 q^{7} - 102 q^{8} + 90 q^{9} + 30 q^{11} - 120 q^{12} - 112 q^{13} + 38 q^{14} + 120 q^{16} - 204 q^{17} - 166 q^{18} - 50 q^{19} - 64 q^{21} - 400 q^{22} - 262 q^{23} - 102 q^{24} - 50 q^{26} - 678 q^{27} - 428 q^{28} + 232 q^{29} + 18 q^{31} - 880 q^{32} - 168 q^{33} + 68 q^{34} + 302 q^{36} - 852 q^{37} + 200 q^{38} + 132 q^{39} + 408 q^{41} - 1794 q^{42} - 876 q^{43} + 52 q^{44} + 104 q^{46} - 1132 q^{47} + 494 q^{48} - 12 q^{49} + 204 q^{51} - 2790 q^{52} - 492 q^{53} - 150 q^{54} + 536 q^{56} - 1842 q^{57} - 866 q^{58} - 134 q^{59} + 712 q^{61} - 1648 q^{62} - 1246 q^{63} - 12 q^{64} - 2068 q^{66} - 2680 q^{67} - 816 q^{68} - 900 q^{69} + 98 q^{71} - 3992 q^{72} - 894 q^{73} - 1236 q^{74} - 1594 q^{76} - 1164 q^{77} - 40 q^{78} - 1134 q^{79} - 608 q^{81} - 5406 q^{82} - 2272 q^{83} + 560 q^{84} - 1932 q^{86} - 2320 q^{87} - 3238 q^{88} - 1622 q^{89} - 120 q^{91} - 2226 q^{92} - 5092 q^{93} + 1982 q^{94} - 1548 q^{96} - 2706 q^{97} + 2582 q^{98} + 614 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 12 * q^3 + 48 * q^4 + 8 * q^6 - 70 * q^7 - 102 * q^8 + 90 * q^9 + 30 * q^11 - 120 * q^12 - 112 * q^13 + 38 * q^14 + 120 * q^16 - 204 * q^17 - 166 * q^18 - 50 * q^19 - 64 * q^21 - 400 * q^22 - 262 * q^23 - 102 * q^24 - 50 * q^26 - 678 * q^27 - 428 * q^28 + 232 * q^29 + 18 * q^31 - 880 * q^32 - 168 * q^33 + 68 * q^34 + 302 * q^36 - 852 * q^37 + 200 * q^38 + 132 * q^39 + 408 * q^41 - 1794 * q^42 - 876 * q^43 + 52 * q^44 + 104 * q^46 - 1132 * q^47 + 494 * q^48 - 12 * q^49 + 204 * q^51 - 2790 * q^52 - 492 * q^53 - 150 * q^54 + 536 * q^56 - 1842 * q^57 - 866 * q^58 - 134 * q^59 + 712 * q^61 - 1648 * q^62 - 1246 * q^63 - 12 * q^64 - 2068 * q^66 - 2680 * q^67 - 816 * q^68 - 900 * q^69 + 98 * q^71 - 3992 * q^72 - 894 * q^73 - 1236 * q^74 - 1594 * q^76 - 1164 * q^77 - 40 * q^78 - 1134 * q^79 - 608 * q^81 - 5406 * q^82 - 2272 * q^83 + 560 * q^84 - 1932 * q^86 - 2320 * q^87 - 3238 * q^88 - 1622 * q^89 - 120 * q^91 - 2226 * q^92 - 5092 * q^93 + 1982 * q^94 - 1548 * q^96 - 2706 * q^97 + 2582 * q^98 + 614 * q^99

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