LMFDB - Embedded newform 5610.2.a.cf.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.52616$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.54997 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.54997 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -1.05232 q^{13} -4.54997 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +6.39400 q^{19} -1.00000 q^{20} +4.54997 q^{21} +1.00000 q^{22} -1.20828 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.05232 q^{26} +1.00000 q^{27} +4.54997 q^{28} -5.60228 q^{29} +1.00000 q^{30} +1.49765 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -4.54997 q^{35} +1.00000 q^{36} +2.00000 q^{37} -6.39400 q^{38} -1.05232 q^{39} +1.00000 q^{40} -1.34169 q^{41} -4.54997 q^{42} +10.6546 q^{43} -1.00000 q^{44} -1.00000 q^{45} +1.20828 q^{46} +1.00000 q^{48} +13.7022 q^{49} -1.00000 q^{50} -1.00000 q^{51} -1.05232 q^{52} +6.81057 q^{53} -1.00000 q^{54} +1.00000 q^{55} -4.54997 q^{56} +6.39400 q^{57} +5.60228 q^{58} -3.05232 q^{59} -1.00000 q^{60} -4.10463 q^{61} -1.49765 q^{62} +4.54997 q^{63} +1.00000 q^{64} +1.05232 q^{65} +1.00000 q^{66} -10.5463 q^{67} -1.00000 q^{68} -1.20828 q^{69} +4.54997 q^{70} +13.2522 q^{71} -1.00000 q^{72} -0.0476242 q^{73} -2.00000 q^{74} +1.00000 q^{75} +6.39400 q^{76} -4.54997 q^{77} +1.05232 q^{78} -5.07737 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.34169 q^{82} -2.68337 q^{83} +4.54997 q^{84} +1.00000 q^{85} -10.6546 q^{86} -5.60228 q^{87} +1.00000 q^{88} +11.0999 q^{89} +1.00000 q^{90} -4.78800 q^{91} -1.20828 q^{92} +1.49765 q^{93} -6.39400 q^{95} -1.00000 q^{96} +3.84403 q^{97} -13.7022 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 6 q^{13} - 5 q^{14} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 8 q^{19} - 4 q^{20} + 5 q^{21} + 4 q^{22} + q^{23} - 4 q^{24} + 4 q^{25} - 6 q^{26} + 4 q^{27} + 5 q^{28} + q^{29} + 4 q^{30} + 3 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{34} - 5 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} + 9 q^{43} - 4 q^{44} - 4 q^{45} - q^{46} + 4 q^{48} + 5 q^{49} - 4 q^{50} - 4 q^{51} + 6 q^{52} - 2 q^{53} - 4 q^{54} + 4 q^{55} - 5 q^{56} + 8 q^{57} - q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{61} - 3 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 4 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} + 5 q^{70} - 10 q^{71} - 4 q^{72} + 16 q^{73} - 8 q^{74} + 4 q^{75} + 8 q^{76} - 5 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 2 q^{82} + 4 q^{83} + 5 q^{84} + 4 q^{85} - 9 q^{86} + q^{87} + 4 q^{88} + 18 q^{89} + 4 q^{90} + 16 q^{91} + q^{92} + 3 q^{93} - 8 q^{95} - 4 q^{96} + 11 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 6 * q^13 - 5 * q^14 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 8 * q^19 - 4 * q^20 + 5 * q^21 + 4 * q^22 + q^23 - 4 * q^24 + 4 * q^25 - 6 * q^26 + 4 * q^27 + 5 * q^28 + q^29 + 4 * q^30 + 3 * q^31 - 4 * q^32 - 4 * q^33 + 4 * q^34 - 5 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 + 9 * q^43 - 4 * q^44 - 4 * q^45 - q^46 + 4 * q^48 + 5 * q^49 - 4 * q^50 - 4 * q^51 + 6 * q^52 - 2 * q^53 - 4 * q^54 + 4 * q^55 - 5 * q^56 + 8 * q^57 - q^58 - 2 * q^59 - 4 * q^60 + 4 * q^61 - 3 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 4 * q^66 + 12 * q^67 - 4 * q^68 + q^69 + 5 * q^70 - 10 * q^71 - 4 * q^72 + 16 * q^73 - 8 * q^74 + 4 * q^75 + 8 * q^76 - 5 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 2 * q^82 + 4 * q^83 + 5 * q^84 + 4 * q^85 - 9 * q^86 + q^87 + 4 * q^88 + 18 * q^89 + 4 * q^90 + 16 * q^91 + q^92 + 3 * q^93 - 8 * q^95 - 4 * q^96 + 11 * q^97 - 5 * q^98 - 4 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	4.54997	1.71973	0.859863	−	0.510524i	$-0.170549\pi$
$7$	4.54997	1.71973	0.859863	+	0.510524i	$0.170549\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−1.05232	−0.291860	−0.145930	−	0.989295i	$-0.546617\pi$
$13$	−1.05232	−0.291860	−0.145930	+	0.989295i	$0.546617\pi$
$14$	−4.54997	−1.21603
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	6.39400	1.46688	0.733442	−	0.679752i	$-0.237912\pi$
$19$	6.39400	1.46688	0.733442	+	0.679752i	$0.237912\pi$
$20$	−1.00000	−0.223607
$21$	4.54997	0.992885
$22$	1.00000	0.213201
$23$	−1.20828	−0.251945	−0.125972	−	0.992034i	$-0.540205\pi$
$23$	−1.20828	−0.251945	−0.125972	+	0.992034i	$0.540205\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	1.05232	0.206376
$27$	1.00000	0.192450
$28$	4.54997	0.859863
$29$	−5.60228	−1.04032	−0.520159	−	0.854069i	$-0.674127\pi$
$29$	−5.60228	−1.04032	−0.520159	+	0.854069i	$0.674127\pi$
$30$	1.00000	0.182574
$31$	1.49765	0.268987	0.134493	−	0.990914i	$-0.457059\pi$
$31$	1.49765	0.268987	0.134493	+	0.990914i	$0.457059\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−4.54997	−0.769085
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−6.39400	−1.03724
$39$	−1.05232	−0.168505
$40$	1.00000	0.158114
$41$	−1.34169	−0.209536	−0.104768	−	0.994497i	$-0.533410\pi$
$41$	−1.34169	−0.209536	−0.104768	+	0.994497i	$0.533410\pi$
$42$	−4.54997	−0.702076
$43$	10.6546	1.62481	0.812406	−	0.583093i	$-0.198158\pi$
$43$	10.6546	1.62481	0.812406	+	0.583093i	$0.198158\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	1.20828	0.178152
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	13.7022	1.95746
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−1.05232	−0.145930
$53$	6.81057	0.935504	0.467752	−	0.883860i	$-0.345064\pi$
$53$	6.81057	0.935504	0.467752	+	0.883860i	$0.345064\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−4.54997	−0.608015
$57$	6.39400	0.846906
$58$	5.60228	0.735616
$59$	−3.05232	−0.397378	−0.198689	−	0.980063i	$-0.563668\pi$
$59$	−3.05232	−0.397378	−0.198689	+	0.980063i	$0.563668\pi$
$60$	−1.00000	−0.129099
$61$	−4.10463	−0.525544	−0.262772	−	0.964858i	$-0.584637\pi$
$61$	−4.10463	−0.525544	−0.262772	+	0.964858i	$0.584637\pi$
$62$	−1.49765	−0.190202
$63$	4.54997	0.573242
$64$	1.00000	0.125000
$65$	1.05232	0.130524
$66$	1.00000	0.123091
$67$	−10.5463	−1.28843	−0.644215	−	0.764844i	$-0.722816\pi$
$67$	−10.5463	−1.28843	−0.644215	+	0.764844i	$0.722816\pi$
$68$	−1.00000	−0.121268
$69$	−1.20828	−0.145460
$70$	4.54997	0.543825
$71$	13.2522	1.57275	0.786373	−	0.617752i	$-0.211956\pi$
$71$	13.2522	1.57275	0.786373	+	0.617752i	$0.211956\pi$
$72$	−1.00000	−0.117851
$73$	−0.0476242	−0.00557399	−0.00278700	−	0.999996i	$-0.500887\pi$
$73$	−0.0476242	−0.00557399	−0.00278700	+	0.999996i	$0.500887\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	6.39400	0.733442
$77$	−4.54997	−0.518517
$78$	1.05232	0.119151
$79$	−5.07737	−0.571249	−0.285625	−	0.958342i	$-0.592201\pi$
$79$	−5.07737	−0.571249	−0.285625	+	0.958342i	$0.592201\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.34169	0.148164
$83$	−2.68337	−0.294538	−0.147269	−	0.989096i	$-0.547048\pi$
$83$	−2.68337	−0.294538	−0.147269	+	0.989096i	$0.547048\pi$
$84$	4.54997	0.496442
$85$	1.00000	0.108465
$86$	−10.6546	−1.14892
$87$	−5.60228	−0.600628
$88$	1.00000	0.106600
$89$	11.0999	1.17659	0.588296	−	0.808646i	$-0.299799\pi$
$89$	11.0999	1.17659	0.588296	+	0.808646i	$0.299799\pi$
$90$	1.00000	0.105409
$91$	−4.78800	−0.501919
$92$	−1.20828	−0.125972
$93$	1.49765	0.155300
$94$	0	0
$95$	−6.39400	−0.656011
$96$	−1.00000	−0.102062
$97$	3.84403	0.390302	0.195151	−	0.980773i	$-0.437480\pi$
$97$	3.84403	0.390302	0.195151	+	0.980773i	$0.437480\pi$
$98$	−13.7022	−1.38413
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	15.2296	1.51540	0.757702	−	0.652600i	$-0.226322\pi$
$101$	15.2296	1.51540	0.757702	+	0.652600i	$0.226322\pi$
$102$	1.00000	0.0990148
$103$	−1.18572	−0.116832	−0.0584161	−	0.998292i	$-0.518605\pi$
$103$	−1.18572	−0.116832	−0.0584161	+	0.998292i	$0.518605\pi$
$104$	1.05232	0.103188
$105$	−4.54997	−0.444032
$106$	−6.81057	−0.661501
$107$	16.7022	1.61466	0.807332	−	0.590097i	$-0.200910\pi$
$107$	16.7022	1.61466	0.807332	+	0.590097i	$0.200910\pi$
$108$	1.00000	0.0962250
$109$	5.68806	0.544818	0.272409	−	0.962182i	$-0.412180\pi$
$109$	5.68806	0.544818	0.272409	+	0.962182i	$0.412180\pi$
$110$	−1.00000	−0.0953463
$111$	2.00000	0.189832
$112$	4.54997	0.429932
$113$	7.07737	0.665783	0.332892	−	0.942965i	$-0.391976\pi$
$113$	7.07737	0.665783	0.332892	+	0.942965i	$0.391976\pi$
$114$	−6.39400	−0.598853
$115$	1.20828	0.112673
$116$	−5.60228	−0.520159
$117$	−1.05232	−0.0972866
$118$	3.05232	0.280988
$119$	−4.54997	−0.417095
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	4.10463	0.371616
$123$	−1.34169	−0.120976
$124$	1.49765	0.134493
$125$	−1.00000	−0.0894427
$126$	−4.54997	−0.405344
$127$	−16.6164	−1.47447	−0.737236	−	0.675636i	$-0.763869\pi$
$127$	−16.6164	−1.47447	−0.737236	+	0.675636i	$0.763869\pi$
$128$	−1.00000	−0.0883883
$129$	10.6546	0.938085
$130$	−1.05232	−0.0922941
$131$	−2.68337	−0.234447	−0.117224	−	0.993106i	$-0.537399\pi$
$131$	−2.68337	−0.234447	−0.117224	+	0.993106i	$0.537399\pi$
$132$	−1.00000	−0.0870388
$133$	29.0925	2.52264
$134$	10.5463	0.911058
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−7.01416	−0.599260	−0.299630	−	0.954055i	$-0.596863\pi$
$137$	−7.01416	−0.599260	−0.299630	+	0.954055i	$0.596863\pi$
$138$	1.20828	0.102856
$139$	0.0857780	0.00727559	0.00363780	−	0.999993i	$-0.498842\pi$
$139$	0.0857780	0.00727559	0.00363780	+	0.999993i	$0.498842\pi$
$140$	−4.54997	−0.384543
$141$	0	0
$142$	−13.2522	−1.11210
$143$	1.05232	0.0879990
$144$	1.00000	0.0833333
$145$	5.60228	0.465244
$146$	0.0476242	0.00394141
$147$	13.7022	1.13014
$148$	2.00000	0.164399
$149$	−4.76294	−0.390196	−0.195098	−	0.980784i	$-0.562502\pi$
$149$	−4.76294	−0.390196	−0.195098	+	0.980784i	$0.562502\pi$
$150$	−1.00000	−0.0816497
$151$	4.57874	0.372613	0.186306	−	0.982492i	$-0.440348\pi$
$151$	4.57874	0.372613	0.186306	+	0.982492i	$0.440348\pi$
$152$	−6.39400	−0.518622
$153$	−1.00000	−0.0808452
$154$	4.54997	0.366647
$155$	−1.49765	−0.120295
$156$	−1.05232	−0.0842526
$157$	9.07488	0.724254	0.362127	−	0.932129i	$-0.382051\pi$
$157$	9.07488	0.724254	0.362127	+	0.932129i	$0.382051\pi$
$158$	5.07737	0.403934
$159$	6.81057	0.540113
$160$	1.00000	0.0790569
$161$	−5.49765	−0.433276
$162$	−1.00000	−0.0785674
$163$	12.9690	1.01581	0.507906	−	0.861412i	$-0.330420\pi$
$163$	12.9690	1.01581	0.507906	+	0.861412i	$0.330420\pi$
$164$	−1.34169	−0.104768
$165$	1.00000	0.0778499
$166$	2.68337	0.208270
$167$	−16.5713	−1.28233	−0.641163	−	0.767404i	$-0.721548\pi$
$167$	−16.5713	−1.28233	−0.641163	+	0.767404i	$0.721548\pi$
$168$	−4.54997	−0.351038
$169$	−11.8926	−0.914818
$170$	−1.00000	−0.0766965
$171$	6.39400	0.488961
$172$	10.6546	0.812406
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	5.60228	0.424708
$175$	4.54997	0.343945
$176$	−1.00000	−0.0753778
$177$	−3.05232	−0.229426
$178$	−11.0999	−0.831976
$179$	3.05232	0.228141	0.114070	−	0.993473i	$-0.463611\pi$
$179$	3.05232	0.228141	0.114070	+	0.993473i	$0.463611\pi$
$180$	−1.00000	−0.0745356
$181$	−8.86440	−0.658886	−0.329443	−	0.944176i	$-0.606861\pi$
$181$	−8.86440	−0.658886	−0.329443	+	0.944176i	$0.606861\pi$
$182$	4.78800	0.354910
$183$	−4.10463	−0.303423
$184$	1.20828	0.0890759
$185$	−2.00000	−0.147043
$186$	−1.49765	−0.109813
$187$	1.00000	0.0731272
$188$	0	0
$189$	4.54997	0.330962
$190$	6.39400	0.463870
$191$	−10.8069	−0.781957	−0.390978	−	0.920400i	$-0.627863\pi$
$191$	−10.8069	−0.781957	−0.390978	+	0.920400i	$0.627863\pi$
$192$	1.00000	0.0721688
$193$	6.05701	0.435993	0.217996	−	0.975950i	$-0.430048\pi$
$193$	6.05701	0.435993	0.217996	+	0.975950i	$0.430048\pi$
$194$	−3.84403	−0.275985
$195$	1.05232	0.0753579
$196$	13.7022	0.978730
$197$	−7.88794	−0.561993	−0.280996	−	0.959709i	$-0.590665\pi$
$197$	−7.88794	−0.561993	−0.280996	+	0.959709i	$0.590665\pi$
$198$	1.00000	0.0710669
$199$	10.6834	0.757324	0.378662	−	0.925535i	$-0.376384\pi$
$199$	10.6834	0.757324	0.378662	+	0.925535i	$0.376384\pi$
$200$	−1.00000	−0.0707107
$201$	−10.5463	−0.743876
$202$	−15.2296	−1.07155
$203$	−25.4902	−1.78906
$204$	−1.00000	−0.0700140
$205$	1.34169	0.0937074
$206$	1.18572	0.0826128
$207$	−1.20828	−0.0839815
$208$	−1.05232	−0.0729649
$209$	−6.39400	−0.442282
$210$	4.54997	0.313978
$211$	−3.60228	−0.247992	−0.123996	−	0.992283i	$-0.539571\pi$
$211$	−3.60228	−0.247992	−0.123996	+	0.992283i	$0.539571\pi$
$212$	6.81057	0.467752
$213$	13.2522	0.908025
$214$	−16.7022	−1.14174
$215$	−10.6546	−0.726638
$216$	−1.00000	−0.0680414
$217$	6.81428	0.462584
$218$	−5.68806	−0.385244
$219$	−0.0476242	−0.00321815
$220$	1.00000	0.0674200
$221$	1.05232	0.0707864
$222$	−2.00000	−0.134231
$223$	−12.1235	−0.811848	−0.405924	−	0.913907i	$-0.633050\pi$
$223$	−12.1235	−0.811848	−0.405924	+	0.913907i	$0.633050\pi$
$224$	−4.54997	−0.304008
$225$	1.00000	0.0666667
$226$	−7.07737	−0.470780
$227$	17.9737	1.19296	0.596479	−	0.802629i	$-0.296566\pi$
$227$	17.9737	1.19296	0.596479	+	0.802629i	$0.296566\pi$
$228$	6.39400	0.423453
$229$	−17.7833	−1.17515	−0.587577	−	0.809168i	$-0.699918\pi$
$229$	−17.7833	−1.17515	−0.587577	+	0.809168i	$0.699918\pi$
$230$	−1.20828	−0.0796719
$231$	−4.54997	−0.299366
$232$	5.60228	0.367808
$233$	−10.9690	−0.718605	−0.359302	−	0.933221i	$-0.616985\pi$
$233$	−10.9690	−0.718605	−0.359302	+	0.933221i	$0.616985\pi$
$234$	1.05232	0.0687920
$235$	0	0
$236$	−3.05232	−0.198689
$237$	−5.07737	−0.329811
$238$	4.54997	0.294931
$239$	6.90006	0.446328	0.223164	−	0.974781i	$-0.428361\pi$
$239$	6.90006	0.446328	0.223164	+	0.974781i	$0.428361\pi$
$240$	−1.00000	−0.0645497
$241$	24.2055	1.55922	0.779608	−	0.626268i	$-0.215418\pi$
$241$	24.2055	1.55922	0.779608	+	0.626268i	$0.215418\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−4.10463	−0.262772
$245$	−13.7022	−0.875403
$246$	1.34169	0.0855428
$247$	−6.72850	−0.428124
$248$	−1.49765	−0.0951012
$249$	−2.68337	−0.170052
$250$	1.00000	0.0632456
$251$	16.9403	1.06926	0.534630	−	0.845086i	$-0.320451\pi$
$251$	16.9403	1.06926	0.534630	+	0.845086i	$0.320451\pi$
$252$	4.54997	0.286621
$253$	1.20828	0.0759641
$254$	16.6164	1.04261
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	1.97177	0.122995	0.0614977	−	0.998107i	$-0.480412\pi$
$257$	1.97177	0.122995	0.0614977	+	0.998107i	$0.480412\pi$
$258$	−10.6546	−0.663326
$259$	9.09994	0.565443
$260$	1.05232	0.0652618
$261$	−5.60228	−0.346773
$262$	2.68337	0.165779
$263$	−20.1235	−1.24087	−0.620434	−	0.784259i	$-0.713043\pi$
$263$	−20.1235	−1.24087	−0.620434	+	0.784259i	$0.713043\pi$
$264$	1.00000	0.0615457
$265$	−6.81057	−0.418370
$266$	−29.0925	−1.78378
$267$	11.0999	0.679305
$268$	−10.5463	−0.644215
$269$	−0.633256	−0.0386103	−0.0193052	−	0.999814i	$-0.506145\pi$
$269$	−0.633256	−0.0386103	−0.0193052	+	0.999814i	$0.506145\pi$
$270$	1.00000	0.0608581
$271$	−0.181026	−0.0109966	−0.00549829	−	0.999985i	$-0.501750\pi$
$271$	−0.181026	−0.0109966	−0.00549829	+	0.999985i	$0.501750\pi$
$272$	−1.00000	−0.0606339
$273$	−4.78800	−0.289783
$274$	7.01416	0.423741
$275$	−1.00000	−0.0603023
$276$	−1.20828	−0.0727301
$277$	20.7786	1.24847	0.624233	−	0.781238i	$-0.285412\pi$
$277$	20.7786	1.24847	0.624233	+	0.781238i	$0.285412\pi$
$278$	−0.0857780	−0.00514462
$279$	1.49765	0.0896622
$280$	4.54997	0.271913
$281$	−1.91422	−0.114193	−0.0570965	−	0.998369i	$-0.518184\pi$
$281$	−1.91422	−0.114193	−0.0570965	+	0.998369i	$0.518184\pi$
$282$	0	0
$283$	−5.88794	−0.350002	−0.175001	−	0.984568i	$-0.555993\pi$
$283$	−5.88794	−0.350002	−0.175001	+	0.984568i	$0.555993\pi$
$284$	13.2522	0.786373
$285$	−6.39400	−0.378748
$286$	−1.05232	−0.0622247
$287$	−6.10463	−0.360345
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−5.60228	−0.328977
$291$	3.84403	0.225341
$292$	−0.0476242	−0.00278700
$293$	1.97177	0.115192	0.0575959	−	0.998340i	$-0.481657\pi$
$293$	1.97177	0.115192	0.0575959	+	0.998340i	$0.481657\pi$
$294$	−13.7022	−0.799130
$295$	3.05232	0.177713
$296$	−2.00000	−0.116248
$297$	−1.00000	−0.0580259
$298$	4.76294	0.275910
$299$	1.27150	0.0735325
$300$	1.00000	0.0577350
$301$	48.4781	2.79423
$302$	−4.57874	−0.263477
$303$	15.2296	0.874919
$304$	6.39400	0.366721
$305$	4.10463	0.235030
$306$	1.00000	0.0571662
$307$	4.68088	0.267152	0.133576	−	0.991039i	$-0.457354\pi$
$307$	4.68088	0.267152	0.133576	+	0.991039i	$0.457354\pi$
$308$	−4.54997	−0.259259
$309$	−1.18572	−0.0674531
$310$	1.49765	0.0850611
$311$	9.56413	0.542332	0.271166	−	0.962533i	$-0.412591\pi$
$311$	9.56413	0.542332	0.271166	+	0.962533i	$0.412591\pi$
$312$	1.05232	0.0595756
$313$	−29.5604	−1.67085	−0.835427	−	0.549602i	$-0.814779\pi$
$313$	−29.5604	−1.67085	−0.835427	+	0.549602i	$0.814779\pi$
$314$	−9.07488	−0.512125
$315$	−4.54997	−0.256362
$316$	−5.07737	−0.285625
$317$	33.6400	1.88941	0.944705	−	0.327921i	$-0.106348\pi$
$317$	33.6400	1.88941	0.944705	+	0.327921i	$0.106348\pi$
$318$	−6.81057	−0.381918
$319$	5.60228	0.313668
$320$	−1.00000	−0.0559017
$321$	16.7022	0.932227
$322$	5.49765	0.306372
$323$	−6.39400	−0.355772
$324$	1.00000	0.0555556
$325$	−1.05232	−0.0583719
$326$	−12.9690	−0.718288
$327$	5.68806	0.314551
$328$	1.34169	0.0740822
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	−25.0643	−1.37766	−0.688829	−	0.724924i	$-0.741875\pi$
$331$	−25.0643	−1.37766	−0.688829	+	0.724924i	$0.741875\pi$
$332$	−2.68337	−0.147269
$333$	2.00000	0.109599
$334$	16.5713	0.906742
$335$	10.5463	0.576204
$336$	4.54997	0.248221
$337$	10.1523	0.553029	0.276514	−	0.961010i	$-0.410821\pi$
$337$	10.1523	0.553029	0.276514	+	0.961010i	$0.410821\pi$
$338$	11.8926	0.646874
$339$	7.07737	0.384390
$340$	1.00000	0.0542326
$341$	−1.49765	−0.0811025
$342$	−6.39400	−0.345748
$343$	30.4949	1.64657
$344$	−10.6546	−0.574458
$345$	1.20828	0.0650518
$346$	−6.00000	−0.322562
$347$	23.8210	1.27878	0.639390	−	0.768883i	$-0.279187\pi$
$347$	23.8210	1.27878	0.639390	+	0.768883i	$0.279187\pi$
$348$	−5.60228	−0.300314
$349$	15.2178	0.814588	0.407294	−	0.913297i	$-0.366472\pi$
$349$	15.2178	0.814588	0.407294	+	0.913297i	$0.366472\pi$
$350$	−4.54997	−0.243206
$351$	−1.05232	−0.0561684
$352$	1.00000	0.0533002
$353$	20.2281	1.07663	0.538317	−	0.842742i	$-0.319060\pi$
$353$	20.2281	1.07663	0.538317	+	0.842742i	$0.319060\pi$
$354$	3.05232	0.162229
$355$	−13.2522	−0.703353
$356$	11.0999	0.588296
$357$	−4.54997	−0.240810
$358$	−3.05232	−0.161320
$359$	14.6258	0.771922	0.385961	−	0.922515i	$-0.373870\pi$
$359$	14.6258	0.771922	0.385961	+	0.922515i	$0.373870\pi$
$360$	1.00000	0.0527046
$361$	21.8833	1.15175
$362$	8.86440	0.465902
$363$	1.00000	0.0524864
$364$	−4.78800	−0.250960
$365$	0.0476242	0.00249276
$366$	4.10463	0.214552
$367$	−34.6341	−1.80788	−0.903942	−	0.427655i	$-0.859340\pi$
$367$	−34.6341	−1.80788	−0.903942	+	0.427655i	$0.859340\pi$
$368$	−1.20828	−0.0629861
$369$	−1.34169	−0.0698454
$370$	2.00000	0.103975
$371$	30.9879	1.60881
$372$	1.49765	0.0776498
$373$	18.2024	0.942483	0.471242	−	0.882004i	$-0.343806\pi$
$373$	18.2024	0.942483	0.471242	+	0.882004i	$0.343806\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	5.89537	0.303627
$378$	−4.54997	−0.234025
$379$	−18.6834	−0.959700	−0.479850	−	0.877350i	$-0.659309\pi$
$379$	−18.6834	−0.959700	−0.479850	+	0.877350i	$0.659309\pi$
$380$	−6.39400	−0.328005
$381$	−16.6164	−0.851286
$382$	10.8069	0.552927
$383$	4.09525	0.209257	0.104629	−	0.994511i	$-0.466635\pi$
$383$	4.09525	0.209257	0.104629	+	0.994511i	$0.466635\pi$
$384$	−1.00000	−0.0510310
$385$	4.54997	0.231888
$386$	−6.05701	−0.308293
$387$	10.6546	0.541604
$388$	3.84403	0.195151
$389$	5.57351	0.282588	0.141294	−	0.989968i	$-0.454874\pi$
$389$	5.57351	0.282588	0.141294	+	0.989968i	$0.454874\pi$
$390$	−1.05232	−0.0532861
$391$	1.20828	0.0611055
$392$	−13.7022	−0.692067
$393$	−2.68337	−0.135358
$394$	7.88794	0.397389
$395$	5.07737	0.255470
$396$	−1.00000	−0.0502519
$397$	18.6928	0.938162	0.469081	−	0.883155i	$-0.344585\pi$
$397$	18.6928	0.938162	0.469081	+	0.883155i	$0.344585\pi$
$398$	−10.6834	−0.535509
$399$	29.0925	1.45645
$400$	1.00000	0.0500000
$401$	2.75923	0.137789	0.0688947	−	0.997624i	$-0.478053\pi$
$401$	2.75923	0.137789	0.0688947	+	0.997624i	$0.478053\pi$
$402$	10.5463	0.525999
$403$	−1.57600	−0.0785064
$404$	15.2296	0.757702
$405$	−1.00000	−0.0496904
$406$	25.4902	1.26506
$407$	−2.00000	−0.0991363
$408$	1.00000	0.0495074
$409$	−0.416568	−0.0205979	−0.0102990	−	0.999947i	$-0.503278\pi$
$409$	−0.416568	−0.0205979	−0.0102990	+	0.999947i	$0.503278\pi$
$410$	−1.34169	−0.0662611
$411$	−7.01416	−0.345983
$412$	−1.18572	−0.0584161
$413$	−13.8879	−0.683381
$414$	1.20828	0.0593839
$415$	2.68337	0.131722
$416$	1.05232	0.0515940
$417$	0.0857780	0.00420057
$418$	6.39400	0.312741
$419$	11.8691	0.579843	0.289921	−	0.957050i	$-0.406371\pi$
$419$	11.8691	0.579843	0.289921	+	0.957050i	$0.406371\pi$
$420$	−4.54997	−0.222016
$421$	−9.20457	−0.448603	−0.224302	−	0.974520i	$-0.572010\pi$
$421$	−9.20457	−0.448603	−0.224302	+	0.974520i	$0.572010\pi$
$422$	3.60228	0.175356
$423$	0	0
$424$	−6.81057	−0.330750
$425$	−1.00000	−0.0485071
$426$	−13.2522	−0.642071
$427$	−18.6759	−0.903792
$428$	16.7022	0.807332
$429$	1.05232	0.0508063
$430$	10.6546	0.513810
$431$	7.68186	0.370022	0.185011	−	0.982736i	$-0.440768\pi$
$431$	7.68186	0.370022	0.185011	+	0.982736i	$0.440768\pi$
$432$	1.00000	0.0481125
$433$	11.4044	0.548063	0.274031	−	0.961721i	$-0.411643\pi$
$433$	11.4044	0.548063	0.274031	+	0.961721i	$0.411643\pi$
$434$	−6.81428	−0.327096
$435$	5.60228	0.268609
$436$	5.68806	0.272409
$437$	−7.72577	−0.369574
$438$	0.0476242	0.00227557
$439$	−38.4818	−1.83664	−0.918319	−	0.395842i	$-0.870453\pi$
$439$	−38.4818	−1.83664	−0.918319	+	0.395842i	$0.870453\pi$
$440$	−1.00000	−0.0476731
$441$	13.7022	0.652487
$442$	−1.05232	−0.0500535
$443$	−2.88696	−0.137164	−0.0685819	−	0.997645i	$-0.521847\pi$
$443$	−2.88696	−0.137164	−0.0685819	+	0.997645i	$0.521847\pi$
$444$	2.00000	0.0949158
$445$	−11.0999	−0.526188
$446$	12.1235	0.574064
$447$	−4.76294	−0.225280
$448$	4.54997	0.214966
$449$	−7.03346	−0.331930	−0.165965	−	0.986132i	$-0.553074\pi$
$449$	−7.03346	−0.331930	−0.165965	+	0.986132i	$0.553074\pi$
$450$	−1.00000	−0.0471405
$451$	1.34169	0.0631775
$452$	7.07737	0.332892
$453$	4.57874	0.215128
$454$	−17.9737	−0.843548
$455$	4.78800	0.224465
$456$	−6.39400	−0.299427
$457$	14.2093	0.664681	0.332341	−	0.943159i	$-0.392162\pi$
$457$	14.2093	0.664681	0.332341	+	0.943159i	$0.392162\pi$
$458$	17.7833	0.830960
$459$	−1.00000	−0.0466760
$460$	1.20828	0.0563365
$461$	−41.0600	−1.91236	−0.956178	−	0.292786i	$-0.905418\pi$
$461$	−41.0600	−1.91236	−0.956178	+	0.292786i	$0.905418\pi$
$462$	4.54997	0.211684
$463$	18.9378	0.880113	0.440056	−	0.897970i	$-0.354958\pi$
$463$	18.9378	0.880113	0.440056	+	0.897970i	$0.354958\pi$
$464$	−5.60228	−0.260080
$465$	−1.49765	−0.0694521
$466$	10.9690	0.508130
$467$	−22.6033	−1.04595	−0.522977	−	0.852347i	$-0.675179\pi$
$467$	−22.6033	−1.04595	−0.522977	+	0.852347i	$0.675179\pi$
$468$	−1.05232	−0.0486433
$469$	−47.9851	−2.21575
$470$	0	0
$471$	9.07488	0.418148
$472$	3.05232	0.140494
$473$	−10.6546	−0.489899
$474$	5.07737	0.233211
$475$	6.39400	0.293377
$476$	−4.54997	−0.208548
$477$	6.81057	0.311835
$478$	−6.90006	−0.315601
$479$	−33.8366	−1.54603	−0.773017	−	0.634385i	$-0.781253\pi$
$479$	−33.8366	−1.54603	−0.773017	+	0.634385i	$0.781253\pi$
$480$	1.00000	0.0456435
$481$	−2.10463	−0.0959629
$482$	−24.2055	−1.10253
$483$	−5.49765	−0.250152
$484$	1.00000	0.0454545
$485$	−3.84403	−0.174548
$486$	−1.00000	−0.0453609
$487$	7.82518	0.354593	0.177296	−	0.984158i	$-0.443265\pi$
$487$	7.82518	0.354593	0.177296	+	0.984158i	$0.443265\pi$
$488$	4.10463	0.185808
$489$	12.9690	0.586480
$490$	13.7022	0.619003
$491$	−23.3794	−1.05510	−0.527549	−	0.849525i	$-0.676889\pi$
$491$	−23.3794	−1.05510	−0.527549	+	0.849525i	$0.676889\pi$
$492$	−1.34169	−0.0604879
$493$	5.60228	0.252314
$494$	6.72850	0.302730
$495$	1.00000	0.0449467
$496$	1.49765	0.0672467
$497$	60.2971	2.70469
$498$	2.68337	0.120245
$499$	0.0952484	0.00426390	0.00213195	−	0.999998i	$-0.499321\pi$
$499$	0.0952484	0.00426390	0.00213195	+	0.999998i	$0.499321\pi$
$500$	−1.00000	−0.0447214
$501$	−16.5713	−0.740352
$502$	−16.9403	−0.756081
$503$	26.2951	1.17244	0.586221	−	0.810151i	$-0.300615\pi$
$503$	26.2951	1.17244	0.586221	+	0.810151i	$0.300615\pi$
$504$	−4.54997	−0.202672
$505$	−15.2296	−0.677710
$506$	−1.20828	−0.0537148
$507$	−11.8926	−0.528170
$508$	−16.6164	−0.737236
$509$	5.57351	0.247042	0.123521	−	0.992342i	$-0.460581\pi$
$509$	5.57351	0.247042	0.123521	+	0.992342i	$0.460581\pi$
$510$	−1.00000	−0.0442807
$511$	−0.216689	−0.00958574
$512$	−1.00000	−0.0441942
$513$	6.39400	0.282302
$514$	−1.97177	−0.0869709
$515$	1.18572	0.0522490
$516$	10.6546	0.469043
$517$	0	0
$518$	−9.09994	−0.399828
$519$	6.00000	0.263371
$520$	−1.05232	−0.0461471
$521$	12.7404	0.558166	0.279083	−	0.960267i	$-0.409970\pi$
$521$	12.7404	0.558166	0.279083	+	0.960267i	$0.409970\pi$
$522$	5.60228	0.245205
$523$	32.3259	1.41351	0.706755	−	0.707458i	$-0.250158\pi$
$523$	32.3259	1.41351	0.706755	+	0.707458i	$0.250158\pi$
$524$	−2.68337	−0.117224
$525$	4.54997	0.198577
$526$	20.1235	0.877426
$527$	−1.49765	−0.0652389
$528$	−1.00000	−0.0435194
$529$	−21.5401	−0.936524
$530$	6.81057	0.295832
$531$	−3.05232	−0.132459
$532$	29.0925	1.26132
$533$	1.41188	0.0611552
$534$	−11.0999	−0.480341
$535$	−16.7022	−0.722100
$536$	10.5463	0.455529
$537$	3.05232	0.131717
$538$	0.633256	0.0273016
$539$	−13.7022	−0.590197
$540$	−1.00000	−0.0430331
$541$	24.4667	1.05190	0.525952	−	0.850514i	$-0.323709\pi$
$541$	24.4667	1.05190	0.525952	+	0.850514i	$0.323709\pi$
$542$	0.181026	0.00777575
$543$	−8.86440	−0.380408
$544$	1.00000	0.0428746
$545$	−5.68806	−0.243650
$546$	4.78800	0.204908
$547$	25.0999	1.07320	0.536598	−	0.843838i	$-0.319709\pi$
$547$	25.0999	1.07320	0.536598	+	0.843838i	$0.319709\pi$
$548$	−7.01416	−0.299630
$549$	−4.10463	−0.175181
$550$	1.00000	0.0426401
$551$	−35.8210	−1.52603
$552$	1.20828	0.0514280
$553$	−23.1019	−0.982392
$554$	−20.7786	−0.882799
$555$	−2.00000	−0.0848953
$556$	0.0857780	0.00363780
$557$	27.5354	1.16671	0.583355	−	0.812217i	$-0.301740\pi$
$557$	27.5354	1.16671	0.583355	+	0.812217i	$0.301740\pi$
$558$	−1.49765	−0.0634008
$559$	−11.2120	−0.474217
$560$	−4.54997	−0.192271
$561$	1.00000	0.0422200
$562$	1.91422	0.0807466
$563$	35.2924	1.48740	0.743698	−	0.668515i	$-0.233070\pi$
$563$	35.2924	1.48740	0.743698	+	0.668515i	$0.233070\pi$
$564$	0	0
$565$	−7.07737	−0.297747
$566$	5.88794	0.247489
$567$	4.54997	0.191081
$568$	−13.2522	−0.556050
$569$	−39.6713	−1.66311	−0.831553	−	0.555446i	$-0.812548\pi$
$569$	−39.6713	−1.66311	−0.831553	+	0.555446i	$0.812548\pi$
$570$	6.39400	0.267815
$571$	34.5044	1.44396	0.721982	−	0.691912i	$-0.243231\pi$
$571$	34.5044	1.44396	0.721982	+	0.691912i	$0.243231\pi$
$572$	1.05232	0.0439995
$573$	−10.8069	−0.451463
$574$	6.10463	0.254802
$575$	−1.20828	−0.0503889
$576$	1.00000	0.0416667
$577$	9.37613	0.390333	0.195167	−	0.980770i	$-0.437475\pi$
$577$	9.37613	0.390333	0.195167	+	0.980770i	$0.437475\pi$
$578$	−1.00000	−0.0415945
$579$	6.05701	0.251721
$580$	5.60228	0.232622
$581$	−12.2093	−0.506525
$582$	−3.84403	−0.159340
$583$	−6.81057	−0.282065
$584$	0.0476242	0.00197070
$585$	1.05232	0.0435079
$586$	−1.97177	−0.0814529
$587$	6.51748	0.269005	0.134503	−	0.990913i	$-0.457056\pi$
$587$	6.51748	0.269005	0.134503	+	0.990913i	$0.457056\pi$
$588$	13.7022	0.565070
$589$	9.57600	0.394572
$590$	−3.05232	−0.125662
$591$	−7.88794	−0.324467
$592$	2.00000	0.0821995
$593$	−15.5259	−0.637572	−0.318786	−	0.947827i	$-0.603275\pi$
$593$	−15.5259	−0.637572	−0.318786	+	0.947827i	$0.603275\pi$
$594$	1.00000	0.0410305
$595$	4.54997	0.186531
$596$	−4.76294	−0.195098
$597$	10.6834	0.437241
$598$	−1.27150	−0.0519953
$599$	−39.3782	−1.60895	−0.804474	−	0.593988i	$-0.797553\pi$
$599$	−39.3782	−1.60895	−0.804474	+	0.593988i	$0.797553\pi$
$600$	−1.00000	−0.0408248
$601$	15.0774	0.615019	0.307509	−	0.951545i	$-0.400504\pi$
$601$	15.0774	0.615019	0.307509	+	0.951545i	$0.400504\pi$
$602$	−48.4781	−1.97582
$603$	−10.5463	−0.429477
$604$	4.57874	0.186306
$605$	−1.00000	−0.0406558
$606$	−15.2296	−0.618661
$607$	36.9403	1.49936	0.749679	−	0.661801i	$-0.230208\pi$
$607$	36.9403	1.49936	0.749679	+	0.661801i	$0.230208\pi$
$608$	−6.39400	−0.259311
$609$	−25.4902	−1.03292
$610$	−4.10463	−0.166192
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	−7.56413	−0.305512	−0.152756	−	0.988264i	$-0.548815\pi$
$613$	−7.56413	−0.305512	−0.152756	+	0.988264i	$0.548815\pi$
$614$	−4.68088	−0.188905
$615$	1.34169	0.0541020
$616$	4.54997	0.183324
$617$	40.0058	1.61057	0.805286	−	0.592887i	$-0.202012\pi$
$617$	40.0058	1.61057	0.805286	+	0.592887i	$0.202012\pi$
$618$	1.18572	0.0476965
$619$	−41.4997	−1.66801	−0.834007	−	0.551754i	$-0.813959\pi$
$619$	−41.4997	−1.66801	−0.834007	+	0.551754i	$0.813959\pi$
$620$	−1.49765	−0.0601473
$621$	−1.20828	−0.0484868
$622$	−9.56413	−0.383487
$623$	50.5044	2.02342
$624$	−1.05232	−0.0421263
$625$	1.00000	0.0400000
$626$	29.5604	1.18147
$627$	−6.39400	−0.255352
$628$	9.07488	0.362127
$629$	−2.00000	−0.0797452
$630$	4.54997	0.181275
$631$	42.1423	1.67766	0.838830	−	0.544394i	$-0.183240\pi$
$631$	42.1423	1.67766	0.838830	+	0.544394i	$0.183240\pi$
$632$	5.07737	0.201967
$633$	−3.60228	−0.143178
$634$	−33.6400	−1.33601
$635$	16.6164	0.659404
$636$	6.81057	0.270057
$637$	−14.4191	−0.571304
$638$	−5.60228	−0.221797
$639$	13.2522	0.524249
$640$	1.00000	0.0395285
$641$	3.55466	0.140401	0.0702003	−	0.997533i	$-0.477636\pi$
$641$	3.55466	0.140401	0.0702003	+	0.997533i	$0.477636\pi$
$642$	−16.7022	−0.659184
$643$	−37.2735	−1.46992	−0.734962	−	0.678108i	$-0.762800\pi$
$643$	−37.2735	−1.46992	−0.734962	+	0.678108i	$0.762800\pi$
$644$	−5.49765	−0.216638
$645$	−10.6546	−0.419524
$646$	6.39400	0.251569
$647$	−30.9303	−1.21600	−0.607999	−	0.793938i	$-0.708027\pi$
$647$	−30.9303	−1.21600	−0.607999	+	0.793938i	$0.708027\pi$
$648$	−1.00000	−0.0392837
$649$	3.05232	0.119814
$650$	1.05232	0.0412752
$651$	6.81428	0.267073
$652$	12.9690	0.507906
$653$	−46.5808	−1.82285	−0.911423	−	0.411470i	$-0.865016\pi$
$653$	−46.5808	−1.82285	−0.911423	+	0.411470i	$0.865016\pi$
$654$	−5.68806	−0.222421
$655$	2.68337	0.104848
$656$	−1.34169	−0.0523840
$657$	−0.0476242	−0.00185800
$658$	0	0
$659$	−13.5133	−0.526405	−0.263202	−	0.964741i	$-0.584779\pi$
$659$	−13.5133	−0.526405	−0.263202	+	0.964741i	$0.584779\pi$
$660$	1.00000	0.0389249
$661$	−3.63355	−0.141329	−0.0706643	−	0.997500i	$-0.522512\pi$
$661$	−3.63355	−0.141329	−0.0706643	+	0.997500i	$0.522512\pi$
$662$	25.0643	0.974151
$663$	1.05232	0.0408685
$664$	2.68337	0.104135
$665$	−29.0925	−1.12816
$666$	−2.00000	−0.0774984
$667$	6.76915	0.262103
$668$	−16.5713	−0.641163
$669$	−12.1235	−0.468721
$670$	−10.5463	−0.407437
$671$	4.10463	0.158457
$672$	−4.54997	−0.175519
$673$	9.67619	0.372990	0.186495	−	0.982456i	$-0.440287\pi$
$673$	9.67619	0.372990	0.186495	+	0.982456i	$0.440287\pi$
$674$	−10.1523	−0.391050
$675$	1.00000	0.0384900
$676$	−11.8926	−0.457409
$677$	18.6740	0.717700	0.358850	−	0.933395i	$-0.383169\pi$
$677$	18.6740	0.717700	0.358850	+	0.933395i	$0.383169\pi$
$678$	−7.07737	−0.271805
$679$	17.4902	0.671213
$680$	−1.00000	−0.0383482
$681$	17.9737	0.688754
$682$	1.49765	0.0573482
$683$	−32.8183	−1.25576	−0.627878	−	0.778312i	$-0.716076\pi$
$683$	−32.8183	−1.25576	−0.627878	+	0.778312i	$0.716076\pi$
$684$	6.39400	0.244481
$685$	7.01416	0.267997
$686$	−30.4949	−1.16430
$687$	−17.7833	−0.678476
$688$	10.6546	0.406203
$689$	−7.16686	−0.273036
$690$	−1.20828	−0.0459986
$691$	0.948222	0.0360721	0.0180360	−	0.999837i	$-0.494259\pi$
$691$	0.948222	0.0360721	0.0180360	+	0.999837i	$0.494259\pi$
$692$	6.00000	0.228086
$693$	−4.54997	−0.172839
$694$	−23.8210	−0.904233
$695$	−0.0857780	−0.00325374
$696$	5.60228	0.212354
$697$	1.34169	0.0508200
$698$	−15.2178	−0.576000
$699$	−10.9690	−0.414887
$700$	4.54997	0.171973
$701$	17.5584	0.663171	0.331585	−	0.943425i	$-0.392417\pi$
$701$	17.5584	0.663171	0.331585	+	0.943425i	$0.392417\pi$
$702$	1.05232	0.0397171
$703$	12.7880	0.482309
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−20.2281	−0.761295
$707$	69.2943	2.60608
$708$	−3.05232	−0.114713
$709$	−42.3998	−1.59236	−0.796178	−	0.605062i	$-0.793148\pi$
$709$	−42.3998	−1.59236	−0.796178	+	0.605062i	$0.793148\pi$
$710$	13.2522	0.497346
$711$	−5.07737	−0.190416
$712$	−11.0999	−0.415988
$713$	−1.80959	−0.0677697
$714$	4.54997	0.170278
$715$	−1.05232	−0.0393544
$716$	3.05232	0.114070
$717$	6.90006	0.257687
$718$	−14.6258	−0.545831
$719$	20.2401	0.754827	0.377414	−	0.926045i	$-0.376813\pi$
$719$	20.2401	0.754827	0.377414	+	0.926045i	$0.376813\pi$
$720$	−1.00000	−0.0372678
$721$	−5.39498	−0.200919
$722$	−21.8833	−0.814410
$723$	24.2055	0.900214
$724$	−8.86440	−0.329443
$725$	−5.60228	−0.208064
$726$	−1.00000	−0.0371135
$727$	1.35727	0.0503385	0.0251692	−	0.999683i	$-0.491988\pi$
$727$	1.35727	0.0503385	0.0251692	+	0.999683i	$0.491988\pi$
$728$	4.78800	0.177455
$729$	1.00000	0.0370370
$730$	−0.0476242	−0.00176265
$731$	−10.6546	−0.394075
$732$	−4.10463	−0.151712
$733$	51.0732	1.88643	0.943216	−	0.332180i	$-0.107784\pi$
$733$	51.0732	1.88643	0.943216	+	0.332180i	$0.107784\pi$
$734$	34.6341	1.27837
$735$	−13.7022	−0.505414
$736$	1.20828	0.0445379
$737$	10.5463	0.388476
$738$	1.34169	0.0493881
$739$	−46.5270	−1.71152	−0.855761	−	0.517372i	$-0.826911\pi$
$739$	−46.5270	−1.71152	−0.855761	+	0.517372i	$0.826911\pi$
$740$	−2.00000	−0.0735215
$741$	−6.72850	−0.247178
$742$	−30.9879	−1.13760
$743$	16.1641	0.593004	0.296502	−	0.955032i	$-0.404180\pi$
$743$	16.1641	0.593004	0.296502	+	0.955032i	$0.404180\pi$
$744$	−1.49765	−0.0549067
$745$	4.76294	0.174501
$746$	−18.2024	−0.666436
$747$	−2.68337	−0.0981794
$748$	1.00000	0.0365636
$749$	75.9946	2.77678
$750$	1.00000	0.0365148
$751$	−1.80216	−0.0657619	−0.0328809	−	0.999459i	$-0.510468\pi$
$751$	−1.80216	−0.0657619	−0.0328809	+	0.999459i	$0.510468\pi$
$752$	0	0
$753$	16.9403	0.617337
$754$	−5.89537	−0.214697
$755$	−4.57874	−0.166637
$756$	4.54997	0.165481
$757$	30.0816	1.09333	0.546667	−	0.837350i	$-0.315896\pi$
$757$	30.0816	1.09333	0.546667	+	0.837350i	$0.315896\pi$
$758$	18.6834	0.678611
$759$	1.20828	0.0438579
$760$	6.39400	0.231935
$761$	−36.2019	−1.31232	−0.656159	−	0.754622i	$-0.727820\pi$
$761$	−36.2019	−1.31232	−0.656159	+	0.754622i	$0.727820\pi$
$762$	16.6164	0.601950
$763$	25.8805	0.936938
$764$	−10.8069	−0.390978
$765$	1.00000	0.0361551
$766$	−4.09525	−0.147967
$767$	3.21200	0.115979
$768$	1.00000	0.0360844
$769$	−0.00938200	−0.000338323 0	−0.000169162	−	1.00000i	$-0.500054\pi$
$769$	−0.00938200	−0.000338323 0	−0.000169162		1.00000i	$0.500054\pi$
$770$	−4.54997	−0.163970
$771$	1.97177	0.0710114
$772$	6.05701	0.217996
$773$	5.60795	0.201704	0.100852	−	0.994901i	$-0.467843\pi$
$773$	5.60795	0.201704	0.100852	+	0.994901i	$0.467843\pi$
$774$	−10.6546	−0.382972
$775$	1.49765	0.0537973
$776$	−3.84403	−0.137993
$777$	9.09994	0.326459
$778$	−5.57351	−0.199820
$779$	−8.57874	−0.307365
$780$	1.05232	0.0376789
$781$	−13.2522	−0.474201
$782$	−1.20828	−0.0432081
$783$	−5.60228	−0.200209
$784$	13.7022	0.489365
$785$	−9.07488	−0.323896
$786$	2.68337	0.0957127
$787$	−22.9879	−0.819429	−0.409715	−	0.912214i	$-0.634372\pi$
$787$	−22.9879	−0.819429	−0.409715	+	0.912214i	$0.634372\pi$
$788$	−7.88794	−0.280996
$789$	−20.1235	−0.716415
$790$	−5.07737	−0.180645
$791$	32.2018	1.14497
$792$	1.00000	0.0355335
$793$	4.31936	0.153385
$794$	−18.6928	−0.663381
$795$	−6.81057	−0.241546
$796$	10.6834	0.378662
$797$	−0.496677	−0.0175932	−0.00879661	−	0.999961i	$-0.502800\pi$
$797$	−0.496677	−0.0175932	−0.00879661	+	0.999961i	$0.502800\pi$
$798$	−29.0925	−1.02986
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	11.0999	0.392197
$802$	−2.75923	−0.0974318
$803$	0.0476242	0.00168062
$804$	−10.5463	−0.371938
$805$	5.49765	0.193767
$806$	1.57600	0.0555124
$807$	−0.633256	−0.0222917
$808$	−15.2296	−0.535776
$809$	16.6415	0.585084	0.292542	−	0.956253i	$-0.405499\pi$
$809$	16.6415	0.585084	0.292542	+	0.956253i	$0.405499\pi$
$810$	1.00000	0.0351364
$811$	−5.09251	−0.178822	−0.0894111	−	0.995995i	$-0.528499\pi$
$811$	−5.09251	−0.178822	−0.0894111	+	0.995995i	$0.528499\pi$
$812$	−25.4902	−0.894532
$813$	−0.181026	−0.00634887
$814$	2.00000	0.0701000
$815$	−12.9690	−0.454285
$816$	−1.00000	−0.0350070
$817$	68.1255	2.38341
$818$	0.416568	0.0145649
$819$	−4.78800	−0.167306
$820$	1.34169	0.0468537
$821$	11.1783	0.390125	0.195062	−	0.980791i	$-0.437509\pi$
$821$	11.1783	0.390125	0.195062	+	0.980791i	$0.437509\pi$
$822$	7.01416	0.244647
$823$	4.96282	0.172993	0.0864966	−	0.996252i	$-0.472433\pi$
$823$	4.96282	0.172993	0.0864966	+	0.996252i	$0.472433\pi$
$824$	1.18572	0.0413064
$825$	−1.00000	−0.0348155
$826$	13.8879	0.483223
$827$	49.7570	1.73022	0.865111	−	0.501581i	$-0.167248\pi$
$827$	49.7570	1.73022	0.865111	+	0.501581i	$0.167248\pi$
$828$	−1.20828	−0.0419908
$829$	25.5017	0.885709	0.442854	−	0.896594i	$-0.353966\pi$
$829$	25.5017	0.885709	0.442854	+	0.896594i	$0.353966\pi$
$830$	−2.68337	−0.0931412
$831$	20.7786	0.720802
$832$	−1.05232	−0.0364825
$833$	−13.7022	−0.474754
$834$	−0.0857780	−0.00297025
$835$	16.5713	0.573474
$836$	−6.39400	−0.221141
$837$	1.49765	0.0517665
$838$	−11.8691	−0.410011
$839$	−21.2973	−0.735265	−0.367633	−	0.929971i	$-0.619832\pi$
$839$	−21.2973	−0.735265	−0.367633	+	0.929971i	$0.619832\pi$
$840$	4.54997	0.156989
$841$	2.38560	0.0822619
$842$	9.20457	0.317210
$843$	−1.91422	−0.0659293
$844$	−3.60228	−0.123996
$845$	11.8926	0.409119
$846$	0	0
$847$	4.54997	0.156339
$848$	6.81057	0.233876
$849$	−5.88794	−0.202074
$850$	1.00000	0.0342997
$851$	−2.41657	−0.0828389
$852$	13.2522	0.454013
$853$	−16.1830	−0.554095	−0.277047	−	0.960856i	$-0.589356\pi$
$853$	−16.1830	−0.554095	−0.277047	+	0.960856i	$0.589356\pi$
$854$	18.6759	0.639078
$855$	−6.39400	−0.218670
$856$	−16.7022	−0.570870
$857$	−18.7523	−0.640568	−0.320284	−	0.947322i	$-0.603778\pi$
$857$	−18.7523	−0.640568	−0.320284	+	0.947322i	$0.603778\pi$
$858$	−1.05232	−0.0359254
$859$	38.9398	1.32861	0.664305	−	0.747462i	$-0.268728\pi$
$859$	38.9398	1.32861	0.664305	+	0.747462i	$0.268728\pi$
$860$	−10.6546	−0.363319
$861$	−6.10463	−0.208045
$862$	−7.68186	−0.261645
$863$	17.1878	0.585078	0.292539	−	0.956254i	$-0.405500\pi$
$863$	17.1878	0.585078	0.292539	+	0.956254i	$0.405500\pi$
$864$	−1.00000	−0.0340207
$865$	−6.00000	−0.204006
$866$	−11.4044	−0.387539
$867$	1.00000	0.0339618
$868$	6.81428	0.231292
$869$	5.07737	0.172238
$870$	−5.60228	−0.189935
$871$	11.0980	0.376041
$872$	−5.68806	−0.192622
$873$	3.84403	0.130101
$874$	7.72577	0.261328
$875$	−4.54997	−0.153817
$876$	−0.0476242	−0.00160907
$877$	36.5450	1.23404	0.617019	−	0.786948i	$-0.288340\pi$
$877$	36.5450	1.23404	0.617019	+	0.786948i	$0.288340\pi$
$878$	38.4818	1.29870
$879$	1.97177	0.0665060
$880$	1.00000	0.0337100
$881$	50.3710	1.69704	0.848521	−	0.529162i	$-0.177494\pi$
$881$	50.3710	1.69704	0.848521	+	0.529162i	$0.177494\pi$
$882$	−13.7022	−0.461378
$883$	−47.2505	−1.59011	−0.795053	−	0.606540i	$-0.792557\pi$
$883$	−47.2505	−1.59011	−0.795053	+	0.606540i	$0.792557\pi$
$884$	1.05232	0.0353932
$885$	3.05232	0.102602
$886$	2.88696	0.0969895
$887$	−8.05012	−0.270296	−0.135148	−	0.990825i	$-0.543151\pi$
$887$	−8.05012	−0.270296	−0.135148	+	0.990825i	$0.543151\pi$
$888$	−2.00000	−0.0671156
$889$	−75.6043	−2.53569
$890$	11.0999	0.372071
$891$	−1.00000	−0.0335013
$892$	−12.1235	−0.405924
$893$	0	0
$894$	4.76294	0.159297
$895$	−3.05232	−0.102028
$896$	−4.54997	−0.152004
$897$	1.27150	0.0424540
$898$	7.03346	0.234710
$899$	−8.39029	−0.279832
$900$	1.00000	0.0333333
$901$	−6.81057	−0.226893
$902$	−1.34169	−0.0446733
$903$	48.4781	1.61325
$904$	−7.07737	−0.235390
$905$	8.86440	0.294663
$906$	−4.57874	−0.152118
$907$	−37.2735	−1.23765	−0.618824	−	0.785530i	$-0.712390\pi$
$907$	−37.2735	−1.23765	−0.618824	+	0.785530i	$0.712390\pi$
$908$	17.9737	0.596479
$909$	15.2296	0.505135
$910$	−4.78800	−0.158721
$911$	−43.0950	−1.42780	−0.713901	−	0.700247i	$-0.753073\pi$
$911$	−43.0950	−1.42780	−0.713901	+	0.700247i	$0.753073\pi$
$912$	6.39400	0.211727
$913$	2.68337	0.0888066
$914$	−14.2093	−0.470001
$915$	4.10463	0.135695
$916$	−17.7833	−0.587577
$917$	−12.2093	−0.403185
$918$	1.00000	0.0330049
$919$	14.4448	0.476490	0.238245	−	0.971205i	$-0.423428\pi$
$919$	14.4448	0.476490	0.238245	+	0.971205i	$0.423428\pi$
$920$	−1.20828	−0.0398359
$921$	4.68088	0.154240
$922$	41.0600	1.35224
$923$	−13.9455	−0.459021
$924$	−4.54997	−0.149683
$925$	2.00000	0.0657596
$926$	−18.9378	−0.622334
$927$	−1.18572	−0.0389441
$928$	5.60228	0.183904
$929$	−10.7405	−0.352383	−0.176192	−	0.984356i	$-0.556378\pi$
$929$	−10.7405	−0.352383	−0.176192	+	0.984356i	$0.556378\pi$
$930$	1.49765	0.0491100
$931$	87.6120	2.87137
$932$	−10.9690	−0.359302
$933$	9.56413	0.313116
$934$	22.6033	0.739601
$935$	−1.00000	−0.0327035
$936$	1.05232	0.0343960
$937$	39.5572	1.29228	0.646139	−	0.763219i	$-0.276382\pi$
$937$	39.5572	1.29228	0.646139	+	0.763219i	$0.276382\pi$
$938$	47.9851	1.56677
$939$	−29.5604	−0.964668
$940$	0	0
$941$	−37.1971	−1.21259	−0.606296	−	0.795239i	$-0.707345\pi$
$941$	−37.1971	−1.21259	−0.606296	+	0.795239i	$0.707345\pi$
$942$	−9.07488	−0.295676
$943$	1.62114	0.0527915
$944$	−3.05232	−0.0993444
$945$	−4.54997	−0.148011
$946$	10.6546	0.346411
$947$	8.70018	0.282718	0.141359	−	0.989958i	$-0.454853\pi$
$947$	8.70018	0.282718	0.141359	+	0.989958i	$0.454853\pi$
$948$	−5.07737	−0.164905
$949$	0.0501157	0.00162682
$950$	−6.39400	−0.207449
$951$	33.6400	1.09085
$952$	4.54997	0.147465
$953$	10.4835	0.339594	0.169797	−	0.985479i	$-0.445689\pi$
$953$	10.4835	0.339594	0.169797	+	0.985479i	$0.445689\pi$
$954$	−6.81057	−0.220500
$955$	10.8069	0.349702
$956$	6.90006	0.223164
$957$	5.60228	0.181096
$958$	33.8366	1.09321
$959$	−31.9142	−1.03056
$960$	−1.00000	−0.0322749
$961$	−28.7570	−0.927646
$962$	2.10463	0.0678560
$963$	16.7022	0.538222
$964$	24.2055	0.779608
$965$	−6.05701	−0.194982
$966$	5.49765	0.176884
$967$	−21.0999	−0.678528	−0.339264	−	0.940691i	$-0.610178\pi$
$967$	−21.0999	−0.678528	−0.339264	+	0.940691i	$0.610178\pi$
$968$	−1.00000	−0.0321412
$969$	−6.39400	−0.205405
$970$	3.84403	0.123424
$971$	−22.3070	−0.715866	−0.357933	−	0.933747i	$-0.616518\pi$
$971$	−22.3070	−0.715866	−0.357933	+	0.933747i	$0.616518\pi$
$972$	1.00000	0.0320750
$973$	0.390287	0.0125120
$974$	−7.82518	−0.250735
$975$	−1.05232	−0.0337011
$976$	−4.10463	−0.131386
$977$	27.1426	0.868370	0.434185	−	0.900824i	$-0.357036\pi$
$977$	27.1426	0.868370	0.434185	+	0.900824i	$0.357036\pi$
$978$	−12.9690	−0.414704
$979$	−11.0999	−0.354756
$980$	−13.7022	−0.437702
$981$	5.68806	0.181606
$982$	23.3794	0.746066
$983$	−27.5673	−0.879261	−0.439630	−	0.898179i	$-0.644891\pi$
$983$	−27.5673	−0.879261	−0.439630	+	0.898179i	$0.644891\pi$
$984$	1.34169	0.0427714
$985$	7.88794	0.251331
$986$	−5.60228	−0.178413
$987$	0	0
$988$	−6.72850	−0.214062
$989$	−12.8738	−0.409362
$990$	−1.00000	−0.0317821
$991$	−14.7190	−0.467566	−0.233783	−	0.972289i	$-0.575110\pi$
$991$	−14.7190	−0.467566	−0.233783	+	0.972289i	$0.575110\pi$
$992$	−1.49765	−0.0475506
$993$	−25.0643	−0.795391
$994$	−60.2971	−1.91251
$995$	−10.6834	−0.338686
$996$	−2.68337	−0.0850259
$997$	25.7540	0.815637	0.407819	−	0.913063i	$-0.366290\pi$
$997$	25.7540	0.815637	0.407819	+	0.913063i	$0.366290\pi$
$998$	−0.0952484	−0.00301504
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cf.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cf.1.4	✓	4	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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.54997 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.54997 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -1.05232 q^{13} -4.54997 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +6.39400 q^{19} -1.00000 q^{20} +4.54997 q^{21} +1.00000 q^{22} -1.20828 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.05232 q^{26} +1.00000 q^{27} +4.54997 q^{28} -5.60228 q^{29} +1.00000 q^{30} +1.49765 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -4.54997 q^{35} +1.00000 q^{36} +2.00000 q^{37} -6.39400 q^{38} -1.05232 q^{39} +1.00000 q^{40} -1.34169 q^{41} -4.54997 q^{42} +10.6546 q^{43} -1.00000 q^{44} -1.00000 q^{45} +1.20828 q^{46} +1.00000 q^{48} +13.7022 q^{49} -1.00000 q^{50} -1.00000 q^{51} -1.05232 q^{52} +6.81057 q^{53} -1.00000 q^{54} +1.00000 q^{55} -4.54997 q^{56} +6.39400 q^{57} +5.60228 q^{58} -3.05232 q^{59} -1.00000 q^{60} -4.10463 q^{61} -1.49765 q^{62} +4.54997 q^{63} +1.00000 q^{64} +1.05232 q^{65} +1.00000 q^{66} -10.5463 q^{67} -1.00000 q^{68} -1.20828 q^{69} +4.54997 q^{70} +13.2522 q^{71} -1.00000 q^{72} -0.0476242 q^{73} -2.00000 q^{74} +1.00000 q^{75} +6.39400 q^{76} -4.54997 q^{77} +1.05232 q^{78} -5.07737 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.34169 q^{82} -2.68337 q^{83} +4.54997 q^{84} +1.00000 q^{85} -10.6546 q^{86} -5.60228 q^{87} +1.00000 q^{88} +11.0999 q^{89} +1.00000 q^{90} -4.78800 q^{91} -1.20828 q^{92} +1.49765 q^{93} -6.39400 q^{95} -1.00000 q^{96} +3.84403 q^{97} -13.7022 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 6 q^{13} - 5 q^{14} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 8 q^{19} - 4 q^{20} + 5 q^{21} + 4 q^{22} + q^{23} - 4 q^{24} + 4 q^{25} - 6 q^{26} + 4 q^{27} + 5 q^{28} + q^{29} + 4 q^{30} + 3 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{34} - 5 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} + 9 q^{43} - 4 q^{44} - 4 q^{45} - q^{46} + 4 q^{48} + 5 q^{49} - 4 q^{50} - 4 q^{51} + 6 q^{52} - 2 q^{53} - 4 q^{54} + 4 q^{55} - 5 q^{56} + 8 q^{57} - q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{61} - 3 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 4 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} + 5 q^{70} - 10 q^{71} - 4 q^{72} + 16 q^{73} - 8 q^{74} + 4 q^{75} + 8 q^{76} - 5 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 2 q^{82} + 4 q^{83} + 5 q^{84} + 4 q^{85} - 9 q^{86} + q^{87} + 4 q^{88} + 18 q^{89} + 4 q^{90} + 16 q^{91} + q^{92} + 3 q^{93} - 8 q^{95} - 4 q^{96} + 11 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 6 * q^13 - 5 * q^14 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 8 * q^19 - 4 * q^20 + 5 * q^21 + 4 * q^22 + q^23 - 4 * q^24 + 4 * q^25 - 6 * q^26 + 4 * q^27 + 5 * q^28 + q^29 + 4 * q^30 + 3 * q^31 - 4 * q^32 - 4 * q^33 + 4 * q^34 - 5 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 + 9 * q^43 - 4 * q^44 - 4 * q^45 - q^46 + 4 * q^48 + 5 * q^49 - 4 * q^50 - 4 * q^51 + 6 * q^52 - 2 * q^53 - 4 * q^54 + 4 * q^55 - 5 * q^56 + 8 * q^57 - q^58 - 2 * q^59 - 4 * q^60 + 4 * q^61 - 3 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 4 * q^66 + 12 * q^67 - 4 * q^68 + q^69 + 5 * q^70 - 10 * q^71 - 4 * q^72 + 16 * q^73 - 8 * q^74 + 4 * q^75 + 8 * q^76 - 5 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 2 * q^82 + 4 * q^83 + 5 * q^84 + 4 * q^85 - 9 * q^86 + q^87 + 4 * q^88 + 18 * q^89 + 4 * q^90 + 16 * q^91 + q^92 + 3 * q^93 - 8 * q^95 - 4 * q^96 + 11 * q^97 - 5 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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