LMFDB - Embedded newform 4034.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.83579 q^{3} +1.00000 q^{4} +4.39396 q^{5} +2.83579 q^{6} -1.33504 q^{7} -1.00000 q^{8} +5.04172 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.83579 q^{3} +1.00000 q^{4} +4.39396 q^{5} +2.83579 q^{6} -1.33504 q^{7} -1.00000 q^{8} +5.04172 q^{9} -4.39396 q^{10} -0.448139 q^{11} -2.83579 q^{12} -2.36627 q^{13} +1.33504 q^{14} -12.4603 q^{15} +1.00000 q^{16} +4.35693 q^{17} -5.04172 q^{18} -3.01101 q^{19} +4.39396 q^{20} +3.78588 q^{21} +0.448139 q^{22} -0.853088 q^{23} +2.83579 q^{24} +14.3068 q^{25} +2.36627 q^{26} -5.78990 q^{27} -1.33504 q^{28} -0.659341 q^{29} +12.4603 q^{30} -8.16118 q^{31} -1.00000 q^{32} +1.27083 q^{33} -4.35693 q^{34} -5.86609 q^{35} +5.04172 q^{36} +8.05772 q^{37} +3.01101 q^{38} +6.71024 q^{39} -4.39396 q^{40} -10.1462 q^{41} -3.78588 q^{42} -6.08641 q^{43} -0.448139 q^{44} +22.1531 q^{45} +0.853088 q^{46} +8.29245 q^{47} -2.83579 q^{48} -5.21768 q^{49} -14.3068 q^{50} -12.3554 q^{51} -2.36627 q^{52} -13.5577 q^{53} +5.78990 q^{54} -1.96910 q^{55} +1.33504 q^{56} +8.53860 q^{57} +0.659341 q^{58} -12.5178 q^{59} -12.4603 q^{60} +1.93267 q^{61} +8.16118 q^{62} -6.73088 q^{63} +1.00000 q^{64} -10.3973 q^{65} -1.27083 q^{66} +0.323643 q^{67} +4.35693 q^{68} +2.41918 q^{69} +5.86609 q^{70} +0.274768 q^{71} -5.04172 q^{72} +1.94413 q^{73} -8.05772 q^{74} -40.5713 q^{75} -3.01101 q^{76} +0.598282 q^{77} -6.71024 q^{78} +5.34697 q^{79} +4.39396 q^{80} +1.29380 q^{81} +10.1462 q^{82} +3.30005 q^{83} +3.78588 q^{84} +19.1442 q^{85} +6.08641 q^{86} +1.86975 q^{87} +0.448139 q^{88} -0.952300 q^{89} -22.1531 q^{90} +3.15905 q^{91} -0.853088 q^{92} +23.1434 q^{93} -8.29245 q^{94} -13.2302 q^{95} +2.83579 q^{96} -16.7742 q^{97} +5.21768 q^{98} -2.25939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.83579	−1.63725	−0.818623	−	0.574331i	$-0.805262\pi$
$3$	−2.83579	−1.63725	−0.818623	+	0.574331i	$0.805262\pi$
$4$	1.00000	0.500000
$5$	4.39396	1.96504	0.982518	−	0.186166i	$-0.0596061\pi$
$5$	4.39396	1.96504	0.982518	+	0.186166i	$0.0596061\pi$
$6$	2.83579	1.15771
$7$	−1.33504	−0.504596	−0.252298	−	0.967650i	$-0.581186\pi$
$7$	−1.33504	−0.504596	−0.252298	+	0.967650i	$0.581186\pi$
$8$	−1.00000	−0.353553
$9$	5.04172	1.68057
$10$	−4.39396	−1.38949
$11$	−0.448139	−0.135119	−0.0675595	−	0.997715i	$-0.521521\pi$
$11$	−0.448139	−0.135119	−0.0675595	+	0.997715i	$0.521521\pi$
$12$	−2.83579	−0.818623
$13$	−2.36627	−0.656284	−0.328142	−	0.944628i	$-0.606423\pi$
$13$	−2.36627	−0.656284	−0.328142	+	0.944628i	$0.606423\pi$
$14$	1.33504	0.356803
$15$	−12.4603	−3.21725
$16$	1.00000	0.250000
$17$	4.35693	1.05671	0.528356	−	0.849023i	$-0.322809\pi$
$17$	4.35693	1.05671	0.528356	+	0.849023i	$0.322809\pi$
$18$	−5.04172	−1.18835
$19$	−3.01101	−0.690773	−0.345386	−	0.938461i	$-0.612252\pi$
$19$	−3.01101	−0.690773	−0.345386	+	0.938461i	$0.612252\pi$
$20$	4.39396	0.982518
$21$	3.78588	0.826148
$22$	0.448139	0.0955436
$23$	−0.853088	−0.177881	−0.0889405	−	0.996037i	$-0.528348\pi$
$23$	−0.853088	−0.177881	−0.0889405	+	0.996037i	$0.528348\pi$
$24$	2.83579	0.578854
$25$	14.3068	2.86137
$26$	2.36627	0.464063
$27$	−5.78990	−1.11427
$28$	−1.33504	−0.252298
$29$	−0.659341	−0.122436	−0.0612182	−	0.998124i	$-0.519499\pi$
$29$	−0.659341	−0.122436	−0.0612182	+	0.998124i	$0.519499\pi$
$30$	12.4603	2.27494
$31$	−8.16118	−1.46579	−0.732896	−	0.680341i	$-0.761832\pi$
$31$	−8.16118	−1.46579	−0.732896	+	0.680341i	$0.761832\pi$
$32$	−1.00000	−0.176777
$33$	1.27083	0.221223
$34$	−4.35693	−0.747208
$35$	−5.86609	−0.991550
$36$	5.04172	0.840287
$37$	8.05772	1.32468	0.662341	−	0.749203i	$-0.269563\pi$
$37$	8.05772	1.32468	0.662341	+	0.749203i	$0.269563\pi$
$38$	3.01101	0.488450
$39$	6.71024	1.07450
$40$	−4.39396	−0.694745
$41$	−10.1462	−1.58457	−0.792285	−	0.610151i	$-0.791109\pi$
$41$	−10.1462	−1.58457	−0.792285	+	0.610151i	$0.791109\pi$
$42$	−3.78588	−0.584175
$43$	−6.08641	−0.928168	−0.464084	−	0.885791i	$-0.653616\pi$
$43$	−6.08641	−0.928168	−0.464084	+	0.885791i	$0.653616\pi$
$44$	−0.448139	−0.0675595
$45$	22.1531	3.30239
$46$	0.853088	0.125781
$47$	8.29245	1.20958	0.604789	−	0.796386i	$-0.293257\pi$
$47$	8.29245	1.20958	0.604789	+	0.796386i	$0.293257\pi$
$48$	−2.83579	−0.409311
$49$	−5.21768	−0.745383
$50$	−14.3068	−2.02329
$51$	−12.3554	−1.73010
$52$	−2.36627	−0.328142
$53$	−13.5577	−1.86229	−0.931144	−	0.364652i	$-0.881188\pi$
$53$	−13.5577	−1.86229	−0.931144	+	0.364652i	$0.881188\pi$
$54$	5.78990	0.787906
$55$	−1.96910	−0.265514
$56$	1.33504	0.178402
$57$	8.53860	1.13096
$58$	0.659341	0.0865757
$59$	−12.5178	−1.62968	−0.814841	−	0.579684i	$-0.803176\pi$
$59$	−12.5178	−1.62968	−0.814841	+	0.579684i	$0.803176\pi$
$60$	−12.4603	−1.60862
$61$	1.93267	0.247454	0.123727	−	0.992316i	$-0.460515\pi$
$61$	1.93267	0.247454	0.123727	+	0.992316i	$0.460515\pi$
$62$	8.16118	1.03647
$63$	−6.73088	−0.848011
$64$	1.00000	0.125000
$65$	−10.3973	−1.28962
$66$	−1.27083	−0.156428
$67$	0.323643	0.0395393	0.0197697	−	0.999805i	$-0.493707\pi$
$67$	0.323643	0.0395393	0.0197697	+	0.999805i	$0.493707\pi$
$68$	4.35693	0.528356
$69$	2.41918	0.291235
$70$	5.86609	0.701132
$71$	0.274768	0.0326090	0.0163045	−	0.999867i	$-0.494810\pi$
$71$	0.274768	0.0326090	0.0163045	+	0.999867i	$0.494810\pi$
$72$	−5.04172	−0.594173
$73$	1.94413	0.227543	0.113771	−	0.993507i	$-0.463707\pi$
$73$	1.94413	0.227543	0.113771	+	0.993507i	$0.463707\pi$
$74$	−8.05772	−0.936691
$75$	−40.5713	−4.68477
$76$	−3.01101	−0.345386
$77$	0.598282	0.0681805
$78$	−6.71024	−0.759786
$79$	5.34697	0.601581	0.300790	−	0.953690i	$-0.402750\pi$
$79$	5.34697	0.601581	0.300790	+	0.953690i	$0.402750\pi$
$80$	4.39396	0.491259
$81$	1.29380	0.143755
$82$	10.1462	1.12046
$83$	3.30005	0.362227	0.181114	−	0.983462i	$-0.442030\pi$
$83$	3.30005	0.362227	0.181114	+	0.983462i	$0.442030\pi$
$84$	3.78588	0.413074
$85$	19.1442	2.07648
$86$	6.08641	0.656314
$87$	1.86975	0.200459
$88$	0.448139	0.0477718
$89$	−0.952300	−0.100944	−0.0504718	−	0.998725i	$-0.516073\pi$
$89$	−0.952300	−0.100944	−0.0504718	+	0.998725i	$0.516073\pi$
$90$	−22.1531	−2.33514
$91$	3.15905	0.331159
$92$	−0.853088	−0.0889405
$93$	23.1434	2.39986
$94$	−8.29245	−0.855301
$95$	−13.2302	−1.35739
$96$	2.83579	0.289427
$97$	−16.7742	−1.70317	−0.851583	−	0.524219i	$-0.824357\pi$
$97$	−16.7742	−1.70317	−0.851583	+	0.524219i	$0.824357\pi$
$98$	5.21768	0.527065
$99$	−2.25939	−0.227078
$100$	14.3068	1.43068
$101$	−4.65756	−0.463444	−0.231722	−	0.972782i	$-0.574436\pi$
$101$	−4.65756	−0.463444	−0.231722	+	0.972782i	$0.574436\pi$
$102$	12.3554	1.22336
$103$	1.44880	0.142755	0.0713774	−	0.997449i	$-0.477261\pi$
$103$	1.44880	0.142755	0.0713774	+	0.997449i	$0.477261\pi$
$104$	2.36627	0.232032
$105$	16.6350	1.62341
$106$	13.5577	1.31684
$107$	14.9136	1.44175	0.720875	−	0.693065i	$-0.243740\pi$
$107$	14.9136	1.44175	0.720875	+	0.693065i	$0.243740\pi$
$108$	−5.78990	−0.557134
$109$	16.1673	1.54855	0.774275	−	0.632849i	$-0.218115\pi$
$109$	16.1673	1.54855	0.774275	+	0.632849i	$0.218115\pi$
$110$	1.96910	0.187747
$111$	−22.8500	−2.16883
$112$	−1.33504	−0.126149
$113$	−11.5114	−1.08290	−0.541449	−	0.840734i	$-0.682124\pi$
$113$	−11.5114	−1.08290	−0.541449	+	0.840734i	$0.682124\pi$
$114$	−8.53860	−0.799713
$115$	−3.74843	−0.349543
$116$	−0.659341	−0.0612182
$117$	−11.9301	−1.10293
$118$	12.5178	1.15236
$119$	−5.81666	−0.533213
$120$	12.4603	1.13747
$121$	−10.7992	−0.981743
$122$	−1.93267	−0.174976
$123$	28.7725	2.59433
$124$	−8.16118	−0.732896
$125$	40.8939	3.65766
$126$	6.73088	0.599634
$127$	0.947273	0.0840568	0.0420284	−	0.999116i	$-0.486618\pi$
$127$	0.947273	0.0840568	0.0420284	+	0.999116i	$0.486618\pi$
$128$	−1.00000	−0.0883883
$129$	17.2598	1.51964
$130$	10.3973	0.911901
$131$	−21.0211	−1.83663	−0.918313	−	0.395855i	$-0.870448\pi$
$131$	−21.0211	−1.83663	−0.918313	+	0.395855i	$0.870448\pi$
$132$	1.27083	0.110612
$133$	4.01980	0.348561
$134$	−0.323643	−0.0279585
$135$	−25.4406	−2.18958
$136$	−4.35693	−0.373604
$137$	−13.0013	−1.11077	−0.555387	−	0.831592i	$-0.687430\pi$
$137$	−13.0013	−1.11077	−0.555387	+	0.831592i	$0.687430\pi$
$138$	−2.41918	−0.205934
$139$	7.46539	0.633206	0.316603	−	0.948558i	$-0.397458\pi$
$139$	7.46539	0.633206	0.316603	+	0.948558i	$0.397458\pi$
$140$	−5.86609	−0.495775
$141$	−23.5157	−1.98038
$142$	−0.274768	−0.0230580
$143$	1.06042	0.0886765
$144$	5.04172	0.420144
$145$	−2.89711	−0.240592
$146$	−1.94413	−0.160897
$147$	14.7963	1.22038
$148$	8.05772	0.662341
$149$	17.8733	1.46424	0.732118	−	0.681178i	$-0.238532\pi$
$149$	17.8733	1.46424	0.732118	+	0.681178i	$0.238532\pi$
$150$	40.5713	3.31263
$151$	24.4001	1.98565	0.992825	−	0.119578i	$-0.0381541\pi$
$151$	24.4001	1.98565	0.992825	+	0.119578i	$0.0381541\pi$
$152$	3.01101	0.244225
$153$	21.9665	1.77588
$154$	−0.598282	−0.0482109
$155$	−35.8599	−2.88033
$156$	6.71024	0.537250
$157$	23.4272	1.86969	0.934845	−	0.355056i	$-0.115538\pi$
$157$	23.4272	1.86969	0.934845	+	0.355056i	$0.115538\pi$
$158$	−5.34697	−0.425382
$159$	38.4467	3.04902
$160$	−4.39396	−0.347373
$161$	1.13890	0.0897581
$162$	−1.29380	−0.101650
$163$	−0.594788	−0.0465874	−0.0232937	−	0.999729i	$-0.507415\pi$
$163$	−0.594788	−0.0465874	−0.0232937	+	0.999729i	$0.507415\pi$
$164$	−10.1462	−0.792285
$165$	5.58397	0.434712
$166$	−3.30005	−0.256133
$167$	0.844999	0.0653880	0.0326940	−	0.999465i	$-0.489591\pi$
$167$	0.844999	0.0653880	0.0326940	+	0.999465i	$0.489591\pi$
$168$	−3.78588	−0.292087
$169$	−7.40078	−0.569291
$170$	−19.1442	−1.46829
$171$	−15.1807	−1.16089
$172$	−6.08641	−0.464084
$173$	11.0445	0.839701	0.419851	−	0.907593i	$-0.362082\pi$
$173$	11.0445	0.839701	0.419851	+	0.907593i	$0.362082\pi$
$174$	−1.86975	−0.141746
$175$	−19.1001	−1.44384
$176$	−0.448139	−0.0337798
$177$	35.4980	2.66819
$178$	0.952300	0.0713779
$179$	−12.1931	−0.911355	−0.455678	−	0.890145i	$-0.650603\pi$
$179$	−12.1931	−0.911355	−0.455678	+	0.890145i	$0.650603\pi$
$180$	22.1531	1.65119
$181$	−17.8419	−1.32618	−0.663090	−	0.748540i	$-0.730755\pi$
$181$	−17.8419	−1.32618	−0.663090	+	0.748540i	$0.730755\pi$
$182$	−3.15905	−0.234164
$183$	−5.48066	−0.405142
$184$	0.853088	0.0628905
$185$	35.4053	2.60305
$186$	−23.1434	−1.69696
$187$	−1.95251	−0.142782
$188$	8.29245	0.604789
$189$	7.72973	0.562255
$190$	13.2302	0.959822
$191$	18.8538	1.36421	0.682106	−	0.731253i	$-0.261064\pi$
$191$	18.8538	1.36421	0.682106	+	0.731253i	$0.261064\pi$
$192$	−2.83579	−0.204656
$193$	−14.1738	−1.02025	−0.510125	−	0.860100i	$-0.670401\pi$
$193$	−14.1738	−1.02025	−0.510125	+	0.860100i	$0.670401\pi$
$194$	16.7742	1.20432
$195$	29.4845	2.11143
$196$	−5.21768	−0.372691
$197$	−3.75940	−0.267846	−0.133923	−	0.990992i	$-0.542758\pi$
$197$	−3.75940	−0.267846	−0.133923	+	0.990992i	$0.542758\pi$
$198$	2.25939	0.160568
$199$	−2.52860	−0.179248	−0.0896238	−	0.995976i	$-0.528566\pi$
$199$	−2.52860	−0.179248	−0.0896238	+	0.995976i	$0.528566\pi$
$200$	−14.3068	−1.01165
$201$	−0.917785	−0.0647356
$202$	4.65756	0.327705
$203$	0.880243	0.0617809
$204$	−12.3554	−0.865049
$205$	−44.5819	−3.11374
$206$	−1.44880	−0.100943
$207$	−4.30103	−0.298942
$208$	−2.36627	−0.164071
$209$	1.34935	0.0933366
$210$	−16.6350	−1.14792
$211$	−8.77179	−0.603875	−0.301938	−	0.953328i	$-0.597633\pi$
$211$	−8.77179	−0.603875	−0.301938	+	0.953328i	$0.597633\pi$
$212$	−13.5577	−0.931144
$213$	−0.779186	−0.0533889
$214$	−14.9136	−1.01947
$215$	−26.7434	−1.82388
$216$	5.78990	0.393953
$217$	10.8955	0.739633
$218$	−16.1673	−1.09499
$219$	−5.51314	−0.372544
$220$	−1.96910	−0.132757
$221$	−10.3097	−0.693504
$222$	22.8500	1.53359
$223$	4.02449	0.269500	0.134750	−	0.990880i	$-0.456977\pi$
$223$	4.02449	0.269500	0.134750	+	0.990880i	$0.456977\pi$
$224$	1.33504	0.0892008
$225$	72.1312	4.80874
$226$	11.5114	0.765724
$227$	−13.7838	−0.914866	−0.457433	−	0.889244i	$-0.651231\pi$
$227$	−13.7838	−0.914866	−0.457433	+	0.889244i	$0.651231\pi$
$228$	8.53860	0.565482
$229$	−13.2737	−0.877151	−0.438576	−	0.898694i	$-0.644517\pi$
$229$	−13.2737	−0.877151	−0.438576	+	0.898694i	$0.644517\pi$
$230$	3.74843	0.247164
$231$	−1.69660	−0.111628
$232$	0.659341	0.0432878
$233$	−15.6580	−1.02579	−0.512895	−	0.858451i	$-0.671427\pi$
$233$	−15.6580	−1.02579	−0.512895	+	0.858451i	$0.671427\pi$
$234$	11.9301	0.779893
$235$	36.4367	2.37687
$236$	−12.5178	−0.814841
$237$	−15.1629	−0.984936
$238$	5.81666	0.377038
$239$	−14.4540	−0.934952	−0.467476	−	0.884006i	$-0.654837\pi$
$239$	−14.4540	−0.934952	−0.467476	+	0.884006i	$0.654837\pi$
$240$	−12.4603	−0.804312
$241$	−7.37157	−0.474845	−0.237422	−	0.971407i	$-0.576303\pi$
$241$	−7.37157	−0.474845	−0.237422	+	0.971407i	$0.576303\pi$
$242$	10.7992	0.694197
$243$	13.7008	0.878904
$244$	1.93267	0.123727
$245$	−22.9263	−1.46470
$246$	−28.7725	−1.83447
$247$	7.12485	0.453343
$248$	8.16118	0.518236
$249$	−9.35825	−0.593055
$250$	−40.8939	−2.58636
$251$	−23.0006	−1.45178	−0.725892	−	0.687808i	$-0.758573\pi$
$251$	−23.0006	−1.45178	−0.725892	+	0.687808i	$0.758573\pi$
$252$	−6.73088	−0.424005
$253$	0.382302	0.0240351
$254$	−0.947273	−0.0594372
$255$	−54.2889	−3.39970
$256$	1.00000	0.0625000
$257$	0.285268	0.0177946	0.00889728	−	0.999960i	$-0.497168\pi$
$257$	0.285268	0.0177946	0.00889728	+	0.999960i	$0.497168\pi$
$258$	−17.2598	−1.07455
$259$	−10.7573	−0.668429
$260$	−10.3973	−0.644812
$261$	−3.32421	−0.205764
$262$	21.0211	1.29869
$263$	15.7849	0.973339	0.486670	−	0.873586i	$-0.338212\pi$
$263$	15.7849	0.973339	0.486670	+	0.873586i	$0.338212\pi$
$264$	−1.27083	−0.0782142
$265$	−59.5717	−3.65946
$266$	−4.01980	−0.246470
$267$	2.70053	0.165270
$268$	0.323643	0.0197697
$269$	−0.142369	−0.00868039	−0.00434019	−	0.999991i	$-0.501382\pi$
$269$	−0.142369	−0.00868039	−0.00434019	+	0.999991i	$0.501382\pi$
$270$	25.4406	1.54826
$271$	−18.3774	−1.11635	−0.558174	−	0.829724i	$-0.688498\pi$
$271$	−18.3774	−1.11635	−0.558174	+	0.829724i	$0.688498\pi$
$272$	4.35693	0.264178
$273$	−8.95841	−0.542188
$274$	13.0013	0.785436
$275$	−6.41146	−0.386626
$276$	2.41918	0.145618
$277$	17.0567	1.02484	0.512418	−	0.858736i	$-0.328750\pi$
$277$	17.0567	1.02484	0.512418	+	0.858736i	$0.328750\pi$
$278$	−7.46539	−0.447745
$279$	−41.1464	−2.46337
$280$	5.86609	0.350566
$281$	−10.3881	−0.619703	−0.309851	−	0.950785i	$-0.600279\pi$
$281$	−10.3881	−0.619703	−0.309851	+	0.950785i	$0.600279\pi$
$282$	23.5157	1.40034
$283$	−31.2416	−1.85712	−0.928561	−	0.371179i	$-0.878953\pi$
$283$	−31.2416	−1.85712	−0.928561	+	0.371179i	$0.878953\pi$
$284$	0.274768	0.0163045
$285$	37.5182	2.22239
$286$	−1.06042	−0.0627038
$287$	13.5455	0.799568
$288$	−5.04172	−0.297086
$289$	1.98288	0.116640
$290$	2.89711	0.170124
$291$	47.5683	2.78850
$292$	1.94413	0.113771
$293$	−1.99603	−0.116609	−0.0583047	−	0.998299i	$-0.518570\pi$
$293$	−1.99603	−0.116609	−0.0583047	+	0.998299i	$0.518570\pi$
$294$	−14.7963	−0.862935
$295$	−55.0028	−3.20239
$296$	−8.05772	−0.468346
$297$	2.59468	0.150559
$298$	−17.8733	−1.03537
$299$	2.01863	0.116741
$300$	−40.5713	−2.34238
$301$	8.12557	0.468350
$302$	−24.4001	−1.40407
$303$	13.2079	0.758772
$304$	−3.01101	−0.172693
$305$	8.49209	0.486255
$306$	−21.9665	−1.25574
$307$	8.50164	0.485214	0.242607	−	0.970125i	$-0.421997\pi$
$307$	8.50164	0.485214	0.242607	+	0.970125i	$0.421997\pi$
$308$	0.598282	0.0340903
$309$	−4.10851	−0.233725
$310$	35.8599	2.03670
$311$	2.16854	0.122967	0.0614834	−	0.998108i	$-0.480417\pi$
$311$	2.16854	0.122967	0.0614834	+	0.998108i	$0.480417\pi$
$312$	−6.71024	−0.379893
$313$	−10.8623	−0.613972	−0.306986	−	0.951714i	$-0.599321\pi$
$313$	−10.8623	−0.613972	−0.306986	+	0.951714i	$0.599321\pi$
$314$	−23.4272	−1.32207
$315$	−29.5752	−1.66637
$316$	5.34697	0.300790
$317$	−5.45494	−0.306380	−0.153190	−	0.988197i	$-0.548955\pi$
$317$	−5.45494	−0.306380	−0.153190	+	0.988197i	$0.548955\pi$
$318$	−38.4467	−2.15598
$319$	0.295476	0.0165435
$320$	4.39396	0.245630
$321$	−42.2918	−2.36050
$322$	−1.13890	−0.0634685
$323$	−13.1188	−0.729948
$324$	1.29380	0.0718776
$325$	−33.8538	−1.87787
$326$	0.594788	0.0329423
$327$	−45.8472	−2.53536
$328$	10.1462	0.560230
$329$	−11.0707	−0.610349
$330$	−5.58397	−0.307388
$331$	23.6167	1.29809	0.649045	−	0.760750i	$-0.275169\pi$
$331$	23.6167	1.29809	0.649045	+	0.760750i	$0.275169\pi$
$332$	3.30005	0.181114
$333$	40.6248	2.22623
$334$	−0.844999	−0.0462363
$335$	1.42207	0.0776962
$336$	3.78588	0.206537
$337$	4.14214	0.225637	0.112818	−	0.993616i	$-0.464012\pi$
$337$	4.14214	0.225637	0.112818	+	0.993616i	$0.464012\pi$
$338$	7.40078	0.402549
$339$	32.6438	1.77297
$340$	19.1442	1.03824
$341$	3.65735	0.198056
$342$	15.1807	0.820877
$343$	16.3110	0.880713
$344$	6.08641	0.328157
$345$	10.6298	0.572288
$346$	−11.0445	−0.593758
$347$	18.5320	0.994851	0.497425	−	0.867507i	$-0.334279\pi$
$347$	18.5320	0.994851	0.497425	+	0.867507i	$0.334279\pi$
$348$	1.86975	0.100229
$349$	−25.4764	−1.36372	−0.681859	−	0.731484i	$-0.738828\pi$
$349$	−25.4764	−1.36372	−0.681859	+	0.731484i	$0.738828\pi$
$350$	19.1001	1.02095
$351$	13.7005	0.731276
$352$	0.448139	0.0238859
$353$	2.40600	0.128058	0.0640291	−	0.997948i	$-0.479605\pi$
$353$	2.40600	0.128058	0.0640291	+	0.997948i	$0.479605\pi$
$354$	−35.4980	−1.88670
$355$	1.20732	0.0640779
$356$	−0.952300	−0.0504718
$357$	16.4949	0.873000
$358$	12.1931	0.644426
$359$	−12.3024	−0.649295	−0.324648	−	0.945835i	$-0.605246\pi$
$359$	−12.3024	−0.649295	−0.324648	+	0.945835i	$0.605246\pi$
$360$	−22.1531	−1.16757
$361$	−9.93383	−0.522833
$362$	17.8419	0.937751
$363$	30.6242	1.60735
$364$	3.15905	0.165579
$365$	8.54241	0.447130
$366$	5.48066	0.286479
$367$	34.7846	1.81574	0.907869	−	0.419253i	$-0.137708\pi$
$367$	34.7846	1.81574	0.907869	+	0.419253i	$0.137708\pi$
$368$	−0.853088	−0.0444703
$369$	−51.1543	−2.66299
$370$	−35.4053	−1.84063
$371$	18.1000	0.939703
$372$	23.1434	1.19993
$373$	19.6864	1.01932	0.509660	−	0.860376i	$-0.329771\pi$
$373$	19.6864	1.01932	0.509660	+	0.860376i	$0.329771\pi$
$374$	1.95251	0.100962
$375$	−115.967	−5.98849
$376$	−8.29245	−0.427651
$377$	1.56018	0.0803531
$378$	−7.72973	−0.397574
$379$	−16.6965	−0.857643	−0.428821	−	0.903389i	$-0.641071\pi$
$379$	−16.6965	−0.857643	−0.428821	+	0.903389i	$0.641071\pi$
$380$	−13.2302	−0.678697
$381$	−2.68627	−0.137622
$382$	−18.8538	−0.964644
$383$	−19.8177	−1.01264	−0.506318	−	0.862347i	$-0.668994\pi$
$383$	−19.8177	−1.01264	−0.506318	+	0.862347i	$0.668994\pi$
$384$	2.83579	0.144713
$385$	2.62882	0.133977
$386$	14.1738	0.721426
$387$	−30.6860	−1.55986
$388$	−16.7742	−0.851583
$389$	−22.6601	−1.14891	−0.574457	−	0.818535i	$-0.694787\pi$
$389$	−22.6601	−1.14891	−0.574457	+	0.818535i	$0.694787\pi$
$390$	−29.4845	−1.49301
$391$	−3.71685	−0.187969
$392$	5.21768	0.263533
$393$	59.6116	3.00701
$394$	3.75940	0.189396
$395$	23.4943	1.18213
$396$	−2.25939	−0.113539
$397$	−16.7456	−0.840439	−0.420220	−	0.907422i	$-0.638047\pi$
$397$	−16.7456	−0.840439	−0.420220	+	0.907422i	$0.638047\pi$
$398$	2.52860	0.126747
$399$	−11.3993	−0.570680
$400$	14.3068	0.715342
$401$	26.6031	1.32849	0.664247	−	0.747513i	$-0.268752\pi$
$401$	26.6031	1.32849	0.664247	+	0.747513i	$0.268752\pi$
$402$	0.917785	0.0457750
$403$	19.3115	0.961976
$404$	−4.65756	−0.231722
$405$	5.68489	0.282484
$406$	−0.880243	−0.0436857
$407$	−3.61098	−0.178990
$408$	12.3554	0.611682
$409$	−14.5602	−0.719954	−0.359977	−	0.932961i	$-0.617215\pi$
$409$	−14.5602	−0.719954	−0.359977	+	0.932961i	$0.617215\pi$
$410$	44.5819	2.20175
$411$	36.8690	1.81861
$412$	1.44880	0.0713774
$413$	16.7117	0.822331
$414$	4.30103	0.211384
$415$	14.5003	0.711790
$416$	2.36627	0.116016
$417$	−21.1703	−1.03671
$418$	−1.34935	−0.0659989
$419$	30.7615	1.50280	0.751400	−	0.659847i	$-0.229379\pi$
$419$	30.7615	1.50280	0.751400	+	0.659847i	$0.229379\pi$
$420$	16.6350	0.811705
$421$	−25.7494	−1.25495	−0.627473	−	0.778638i	$-0.715911\pi$
$421$	−25.7494	−1.25495	−0.627473	+	0.778638i	$0.715911\pi$
$422$	8.77179	0.427004
$423$	41.8082	2.03279
$424$	13.5577	0.658418
$425$	62.3340	3.02364
$426$	0.779186	0.0377517
$427$	−2.58019	−0.124864
$428$	14.9136	0.720875
$429$	−3.00712	−0.145185
$430$	26.7434	1.28968
$431$	−13.3900	−0.644972	−0.322486	−	0.946574i	$-0.604518\pi$
$431$	−13.3900	−0.644972	−0.322486	+	0.946574i	$0.604518\pi$
$432$	−5.78990	−0.278567
$433$	−29.7637	−1.43035	−0.715175	−	0.698945i	$-0.753653\pi$
$433$	−29.7637	−1.43035	−0.715175	+	0.698945i	$0.753653\pi$
$434$	−10.8955	−0.522999
$435$	8.21561	0.393909
$436$	16.1673	0.774275
$437$	2.56865	0.122875
$438$	5.51314	0.263428
$439$	−5.58421	−0.266520	−0.133260	−	0.991081i	$-0.542544\pi$
$439$	−5.58421	−0.266520	−0.133260	+	0.991081i	$0.542544\pi$
$440$	1.96910	0.0938733
$441$	−26.3061	−1.25267
$442$	10.3097	0.490381
$443$	−31.3242	−1.48826	−0.744129	−	0.668036i	$-0.767135\pi$
$443$	−31.3242	−1.48826	−0.744129	+	0.668036i	$0.767135\pi$
$444$	−22.8500	−1.08441
$445$	−4.18437	−0.198358
$446$	−4.02449	−0.190565
$447$	−50.6849	−2.39731
$448$	−1.33504	−0.0630745
$449$	−5.88375	−0.277671	−0.138836	−	0.990315i	$-0.544336\pi$
$449$	−5.88375	−0.277671	−0.138836	+	0.990315i	$0.544336\pi$
$450$	−72.1312	−3.40030
$451$	4.54691	0.214106
$452$	−11.5114	−0.541449
$453$	−69.1936	−3.25100
$454$	13.7838	0.646908
$455$	13.8807	0.650739
$456$	−8.53860	−0.399856
$457$	−14.6856	−0.686961	−0.343481	−	0.939160i	$-0.611606\pi$
$457$	−14.6856	−0.686961	−0.343481	+	0.939160i	$0.611606\pi$
$458$	13.2737	0.620239
$459$	−25.2262	−1.17746
$460$	−3.74843	−0.174771
$461$	−20.4244	−0.951260	−0.475630	−	0.879646i	$-0.657780\pi$
$461$	−20.4244	−0.951260	−0.475630	+	0.879646i	$0.657780\pi$
$462$	1.69660	0.0789331
$463$	14.7432	0.685177	0.342588	−	0.939486i	$-0.388696\pi$
$463$	14.7432	0.685177	0.342588	+	0.939486i	$0.388696\pi$
$464$	−0.659341	−0.0306091
$465$	101.691	4.71582
$466$	15.6580	0.725343
$467$	11.8245	0.547173	0.273586	−	0.961847i	$-0.411790\pi$
$467$	11.8245	0.547173	0.273586	+	0.961847i	$0.411790\pi$
$468$	−11.9301	−0.551467
$469$	−0.432075	−0.0199514
$470$	−36.4367	−1.68070
$471$	−66.4346	−3.06114
$472$	12.5178	0.576180
$473$	2.72756	0.125413
$474$	15.1629	0.696455
$475$	−43.0780	−1.97656
$476$	−5.81666	−0.266606
$477$	−68.3539	−3.12971
$478$	14.4540	0.661111
$479$	−8.73494	−0.399110	−0.199555	−	0.979887i	$-0.563950\pi$
$479$	−8.73494	−0.399110	−0.199555	+	0.979887i	$0.563950\pi$
$480$	12.4603	0.568735
$481$	−19.0667	−0.869368
$482$	7.37157	0.335766
$483$	−3.22969	−0.146956
$484$	−10.7992	−0.490871
$485$	−73.7053	−3.34679
$486$	−13.7008	−0.621479
$487$	−16.8507	−0.763580	−0.381790	−	0.924249i	$-0.624692\pi$
$487$	−16.8507	−0.763580	−0.381790	+	0.924249i	$0.624692\pi$
$488$	−1.93267	−0.0874881
$489$	1.68670	0.0762751
$490$	22.9263	1.03570
$491$	−14.3719	−0.648597	−0.324298	−	0.945955i	$-0.605128\pi$
$491$	−14.3719	−0.648597	−0.324298	+	0.945955i	$0.605128\pi$
$492$	28.7725	1.29717
$493$	−2.87270	−0.129380
$494$	−7.12485	−0.320562
$495$	−9.92768	−0.446216
$496$	−8.16118	−0.366448
$497$	−0.366825	−0.0164544
$498$	9.35825	0.419353
$499$	13.9718	0.625463	0.312732	−	0.949842i	$-0.398756\pi$
$499$	13.9718	0.625463	0.312732	+	0.949842i	$0.398756\pi$
$500$	40.8939	1.82883
$501$	−2.39624	−0.107056
$502$	23.0006	1.02657
$503$	−18.8373	−0.839915	−0.419958	−	0.907544i	$-0.637955\pi$
$503$	−18.8373	−0.839915	−0.419958	+	0.907544i	$0.637955\pi$
$504$	6.73088	0.299817
$505$	−20.4651	−0.910685
$506$	−0.382302	−0.0169954
$507$	20.9871	0.932069
$508$	0.947273	0.0420284
$509$	−0.227788	−0.0100965	−0.00504826	−	0.999987i	$-0.501607\pi$
$509$	−0.227788	−0.0100965	−0.00504826	+	0.999987i	$0.501607\pi$
$510$	54.2889	2.40395
$511$	−2.59548	−0.114817
$512$	−1.00000	−0.0441942
$513$	17.4334	0.769705
$514$	−0.285268	−0.0125826
$515$	6.36598	0.280518
$516$	17.2598	0.759820
$517$	−3.71617	−0.163437
$518$	10.7573	0.472651
$519$	−31.3200	−1.37480
$520$	10.3973	0.455951
$521$	30.4278	1.33307	0.666533	−	0.745476i	$-0.267778\pi$
$521$	30.4278	1.33307	0.666533	+	0.745476i	$0.267778\pi$
$522$	3.32421	0.145497
$523$	−25.3822	−1.10989	−0.554943	−	0.831888i	$-0.687260\pi$
$523$	−25.3822	−1.10989	−0.554943	+	0.831888i	$0.687260\pi$
$524$	−21.0211	−0.918313
$525$	54.1641	2.36391
$526$	−15.7849	−0.688255
$527$	−35.5577	−1.54892
$528$	1.27083	0.0553058
$529$	−22.2722	−0.968358
$530$	59.5717	2.58763
$531$	−63.1114	−2.73880
$532$	4.01980	0.174281
$533$	24.0086	1.03993
$534$	−2.70053	−0.116863
$535$	65.5296	2.83309
$536$	−0.323643	−0.0139793
$537$	34.5771	1.49211
$538$	0.142369	0.00613796
$539$	2.33825	0.100715
$540$	−25.4406	−1.09479
$541$	1.29012	0.0554668	0.0277334	−	0.999615i	$-0.491171\pi$
$541$	1.29012	0.0554668	0.0277334	+	0.999615i	$0.491171\pi$
$542$	18.3774	0.789378
$543$	50.5960	2.17128
$544$	−4.35693	−0.186802
$545$	71.0386	3.04296
$546$	8.95841	0.383385
$547$	15.2790	0.653283	0.326642	−	0.945148i	$-0.394083\pi$
$547$	15.2790	0.653283	0.326642	+	0.945148i	$0.394083\pi$
$548$	−13.0013	−0.555387
$549$	9.74401	0.415864
$550$	6.41146	0.273386
$551$	1.98528	0.0845758
$552$	−2.41918	−0.102967
$553$	−7.13839	−0.303555
$554$	−17.0567	−0.724669
$555$	−100.402	−4.26183
$556$	7.46539	0.316603
$557$	42.8050	1.81370	0.906852	−	0.421449i	$-0.138478\pi$
$557$	42.8050	1.81370	0.906852	+	0.421449i	$0.138478\pi$
$558$	41.1464	1.74187
$559$	14.4021	0.609142
$560$	−5.86609	−0.247887
$561$	5.53692	0.233769
$562$	10.3881	0.438196
$563$	−0.229178	−0.00965870	−0.00482935	−	0.999988i	$-0.501537\pi$
$563$	−0.229178	−0.00965870	−0.00482935	+	0.999988i	$0.501537\pi$
$564$	−23.5157	−0.990189
$565$	−50.5804	−2.12793
$566$	31.2416	1.31318
$567$	−1.72727	−0.0725383
$568$	−0.274768	−0.0115290
$569$	−10.2641	−0.430295	−0.215148	−	0.976582i	$-0.569023\pi$
$569$	−10.2641	−0.430295	−0.215148	+	0.976582i	$0.569023\pi$
$570$	−37.5182	−1.57147
$571$	−41.3427	−1.73014	−0.865070	−	0.501651i	$-0.832726\pi$
$571$	−41.3427	−1.73014	−0.865070	+	0.501651i	$0.832726\pi$
$572$	1.06042	0.0443383
$573$	−53.4654	−2.23355
$574$	−13.5455	−0.565380
$575$	−12.2050	−0.508983
$576$	5.04172	0.210072
$577$	29.1464	1.21338	0.606690	−	0.794939i	$-0.292497\pi$
$577$	29.1464	1.21338	0.606690	+	0.794939i	$0.292497\pi$
$578$	−1.98288	−0.0824770
$579$	40.1939	1.67040
$580$	−2.89711	−0.120296
$581$	−4.40568	−0.182778
$582$	−47.5683	−1.97177
$583$	6.07572	0.251631
$584$	−1.94413	−0.0804486
$585$	−52.4202	−2.16731
$586$	1.99603	0.0824554
$587$	−13.1632	−0.543305	−0.271653	−	0.962395i	$-0.587570\pi$
$587$	−13.1632	−0.543305	−0.271653	+	0.962395i	$0.587570\pi$
$588$	14.7963	0.610188
$589$	24.5734	1.01253
$590$	55.0028	2.26443
$591$	10.6609	0.438530
$592$	8.05772	0.331170
$593$	17.0674	0.700876	0.350438	−	0.936586i	$-0.386033\pi$
$593$	17.0674	0.700876	0.350438	+	0.936586i	$0.386033\pi$
$594$	−2.59468	−0.106461
$595$	−25.5582	−1.04778
$596$	17.8733	0.732118
$597$	7.17058	0.293472
$598$	−2.01863	−0.0825481
$599$	−14.8208	−0.605562	−0.302781	−	0.953060i	$-0.597915\pi$
$599$	−14.8208	−0.605562	−0.302781	+	0.953060i	$0.597915\pi$
$600$	40.5713	1.65631
$601$	−29.0408	−1.18460	−0.592299	−	0.805718i	$-0.701780\pi$
$601$	−29.0408	−1.18460	−0.592299	+	0.805718i	$0.701780\pi$
$602$	−8.12557	−0.331173
$603$	1.63172	0.0664487
$604$	24.4001	0.992825
$605$	−47.4511	−1.92916
$606$	−13.2079	−0.536533
$607$	22.3709	0.908008	0.454004	−	0.891000i	$-0.349995\pi$
$607$	22.3709	0.908008	0.454004	+	0.891000i	$0.349995\pi$
$608$	3.01101	0.122113
$609$	−2.49619	−0.101151
$610$	−8.49209	−0.343835
$611$	−19.6222	−0.793828
$612$	21.9665	0.887941
$613$	18.6986	0.755230	0.377615	−	0.925963i	$-0.376744\pi$
$613$	18.6986	0.755230	0.377615	+	0.925963i	$0.376744\pi$
$614$	−8.50164	−0.343098
$615$	126.425	5.09795
$616$	−0.598282	−0.0241055
$617$	−17.1686	−0.691184	−0.345592	−	0.938385i	$-0.612322\pi$
$617$	−17.1686	−0.691184	−0.345592	+	0.938385i	$0.612322\pi$
$618$	4.10851	0.165268
$619$	−9.01361	−0.362288	−0.181144	−	0.983457i	$-0.557980\pi$
$619$	−9.01361	−0.362288	−0.181144	+	0.983457i	$0.557980\pi$
$620$	−35.8599	−1.44017
$621$	4.93929	0.198207
$622$	−2.16854	−0.0869506
$623$	1.27135	0.0509358
$624$	6.71024	0.268625
$625$	108.152	4.32607
$626$	10.8623	0.434144
$627$	−3.82648	−0.152815
$628$	23.4272	0.934845
$629$	35.1070	1.39981
$630$	29.5752	1.17830
$631$	−33.1002	−1.31770	−0.658849	−	0.752275i	$-0.728956\pi$
$631$	−33.1002	−1.31770	−0.658849	+	0.752275i	$0.728956\pi$
$632$	−5.34697	−0.212691
$633$	24.8750	0.988692
$634$	5.45494	0.216643
$635$	4.16227	0.165175
$636$	38.4467	1.52451
$637$	12.3464	0.489183
$638$	−0.295476	−0.0116980
$639$	1.38531	0.0548018
$640$	−4.39396	−0.173686
$641$	7.47215	0.295132	0.147566	−	0.989052i	$-0.452856\pi$
$641$	7.47215	0.295132	0.147566	+	0.989052i	$0.452856\pi$
$642$	42.2918	1.66913
$643$	−42.9952	−1.69556	−0.847782	−	0.530344i	$-0.822063\pi$
$643$	−42.9952	−1.69556	−0.847782	+	0.530344i	$0.822063\pi$
$644$	1.13890	0.0448790
$645$	75.8388	2.98615
$646$	13.1188	0.516151
$647$	−0.0272818	−0.00107256	−0.000536278	−	1.00000i	$-0.500171\pi$
$647$	−0.0272818	−0.00107256	−0.000536278		1.00000i	$0.500171\pi$
$648$	−1.29380	−0.0508252
$649$	5.60973	0.220201
$650$	33.8538	1.32786
$651$	−30.8973	−1.21096
$652$	−0.594788	−0.0232937
$653$	32.9612	1.28987	0.644936	−	0.764237i	$-0.276884\pi$
$653$	32.9612	1.28987	0.644936	+	0.764237i	$0.276884\pi$
$654$	45.8472	1.79277
$655$	−92.3660	−3.60904
$656$	−10.1462	−0.396142
$657$	9.80175	0.382403
$658$	11.0707	0.431582
$659$	30.7847	1.19920	0.599602	−	0.800299i	$-0.295326\pi$
$659$	30.7847	1.19920	0.599602	+	0.800299i	$0.295326\pi$
$660$	5.58397	0.217356
$661$	10.1915	0.396403	0.198201	−	0.980161i	$-0.436490\pi$
$661$	10.1915	0.396403	0.198201	+	0.980161i	$0.436490\pi$
$662$	−23.6167	−0.917888
$663$	29.2361	1.13544
$664$	−3.30005	−0.128067
$665$	17.6628	0.684935
$666$	−40.6248	−1.57418
$667$	0.562475	0.0217791
$668$	0.844999	0.0326940
$669$	−11.4126	−0.441237
$670$	−1.42207	−0.0549395
$671$	−0.866107	−0.0334357
$672$	−3.78588	−0.146044
$673$	6.30932	0.243206	0.121603	−	0.992579i	$-0.461196\pi$
$673$	6.30932	0.243206	0.121603	+	0.992579i	$0.461196\pi$
$674$	−4.14214	−0.159549
$675$	−82.8352	−3.18833
$676$	−7.40078	−0.284645
$677$	−36.7931	−1.41408	−0.707038	−	0.707176i	$-0.749969\pi$
$677$	−36.7931	−1.41408	−0.707038	+	0.707176i	$0.749969\pi$
$678$	−32.6438	−1.25368
$679$	22.3942	0.859411
$680$	−19.1442	−0.734146
$681$	39.0881	1.49786
$682$	−3.65735	−0.140047
$683$	−22.8658	−0.874936	−0.437468	−	0.899234i	$-0.644125\pi$
$683$	−22.8658	−0.874936	−0.437468	+	0.899234i	$0.644125\pi$
$684$	−15.1807	−0.580447
$685$	−57.1271	−2.18271
$686$	−16.3110	−0.622758
$687$	37.6415	1.43611
$688$	−6.08641	−0.232042
$689$	32.0810	1.22219
$690$	−10.6298	−0.404668
$691$	33.2727	1.26575	0.632876	−	0.774253i	$-0.281874\pi$
$691$	33.2727	1.26575	0.632876	+	0.774253i	$0.281874\pi$
$692$	11.0445	0.419851
$693$	3.01637	0.114582
$694$	−18.5320	−0.703466
$695$	32.8026	1.24427
$696$	−1.86975	−0.0708728
$697$	−44.2063	−1.67443
$698$	25.4764	0.964294
$699$	44.4028	1.67947
$700$	−19.1001	−0.721918
$701$	29.6390	1.11945	0.559726	−	0.828678i	$-0.310907\pi$
$701$	29.6390	1.11945	0.559726	+	0.828678i	$0.310907\pi$
$702$	−13.7005	−0.517090
$703$	−24.2619	−0.915054
$704$	−0.448139	−0.0168899
$705$	−103.327	−3.89151
$706$	−2.40600	−0.0905509
$707$	6.21800	0.233852
$708$	35.4980	1.33410
$709$	−18.7886	−0.705622	−0.352811	−	0.935695i	$-0.614774\pi$
$709$	−18.7886	−0.705622	−0.352811	+	0.935695i	$0.614774\pi$
$710$	−1.20732	−0.0453099
$711$	26.9579	1.01100
$712$	0.952300	0.0356890
$713$	6.96220	0.260737
$714$	−16.4949	−0.617304
$715$	4.65943	0.174253
$716$	−12.1931	−0.455678
$717$	40.9886	1.53075
$718$	12.3024	0.459121
$719$	2.01719	0.0752285	0.0376143	−	0.999292i	$-0.488024\pi$
$719$	2.01719	0.0752285	0.0376143	+	0.999292i	$0.488024\pi$
$720$	22.1531	0.825597
$721$	−1.93420	−0.0720335
$722$	9.93383	0.369699
$723$	20.9043	0.777438
$724$	−17.8419	−0.663090
$725$	−9.43308	−0.350336
$726$	−30.6242	−1.13657
$727$	13.1361	0.487191	0.243596	−	0.969877i	$-0.421673\pi$
$727$	13.1361	0.487191	0.243596	+	0.969877i	$0.421673\pi$
$728$	−3.15905	−0.117082
$729$	−42.7339	−1.58274
$730$	−8.54241	−0.316169
$731$	−26.5181	−0.980806
$732$	−5.48066	−0.202571
$733$	32.5710	1.20304	0.601518	−	0.798859i	$-0.294563\pi$
$733$	32.5710	1.20304	0.601518	+	0.798859i	$0.294563\pi$
$734$	−34.7846	−1.28392
$735$	65.0141	2.39808
$736$	0.853088	0.0314452
$737$	−0.145037	−0.00534251
$738$	51.1543	1.88302
$739$	−23.5099	−0.864826	−0.432413	−	0.901676i	$-0.642338\pi$
$739$	−23.5099	−0.864826	−0.432413	+	0.901676i	$0.642338\pi$
$740$	35.4053	1.30152
$741$	−20.2046	−0.742235
$742$	−18.1000	−0.664470
$743$	−2.39977	−0.0880392	−0.0440196	−	0.999031i	$-0.514016\pi$
$743$	−2.39977	−0.0880392	−0.0440196	+	0.999031i	$0.514016\pi$
$744$	−23.1434	−0.848479
$745$	78.5344	2.87728
$746$	−19.6864	−0.720769
$747$	16.6379	0.608750
$748$	−1.95251	−0.0713910
$749$	−19.9102	−0.727502
$750$	115.967	4.23450
$751$	−8.87840	−0.323977	−0.161989	−	0.986793i	$-0.551791\pi$
$751$	−8.87840	−0.323977	−0.161989	+	0.986793i	$0.551791\pi$
$752$	8.29245	0.302395
$753$	65.2249	2.37693
$754$	−1.56018	−0.0568183
$755$	107.213	3.90187
$756$	7.72973	0.281127
$757$	−6.79164	−0.246846	−0.123423	−	0.992354i	$-0.539387\pi$
$757$	−6.79164	−0.246846	−0.123423	+	0.992354i	$0.539387\pi$
$758$	16.6965	0.606445
$759$	−1.08413	−0.0393514
$760$	13.2302	0.479911
$761$	50.1039	1.81626	0.908132	−	0.418683i	$-0.137508\pi$
$761$	50.1039	1.81626	0.908132	+	0.418683i	$0.137508\pi$
$762$	2.68627	0.0973133
$763$	−21.5840	−0.781392
$764$	18.8538	0.682106
$765$	96.5196	3.48967
$766$	19.8177	0.716041
$767$	29.6205	1.06954
$768$	−2.83579	−0.102328
$769$	1.70852	0.0616109	0.0308055	−	0.999525i	$-0.490193\pi$
$769$	1.70852	0.0616109	0.0308055	+	0.999525i	$0.490193\pi$
$770$	−2.62882	−0.0947362
$771$	−0.808962	−0.0291341
$772$	−14.1738	−0.510125
$773$	−31.5283	−1.13400	−0.566998	−	0.823719i	$-0.691895\pi$
$773$	−31.5283	−1.13400	−0.566998	+	0.823719i	$0.691895\pi$
$774$	30.6860	1.10298
$775$	−116.761	−4.19417
$776$	16.7742	0.602160
$777$	30.5056	1.09438
$778$	22.6601	0.812404
$779$	30.5503	1.09458
$780$	29.4845	1.05572
$781$	−0.123134	−0.00440610
$782$	3.71685	0.132914
$783$	3.81752	0.136427
$784$	−5.21768	−0.186346
$785$	102.938	3.67401
$786$	−59.6116	−2.12628
$787$	−8.91241	−0.317693	−0.158847	−	0.987303i	$-0.550778\pi$
$787$	−8.91241	−0.317693	−0.158847	+	0.987303i	$0.550778\pi$
$788$	−3.75940	−0.133923
$789$	−44.7627	−1.59360
$790$	−23.4943	−0.835891
$791$	15.3681	0.546426
$792$	2.25939	0.0802841
$793$	−4.57322	−0.162400
$794$	16.7456	0.594280
$795$	168.933	5.99144
$796$	−2.52860	−0.0896238
$797$	5.73799	0.203250	0.101625	−	0.994823i	$-0.467596\pi$
$797$	5.73799	0.203250	0.101625	+	0.994823i	$0.467596\pi$
$798$	11.3993	0.403532
$799$	36.1297	1.27818
$800$	−14.3068	−0.505823
$801$	−4.80123	−0.169643
$802$	−26.6031	−0.939387
$803$	−0.871240	−0.0307454
$804$	−0.917785	−0.0323678
$805$	5.00429	0.176378
$806$	−19.3115	−0.680220
$807$	0.403729	0.0142119
$808$	4.65756	0.163852
$809$	−21.5558	−0.757861	−0.378931	−	0.925425i	$-0.623708\pi$
$809$	−21.5558	−0.757861	−0.378931	+	0.925425i	$0.623708\pi$
$810$	−5.68489	−0.199747
$811$	23.0128	0.808088	0.404044	−	0.914740i	$-0.367604\pi$
$811$	23.0128	0.808088	0.404044	+	0.914740i	$0.367604\pi$
$812$	0.880243	0.0308905
$813$	52.1146	1.82774
$814$	3.61098	0.126565
$815$	−2.61347	−0.0915460
$816$	−12.3554	−0.432524
$817$	18.3262	0.641153
$818$	14.5602	0.509084
$819$	15.9271	0.556536
$820$	−44.5819	−1.55687
$821$	11.1378	0.388711	0.194356	−	0.980931i	$-0.437738\pi$
$821$	11.1378	0.388711	0.194356	+	0.980931i	$0.437738\pi$
$822$	−36.8690	−1.28595
$823$	−34.9534	−1.21840	−0.609199	−	0.793017i	$-0.708509\pi$
$823$	−34.9534	−1.21840	−0.609199	+	0.793017i	$0.708509\pi$
$824$	−1.44880	−0.0504714
$825$	18.1816	0.633001
$826$	−16.7117	−0.581476
$827$	42.5398	1.47925	0.739627	−	0.673017i	$-0.235002\pi$
$827$	42.5398	1.47925	0.739627	+	0.673017i	$0.235002\pi$
$828$	−4.30103	−0.149471
$829$	−32.2665	−1.12066	−0.560332	−	0.828268i	$-0.689326\pi$
$829$	−32.2665	−1.12066	−0.560332	+	0.828268i	$0.689326\pi$
$830$	−14.5003	−0.503312
$831$	−48.3692	−1.67791
$832$	−2.36627	−0.0820356
$833$	−22.7331	−0.787655
$834$	21.1703	0.733068
$835$	3.71289	0.128490
$836$	1.34935	0.0466683
$837$	47.2524	1.63328
$838$	−30.7615	−1.06264
$839$	18.8822	0.651885	0.325942	−	0.945390i	$-0.394318\pi$
$839$	18.8822	0.651885	0.325942	+	0.945390i	$0.394318\pi$
$840$	−16.6350	−0.573962
$841$	−28.5653	−0.985009
$842$	25.7494	0.887382
$843$	29.4585	1.01461
$844$	−8.77179	−0.301938
$845$	−32.5187	−1.11868
$846$	−41.8082	−1.43740
$847$	14.4173	0.495384
$848$	−13.5577	−0.465572
$849$	88.5948	3.04057
$850$	−62.3340	−2.13804
$851$	−6.87394	−0.235636
$852$	−0.779186	−0.0266945
$853$	53.3641	1.82715	0.913575	−	0.406670i	$-0.133310\pi$
$853$	53.3641	1.82715	0.913575	+	0.406670i	$0.133310\pi$
$854$	2.58019	0.0882923
$855$	−66.7032	−2.28120
$856$	−14.9136	−0.509736
$857$	10.6920	0.365233	0.182616	−	0.983184i	$-0.441543\pi$
$857$	10.6920	0.365233	0.182616	+	0.983184i	$0.441543\pi$
$858$	3.00712	0.102662
$859$	−56.8640	−1.94017	−0.970087	−	0.242756i	$-0.921949\pi$
$859$	−56.8640	−1.94017	−0.970087	+	0.242756i	$0.921949\pi$
$860$	−26.7434	−0.911942
$861$	−38.4123	−1.30909
$862$	13.3900	0.456064
$863$	−0.179866	−0.00612273	−0.00306136	−	0.999995i	$-0.500974\pi$
$863$	−0.179866	−0.00612273	−0.00306136	+	0.999995i	$0.500974\pi$
$864$	5.78990	0.196976
$865$	48.5292	1.65004
$866$	29.7637	1.01141
$867$	−5.62304	−0.190968
$868$	10.8955	0.369816
$869$	−2.39619	−0.0812850
$870$	−8.21561	−0.278535
$871$	−0.765826	−0.0259490
$872$	−16.1673	−0.547495
$873$	−84.5711	−2.86230
$874$	−2.56865	−0.0868860
$875$	−54.5948	−1.84564
$876$	−5.51314	−0.186272
$877$	−39.0982	−1.32025	−0.660126	−	0.751155i	$-0.729497\pi$
$877$	−39.0982	−1.32025	−0.660126	+	0.751155i	$0.729497\pi$
$878$	5.58421	0.188458
$879$	5.66034	0.190918
$880$	−1.96910	−0.0663785
$881$	−40.7107	−1.37158	−0.685789	−	0.727800i	$-0.740543\pi$
$881$	−40.7107	−1.37158	−0.685789	+	0.727800i	$0.740543\pi$
$882$	26.3061	0.885772
$883$	−27.3346	−0.919883	−0.459941	−	0.887949i	$-0.652130\pi$
$883$	−27.3346	−0.919883	−0.459941	+	0.887949i	$0.652130\pi$
$884$	−10.3097	−0.346752
$885$	155.977	5.24309
$886$	31.3242	1.05236
$887$	−38.9191	−1.30678	−0.653388	−	0.757023i	$-0.726653\pi$
$887$	−38.9191	−1.30678	−0.653388	+	0.757023i	$0.726653\pi$
$888$	22.8500	0.766797
$889$	−1.26464	−0.0424147
$890$	4.18437	0.140260
$891$	−0.579801	−0.0194241
$892$	4.02449	0.134750
$893$	−24.9686	−0.835544
$894$	50.6849	1.69516
$895$	−53.5760	−1.79085
$896$	1.33504	0.0446004
$897$	−5.72443	−0.191133
$898$	5.88375	0.196343
$899$	5.38100	0.179466
$900$	72.1312	2.40437
$901$	−59.0698	−1.96790
$902$	−4.54691	−0.151396
$903$	−23.0424	−0.766804
$904$	11.5114	0.382862
$905$	−78.3966	−2.60599
$906$	69.1936	2.29880
$907$	−17.2353	−0.572288	−0.286144	−	0.958187i	$-0.592374\pi$
$907$	−17.2353	−0.572288	−0.286144	+	0.958187i	$0.592374\pi$
$908$	−13.7838	−0.457433
$909$	−23.4821	−0.778852
$910$	−13.8807	−0.460142
$911$	11.1717	0.370135	0.185068	−	0.982726i	$-0.440750\pi$
$911$	11.1717	0.370135	0.185068	+	0.982726i	$0.440750\pi$
$912$	8.53860	0.282741
$913$	−1.47888	−0.0489438
$914$	14.6856	0.485755
$915$	−24.0818	−0.796120
$916$	−13.2737	−0.438576
$917$	28.0640	0.926754
$918$	25.2262	0.832590
$919$	37.4284	1.23465	0.617325	−	0.786709i	$-0.288217\pi$
$919$	37.4284	1.23465	0.617325	+	0.786709i	$0.288217\pi$
$920$	3.74843	0.123582
$921$	−24.1089	−0.794415
$922$	20.4244	0.672642
$923$	−0.650175	−0.0214008
$924$	−1.69660	−0.0558142
$925$	115.281	3.79040
$926$	−14.7432	−0.484493
$927$	7.30446	0.239910
$928$	0.659341	0.0216439
$929$	−24.1617	−0.792721	−0.396360	−	0.918095i	$-0.629727\pi$
$929$	−24.1617	−0.792721	−0.396360	+	0.918095i	$0.629727\pi$
$930$	−101.691	−3.33459
$931$	15.7105	0.514890
$932$	−15.6580	−0.512895
$933$	−6.14954	−0.201327
$934$	−11.8245	−0.386910
$935$	−8.57926	−0.280572
$936$	11.9301	0.389946
$937$	30.1788	0.985898	0.492949	−	0.870058i	$-0.335919\pi$
$937$	30.1788	0.985898	0.492949	+	0.870058i	$0.335919\pi$
$938$	0.432075	0.0141078
$939$	30.8032	1.00522
$940$	36.4367	1.18843
$941$	4.74670	0.154738	0.0773691	−	0.997003i	$-0.475348\pi$
$941$	4.74670	0.154738	0.0773691	+	0.997003i	$0.475348\pi$
$942$	66.4346	2.16455
$943$	8.65560	0.281865
$944$	−12.5178	−0.407421
$945$	33.9641	1.10485
$946$	−2.72756	−0.0886805
$947$	−12.7705	−0.414985	−0.207492	−	0.978237i	$-0.566530\pi$
$947$	−12.7705	−0.414985	−0.207492	+	0.978237i	$0.566530\pi$
$948$	−15.1629	−0.492468
$949$	−4.60032	−0.149333
$950$	43.0780	1.39764
$951$	15.4691	0.501619
$952$	5.81666	0.188519
$953$	15.5551	0.503878	0.251939	−	0.967743i	$-0.418932\pi$
$953$	15.5551	0.503878	0.251939	+	0.967743i	$0.418932\pi$
$954$	68.3539	2.21304
$955$	82.8427	2.68073
$956$	−14.4540	−0.467476
$957$	−0.837910	−0.0270858
$958$	8.73494	0.282213
$959$	17.3572	0.560492
$960$	−12.4603	−0.402156
$961$	35.6049	1.14855
$962$	19.0667	0.614736
$963$	75.1901	2.42297
$964$	−7.37157	−0.237422
$965$	−62.2789	−2.00483
$966$	3.22969	0.103914
$967$	−15.4852	−0.497972	−0.248986	−	0.968507i	$-0.580097\pi$
$967$	−15.4852	−0.497972	−0.248986	+	0.968507i	$0.580097\pi$
$968$	10.7992	0.347099
$969$	37.2021	1.19510
$970$	73.7053	2.36653
$971$	47.0953	1.51136	0.755680	−	0.654941i	$-0.227306\pi$
$971$	47.0953	1.51136	0.755680	+	0.654941i	$0.227306\pi$
$972$	13.7008	0.439452
$973$	−9.96657	−0.319513
$974$	16.8507	0.539933
$975$	96.0024	3.07454
$976$	1.93267	0.0618634
$977$	−46.8512	−1.49890	−0.749451	−	0.662060i	$-0.769682\pi$
$977$	−46.8512	−1.49890	−0.749451	+	0.662060i	$0.769682\pi$
$978$	−1.68670	−0.0539346
$979$	0.426763	0.0136394
$980$	−22.9263	−0.732352
$981$	81.5113	2.60245
$982$	14.3719	0.458627
$983$	3.61312	0.115241	0.0576203	−	0.998339i	$-0.481649\pi$
$983$	3.61312	0.115241	0.0576203	+	0.998339i	$0.481649\pi$
$984$	−28.7725	−0.917234
$985$	−16.5186	−0.526328
$986$	2.87270	0.0914855
$987$	31.3943	0.999291
$988$	7.12485	0.226672
$989$	5.19224	0.165104
$990$	9.92768	0.315522
$991$	−49.5382	−1.57363	−0.786816	−	0.617187i	$-0.788272\pi$
$991$	−49.5382	−1.57363	−0.786816	+	0.617187i	$0.788272\pi$
$992$	8.16118	0.259118
$993$	−66.9720	−2.12529
$994$	0.366825	0.0116350
$995$	−11.1106	−0.352228
$996$	−9.35825	−0.296528
$997$	43.5946	1.38066	0.690328	−	0.723497i	$-0.257466\pi$
$997$	43.5946	1.38066	0.690328	+	0.723497i	$0.257466\pi$
$998$	−13.9718	−0.442269
$999$	−46.6534	−1.47605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.4	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.4	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.83579 q^{3} +1.00000 q^{4} +4.39396 q^{5} +2.83579 q^{6} -1.33504 q^{7} -1.00000 q^{8} +5.04172 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.83579 q^{3} +1.00000 q^{4} +4.39396 q^{5} +2.83579 q^{6} -1.33504 q^{7} -1.00000 q^{8} +5.04172 q^{9} -4.39396 q^{10} -0.448139 q^{11} -2.83579 q^{12} -2.36627 q^{13} +1.33504 q^{14} -12.4603 q^{15} +1.00000 q^{16} +4.35693 q^{17} -5.04172 q^{18} -3.01101 q^{19} +4.39396 q^{20} +3.78588 q^{21} +0.448139 q^{22} -0.853088 q^{23} +2.83579 q^{24} +14.3068 q^{25} +2.36627 q^{26} -5.78990 q^{27} -1.33504 q^{28} -0.659341 q^{29} +12.4603 q^{30} -8.16118 q^{31} -1.00000 q^{32} +1.27083 q^{33} -4.35693 q^{34} -5.86609 q^{35} +5.04172 q^{36} +8.05772 q^{37} +3.01101 q^{38} +6.71024 q^{39} -4.39396 q^{40} -10.1462 q^{41} -3.78588 q^{42} -6.08641 q^{43} -0.448139 q^{44} +22.1531 q^{45} +0.853088 q^{46} +8.29245 q^{47} -2.83579 q^{48} -5.21768 q^{49} -14.3068 q^{50} -12.3554 q^{51} -2.36627 q^{52} -13.5577 q^{53} +5.78990 q^{54} -1.96910 q^{55} +1.33504 q^{56} +8.53860 q^{57} +0.659341 q^{58} -12.5178 q^{59} -12.4603 q^{60} +1.93267 q^{61} +8.16118 q^{62} -6.73088 q^{63} +1.00000 q^{64} -10.3973 q^{65} -1.27083 q^{66} +0.323643 q^{67} +4.35693 q^{68} +2.41918 q^{69} +5.86609 q^{70} +0.274768 q^{71} -5.04172 q^{72} +1.94413 q^{73} -8.05772 q^{74} -40.5713 q^{75} -3.01101 q^{76} +0.598282 q^{77} -6.71024 q^{78} +5.34697 q^{79} +4.39396 q^{80} +1.29380 q^{81} +10.1462 q^{82} +3.30005 q^{83} +3.78588 q^{84} +19.1442 q^{85} +6.08641 q^{86} +1.86975 q^{87} +0.448139 q^{88} -0.952300 q^{89} -22.1531 q^{90} +3.15905 q^{91} -0.853088 q^{92} +23.1434 q^{93} -8.29245 q^{94} -13.2302 q^{95} +2.83579 q^{96} -16.7742 q^{97} +5.21768 q^{98} -2.25939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more