LMFDB - Embedded newform 6025.2.a.i.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.00750$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00750 q^{2} +2.74497 q^{3} -0.984941 q^{4} +2.76556 q^{6} +1.78457 q^{7} -3.00733 q^{8} +4.53484 q^{9} +O(q^{10})$	\(q+1.00750 q^{2} +2.74497 q^{3} -0.984941 q^{4} +2.76556 q^{6} +1.78457 q^{7} -3.00733 q^{8} +4.53484 q^{9} -5.50233 q^{11} -2.70363 q^{12} -0.207802 q^{13} +1.79795 q^{14} -1.06001 q^{16} -5.58081 q^{17} +4.56886 q^{18} +1.05539 q^{19} +4.89858 q^{21} -5.54361 q^{22} -5.66964 q^{23} -8.25503 q^{24} -0.209361 q^{26} +4.21310 q^{27} -1.75769 q^{28} -6.52025 q^{29} +7.75270 q^{31} +4.94671 q^{32} -15.1037 q^{33} -5.62267 q^{34} -4.46656 q^{36} -3.26737 q^{37} +1.06331 q^{38} -0.570410 q^{39} +5.02548 q^{41} +4.93532 q^{42} +10.9987 q^{43} +5.41948 q^{44} -5.71217 q^{46} -7.57472 q^{47} -2.90969 q^{48} -3.81532 q^{49} -15.3191 q^{51} +0.204673 q^{52} -9.19155 q^{53} +4.24470 q^{54} -5.36678 q^{56} +2.89701 q^{57} -6.56916 q^{58} +0.353669 q^{59} -2.42137 q^{61} +7.81086 q^{62} +8.09273 q^{63} +7.10383 q^{64} -15.2170 q^{66} +2.81825 q^{67} +5.49677 q^{68} -15.5630 q^{69} -11.3297 q^{71} -13.6378 q^{72} -12.8426 q^{73} -3.29188 q^{74} -1.03950 q^{76} -9.81928 q^{77} -0.574688 q^{78} -12.9021 q^{79} -2.03972 q^{81} +5.06318 q^{82} +16.8314 q^{83} -4.82481 q^{84} +11.0812 q^{86} -17.8979 q^{87} +16.5473 q^{88} -6.49446 q^{89} -0.370837 q^{91} +5.58426 q^{92} +21.2809 q^{93} -7.63154 q^{94} +13.5785 q^{96} -12.2649 q^{97} -3.84394 q^{98} -24.9522 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * 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 $

$2$	1.00750	0.712411	0.356205	−	0.934408i	$-0.384070\pi$
$2$	1.00750	0.712411	0.356205	+	0.934408i	$0.384070\pi$
$3$	2.74497	1.58481	0.792404	−	0.609997i	$-0.208829\pi$
$3$	2.74497	1.58481	0.792404	+	0.609997i	$0.208829\pi$
$4$	−0.984941	−0.492471
$5$	0	0
$5$	0	0
$6$	2.76556	1.12903
$7$	1.78457	0.674503	0.337251	−	0.941415i	$-0.390503\pi$
$7$	1.78457	0.674503	0.337251	+	0.941415i	$0.390503\pi$
$8$	−3.00733	−1.06325
$9$	4.53484	1.51161
$10$	0	0
$11$	−5.50233	−1.65902	−0.829508	−	0.558495i	$-0.811379\pi$
$11$	−5.50233	−1.65902	−0.829508	+	0.558495i	$0.811379\pi$
$12$	−2.70363	−0.780471
$13$	−0.207802	−0.0576339	−0.0288169	−	0.999585i	$-0.509174\pi$
$13$	−0.207802	−0.0576339	−0.0288169	+	0.999585i	$0.509174\pi$
$14$	1.79795	0.480523
$15$	0	0
$16$	−1.06001	−0.265002
$17$	−5.58081	−1.35354	−0.676772	−	0.736192i	$-0.736622\pi$
$17$	−5.58081	−1.35354	−0.676772	+	0.736192i	$0.736622\pi$
$18$	4.56886	1.07689
$19$	1.05539	0.242123	0.121062	−	0.992645i	$-0.461370\pi$
$19$	1.05539	0.242123	0.121062	+	0.992645i	$0.461370\pi$
$20$	0	0
$21$	4.89858	1.06896
$22$	−5.54361	−1.18190
$23$	−5.66964	−1.18220	−0.591101	−	0.806598i	$-0.701306\pi$
$23$	−5.66964	−1.18220	−0.591101	+	0.806598i	$0.701306\pi$
$24$	−8.25503	−1.68505
$25$	0	0
$26$	−0.209361	−0.0410590
$27$	4.21310	0.810811
$28$	−1.75769	−0.332173
$29$	−6.52025	−1.21078	−0.605390	−	0.795929i	$-0.706983\pi$
$29$	−6.52025	−1.21078	−0.605390	+	0.795929i	$0.706983\pi$
$30$	0	0
$31$	7.75270	1.39243	0.696213	−	0.717835i	$-0.254867\pi$
$31$	7.75270	1.39243	0.696213	+	0.717835i	$0.254867\pi$
$32$	4.94671	0.874462
$33$	−15.1037	−2.62922
$34$	−5.62267	−0.964280
$35$	0	0
$36$	−4.46656	−0.744426
$37$	−3.26737	−0.537153	−0.268577	−	0.963258i	$-0.586553\pi$
$37$	−3.26737	−0.537153	−0.268577	+	0.963258i	$0.586553\pi$
$38$	1.06331	0.172491
$39$	−0.570410	−0.0913386
$40$	0	0
$41$	5.02548	0.784848	0.392424	−	0.919784i	$-0.371637\pi$
$41$	5.02548	0.784848	0.392424	+	0.919784i	$0.371637\pi$
$42$	4.93532	0.761537
$43$	10.9987	1.67729	0.838644	−	0.544680i	$-0.183349\pi$
$43$	10.9987	1.67729	0.838644	+	0.544680i	$0.183349\pi$
$44$	5.41948	0.817017
$45$	0	0
$46$	−5.71217	−0.842213
$47$	−7.57472	−1.10489	−0.552443	−	0.833551i	$-0.686304\pi$
$47$	−7.57472	−1.10489	−0.552443	+	0.833551i	$0.686304\pi$
$48$	−2.90969	−0.419977
$49$	−3.81532	−0.545046
$50$	0	0
$51$	−15.3191	−2.14511
$52$	0.204673	0.0283830
$53$	−9.19155	−1.26256	−0.631278	−	0.775557i	$-0.717469\pi$
$53$	−9.19155	−1.26256	−0.631278	+	0.775557i	$0.717469\pi$
$54$	4.24470	0.577631
$55$	0	0
$56$	−5.36678	−0.717167
$57$	2.89701	0.383719
$58$	−6.56916	−0.862573
$59$	0.353669	0.0460438	0.0230219	−	0.999735i	$-0.492671\pi$
$59$	0.353669	0.0460438	0.0230219	+	0.999735i	$0.492671\pi$
$60$	0	0
$61$	−2.42137	−0.310025	−0.155012	−	0.987913i	$-0.549542\pi$
$61$	−2.42137	−0.310025	−0.155012	+	0.987913i	$0.549542\pi$
$62$	7.81086	0.991980
$63$	8.09273	1.01959
$64$	7.10383	0.887978
$65$	0	0
$66$	−15.2170	−1.87309
$67$	2.81825	0.344304	0.172152	−	0.985070i	$-0.444928\pi$
$67$	2.81825	0.344304	0.172152	+	0.985070i	$0.444928\pi$
$68$	5.49677	0.666581
$69$	−15.5630	−1.87356
$70$	0	0
$71$	−11.3297	−1.34458	−0.672292	−	0.740286i	$-0.734690\pi$
$71$	−11.3297	−1.34458	−0.672292	+	0.740286i	$0.734690\pi$
$72$	−13.6378	−1.60723
$73$	−12.8426	−1.50311	−0.751557	−	0.659669i	$-0.770697\pi$
$73$	−12.8426	−1.50311	−0.751557	+	0.659669i	$0.770697\pi$
$74$	−3.29188	−0.382674
$75$	0	0
$76$	−1.03950	−0.119239
$77$	−9.81928	−1.11901
$78$	−0.574688	−0.0650706
$79$	−12.9021	−1.45160	−0.725802	−	0.687903i	$-0.758531\pi$
$79$	−12.9021	−1.45160	−0.725802	+	0.687903i	$0.758531\pi$
$80$	0	0
$81$	−2.03972	−0.226635
$82$	5.06318	0.559135
$83$	16.8314	1.84748	0.923741	−	0.383017i	$-0.125115\pi$
$83$	16.8314	1.84748	0.923741	+	0.383017i	$0.125115\pi$
$84$	−4.82481	−0.526430
$85$	0	0
$86$	11.0812	1.19492
$87$	−17.8979	−1.91885
$88$	16.5473	1.76395
$89$	−6.49446	−0.688412	−0.344206	−	0.938894i	$-0.611852\pi$
$89$	−6.49446	−0.688412	−0.344206	+	0.938894i	$0.611852\pi$
$90$	0	0
$91$	−0.370837	−0.0388742
$92$	5.58426	0.582199
$93$	21.2809	2.20673
$94$	−7.63154	−0.787133
$95$	0	0
$96$	13.5785	1.38585
$97$	−12.2649	−1.24531	−0.622654	−	0.782497i	$-0.713946\pi$
$97$	−12.2649	−1.24531	−0.622654	+	0.782497i	$0.713946\pi$
$98$	−3.84394	−0.388297
$99$	−24.9522	−2.50779
$100$	0	0
$101$	−8.19946	−0.815876	−0.407938	−	0.913010i	$-0.633752\pi$
$101$	−8.19946	−0.815876	−0.407938	+	0.913010i	$0.633752\pi$
$102$	−15.4340	−1.52820
$103$	15.6245	1.53953	0.769764	−	0.638328i	$-0.220374\pi$
$103$	15.6245	1.53953	0.769764	+	0.638328i	$0.220374\pi$
$104$	0.624930	0.0612794
$105$	0	0
$106$	−9.26049	−0.899459
$107$	−15.8920	−1.53633	−0.768167	−	0.640250i	$-0.778831\pi$
$107$	−15.8920	−1.53633	−0.768167	+	0.640250i	$0.778831\pi$
$108$	−4.14966	−0.399301
$109$	−6.84872	−0.655988	−0.327994	−	0.944680i	$-0.606373\pi$
$109$	−6.84872	−0.655988	−0.327994	+	0.944680i	$0.606373\pi$
$110$	0	0
$111$	−8.96884	−0.851284
$112$	−1.89165	−0.178744
$113$	9.15941	0.861644	0.430822	−	0.902437i	$-0.358224\pi$
$113$	9.15941	0.861644	0.430822	+	0.902437i	$0.358224\pi$
$114$	2.91874	0.273365
$115$	0	0
$116$	6.42206	0.596274
$117$	−0.942350	−0.0871203
$118$	0.356322	0.0328021
$119$	−9.95932	−0.912970
$120$	0	0
$121$	19.2757	1.75233
$122$	−2.43953	−0.220865
$123$	13.7948	1.24383
$124$	−7.63596	−0.685730
$125$	0	0
$126$	8.15344	0.726366
$127$	−1.00836	−0.0894774	−0.0447387	−	0.998999i	$-0.514246\pi$
$127$	−1.00836	−0.0894774	−0.0447387	+	0.998999i	$0.514246\pi$
$128$	−2.73630	−0.241857
$129$	30.1911	2.65818
$130$	0	0
$131$	2.44839	0.213917	0.106959	−	0.994263i	$-0.465889\pi$
$131$	2.44839	0.213917	0.106959	+	0.994263i	$0.465889\pi$
$132$	14.8763	1.29481
$133$	1.88341	0.163313
$134$	2.83939	0.245286
$135$	0	0
$136$	16.7833	1.43916
$137$	−18.1980	−1.55476	−0.777378	−	0.629033i	$-0.783451\pi$
$137$	−18.1980	−1.55476	−0.777378	+	0.629033i	$0.783451\pi$
$138$	−15.6797	−1.33475
$139$	10.8048	0.916452	0.458226	−	0.888836i	$-0.348485\pi$
$139$	10.8048	0.916452	0.458226	+	0.888836i	$0.348485\pi$
$140$	0	0
$141$	−20.7924	−1.75103
$142$	−11.4147	−0.957897
$143$	1.14340	0.0956156
$144$	−4.80697	−0.400581
$145$	0	0
$146$	−12.9389	−1.07083
$147$	−10.4729	−0.863793
$148$	3.21817	0.264532
$149$	6.24778	0.511838	0.255919	−	0.966698i	$-0.417622\pi$
$149$	6.24778	0.511838	0.255919	+	0.966698i	$0.417622\pi$
$150$	0	0
$151$	15.3771	1.25137	0.625686	−	0.780075i	$-0.284819\pi$
$151$	15.3771	1.25137	0.625686	+	0.780075i	$0.284819\pi$
$152$	−3.17391	−0.257438
$153$	−25.3081	−2.04604
$154$	−9.89294	−0.797196
$155$	0	0
$156$	0.561820	0.0449816
$157$	8.45489	0.674774	0.337387	−	0.941366i	$-0.390457\pi$
$157$	8.45489	0.674774	0.337387	+	0.941366i	$0.390457\pi$
$158$	−12.9989	−1.03414
$159$	−25.2305	−2.00091
$160$	0	0
$161$	−10.1178	−0.797398
$162$	−2.05502	−0.161457
$163$	22.7243	1.77991	0.889953	−	0.456052i	$-0.150737\pi$
$163$	22.7243	1.77991	0.889953	+	0.456052i	$0.150737\pi$
$164$	−4.94981	−0.386515
$165$	0	0
$166$	16.9576	1.31617
$167$	14.0204	1.08493	0.542464	−	0.840079i	$-0.317491\pi$
$167$	14.0204	1.08493	0.542464	+	0.840079i	$0.317491\pi$
$168$	−14.7316	−1.13657
$169$	−12.9568	−0.996678
$170$	0	0
$171$	4.78603	0.365997
$172$	−10.8331	−0.826015
$173$	−19.1163	−1.45339	−0.726694	−	0.686962i	$-0.758944\pi$
$173$	−19.1163	−1.45339	−0.726694	+	0.686962i	$0.758944\pi$
$174$	−18.0321	−1.36701
$175$	0	0
$176$	5.83251	0.439642
$177$	0.970810	0.0729706
$178$	−6.54318	−0.490432
$179$	14.4267	1.07830	0.539150	−	0.842210i	$-0.318745\pi$
$179$	14.4267	1.07830	0.539150	+	0.842210i	$0.318745\pi$
$180$	0	0
$181$	0.321572	0.0239023	0.0119511	−	0.999929i	$-0.496196\pi$
$181$	0.321572	0.0239023	0.0119511	+	0.999929i	$0.496196\pi$
$182$	−0.373618	−0.0276944
$183$	−6.64658	−0.491329
$184$	17.0505	1.25698
$185$	0	0
$186$	21.4406	1.57210
$187$	30.7075	2.24555
$188$	7.46066	0.544124
$189$	7.51856	0.546895
$190$	0	0
$191$	11.8364	0.856455	0.428227	−	0.903671i	$-0.359138\pi$
$191$	11.8364	0.856455	0.428227	+	0.903671i	$0.359138\pi$
$192$	19.4998	1.40727
$193$	17.9696	1.29348	0.646739	−	0.762711i	$-0.276132\pi$
$193$	17.9696	1.29348	0.646739	+	0.762711i	$0.276132\pi$
$194$	−12.3569	−0.887171
$195$	0	0
$196$	3.75787	0.268419
$197$	−17.8489	−1.27168	−0.635840	−	0.771821i	$-0.719346\pi$
$197$	−17.8489	−1.27168	−0.635840	+	0.771821i	$0.719346\pi$
$198$	−25.1394	−1.78658
$199$	−3.39562	−0.240709	−0.120355	−	0.992731i	$-0.538403\pi$
$199$	−3.39562	−0.240709	−0.120355	+	0.992731i	$0.538403\pi$
$200$	0	0
$201$	7.73601	0.545656
$202$	−8.26096	−0.581239
$203$	−11.6358	−0.816675
$204$	15.0884	1.05640
$205$	0	0
$206$	15.7417	1.09678
$207$	−25.7109	−1.78703
$208$	0.220272	0.0152731
$209$	−5.80711	−0.401686
$210$	0	0
$211$	1.26930	0.0873820	0.0436910	−	0.999045i	$-0.486088\pi$
$211$	1.26930	0.0873820	0.0436910	+	0.999045i	$0.486088\pi$
$212$	9.05313	0.621772
$213$	−31.0996	−2.13091
$214$	−16.0112	−1.09450
$215$	0	0
$216$	−12.6702	−0.862097
$217$	13.8352	0.939196
$218$	−6.90009	−0.467333
$219$	−35.2525	−2.38215
$220$	0	0
$221$	1.15970	0.0780101
$222$	−9.03611	−0.606464
$223$	18.3847	1.23113	0.615565	−	0.788086i	$-0.288928\pi$
$223$	18.3847	1.23113	0.615565	+	0.788086i	$0.288928\pi$
$224$	8.82773	0.589827
$225$	0	0
$226$	9.22811	0.613845
$227$	−1.04449	−0.0693251	−0.0346625	−	0.999399i	$-0.511036\pi$
$227$	−1.04449	−0.0693251	−0.0346625	+	0.999399i	$0.511036\pi$
$228$	−2.85339	−0.188970
$229$	−7.30721	−0.482874	−0.241437	−	0.970416i	$-0.577619\pi$
$229$	−7.30721	−0.482874	−0.241437	+	0.970416i	$0.577619\pi$
$230$	0	0
$231$	−26.9536	−1.77342
$232$	19.6086	1.28736
$233$	−19.9317	−1.30577	−0.652886	−	0.757456i	$-0.726442\pi$
$233$	−19.9317	−1.30577	−0.652886	+	0.757456i	$0.726442\pi$
$234$	−0.949418	−0.0620654
$235$	0	0
$236$	−0.348343	−0.0226752
$237$	−35.4160	−2.30051
$238$	−10.0340	−0.650410
$239$	6.22563	0.402702	0.201351	−	0.979519i	$-0.435467\pi$
$239$	6.22563	0.402702	0.201351	+	0.979519i	$0.435467\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	19.4203	1.24838
$243$	−18.2383	−1.16998
$244$	2.38491	0.152678
$245$	0	0
$246$	13.8983	0.886121
$247$	−0.219312	−0.0139545
$248$	−23.3150	−1.48050
$249$	46.2016	2.92790
$250$	0	0
$251$	−6.50832	−0.410801	−0.205401	−	0.978678i	$-0.565850\pi$
$251$	−6.50832	−0.410801	−0.205401	+	0.978678i	$0.565850\pi$
$252$	−7.97087	−0.502118
$253$	31.1962	1.96129
$254$	−1.01592	−0.0637446
$255$	0	0
$256$	−16.9645	−1.06028
$257$	17.6646	1.10189	0.550943	−	0.834543i	$-0.314268\pi$
$257$	17.6646	1.10189	0.550943	+	0.834543i	$0.314268\pi$
$258$	30.4176	1.89372
$259$	−5.83085	−0.362311
$260$	0	0
$261$	−29.5683	−1.83023
$262$	2.46676	0.152397
$263$	10.7867	0.665137	0.332569	−	0.943079i	$-0.392085\pi$
$263$	10.7867	0.665137	0.332569	+	0.943079i	$0.392085\pi$
$264$	45.4219	2.79553
$265$	0	0
$266$	1.89754	0.116346
$267$	−17.8271	−1.09100
$268$	−2.77581	−0.169560
$269$	−5.76469	−0.351480	−0.175740	−	0.984437i	$-0.556232\pi$
$269$	−5.76469	−0.351480	−0.175740	+	0.984437i	$0.556232\pi$
$270$	0	0
$271$	−20.0234	−1.21633	−0.608166	−	0.793810i	$-0.708095\pi$
$271$	−20.0234	−1.21633	−0.608166	+	0.793810i	$0.708095\pi$
$272$	5.91570	0.358692
$273$	−1.01793	−0.0616082
$274$	−18.3345	−1.10763
$275$	0	0
$276$	15.3286	0.922674
$277$	7.27224	0.436947	0.218473	−	0.975843i	$-0.429892\pi$
$277$	7.27224	0.436947	0.218473	+	0.975843i	$0.429892\pi$
$278$	10.8859	0.652890
$279$	35.1573	2.10481
$280$	0	0
$281$	23.8433	1.42237	0.711185	−	0.703005i	$-0.248159\pi$
$281$	23.8433	1.42237	0.711185	+	0.703005i	$0.248159\pi$
$282$	−20.9483	−1.24745
$283$	−13.9561	−0.829603	−0.414801	−	0.909912i	$-0.636149\pi$
$283$	−13.9561	−0.829603	−0.414801	+	0.909912i	$0.636149\pi$
$284$	11.1591	0.662168
$285$	0	0
$286$	1.15197	0.0681176
$287$	8.96831	0.529383
$288$	22.4325	1.32185
$289$	14.1454	0.832083
$290$	0	0
$291$	−33.6667	−1.97357
$292$	12.6492	0.740239
$293$	26.8405	1.56804	0.784020	−	0.620735i	$-0.213166\pi$
$293$	26.8405	1.56804	0.784020	+	0.620735i	$0.213166\pi$
$294$	−10.5515	−0.615375
$295$	0	0
$296$	9.82608	0.571129
$297$	−23.1819	−1.34515
$298$	6.29464	0.364639
$299$	1.17816	0.0681349
$300$	0	0
$301$	19.6279	1.13134
$302$	15.4925	0.891492
$303$	−22.5072	−1.29301
$304$	−1.11872	−0.0641631
$305$	0	0
$306$	−25.4979	−1.45762
$307$	9.74369	0.556102	0.278051	−	0.960566i	$-0.410312\pi$
$307$	9.74369	0.556102	0.278051	+	0.960566i	$0.410312\pi$
$308$	9.67142	0.551080
$309$	42.8888	2.43986
$310$	0	0
$311$	14.0249	0.795281	0.397640	−	0.917541i	$-0.369829\pi$
$311$	14.0249	0.795281	0.397640	+	0.917541i	$0.369829\pi$
$312$	1.71541	0.0971160
$313$	18.0827	1.02209	0.511047	−	0.859553i	$-0.329258\pi$
$313$	18.0827	1.02209	0.511047	+	0.859553i	$0.329258\pi$
$314$	8.51831	0.480716
$315$	0	0
$316$	12.7079	0.714873
$317$	−4.68864	−0.263340	−0.131670	−	0.991294i	$-0.542034\pi$
$317$	−4.68864	−0.263340	−0.131670	+	0.991294i	$0.542034\pi$
$318$	−25.4197	−1.42547
$319$	35.8766	2.00870
$320$	0	0
$321$	−43.6229	−2.43479
$322$	−10.1937	−0.568075
$323$	−5.88993	−0.327724
$324$	2.00900	0.111611
$325$	0	0
$326$	22.8948	1.26802
$327$	−18.7995	−1.03962
$328$	−15.1133	−0.834492
$329$	−13.5176	−0.745249
$330$	0	0
$331$	−4.32580	−0.237768	−0.118884	−	0.992908i	$-0.537932\pi$
$331$	−4.32580	−0.237768	−0.118884	+	0.992908i	$0.537932\pi$
$332$	−16.5779	−0.909831
$333$	−14.8170	−0.811969
$334$	14.1255	0.772915
$335$	0	0
$336$	−5.19253	−0.283276
$337$	−11.2184	−0.611107	−0.305553	−	0.952175i	$-0.598841\pi$
$337$	−11.2184	−0.611107	−0.305553	+	0.952175i	$0.598841\pi$
$338$	−13.0540	−0.710044
$339$	25.1423	1.36554
$340$	0	0
$341$	−42.6580	−2.31006
$342$	4.82193	0.260740
$343$	−19.3007	−1.04214
$344$	−33.0768	−1.78338
$345$	0	0
$346$	−19.2597	−1.03541
$347$	1.15130	0.0618052	0.0309026	−	0.999522i	$-0.490162\pi$
$347$	1.15130	0.0618052	0.0309026	+	0.999522i	$0.490162\pi$
$348$	17.6284	0.944979
$349$	−18.9911	−1.01657	−0.508284	−	0.861189i	$-0.669720\pi$
$349$	−18.9911	−1.01657	−0.508284	+	0.861189i	$0.669720\pi$
$350$	0	0
$351$	−0.875490	−0.0467302
$352$	−27.2184	−1.45075
$353$	−4.40157	−0.234272	−0.117136	−	0.993116i	$-0.537371\pi$
$353$	−4.40157	−0.234272	−0.117136	+	0.993116i	$0.537371\pi$
$354$	0.978092	0.0519850
$355$	0	0
$356$	6.39667	0.339023
$357$	−27.3380	−1.44688
$358$	14.5349	0.768193
$359$	−31.4767	−1.66128	−0.830638	−	0.556813i	$-0.812024\pi$
$359$	−31.4767	−1.66128	−0.830638	+	0.556813i	$0.812024\pi$
$360$	0	0
$361$	−17.8862	−0.941376
$362$	0.323984	0.0170282
$363$	52.9111	2.77711
$364$	0.365252	0.0191444
$365$	0	0
$366$	−6.69644	−0.350028
$367$	17.6258	0.920061	0.460030	−	0.887903i	$-0.347839\pi$
$367$	17.6258	0.920061	0.460030	+	0.887903i	$0.347839\pi$
$368$	6.00986	0.313285
$369$	22.7898	1.18639
$370$	0	0
$371$	−16.4029	−0.851598
$372$	−20.9605	−1.08675
$373$	11.3860	0.589544	0.294772	−	0.955568i	$-0.404756\pi$
$373$	11.3860	0.589544	0.294772	+	0.955568i	$0.404756\pi$
$374$	30.9378	1.59976
$375$	0	0
$376$	22.7797	1.17477
$377$	1.35492	0.0697820
$378$	7.57495	0.389614
$379$	−18.9612	−0.973970	−0.486985	−	0.873410i	$-0.661903\pi$
$379$	−18.9612	−0.973970	−0.486985	+	0.873410i	$0.661903\pi$
$380$	0	0
$381$	−2.76791	−0.141804
$382$	11.9252	0.610148
$383$	21.6188	1.10467	0.552335	−	0.833622i	$-0.313737\pi$
$383$	21.6188	1.10467	0.552335	+	0.833622i	$0.313737\pi$
$384$	−7.51105	−0.383297
$385$	0	0
$386$	18.1044	0.921488
$387$	49.8775	2.53541
$388$	12.0802	0.613278
$389$	3.71646	0.188432	0.0942159	−	0.995552i	$-0.469966\pi$
$389$	3.71646	0.188432	0.0942159	+	0.995552i	$0.469966\pi$
$390$	0	0
$391$	31.6412	1.60016
$392$	11.4739	0.579521
$393$	6.72076	0.339017
$394$	−17.9828	−0.905959
$395$	0	0
$396$	24.5765	1.23501
$397$	−11.1817	−0.561192	−0.280596	−	0.959826i	$-0.590532\pi$
$397$	−11.1817	−0.561192	−0.280596	+	0.959826i	$0.590532\pi$
$398$	−3.42110	−0.171484
$399$	5.16991	0.258819
$400$	0	0
$401$	−8.77313	−0.438109	−0.219055	−	0.975713i	$-0.570297\pi$
$401$	−8.77313	−0.438109	−0.219055	+	0.975713i	$0.570297\pi$
$402$	7.79404	0.388731
$403$	−1.61103	−0.0802510
$404$	8.07598	0.401795
$405$	0	0
$406$	−11.7231	−0.581808
$407$	17.9782	0.891146
$408$	46.0697	2.28079
$409$	−25.1190	−1.24205	−0.621027	−	0.783790i	$-0.713284\pi$
$409$	−25.1190	−1.24205	−0.621027	+	0.783790i	$0.713284\pi$
$410$	0	0
$411$	−49.9528	−2.46399
$412$	−15.3892	−0.758173
$413$	0.631146	0.0310567
$414$	−25.9038	−1.27310
$415$	0	0
$416$	−1.02794	−0.0503987
$417$	29.6588	1.45240
$418$	−5.85067	−0.286166
$419$	0.733694	0.0358433	0.0179217	−	0.999839i	$-0.494295\pi$
$419$	0.733694	0.0358433	0.0179217	+	0.999839i	$0.494295\pi$
$420$	0	0
$421$	25.4810	1.24187	0.620934	−	0.783863i	$-0.286753\pi$
$421$	25.4810	1.24187	0.620934	+	0.783863i	$0.286753\pi$
$422$	1.27882	0.0622519
$423$	−34.3502	−1.67016
$424$	27.6420	1.34242
$425$	0	0
$426$	−31.3329	−1.51808
$427$	−4.32110	−0.209113
$428$	15.6526	0.756599
$429$	3.13858	0.151532
$430$	0	0
$431$	15.1415	0.729339	0.364670	−	0.931137i	$-0.381182\pi$
$431$	15.1415	0.729339	0.364670	+	0.931137i	$0.381182\pi$
$432$	−4.46592	−0.214866
$433$	22.4813	1.08038	0.540192	−	0.841542i	$-0.318352\pi$
$433$	22.4813	1.08038	0.540192	+	0.841542i	$0.318352\pi$
$434$	13.9390	0.669093
$435$	0	0
$436$	6.74559	0.323055
$437$	−5.98368	−0.286238
$438$	−35.5170	−1.69707
$439$	−37.6335	−1.79615	−0.898074	−	0.439844i	$-0.855034\pi$
$439$	−37.6335	−1.79615	−0.898074	+	0.439844i	$0.855034\pi$
$440$	0	0
$441$	−17.3019	−0.823899
$442$	1.16840	0.0555752
$443$	−34.3378	−1.63144	−0.815719	−	0.578449i	$-0.803658\pi$
$443$	−34.3378	−1.63144	−0.815719	+	0.578449i	$0.803658\pi$
$444$	8.83378	0.419233
$445$	0	0
$446$	18.5226	0.877070
$447$	17.1499	0.811165
$448$	12.6773	0.598944
$449$	−34.0031	−1.60470	−0.802352	−	0.596851i	$-0.796418\pi$
$449$	−34.0031	−1.60470	−0.802352	+	0.596851i	$0.796418\pi$
$450$	0	0
$451$	−27.6519	−1.30208
$452$	−9.02148	−0.424335
$453$	42.2097	1.98318
$454$	−1.05232	−0.0493879
$455$	0	0
$456$	−8.71227	−0.407990
$457$	24.6811	1.15453	0.577267	−	0.816555i	$-0.304119\pi$
$457$	24.6811	1.15453	0.577267	+	0.816555i	$0.304119\pi$
$458$	−7.36202	−0.344005
$459$	−23.5125	−1.09747
$460$	0	0
$461$	−2.45386	−0.114288	−0.0571438	−	0.998366i	$-0.518199\pi$
$461$	−2.45386	−0.114288	−0.0571438	+	0.998366i	$0.518199\pi$
$462$	−27.1558	−1.26340
$463$	11.1415	0.517791	0.258896	−	0.965905i	$-0.416641\pi$
$463$	11.1415	0.517791	0.258896	+	0.965905i	$0.416641\pi$
$464$	6.91151	0.320859
$465$	0	0
$466$	−20.0813	−0.930246
$467$	−8.87020	−0.410464	−0.205232	−	0.978713i	$-0.565795\pi$
$467$	−8.87020	−0.410464	−0.205232	+	0.978713i	$0.565795\pi$
$468$	0.928159	0.0429042
$469$	5.02936	0.232234
$470$	0	0
$471$	23.2084	1.06939
$472$	−1.06360	−0.0489562
$473$	−60.5186	−2.78265
$474$	−35.6816	−1.63891
$475$	0	0
$476$	9.80935	0.449611
$477$	−41.6822	−1.90850
$478$	6.27233	0.286890
$479$	−9.65558	−0.441175	−0.220587	−	0.975367i	$-0.570797\pi$
$479$	−9.65558	−0.441175	−0.220587	+	0.975367i	$0.570797\pi$
$480$	0	0
$481$	0.678967	0.0309582
$482$	−1.00750	−0.0458904
$483$	−27.7732	−1.26372
$484$	−18.9854	−0.862973
$485$	0	0
$486$	−18.3751	−0.833510
$487$	−32.3335	−1.46517	−0.732585	−	0.680675i	$-0.761686\pi$
$487$	−32.3335	−1.46517	−0.732585	+	0.680675i	$0.761686\pi$
$488$	7.28186	0.329634
$489$	62.3775	2.82081
$490$	0	0
$491$	3.06284	0.138224	0.0691121	−	0.997609i	$-0.477983\pi$
$491$	3.06284	0.138224	0.0691121	+	0.997609i	$0.477983\pi$
$492$	−13.5871	−0.612552
$493$	36.3883	1.63884
$494$	−0.220957	−0.00994134
$495$	0	0
$496$	−8.21792	−0.368996
$497$	−20.2186	−0.906926
$498$	46.5481	2.08587
$499$	1.17053	0.0524002	0.0262001	−	0.999657i	$-0.491659\pi$
$499$	1.17053	0.0524002	0.0262001	+	0.999657i	$0.491659\pi$
$500$	0	0
$501$	38.4855	1.71940
$502$	−6.55714	−0.292659
$503$	0.0532019	0.00237215	0.00118608	−	0.999999i	$-0.499622\pi$
$503$	0.0532019	0.00237215	0.00118608	+	0.999999i	$0.499622\pi$
$504$	−24.3375	−1.08408
$505$	0	0
$506$	31.4302	1.39724
$507$	−35.5660	−1.57954
$508$	0.993174	0.0440650
$509$	15.7788	0.699385	0.349693	−	0.936865i	$-0.386286\pi$
$509$	15.7788	0.699385	0.349693	+	0.936865i	$0.386286\pi$
$510$	0	0
$511$	−22.9185	−1.01385
$512$	−11.6191	−0.513498
$513$	4.44646	0.196316
$514$	17.7971	0.784995
$515$	0	0
$516$	−29.7365	−1.30908
$517$	41.6786	1.83302
$518$	−5.87459	−0.258115
$519$	−52.4737	−2.30334
$520$	0	0
$521$	−29.7955	−1.30537	−0.652683	−	0.757631i	$-0.726357\pi$
$521$	−29.7955	−1.30537	−0.652683	+	0.757631i	$0.726357\pi$
$522$	−29.7901	−1.30388
$523$	−13.1381	−0.574489	−0.287244	−	0.957857i	$-0.592739\pi$
$523$	−13.1381	−0.574489	−0.287244	+	0.957857i	$0.592739\pi$
$524$	−2.41152	−0.105348
$525$	0	0
$526$	10.8676	0.473851
$527$	−43.2664	−1.88471
$528$	16.0101	0.696748
$529$	9.14479	0.397600
$530$	0	0
$531$	1.60383	0.0696005
$532$	−1.85505	−0.0804267
$533$	−1.04431	−0.0452339
$534$	−17.9608	−0.777240
$535$	0	0
$536$	−8.47542	−0.366082
$537$	39.6008	1.70890
$538$	−5.80794	−0.250398
$539$	20.9932	0.904240
$540$	0	0
$541$	−9.02109	−0.387847	−0.193924	−	0.981017i	$-0.562121\pi$
$541$	−9.02109	−0.387847	−0.193924	+	0.981017i	$0.562121\pi$
$542$	−20.1736	−0.866529
$543$	0.882704	0.0378805
$544$	−27.6066	−1.18362
$545$	0	0
$546$	−1.02557	−0.0438903
$547$	−20.1105	−0.859862	−0.429931	−	0.902862i	$-0.641462\pi$
$547$	−20.1105	−0.859862	−0.429931	+	0.902862i	$0.641462\pi$
$548$	17.9239	0.765672
$549$	−10.9805	−0.468638
$550$	0	0
$551$	−6.88141	−0.293158
$552$	46.8030	1.99207
$553$	−23.0247	−0.979112
$554$	7.32679	0.311286
$555$	0	0
$556$	−10.6421	−0.451326
$557$	6.75516	0.286226	0.143113	−	0.989706i	$-0.454289\pi$
$557$	6.75516	0.286226	0.143113	+	0.989706i	$0.454289\pi$
$558$	35.4210	1.49949
$559$	−2.28555	−0.0966686
$560$	0	0
$561$	84.2910	3.55877
$562$	24.0221	1.01331
$563$	−33.1728	−1.39807	−0.699033	−	0.715090i	$-0.746386\pi$
$563$	−33.1728	−1.39807	−0.699033	+	0.715090i	$0.746386\pi$
$564$	20.4793	0.862332
$565$	0	0
$566$	−14.0608	−0.591018
$567$	−3.64001	−0.152866
$568$	34.0721	1.42963
$569$	19.4186	0.814068	0.407034	−	0.913413i	$-0.366563\pi$
$569$	19.4186	0.814068	0.407034	+	0.913413i	$0.366563\pi$
$570$	0	0
$571$	−38.0112	−1.59072	−0.795360	−	0.606138i	$-0.792718\pi$
$571$	−38.0112	−1.59072	−0.795360	+	0.606138i	$0.792718\pi$
$572$	−1.12618	−0.0470879
$573$	32.4906	1.35732
$574$	9.03558	0.377138
$575$	0	0
$576$	32.2147	1.34228
$577$	39.8084	1.65724	0.828622	−	0.559808i	$-0.189125\pi$
$577$	39.8084	1.65724	0.828622	+	0.559808i	$0.189125\pi$
$578$	14.2515	0.592785
$579$	49.3259	2.04991
$580$	0	0
$581$	30.0367	1.24613
$582$	−33.9192	−1.40600
$583$	50.5749	2.09460
$584$	38.6220	1.59819
$585$	0	0
$586$	27.0419	1.11709
$587$	23.1379	0.955002	0.477501	−	0.878631i	$-0.341543\pi$
$587$	23.1379	0.955002	0.477501	+	0.878631i	$0.341543\pi$
$588$	10.3152	0.425393
$589$	8.18213	0.337139
$590$	0	0
$591$	−48.9946	−2.01537
$592$	3.46344	0.142347
$593$	−17.6299	−0.723974	−0.361987	−	0.932183i	$-0.617901\pi$
$593$	−17.6299	−0.723974	−0.361987	+	0.932183i	$0.617901\pi$
$594$	−23.3558	−0.958299
$595$	0	0
$596$	−6.15370	−0.252065
$597$	−9.32088	−0.381478
$598$	1.18700	0.0485400
$599$	8.46130	0.345719	0.172860	−	0.984946i	$-0.444699\pi$
$599$	8.46130	0.345719	0.172860	+	0.984946i	$0.444699\pi$
$600$	0	0
$601$	11.2936	0.460676	0.230338	−	0.973111i	$-0.426017\pi$
$601$	11.2936	0.460676	0.230338	+	0.973111i	$0.426017\pi$
$602$	19.7752	0.805976
$603$	12.7803	0.520456
$604$	−15.1456	−0.616264
$605$	0	0
$606$	−22.6761	−0.921152
$607$	3.75489	0.152406	0.0762031	−	0.997092i	$-0.475720\pi$
$607$	3.75489	0.152406	0.0762031	+	0.997092i	$0.475720\pi$
$608$	5.22070	0.211728
$609$	−31.9399	−1.29427
$610$	0	0
$611$	1.57404	0.0636789
$612$	24.9270	1.00761
$613$	−21.3730	−0.863248	−0.431624	−	0.902054i	$-0.642059\pi$
$613$	−21.3730	−0.863248	−0.431624	+	0.902054i	$0.642059\pi$
$614$	9.81678	0.396173
$615$	0	0
$616$	29.5298	1.18979
$617$	41.6036	1.67490	0.837449	−	0.546516i	$-0.184046\pi$
$617$	41.6036	1.67490	0.837449	+	0.546516i	$0.184046\pi$
$618$	43.2105	1.73818
$619$	−11.8359	−0.475725	−0.237863	−	0.971299i	$-0.576447\pi$
$619$	−11.8359	−0.475725	−0.237863	+	0.971299i	$0.576447\pi$
$620$	0	0
$621$	−23.8867	−0.958542
$622$	14.1301	0.566567
$623$	−11.5898	−0.464336
$624$	0.604638	0.0242049
$625$	0	0
$626$	18.2183	0.728151
$627$	−15.9403	−0.636595
$628$	−8.32758	−0.332306
$629$	18.2346	0.727061
$630$	0	0
$631$	30.1234	1.19919	0.599597	−	0.800302i	$-0.295327\pi$
$631$	30.1234	1.19919	0.599597	+	0.800302i	$0.295327\pi$
$632$	38.8010	1.54342
$633$	3.48418	0.138484
$634$	−4.72381	−0.187607
$635$	0	0
$636$	24.8506	0.985389
$637$	0.792831	0.0314131
$638$	36.1457	1.43102
$639$	−51.3783	−2.03249
$640$	0	0
$641$	−30.4372	−1.20220	−0.601098	−	0.799175i	$-0.705270\pi$
$641$	−30.4372	−1.20220	−0.601098	+	0.799175i	$0.705270\pi$
$642$	−43.9501	−1.73457
$643$	−33.0159	−1.30202	−0.651011	−	0.759068i	$-0.725655\pi$
$643$	−33.0159	−1.30202	−0.651011	+	0.759068i	$0.725655\pi$
$644$	9.96549	0.392695
$645$	0	0
$646$	−5.93411	−0.233474
$647$	37.3333	1.46772	0.733862	−	0.679299i	$-0.237716\pi$
$647$	37.3333	1.46772	0.733862	+	0.679299i	$0.237716\pi$
$648$	6.13410	0.240970
$649$	−1.94601	−0.0763874
$650$	0	0
$651$	37.9772	1.48844
$652$	−22.3821	−0.876552
$653$	−9.21724	−0.360699	−0.180349	−	0.983603i	$-0.557723\pi$
$653$	−9.21724	−0.360699	−0.180349	+	0.983603i	$0.557723\pi$
$654$	−18.9405	−0.740633
$655$	0	0
$656$	−5.32705	−0.207986
$657$	−58.2392	−2.27213
$658$	−13.6190	−0.530924
$659$	−7.40132	−0.288315	−0.144157	−	0.989555i	$-0.546047\pi$
$659$	−7.40132	−0.288315	−0.144157	+	0.989555i	$0.546047\pi$
$660$	0	0
$661$	−2.61372	−0.101662	−0.0508309	−	0.998707i	$-0.516187\pi$
$661$	−2.61372	−0.101662	−0.0508309	+	0.998707i	$0.516187\pi$
$662$	−4.35825	−0.169388
$663$	3.18335	0.123631
$664$	−50.6175	−1.96434
$665$	0	0
$666$	−14.9282	−0.578455
$667$	36.9675	1.43139
$668$	−13.8092	−0.534296
$669$	50.4654	1.95110
$670$	0	0
$671$	13.3232	0.514336
$672$	24.2318	0.934763
$673$	43.7488	1.68639	0.843195	−	0.537607i	$-0.180672\pi$
$673$	43.7488	1.68639	0.843195	+	0.537607i	$0.180672\pi$
$674$	−11.3026	−0.435359
$675$	0	0
$676$	12.7617	0.490835
$677$	6.14170	0.236045	0.118022	−	0.993011i	$-0.462345\pi$
$677$	6.14170	0.236045	0.118022	+	0.993011i	$0.462345\pi$
$678$	25.3309	0.972826
$679$	−21.8875	−0.839964
$680$	0	0
$681$	−2.86708	−0.109867
$682$	−42.9779	−1.64571
$683$	41.8008	1.59946	0.799732	−	0.600358i	$-0.204975\pi$
$683$	41.8008	1.59946	0.799732	+	0.600358i	$0.204975\pi$
$684$	−4.71396	−0.180243
$685$	0	0
$686$	−19.4454	−0.742430
$687$	−20.0581	−0.765262
$688$	−11.6587	−0.444484
$689$	1.91002	0.0727660
$690$	0	0
$691$	23.9577	0.911393	0.455697	−	0.890135i	$-0.349390\pi$
$691$	23.9577	0.911393	0.455697	+	0.890135i	$0.349390\pi$
$692$	18.8285	0.715751
$693$	−44.5289	−1.69151
$694$	1.15994	0.0440307
$695$	0	0
$696$	53.8248	2.04023
$697$	−28.0462	−1.06233
$698$	−19.1335	−0.724215
$699$	−54.7120	−2.06940
$700$	0	0
$701$	−14.7306	−0.556365	−0.278183	−	0.960528i	$-0.589732\pi$
$701$	−14.7306	−0.556365	−0.278183	+	0.960528i	$0.589732\pi$
$702$	−0.882058	−0.0332911
$703$	−3.44836	−0.130057
$704$	−39.0876	−1.47317
$705$	0	0
$706$	−4.43458	−0.166898
$707$	−14.6325	−0.550311
$708$	−0.956191	−0.0359359
$709$	0.389972	0.0146457	0.00732286	−	0.999973i	$-0.497669\pi$
$709$	0.389972	0.0146457	0.00732286	+	0.999973i	$0.497669\pi$
$710$	0	0
$711$	−58.5092	−2.19427
$712$	19.5310	0.731955
$713$	−43.9550	−1.64613
$714$	−27.5431	−1.03077
$715$	0	0
$716$	−14.2094	−0.531032
$717$	17.0891	0.638206
$718$	−31.7128	−1.18351
$719$	27.7168	1.03366	0.516831	−	0.856087i	$-0.327111\pi$
$719$	27.7168	1.03366	0.516831	+	0.856087i	$0.327111\pi$
$720$	0	0
$721$	27.8830	1.03842
$722$	−18.0203	−0.670647
$723$	−2.74497	−0.102086
$724$	−0.316730	−0.0117712
$725$	0	0
$726$	53.3080	1.97844
$727$	15.2729	0.566439	0.283220	−	0.959055i	$-0.408597\pi$
$727$	15.2729	0.566439	0.283220	+	0.959055i	$0.408597\pi$
$728$	1.11523	0.0413331
$729$	−43.9443	−1.62756
$730$	0	0
$731$	−61.3817	−2.27028
$732$	6.54649	0.241965
$733$	−12.2421	−0.452171	−0.226085	−	0.974107i	$-0.572593\pi$
$733$	−12.2421	−0.452171	−0.226085	+	0.974107i	$0.572593\pi$
$734$	17.7580	0.655461
$735$	0	0
$736$	−28.0460	−1.03379
$737$	−15.5070	−0.571206
$738$	22.9607	0.845196
$739$	32.3832	1.19124	0.595619	−	0.803267i	$-0.296907\pi$
$739$	32.3832	1.19124	0.595619	+	0.803267i	$0.296907\pi$
$740$	0	0
$741$	−0.602005	−0.0221152
$742$	−16.5260	−0.606687
$743$	51.9139	1.90454	0.952269	−	0.305261i	$-0.0987436\pi$
$743$	51.9139	1.90454	0.952269	+	0.305261i	$0.0987436\pi$
$744$	−63.9988	−2.34631
$745$	0	0
$746$	11.4714	0.419997
$747$	76.3277	2.79268
$748$	−30.2451	−1.10587
$749$	−28.3603	−1.03626
$750$	0	0
$751$	−13.6309	−0.497398	−0.248699	−	0.968581i	$-0.580003\pi$
$751$	−13.6309	−0.497398	−0.248699	+	0.968581i	$0.580003\pi$
$752$	8.02926	0.292797
$753$	−17.8651	−0.651041
$754$	1.36508	0.0497134
$755$	0	0
$756$	−7.40534	−0.269330
$757$	49.8016	1.81007	0.905035	−	0.425337i	$-0.139844\pi$
$757$	49.8016	1.81007	0.905035	+	0.425337i	$0.139844\pi$
$758$	−19.1034	−0.693867
$759$	85.6326	3.10827
$760$	0	0
$761$	32.4276	1.17550	0.587750	−	0.809043i	$-0.300014\pi$
$761$	32.4276	1.17550	0.587750	+	0.809043i	$0.300014\pi$
$762$	−2.78867	−0.101023
$763$	−12.2220	−0.442466
$764$	−11.6582	−0.421779
$765$	0	0
$766$	21.7810	0.786978
$767$	−0.0734931	−0.00265368
$768$	−46.5669	−1.68034
$769$	10.2097	0.368171	0.184086	−	0.982910i	$-0.441068\pi$
$769$	10.2097	0.368171	0.184086	+	0.982910i	$0.441068\pi$
$770$	0	0
$771$	48.4887	1.74628
$772$	−17.6990	−0.637000
$773$	8.61762	0.309954	0.154977	−	0.987918i	$-0.450470\pi$
$773$	8.61762	0.309954	0.154977	+	0.987918i	$0.450470\pi$
$774$	50.2516	1.80626
$775$	0	0
$776$	36.8845	1.32408
$777$	−16.0055	−0.574194
$778$	3.74433	0.134241
$779$	5.30384	0.190030
$780$	0	0
$781$	62.3396	2.23069
$782$	31.8785	1.13997
$783$	−27.4705	−0.981714
$784$	4.04427	0.144438
$785$	0	0
$786$	6.77117	0.241520
$787$	32.3988	1.15489	0.577447	−	0.816428i	$-0.304049\pi$
$787$	32.3988	1.15489	0.577447	+	0.816428i	$0.304049\pi$
$788$	17.5801	0.626265
$789$	29.6092	1.05411
$790$	0	0
$791$	16.3456	0.581182
$792$	75.0396	2.66642
$793$	0.503166	0.0178679
$794$	−11.2655	−0.399799
$795$	0	0
$796$	3.34449	0.118542
$797$	−17.3131	−0.613262	−0.306631	−	0.951829i	$-0.599202\pi$
$797$	−17.3131	−0.613262	−0.306631	+	0.951829i	$0.599202\pi$
$798$	5.20869	0.184386
$799$	42.2731	1.49551
$800$	0	0
$801$	−29.4514	−1.04061
$802$	−8.83894	−0.312114
$803$	70.6643	2.49369
$804$	−7.61952	−0.268720
$805$	0	0
$806$	−1.62311	−0.0571717
$807$	−15.8239	−0.557028
$808$	24.6585	0.867483
$809$	31.2502	1.09870	0.549350	−	0.835592i	$-0.314875\pi$
$809$	31.2502	1.09870	0.549350	+	0.835592i	$0.314875\pi$
$810$	0	0
$811$	−46.0831	−1.61820	−0.809098	−	0.587674i	$-0.800044\pi$
$811$	−46.0831	−1.61820	−0.809098	+	0.587674i	$0.800044\pi$
$812$	11.4606	0.402188
$813$	−54.9635	−1.92765
$814$	18.1130	0.634862
$815$	0	0
$816$	16.2384	0.568457
$817$	11.6079	0.406110
$818$	−25.3074	−0.884852
$819$	−1.68169	−0.0587629
$820$	0	0
$821$	−21.3041	−0.743519	−0.371760	−	0.928329i	$-0.621245\pi$
$821$	−21.3041	−0.743519	−0.371760	+	0.928329i	$0.621245\pi$
$822$	−50.3275	−1.75537
$823$	23.3806	0.814997	0.407499	−	0.913206i	$-0.366401\pi$
$823$	23.3806	0.814997	0.407499	+	0.913206i	$0.366401\pi$
$824$	−46.9881	−1.63691
$825$	0	0
$826$	0.635881	0.0221251
$827$	−12.6141	−0.438636	−0.219318	−	0.975653i	$-0.570383\pi$
$827$	−12.6141	−0.438636	−0.219318	+	0.975653i	$0.570383\pi$
$828$	25.3238	0.880061
$829$	−24.4708	−0.849905	−0.424953	−	0.905216i	$-0.639709\pi$
$829$	−24.4708	−0.849905	−0.424953	+	0.905216i	$0.639709\pi$
$830$	0	0
$831$	19.9621	0.692477
$832$	−1.47619	−0.0511776
$833$	21.2926	0.737744
$834$	29.8813	1.03471
$835$	0	0
$836$	5.71966	0.197819
$837$	32.6629	1.12900
$838$	0.739198	0.0255352
$839$	46.3804	1.60123	0.800614	−	0.599181i	$-0.204507\pi$
$839$	46.3804	1.60123	0.800614	+	0.599181i	$0.204507\pi$
$840$	0	0
$841$	13.5137	0.465988
$842$	25.6721	0.884721
$843$	65.4489	2.25418
$844$	−1.25018	−0.0430331
$845$	0	0
$846$	−34.6078	−1.18984
$847$	34.3987	1.18195
$848$	9.74311	0.334580
$849$	−38.3090	−1.31476
$850$	0	0
$851$	18.5248	0.635023
$852$	30.6313	1.04941
$853$	−34.5483	−1.18291	−0.591455	−	0.806338i	$-0.701446\pi$
$853$	−34.5483	−1.18291	−0.591455	+	0.806338i	$0.701446\pi$
$854$	−4.35351	−0.148974
$855$	0	0
$856$	47.7924	1.63351
$857$	26.9165	0.919449	0.459724	−	0.888062i	$-0.347948\pi$
$857$	26.9165	0.919449	0.459724	+	0.888062i	$0.347948\pi$
$858$	3.16213	0.107953
$859$	3.25152	0.110940	0.0554702	−	0.998460i	$-0.482334\pi$
$859$	3.25152	0.110940	0.0554702	+	0.998460i	$0.482334\pi$
$860$	0	0
$861$	24.6177	0.838969
$862$	15.2551	0.519589
$863$	−1.12241	−0.0382073	−0.0191036	−	0.999818i	$-0.506081\pi$
$863$	−1.12241	−0.0382073	−0.0191036	+	0.999818i	$0.506081\pi$
$864$	20.8410	0.709024
$865$	0	0
$866$	22.6500	0.769677
$867$	38.8287	1.31869
$868$	−13.6269	−0.462527
$869$	70.9919	2.40824
$870$	0	0
$871$	−0.585638	−0.0198436
$872$	20.5964	0.697481
$873$	−55.6193	−1.88243
$874$	−6.02856	−0.203919
$875$	0	0
$876$	34.7217	1.17314
$877$	−49.1997	−1.66136	−0.830678	−	0.556753i	$-0.812047\pi$
$877$	−49.1997	−1.66136	−0.830678	+	0.556753i	$0.812047\pi$
$878$	−37.9158	−1.27960
$879$	73.6764	2.48504
$880$	0	0
$881$	−26.4868	−0.892361	−0.446181	−	0.894943i	$-0.647216\pi$
$881$	−26.4868	−0.892361	−0.446181	+	0.894943i	$0.647216\pi$
$882$	−17.4317	−0.586955
$883$	−7.74946	−0.260790	−0.130395	−	0.991462i	$-0.541625\pi$
$883$	−7.74946	−0.260790	−0.130395	+	0.991462i	$0.541625\pi$
$884$	−1.14224	−0.0384177
$885$	0	0
$886$	−34.5954	−1.16225
$887$	−51.1505	−1.71747	−0.858733	−	0.512424i	$-0.828748\pi$
$887$	−51.1505	−1.71747	−0.858733	+	0.512424i	$0.828748\pi$
$888$	26.9723	0.905130
$889$	−1.79948	−0.0603527
$890$	0	0
$891$	11.2232	0.375991
$892$	−18.1078	−0.606295
$893$	−7.99429	−0.267519
$894$	17.2786	0.577882
$895$	0	0
$896$	−4.88311	−0.163133
$897$	3.23402	0.107981
$898$	−34.2581	−1.14321
$899$	−50.5496	−1.68592
$900$	0	0
$901$	51.2962	1.70893
$902$	−27.8593	−0.927613
$903$	53.8780	1.79295
$904$	−27.5454	−0.916145
$905$	0	0
$906$	42.5263	1.41284
$907$	17.0524	0.566214	0.283107	−	0.959088i	$-0.408635\pi$
$907$	17.0524	0.566214	0.283107	+	0.959088i	$0.408635\pi$
$908$	1.02876	0.0341406
$909$	−37.1833	−1.23329
$910$	0	0
$911$	−11.6362	−0.385525	−0.192763	−	0.981245i	$-0.561745\pi$
$911$	−11.6362	−0.385525	−0.192763	+	0.981245i	$0.561745\pi$
$912$	−3.07085	−0.101686
$913$	−92.6118	−3.06500
$914$	24.8663	0.822503
$915$	0	0
$916$	7.19717	0.237801
$917$	4.36932	0.144288
$918$	−23.6889	−0.781849
$919$	−43.8257	−1.44568	−0.722838	−	0.691018i	$-0.757163\pi$
$919$	−43.8257	−1.44568	−0.722838	+	0.691018i	$0.757163\pi$
$920$	0	0
$921$	26.7461	0.881314
$922$	−2.47227	−0.0814198
$923$	2.35433	0.0774936
$924$	26.5477	0.873356
$925$	0	0
$926$	11.2251	0.368880
$927$	70.8547	2.32717
$928$	−32.2538	−1.05878
$929$	48.2895	1.58433	0.792163	−	0.610309i	$-0.208955\pi$
$929$	48.2895	1.58433	0.792163	+	0.610309i	$0.208955\pi$
$930$	0	0
$931$	−4.02665	−0.131968
$932$	19.6316	0.643055
$933$	38.4980	1.26037
$934$	−8.93674	−0.292419
$935$	0	0
$936$	2.83396	0.0926308
$937$	−42.5736	−1.39082	−0.695409	−	0.718614i	$-0.744777\pi$
$937$	−42.5736	−1.39082	−0.695409	+	0.718614i	$0.744777\pi$
$938$	5.06709	0.165446
$939$	49.6364	1.61982
$940$	0	0
$941$	−5.74619	−0.187320	−0.0936602	−	0.995604i	$-0.529857\pi$
$941$	−5.74619	−0.187320	−0.0936602	+	0.995604i	$0.529857\pi$
$942$	23.3825	0.761843
$943$	−28.4927	−0.927849
$944$	−0.374892	−0.0122017
$945$	0	0
$946$	−60.9725	−1.98239
$947$	−18.4891	−0.600814	−0.300407	−	0.953811i	$-0.597122\pi$
$947$	−18.4891	−0.600814	−0.300407	+	0.953811i	$0.597122\pi$
$948$	34.8827	1.13294
$949$	2.66872	0.0866303
$950$	0	0
$951$	−12.8702	−0.417344
$952$	29.9510	0.970717
$953$	−2.92733	−0.0948256	−0.0474128	−	0.998875i	$-0.515098\pi$
$953$	−2.92733	−0.0948256	−0.0474128	+	0.998875i	$0.515098\pi$
$954$	−41.9949	−1.35963
$955$	0	0
$956$	−6.13188	−0.198319
$957$	98.4801	3.18341
$958$	−9.72801	−0.314298
$959$	−32.4755	−1.04869
$960$	0	0
$961$	29.1044	0.938853
$962$	0.684060	0.0220550
$963$	−72.0676	−2.32234
$964$	0.984941	0.0317228
$965$	0	0
$966$	−27.9815	−0.900290
$967$	−39.4409	−1.26833	−0.634167	−	0.773196i	$-0.718657\pi$
$967$	−39.4409	−1.26833	−0.634167	+	0.773196i	$0.718657\pi$
$968$	−57.9683	−1.86317
$969$	−16.1677	−0.519380
$970$	0	0
$971$	−39.7873	−1.27684	−0.638418	−	0.769690i	$-0.720411\pi$
$971$	−39.7873	−1.27684	−0.638418	+	0.769690i	$0.720411\pi$
$972$	17.9636	0.576183
$973$	19.2819	0.618149
$974$	−32.5760	−1.04380
$975$	0	0
$976$	2.56667	0.0821571
$977$	59.4591	1.90226	0.951132	−	0.308784i	$-0.0999219\pi$
$977$	59.4591	1.90226	0.951132	+	0.308784i	$0.0999219\pi$
$978$	62.8454	2.00957
$979$	35.7347	1.14209
$980$	0	0
$981$	−31.0579	−0.991602
$982$	3.08582	0.0984724
$983$	−17.4697	−0.557198	−0.278599	−	0.960407i	$-0.589870\pi$
$983$	−17.4697	−0.557198	−0.278599	+	0.960407i	$0.589870\pi$
$984$	−41.4855	−1.32251
$985$	0	0
$986$	36.6612	1.16753
$987$	−37.1054	−1.18108
$988$	0.216010	0.00687218
$989$	−62.3587	−1.98289
$990$	0	0
$991$	4.10723	0.130470	0.0652352	−	0.997870i	$-0.479220\pi$
$991$	4.10723	0.130470	0.0652352	+	0.997870i	$0.479220\pi$
$992$	38.3503	1.21762
$993$	−11.8742	−0.376816
$994$	−20.3702	−0.646104
$995$	0	0
$996$	−45.5058	−1.44191
$997$	3.91021	0.123837	0.0619187	−	0.998081i	$-0.480278\pi$
$997$	3.91021	0.123837	0.0619187	+	0.998081i	$0.480278\pi$
$998$	1.17931	0.0373304
$999$	−13.7658	−0.435530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.11		15
5.4	even	2		1205.2.a.c.1.5	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.5	✓	15	5.4	even	2
6025.2.a.i.1.11		15	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00750 q^{2} +2.74497 q^{3} -0.984941 q^{4} +2.76556 q^{6} +1.78457 q^{7} -3.00733 q^{8} +4.53484 q^{9} +O(q^{10})\)	\(q+1.00750 q^{2} +2.74497 q^{3} -0.984941 q^{4} +2.76556 q^{6} +1.78457 q^{7} -3.00733 q^{8} +4.53484 q^{9} -5.50233 q^{11} -2.70363 q^{12} -0.207802 q^{13} +1.79795 q^{14} -1.06001 q^{16} -5.58081 q^{17} +4.56886 q^{18} +1.05539 q^{19} +4.89858 q^{21} -5.54361 q^{22} -5.66964 q^{23} -8.25503 q^{24} -0.209361 q^{26} +4.21310 q^{27} -1.75769 q^{28} -6.52025 q^{29} +7.75270 q^{31} +4.94671 q^{32} -15.1037 q^{33} -5.62267 q^{34} -4.46656 q^{36} -3.26737 q^{37} +1.06331 q^{38} -0.570410 q^{39} +5.02548 q^{41} +4.93532 q^{42} +10.9987 q^{43} +5.41948 q^{44} -5.71217 q^{46} -7.57472 q^{47} -2.90969 q^{48} -3.81532 q^{49} -15.3191 q^{51} +0.204673 q^{52} -9.19155 q^{53} +4.24470 q^{54} -5.36678 q^{56} +2.89701 q^{57} -6.56916 q^{58} +0.353669 q^{59} -2.42137 q^{61} +7.81086 q^{62} +8.09273 q^{63} +7.10383 q^{64} -15.2170 q^{66} +2.81825 q^{67} +5.49677 q^{68} -15.5630 q^{69} -11.3297 q^{71} -13.6378 q^{72} -12.8426 q^{73} -3.29188 q^{74} -1.03950 q^{76} -9.81928 q^{77} -0.574688 q^{78} -12.9021 q^{79} -2.03972 q^{81} +5.06318 q^{82} +16.8314 q^{83} -4.82481 q^{84} +11.0812 q^{86} -17.8979 q^{87} +16.5473 q^{88} -6.49446 q^{89} -0.370837 q^{91} +5.58426 q^{92} +21.2809 q^{93} -7.63154 q^{94} +13.5785 q^{96} -12.2649 q^{97} -3.84394 q^{98} -24.9522 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

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