LMFDB - Embedded newform 6275.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6275,2,Mod(1,6275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6275, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6275 = 5^{2} \cdot 251 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6275.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:	$50.1061272684$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 $ x^17 - 2x^16 - 28x^15 + 54x^14 + 317x^13 - 582x^12 - 1867x^11 + 3178x^10 + 6186x^9 - 9216x^8 - 11921x^7 + 13680x^6 + 13752x^5 - 9400x^4 - 8800x^3 + 1920x^2 + 2240x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 251)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.779516$ of defining polynomial
Character	$\chi$	$=$	6275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.779516 q^{2} +3.14584 q^{3} -1.39236 q^{4} -2.45223 q^{6} -2.07256 q^{7} +2.64439 q^{8} +6.89631 q^{9} +O(q^{10})$	\(q-0.779516 q^{2} +3.14584 q^{3} -1.39236 q^{4} -2.45223 q^{6} -2.07256 q^{7} +2.64439 q^{8} +6.89631 q^{9} +4.31307 q^{11} -4.38013 q^{12} -0.691540 q^{13} +1.61559 q^{14} +0.723363 q^{16} -4.59213 q^{17} -5.37578 q^{18} +1.42603 q^{19} -6.51995 q^{21} -3.36210 q^{22} +7.21258 q^{23} +8.31884 q^{24} +0.539067 q^{26} +12.2572 q^{27} +2.88574 q^{28} +6.96732 q^{29} +2.81029 q^{31} -5.85266 q^{32} +13.5682 q^{33} +3.57964 q^{34} -9.60211 q^{36} -5.24691 q^{37} -1.11162 q^{38} -2.17548 q^{39} +4.77869 q^{41} +5.08240 q^{42} +0.0696559 q^{43} -6.00532 q^{44} -5.62232 q^{46} +11.4139 q^{47} +2.27559 q^{48} -2.70449 q^{49} -14.4461 q^{51} +0.962870 q^{52} -8.68993 q^{53} -9.55465 q^{54} -5.48067 q^{56} +4.48607 q^{57} -5.43114 q^{58} -7.99534 q^{59} -7.84861 q^{61} -2.19066 q^{62} -14.2930 q^{63} +3.11552 q^{64} -10.5766 q^{66} -14.4895 q^{67} +6.39387 q^{68} +22.6896 q^{69} +10.8406 q^{71} +18.2366 q^{72} +0.113363 q^{73} +4.09005 q^{74} -1.98555 q^{76} -8.93909 q^{77} +1.69582 q^{78} -6.17996 q^{79} +17.8702 q^{81} -3.72506 q^{82} +11.1760 q^{83} +9.07808 q^{84} -0.0542979 q^{86} +21.9181 q^{87} +11.4054 q^{88} -2.35477 q^{89} +1.43326 q^{91} -10.0425 q^{92} +8.84072 q^{93} -8.89734 q^{94} -18.4115 q^{96} +2.40260 q^{97} +2.10819 q^{98} +29.7442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * 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 $

$2$	−0.779516	−0.551201	−0.275600	−	0.961272i	$-0.588877\pi$
$2$	−0.779516	−0.551201	−0.275600	+	0.961272i	$0.588877\pi$
$3$	3.14584	1.81625	0.908126	−	0.418697i	$-0.137513\pi$
$3$	3.14584	1.81625	0.908126	+	0.418697i	$0.137513\pi$
$4$	−1.39236	−0.696178
$5$	0	0
$5$	0	0
$6$	−2.45223	−1.00112
$7$	−2.07256	−0.783355	−0.391677	−	0.920103i	$-0.628105\pi$
$7$	−2.07256	−0.783355	−0.391677	+	0.920103i	$0.628105\pi$
$8$	2.64439	0.934935
$9$	6.89631	2.29877
$10$	0	0
$11$	4.31307	1.30044	0.650219	−	0.759747i	$-0.274677\pi$
$11$	4.31307	1.30044	0.650219	+	0.759747i	$0.274677\pi$
$12$	−4.38013	−1.26443
$13$	−0.691540	−0.191799	−0.0958994	−	0.995391i	$-0.530573\pi$
$13$	−0.691540	−0.191799	−0.0958994	+	0.995391i	$0.530573\pi$
$14$	1.61559	0.431786
$15$	0	0
$16$	0.723363	0.180841
$17$	−4.59213	−1.11375	−0.556877	−	0.830595i	$-0.688001\pi$
$17$	−4.59213	−1.11375	−0.556877	+	0.830595i	$0.688001\pi$
$18$	−5.37578	−1.26708
$19$	1.42603	0.327155	0.163577	−	0.986531i	$-0.447697\pi$
$19$	1.42603	0.327155	0.163577	+	0.986531i	$0.447697\pi$
$20$	0	0
$21$	−6.51995	−1.42277
$22$	−3.36210	−0.716803
$23$	7.21258	1.50393	0.751964	−	0.659204i	$-0.229107\pi$
$23$	7.21258	1.50393	0.751964	+	0.659204i	$0.229107\pi$
$24$	8.31884	1.69808
$25$	0	0
$26$	0.539067	0.105720
$27$	12.2572	2.35889
$28$	2.88574	0.545354
$29$	6.96732	1.29380	0.646900	−	0.762575i	$-0.276065\pi$
$29$	6.96732	1.29380	0.646900	+	0.762575i	$0.276065\pi$
$30$	0	0
$31$	2.81029	0.504743	0.252371	−	0.967630i	$-0.418790\pi$
$31$	2.81029	0.504743	0.252371	+	0.967630i	$0.418790\pi$
$32$	−5.85266	−1.03461
$33$	13.5682	2.36192
$34$	3.57964	0.613903
$35$	0	0
$36$	−9.60211	−1.60035
$37$	−5.24691	−0.862587	−0.431294	−	0.902212i	$-0.641943\pi$
$37$	−5.24691	−0.862587	−0.431294	+	0.902212i	$0.641943\pi$
$38$	−1.11162	−0.180328
$39$	−2.17548	−0.348355
$40$	0	0
$41$	4.77869	0.746306	0.373153	−	0.927770i	$-0.378277\pi$
$41$	4.77869	0.746306	0.373153	+	0.927770i	$0.378277\pi$
$42$	5.08240	0.784231
$43$	0.0696559	0.0106224	0.00531122	−	0.999986i	$-0.498309\pi$
$43$	0.0696559	0.0106224	0.00531122	+	0.999986i	$0.498309\pi$
$44$	−6.00532	−0.905336
$45$	0	0
$46$	−5.62232	−0.828966
$47$	11.4139	1.66489	0.832446	−	0.554106i	$-0.186940\pi$
$47$	11.4139	1.66489	0.832446	+	0.554106i	$0.186940\pi$
$48$	2.27559	0.328452
$49$	−2.70449	−0.386356
$50$	0	0
$51$	−14.4461	−2.02286
$52$	0.962870	0.133526
$53$	−8.68993	−1.19365	−0.596827	−	0.802370i	$-0.703572\pi$
$53$	−8.68993	−1.19365	−0.596827	+	0.802370i	$0.703572\pi$
$54$	−9.55465	−1.30022
$55$	0	0
$56$	−5.48067	−0.732385
$57$	4.48607	0.594195
$58$	−5.43114	−0.713143
$59$	−7.99534	−1.04090	−0.520452	−	0.853891i	$-0.674237\pi$
$59$	−7.99534	−1.04090	−0.520452	+	0.853891i	$0.674237\pi$
$60$	0	0
$61$	−7.84861	−1.00491	−0.502456	−	0.864603i	$-0.667570\pi$
$61$	−7.84861	−1.00491	−0.502456	+	0.864603i	$0.667570\pi$
$62$	−2.19066	−0.278215
$63$	−14.2930	−1.80075
$64$	3.11552	0.389439
$65$	0	0
$66$	−10.5766	−1.30189
$67$	−14.4895	−1.77017	−0.885087	−	0.465426i	$-0.845901\pi$
$67$	−14.4895	−1.77017	−0.885087	+	0.465426i	$0.845901\pi$
$68$	6.39387	0.775371
$69$	22.6896	2.73151
$70$	0	0
$71$	10.8406	1.28654	0.643268	−	0.765641i	$-0.277578\pi$
$71$	10.8406	1.28654	0.643268	+	0.765641i	$0.277578\pi$
$72$	18.2366	2.14920
$73$	0.113363	0.0132682	0.00663409	−	0.999978i	$-0.497888\pi$
$73$	0.113363	0.0132682	0.00663409	+	0.999978i	$0.497888\pi$
$74$	4.09005	0.475459
$75$	0	0
$76$	−1.98555	−0.227758
$77$	−8.93909	−1.01870
$78$	1.69582	0.192014
$79$	−6.17996	−0.695300	−0.347650	−	0.937624i	$-0.613020\pi$
$79$	−6.17996	−0.695300	−0.347650	+	0.937624i	$0.613020\pi$
$80$	0	0
$81$	17.8702	1.98557
$82$	−3.72506	−0.411364
$83$	11.1760	1.22673	0.613363	−	0.789801i	$-0.289816\pi$
$83$	11.1760	1.22673	0.613363	+	0.789801i	$0.289816\pi$
$84$	9.07808	0.990500
$85$	0	0
$86$	−0.0542979	−0.00585509
$87$	21.9181	2.34986
$88$	11.4054	1.21582
$89$	−2.35477	−0.249605	−0.124803	−	0.992182i	$-0.539830\pi$
$89$	−2.35477	−0.249605	−0.124803	+	0.992182i	$0.539830\pi$
$90$	0	0
$91$	1.43326	0.150246
$92$	−10.0425	−1.04700
$93$	8.84072	0.916740
$94$	−8.89734	−0.917690
$95$	0	0
$96$	−18.4115	−1.87912
$97$	2.40260	0.243947	0.121973	−	0.992533i	$-0.461078\pi$
$97$	2.40260	0.243947	0.121973	+	0.992533i	$0.461078\pi$
$98$	2.10819	0.212960
$99$	29.7442	2.98941
$100$	0	0
$101$	−0.196664	−0.0195688	−0.00978438	−	0.999952i	$-0.503115\pi$
$101$	−0.196664	−0.0195688	−0.00978438	+	0.999952i	$0.503115\pi$
$102$	11.2610	1.11500
$103$	−8.71179	−0.858398	−0.429199	−	0.903210i	$-0.641204\pi$
$103$	−8.71179	−0.858398	−0.429199	+	0.903210i	$0.641204\pi$
$104$	−1.82871	−0.179319
$105$	0	0
$106$	6.77394	0.657943
$107$	4.84459	0.468344	0.234172	−	0.972195i	$-0.424762\pi$
$107$	4.84459	0.468344	0.234172	+	0.972195i	$0.424762\pi$
$108$	−17.0663	−1.64221
$109$	20.3490	1.94908	0.974541	−	0.224208i	$-0.0719796\pi$
$109$	20.3490	1.94908	0.974541	+	0.224208i	$0.0719796\pi$
$110$	0	0
$111$	−16.5060	−1.56668
$112$	−1.49921	−0.141663
$113$	16.1506	1.51932	0.759659	−	0.650322i	$-0.225366\pi$
$113$	16.1506	1.51932	0.759659	+	0.650322i	$0.225366\pi$
$114$	−3.49696	−0.327521
$115$	0	0
$116$	−9.70099	−0.900714
$117$	−4.76908	−0.440901
$118$	6.23249	0.573748
$119$	9.51747	0.872465
$120$	0	0
$121$	7.60253	0.691139
$122$	6.11811	0.553908
$123$	15.0330	1.35548
$124$	−3.91292	−0.351391
$125$	0	0
$126$	11.1416	0.992576
$127$	21.5000	1.90782	0.953909	−	0.300097i	$-0.0970191\pi$
$127$	21.5000	1.90782	0.953909	+	0.300097i	$0.0970191\pi$
$128$	9.27673	0.819955
$129$	0.219126	0.0192930
$130$	0	0
$131$	−10.4234	−0.910697	−0.455349	−	0.890313i	$-0.650485\pi$
$131$	−10.4234	−0.910697	−0.455349	+	0.890313i	$0.650485\pi$
$132$	−18.8918	−1.64432
$133$	−2.95554	−0.256278
$134$	11.2948	0.975721
$135$	0	0
$136$	−12.1434	−1.04129
$137$	17.0007	1.45246	0.726232	−	0.687449i	$-0.241270\pi$
$137$	17.0007	1.45246	0.726232	+	0.687449i	$0.241270\pi$
$138$	−17.6869	−1.50561
$139$	15.9865	1.35596	0.677980	−	0.735081i	$-0.262856\pi$
$139$	15.9865	1.35596	0.677980	+	0.735081i	$0.262856\pi$
$140$	0	0
$141$	35.9064	3.02386
$142$	−8.45038	−0.709140
$143$	−2.98266	−0.249422
$144$	4.98854	0.415711
$145$	0	0
$146$	−0.0883686	−0.00731343
$147$	−8.50789	−0.701719
$148$	7.30557	0.600514
$149$	−14.2480	−1.16725	−0.583623	−	0.812025i	$-0.698365\pi$
$149$	−14.2480	−1.16725	−0.583623	+	0.812025i	$0.698365\pi$
$150$	0	0
$151$	13.4756	1.09663	0.548316	−	0.836271i	$-0.315269\pi$
$151$	13.4756	1.09663	0.548316	+	0.836271i	$0.315269\pi$
$152$	3.77099	0.305868
$153$	−31.6687	−2.56027
$154$	6.96816	0.561511
$155$	0	0
$156$	3.02903	0.242517
$157$	−10.2729	−0.819870	−0.409935	−	0.912115i	$-0.634449\pi$
$157$	−10.2729	−0.819870	−0.409935	+	0.912115i	$0.634449\pi$
$158$	4.81738	0.383250
$159$	−27.3371	−2.16798
$160$	0	0
$161$	−14.9485	−1.17811
$162$	−13.9301	−1.09445
$163$	−12.4576	−0.975753	−0.487877	−	0.872913i	$-0.662228\pi$
$163$	−12.4576	−0.975753	−0.487877	+	0.872913i	$0.662228\pi$
$164$	−6.65363	−0.519561
$165$	0	0
$166$	−8.71188	−0.676173
$167$	17.4629	1.35132	0.675659	−	0.737214i	$-0.263859\pi$
$167$	17.4629	1.35132	0.675659	+	0.737214i	$0.263859\pi$
$168$	−17.2413	−1.33020
$169$	−12.5218	−0.963213
$170$	0	0
$171$	9.83437	0.752053
$172$	−0.0969858	−0.00739510
$173$	13.2820	1.00982	0.504908	−	0.863173i	$-0.331527\pi$
$173$	13.2820	1.00982	0.504908	+	0.863173i	$0.331527\pi$
$174$	−17.0855	−1.29525
$175$	0	0
$176$	3.11991	0.235172
$177$	−25.1521	−1.89054
$178$	1.83558	0.137583
$179$	16.9053	1.26357	0.631783	−	0.775146i	$-0.282324\pi$
$179$	16.9053	1.26357	0.631783	+	0.775146i	$0.282324\pi$
$180$	0	0
$181$	−8.95143	−0.665354	−0.332677	−	0.943041i	$-0.607952\pi$
$181$	−8.95143	−0.665354	−0.332677	+	0.943041i	$0.607952\pi$
$182$	−1.11725	−0.0828160
$183$	−24.6905	−1.82517
$184$	19.0729	1.40607
$185$	0	0
$186$	−6.89148	−0.505308
$187$	−19.8062	−1.44837
$188$	−15.8922	−1.15906
$189$	−25.4037	−1.84785
$190$	0	0
$191$	6.87340	0.497342	0.248671	−	0.968588i	$-0.420006\pi$
$191$	6.87340	0.497342	0.248671	+	0.968588i	$0.420006\pi$
$192$	9.80091	0.707320
$193$	−10.7691	−0.775174	−0.387587	−	0.921833i	$-0.626691\pi$
$193$	−10.7691	−0.775174	−0.387587	+	0.921833i	$0.626691\pi$
$194$	−1.87286	−0.134464
$195$	0	0
$196$	3.76561	0.268972
$197$	15.3371	1.09273	0.546363	−	0.837548i	$-0.316012\pi$
$197$	15.3371	1.09273	0.546363	+	0.837548i	$0.316012\pi$
$198$	−23.1861	−1.64776
$199$	−5.96752	−0.423026	−0.211513	−	0.977375i	$-0.567839\pi$
$199$	−5.96752	−0.423026	−0.211513	+	0.977375i	$0.567839\pi$
$200$	0	0
$201$	−45.5816	−3.21508
$202$	0.153302	0.0107863
$203$	−14.4402	−1.01350
$204$	20.1141	1.40827
$205$	0	0
$206$	6.79098	0.473150
$207$	49.7402	3.45718
$208$	−0.500235	−0.0346851
$209$	6.15058	0.425444
$210$	0	0
$211$	−0.312277	−0.0214981	−0.0107490	−	0.999942i	$-0.503422\pi$
$211$	−0.312277	−0.0214981	−0.0107490	+	0.999942i	$0.503422\pi$
$212$	12.0995	0.830995
$213$	34.1026	2.33667
$214$	−3.77644	−0.258152
$215$	0	0
$216$	32.4128	2.20541
$217$	−5.82449	−0.395392
$218$	−15.8624	−1.07434
$219$	0.356623	0.0240984
$220$	0	0
$221$	3.17564	0.213617
$222$	12.8666	0.863553
$223$	9.92618	0.664706	0.332353	−	0.943155i	$-0.392157\pi$
$223$	9.92618	0.664706	0.332353	+	0.943155i	$0.392157\pi$
$224$	12.1300	0.810470
$225$	0	0
$226$	−12.5896	−0.837449
$227$	21.8928	1.45307	0.726537	−	0.687128i	$-0.241129\pi$
$227$	21.8928	1.45307	0.726537	+	0.687128i	$0.241129\pi$
$228$	−6.24621	−0.413665
$229$	−3.74494	−0.247473	−0.123736	−	0.992315i	$-0.539488\pi$
$229$	−3.74494	−0.247473	−0.123736	+	0.992315i	$0.539488\pi$
$230$	0	0
$231$	−28.1210	−1.85022
$232$	18.4243	1.20962
$233$	−22.6997	−1.48710	−0.743552	−	0.668678i	$-0.766860\pi$
$233$	−22.6997	−1.48710	−0.743552	+	0.668678i	$0.766860\pi$
$234$	3.71757	0.243025
$235$	0	0
$236$	11.1324	0.724655
$237$	−19.4412	−1.26284
$238$	−7.41902	−0.480903
$239$	4.32556	0.279797	0.139899	−	0.990166i	$-0.455322\pi$
$239$	4.32556	0.279797	0.139899	+	0.990166i	$0.455322\pi$
$240$	0	0
$241$	−12.9477	−0.834034	−0.417017	−	0.908899i	$-0.636924\pi$
$241$	−12.9477	−0.834034	−0.417017	+	0.908899i	$0.636924\pi$
$242$	−5.92629	−0.380956
$243$	19.4452	1.24741
$244$	10.9280	0.699597
$245$	0	0
$246$	−11.7185	−0.747141
$247$	−0.986160	−0.0627478
$248$	7.43151	0.471901
$249$	35.1580	2.22804
$250$	0	0
$251$	1.00000	0.0631194
$251$	1.00000	0.0631194
$252$	19.9010	1.25364
$253$	31.1083	1.95576
$254$	−16.7596	−1.05159
$255$	0	0
$256$	−13.4624	−0.841399
$257$	0.394093	0.0245828	0.0122914	−	0.999924i	$-0.496087\pi$
$257$	0.394093	0.0245828	0.0122914	+	0.999924i	$0.496087\pi$
$258$	−0.170813	−0.0106343
$259$	10.8746	0.675712
$260$	0	0
$261$	48.0488	2.97415
$262$	8.12521	0.501977
$263$	−1.53116	−0.0944155	−0.0472077	−	0.998885i	$-0.515032\pi$
$263$	−1.53116	−0.0944155	−0.0472077	+	0.998885i	$0.515032\pi$
$264$	35.8797	2.20824
$265$	0	0
$266$	2.30389	0.141261
$267$	−7.40773	−0.453346
$268$	20.1745	1.23235
$269$	−3.68392	−0.224612	−0.112306	−	0.993674i	$-0.535824\pi$
$269$	−3.68392	−0.224612	−0.112306	+	0.993674i	$0.535824\pi$
$270$	0	0
$271$	10.8632	0.659892	0.329946	−	0.944000i	$-0.392969\pi$
$271$	10.8632	0.659892	0.329946	+	0.944000i	$0.392969\pi$
$272$	−3.32178	−0.201412
$273$	4.50881	0.272885
$274$	−13.2523	−0.800600
$275$	0	0
$276$	−31.5920	−1.90162
$277$	3.92556	0.235864	0.117932	−	0.993022i	$-0.462373\pi$
$277$	3.92556	0.235864	0.117932	+	0.993022i	$0.462373\pi$
$278$	−12.4618	−0.747406
$279$	19.3806	1.16029
$280$	0	0
$281$	−1.81456	−0.108248	−0.0541239	−	0.998534i	$-0.517237\pi$
$281$	−1.81456	−0.108248	−0.0541239	+	0.998534i	$0.517237\pi$
$282$	−27.9896	−1.66676
$283$	−20.4093	−1.21321	−0.606604	−	0.795004i	$-0.707469\pi$
$283$	−20.4093	−1.21321	−0.606604	+	0.795004i	$0.707469\pi$
$284$	−15.0939	−0.895658
$285$	0	0
$286$	2.32503	0.137482
$287$	−9.90412	−0.584622
$288$	−40.3618	−2.37834
$289$	4.08765	0.240450
$290$	0	0
$291$	7.55819	0.443069
$292$	−0.157842	−0.00923701
$293$	19.2694	1.12573	0.562865	−	0.826549i	$-0.309699\pi$
$293$	19.2694	1.12573	0.562865	+	0.826549i	$0.309699\pi$
$294$	6.63204	0.386788
$295$	0	0
$296$	−13.8749	−0.806463
$297$	52.8660	3.06759
$298$	11.1066	0.643386
$299$	−4.98779	−0.288452
$300$	0	0
$301$	−0.144366	−0.00832113
$302$	−10.5045	−0.604464
$303$	−0.618672	−0.0355418
$304$	1.03154	0.0591629
$305$	0	0
$306$	24.6863	1.41122
$307$	−19.9296	−1.13744	−0.568720	−	0.822531i	$-0.692561\pi$
$307$	−19.9296	−1.13744	−0.568720	+	0.822531i	$0.692561\pi$
$308$	12.4464	0.709199
$309$	−27.4059	−1.55907
$310$	0	0
$311$	29.0820	1.64909	0.824545	−	0.565797i	$-0.191431\pi$
$311$	29.0820	1.64909	0.824545	+	0.565797i	$0.191431\pi$
$312$	−5.75282	−0.325689
$313$	25.4848	1.44049	0.720243	−	0.693722i	$-0.244030\pi$
$313$	25.4848	1.44049	0.720243	+	0.693722i	$0.244030\pi$
$314$	8.00792	0.451913
$315$	0	0
$316$	8.60470	0.484052
$317$	−22.9102	−1.28677	−0.643383	−	0.765544i	$-0.722470\pi$
$317$	−22.9102	−1.28677	−0.643383	+	0.765544i	$0.722470\pi$
$318$	21.3097	1.19499
$319$	30.0505	1.68251
$320$	0	0
$321$	15.2403	0.850631
$322$	11.6526	0.649375
$323$	−6.54853	−0.364370
$324$	−24.8816	−1.38231
$325$	0	0
$326$	9.71088	0.537836
$327$	64.0148	3.54002
$328$	12.6367	0.697747
$329$	−23.6561	−1.30420
$330$	0	0
$331$	24.7108	1.35823	0.679113	−	0.734034i	$-0.262365\pi$
$331$	24.7108	1.35823	0.679113	+	0.734034i	$0.262365\pi$
$332$	−15.5610	−0.854020
$333$	−36.1843	−1.98289
$334$	−13.6126	−0.744848
$335$	0	0
$336$	−4.71629	−0.257295
$337$	−17.8271	−0.971102	−0.485551	−	0.874208i	$-0.661381\pi$
$337$	−17.8271	−0.971102	−0.485551	+	0.874208i	$0.661381\pi$
$338$	9.76092	0.530924
$339$	50.8071	2.75946
$340$	0	0
$341$	12.1210	0.656387
$342$	−7.66604	−0.414532
$343$	20.1131	1.08601
$344$	0.184198	0.00993128
$345$	0	0
$346$	−10.3536	−0.556611
$347$	26.3885	1.41661	0.708305	−	0.705907i	$-0.249460\pi$
$347$	26.3885	1.41661	0.708305	+	0.705907i	$0.249460\pi$
$348$	−30.5177	−1.63592
$349$	−16.0414	−0.858677	−0.429339	−	0.903144i	$-0.641253\pi$
$349$	−16.0414	−0.858677	−0.429339	+	0.903144i	$0.641253\pi$
$350$	0	0
$351$	−8.47633	−0.452433
$352$	−25.2429	−1.34545
$353$	−9.77533	−0.520289	−0.260144	−	0.965570i	$-0.583770\pi$
$353$	−9.77533	−0.520289	−0.260144	+	0.965570i	$0.583770\pi$
$354$	19.6064	1.04207
$355$	0	0
$356$	3.27868	0.173769
$357$	29.9404	1.58462
$358$	−13.1780	−0.696478
$359$	9.93170	0.524175	0.262088	−	0.965044i	$-0.415589\pi$
$359$	9.93170	0.524175	0.262088	+	0.965044i	$0.415589\pi$
$360$	0	0
$361$	−16.9664	−0.892970
$362$	6.97778	0.366744
$363$	23.9163	1.25528
$364$	−1.99561	−0.104598
$365$	0	0
$366$	19.2466	1.00604
$367$	−7.88573	−0.411632	−0.205816	−	0.978591i	$-0.565985\pi$
$367$	−7.88573	−0.411632	−0.205816	+	0.978591i	$0.565985\pi$
$368$	5.21732	0.271972
$369$	32.9553	1.71559
$370$	0	0
$371$	18.0104	0.935054
$372$	−12.3094	−0.638214
$373$	9.68592	0.501518	0.250759	−	0.968050i	$-0.419320\pi$
$373$	9.68592	0.501518	0.250759	+	0.968050i	$0.419320\pi$
$374$	15.4392	0.798342
$375$	0	0
$376$	30.1829	1.55657
$377$	−4.81818	−0.248149
$378$	19.8026	1.01854
$379$	6.40384	0.328943	0.164471	−	0.986382i	$-0.447408\pi$
$379$	6.40384	0.328943	0.164471	+	0.986382i	$0.447408\pi$
$380$	0	0
$381$	67.6356	3.46508
$382$	−5.35793	−0.274135
$383$	3.01090	0.153850	0.0769248	−	0.997037i	$-0.475490\pi$
$383$	3.01090	0.153850	0.0769248	+	0.997037i	$0.475490\pi$
$384$	29.1831	1.48924
$385$	0	0
$386$	8.39465	0.427277
$387$	0.480369	0.0244185
$388$	−3.34527	−0.169830
$389$	−3.05939	−0.155117	−0.0775586	−	0.996988i	$-0.524713\pi$
$389$	−3.05939	−0.155117	−0.0775586	+	0.996988i	$0.524713\pi$
$390$	0	0
$391$	−33.1211	−1.67501
$392$	−7.15174	−0.361217
$393$	−32.7904	−1.65406
$394$	−11.9555	−0.602312
$395$	0	0
$396$	−41.4145	−2.08116
$397$	−11.8686	−0.595668	−0.297834	−	0.954618i	$-0.596264\pi$
$397$	−11.8686	−0.595668	−0.297834	+	0.954618i	$0.596264\pi$
$398$	4.65177	0.233172
$399$	−9.29766	−0.465465
$400$	0	0
$401$	−3.21244	−0.160422	−0.0802109	−	0.996778i	$-0.525559\pi$
$401$	−3.21244	−0.160422	−0.0802109	+	0.996778i	$0.525559\pi$
$402$	35.5316	1.77215
$403$	−1.94343	−0.0968090
$404$	0.273826	0.0136233
$405$	0	0
$406$	11.2564	0.558644
$407$	−22.6303	−1.12174
$408$	−38.2012	−1.89124
$409$	−39.8967	−1.97277	−0.986383	−	0.164462i	$-0.947411\pi$
$409$	−39.8967	−1.97277	−0.986383	+	0.164462i	$0.947411\pi$
$410$	0	0
$411$	53.4814	2.63804
$412$	12.1299	0.597598
$413$	16.5708	0.815397
$414$	−38.7733	−1.90560
$415$	0	0
$416$	4.04735	0.198438
$417$	50.2911	2.46276
$418$	−4.79447	−0.234505
$419$	21.7394	1.06204	0.531020	−	0.847359i	$-0.321809\pi$
$419$	21.7394	1.06204	0.531020	+	0.847359i	$0.321809\pi$
$420$	0	0
$421$	4.07730	0.198715	0.0993577	−	0.995052i	$-0.468321\pi$
$421$	4.07730	0.198715	0.0993577	+	0.995052i	$0.468321\pi$
$422$	0.243425	0.0118498
$423$	78.7140	3.82721
$424$	−22.9796	−1.11599
$425$	0	0
$426$	−26.5835	−1.28798
$427$	16.2667	0.787202
$428$	−6.74539	−0.326051
$429$	−9.38297	−0.453014
$430$	0	0
$431$	12.9221	0.622436	0.311218	−	0.950339i	$-0.399263\pi$
$431$	12.9221	0.622436	0.311218	+	0.950339i	$0.399263\pi$
$432$	8.86639	0.426584
$433$	−24.6228	−1.18330	−0.591649	−	0.806196i	$-0.701523\pi$
$433$	−24.6228	−1.18330	−0.591649	+	0.806196i	$0.701523\pi$
$434$	4.54029	0.217941
$435$	0	0
$436$	−28.3331	−1.35691
$437$	10.2854	0.492017
$438$	−0.277993	−0.0132830
$439$	−21.7282	−1.03703	−0.518515	−	0.855068i	$-0.673515\pi$
$439$	−21.7282	−1.03703	−0.518515	+	0.855068i	$0.673515\pi$
$440$	0	0
$441$	−18.6510	−0.888143
$442$	−2.47546	−0.117746
$443$	35.5501	1.68904	0.844518	−	0.535527i	$-0.179887\pi$
$443$	35.5501	1.68904	0.844518	+	0.535527i	$0.179887\pi$
$444$	22.9821	1.09068
$445$	0	0
$446$	−7.73761	−0.366387
$447$	−44.8221	−2.12001
$448$	−6.45710	−0.305069
$449$	−30.4969	−1.43924	−0.719619	−	0.694370i	$-0.755683\pi$
$449$	−30.4969	−1.43924	−0.719619	+	0.694370i	$0.755683\pi$
$450$	0	0
$451$	20.6108	0.970524
$452$	−22.4873	−1.05772
$453$	42.3922	1.99176
$454$	−17.0658	−0.800935
$455$	0	0
$456$	11.8629	0.555533
$457$	−23.1694	−1.08382	−0.541908	−	0.840437i	$-0.682298\pi$
$457$	−23.1694	−1.08382	−0.541908	+	0.840437i	$0.682298\pi$
$458$	2.91924	0.136407
$459$	−56.2865	−2.62723
$460$	0	0
$461$	24.0832	1.12167	0.560833	−	0.827929i	$-0.310481\pi$
$461$	24.0832	1.12167	0.560833	+	0.827929i	$0.310481\pi$
$462$	21.9207	1.01984
$463$	−5.04661	−0.234536	−0.117268	−	0.993100i	$-0.537414\pi$
$463$	−5.04661	−0.234536	−0.117268	+	0.993100i	$0.537414\pi$
$464$	5.03991	0.233972
$465$	0	0
$466$	17.6947	0.819693
$467$	15.4324	0.714128	0.357064	−	0.934080i	$-0.383778\pi$
$467$	15.4324	0.714128	0.357064	+	0.934080i	$0.383778\pi$
$468$	6.64025	0.306946
$469$	30.0304	1.38667
$470$	0	0
$471$	−32.3170	−1.48909
$472$	−21.1428	−0.973178
$473$	0.300431	0.0138138
$474$	15.1547	0.696078
$475$	0	0
$476$	−13.2517	−0.607391
$477$	−59.9285	−2.74394
$478$	−3.37184	−0.154224
$479$	3.51010	0.160381	0.0801903	−	0.996780i	$-0.474447\pi$
$479$	3.51010	0.160381	0.0801903	+	0.996780i	$0.474447\pi$
$480$	0	0
$481$	3.62845	0.165443
$482$	10.0929	0.459720
$483$	−47.0257	−2.13974
$484$	−10.5854	−0.481156
$485$	0	0
$486$	−15.1578	−0.687572
$487$	−25.8708	−1.17232	−0.586158	−	0.810196i	$-0.699360\pi$
$487$	−25.8708	−1.17232	−0.586158	+	0.810196i	$0.699360\pi$
$488$	−20.7548	−0.939526
$489$	−39.1896	−1.77221
$490$	0	0
$491$	−20.4715	−0.923868	−0.461934	−	0.886914i	$-0.652844\pi$
$491$	−20.4715	−0.923868	−0.461934	+	0.886914i	$0.652844\pi$
$492$	−20.9313	−0.943654
$493$	−31.9948	−1.44098
$494$	0.768727	0.0345867
$495$	0	0
$496$	2.03286	0.0912781
$497$	−22.4677	−1.00781
$498$	−27.4062	−1.22810
$499$	−31.6343	−1.41615	−0.708073	−	0.706139i	$-0.750435\pi$
$499$	−31.6343	−1.41615	−0.708073	+	0.706139i	$0.750435\pi$
$500$	0	0
$501$	54.9354	2.45433
$502$	−0.779516	−0.0347915
$503$	7.48882	0.333910	0.166955	−	0.985965i	$-0.446607\pi$
$503$	7.48882	0.333910	0.166955	+	0.985965i	$0.446607\pi$
$504$	−37.7964	−1.68359
$505$	0	0
$506$	−24.2494	−1.07802
$507$	−39.3915	−1.74944
$508$	−29.9357	−1.32818
$509$	3.71394	0.164618	0.0823088	−	0.996607i	$-0.473771\pi$
$509$	3.71394	0.164618	0.0823088	+	0.996607i	$0.473771\pi$
$510$	0	0
$511$	−0.234953	−0.0103937
$512$	−8.05932	−0.356175
$513$	17.4791	0.771722
$514$	−0.307202	−0.0135501
$515$	0	0
$516$	−0.305102	−0.0134314
$517$	49.2290	2.16509
$518$	−8.47688	−0.372453
$519$	41.7832	1.83408
$520$	0	0
$521$	−17.6405	−0.772846	−0.386423	−	0.922322i	$-0.626289\pi$
$521$	−17.6405	−0.772846	−0.386423	+	0.922322i	$0.626289\pi$
$522$	−37.4548	−1.63935
$523$	11.7757	0.514915	0.257458	−	0.966290i	$-0.417115\pi$
$523$	11.7757	0.514915	0.257458	+	0.966290i	$0.417115\pi$
$524$	14.5131	0.634007
$525$	0	0
$526$	1.19356	0.0520419
$527$	−12.9052	−0.562160
$528$	9.81475	0.427132
$529$	29.0214	1.26180
$530$	0	0
$531$	−55.1383	−2.39280
$532$	4.11516	0.178415
$533$	−3.30466	−0.143141
$534$	5.77444	0.249885
$535$	0	0
$536$	−38.3159	−1.65500
$537$	53.1815	2.29495
$538$	2.87167	0.123807
$539$	−11.6646	−0.502432
$540$	0	0
$541$	17.0425	0.732715	0.366357	−	0.930474i	$-0.380605\pi$
$541$	17.0425	0.732715	0.366357	+	0.930474i	$0.380605\pi$
$542$	−8.46804	−0.363733
$543$	−28.1598	−1.20845
$544$	26.8762	1.15231
$545$	0	0
$546$	−3.51469	−0.150415
$547$	20.9090	0.894004	0.447002	−	0.894533i	$-0.352492\pi$
$547$	20.9090	0.894004	0.447002	+	0.894533i	$0.352492\pi$
$548$	−23.6710	−1.01117
$549$	−54.1264	−2.31006
$550$	0	0
$551$	9.93563	0.423272
$552$	60.0003	2.55378
$553$	12.8084	0.544666
$554$	−3.06004	−0.130008
$555$	0	0
$556$	−22.2589	−0.943989
$557$	14.3266	0.607037	0.303518	−	0.952826i	$-0.401839\pi$
$557$	14.3266	0.607037	0.303518	+	0.952826i	$0.401839\pi$
$558$	−15.1075	−0.639551
$559$	−0.0481699	−0.00203737
$560$	0	0
$561$	−62.3070	−2.63060
$562$	1.41448	0.0596663
$563$	2.48884	0.104892	0.0524460	−	0.998624i	$-0.483298\pi$
$563$	2.48884	0.104892	0.0524460	+	0.998624i	$0.483298\pi$
$564$	−49.9945	−2.10515
$565$	0	0
$566$	15.9094	0.668722
$567$	−37.0370	−1.55541
$568$	28.6667	1.20283
$569$	−5.07011	−0.212550	−0.106275	−	0.994337i	$-0.533892\pi$
$569$	−5.07011	−0.212550	−0.106275	+	0.994337i	$0.533892\pi$
$570$	0	0
$571$	−35.7515	−1.49615	−0.748077	−	0.663612i	$-0.769023\pi$
$571$	−35.7515	−1.49615	−0.748077	+	0.663612i	$0.769023\pi$
$572$	4.15292	0.173642
$573$	21.6226	0.903298
$574$	7.72042	0.322244
$575$	0	0
$576$	21.4856	0.895232
$577$	−12.8559	−0.535197	−0.267599	−	0.963530i	$-0.586230\pi$
$577$	−12.8559	−0.535197	−0.267599	+	0.963530i	$0.586230\pi$
$578$	−3.18639	−0.132536
$579$	−33.8777	−1.40791
$580$	0	0
$581$	−23.1630	−0.960962
$582$	−5.89173	−0.244220
$583$	−37.4803	−1.55227
$584$	0.299778	0.0124049
$585$	0	0
$586$	−15.0208	−0.620504
$587$	−30.4149	−1.25536	−0.627679	−	0.778472i	$-0.715995\pi$
$587$	−30.4149	−1.25536	−0.627679	+	0.778472i	$0.715995\pi$
$588$	11.8460	0.488521
$589$	4.00757	0.165129
$590$	0	0
$591$	48.2482	1.98467
$592$	−3.79543	−0.155991
$593$	−28.6314	−1.17575	−0.587876	−	0.808951i	$-0.700036\pi$
$593$	−28.6314	−1.17575	−0.587876	+	0.808951i	$0.700036\pi$
$594$	−41.2098	−1.69086
$595$	0	0
$596$	19.8383	0.812610
$597$	−18.7729	−0.768322
$598$	3.88806	0.158995
$599$	−11.0037	−0.449600	−0.224800	−	0.974405i	$-0.572173\pi$
$599$	−11.0037	−0.449600	−0.224800	+	0.974405i	$0.572173\pi$
$600$	0	0
$601$	0.423259	0.0172651	0.00863255	−	0.999963i	$-0.497252\pi$
$601$	0.423259	0.0172651	0.00863255	+	0.999963i	$0.497252\pi$
$602$	0.112536	0.00458661
$603$	−99.9240	−4.06922
$604$	−18.7629	−0.763451
$605$	0	0
$606$	0.482265	0.0195907
$607$	40.7175	1.65267	0.826336	−	0.563177i	$-0.190421\pi$
$607$	40.7175	1.65267	0.826336	+	0.563177i	$0.190421\pi$
$608$	−8.34609	−0.338479
$609$	−45.4266	−1.84078
$610$	0	0
$611$	−7.89319	−0.319324
$612$	44.0941	1.78240
$613$	−4.87460	−0.196883	−0.0984417	−	0.995143i	$-0.531386\pi$
$613$	−4.87460	−0.196883	−0.0984417	+	0.995143i	$0.531386\pi$
$614$	15.5354	0.626958
$615$	0	0
$616$	−23.6385	−0.952422
$617$	7.06448	0.284405	0.142203	−	0.989838i	$-0.454582\pi$
$617$	7.06448	0.284405	0.142203	+	0.989838i	$0.454582\pi$
$618$	21.3633	0.859359
$619$	−10.4543	−0.420195	−0.210098	−	0.977680i	$-0.567378\pi$
$619$	−10.4543	−0.420195	−0.210098	+	0.977680i	$0.567378\pi$
$620$	0	0
$621$	88.4058	3.54760
$622$	−22.6699	−0.908980
$623$	4.88041	0.195529
$624$	−1.57366	−0.0629968
$625$	0	0
$626$	−19.8658	−0.793997
$627$	19.3487	0.772714
$628$	14.3036	0.570775
$629$	24.0945	0.960711
$630$	0	0
$631$	−8.50745	−0.338676	−0.169338	−	0.985558i	$-0.554163\pi$
$631$	−8.50745	−0.338676	−0.169338	+	0.985558i	$0.554163\pi$
$632$	−16.3423	−0.650060
$633$	−0.982375	−0.0390459
$634$	17.8589	0.709267
$635$	0	0
$636$	38.0630	1.50930
$637$	1.87026	0.0741026
$638$	−23.4248	−0.927398
$639$	74.7598	2.95745
$640$	0	0
$641$	17.1989	0.679315	0.339657	−	0.940549i	$-0.389689\pi$
$641$	17.1989	0.679315	0.339657	+	0.940549i	$0.389689\pi$
$642$	−11.8801	−0.468869
$643$	30.4905	1.20243	0.601215	−	0.799088i	$-0.294684\pi$
$643$	30.4905	1.20243	0.601215	+	0.799088i	$0.294684\pi$
$644$	20.8137	0.820173
$645$	0	0
$646$	5.10468	0.200841
$647$	23.5857	0.927250	0.463625	−	0.886031i	$-0.346548\pi$
$647$	23.5857	0.927250	0.463625	+	0.886031i	$0.346548\pi$
$648$	47.2557	1.85638
$649$	−34.4844	−1.35363
$650$	0	0
$651$	−18.3229	−0.718132
$652$	17.3454	0.679297
$653$	−11.0925	−0.434081	−0.217041	−	0.976163i	$-0.569640\pi$
$653$	−11.0925	−0.434081	−0.217041	+	0.976163i	$0.569640\pi$
$654$	−49.9005	−1.95126
$655$	0	0
$656$	3.45673	0.134963
$657$	0.781789	0.0305005
$658$	18.4403	0.718877
$659$	31.0542	1.20970	0.604850	−	0.796339i	$-0.293233\pi$
$659$	31.0542	1.20970	0.604850	+	0.796339i	$0.293233\pi$
$660$	0	0
$661$	7.18698	0.279541	0.139771	−	0.990184i	$-0.455364\pi$
$661$	7.18698	0.279541	0.139771	+	0.990184i	$0.455364\pi$
$662$	−19.2624	−0.748655
$663$	9.99006	0.387982
$664$	29.5538	1.14691
$665$	0	0
$666$	28.2063	1.09297
$667$	50.2524	1.94578
$668$	−24.3145	−0.940757
$669$	31.2262	1.20727
$670$	0	0
$671$	−33.8515	−1.30682
$672$	38.1590	1.47202
$673$	29.4721	1.13607	0.568034	−	0.823005i	$-0.307704\pi$
$673$	29.4721	1.13607	0.568034	+	0.823005i	$0.307704\pi$
$674$	13.8965	0.535272
$675$	0	0
$676$	17.4348	0.670567
$677$	46.4622	1.78569	0.892843	−	0.450368i	$-0.148707\pi$
$677$	46.4622	1.78569	0.892843	+	0.450368i	$0.148707\pi$
$678$	−39.6049	−1.52102
$679$	−4.97953	−0.191097
$680$	0	0
$681$	68.8711	2.63915
$682$	−9.44848	−0.361801
$683$	9.60289	0.367444	0.183722	−	0.982978i	$-0.441185\pi$
$683$	9.60289	0.367444	0.183722	+	0.982978i	$0.441185\pi$
$684$	−13.6929	−0.523562
$685$	0	0
$686$	−15.6785	−0.598609
$687$	−11.7810	−0.449473
$688$	0.0503866	0.00192097
$689$	6.00944	0.228941
$690$	0	0
$691$	8.92238	0.339423	0.169712	−	0.985494i	$-0.445716\pi$
$691$	8.92238	0.339423	0.169712	+	0.985494i	$0.445716\pi$
$692$	−18.4933	−0.703011
$693$	−61.6467	−2.34177
$694$	−20.5703	−0.780836
$695$	0	0
$696$	57.9600	2.19697
$697$	−21.9444	−0.831202
$698$	12.5045	0.473304
$699$	−71.4095	−2.70095
$700$	0	0
$701$	−3.79254	−0.143242	−0.0716212	−	0.997432i	$-0.522817\pi$
$701$	−3.79254	−0.143242	−0.0716212	+	0.997432i	$0.522817\pi$
$702$	6.60743	0.249381
$703$	−7.48228	−0.282199
$704$	13.4374	0.506442
$705$	0	0
$706$	7.62003	0.286783
$707$	0.407597	0.0153293
$708$	35.0206	1.31616
$709$	−13.0451	−0.489920	−0.244960	−	0.969533i	$-0.578775\pi$
$709$	−13.0451	−0.489920	−0.244960	+	0.969533i	$0.578775\pi$
$710$	0	0
$711$	−42.6189	−1.59833
$712$	−6.22694	−0.233364
$713$	20.2694	0.759097
$714$	−23.3390	−0.873442
$715$	0	0
$716$	−23.5383	−0.879666
$717$	13.6075	0.508182
$718$	−7.74192	−0.288926
$719$	−49.9742	−1.86372	−0.931861	−	0.362814i	$-0.881816\pi$
$719$	−49.9742	−1.86372	−0.931861	+	0.362814i	$0.881816\pi$
$720$	0	0
$721$	18.0557	0.672430
$722$	13.2256	0.492206
$723$	−40.7313	−1.51482
$724$	12.4636	0.463205
$725$	0	0
$726$	−18.6432	−0.691913
$727$	−44.0322	−1.63306	−0.816532	−	0.577301i	$-0.804106\pi$
$727$	−44.0322	−1.63306	−0.816532	+	0.577301i	$0.804106\pi$
$728$	3.79010	0.140471
$729$	7.56087	0.280032
$730$	0	0
$731$	−0.319869	−0.0118308
$732$	34.3779	1.27064
$733$	−26.0442	−0.961963	−0.480981	−	0.876731i	$-0.659720\pi$
$733$	−26.0442	−0.961963	−0.480981	+	0.876731i	$0.659720\pi$
$734$	6.14705	0.226892
$735$	0	0
$736$	−42.2128	−1.55599
$737$	−62.4941	−2.30200
$738$	−25.6892	−0.945632
$739$	48.8930	1.79856	0.899278	−	0.437377i	$-0.144092\pi$
$739$	48.8930	1.79856	0.899278	+	0.437377i	$0.144092\pi$
$740$	0	0
$741$	−3.10230	−0.113966
$742$	−14.0394	−0.515403
$743$	−12.1636	−0.446241	−0.223120	−	0.974791i	$-0.571624\pi$
$743$	−12.1636	−0.446241	−0.223120	+	0.974791i	$0.571624\pi$
$744$	23.3783	0.857092
$745$	0	0
$746$	−7.55033	−0.276437
$747$	77.0733	2.81996
$748$	27.5772	1.00832
$749$	−10.0407	−0.366880
$750$	0	0
$751$	−24.7050	−0.901500	−0.450750	−	0.892650i	$-0.648843\pi$
$751$	−24.7050	−0.901500	−0.450750	+	0.892650i	$0.648843\pi$
$752$	8.25642	0.301081
$753$	3.14584	0.114641
$754$	3.75585	0.136780
$755$	0	0
$756$	35.3710	1.28643
$757$	11.9146	0.433042	0.216521	−	0.976278i	$-0.430529\pi$
$757$	11.9146	0.433042	0.216521	+	0.976278i	$0.430529\pi$
$758$	−4.99189	−0.181314
$759$	97.8619	3.55216
$760$	0	0
$761$	−7.04012	−0.255204	−0.127602	−	0.991825i	$-0.540728\pi$
$761$	−7.04012	−0.255204	−0.127602	+	0.991825i	$0.540728\pi$
$762$	−52.7230	−1.90995
$763$	−42.1746	−1.52682
$764$	−9.57022	−0.346238
$765$	0	0
$766$	−2.34704	−0.0848021
$767$	5.52910	0.199644
$768$	−42.3505	−1.52819
$769$	12.7885	0.461164	0.230582	−	0.973053i	$-0.425937\pi$
$769$	12.7885	0.461164	0.230582	+	0.973053i	$0.425937\pi$
$770$	0	0
$771$	1.23975	0.0446486
$772$	14.9944	0.539659
$773$	−43.1745	−1.55288	−0.776439	−	0.630192i	$-0.782976\pi$
$773$	−43.1745	−1.55288	−0.776439	+	0.630192i	$0.782976\pi$
$774$	−0.374455	−0.0134595
$775$	0	0
$776$	6.35342	0.228074
$777$	34.2096	1.22726
$778$	2.38484	0.0855008
$779$	6.81457	0.244157
$780$	0	0
$781$	46.7560	1.67306
$782$	25.8184	0.923265
$783$	85.3996	3.05193
$784$	−1.95633	−0.0698689
$785$	0	0
$786$	25.5606	0.911717
$787$	−22.3365	−0.796212	−0.398106	−	0.917339i	$-0.630332\pi$
$787$	−22.3365	−0.796212	−0.398106	+	0.917339i	$0.630332\pi$
$788$	−21.3547	−0.760731
$789$	−4.81679	−0.171482
$790$	0	0
$791$	−33.4731	−1.19016
$792$	78.6555	2.79490
$793$	5.42763	0.192741
$794$	9.25176	0.328333
$795$	0	0
$796$	8.30890	0.294501
$797$	−39.2565	−1.39054	−0.695269	−	0.718750i	$-0.744715\pi$
$797$	−39.2565	−1.39054	−0.695269	+	0.718750i	$0.744715\pi$
$798$	7.24767	0.256565
$799$	−52.4142	−1.85428
$800$	0	0
$801$	−16.2392	−0.573785
$802$	2.50415	0.0884246
$803$	0.488944	0.0172545
$804$	63.4658	2.23827
$805$	0	0
$806$	1.51493	0.0533612
$807$	−11.5890	−0.407952
$808$	−0.520056	−0.0182955
$809$	−4.53751	−0.159530	−0.0797651	−	0.996814i	$-0.525417\pi$
$809$	−4.53751	−0.159530	−0.0797651	+	0.996814i	$0.525417\pi$
$810$	0	0
$811$	12.1635	0.427118	0.213559	−	0.976930i	$-0.431494\pi$
$811$	12.1635	0.427118	0.213559	+	0.976930i	$0.431494\pi$
$812$	20.1059	0.705578
$813$	34.1739	1.19853
$814$	17.6407	0.618305
$815$	0	0
$816$	−10.4498	−0.365816
$817$	0.0993317	0.00347518
$818$	31.1001	1.08739
$819$	9.88420	0.345382
$820$	0	0
$821$	−12.4541	−0.434650	−0.217325	−	0.976099i	$-0.569733\pi$
$821$	−12.4541	−0.434650	−0.217325	+	0.976099i	$0.569733\pi$
$822$	−41.6896	−1.45409
$823$	21.5162	0.750009	0.375005	−	0.927023i	$-0.377641\pi$
$823$	21.5162	0.750009	0.375005	+	0.927023i	$0.377641\pi$
$824$	−23.0374	−0.802546
$825$	0	0
$826$	−12.9172	−0.449448
$827$	−21.6544	−0.752997	−0.376499	−	0.926417i	$-0.622872\pi$
$827$	−21.6544	−0.752997	−0.376499	+	0.926417i	$0.622872\pi$
$828$	−69.2560	−2.40681
$829$	23.6207	0.820382	0.410191	−	0.912000i	$-0.365462\pi$
$829$	23.6207	0.820382	0.410191	+	0.912000i	$0.365462\pi$
$830$	0	0
$831$	12.3492	0.428389
$832$	−2.15450	−0.0746940
$833$	12.4194	0.430306
$834$	−39.2027	−1.35748
$835$	0	0
$836$	−8.56379	−0.296185
$837$	34.4462	1.19063
$838$	−16.9462	−0.585397
$839$	7.82348	0.270096	0.135048	−	0.990839i	$-0.456881\pi$
$839$	7.82348	0.270096	0.135048	+	0.990839i	$0.456881\pi$
$840$	0	0
$841$	19.5436	0.673916
$842$	−3.17832	−0.109532
$843$	−5.70833	−0.196605
$844$	0.434801	0.0149665
$845$	0	0
$846$	−61.3588	−2.10956
$847$	−15.7567	−0.541407
$848$	−6.28598	−0.215861
$849$	−64.2045	−2.20349
$850$	0	0
$851$	−37.8438	−1.29727
$852$	−47.4830	−1.62674
$853$	20.1784	0.690896	0.345448	−	0.938438i	$-0.387727\pi$
$853$	20.1784	0.690896	0.345448	+	0.938438i	$0.387727\pi$
$854$	−12.6802	−0.433906
$855$	0	0
$856$	12.8110	0.437871
$857$	7.59263	0.259359	0.129680	−	0.991556i	$-0.458605\pi$
$857$	7.59263	0.259359	0.129680	+	0.991556i	$0.458605\pi$
$858$	7.31417	0.249702
$859$	−26.8210	−0.915122	−0.457561	−	0.889178i	$-0.651277\pi$
$859$	−26.8210	−0.915122	−0.457561	+	0.889178i	$0.651277\pi$
$860$	0	0
$861$	−31.1568	−1.06182
$862$	−10.0730	−0.343087
$863$	2.72517	0.0927660	0.0463830	−	0.998924i	$-0.485231\pi$
$863$	2.72517	0.0927660	0.0463830	+	0.998924i	$0.485231\pi$
$864$	−71.7370	−2.44054
$865$	0	0
$866$	19.1939	0.652235
$867$	12.8591	0.436718
$868$	8.10977	0.275263
$869$	−26.6546	−0.904195
$870$	0	0
$871$	10.0201	0.339517
$872$	53.8108	1.82226
$873$	16.5691	0.560778
$874$	−8.01762	−0.271200
$875$	0	0
$876$	−0.496546	−0.0167767
$877$	−44.9386	−1.51747	−0.758735	−	0.651400i	$-0.774182\pi$
$877$	−44.9386	−1.51747	−0.758735	+	0.651400i	$0.774182\pi$
$878$	16.9375	0.571612
$879$	60.6185	2.04461
$880$	0	0
$881$	−56.3147	−1.89729	−0.948645	−	0.316344i	$-0.897545\pi$
$881$	−56.3147	−1.89729	−0.948645	+	0.316344i	$0.897545\pi$
$882$	14.5387	0.489545
$883$	46.7714	1.57398	0.786992	−	0.616963i	$-0.211637\pi$
$883$	46.7714	1.57398	0.786992	+	0.616963i	$0.211637\pi$
$884$	−4.42162	−0.148715
$885$	0	0
$886$	−27.7119	−0.930998
$887$	43.3251	1.45472	0.727358	−	0.686259i	$-0.240748\pi$
$887$	43.3251	1.45472	0.727358	+	0.686259i	$0.240748\pi$
$888$	−43.6482	−1.46474
$889$	−44.5601	−1.49450
$890$	0	0
$891$	77.0751	2.58211
$892$	−13.8208	−0.462754
$893$	16.2766	0.544677
$894$	34.9395	1.16855
$895$	0	0
$896$	−19.2266	−0.642315
$897$	−15.6908	−0.523901
$898$	23.7728	0.793309
$899$	19.5802	0.653036
$900$	0	0
$901$	39.9053	1.32944
$902$	−16.0664	−0.534954
$903$	−0.454153	−0.0151133
$904$	42.7085	1.42046
$905$	0	0
$906$	−33.0454	−1.09786
$907$	−34.0973	−1.13218	−0.566091	−	0.824343i	$-0.691545\pi$
$907$	−34.0973	−1.13218	−0.566091	+	0.824343i	$0.691545\pi$
$908$	−30.4825	−1.01160
$909$	−1.35625	−0.0449841
$910$	0	0
$911$	−9.81857	−0.325304	−0.162652	−	0.986684i	$-0.552005\pi$
$911$	−9.81857	−0.325304	−0.162652	+	0.986684i	$0.552005\pi$
$912$	3.24506	0.107455
$913$	48.2029	1.59528
$914$	18.0609	0.597401
$915$	0	0
$916$	5.21429	0.172285
$917$	21.6032	0.713399
$918$	43.8762	1.44813
$919$	38.2375	1.26134	0.630670	−	0.776051i	$-0.282780\pi$
$919$	38.2375	1.26134	0.630670	+	0.776051i	$0.282780\pi$
$920$	0	0
$921$	−62.6952	−2.06588
$922$	−18.7732	−0.618263
$923$	−7.49668	−0.246756
$924$	39.1544	1.28808
$925$	0	0
$926$	3.93391	0.129276
$927$	−60.0792	−1.97326
$928$	−40.7774	−1.33858
$929$	−8.67986	−0.284777	−0.142388	−	0.989811i	$-0.545478\pi$
$929$	−8.67986	−0.284777	−0.142388	+	0.989811i	$0.545478\pi$
$930$	0	0
$931$	−3.85669	−0.126398
$932$	31.6060	1.03529
$933$	91.4873	2.99516
$934$	−12.0298	−0.393628
$935$	0	0
$936$	−12.6113	−0.412214
$937$	−25.5923	−0.836063	−0.418032	−	0.908432i	$-0.637280\pi$
$937$	−25.5923	−0.836063	−0.418032	+	0.908432i	$0.637280\pi$
$938$	−23.4091	−0.764335
$939$	80.1711	2.61628
$940$	0	0
$941$	−12.9227	−0.421267	−0.210633	−	0.977565i	$-0.567553\pi$
$941$	−12.9227	−0.421267	−0.210633	+	0.977565i	$0.567553\pi$
$942$	25.1916	0.820788
$943$	34.4667	1.12239
$944$	−5.78354	−0.188238
$945$	0	0
$946$	−0.234190	−0.00761419
$947$	−51.5358	−1.67469	−0.837345	−	0.546675i	$-0.815893\pi$
$947$	−51.5358	−1.67469	−0.837345	+	0.546675i	$0.815893\pi$
$948$	27.0690	0.879161
$949$	−0.0783954	−0.00254482
$950$	0	0
$951$	−72.0719	−2.33709
$952$	25.1679	0.815698
$953$	20.2468	0.655859	0.327929	−	0.944702i	$-0.393649\pi$
$953$	20.2468	0.655859	0.327929	+	0.944702i	$0.393649\pi$
$954$	46.7152	1.51246
$955$	0	0
$956$	−6.02271	−0.194788
$957$	94.5341	3.05585
$958$	−2.73618	−0.0884019
$959$	−35.2349	−1.13779
$960$	0	0
$961$	−23.1023	−0.745235
$962$	−2.82844	−0.0911925
$963$	33.4098	1.07662
$964$	18.0278	0.580636
$965$	0	0
$966$	36.6572	1.17943
$967$	−16.6869	−0.536616	−0.268308	−	0.963333i	$-0.586465\pi$
$967$	−16.6869	−0.536616	−0.268308	+	0.963333i	$0.586465\pi$
$968$	20.1041	0.646170
$969$	−20.6006	−0.661787
$970$	0	0
$971$	37.5064	1.20364	0.601819	−	0.798633i	$-0.294443\pi$
$971$	37.5064	1.20364	0.601819	+	0.798633i	$0.294443\pi$
$972$	−27.0746	−0.868417
$973$	−33.1331	−1.06220
$974$	20.1667	0.646182
$975$	0	0
$976$	−5.67739	−0.181729
$977$	8.01221	0.256333	0.128167	−	0.991753i	$-0.459091\pi$
$977$	8.01221	0.256333	0.128167	+	0.991753i	$0.459091\pi$
$978$	30.5489	0.976845
$979$	−10.1563	−0.324596
$980$	0	0
$981$	140.333	4.48049
$982$	15.9579	0.509237
$983$	−27.5705	−0.879362	−0.439681	−	0.898154i	$-0.644909\pi$
$983$	−27.5705	−0.879362	−0.439681	+	0.898154i	$0.644909\pi$
$984$	39.7532	1.26728
$985$	0	0
$986$	24.9405	0.794267
$987$	−74.4182	−2.36876
$988$	1.37308	0.0436836
$989$	0.502399	0.0159754
$990$	0	0
$991$	11.0011	0.349463	0.174731	−	0.984616i	$-0.444094\pi$
$991$	11.0011	0.349463	0.174731	+	0.984616i	$0.444094\pi$
$992$	−16.4477	−0.522214
$993$	77.7361	2.46688
$994$	17.5139	0.555508
$995$	0	0
$996$	−48.9524	−1.55111
$997$	29.1077	0.921849	0.460925	−	0.887439i	$-0.347518\pi$
$997$	29.1077	0.921849	0.460925	+	0.887439i	$0.347518\pi$
$998$	24.6595	0.780581
$999$	−64.3123	−2.03475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6275.2.a.e.1.8		17
5.4	even	2		251.2.a.b.1.10	✓	17
15.14	odd	2		2259.2.a.k.1.8		17
20.19	odd	2		4016.2.a.k.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
251.2.a.b.1.10	✓	17	5.4	even	2
2259.2.a.k.1.8		17	15.14	odd	2
4016.2.a.k.1.17		17	20.19	odd	2
6275.2.a.e.1.8		17	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6275 = 5^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6275.a (trivial)

\(f(q)\)	\(=\)	\(q-0.779516 q^{2} +3.14584 q^{3} -1.39236 q^{4} -2.45223 q^{6} -2.07256 q^{7} +2.64439 q^{8} +6.89631 q^{9} +O(q^{10})\)	\(q-0.779516 q^{2} +3.14584 q^{3} -1.39236 q^{4} -2.45223 q^{6} -2.07256 q^{7} +2.64439 q^{8} +6.89631 q^{9} +4.31307 q^{11} -4.38013 q^{12} -0.691540 q^{13} +1.61559 q^{14} +0.723363 q^{16} -4.59213 q^{17} -5.37578 q^{18} +1.42603 q^{19} -6.51995 q^{21} -3.36210 q^{22} +7.21258 q^{23} +8.31884 q^{24} +0.539067 q^{26} +12.2572 q^{27} +2.88574 q^{28} +6.96732 q^{29} +2.81029 q^{31} -5.85266 q^{32} +13.5682 q^{33} +3.57964 q^{34} -9.60211 q^{36} -5.24691 q^{37} -1.11162 q^{38} -2.17548 q^{39} +4.77869 q^{41} +5.08240 q^{42} +0.0696559 q^{43} -6.00532 q^{44} -5.62232 q^{46} +11.4139 q^{47} +2.27559 q^{48} -2.70449 q^{49} -14.4461 q^{51} +0.962870 q^{52} -8.68993 q^{53} -9.55465 q^{54} -5.48067 q^{56} +4.48607 q^{57} -5.43114 q^{58} -7.99534 q^{59} -7.84861 q^{61} -2.19066 q^{62} -14.2930 q^{63} +3.11552 q^{64} -10.5766 q^{66} -14.4895 q^{67} +6.39387 q^{68} +22.6896 q^{69} +10.8406 q^{71} +18.2366 q^{72} +0.113363 q^{73} +4.09005 q^{74} -1.98555 q^{76} -8.93909 q^{77} +1.69582 q^{78} -6.17996 q^{79} +17.8702 q^{81} -3.72506 q^{82} +11.1760 q^{83} +9.07808 q^{84} -0.0542979 q^{86} +21.9181 q^{87} +11.4054 q^{88} -2.35477 q^{89} +1.43326 q^{91} -10.0425 q^{92} +8.84072 q^{93} -8.89734 q^{94} -18.4115 q^{96} +2.40260 q^{97} +2.10819 q^{98} +29.7442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * q^99

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