LMFDB - Embedded newform 7098.2.a.bw.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.56155 q^{10} +2.56155 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.56155 q^{15} +1.00000 q^{16} -5.00000 q^{17} +1.00000 q^{18} +7.68466 q^{19} -3.56155 q^{20} -1.00000 q^{21} +2.56155 q^{22} -9.12311 q^{23} +1.00000 q^{24} +7.68466 q^{25} +1.00000 q^{27} -1.00000 q^{28} -1.00000 q^{29} -3.56155 q^{30} +5.12311 q^{31} +1.00000 q^{32} +2.56155 q^{33} -5.00000 q^{34} +3.56155 q^{35} +1.00000 q^{36} -9.80776 q^{37} +7.68466 q^{38} -3.56155 q^{40} +4.12311 q^{41} -1.00000 q^{42} -2.87689 q^{43} +2.56155 q^{44} -3.56155 q^{45} -9.12311 q^{46} -7.68466 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.68466 q^{50} -5.00000 q^{51} -3.87689 q^{53} +1.00000 q^{54} -9.12311 q^{55} -1.00000 q^{56} +7.68466 q^{57} -1.00000 q^{58} +13.1231 q^{59} -3.56155 q^{60} -1.00000 q^{61} +5.12311 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.56155 q^{66} +1.12311 q^{67} -5.00000 q^{68} -9.12311 q^{69} +3.56155 q^{70} -4.00000 q^{71} +1.00000 q^{72} -2.43845 q^{73} -9.80776 q^{74} +7.68466 q^{75} +7.68466 q^{76} -2.56155 q^{77} +1.43845 q^{79} -3.56155 q^{80} +1.00000 q^{81} +4.12311 q^{82} -10.2462 q^{83} -1.00000 q^{84} +17.8078 q^{85} -2.87689 q^{86} -1.00000 q^{87} +2.56155 q^{88} -9.68466 q^{89} -3.56155 q^{90} -9.12311 q^{92} +5.12311 q^{93} -7.68466 q^{94} -27.3693 q^{95} +1.00000 q^{96} +12.2462 q^{97} +1.00000 q^{98} +2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + q^{11} + 2 q^{12} - 2 q^{14} - 3 q^{15} + 2 q^{16} - 10 q^{17} + 2 q^{18} + 3 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} - 10 q^{23} + 2 q^{24} + 3 q^{25} + 2 q^{27} - 2 q^{28} - 2 q^{29} - 3 q^{30} + 2 q^{31} + 2 q^{32} + q^{33} - 10 q^{34} + 3 q^{35} + 2 q^{36} + q^{37} + 3 q^{38} - 3 q^{40} - 2 q^{42} - 14 q^{43} + q^{44} - 3 q^{45} - 10 q^{46} - 3 q^{47} + 2 q^{48} + 2 q^{49} + 3 q^{50} - 10 q^{51} - 16 q^{53} + 2 q^{54} - 10 q^{55} - 2 q^{56} + 3 q^{57} - 2 q^{58} + 18 q^{59} - 3 q^{60} - 2 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + q^{66} - 6 q^{67} - 10 q^{68} - 10 q^{69} + 3 q^{70} - 8 q^{71} + 2 q^{72} - 9 q^{73} + q^{74} + 3 q^{75} + 3 q^{76} - q^{77} + 7 q^{79} - 3 q^{80} + 2 q^{81} - 4 q^{83} - 2 q^{84} + 15 q^{85} - 14 q^{86} - 2 q^{87} + q^{88} - 7 q^{89} - 3 q^{90} - 10 q^{92} + 2 q^{93} - 3 q^{94} - 30 q^{95} + 2 q^{96} + 8 q^{97} + 2 q^{98} + q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + q^11 + 2 * q^12 - 2 * q^14 - 3 * q^15 + 2 * q^16 - 10 * q^17 + 2 * q^18 + 3 * q^19 - 3 * q^20 - 2 * q^21 + q^22 - 10 * q^23 + 2 * q^24 + 3 * q^25 + 2 * q^27 - 2 * q^28 - 2 * q^29 - 3 * q^30 + 2 * q^31 + 2 * q^32 + q^33 - 10 * q^34 + 3 * q^35 + 2 * q^36 + q^37 + 3 * q^38 - 3 * q^40 - 2 * q^42 - 14 * q^43 + q^44 - 3 * q^45 - 10 * q^46 - 3 * q^47 + 2 * q^48 + 2 * q^49 + 3 * q^50 - 10 * q^51 - 16 * q^53 + 2 * q^54 - 10 * q^55 - 2 * q^56 + 3 * q^57 - 2 * q^58 + 18 * q^59 - 3 * q^60 - 2 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + q^66 - 6 * q^67 - 10 * q^68 - 10 * q^69 + 3 * q^70 - 8 * q^71 + 2 * q^72 - 9 * q^73 + q^74 + 3 * q^75 + 3 * q^76 - q^77 + 7 * q^79 - 3 * q^80 + 2 * q^81 - 4 * q^83 - 2 * q^84 + 15 * q^85 - 14 * q^86 - 2 * q^87 + q^88 - 7 * q^89 - 3 * q^90 - 10 * q^92 + 2 * q^93 - 3 * q^94 - 30 * q^95 + 2 * q^96 + 8 * q^97 + 2 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.56155	−1.59277	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−3.56155	−1.59277	−0.796387	+	0.604787i	$0.793258\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.56155	−1.12626
$11$	2.56155	0.772337	0.386169	−	0.922428i	$-0.373798\pi$
$11$	2.56155	0.772337	0.386169	+	0.922428i	$0.373798\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−3.56155	−0.919589
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	1.00000	0.235702
$19$	7.68466	1.76298	0.881491	−	0.472201i	$-0.156540\pi$
$19$	7.68466	1.76298	0.881491	+	0.472201i	$0.156540\pi$
$20$	−3.56155	−0.796387
$21$	−1.00000	−0.218218
$22$	2.56155	0.546125
$23$	−9.12311	−1.90230	−0.951150	−	0.308731i	$-0.900096\pi$
$23$	−9.12311	−1.90230	−0.951150	+	0.308731i	$0.900096\pi$
$24$	1.00000	0.204124
$25$	7.68466	1.53693
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−3.56155	−0.650248
$31$	5.12311	0.920137	0.460068	−	0.887883i	$-0.347825\pi$
$31$	5.12311	0.920137	0.460068	+	0.887883i	$0.347825\pi$
$32$	1.00000	0.176777
$33$	2.56155	0.445909
$34$	−5.00000	−0.857493
$35$	3.56155	0.602012
$36$	1.00000	0.166667
$37$	−9.80776	−1.61239	−0.806193	−	0.591652i	$-0.798476\pi$
$37$	−9.80776	−1.61239	−0.806193	+	0.591652i	$0.798476\pi$
$38$	7.68466	1.24662
$39$	0	0
$40$	−3.56155	−0.563131
$41$	4.12311	0.643921	0.321960	−	0.946753i	$-0.395658\pi$
$41$	4.12311	0.643921	0.321960	+	0.946753i	$0.395658\pi$
$42$	−1.00000	−0.154303
$43$	−2.87689	−0.438722	−0.219361	−	0.975644i	$-0.570397\pi$
$43$	−2.87689	−0.438722	−0.219361	+	0.975644i	$0.570397\pi$
$44$	2.56155	0.386169
$45$	−3.56155	−0.530925
$46$	−9.12311	−1.34513
$47$	−7.68466	−1.12092	−0.560461	−	0.828181i	$-0.689376\pi$
$47$	−7.68466	−1.12092	−0.560461	+	0.828181i	$0.689376\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	7.68466	1.08677
$51$	−5.00000	−0.700140
$52$	0	0
$53$	−3.87689	−0.532532	−0.266266	−	0.963900i	$-0.585790\pi$
$53$	−3.87689	−0.532532	−0.266266	+	0.963900i	$0.585790\pi$
$54$	1.00000	0.136083
$55$	−9.12311	−1.23016
$56$	−1.00000	−0.133631
$57$	7.68466	1.01786
$58$	−1.00000	−0.131306
$59$	13.1231	1.70848	0.854241	−	0.519877i	$-0.174022\pi$
$59$	13.1231	1.70848	0.854241	+	0.519877i	$0.174022\pi$
$60$	−3.56155	−0.459794
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	5.12311	0.650635
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	2.56155	0.315305
$67$	1.12311	0.137209	0.0686046	−	0.997644i	$-0.478145\pi$
$67$	1.12311	0.137209	0.0686046	+	0.997644i	$0.478145\pi$
$68$	−5.00000	−0.606339
$69$	−9.12311	−1.09829
$70$	3.56155	0.425687
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	1.00000	0.117851
$73$	−2.43845	−0.285399	−0.142699	−	0.989766i	$-0.545578\pi$
$73$	−2.43845	−0.285399	−0.142699	+	0.989766i	$0.545578\pi$
$74$	−9.80776	−1.14013
$75$	7.68466	0.887348
$76$	7.68466	0.881491
$77$	−2.56155	−0.291916
$78$	0	0
$79$	1.43845	0.161838	0.0809190	−	0.996721i	$-0.474214\pi$
$79$	1.43845	0.161838	0.0809190	+	0.996721i	$0.474214\pi$
$80$	−3.56155	−0.398194
$81$	1.00000	0.111111
$82$	4.12311	0.455321
$83$	−10.2462	−1.12467	−0.562334	−	0.826910i	$-0.690096\pi$
$83$	−10.2462	−1.12467	−0.562334	+	0.826910i	$0.690096\pi$
$84$	−1.00000	−0.109109
$85$	17.8078	1.93152
$86$	−2.87689	−0.310223
$87$	−1.00000	−0.107211
$88$	2.56155	0.273062
$89$	−9.68466	−1.02657	−0.513286	−	0.858218i	$-0.671572\pi$
$89$	−9.68466	−1.02657	−0.513286	+	0.858218i	$0.671572\pi$
$90$	−3.56155	−0.375421
$91$	0	0
$92$	−9.12311	−0.951150
$93$	5.12311	0.531241
$94$	−7.68466	−0.792612
$95$	−27.3693	−2.80803
$96$	1.00000	0.102062
$97$	12.2462	1.24341	0.621707	−	0.783250i	$-0.286439\pi$
$97$	12.2462	1.24341	0.621707	+	0.783250i	$0.286439\pi$
$98$	1.00000	0.101015
$99$	2.56155	0.257446
$100$	7.68466	0.768466
$101$	−19.5616	−1.94645	−0.973224	−	0.229860i	$-0.926173\pi$
$101$	−19.5616	−1.94645	−0.973224	+	0.229860i	$0.926173\pi$
$102$	−5.00000	−0.495074
$103$	−11.3693	−1.12025	−0.560126	−	0.828407i	$-0.689247\pi$
$103$	−11.3693	−1.12025	−0.560126	+	0.828407i	$0.689247\pi$
$104$	0	0
$105$	3.56155	0.347572
$106$	−3.87689	−0.376557
$107$	−9.43845	−0.912449	−0.456225	−	0.889865i	$-0.650799\pi$
$107$	−9.43845	−0.912449	−0.456225	+	0.889865i	$0.650799\pi$
$108$	1.00000	0.0962250
$109$	0.876894	0.0839912	0.0419956	−	0.999118i	$-0.486628\pi$
$109$	0.876894	0.0839912	0.0419956	+	0.999118i	$0.486628\pi$
$110$	−9.12311	−0.869854
$111$	−9.80776	−0.930912
$112$	−1.00000	−0.0944911
$113$	16.9309	1.59272	0.796361	−	0.604821i	$-0.206756\pi$
$113$	16.9309	1.59272	0.796361	+	0.604821i	$0.206756\pi$
$114$	7.68466	0.719734
$115$	32.4924	3.02993
$116$	−1.00000	−0.0928477
$117$	0	0
$118$	13.1231	1.20808
$119$	5.00000	0.458349
$120$	−3.56155	−0.325124
$121$	−4.43845	−0.403495
$122$	−1.00000	−0.0905357
$123$	4.12311	0.371768
$124$	5.12311	0.460068
$125$	−9.56155	−0.855211
$126$	−1.00000	−0.0890871
$127$	2.24621	0.199319	0.0996595	−	0.995022i	$-0.468225\pi$
$127$	2.24621	0.199319	0.0996595	+	0.995022i	$0.468225\pi$
$128$	1.00000	0.0883883
$129$	−2.87689	−0.253296
$130$	0	0
$131$	−16.4924	−1.44095	−0.720475	−	0.693481i	$-0.756076\pi$
$131$	−16.4924	−1.44095	−0.720475	+	0.693481i	$0.756076\pi$
$132$	2.56155	0.222955
$133$	−7.68466	−0.666344
$134$	1.12311	0.0970215
$135$	−3.56155	−0.306530
$136$	−5.00000	−0.428746
$137$	−5.80776	−0.496191	−0.248095	−	0.968736i	$-0.579805\pi$
$137$	−5.80776	−0.496191	−0.248095	+	0.968736i	$0.579805\pi$
$138$	−9.12311	−0.776610
$139$	−7.68466	−0.651804	−0.325902	−	0.945404i	$-0.605668\pi$
$139$	−7.68466	−0.651804	−0.325902	+	0.945404i	$0.605668\pi$
$140$	3.56155	0.301006
$141$	−7.68466	−0.647165
$142$	−4.00000	−0.335673
$143$	0	0
$144$	1.00000	0.0833333
$145$	3.56155	0.295771
$146$	−2.43845	−0.201807
$147$	1.00000	0.0824786
$148$	−9.80776	−0.806193
$149$	−17.8078	−1.45887	−0.729434	−	0.684051i	$-0.760217\pi$
$149$	−17.8078	−1.45887	−0.729434	+	0.684051i	$0.760217\pi$
$150$	7.68466	0.627450
$151$	−17.4384	−1.41912	−0.709560	−	0.704645i	$-0.751106\pi$
$151$	−17.4384	−1.41912	−0.709560	+	0.704645i	$0.751106\pi$
$152$	7.68466	0.623308
$153$	−5.00000	−0.404226
$154$	−2.56155	−0.206416
$155$	−18.2462	−1.46557
$156$	0	0
$157$	−5.80776	−0.463510	−0.231755	−	0.972774i	$-0.574447\pi$
$157$	−5.80776	−0.463510	−0.231755	+	0.972774i	$0.574447\pi$
$158$	1.43845	0.114437
$159$	−3.87689	−0.307458
$160$	−3.56155	−0.281565
$161$	9.12311	0.719001
$162$	1.00000	0.0785674
$163$	−1.12311	−0.0879684	−0.0439842	−	0.999032i	$-0.514005\pi$
$163$	−1.12311	−0.0879684	−0.0439842	+	0.999032i	$0.514005\pi$
$164$	4.12311	0.321960
$165$	−9.12311	−0.710233
$166$	−10.2462	−0.795260
$167$	20.4924	1.58575	0.792876	−	0.609383i	$-0.208583\pi$
$167$	20.4924	1.58575	0.792876	+	0.609383i	$0.208583\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	17.8078	1.36579
$171$	7.68466	0.587661
$172$	−2.87689	−0.219361
$173$	−4.87689	−0.370783	−0.185392	−	0.982665i	$-0.559355\pi$
$173$	−4.87689	−0.370783	−0.185392	+	0.982665i	$0.559355\pi$
$174$	−1.00000	−0.0758098
$175$	−7.68466	−0.580906
$176$	2.56155	0.193084
$177$	13.1231	0.986393
$178$	−9.68466	−0.725896
$179$	−16.4924	−1.23270	−0.616351	−	0.787472i	$-0.711390\pi$
$179$	−16.4924	−1.23270	−0.616351	+	0.787472i	$0.711390\pi$
$180$	−3.56155	−0.265462
$181$	13.2462	0.984583	0.492292	−	0.870430i	$-0.336159\pi$
$181$	13.2462	0.984583	0.492292	+	0.870430i	$0.336159\pi$
$182$	0	0
$183$	−1.00000	−0.0739221
$184$	−9.12311	−0.672564
$185$	34.9309	2.56817
$186$	5.12311	0.375644
$187$	−12.8078	−0.936596
$188$	−7.68466	−0.560461
$189$	−1.00000	−0.0727393
$190$	−27.3693	−1.98558
$191$	5.75379	0.416330	0.208165	−	0.978094i	$-0.433251\pi$
$191$	5.75379	0.416330	0.208165	+	0.978094i	$0.433251\pi$
$192$	1.00000	0.0721688
$193$	−20.3693	−1.46622	−0.733108	−	0.680113i	$-0.761931\pi$
$193$	−20.3693	−1.46622	−0.733108	+	0.680113i	$0.761931\pi$
$194$	12.2462	0.879227
$195$	0	0
$196$	1.00000	0.0714286
$197$	−0.561553	−0.0400090	−0.0200045	−	0.999800i	$-0.506368\pi$
$197$	−0.561553	−0.0400090	−0.0200045	+	0.999800i	$0.506368\pi$
$198$	2.56155	0.182042
$199$	−17.6155	−1.24873	−0.624366	−	0.781132i	$-0.714643\pi$
$199$	−17.6155	−1.24873	−0.624366	+	0.781132i	$0.714643\pi$
$200$	7.68466	0.543387
$201$	1.12311	0.0792178
$202$	−19.5616	−1.37635
$203$	1.00000	0.0701862
$204$	−5.00000	−0.350070
$205$	−14.6847	−1.02562
$206$	−11.3693	−0.792138
$207$	−9.12311	−0.634100
$208$	0	0
$209$	19.6847	1.36162
$210$	3.56155	0.245770
$211$	−2.87689	−0.198054	−0.0990268	−	0.995085i	$-0.531573\pi$
$211$	−2.87689	−0.198054	−0.0990268	+	0.995085i	$0.531573\pi$
$212$	−3.87689	−0.266266
$213$	−4.00000	−0.274075
$214$	−9.43845	−0.645199
$215$	10.2462	0.698786
$216$	1.00000	0.0680414
$217$	−5.12311	−0.347779
$218$	0.876894	0.0593908
$219$	−2.43845	−0.164775
$220$	−9.12311	−0.615080
$221$	0	0
$222$	−9.80776	−0.658254
$223$	−16.4924	−1.10441	−0.552207	−	0.833707i	$-0.686214\pi$
$223$	−16.4924	−1.10441	−0.552207	+	0.833707i	$0.686214\pi$
$224$	−1.00000	−0.0668153
$225$	7.68466	0.512311
$226$	16.9309	1.12622
$227$	13.1231	0.871011	0.435506	−	0.900186i	$-0.356570\pi$
$227$	13.1231	0.871011	0.435506	+	0.900186i	$0.356570\pi$
$228$	7.68466	0.508929
$229$	22.8078	1.50718	0.753590	−	0.657345i	$-0.228321\pi$
$229$	22.8078	1.50718	0.753590	+	0.657345i	$0.228321\pi$
$230$	32.4924	2.14249
$231$	−2.56155	−0.168538
$232$	−1.00000	−0.0656532
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	27.3693	1.78538
$236$	13.1231	0.854241
$237$	1.43845	0.0934372
$238$	5.00000	0.324102
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	−3.56155	−0.229897
$241$	11.3153	0.728885	0.364443	−	0.931226i	$-0.381260\pi$
$241$	11.3153	0.728885	0.364443	+	0.931226i	$0.381260\pi$
$242$	−4.43845	−0.285314
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−3.56155	−0.227539
$246$	4.12311	0.262880
$247$	0	0
$248$	5.12311	0.325318
$249$	−10.2462	−0.649327
$250$	−9.56155	−0.604726
$251$	8.49242	0.536037	0.268018	−	0.963414i	$-0.413631\pi$
$251$	8.49242	0.536037	0.268018	+	0.963414i	$0.413631\pi$
$252$	−1.00000	−0.0629941
$253$	−23.3693	−1.46922
$254$	2.24621	0.140940
$255$	17.8078	1.11517
$256$	1.00000	0.0625000
$257$	−14.7538	−0.920316	−0.460158	−	0.887837i	$-0.652207\pi$
$257$	−14.7538	−0.920316	−0.460158	+	0.887837i	$0.652207\pi$
$258$	−2.87689	−0.179108
$259$	9.80776	0.609425
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	−16.4924	−1.01891
$263$	−20.4924	−1.26362	−0.631808	−	0.775125i	$-0.717687\pi$
$263$	−20.4924	−1.26362	−0.631808	+	0.775125i	$0.717687\pi$
$264$	2.56155	0.157653
$265$	13.8078	0.848204
$266$	−7.68466	−0.471177
$267$	−9.68466	−0.592691
$268$	1.12311	0.0686046
$269$	−4.87689	−0.297349	−0.148675	−	0.988886i	$-0.547501\pi$
$269$	−4.87689	−0.297349	−0.148675	+	0.988886i	$0.547501\pi$
$270$	−3.56155	−0.216749
$271$	13.1231	0.797172	0.398586	−	0.917131i	$-0.369501\pi$
$271$	13.1231	0.797172	0.398586	+	0.917131i	$0.369501\pi$
$272$	−5.00000	−0.303170
$273$	0	0
$274$	−5.80776	−0.350860
$275$	19.6847	1.18703
$276$	−9.12311	−0.549146
$277$	−3.56155	−0.213993	−0.106996	−	0.994259i	$-0.534123\pi$
$277$	−3.56155	−0.213993	−0.106996	+	0.994259i	$0.534123\pi$
$278$	−7.68466	−0.460895
$279$	5.12311	0.306712
$280$	3.56155	0.212843
$281$	7.80776	0.465772	0.232886	−	0.972504i	$-0.425183\pi$
$281$	7.80776	0.465772	0.232886	+	0.972504i	$0.425183\pi$
$282$	−7.68466	−0.457615
$283$	8.49242	0.504822	0.252411	−	0.967620i	$-0.418776\pi$
$283$	8.49242	0.504822	0.252411	+	0.967620i	$0.418776\pi$
$284$	−4.00000	−0.237356
$285$	−27.3693	−1.62122
$286$	0	0
$287$	−4.12311	−0.243379
$288$	1.00000	0.0589256
$289$	8.00000	0.470588
$290$	3.56155	0.209142
$291$	12.2462	0.717886
$292$	−2.43845	−0.142699
$293$	−4.68466	−0.273681	−0.136840	−	0.990593i	$-0.543695\pi$
$293$	−4.68466	−0.273681	−0.136840	+	0.990593i	$0.543695\pi$
$294$	1.00000	0.0583212
$295$	−46.7386	−2.72123
$296$	−9.80776	−0.570065
$297$	2.56155	0.148636
$298$	−17.8078	−1.03158
$299$	0	0
$300$	7.68466	0.443674
$301$	2.87689	0.165821
$302$	−17.4384	−1.00347
$303$	−19.5616	−1.12378
$304$	7.68466	0.440745
$305$	3.56155	0.203934
$306$	−5.00000	−0.285831
$307$	−33.9309	−1.93654	−0.968269	−	0.249912i	$-0.919598\pi$
$307$	−33.9309	−1.93654	−0.968269	+	0.249912i	$0.919598\pi$
$308$	−2.56155	−0.145958
$309$	−11.3693	−0.646778
$310$	−18.2462	−1.03632
$311$	22.5616	1.27935	0.639674	−	0.768646i	$-0.279069\pi$
$311$	22.5616	1.27935	0.639674	+	0.768646i	$0.279069\pi$
$312$	0	0
$313$	27.6155	1.56092	0.780461	−	0.625205i	$-0.214984\pi$
$313$	27.6155	1.56092	0.780461	+	0.625205i	$0.214984\pi$
$314$	−5.80776	−0.327751
$315$	3.56155	0.200671
$316$	1.43845	0.0809190
$317$	−11.5616	−0.649362	−0.324681	−	0.945824i	$-0.605257\pi$
$317$	−11.5616	−0.649362	−0.324681	+	0.945824i	$0.605257\pi$
$318$	−3.87689	−0.217405
$319$	−2.56155	−0.143419
$320$	−3.56155	−0.199097
$321$	−9.43845	−0.526803
$322$	9.12311	0.508411
$323$	−38.4233	−2.13793
$324$	1.00000	0.0555556
$325$	0	0
$326$	−1.12311	−0.0622031
$327$	0.876894	0.0484924
$328$	4.12311	0.227660
$329$	7.68466	0.423669
$330$	−9.12311	−0.502210
$331$	−35.3693	−1.94407	−0.972037	−	0.234829i	$-0.924547\pi$
$331$	−35.3693	−1.94407	−0.972037	+	0.234829i	$0.924547\pi$
$332$	−10.2462	−0.562334
$333$	−9.80776	−0.537462
$334$	20.4924	1.12130
$335$	−4.00000	−0.218543
$336$	−1.00000	−0.0545545
$337$	−29.4924	−1.60655	−0.803277	−	0.595605i	$-0.796912\pi$
$337$	−29.4924	−1.60655	−0.803277	+	0.595605i	$0.796912\pi$
$338$	0	0
$339$	16.9309	0.919559
$340$	17.8078	0.965762
$341$	13.1231	0.710656
$342$	7.68466	0.415539
$343$	−1.00000	−0.0539949
$344$	−2.87689	−0.155112
$345$	32.4924	1.74933
$346$	−4.87689	−0.262183
$347$	−0.315342	−0.0169284	−0.00846421	−	0.999964i	$-0.502694\pi$
$347$	−0.315342	−0.0169284	−0.00846421	+	0.999964i	$0.502694\pi$
$348$	−1.00000	−0.0536056
$349$	−6.49242	−0.347531	−0.173766	−	0.984787i	$-0.555594\pi$
$349$	−6.49242	−0.347531	−0.173766	+	0.984787i	$0.555594\pi$
$350$	−7.68466	−0.410762
$351$	0	0
$352$	2.56155	0.136531
$353$	−9.80776	−0.522015	−0.261007	−	0.965337i	$-0.584055\pi$
$353$	−9.80776	−0.522015	−0.261007	+	0.965337i	$0.584055\pi$
$354$	13.1231	0.697485
$355$	14.2462	0.756110
$356$	−9.68466	−0.513286
$357$	5.00000	0.264628
$358$	−16.4924	−0.871652
$359$	−4.63068	−0.244398	−0.122199	−	0.992506i	$-0.538995\pi$
$359$	−4.63068	−0.244398	−0.122199	+	0.992506i	$0.538995\pi$
$360$	−3.56155	−0.187710
$361$	40.0540	2.10810
$362$	13.2462	0.696205
$363$	−4.43845	−0.232958
$364$	0	0
$365$	8.68466	0.454576
$366$	−1.00000	−0.0522708
$367$	11.3693	0.593474	0.296737	−	0.954959i	$-0.404102\pi$
$367$	11.3693	0.593474	0.296737	+	0.954959i	$0.404102\pi$
$368$	−9.12311	−0.475575
$369$	4.12311	0.214640
$370$	34.9309	1.81597
$371$	3.87689	0.201278
$372$	5.12311	0.265621
$373$	21.5616	1.11641	0.558207	−	0.829701i	$-0.311489\pi$
$373$	21.5616	1.11641	0.558207	+	0.829701i	$0.311489\pi$
$374$	−12.8078	−0.662274
$375$	−9.56155	−0.493756
$376$	−7.68466	−0.396306
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	0.492423	0.0252940	0.0126470	−	0.999920i	$-0.495974\pi$
$379$	0.492423	0.0252940	0.0126470	+	0.999920i	$0.495974\pi$
$380$	−27.3693	−1.40402
$381$	2.24621	0.115077
$382$	5.75379	0.294389
$383$	8.31534	0.424894	0.212447	−	0.977173i	$-0.431857\pi$
$383$	8.31534	0.424894	0.212447	+	0.977173i	$0.431857\pi$
$384$	1.00000	0.0510310
$385$	9.12311	0.464957
$386$	−20.3693	−1.03677
$387$	−2.87689	−0.146241
$388$	12.2462	0.621707
$389$	18.6847	0.947350	0.473675	−	0.880700i	$-0.342927\pi$
$389$	18.6847	0.947350	0.473675	+	0.880700i	$0.342927\pi$
$390$	0	0
$391$	45.6155	2.30688
$392$	1.00000	0.0505076
$393$	−16.4924	−0.831933
$394$	−0.561553	−0.0282906
$395$	−5.12311	−0.257771
$396$	2.56155	0.128723
$397$	1.68466	0.0845506	0.0422753	−	0.999106i	$-0.486539\pi$
$397$	1.68466	0.0845506	0.0422753	+	0.999106i	$0.486539\pi$
$398$	−17.6155	−0.882987
$399$	−7.68466	−0.384714
$400$	7.68466	0.384233
$401$	15.1771	0.757907	0.378954	−	0.925416i	$-0.376284\pi$
$401$	15.1771	0.757907	0.378954	+	0.925416i	$0.376284\pi$
$402$	1.12311	0.0560154
$403$	0	0
$404$	−19.5616	−0.973224
$405$	−3.56155	−0.176975
$406$	1.00000	0.0496292
$407$	−25.1231	−1.24531
$408$	−5.00000	−0.247537
$409$	−30.4384	−1.50508	−0.752542	−	0.658544i	$-0.771173\pi$
$409$	−30.4384	−1.50508	−0.752542	+	0.658544i	$0.771173\pi$
$410$	−14.6847	−0.725224
$411$	−5.80776	−0.286476
$412$	−11.3693	−0.560126
$413$	−13.1231	−0.645746
$414$	−9.12311	−0.448376
$415$	36.4924	1.79134
$416$	0	0
$417$	−7.68466	−0.376319
$418$	19.6847	0.962808
$419$	22.7386	1.11085	0.555427	−	0.831565i	$-0.312555\pi$
$419$	22.7386	1.11085	0.555427	+	0.831565i	$0.312555\pi$
$420$	3.56155	0.173786
$421$	8.43845	0.411265	0.205632	−	0.978629i	$-0.434075\pi$
$421$	8.43845	0.411265	0.205632	+	0.978629i	$0.434075\pi$
$422$	−2.87689	−0.140045
$423$	−7.68466	−0.373641
$424$	−3.87689	−0.188279
$425$	−38.4233	−1.86380
$426$	−4.00000	−0.193801
$427$	1.00000	0.0483934
$428$	−9.43845	−0.456225
$429$	0	0
$430$	10.2462	0.494116
$431$	−18.7386	−0.902608	−0.451304	−	0.892370i	$-0.649041\pi$
$431$	−18.7386	−0.902608	−0.451304	+	0.892370i	$0.649041\pi$
$432$	1.00000	0.0481125
$433$	−5.31534	−0.255439	−0.127720	−	0.991810i	$-0.540766\pi$
$433$	−5.31534	−0.255439	−0.127720	+	0.991810i	$0.540766\pi$
$434$	−5.12311	−0.245917
$435$	3.56155	0.170763
$436$	0.876894	0.0419956
$437$	−70.1080	−3.35372
$438$	−2.43845	−0.116514
$439$	−28.4924	−1.35987	−0.679935	−	0.733273i	$-0.737992\pi$
$439$	−28.4924	−1.35987	−0.679935	+	0.733273i	$0.737992\pi$
$440$	−9.12311	−0.434927
$441$	1.00000	0.0476190
$442$	0	0
$443$	−34.4233	−1.63550	−0.817750	−	0.575574i	$-0.804779\pi$
$443$	−34.4233	−1.63550	−0.817750	+	0.575574i	$0.804779\pi$
$444$	−9.80776	−0.465456
$445$	34.4924	1.63510
$446$	−16.4924	−0.780939
$447$	−17.8078	−0.842278
$448$	−1.00000	−0.0472456
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	7.68466	0.362258
$451$	10.5616	0.497324
$452$	16.9309	0.796361
$453$	−17.4384	−0.819330
$454$	13.1231	0.615898
$455$	0	0
$456$	7.68466	0.359867
$457$	−13.3153	−0.622865	−0.311433	−	0.950268i	$-0.600809\pi$
$457$	−13.3153	−0.622865	−0.311433	+	0.950268i	$0.600809\pi$
$458$	22.8078	1.06574
$459$	−5.00000	−0.233380
$460$	32.4924	1.51497
$461$	30.0540	1.39975	0.699877	−	0.714264i	$-0.253238\pi$
$461$	30.0540	1.39975	0.699877	+	0.714264i	$0.253238\pi$
$462$	−2.56155	−0.119174
$463$	−11.6847	−0.543032	−0.271516	−	0.962434i	$-0.587525\pi$
$463$	−11.6847	−0.543032	−0.271516	+	0.962434i	$0.587525\pi$
$464$	−1.00000	−0.0464238
$465$	−18.2462	−0.846148
$466$	−6.00000	−0.277945
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	−1.12311	−0.0518602
$470$	27.3693	1.26245
$471$	−5.80776	−0.267608
$472$	13.1231	0.604040
$473$	−7.36932	−0.338842
$474$	1.43845	0.0660701
$475$	59.0540	2.70958
$476$	5.00000	0.229175
$477$	−3.87689	−0.177511
$478$	4.00000	0.182956
$479$	−2.56155	−0.117040	−0.0585202	−	0.998286i	$-0.518638\pi$
$479$	−2.56155	−0.117040	−0.0585202	+	0.998286i	$0.518638\pi$
$480$	−3.56155	−0.162562
$481$	0	0
$482$	11.3153	0.515400
$483$	9.12311	0.415116
$484$	−4.43845	−0.201748
$485$	−43.6155	−1.98048
$486$	1.00000	0.0453609
$487$	23.6847	1.07325	0.536627	−	0.843819i	$-0.319698\pi$
$487$	23.6847	1.07325	0.536627	+	0.843819i	$0.319698\pi$
$488$	−1.00000	−0.0452679
$489$	−1.12311	−0.0507886
$490$	−3.56155	−0.160895
$491$	−1.75379	−0.0791474	−0.0395737	−	0.999217i	$-0.512600\pi$
$491$	−1.75379	−0.0791474	−0.0395737	+	0.999217i	$0.512600\pi$
$492$	4.12311	0.185884
$493$	5.00000	0.225189
$494$	0	0
$495$	−9.12311	−0.410053
$496$	5.12311	0.230034
$497$	4.00000	0.179425
$498$	−10.2462	−0.459144
$499$	−27.3693	−1.22522	−0.612609	−	0.790386i	$-0.709880\pi$
$499$	−27.3693	−1.22522	−0.612609	+	0.790386i	$0.709880\pi$
$500$	−9.56155	−0.427606
$501$	20.4924	0.915534
$502$	8.49242	0.379035
$503$	20.4924	0.913712	0.456856	−	0.889541i	$-0.348975\pi$
$503$	20.4924	0.913712	0.456856	+	0.889541i	$0.348975\pi$
$504$	−1.00000	−0.0445435
$505$	69.6695	3.10025
$506$	−23.3693	−1.03889
$507$	0	0
$508$	2.24621	0.0996595
$509$	27.3153	1.21073	0.605366	−	0.795948i	$-0.293027\pi$
$509$	27.3153	1.21073	0.605366	+	0.795948i	$0.293027\pi$
$510$	17.8078	0.788541
$511$	2.43845	0.107871
$512$	1.00000	0.0441942
$513$	7.68466	0.339286
$514$	−14.7538	−0.650762
$515$	40.4924	1.78431
$516$	−2.87689	−0.126648
$517$	−19.6847	−0.865730
$518$	9.80776	0.430928
$519$	−4.87689	−0.214072
$520$	0	0
$521$	−17.0000	−0.744784	−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000	−0.744784	−0.372392	+	0.928076i	$0.621462\pi$
$522$	−1.00000	−0.0437688
$523$	15.1922	0.664310	0.332155	−	0.943225i	$-0.392224\pi$
$523$	15.1922	0.664310	0.332155	+	0.943225i	$0.392224\pi$
$524$	−16.4924	−0.720475
$525$	−7.68466	−0.335386
$526$	−20.4924	−0.893512
$527$	−25.6155	−1.11583
$528$	2.56155	0.111477
$529$	60.2311	2.61874
$530$	13.8078	0.599771
$531$	13.1231	0.569494
$532$	−7.68466	−0.333172
$533$	0	0
$534$	−9.68466	−0.419096
$535$	33.6155	1.45333
$536$	1.12311	0.0485108
$537$	−16.4924	−0.711701
$538$	−4.87689	−0.210258
$539$	2.56155	0.110334
$540$	−3.56155	−0.153265
$541$	1.56155	0.0671364	0.0335682	−	0.999436i	$-0.489313\pi$
$541$	1.56155	0.0671364	0.0335682	+	0.999436i	$0.489313\pi$
$542$	13.1231	0.563686
$543$	13.2462	0.568449
$544$	−5.00000	−0.214373
$545$	−3.12311	−0.133779
$546$	0	0
$547$	−22.7386	−0.972234	−0.486117	−	0.873894i	$-0.661587\pi$
$547$	−22.7386	−0.972234	−0.486117	+	0.873894i	$0.661587\pi$
$548$	−5.80776	−0.248095
$549$	−1.00000	−0.0426790
$550$	19.6847	0.839357
$551$	−7.68466	−0.327377
$552$	−9.12311	−0.388305
$553$	−1.43845	−0.0611690
$554$	−3.56155	−0.151316
$555$	34.9309	1.48273
$556$	−7.68466	−0.325902
$557$	21.7386	0.921095	0.460548	−	0.887635i	$-0.347653\pi$
$557$	21.7386	0.921095	0.460548	+	0.887635i	$0.347653\pi$
$558$	5.12311	0.216878
$559$	0	0
$560$	3.56155	0.150503
$561$	−12.8078	−0.540744
$562$	7.80776	0.329351
$563$	−0.630683	−0.0265801	−0.0132901	−	0.999912i	$-0.504230\pi$
$563$	−0.630683	−0.0265801	−0.0132901	+	0.999912i	$0.504230\pi$
$564$	−7.68466	−0.323582
$565$	−60.3002	−2.53685
$566$	8.49242	0.356963
$567$	−1.00000	−0.0419961
$568$	−4.00000	−0.167836
$569$	11.6155	0.486948	0.243474	−	0.969907i	$-0.421713\pi$
$569$	11.6155	0.486948	0.243474	+	0.969907i	$0.421713\pi$
$570$	−27.3693	−1.14637
$571$	13.7538	0.575578	0.287789	−	0.957694i	$-0.407080\pi$
$571$	13.7538	0.575578	0.287789	+	0.957694i	$0.407080\pi$
$572$	0	0
$573$	5.75379	0.240368
$574$	−4.12311	−0.172095
$575$	−70.1080	−2.92370
$576$	1.00000	0.0416667
$577$	31.3153	1.30367	0.651837	−	0.758359i	$-0.273998\pi$
$577$	31.3153	1.30367	0.651837	+	0.758359i	$0.273998\pi$
$578$	8.00000	0.332756
$579$	−20.3693	−0.846520
$580$	3.56155	0.147885
$581$	10.2462	0.425084
$582$	12.2462	0.507622
$583$	−9.93087	−0.411295
$584$	−2.43845	−0.100904
$585$	0	0
$586$	−4.68466	−0.193521
$587$	31.3693	1.29475	0.647375	−	0.762172i	$-0.275867\pi$
$587$	31.3693	1.29475	0.647375	+	0.762172i	$0.275867\pi$
$588$	1.00000	0.0412393
$589$	39.3693	1.62218
$590$	−46.7386	−1.92420
$591$	−0.561553	−0.0230992
$592$	−9.80776	−0.403097
$593$	32.6155	1.33936	0.669680	−	0.742650i	$-0.266431\pi$
$593$	32.6155	1.33936	0.669680	+	0.742650i	$0.266431\pi$
$594$	2.56155	0.105102
$595$	−17.8078	−0.730047
$596$	−17.8078	−0.729434
$597$	−17.6155	−0.720956
$598$	0	0
$599$	−22.8769	−0.934725	−0.467362	−	0.884066i	$-0.654796\pi$
$599$	−22.8769	−0.934725	−0.467362	+	0.884066i	$0.654796\pi$
$600$	7.68466	0.313725
$601$	36.9309	1.50644	0.753221	−	0.657768i	$-0.228499\pi$
$601$	36.9309	1.50644	0.753221	+	0.657768i	$0.228499\pi$
$602$	2.87689	0.117253
$603$	1.12311	0.0457364
$604$	−17.4384	−0.709560
$605$	15.8078	0.642677
$606$	−19.5616	−0.794634
$607$	21.1231	0.857360	0.428680	−	0.903456i	$-0.358979\pi$
$607$	21.1231	0.857360	0.428680	+	0.903456i	$0.358979\pi$
$608$	7.68466	0.311654
$609$	1.00000	0.0405220
$610$	3.56155	0.144203
$611$	0	0
$612$	−5.00000	−0.202113
$613$	36.3002	1.46615	0.733075	−	0.680147i	$-0.238084\pi$
$613$	36.3002	1.46615	0.733075	+	0.680147i	$0.238084\pi$
$614$	−33.9309	−1.36934
$615$	−14.6847	−0.592143
$616$	−2.56155	−0.103208
$617$	−27.4233	−1.10402	−0.552010	−	0.833837i	$-0.686139\pi$
$617$	−27.4233	−1.10402	−0.552010	+	0.833837i	$0.686139\pi$
$618$	−11.3693	−0.457341
$619$	4.31534	0.173448	0.0867241	−	0.996232i	$-0.472360\pi$
$619$	4.31534	0.173448	0.0867241	+	0.996232i	$0.472360\pi$
$620$	−18.2462	−0.732785
$621$	−9.12311	−0.366098
$622$	22.5616	0.904636
$623$	9.68466	0.388008
$624$	0	0
$625$	−4.36932	−0.174773
$626$	27.6155	1.10374
$627$	19.6847	0.786130
$628$	−5.80776	−0.231755
$629$	49.0388	1.95531
$630$	3.56155	0.141896
$631$	23.1922	0.923268	0.461634	−	0.887070i	$-0.347263\pi$
$631$	23.1922	0.923268	0.461634	+	0.887070i	$0.347263\pi$
$632$	1.43845	0.0572184
$633$	−2.87689	−0.114346
$634$	−11.5616	−0.459168
$635$	−8.00000	−0.317470
$636$	−3.87689	−0.153729
$637$	0	0
$638$	−2.56155	−0.101413
$639$	−4.00000	−0.158238
$640$	−3.56155	−0.140783
$641$	36.9309	1.45868	0.729341	−	0.684151i	$-0.239827\pi$
$641$	36.9309	1.45868	0.729341	+	0.684151i	$0.239827\pi$
$642$	−9.43845	−0.372506
$643$	−26.5616	−1.04749	−0.523743	−	0.851877i	$-0.675465\pi$
$643$	−26.5616	−1.04749	−0.523743	+	0.851877i	$0.675465\pi$
$644$	9.12311	0.359501
$645$	10.2462	0.403444
$646$	−38.4233	−1.51174
$647$	−20.8078	−0.818038	−0.409019	−	0.912526i	$-0.634129\pi$
$647$	−20.8078	−0.818038	−0.409019	+	0.912526i	$0.634129\pi$
$648$	1.00000	0.0392837
$649$	33.6155	1.31952
$650$	0	0
$651$	−5.12311	−0.200790
$652$	−1.12311	−0.0439842
$653$	−18.8078	−0.736005	−0.368002	−	0.929825i	$-0.619958\pi$
$653$	−18.8078	−0.736005	−0.368002	+	0.929825i	$0.619958\pi$
$654$	0.876894	0.0342893
$655$	58.7386	2.29511
$656$	4.12311	0.160980
$657$	−2.43845	−0.0951329
$658$	7.68466	0.299579
$659$	−28.3153	−1.10301	−0.551505	−	0.834172i	$-0.685946\pi$
$659$	−28.3153	−1.10301	−0.551505	+	0.834172i	$0.685946\pi$
$660$	−9.12311	−0.355116
$661$	−9.80776	−0.381478	−0.190739	−	0.981641i	$-0.561088\pi$
$661$	−9.80776	−0.381478	−0.190739	+	0.981641i	$0.561088\pi$
$662$	−35.3693	−1.37467
$663$	0	0
$664$	−10.2462	−0.397630
$665$	27.3693	1.06134
$666$	−9.80776	−0.380043
$667$	9.12311	0.353248
$668$	20.4924	0.792876
$669$	−16.4924	−0.637634
$670$	−4.00000	−0.154533
$671$	−2.56155	−0.0988876
$672$	−1.00000	−0.0385758
$673$	8.75379	0.337434	0.168717	−	0.985665i	$-0.446038\pi$
$673$	8.75379	0.337434	0.168717	+	0.985665i	$0.446038\pi$
$674$	−29.4924	−1.13601
$675$	7.68466	0.295783
$676$	0	0
$677$	−8.38447	−0.322241	−0.161121	−	0.986935i	$-0.551511\pi$
$677$	−8.38447	−0.322241	−0.161121	+	0.986935i	$0.551511\pi$
$678$	16.9309	0.650226
$679$	−12.2462	−0.469966
$680$	17.8078	0.682897
$681$	13.1231	0.502879
$682$	13.1231	0.502510
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	7.68466	0.293830
$685$	20.6847	0.790320
$686$	−1.00000	−0.0381802
$687$	22.8078	0.870170
$688$	−2.87689	−0.109681
$689$	0	0
$690$	32.4924	1.23697
$691$	−28.4924	−1.08390	−0.541951	−	0.840410i	$-0.682314\pi$
$691$	−28.4924	−1.08390	−0.541951	+	0.840410i	$0.682314\pi$
$692$	−4.87689	−0.185392
$693$	−2.56155	−0.0973053
$694$	−0.315342	−0.0119702
$695$	27.3693	1.03818
$696$	−1.00000	−0.0379049
$697$	−20.6155	−0.780869
$698$	−6.49242	−0.245742
$699$	−6.00000	−0.226941
$700$	−7.68466	−0.290453
$701$	9.05398	0.341964	0.170982	−	0.985274i	$-0.445306\pi$
$701$	9.05398	0.341964	0.170982	+	0.985274i	$0.445306\pi$
$702$	0	0
$703$	−75.3693	−2.84261
$704$	2.56155	0.0965422
$705$	27.3693	1.03079
$706$	−9.80776	−0.369120
$707$	19.5616	0.735688
$708$	13.1231	0.493197
$709$	20.3002	0.762390	0.381195	−	0.924495i	$-0.375513\pi$
$709$	20.3002	0.762390	0.381195	+	0.924495i	$0.375513\pi$
$710$	14.2462	0.534651
$711$	1.43845	0.0539460
$712$	−9.68466	−0.362948
$713$	−46.7386	−1.75038
$714$	5.00000	0.187120
$715$	0	0
$716$	−16.4924	−0.616351
$717$	4.00000	0.149383
$718$	−4.63068	−0.172816
$719$	21.9309	0.817883	0.408942	−	0.912561i	$-0.365898\pi$
$719$	21.9309	0.817883	0.408942	+	0.912561i	$0.365898\pi$
$720$	−3.56155	−0.132731
$721$	11.3693	0.423415
$722$	40.0540	1.49065
$723$	11.3153	0.420822
$724$	13.2462	0.492292
$725$	−7.68466	−0.285401
$726$	−4.43845	−0.164726
$727$	50.2462	1.86353	0.931764	−	0.363063i	$-0.118269\pi$
$727$	50.2462	1.86353	0.931764	+	0.363063i	$0.118269\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.68466	0.321434
$731$	14.3845	0.532029
$732$	−1.00000	−0.0369611
$733$	32.6155	1.20468	0.602341	−	0.798239i	$-0.294235\pi$
$733$	32.6155	1.20468	0.602341	+	0.798239i	$0.294235\pi$
$734$	11.3693	0.419649
$735$	−3.56155	−0.131370
$736$	−9.12311	−0.336282
$737$	2.87689	0.105972
$738$	4.12311	0.151774
$739$	47.3693	1.74251	0.871254	−	0.490832i	$-0.163307\pi$
$739$	47.3693	1.74251	0.871254	+	0.490832i	$0.163307\pi$
$740$	34.9309	1.28408
$741$	0	0
$742$	3.87689	0.142325
$743$	8.63068	0.316629	0.158315	−	0.987389i	$-0.449394\pi$
$743$	8.63068	0.316629	0.158315	+	0.987389i	$0.449394\pi$
$744$	5.12311	0.187822
$745$	63.4233	2.32365
$746$	21.5616	0.789425
$747$	−10.2462	−0.374889
$748$	−12.8078	−0.468298
$749$	9.43845	0.344873
$750$	−9.56155	−0.349139
$751$	−0.807764	−0.0294757	−0.0147379	−	0.999891i	$-0.504691\pi$
$751$	−0.807764	−0.0294757	−0.0147379	+	0.999891i	$0.504691\pi$
$752$	−7.68466	−0.280231
$753$	8.49242	0.309481
$754$	0	0
$755$	62.1080	2.26034
$756$	−1.00000	−0.0363696
$757$	−7.12311	−0.258894	−0.129447	−	0.991586i	$-0.541320\pi$
$757$	−7.12311	−0.258894	−0.129447	+	0.991586i	$0.541320\pi$
$758$	0.492423	0.0178856
$759$	−23.3693	−0.848252
$760$	−27.3693	−0.992789
$761$	−42.4924	−1.54035	−0.770175	−	0.637833i	$-0.779831\pi$
$761$	−42.4924	−1.54035	−0.770175	+	0.637833i	$0.779831\pi$
$762$	2.24621	0.0813716
$763$	−0.876894	−0.0317457
$764$	5.75379	0.208165
$765$	17.8078	0.643841
$766$	8.31534	0.300446
$767$	0	0
$768$	1.00000	0.0360844
$769$	−22.9848	−0.828855	−0.414427	−	0.910082i	$-0.636018\pi$
$769$	−22.9848	−0.828855	−0.414427	+	0.910082i	$0.636018\pi$
$770$	9.12311	0.328774
$771$	−14.7538	−0.531345
$772$	−20.3693	−0.733108
$773$	26.4924	0.952866	0.476433	−	0.879211i	$-0.341929\pi$
$773$	26.4924	0.952866	0.476433	+	0.879211i	$0.341929\pi$
$774$	−2.87689	−0.103408
$775$	39.3693	1.41419
$776$	12.2462	0.439613
$777$	9.80776	0.351852
$778$	18.6847	0.669877
$779$	31.6847	1.13522
$780$	0	0
$781$	−10.2462	−0.366638
$782$	45.6155	1.63121
$783$	−1.00000	−0.0357371
$784$	1.00000	0.0357143
$785$	20.6847	0.738267
$786$	−16.4924	−0.588265
$787$	0.807764	0.0287937	0.0143968	−	0.999896i	$-0.495417\pi$
$787$	0.807764	0.0287937	0.0143968	+	0.999896i	$0.495417\pi$
$788$	−0.561553	−0.0200045
$789$	−20.4924	−0.729550
$790$	−5.12311	−0.182272
$791$	−16.9309	−0.601992
$792$	2.56155	0.0910208
$793$	0	0
$794$	1.68466	0.0597863
$795$	13.8078	0.489711
$796$	−17.6155	−0.624366
$797$	−24.1080	−0.853947	−0.426974	−	0.904264i	$-0.640420\pi$
$797$	−24.1080	−0.853947	−0.426974	+	0.904264i	$0.640420\pi$
$798$	−7.68466	−0.272034
$799$	38.4233	1.35932
$800$	7.68466	0.271694
$801$	−9.68466	−0.342191
$802$	15.1771	0.535921
$803$	−6.24621	−0.220424
$804$	1.12311	0.0396089
$805$	−32.4924	−1.14521
$806$	0	0
$807$	−4.87689	−0.171675
$808$	−19.5616	−0.688173
$809$	−10.9309	−0.384309	−0.192154	−	0.981365i	$-0.561547\pi$
$809$	−10.9309	−0.384309	−0.192154	+	0.981365i	$0.561547\pi$
$810$	−3.56155	−0.125140
$811$	5.75379	0.202043	0.101021	−	0.994884i	$-0.467789\pi$
$811$	5.75379	0.202043	0.101021	+	0.994884i	$0.467789\pi$
$812$	1.00000	0.0350931
$813$	13.1231	0.460247
$814$	−25.1231	−0.880564
$815$	4.00000	0.140114
$816$	−5.00000	−0.175035
$817$	−22.1080	−0.773459
$818$	−30.4384	−1.06426
$819$	0	0
$820$	−14.6847	−0.512811
$821$	−12.0691	−0.421216	−0.210608	−	0.977571i	$-0.567544\pi$
$821$	−12.0691	−0.421216	−0.210608	+	0.977571i	$0.567544\pi$
$822$	−5.80776	−0.202569
$823$	14.2462	0.496592	0.248296	−	0.968684i	$-0.420129\pi$
$823$	14.2462	0.496592	0.248296	+	0.968684i	$0.420129\pi$
$824$	−11.3693	−0.396069
$825$	19.6847	0.685332
$826$	−13.1231	−0.456611
$827$	−11.5076	−0.400158	−0.200079	−	0.979780i	$-0.564120\pi$
$827$	−11.5076	−0.400158	−0.200079	+	0.979780i	$0.564120\pi$
$828$	−9.12311	−0.317050
$829$	29.1080	1.01096	0.505480	−	0.862838i	$-0.331315\pi$
$829$	29.1080	1.01096	0.505480	+	0.862838i	$0.331315\pi$
$830$	36.4924	1.26667
$831$	−3.56155	−0.123549
$832$	0	0
$833$	−5.00000	−0.173240
$834$	−7.68466	−0.266098
$835$	−72.9848	−2.52574
$836$	19.6847	0.680808
$837$	5.12311	0.177080
$838$	22.7386	0.785493
$839$	8.00000	0.276191	0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000	0.276191	0.138095	+	0.990419i	$0.455902\pi$
$840$	3.56155	0.122885
$841$	−28.0000	−0.965517
$842$	8.43845	0.290808
$843$	7.80776	0.268914
$844$	−2.87689	−0.0990268
$845$	0	0
$846$	−7.68466	−0.264204
$847$	4.43845	0.152507
$848$	−3.87689	−0.133133
$849$	8.49242	0.291459
$850$	−38.4233	−1.31791
$851$	89.4773	3.06724
$852$	−4.00000	−0.137038
$853$	−0.369317	−0.0126452	−0.00632258	−	0.999980i	$-0.502013\pi$
$853$	−0.369317	−0.0126452	−0.00632258	+	0.999980i	$0.502013\pi$
$854$	1.00000	0.0342193
$855$	−27.3693	−0.936011
$856$	−9.43845	−0.322599
$857$	−22.3002	−0.761760	−0.380880	−	0.924625i	$-0.624379\pi$
$857$	−22.3002	−0.761760	−0.380880	+	0.924625i	$0.624379\pi$
$858$	0	0
$859$	−36.8078	−1.25586	−0.627932	−	0.778268i	$-0.716099\pi$
$859$	−36.8078	−1.25586	−0.627932	+	0.778268i	$0.716099\pi$
$860$	10.2462	0.349393
$861$	−4.12311	−0.140515
$862$	−18.7386	−0.638240
$863$	26.1080	0.888725	0.444362	−	0.895847i	$-0.353430\pi$
$863$	26.1080	0.888725	0.444362	+	0.895847i	$0.353430\pi$
$864$	1.00000	0.0340207
$865$	17.3693	0.590574
$866$	−5.31534	−0.180623
$867$	8.00000	0.271694
$868$	−5.12311	−0.173890
$869$	3.68466	0.124993
$870$	3.56155	0.120748
$871$	0	0
$872$	0.876894	0.0296954
$873$	12.2462	0.414471
$874$	−70.1080	−2.37144
$875$	9.56155	0.323239
$876$	−2.43845	−0.0823875
$877$	8.30019	0.280277	0.140139	−	0.990132i	$-0.455245\pi$
$877$	8.30019	0.280277	0.140139	+	0.990132i	$0.455245\pi$
$878$	−28.4924	−0.961573
$879$	−4.68466	−0.158010
$880$	−9.12311	−0.307540
$881$	47.1771	1.58944	0.794718	−	0.606979i	$-0.207619\pi$
$881$	47.1771	1.58944	0.794718	+	0.606979i	$0.207619\pi$
$882$	1.00000	0.0336718
$883$	17.1231	0.576238	0.288119	−	0.957595i	$-0.406970\pi$
$883$	17.1231	0.576238	0.288119	+	0.957595i	$0.406970\pi$
$884$	0	0
$885$	−46.7386	−1.57110
$886$	−34.4233	−1.15647
$887$	5.43845	0.182605	0.0913026	−	0.995823i	$-0.470897\pi$
$887$	5.43845	0.182605	0.0913026	+	0.995823i	$0.470897\pi$
$888$	−9.80776	−0.329127
$889$	−2.24621	−0.0753355
$890$	34.4924	1.15619
$891$	2.56155	0.0858152
$892$	−16.4924	−0.552207
$893$	−59.0540	−1.97617
$894$	−17.8078	−0.595581
$895$	58.7386	1.96342
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0000	0.600668
$899$	−5.12311	−0.170865
$900$	7.68466	0.256155
$901$	19.3845	0.645790
$902$	10.5616	0.351661
$903$	2.87689	0.0957371
$904$	16.9309	0.563112
$905$	−47.1771	−1.56822
$906$	−17.4384	−0.579354
$907$	22.8769	0.759615	0.379807	−	0.925066i	$-0.375990\pi$
$907$	22.8769	0.759615	0.379807	+	0.925066i	$0.375990\pi$
$908$	13.1231	0.435506
$909$	−19.5616	−0.648816
$910$	0	0
$911$	−5.26137	−0.174317	−0.0871584	−	0.996194i	$-0.527779\pi$
$911$	−5.26137	−0.174317	−0.0871584	+	0.996194i	$0.527779\pi$
$912$	7.68466	0.254464
$913$	−26.2462	−0.868623
$914$	−13.3153	−0.440432
$915$	3.56155	0.117741
$916$	22.8078	0.753590
$917$	16.4924	0.544628
$918$	−5.00000	−0.165025
$919$	6.56155	0.216446	0.108223	−	0.994127i	$-0.465484\pi$
$919$	6.56155	0.216446	0.108223	+	0.994127i	$0.465484\pi$
$920$	32.4924	1.07124
$921$	−33.9309	−1.11806
$922$	30.0540	0.989775
$923$	0	0
$924$	−2.56155	−0.0842689
$925$	−75.3693	−2.47813
$926$	−11.6847	−0.383982
$927$	−11.3693	−0.373417
$928$	−1.00000	−0.0328266
$929$	−6.61553	−0.217048	−0.108524	−	0.994094i	$-0.534613\pi$
$929$	−6.61553	−0.217048	−0.108524	+	0.994094i	$0.534613\pi$
$930$	−18.2462	−0.598317
$931$	7.68466	0.251855
$932$	−6.00000	−0.196537
$933$	22.5616	0.738632
$934$	28.0000	0.916188
$935$	45.6155	1.49179
$936$	0	0
$937$	13.5616	0.443037	0.221518	−	0.975156i	$-0.428899\pi$
$937$	13.5616	0.443037	0.221518	+	0.975156i	$0.428899\pi$
$938$	−1.12311	−0.0366707
$939$	27.6155	0.901199
$940$	27.3693	0.892689
$941$	53.3693	1.73979	0.869895	−	0.493237i	$-0.164186\pi$
$941$	53.3693	1.73979	0.869895	+	0.493237i	$0.164186\pi$
$942$	−5.80776	−0.189227
$943$	−37.6155	−1.22493
$944$	13.1231	0.427121
$945$	3.56155	0.115857
$946$	−7.36932	−0.239597
$947$	−0.315342	−0.0102472	−0.00512361	−	0.999987i	$-0.501631\pi$
$947$	−0.315342	−0.0102472	−0.00512361	+	0.999987i	$0.501631\pi$
$948$	1.43845	0.0467186
$949$	0	0
$950$	59.0540	1.91596
$951$	−11.5616	−0.374909
$952$	5.00000	0.162051
$953$	−52.7386	−1.70837	−0.854186	−	0.519968i	$-0.825944\pi$
$953$	−52.7386	−1.70837	−0.854186	+	0.519968i	$0.825944\pi$
$954$	−3.87689	−0.125519
$955$	−20.4924	−0.663119
$956$	4.00000	0.129369
$957$	−2.56155	−0.0828032
$958$	−2.56155	−0.0827600
$959$	5.80776	0.187542
$960$	−3.56155	−0.114949
$961$	−4.75379	−0.153348
$962$	0	0
$963$	−9.43845	−0.304150
$964$	11.3153	0.364443
$965$	72.5464	2.33535
$966$	9.12311	0.293531
$967$	−4.49242	−0.144467	−0.0722333	−	0.997388i	$-0.523013\pi$
$967$	−4.49242	−0.144467	−0.0722333	+	0.997388i	$0.523013\pi$
$968$	−4.43845	−0.142657
$969$	−38.4233	−1.23433
$970$	−43.6155	−1.40041
$971$	−10.8769	−0.349056	−0.174528	−	0.984652i	$-0.555840\pi$
$971$	−10.8769	−0.349056	−0.174528	+	0.984652i	$0.555840\pi$
$972$	1.00000	0.0320750
$973$	7.68466	0.246359
$974$	23.6847	0.758905
$975$	0	0
$976$	−1.00000	−0.0320092
$977$	2.05398	0.0657125	0.0328562	−	0.999460i	$-0.489540\pi$
$977$	2.05398	0.0657125	0.0328562	+	0.999460i	$0.489540\pi$
$978$	−1.12311	−0.0359130
$979$	−24.8078	−0.792860
$980$	−3.56155	−0.113770
$981$	0.876894	0.0279971
$982$	−1.75379	−0.0559656
$983$	55.2311	1.76160	0.880799	−	0.473491i	$-0.157006\pi$
$983$	55.2311	1.76160	0.880799	+	0.473491i	$0.157006\pi$
$984$	4.12311	0.131440
$985$	2.00000	0.0637253
$986$	5.00000	0.159232
$987$	7.68466	0.244605
$988$	0	0
$989$	26.2462	0.834581
$990$	−9.12311	−0.289951
$991$	−1.43845	−0.0456938	−0.0228469	−	0.999739i	$-0.507273\pi$
$991$	−1.43845	−0.0456938	−0.0228469	+	0.999739i	$0.507273\pi$
$992$	5.12311	0.162659
$993$	−35.3693	−1.12241
$994$	4.00000	0.126872
$995$	62.7386	1.98895
$996$	−10.2462	−0.324664
$997$	−17.0000	−0.538395	−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000	−0.538395	−0.269198	+	0.963085i	$0.586759\pi$
$998$	−27.3693	−0.866361
$999$	−9.80776	−0.310304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bw.1.1		2
13.3	even	3		546.2.l.i.295.1	yes	4
13.9	even	3		546.2.l.i.211.1	✓	4
13.12	even	2		7098.2.a.bq.1.2		2
39.29	odd	6		1638.2.r.z.1387.2		4
39.35	odd	6		1638.2.r.z.757.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.i.211.1	✓	4	13.9	even	3
546.2.l.i.295.1	yes	4	13.3	even	3
1638.2.r.z.757.2		4	39.35	odd	6
1638.2.r.z.1387.2		4	39.29	odd	6
7098.2.a.bq.1.2		2	13.12	even	2
7098.2.a.bw.1.1		2	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:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.56155 q^{10} +2.56155 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.56155 q^{15} +1.00000 q^{16} -5.00000 q^{17} +1.00000 q^{18} +7.68466 q^{19} -3.56155 q^{20} -1.00000 q^{21} +2.56155 q^{22} -9.12311 q^{23} +1.00000 q^{24} +7.68466 q^{25} +1.00000 q^{27} -1.00000 q^{28} -1.00000 q^{29} -3.56155 q^{30} +5.12311 q^{31} +1.00000 q^{32} +2.56155 q^{33} -5.00000 q^{34} +3.56155 q^{35} +1.00000 q^{36} -9.80776 q^{37} +7.68466 q^{38} -3.56155 q^{40} +4.12311 q^{41} -1.00000 q^{42} -2.87689 q^{43} +2.56155 q^{44} -3.56155 q^{45} -9.12311 q^{46} -7.68466 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.68466 q^{50} -5.00000 q^{51} -3.87689 q^{53} +1.00000 q^{54} -9.12311 q^{55} -1.00000 q^{56} +7.68466 q^{57} -1.00000 q^{58} +13.1231 q^{59} -3.56155 q^{60} -1.00000 q^{61} +5.12311 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.56155 q^{66} +1.12311 q^{67} -5.00000 q^{68} -9.12311 q^{69} +3.56155 q^{70} -4.00000 q^{71} +1.00000 q^{72} -2.43845 q^{73} -9.80776 q^{74} +7.68466 q^{75} +7.68466 q^{76} -2.56155 q^{77} +1.43845 q^{79} -3.56155 q^{80} +1.00000 q^{81} +4.12311 q^{82} -10.2462 q^{83} -1.00000 q^{84} +17.8078 q^{85} -2.87689 q^{86} -1.00000 q^{87} +2.56155 q^{88} -9.68466 q^{89} -3.56155 q^{90} -9.12311 q^{92} +5.12311 q^{93} -7.68466 q^{94} -27.3693 q^{95} +1.00000 q^{96} +12.2462 q^{97} +1.00000 q^{98} +2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + q^{11} + 2 q^{12} - 2 q^{14} - 3 q^{15} + 2 q^{16} - 10 q^{17} + 2 q^{18} + 3 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} - 10 q^{23} + 2 q^{24} + 3 q^{25} + 2 q^{27} - 2 q^{28} - 2 q^{29} - 3 q^{30} + 2 q^{31} + 2 q^{32} + q^{33} - 10 q^{34} + 3 q^{35} + 2 q^{36} + q^{37} + 3 q^{38} - 3 q^{40} - 2 q^{42} - 14 q^{43} + q^{44} - 3 q^{45} - 10 q^{46} - 3 q^{47} + 2 q^{48} + 2 q^{49} + 3 q^{50} - 10 q^{51} - 16 q^{53} + 2 q^{54} - 10 q^{55} - 2 q^{56} + 3 q^{57} - 2 q^{58} + 18 q^{59} - 3 q^{60} - 2 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + q^{66} - 6 q^{67} - 10 q^{68} - 10 q^{69} + 3 q^{70} - 8 q^{71} + 2 q^{72} - 9 q^{73} + q^{74} + 3 q^{75} + 3 q^{76} - q^{77} + 7 q^{79} - 3 q^{80} + 2 q^{81} - 4 q^{83} - 2 q^{84} + 15 q^{85} - 14 q^{86} - 2 q^{87} + q^{88} - 7 q^{89} - 3 q^{90} - 10 q^{92} + 2 q^{93} - 3 q^{94} - 30 q^{95} + 2 q^{96} + 8 q^{97} + 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + q^11 + 2 * q^12 - 2 * q^14 - 3 * q^15 + 2 * q^16 - 10 * q^17 + 2 * q^18 + 3 * q^19 - 3 * q^20 - 2 * q^21 + q^22 - 10 * q^23 + 2 * q^24 + 3 * q^25 + 2 * q^27 - 2 * q^28 - 2 * q^29 - 3 * q^30 + 2 * q^31 + 2 * q^32 + q^33 - 10 * q^34 + 3 * q^35 + 2 * q^36 + q^37 + 3 * q^38 - 3 * q^40 - 2 * q^42 - 14 * q^43 + q^44 - 3 * q^45 - 10 * q^46 - 3 * q^47 + 2 * q^48 + 2 * q^49 + 3 * q^50 - 10 * q^51 - 16 * q^53 + 2 * q^54 - 10 * q^55 - 2 * q^56 + 3 * q^57 - 2 * q^58 + 18 * q^59 - 3 * q^60 - 2 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + q^66 - 6 * q^67 - 10 * q^68 - 10 * q^69 + 3 * q^70 - 8 * q^71 + 2 * q^72 - 9 * q^73 + q^74 + 3 * q^75 + 3 * q^76 - q^77 + 7 * q^79 - 3 * q^80 + 2 * q^81 - 4 * q^83 - 2 * q^84 + 15 * q^85 - 14 * q^86 - 2 * q^87 + q^88 - 7 * q^89 - 3 * q^90 - 10 * q^92 + 2 * q^93 - 3 * q^94 - 30 * q^95 + 2 * q^96 + 8 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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