LMFDB - Embedded newform 6011.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76662 q^{2} +0.922557 q^{3} +5.65417 q^{4} +0.0715024 q^{5} -2.55236 q^{6} +5.08559 q^{7} -10.1097 q^{8} -2.14889 q^{9} +O(q^{10})$	\(q-2.76662 q^{2} +0.922557 q^{3} +5.65417 q^{4} +0.0715024 q^{5} -2.55236 q^{6} +5.08559 q^{7} -10.1097 q^{8} -2.14889 q^{9} -0.197820 q^{10} +3.43068 q^{11} +5.21629 q^{12} +1.42754 q^{13} -14.0699 q^{14} +0.0659650 q^{15} +16.6613 q^{16} -2.59756 q^{17} +5.94515 q^{18} +4.11852 q^{19} +0.404286 q^{20} +4.69175 q^{21} -9.49137 q^{22} -5.11986 q^{23} -9.32675 q^{24} -4.99489 q^{25} -3.94945 q^{26} -4.75014 q^{27} +28.7548 q^{28} -0.357853 q^{29} -0.182500 q^{30} +3.59851 q^{31} -25.8760 q^{32} +3.16500 q^{33} +7.18646 q^{34} +0.363632 q^{35} -12.1502 q^{36} +3.35904 q^{37} -11.3944 q^{38} +1.31699 q^{39} -0.722866 q^{40} +0.266990 q^{41} -12.9803 q^{42} -3.74629 q^{43} +19.3976 q^{44} -0.153651 q^{45} +14.1647 q^{46} -2.41792 q^{47} +15.3710 q^{48} +18.8632 q^{49} +13.8189 q^{50} -2.39640 q^{51} +8.07154 q^{52} +3.92849 q^{53} +13.1418 q^{54} +0.245302 q^{55} -51.4137 q^{56} +3.79957 q^{57} +0.990042 q^{58} +8.67788 q^{59} +0.372977 q^{60} +6.32331 q^{61} -9.95571 q^{62} -10.9284 q^{63} +38.2663 q^{64} +0.102072 q^{65} -8.75633 q^{66} -7.27108 q^{67} -14.6870 q^{68} -4.72336 q^{69} -1.00603 q^{70} -5.76170 q^{71} +21.7246 q^{72} -5.78816 q^{73} -9.29318 q^{74} -4.60807 q^{75} +23.2868 q^{76} +17.4470 q^{77} -3.64359 q^{78} +0.949801 q^{79} +1.19132 q^{80} +2.06439 q^{81} -0.738658 q^{82} -7.75787 q^{83} +26.5279 q^{84} -0.185732 q^{85} +10.3645 q^{86} -0.330140 q^{87} -34.6830 q^{88} +6.58467 q^{89} +0.425092 q^{90} +7.25988 q^{91} -28.9486 q^{92} +3.31983 q^{93} +6.68947 q^{94} +0.294484 q^{95} -23.8720 q^{96} +3.55282 q^{97} -52.1873 q^{98} -7.37215 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.76662	−1.95629	−0.978147	−	0.207916i	$-0.933332\pi$
$2$	−2.76662	−1.95629	−0.978147	+	0.207916i	$0.933332\pi$
$3$	0.922557	0.532638	0.266319	−	0.963885i	$-0.414192\pi$
$3$	0.922557	0.532638	0.266319	+	0.963885i	$0.414192\pi$
$4$	5.65417	2.82708
$5$	0.0715024	0.0319768	0.0159884	−	0.999872i	$-0.494911\pi$
$5$	0.0715024	0.0319768	0.0159884	+	0.999872i	$0.494911\pi$
$6$	−2.55236	−1.04200
$7$	5.08559	1.92217	0.961086	−	0.276248i	$-0.0890911\pi$
$7$	5.08559	1.92217	0.961086	+	0.276248i	$0.0890911\pi$
$8$	−10.1097	−3.57431
$9$	−2.14889	−0.716296
$10$	−0.197820	−0.0625561
$11$	3.43068	1.03439	0.517194	−	0.855868i	$-0.326976\pi$
$11$	3.43068	1.03439	0.517194	+	0.855868i	$0.326976\pi$
$12$	5.21629	1.50581
$13$	1.42754	0.395928	0.197964	−	0.980209i	$-0.436567\pi$
$13$	1.42754	0.395928	0.197964	+	0.980209i	$0.436567\pi$
$14$	−14.0699	−3.76033
$15$	0.0659650	0.0170321
$16$	16.6613	4.16532
$17$	−2.59756	−0.630001	−0.315001	−	0.949091i	$-0.602005\pi$
$17$	−2.59756	−0.630001	−0.315001	+	0.949091i	$0.602005\pi$
$18$	5.94515	1.40129
$19$	4.11852	0.944854	0.472427	−	0.881370i	$-0.343378\pi$
$19$	4.11852	0.944854	0.472427	+	0.881370i	$0.343378\pi$
$20$	0.404286	0.0904012
$21$	4.69175	1.02382
$22$	−9.49137	−2.02357
$23$	−5.11986	−1.06757	−0.533783	−	0.845622i	$-0.679230\pi$
$23$	−5.11986	−1.06757	−0.533783	+	0.845622i	$0.679230\pi$
$24$	−9.32675	−1.90381
$25$	−4.99489	−0.998977
$26$	−3.94945	−0.774551
$27$	−4.75014	−0.914165
$28$	28.7548	5.43414
$29$	−0.357853	−0.0664516	−0.0332258	−	0.999448i	$-0.510578\pi$
$29$	−0.357853	−0.0664516	−0.0332258	+	0.999448i	$0.510578\pi$
$30$	−0.182500	−0.0333198
$31$	3.59851	0.646312	0.323156	−	0.946346i	$-0.395256\pi$
$31$	3.59851	0.646312	0.323156	+	0.946346i	$0.395256\pi$
$32$	−25.8760	−4.57427
$33$	3.16500	0.550955
$34$	7.18646	1.23247
$35$	0.363632	0.0614650
$36$	−12.1502	−2.02503
$37$	3.35904	0.552223	0.276112	−	0.961126i	$-0.410954\pi$
$37$	3.35904	0.552223	0.276112	+	0.961126i	$0.410954\pi$
$38$	−11.3944	−1.84841
$39$	1.31699	0.210886
$40$	−0.722866	−0.114295
$41$	0.266990	0.0416968	0.0208484	−	0.999783i	$-0.493363\pi$
$41$	0.266990	0.0416968	0.0208484	+	0.999783i	$0.493363\pi$
$42$	−12.9803	−2.00290
$43$	−3.74629	−0.571303	−0.285652	−	0.958334i	$-0.592210\pi$
$43$	−3.74629	−0.571303	−0.285652	+	0.958334i	$0.592210\pi$
$44$	19.3976	2.92430
$45$	−0.153651	−0.0229049
$46$	14.1647	2.08847
$47$	−2.41792	−0.352690	−0.176345	−	0.984328i	$-0.556428\pi$
$47$	−2.41792	−0.352690	−0.176345	+	0.984328i	$0.556428\pi$
$48$	15.3710	2.21861
$49$	18.8632	2.69475
$50$	13.8189	1.95429
$51$	−2.39640	−0.335563
$52$	8.07154	1.11932
$53$	3.92849	0.539620	0.269810	−	0.962914i	$-0.413039\pi$
$53$	3.92849	0.539620	0.269810	+	0.962914i	$0.413039\pi$
$54$	13.1418	1.78838
$55$	0.245302	0.0330765
$56$	−51.4137	−6.87044
$57$	3.79957	0.503265
$58$	0.990042	0.129999
$59$	8.67788	1.12976	0.564882	−	0.825172i	$-0.308922\pi$
$59$	8.67788	1.12976	0.564882	+	0.825172i	$0.308922\pi$
$60$	0.372977	0.0481511
$61$	6.32331	0.809617	0.404808	−	0.914402i	$-0.367338\pi$
$61$	6.32331	0.809617	0.404808	+	0.914402i	$0.367338\pi$
$62$	−9.95571	−1.26438
$63$	−10.9284	−1.37685
$64$	38.2663	4.78329
$65$	0.102072	0.0126605
$66$	−8.75633	−1.07783
$67$	−7.27108	−0.888304	−0.444152	−	0.895952i	$-0.646495\pi$
$67$	−7.27108	−0.888304	−0.444152	+	0.895952i	$0.646495\pi$
$68$	−14.6870	−1.78107
$69$	−4.72336	−0.568626
$70$	−1.00603	−0.120244
$71$	−5.76170	−0.683788	−0.341894	−	0.939739i	$-0.611068\pi$
$71$	−5.76170	−0.683788	−0.341894	+	0.939739i	$0.611068\pi$
$72$	21.7246	2.56027
$73$	−5.78816	−0.677453	−0.338727	−	0.940885i	$-0.609996\pi$
$73$	−5.78816	−0.677453	−0.338727	+	0.940885i	$0.609996\pi$
$74$	−9.29318	−1.08031
$75$	−4.60807	−0.532094
$76$	23.2868	2.67118
$77$	17.4470	1.98827
$78$	−3.64359	−0.412556
$79$	0.949801	0.106861	0.0534305	−	0.998572i	$-0.482984\pi$
$79$	0.949801	0.106861	0.0534305	+	0.998572i	$0.482984\pi$
$80$	1.19132	0.133194
$81$	2.06439	0.229377
$82$	−0.738658	−0.0815711
$83$	−7.75787	−0.851537	−0.425768	−	0.904832i	$-0.639996\pi$
$83$	−7.75787	−0.851537	−0.425768	+	0.904832i	$0.639996\pi$
$84$	26.5279	2.89443
$85$	−0.185732	−0.0201454
$86$	10.3645	1.11764
$87$	−0.330140	−0.0353947
$88$	−34.6830	−3.69723
$89$	6.58467	0.697974	0.348987	−	0.937128i	$-0.386526\pi$
$89$	6.58467	0.697974	0.348987	+	0.937128i	$0.386526\pi$
$90$	0.425092	0.0448087
$91$	7.25988	0.761042
$92$	−28.9486	−3.01810
$93$	3.31983	0.344251
$94$	6.68947	0.689966
$95$	0.294484	0.0302134
$96$	−23.8720	−2.43643
$97$	3.55282	0.360734	0.180367	−	0.983599i	$-0.442271\pi$
$97$	3.55282	0.360734	0.180367	+	0.983599i	$0.442271\pi$
$98$	−52.1873	−5.27172
$99$	−7.37215	−0.740929
$100$	−28.2419	−2.82419
$101$	17.7055	1.76176	0.880881	−	0.473339i	$-0.156951\pi$
$101$	17.7055	1.76176	0.880881	+	0.473339i	$0.156951\pi$
$102$	6.62991	0.656459
$103$	10.5999	1.04444	0.522222	−	0.852810i	$-0.325103\pi$
$103$	10.5999	1.04444	0.522222	+	0.852810i	$0.325103\pi$
$104$	−14.4320	−1.41517
$105$	0.335471	0.0327386
$106$	−10.8686	−1.05566
$107$	13.5548	1.31039	0.655195	−	0.755459i	$-0.272586\pi$
$107$	13.5548	1.31039	0.655195	+	0.755459i	$0.272586\pi$
$108$	−26.8581	−2.58442
$109$	−8.63912	−0.827478	−0.413739	−	0.910396i	$-0.635777\pi$
$109$	−8.63912	−0.827478	−0.413739	+	0.910396i	$0.635777\pi$
$110$	−0.678656	−0.0647073
$111$	3.09891	0.294135
$112$	84.7324	8.00646
$113$	7.86598	0.739969	0.369984	−	0.929038i	$-0.379363\pi$
$113$	7.86598	0.739969	0.369984	+	0.929038i	$0.379363\pi$
$114$	−10.5120	−0.984535
$115$	−0.366082	−0.0341374
$116$	−2.02336	−0.187864
$117$	−3.06762	−0.283602
$118$	−24.0084	−2.21015
$119$	−13.2101	−1.21097
$120$	−0.666885	−0.0608780
$121$	0.769555	0.0699595
$122$	−17.4942	−1.58385
$123$	0.246313	0.0222093
$124$	20.3466	1.82718
$125$	−0.714658	−0.0639210
$126$	30.2346	2.69351
$127$	−1.15181	−0.102206	−0.0511031	−	0.998693i	$-0.516274\pi$
$127$	−1.15181	−0.102206	−0.0511031	+	0.998693i	$0.516274\pi$
$128$	−54.1164	−4.78326
$129$	−3.45616	−0.304298
$130$	−0.282395	−0.0247677
$131$	6.45625	0.564085	0.282043	−	0.959402i	$-0.408988\pi$
$131$	6.45625	0.564085	0.282043	+	0.959402i	$0.408988\pi$
$132$	17.8954	1.55760
$133$	20.9451	1.81617
$134$	20.1163	1.73778
$135$	−0.339646	−0.0292321
$136$	26.2605	2.25182
$137$	16.2348	1.38703	0.693517	−	0.720440i	$-0.256060\pi$
$137$	16.2348	1.38703	0.693517	+	0.720440i	$0.256060\pi$
$138$	13.0677	1.11240
$139$	18.6551	1.58231	0.791154	−	0.611617i	$-0.209480\pi$
$139$	18.6551	1.58231	0.791154	+	0.611617i	$0.209480\pi$
$140$	2.05603	0.173767
$141$	−2.23067	−0.187856
$142$	15.9404	1.33769
$143$	4.89743	0.409543
$144$	−35.8032	−2.98360
$145$	−0.0255873	−0.00212491
$146$	16.0136	1.32530
$147$	17.4024	1.43533
$148$	18.9926	1.56118
$149$	−3.11146	−0.254900	−0.127450	−	0.991845i	$-0.540679\pi$
$149$	−3.11146	−0.254900	−0.127450	+	0.991845i	$0.540679\pi$
$150$	12.7488	1.04093
$151$	15.4611	1.25821	0.629104	−	0.777321i	$-0.283422\pi$
$151$	15.4611	1.25821	0.629104	+	0.777321i	$0.283422\pi$
$152$	−41.6369	−3.37720
$153$	5.58187	0.451268
$154$	−48.2692	−3.88965
$155$	0.257302	0.0206670
$156$	7.44645	0.596194
$157$	12.5908	1.00486	0.502429	−	0.864619i	$-0.332440\pi$
$157$	12.5908	1.00486	0.502429	+	0.864619i	$0.332440\pi$
$158$	−2.62773	−0.209051
$159$	3.62426	0.287422
$160$	−1.85019	−0.146271
$161$	−26.0375	−2.05204
$162$	−5.71138	−0.448728
$163$	20.6888	1.62047	0.810235	−	0.586105i	$-0.199339\pi$
$163$	20.6888	1.62047	0.810235	+	0.586105i	$0.199339\pi$
$164$	1.50960	0.117880
$165$	0.226305	0.0176178
$166$	21.4630	1.66586
$167$	8.87756	0.686966	0.343483	−	0.939159i	$-0.388393\pi$
$167$	8.87756	0.686966	0.343483	+	0.939159i	$0.388393\pi$
$168$	−47.4320	−3.65946
$169$	−10.9621	−0.843241
$170$	0.513849	0.0394104
$171$	−8.85025	−0.676796
$172$	−21.1821	−1.61512
$173$	15.7970	1.20103	0.600513	−	0.799615i	$-0.294963\pi$
$173$	15.7970	1.20103	0.600513	+	0.799615i	$0.294963\pi$
$174$	0.913370	0.0692424
$175$	−25.4020	−1.92021
$176$	57.1594	4.30855
$177$	8.00583	0.601755
$178$	−18.2173	−1.36544
$179$	9.15598	0.684350	0.342175	−	0.939636i	$-0.388836\pi$
$179$	9.15598	0.684350	0.342175	+	0.939636i	$0.388836\pi$
$180$	−0.868766	−0.0647540
$181$	−20.0808	−1.49259	−0.746296	−	0.665614i	$-0.768170\pi$
$181$	−20.0808	−1.49259	−0.746296	+	0.665614i	$0.768170\pi$
$182$	−20.0853	−1.48882
$183$	5.83361	0.431233
$184$	51.7602	3.81581
$185$	0.240180	0.0176584
$186$	−9.18471	−0.673455
$187$	−8.91140	−0.651666
$188$	−13.6713	−0.997085
$189$	−24.1573	−1.75718
$190$	−0.814725	−0.0591063
$191$	19.9198	1.44135	0.720673	−	0.693275i	$-0.243833\pi$
$191$	19.9198	1.44135	0.720673	+	0.693275i	$0.243833\pi$
$192$	35.3029	2.54777
$193$	−11.5347	−0.830284	−0.415142	−	0.909757i	$-0.636268\pi$
$193$	−11.5347	−0.830284	−0.415142	+	0.909757i	$0.636268\pi$
$194$	−9.82930	−0.705702
$195$	0.0941676	0.00674348
$196$	106.656	7.61828
$197$	−14.7582	−1.05148	−0.525740	−	0.850646i	$-0.676211\pi$
$197$	−14.7582	−1.05148	−0.525740	+	0.850646i	$0.676211\pi$
$198$	20.3959	1.44947
$199$	13.0240	0.923249	0.461624	−	0.887076i	$-0.347267\pi$
$199$	13.0240	0.923249	0.461624	+	0.887076i	$0.347267\pi$
$200$	50.4967	3.57066
$201$	−6.70798	−0.473145
$202$	−48.9843	−3.44652
$203$	−1.81989	−0.127732
$204$	−13.5496	−0.948664
$205$	0.0190904	0.00133333
$206$	−29.3260	−2.04324
$207$	11.0020	0.764693
$208$	23.7846	1.64917
$209$	14.1293	0.977346
$210$	−0.928120	−0.0640463
$211$	−26.3814	−1.81617	−0.908087	−	0.418782i	$-0.862457\pi$
$211$	−26.3814	−1.81617	−0.908087	+	0.418782i	$0.862457\pi$
$212$	22.2124	1.52555
$213$	−5.31549	−0.364212
$214$	−37.5009	−2.56351
$215$	−0.267868	−0.0182685
$216$	48.0224	3.26751
$217$	18.3006	1.24232
$218$	23.9011	1.61879
$219$	−5.33991	−0.360838
$220$	1.38698	0.0935099
$221$	−3.70812	−0.249435
$222$	−8.57349	−0.575415
$223$	27.2508	1.82485	0.912425	−	0.409244i	$-0.134207\pi$
$223$	27.2508	1.82485	0.912425	+	0.409244i	$0.134207\pi$
$224$	−131.595	−8.79253
$225$	10.7335	0.715564
$226$	−21.7621	−1.44760
$227$	−21.2411	−1.40982	−0.704910	−	0.709297i	$-0.749012\pi$
$227$	−21.2411	−1.40982	−0.704910	+	0.709297i	$0.749012\pi$
$228$	21.4834	1.42277
$229$	−22.0431	−1.45665	−0.728324	−	0.685233i	$-0.759701\pi$
$229$	−22.0431	−1.45665	−0.728324	+	0.685233i	$0.759701\pi$
$230$	1.01281	0.0667827
$231$	16.0959	1.05903
$232$	3.61778	0.237519
$233$	16.2893	1.06715	0.533574	−	0.845753i	$-0.320848\pi$
$233$	16.2893	1.06715	0.533574	+	0.845753i	$0.320848\pi$
$234$	8.48694	0.554808
$235$	−0.172887	−0.0112779
$236$	49.0662	3.19393
$237$	0.876245	0.0569182
$238$	36.5474	2.36901
$239$	9.92709	0.642130	0.321065	−	0.947057i	$-0.395959\pi$
$239$	9.92709	0.642130	0.321065	+	0.947057i	$0.395959\pi$
$240$	1.09906	0.0709440
$241$	−3.03176	−0.195293	−0.0976464	−	0.995221i	$-0.531131\pi$
$241$	−3.03176	−0.195293	−0.0976464	+	0.995221i	$0.531131\pi$
$242$	−2.12906	−0.136861
$243$	16.1549	1.03634
$244$	35.7530	2.28885
$245$	1.34877	0.0861695
$246$	−0.681453	−0.0434479
$247$	5.87935	0.374094
$248$	−36.3798	−2.31012
$249$	−7.15707	−0.453561
$250$	1.97719	0.125048
$251$	7.31733	0.461866	0.230933	−	0.972970i	$-0.425822\pi$
$251$	7.31733	0.461866	0.230933	+	0.972970i	$0.425822\pi$
$252$	−61.7908	−3.89246
$253$	−17.5646	−1.10428
$254$	3.18660	0.199945
$255$	−0.171348	−0.0107302
$256$	73.1865	4.57416
$257$	9.70232	0.605214	0.302607	−	0.953115i	$-0.402143\pi$
$257$	9.70232	0.605214	0.302607	+	0.953115i	$0.402143\pi$
$258$	9.56187	0.595296
$259$	17.0827	1.06147
$260$	0.577134	0.0357924
$261$	0.768987	0.0475991
$262$	−17.8620	−1.10352
$263$	−18.8143	−1.16014	−0.580069	−	0.814567i	$-0.696975\pi$
$263$	−18.8143	−1.16014	−0.580069	+	0.814567i	$0.696975\pi$
$264$	−31.9971	−1.96928
$265$	0.280897	0.0172553
$266$	−57.9471	−3.55297
$267$	6.07473	0.371768
$268$	−41.1119	−2.51131
$269$	4.03928	0.246279	0.123139	−	0.992389i	$-0.460704\pi$
$269$	4.03928	0.246279	0.123139	+	0.992389i	$0.460704\pi$
$270$	0.939671	0.0571866
$271$	14.3135	0.869484	0.434742	−	0.900555i	$-0.356840\pi$
$271$	14.3135	0.869484	0.434742	+	0.900555i	$0.356840\pi$
$272$	−43.2786	−2.62415
$273$	6.69765	0.405360
$274$	−44.9155	−2.71345
$275$	−17.1359	−1.03333
$276$	−26.7067	−1.60755
$277$	−22.4777	−1.35056	−0.675278	−	0.737563i	$-0.735976\pi$
$277$	−22.4777	−1.35056	−0.675278	+	0.737563i	$0.735976\pi$
$278$	−51.6116	−3.09546
$279$	−7.73281	−0.462951
$280$	−3.67620	−0.219695
$281$	3.64234	0.217284	0.108642	−	0.994081i	$-0.465350\pi$
$281$	3.64234	0.217284	0.108642	+	0.994081i	$0.465350\pi$
$282$	6.17141	0.367502
$283$	22.3736	1.32997	0.664985	−	0.746857i	$-0.268438\pi$
$283$	22.3736	1.32997	0.664985	+	0.746857i	$0.268438\pi$
$284$	−32.5776	−1.93312
$285$	0.271678	0.0160928
$286$	−13.5493	−0.801187
$287$	1.35780	0.0801484
$288$	55.6046	3.27653
$289$	−10.2527	−0.603098
$290$	0.0707904	0.00415695
$291$	3.27768	0.192141
$292$	−32.7272	−1.91522
$293$	−13.0979	−0.765188	−0.382594	−	0.923917i	$-0.624969\pi$
$293$	−13.0979	−0.765188	−0.382594	+	0.923917i	$0.624969\pi$
$294$	−48.1458	−2.80792
$295$	0.620489	0.0361263
$296$	−33.9588	−1.97382
$297$	−16.2962	−0.945602
$298$	8.60821	0.498660
$299$	−7.30880	−0.422679
$300$	−26.0548	−1.50427
$301$	−19.0521	−1.09814
$302$	−42.7750	−2.46142
$303$	16.3343	0.938382
$304$	68.6198	3.93561
$305$	0.452132	0.0258890
$306$	−15.4429	−0.882812
$307$	11.6526	0.665049	0.332525	−	0.943095i	$-0.392100\pi$
$307$	11.6526	0.665049	0.332525	+	0.943095i	$0.392100\pi$
$308$	98.6484	5.62101
$309$	9.77905	0.556311
$310$	−0.711857	−0.0404308
$311$	17.1105	0.970246	0.485123	−	0.874446i	$-0.338775\pi$
$311$	17.1105	0.970246	0.485123	+	0.874446i	$0.338775\pi$
$312$	−13.3143	−0.753774
$313$	−20.2432	−1.14421	−0.572106	−	0.820180i	$-0.693873\pi$
$313$	−20.2432	−1.14421	−0.572106	+	0.820180i	$0.693873\pi$
$314$	−34.8340	−1.96580
$315$	−0.781405	−0.0440272
$316$	5.37033	0.302105
$317$	−30.3897	−1.70686	−0.853428	−	0.521211i	$-0.825480\pi$
$317$	−30.3897	−1.70686	−0.853428	+	0.521211i	$0.825480\pi$
$318$	−10.0269	−0.562282
$319$	−1.22768	−0.0687368
$320$	2.73613	0.152955
$321$	12.5051	0.697964
$322$	72.0359	4.01440
$323$	−10.6981	−0.595259
$324$	11.6724	0.648468
$325$	−7.13040	−0.395523
$326$	−57.2379	−3.17011
$327$	−7.97008	−0.440746
$328$	−2.69918	−0.149037
$329$	−12.2966	−0.677932
$330$	−0.626098	−0.0344656
$331$	7.07007	0.388606	0.194303	−	0.980942i	$-0.437755\pi$
$331$	7.07007	0.388606	0.194303	+	0.980942i	$0.437755\pi$
$332$	−43.8643	−2.40737
$333$	−7.21821	−0.395556
$334$	−24.5608	−1.34391
$335$	−0.519899	−0.0284051
$336$	78.1704	4.26455
$337$	−19.0094	−1.03551	−0.517753	−	0.855530i	$-0.673231\pi$
$337$	−19.0094	−1.03551	−0.517753	+	0.855530i	$0.673231\pi$
$338$	30.3280	1.64963
$339$	7.25681	0.394136
$340$	−1.05016	−0.0569528
$341$	12.3453	0.668538
$342$	24.4852	1.32401
$343$	60.3316	3.25760
$344$	37.8737	2.04202
$345$	−0.337732	−0.0181829
$346$	−43.7043	−2.34956
$347$	−16.0341	−0.860755	−0.430377	−	0.902649i	$-0.641619\pi$
$347$	−16.0341	−0.860755	−0.430377	+	0.902649i	$0.641619\pi$
$348$	−1.86666	−0.100064
$349$	7.14335	0.382375	0.191187	−	0.981554i	$-0.438766\pi$
$349$	7.14335	0.382375	0.191187	+	0.981554i	$0.438766\pi$
$350$	70.2775	3.75649
$351$	−6.78101	−0.361944
$352$	−88.7721	−4.73157
$353$	21.6144	1.15042	0.575210	−	0.818006i	$-0.304920\pi$
$353$	21.6144	1.15042	0.575210	+	0.818006i	$0.304920\pi$
$354$	−22.1491	−1.17721
$355$	−0.411975	−0.0218654
$356$	37.2308	1.97323
$357$	−12.1871	−0.645010
$358$	−25.3311	−1.33879
$359$	−31.1165	−1.64227	−0.821133	−	0.570737i	$-0.806657\pi$
$359$	−31.1165	−1.64227	−0.821133	+	0.570737i	$0.806657\pi$
$360$	1.55336	0.0818692
$361$	−2.03777	−0.107251
$362$	55.5558	2.91995
$363$	0.709958	0.0372631
$364$	41.0486	2.15153
$365$	−0.413867	−0.0216628
$366$	−16.1394	−0.843618
$367$	−15.0869	−0.787528	−0.393764	−	0.919212i	$-0.628827\pi$
$367$	−15.0869	−0.787528	−0.393764	+	0.919212i	$0.628827\pi$
$368$	−85.3034	−4.44675
$369$	−0.573731	−0.0298672
$370$	−0.664485	−0.0345449
$371$	19.9787	1.03724
$372$	18.7709	0.973225
$373$	19.7172	1.02092	0.510460	−	0.859902i	$-0.329475\pi$
$373$	19.7172	1.02092	0.510460	+	0.859902i	$0.329475\pi$
$374$	24.6544	1.27485
$375$	−0.659313	−0.0340468
$376$	24.4444	1.26062
$377$	−0.510849	−0.0263101
$378$	66.8339	3.43757
$379$	12.5148	0.642841	0.321420	−	0.946937i	$-0.395840\pi$
$379$	12.5148	0.642841	0.321420	+	0.946937i	$0.395840\pi$
$380$	1.66506	0.0854159
$381$	−1.06261	−0.0544389
$382$	−55.1104	−2.81970
$383$	14.7140	0.751852	0.375926	−	0.926650i	$-0.377325\pi$
$383$	14.7140	0.751852	0.375926	+	0.926650i	$0.377325\pi$
$384$	−49.9254	−2.54775
$385$	1.24750	0.0635787
$386$	31.9120	1.62428
$387$	8.05036	0.409223
$388$	20.0882	1.01983
$389$	−31.8290	−1.61379	−0.806897	−	0.590692i	$-0.798855\pi$
$389$	−31.8290	−1.61379	−0.806897	+	0.590692i	$0.798855\pi$
$390$	−0.260526	−0.0131922
$391$	13.2992	0.672567
$392$	−190.701	−9.63186
$393$	5.95626	0.300453
$394$	40.8303	2.05700
$395$	0.0679130	0.00341707
$396$	−41.6833	−2.09467
$397$	−13.3655	−0.670795	−0.335398	−	0.942077i	$-0.608871\pi$
$397$	−13.3655	−0.670795	−0.335398	+	0.942077i	$0.608871\pi$
$398$	−36.0325	−1.80614
$399$	19.3231	0.967363
$400$	−83.2211	−4.16106
$401$	−4.56917	−0.228174	−0.114087	−	0.993471i	$-0.536394\pi$
$401$	−4.56917	−0.228174	−0.114087	+	0.993471i	$0.536394\pi$
$402$	18.5584	0.925610
$403$	5.13702	0.255893
$404$	100.110	4.98064
$405$	0.147609	0.00733475
$406$	5.03495	0.249880
$407$	11.5238	0.571213
$408$	24.2268	1.19941
$409$	−24.3122	−1.20216	−0.601081	−	0.799188i	$-0.705263\pi$
$409$	−24.3122	−1.20216	−0.601081	+	0.799188i	$0.705263\pi$
$410$	−0.0528158	−0.00260838
$411$	14.9775	0.738788
$412$	59.9339	2.95273
$413$	44.1321	2.17160
$414$	−30.4384	−1.49596
$415$	−0.554706	−0.0272295
$416$	−36.9389	−1.81108
$417$	17.2104	0.842798
$418$	−39.0904	−1.91198
$419$	−21.3116	−1.04114	−0.520571	−	0.853818i	$-0.674281\pi$
$419$	−21.3116	−1.04114	−0.520571	+	0.853818i	$0.674281\pi$
$420$	1.89681	0.0925548
$421$	11.6435	0.567472	0.283736	−	0.958902i	$-0.408426\pi$
$421$	11.6435	0.567472	0.283736	+	0.958902i	$0.408426\pi$
$422$	72.9873	3.55297
$423$	5.19585	0.252631
$424$	−39.7158	−1.92877
$425$	12.9745	0.629357
$426$	14.7059	0.712505
$427$	32.1578	1.55622
$428$	76.6410	3.70458
$429$	4.51815	0.218139
$430$	0.741089	0.0357385
$431$	28.5690	1.37612	0.688059	−	0.725654i	$-0.258463\pi$
$431$	28.5690	1.37612	0.688059	+	0.725654i	$0.258463\pi$
$432$	−79.1434	−3.80779
$433$	−35.1604	−1.68970	−0.844852	−	0.535001i	$-0.820311\pi$
$433$	−35.1604	−1.68970	−0.844852	+	0.535001i	$0.820311\pi$
$434$	−50.6307	−2.43035
$435$	−0.0236058	−0.00113181
$436$	−48.8470	−2.33935
$437$	−21.0863	−1.00869
$438$	14.7735	0.705904
$439$	−17.7995	−0.849522	−0.424761	−	0.905306i	$-0.639642\pi$
$439$	−17.7995	−0.849522	−0.424761	+	0.905306i	$0.639642\pi$
$440$	−2.47992	−0.118226
$441$	−40.5350	−1.93024
$442$	10.2589	0.487968
$443$	−2.47835	−0.117750	−0.0588749	−	0.998265i	$-0.518751\pi$
$443$	−2.47835	−0.117750	−0.0588749	+	0.998265i	$0.518751\pi$
$444$	17.5217	0.831545
$445$	0.470820	0.0223190
$446$	−75.3926	−3.56994
$447$	−2.87049	−0.135770
$448$	194.607	9.19432
$449$	1.82851	0.0862926	0.0431463	−	0.999069i	$-0.486262\pi$
$449$	1.82851	0.0862926	0.0431463	+	0.999069i	$0.486262\pi$
$450$	−29.6954	−1.39985
$451$	0.915955	0.0431306
$452$	44.4755	2.09195
$453$	14.2638	0.670170
$454$	58.7659	2.75802
$455$	0.519099	0.0243357
$456$	−38.4124	−1.79883
$457$	33.4393	1.56423	0.782113	−	0.623136i	$-0.214142\pi$
$457$	33.4393	1.56423	0.782113	+	0.623136i	$0.214142\pi$
$458$	60.9848	2.84963
$459$	12.3388	0.575925
$460$	−2.06989	−0.0965091
$461$	−35.6398	−1.65991	−0.829956	−	0.557829i	$-0.811634\pi$
$461$	−35.6398	−1.65991	−0.829956	+	0.557829i	$0.811634\pi$
$462$	−44.5311	−2.07177
$463$	−8.28048	−0.384827	−0.192413	−	0.981314i	$-0.561631\pi$
$463$	−8.28048	−0.384827	−0.192413	+	0.981314i	$0.561631\pi$
$464$	−5.96228	−0.276792
$465$	0.237376	0.0110080
$466$	−45.0663	−2.08766
$467$	−11.9542	−0.553175	−0.276588	−	0.960989i	$-0.589204\pi$
$467$	−11.9542	−0.553175	−0.276588	+	0.960989i	$0.589204\pi$
$468$	−17.3448	−0.801766
$469$	−36.9777	−1.70747
$470$	0.478313	0.0220629
$471$	11.6158	0.535226
$472$	−87.7305	−4.03812
$473$	−12.8523	−0.590950
$474$	−2.42423	−0.111349
$475$	−20.5716	−0.943888
$476$	−74.6923	−3.42352
$477$	−8.44190	−0.386528
$478$	−27.4644	−1.25619
$479$	16.2700	0.743397	0.371699	−	0.928353i	$-0.378775\pi$
$479$	16.2700	0.743397	0.371699	+	0.928353i	$0.378775\pi$
$480$	−1.70691	−0.0779093
$481$	4.79517	0.218641
$482$	8.38771	0.382050
$483$	−24.0211	−1.09300
$484$	4.35119	0.197781
$485$	0.254035	0.0115351
$486$	−44.6945	−2.02739
$487$	−32.8828	−1.49006	−0.745031	−	0.667030i	$-0.767565\pi$
$487$	−32.8828	−1.49006	−0.745031	+	0.667030i	$0.767565\pi$
$488$	−63.9266	−2.89382
$489$	19.0866	0.863125
$490$	−3.73152	−0.168573
$491$	17.0182	0.768021	0.384010	−	0.923329i	$-0.374543\pi$
$491$	17.0182	0.768021	0.384010	+	0.923329i	$0.374543\pi$
$492$	1.39269	0.0627875
$493$	0.929545	0.0418646
$494$	−16.2659	−0.731838
$495$	−0.527126	−0.0236926
$496$	59.9558	2.69209
$497$	−29.3016	−1.31436
$498$	19.8009	0.887299
$499$	−10.9739	−0.491258	−0.245629	−	0.969364i	$-0.578995\pi$
$499$	−10.9739	−0.491258	−0.245629	+	0.969364i	$0.578995\pi$
$500$	−4.04080	−0.180710
$501$	8.19005	0.365905
$502$	−20.2442	−0.903545
$503$	−3.15336	−0.140601	−0.0703006	−	0.997526i	$-0.522396\pi$
$503$	−3.15336	−0.140601	−0.0703006	+	0.997526i	$0.522396\pi$
$504$	110.482	4.92127
$505$	1.26598	0.0563355
$506$	48.5945	2.16029
$507$	−10.1132	−0.449142
$508$	−6.51250	−0.288945
$509$	2.01654	0.0893814	0.0446907	−	0.999001i	$-0.485770\pi$
$509$	2.01654	0.0893814	0.0446907	+	0.999001i	$0.485770\pi$
$510$	0.474055	0.0209915
$511$	−29.4362	−1.30218
$512$	−94.2463	−4.16514
$513$	−19.5636	−0.863753
$514$	−26.8426	−1.18398
$515$	0.757921	0.0333980
$516$	−19.5417	−0.860276
$517$	−8.29512	−0.364819
$518$	−47.2613	−2.07654
$519$	14.5737	0.639713
$520$	−1.03192	−0.0452526
$521$	29.0192	1.27135	0.635676	−	0.771956i	$-0.280721\pi$
$521$	29.0192	1.27135	0.635676	+	0.771956i	$0.280721\pi$
$522$	−2.12749	−0.0931177
$523$	−4.48348	−0.196049	−0.0980245	−	0.995184i	$-0.531252\pi$
$523$	−4.48348	−0.196049	−0.0980245	+	0.995184i	$0.531252\pi$
$524$	36.5047	1.59472
$525$	−23.4347	−1.02278
$526$	52.0519	2.26957
$527$	−9.34736	−0.407178
$528$	52.7328	2.29490
$529$	3.21300	0.139696
$530$	−0.777133	−0.0337565
$531$	−18.6478	−0.809245
$532$	118.427	5.13447
$533$	0.381138	0.0165089
$534$	−16.8065	−0.727286
$535$	0.969200	0.0419022
$536$	73.5082	3.17507
$537$	8.44691	0.364511
$538$	−11.1751	−0.481794
$539$	64.7137	2.78742
$540$	−1.92042	−0.0826416
$541$	15.8858	0.682984	0.341492	−	0.939885i	$-0.389068\pi$
$541$	15.8858	0.682984	0.341492	+	0.939885i	$0.389068\pi$
$542$	−39.6000	−1.70097
$543$	−18.5257	−0.795012
$544$	67.2144	2.88179
$545$	−0.617718	−0.0264601
$546$	−18.5298	−0.793003
$547$	14.6820	0.627758	0.313879	−	0.949463i	$-0.398371\pi$
$547$	14.6820	0.627758	0.313879	+	0.949463i	$0.398371\pi$
$548$	91.7944	3.92126
$549$	−13.5881	−0.579925
$550$	47.4083	2.02150
$551$	−1.47383	−0.0627871
$552$	47.7517	2.03245
$553$	4.83030	0.205405
$554$	62.1873	2.64208
$555$	0.221579	0.00940552
$556$	105.479	4.47332
$557$	5.83248	0.247130	0.123565	−	0.992336i	$-0.460567\pi$
$557$	5.83248	0.247130	0.123565	+	0.992336i	$0.460567\pi$
$558$	21.3937	0.905668
$559$	−5.34797	−0.226195
$560$	6.05856	0.256021
$561$	−8.22127	−0.347102
$562$	−10.0770	−0.425071
$563$	7.74767	0.326526	0.163263	−	0.986583i	$-0.447798\pi$
$563$	7.74767	0.326526	0.163263	+	0.986583i	$0.447798\pi$
$564$	−12.6126	−0.531086
$565$	0.562436	0.0236619
$566$	−61.8990	−2.60181
$567$	10.4987	0.440902
$568$	58.2489	2.44407
$569$	−7.75528	−0.325118	−0.162559	−	0.986699i	$-0.551975\pi$
$569$	−7.75528	−0.325118	−0.162559	+	0.986699i	$0.551975\pi$
$570$	−0.751630	−0.0314823
$571$	−34.4399	−1.44126	−0.720632	−	0.693318i	$-0.756148\pi$
$571$	−34.4399	−1.44126	−0.720632	+	0.693318i	$0.756148\pi$
$572$	27.6909	1.15781
$573$	18.3771	0.767716
$574$	−3.75651	−0.156794
$575$	25.5731	1.06647
$576$	−82.2301	−3.42626
$577$	23.2266	0.966934	0.483467	−	0.875362i	$-0.339377\pi$
$577$	23.2266	0.966934	0.483467	+	0.875362i	$0.339377\pi$
$578$	28.3652	1.17984
$579$	−10.6414	−0.442241
$580$	−0.144675	−0.00600731
$581$	−39.4534	−1.63680
$582$	−9.06808	−0.375884
$583$	13.4774	0.558177
$584$	58.5164	2.42143
$585$	−0.219342	−0.00906869
$586$	36.2369	1.49693
$587$	−2.30270	−0.0950424	−0.0475212	−	0.998870i	$-0.515132\pi$
$587$	−2.30270	−0.0950424	−0.0475212	+	0.998870i	$0.515132\pi$
$588$	98.3961	4.05779
$589$	14.8206	0.610671
$590$	−1.71665	−0.0706735
$591$	−13.6153	−0.560058
$592$	55.9659	2.30018
$593$	31.7647	1.30442	0.652211	−	0.758038i	$-0.273842\pi$
$593$	31.7647	1.30442	0.652211	+	0.758038i	$0.273842\pi$
$594$	45.0854	1.84987
$595$	−0.944556	−0.0387230
$596$	−17.5927	−0.720625
$597$	12.0154	0.491758
$598$	20.2207	0.826884
$599$	−23.7842	−0.971794	−0.485897	−	0.874016i	$-0.661507\pi$
$599$	−23.7842	−0.971794	−0.485897	+	0.874016i	$0.661507\pi$
$600$	46.5861	1.90187
$601$	40.9640	1.67096	0.835478	−	0.549523i	$-0.185191\pi$
$601$	40.9640	1.67096	0.835478	+	0.549523i	$0.185191\pi$
$602$	52.7098	2.14829
$603$	15.6247	0.636289
$604$	87.4197	3.55706
$605$	0.0550250	0.00223708
$606$	−45.1908	−1.83575
$607$	13.2887	0.539371	0.269686	−	0.962948i	$-0.413080\pi$
$607$	13.2887	0.539371	0.269686	+	0.962948i	$0.413080\pi$
$608$	−106.571	−4.32202
$609$	−1.67896	−0.0680347
$610$	−1.25087	−0.0506464
$611$	−3.45168	−0.139640
$612$	31.5608	1.27577
$613$	−13.3881	−0.540742	−0.270371	−	0.962756i	$-0.587146\pi$
$613$	−13.3881	−0.540742	−0.270371	+	0.962756i	$0.587146\pi$
$614$	−32.2383	−1.30103
$615$	0.0176120	0.000710183 0
$616$	−176.384	−7.10671
$617$	−19.5615	−0.787516	−0.393758	−	0.919214i	$-0.628825\pi$
$617$	−19.5615	−0.787516	−0.393758	+	0.919214i	$0.628825\pi$
$618$	−27.0549	−1.08831
$619$	9.06569	0.364381	0.182190	−	0.983263i	$-0.441681\pi$
$619$	9.06569	0.364381	0.182190	+	0.983263i	$0.441681\pi$
$620$	1.45483	0.0584274
$621$	24.3201	0.975931
$622$	−47.3381	−1.89809
$623$	33.4869	1.34163
$624$	21.9426	0.878409
$625$	24.9233	0.996933
$626$	56.0051	2.23841
$627$	13.0351	0.520572
$628$	71.1906	2.84082
$629$	−8.72532	−0.347901
$630$	2.16185	0.0861300
$631$	18.5903	0.740068	0.370034	−	0.929018i	$-0.379346\pi$
$631$	18.5903	0.740068	0.370034	+	0.929018i	$0.379346\pi$
$632$	−9.60218	−0.381954
$633$	−24.3384	−0.967364
$634$	84.0766	3.33911
$635$	−0.0823568	−0.00326823
$636$	20.4922	0.812567
$637$	26.9280	1.06693
$638$	3.39652	0.134469
$639$	12.3812	0.489795
$640$	−3.86945	−0.152953
$641$	−26.6071	−1.05092	−0.525459	−	0.850819i	$-0.676106\pi$
$641$	−26.6071	−1.05092	−0.525459	+	0.850819i	$0.676106\pi$
$642$	−34.5967	−1.36542
$643$	−26.0900	−1.02889	−0.514444	−	0.857524i	$-0.672002\pi$
$643$	−26.0900	−1.02889	−0.514444	+	0.857524i	$0.672002\pi$
$644$	−147.221	−5.80130
$645$	−0.247124	−0.00973049
$646$	29.5976	1.16450
$647$	−20.4619	−0.804442	−0.402221	−	0.915543i	$-0.631762\pi$
$647$	−20.4619	−0.804442	−0.402221	+	0.915543i	$0.631762\pi$
$648$	−20.8703	−0.819864
$649$	29.7710	1.16861
$650$	19.7271	0.773759
$651$	16.8833	0.661709
$652$	116.978	4.58120
$653$	−6.23156	−0.243860	−0.121930	−	0.992539i	$-0.538908\pi$
$653$	−6.23156	−0.243860	−0.121930	+	0.992539i	$0.538908\pi$
$654$	22.0502	0.862229
$655$	0.461637	0.0180377
$656$	4.44838	0.173680
$657$	12.4381	0.485257
$658$	34.0199	1.32623
$659$	37.5885	1.46424	0.732121	−	0.681175i	$-0.238531\pi$
$659$	37.5885	1.46424	0.732121	+	0.681175i	$0.238531\pi$
$660$	1.27956	0.0498070
$661$	47.3194	1.84051	0.920256	−	0.391316i	$-0.127980\pi$
$661$	47.3194	1.84051	0.920256	+	0.391316i	$0.127980\pi$
$662$	−19.5602	−0.760228
$663$	−3.42095	−0.132859
$664$	78.4295	3.04366
$665$	1.49763	0.0580755
$666$	19.9700	0.773823
$667$	1.83216	0.0709415
$668$	50.1952	1.94211
$669$	25.1404	0.971985
$670$	1.43836	0.0555688
$671$	21.6932	0.837458
$672$	−121.403	−4.68324
$673$	12.2059	0.470502	0.235251	−	0.971935i	$-0.424409\pi$
$673$	12.2059	0.470502	0.235251	+	0.971935i	$0.424409\pi$
$674$	52.5916	2.02575
$675$	23.7264	0.913231
$676$	−61.9817	−2.38391
$677$	−16.0955	−0.618602	−0.309301	−	0.950964i	$-0.600095\pi$
$677$	−16.0955	−0.618602	−0.309301	+	0.950964i	$0.600095\pi$
$678$	−20.0768	−0.771045
$679$	18.0682	0.693394
$680$	1.87769	0.0720061
$681$	−19.5961	−0.750924
$682$	−34.1548	−1.30786
$683$	−45.2113	−1.72996	−0.864981	−	0.501805i	$-0.832669\pi$
$683$	−45.2113	−1.72996	−0.864981	+	0.501805i	$0.832669\pi$
$684$	−50.0408	−1.91336
$685$	1.16083	0.0443530
$686$	−166.914	−6.37282
$687$	−20.3360	−0.775867
$688$	−62.4179	−2.37966
$689$	5.60808	0.213651
$690$	0.934374	0.0355710
$691$	16.6480	0.633319	0.316660	−	0.948539i	$-0.397439\pi$
$691$	16.6480	0.633319	0.316660	+	0.948539i	$0.397439\pi$
$692$	89.3190	3.39540
$693$	−37.4917	−1.42419
$694$	44.3602	1.68389
$695$	1.33389	0.0505972
$696$	3.33761	0.126512
$697$	−0.693522	−0.0262690
$698$	−19.7629	−0.748037
$699$	15.0278	0.568404
$700$	−143.627	−5.42859
$701$	−18.1637	−0.686034	−0.343017	−	0.939329i	$-0.611449\pi$
$701$	−18.1637	−0.686034	−0.343017	+	0.939329i	$0.611449\pi$
$702$	18.7605	0.708068
$703$	13.8343	0.521770
$704$	131.280	4.94778
$705$	−0.159498	−0.00600705
$706$	−59.7989	−2.25056
$707$	90.0428	3.38641
$708$	45.2663	1.70121
$709$	26.8330	1.00773	0.503867	−	0.863781i	$-0.331910\pi$
$709$	26.8330	1.00773	0.503867	+	0.863781i	$0.331910\pi$
$710$	1.13978	0.0427751
$711$	−2.04102	−0.0765441
$712$	−66.5689	−2.49477
$713$	−18.4239	−0.689981
$714$	33.7170	1.26183
$715$	0.350178	0.0130959
$716$	51.7694	1.93471
$717$	9.15830	0.342023
$718$	86.0874	3.21275
$719$	−15.3728	−0.573307	−0.286654	−	0.958034i	$-0.592543\pi$
$719$	−15.3728	−0.573307	−0.286654	+	0.958034i	$0.592543\pi$
$720$	−2.56001	−0.0954061
$721$	53.9070	2.00760
$722$	5.63772	0.209814
$723$	−2.79697	−0.104020
$724$	−113.540	−4.21968
$725$	1.78744	0.0663837
$726$	−1.96418	−0.0728976
$727$	−10.6465	−0.394858	−0.197429	−	0.980317i	$-0.563259\pi$
$727$	−10.6465	−0.394858	−0.197429	+	0.980317i	$0.563259\pi$
$728$	−73.3950	−2.72020
$729$	8.71068	0.322618
$730$	1.14501	0.0423788
$731$	9.73121	0.359922
$732$	32.9842	1.21913
$733$	−50.2308	−1.85532	−0.927658	−	0.373431i	$-0.878181\pi$
$733$	−50.2308	−1.85532	−0.927658	+	0.373431i	$0.878181\pi$
$734$	41.7396	1.54064
$735$	1.24431	0.0458972
$736$	132.481	4.88333
$737$	−24.9447	−0.918851
$738$	1.58729	0.0584291
$739$	−19.9439	−0.733647	−0.366823	−	0.930291i	$-0.619555\pi$
$739$	−19.9439	−0.733647	−0.366823	+	0.930291i	$0.619555\pi$
$740$	1.35802	0.0499216
$741$	5.42404	0.199257
$742$	−55.2734	−2.02915
$743$	−17.3534	−0.636634	−0.318317	−	0.947984i	$-0.603118\pi$
$743$	−17.3534	−0.636634	−0.318317	+	0.947984i	$0.603118\pi$
$744$	−33.5624	−1.23046
$745$	−0.222477	−0.00815091
$746$	−54.5500	−1.99722
$747$	16.6708	0.609953
$748$	−50.3865	−1.84231
$749$	68.9341	2.51880
$750$	1.82407	0.0666054
$751$	−5.10010	−0.186105	−0.0930527	−	0.995661i	$-0.529662\pi$
$751$	−5.10010	−0.186105	−0.0930527	+	0.995661i	$0.529662\pi$
$752$	−40.2857	−1.46907
$753$	6.75065	0.246007
$754$	1.41332	0.0514702
$755$	1.10551	0.0402335
$756$	−136.589	−4.96770
$757$	21.0092	0.763592	0.381796	−	0.924247i	$-0.375306\pi$
$757$	21.0092	0.763592	0.381796	+	0.924247i	$0.375306\pi$
$758$	−34.6236	−1.25759
$759$	−16.2043	−0.588180
$760$	−2.97714	−0.107992
$761$	−26.2922	−0.953092	−0.476546	−	0.879149i	$-0.658111\pi$
$761$	−26.2922	−0.953092	−0.476546	+	0.879149i	$0.658111\pi$
$762$	2.93982	0.106498
$763$	−43.9350	−1.59056
$764$	112.630	4.07480
$765$	0.399117	0.0144301
$766$	−40.7081	−1.47084
$767$	12.3880	0.447305
$768$	67.5187	2.43637
$769$	11.5171	0.415317	0.207659	−	0.978201i	$-0.433416\pi$
$769$	11.5171	0.415317	0.207659	+	0.978201i	$0.433416\pi$
$770$	−3.45136	−0.124379
$771$	8.95094	0.322360
$772$	−65.2189	−2.34728
$773$	29.5164	1.06163	0.530816	−	0.847487i	$-0.321885\pi$
$773$	29.5164	1.06163	0.530816	+	0.847487i	$0.321885\pi$
$774$	−22.2722	−0.800559
$775$	−17.9742	−0.645651
$776$	−35.9179	−1.28938
$777$	15.7598	0.565379
$778$	88.0586	3.15705
$779$	1.09960	0.0393973
$780$	0.532439	0.0190644
$781$	−19.7665	−0.707302
$782$	−36.7937	−1.31574
$783$	1.69985	0.0607478
$784$	314.285	11.2245
$785$	0.900274	0.0321322
$786$	−16.4787	−0.587775
$787$	36.1461	1.28847	0.644234	−	0.764829i	$-0.277176\pi$
$787$	36.1461	1.28847	0.644234	+	0.764829i	$0.277176\pi$
$788$	−83.4454	−2.97262
$789$	−17.3572	−0.617934
$790$	−0.187889	−0.00668480
$791$	40.0031	1.42235
$792$	74.5300	2.64831
$793$	9.02677	0.320550
$794$	36.9772	1.31227
$795$	0.259143	0.00919086
$796$	73.6400	2.61010
$797$	−20.3715	−0.721595	−0.360798	−	0.932644i	$-0.617495\pi$
$797$	−20.3715	−0.721595	−0.360798	+	0.932644i	$0.617495\pi$
$798$	−53.4595	−1.89245
$799$	6.28071	0.222195
$800$	129.248	4.56959
$801$	−14.1497	−0.499956
$802$	12.6412	0.446375
$803$	−19.8573	−0.700750
$804$	−37.9280	−1.33762
$805$	−1.86175	−0.0656179
$806$	−14.2122	−0.500602
$807$	3.72646	0.131178
$808$	−178.997	−6.29708
$809$	54.8490	1.92839	0.964194	−	0.265199i	$-0.0854375\pi$
$809$	54.8490	1.92839	0.964194	+	0.265199i	$0.0854375\pi$
$810$	−0.408377	−0.0143489
$811$	20.3552	0.714769	0.357384	−	0.933957i	$-0.383669\pi$
$811$	20.3552	0.714769	0.357384	+	0.933957i	$0.383669\pi$
$812$	−10.2900	−0.361108
$813$	13.2050	0.463121
$814$	−31.8819	−1.11746
$815$	1.47930	0.0518175
$816$	−39.9270	−1.39772
$817$	−15.4292	−0.539798
$818$	67.2626	2.35178
$819$	−15.6007	−0.545132
$820$	0.107940	0.00376944
$821$	6.55169	0.228655	0.114328	−	0.993443i	$-0.463529\pi$
$821$	6.55169	0.228655	0.114328	+	0.993443i	$0.463529\pi$
$822$	−41.4371	−1.44529
$823$	−49.3887	−1.72158	−0.860791	−	0.508959i	$-0.830031\pi$
$823$	−49.3887	−1.72158	−0.860791	+	0.508959i	$0.830031\pi$
$824$	−107.162	−3.73317
$825$	−15.8088	−0.550392
$826$	−122.097	−4.24829
$827$	4.58007	0.159264	0.0796322	−	0.996824i	$-0.474625\pi$
$827$	4.58007	0.159264	0.0796322	+	0.996824i	$0.474625\pi$
$828$	62.2072	2.16185
$829$	13.2943	0.461729	0.230865	−	0.972986i	$-0.425845\pi$
$829$	13.2943	0.461729	0.230865	+	0.972986i	$0.425845\pi$
$830$	1.53466	0.0532688
$831$	−20.7370	−0.719358
$832$	54.6267	1.89384
$833$	−48.9984	−1.69769
$834$	−47.6147	−1.64876
$835$	0.634767	0.0219670
$836$	79.8896	2.76304
$837$	−17.0935	−0.590836
$838$	58.9611	2.03678
$839$	44.1969	1.52585	0.762924	−	0.646489i	$-0.223763\pi$
$839$	44.1969	1.52585	0.762924	+	0.646489i	$0.223763\pi$
$840$	−3.39150	−0.117018
$841$	−28.8719	−0.995584
$842$	−32.2132	−1.11014
$843$	3.36027	0.115734
$844$	−149.165	−5.13447
$845$	−0.783819	−0.0269642
$846$	−14.3749	−0.494220
$847$	3.91364	0.134474
$848$	65.4537	2.24769
$849$	20.6409	0.708393
$850$	−35.8955	−1.23121
$851$	−17.1978	−0.589534
$852$	−30.0547	−1.02966
$853$	41.5134	1.42139	0.710696	−	0.703499i	$-0.248380\pi$
$853$	41.5134	1.42139	0.710696	+	0.703499i	$0.248380\pi$
$854$	−88.9682	−3.04443
$855$	−0.632814	−0.0216418
$856$	−137.035	−4.68374
$857$	22.0481	0.753149	0.376574	−	0.926386i	$-0.377102\pi$
$857$	22.0481	0.753149	0.376574	+	0.926386i	$0.377102\pi$
$858$	−12.5000	−0.426743
$859$	37.0443	1.26393	0.631967	−	0.774995i	$-0.282248\pi$
$859$	37.0443	1.26393	0.631967	+	0.774995i	$0.282248\pi$
$860$	−1.51457	−0.0516465
$861$	1.25265	0.0426901
$862$	−79.0394	−2.69209
$863$	−6.80963	−0.231802	−0.115901	−	0.993261i	$-0.536976\pi$
$863$	−6.80963	−0.231802	−0.115901	+	0.993261i	$0.536976\pi$
$864$	122.915	4.18164
$865$	1.12953	0.0384050
$866$	97.2755	3.30555
$867$	−9.45867	−0.321233
$868$	103.474	3.51215
$869$	3.25846	0.110536
$870$	0.0653081	0.00221415
$871$	−10.3797	−0.351704
$872$	87.3387	2.95766
$873$	−7.63462	−0.258393
$874$	58.3376	1.97330
$875$	−3.63446	−0.122867
$876$	−30.1927	−1.02012
$877$	−25.5099	−0.861408	−0.430704	−	0.902493i	$-0.641735\pi$
$877$	−25.5099	−0.861408	−0.430704	+	0.902493i	$0.641735\pi$
$878$	49.2443	1.66191
$879$	−12.0836	−0.407568
$880$	4.08703	0.137774
$881$	−9.62457	−0.324260	−0.162130	−	0.986769i	$-0.551836\pi$
$881$	−9.62457	−0.324260	−0.162130	+	0.986769i	$0.551836\pi$
$882$	112.145	3.77611
$883$	14.0021	0.471208	0.235604	−	0.971849i	$-0.424293\pi$
$883$	14.0021	0.471208	0.235604	+	0.971849i	$0.424293\pi$
$884$	−20.9663	−0.705174
$885$	0.572436	0.0192422
$886$	6.85663	0.230353
$887$	−34.0375	−1.14287	−0.571434	−	0.820648i	$-0.693613\pi$
$887$	−34.0375	−1.14287	−0.571434	+	0.820648i	$0.693613\pi$
$888$	−31.3290	−1.05133
$889$	−5.85761	−0.196458
$890$	−1.30258	−0.0436625
$891$	7.08227	0.237265
$892$	154.081	5.15900
$893$	−9.95828	−0.333241
$894$	7.94156	0.265605
$895$	0.654674	0.0218834
$896$	−275.214	−9.19425
$897$	−6.74279	−0.225135
$898$	−5.05878	−0.168814
$899$	−1.28774	−0.0429485
$900$	60.6888	2.02296
$901$	−10.2045	−0.339961
$902$	−2.53410	−0.0843762
$903$	−17.5766	−0.584913
$904$	−79.5225	−2.64488
$905$	−1.43582	−0.0477284
$906$	−39.4623	−1.31105
$907$	26.0904	0.866318	0.433159	−	0.901317i	$-0.357399\pi$
$907$	26.0904	0.866318	0.433159	+	0.901317i	$0.357399\pi$
$908$	−120.101	−3.98568
$909$	−38.0471	−1.26194
$910$	−1.43615	−0.0476078
$911$	59.6332	1.97574	0.987868	−	0.155293i	$-0.0496321\pi$
$911$	59.6332	1.97574	0.987868	+	0.155293i	$0.0496321\pi$
$912$	63.3056	2.09626
$913$	−26.6148	−0.880820
$914$	−92.5138	−3.06009
$915$	0.417117	0.0137895
$916$	−124.635	−4.11807
$917$	32.8339	1.08427
$918$	−34.1367	−1.12668
$919$	24.7324	0.815848	0.407924	−	0.913016i	$-0.366253\pi$
$919$	24.7324	0.815848	0.407924	+	0.913016i	$0.366253\pi$
$920$	3.70097	0.122017
$921$	10.7502	0.354231
$922$	98.6017	3.24727
$923$	−8.22505	−0.270731
$924$	91.0087	2.99397
$925$	−16.7780	−0.551659
$926$	22.9089	0.752834
$927$	−22.7781	−0.748131
$928$	9.25979	0.303968
$929$	−35.2500	−1.15651	−0.578257	−	0.815854i	$-0.696267\pi$
$929$	−35.2500	−1.15651	−0.578257	+	0.815854i	$0.696267\pi$
$930$	−0.656728	−0.0215350
$931$	77.6887	2.54614
$932$	92.1025	3.01692
$933$	15.7854	0.516790
$934$	33.0727	1.08217
$935$	−0.637186	−0.0208382
$936$	31.0127	1.01368
$937$	43.9841	1.43690	0.718449	−	0.695580i	$-0.244852\pi$
$937$	43.9841	1.43690	0.718449	+	0.695580i	$0.244852\pi$
$938$	102.303	3.34032
$939$	−18.6755	−0.609451
$940$	−0.977533	−0.0318836
$941$	52.7697	1.72024	0.860122	−	0.510089i	$-0.170388\pi$
$941$	52.7697	1.72024	0.860122	+	0.510089i	$0.170388\pi$
$942$	−32.1363	−1.04706
$943$	−1.36695	−0.0445140
$944$	144.584	4.70582
$945$	−1.72730	−0.0561892
$946$	35.5574	1.15607
$947$	−21.8481	−0.709968	−0.354984	−	0.934872i	$-0.615514\pi$
$947$	−21.8481	−0.709968	−0.354984	+	0.934872i	$0.615514\pi$
$948$	4.95444	0.160913
$949$	−8.26283	−0.268223
$950$	56.9136	1.84652
$951$	−28.0362	−0.909137
$952$	133.550	4.32839
$953$	15.9703	0.517327	0.258664	−	0.965967i	$-0.416718\pi$
$953$	15.9703	0.517327	0.258664	+	0.965967i	$0.416718\pi$
$954$	23.3555	0.756162
$955$	1.42431	0.0460897
$956$	56.1294	1.81535
$957$	−1.13260	−0.0366119
$958$	−45.0130	−1.45430
$959$	82.5637	2.66612
$960$	2.52424	0.0814695
$961$	−18.0507	−0.582280
$962$	−13.2664	−0.427725
$963$	−29.1277	−0.938628
$964$	−17.1421	−0.552109
$965$	−0.824756	−0.0265498
$966$	66.4572	2.13822
$967$	−56.1222	−1.80477	−0.902385	−	0.430931i	$-0.858185\pi$
$967$	−56.1222	−1.80477	−0.902385	+	0.430931i	$0.858185\pi$
$968$	−7.77995	−0.250057
$969$	−9.86962	−0.317058
$970$	−0.702818	−0.0225661
$971$	2.87793	0.0923572	0.0461786	−	0.998933i	$-0.485296\pi$
$971$	2.87793	0.0923572	0.0461786	+	0.998933i	$0.485296\pi$
$972$	91.3427	2.92982
$973$	94.8724	3.04147
$974$	90.9741	2.91500
$975$	−6.57819	−0.210671
$976$	105.354	3.37231
$977$	−9.88076	−0.316114	−0.158057	−	0.987430i	$-0.550523\pi$
$977$	−9.88076	−0.316114	−0.158057	+	0.987430i	$0.550523\pi$
$978$	−52.8052	−1.68852
$979$	22.5899	0.721976
$980$	7.62615	0.243608
$981$	18.5645	0.592719
$982$	−47.0829	−1.50247
$983$	9.37571	0.299039	0.149519	−	0.988759i	$-0.452227\pi$
$983$	9.37571	0.299039	0.149519	+	0.988759i	$0.452227\pi$
$984$	−2.49014	−0.0793829
$985$	−1.05525	−0.0336230
$986$	−2.57170	−0.0818995
$987$	−11.3443	−0.361093
$988$	33.2428	1.05760
$989$	19.1805	0.609904
$990$	1.45836	0.0463496
$991$	40.6505	1.29131	0.645653	−	0.763631i	$-0.276585\pi$
$991$	40.6505	1.29131	0.645653	+	0.763631i	$0.276585\pi$
$992$	−93.1150	−2.95641
$993$	6.52254	0.206987
$994$	81.0664	2.57127
$995$	0.931249	0.0295226
$996$	−40.4673	−1.28226
$997$	9.92219	0.314239	0.157120	−	0.987580i	$-0.449779\pi$
$997$	9.92219	0.314239	0.157120	+	0.987580i	$0.449779\pi$
$998$	30.3605	0.961046
$999$	−15.9559	−0.504823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.4	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.4	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76662 q^{2} +0.922557 q^{3} +5.65417 q^{4} +0.0715024 q^{5} -2.55236 q^{6} +5.08559 q^{7} -10.1097 q^{8} -2.14889 q^{9} +O(q^{10})\)	\(q-2.76662 q^{2} +0.922557 q^{3} +5.65417 q^{4} +0.0715024 q^{5} -2.55236 q^{6} +5.08559 q^{7} -10.1097 q^{8} -2.14889 q^{9} -0.197820 q^{10} +3.43068 q^{11} +5.21629 q^{12} +1.42754 q^{13} -14.0699 q^{14} +0.0659650 q^{15} +16.6613 q^{16} -2.59756 q^{17} +5.94515 q^{18} +4.11852 q^{19} +0.404286 q^{20} +4.69175 q^{21} -9.49137 q^{22} -5.11986 q^{23} -9.32675 q^{24} -4.99489 q^{25} -3.94945 q^{26} -4.75014 q^{27} +28.7548 q^{28} -0.357853 q^{29} -0.182500 q^{30} +3.59851 q^{31} -25.8760 q^{32} +3.16500 q^{33} +7.18646 q^{34} +0.363632 q^{35} -12.1502 q^{36} +3.35904 q^{37} -11.3944 q^{38} +1.31699 q^{39} -0.722866 q^{40} +0.266990 q^{41} -12.9803 q^{42} -3.74629 q^{43} +19.3976 q^{44} -0.153651 q^{45} +14.1647 q^{46} -2.41792 q^{47} +15.3710 q^{48} +18.8632 q^{49} +13.8189 q^{50} -2.39640 q^{51} +8.07154 q^{52} +3.92849 q^{53} +13.1418 q^{54} +0.245302 q^{55} -51.4137 q^{56} +3.79957 q^{57} +0.990042 q^{58} +8.67788 q^{59} +0.372977 q^{60} +6.32331 q^{61} -9.95571 q^{62} -10.9284 q^{63} +38.2663 q^{64} +0.102072 q^{65} -8.75633 q^{66} -7.27108 q^{67} -14.6870 q^{68} -4.72336 q^{69} -1.00603 q^{70} -5.76170 q^{71} +21.7246 q^{72} -5.78816 q^{73} -9.29318 q^{74} -4.60807 q^{75} +23.2868 q^{76} +17.4470 q^{77} -3.64359 q^{78} +0.949801 q^{79} +1.19132 q^{80} +2.06439 q^{81} -0.738658 q^{82} -7.75787 q^{83} +26.5279 q^{84} -0.185732 q^{85} +10.3645 q^{86} -0.330140 q^{87} -34.6830 q^{88} +6.58467 q^{89} +0.425092 q^{90} +7.25988 q^{91} -28.9486 q^{92} +3.31983 q^{93} +6.68947 q^{94} +0.294484 q^{95} -23.8720 q^{96} +3.55282 q^{97} -52.1873 q^{98} -7.37215 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more