LMFDB - Embedded newform 4017.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25716 q^{2} -1.00000 q^{3} +3.09477 q^{4} -2.92277 q^{5} +2.25716 q^{6} -0.587921 q^{7} -2.47106 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.25716 q^{2} -1.00000 q^{3} +3.09477 q^{4} -2.92277 q^{5} +2.25716 q^{6} -0.587921 q^{7} -2.47106 q^{8} +1.00000 q^{9} +6.59715 q^{10} -5.37503 q^{11} -3.09477 q^{12} -1.00000 q^{13} +1.32703 q^{14} +2.92277 q^{15} -0.611949 q^{16} -6.46179 q^{17} -2.25716 q^{18} +7.52687 q^{19} -9.04529 q^{20} +0.587921 q^{21} +12.1323 q^{22} -5.75965 q^{23} +2.47106 q^{24} +3.54257 q^{25} +2.25716 q^{26} -1.00000 q^{27} -1.81948 q^{28} +9.64388 q^{29} -6.59715 q^{30} +9.29536 q^{31} +6.32340 q^{32} +5.37503 q^{33} +14.5853 q^{34} +1.71835 q^{35} +3.09477 q^{36} -8.26104 q^{37} -16.9893 q^{38} +1.00000 q^{39} +7.22235 q^{40} +5.57815 q^{41} -1.32703 q^{42} +3.50825 q^{43} -16.6345 q^{44} -2.92277 q^{45} +13.0004 q^{46} -0.0118009 q^{47} +0.611949 q^{48} -6.65435 q^{49} -7.99614 q^{50} +6.46179 q^{51} -3.09477 q^{52} -1.48859 q^{53} +2.25716 q^{54} +15.7100 q^{55} +1.45279 q^{56} -7.52687 q^{57} -21.7678 q^{58} +5.63826 q^{59} +9.04529 q^{60} -8.71242 q^{61} -20.9811 q^{62} -0.587921 q^{63} -13.0490 q^{64} +2.92277 q^{65} -12.1323 q^{66} +2.08129 q^{67} -19.9977 q^{68} +5.75965 q^{69} -3.87860 q^{70} +2.18111 q^{71} -2.47106 q^{72} -4.53662 q^{73} +18.6465 q^{74} -3.54257 q^{75} +23.2939 q^{76} +3.16009 q^{77} -2.25716 q^{78} +12.6892 q^{79} +1.78858 q^{80} +1.00000 q^{81} -12.5908 q^{82} +10.9485 q^{83} +1.81948 q^{84} +18.8863 q^{85} -7.91869 q^{86} -9.64388 q^{87} +13.2820 q^{88} -7.79969 q^{89} +6.59715 q^{90} +0.587921 q^{91} -17.8248 q^{92} -9.29536 q^{93} +0.0266366 q^{94} -21.9993 q^{95} -6.32340 q^{96} -2.18498 q^{97} +15.0199 q^{98} -5.37503 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−2.25716	−1.59605	−0.798026	−	0.602623i	$-0.794122\pi$
$2$	−2.25716	−1.59605	−0.798026	+	0.602623i	$0.794122\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.09477	1.54738
$5$	−2.92277	−1.30710	−0.653551	−	0.756883i	$-0.726721\pi$
$5$	−2.92277	−1.30710	−0.653551	+	0.756883i	$0.726721\pi$
$6$	2.25716	0.921481
$7$	−0.587921	−0.222213	−0.111107	−	0.993809i	$-0.535439\pi$
$7$	−0.587921	−0.222213	−0.111107	+	0.993809i	$0.535439\pi$
$8$	−2.47106	−0.873653
$9$	1.00000	0.333333
$10$	6.59715	2.08620
$11$	−5.37503	−1.62063	−0.810316	−	0.585993i	$-0.800704\pi$
$11$	−5.37503	−1.62063	−0.810316	+	0.585993i	$0.800704\pi$
$12$	−3.09477	−0.893382
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.32703	0.354664
$15$	2.92277	0.754655
$16$	−0.611949	−0.152987
$17$	−6.46179	−1.56721	−0.783607	−	0.621256i	$-0.786623\pi$
$17$	−6.46179	−1.56721	−0.783607	+	0.621256i	$0.786623\pi$
$18$	−2.25716	−0.532018
$19$	7.52687	1.72678	0.863391	−	0.504535i	$-0.168336\pi$
$19$	7.52687	1.72678	0.863391	+	0.504535i	$0.168336\pi$
$20$	−9.04529	−2.02259
$21$	0.587921	0.128295
$22$	12.1323	2.58661
$23$	−5.75965	−1.20097	−0.600485	−	0.799636i	$-0.705026\pi$
$23$	−5.75965	−1.20097	−0.600485	+	0.799636i	$0.705026\pi$
$24$	2.47106	0.504404
$25$	3.54257	0.708514
$26$	2.25716	0.442665
$27$	−1.00000	−0.192450
$28$	−1.81948	−0.343849
$29$	9.64388	1.79082	0.895412	−	0.445239i	$-0.146881\pi$
$29$	9.64388	1.79082	0.895412	+	0.445239i	$0.146881\pi$
$30$	−6.59715	−1.20447
$31$	9.29536	1.66950	0.834748	−	0.550632i	$-0.185613\pi$
$31$	9.29536	1.66950	0.834748	+	0.550632i	$0.185613\pi$
$32$	6.32340	1.11783
$33$	5.37503	0.935672
$34$	14.5853	2.50136
$35$	1.71835	0.290455
$36$	3.09477	0.515795
$37$	−8.26104	−1.35811	−0.679053	−	0.734089i	$-0.737609\pi$
$37$	−8.26104	−1.35811	−0.679053	+	0.734089i	$0.737609\pi$
$38$	−16.9893	−2.75603
$39$	1.00000	0.160128
$40$	7.22235	1.14195
$41$	5.57815	0.871161	0.435580	−	0.900150i	$-0.356543\pi$
$41$	5.57815	0.871161	0.435580	+	0.900150i	$0.356543\pi$
$42$	−1.32703	−0.204765
$43$	3.50825	0.535004	0.267502	−	0.963557i	$-0.413802\pi$
$43$	3.50825	0.535004	0.267502	+	0.963557i	$0.413802\pi$
$44$	−16.6345	−2.50774
$45$	−2.92277	−0.435700
$46$	13.0004	1.91681
$47$	−0.0118009	−0.00172134	−0.000860672	−	1.00000i	$-0.500274\pi$
$47$	−0.0118009	−0.00172134	−0.000860672		1.00000i	$0.500274\pi$
$48$	0.611949	0.0883272
$49$	−6.65435	−0.950621
$50$	−7.99614	−1.13082
$51$	6.46179	0.904832
$52$	−3.09477	−0.429167
$53$	−1.48859	−0.204474	−0.102237	−	0.994760i	$-0.532600\pi$
$53$	−1.48859	−0.204474	−0.102237	+	0.994760i	$0.532600\pi$
$54$	2.25716	0.307160
$55$	15.7100	2.11833
$56$	1.45279	0.194137
$57$	−7.52687	−0.996958
$58$	−21.7678	−2.85825
$59$	5.63826	0.734039	0.367020	−	0.930213i	$-0.380378\pi$
$59$	5.63826	0.734039	0.367020	+	0.930213i	$0.380378\pi$
$60$	9.04529	1.16774
$61$	−8.71242	−1.11551	−0.557756	−	0.830005i	$-0.688337\pi$
$61$	−8.71242	−1.11551	−0.557756	+	0.830005i	$0.688337\pi$
$62$	−20.9811	−2.66460
$63$	−0.587921	−0.0740710
$64$	−13.0490	−1.63113
$65$	2.92277	0.362525
$66$	−12.1323	−1.49338
$67$	2.08129	0.254270	0.127135	−	0.991885i	$-0.459422\pi$
$67$	2.08129	0.254270	0.127135	+	0.991885i	$0.459422\pi$
$68$	−19.9977	−2.42508
$69$	5.75965	0.693380
$70$	−3.87860	−0.463581
$71$	2.18111	0.258850	0.129425	−	0.991589i	$-0.458687\pi$
$71$	2.18111	0.258850	0.129425	+	0.991589i	$0.458687\pi$
$72$	−2.47106	−0.291218
$73$	−4.53662	−0.530971	−0.265485	−	0.964115i	$-0.585532\pi$
$73$	−4.53662	−0.530971	−0.265485	+	0.964115i	$0.585532\pi$
$74$	18.6465	2.16761
$75$	−3.54257	−0.409061
$76$	23.2939	2.67199
$77$	3.16009	0.360126
$78$	−2.25716	−0.255573
$79$	12.6892	1.42764	0.713820	−	0.700329i	$-0.246963\pi$
$79$	12.6892	1.42764	0.713820	+	0.700329i	$0.246963\pi$
$80$	1.78858	0.199970
$81$	1.00000	0.111111
$82$	−12.5908	−1.39042
$83$	10.9485	1.20175	0.600876	−	0.799342i	$-0.294818\pi$
$83$	10.9485	1.20175	0.600876	+	0.799342i	$0.294818\pi$
$84$	1.81948	0.198521
$85$	18.8863	2.04851
$86$	−7.91869	−0.853894
$87$	−9.64388	−1.03393
$88$	13.2820	1.41587
$89$	−7.79969	−0.826766	−0.413383	−	0.910557i	$-0.635653\pi$
$89$	−7.79969	−0.826766	−0.413383	+	0.910557i	$0.635653\pi$
$90$	6.59715	0.695401
$91$	0.587921	0.0616308
$92$	−17.8248	−1.85836
$93$	−9.29536	−0.963884
$94$	0.0266366	0.00274736
$95$	−21.9993	−2.25708
$96$	−6.32340	−0.645379
$97$	−2.18498	−0.221851	−0.110925	−	0.993829i	$-0.535381\pi$
$97$	−2.18498	−0.221851	−0.110925	+	0.993829i	$0.535381\pi$
$98$	15.0199	1.51724
$99$	−5.37503	−0.540211
$100$	10.9634	1.09634
$101$	14.9541	1.48799	0.743996	−	0.668184i	$-0.232928\pi$
$101$	14.9541	1.48799	0.743996	+	0.668184i	$0.232928\pi$
$102$	−14.5853	−1.44416
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.47106	0.242308
$105$	−1.71835	−0.167694
$106$	3.35999	0.326351
$107$	−2.92624	−0.282890	−0.141445	−	0.989946i	$-0.545175\pi$
$107$	−2.92624	−0.282890	−0.141445	+	0.989946i	$0.545175\pi$
$108$	−3.09477	−0.297794
$109$	−5.75011	−0.550761	−0.275380	−	0.961335i	$-0.588804\pi$
$109$	−5.75011	−0.550761	−0.275380	+	0.961335i	$0.588804\pi$
$110$	−35.4599	−3.38097
$111$	8.26104	0.784103
$112$	0.359777	0.0339958
$113$	19.9754	1.87913	0.939564	−	0.342372i	$-0.111230\pi$
$113$	19.9754	1.87913	0.939564	+	0.342372i	$0.111230\pi$
$114$	16.9893	1.59120
$115$	16.8341	1.56979
$116$	29.8456	2.77109
$117$	−1.00000	−0.0924500
$118$	−12.7265	−1.17157
$119$	3.79902	0.348256
$120$	−7.22235	−0.659307
$121$	17.8909	1.62645
$122$	19.6653	1.78041
$123$	−5.57815	−0.502965
$124$	28.7670	2.58335
$125$	4.25973	0.381002
$126$	1.32703	0.118221
$127$	8.39159	0.744633	0.372317	−	0.928106i	$-0.378564\pi$
$127$	8.39159	0.744633	0.372317	+	0.928106i	$0.378564\pi$
$128$	16.8069	1.48553
$129$	−3.50825	−0.308885
$130$	−6.59715	−0.578608
$131$	−7.71124	−0.673734	−0.336867	−	0.941552i	$-0.609367\pi$
$131$	−7.71124	−0.673734	−0.336867	+	0.941552i	$0.609367\pi$
$132$	16.6345	1.44784
$133$	−4.42520	−0.383714
$134$	−4.69780	−0.405828
$135$	2.92277	0.251552
$136$	15.9675	1.36920
$137$	14.0002	1.19612	0.598060	−	0.801451i	$-0.295938\pi$
$137$	14.0002	1.19612	0.598060	+	0.801451i	$0.295938\pi$
$138$	−13.0004	−1.10667
$139$	−21.6096	−1.83290	−0.916451	−	0.400146i	$-0.868959\pi$
$139$	−21.6096	−1.83290	−0.916451	+	0.400146i	$0.868959\pi$
$140$	5.31791	0.449445
$141$	0.0118009	0.000993818 0
$142$	−4.92311	−0.413138
$143$	5.37503	0.449482
$144$	−0.611949	−0.0509957
$145$	−28.1868	−2.34079
$146$	10.2399	0.847457
$147$	6.65435	0.548841
$148$	−25.5660	−2.10151
$149$	−5.11715	−0.419213	−0.209607	−	0.977786i	$-0.567218\pi$
$149$	−5.11715	−0.419213	−0.209607	+	0.977786i	$0.567218\pi$
$150$	7.99614	0.652882
$151$	7.65105	0.622634	0.311317	−	0.950306i	$-0.399230\pi$
$151$	7.65105	0.622634	0.311317	+	0.950306i	$0.399230\pi$
$152$	−18.5994	−1.50861
$153$	−6.46179	−0.522405
$154$	−7.13282	−0.574779
$155$	−27.1682	−2.18220
$156$	3.09477	0.247780
$157$	20.1095	1.60491	0.802456	−	0.596711i	$-0.203526\pi$
$157$	20.1095	1.60491	0.802456	+	0.596711i	$0.203526\pi$
$158$	−28.6414	−2.27859
$159$	1.48859	0.118053
$160$	−18.4818	−1.46112
$161$	3.38622	0.266871
$162$	−2.25716	−0.177339
$163$	21.6686	1.69722	0.848608	−	0.529022i	$-0.177441\pi$
$163$	21.6686	1.69722	0.848608	+	0.529022i	$0.177441\pi$
$164$	17.2631	1.34802
$165$	−15.7100	−1.22302
$166$	−24.7125	−1.91806
$167$	−15.5209	−1.20104	−0.600520	−	0.799610i	$-0.705040\pi$
$167$	−15.5209	−1.20104	−0.600520	+	0.799610i	$0.705040\pi$
$168$	−1.45279	−0.112085
$169$	1.00000	0.0769231
$170$	−42.6294	−3.26953
$171$	7.52687	0.575594
$172$	10.8572	0.827856
$173$	−17.1058	−1.30053	−0.650267	−	0.759706i	$-0.725343\pi$
$173$	−17.1058	−1.30053	−0.650267	+	0.759706i	$0.725343\pi$
$174$	21.7678	1.65021
$175$	−2.08275	−0.157441
$176$	3.28924	0.247936
$177$	−5.63826	−0.423798
$178$	17.6052	1.31956
$179$	−21.9200	−1.63837	−0.819187	−	0.573526i	$-0.805575\pi$
$179$	−21.9200	−1.63837	−0.819187	+	0.573526i	$0.805575\pi$
$180$	−9.04529	−0.674196
$181$	2.14057	0.159107	0.0795536	−	0.996831i	$-0.474651\pi$
$181$	2.14057	0.159107	0.0795536	+	0.996831i	$0.474651\pi$
$182$	−1.32703	−0.0983660
$183$	8.71242	0.644041
$184$	14.2325	1.04923
$185$	24.1451	1.77518
$186$	20.9811	1.53841
$187$	34.7323	2.53988
$188$	−0.0365212	−0.00266358
$189$	0.587921	0.0427649
$190$	49.6559	3.60242
$191$	11.5993	0.839295	0.419647	−	0.907687i	$-0.362154\pi$
$191$	11.5993	0.839295	0.419647	+	0.907687i	$0.362154\pi$
$192$	13.0490	0.941731
$193$	−6.05154	−0.435599	−0.217800	−	0.975994i	$-0.569888\pi$
$193$	−6.05154	−0.435599	−0.217800	+	0.975994i	$0.569888\pi$
$194$	4.93184	0.354085
$195$	−2.92277	−0.209304
$196$	−20.5937	−1.47098
$197$	7.99866	0.569881	0.284941	−	0.958545i	$-0.408026\pi$
$197$	7.99866	0.569881	0.284941	+	0.958545i	$0.408026\pi$
$198$	12.1323	0.862204
$199$	5.59952	0.396940	0.198470	−	0.980107i	$-0.436403\pi$
$199$	5.59952	0.396940	0.198470	+	0.980107i	$0.436403\pi$
$200$	−8.75391	−0.618995
$201$	−2.08129	−0.146803
$202$	−33.7539	−2.37491
$203$	−5.66984	−0.397944
$204$	19.9977	1.40012
$205$	−16.3036	−1.13870
$206$	2.25716	0.157264
$207$	−5.75965	−0.400323
$208$	0.611949	0.0424310
$209$	−40.4571	−2.79848
$210$	3.87860	0.267649
$211$	−20.9278	−1.44073	−0.720364	−	0.693596i	$-0.756025\pi$
$211$	−20.9278	−1.44073	−0.720364	+	0.693596i	$0.756025\pi$
$212$	−4.60685	−0.316400
$213$	−2.18111	−0.149447
$214$	6.60499	0.451508
$215$	−10.2538	−0.699304
$216$	2.47106	0.168135
$217$	−5.46494	−0.370984
$218$	12.9789	0.879043
$219$	4.53662	0.306556
$220$	48.6187	3.27787
$221$	6.46179	0.434667
$222$	−18.6465	−1.25147
$223$	−3.40291	−0.227876	−0.113938	−	0.993488i	$-0.536346\pi$
$223$	−3.40291	−0.227876	−0.113938	+	0.993488i	$0.536346\pi$
$224$	−3.71765	−0.248396
$225$	3.54257	0.236171
$226$	−45.0877	−2.99919
$227$	17.2965	1.14801	0.574003	−	0.818853i	$-0.305390\pi$
$227$	17.2965	1.14801	0.574003	+	0.818853i	$0.305390\pi$
$228$	−23.2939	−1.54268
$229$	2.42097	0.159982	0.0799912	−	0.996796i	$-0.474511\pi$
$229$	2.42097	0.159982	0.0799912	+	0.996796i	$0.474511\pi$
$230$	−37.9973	−2.50547
$231$	−3.16009	−0.207919
$232$	−23.8307	−1.56456
$233$	−20.9613	−1.37322	−0.686611	−	0.727025i	$-0.740902\pi$
$233$	−20.9613	−1.37322	−0.686611	+	0.727025i	$0.740902\pi$
$234$	2.25716	0.147555
$235$	0.0344914	0.00224997
$236$	17.4491	1.13584
$237$	−12.6892	−0.824249
$238$	−8.57499	−0.555834
$239$	−4.82336	−0.311997	−0.155999	−	0.987757i	$-0.549860\pi$
$239$	−4.82336	−0.311997	−0.155999	+	0.987757i	$0.549860\pi$
$240$	−1.78858	−0.115453
$241$	28.3011	1.82304	0.911518	−	0.411260i	$-0.134911\pi$
$241$	28.3011	1.82304	0.911518	+	0.411260i	$0.134911\pi$
$242$	−40.3826	−2.59590
$243$	−1.00000	−0.0641500
$244$	−26.9629	−1.72612
$245$	19.4491	1.24256
$246$	12.5908	0.802758
$247$	−7.52687	−0.478923
$248$	−22.9694	−1.45856
$249$	−10.9485	−0.693832
$250$	−9.61490	−0.608100
$251$	15.8831	1.00253	0.501266	−	0.865293i	$-0.332868\pi$
$251$	15.8831	1.00253	0.501266	+	0.865293i	$0.332868\pi$
$252$	−1.81948	−0.114616
$253$	30.9583	1.94633
$254$	−18.9412	−1.18847
$255$	−18.8863	−1.18271
$256$	−11.8378	−0.739865
$257$	−5.00871	−0.312435	−0.156217	−	0.987723i	$-0.549930\pi$
$257$	−5.00871	−0.312435	−0.156217	+	0.987723i	$0.549930\pi$
$258$	7.91869	0.492996
$259$	4.85683	0.301789
$260$	9.04529	0.560965
$261$	9.64388	0.596941
$262$	17.4055	1.07531
$263$	−21.0825	−1.30000	−0.650001	−	0.759934i	$-0.725231\pi$
$263$	−21.0825	−1.30000	−0.650001	+	0.759934i	$0.725231\pi$
$264$	−13.2820	−0.817453
$265$	4.35081	0.267268
$266$	9.98838	0.612427
$267$	7.79969	0.477334
$268$	6.44110	0.393453
$269$	−9.58511	−0.584415	−0.292207	−	0.956355i	$-0.594390\pi$
$269$	−9.58511	−0.584415	−0.292207	+	0.956355i	$0.594390\pi$
$270$	−6.59715	−0.401490
$271$	−7.13890	−0.433657	−0.216829	−	0.976210i	$-0.569571\pi$
$271$	−7.13890	−0.433657	−0.216829	+	0.976210i	$0.569571\pi$
$272$	3.95429	0.239764
$273$	−0.587921	−0.0355826
$274$	−31.6007	−1.90907
$275$	−19.0414	−1.14824
$276$	17.8248	1.07293
$277$	5.66932	0.340636	0.170318	−	0.985389i	$-0.445520\pi$
$277$	5.66932	0.340636	0.170318	+	0.985389i	$0.445520\pi$
$278$	48.7763	2.92541
$279$	9.29536	0.556499
$280$	−4.24617	−0.253757
$281$	3.96625	0.236607	0.118303	−	0.992978i	$-0.462255\pi$
$281$	3.96625	0.236607	0.118303	+	0.992978i	$0.462255\pi$
$282$	−0.0266366	−0.00158619
$283$	−27.8791	−1.65724	−0.828620	−	0.559811i	$-0.810874\pi$
$283$	−27.8791	−1.65724	−0.828620	+	0.559811i	$0.810874\pi$
$284$	6.75002	0.400540
$285$	21.9993	1.30313
$286$	−12.1323	−0.717397
$287$	−3.27951	−0.193583
$288$	6.32340	0.372610
$289$	24.7548	1.45616
$290$	63.6221	3.73602
$291$	2.18498	0.128086
$292$	−14.0398	−0.821616
$293$	−3.10826	−0.181587	−0.0907933	−	0.995870i	$-0.528940\pi$
$293$	−3.10826	−0.181587	−0.0907933	+	0.995870i	$0.528940\pi$
$294$	−15.0199	−0.875980
$295$	−16.4793	−0.959464
$296$	20.4136	1.18651
$297$	5.37503	0.311891
$298$	11.5502	0.669086
$299$	5.75965	0.333089
$300$	−10.9634	−0.632974
$301$	−2.06257	−0.118885
$302$	−17.2696	−0.993756
$303$	−14.9541	−0.859093
$304$	−4.60606	−0.264176
$305$	25.4644	1.45809
$306$	14.5853	0.833786
$307$	−0.938215	−0.0535467	−0.0267734	−	0.999642i	$-0.508523\pi$
$307$	−0.938215	−0.0535467	−0.0267734	+	0.999642i	$0.508523\pi$
$308$	9.77974	0.557252
$309$	1.00000	0.0568880
$310$	61.3229	3.48291
$311$	−16.7680	−0.950827	−0.475413	−	0.879762i	$-0.657702\pi$
$311$	−16.7680	−0.950827	−0.475413	+	0.879762i	$0.657702\pi$
$312$	−2.47106	−0.139896
$313$	−26.4672	−1.49601	−0.748007	−	0.663691i	$-0.768989\pi$
$313$	−26.4672	−1.49601	−0.748007	+	0.663691i	$0.768989\pi$
$314$	−45.3903	−2.56152
$315$	1.71835	0.0968183
$316$	39.2700	2.20911
$317$	31.9797	1.79616	0.898078	−	0.439836i	$-0.144963\pi$
$317$	31.9797	1.79616	0.898078	+	0.439836i	$0.144963\pi$
$318$	−3.35999	−0.188419
$319$	−51.8361	−2.90227
$320$	38.1392	2.13205
$321$	2.92624	0.163327
$322$	−7.64323	−0.425941
$323$	−48.6371	−2.70624
$324$	3.09477	0.171932
$325$	−3.54257	−0.196506
$326$	−48.9095	−2.70885
$327$	5.75011	0.317982
$328$	−13.7840	−0.761092
$329$	0.00693802	0.000382505 0
$330$	35.4599	1.95200
$331$	17.4416	0.958676	0.479338	−	0.877630i	$-0.340877\pi$
$331$	17.4416	0.958676	0.479338	+	0.877630i	$0.340877\pi$
$332$	33.8830	1.85957
$333$	−8.26104	−0.452702
$334$	35.0331	1.91692
$335$	−6.08312	−0.332356
$336$	−0.359777	−0.0196275
$337$	−1.36939	−0.0745956	−0.0372978	−	0.999304i	$-0.511875\pi$
$337$	−1.36939	−0.0745956	−0.0372978	+	0.999304i	$0.511875\pi$
$338$	−2.25716	−0.122773
$339$	−19.9754	−1.08492
$340$	58.4488	3.16983
$341$	−49.9628	−2.70564
$342$	−16.9893	−0.918678
$343$	8.02767	0.433454
$344$	−8.66912	−0.467408
$345$	−16.8341	−0.906318
$346$	38.6106	2.07572
$347$	−26.3269	−1.41330	−0.706650	−	0.707563i	$-0.749794\pi$
$347$	−26.3269	−1.41330	−0.706650	+	0.707563i	$0.749794\pi$
$348$	−29.8456	−1.59989
$349$	−1.01136	−0.0541366	−0.0270683	−	0.999634i	$-0.508617\pi$
$349$	−1.01136	−0.0541366	−0.0270683	+	0.999634i	$0.508617\pi$
$350$	4.70110	0.251284
$351$	1.00000	0.0533761
$352$	−33.9884	−1.81159
$353$	5.01827	0.267096	0.133548	−	0.991042i	$-0.457363\pi$
$353$	5.01827	0.267096	0.133548	+	0.991042i	$0.457363\pi$
$354$	12.7265	0.676404
$355$	−6.37487	−0.338343
$356$	−24.1382	−1.27932
$357$	−3.79902	−0.201066
$358$	49.4768	2.61493
$359$	−5.14578	−0.271584	−0.135792	−	0.990737i	$-0.543358\pi$
$359$	−5.14578	−0.271584	−0.135792	+	0.990737i	$0.543358\pi$
$360$	7.22235	0.380651
$361$	37.6537	1.98178
$362$	−4.83161	−0.253944
$363$	−17.8909	−0.939030
$364$	1.81948	0.0953665
$365$	13.2595	0.694033
$366$	−19.6653	−1.02792
$367$	−4.09823	−0.213926	−0.106963	−	0.994263i	$-0.534113\pi$
$367$	−4.09823	−0.213926	−0.106963	+	0.994263i	$0.534113\pi$
$368$	3.52461	0.183733
$369$	5.57815	0.290387
$370$	−54.4993	−2.83328
$371$	0.875175	0.0454368
$372$	−28.7670	−1.49150
$373$	−12.6230	−0.653594	−0.326797	−	0.945095i	$-0.605969\pi$
$373$	−12.6230	−0.653594	−0.326797	+	0.945095i	$0.605969\pi$
$374$	−78.3964	−4.05378
$375$	−4.25973	−0.219972
$376$	0.0291609	0.00150386
$377$	−9.64388	−0.496685
$378$	−1.32703	−0.0682551
$379$	21.4445	1.10153	0.550764	−	0.834661i	$-0.314336\pi$
$379$	21.4445	1.10153	0.550764	+	0.834661i	$0.314336\pi$
$380$	−68.0827	−3.49257
$381$	−8.39159	−0.429914
$382$	−26.1814	−1.33956
$383$	−12.7951	−0.653801	−0.326900	−	0.945059i	$-0.606004\pi$
$383$	−12.7951	−0.653801	−0.326900	+	0.945059i	$0.606004\pi$
$384$	−16.8069	−0.857674
$385$	−9.23620	−0.470721
$386$	13.6593	0.695239
$387$	3.50825	0.178335
$388$	−6.76199	−0.343288
$389$	−13.8726	−0.703366	−0.351683	−	0.936119i	$-0.614391\pi$
$389$	−13.8726	−0.703366	−0.351683	+	0.936119i	$0.614391\pi$
$390$	6.59715	0.334060
$391$	37.2177	1.88218
$392$	16.4433	0.830513
$393$	7.71124	0.388980
$394$	−18.0543	−0.909560
$395$	−37.0874	−1.86607
$396$	−16.6345	−0.835913
$397$	−11.1321	−0.558705	−0.279352	−	0.960189i	$-0.590120\pi$
$397$	−11.1321	−0.558705	−0.279352	+	0.960189i	$0.590120\pi$
$398$	−12.6390	−0.633537
$399$	4.42520	0.221537
$400$	−2.16787	−0.108394
$401$	−15.2707	−0.762583	−0.381291	−	0.924455i	$-0.624521\pi$
$401$	−15.2707	−0.762583	−0.381291	+	0.924455i	$0.624521\pi$
$402$	4.69780	0.234305
$403$	−9.29536	−0.463035
$404$	46.2796	2.30250
$405$	−2.92277	−0.145233
$406$	12.7977	0.635140
$407$	44.4033	2.20099
$408$	−15.9675	−0.790509
$409$	−37.9865	−1.87831	−0.939155	−	0.343494i	$-0.888389\pi$
$409$	−37.9865	−1.87831	−0.939155	+	0.343494i	$0.888389\pi$
$410$	36.7999	1.81742
$411$	−14.0002	−0.690580
$412$	−3.09477	−0.152468
$413$	−3.31485	−0.163113
$414$	13.0004	0.638937
$415$	−31.9999	−1.57081
$416$	−6.32340	−0.310030
$417$	21.6096	1.05823
$418$	91.3182	4.46652
$419$	20.0156	0.977828	0.488914	−	0.872332i	$-0.337393\pi$
$419$	20.0156	0.977828	0.488914	+	0.872332i	$0.337393\pi$
$420$	−5.31791	−0.259487
$421$	−9.03489	−0.440334	−0.220167	−	0.975462i	$-0.570660\pi$
$421$	−9.03489	−0.440334	−0.220167	+	0.975462i	$0.570660\pi$
$422$	47.2373	2.29948
$423$	−0.0118009	−0.000573781 0
$424$	3.67841	0.178640
$425$	−22.8913	−1.11039
$426$	4.92311	0.238525
$427$	5.12221	0.247881
$428$	−9.05604	−0.437740
$429$	−5.37503	−0.259509
$430$	23.1445	1.11613
$431$	−10.9479	−0.527344	−0.263672	−	0.964612i	$-0.584934\pi$
$431$	−10.9479	−0.527344	−0.263672	+	0.964612i	$0.584934\pi$
$432$	0.611949	0.0294424
$433$	0.0318180	0.00152907	0.000764537	−	1.00000i	$-0.499757\pi$
$433$	0.0318180	0.00152907	0.000764537		1.00000i	$0.499757\pi$
$434$	12.3352	0.592110
$435$	28.1868	1.35145
$436$	−17.7953	−0.852238
$437$	−43.3521	−2.07381
$438$	−10.2399	−0.489280
$439$	−29.2446	−1.39577	−0.697884	−	0.716211i	$-0.745875\pi$
$439$	−29.2446	−1.39577	−0.697884	+	0.716211i	$0.745875\pi$
$440$	−38.8203	−1.85069
$441$	−6.65435	−0.316874
$442$	−14.5853	−0.693752
$443$	15.3915	0.731272	0.365636	−	0.930758i	$-0.380852\pi$
$443$	15.3915	0.731272	0.365636	+	0.930758i	$0.380852\pi$
$444$	25.5660	1.21331
$445$	22.7967	1.08067
$446$	7.68090	0.363701
$447$	5.11715	0.242033
$448$	7.67178	0.362458
$449$	−6.42926	−0.303415	−0.151708	−	0.988425i	$-0.548477\pi$
$449$	−6.42926	−0.303415	−0.151708	+	0.988425i	$0.548477\pi$
$450$	−7.99614	−0.376942
$451$	−29.9827	−1.41183
$452$	61.8193	2.90773
$453$	−7.65105	−0.359478
$454$	−39.0409	−1.83228
$455$	−1.71835	−0.0805577
$456$	18.5994	0.870996
$457$	−13.4602	−0.629642	−0.314821	−	0.949151i	$-0.601944\pi$
$457$	−13.4602	−0.629642	−0.314821	+	0.949151i	$0.601944\pi$
$458$	−5.46452	−0.255340
$459$	6.46179	0.301611
$460$	52.0977	2.42907
$461$	11.1647	0.519992	0.259996	−	0.965610i	$-0.416279\pi$
$461$	11.1647	0.519992	0.259996	+	0.965610i	$0.416279\pi$
$462$	7.13282	0.331849
$463$	−38.5811	−1.79302	−0.896509	−	0.443026i	$-0.853905\pi$
$463$	−38.5811	−1.79302	−0.896509	+	0.443026i	$0.853905\pi$
$464$	−5.90156	−0.273973
$465$	27.1682	1.25989
$466$	47.3130	2.19173
$467$	−9.57923	−0.443274	−0.221637	−	0.975129i	$-0.571140\pi$
$467$	−9.57923	−0.443274	−0.221637	+	0.975129i	$0.571140\pi$
$468$	−3.09477	−0.143056
$469$	−1.22363	−0.0565020
$470$	−0.0778526	−0.00359107
$471$	−20.1095	−0.926597
$472$	−13.9325	−0.641296
$473$	−18.8570	−0.867044
$474$	28.6414	1.31554
$475$	26.6644	1.22345
$476$	11.7571	0.538885
$477$	−1.48859	−0.0681580
$478$	10.8871	0.497964
$479$	29.4989	1.34784	0.673919	−	0.738805i	$-0.264610\pi$
$479$	29.4989	1.34784	0.673919	+	0.738805i	$0.264610\pi$
$480$	18.4818	0.843575
$481$	8.26104	0.376671
$482$	−63.8802	−2.90966
$483$	−3.38622	−0.154078
$484$	55.3682	2.51674
$485$	6.38617	0.289981
$486$	2.25716	0.102387
$487$	−11.0249	−0.499585	−0.249792	−	0.968299i	$-0.580362\pi$
$487$	−11.0249	−0.499585	−0.249792	+	0.968299i	$0.580362\pi$
$488$	21.5290	0.974570
$489$	−21.6686	−0.979888
$490$	−43.8997	−1.98319
$491$	−8.24834	−0.372242	−0.186121	−	0.982527i	$-0.559592\pi$
$491$	−8.24834	−0.372242	−0.186121	+	0.982527i	$0.559592\pi$
$492$	−17.2631	−0.778280
$493$	−62.3168	−2.80661
$494$	16.9893	0.764387
$495$	15.7100	0.706110
$496$	−5.68829	−0.255412
$497$	−1.28232	−0.0575198
$498$	24.7125	1.10739
$499$	18.8563	0.844122	0.422061	−	0.906567i	$-0.361307\pi$
$499$	18.8563	0.844122	0.422061	+	0.906567i	$0.361307\pi$
$500$	13.1829	0.589557
$501$	15.5209	0.693421
$502$	−35.8507	−1.60009
$503$	14.9861	0.668196	0.334098	−	0.942538i	$-0.391568\pi$
$503$	14.9861	0.668196	0.334098	+	0.942538i	$0.391568\pi$
$504$	1.45279	0.0647124
$505$	−43.7075	−1.94496
$506$	−69.8777	−3.10644
$507$	−1.00000	−0.0444116
$508$	25.9700	1.15223
$509$	−3.03525	−0.134535	−0.0672676	−	0.997735i	$-0.521428\pi$
$509$	−3.03525	−0.134535	−0.0672676	+	0.997735i	$0.521428\pi$
$510$	42.6294	1.88766
$511$	2.66717	0.117989
$512$	−6.89392	−0.304671
$513$	−7.52687	−0.332319
$514$	11.3055	0.498662
$515$	2.92277	0.128793
$516$	−10.8572	−0.477963
$517$	0.0634304	0.00278966
$518$	−10.9626	−0.481671
$519$	17.1058	0.750863
$520$	−7.22235	−0.316721
$521$	1.52073	0.0666245	0.0333123	−	0.999445i	$-0.489394\pi$
$521$	1.52073	0.0666245	0.0333123	+	0.999445i	$0.489394\pi$
$522$	−21.7678	−0.952749
$523$	13.7122	0.599591	0.299795	−	0.954004i	$-0.403082\pi$
$523$	13.7122	0.599591	0.299795	+	0.954004i	$0.403082\pi$
$524$	−23.8645	−1.04252
$525$	2.08275	0.0908986
$526$	47.5865	2.07487
$527$	−60.0647	−2.61646
$528$	−3.28924	−0.143146
$529$	10.1736	0.442329
$530$	−9.82048	−0.426574
$531$	5.63826	0.244680
$532$	−13.6950	−0.593752
$533$	−5.57815	−0.241617
$534$	−17.6052	−0.761849
$535$	8.55272	0.369766
$536$	−5.14299	−0.222144
$537$	21.9200	0.945916
$538$	21.6351	0.932757
$539$	35.7673	1.54061
$540$	9.04529	0.389247
$541$	−26.2097	−1.12684	−0.563421	−	0.826170i	$-0.690515\pi$
$541$	−26.2097	−1.12684	−0.563421	+	0.826170i	$0.690515\pi$
$542$	16.1136	0.692139
$543$	−2.14057	−0.0918606
$544$	−40.8605	−1.75188
$545$	16.8062	0.719900
$546$	1.32703	0.0567917
$547$	1.67777	0.0717363	0.0358681	−	0.999357i	$-0.488580\pi$
$547$	1.67777	0.0717363	0.0358681	+	0.999357i	$0.488580\pi$
$548$	43.3274	1.85086
$549$	−8.71242	−0.371837
$550$	42.9795	1.83265
$551$	72.5882	3.09236
$552$	−14.2325	−0.605774
$553$	−7.46021	−0.317241
$554$	−12.7966	−0.543674
$555$	−24.1451	−1.02490
$556$	−66.8767	−2.83620
$557$	3.24833	0.137636	0.0688181	−	0.997629i	$-0.478077\pi$
$557$	3.24833	0.137636	0.0688181	+	0.997629i	$0.478077\pi$
$558$	−20.9811	−0.888202
$559$	−3.50825	−0.148383
$560$	−1.05155	−0.0444359
$561$	−34.7323	−1.46640
$562$	−8.95245	−0.377636
$563$	29.1475	1.22842	0.614209	−	0.789143i	$-0.289475\pi$
$563$	29.1475	1.22842	0.614209	+	0.789143i	$0.289475\pi$
$564$	0.0365212	0.00153782
$565$	−58.3835	−2.45621
$566$	62.9276	2.64504
$567$	−0.587921	−0.0246903
$568$	−5.38966	−0.226145
$569$	6.49901	0.272452	0.136226	−	0.990678i	$-0.456503\pi$
$569$	6.49901	0.272452	0.136226	+	0.990678i	$0.456503\pi$
$570$	−49.6559	−2.07986
$571$	−43.5132	−1.82097	−0.910485	−	0.413541i	$-0.864292\pi$
$571$	−43.5132	−1.82097	−0.910485	+	0.413541i	$0.864292\pi$
$572$	16.6345	0.695522
$573$	−11.5993	−0.484567
$574$	7.40237	0.308969
$575$	−20.4039	−0.850904
$576$	−13.0490	−0.543709
$577$	−27.3060	−1.13676	−0.568382	−	0.822765i	$-0.692430\pi$
$577$	−27.3060	−1.13676	−0.568382	+	0.822765i	$0.692430\pi$
$578$	−55.8754	−2.32411
$579$	6.05154	0.251493
$580$	−87.2316	−3.62210
$581$	−6.43684	−0.267045
$582$	−4.93184	−0.204431
$583$	8.00123	0.331377
$584$	11.2103	0.463884
$585$	2.92277	0.120842
$586$	7.01584	0.289822
$587$	−24.9536	−1.02994	−0.514972	−	0.857207i	$-0.672198\pi$
$587$	−24.9536	−1.02994	−0.514972	+	0.857207i	$0.672198\pi$
$588$	20.5937	0.849268
$589$	69.9650	2.88286
$590$	37.1965	1.53135
$591$	−7.99866	−0.329021
$592$	5.05533	0.207773
$593$	40.1282	1.64787	0.823934	−	0.566686i	$-0.191775\pi$
$593$	40.1282	1.64787	0.823934	+	0.566686i	$0.191775\pi$
$594$	−12.1323	−0.497794
$595$	−11.1037	−0.455205
$596$	−15.8364	−0.648684
$597$	−5.59952	−0.229173
$598$	−13.0004	−0.531628
$599$	−19.7756	−0.808011	−0.404005	−	0.914757i	$-0.632382\pi$
$599$	−19.7756	−0.808011	−0.404005	+	0.914757i	$0.632382\pi$
$600$	8.75391	0.357377
$601$	−31.0460	−1.26639	−0.633196	−	0.773991i	$-0.718257\pi$
$601$	−31.0460	−1.26639	−0.633196	+	0.773991i	$0.718257\pi$
$602$	4.65556	0.189746
$603$	2.08129	0.0847566
$604$	23.6782	0.963453
$605$	−52.2910	−2.12593
$606$	33.7539	1.37116
$607$	−44.2660	−1.79670	−0.898350	−	0.439280i	$-0.855234\pi$
$607$	−44.2660	−1.79670	−0.898350	+	0.439280i	$0.855234\pi$
$608$	47.5954	1.93025
$609$	5.66984	0.229753
$610$	−57.4772	−2.32718
$611$	0.0118009	0.000477415 0
$612$	−19.9977	−0.808361
$613$	43.2387	1.74640	0.873198	−	0.487366i	$-0.162042\pi$
$613$	43.2387	1.74640	0.873198	+	0.487366i	$0.162042\pi$
$614$	2.11770	0.0854634
$615$	16.3036	0.657426
$616$	−7.80878	−0.314625
$617$	−15.5263	−0.625066	−0.312533	−	0.949907i	$-0.601178\pi$
$617$	−15.5263	−0.625066	−0.312533	+	0.949907i	$0.601178\pi$
$618$	−2.25716	−0.0907963
$619$	37.3677	1.50194	0.750968	−	0.660339i	$-0.229587\pi$
$619$	37.3677	1.50194	0.750968	+	0.660339i	$0.229587\pi$
$620$	−84.0792	−3.37670
$621$	5.75965	0.231127
$622$	37.8481	1.51757
$623$	4.58560	0.183718
$624$	−0.611949	−0.0244976
$625$	−30.1631	−1.20652
$626$	59.7406	2.38772
$627$	40.4571	1.61570
$628$	62.2342	2.48342
$629$	53.3811	2.12844
$630$	−3.87860	−0.154527
$631$	−7.46990	−0.297372	−0.148686	−	0.988884i	$-0.547504\pi$
$631$	−7.46990	−0.297372	−0.148686	+	0.988884i	$0.547504\pi$
$632$	−31.3557	−1.24726
$633$	20.9278	0.831805
$634$	−72.1832	−2.86676
$635$	−24.5267	−0.973311
$636$	4.60685	0.182674
$637$	6.65435	0.263655
$638$	117.002	4.63217
$639$	2.18111	0.0862833
$640$	−49.1227	−1.94174
$641$	43.8085	1.73033	0.865166	−	0.501485i	$-0.167213\pi$
$641$	43.8085	1.73033	0.865166	+	0.501485i	$0.167213\pi$
$642$	−6.60499	−0.260678
$643$	0.0232622	0.000917370 0	0.000458685	−	1.00000i	$-0.499854\pi$
$643$	0.0232622	0.000917370 0	0.000458685		1.00000i	$0.499854\pi$
$644$	10.4796	0.412952
$645$	10.2538	0.403743
$646$	109.782	4.31930
$647$	−2.25378	−0.0886052	−0.0443026	−	0.999018i	$-0.514107\pi$
$647$	−2.25378	−0.0886052	−0.0443026	+	0.999018i	$0.514107\pi$
$648$	−2.47106	−0.0970726
$649$	−30.3058	−1.18961
$650$	7.99614	0.313634
$651$	5.46494	0.214188
$652$	67.0593	2.62625
$653$	25.5129	0.998396	0.499198	−	0.866488i	$-0.333628\pi$
$653$	25.5129	0.998396	0.499198	+	0.866488i	$0.333628\pi$
$654$	−12.9789	−0.507516
$655$	22.5382	0.880638
$656$	−3.41354	−0.133276
$657$	−4.53662	−0.176990
$658$	−0.0156602	−0.000610498 0
$659$	−4.72705	−0.184140	−0.0920699	−	0.995753i	$-0.529348\pi$
$659$	−4.72705	−0.184140	−0.0920699	+	0.995753i	$0.529348\pi$
$660$	−48.6187	−1.89248
$661$	13.3566	0.519510	0.259755	−	0.965675i	$-0.416358\pi$
$661$	13.3566	0.519510	0.259755	+	0.965675i	$0.416358\pi$
$662$	−39.3684	−1.53010
$663$	−6.46179	−0.250955
$664$	−27.0544	−1.04991
$665$	12.9338	0.501552
$666$	18.6465	0.722536
$667$	−55.5454	−2.15073
$668$	−48.0335	−1.85847
$669$	3.40291	0.131564
$670$	13.7306	0.530458
$671$	46.8295	1.80783
$672$	3.71765	0.143412
$673$	2.55711	0.0985692	0.0492846	−	0.998785i	$-0.484306\pi$
$673$	2.55711	0.0985692	0.0492846	+	0.998785i	$0.484306\pi$
$674$	3.09094	0.119059
$675$	−3.54257	−0.136354
$676$	3.09477	0.119030
$677$	−23.5234	−0.904076	−0.452038	−	0.891999i	$-0.649303\pi$
$677$	−23.5234	−0.904076	−0.452038	+	0.891999i	$0.649303\pi$
$678$	45.0877	1.73158
$679$	1.28459	0.0492981
$680$	−46.6693	−1.78969
$681$	−17.2965	−0.662802
$682$	112.774	4.31834
$683$	−36.4566	−1.39497	−0.697486	−	0.716598i	$-0.745698\pi$
$683$	−36.4566	−1.39497	−0.697486	+	0.716598i	$0.745698\pi$
$684$	23.2939	0.890665
$685$	−40.9194	−1.56345
$686$	−18.1197	−0.691815
$687$	−2.42097	−0.0923659
$688$	−2.14687	−0.0818487
$689$	1.48859	0.0567109
$690$	37.9973	1.44653
$691$	−19.5889	−0.745196	−0.372598	−	0.927993i	$-0.621533\pi$
$691$	−19.5889	−0.745196	−0.372598	+	0.927993i	$0.621533\pi$
$692$	−52.9386	−2.01242
$693$	3.16009	0.120042
$694$	59.4239	2.25570
$695$	63.1598	2.39579
$696$	23.8307	0.903298
$697$	−36.0449	−1.36530
$698$	2.28279	0.0864049
$699$	20.9613	0.792830
$700$	−6.44562	−0.243622
$701$	−9.27560	−0.350335	−0.175167	−	0.984539i	$-0.556047\pi$
$701$	−9.27560	−0.350335	−0.175167	+	0.984539i	$0.556047\pi$
$702$	−2.25716	−0.0851910
$703$	−62.1797	−2.34515
$704$	70.1388	2.64346
$705$	−0.0344914	−0.00129902
$706$	−11.3270	−0.426299
$707$	−8.79185	−0.330651
$708$	−17.4491	−0.655778
$709$	−15.0058	−0.563555	−0.281777	−	0.959480i	$-0.590924\pi$
$709$	−15.0058	−0.563555	−0.281777	+	0.959480i	$0.590924\pi$
$710$	14.3891	0.540013
$711$	12.6892	0.475880
$712$	19.2735	0.722307
$713$	−53.5380	−2.00502
$714$	8.57499	0.320911
$715$	−15.7100	−0.587519
$716$	−67.8372	−2.53519
$717$	4.82336	0.180132
$718$	11.6149	0.433463
$719$	−28.9636	−1.08016	−0.540079	−	0.841614i	$-0.681606\pi$
$719$	−28.9636	−1.08016	−0.540079	+	0.841614i	$0.681606\pi$
$720$	1.78858	0.0666566
$721$	0.587921	0.0218953
$722$	−84.9905	−3.16302
$723$	−28.3011	−1.05253
$724$	6.62456	0.246200
$725$	34.1641	1.26882
$726$	40.3826	1.49874
$727$	−4.24767	−0.157537	−0.0787686	−	0.996893i	$-0.525099\pi$
$727$	−4.24767	−0.157537	−0.0787686	+	0.996893i	$0.525099\pi$
$728$	−1.45279	−0.0538440
$729$	1.00000	0.0370370
$730$	−29.9287	−1.10771
$731$	−22.6696	−0.838466
$732$	26.9629	0.996578
$733$	−2.04909	−0.0756848	−0.0378424	−	0.999284i	$-0.512048\pi$
$733$	−2.04909	−0.0756848	−0.0378424	+	0.999284i	$0.512048\pi$
$734$	9.25035	0.341437
$735$	−19.4491	−0.717391
$736$	−36.4205	−1.34248
$737$	−11.1870	−0.412077
$738$	−12.5908	−0.463473
$739$	−37.2102	−1.36880	−0.684400	−	0.729107i	$-0.739936\pi$
$739$	−37.2102	−1.36880	−0.684400	+	0.729107i	$0.739936\pi$
$740$	74.7234	2.74689
$741$	7.52687	0.276506
$742$	−1.97541	−0.0725196
$743$	24.1811	0.887120	0.443560	−	0.896245i	$-0.353715\pi$
$743$	24.1811	0.887120	0.443560	+	0.896245i	$0.353715\pi$
$744$	22.9694	0.842101
$745$	14.9562	0.547954
$746$	28.4921	1.04317
$747$	10.9485	0.400584
$748$	107.488	3.93017
$749$	1.72040	0.0628620
$750$	9.61490	0.351086
$751$	17.1348	0.625258	0.312629	−	0.949875i	$-0.398790\pi$
$751$	17.1348	0.625258	0.312629	+	0.949875i	$0.398790\pi$
$752$	0.00722157	0.000263344 0
$753$	−15.8831	−0.578812
$754$	21.7678	0.792735
$755$	−22.3622	−0.813845
$756$	1.81948	0.0661738
$757$	3.70836	0.134783	0.0673913	−	0.997727i	$-0.478532\pi$
$757$	3.70836	0.134783	0.0673913	+	0.997727i	$0.478532\pi$
$758$	−48.4036	−1.75810
$759$	−30.9583	−1.12371
$760$	54.3617	1.97190
$761$	10.1752	0.368849	0.184425	−	0.982847i	$-0.440958\pi$
$761$	10.1752	0.368849	0.184425	+	0.982847i	$0.440958\pi$
$762$	18.9412	0.686166
$763$	3.38061	0.122386
$764$	35.8971	1.29871
$765$	18.8863	0.682836
$766$	28.8806	1.04350
$767$	−5.63826	−0.203586
$768$	11.8378	0.427161
$769$	11.0706	0.399215	0.199608	−	0.979876i	$-0.436033\pi$
$769$	11.0706	0.399215	0.199608	+	0.979876i	$0.436033\pi$
$770$	20.8476	0.751295
$771$	5.00871	0.180384
$772$	−18.7281	−0.674039
$773$	3.62253	0.130293	0.0651466	−	0.997876i	$-0.479248\pi$
$773$	3.62253	0.130293	0.0651466	+	0.997876i	$0.479248\pi$
$774$	−7.91869	−0.284631
$775$	32.9295	1.18286
$776$	5.39921	0.193821
$777$	−4.85683	−0.174238
$778$	31.3126	1.12261
$779$	41.9860	1.50430
$780$	−9.04529	−0.323873
$781$	−11.7235	−0.419500
$782$	−84.0062	−3.00405
$783$	−9.64388	−0.344644
$784$	4.07212	0.145433
$785$	−58.7754	−2.09778
$786$	−17.4055	−0.620833
$787$	31.2494	1.11392	0.556961	−	0.830539i	$-0.311967\pi$
$787$	31.2494	1.11392	0.556961	+	0.830539i	$0.311967\pi$
$788$	24.7540	0.881825
$789$	21.0825	0.750556
$790$	83.7122	2.97835
$791$	−11.7440	−0.417567
$792$	13.2820	0.471957
$793$	8.71242	0.309387
$794$	25.1269	0.891722
$795$	−4.35081	−0.154307
$796$	17.3292	0.614218
$797$	−30.8334	−1.09218	−0.546088	−	0.837728i	$-0.683884\pi$
$797$	−30.8334	−1.09218	−0.546088	+	0.837728i	$0.683884\pi$
$798$	−9.98838	−0.353585
$799$	0.0762552	0.00269772
$800$	22.4011	0.791997
$801$	−7.79969	−0.275589
$802$	34.4684	1.21712
$803$	24.3844	0.860508
$804$	−6.44110	−0.227160
$805$	−9.89712	−0.348828
$806$	20.9811	0.739028
$807$	9.58511	0.337412
$808$	−36.9527	−1.29999
$809$	41.4287	1.45655	0.728277	−	0.685282i	$-0.240321\pi$
$809$	41.4287	1.45655	0.728277	+	0.685282i	$0.240321\pi$
$810$	6.59715	0.231800
$811$	38.3252	1.34578	0.672890	−	0.739743i	$-0.265053\pi$
$811$	38.3252	1.34578	0.672890	+	0.739743i	$0.265053\pi$
$812$	−17.5468	−0.615773
$813$	7.13890	0.250372
$814$	−100.225	−3.51290
$815$	−63.3323	−2.21843
$816$	−3.95429	−0.138428
$817$	26.4062	0.923835
$818$	85.7415	2.99788
$819$	0.587921	0.0205436
$820$	−50.4560	−1.76200
$821$	27.8590	0.972285	0.486142	−	0.873880i	$-0.338404\pi$
$821$	27.8590	0.972285	0.486142	+	0.873880i	$0.338404\pi$
$822$	31.6007	1.10220
$823$	−43.3611	−1.51147	−0.755736	−	0.654876i	$-0.772721\pi$
$823$	−43.3611	−1.51147	−0.755736	+	0.654876i	$0.772721\pi$
$824$	2.47106	0.0860836
$825$	19.0414	0.662936
$826$	7.48215	0.260337
$827$	−18.7118	−0.650674	−0.325337	−	0.945598i	$-0.605478\pi$
$827$	−18.7118	−0.650674	−0.325337	+	0.945598i	$0.605478\pi$
$828$	−17.8248	−0.619454
$829$	−6.07930	−0.211143	−0.105571	−	0.994412i	$-0.533667\pi$
$829$	−6.07930	−0.211143	−0.105571	+	0.994412i	$0.533667\pi$
$830$	72.2288	2.50710
$831$	−5.66932	−0.196667
$832$	13.0490	0.452393
$833$	42.9990	1.48983
$834$	−48.7763	−1.68899
$835$	45.3639	1.56988
$836$	−125.205	−4.33032
$837$	−9.29536	−0.321295
$838$	−45.1785	−1.56066
$839$	−14.0997	−0.486776	−0.243388	−	0.969929i	$-0.578259\pi$
$839$	−14.0997	−0.486776	−0.243388	+	0.969929i	$0.578259\pi$
$840$	4.24617	0.146507
$841$	64.0044	2.20705
$842$	20.3932	0.702796
$843$	−3.96625	−0.136605
$844$	−64.7666	−2.22936
$845$	−2.92277	−0.100546
$846$	0.0266366	0.000915785 0
$847$	−10.5184	−0.361418
$848$	0.910943	0.0312819
$849$	27.8791	0.956808
$850$	51.6694	1.77225
$851$	47.5807	1.63104
$852$	−6.75002	−0.231252
$853$	25.1223	0.860170	0.430085	−	0.902789i	$-0.358484\pi$
$853$	25.1223	0.860170	0.430085	+	0.902789i	$0.358484\pi$
$854$	−11.5616	−0.395631
$855$	−21.9993	−0.752360
$856$	7.23093	0.247148
$857$	−0.0728092	−0.00248712	−0.00124356	−	0.999999i	$-0.500396\pi$
$857$	−0.0728092	−0.00248712	−0.00124356	+	0.999999i	$0.500396\pi$
$858$	12.1323	0.414190
$859$	25.5077	0.870313	0.435157	−	0.900355i	$-0.356693\pi$
$859$	25.5077	0.870313	0.435157	+	0.900355i	$0.356693\pi$
$860$	−31.7332	−1.08209
$861$	3.27951	0.111765
$862$	24.7112	0.841668
$863$	−12.6172	−0.429494	−0.214747	−	0.976670i	$-0.568893\pi$
$863$	−12.6172	−0.429494	−0.214747	+	0.976670i	$0.568893\pi$
$864$	−6.32340	−0.215126
$865$	49.9964	1.69993
$866$	−0.0718183	−0.00244048
$867$	−24.7548	−0.840716
$868$	−16.9127	−0.574055
$869$	−68.2045	−2.31368
$870$	−63.6221	−2.15699
$871$	−2.08129	−0.0705217
$872$	14.2089	0.481174
$873$	−2.18498	−0.0739502
$874$	97.8526	3.30991
$875$	−2.50439	−0.0846637
$876$	14.0398	0.474360
$877$	24.2728	0.819634	0.409817	−	0.912168i	$-0.365593\pi$
$877$	24.2728	0.819634	0.409817	+	0.912168i	$0.365593\pi$
$878$	66.0096	2.22772
$879$	3.10826	0.104839
$880$	−9.61369	−0.324077
$881$	−21.4978	−0.724279	−0.362140	−	0.932124i	$-0.617954\pi$
$881$	−21.4978	−0.724279	−0.362140	+	0.932124i	$0.617954\pi$
$882$	15.0199	0.505747
$883$	44.2833	1.49025	0.745125	−	0.666925i	$-0.232390\pi$
$883$	44.2833	1.49025	0.745125	+	0.666925i	$0.232390\pi$
$884$	19.9977	0.672597
$885$	16.4793	0.553947
$886$	−34.7410	−1.16715
$887$	44.5090	1.49447	0.747233	−	0.664562i	$-0.231382\pi$
$887$	44.5090	1.49447	0.747233	+	0.664562i	$0.231382\pi$
$888$	−20.4136	−0.685034
$889$	−4.93359	−0.165467
$890$	−51.4558	−1.72480
$891$	−5.37503	−0.180070
$892$	−10.5312	−0.352611
$893$	−0.0888241	−0.00297239
$894$	−11.5502	−0.386297
$895$	64.0669	2.14152
$896$	−9.88113	−0.330105
$897$	−5.75965	−0.192309
$898$	14.5119	0.484267
$899$	89.6434	2.98977
$900$	10.9634	0.365447
$901$	9.61899	0.320455
$902$	67.6757	2.25336
$903$	2.06257	0.0686382
$904$	−49.3605	−1.64171
$905$	−6.25639	−0.207969
$906$	17.2696	0.573745
$907$	3.12898	0.103896	0.0519481	−	0.998650i	$-0.483457\pi$
$907$	3.12898	0.103896	0.0519481	+	0.998650i	$0.483457\pi$
$908$	53.5285	1.77641
$909$	14.9541	0.495998
$910$	3.87860	0.128574
$911$	−30.9253	−1.02460	−0.512301	−	0.858806i	$-0.671207\pi$
$911$	−30.9253	−1.02460	−0.512301	+	0.858806i	$0.671207\pi$
$912$	4.60606	0.152522
$913$	−58.8484	−1.94760
$914$	30.3818	1.00494
$915$	−25.4644	−0.841826
$916$	7.49235	0.247554
$917$	4.53359	0.149712
$918$	−14.5853	−0.481386
$919$	34.0104	1.12190	0.560949	−	0.827850i	$-0.310436\pi$
$919$	34.0104	1.12190	0.560949	+	0.827850i	$0.310436\pi$
$920$	−41.5982	−1.37145
$921$	0.938215	0.0309152
$922$	−25.2005	−0.829934
$923$	−2.18111	−0.0717920
$924$	−9.77974	−0.321730
$925$	−29.2653	−0.962237
$926$	87.0837	2.86175
$927$	−1.00000	−0.0328443
$928$	60.9821	2.00183
$929$	−27.6205	−0.906200	−0.453100	−	0.891460i	$-0.649682\pi$
$929$	−27.6205	−0.906200	−0.453100	+	0.891460i	$0.649682\pi$
$930$	−61.3229	−2.01086
$931$	−50.0864	−1.64152
$932$	−64.8704	−2.12490
$933$	16.7680	0.548960
$934$	21.6218	0.707488
$935$	−101.514	−3.31988
$936$	2.47106	0.0807693
$937$	14.1863	0.463446	0.231723	−	0.972782i	$-0.425564\pi$
$937$	14.1863	0.463446	0.231723	+	0.972782i	$0.425564\pi$
$938$	2.76193	0.0901802
$939$	26.4672	0.863724
$940$	0.106743	0.00348157
$941$	−11.5513	−0.376561	−0.188281	−	0.982115i	$-0.560291\pi$
$941$	−11.5513	−0.376561	−0.188281	+	0.982115i	$0.560291\pi$
$942$	45.3903	1.47890
$943$	−32.1282	−1.04624
$944$	−3.45033	−0.112299
$945$	−1.71835	−0.0558981
$946$	42.5632	1.38385
$947$	17.8371	0.579627	0.289813	−	0.957083i	$-0.406407\pi$
$947$	17.8371	0.579627	0.289813	+	0.957083i	$0.406407\pi$
$948$	−39.2700	−1.27543
$949$	4.53662	0.147265
$950$	−60.1859	−1.95269
$951$	−31.9797	−1.03701
$952$	−9.38763	−0.304255
$953$	−42.0922	−1.36350	−0.681749	−	0.731586i	$-0.738781\pi$
$953$	−42.0922	−1.36350	−0.681749	+	0.731586i	$0.738781\pi$
$954$	3.35999	0.108784
$955$	−33.9020	−1.09704
$956$	−14.9272	−0.482780
$957$	51.8361	1.67562
$958$	−66.5837	−2.15122
$959$	−8.23102	−0.265794
$960$	−38.1392	−1.23094
$961$	55.4038	1.78722
$962$	−18.6465	−0.601186
$963$	−2.92624	−0.0942968
$964$	87.5854	2.82094
$965$	17.6872	0.569372
$966$	7.64323	0.245917
$967$	−3.90829	−0.125682	−0.0628411	−	0.998024i	$-0.520016\pi$
$967$	−3.90829	−0.125682	−0.0628411	+	0.998024i	$0.520016\pi$
$968$	−44.2096	−1.42095
$969$	48.6371	1.56245
$970$	−14.4146	−0.462825
$971$	44.4024	1.42494	0.712470	−	0.701702i	$-0.247576\pi$
$971$	44.4024	1.42494	0.712470	+	0.701702i	$0.247576\pi$
$972$	−3.09477	−0.0992647
$973$	12.7047	0.407295
$974$	24.8849	0.797363
$975$	3.54257	0.113453
$976$	5.33156	0.170659
$977$	1.21235	0.0387864	0.0193932	−	0.999812i	$-0.493827\pi$
$977$	1.21235	0.0387864	0.0193932	+	0.999812i	$0.493827\pi$
$978$	48.9095	1.56395
$979$	41.9236	1.33988
$980$	60.1905	1.92271
$981$	−5.75011	−0.183587
$982$	18.6178	0.594118
$983$	−46.5474	−1.48463	−0.742315	−	0.670051i	$-0.766272\pi$
$983$	−46.5474	−1.48463	−0.742315	+	0.670051i	$0.766272\pi$
$984$	13.7840	0.439417
$985$	−23.3782	−0.744892
$986$	140.659	4.47949
$987$	−0.00693802	−0.000220839 0
$988$	−23.2939	−0.741078
$989$	−20.2063	−0.642523
$990$	−35.4599	−1.12699
$991$	−53.1887	−1.68960	−0.844798	−	0.535086i	$-0.820279\pi$
$991$	−53.1887	−1.68960	−0.844798	+	0.535086i	$0.820279\pi$
$992$	58.7783	1.86621
$993$	−17.4416	−0.553492
$994$	2.89440	0.0918047
$995$	−16.3661	−0.518840
$996$	−33.8830	−1.07362
$997$	15.4428	0.489077	0.244539	−	0.969640i	$-0.421363\pi$
$997$	15.4428	0.489077	0.244539	+	0.969640i	$0.421363\pi$
$998$	−42.5616	−1.34726
$999$	8.26104	0.261368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.5	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.5	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25716 q^{2} -1.00000 q^{3} +3.09477 q^{4} -2.92277 q^{5} +2.25716 q^{6} -0.587921 q^{7} -2.47106 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.25716 q^{2} -1.00000 q^{3} +3.09477 q^{4} -2.92277 q^{5} +2.25716 q^{6} -0.587921 q^{7} -2.47106 q^{8} +1.00000 q^{9} +6.59715 q^{10} -5.37503 q^{11} -3.09477 q^{12} -1.00000 q^{13} +1.32703 q^{14} +2.92277 q^{15} -0.611949 q^{16} -6.46179 q^{17} -2.25716 q^{18} +7.52687 q^{19} -9.04529 q^{20} +0.587921 q^{21} +12.1323 q^{22} -5.75965 q^{23} +2.47106 q^{24} +3.54257 q^{25} +2.25716 q^{26} -1.00000 q^{27} -1.81948 q^{28} +9.64388 q^{29} -6.59715 q^{30} +9.29536 q^{31} +6.32340 q^{32} +5.37503 q^{33} +14.5853 q^{34} +1.71835 q^{35} +3.09477 q^{36} -8.26104 q^{37} -16.9893 q^{38} +1.00000 q^{39} +7.22235 q^{40} +5.57815 q^{41} -1.32703 q^{42} +3.50825 q^{43} -16.6345 q^{44} -2.92277 q^{45} +13.0004 q^{46} -0.0118009 q^{47} +0.611949 q^{48} -6.65435 q^{49} -7.99614 q^{50} +6.46179 q^{51} -3.09477 q^{52} -1.48859 q^{53} +2.25716 q^{54} +15.7100 q^{55} +1.45279 q^{56} -7.52687 q^{57} -21.7678 q^{58} +5.63826 q^{59} +9.04529 q^{60} -8.71242 q^{61} -20.9811 q^{62} -0.587921 q^{63} -13.0490 q^{64} +2.92277 q^{65} -12.1323 q^{66} +2.08129 q^{67} -19.9977 q^{68} +5.75965 q^{69} -3.87860 q^{70} +2.18111 q^{71} -2.47106 q^{72} -4.53662 q^{73} +18.6465 q^{74} -3.54257 q^{75} +23.2939 q^{76} +3.16009 q^{77} -2.25716 q^{78} +12.6892 q^{79} +1.78858 q^{80} +1.00000 q^{81} -12.5908 q^{82} +10.9485 q^{83} +1.81948 q^{84} +18.8863 q^{85} -7.91869 q^{86} -9.64388 q^{87} +13.2820 q^{88} -7.79969 q^{89} +6.59715 q^{90} +0.587921 q^{91} -17.8248 q^{92} -9.29536 q^{93} +0.0266366 q^{94} -21.9993 q^{95} -6.32340 q^{96} -2.18498 q^{97} +15.0199 q^{98} -5.37503 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more