LMFDB - Embedded newform 5290.2.a.bj.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 15x^{8} + 35x^{7} + 78x^{6} - 123x^{5} - 185x^{4} + 140x^{3} + 177x^{2} - 15x - 23 $ x^10 - 3x^9 - 15x^8 + 35x^7 + 78x^6 - 123x^5 - 185x^4 + 140x^3 + 177x^2 - 15*x - 23
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.00869$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.259097 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.259097 q^{6} -4.66427 q^{7} -1.00000 q^{8} -2.93287 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.259097 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.259097 q^{6} -4.66427 q^{7} -1.00000 q^{8} -2.93287 q^{9} -1.00000 q^{10} -3.14316 q^{11} +0.259097 q^{12} -5.01132 q^{13} +4.66427 q^{14} +0.259097 q^{15} +1.00000 q^{16} -6.42863 q^{17} +2.93287 q^{18} -5.69216 q^{19} +1.00000 q^{20} -1.20850 q^{21} +3.14316 q^{22} -0.259097 q^{24} +1.00000 q^{25} +5.01132 q^{26} -1.53719 q^{27} -4.66427 q^{28} +4.01088 q^{29} -0.259097 q^{30} +0.125770 q^{31} -1.00000 q^{32} -0.814383 q^{33} +6.42863 q^{34} -4.66427 q^{35} -2.93287 q^{36} +0.835045 q^{37} +5.69216 q^{38} -1.29842 q^{39} -1.00000 q^{40} -11.4525 q^{41} +1.20850 q^{42} -7.19399 q^{43} -3.14316 q^{44} -2.93287 q^{45} +5.35505 q^{47} +0.259097 q^{48} +14.7554 q^{49} -1.00000 q^{50} -1.66564 q^{51} -5.01132 q^{52} -2.68108 q^{53} +1.53719 q^{54} -3.14316 q^{55} +4.66427 q^{56} -1.47482 q^{57} -4.01088 q^{58} -5.38922 q^{59} +0.259097 q^{60} +4.91488 q^{61} -0.125770 q^{62} +13.6797 q^{63} +1.00000 q^{64} -5.01132 q^{65} +0.814383 q^{66} +7.13595 q^{67} -6.42863 q^{68} +4.66427 q^{70} +8.75253 q^{71} +2.93287 q^{72} -15.3642 q^{73} -0.835045 q^{74} +0.259097 q^{75} -5.69216 q^{76} +14.6605 q^{77} +1.29842 q^{78} +5.16621 q^{79} +1.00000 q^{80} +8.40033 q^{81} +11.4525 q^{82} -13.8710 q^{83} -1.20850 q^{84} -6.42863 q^{85} +7.19399 q^{86} +1.03921 q^{87} +3.14316 q^{88} -11.2685 q^{89} +2.93287 q^{90} +23.3741 q^{91} +0.0325866 q^{93} -5.35505 q^{94} -5.69216 q^{95} -0.259097 q^{96} -1.58353 q^{97} -14.7554 q^{98} +9.21847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * 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
$3$	0.259097	0.149590	0.0747948	−	0.997199i	$-0.476170\pi$
$3$	0.259097	0.149590	0.0747948	+	0.997199i	$0.476170\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.259097	−0.105776
$7$	−4.66427	−1.76293	−0.881464	−	0.472252i	$-0.843441\pi$
$7$	−4.66427	−1.76293	−0.881464	+	0.472252i	$0.843441\pi$
$8$	−1.00000	−0.353553
$9$	−2.93287	−0.977623
$10$	−1.00000	−0.316228
$11$	−3.14316	−0.947698	−0.473849	−	0.880606i	$-0.657136\pi$
$11$	−3.14316	−0.947698	−0.473849	+	0.880606i	$0.657136\pi$
$12$	0.259097	0.0747948
$13$	−5.01132	−1.38989	−0.694946	−	0.719062i	$-0.744572\pi$
$13$	−5.01132	−1.38989	−0.694946	+	0.719062i	$0.744572\pi$
$14$	4.66427	1.24658
$15$	0.259097	0.0668985
$16$	1.00000	0.250000
$17$	−6.42863	−1.55917	−0.779586	−	0.626295i	$-0.784571\pi$
$17$	−6.42863	−1.55917	−0.779586	+	0.626295i	$0.784571\pi$
$18$	2.93287	0.691284
$19$	−5.69216	−1.30587	−0.652935	−	0.757414i	$-0.726463\pi$
$19$	−5.69216	−1.30587	−0.652935	+	0.757414i	$0.726463\pi$
$20$	1.00000	0.223607
$21$	−1.20850	−0.263716
$22$	3.14316	0.670124
$23$	0	0
$23$	0	0
$24$	−0.259097	−0.0528879
$25$	1.00000	0.200000
$26$	5.01132	0.982801
$27$	−1.53719	−0.295832
$28$	−4.66427	−0.881464
$29$	4.01088	0.744802	0.372401	−	0.928072i	$-0.378535\pi$
$29$	4.01088	0.744802	0.372401	+	0.928072i	$0.378535\pi$
$30$	−0.259097	−0.0473044
$31$	0.125770	0.0225890	0.0112945	−	0.999936i	$-0.496405\pi$
$31$	0.125770	0.0225890	0.0112945	+	0.999936i	$0.496405\pi$
$32$	−1.00000	−0.176777
$33$	−0.814383	−0.141766
$34$	6.42863	1.10250
$35$	−4.66427	−0.788405
$36$	−2.93287	−0.488811
$37$	0.835045	0.137281	0.0686403	−	0.997641i	$-0.478134\pi$
$37$	0.835045	0.137281	0.0686403	+	0.997641i	$0.478134\pi$
$38$	5.69216	0.923390
$39$	−1.29842	−0.207913
$40$	−1.00000	−0.158114
$41$	−11.4525	−1.78857	−0.894287	−	0.447493i	$-0.852317\pi$
$41$	−11.4525	−1.78857	−0.894287	+	0.447493i	$0.852317\pi$
$42$	1.20850	0.186475
$43$	−7.19399	−1.09707	−0.548537	−	0.836126i	$-0.684815\pi$
$43$	−7.19399	−1.09707	−0.548537	+	0.836126i	$0.684815\pi$
$44$	−3.14316	−0.473849
$45$	−2.93287	−0.437206
$46$	0	0
$47$	5.35505	0.781115	0.390557	−	0.920579i	$-0.372282\pi$
$47$	5.35505	0.781115	0.390557	+	0.920579i	$0.372282\pi$
$48$	0.259097	0.0373974
$49$	14.7554	2.10791
$50$	−1.00000	−0.141421
$51$	−1.66564	−0.233236
$52$	−5.01132	−0.694946
$53$	−2.68108	−0.368275	−0.184138	−	0.982900i	$-0.558949\pi$
$53$	−2.68108	−0.368275	−0.184138	+	0.982900i	$0.558949\pi$
$54$	1.53719	0.209185
$55$	−3.14316	−0.423823
$56$	4.66427	0.623289
$57$	−1.47482	−0.195345
$58$	−4.01088	−0.526654
$59$	−5.38922	−0.701617	−0.350808	−	0.936447i	$-0.614093\pi$
$59$	−5.38922	−0.701617	−0.350808	+	0.936447i	$0.614093\pi$
$60$	0.259097	0.0334493
$61$	4.91488	0.629286	0.314643	−	0.949210i	$-0.398115\pi$
$61$	4.91488	0.629286	0.314643	+	0.949210i	$0.398115\pi$
$62$	−0.125770	−0.0159728
$63$	13.6797	1.72348
$64$	1.00000	0.125000
$65$	−5.01132	−0.621578
$66$	0.814383	0.100244
$67$	7.13595	0.871795	0.435897	−	0.899996i	$-0.356431\pi$
$67$	7.13595	0.871795	0.435897	+	0.899996i	$0.356431\pi$
$68$	−6.42863	−0.779586
$69$	0	0
$70$	4.66427	0.557486
$71$	8.75253	1.03873	0.519367	−	0.854551i	$-0.326168\pi$
$71$	8.75253	1.03873	0.519367	+	0.854551i	$0.326168\pi$
$72$	2.93287	0.345642
$73$	−15.3642	−1.79825	−0.899123	−	0.437696i	$-0.855795\pi$
$73$	−15.3642	−1.79825	−0.899123	+	0.437696i	$0.855795\pi$
$74$	−0.835045	−0.0970720
$75$	0.259097	0.0299179
$76$	−5.69216	−0.652935
$77$	14.6605	1.67072
$78$	1.29842	0.147017
$79$	5.16621	0.581244	0.290622	−	0.956838i	$-0.406138\pi$
$79$	5.16621	0.581244	0.290622	+	0.956838i	$0.406138\pi$
$80$	1.00000	0.111803
$81$	8.40033	0.933370
$82$	11.4525	1.26471
$83$	−13.8710	−1.52254	−0.761272	−	0.648432i	$-0.775425\pi$
$83$	−13.8710	−1.52254	−0.761272	+	0.648432i	$0.775425\pi$
$84$	−1.20850	−0.131858
$85$	−6.42863	−0.697283
$86$	7.19399	0.775748
$87$	1.03921	0.111415
$88$	3.14316	0.335062
$89$	−11.2685	−1.19445	−0.597227	−	0.802072i	$-0.703731\pi$
$89$	−11.2685	−1.19445	−0.597227	+	0.802072i	$0.703731\pi$
$90$	2.93287	0.309152
$91$	23.3741	2.45028
$92$	0	0
$93$	0.0325866	0.00337908
$94$	−5.35505	−0.552332
$95$	−5.69216	−0.584003
$96$	−0.259097	−0.0264440
$97$	−1.58353	−0.160783	−0.0803914	−	0.996763i	$-0.525617\pi$
$97$	−1.58353	−0.160783	−0.0803914	+	0.996763i	$0.525617\pi$
$98$	−14.7554	−1.49052
$99$	9.21847	0.926491
$100$	1.00000	0.100000
$101$	16.1749	1.60947	0.804733	−	0.593636i	$-0.202308\pi$
$101$	16.1749	1.60947	0.804733	+	0.593636i	$0.202308\pi$
$102$	1.66564	0.164923
$103$	10.7046	1.05476	0.527378	−	0.849631i	$-0.323175\pi$
$103$	10.7046	1.05476	0.527378	+	0.849631i	$0.323175\pi$
$104$	5.01132	0.491401
$105$	−1.20850	−0.117937
$106$	2.68108	0.260410
$107$	5.65139	0.546341	0.273170	−	0.961966i	$-0.411928\pi$
$107$	5.65139	0.546341	0.273170	+	0.961966i	$0.411928\pi$
$108$	−1.53719	−0.147916
$109$	−4.41441	−0.422824	−0.211412	−	0.977397i	$-0.567806\pi$
$109$	−4.41441	−0.422824	−0.211412	+	0.977397i	$0.567806\pi$
$110$	3.14316	0.299688
$111$	0.216358	0.0205358
$112$	−4.66427	−0.440732
$113$	−4.78510	−0.450145	−0.225072	−	0.974342i	$-0.572262\pi$
$113$	−4.78510	−0.450145	−0.225072	+	0.974342i	$0.572262\pi$
$114$	1.47482	0.138130
$115$	0	0
$116$	4.01088	0.372401
$117$	14.6976	1.35879
$118$	5.38922	0.496118
$119$	29.9849	2.74871
$120$	−0.259097	−0.0236522
$121$	−1.12056	−0.101869
$122$	−4.91488	−0.444972
$123$	−2.96730	−0.267552
$124$	0.125770	0.0112945
$125$	1.00000	0.0894427
$126$	−13.6797	−1.21868
$127$	16.9439	1.50353	0.751766	−	0.659430i	$-0.229202\pi$
$127$	16.9439	1.50353	0.751766	+	0.659430i	$0.229202\pi$
$128$	−1.00000	−0.0883883
$129$	−1.86394	−0.164111
$130$	5.01132	0.439522
$131$	−4.19592	−0.366600	−0.183300	−	0.983057i	$-0.558678\pi$
$131$	−4.19592	−0.366600	−0.183300	+	0.983057i	$0.558678\pi$
$132$	−0.814383	−0.0708829
$133$	26.5497	2.30215
$134$	−7.13595	−0.616452
$135$	−1.53719	−0.132300
$136$	6.42863	0.551251
$137$	−11.6712	−0.997137	−0.498568	−	0.866850i	$-0.666141\pi$
$137$	−11.6712	−0.997137	−0.498568	+	0.866850i	$0.666141\pi$
$138$	0	0
$139$	5.31325	0.450664	0.225332	−	0.974282i	$-0.427653\pi$
$139$	5.31325	0.450664	0.225332	+	0.974282i	$0.427653\pi$
$140$	−4.66427	−0.394202
$141$	1.38748	0.116847
$142$	−8.75253	−0.734496
$143$	15.7514	1.31720
$144$	−2.93287	−0.244406
$145$	4.01088	0.333086
$146$	15.3642	1.27155
$147$	3.82307	0.315322
$148$	0.835045	0.0686403
$149$	4.00187	0.327846	0.163923	−	0.986473i	$-0.447585\pi$
$149$	4.00187	0.327846	0.163923	+	0.986473i	$0.447585\pi$
$150$	−0.259097	−0.0211552
$151$	−8.15202	−0.663402	−0.331701	−	0.943385i	$-0.607622\pi$
$151$	−8.15202	−0.663402	−0.331701	+	0.943385i	$0.607622\pi$
$152$	5.69216	0.461695
$153$	18.8543	1.52428
$154$	−14.6605	−1.18138
$155$	0.125770	0.0101021
$156$	−1.29842	−0.103957
$157$	−17.0474	−1.36053	−0.680265	−	0.732966i	$-0.738135\pi$
$157$	−17.0474	−1.36053	−0.680265	+	0.732966i	$0.738135\pi$
$158$	−5.16621	−0.411002
$159$	−0.694661	−0.0550902
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−8.40033	−0.659992
$163$	−14.5346	−1.13844	−0.569218	−	0.822187i	$-0.692754\pi$
$163$	−14.5346	−1.13844	−0.569218	+	0.822187i	$0.692754\pi$
$164$	−11.4525	−0.894287
$165$	−0.814383	−0.0633996
$166$	13.8710	1.07660
$167$	−12.6392	−0.978054	−0.489027	−	0.872269i	$-0.662648\pi$
$167$	−12.6392	−0.978054	−0.489027	+	0.872269i	$0.662648\pi$
$168$	1.20850	0.0932376
$169$	12.1134	0.931797
$170$	6.42863	0.493054
$171$	16.6943	1.27665
$172$	−7.19399	−0.548537
$173$	−3.07061	−0.233454	−0.116727	−	0.993164i	$-0.537240\pi$
$173$	−3.07061	−0.233454	−0.116727	+	0.993164i	$0.537240\pi$
$174$	−1.03921	−0.0787821
$175$	−4.66427	−0.352585
$176$	−3.14316	−0.236924
$177$	−1.39633	−0.104955
$178$	11.2685	0.844606
$179$	−3.70124	−0.276644	−0.138322	−	0.990387i	$-0.544171\pi$
$179$	−3.70124	−0.276644	−0.138322	+	0.990387i	$0.544171\pi$
$180$	−2.93287	−0.218603
$181$	4.36736	0.324623	0.162312	−	0.986740i	$-0.448105\pi$
$181$	4.36736	0.324623	0.162312	+	0.986740i	$0.448105\pi$
$182$	−23.3741	−1.73261
$183$	1.27343	0.0941346
$184$	0	0
$185$	0.835045	0.0613937
$186$	−0.0325866	−0.00238937
$187$	20.2062	1.47762
$188$	5.35505	0.390557
$189$	7.16986	0.521530
$190$	5.69216	0.412952
$191$	−2.38501	−0.172574	−0.0862868	−	0.996270i	$-0.527500\pi$
$191$	−2.38501	−0.172574	−0.0862868	+	0.996270i	$0.527500\pi$
$192$	0.259097	0.0186987
$193$	−9.40122	−0.676714	−0.338357	−	0.941018i	$-0.609871\pi$
$193$	−9.40122	−0.676714	−0.338357	+	0.941018i	$0.609871\pi$
$194$	1.58353	0.113691
$195$	−1.29842	−0.0929817
$196$	14.7554	1.05396
$197$	1.83876	0.131006	0.0655029	−	0.997852i	$-0.479135\pi$
$197$	1.83876	0.131006	0.0655029	+	0.997852i	$0.479135\pi$
$198$	−9.21847	−0.655128
$199$	4.87022	0.345241	0.172620	−	0.984988i	$-0.444777\pi$
$199$	4.87022	0.345241	0.172620	+	0.984988i	$0.444777\pi$
$200$	−1.00000	−0.0707107
$201$	1.84890	0.130412
$202$	−16.1749	−1.13807
$203$	−18.7078	−1.31303
$204$	−1.66564	−0.116618
$205$	−11.4525	−0.799875
$206$	−10.7046	−0.745825
$207$	0	0
$208$	−5.01132	−0.347473
$209$	17.8913	1.23757
$210$	1.20850	0.0833942
$211$	16.6046	1.14311	0.571553	−	0.820565i	$-0.306341\pi$
$211$	16.6046	1.14311	0.571553	+	0.820565i	$0.306341\pi$
$212$	−2.68108	−0.184138
$213$	2.26775	0.155384
$214$	−5.65139	−0.386321
$215$	−7.19399	−0.490626
$216$	1.53719	0.104592
$217$	−0.586625	−0.0398227
$218$	4.41441	0.298982
$219$	−3.98082	−0.268999
$220$	−3.14316	−0.211912
$221$	32.2160	2.16708
$222$	−0.216358	−0.0145210
$223$	−17.2501	−1.15515	−0.577576	−	0.816337i	$-0.696001\pi$
$223$	−17.2501	−1.15515	−0.577576	+	0.816337i	$0.696001\pi$
$224$	4.66427	0.311644
$225$	−2.93287	−0.195525
$226$	4.78510	0.318300
$227$	0.800560	0.0531350	0.0265675	−	0.999647i	$-0.491542\pi$
$227$	0.800560	0.0531350	0.0265675	+	0.999647i	$0.491542\pi$
$228$	−1.47482	−0.0976724
$229$	−2.48769	−0.164391	−0.0821956	−	0.996616i	$-0.526193\pi$
$229$	−2.48769	−0.164391	−0.0821956	+	0.996616i	$0.526193\pi$
$230$	0	0
$231$	3.79850	0.249923
$232$	−4.01088	−0.263327
$233$	3.72567	0.244077	0.122038	−	0.992525i	$-0.461057\pi$
$233$	3.72567	0.244077	0.122038	+	0.992525i	$0.461057\pi$
$234$	−14.6976	−0.960809
$235$	5.35505	0.349325
$236$	−5.38922	−0.350808
$237$	1.33855	0.0869481
$238$	−29.9849	−1.94363
$239$	4.39816	0.284493	0.142247	−	0.989831i	$-0.454567\pi$
$239$	4.39816	0.284493	0.142247	+	0.989831i	$0.454567\pi$
$240$	0.259097	0.0167246
$241$	2.46589	0.158842	0.0794211	−	0.996841i	$-0.474693\pi$
$241$	2.46589	0.158842	0.0794211	+	0.996841i	$0.474693\pi$
$242$	1.12056	0.0720322
$243$	6.78806	0.435454
$244$	4.91488	0.314643
$245$	14.7554	0.942687
$246$	2.96730	0.189188
$247$	28.5252	1.81502
$248$	−0.125770	−0.00798641
$249$	−3.59394	−0.227757
$250$	−1.00000	−0.0632456
$251$	−12.2154	−0.771029	−0.385515	−	0.922702i	$-0.625976\pi$
$251$	−12.2154	−0.771029	−0.385515	+	0.922702i	$0.625976\pi$
$252$	13.6797	0.861739
$253$	0	0
$254$	−16.9439	−1.06316
$255$	−1.66564	−0.104306
$256$	1.00000	0.0625000
$257$	10.3228	0.643917	0.321958	−	0.946754i	$-0.395659\pi$
$257$	10.3228	0.643917	0.321958	+	0.946754i	$0.395659\pi$
$258$	1.86394	0.116044
$259$	−3.89487	−0.242016
$260$	−5.01132	−0.310789
$261$	−11.7634	−0.728135
$262$	4.19592	0.259225
$263$	2.13852	0.131867	0.0659334	−	0.997824i	$-0.478998\pi$
$263$	2.13852	0.131867	0.0659334	+	0.997824i	$0.478998\pi$
$264$	0.814383	0.0501218
$265$	−2.68108	−0.164698
$266$	−26.5497	−1.62787
$267$	−2.91962	−0.178678
$268$	7.13595	0.435897
$269$	−13.3162	−0.811905	−0.405952	−	0.913894i	$-0.633060\pi$
$269$	−13.3162	−0.811905	−0.405952	+	0.913894i	$0.633060\pi$
$270$	1.53719	0.0935503
$271$	−12.8185	−0.778671	−0.389336	−	0.921096i	$-0.627295\pi$
$271$	−12.8185	−0.778671	−0.389336	+	0.921096i	$0.627295\pi$
$272$	−6.42863	−0.389793
$273$	6.05617	0.366536
$274$	11.6712	0.705082
$275$	−3.14316	−0.189540
$276$	0	0
$277$	18.2786	1.09825	0.549126	−	0.835740i	$-0.314961\pi$
$277$	18.2786	1.09825	0.549126	+	0.835740i	$0.314961\pi$
$278$	−5.31325	−0.318668
$279$	−0.368867	−0.0220835
$280$	4.66427	0.278743
$281$	−18.7519	−1.11864	−0.559321	−	0.828951i	$-0.688938\pi$
$281$	−18.7519	−1.11864	−0.559321	+	0.828951i	$0.688938\pi$
$282$	−1.38748	−0.0826231
$283$	−22.0875	−1.31297	−0.656484	−	0.754340i	$-0.727957\pi$
$283$	−22.0875	−1.31297	−0.656484	+	0.754340i	$0.727957\pi$
$284$	8.75253	0.519367
$285$	−1.47482	−0.0873608
$286$	−15.7514	−0.931399
$287$	53.4174	3.15313
$288$	2.93287	0.172821
$289$	24.3273	1.43102
$290$	−4.01088	−0.235527
$291$	−0.410287	−0.0240515
$292$	−15.3642	−0.899123
$293$	−30.2196	−1.76545	−0.882723	−	0.469894i	$-0.844292\pi$
$293$	−30.2196	−1.76545	−0.882723	+	0.469894i	$0.844292\pi$
$294$	−3.82307	−0.222966
$295$	−5.38922	−0.313773
$296$	−0.835045	−0.0485360
$297$	4.83163	0.280359
$298$	−4.00187	−0.231822
$299$	0	0
$300$	0.259097	0.0149590
$301$	33.5547	1.93406
$302$	8.15202	0.469096
$303$	4.19088	0.240760
$304$	−5.69216	−0.326468
$305$	4.91488	0.281425
$306$	−18.8543	−1.07783
$307$	16.6139	0.948207	0.474103	−	0.880469i	$-0.342772\pi$
$307$	16.6139	0.948207	0.474103	+	0.880469i	$0.342772\pi$
$308$	14.6605	0.835361
$309$	2.77353	0.157781
$310$	−0.125770	−0.00714326
$311$	−11.1062	−0.629772	−0.314886	−	0.949129i	$-0.601966\pi$
$311$	−11.1062	−0.629772	−0.314886	+	0.949129i	$0.601966\pi$
$312$	1.29842	0.0735085
$313$	−31.6253	−1.78757	−0.893783	−	0.448500i	$-0.851958\pi$
$313$	−31.6253	−1.78757	−0.893783	+	0.448500i	$0.851958\pi$
$314$	17.0474	0.962040
$315$	13.6797	0.770763
$316$	5.16621	0.290622
$317$	−6.06382	−0.340578	−0.170289	−	0.985394i	$-0.554470\pi$
$317$	−6.06382	−0.340578	−0.170289	+	0.985394i	$0.554470\pi$
$318$	0.694661	0.0389546
$319$	−12.6068	−0.705847
$320$	1.00000	0.0559017
$321$	1.46426	0.0817270
$322$	0	0
$323$	36.5928	2.03608
$324$	8.40033	0.466685
$325$	−5.01132	−0.277978
$326$	14.5346	0.804995
$327$	−1.14376	−0.0632502
$328$	11.4525	0.632357
$329$	−24.9774	−1.37705
$330$	0.814383	0.0448303
$331$	−26.7826	−1.47211	−0.736053	−	0.676924i	$-0.763313\pi$
$331$	−26.7826	−1.47211	−0.736053	+	0.676924i	$0.763313\pi$
$332$	−13.8710	−0.761272
$333$	−2.44908	−0.134209
$334$	12.6392	0.691588
$335$	7.13595	0.389879
$336$	−1.20850	−0.0659289
$337$	−30.5482	−1.66407	−0.832033	−	0.554727i	$-0.812823\pi$
$337$	−30.5482	−1.66407	−0.832033	+	0.554727i	$0.812823\pi$
$338$	−12.1134	−0.658880
$339$	−1.23981	−0.0673370
$340$	−6.42863	−0.348642
$341$	−0.395315	−0.0214075
$342$	−16.6943	−0.902727
$343$	−36.1732	−1.95317
$344$	7.19399	0.387874
$345$	0	0
$346$	3.07061	0.165077
$347$	3.43903	0.184617	0.0923083	−	0.995730i	$-0.470575\pi$
$347$	3.43903	0.184617	0.0923083	+	0.995730i	$0.470575\pi$
$348$	1.03921	0.0557073
$349$	−23.8768	−1.27810	−0.639049	−	0.769166i	$-0.720672\pi$
$349$	−23.8768	−1.27810	−0.639049	+	0.769166i	$0.720672\pi$
$350$	4.66427	0.249316
$351$	7.70335	0.411174
$352$	3.14316	0.167531
$353$	−4.10417	−0.218443	−0.109221	−	0.994017i	$-0.534836\pi$
$353$	−4.10417	−0.218443	−0.109221	+	0.994017i	$0.534836\pi$
$354$	1.39633	0.0742142
$355$	8.75253	0.464536
$356$	−11.2685	−0.597227
$357$	7.76899	0.411178
$358$	3.70124	0.195617
$359$	1.74673	0.0921889	0.0460944	−	0.998937i	$-0.485322\pi$
$359$	1.74673	0.0921889	0.0460944	+	0.998937i	$0.485322\pi$
$360$	2.93287	0.154576
$361$	13.4006	0.705297
$362$	−4.36736	−0.229543
$363$	−0.290333	−0.0152385
$364$	23.3741	1.22514
$365$	−15.3642	−0.804200
$366$	−1.27343	−0.0665632
$367$	−2.76843	−0.144511	−0.0722554	−	0.997386i	$-0.523020\pi$
$367$	−2.76843	−0.144511	−0.0722554	+	0.997386i	$0.523020\pi$
$368$	0	0
$369$	33.5886	1.74855
$370$	−0.835045	−0.0434119
$371$	12.5053	0.649242
$372$	0.0325866	0.00168954
$373$	−12.4141	−0.642778	−0.321389	−	0.946947i	$-0.604150\pi$
$373$	−12.4141	−0.642778	−0.321389	+	0.946947i	$0.604150\pi$
$374$	−20.2062	−1.04484
$375$	0.259097	0.0133797
$376$	−5.35505	−0.276166
$377$	−20.0998	−1.03519
$378$	−7.16986	−0.368778
$379$	9.27872	0.476616	0.238308	−	0.971190i	$-0.423407\pi$
$379$	9.27872	0.476616	0.238308	+	0.971190i	$0.423407\pi$
$380$	−5.69216	−0.292001
$381$	4.39012	0.224913
$382$	2.38501	0.122028
$383$	−11.4000	−0.582511	−0.291256	−	0.956645i	$-0.594073\pi$
$383$	−11.4000	−0.582511	−0.291256	+	0.956645i	$0.594073\pi$
$384$	−0.259097	−0.0132220
$385$	14.6605	0.747170
$386$	9.40122	0.478509
$387$	21.0990	1.07252
$388$	−1.58353	−0.0803914
$389$	−22.5111	−1.14136	−0.570679	−	0.821174i	$-0.693320\pi$
$389$	−22.5111	−1.14136	−0.570679	+	0.821174i	$0.693320\pi$
$390$	1.29842	0.0657480
$391$	0	0
$392$	−14.7554	−0.745259
$393$	−1.08715	−0.0548395
$394$	−1.83876	−0.0926352
$395$	5.16621	0.259940
$396$	9.21847	0.463246
$397$	−18.9406	−0.950602	−0.475301	−	0.879823i	$-0.657661\pi$
$397$	−18.9406	−0.950602	−0.475301	+	0.879823i	$0.657661\pi$
$398$	−4.87022	−0.244122
$399$	6.87896	0.344379
$400$	1.00000	0.0500000
$401$	5.16517	0.257936	0.128968	−	0.991649i	$-0.458833\pi$
$401$	5.16517	0.257936	0.128968	+	0.991649i	$0.458833\pi$
$402$	−1.84890	−0.0922149
$403$	−0.630274	−0.0313962
$404$	16.1749	0.804733
$405$	8.40033	0.417416
$406$	18.7078	0.928453
$407$	−2.62468	−0.130100
$408$	1.66564	0.0824614
$409$	2.31427	0.114433	0.0572166	−	0.998362i	$-0.481777\pi$
$409$	2.31427	0.114433	0.0572166	+	0.998362i	$0.481777\pi$
$410$	11.4525	0.565597
$411$	−3.02397	−0.149161
$412$	10.7046	0.527378
$413$	25.1368	1.23690
$414$	0	0
$415$	−13.8710	−0.680903
$416$	5.01132	0.245700
$417$	1.37665	0.0674148
$418$	−17.8913	−0.875094
$419$	−30.1439	−1.47263	−0.736313	−	0.676642i	$-0.763435\pi$
$419$	−30.1439	−1.47263	−0.736313	+	0.676642i	$0.763435\pi$
$420$	−1.20850	−0.0589686
$421$	22.2534	1.08456	0.542281	−	0.840197i	$-0.317561\pi$
$421$	22.2534	1.08456	0.542281	+	0.840197i	$0.317561\pi$
$422$	−16.6046	−0.808298
$423$	−15.7057	−0.763636
$424$	2.68108	0.130205
$425$	−6.42863	−0.311835
$426$	−2.26775	−0.109873
$427$	−22.9243	−1.10938
$428$	5.65139	0.273170
$429$	4.08113	0.197039
$430$	7.19399	0.346925
$431$	−9.81670	−0.472854	−0.236427	−	0.971649i	$-0.575976\pi$
$431$	−9.81670	−0.472854	−0.236427	+	0.971649i	$0.575976\pi$
$432$	−1.53719	−0.0739580
$433$	−27.0085	−1.29795	−0.648974	−	0.760811i	$-0.724801\pi$
$433$	−27.0085	−1.29795	−0.648974	+	0.760811i	$0.724801\pi$
$434$	0.586625	0.0281589
$435$	1.03921	0.0498262
$436$	−4.41441	−0.211412
$437$	0	0
$438$	3.98082	0.190211
$439$	−30.6254	−1.46167	−0.730836	−	0.682553i	$-0.760870\pi$
$439$	−30.6254	−1.46167	−0.730836	+	0.682553i	$0.760870\pi$
$440$	3.14316	0.149844
$441$	−43.2756	−2.06074
$442$	−32.2160	−1.53236
$443$	34.8461	1.65559	0.827794	−	0.561033i	$-0.189596\pi$
$443$	34.8461	1.65559	0.827794	+	0.561033i	$0.189596\pi$
$444$	0.216358	0.0102679
$445$	−11.2685	−0.534176
$446$	17.2501	0.816816
$447$	1.03687	0.0490424
$448$	−4.66427	−0.220366
$449$	33.8605	1.59798	0.798989	−	0.601346i	$-0.205369\pi$
$449$	33.8605	1.59798	0.798989	+	0.601346i	$0.205369\pi$
$450$	2.93287	0.138257
$451$	35.9969	1.69503
$452$	−4.78510	−0.225072
$453$	−2.11216	−0.0992381
$454$	−0.800560	−0.0375721
$455$	23.3741	1.09580
$456$	1.47482	0.0690648
$457$	10.9350	0.511516	0.255758	−	0.966741i	$-0.417675\pi$
$457$	10.9350	0.511516	0.255758	+	0.966741i	$0.417675\pi$
$458$	2.48769	0.116242
$459$	9.88202	0.461253
$460$	0	0
$461$	10.7264	0.499580	0.249790	−	0.968300i	$-0.419638\pi$
$461$	10.7264	0.499580	0.249790	+	0.968300i	$0.419638\pi$
$462$	−3.79850	−0.176722
$463$	15.4545	0.718229	0.359115	−	0.933293i	$-0.383079\pi$
$463$	15.4545	0.718229	0.359115	+	0.933293i	$0.383079\pi$
$464$	4.01088	0.186200
$465$	0.0325866	0.00151117
$466$	−3.72567	−0.172588
$467$	14.6325	0.677110	0.338555	−	0.940947i	$-0.390062\pi$
$467$	14.6325	0.677110	0.338555	+	0.940947i	$0.390062\pi$
$468$	14.6976	0.679395
$469$	−33.2840	−1.53691
$470$	−5.35505	−0.247010
$471$	−4.41693	−0.203521
$472$	5.38922	0.248059
$473$	22.6119	1.03969
$474$	−1.33855	−0.0614816
$475$	−5.69216	−0.261174
$476$	29.9849	1.37435
$477$	7.86327	0.360034
$478$	−4.39816	−0.201167
$479$	11.6251	0.531166	0.265583	−	0.964088i	$-0.414436\pi$
$479$	11.6251	0.531166	0.265583	+	0.964088i	$0.414436\pi$
$480$	−0.259097	−0.0118261
$481$	−4.18468	−0.190805
$482$	−2.46589	−0.112318
$483$	0	0
$484$	−1.12056	−0.0509345
$485$	−1.58353	−0.0719043
$486$	−6.78806	−0.307913
$487$	19.5401	0.885448	0.442724	−	0.896658i	$-0.354012\pi$
$487$	19.5401	0.885448	0.442724	+	0.896658i	$0.354012\pi$
$488$	−4.91488	−0.222486
$489$	−3.76586	−0.170298
$490$	−14.7554	−0.666580
$491$	10.5517	0.476190	0.238095	−	0.971242i	$-0.423477\pi$
$491$	10.5517	0.476190	0.238095	+	0.971242i	$0.423477\pi$
$492$	−2.96730	−0.133776
$493$	−25.7845	−1.16127
$494$	−28.5252	−1.28341
$495$	9.21847	0.414339
$496$	0.125770	0.00564724
$497$	−40.8241	−1.83121
$498$	3.59394	0.161049
$499$	27.4205	1.22751	0.613756	−	0.789496i	$-0.289658\pi$
$499$	27.4205	1.22751	0.613756	+	0.789496i	$0.289658\pi$
$500$	1.00000	0.0447214
$501$	−3.27479	−0.146307
$502$	12.2154	0.545200
$503$	9.59985	0.428036	0.214018	−	0.976830i	$-0.431345\pi$
$503$	9.59985	0.428036	0.214018	+	0.976830i	$0.431345\pi$
$504$	−13.6797	−0.609341
$505$	16.1749	0.719776
$506$	0	0
$507$	3.13854	0.139387
$508$	16.9439	0.751766
$509$	9.62884	0.426791	0.213395	−	0.976966i	$-0.431548\pi$
$509$	9.62884	0.426791	0.213395	+	0.976966i	$0.431548\pi$
$510$	1.66564	0.0737558
$511$	71.6628	3.17018
$512$	−1.00000	−0.0441942
$513$	8.74992	0.386318
$514$	−10.3228	−0.455318
$515$	10.7046	0.471701
$516$	−1.86394	−0.0820554
$517$	−16.8318	−0.740261
$518$	3.89487	0.171131
$519$	−0.795586	−0.0349224
$520$	5.01132	0.219761
$521$	25.8153	1.13099	0.565495	−	0.824752i	$-0.308685\pi$
$521$	25.8153	1.13099	0.565495	+	0.824752i	$0.308685\pi$
$522$	11.7634	0.514869
$523$	28.7445	1.25691	0.628454	−	0.777847i	$-0.283688\pi$
$523$	28.7445	1.25691	0.628454	+	0.777847i	$0.283688\pi$
$524$	−4.19592	−0.183300
$525$	−1.20850	−0.0527431
$526$	−2.13852	−0.0932439
$527$	−0.808530	−0.0352201
$528$	−0.814383	−0.0354415
$529$	0	0
$530$	2.68108	0.116459
$531$	15.8059	0.685917
$532$	26.5497	1.15108
$533$	57.3920	2.48592
$534$	2.91962	0.126344
$535$	5.65139	0.244331
$536$	−7.13595	−0.308226
$537$	−0.958981	−0.0413831
$538$	13.3162	0.574103
$539$	−46.3785	−1.99766
$540$	−1.53719	−0.0661500
$541$	−26.2444	−1.12834	−0.564168	−	0.825660i	$-0.690803\pi$
$541$	−26.2444	−1.12834	−0.564168	+	0.825660i	$0.690803\pi$
$542$	12.8185	0.550604
$543$	1.13157	0.0485603
$544$	6.42863	0.275625
$545$	−4.41441	−0.189093
$546$	−6.05617	−0.259180
$547$	4.29766	0.183755	0.0918774	−	0.995770i	$-0.470713\pi$
$547$	4.29766	0.183755	0.0918774	+	0.995770i	$0.470713\pi$
$548$	−11.6712	−0.498568
$549$	−14.4147	−0.615204
$550$	3.14316	0.134025
$551$	−22.8306	−0.972615
$552$	0	0
$553$	−24.0966	−1.02469
$554$	−18.2786	−0.776581
$555$	0.216358	0.00918387
$556$	5.31325	0.225332
$557$	18.8830	0.800098	0.400049	−	0.916494i	$-0.368993\pi$
$557$	18.8830	0.800098	0.400049	+	0.916494i	$0.368993\pi$
$558$	0.368867	0.0156154
$559$	36.0514	1.52481
$560$	−4.66427	−0.197101
$561$	5.23537	0.221037
$562$	18.7519	0.791000
$563$	−4.36230	−0.183849	−0.0919245	−	0.995766i	$-0.529302\pi$
$563$	−4.36230	−0.183849	−0.0919245	+	0.995766i	$0.529302\pi$
$564$	1.38748	0.0584234
$565$	−4.78510	−0.201311
$566$	22.0875	0.928409
$567$	−39.1814	−1.64546
$568$	−8.75253	−0.367248
$569$	21.5058	0.901571	0.450786	−	0.892632i	$-0.351144\pi$
$569$	21.5058	0.901571	0.450786	+	0.892632i	$0.351144\pi$
$570$	1.47482	0.0617734
$571$	2.58443	0.108155	0.0540775	−	0.998537i	$-0.482778\pi$
$571$	2.58443	0.108155	0.0540775	+	0.998537i	$0.482778\pi$
$572$	15.7514	0.658598
$573$	−0.617950	−0.0258152
$574$	−53.4174	−2.22960
$575$	0	0
$576$	−2.93287	−0.122203
$577$	−6.80722	−0.283388	−0.141694	−	0.989910i	$-0.545255\pi$
$577$	−6.80722	−0.283388	−0.141694	+	0.989910i	$0.545255\pi$
$578$	−24.3273	−1.01188
$579$	−2.43583	−0.101230
$580$	4.01088	0.166543
$581$	64.6982	2.68414
$582$	0.410287	0.0170069
$583$	8.42707	0.349014
$584$	15.3642	0.635776
$585$	14.6976	0.607669
$586$	30.2196	1.24836
$587$	−1.34941	−0.0556962	−0.0278481	−	0.999612i	$-0.508865\pi$
$587$	−1.34941	−0.0556962	−0.0278481	+	0.999612i	$0.508865\pi$
$588$	3.82307	0.157661
$589$	−0.715903	−0.0294983
$590$	5.38922	0.221871
$591$	0.476416	0.0195971
$592$	0.835045	0.0343201
$593$	6.52390	0.267905	0.133952	−	0.990988i	$-0.457233\pi$
$593$	6.52390	0.267905	0.133952	+	0.990988i	$0.457233\pi$
$594$	−4.83163	−0.198244
$595$	29.9849	1.22926
$596$	4.00187	0.163923
$597$	1.26186	0.0516444
$598$	0	0
$599$	29.7565	1.21582	0.607910	−	0.794006i	$-0.292008\pi$
$599$	29.7565	1.21582	0.607910	+	0.794006i	$0.292008\pi$
$600$	−0.259097	−0.0105776
$601$	−7.36636	−0.300480	−0.150240	−	0.988650i	$-0.548005\pi$
$601$	−7.36636	−0.300480	−0.150240	+	0.988650i	$0.548005\pi$
$602$	−33.5547	−1.36759
$603$	−20.9288	−0.852287
$604$	−8.15202	−0.331701
$605$	−1.12056	−0.0455572
$606$	−4.19088	−0.170243
$607$	18.5931	0.754670	0.377335	−	0.926077i	$-0.376841\pi$
$607$	18.5931	0.754670	0.377335	+	0.926077i	$0.376841\pi$
$608$	5.69216	0.230847
$609$	−4.84714	−0.196416
$610$	−4.91488	−0.198998
$611$	−26.8359	−1.08566
$612$	18.8543	0.762141
$613$	−37.6043	−1.51882	−0.759412	−	0.650610i	$-0.774513\pi$
$613$	−37.6043	−1.51882	−0.759412	+	0.650610i	$0.774513\pi$
$614$	−16.6139	−0.670483
$615$	−2.96730	−0.119653
$616$	−14.6605	−0.590689
$617$	0.704562	0.0283646	0.0141823	−	0.999899i	$-0.495485\pi$
$617$	0.704562	0.0283646	0.0141823	+	0.999899i	$0.495485\pi$
$618$	−2.77353	−0.111568
$619$	46.9660	1.88772	0.943861	−	0.330342i	$-0.107164\pi$
$619$	46.9660	1.88772	0.943861	+	0.330342i	$0.107164\pi$
$620$	0.125770	0.00505105
$621$	0	0
$622$	11.1062	0.445316
$623$	52.5591	2.10573
$624$	−1.29842	−0.0519783
$625$	1.00000	0.0400000
$626$	31.6253	1.26400
$627$	4.63559	0.185128
$628$	−17.0474	−0.680265
$629$	−5.36820	−0.214044
$630$	−13.6797	−0.545012
$631$	45.4882	1.81086	0.905429	−	0.424497i	$-0.139549\pi$
$631$	45.4882	1.81086	0.905429	+	0.424497i	$0.139549\pi$
$632$	−5.16621	−0.205501
$633$	4.30219	0.170997
$634$	6.06382	0.240825
$635$	16.9439	0.672400
$636$	−0.694661	−0.0275451
$637$	−73.9440	−2.92977
$638$	12.6068	0.499109
$639$	−25.6700	−1.01549
$640$	−1.00000	−0.0395285
$641$	33.8883	1.33851	0.669254	−	0.743034i	$-0.266614\pi$
$641$	33.8883	1.33851	0.669254	+	0.743034i	$0.266614\pi$
$642$	−1.46426	−0.0577897
$643$	−43.7168	−1.72402	−0.862011	−	0.506890i	$-0.830795\pi$
$643$	−43.7168	−1.72402	−0.862011	+	0.506890i	$0.830795\pi$
$644$	0	0
$645$	−1.86394	−0.0733926
$646$	−36.5928	−1.43972
$647$	12.7514	0.501309	0.250655	−	0.968077i	$-0.419354\pi$
$647$	12.7514	0.501309	0.250655	+	0.968077i	$0.419354\pi$
$648$	−8.40033	−0.329996
$649$	16.9392	0.664921
$650$	5.01132	0.196560
$651$	−0.151993	−0.00595707
$652$	−14.5346	−0.569218
$653$	32.5678	1.27448	0.637238	−	0.770667i	$-0.280077\pi$
$653$	32.5678	1.27448	0.637238	+	0.770667i	$0.280077\pi$
$654$	1.14376	0.0447246
$655$	−4.19592	−0.163948
$656$	−11.4525	−0.447144
$657$	45.0612	1.75801
$658$	24.9774	0.973720
$659$	−13.6442	−0.531501	−0.265751	−	0.964042i	$-0.585620\pi$
$659$	−13.6442	−0.531501	−0.265751	+	0.964042i	$0.585620\pi$
$660$	−0.814383	−0.0316998
$661$	−28.6495	−1.11434	−0.557169	−	0.830399i	$-0.688112\pi$
$661$	−28.6495	−1.11434	−0.557169	+	0.830399i	$0.688112\pi$
$662$	26.7826	1.04094
$663$	8.34706	0.324173
$664$	13.8710	0.538301
$665$	26.5497	1.02955
$666$	2.44908	0.0948998
$667$	0	0
$668$	−12.6392	−0.489027
$669$	−4.46945	−0.172799
$670$	−7.13595	−0.275686
$671$	−15.4482	−0.596373
$672$	1.20850	0.0466188
$673$	−4.88784	−0.188413	−0.0942063	−	0.995553i	$-0.530031\pi$
$673$	−4.88784	−0.188413	−0.0942063	+	0.995553i	$0.530031\pi$
$674$	30.5482	1.17667
$675$	−1.53719	−0.0591664
$676$	12.1134	0.465899
$677$	−5.82792	−0.223985	−0.111993	−	0.993709i	$-0.535723\pi$
$677$	−5.82792	−0.223985	−0.111993	+	0.993709i	$0.535723\pi$
$678$	1.23981	0.0476145
$679$	7.38599	0.283448
$680$	6.42863	0.246527
$681$	0.207423	0.00794845
$682$	0.395315	0.0151374
$683$	15.4277	0.590324	0.295162	−	0.955447i	$-0.404626\pi$
$683$	15.4277	0.590324	0.295162	+	0.955447i	$0.404626\pi$
$684$	16.6943	0.638324
$685$	−11.6712	−0.445933
$686$	36.1732	1.38110
$687$	−0.644553	−0.0245912
$688$	−7.19399	−0.274268
$689$	13.4358	0.511862
$690$	0	0
$691$	0.453717	0.0172602	0.00863011	−	0.999963i	$-0.497253\pi$
$691$	0.453717	0.0172602	0.00863011	+	0.999963i	$0.497253\pi$
$692$	−3.07061	−0.116727
$693$	−42.9974	−1.63334
$694$	−3.43903	−0.130544
$695$	5.31325	0.201543
$696$	−1.03921	−0.0393910
$697$	73.6237	2.78870
$698$	23.8768	0.903751
$699$	0.965310	0.0365114
$700$	−4.66427	−0.176293
$701$	−5.40376	−0.204097	−0.102049	−	0.994779i	$-0.532540\pi$
$701$	−5.40376	−0.204097	−0.102049	+	0.994779i	$0.532540\pi$
$702$	−7.70335	−0.290744
$703$	−4.75321	−0.179271
$704$	−3.14316	−0.118462
$705$	1.38748	0.0522554
$706$	4.10417	0.154462
$707$	−75.4442	−2.83737
$708$	−1.39633	−0.0524773
$709$	−12.4084	−0.466005	−0.233003	−	0.972476i	$-0.574855\pi$
$709$	−12.4084	−0.466005	−0.233003	+	0.972476i	$0.574855\pi$
$710$	−8.75253	−0.328477
$711$	−15.1518	−0.568238
$712$	11.2685	0.422303
$713$	0	0
$714$	−7.76899	−0.290747
$715$	15.7514	0.589068
$716$	−3.70124	−0.138322
$717$	1.13955	0.0425573
$718$	−1.74673	−0.0651874
$719$	−26.5277	−0.989315	−0.494658	−	0.869088i	$-0.664707\pi$
$719$	−26.5277	−0.989315	−0.494658	+	0.869088i	$0.664707\pi$
$720$	−2.93287	−0.109302
$721$	−49.9291	−1.85946
$722$	−13.4006	−0.498720
$723$	0.638906	0.0237612
$724$	4.36736	0.162312
$725$	4.01088	0.148960
$726$	0.290333	0.0107753
$727$	−35.6584	−1.32250	−0.661248	−	0.750167i	$-0.729973\pi$
$727$	−35.6584	−1.32250	−0.661248	+	0.750167i	$0.729973\pi$
$728$	−23.3741	−0.866304
$729$	−23.4422	−0.868230
$730$	15.3642	0.568655
$731$	46.2475	1.71053
$732$	1.27343	0.0470673
$733$	−3.16685	−0.116970	−0.0584852	−	0.998288i	$-0.518627\pi$
$733$	−3.16685	−0.116970	−0.0584852	+	0.998288i	$0.518627\pi$
$734$	2.76843	0.102185
$735$	3.82307	0.141016
$736$	0	0
$737$	−22.4294	−0.826198
$738$	−33.5886	−1.23641
$739$	1.83846	0.0676288	0.0338144	−	0.999428i	$-0.489234\pi$
$739$	1.83846	0.0676288	0.0338144	+	0.999428i	$0.489234\pi$
$740$	0.835045	0.0306969
$741$	7.39080	0.271508
$742$	−12.5053	−0.459084
$743$	−24.3944	−0.894943	−0.447471	−	0.894298i	$-0.647675\pi$
$743$	−24.3944	−0.894943	−0.447471	+	0.894298i	$0.647675\pi$
$744$	−0.0325866	−0.00119468
$745$	4.00187	0.146617
$746$	12.4141	0.454513
$747$	40.6819	1.48847
$748$	20.2062	0.738812
$749$	−26.3596	−0.963159
$750$	−0.259097	−0.00946088
$751$	28.4190	1.03702	0.518512	−	0.855070i	$-0.326486\pi$
$751$	28.4190	1.03702	0.518512	+	0.855070i	$0.326486\pi$
$752$	5.35505	0.195279
$753$	−3.16497	−0.115338
$754$	20.0998	0.731992
$755$	−8.15202	−0.296682
$756$	7.16986	0.260765
$757$	−7.18028	−0.260972	−0.130486	−	0.991450i	$-0.541654\pi$
$757$	−7.18028	−0.260972	−0.130486	+	0.991450i	$0.541654\pi$
$758$	−9.27872	−0.337018
$759$	0	0
$760$	5.69216	0.206476
$761$	−15.8445	−0.574364	−0.287182	−	0.957876i	$-0.592718\pi$
$761$	−15.8445	−0.574364	−0.287182	+	0.957876i	$0.592718\pi$
$762$	−4.39012	−0.159037
$763$	20.5900	0.745408
$764$	−2.38501	−0.0862868
$765$	18.8543	0.681680
$766$	11.4000	0.411898
$767$	27.0071	0.975171
$768$	0.259097	0.00934936
$769$	−8.26978	−0.298216	−0.149108	−	0.988821i	$-0.547640\pi$
$769$	−8.26978	−0.298216	−0.149108	+	0.988821i	$0.547640\pi$
$770$	−14.6605	−0.528329
$771$	2.67460	0.0963233
$772$	−9.40122	−0.338357
$773$	13.6265	0.490109	0.245055	−	0.969509i	$-0.421194\pi$
$773$	13.6265	0.490109	0.245055	+	0.969509i	$0.421194\pi$
$774$	−21.0990	−0.758389
$775$	0.125770	0.00451779
$776$	1.58353	0.0568453
$777$	−1.00915	−0.0362030
$778$	22.5111	0.807061
$779$	65.1892	2.33565
$780$	−1.29842	−0.0464908
$781$	−27.5106	−0.984406
$782$	0	0
$783$	−6.16548	−0.220336
$784$	14.7554	0.526978
$785$	−17.0474	−0.608448
$786$	1.08715	0.0387774
$787$	8.31222	0.296299	0.148149	−	0.988965i	$-0.452668\pi$
$787$	8.31222	0.296299	0.148149	+	0.988965i	$0.452668\pi$
$788$	1.83876	0.0655029
$789$	0.554084	0.0197259
$790$	−5.16621	−0.183806
$791$	22.3190	0.793572
$792$	−9.21847	−0.327564
$793$	−24.6300	−0.874638
$794$	18.9406	0.672177
$795$	−0.694661	−0.0246371
$796$	4.87022	0.172620
$797$	19.7820	0.700713	0.350356	−	0.936616i	$-0.386060\pi$
$797$	19.7820	0.700713	0.350356	+	0.936616i	$0.386060\pi$
$798$	−6.87896	−0.243512
$799$	−34.4257	−1.21789
$800$	−1.00000	−0.0353553
$801$	33.0489	1.16773
$802$	−5.16517	−0.182389
$803$	48.2922	1.70419
$804$	1.84890	0.0652058
$805$	0	0
$806$	0.630274	0.0222005
$807$	−3.45019	−0.121453
$808$	−16.1749	−0.569033
$809$	−20.1183	−0.707322	−0.353661	−	0.935374i	$-0.615063\pi$
$809$	−20.1183	−0.707322	−0.353661	+	0.935374i	$0.615063\pi$
$810$	−8.40033	−0.295157
$811$	17.3046	0.607648	0.303824	−	0.952728i	$-0.401736\pi$
$811$	17.3046	0.607648	0.303824	+	0.952728i	$0.401736\pi$
$812$	−18.7078	−0.656516
$813$	−3.32125	−0.116481
$814$	2.62468	0.0919949
$815$	−14.5346	−0.509124
$816$	−1.66564	−0.0583090
$817$	40.9493	1.43264
$818$	−2.31427	−0.0809165
$819$	−68.5533	−2.39545
$820$	−11.4525	−0.399937
$821$	46.1067	1.60914	0.804568	−	0.593861i	$-0.202397\pi$
$821$	46.1067	1.60914	0.804568	+	0.593861i	$0.202397\pi$
$822$	3.02397	0.105473
$823$	−9.42792	−0.328637	−0.164318	−	0.986407i	$-0.552542\pi$
$823$	−9.42792	−0.328637	−0.164318	+	0.986407i	$0.552542\pi$
$824$	−10.7046	−0.372913
$825$	−0.814383	−0.0283532
$826$	−25.1368	−0.874620
$827$	−44.5622	−1.54958	−0.774790	−	0.632218i	$-0.782145\pi$
$827$	−44.5622	−1.54958	−0.774790	+	0.632218i	$0.782145\pi$
$828$	0	0
$829$	−40.8816	−1.41988	−0.709939	−	0.704264i	$-0.751277\pi$
$829$	−40.8816	−1.41988	−0.709939	+	0.704264i	$0.751277\pi$
$830$	13.8710	0.481471
$831$	4.73592	0.164287
$832$	−5.01132	−0.173736
$833$	−94.8569	−3.28660
$834$	−1.37665	−0.0476694
$835$	−12.6392	−0.437399
$836$	17.8913	0.618785
$837$	−0.193332	−0.00668254
$838$	30.1439	1.04130
$839$	26.3544	0.909853	0.454927	−	0.890529i	$-0.349665\pi$
$839$	26.3544	0.909853	0.454927	+	0.890529i	$0.349665\pi$
$840$	1.20850	0.0416971
$841$	−12.9128	−0.445270
$842$	−22.2534	−0.766902
$843$	−4.85855	−0.167337
$844$	16.6046	0.571553
$845$	12.1134	0.416712
$846$	15.7057	0.539972
$847$	5.22658	0.179587
$848$	−2.68108	−0.0920688
$849$	−5.72281	−0.196406
$850$	6.42863	0.220500
$851$	0	0
$852$	2.26775	0.0776920
$853$	18.6874	0.639843	0.319922	−	0.947444i	$-0.396343\pi$
$853$	18.6874	0.639843	0.319922	+	0.947444i	$0.396343\pi$
$854$	22.9243	0.784453
$855$	16.6943	0.570935
$856$	−5.65139	−0.193161
$857$	−46.6408	−1.59322	−0.796610	−	0.604494i	$-0.793375\pi$
$857$	−46.6408	−1.59322	−0.796610	+	0.604494i	$0.793375\pi$
$858$	−4.08113	−0.139328
$859$	−21.0275	−0.717450	−0.358725	−	0.933443i	$-0.616788\pi$
$859$	−21.0275	−0.717450	−0.358725	+	0.933443i	$0.616788\pi$
$860$	−7.19399	−0.245313
$861$	13.8403	0.471675
$862$	9.81670	0.334358
$863$	30.4334	1.03596	0.517982	−	0.855392i	$-0.326684\pi$
$863$	30.4334	1.03596	0.517982	+	0.855392i	$0.326684\pi$
$864$	1.53719	0.0522962
$865$	−3.07061	−0.104404
$866$	27.0085	0.917787
$867$	6.30314	0.214066
$868$	−0.586625	−0.0199114
$869$	−16.2382	−0.550844
$870$	−1.03921	−0.0352324
$871$	−35.7605	−1.21170
$872$	4.41441	0.149491
$873$	4.64428	0.157185
$874$	0	0
$875$	−4.66427	−0.157681
$876$	−3.98082	−0.134500
$877$	−35.0555	−1.18374	−0.591871	−	0.806033i	$-0.701610\pi$
$877$	−35.0555	−1.18374	−0.591871	+	0.806033i	$0.701610\pi$
$878$	30.6254	1.03356
$879$	−7.82980	−0.264092
$880$	−3.14316	−0.105956
$881$	58.9809	1.98712	0.993558	−	0.113323i	$-0.0361496\pi$
$881$	58.9809	1.98712	0.993558	+	0.113323i	$0.0361496\pi$
$882$	43.2756	1.45717
$883$	−22.8580	−0.769231	−0.384616	−	0.923077i	$-0.625666\pi$
$883$	−22.8580	−0.769231	−0.384616	+	0.923077i	$0.625666\pi$
$884$	32.2160	1.08354
$885$	−1.39633	−0.0469372
$886$	−34.8461	−1.17068
$887$	20.0706	0.673906	0.336953	−	0.941521i	$-0.390604\pi$
$887$	20.0706	0.673906	0.336953	+	0.941521i	$0.390604\pi$
$888$	−0.216358	−0.00726048
$889$	−79.0310	−2.65062
$890$	11.2685	0.377719
$891$	−26.4035	−0.884552
$892$	−17.2501	−0.577576
$893$	−30.4818	−1.02003
$894$	−1.03687	−0.0346782
$895$	−3.70124	−0.123719
$896$	4.66427	0.155822
$897$	0	0
$898$	−33.8605	−1.12994
$899$	0.504449	0.0168243
$900$	−2.93287	−0.0977623
$901$	17.2357	0.574205
$902$	−35.9969	−1.19857
$903$	8.69392	0.289316
$904$	4.78510	0.159150
$905$	4.36736	0.145176
$906$	2.11216	0.0701719
$907$	−40.8389	−1.35603	−0.678017	−	0.735046i	$-0.737160\pi$
$907$	−40.8389	−1.35603	−0.678017	+	0.735046i	$0.737160\pi$
$908$	0.800560	0.0265675
$909$	−47.4390	−1.57345
$910$	−23.3741	−0.774845
$911$	−22.8314	−0.756437	−0.378219	−	0.925716i	$-0.623463\pi$
$911$	−22.8314	−0.756437	−0.378219	+	0.925716i	$0.623463\pi$
$912$	−1.47482	−0.0488362
$913$	43.5989	1.44291
$914$	−10.9350	−0.361697
$915$	1.27343	0.0420983
$916$	−2.48769	−0.0821956
$917$	19.5709	0.646288
$918$	−9.88202	−0.326155
$919$	23.3350	0.769750	0.384875	−	0.922969i	$-0.374245\pi$
$919$	23.3350	0.769750	0.384875	+	0.922969i	$0.374245\pi$
$920$	0	0
$921$	4.30462	0.141842
$922$	−10.7264	−0.353256
$923$	−43.8618	−1.44373
$924$	3.79850	0.124961
$925$	0.835045	0.0274561
$926$	−15.4545	−0.507865
$927$	−31.3952	−1.03115
$928$	−4.01088	−0.131664
$929$	−31.7745	−1.04249	−0.521244	−	0.853408i	$-0.674532\pi$
$929$	−31.7745	−1.04249	−0.521244	+	0.853408i	$0.674532\pi$
$930$	−0.0325866	−0.00106856
$931$	−83.9899	−2.75266
$932$	3.72567	0.122038
$933$	−2.87757	−0.0942074
$934$	−14.6325	−0.478789
$935$	20.2062	0.660814
$936$	−14.6976	−0.480405
$937$	7.06645	0.230851	0.115425	−	0.993316i	$-0.463177\pi$
$937$	7.06645	0.230851	0.115425	+	0.993316i	$0.463177\pi$
$938$	33.2840	1.08676
$939$	−8.19401	−0.267401
$940$	5.35505	0.174663
$941$	2.53737	0.0827158	0.0413579	−	0.999144i	$-0.486832\pi$
$941$	2.53737	0.0827158	0.0413579	+	0.999144i	$0.486832\pi$
$942$	4.41693	0.143911
$943$	0	0
$944$	−5.38922	−0.175404
$945$	7.16986	0.233235
$946$	−22.6119	−0.735175
$947$	−56.5337	−1.83710	−0.918549	−	0.395307i	$-0.870638\pi$
$947$	−56.5337	−1.83710	−0.918549	+	0.395307i	$0.870638\pi$
$948$	1.33855	0.0434741
$949$	76.9951	2.49937
$950$	5.69216	0.184678
$951$	−1.57112	−0.0509469
$952$	−29.9849	−0.971815
$953$	7.04172	0.228104	0.114052	−	0.993475i	$-0.463617\pi$
$953$	7.04172	0.228104	0.114052	+	0.993475i	$0.463617\pi$
$954$	−7.86327	−0.254583
$955$	−2.38501	−0.0771772
$956$	4.39816	0.142247
$957$	−3.26639	−0.105587
$958$	−11.6251	−0.375591
$959$	54.4375	1.75788
$960$	0.259097	0.00836232
$961$	−30.9842	−0.999490
$962$	4.18468	0.134919
$963$	−16.5748	−0.534115
$964$	2.46589	0.0794211
$965$	−9.40122	−0.302636
$966$	0	0
$967$	0.315127	0.0101338	0.00506690	−	0.999987i	$-0.498387\pi$
$967$	0.315127	0.0101338	0.00506690	+	0.999987i	$0.498387\pi$
$968$	1.12056	0.0360161
$969$	9.48108	0.304576
$970$	1.58353	0.0508440
$971$	16.3322	0.524125	0.262062	−	0.965051i	$-0.415597\pi$
$971$	16.3322	0.524125	0.262062	+	0.965051i	$0.415597\pi$
$972$	6.78806	0.217727
$973$	−24.7824	−0.794488
$974$	−19.5401	−0.626106
$975$	−1.29842	−0.0415827
$976$	4.91488	0.157321
$977$	37.6327	1.20398	0.601989	−	0.798504i	$-0.294375\pi$
$977$	37.6327	1.20398	0.601989	+	0.798504i	$0.294375\pi$
$978$	3.76586	0.120419
$979$	35.4185	1.13198
$980$	14.7554	0.471343
$981$	12.9469	0.413363
$982$	−10.5517	−0.336717
$983$	31.9347	1.01856	0.509279	−	0.860602i	$-0.329912\pi$
$983$	31.9347	1.01856	0.509279	+	0.860602i	$0.329912\pi$
$984$	2.96730	0.0945940
$985$	1.83876	0.0585876
$986$	25.7845	0.821145
$987$	−6.47157	−0.205992
$988$	28.5252	0.907509
$989$	0	0
$990$	−9.21847	−0.292982
$991$	−54.2815	−1.72431	−0.862155	−	0.506645i	$-0.830886\pi$
$991$	−54.2815	−1.72431	−0.862155	+	0.506645i	$0.830886\pi$
$992$	−0.125770	−0.00399320
$993$	−6.93930	−0.220212
$994$	40.8241	1.29486
$995$	4.87022	0.154396
$996$	−3.59394	−0.113878
$997$	20.7290	0.656493	0.328247	−	0.944592i	$-0.393542\pi$
$997$	20.7290	0.656493	0.328247	+	0.944592i	$0.393542\pi$
$998$	−27.4205	−0.867982
$999$	−1.28362	−0.0406120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bj.1.5		10
23.2	even	11		230.2.g.b.211.2	yes	20
23.12	even	11		230.2.g.b.121.2	✓	20
23.22	odd	2		5290.2.a.bi.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.121.2	✓	20	23.12	even	11
230.2.g.b.211.2	yes	20	23.2	even	11
5290.2.a.bi.1.5		10	23.22	odd	2
5290.2.a.bj.1.5		10	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.259097 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.259097 q^{6} -4.66427 q^{7} -1.00000 q^{8} -2.93287 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.259097 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.259097 q^{6} -4.66427 q^{7} -1.00000 q^{8} -2.93287 q^{9} -1.00000 q^{10} -3.14316 q^{11} +0.259097 q^{12} -5.01132 q^{13} +4.66427 q^{14} +0.259097 q^{15} +1.00000 q^{16} -6.42863 q^{17} +2.93287 q^{18} -5.69216 q^{19} +1.00000 q^{20} -1.20850 q^{21} +3.14316 q^{22} -0.259097 q^{24} +1.00000 q^{25} +5.01132 q^{26} -1.53719 q^{27} -4.66427 q^{28} +4.01088 q^{29} -0.259097 q^{30} +0.125770 q^{31} -1.00000 q^{32} -0.814383 q^{33} +6.42863 q^{34} -4.66427 q^{35} -2.93287 q^{36} +0.835045 q^{37} +5.69216 q^{38} -1.29842 q^{39} -1.00000 q^{40} -11.4525 q^{41} +1.20850 q^{42} -7.19399 q^{43} -3.14316 q^{44} -2.93287 q^{45} +5.35505 q^{47} +0.259097 q^{48} +14.7554 q^{49} -1.00000 q^{50} -1.66564 q^{51} -5.01132 q^{52} -2.68108 q^{53} +1.53719 q^{54} -3.14316 q^{55} +4.66427 q^{56} -1.47482 q^{57} -4.01088 q^{58} -5.38922 q^{59} +0.259097 q^{60} +4.91488 q^{61} -0.125770 q^{62} +13.6797 q^{63} +1.00000 q^{64} -5.01132 q^{65} +0.814383 q^{66} +7.13595 q^{67} -6.42863 q^{68} +4.66427 q^{70} +8.75253 q^{71} +2.93287 q^{72} -15.3642 q^{73} -0.835045 q^{74} +0.259097 q^{75} -5.69216 q^{76} +14.6605 q^{77} +1.29842 q^{78} +5.16621 q^{79} +1.00000 q^{80} +8.40033 q^{81} +11.4525 q^{82} -13.8710 q^{83} -1.20850 q^{84} -6.42863 q^{85} +7.19399 q^{86} +1.03921 q^{87} +3.14316 q^{88} -11.2685 q^{89} +2.93287 q^{90} +23.3741 q^{91} +0.0325866 q^{93} -5.35505 q^{94} -5.69216 q^{95} -0.259097 q^{96} -1.58353 q^{97} -14.7554 q^{98} +9.21847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more