LMFDB - Embedded newform 4235.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.580017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 4x^{2} + 6x + 3 $ x^5 - 7x^3 - 4x^2 + 6*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.470042$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.470042 q^{2} -0.577925 q^{3} -1.77906 q^{4} -1.00000 q^{5} -0.271649 q^{6} +1.00000 q^{7} -1.77632 q^{8} -2.66600 q^{9} +O(q^{10})$	\(q+0.470042 q^{2} -0.577925 q^{3} -1.77906 q^{4} -1.00000 q^{5} -0.271649 q^{6} +1.00000 q^{7} -1.77632 q^{8} -2.66600 q^{9} -0.470042 q^{10} +1.02816 q^{12} -1.19839 q^{13} +0.470042 q^{14} +0.577925 q^{15} +2.72318 q^{16} +1.08534 q^{17} -1.25313 q^{18} +6.29189 q^{19} +1.77906 q^{20} -0.577925 q^{21} -6.35986 q^{23} +1.02658 q^{24} +1.00000 q^{25} -0.563295 q^{26} +3.27452 q^{27} -1.77906 q^{28} +6.79931 q^{29} +0.271649 q^{30} +9.46531 q^{31} +4.83264 q^{32} +0.510154 q^{34} -1.00000 q^{35} +4.74298 q^{36} -8.49980 q^{37} +2.95746 q^{38} +0.692581 q^{39} +1.77632 q^{40} +9.51571 q^{41} -0.271649 q^{42} -5.07339 q^{43} +2.66600 q^{45} -2.98940 q^{46} +3.89889 q^{47} -1.57379 q^{48} +1.00000 q^{49} +0.470042 q^{50} -0.627242 q^{51} +2.13201 q^{52} -12.2191 q^{53} +1.53916 q^{54} -1.77632 q^{56} -3.63624 q^{57} +3.19596 q^{58} -4.91466 q^{59} -1.02816 q^{60} -10.6033 q^{61} +4.44909 q^{62} -2.66600 q^{63} -3.17481 q^{64} +1.19839 q^{65} -5.09350 q^{67} -1.93088 q^{68} +3.67552 q^{69} -0.470042 q^{70} -7.24680 q^{71} +4.73567 q^{72} +10.2495 q^{73} -3.99527 q^{74} -0.577925 q^{75} -11.1937 q^{76} +0.325542 q^{78} -0.0718642 q^{79} -2.72318 q^{80} +6.10558 q^{81} +4.47278 q^{82} -9.16537 q^{83} +1.02816 q^{84} -1.08534 q^{85} -2.38471 q^{86} -3.92949 q^{87} -3.20656 q^{89} +1.25313 q^{90} -1.19839 q^{91} +11.3146 q^{92} -5.47024 q^{93} +1.83264 q^{94} -6.29189 q^{95} -2.79290 q^{96} -9.05358 q^{97} +0.470042 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} - 23 q^{12} - 10 q^{13} + 2 q^{15} + 10 q^{16} - 2 q^{17} - 5 q^{18} + 3 q^{19} - 4 q^{20} - 2 q^{21} + 3 q^{23} + 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} + 4 q^{28} - q^{29} - 5 q^{30} - 12 q^{31} - 29 q^{32} - 20 q^{34} - 5 q^{35} + 45 q^{36} + 9 q^{38} + 2 q^{39} + 12 q^{40} + 11 q^{41} + 5 q^{42} - 10 q^{43} - 11 q^{45} - 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} - 6 q^{51} - 30 q^{52} + 4 q^{53} + 34 q^{54} - 12 q^{56} - 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} - 40 q^{61} - q^{62} + 11 q^{63} + 38 q^{64} + 10 q^{65} + 7 q^{67} + 19 q^{68} - 24 q^{69} + 10 q^{71} - 72 q^{72} - 11 q^{73} + 37 q^{74} - 2 q^{75} - 3 q^{76} - 87 q^{78} - 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} - 26 q^{83} - 23 q^{84} + 2 q^{85} - 17 q^{86} - 14 q^{87} + 5 q^{89} + 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} - 44 q^{94} - 3 q^{95} + 84 q^{96} - 5 q^{97}+O(q^{100}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9 - 23 * q^12 - 10 * q^13 + 2 * q^15 + 10 * q^16 - 2 * q^17 - 5 * q^18 + 3 * q^19 - 4 * q^20 - 2 * q^21 + 3 * q^23 + 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 + 4 * q^28 - q^29 - 5 * q^30 - 12 * q^31 - 29 * q^32 - 20 * q^34 - 5 * q^35 + 45 * q^36 + 9 * q^38 + 2 * q^39 + 12 * q^40 + 11 * q^41 + 5 * q^42 - 10 * q^43 - 11 * q^45 - 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 - 6 * q^51 - 30 * q^52 + 4 * q^53 + 34 * q^54 - 12 * q^56 - 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 - 40 * q^61 - q^62 + 11 * q^63 + 38 * q^64 + 10 * q^65 + 7 * q^67 + 19 * q^68 - 24 * q^69 + 10 * q^71 - 72 * q^72 - 11 * q^73 + 37 * q^74 - 2 * q^75 - 3 * q^76 - 87 * q^78 - 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 - 26 * q^83 - 23 * q^84 + 2 * q^85 - 17 * q^86 - 14 * q^87 + 5 * q^89 + 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 - 44 * q^94 - 3 * q^95 + 84 * q^96 - 5 * q^97

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 $

$2$	0.470042	0.332370	0.166185	−	0.986095i	$-0.446855\pi$
$2$	0.470042	0.332370	0.166185	+	0.986095i	$0.446855\pi$
$3$	−0.577925	−0.333665	−0.166832	−	0.985985i	$-0.553354\pi$
$3$	−0.577925	−0.333665	−0.166832	+	0.985985i	$0.553354\pi$
$4$	−1.77906	−0.889530
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.271649	−0.110900
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.77632	−0.628023
$9$	−2.66600	−0.888668
$10$	−0.470042	−0.148640
$11$	0	0
$11$	0	0
$12$	1.02816	0.296805
$13$	−1.19839	−0.332374	−0.166187	−	0.986094i	$-0.553146\pi$
$13$	−1.19839	−0.332374	−0.166187	+	0.986094i	$0.553146\pi$
$14$	0.470042	0.125624
$15$	0.577925	0.149220
$16$	2.72318	0.680794
$17$	1.08534	0.263233	0.131616	−	0.991301i	$-0.457983\pi$
$17$	1.08534	0.263233	0.131616	+	0.991301i	$0.457983\pi$
$18$	−1.25313	−0.295367
$19$	6.29189	1.44346	0.721730	−	0.692175i	$-0.243347\pi$
$19$	6.29189	1.44346	0.721730	+	0.692175i	$0.243347\pi$
$20$	1.77906	0.397810
$21$	−0.577925	−0.126114
$22$	0	0
$23$	−6.35986	−1.32612	−0.663061	−	0.748565i	$-0.730743\pi$
$23$	−6.35986	−1.32612	−0.663061	+	0.748565i	$0.730743\pi$
$24$	1.02658	0.209549
$25$	1.00000	0.200000
$26$	−0.563295	−0.110471
$27$	3.27452	0.630182
$28$	−1.77906	−0.336211
$29$	6.79931	1.26260	0.631300	−	0.775539i	$-0.282522\pi$
$29$	6.79931	1.26260	0.631300	+	0.775539i	$0.282522\pi$
$30$	0.271649	0.0495961
$31$	9.46531	1.70002	0.850010	−	0.526767i	$-0.176596\pi$
$31$	9.46531	1.70002	0.850010	+	0.526767i	$0.176596\pi$
$32$	4.83264	0.854299
$33$	0	0
$34$	0.510154	0.0874906
$35$	−1.00000	−0.169031
$36$	4.74298	0.790497
$37$	−8.49980	−1.39736	−0.698680	−	0.715435i	$-0.746229\pi$
$37$	−8.49980	−1.39736	−0.698680	+	0.715435i	$0.746229\pi$
$38$	2.95746	0.479763
$39$	0.692581	0.110902
$40$	1.77632	0.280861
$41$	9.51571	1.48610	0.743052	−	0.669234i	$-0.233377\pi$
$41$	9.51571	1.48610	0.743052	+	0.669234i	$0.233377\pi$
$42$	−0.271649	−0.0419163
$43$	−5.07339	−0.773684	−0.386842	−	0.922146i	$-0.626434\pi$
$43$	−5.07339	−0.773684	−0.386842	+	0.922146i	$0.626434\pi$
$44$	0	0
$45$	2.66600	0.397424
$46$	−2.98940	−0.440763
$47$	3.89889	0.568712	0.284356	−	0.958719i	$-0.408220\pi$
$47$	3.89889	0.568712	0.284356	+	0.958719i	$0.408220\pi$
$48$	−1.57379	−0.227157
$49$	1.00000	0.142857
$50$	0.470042	0.0664740
$51$	−0.627242	−0.0878315
$52$	2.13201	0.295657
$53$	−12.2191	−1.67842	−0.839210	−	0.543808i	$-0.816982\pi$
$53$	−12.2191	−1.67842	−0.839210	+	0.543808i	$0.816982\pi$
$54$	1.53916	0.209454
$55$	0	0
$56$	−1.77632	−0.237370
$57$	−3.63624	−0.481632
$58$	3.19596	0.419650
$59$	−4.91466	−0.639835	−0.319917	−	0.947445i	$-0.603655\pi$
$59$	−4.91466	−0.639835	−0.319917	+	0.947445i	$0.603655\pi$
$60$	−1.02816	−0.132735
$61$	−10.6033	−1.35762	−0.678810	−	0.734314i	$-0.737504\pi$
$61$	−10.6033	−1.35762	−0.678810	+	0.734314i	$0.737504\pi$
$62$	4.44909	0.565036
$63$	−2.66600	−0.335885
$64$	−3.17481	−0.396851
$65$	1.19839	0.148642
$66$	0	0
$67$	−5.09350	−0.622270	−0.311135	−	0.950366i	$-0.600709\pi$
$67$	−5.09350	−0.622270	−0.311135	+	0.950366i	$0.600709\pi$
$68$	−1.93088	−0.234153
$69$	3.67552	0.442481
$70$	−0.470042	−0.0561808
$71$	−7.24680	−0.860037	−0.430019	−	0.902820i	$-0.641493\pi$
$71$	−7.24680	−0.860037	−0.430019	+	0.902820i	$0.641493\pi$
$72$	4.73567	0.558104
$73$	10.2495	1.19962	0.599809	−	0.800143i	$-0.295243\pi$
$73$	10.2495	1.19962	0.599809	+	0.800143i	$0.295243\pi$
$74$	−3.99527	−0.464440
$75$	−0.577925	−0.0667330
$76$	−11.1937	−1.28400
$77$	0	0
$78$	0.325542	0.0368604
$79$	−0.0718642	−0.00808536	−0.00404268	−	0.999992i	$-0.501287\pi$
$79$	−0.0718642	−0.00808536	−0.00404268	+	0.999992i	$0.501287\pi$
$80$	−2.72318	−0.304460
$81$	6.10558	0.678398
$82$	4.47278	0.493936
$83$	−9.16537	−1.00603	−0.503015	−	0.864278i	$-0.667776\pi$
$83$	−9.16537	−1.00603	−0.503015	+	0.864278i	$0.667776\pi$
$84$	1.02816	0.112182
$85$	−1.08534	−0.117721
$86$	−2.38471	−0.257149
$87$	−3.92949	−0.421285
$88$	0	0
$89$	−3.20656	−0.339895	−0.169947	−	0.985453i	$-0.554360\pi$
$89$	−3.20656	−0.339895	−0.169947	+	0.985453i	$0.554360\pi$
$90$	1.25313	0.132092
$91$	−1.19839	−0.125626
$92$	11.3146	1.17963
$93$	−5.47024	−0.567237
$94$	1.83264	0.189023
$95$	−6.29189	−0.645535
$96$	−2.79290	−0.285050
$97$	−9.05358	−0.919252	−0.459626	−	0.888113i	$-0.652017\pi$
$97$	−9.05358	−0.919252	−0.459626	+	0.888113i	$0.652017\pi$
$98$	0.470042	0.0474814
$99$	0	0
$100$	−1.77906	−0.177906
$101$	−2.41665	−0.240466	−0.120233	−	0.992746i	$-0.538364\pi$
$101$	−2.41665	−0.240466	−0.120233	+	0.992746i	$0.538364\pi$
$102$	−0.294830	−0.0291926
$103$	−13.1214	−1.29289	−0.646443	−	0.762963i	$-0.723744\pi$
$103$	−13.1214	−1.29289	−0.646443	+	0.762963i	$0.723744\pi$
$104$	2.12873	0.208739
$105$	0.577925	0.0563997
$106$	−5.74348	−0.557856
$107$	13.6316	1.31782	0.658910	−	0.752222i	$-0.271018\pi$
$107$	13.6316	1.31782	0.658910	+	0.752222i	$0.271018\pi$
$108$	−5.82557	−0.560566
$109$	7.14569	0.684433	0.342217	−	0.939621i	$-0.388822\pi$
$109$	7.14569	0.684433	0.342217	+	0.939621i	$0.388822\pi$
$110$	0	0
$111$	4.91225	0.466250
$112$	2.72318	0.257316
$113$	10.9216	1.02742	0.513710	−	0.857964i	$-0.328271\pi$
$113$	10.9216	1.02742	0.513710	+	0.857964i	$0.328271\pi$
$114$	−1.70919	−0.160080
$115$	6.35986	0.593060
$116$	−12.0964	−1.12312
$117$	3.19492	0.295370
$118$	−2.31010	−0.212662
$119$	1.08534	0.0994926
$120$	−1.02658	−0.0937133
$121$	0	0
$122$	−4.98402	−0.451232
$123$	−5.49936	−0.495861
$124$	−16.8394	−1.51222
$125$	−1.00000	−0.0894427
$126$	−1.25313	−0.111638
$127$	−11.2229	−0.995872	−0.497936	−	0.867214i	$-0.665909\pi$
$127$	−11.2229	−0.995872	−0.497936	+	0.867214i	$0.665909\pi$
$128$	−11.1576	−0.986200
$129$	2.93204	0.258151
$130$	0.563295	0.0494043
$131$	17.3578	1.51656	0.758279	−	0.651930i	$-0.226040\pi$
$131$	17.3578	1.51656	0.758279	+	0.651930i	$0.226040\pi$
$132$	0	0
$133$	6.29189	0.545576
$134$	−2.39416	−0.206824
$135$	−3.27452	−0.281826
$136$	−1.92790	−0.165316
$137$	18.8358	1.60925	0.804627	−	0.593780i	$-0.202365\pi$
$137$	18.8358	1.60925	0.804627	+	0.593780i	$0.202365\pi$
$138$	1.72765	0.147067
$139$	−20.0886	−1.70390	−0.851948	−	0.523626i	$-0.824579\pi$
$139$	−20.0886	−1.70390	−0.851948	+	0.523626i	$0.824579\pi$
$140$	1.77906	0.150358
$141$	−2.25327	−0.189759
$142$	−3.40630	−0.285851
$143$	0	0
$144$	−7.26000	−0.605000
$145$	−6.79931	−0.564652
$146$	4.81772	0.398717
$147$	−0.577925	−0.0476664
$148$	15.1217	1.24299
$149$	−11.3747	−0.931850	−0.465925	−	0.884824i	$-0.654278\pi$
$149$	−11.3747	−0.931850	−0.465925	+	0.884824i	$0.654278\pi$
$150$	−0.271649	−0.0221800
$151$	−12.8036	−1.04195	−0.520973	−	0.853573i	$-0.674431\pi$
$151$	−12.8036	−1.04195	−0.520973	+	0.853573i	$0.674431\pi$
$152$	−11.1764	−0.906526
$153$	−2.89351	−0.233926
$154$	0	0
$155$	−9.46531	−0.760272
$156$	−1.23214	−0.0986504
$157$	8.23103	0.656908	0.328454	−	0.944520i	$-0.393472\pi$
$157$	8.23103	0.656908	0.328454	+	0.944520i	$0.393472\pi$
$158$	−0.0337792	−0.00268733
$159$	7.06171	0.560030
$160$	−4.83264	−0.382054
$161$	−6.35986	−0.501227
$162$	2.86988	0.225479
$163$	6.30685	0.493991	0.246995	−	0.969017i	$-0.420557\pi$
$163$	6.30685	0.493991	0.246995	+	0.969017i	$0.420557\pi$
$164$	−16.9290	−1.32193
$165$	0	0
$166$	−4.30811	−0.334374
$167$	−9.35034	−0.723551	−0.361776	−	0.932265i	$-0.617829\pi$
$167$	−9.35034	−0.723551	−0.361776	+	0.932265i	$0.617829\pi$
$168$	1.02658	0.0792022
$169$	−11.5639	−0.889527
$170$	−0.510154	−0.0391270
$171$	−16.7742	−1.28276
$172$	9.02586	0.688216
$173$	−6.98410	−0.530991	−0.265495	−	0.964112i	$-0.585536\pi$
$173$	−6.98410	−0.530991	−0.265495	+	0.964112i	$0.585536\pi$
$174$	−1.84702	−0.140023
$175$	1.00000	0.0755929
$176$	0	0
$177$	2.84031	0.213490
$178$	−1.50722	−0.112971
$179$	13.0020	0.971812	0.485906	−	0.874011i	$-0.338490\pi$
$179$	13.0020	0.971812	0.485906	+	0.874011i	$0.338490\pi$
$180$	−4.74298	−0.353521
$181$	−18.2396	−1.35574	−0.677871	−	0.735181i	$-0.737097\pi$
$181$	−18.2396	−1.35574	−0.677871	+	0.735181i	$0.737097\pi$
$182$	−0.563295	−0.0417542
$183$	6.12793	0.452990
$184$	11.2971	0.832836
$185$	8.49980	0.624918
$186$	−2.57124	−0.188533
$187$	0	0
$188$	−6.93636	−0.505886
$189$	3.27452	0.238186
$190$	−2.95746	−0.214556
$191$	−14.8793	−1.07663	−0.538315	−	0.842743i	$-0.680939\pi$
$191$	−14.8793	−1.07663	−0.538315	+	0.842743i	$0.680939\pi$
$192$	1.83480	0.132415
$193$	4.87672	0.351034	0.175517	−	0.984476i	$-0.443840\pi$
$193$	4.87672	0.351034	0.175517	+	0.984476i	$0.443840\pi$
$194$	−4.25557	−0.305532
$195$	−0.692581	−0.0495968
$196$	−1.77906	−0.127076
$197$	−21.3123	−1.51844	−0.759220	−	0.650834i	$-0.774420\pi$
$197$	−21.3123	−1.51844	−0.759220	+	0.650834i	$0.774420\pi$
$198$	0	0
$199$	1.08916	0.0772085	0.0386042	−	0.999255i	$-0.487709\pi$
$199$	1.08916	0.0772085	0.0386042	+	0.999255i	$0.487709\pi$
$200$	−1.77632	−0.125605
$201$	2.94366	0.207630
$202$	−1.13593	−0.0799237
$203$	6.79931	0.477218
$204$	1.11590	0.0781288
$205$	−9.51571	−0.664606
$206$	−6.16759	−0.429716
$207$	16.9554	1.17848
$208$	−3.26344	−0.226279
$209$	0	0
$210$	0.271649	0.0187456
$211$	−22.9845	−1.58232	−0.791158	−	0.611612i	$-0.790521\pi$
$211$	−22.9845	−1.58232	−0.791158	+	0.611612i	$0.790521\pi$
$212$	21.7385	1.49301
$213$	4.18811	0.286964
$214$	6.40745	0.438004
$215$	5.07339	0.346002
$216$	−5.81659	−0.395769
$217$	9.46531	0.642547
$218$	3.35878	0.227485
$219$	−5.92346	−0.400271
$220$	0	0
$221$	−1.30066	−0.0874918
$222$	2.30896	0.154967
$223$	−23.3688	−1.56489	−0.782447	−	0.622717i	$-0.786029\pi$
$223$	−23.3688	−1.56489	−0.782447	+	0.622717i	$0.786029\pi$
$224$	4.83264	0.322895
$225$	−2.66600	−0.177734
$226$	5.13363	0.341484
$227$	−9.26282	−0.614795	−0.307398	−	0.951581i	$-0.599458\pi$
$227$	−9.26282	−0.614795	−0.307398	+	0.951581i	$0.599458\pi$
$228$	6.46909	0.428426
$229$	22.3739	1.47851	0.739255	−	0.673426i	$-0.235178\pi$
$229$	22.3739	1.47851	0.739255	+	0.673426i	$0.235178\pi$
$230$	2.98940	0.197115
$231$	0	0
$232$	−12.0777	−0.792942
$233$	−0.300984	−0.0197181	−0.00985907	−	0.999951i	$-0.503138\pi$
$233$	−0.300984	−0.0197181	−0.00985907	+	0.999951i	$0.503138\pi$
$234$	1.50175	0.0981723
$235$	−3.89889	−0.254336
$236$	8.74348	0.569152
$237$	0.0415321	0.00269780
$238$	0.510154	0.0330684
$239$	17.8086	1.15194	0.575972	−	0.817469i	$-0.304624\pi$
$239$	17.8086	1.15194	0.575972	+	0.817469i	$0.304624\pi$
$240$	1.57379	0.101588
$241$	−14.8175	−0.954480	−0.477240	−	0.878773i	$-0.658363\pi$
$241$	−14.8175	−0.954480	−0.477240	+	0.878773i	$0.658363\pi$
$242$	0	0
$243$	−13.3521	−0.856540
$244$	18.8640	1.20764
$245$	−1.00000	−0.0638877
$246$	−2.58493	−0.164809
$247$	−7.54016	−0.479769
$248$	−16.8134	−1.06765
$249$	5.29689	0.335677
$250$	−0.470042	−0.0297281
$251$	4.92595	0.310923	0.155462	−	0.987842i	$-0.450313\pi$
$251$	4.92595	0.310923	0.155462	+	0.987842i	$0.450313\pi$
$252$	4.74298	0.298780
$253$	0	0
$254$	−5.27524	−0.330998
$255$	0.627242	0.0392794
$256$	1.10508	0.0690674
$257$	10.6277	0.662940	0.331470	−	0.943466i	$-0.392455\pi$
$257$	10.6277	0.662940	0.331470	+	0.943466i	$0.392455\pi$
$258$	1.37818	0.0858018
$259$	−8.49980	−0.528152
$260$	−2.13201	−0.132222
$261$	−18.1270	−1.12203
$262$	8.15890	0.504059
$263$	−6.62908	−0.408766	−0.204383	−	0.978891i	$-0.565519\pi$
$263$	−6.62908	−0.408766	−0.204383	+	0.978891i	$0.565519\pi$
$264$	0	0
$265$	12.2191	0.750612
$266$	2.95746	0.181333
$267$	1.85315	0.113411
$268$	9.06165	0.553528
$269$	14.6214	0.891480	0.445740	−	0.895163i	$-0.352941\pi$
$269$	14.6214	0.891480	0.445740	+	0.895163i	$0.352941\pi$
$270$	−1.53916	−0.0936705
$271$	5.00420	0.303984	0.151992	−	0.988382i	$-0.451431\pi$
$271$	5.00420	0.303984	0.151992	+	0.988382i	$0.451431\pi$
$272$	2.95556	0.179207
$273$	0.692581	0.0419169
$274$	8.85364	0.534868
$275$	0	0
$276$	−6.53897	−0.393600
$277$	−3.50429	−0.210552	−0.105276	−	0.994443i	$-0.533573\pi$
$277$	−3.50429	−0.210552	−0.105276	+	0.994443i	$0.533573\pi$
$278$	−9.44251	−0.566324
$279$	−25.2345	−1.51075
$280$	1.77632	0.106155
$281$	9.42495	0.562245	0.281123	−	0.959672i	$-0.409293\pi$
$281$	9.42495	0.562245	0.281123	+	0.959672i	$0.409293\pi$
$282$	−1.05913	−0.0630703
$283$	−15.9110	−0.945812	−0.472906	−	0.881113i	$-0.656795\pi$
$283$	−15.9110	−0.945812	−0.472906	+	0.881113i	$0.656795\pi$
$284$	12.8925	0.765029
$285$	3.63624	0.215392
$286$	0	0
$287$	9.51571	0.561695
$288$	−12.8838	−0.759188
$289$	−15.8220	−0.930709
$290$	−3.19596	−0.187673
$291$	5.23229	0.306722
$292$	−18.2346	−1.06710
$293$	−15.3574	−0.897187	−0.448593	−	0.893736i	$-0.648075\pi$
$293$	−15.3574	−0.897187	−0.448593	+	0.893736i	$0.648075\pi$
$294$	−0.271649	−0.0158429
$295$	4.91466	0.286143
$296$	15.0984	0.877574
$297$	0	0
$298$	−5.34658	−0.309719
$299$	7.62161	0.440769
$300$	1.02816	0.0593610
$301$	−5.07339	−0.292425
$302$	−6.01825	−0.346312
$303$	1.39664	0.0802350
$304$	17.1339	0.982699
$305$	10.6033	0.607146
$306$	−1.36007	−0.0777501
$307$	16.0662	0.916944	0.458472	−	0.888709i	$-0.348397\pi$
$307$	16.0662	0.916944	0.458472	+	0.888709i	$0.348397\pi$
$308$	0	0
$309$	7.58315	0.431391
$310$	−4.44909	−0.252692
$311$	3.67098	0.208162	0.104081	−	0.994569i	$-0.466810\pi$
$311$	3.67098	0.208162	0.104081	+	0.994569i	$0.466810\pi$
$312$	−1.23024	−0.0696489
$313$	−4.45248	−0.251669	−0.125834	−	0.992051i	$-0.540161\pi$
$313$	−4.45248	−0.251669	−0.125834	+	0.992051i	$0.540161\pi$
$314$	3.86893	0.218336
$315$	2.66600	0.150212
$316$	0.127851	0.00719217
$317$	−22.3020	−1.25261	−0.626304	−	0.779579i	$-0.715433\pi$
$317$	−22.3020	−1.25261	−0.626304	+	0.779579i	$0.715433\pi$
$318$	3.31930	0.186137
$319$	0	0
$320$	3.17481	0.177477
$321$	−7.87806	−0.439710
$322$	−2.98940	−0.166593
$323$	6.82882	0.379966
$324$	−10.8622	−0.603455
$325$	−1.19839	−0.0664749
$326$	2.96449	0.164188
$327$	−4.12967	−0.228371
$328$	−16.9029	−0.933308
$329$	3.89889	0.214953
$330$	0	0
$331$	−8.43313	−0.463527	−0.231763	−	0.972772i	$-0.574450\pi$
$331$	−8.43313	−0.463527	−0.231763	+	0.972772i	$0.574450\pi$
$332$	16.3057	0.894894
$333$	22.6605	1.24179
$334$	−4.39506	−0.240487
$335$	5.09350	0.278288
$336$	−1.57379	−0.0858573
$337$	−30.2983	−1.65045	−0.825226	−	0.564803i	$-0.808952\pi$
$337$	−30.2983	−1.65045	−0.825226	+	0.564803i	$0.808952\pi$
$338$	−5.43550	−0.295652
$339$	−6.31188	−0.342814
$340$	1.93088	0.104717
$341$	0	0
$342$	−7.88459	−0.426350
$343$	1.00000	0.0539949
$344$	9.01195	0.485892
$345$	−3.67552	−0.197883
$346$	−3.28282	−0.176485
$347$	−1.68714	−0.0905706	−0.0452853	−	0.998974i	$-0.514420\pi$
$347$	−1.68714	−0.0905706	−0.0452853	+	0.998974i	$0.514420\pi$
$348$	6.99079	0.374746
$349$	26.2092	1.40295	0.701474	−	0.712695i	$-0.252526\pi$
$349$	26.2092	1.40295	0.701474	+	0.712695i	$0.252526\pi$
$350$	0.470042	0.0251248
$351$	−3.92417	−0.209456
$352$	0	0
$353$	17.6788	0.940948	0.470474	−	0.882414i	$-0.344083\pi$
$353$	17.6788	0.940948	0.470474	+	0.882414i	$0.344083\pi$
$354$	1.33506	0.0709578
$355$	7.24680	0.384620
$356$	5.70466	0.302346
$357$	−0.627242	−0.0331972
$358$	6.11147	0.323001
$359$	−7.06393	−0.372820	−0.186410	−	0.982472i	$-0.559685\pi$
$359$	−7.06393	−0.372820	−0.186410	+	0.982472i	$0.559685\pi$
$360$	−4.73567	−0.249592
$361$	20.5879	1.08358
$362$	−8.57340	−0.450608
$363$	0	0
$364$	2.13201	0.111748
$365$	−10.2495	−0.536486
$366$	2.88039	0.150560
$367$	9.09662	0.474840	0.237420	−	0.971407i	$-0.423698\pi$
$367$	9.09662	0.474840	0.237420	+	0.971407i	$0.423698\pi$
$368$	−17.3190	−0.902816
$369$	−25.3689	−1.32065
$370$	3.99527	0.207704
$371$	−12.2191	−0.634383
$372$	9.73188	0.504574
$373$	−33.9587	−1.75832	−0.879158	−	0.476531i	$-0.841894\pi$
$373$	−33.9587	−1.75832	−0.879158	+	0.476531i	$0.841894\pi$
$374$	0	0
$375$	0.577925	0.0298439
$376$	−6.92567	−0.357164
$377$	−8.14824	−0.419656
$378$	1.53916	0.0791661
$379$	20.7225	1.06445	0.532223	−	0.846604i	$-0.321357\pi$
$379$	20.7225	1.06445	0.532223	+	0.846604i	$0.321357\pi$
$380$	11.1937	0.574223
$381$	6.48599	0.332288
$382$	−6.99392	−0.357840
$383$	−17.5943	−0.899028	−0.449514	−	0.893273i	$-0.648403\pi$
$383$	−17.5943	−0.899028	−0.449514	+	0.893273i	$0.648403\pi$
$384$	6.44824	0.329060
$385$	0	0
$386$	2.29227	0.116673
$387$	13.5257	0.687548
$388$	16.1069	0.817702
$389$	−23.3951	−1.18618	−0.593089	−	0.805137i	$-0.702092\pi$
$389$	−23.3951	−1.18618	−0.593089	+	0.805137i	$0.702092\pi$
$390$	−0.325542	−0.0164845
$391$	−6.90258	−0.349079
$392$	−1.77632	−0.0897176
$393$	−10.0315	−0.506022
$394$	−10.0177	−0.504684
$395$	0.0718642	0.00361588
$396$	0	0
$397$	6.31381	0.316881	0.158441	−	0.987369i	$-0.449353\pi$
$397$	6.31381	0.316881	0.158441	+	0.987369i	$0.449353\pi$
$398$	0.511951	0.0256618
$399$	−3.63624	−0.182040
$400$	2.72318	0.136159
$401$	−29.4882	−1.47257	−0.736284	−	0.676672i	$-0.763421\pi$
$401$	−29.4882	−1.47257	−0.736284	+	0.676672i	$0.763421\pi$
$402$	1.38364	0.0690099
$403$	−11.3432	−0.565043
$404$	4.29937	0.213902
$405$	−6.10558	−0.303389
$406$	3.19596	0.158613
$407$	0	0
$408$	1.11418	0.0551602
$409$	−22.1755	−1.09651	−0.548253	−	0.836313i	$-0.684707\pi$
$409$	−22.1755	−1.09651	−0.548253	+	0.836313i	$0.684707\pi$
$410$	−4.47278	−0.220895
$411$	−10.8857	−0.536952
$412$	23.3437	1.15006
$413$	−4.91466	−0.241835
$414$	7.96976	0.391692
$415$	9.16537	0.449910
$416$	−5.79141	−0.283947
$417$	11.6097	0.568530
$418$	0	0
$419$	−23.8536	−1.16532	−0.582662	−	0.812715i	$-0.697989\pi$
$419$	−23.8536	−1.16532	−0.582662	+	0.812715i	$0.697989\pi$
$420$	−1.02816	−0.0501692
$421$	15.7409	0.767162	0.383581	−	0.923507i	$-0.374691\pi$
$421$	15.7409	0.767162	0.383581	+	0.923507i	$0.374691\pi$
$422$	−10.8037	−0.525914
$423$	−10.3945	−0.505396
$424$	21.7050	1.05409
$425$	1.08534	0.0526465
$426$	1.96859	0.0953783
$427$	−10.6033	−0.513132
$428$	−24.2515	−1.17224
$429$	0	0
$430$	2.38471	0.115001
$431$	1.50575	0.0725294	0.0362647	−	0.999342i	$-0.488454\pi$
$431$	1.50575	0.0725294	0.0362647	+	0.999342i	$0.488454\pi$
$432$	8.91710	0.429024
$433$	6.62788	0.318516	0.159258	−	0.987237i	$-0.449090\pi$
$433$	6.62788	0.318516	0.159258	+	0.987237i	$0.449090\pi$
$434$	4.44909	0.213563
$435$	3.92949	0.188404
$436$	−12.7126	−0.608824
$437$	−40.0156	−1.91420
$438$	−2.78428	−0.133038
$439$	5.96524	0.284705	0.142353	−	0.989816i	$-0.454533\pi$
$439$	5.96524	0.284705	0.142353	+	0.989816i	$0.454533\pi$
$440$	0	0
$441$	−2.66600	−0.126953
$442$	−0.611365	−0.0290797
$443$	26.5172	1.25987	0.629936	−	0.776647i	$-0.283081\pi$
$443$	26.5172	1.25987	0.629936	+	0.776647i	$0.283081\pi$
$444$	−8.73918	−0.414743
$445$	3.20656	0.152005
$446$	−10.9843	−0.520124
$447$	6.57371	0.310926
$448$	−3.17481	−0.149995
$449$	37.4390	1.76686	0.883429	−	0.468565i	$-0.155229\pi$
$449$	37.4390	1.76686	0.883429	+	0.468565i	$0.155229\pi$
$450$	−1.25313	−0.0590733
$451$	0	0
$452$	−19.4302	−0.913922
$453$	7.39954	0.347661
$454$	−4.35392	−0.204339
$455$	1.19839	0.0561815
$456$	6.45912	0.302476
$457$	−1.42603	−0.0667069	−0.0333535	−	0.999444i	$-0.510619\pi$
$457$	−1.42603	−0.0667069	−0.0333535	+	0.999444i	$0.510619\pi$
$458$	10.5167	0.491412
$459$	3.55396	0.165885
$460$	−11.3146	−0.527545
$461$	−0.554469	−0.0258242	−0.0129121	−	0.999917i	$-0.504110\pi$
$461$	−0.554469	−0.0258242	−0.0129121	+	0.999917i	$0.504110\pi$
$462$	0	0
$463$	16.2994	0.757495	0.378748	−	0.925500i	$-0.376355\pi$
$463$	16.2994	0.757495	0.378748	+	0.925500i	$0.376355\pi$
$464$	18.5157	0.859570
$465$	5.47024	0.253676
$466$	−0.141475	−0.00655372
$467$	−22.7720	−1.05376	−0.526880	−	0.849939i	$-0.676638\pi$
$467$	−22.7720	−1.05376	−0.526880	+	0.849939i	$0.676638\pi$
$468$	−5.68396	−0.262741
$469$	−5.09350	−0.235196
$470$	−1.83264	−0.0845335
$471$	−4.75691	−0.219187
$472$	8.73001	0.401831
$473$	0	0
$474$	0.0195218	0.000896668 0
$475$	6.29189	0.288692
$476$	−1.93088	−0.0885017
$477$	32.5761	1.49156
$478$	8.37081	0.382872
$479$	14.7738	0.675033	0.337516	−	0.941320i	$-0.390413\pi$
$479$	14.7738	0.675033	0.337516	+	0.941320i	$0.390413\pi$
$480$	2.79290	0.127478
$481$	10.1861	0.464447
$482$	−6.96486	−0.317240
$483$	3.67552	0.167242
$484$	0	0
$485$	9.05358	0.411102
$486$	−6.27607	−0.284688
$487$	−6.18415	−0.280231	−0.140115	−	0.990135i	$-0.544747\pi$
$487$	−6.18415	−0.280231	−0.140115	+	0.990135i	$0.544747\pi$
$488$	18.8349	0.852616
$489$	−3.64488	−0.164827
$490$	−0.470042	−0.0212343
$491$	36.2148	1.63435	0.817175	−	0.576389i	$-0.195539\pi$
$491$	36.2148	1.63435	0.817175	+	0.576389i	$0.195539\pi$
$492$	9.78370	0.441083
$493$	7.37953	0.332357
$494$	−3.54420	−0.159461
$495$	0	0
$496$	25.7757	1.15736
$497$	−7.24680	−0.325063
$498$	2.48976	0.111569
$499$	−17.9874	−0.805227	−0.402614	−	0.915370i	$-0.631898\pi$
$499$	−17.9874	−0.805227	−0.402614	+	0.915370i	$0.631898\pi$
$500$	1.77906	0.0795620
$501$	5.40379	0.241424
$502$	2.31541	0.103342
$503$	−20.1263	−0.897389	−0.448694	−	0.893685i	$-0.648111\pi$
$503$	−20.1263	−0.897389	−0.448694	+	0.893685i	$0.648111\pi$
$504$	4.73567	0.210943
$505$	2.41665	0.107540
$506$	0	0
$507$	6.68304	0.296804
$508$	19.9662	0.885858
$509$	−22.3565	−0.990936	−0.495468	−	0.868626i	$-0.665003\pi$
$509$	−22.3565	−0.990936	−0.495468	+	0.868626i	$0.665003\pi$
$510$	0.294830	0.0130553
$511$	10.2495	0.453413
$512$	22.8346	1.00916
$513$	20.6030	0.909643
$514$	4.99549	0.220341
$515$	13.1214	0.578196
$516$	−5.21627	−0.229633
$517$	0	0
$518$	−3.99527	−0.175542
$519$	4.03628	0.177173
$520$	−2.12873	−0.0933509
$521$	−4.65362	−0.203879	−0.101939	−	0.994791i	$-0.532505\pi$
$521$	−4.65362	−0.203879	−0.101939	+	0.994791i	$0.532505\pi$
$522$	−8.52044	−0.372930
$523$	−28.6197	−1.25145	−0.625726	−	0.780043i	$-0.715197\pi$
$523$	−28.6197	−1.25145	−0.625726	+	0.780043i	$0.715197\pi$
$524$	−30.8806	−1.34902
$525$	−0.577925	−0.0252227
$526$	−3.11595	−0.135862
$527$	10.2730	0.447501
$528$	0	0
$529$	17.4478	0.758600
$530$	5.74348	0.249481
$531$	13.1025	0.568600
$532$	−11.1937	−0.485307
$533$	−11.4036	−0.493943
$534$	0.871058	0.0376944
$535$	−13.6316	−0.589347
$536$	9.04768	0.390800
$537$	−7.51416	−0.324260
$538$	6.87265	0.296301
$539$	0	0
$540$	5.82557	0.250693
$541$	1.53468	0.0659810	0.0329905	−	0.999456i	$-0.489497\pi$
$541$	1.53468	0.0659810	0.0329905	+	0.999456i	$0.489497\pi$
$542$	2.35219	0.101035
$543$	10.5411	0.452363
$544$	5.24504	0.224879
$545$	−7.14569	−0.306088
$546$	0.325542	0.0139319
$547$	32.9352	1.40821	0.704104	−	0.710097i	$-0.251349\pi$
$547$	32.9352	1.40821	0.704104	+	0.710097i	$0.251349\pi$
$548$	−33.5101	−1.43148
$549$	28.2686	1.20647
$550$	0	0
$551$	42.7805	1.82251
$552$	−6.52889	−0.277888
$553$	−0.0718642	−0.00305598
$554$	−1.64716	−0.0699813
$555$	−4.91225	−0.208513
$556$	35.7389	1.51567
$557$	25.5992	1.08467	0.542337	−	0.840161i	$-0.317539\pi$
$557$	25.5992	1.08467	0.542337	+	0.840161i	$0.317539\pi$
$558$	−11.8613	−0.502129
$559$	6.07991	0.257153
$560$	−2.72318	−0.115075
$561$	0	0
$562$	4.43012	0.186874
$563$	−14.5421	−0.612876	−0.306438	−	0.951891i	$-0.599137\pi$
$563$	−14.5421	−0.612876	−0.306438	+	0.951891i	$0.599137\pi$
$564$	4.00870	0.168797
$565$	−10.9216	−0.459476
$566$	−7.47885	−0.314359
$567$	6.10558	0.256410
$568$	12.8726	0.540123
$569$	−4.43273	−0.185830	−0.0929148	−	0.995674i	$-0.529618\pi$
$569$	−4.43273	−0.185830	−0.0929148	+	0.995674i	$0.529618\pi$
$570$	1.70919	0.0715900
$571$	25.7504	1.07762	0.538811	−	0.842427i	$-0.318874\pi$
$571$	25.7504	1.07762	0.538811	+	0.842427i	$0.318874\pi$
$572$	0	0
$573$	8.59914	0.359234
$574$	4.47278	0.186690
$575$	−6.35986	−0.265224
$576$	8.46404	0.352668
$577$	42.5310	1.77059	0.885294	−	0.465031i	$-0.153957\pi$
$577$	42.5310	1.77059	0.885294	+	0.465031i	$0.153957\pi$
$578$	−7.43703	−0.309340
$579$	−2.81838	−0.117128
$580$	12.0964	0.502275
$581$	−9.16537	−0.380243
$582$	2.45940	0.101945
$583$	0	0
$584$	−18.2064	−0.753388
$585$	−3.19492	−0.132094
$586$	−7.21861	−0.298198
$587$	2.68746	0.110923	0.0554617	−	0.998461i	$-0.482337\pi$
$587$	2.68746	0.110923	0.0554617	+	0.998461i	$0.482337\pi$
$588$	1.02816	0.0424007
$589$	59.5547	2.45391
$590$	2.31010	0.0951053
$591$	12.3169	0.506651
$592$	−23.1465	−0.951314
$593$	27.0766	1.11190	0.555952	−	0.831214i	$-0.312354\pi$
$593$	27.0766	1.11190	0.555952	+	0.831214i	$0.312354\pi$
$594$	0	0
$595$	−1.08534	−0.0444944
$596$	20.2362	0.828909
$597$	−0.629452	−0.0257618
$598$	3.58248	0.146498
$599$	−16.1515	−0.659933	−0.329966	−	0.943993i	$-0.607037\pi$
$599$	−16.1515	−0.659933	−0.329966	+	0.943993i	$0.607037\pi$
$600$	1.02658	0.0419099
$601$	12.3469	0.503640	0.251820	−	0.967774i	$-0.418971\pi$
$601$	12.3469	0.503640	0.251820	+	0.967774i	$0.418971\pi$
$602$	−2.38471	−0.0971934
$603$	13.5793	0.552991
$604$	22.7785	0.926842
$605$	0	0
$606$	0.656481	0.0266677
$607$	13.0242	0.528635	0.264318	−	0.964436i	$-0.414853\pi$
$607$	13.0242	0.528635	0.264318	+	0.964436i	$0.414853\pi$
$608$	30.4065	1.23315
$609$	−3.92949	−0.159231
$610$	4.98402	0.201797
$611$	−4.67241	−0.189025
$612$	5.14773	0.208085
$613$	−21.3235	−0.861249	−0.430624	−	0.902531i	$-0.641707\pi$
$613$	−21.3235	−0.861249	−0.430624	+	0.902531i	$0.641707\pi$
$614$	7.55177	0.304765
$615$	5.49936	0.221756
$616$	0	0
$617$	−38.5851	−1.55338	−0.776688	−	0.629886i	$-0.783102\pi$
$617$	−38.5851	−1.55338	−0.776688	+	0.629886i	$0.783102\pi$
$618$	3.56440	0.143381
$619$	−43.6172	−1.75312	−0.876561	−	0.481290i	$-0.840168\pi$
$619$	−43.6172	−1.75312	−0.876561	+	0.481290i	$0.840168\pi$
$620$	16.8394	0.676285
$621$	−20.8255	−0.835699
$622$	1.72552	0.0691870
$623$	−3.20656	−0.128468
$624$	1.88602	0.0755012
$625$	1.00000	0.0400000
$626$	−2.09285	−0.0836472
$627$	0	0
$628$	−14.6435	−0.584339
$629$	−9.22514	−0.367831
$630$	1.25313	0.0499261
$631$	4.87238	0.193966	0.0969831	−	0.995286i	$-0.469081\pi$
$631$	4.87238	0.193966	0.0969831	+	0.995286i	$0.469081\pi$
$632$	0.127654	0.00507779
$633$	13.2833	0.527963
$634$	−10.4829	−0.416329
$635$	11.2229	0.445367
$636$	−12.5632	−0.498163
$637$	−1.19839	−0.0474821
$638$	0	0
$639$	19.3200	0.764287
$640$	11.1576	0.441042
$641$	34.8401	1.37610	0.688052	−	0.725662i	$-0.258466\pi$
$641$	34.8401	1.37610	0.688052	+	0.725662i	$0.258466\pi$
$642$	−3.70302	−0.146147
$643$	−32.0891	−1.26547	−0.632735	−	0.774368i	$-0.718068\pi$
$643$	−32.0891	−1.26547	−0.632735	+	0.774368i	$0.718068\pi$
$644$	11.3146	0.445857
$645$	−2.93204	−0.115449
$646$	3.20983	0.126289
$647$	19.5279	0.767719	0.383860	−	0.923392i	$-0.374595\pi$
$647$	19.5279	0.767719	0.383860	+	0.923392i	$0.374595\pi$
$648$	−10.8455	−0.426050
$649$	0	0
$650$	−0.563295	−0.0220943
$651$	−5.47024	−0.214395
$652$	−11.2203	−0.439419
$653$	1.40985	0.0551716	0.0275858	−	0.999619i	$-0.491218\pi$
$653$	1.40985	0.0551716	0.0275858	+	0.999619i	$0.491218\pi$
$654$	−1.94112	−0.0759038
$655$	−17.3578	−0.678226
$656$	25.9130	1.01173
$657$	−27.3253	−1.06606
$658$	1.83264	0.0714439
$659$	−18.6595	−0.726871	−0.363435	−	0.931619i	$-0.618396\pi$
$659$	−18.6595	−0.726871	−0.363435	+	0.931619i	$0.618396\pi$
$660$	0	0
$661$	−2.08885	−0.0812468	−0.0406234	−	0.999175i	$-0.512934\pi$
$661$	−2.08885	−0.0812468	−0.0406234	+	0.999175i	$0.512934\pi$
$662$	−3.96393	−0.154062
$663$	0.751683	0.0291930
$664$	16.2806	0.631810
$665$	−6.29189	−0.243989
$666$	10.6514	0.412733
$667$	−43.2426	−1.67436
$668$	16.6348	0.643621
$669$	13.5054	0.522150
$670$	2.39416	0.0924945
$671$	0	0
$672$	−2.79290	−0.107739
$673$	−31.9112	−1.23009	−0.615043	−	0.788493i	$-0.710861\pi$
$673$	−31.9112	−1.23009	−0.615043	+	0.788493i	$0.710861\pi$
$674$	−14.2415	−0.548561
$675$	3.27452	0.126036
$676$	20.5728	0.791261
$677$	−4.07020	−0.156431	−0.0782153	−	0.996936i	$-0.524922\pi$
$677$	−4.07020	−0.156431	−0.0782153	+	0.996936i	$0.524922\pi$
$678$	−2.96685	−0.113941
$679$	−9.05358	−0.347445
$680$	1.92790	0.0739317
$681$	5.35321	0.205136
$682$	0	0
$683$	38.8897	1.48807	0.744036	−	0.668139i	$-0.232909\pi$
$683$	38.8897	1.48807	0.744036	+	0.668139i	$0.232909\pi$
$684$	29.8423	1.14105
$685$	−18.8358	−0.719681
$686$	0.470042	0.0179463
$687$	−12.9304	−0.493327
$688$	−13.8157	−0.526720
$689$	14.6433	0.557864
$690$	−1.72765	−0.0657705
$691$	−47.2979	−1.79930	−0.899649	−	0.436613i	$-0.856178\pi$
$691$	−47.2979	−1.79930	−0.899649	+	0.436613i	$0.856178\pi$
$692$	12.4251	0.472332
$693$	0	0
$694$	−0.793029	−0.0301030
$695$	20.0886	0.762005
$696$	6.98002	0.264577
$697$	10.3277	0.391191
$698$	12.3194	0.466298
$699$	0.173946	0.00657925
$700$	−1.77906	−0.0672422
$701$	−13.4974	−0.509791	−0.254896	−	0.966969i	$-0.582041\pi$
$701$	−13.4974	−0.509791	−0.254896	+	0.966969i	$0.582041\pi$
$702$	−1.84452	−0.0696171
$703$	−53.4799	−2.01703
$704$	0	0
$705$	2.25327	0.0848629
$706$	8.30979	0.312743
$707$	−2.41665	−0.0908876
$708$	−5.05307	−0.189906
$709$	16.3431	0.613776	0.306888	−	0.951746i	$-0.400712\pi$
$709$	16.3431	0.613776	0.306888	+	0.951746i	$0.400712\pi$
$710$	3.40630	0.127836
$711$	0.191590	0.00718520
$712$	5.69587	0.213462
$713$	−60.1980	−2.25443
$714$	−0.294830	−0.0110338
$715$	0	0
$716$	−23.1313	−0.864456
$717$	−10.2920	−0.384364
$718$	−3.32035	−0.123914
$719$	5.59133	0.208521	0.104261	−	0.994550i	$-0.466752\pi$
$719$	5.59133	0.208521	0.104261	+	0.994550i	$0.466752\pi$
$720$	7.26000	0.270564
$721$	−13.1214	−0.488665
$722$	9.67720	0.360148
$723$	8.56341	0.318476
$724$	32.4494	1.20597
$725$	6.79931	0.252520
$726$	0	0
$727$	15.1035	0.560159	0.280080	−	0.959977i	$-0.409639\pi$
$727$	15.1035	0.560159	0.280080	+	0.959977i	$0.409639\pi$
$728$	2.12873	0.0788959
$729$	−10.6002	−0.392601
$730$	−4.81772	−0.178312
$731$	−5.50633	−0.203659
$732$	−10.9020	−0.402948
$733$	−13.0144	−0.480696	−0.240348	−	0.970687i	$-0.577262\pi$
$733$	−13.0144	−0.480696	−0.240348	+	0.970687i	$0.577262\pi$
$734$	4.27580	0.157823
$735$	0.577925	0.0213171
$736$	−30.7349	−1.13290
$737$	0	0
$738$	−11.9245	−0.438945
$739$	25.1956	0.926836	0.463418	−	0.886140i	$-0.346623\pi$
$739$	25.1956	0.926836	0.463418	+	0.886140i	$0.346623\pi$
$740$	−15.1217	−0.555883
$741$	4.35765	0.160082
$742$	−5.74348	−0.210850
$743$	38.2296	1.40251	0.701254	−	0.712911i	$-0.252624\pi$
$743$	38.2296	1.40251	0.701254	+	0.712911i	$0.252624\pi$
$744$	9.71688	0.356238
$745$	11.3747	0.416736
$746$	−15.9620	−0.584412
$747$	24.4349	0.894026
$748$	0	0
$749$	13.6316	0.498089
$750$	0.271649	0.00991922
$751$	−24.3760	−0.889494	−0.444747	−	0.895656i	$-0.646706\pi$
$751$	−24.3760	−0.889494	−0.444747	+	0.895656i	$0.646706\pi$
$752$	10.6174	0.387176
$753$	−2.84683	−0.103744
$754$	−3.83002	−0.139481
$755$	12.8036	0.465972
$756$	−5.82557	−0.211874
$757$	28.9119	1.05082	0.525410	−	0.850849i	$-0.323912\pi$
$757$	28.9119	1.05082	0.525410	+	0.850849i	$0.323912\pi$
$758$	9.74047	0.353790
$759$	0	0
$760$	11.1764	0.405411
$761$	17.6334	0.639212	0.319606	−	0.947551i	$-0.396449\pi$
$761$	17.6334	0.639212	0.319606	+	0.947551i	$0.396449\pi$
$762$	3.04869	0.110442
$763$	7.14569	0.258691
$764$	26.4712	0.957696
$765$	2.89351	0.104615
$766$	−8.27008	−0.298810
$767$	5.88970	0.212665
$768$	−0.638652	−0.0230454
$769$	−30.2925	−1.09237	−0.546187	−	0.837663i	$-0.683921\pi$
$769$	−30.2925	−1.09237	−0.546187	+	0.837663i	$0.683921\pi$
$770$	0	0
$771$	−6.14203	−0.221200
$772$	−8.67599	−0.312256
$773$	−30.0549	−1.08100	−0.540500	−	0.841344i	$-0.681765\pi$
$773$	−30.0549	−1.08100	−0.540500	+	0.841344i	$0.681765\pi$
$774$	6.35763	0.228520
$775$	9.46531	0.340004
$776$	16.0820	0.577312
$777$	4.91225	0.176226
$778$	−10.9967	−0.394250
$779$	59.8718	2.14513
$780$	1.23214	0.0441178
$781$	0	0
$782$	−3.24451	−0.116023
$783$	22.2645	0.795668
$784$	2.72318	0.0972563
$785$	−8.23103	−0.293778
$786$	−4.71523	−0.168187
$787$	38.2530	1.36357	0.681787	−	0.731551i	$-0.261203\pi$
$787$	38.2530	1.36357	0.681787	+	0.731551i	$0.261203\pi$
$788$	37.9159	1.35070
$789$	3.83111	0.136391
$790$	0.0337792	0.00120181
$791$	10.9216	0.388329
$792$	0	0
$793$	12.7070	0.451238
$794$	2.96776	0.105322
$795$	−7.06171	−0.250453
$796$	−1.93768	−0.0686793
$797$	−12.7361	−0.451135	−0.225568	−	0.974228i	$-0.572424\pi$
$797$	−12.7361	−0.451135	−0.225568	+	0.974228i	$0.572424\pi$
$798$	−1.70919	−0.0605046
$799$	4.23161	0.149704
$800$	4.83264	0.170860
$801$	8.54870	0.302053
$802$	−13.8607	−0.489438
$803$	0	0
$804$	−5.23695	−0.184693
$805$	6.35986	0.224156
$806$	−5.33177	−0.187803
$807$	−8.45004	−0.297455
$808$	4.29274	0.151018
$809$	13.6911	0.481354	0.240677	−	0.970605i	$-0.422631\pi$
$809$	13.6911	0.481354	0.240677	+	0.970605i	$0.422631\pi$
$810$	−2.86988	−0.100837
$811$	−42.2475	−1.48351	−0.741756	−	0.670670i	$-0.766007\pi$
$811$	−42.2475	−1.48351	−0.741756	+	0.670670i	$0.766007\pi$
$812$	−12.0964	−0.424500
$813$	−2.89205	−0.101429
$814$	0	0
$815$	−6.30685	−0.220919
$816$	−1.70809	−0.0597952
$817$	−31.9212	−1.11678
$818$	−10.4234	−0.364446
$819$	3.19492	0.111640
$820$	16.9290	0.591187
$821$	−31.6222	−1.10362	−0.551810	−	0.833970i	$-0.686063\pi$
$821$	−31.6222	−1.10362	−0.551810	+	0.833970i	$0.686063\pi$
$822$	−5.11674	−0.178467
$823$	32.4818	1.13224	0.566122	−	0.824322i	$-0.308443\pi$
$823$	32.4818	1.13224	0.566122	+	0.824322i	$0.308443\pi$
$824$	23.3077	0.811962
$825$	0	0
$826$	−2.31010	−0.0803786
$827$	−51.6677	−1.79666	−0.898330	−	0.439321i	$-0.855219\pi$
$827$	−51.6677	−1.79666	−0.898330	+	0.439321i	$0.855219\pi$
$828$	−30.1647	−1.04830
$829$	3.81406	0.132468	0.0662339	−	0.997804i	$-0.478902\pi$
$829$	3.81406	0.132468	0.0662339	+	0.997804i	$0.478902\pi$
$830$	4.30811	0.149537
$831$	2.02522	0.0702539
$832$	3.80467	0.131903
$833$	1.08534	0.0376047
$834$	5.45706	0.188962
$835$	9.35034	0.323582
$836$	0	0
$837$	30.9944	1.07132
$838$	−11.2122	−0.387319
$839$	−34.9994	−1.20831	−0.604157	−	0.796865i	$-0.706490\pi$
$839$	−34.9994	−1.20831	−0.604157	+	0.796865i	$0.706490\pi$
$840$	−1.02658	−0.0354203
$841$	17.2306	0.594157
$842$	7.39887	0.254982
$843$	−5.44691	−0.187602
$844$	40.8907	1.40752
$845$	11.5639	0.397809
$846$	−4.88583	−0.167978
$847$	0	0
$848$	−33.2747	−1.14266
$849$	9.19537	0.315584
$850$	0.510154	0.0174981
$851$	54.0576	1.85307
$852$	−7.45089	−0.255263
$853$	51.6573	1.76871	0.884357	−	0.466812i	$-0.154597\pi$
$853$	51.6573	1.76871	0.884357	+	0.466812i	$0.154597\pi$
$854$	−4.98402	−0.170550
$855$	16.7742	0.573666
$856$	−24.2141	−0.827622
$857$	11.4832	0.392258	0.196129	−	0.980578i	$-0.437163\pi$
$857$	11.4832	0.392258	0.196129	+	0.980578i	$0.437163\pi$
$858$	0	0
$859$	11.5148	0.392880	0.196440	−	0.980516i	$-0.437062\pi$
$859$	11.5148	0.392880	0.196440	+	0.980516i	$0.437062\pi$
$860$	−9.02586	−0.307779
$861$	−5.49936	−0.187418
$862$	0.707766	0.0241066
$863$	−27.5849	−0.938999	−0.469500	−	0.882933i	$-0.655566\pi$
$863$	−27.5849	−0.938999	−0.469500	+	0.882933i	$0.655566\pi$
$864$	15.8246	0.538364
$865$	6.98410	0.237466
$866$	3.11538	0.105865
$867$	9.14395	0.310545
$868$	−16.8394	−0.571565
$869$	0	0
$870$	1.84702	0.0626200
$871$	6.10402	0.206827
$872$	−12.6930	−0.429840
$873$	24.1369	0.816910
$874$	−18.8090	−0.636224
$875$	−1.00000	−0.0338062
$876$	10.5382	0.356053
$877$	−50.2969	−1.69841	−0.849203	−	0.528067i	$-0.822917\pi$
$877$	−50.2969	−1.69841	−0.849203	+	0.528067i	$0.822917\pi$
$878$	2.80392	0.0946276
$879$	8.87540	0.299360
$880$	0	0
$881$	−29.4455	−0.992044	−0.496022	−	0.868310i	$-0.665207\pi$
$881$	−29.4455	−0.992044	−0.496022	+	0.868310i	$0.665207\pi$
$882$	−1.25313	−0.0421952
$883$	27.3839	0.921542	0.460771	−	0.887519i	$-0.347573\pi$
$883$	27.3839	0.921542	0.460771	+	0.887519i	$0.347573\pi$
$884$	2.31395	0.0778266
$885$	−2.84031	−0.0954758
$886$	12.4642	0.418744
$887$	−43.0693	−1.44612	−0.723062	−	0.690783i	$-0.757266\pi$
$887$	−43.0693	−1.44612	−0.723062	+	0.690783i	$0.757266\pi$
$888$	−8.72571	−0.292816
$889$	−11.2229	−0.376404
$890$	1.50722	0.0505221
$891$	0	0
$892$	41.5746	1.39202
$893$	24.5314	0.820912
$894$	3.08992	0.103342
$895$	−13.0020	−0.434608
$896$	−11.1576	−0.372749
$897$	−4.40472	−0.147069
$898$	17.5979	0.587251
$899$	64.3575	2.14644
$900$	4.74298	0.158099
$901$	−13.2618	−0.441815
$902$	0	0
$903$	2.93204	0.0975720
$904$	−19.4003	−0.645244
$905$	18.2396	0.606306
$906$	3.47810	0.115552
$907$	−30.1364	−1.00066	−0.500332	−	0.865834i	$-0.666789\pi$
$907$	−30.1364	−1.00066	−0.500332	+	0.865834i	$0.666789\pi$
$908$	16.4791	0.546879
$909$	6.44280	0.213694
$910$	0.563295	0.0186731
$911$	39.4333	1.30648	0.653242	−	0.757149i	$-0.273409\pi$
$911$	39.4333	1.30648	0.653242	+	0.757149i	$0.273409\pi$
$912$	−9.90213	−0.327892
$913$	0	0
$914$	−0.670295	−0.0221714
$915$	−6.12793	−0.202583
$916$	−39.8045	−1.31518
$917$	17.3578	0.573205
$918$	1.67051	0.0551350
$919$	16.9203	0.558149	0.279075	−	0.960269i	$-0.409972\pi$
$919$	16.9203	0.558149	0.279075	+	0.960269i	$0.409972\pi$
$920$	−11.2971	−0.372455
$921$	−9.28503	−0.305952
$922$	−0.260624	−0.00858319
$923$	8.68452	0.285854
$924$	0	0
$925$	−8.49980	−0.279472
$926$	7.66139	0.251769
$927$	34.9816	1.14895
$928$	32.8586	1.07864
$929$	−41.8149	−1.37190	−0.685951	−	0.727648i	$-0.740613\pi$
$929$	−41.8149	−1.37190	−0.685951	+	0.727648i	$0.740613\pi$
$930$	2.57124	0.0843143
$931$	6.29189	0.206209
$932$	0.535469	0.0175399
$933$	−2.12155	−0.0694565
$934$	−10.7038	−0.350239
$935$	0	0
$936$	−5.67519	−0.185500
$937$	10.7732	0.351947	0.175973	−	0.984395i	$-0.443693\pi$
$937$	10.7732	0.351947	0.175973	+	0.984395i	$0.443693\pi$
$938$	−2.39416	−0.0781721
$939$	2.57320	0.0839731
$940$	6.93636	0.226239
$941$	10.4374	0.340249	0.170125	−	0.985423i	$-0.445583\pi$
$941$	10.4374	0.340249	0.170125	+	0.985423i	$0.445583\pi$
$942$	−2.23595	−0.0728512
$943$	−60.5186	−1.97076
$944$	−13.3835	−0.435596
$945$	−3.27452	−0.106520
$946$	0	0
$947$	25.7372	0.836348	0.418174	−	0.908367i	$-0.362670\pi$
$947$	25.7372	0.836348	0.418174	+	0.908367i	$0.362670\pi$
$948$	−0.0738881	−0.00239978
$949$	−12.2830	−0.398723
$950$	2.95746	0.0959525
$951$	12.8889	0.417951
$952$	−1.92790	−0.0624837
$953$	22.0261	0.713496	0.356748	−	0.934201i	$-0.383885\pi$
$953$	22.0261	0.713496	0.356748	+	0.934201i	$0.383885\pi$
$954$	15.3121	0.495749
$955$	14.8793	0.481484
$956$	−31.6826	−1.02469
$957$	0	0
$958$	6.94431	0.224361
$959$	18.8358	0.608241
$960$	−1.83480	−0.0592179
$961$	58.5921	1.89007
$962$	4.78790	0.154368
$963$	−36.3420	−1.17110
$964$	26.3612	0.849039
$965$	−4.87672	−0.156987
$966$	1.72765	0.0555862
$967$	−39.0647	−1.25624	−0.628118	−	0.778118i	$-0.716174\pi$
$967$	−39.0647	−1.25624	−0.628118	+	0.778118i	$0.716174\pi$
$968$	0	0
$969$	−3.94654	−0.126781
$970$	4.25557	0.136638
$971$	27.4441	0.880723	0.440362	−	0.897820i	$-0.354850\pi$
$971$	27.4441	0.880723	0.440362	+	0.897820i	$0.354850\pi$
$972$	23.7543	0.761918
$973$	−20.0886	−0.644012
$974$	−2.90681	−0.0931403
$975$	0.692581	0.0221803
$976$	−28.8748	−0.924259
$977$	13.7037	0.438420	0.219210	−	0.975678i	$-0.429652\pi$
$977$	13.7037	0.438420	0.219210	+	0.975678i	$0.429652\pi$
$978$	−1.71325	−0.0547837
$979$	0	0
$980$	1.77906	0.0568300
$981$	−19.0504	−0.608234
$982$	17.0225	0.543209
$983$	26.5600	0.847133	0.423566	−	0.905865i	$-0.360778\pi$
$983$	26.5600	0.847133	0.423566	+	0.905865i	$0.360778\pi$
$984$	9.76862	0.311412
$985$	21.3123	0.679067
$986$	3.46869	0.110466
$987$	−2.25327	−0.0717222
$988$	13.4144	0.426769
$989$	32.2660	1.02600
$990$	0	0
$991$	−55.9346	−1.77682	−0.888410	−	0.459051i	$-0.848190\pi$
$991$	−55.9346	−1.77682	−0.888410	+	0.459051i	$0.848190\pi$
$992$	45.7425	1.45232
$993$	4.87371	0.154663
$994$	−3.40630	−0.108041
$995$	−1.08916	−0.0345287
$996$	−9.42349	−0.298595
$997$	−1.89634	−0.0600578	−0.0300289	−	0.999549i	$-0.509560\pi$
$997$	−1.89634	−0.0600578	−0.0300289	+	0.999549i	$0.509560\pi$
$998$	−8.45484	−0.267633
$999$	−27.8328	−0.880591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bb.1.3	yes	5
11.10	odd	2		4235.2.a.ba.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.ba.1.3	✓	5	11.10	odd	2
4235.2.a.bb.1.3	yes	5	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+0.470042 q^{2} -0.577925 q^{3} -1.77906 q^{4} -1.00000 q^{5} -0.271649 q^{6} +1.00000 q^{7} -1.77632 q^{8} -2.66600 q^{9} +O(q^{10})\)	\(q+0.470042 q^{2} -0.577925 q^{3} -1.77906 q^{4} -1.00000 q^{5} -0.271649 q^{6} +1.00000 q^{7} -1.77632 q^{8} -2.66600 q^{9} -0.470042 q^{10} +1.02816 q^{12} -1.19839 q^{13} +0.470042 q^{14} +0.577925 q^{15} +2.72318 q^{16} +1.08534 q^{17} -1.25313 q^{18} +6.29189 q^{19} +1.77906 q^{20} -0.577925 q^{21} -6.35986 q^{23} +1.02658 q^{24} +1.00000 q^{25} -0.563295 q^{26} +3.27452 q^{27} -1.77906 q^{28} +6.79931 q^{29} +0.271649 q^{30} +9.46531 q^{31} +4.83264 q^{32} +0.510154 q^{34} -1.00000 q^{35} +4.74298 q^{36} -8.49980 q^{37} +2.95746 q^{38} +0.692581 q^{39} +1.77632 q^{40} +9.51571 q^{41} -0.271649 q^{42} -5.07339 q^{43} +2.66600 q^{45} -2.98940 q^{46} +3.89889 q^{47} -1.57379 q^{48} +1.00000 q^{49} +0.470042 q^{50} -0.627242 q^{51} +2.13201 q^{52} -12.2191 q^{53} +1.53916 q^{54} -1.77632 q^{56} -3.63624 q^{57} +3.19596 q^{58} -4.91466 q^{59} -1.02816 q^{60} -10.6033 q^{61} +4.44909 q^{62} -2.66600 q^{63} -3.17481 q^{64} +1.19839 q^{65} -5.09350 q^{67} -1.93088 q^{68} +3.67552 q^{69} -0.470042 q^{70} -7.24680 q^{71} +4.73567 q^{72} +10.2495 q^{73} -3.99527 q^{74} -0.577925 q^{75} -11.1937 q^{76} +0.325542 q^{78} -0.0718642 q^{79} -2.72318 q^{80} +6.10558 q^{81} +4.47278 q^{82} -9.16537 q^{83} +1.02816 q^{84} -1.08534 q^{85} -2.38471 q^{86} -3.92949 q^{87} -3.20656 q^{89} +1.25313 q^{90} -1.19839 q^{91} +11.3146 q^{92} -5.47024 q^{93} +1.83264 q^{94} -6.29189 q^{95} -2.79290 q^{96} -9.05358 q^{97} +0.470042 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} - 23 q^{12} - 10 q^{13} + 2 q^{15} + 10 q^{16} - 2 q^{17} - 5 q^{18} + 3 q^{19} - 4 q^{20} - 2 q^{21} + 3 q^{23} + 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} + 4 q^{28} - q^{29} - 5 q^{30} - 12 q^{31} - 29 q^{32} - 20 q^{34} - 5 q^{35} + 45 q^{36} + 9 q^{38} + 2 q^{39} + 12 q^{40} + 11 q^{41} + 5 q^{42} - 10 q^{43} - 11 q^{45} - 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} - 6 q^{51} - 30 q^{52} + 4 q^{53} + 34 q^{54} - 12 q^{56} - 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} - 40 q^{61} - q^{62} + 11 q^{63} + 38 q^{64} + 10 q^{65} + 7 q^{67} + 19 q^{68} - 24 q^{69} + 10 q^{71} - 72 q^{72} - 11 q^{73} + 37 q^{74} - 2 q^{75} - 3 q^{76} - 87 q^{78} - 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} - 26 q^{83} - 23 q^{84} + 2 q^{85} - 17 q^{86} - 14 q^{87} + 5 q^{89} + 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} - 44 q^{94} - 3 q^{95} + 84 q^{96} - 5 q^{97}+O(q^{100}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9 - 23 * q^12 - 10 * q^13 + 2 * q^15 + 10 * q^16 - 2 * q^17 - 5 * q^18 + 3 * q^19 - 4 * q^20 - 2 * q^21 + 3 * q^23 + 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 + 4 * q^28 - q^29 - 5 * q^30 - 12 * q^31 - 29 * q^32 - 20 * q^34 - 5 * q^35 + 45 * q^36 + 9 * q^38 + 2 * q^39 + 12 * q^40 + 11 * q^41 + 5 * q^42 - 10 * q^43 - 11 * q^45 - 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 - 6 * q^51 - 30 * q^52 + 4 * q^53 + 34 * q^54 - 12 * q^56 - 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 - 40 * q^61 - q^62 + 11 * q^63 + 38 * q^64 + 10 * q^65 + 7 * q^67 + 19 * q^68 - 24 * q^69 + 10 * q^71 - 72 * q^72 - 11 * q^73 + 37 * q^74 - 2 * q^75 - 3 * q^76 - 87 * q^78 - 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 - 26 * q^83 - 23 * q^84 + 2 * q^85 - 17 * q^86 - 14 * q^87 + 5 * q^89 + 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 - 44 * q^94 - 3 * q^95 + 84 * q^96 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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