LMFDB - Embedded newform 7098.2.a.cb.1.3

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:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.692021 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.692021 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.692021 q^{10} +0.664874 q^{11} -1.00000 q^{12} -1.00000 q^{14} -0.692021 q^{15} +1.00000 q^{16} -7.74094 q^{17} -1.00000 q^{18} +3.89977 q^{19} +0.692021 q^{20} -1.00000 q^{21} -0.664874 q^{22} +0.841166 q^{23} +1.00000 q^{24} -4.52111 q^{25} -1.00000 q^{27} +1.00000 q^{28} +8.98792 q^{29} +0.692021 q^{30} -6.26875 q^{31} -1.00000 q^{32} -0.664874 q^{33} +7.74094 q^{34} +0.692021 q^{35} +1.00000 q^{36} -11.1685 q^{37} -3.89977 q^{38} -0.692021 q^{40} +11.7409 q^{41} +1.00000 q^{42} +9.87800 q^{43} +0.664874 q^{44} +0.692021 q^{45} -0.841166 q^{46} +10.3177 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.52111 q^{50} +7.74094 q^{51} -7.92154 q^{53} +1.00000 q^{54} +0.460107 q^{55} -1.00000 q^{56} -3.89977 q^{57} -8.98792 q^{58} -10.8901 q^{59} -0.692021 q^{60} -6.05429 q^{61} +6.26875 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.664874 q^{66} +2.98792 q^{67} -7.74094 q^{68} -0.841166 q^{69} -0.692021 q^{70} -9.93661 q^{71} -1.00000 q^{72} -14.5918 q^{73} +11.1685 q^{74} +4.52111 q^{75} +3.89977 q^{76} +0.664874 q^{77} -1.60388 q^{79} +0.692021 q^{80} +1.00000 q^{81} -11.7409 q^{82} -4.39612 q^{83} -1.00000 q^{84} -5.35690 q^{85} -9.87800 q^{86} -8.98792 q^{87} -0.664874 q^{88} -0.454731 q^{89} -0.692021 q^{90} +0.841166 q^{92} +6.26875 q^{93} -10.3177 q^{94} +2.69873 q^{95} +1.00000 q^{96} -8.61596 q^{97} -1.00000 q^{98} +0.664874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{15} + 3 q^{16} - 9 q^{17} - 3 q^{18} - 11 q^{19} - 3 q^{20} - 3 q^{21} - 3 q^{22} + 11 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{27} + 3 q^{28} + 8 q^{29} - 3 q^{30} - 11 q^{31} - 3 q^{32} - 3 q^{33} + 9 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} + 11 q^{38} + 3 q^{40} + 21 q^{41} + 3 q^{42} + 10 q^{43} + 3 q^{44} - 3 q^{45} - 11 q^{46} + 14 q^{47} - 3 q^{48} + 3 q^{49} - 2 q^{50} + 9 q^{51} + 2 q^{53} + 3 q^{54} - 24 q^{55} - 3 q^{56} + 11 q^{57} - 8 q^{58} - 32 q^{59} + 3 q^{60} - 6 q^{61} + 11 q^{62} + 3 q^{63} + 3 q^{64} + 3 q^{66} - 10 q^{67} - 9 q^{68} - 11 q^{69} + 3 q^{70} + 21 q^{71} - 3 q^{72} - 16 q^{73} + 3 q^{74} - 2 q^{75} - 11 q^{76} + 3 q^{77} + 4 q^{79} - 3 q^{80} + 3 q^{81} - 21 q^{82} - 22 q^{83} - 3 q^{84} - 12 q^{85} - 10 q^{86} - 8 q^{87} - 3 q^{88} + 21 q^{89} + 3 q^{90} + 11 q^{92} + 11 q^{93} - 14 q^{94} + 25 q^{95} + 3 q^{96} - 36 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 + 3 * q^15 + 3 * q^16 - 9 * q^17 - 3 * q^18 - 11 * q^19 - 3 * q^20 - 3 * q^21 - 3 * q^22 + 11 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^27 + 3 * q^28 + 8 * q^29 - 3 * q^30 - 11 * q^31 - 3 * q^32 - 3 * q^33 + 9 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 + 11 * q^38 + 3 * q^40 + 21 * q^41 + 3 * q^42 + 10 * q^43 + 3 * q^44 - 3 * q^45 - 11 * q^46 + 14 * q^47 - 3 * q^48 + 3 * q^49 - 2 * q^50 + 9 * q^51 + 2 * q^53 + 3 * q^54 - 24 * q^55 - 3 * q^56 + 11 * q^57 - 8 * q^58 - 32 * q^59 + 3 * q^60 - 6 * q^61 + 11 * q^62 + 3 * q^63 + 3 * q^64 + 3 * q^66 - 10 * q^67 - 9 * q^68 - 11 * q^69 + 3 * q^70 + 21 * q^71 - 3 * q^72 - 16 * q^73 + 3 * q^74 - 2 * q^75 - 11 * q^76 + 3 * q^77 + 4 * q^79 - 3 * q^80 + 3 * q^81 - 21 * q^82 - 22 * q^83 - 3 * q^84 - 12 * q^85 - 10 * q^86 - 8 * q^87 - 3 * q^88 + 21 * q^89 + 3 * q^90 + 11 * q^92 + 11 * q^93 - 14 * q^94 + 25 * q^95 + 3 * q^96 - 36 * q^97 - 3 * q^98 + 3 * 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
$5$	0.692021	0.309481	0.154741	−	0.987955i	$-0.450546\pi$
$5$	0.692021	0.309481	0.154741	+	0.987955i	$0.450546\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.692021	−0.218836
$11$	0.664874	0.200467	0.100234	−	0.994964i	$-0.468041\pi$
$11$	0.664874	0.200467	0.100234	+	0.994964i	$0.468041\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−0.692021	−0.178679
$16$	1.00000	0.250000
$17$	−7.74094	−1.87745	−0.938727	−	0.344662i	$-0.887993\pi$
$17$	−7.74094	−1.87745	−0.938727	+	0.344662i	$0.887993\pi$
$18$	−1.00000	−0.235702
$19$	3.89977	0.894669	0.447335	−	0.894367i	$-0.352373\pi$
$19$	3.89977	0.894669	0.447335	+	0.894367i	$0.352373\pi$
$20$	0.692021	0.154741
$21$	−1.00000	−0.218218
$22$	−0.664874	−0.141752
$23$	0.841166	0.175395	0.0876977	−	0.996147i	$-0.472049\pi$
$23$	0.841166	0.175395	0.0876977	+	0.996147i	$0.472049\pi$
$24$	1.00000	0.204124
$25$	−4.52111	−0.904221
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	8.98792	1.66901	0.834507	−	0.550997i	$-0.185752\pi$
$29$	8.98792	1.66901	0.834507	+	0.550997i	$0.185752\pi$
$30$	0.692021	0.126345
$31$	−6.26875	−1.12590	−0.562950	−	0.826491i	$-0.690334\pi$
$31$	−6.26875	−1.12590	−0.562950	+	0.826491i	$0.690334\pi$
$32$	−1.00000	−0.176777
$33$	−0.664874	−0.115740
$34$	7.74094	1.32756
$35$	0.692021	0.116973
$36$	1.00000	0.166667
$37$	−11.1685	−1.83609	−0.918047	−	0.396472i	$-0.870234\pi$
$37$	−11.1685	−1.83609	−0.918047	+	0.396472i	$0.870234\pi$
$38$	−3.89977	−0.632627
$39$	0	0
$40$	−0.692021	−0.109418
$41$	11.7409	1.83363	0.916813	−	0.399316i	$-0.130752\pi$
$41$	11.7409	1.83363	0.916813	+	0.399316i	$0.130752\pi$
$42$	1.00000	0.154303
$43$	9.87800	1.50638	0.753191	−	0.657802i	$-0.228514\pi$
$43$	9.87800	1.50638	0.753191	+	0.657802i	$0.228514\pi$
$44$	0.664874	0.100234
$45$	0.692021	0.103160
$46$	−0.841166	−0.124023
$47$	10.3177	1.50499	0.752493	−	0.658600i	$-0.228851\pi$
$47$	10.3177	1.50499	0.752493	+	0.658600i	$0.228851\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.52111	0.639381
$51$	7.74094	1.08395
$52$	0	0
$53$	−7.92154	−1.08811	−0.544054	−	0.839050i	$-0.683111\pi$
$53$	−7.92154	−1.08811	−0.544054	+	0.839050i	$0.683111\pi$
$54$	1.00000	0.136083
$55$	0.460107	0.0620409
$56$	−1.00000	−0.133631
$57$	−3.89977	−0.516537
$58$	−8.98792	−1.18017
$59$	−10.8901	−1.41777	−0.708884	−	0.705325i	$-0.750801\pi$
$59$	−10.8901	−1.41777	−0.708884	+	0.705325i	$0.750801\pi$
$60$	−0.692021	−0.0893396
$61$	−6.05429	−0.775173	−0.387586	−	0.921833i	$-0.626691\pi$
$61$	−6.05429	−0.775173	−0.387586	+	0.921833i	$0.626691\pi$
$62$	6.26875	0.796132
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	0.664874	0.0818404
$67$	2.98792	0.365032	0.182516	−	0.983203i	$-0.441576\pi$
$67$	2.98792	0.365032	0.182516	+	0.983203i	$0.441576\pi$
$68$	−7.74094	−0.938727
$69$	−0.841166	−0.101265
$70$	−0.692021	−0.0827124
$71$	−9.93661	−1.17926	−0.589629	−	0.807674i	$-0.700726\pi$
$71$	−9.93661	−1.17926	−0.589629	+	0.807674i	$0.700726\pi$
$72$	−1.00000	−0.117851
$73$	−14.5918	−1.70784	−0.853920	−	0.520404i	$-0.825781\pi$
$73$	−14.5918	−1.70784	−0.853920	+	0.520404i	$0.825781\pi$
$74$	11.1685	1.29831
$75$	4.52111	0.522052
$76$	3.89977	0.447335
$77$	0.664874	0.0757695
$78$	0	0
$79$	−1.60388	−0.180450	−0.0902250	−	0.995921i	$-0.528759\pi$
$79$	−1.60388	−0.180450	−0.0902250	+	0.995921i	$0.528759\pi$
$80$	0.692021	0.0773704
$81$	1.00000	0.111111
$82$	−11.7409	−1.29657
$83$	−4.39612	−0.482537	−0.241269	−	0.970458i	$-0.577564\pi$
$83$	−4.39612	−0.482537	−0.241269	+	0.970458i	$0.577564\pi$
$84$	−1.00000	−0.109109
$85$	−5.35690	−0.581037
$86$	−9.87800	−1.06517
$87$	−8.98792	−0.963606
$88$	−0.664874	−0.0708758
$89$	−0.454731	−0.0482013	−0.0241007	−	0.999710i	$-0.507672\pi$
$89$	−0.454731	−0.0482013	−0.0241007	+	0.999710i	$0.507672\pi$
$90$	−0.692021	−0.0729455
$91$	0	0
$92$	0.841166	0.0876977
$93$	6.26875	0.650039
$94$	−10.3177	−1.06419
$95$	2.69873	0.276883
$96$	1.00000	0.102062
$97$	−8.61596	−0.874818	−0.437409	−	0.899263i	$-0.644104\pi$
$97$	−8.61596	−0.874818	−0.437409	+	0.899263i	$0.644104\pi$
$98$	−1.00000	−0.101015
$99$	0.664874	0.0668224
$100$	−4.52111	−0.452111
$101$	17.7235	1.76355	0.881776	−	0.471668i	$-0.156348\pi$
$101$	17.7235	1.76355	0.881776	+	0.471668i	$0.156348\pi$
$102$	−7.74094	−0.766467
$103$	−12.5972	−1.24124	−0.620618	−	0.784113i	$-0.713118\pi$
$103$	−12.5972	−1.24124	−0.620618	+	0.784113i	$0.713118\pi$
$104$	0	0
$105$	−0.692021	−0.0675344
$106$	7.92154	0.769408
$107$	−0.692021	−0.0669002	−0.0334501	−	0.999440i	$-0.510649\pi$
$107$	−0.692021	−0.0669002	−0.0334501	+	0.999440i	$0.510649\pi$
$108$	−1.00000	−0.0962250
$109$	−8.03923	−0.770018	−0.385009	−	0.922913i	$-0.625802\pi$
$109$	−8.03923	−0.770018	−0.385009	+	0.922913i	$0.625802\pi$
$110$	−0.460107	−0.0438695
$111$	11.1685	1.06007
$112$	1.00000	0.0944911
$113$	12.5918	1.18454	0.592268	−	0.805741i	$-0.298233\pi$
$113$	12.5918	1.18454	0.592268	+	0.805741i	$0.298233\pi$
$114$	3.89977	0.365247
$115$	0.582105	0.0542816
$116$	8.98792	0.834507
$117$	0	0
$118$	10.8901	1.00251
$119$	−7.74094	−0.709611
$120$	0.692021	0.0631726
$121$	−10.5579	−0.959813
$122$	6.05429	0.548130
$123$	−11.7409	−1.05864
$124$	−6.26875	−0.562950
$125$	−6.58881	−0.589321
$126$	−1.00000	−0.0890871
$127$	6.76809	0.600571	0.300285	−	0.953849i	$-0.402918\pi$
$127$	6.76809	0.600571	0.300285	+	0.953849i	$0.402918\pi$
$128$	−1.00000	−0.0883883
$129$	−9.87800	−0.869710
$130$	0	0
$131$	0.987918	0.0863148	0.0431574	−	0.999068i	$-0.486258\pi$
$131$	0.987918	0.0863148	0.0431574	+	0.999068i	$0.486258\pi$
$132$	−0.664874	−0.0578699
$133$	3.89977	0.338153
$134$	−2.98792	−0.258117
$135$	−0.692021	−0.0595597
$136$	7.74094	0.663780
$137$	0.572417	0.0489048	0.0244524	−	0.999701i	$-0.492216\pi$
$137$	0.572417	0.0489048	0.0244524	+	0.999701i	$0.492216\pi$
$138$	0.841166	0.0716048
$139$	16.7627	1.42179	0.710897	−	0.703296i	$-0.248289\pi$
$139$	16.7627	1.42179	0.710897	+	0.703296i	$0.248289\pi$
$140$	0.692021	0.0584865
$141$	−10.3177	−0.868904
$142$	9.93661	0.833862
$143$	0	0
$144$	1.00000	0.0833333
$145$	6.21983	0.516529
$146$	14.5918	1.20763
$147$	−1.00000	−0.0824786
$148$	−11.1685	−0.918047
$149$	12.0194	0.984666	0.492333	−	0.870407i	$-0.336144\pi$
$149$	12.0194	0.984666	0.492333	+	0.870407i	$0.336144\pi$
$150$	−4.52111	−0.369147
$151$	19.3491	1.57461	0.787305	−	0.616564i	$-0.211476\pi$
$151$	19.3491	1.57461	0.787305	+	0.616564i	$0.211476\pi$
$152$	−3.89977	−0.316313
$153$	−7.74094	−0.625818
$154$	−0.664874	−0.0535771
$155$	−4.33811	−0.348445
$156$	0	0
$157$	−2.19567	−0.175233	−0.0876167	−	0.996154i	$-0.527925\pi$
$157$	−2.19567	−0.175233	−0.0876167	+	0.996154i	$0.527925\pi$
$158$	1.60388	0.127597
$159$	7.92154	0.628219
$160$	−0.692021	−0.0547091
$161$	0.841166	0.0662932
$162$	−1.00000	−0.0785674
$163$	−19.3599	−1.51638	−0.758191	−	0.652032i	$-0.773917\pi$
$163$	−19.3599	−1.51638	−0.758191	+	0.652032i	$0.773917\pi$
$164$	11.7409	0.916813
$165$	−0.460107	−0.0358193
$166$	4.39612	0.341205
$167$	−20.5133	−1.58737	−0.793685	−	0.608329i	$-0.791840\pi$
$167$	−20.5133	−1.58737	−0.793685	+	0.608329i	$0.791840\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	5.35690	0.410855
$171$	3.89977	0.298223
$172$	9.87800	0.753191
$173$	9.08815	0.690959	0.345479	−	0.938426i	$-0.387716\pi$
$173$	9.08815	0.690959	0.345479	+	0.938426i	$0.387716\pi$
$174$	8.98792	0.681372
$175$	−4.52111	−0.341764
$176$	0.664874	0.0501168
$177$	10.8901	0.818549
$178$	0.454731	0.0340835
$179$	8.98792	0.671789	0.335894	−	0.941900i	$-0.390962\pi$
$179$	8.98792	0.671789	0.335894	+	0.941900i	$0.390962\pi$
$180$	0.692021	0.0515802
$181$	−1.76941	−0.131519	−0.0657597	−	0.997835i	$-0.520947\pi$
$181$	−1.76941	−0.131519	−0.0657597	+	0.997835i	$0.520947\pi$
$182$	0	0
$183$	6.05429	0.447546
$184$	−0.841166	−0.0620116
$185$	−7.72886	−0.568237
$186$	−6.26875	−0.459647
$187$	−5.14675	−0.376368
$188$	10.3177	0.752493
$189$	−1.00000	−0.0727393
$190$	−2.69873	−0.195786
$191$	−16.7657	−1.21312	−0.606561	−	0.795037i	$-0.707452\pi$
$191$	−16.7657	−1.21312	−0.606561	+	0.795037i	$0.707452\pi$
$192$	−1.00000	−0.0721688
$193$	−16.9933	−1.22320	−0.611602	−	0.791166i	$-0.709475\pi$
$193$	−16.9933	−1.22320	−0.611602	+	0.791166i	$0.709475\pi$
$194$	8.61596	0.618590
$195$	0	0
$196$	1.00000	0.0714286
$197$	4.90946	0.349785	0.174892	−	0.984588i	$-0.444042\pi$
$197$	4.90946	0.349785	0.174892	+	0.984588i	$0.444042\pi$
$198$	−0.664874	−0.0472506
$199$	−14.9729	−1.06140	−0.530699	−	0.847561i	$-0.678070\pi$
$199$	−14.9729	−1.06140	−0.530699	+	0.847561i	$0.678070\pi$
$200$	4.52111	0.319690
$201$	−2.98792	−0.210752
$202$	−17.7235	−1.24702
$203$	8.98792	0.630828
$204$	7.74094	0.541974
$205$	8.12498	0.567473
$206$	12.5972	0.877686
$207$	0.841166	0.0584651
$208$	0	0
$209$	2.59286	0.179352
$210$	0.692021	0.0477540
$211$	−6.98792	−0.481068	−0.240534	−	0.970641i	$-0.577323\pi$
$211$	−6.98792	−0.481068	−0.240534	+	0.970641i	$0.577323\pi$
$212$	−7.92154	−0.544054
$213$	9.93661	0.680845
$214$	0.692021	0.0473056
$215$	6.83579	0.466197
$216$	1.00000	0.0680414
$217$	−6.26875	−0.425550
$218$	8.03923	0.544485
$219$	14.5918	0.986022
$220$	0.460107	0.0310204
$221$	0	0
$222$	−11.1685	−0.749582
$223$	1.13467	0.0759832	0.0379916	−	0.999278i	$-0.487904\pi$
$223$	1.13467	0.0759832	0.0379916	+	0.999278i	$0.487904\pi$
$224$	−1.00000	−0.0668153
$225$	−4.52111	−0.301407
$226$	−12.5918	−0.837594
$227$	−5.26205	−0.349254	−0.174627	−	0.984635i	$-0.555872\pi$
$227$	−5.26205	−0.349254	−0.174627	+	0.984635i	$0.555872\pi$
$228$	−3.89977	−0.258269
$229$	−3.40821	−0.225221	−0.112610	−	0.993639i	$-0.535921\pi$
$229$	−3.40821	−0.225221	−0.112610	+	0.993639i	$0.535921\pi$
$230$	−0.582105	−0.0383829
$231$	−0.664874	−0.0437455
$232$	−8.98792	−0.590086
$233$	−23.6775	−1.55117	−0.775584	−	0.631245i	$-0.782544\pi$
$233$	−23.6775	−1.55117	−0.775584	+	0.631245i	$0.782544\pi$
$234$	0	0
$235$	7.14005	0.465765
$236$	−10.8901	−0.708884
$237$	1.60388	0.104183
$238$	7.74094	0.501771
$239$	20.2610	1.31057	0.655287	−	0.755380i	$-0.272548\pi$
$239$	20.2610	1.31057	0.655287	+	0.755380i	$0.272548\pi$
$240$	−0.692021	−0.0446698
$241$	−0.0435405	−0.00280469	−0.00140235	−	0.999999i	$-0.500446\pi$
$241$	−0.0435405	−0.00280469	−0.00140235	+	0.999999i	$0.500446\pi$
$242$	10.5579	0.678690
$243$	−1.00000	−0.0641500
$244$	−6.05429	−0.387586
$245$	0.692021	0.0442116
$246$	11.7409	0.748575
$247$	0	0
$248$	6.26875	0.398066
$249$	4.39612	0.278593
$250$	6.58881	0.416713
$251$	−27.3056	−1.72351	−0.861757	−	0.507322i	$-0.830636\pi$
$251$	−27.3056	−1.72351	−0.861757	+	0.507322i	$0.830636\pi$
$252$	1.00000	0.0629941
$253$	0.559270	0.0351610
$254$	−6.76809	−0.424667
$255$	5.35690	0.335462
$256$	1.00000	0.0625000
$257$	7.97584	0.497519	0.248760	−	0.968565i	$-0.419977\pi$
$257$	7.97584	0.497519	0.248760	+	0.968565i	$0.419977\pi$
$258$	9.87800	0.614978
$259$	−11.1685	−0.693978
$260$	0	0
$261$	8.98792	0.556338
$262$	−0.987918	−0.0610338
$263$	9.37867	0.578313	0.289157	−	0.957282i	$-0.406625\pi$
$263$	9.37867	0.578313	0.289157	+	0.957282i	$0.406625\pi$
$264$	0.664874	0.0409202
$265$	−5.48188	−0.336749
$266$	−3.89977	−0.239110
$267$	0.454731	0.0278291
$268$	2.98792	0.182516
$269$	7.96077	0.485377	0.242688	−	0.970104i	$-0.421971\pi$
$269$	7.96077	0.485377	0.242688	+	0.970104i	$0.421971\pi$
$270$	0.692021	0.0421151
$271$	−10.6377	−0.646196	−0.323098	−	0.946366i	$-0.604724\pi$
$271$	−10.6377	−0.646196	−0.323098	+	0.946366i	$0.604724\pi$
$272$	−7.74094	−0.469363
$273$	0	0
$274$	−0.572417	−0.0345809
$275$	−3.00597	−0.181267
$276$	−0.841166	−0.0506323
$277$	26.4674	1.59027	0.795136	−	0.606431i	$-0.207399\pi$
$277$	26.4674	1.59027	0.795136	+	0.606431i	$0.207399\pi$
$278$	−16.7627	−1.00536
$279$	−6.26875	−0.375300
$280$	−0.692021	−0.0413562
$281$	−5.60388	−0.334299	−0.167150	−	0.985932i	$-0.553456\pi$
$281$	−5.60388	−0.334299	−0.167150	+	0.985932i	$0.553456\pi$
$282$	10.3177	0.614408
$283$	−11.3351	−0.673803	−0.336902	−	0.941540i	$-0.609379\pi$
$283$	−11.3351	−0.673803	−0.336902	+	0.941540i	$0.609379\pi$
$284$	−9.93661	−0.589629
$285$	−2.69873	−0.159859
$286$	0	0
$287$	11.7409	0.693046
$288$	−1.00000	−0.0589256
$289$	42.9221	2.52483
$290$	−6.21983	−0.365241
$291$	8.61596	0.505076
$292$	−14.5918	−0.853920
$293$	−20.7530	−1.21240	−0.606202	−	0.795311i	$-0.707308\pi$
$293$	−20.7530	−1.21240	−0.606202	+	0.795311i	$0.707308\pi$
$294$	1.00000	0.0583212
$295$	−7.53617	−0.438773
$296$	11.1685	0.649157
$297$	−0.664874	−0.0385799
$298$	−12.0194	−0.696264
$299$	0	0
$300$	4.52111	0.261026
$301$	9.87800	0.569359
$302$	−19.3491	−1.11342
$303$	−17.7235	−1.01819
$304$	3.89977	0.223667
$305$	−4.18970	−0.239902
$306$	7.74094	0.442520
$307$	−14.5961	−0.833044	−0.416522	−	0.909126i	$-0.636751\pi$
$307$	−14.5961	−0.833044	−0.416522	+	0.909126i	$0.636751\pi$
$308$	0.664874	0.0378847
$309$	12.5972	0.716628
$310$	4.33811	0.246388
$311$	−1.82371	−0.103413	−0.0517065	−	0.998662i	$-0.516466\pi$
$311$	−1.82371	−0.103413	−0.0517065	+	0.998662i	$0.516466\pi$
$312$	0	0
$313$	34.6112	1.95634	0.978170	−	0.207808i	$-0.0666331\pi$
$313$	34.6112	1.95634	0.978170	+	0.207808i	$0.0666331\pi$
$314$	2.19567	0.123909
$315$	0.692021	0.0389910
$316$	−1.60388	−0.0902250
$317$	4.49396	0.252406	0.126203	−	0.992004i	$-0.459721\pi$
$317$	4.49396	0.252406	0.126203	+	0.992004i	$0.459721\pi$
$318$	−7.92154	−0.444218
$319$	5.97584	0.334583
$320$	0.692021	0.0386852
$321$	0.692021	0.0386249
$322$	−0.841166	−0.0468764
$323$	−30.1879	−1.67970
$324$	1.00000	0.0555556
$325$	0	0
$326$	19.3599	1.07224
$327$	8.03923	0.444570
$328$	−11.7409	−0.648285
$329$	10.3177	0.568831
$330$	0.460107	0.0253281
$331$	8.75733	0.481347	0.240673	−	0.970606i	$-0.422632\pi$
$331$	8.75733	0.481347	0.240673	+	0.970606i	$0.422632\pi$
$332$	−4.39612	−0.241269
$333$	−11.1685	−0.612031
$334$	20.5133	1.12244
$335$	2.06770	0.112971
$336$	−1.00000	−0.0545545
$337$	12.6136	0.687105	0.343552	−	0.939134i	$-0.388370\pi$
$337$	12.6136	0.687105	0.343552	+	0.939134i	$0.388370\pi$
$338$	0	0
$339$	−12.5918	−0.683892
$340$	−5.35690	−0.290518
$341$	−4.16793	−0.225706
$342$	−3.89977	−0.210876
$343$	1.00000	0.0539949
$344$	−9.87800	−0.532586
$345$	−0.582105	−0.0313395
$346$	−9.08815	−0.488582
$347$	19.4034	1.04163	0.520815	−	0.853670i	$-0.325628\pi$
$347$	19.4034	1.04163	0.520815	+	0.853670i	$0.325628\pi$
$348$	−8.98792	−0.481803
$349$	−0.415502	−0.0222413	−0.0111207	−	0.999938i	$-0.503540\pi$
$349$	−0.415502	−0.0222413	−0.0111207	+	0.999938i	$0.503540\pi$
$350$	4.52111	0.241663
$351$	0	0
$352$	−0.664874	−0.0354379
$353$	−16.4450	−0.875281	−0.437641	−	0.899150i	$-0.644186\pi$
$353$	−16.4450	−0.875281	−0.437641	+	0.899150i	$0.644186\pi$
$354$	−10.8901	−0.578801
$355$	−6.87635	−0.364959
$356$	−0.454731	−0.0241007
$357$	7.74094	0.409694
$358$	−8.98792	−0.475026
$359$	−6.61058	−0.348893	−0.174447	−	0.984667i	$-0.555814\pi$
$359$	−6.61058	−0.348893	−0.174447	+	0.984667i	$0.555814\pi$
$360$	−0.692021	−0.0364727
$361$	−3.79178	−0.199567
$362$	1.76941	0.0929983
$363$	10.5579	0.554148
$364$	0	0
$365$	−10.0978	−0.528545
$366$	−6.05429	−0.316463
$367$	15.5773	0.813129	0.406565	−	0.913622i	$-0.366727\pi$
$367$	15.5773	0.813129	0.406565	+	0.913622i	$0.366727\pi$
$368$	0.841166	0.0438488
$369$	11.7409	0.611209
$370$	7.72886	0.401804
$371$	−7.92154	−0.411266
$372$	6.26875	0.325020
$373$	−1.81940	−0.0942048	−0.0471024	−	0.998890i	$-0.514999\pi$
$373$	−1.81940	−0.0942048	−0.0471024	+	0.998890i	$0.514999\pi$
$374$	5.14675	0.266132
$375$	6.58881	0.340245
$376$	−10.3177	−0.532093
$377$	0	0
$378$	1.00000	0.0514344
$379$	7.53617	0.387107	0.193554	−	0.981090i	$-0.437999\pi$
$379$	7.53617	0.387107	0.193554	+	0.981090i	$0.437999\pi$
$380$	2.69873	0.138442
$381$	−6.76809	−0.346740
$382$	16.7657	0.857807
$383$	−3.78017	−0.193158	−0.0965788	−	0.995325i	$-0.530790\pi$
$383$	−3.78017	−0.193158	−0.0965788	+	0.995325i	$0.530790\pi$
$384$	1.00000	0.0510310
$385$	0.460107	0.0234492
$386$	16.9933	0.864936
$387$	9.87800	0.502127
$388$	−8.61596	−0.437409
$389$	5.01208	0.254123	0.127061	−	0.991895i	$-0.459446\pi$
$389$	5.01208	0.254123	0.127061	+	0.991895i	$0.459446\pi$
$390$	0	0
$391$	−6.51142	−0.329297
$392$	−1.00000	−0.0505076
$393$	−0.987918	−0.0498339
$394$	−4.90946	−0.247335
$395$	−1.10992	−0.0558459
$396$	0.664874	0.0334112
$397$	5.05562	0.253734	0.126867	−	0.991920i	$-0.459508\pi$
$397$	5.05562	0.253734	0.126867	+	0.991920i	$0.459508\pi$
$398$	14.9729	0.750521
$399$	−3.89977	−0.195233
$400$	−4.52111	−0.226055
$401$	−38.8745	−1.94130	−0.970651	−	0.240492i	$-0.922691\pi$
$401$	−38.8745	−1.94130	−0.970651	+	0.240492i	$0.922691\pi$
$402$	2.98792	0.149024
$403$	0	0
$404$	17.7235	0.881776
$405$	0.692021	0.0343868
$406$	−8.98792	−0.446063
$407$	−7.42566	−0.368077
$408$	−7.74094	−0.383234
$409$	−32.6461	−1.61425	−0.807123	−	0.590384i	$-0.798976\pi$
$409$	−32.6461	−1.61425	−0.807123	+	0.590384i	$0.798976\pi$
$410$	−8.12498	−0.401264
$411$	−0.572417	−0.0282352
$412$	−12.5972	−0.620618
$413$	−10.8901	−0.535866
$414$	−0.841166	−0.0413411
$415$	−3.04221	−0.149336
$416$	0	0
$417$	−16.7627	−0.820873
$418$	−2.59286	−0.126821
$419$	23.3250	1.13950	0.569750	−	0.821818i	$-0.307040\pi$
$419$	23.3250	1.13950	0.569750	+	0.821818i	$0.307040\pi$
$420$	−0.692021	−0.0337672
$421$	−18.2282	−0.888388	−0.444194	−	0.895931i	$-0.646510\pi$
$421$	−18.2282	−0.888388	−0.444194	+	0.895931i	$0.646510\pi$
$422$	6.98792	0.340167
$423$	10.3177	0.501662
$424$	7.92154	0.384704
$425$	34.9976	1.69763
$426$	−9.93661	−0.481430
$427$	−6.05429	−0.292988
$428$	−0.692021	−0.0334501
$429$	0	0
$430$	−6.83579	−0.329651
$431$	4.02177	0.193722	0.0968609	−	0.995298i	$-0.469120\pi$
$431$	4.02177	0.193722	0.0968609	+	0.995298i	$0.469120\pi$
$432$	−1.00000	−0.0481125
$433$	−11.4470	−0.550106	−0.275053	−	0.961429i	$-0.588695\pi$
$433$	−11.4470	−0.550106	−0.275053	+	0.961429i	$0.588695\pi$
$434$	6.26875	0.300910
$435$	−6.21983	−0.298218
$436$	−8.03923	−0.385009
$437$	3.28036	0.156921
$438$	−14.5918	−0.697223
$439$	−37.6450	−1.79670	−0.898349	−	0.439282i	$-0.855233\pi$
$439$	−37.6450	−1.79670	−0.898349	+	0.439282i	$0.855233\pi$
$440$	−0.460107	−0.0219348
$441$	1.00000	0.0476190
$442$	0	0
$443$	−31.7797	−1.50990	−0.754949	−	0.655783i	$-0.772339\pi$
$443$	−31.7797	−1.50990	−0.754949	+	0.655783i	$0.772339\pi$
$444$	11.1685	0.530035
$445$	−0.314683	−0.0149174
$446$	−1.13467	−0.0537282
$447$	−12.0194	−0.568497
$448$	1.00000	0.0472456
$449$	−1.82371	−0.0860661	−0.0430331	−	0.999074i	$-0.513702\pi$
$449$	−1.82371	−0.0860661	−0.0430331	+	0.999074i	$0.513702\pi$
$450$	4.52111	0.213127
$451$	7.80625	0.367582
$452$	12.5918	0.592268
$453$	−19.3491	−0.909101
$454$	5.26205	0.246960
$455$	0	0
$456$	3.89977	0.182624
$457$	−11.0774	−0.518179	−0.259089	−	0.965853i	$-0.583422\pi$
$457$	−11.0774	−0.518179	−0.259089	+	0.965853i	$0.583422\pi$
$458$	3.40821	0.159255
$459$	7.74094	0.361316
$460$	0.582105	0.0271408
$461$	3.82908	0.178338	0.0891691	−	0.996016i	$-0.471579\pi$
$461$	3.82908	0.178338	0.0891691	+	0.996016i	$0.471579\pi$
$462$	0.664874	0.0309328
$463$	−36.0737	−1.67649	−0.838243	−	0.545297i	$-0.816417\pi$
$463$	−36.0737	−1.67649	−0.838243	+	0.545297i	$0.816417\pi$
$464$	8.98792	0.417254
$465$	4.33811	0.201175
$466$	23.6775	1.09684
$467$	−38.3806	−1.77604	−0.888021	−	0.459803i	$-0.847920\pi$
$467$	−38.3806	−1.77604	−0.888021	+	0.459803i	$0.847920\pi$
$468$	0	0
$469$	2.98792	0.137969
$470$	−7.14005	−0.329346
$471$	2.19567	0.101171
$472$	10.8901	0.501257
$473$	6.56763	0.301980
$474$	−1.60388	−0.0736684
$475$	−17.6313	−0.808979
$476$	−7.74094	−0.354805
$477$	−7.92154	−0.362703
$478$	−20.2610	−0.926716
$479$	−11.3599	−0.519046	−0.259523	−	0.965737i	$-0.583565\pi$
$479$	−11.3599	−0.519046	−0.259523	+	0.965737i	$0.583565\pi$
$480$	0.692021	0.0315863
$481$	0	0
$482$	0.0435405	0.00198322
$483$	−0.841166	−0.0382744
$484$	−10.5579	−0.479906
$485$	−5.96243	−0.270740
$486$	1.00000	0.0453609
$487$	−37.4577	−1.69737	−0.848686	−	0.528898i	$-0.822605\pi$
$487$	−37.4577	−1.69737	−0.848686	+	0.528898i	$0.822605\pi$
$488$	6.05429	0.274065
$489$	19.3599	0.875484
$490$	−0.692021	−0.0312623
$491$	24.0200	1.08401	0.542003	−	0.840377i	$-0.317666\pi$
$491$	24.0200	1.08401	0.542003	+	0.840377i	$0.317666\pi$
$492$	−11.7409	−0.529322
$493$	−69.5749	−3.13350
$494$	0	0
$495$	0.460107	0.0206803
$496$	−6.26875	−0.281475
$497$	−9.93661	−0.445718
$498$	−4.39612	−0.196995
$499$	−36.3043	−1.62520	−0.812601	−	0.582821i	$-0.801949\pi$
$499$	−36.3043	−1.62520	−0.812601	+	0.582821i	$0.801949\pi$
$500$	−6.58881	−0.294661
$501$	20.5133	0.916468
$502$	27.3056	1.21871
$503$	−15.6340	−0.697086	−0.348543	−	0.937293i	$-0.613323\pi$
$503$	−15.6340	−0.697086	−0.348543	+	0.937293i	$0.613323\pi$
$504$	−1.00000	−0.0445435
$505$	12.2650	0.545787
$506$	−0.559270	−0.0248626
$507$	0	0
$508$	6.76809	0.300285
$509$	−12.0248	−0.532988	−0.266494	−	0.963837i	$-0.585865\pi$
$509$	−12.0248	−0.532988	−0.266494	+	0.963837i	$0.585865\pi$
$510$	−5.35690	−0.237207
$511$	−14.5918	−0.645503
$512$	−1.00000	−0.0441942
$513$	−3.89977	−0.172179
$514$	−7.97584	−0.351799
$515$	−8.71751	−0.384140
$516$	−9.87800	−0.434855
$517$	6.85995	0.301700
$518$	11.1685	0.490717
$519$	−9.08815	−0.398925
$520$	0	0
$521$	−16.0054	−0.701208	−0.350604	−	0.936524i	$-0.614024\pi$
$521$	−16.0054	−0.701208	−0.350604	+	0.936524i	$0.614024\pi$
$522$	−8.98792	−0.393391
$523$	0.143768	0.00628654	0.00314327	−	0.999995i	$-0.498999\pi$
$523$	0.143768	0.00628654	0.00314327	+	0.999995i	$0.498999\pi$
$524$	0.987918	0.0431574
$525$	4.52111	0.197317
$526$	−9.37867	−0.408929
$527$	48.5260	2.11383
$528$	−0.664874	−0.0289349
$529$	−22.2924	−0.969236
$530$	5.48188	0.238118
$531$	−10.8901	−0.472589
$532$	3.89977	0.169077
$533$	0	0
$534$	−0.454731	−0.0196781
$535$	−0.478894	−0.0207044
$536$	−2.98792	−0.129058
$537$	−8.98792	−0.387857
$538$	−7.96077	−0.343213
$539$	0.664874	0.0286382
$540$	−0.692021	−0.0297799
$541$	30.2717	1.30148	0.650742	−	0.759299i	$-0.274458\pi$
$541$	30.2717	1.30148	0.650742	+	0.759299i	$0.274458\pi$
$542$	10.6377	0.456930
$543$	1.76941	0.0759328
$544$	7.74094	0.331890
$545$	−5.56332	−0.238306
$546$	0	0
$547$	30.7681	1.31555	0.657774	−	0.753215i	$-0.271498\pi$
$547$	30.7681	1.31555	0.657774	+	0.753215i	$0.271498\pi$
$548$	0.572417	0.0244524
$549$	−6.05429	−0.258391
$550$	3.00597	0.128175
$551$	35.0508	1.49322
$552$	0.841166	0.0358024
$553$	−1.60388	−0.0682037
$554$	−26.4674	−1.12449
$555$	7.72886	0.328072
$556$	16.7627	0.710897
$557$	5.01208	0.212369	0.106184	−	0.994346i	$-0.466137\pi$
$557$	5.01208	0.212369	0.106184	+	0.994346i	$0.466137\pi$
$558$	6.26875	0.265377
$559$	0	0
$560$	0.692021	0.0292432
$561$	5.14675	0.217296
$562$	5.60388	0.236385
$563$	23.3793	0.985318	0.492659	−	0.870222i	$-0.336025\pi$
$563$	23.3793	0.985318	0.492659	+	0.870222i	$0.336025\pi$
$564$	−10.3177	−0.434452
$565$	8.71379	0.366592
$566$	11.3351	0.476451
$567$	1.00000	0.0419961
$568$	9.93661	0.416931
$569$	25.9168	1.08649	0.543243	−	0.839575i	$-0.317196\pi$
$569$	25.9168	1.08649	0.543243	+	0.839575i	$0.317196\pi$
$570$	2.69873	0.113037
$571$	−19.3163	−0.808364	−0.404182	−	0.914679i	$-0.632444\pi$
$571$	−19.3163	−0.808364	−0.404182	+	0.914679i	$0.632444\pi$
$572$	0	0
$573$	16.7657	0.700397
$574$	−11.7409	−0.490057
$575$	−3.80300	−0.158596
$576$	1.00000	0.0416667
$577$	−17.7802	−0.740198	−0.370099	−	0.928992i	$-0.620676\pi$
$577$	−17.7802	−0.740198	−0.370099	+	0.928992i	$0.620676\pi$
$578$	−42.9221	−1.78533
$579$	16.9933	0.706217
$580$	6.21983	0.258264
$581$	−4.39612	−0.182382
$582$	−8.61596	−0.357143
$583$	−5.26683	−0.218130
$584$	14.5918	0.603813
$585$	0	0
$586$	20.7530	0.857299
$587$	2.95300	0.121883	0.0609417	−	0.998141i	$-0.480590\pi$
$587$	2.95300	0.121883	0.0609417	+	0.998141i	$0.480590\pi$
$588$	−1.00000	−0.0412393
$589$	−24.4467	−1.00731
$590$	7.53617	0.310259
$591$	−4.90946	−0.201948
$592$	−11.1685	−0.459023
$593$	27.9758	1.14883	0.574415	−	0.818564i	$-0.305230\pi$
$593$	27.9758	1.14883	0.574415	+	0.818564i	$0.305230\pi$
$594$	0.664874	0.0272801
$595$	−5.35690	−0.219611
$596$	12.0194	0.492333
$597$	14.9729	0.612798
$598$	0	0
$599$	−9.53617	−0.389637	−0.194819	−	0.980839i	$-0.562412\pi$
$599$	−9.53617	−0.389637	−0.194819	+	0.980839i	$0.562412\pi$
$600$	−4.52111	−0.184573
$601$	21.9215	0.894198	0.447099	−	0.894484i	$-0.352457\pi$
$601$	21.9215	0.894198	0.447099	+	0.894484i	$0.352457\pi$
$602$	−9.87800	−0.402597
$603$	2.98792	0.121677
$604$	19.3491	0.787305
$605$	−7.30632	−0.297044
$606$	17.7235	0.719967
$607$	−45.6625	−1.85338	−0.926691	−	0.375823i	$-0.877360\pi$
$607$	−45.6625	−1.85338	−0.926691	+	0.375823i	$0.877360\pi$
$608$	−3.89977	−0.158157
$609$	−8.98792	−0.364209
$610$	4.18970	0.169636
$611$	0	0
$612$	−7.74094	−0.312909
$613$	−29.7071	−1.19986	−0.599929	−	0.800053i	$-0.704805\pi$
$613$	−29.7071	−1.19986	−0.599929	+	0.800053i	$0.704805\pi$
$614$	14.5961	0.589051
$615$	−8.12498	−0.327631
$616$	−0.664874	−0.0267886
$617$	37.4034	1.50581	0.752903	−	0.658132i	$-0.228653\pi$
$617$	37.4034	1.50581	0.752903	+	0.658132i	$0.228653\pi$
$618$	−12.5972	−0.506733
$619$	12.0000	0.482321	0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000	0.482321	0.241160	+	0.970485i	$0.422472\pi$
$620$	−4.33811	−0.174223
$621$	−0.841166	−0.0337548
$622$	1.82371	0.0731240
$623$	−0.454731	−0.0182184
$624$	0	0
$625$	18.0459	0.721837
$626$	−34.6112	−1.38334
$627$	−2.59286	−0.103549
$628$	−2.19567	−0.0876167
$629$	86.4548	3.44718
$630$	−0.692021	−0.0275708
$631$	−17.3163	−0.689353	−0.344676	−	0.938722i	$-0.612011\pi$
$631$	−17.3163	−0.689353	−0.344676	+	0.938722i	$0.612011\pi$
$632$	1.60388	0.0637987
$633$	6.98792	0.277745
$634$	−4.49396	−0.178478
$635$	4.68366	0.185865
$636$	7.92154	0.314110
$637$	0	0
$638$	−5.97584	−0.236586
$639$	−9.93661	−0.393086
$640$	−0.692021	−0.0273546
$641$	−27.3599	−1.08065	−0.540325	−	0.841456i	$-0.681699\pi$
$641$	−27.3599	−1.08065	−0.540325	+	0.841456i	$0.681699\pi$
$642$	−0.692021	−0.0273119
$643$	19.1675	0.755891	0.377945	−	0.925828i	$-0.376631\pi$
$643$	19.1675	0.755891	0.377945	+	0.925828i	$0.376631\pi$
$644$	0.841166	0.0331466
$645$	−6.83579	−0.269159
$646$	30.1879	1.18773
$647$	−27.4711	−1.08000	−0.540001	−	0.841665i	$-0.681576\pi$
$647$	−27.4711	−1.08000	−0.540001	+	0.841665i	$0.681576\pi$
$648$	−1.00000	−0.0392837
$649$	−7.24054	−0.284216
$650$	0	0
$651$	6.26875	0.245692
$652$	−19.3599	−0.758191
$653$	43.2680	1.69321	0.846604	−	0.532223i	$-0.178643\pi$
$653$	43.2680	1.69321	0.846604	+	0.532223i	$0.178643\pi$
$654$	−8.03923	−0.314359
$655$	0.683661	0.0267128
$656$	11.7409	0.458407
$657$	−14.5918	−0.569280
$658$	−10.3177	−0.402225
$659$	−19.8619	−0.773709	−0.386854	−	0.922141i	$-0.626438\pi$
$659$	−19.8619	−0.773709	−0.386854	+	0.922141i	$0.626438\pi$
$660$	−0.460107	−0.0179097
$661$	13.4625	0.523631	0.261815	−	0.965118i	$-0.415679\pi$
$661$	13.4625	0.523631	0.261815	+	0.965118i	$0.415679\pi$
$662$	−8.75733	−0.340363
$663$	0	0
$664$	4.39612	0.170603
$665$	2.69873	0.104652
$666$	11.1685	0.432771
$667$	7.56033	0.292737
$668$	−20.5133	−0.793685
$669$	−1.13467	−0.0438689
$670$	−2.06770	−0.0798824
$671$	−4.02535	−0.155397
$672$	1.00000	0.0385758
$673$	−19.2731	−0.742922	−0.371461	−	0.928449i	$-0.621143\pi$
$673$	−19.2731	−0.742922	−0.371461	+	0.928449i	$0.621143\pi$
$674$	−12.6136	−0.485856
$675$	4.52111	0.174017
$676$	0	0
$677$	−20.5241	−0.788805	−0.394402	−	0.918938i	$-0.629048\pi$
$677$	−20.5241	−0.788805	−0.394402	+	0.918938i	$0.629048\pi$
$678$	12.5918	0.483585
$679$	−8.61596	−0.330650
$680$	5.35690	0.205428
$681$	5.26205	0.201642
$682$	4.16793	0.159598
$683$	−4.07202	−0.155811	−0.0779057	−	0.996961i	$-0.524823\pi$
$683$	−4.07202	−0.155811	−0.0779057	+	0.996961i	$0.524823\pi$
$684$	3.89977	0.149112
$685$	0.396125	0.0151351
$686$	−1.00000	−0.0381802
$687$	3.40821	0.130031
$688$	9.87800	0.376595
$689$	0	0
$690$	0.582105	0.0221604
$691$	−35.3739	−1.34569	−0.672843	−	0.739785i	$-0.734927\pi$
$691$	−35.3739	−1.34569	−0.672843	+	0.739785i	$0.734927\pi$
$692$	9.08815	0.345479
$693$	0.664874	0.0252565
$694$	−19.4034	−0.736544
$695$	11.6002	0.440019
$696$	8.98792	0.340686
$697$	−90.8859	−3.44255
$698$	0.415502	0.0157270
$699$	23.6775	0.895567
$700$	−4.52111	−0.170882
$701$	−9.27280	−0.350229	−0.175114	−	0.984548i	$-0.556030\pi$
$701$	−9.27280	−0.350229	−0.175114	+	0.984548i	$0.556030\pi$
$702$	0	0
$703$	−43.5547	−1.64270
$704$	0.664874	0.0250584
$705$	−7.14005	−0.268910
$706$	16.4450	0.618917
$707$	17.7235	0.666560
$708$	10.8901	0.409274
$709$	2.31527	0.0869520	0.0434760	−	0.999054i	$-0.486157\pi$
$709$	2.31527	0.0869520	0.0434760	+	0.999054i	$0.486157\pi$
$710$	6.87635	0.258065
$711$	−1.60388	−0.0601500
$712$	0.454731	0.0170417
$713$	−5.27306	−0.197478
$714$	−7.74094	−0.289697
$715$	0	0
$716$	8.98792	0.335894
$717$	−20.2610	−0.756660
$718$	6.61058	0.246705
$719$	0.987918	0.0368431	0.0184216	−	0.999830i	$-0.494136\pi$
$719$	0.987918	0.0368431	0.0184216	+	0.999830i	$0.494136\pi$
$720$	0.692021	0.0257901
$721$	−12.5972	−0.469143
$722$	3.79178	0.141115
$723$	0.0435405	0.00161929
$724$	−1.76941	−0.0657597
$725$	−40.6353	−1.50916
$726$	−10.5579	−0.391842
$727$	−23.1860	−0.859920	−0.429960	−	0.902848i	$-0.641472\pi$
$727$	−23.1860	−0.859920	−0.429960	+	0.902848i	$0.641472\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.0978	0.373738
$731$	−76.4650	−2.82816
$732$	6.05429	0.223773
$733$	−26.5435	−0.980405	−0.490203	−	0.871608i	$-0.663077\pi$
$733$	−26.5435	−0.980405	−0.490203	+	0.871608i	$0.663077\pi$
$734$	−15.5773	−0.574969
$735$	−0.692021	−0.0255256
$736$	−0.841166	−0.0310058
$737$	1.98659	0.0731770
$738$	−11.7409	−0.432190
$739$	−19.3491	−0.711769	−0.355885	−	0.934530i	$-0.615820\pi$
$739$	−19.3491	−0.711769	−0.355885	+	0.934530i	$0.615820\pi$
$740$	−7.72886	−0.284118
$741$	0	0
$742$	7.92154	0.290809
$743$	51.8437	1.90196	0.950980	−	0.309252i	$-0.100079\pi$
$743$	51.8437	1.90196	0.950980	+	0.309252i	$0.100079\pi$
$744$	−6.26875	−0.229824
$745$	8.31767	0.304736
$746$	1.81940	0.0666128
$747$	−4.39612	−0.160846
$748$	−5.14675	−0.188184
$749$	−0.692021	−0.0252859
$750$	−6.58881	−0.240589
$751$	−16.9095	−0.617035	−0.308517	−	0.951219i	$-0.599833\pi$
$751$	−16.9095	−0.617035	−0.308517	+	0.951219i	$0.599833\pi$
$752$	10.3177	0.376247
$753$	27.3056	0.995071
$754$	0	0
$755$	13.3900	0.487312
$756$	−1.00000	−0.0363696
$757$	−23.5297	−0.855203	−0.427601	−	0.903967i	$-0.640641\pi$
$757$	−23.5297	−0.855203	−0.427601	+	0.903967i	$0.640641\pi$
$758$	−7.53617	−0.273726
$759$	−0.559270	−0.0203002
$760$	−2.69873	−0.0978931
$761$	9.60627	0.348227	0.174113	−	0.984726i	$-0.444294\pi$
$761$	9.60627	0.348227	0.174113	+	0.984726i	$0.444294\pi$
$762$	6.76809	0.245182
$763$	−8.03923	−0.291040
$764$	−16.7657	−0.606561
$765$	−5.35690	−0.193679
$766$	3.78017	0.136583
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	2.29829	0.0828785	0.0414392	−	0.999141i	$-0.486806\pi$
$769$	2.29829	0.0828785	0.0414392	+	0.999141i	$0.486806\pi$
$770$	−0.460107	−0.0165811
$771$	−7.97584	−0.287243
$772$	−16.9933	−0.611602
$773$	−10.2828	−0.369845	−0.184922	−	0.982753i	$-0.559203\pi$
$773$	−10.2828	−0.369845	−0.184922	+	0.982753i	$0.559203\pi$
$774$	−9.87800	−0.355057
$775$	28.3417	1.01806
$776$	8.61596	0.309295
$777$	11.1685	0.400669
$778$	−5.01208	−0.179692
$779$	45.7870	1.64049
$780$	0	0
$781$	−6.60660	−0.236403
$782$	6.51142	0.232848
$783$	−8.98792	−0.321202
$784$	1.00000	0.0357143
$785$	−1.51945	−0.0542315
$786$	0.987918	0.0352379
$787$	26.2398	0.935348	0.467674	−	0.883901i	$-0.345092\pi$
$787$	26.2398	0.935348	0.467674	+	0.883901i	$0.345092\pi$
$788$	4.90946	0.174892
$789$	−9.37867	−0.333889
$790$	1.10992	0.0394890
$791$	12.5918	0.447713
$792$	−0.664874	−0.0236253
$793$	0	0
$794$	−5.05562	−0.179417
$795$	5.48188	0.194422
$796$	−14.9729	−0.530699
$797$	−10.6203	−0.376189	−0.188095	−	0.982151i	$-0.560231\pi$
$797$	−10.6203	−0.376189	−0.188095	+	0.982151i	$0.560231\pi$
$798$	3.89977	0.138050
$799$	−79.8684	−2.82554
$800$	4.52111	0.159845
$801$	−0.454731	−0.0160671
$802$	38.8745	1.37271
$803$	−9.70171	−0.342366
$804$	−2.98792	−0.105376
$805$	0.582105	0.0205165
$806$	0	0
$807$	−7.96077	−0.280232
$808$	−17.7235	−0.623510
$809$	−32.0435	−1.12659	−0.563295	−	0.826256i	$-0.690467\pi$
$809$	−32.0435	−1.12659	−0.563295	+	0.826256i	$0.690467\pi$
$810$	−0.692021	−0.0243152
$811$	25.9909	0.912664	0.456332	−	0.889810i	$-0.349163\pi$
$811$	25.9909	0.912664	0.456332	+	0.889810i	$0.349163\pi$
$812$	8.98792	0.315414
$813$	10.6377	0.373081
$814$	7.42566	0.260269
$815$	−13.3975	−0.469292
$816$	7.74094	0.270987
$817$	38.5220	1.34771
$818$	32.6461	1.14144
$819$	0	0
$820$	8.12498	0.283737
$821$	34.5133	1.20452	0.602262	−	0.798299i	$-0.294266\pi$
$821$	34.5133	1.20452	0.602262	+	0.798299i	$0.294266\pi$
$822$	0.572417	0.0199653
$823$	9.84309	0.343108	0.171554	−	0.985175i	$-0.445121\pi$
$823$	9.84309	0.343108	0.171554	+	0.985175i	$0.445121\pi$
$824$	12.5972	0.438843
$825$	3.00597	0.104654
$826$	10.8901	0.378914
$827$	−16.2892	−0.566431	−0.283215	−	0.959056i	$-0.591401\pi$
$827$	−16.2892	−0.566431	−0.283215	+	0.959056i	$0.591401\pi$
$828$	0.841166	0.0292326
$829$	13.9323	0.483889	0.241944	−	0.970290i	$-0.422215\pi$
$829$	13.9323	0.483889	0.241944	+	0.970290i	$0.422215\pi$
$830$	3.04221	0.105597
$831$	−26.4674	−0.918144
$832$	0	0
$833$	−7.74094	−0.268208
$834$	16.7627	0.580445
$835$	−14.1957	−0.491261
$836$	2.59286	0.0896759
$837$	6.26875	0.216680
$838$	−23.3250	−0.805747
$839$	6.49396	0.224196	0.112098	−	0.993697i	$-0.464243\pi$
$839$	6.49396	0.224196	0.112098	+	0.993697i	$0.464243\pi$
$840$	0.692021	0.0238770
$841$	51.7827	1.78561
$842$	18.2282	0.628185
$843$	5.60388	0.193008
$844$	−6.98792	−0.240534
$845$	0	0
$846$	−10.3177	−0.354729
$847$	−10.5579	−0.362775
$848$	−7.92154	−0.272027
$849$	11.3351	0.389021
$850$	−34.9976	−1.20041
$851$	−9.39459	−0.322042
$852$	9.93661	0.340423
$853$	−45.1099	−1.54453	−0.772267	−	0.635298i	$-0.780877\pi$
$853$	−45.1099	−1.54453	−0.772267	+	0.635298i	$0.780877\pi$
$854$	6.05429	0.207174
$855$	2.69873	0.0922945
$856$	0.692021	0.0236528
$857$	−4.66189	−0.159247	−0.0796236	−	0.996825i	$-0.525372\pi$
$857$	−4.66189	−0.159247	−0.0796236	+	0.996825i	$0.525372\pi$
$858$	0	0
$859$	−37.6364	−1.28414	−0.642069	−	0.766647i	$-0.721924\pi$
$859$	−37.6364	−1.28414	−0.642069	+	0.766647i	$0.721924\pi$
$860$	6.83579	0.233098
$861$	−11.7409	−0.400130
$862$	−4.02177	−0.136982
$863$	−14.1021	−0.480043	−0.240021	−	0.970768i	$-0.577154\pi$
$863$	−14.1021	−0.480043	−0.240021	+	0.970768i	$0.577154\pi$
$864$	1.00000	0.0340207
$865$	6.28919	0.213839
$866$	11.4470	0.388984
$867$	−42.9221	−1.45771
$868$	−6.26875	−0.212775
$869$	−1.06638	−0.0361743
$870$	6.21983	0.210872
$871$	0	0
$872$	8.03923	0.272243
$873$	−8.61596	−0.291606
$874$	−3.28036	−0.110960
$875$	−6.58881	−0.222742
$876$	14.5918	0.493011
$877$	8.51765	0.287621	0.143810	−	0.989605i	$-0.454064\pi$
$877$	8.51765	0.287621	0.143810	+	0.989605i	$0.454064\pi$
$878$	37.6450	1.27046
$879$	20.7530	0.699982
$880$	0.460107	0.0155102
$881$	5.84548	0.196939	0.0984696	−	0.995140i	$-0.468605\pi$
$881$	5.84548	0.196939	0.0984696	+	0.995140i	$0.468605\pi$
$882$	−1.00000	−0.0336718
$883$	−26.8358	−0.903096	−0.451548	−	0.892247i	$-0.649128\pi$
$883$	−26.8358	−0.903096	−0.451548	+	0.892247i	$0.649128\pi$
$884$	0	0
$885$	7.53617	0.253326
$886$	31.7797	1.06766
$887$	−41.9758	−1.40941	−0.704705	−	0.709500i	$-0.748921\pi$
$887$	−41.9758	−1.40941	−0.704705	+	0.709500i	$0.748921\pi$
$888$	−11.1685	−0.374791
$889$	6.76809	0.226994
$890$	0.314683	0.0105482
$891$	0.664874	0.0222741
$892$	1.13467	0.0379916
$893$	40.2366	1.34646
$894$	12.0194	0.401988
$895$	6.21983	0.207906
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	1.82371	0.0608579
$899$	−56.3430	−1.87914
$900$	−4.52111	−0.150704
$901$	61.3202	2.04287
$902$	−7.80625	−0.259920
$903$	−9.87800	−0.328719
$904$	−12.5918	−0.418797
$905$	−1.22447	−0.0407028
$906$	19.3491	0.642832
$907$	−34.3043	−1.13905	−0.569527	−	0.821973i	$-0.692874\pi$
$907$	−34.3043	−1.13905	−0.569527	+	0.821973i	$0.692874\pi$
$908$	−5.26205	−0.174627
$909$	17.7235	0.587851
$910$	0	0
$911$	−16.4179	−0.543949	−0.271975	−	0.962304i	$-0.587677\pi$
$911$	−16.4179	−0.543949	−0.271975	+	0.962304i	$0.587677\pi$
$912$	−3.89977	−0.129134
$913$	−2.92287	−0.0967329
$914$	11.0774	0.366408
$915$	4.18970	0.138507
$916$	−3.40821	−0.112610
$917$	0.987918	0.0326239
$918$	−7.74094	−0.255489
$919$	−44.9697	−1.48341	−0.741707	−	0.670724i	$-0.765984\pi$
$919$	−44.9697	−1.48341	−0.741707	+	0.670724i	$0.765984\pi$
$920$	−0.582105	−0.0191914
$921$	14.5961	0.480958
$922$	−3.82908	−0.126104
$923$	0	0
$924$	−0.664874	−0.0218728
$925$	50.4941	1.66024
$926$	36.0737	1.18545
$927$	−12.5972	−0.413745
$928$	−8.98792	−0.295043
$929$	16.5724	0.543723	0.271862	−	0.962336i	$-0.412361\pi$
$929$	16.5724	0.543723	0.271862	+	0.962336i	$0.412361\pi$
$930$	−4.33811	−0.142252
$931$	3.89977	0.127810
$932$	−23.6775	−0.775584
$933$	1.82371	0.0597055
$934$	38.3806	1.25585
$935$	−3.56166	−0.116479
$936$	0	0
$937$	50.5435	1.65118	0.825592	−	0.564268i	$-0.190842\pi$
$937$	50.5435	1.65118	0.825592	+	0.564268i	$0.190842\pi$
$938$	−2.98792	−0.0975590
$939$	−34.6112	−1.12949
$940$	7.14005	0.232883
$941$	−37.9191	−1.23613	−0.618064	−	0.786127i	$-0.712083\pi$
$941$	−37.9191	−1.23613	−0.618064	+	0.786127i	$0.712083\pi$
$942$	−2.19567	−0.0715388
$943$	9.87608	0.321610
$944$	−10.8901	−0.354442
$945$	−0.692021	−0.0225115
$946$	−6.56763	−0.213532
$947$	−10.2067	−0.331673	−0.165836	−	0.986153i	$-0.553032\pi$
$947$	−10.2067	−0.331673	−0.165836	+	0.986153i	$0.553032\pi$
$948$	1.60388	0.0520915
$949$	0	0
$950$	17.6313	0.572034
$951$	−4.49396	−0.145727
$952$	7.74094	0.250885
$953$	49.6292	1.60765	0.803824	−	0.594867i	$-0.202795\pi$
$953$	49.6292	1.60765	0.803824	+	0.594867i	$0.202795\pi$
$954$	7.92154	0.256469
$955$	−11.6022	−0.375439
$956$	20.2610	0.655287
$957$	−5.97584	−0.193171
$958$	11.3599	0.367021
$959$	0.572417	0.0184843
$960$	−0.692021	−0.0223349
$961$	8.29722	0.267652
$962$	0	0
$963$	−0.692021	−0.0223001
$964$	−0.0435405	−0.00140235
$965$	−11.7597	−0.378559
$966$	0.841166	0.0270641
$967$	−38.5461	−1.23956	−0.619780	−	0.784776i	$-0.712778\pi$
$967$	−38.5461	−1.23956	−0.619780	+	0.784776i	$0.712778\pi$
$968$	10.5579	0.339345
$969$	30.1879	0.969775
$970$	5.96243	0.191442
$971$	−6.45904	−0.207281	−0.103640	−	0.994615i	$-0.533049\pi$
$971$	−6.45904	−0.207281	−0.103640	+	0.994615i	$0.533049\pi$
$972$	−1.00000	−0.0320750
$973$	16.7627	0.537388
$974$	37.4577	1.20022
$975$	0	0
$976$	−6.05429	−0.193793
$977$	−9.85649	−0.315337	−0.157669	−	0.987492i	$-0.550398\pi$
$977$	−9.85649	−0.315337	−0.157669	+	0.987492i	$0.550398\pi$
$978$	−19.3599	−0.619061
$979$	−0.302339	−0.00966279
$980$	0.692021	0.0221058
$981$	−8.03923	−0.256673
$982$	−24.0200	−0.766508
$983$	−17.2728	−0.550917	−0.275458	−	0.961313i	$-0.588830\pi$
$983$	−17.2728	−0.550917	−0.275458	+	0.961313i	$0.588830\pi$
$984$	11.7409	0.374287
$985$	3.39745	0.108252
$986$	69.5749	2.21572
$987$	−10.3177	−0.328415
$988$	0	0
$989$	8.30904	0.264212
$990$	−0.460107	−0.0146232
$991$	21.0992	0.670237	0.335118	−	0.942176i	$-0.391224\pi$
$991$	21.0992	0.670237	0.335118	+	0.942176i	$0.391224\pi$
$992$	6.26875	0.199033
$993$	−8.75733	−0.277906
$994$	9.93661	0.315170
$995$	−10.3615	−0.328483
$996$	4.39612	0.139297
$997$	4.86113	0.153954	0.0769768	−	0.997033i	$-0.475473\pi$
$997$	4.86113	0.153954	0.0769768	+	0.997033i	$0.475473\pi$
$998$	36.3043	1.14919
$999$	11.1685	0.353356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cb.1.3	✓	3
13.12	even	2		7098.2.a.ck.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cb.1.3	✓	3	1.1	even	1	trivial
7098.2.a.ck.1.1	yes	3	13.12	even	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.692021 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.692021 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.692021 q^{10} +0.664874 q^{11} -1.00000 q^{12} -1.00000 q^{14} -0.692021 q^{15} +1.00000 q^{16} -7.74094 q^{17} -1.00000 q^{18} +3.89977 q^{19} +0.692021 q^{20} -1.00000 q^{21} -0.664874 q^{22} +0.841166 q^{23} +1.00000 q^{24} -4.52111 q^{25} -1.00000 q^{27} +1.00000 q^{28} +8.98792 q^{29} +0.692021 q^{30} -6.26875 q^{31} -1.00000 q^{32} -0.664874 q^{33} +7.74094 q^{34} +0.692021 q^{35} +1.00000 q^{36} -11.1685 q^{37} -3.89977 q^{38} -0.692021 q^{40} +11.7409 q^{41} +1.00000 q^{42} +9.87800 q^{43} +0.664874 q^{44} +0.692021 q^{45} -0.841166 q^{46} +10.3177 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.52111 q^{50} +7.74094 q^{51} -7.92154 q^{53} +1.00000 q^{54} +0.460107 q^{55} -1.00000 q^{56} -3.89977 q^{57} -8.98792 q^{58} -10.8901 q^{59} -0.692021 q^{60} -6.05429 q^{61} +6.26875 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.664874 q^{66} +2.98792 q^{67} -7.74094 q^{68} -0.841166 q^{69} -0.692021 q^{70} -9.93661 q^{71} -1.00000 q^{72} -14.5918 q^{73} +11.1685 q^{74} +4.52111 q^{75} +3.89977 q^{76} +0.664874 q^{77} -1.60388 q^{79} +0.692021 q^{80} +1.00000 q^{81} -11.7409 q^{82} -4.39612 q^{83} -1.00000 q^{84} -5.35690 q^{85} -9.87800 q^{86} -8.98792 q^{87} -0.664874 q^{88} -0.454731 q^{89} -0.692021 q^{90} +0.841166 q^{92} +6.26875 q^{93} -10.3177 q^{94} +2.69873 q^{95} +1.00000 q^{96} -8.61596 q^{97} -1.00000 q^{98} +0.664874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{15} + 3 q^{16} - 9 q^{17} - 3 q^{18} - 11 q^{19} - 3 q^{20} - 3 q^{21} - 3 q^{22} + 11 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{27} + 3 q^{28} + 8 q^{29} - 3 q^{30} - 11 q^{31} - 3 q^{32} - 3 q^{33} + 9 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} + 11 q^{38} + 3 q^{40} + 21 q^{41} + 3 q^{42} + 10 q^{43} + 3 q^{44} - 3 q^{45} - 11 q^{46} + 14 q^{47} - 3 q^{48} + 3 q^{49} - 2 q^{50} + 9 q^{51} + 2 q^{53} + 3 q^{54} - 24 q^{55} - 3 q^{56} + 11 q^{57} - 8 q^{58} - 32 q^{59} + 3 q^{60} - 6 q^{61} + 11 q^{62} + 3 q^{63} + 3 q^{64} + 3 q^{66} - 10 q^{67} - 9 q^{68} - 11 q^{69} + 3 q^{70} + 21 q^{71} - 3 q^{72} - 16 q^{73} + 3 q^{74} - 2 q^{75} - 11 q^{76} + 3 q^{77} + 4 q^{79} - 3 q^{80} + 3 q^{81} - 21 q^{82} - 22 q^{83} - 3 q^{84} - 12 q^{85} - 10 q^{86} - 8 q^{87} - 3 q^{88} + 21 q^{89} + 3 q^{90} + 11 q^{92} + 11 q^{93} - 14 q^{94} + 25 q^{95} + 3 q^{96} - 36 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 + 3 * q^15 + 3 * q^16 - 9 * q^17 - 3 * q^18 - 11 * q^19 - 3 * q^20 - 3 * q^21 - 3 * q^22 + 11 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^27 + 3 * q^28 + 8 * q^29 - 3 * q^30 - 11 * q^31 - 3 * q^32 - 3 * q^33 + 9 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 + 11 * q^38 + 3 * q^40 + 21 * q^41 + 3 * q^42 + 10 * q^43 + 3 * q^44 - 3 * q^45 - 11 * q^46 + 14 * q^47 - 3 * q^48 + 3 * q^49 - 2 * q^50 + 9 * q^51 + 2 * q^53 + 3 * q^54 - 24 * q^55 - 3 * q^56 + 11 * q^57 - 8 * q^58 - 32 * q^59 + 3 * q^60 - 6 * q^61 + 11 * q^62 + 3 * q^63 + 3 * q^64 + 3 * q^66 - 10 * q^67 - 9 * q^68 - 11 * q^69 + 3 * q^70 + 21 * q^71 - 3 * q^72 - 16 * q^73 + 3 * q^74 - 2 * q^75 - 11 * q^76 + 3 * q^77 + 4 * q^79 - 3 * q^80 + 3 * q^81 - 21 * q^82 - 22 * q^83 - 3 * q^84 - 12 * q^85 - 10 * q^86 - 8 * q^87 - 3 * q^88 + 21 * q^89 + 3 * q^90 + 11 * q^92 + 11 * q^93 - 14 * q^94 + 25 * q^95 + 3 * q^96 - 36 * q^97 - 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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