LMFDB - Embedded newform 4235.2.a.bh.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:	$8$
Coefficient field:	8.8.32694400625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 16x^{6} + 44x^{5} + 83x^{4} - 200x^{3} - 132x^{2} + 288x - 16 $ x^8 - 3x^7 - 16x^6 + 44x^5 + 83x^4 - 200x^3 - 132x^2 + 288*x - 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.64523$ 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)

$f(q)$	$=$	$q-0.477260 q^{2} -1.87300 q^{3} -1.77222 q^{4} -1.00000 q^{5} +0.893910 q^{6} +1.00000 q^{7} +1.80033 q^{8} +0.508144 q^{9} +O(q^{10})$	\(q-0.477260 q^{2} -1.87300 q^{3} -1.77222 q^{4} -1.00000 q^{5} +0.893910 q^{6} +1.00000 q^{7} +1.80033 q^{8} +0.508144 q^{9} +0.477260 q^{10} +3.31938 q^{12} -3.98510 q^{13} -0.477260 q^{14} +1.87300 q^{15} +2.68522 q^{16} +3.06241 q^{17} -0.242517 q^{18} +0.112100 q^{19} +1.77222 q^{20} -1.87300 q^{21} -7.20351 q^{23} -3.37203 q^{24} +1.00000 q^{25} +1.90193 q^{26} +4.66726 q^{27} -1.77222 q^{28} -3.20232 q^{29} -0.893910 q^{30} -1.87450 q^{31} -4.88221 q^{32} -1.46156 q^{34} -1.00000 q^{35} -0.900544 q^{36} +6.55792 q^{37} -0.0535009 q^{38} +7.46412 q^{39} -1.80033 q^{40} +1.40849 q^{41} +0.893910 q^{42} -4.27596 q^{43} -0.508144 q^{45} +3.43795 q^{46} +4.59397 q^{47} -5.02943 q^{48} +1.00000 q^{49} -0.477260 q^{50} -5.73590 q^{51} +7.06249 q^{52} +1.38466 q^{53} -2.22749 q^{54} +1.80033 q^{56} -0.209964 q^{57} +1.52834 q^{58} +14.2451 q^{59} -3.31938 q^{60} -1.19518 q^{61} +0.894625 q^{62} +0.508144 q^{63} -3.04036 q^{64} +3.98510 q^{65} +7.12333 q^{67} -5.42727 q^{68} +13.4922 q^{69} +0.477260 q^{70} +10.0943 q^{71} +0.914827 q^{72} +10.3155 q^{73} -3.12983 q^{74} -1.87300 q^{75} -0.198666 q^{76} -3.56232 q^{78} +3.99020 q^{79} -2.68522 q^{80} -10.2662 q^{81} -0.672214 q^{82} +3.57680 q^{83} +3.31938 q^{84} -3.06241 q^{85} +2.04075 q^{86} +5.99796 q^{87} -3.94546 q^{89} +0.242517 q^{90} -3.98510 q^{91} +12.7662 q^{92} +3.51095 q^{93} -2.19252 q^{94} -0.112100 q^{95} +9.14440 q^{96} -13.6588 q^{97} -0.477260 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 8 q^{5} - 6 q^{6} + 8 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 8 * q^5 - 6 * q^6 + 8 * q^7 + 6 * q^8 + 17 * q^9	$ 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 8 q^{5} - 6 q^{6} + 8 q^{7} + 6 q^{8} + 17 q^{9} - 2 q^{10} - 10 q^{12} + 2 q^{14} + 3 q^{15} - 6 q^{16} + 7 q^{17} - 3 q^{18} - 19 q^{19} + 2 q^{20} - 3 q^{21} - 16 q^{23} - 5 q^{24} + 8 q^{25} + 15 q^{26} - 21 q^{27} - 2 q^{28} - 8 q^{29} + 6 q^{30} - 6 q^{31} - 16 q^{32} - 3 q^{34} - 8 q^{35} + 4 q^{36} - 26 q^{37} - 25 q^{38} + 11 q^{39} - 6 q^{40} - 9 q^{41} - 6 q^{42} + 4 q^{43} - 17 q^{45} + 20 q^{46} + 9 q^{47} + 16 q^{48} + 8 q^{49} + 2 q^{50} - 44 q^{51} + 5 q^{52} - 7 q^{53} - 21 q^{54} + 6 q^{56} + 36 q^{57} + 15 q^{58} + 20 q^{59} + 10 q^{60} - 13 q^{61} - 9 q^{62} + 17 q^{63} - 6 q^{64} - 21 q^{67} - q^{68} - 12 q^{69} - 2 q^{70} + 3 q^{71} + 38 q^{72} - 16 q^{73} + 2 q^{74} - 3 q^{75} - 11 q^{76} + 7 q^{78} + 14 q^{79} + 6 q^{80} + 12 q^{81} - 16 q^{82} - 4 q^{83} - 10 q^{84} - 7 q^{85} + 7 q^{86} - 8 q^{87} - 23 q^{89} + 3 q^{90} + 26 q^{92} - 67 q^{93} + 12 q^{94} + 19 q^{95} + 27 q^{96} - 38 q^{97} + 2 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 8 * q^5 - 6 * q^6 + 8 * q^7 + 6 * q^8 + 17 * q^9 - 2 * q^10 - 10 * q^12 + 2 * q^14 + 3 * q^15 - 6 * q^16 + 7 * q^17 - 3 * q^18 - 19 * q^19 + 2 * q^20 - 3 * q^21 - 16 * q^23 - 5 * q^24 + 8 * q^25 + 15 * q^26 - 21 * q^27 - 2 * q^28 - 8 * q^29 + 6 * q^30 - 6 * q^31 - 16 * q^32 - 3 * q^34 - 8 * q^35 + 4 * q^36 - 26 * q^37 - 25 * q^38 + 11 * q^39 - 6 * q^40 - 9 * q^41 - 6 * q^42 + 4 * q^43 - 17 * q^45 + 20 * q^46 + 9 * q^47 + 16 * q^48 + 8 * q^49 + 2 * q^50 - 44 * q^51 + 5 * q^52 - 7 * q^53 - 21 * q^54 + 6 * q^56 + 36 * q^57 + 15 * q^58 + 20 * q^59 + 10 * q^60 - 13 * q^61 - 9 * q^62 + 17 * q^63 - 6 * q^64 - 21 * q^67 - q^68 - 12 * q^69 - 2 * q^70 + 3 * q^71 + 38 * q^72 - 16 * q^73 + 2 * q^74 - 3 * q^75 - 11 * q^76 + 7 * q^78 + 14 * q^79 + 6 * q^80 + 12 * q^81 - 16 * q^82 - 4 * q^83 - 10 * q^84 - 7 * q^85 + 7 * q^86 - 8 * q^87 - 23 * q^89 + 3 * q^90 + 26 * q^92 - 67 * q^93 + 12 * q^94 + 19 * q^95 + 27 * q^96 - 38 * q^97 + 2 * q^98

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 $

$2$	−0.477260	−0.337474	−0.168737	−	0.985661i	$-0.553969\pi$
$2$	−0.477260	−0.337474	−0.168737	+	0.985661i	$0.553969\pi$
$3$	−1.87300	−1.08138	−0.540690	−	0.841222i	$-0.681837\pi$
$3$	−1.87300	−1.08138	−0.540690	+	0.841222i	$0.681837\pi$
$4$	−1.77222	−0.886111
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.893910	0.364937
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.80033	0.636513
$9$	0.508144	0.169381
$10$	0.477260	0.150923
$11$	0	0
$11$	0	0
$12$	3.31938	0.958223
$13$	−3.98510	−1.10527	−0.552634	−	0.833424i	$-0.686377\pi$
$13$	−3.98510	−1.10527	−0.552634	+	0.833424i	$0.686377\pi$
$14$	−0.477260	−0.127553
$15$	1.87300	0.483608
$16$	2.68522	0.671305
$17$	3.06241	0.742743	0.371371	−	0.928484i	$-0.378888\pi$
$17$	3.06241	0.742743	0.371371	+	0.928484i	$0.378888\pi$
$18$	−0.242517	−0.0571617
$19$	0.112100	0.0257175	0.0128588	−	0.999917i	$-0.495907\pi$
$19$	0.112100	0.0257175	0.0128588	+	0.999917i	$0.495907\pi$
$20$	1.77222	0.396281
$21$	−1.87300	−0.408723
$22$	0	0
$23$	−7.20351	−1.50204	−0.751018	−	0.660282i	$-0.770437\pi$
$23$	−7.20351	−1.50204	−0.751018	+	0.660282i	$0.770437\pi$
$24$	−3.37203	−0.688312
$25$	1.00000	0.200000
$26$	1.90193	0.372999
$27$	4.66726	0.898214
$28$	−1.77222	−0.334919
$29$	−3.20232	−0.594656	−0.297328	−	0.954775i	$-0.596096\pi$
$29$	−3.20232	−0.594656	−0.297328	+	0.954775i	$0.596096\pi$
$30$	−0.893910	−0.163205
$31$	−1.87450	−0.336670	−0.168335	−	0.985730i	$-0.553839\pi$
$31$	−1.87450	−0.336670	−0.168335	+	0.985730i	$0.553839\pi$
$32$	−4.88221	−0.863061
$33$	0	0
$34$	−1.46156	−0.250656
$35$	−1.00000	−0.169031
$36$	−0.900544	−0.150091
$37$	6.55792	1.07812	0.539058	−	0.842269i	$-0.318780\pi$
$37$	6.55792	1.07812	0.539058	+	0.842269i	$0.318780\pi$
$38$	−0.0535009	−0.00867899
$39$	7.46412	1.19521
$40$	−1.80033	−0.284657
$41$	1.40849	0.219969	0.109984	−	0.993933i	$-0.464920\pi$
$41$	1.40849	0.219969	0.109984	+	0.993933i	$0.464920\pi$
$42$	0.893910	0.137933
$43$	−4.27596	−0.652078	−0.326039	−	0.945356i	$-0.605714\pi$
$43$	−4.27596	−0.652078	−0.326039	+	0.945356i	$0.605714\pi$
$44$	0	0
$45$	−0.508144	−0.0757496
$46$	3.43795	0.506898
$47$	4.59397	0.670099	0.335049	−	0.942201i	$-0.391247\pi$
$47$	4.59397	0.670099	0.335049	+	0.942201i	$0.391247\pi$
$48$	−5.02943	−0.725935
$49$	1.00000	0.142857
$50$	−0.477260	−0.0674948
$51$	−5.73590	−0.803187
$52$	7.06249	0.979391
$53$	1.38466	0.190197	0.0950986	−	0.995468i	$-0.469683\pi$
$53$	1.38466	0.190197	0.0950986	+	0.995468i	$0.469683\pi$
$54$	−2.22749	−0.303124
$55$	0	0
$56$	1.80033	0.240579
$57$	−0.209964	−0.0278104
$58$	1.52834	0.200681
$59$	14.2451	1.85455	0.927274	−	0.374382i	$-0.122145\pi$
$59$	14.2451	1.85455	0.927274	+	0.374382i	$0.122145\pi$
$60$	−3.31938	−0.428530
$61$	−1.19518	−0.153027	−0.0765135	−	0.997069i	$-0.524379\pi$
$61$	−1.19518	−0.153027	−0.0765135	+	0.997069i	$0.524379\pi$
$62$	0.894625	0.113617
$63$	0.508144	0.0640201
$64$	−3.04036	−0.380044
$65$	3.98510	0.494291
$66$	0	0
$67$	7.12333	0.870254	0.435127	−	0.900369i	$-0.356704\pi$
$67$	7.12333	0.870254	0.435127	+	0.900369i	$0.356704\pi$
$68$	−5.42727	−0.658153
$69$	13.4922	1.62427
$70$	0.477260	0.0570435
$71$	10.0943	1.19797	0.598984	−	0.800761i	$-0.295571\pi$
$71$	10.0943	1.19797	0.598984	+	0.800761i	$0.295571\pi$
$72$	0.914827	0.107813
$73$	10.3155	1.20734	0.603668	−	0.797236i	$-0.293705\pi$
$73$	10.3155	1.20734	0.603668	+	0.797236i	$0.293705\pi$
$74$	−3.12983	−0.363836
$75$	−1.87300	−0.216276
$76$	−0.198666	−0.0227886
$77$	0	0
$78$	−3.56232	−0.403354
$79$	3.99020	0.448933	0.224466	−	0.974482i	$-0.427936\pi$
$79$	3.99020	0.448933	0.224466	+	0.974482i	$0.427936\pi$
$80$	−2.68522	−0.300217
$81$	−10.2662	−1.14069
$82$	−0.672214	−0.0742337
$83$	3.57680	0.392605	0.196303	−	0.980543i	$-0.437107\pi$
$83$	3.57680	0.392605	0.196303	+	0.980543i	$0.437107\pi$
$84$	3.31938	0.362174
$85$	−3.06241	−0.332165
$86$	2.04075	0.220059
$87$	5.99796	0.643049
$88$	0	0
$89$	−3.94546	−0.418218	−0.209109	−	0.977892i	$-0.567056\pi$
$89$	−3.94546	−0.418218	−0.209109	+	0.977892i	$0.567056\pi$
$90$	0.242517	0.0255635
$91$	−3.98510	−0.417752
$92$	12.7662	1.33097
$93$	3.51095	0.364069
$94$	−2.19252	−0.226141
$95$	−0.112100	−0.0115012
$96$	9.14440	0.933296
$97$	−13.6588	−1.38684	−0.693419	−	0.720535i	$-0.743896\pi$
$97$	−13.6588	−1.38684	−0.693419	+	0.720535i	$0.743896\pi$
$98$	−0.477260	−0.0482105
$99$	0	0
$100$	−1.77222	−0.177222
$101$	4.26451	0.424335	0.212167	−	0.977233i	$-0.431948\pi$
$101$	4.26451	0.424335	0.212167	+	0.977233i	$0.431948\pi$
$102$	2.73752	0.271054
$103$	−7.94190	−0.782539	−0.391269	−	0.920276i	$-0.627964\pi$
$103$	−7.94190	−0.782539	−0.391269	+	0.920276i	$0.627964\pi$
$104$	−7.17451	−0.703518
$105$	1.87300	0.182786
$106$	−0.660841	−0.0641866
$107$	−8.80372	−0.851087	−0.425544	−	0.904938i	$-0.639917\pi$
$107$	−8.80372	−0.851087	−0.425544	+	0.904938i	$0.639917\pi$
$108$	−8.27142	−0.795918
$109$	8.37070	0.801767	0.400884	−	0.916129i	$-0.368703\pi$
$109$	8.37070	0.801767	0.400884	+	0.916129i	$0.368703\pi$
$110$	0	0
$111$	−12.2830	−1.16585
$112$	2.68522	0.253729
$113$	3.24373	0.305144	0.152572	−	0.988292i	$-0.451244\pi$
$113$	3.24373	0.305144	0.152572	+	0.988292i	$0.451244\pi$
$114$	0.100207	0.00938528
$115$	7.20351	0.671731
$116$	5.67523	0.526932
$117$	−2.02500	−0.187212
$118$	−6.79860	−0.625862
$119$	3.06241	0.280730
$120$	3.37203	0.307823
$121$	0	0
$122$	0.570411	0.0516426
$123$	−2.63810	−0.237870
$124$	3.32204	0.298328
$125$	−1.00000	−0.0894427
$126$	−0.242517	−0.0216051
$127$	13.7235	1.21777	0.608883	−	0.793260i	$-0.291618\pi$
$127$	13.7235	1.21777	0.608883	+	0.793260i	$0.291618\pi$
$128$	11.2155	0.991316
$129$	8.00889	0.705144
$130$	−1.90193	−0.166810
$131$	−20.1983	−1.76473	−0.882365	−	0.470566i	$-0.844050\pi$
$131$	−20.1983	−1.76473	−0.882365	+	0.470566i	$0.844050\pi$
$132$	0	0
$133$	0.112100	0.00972031
$134$	−3.39968	−0.293688
$135$	−4.66726	−0.401694
$136$	5.51335	0.472765
$137$	0.709895	0.0606504	0.0303252	−	0.999540i	$-0.490346\pi$
$137$	0.709895	0.0606504	0.0303252	+	0.999540i	$0.490346\pi$
$138$	−6.43929	−0.548149
$139$	−16.3064	−1.38309	−0.691544	−	0.722335i	$-0.743069\pi$
$139$	−16.3064	−1.38309	−0.691544	+	0.722335i	$0.743069\pi$
$140$	1.77222	0.149780
$141$	−8.60452	−0.724631
$142$	−4.81758	−0.404283
$143$	0	0
$144$	1.36448	0.113706
$145$	3.20232	0.265938
$146$	−4.92317	−0.407444
$147$	−1.87300	−0.154483
$148$	−11.6221	−0.955331
$149$	19.2250	1.57497	0.787486	−	0.616332i	$-0.211382\pi$
$149$	19.2250	1.57497	0.787486	+	0.616332i	$0.211382\pi$
$150$	0.893910	0.0729874
$151$	12.2656	0.998163	0.499082	−	0.866555i	$-0.333671\pi$
$151$	12.2656	0.998163	0.499082	+	0.866555i	$0.333671\pi$
$152$	0.201817	0.0163695
$153$	1.55614	0.125807
$154$	0	0
$155$	1.87450	0.150564
$156$	−13.2281	−1.05909
$157$	−22.6083	−1.80434	−0.902168	−	0.431384i	$-0.858025\pi$
$157$	−22.6083	−1.80434	−0.902168	+	0.431384i	$0.858025\pi$
$158$	−1.90436	−0.151503
$159$	−2.59347	−0.205675
$160$	4.88221	0.385973
$161$	−7.20351	−0.567716
$162$	4.89966	0.384953
$163$	−18.1652	−1.42281	−0.711406	−	0.702781i	$-0.751941\pi$
$163$	−18.1652	−1.42281	−0.711406	+	0.702781i	$0.751941\pi$
$164$	−2.49615	−0.194917
$165$	0	0
$166$	−1.70707	−0.132494
$167$	−10.2037	−0.789588	−0.394794	−	0.918770i	$-0.629184\pi$
$167$	−10.2037	−0.789588	−0.394794	+	0.918770i	$0.629184\pi$
$168$	−3.37203	−0.260158
$169$	2.88105	0.221619
$170$	1.46156	0.112097
$171$	0.0569629	0.00435606
$172$	7.57796	0.577814
$173$	5.22413	0.397183	0.198592	−	0.980082i	$-0.436363\pi$
$173$	5.22413	0.397183	0.198592	+	0.980082i	$0.436363\pi$
$174$	−2.86259	−0.217012
$175$	1.00000	0.0755929
$176$	0	0
$177$	−26.6811	−2.00547
$178$	1.88301	0.141137
$179$	−26.0844	−1.94964	−0.974821	−	0.222988i	$-0.928419\pi$
$179$	−26.0844	−1.94964	−0.974821	+	0.222988i	$0.928419\pi$
$180$	0.900544	0.0671226
$181$	−0.424470	−0.0315506	−0.0157753	−	0.999876i	$-0.505022\pi$
$181$	−0.424470	−0.0315506	−0.0157753	+	0.999876i	$0.505022\pi$
$182$	1.90193	0.140980
$183$	2.23857	0.165480
$184$	−12.9687	−0.956065
$185$	−6.55792	−0.482148
$186$	−1.67564	−0.122864
$187$	0	0
$188$	−8.14153	−0.593782
$189$	4.66726	0.339493
$190$	0.0535009	0.00388136
$191$	−1.36278	−0.0986072	−0.0493036	−	0.998784i	$-0.515700\pi$
$191$	−1.36278	−0.0986072	−0.0493036	+	0.998784i	$0.515700\pi$
$192$	5.69460	0.410972
$193$	23.2290	1.67206	0.836029	−	0.548685i	$-0.184871\pi$
$193$	23.2290	1.67206	0.836029	+	0.548685i	$0.184871\pi$
$194$	6.51878	0.468021
$195$	−7.46412	−0.534516
$196$	−1.77222	−0.126587
$197$	−14.7520	−1.05104	−0.525518	−	0.850783i	$-0.676128\pi$
$197$	−14.7520	−1.05104	−0.525518	+	0.850783i	$0.676128\pi$
$198$	0	0
$199$	20.3953	1.44578	0.722891	−	0.690962i	$-0.242813\pi$
$199$	20.3953	1.44578	0.722891	+	0.690962i	$0.242813\pi$
$200$	1.80033	0.127303
$201$	−13.3420	−0.941074
$202$	−2.03528	−0.143202
$203$	−3.20232	−0.224759
$204$	10.1653	0.711713
$205$	−1.40849	−0.0983730
$206$	3.79035	0.264086
$207$	−3.66042	−0.254417
$208$	−10.7009	−0.741973
$209$	0	0
$210$	−0.893910	−0.0616856
$211$	27.3698	1.88421	0.942106	−	0.335316i	$-0.108843\pi$
$211$	27.3698	1.88421	0.942106	+	0.335316i	$0.108843\pi$
$212$	−2.45392	−0.168536
$213$	−18.9066	−1.29546
$214$	4.20166	0.287220
$215$	4.27596	0.291618
$216$	8.40261	0.571725
$217$	−1.87450	−0.127249
$218$	−3.99500	−0.270575
$219$	−19.3209	−1.30559
$220$	0	0
$221$	−12.2040	−0.820930
$222$	5.86219	0.393445
$223$	−8.84155	−0.592074	−0.296037	−	0.955176i	$-0.595665\pi$
$223$	−8.84155	−0.592074	−0.296037	+	0.955176i	$0.595665\pi$
$224$	−4.88221	−0.326206
$225$	0.508144	0.0338762
$226$	−1.54810	−0.102978
$227$	3.89425	0.258470	0.129235	−	0.991614i	$-0.458748\pi$
$227$	3.89425	0.258470	0.129235	+	0.991614i	$0.458748\pi$
$228$	0.372103	0.0246431
$229$	−5.03752	−0.332888	−0.166444	−	0.986051i	$-0.553229\pi$
$229$	−5.03752	−0.332888	−0.166444	+	0.986051i	$0.553229\pi$
$230$	−3.43795	−0.226691
$231$	0	0
$232$	−5.76524	−0.378507
$233$	−8.38605	−0.549388	−0.274694	−	0.961532i	$-0.588577\pi$
$233$	−8.38605	−0.549388	−0.274694	+	0.961532i	$0.588577\pi$
$234$	0.966454	0.0631791
$235$	−4.59397	−0.299677
$236$	−25.2454	−1.64334
$237$	−7.47366	−0.485466
$238$	−1.46156	−0.0947391
$239$	0.463366	0.0299726	0.0149863	−	0.999888i	$-0.495230\pi$
$239$	0.463366	0.0299726	0.0149863	+	0.999888i	$0.495230\pi$
$240$	5.02943	0.324648
$241$	6.40910	0.412847	0.206423	−	0.978463i	$-0.433818\pi$
$241$	6.40910	0.412847	0.206423	+	0.978463i	$0.433818\pi$
$242$	0	0
$243$	5.22690	0.335306
$244$	2.11812	0.135599
$245$	−1.00000	−0.0638877
$246$	1.25906	0.0802747
$247$	−0.446730	−0.0284248
$248$	−3.37472	−0.214295
$249$	−6.69937	−0.424555
$250$	0.477260	0.0301846
$251$	21.9638	1.38634	0.693172	−	0.720772i	$-0.256213\pi$
$251$	21.9638	1.38634	0.693172	+	0.720772i	$0.256213\pi$
$252$	−0.900544	−0.0567289
$253$	0	0
$254$	−6.54969	−0.410964
$255$	5.73590	0.359196
$256$	0.728021	0.0455013
$257$	8.52476	0.531760	0.265880	−	0.964006i	$-0.414338\pi$
$257$	8.52476	0.531760	0.265880	+	0.964006i	$0.414338\pi$
$258$	−3.82232	−0.237968
$259$	6.55792	0.407490
$260$	−7.06249	−0.437997
$261$	−1.62724	−0.100724
$262$	9.63982	0.595550
$263$	22.8634	1.40982	0.704909	−	0.709298i	$-0.250988\pi$
$263$	22.8634	1.40982	0.704909	+	0.709298i	$0.250988\pi$
$264$	0	0
$265$	−1.38466	−0.0850588
$266$	−0.0535009	−0.00328035
$267$	7.38986	0.452252
$268$	−12.6241	−0.771142
$269$	3.19477	0.194788	0.0973941	−	0.995246i	$-0.468949\pi$
$269$	3.19477	0.194788	0.0973941	+	0.995246i	$0.468949\pi$
$270$	2.22749	0.135561
$271$	−26.4440	−1.60636	−0.803179	−	0.595737i	$-0.796860\pi$
$271$	−26.4440	−1.60636	−0.803179	+	0.595737i	$0.796860\pi$
$272$	8.22323	0.498607
$273$	7.46412	0.451749
$274$	−0.338805	−0.0204679
$275$	0	0
$276$	−23.9112	−1.43928
$277$	−18.0857	−1.08667	−0.543334	−	0.839517i	$-0.682838\pi$
$277$	−18.0857	−1.08667	−0.543334	+	0.839517i	$0.682838\pi$
$278$	7.78237	0.466756
$279$	−0.952516	−0.0570256
$280$	−1.80033	−0.107590
$281$	−30.0360	−1.79180	−0.895899	−	0.444259i	$-0.853467\pi$
$281$	−30.0360	−1.79180	−0.895899	+	0.444259i	$0.853467\pi$
$282$	4.10659	0.244544
$283$	−8.25921	−0.490959	−0.245479	−	0.969402i	$-0.578945\pi$
$283$	−8.25921	−0.490959	−0.245479	+	0.969402i	$0.578945\pi$
$284$	−17.8893	−1.06153
$285$	0.209964	0.0124372
$286$	0	0
$287$	1.40849	0.0831403
$288$	−2.48086	−0.146186
$289$	−7.62167	−0.448333
$290$	−1.52834	−0.0897473
$291$	25.5829	1.49970
$292$	−18.2813	−1.06983
$293$	−32.6748	−1.90888	−0.954442	−	0.298398i	$-0.903548\pi$
$293$	−32.6748	−1.90888	−0.954442	+	0.298398i	$0.903548\pi$
$294$	0.893910	0.0521339
$295$	−14.2451	−0.829379
$296$	11.8064	0.686235
$297$	0	0
$298$	−9.17532	−0.531512
$299$	28.7067	1.66015
$300$	3.31938	0.191645
$301$	−4.27596	−0.246462
$302$	−5.85390	−0.336854
$303$	−7.98745	−0.458867
$304$	0.301013	0.0172643
$305$	1.19518	0.0684357
$306$	−0.742684	−0.0424564
$307$	−32.6700	−1.86457	−0.932287	−	0.361720i	$-0.882190\pi$
$307$	−32.6700	−1.86457	−0.932287	+	0.361720i	$0.882190\pi$
$308$	0	0
$309$	14.8752	0.846221
$310$	−0.894625	−0.0508113
$311$	−31.2623	−1.77272	−0.886361	−	0.462996i	$-0.846775\pi$
$311$	−31.2623	−1.77272	−0.886361	+	0.462996i	$0.846775\pi$
$312$	13.4379	0.760770
$313$	−30.4885	−1.72331	−0.861656	−	0.507493i	$-0.830572\pi$
$313$	−30.4885	−1.72331	−0.861656	+	0.507493i	$0.830572\pi$
$314$	10.7900	0.608916
$315$	−0.508144	−0.0286306
$316$	−7.07152	−0.397804
$317$	1.28836	0.0723616	0.0361808	−	0.999345i	$-0.488481\pi$
$317$	1.28836	0.0723616	0.0361808	+	0.999345i	$0.488481\pi$
$318$	1.23776	0.0694100
$319$	0	0
$320$	3.04036	0.169961
$321$	16.4894	0.920348
$322$	3.43795	0.191589
$323$	0.343296	0.0191015
$324$	18.1940	1.01078
$325$	−3.98510	−0.221054
$326$	8.66955	0.480162
$327$	−15.6783	−0.867014
$328$	2.53574	0.140013
$329$	4.59397	0.253274
$330$	0	0
$331$	5.04673	0.277393	0.138697	−	0.990335i	$-0.455709\pi$
$331$	5.04673	0.277393	0.138697	+	0.990335i	$0.455709\pi$
$332$	−6.33889	−0.347892
$333$	3.33237	0.182613
$334$	4.86983	0.266465
$335$	−7.12333	−0.389189
$336$	−5.02943	−0.274378
$337$	10.0006	0.544768	0.272384	−	0.962189i	$-0.412188\pi$
$337$	10.0006	0.544768	0.272384	+	0.962189i	$0.412188\pi$
$338$	−1.37501	−0.0747908
$339$	−6.07552	−0.329977
$340$	5.42727	0.294335
$341$	0	0
$342$	−0.0271861	−0.00147006
$343$	1.00000	0.0539949
$344$	−7.69815	−0.415056
$345$	−13.4922	−0.726396
$346$	−2.49327	−0.134039
$347$	−33.1050	−1.77717	−0.888586	−	0.458711i	$-0.848311\pi$
$347$	−33.1050	−1.77717	−0.888586	+	0.458711i	$0.848311\pi$
$348$	−10.6297	−0.569813
$349$	−13.2905	−0.711425	−0.355712	−	0.934595i	$-0.615762\pi$
$349$	−13.2905	−0.711425	−0.355712	+	0.934595i	$0.615762\pi$
$350$	−0.477260	−0.0255106
$351$	−18.5995	−0.992768
$352$	0	0
$353$	−5.38061	−0.286381	−0.143191	−	0.989695i	$-0.545736\pi$
$353$	−5.38061	−0.286381	−0.143191	+	0.989695i	$0.545736\pi$
$354$	12.7338	0.676794
$355$	−10.0943	−0.535747
$356$	6.99223	0.370587
$357$	−5.73590	−0.303576
$358$	12.4491	0.657953
$359$	−5.02616	−0.265271	−0.132635	−	0.991165i	$-0.542344\pi$
$359$	−5.02616	−0.265271	−0.132635	+	0.991165i	$0.542344\pi$
$360$	−0.914827	−0.0482156
$361$	−18.9874	−0.999339
$362$	0.202583	0.0106475
$363$	0	0
$364$	7.06249	0.370175
$365$	−10.3155	−0.539937
$366$	−1.06838	−0.0558452
$367$	12.7517	0.665633	0.332817	−	0.942992i	$-0.392001\pi$
$367$	12.7517	0.665633	0.332817	+	0.942992i	$0.392001\pi$
$368$	−19.3430	−1.00832
$369$	0.715713	0.0372585
$370$	3.12983	0.162712
$371$	1.38466	0.0718878
$372$	−6.22219	−0.322605
$373$	9.44532	0.489060	0.244530	−	0.969642i	$-0.421366\pi$
$373$	9.44532	0.489060	0.244530	+	0.969642i	$0.421366\pi$
$374$	0	0
$375$	1.87300	0.0967215
$376$	8.27066	0.426527
$377$	12.7616	0.657255
$378$	−2.22749	−0.114570
$379$	30.1944	1.55098	0.775491	−	0.631358i	$-0.217502\pi$
$379$	30.1944	1.55098	0.775491	+	0.631358i	$0.217502\pi$
$380$	0.198666	0.0101914
$381$	−25.7042	−1.31687
$382$	0.650399	0.0332773
$383$	−32.4674	−1.65900	−0.829502	−	0.558503i	$-0.811376\pi$
$383$	−32.4674	−1.65900	−0.829502	+	0.558503i	$0.811376\pi$
$384$	−21.0066	−1.07199
$385$	0	0
$386$	−11.0863	−0.564276
$387$	−2.17280	−0.110450
$388$	24.2064	1.22889
$389$	3.77335	0.191316	0.0956581	−	0.995414i	$-0.469504\pi$
$389$	3.77335	0.191316	0.0956581	+	0.995414i	$0.469504\pi$
$390$	3.56232	0.180385
$391$	−22.0601	−1.11563
$392$	1.80033	0.0909305
$393$	37.8314	1.90834
$394$	7.04054	0.354697
$395$	−3.99020	−0.200769
$396$	0	0
$397$	−6.38757	−0.320583	−0.160292	−	0.987070i	$-0.551243\pi$
$397$	−6.38757	−0.320583	−0.160292	+	0.987070i	$0.551243\pi$
$398$	−9.73384	−0.487913
$399$	−0.209964	−0.0105113
$400$	2.68522	0.134261
$401$	4.48011	0.223726	0.111863	−	0.993724i	$-0.464318\pi$
$401$	4.48011	0.223726	0.111863	+	0.993724i	$0.464318\pi$
$402$	6.36762	0.317588
$403$	7.47009	0.372111
$404$	−7.55767	−0.376008
$405$	10.2662	0.510133
$406$	1.52834	0.0758503
$407$	0	0
$408$	−10.3265	−0.511239
$409$	11.5916	0.573170	0.286585	−	0.958055i	$-0.407480\pi$
$409$	11.5916	0.573170	0.286585	+	0.958055i	$0.407480\pi$
$410$	0.672214	0.0331983
$411$	−1.32964	−0.0655861
$412$	14.0748	0.693416
$413$	14.2451	0.700954
$414$	1.74697	0.0858589
$415$	−3.57680	−0.175578
$416$	19.4561	0.953915
$417$	30.5419	1.49564
$418$	0	0
$419$	25.2234	1.23224	0.616121	−	0.787651i	$-0.288703\pi$
$419$	25.2234	1.23224	0.616121	+	0.787651i	$0.288703\pi$
$420$	−3.31938	−0.161969
$421$	0.152957	0.00745469	0.00372734	−	0.999993i	$-0.498814\pi$
$421$	0.152957	0.00745469	0.00372734	+	0.999993i	$0.498814\pi$
$422$	−13.0625	−0.635872
$423$	2.33439	0.113502
$424$	2.49284	0.121063
$425$	3.06241	0.148549
$426$	9.02335	0.437183
$427$	−1.19518	−0.0578387
$428$	15.6021	0.754158
$429$	0	0
$430$	−2.04075	−0.0984135
$431$	29.7094	1.43105	0.715526	−	0.698586i	$-0.246187\pi$
$431$	29.7094	1.43105	0.715526	+	0.698586i	$0.246187\pi$
$432$	12.5326	0.602976
$433$	−20.6013	−0.990037	−0.495018	−	0.868883i	$-0.664839\pi$
$433$	−20.6013	−0.990037	−0.495018	+	0.868883i	$0.664839\pi$
$434$	0.894625	0.0429434
$435$	−5.99796	−0.287580
$436$	−14.8347	−0.710455
$437$	−0.807514	−0.0386286
$438$	9.22111	0.440602
$439$	−9.44399	−0.450737	−0.225369	−	0.974274i	$-0.572359\pi$
$439$	−9.44399	−0.450737	−0.225369	+	0.974274i	$0.572359\pi$
$440$	0	0
$441$	0.508144	0.0241973
$442$	5.82448	0.277042
$443$	−7.16965	−0.340640	−0.170320	−	0.985389i	$-0.554480\pi$
$443$	−7.16965	−0.340640	−0.170320	+	0.985389i	$0.554480\pi$
$444$	21.7682	1.03308
$445$	3.94546	0.187033
$446$	4.21972	0.199810
$447$	−36.0085	−1.70314
$448$	−3.04036	−0.143643
$449$	−31.5653	−1.48966	−0.744830	−	0.667255i	$-0.767469\pi$
$449$	−31.5653	−1.48966	−0.744830	+	0.667255i	$0.767469\pi$
$450$	−0.242517	−0.0114323
$451$	0	0
$452$	−5.74861	−0.270392
$453$	−22.9736	−1.07939
$454$	−1.85857	−0.0872269
$455$	3.98510	0.186825
$456$	−0.378004	−0.0177017
$457$	32.5923	1.52460	0.762301	−	0.647223i	$-0.224070\pi$
$457$	32.5923	1.52460	0.762301	+	0.647223i	$0.224070\pi$
$458$	2.40420	0.112341
$459$	14.2930	0.667142
$460$	−12.7662	−0.595228
$461$	−17.6512	−0.822099	−0.411049	−	0.911613i	$-0.634838\pi$
$461$	−17.6512	−0.822099	−0.411049	+	0.911613i	$0.634838\pi$
$462$	0	0
$463$	−38.8001	−1.80319	−0.901597	−	0.432578i	$-0.857604\pi$
$463$	−38.8001	−1.80319	−0.901597	+	0.432578i	$0.857604\pi$
$464$	−8.59894	−0.399196
$465$	−3.51095	−0.162816
$466$	4.00233	0.185404
$467$	−21.5820	−0.998695	−0.499348	−	0.866402i	$-0.666427\pi$
$467$	−21.5820	−0.998695	−0.499348	+	0.866402i	$0.666427\pi$
$468$	3.58876	0.165890
$469$	7.12333	0.328925
$470$	2.19252	0.101133
$471$	42.3454	1.95117
$472$	25.6458	1.18044
$473$	0	0
$474$	3.56688	0.163832
$475$	0.112100	0.00514350
$476$	−5.42727	−0.248758
$477$	0.703604	0.0322158
$478$	−0.221146	−0.0101150
$479$	14.4137	0.658578	0.329289	−	0.944229i	$-0.393191\pi$
$479$	14.4137	0.658578	0.329289	+	0.944229i	$0.393191\pi$
$480$	−9.14440	−0.417383
$481$	−26.1340	−1.19161
$482$	−3.05881	−0.139325
$483$	13.4922	0.613916
$484$	0	0
$485$	13.6588	0.620213
$486$	−2.49459	−0.113157
$487$	−29.4059	−1.33251	−0.666255	−	0.745724i	$-0.732104\pi$
$487$	−29.4059	−1.33251	−0.666255	+	0.745724i	$0.732104\pi$
$488$	−2.15172	−0.0974036
$489$	34.0236	1.53860
$490$	0.477260	0.0215604
$491$	38.5860	1.74136	0.870682	−	0.491847i	$-0.163678\pi$
$491$	38.5860	1.74136	0.870682	+	0.491847i	$0.163678\pi$
$492$	4.67530	0.210779
$493$	−9.80681	−0.441677
$494$	0.213207	0.00959261
$495$	0	0
$496$	−5.03345	−0.226009
$497$	10.0943	0.452789
$498$	3.19734	0.143276
$499$	−12.8786	−0.576526	−0.288263	−	0.957551i	$-0.593078\pi$
$499$	−12.8786	−0.576526	−0.288263	+	0.957551i	$0.593078\pi$
$500$	1.77222	0.0792562
$501$	19.1116	0.853845
$502$	−10.4824	−0.467855
$503$	27.3219	1.21822	0.609111	−	0.793085i	$-0.291527\pi$
$503$	27.3219	1.21822	0.609111	+	0.793085i	$0.291527\pi$
$504$	0.914827	0.0407496
$505$	−4.26451	−0.189768
$506$	0	0
$507$	−5.39622	−0.239655
$508$	−24.3211	−1.07908
$509$	25.9809	1.15158	0.575791	−	0.817597i	$-0.304694\pi$
$509$	25.9809	1.15158	0.575791	+	0.817597i	$0.304694\pi$
$510$	−2.73752	−0.121219
$511$	10.3155	0.456330
$512$	−22.7784	−1.00667
$513$	0.523200	0.0230998
$514$	−4.06852	−0.179455
$515$	7.94190	0.349962
$516$	−14.1935	−0.624836
$517$	0	0
$518$	−3.12983	−0.137517
$519$	−9.78481	−0.429505
$520$	7.17451	0.314623
$521$	38.4717	1.68548	0.842738	−	0.538325i	$-0.180943\pi$
$521$	38.4717	1.68548	0.842738	+	0.538325i	$0.180943\pi$
$522$	0.776616	0.0339916
$523$	−32.3792	−1.41584	−0.707921	−	0.706292i	$-0.750367\pi$
$523$	−32.3792	−1.41584	−0.707921	+	0.706292i	$0.750367\pi$
$524$	35.7958	1.56375
$525$	−1.87300	−0.0817446
$526$	−10.9118	−0.475776
$527$	−5.74049	−0.250060
$528$	0	0
$529$	28.8905	1.25611
$530$	0.660841	0.0287051
$531$	7.23853	0.314126
$532$	−0.198666	−0.00861328
$533$	−5.61297	−0.243125
$534$	−3.52688	−0.152623
$535$	8.80372	0.380618
$536$	12.8244	0.553928
$537$	48.8563	2.10830
$538$	−1.52473	−0.0657359
$539$	0	0
$540$	8.27142	0.355945
$541$	−30.9402	−1.33022	−0.665111	−	0.746745i	$-0.731616\pi$
$541$	−30.9402	−1.33022	−0.665111	+	0.746745i	$0.731616\pi$
$542$	12.6207	0.542104
$543$	0.795034	0.0341182
$544$	−14.9513	−0.641032
$545$	−8.37070	−0.358561
$546$	−3.56232	−0.152453
$547$	30.9387	1.32285	0.661423	−	0.750013i	$-0.269953\pi$
$547$	30.9387	1.32285	0.661423	+	0.750013i	$0.269953\pi$
$548$	−1.25809	−0.0537430
$549$	−0.607322	−0.0259199
$550$	0	0
$551$	−0.358981	−0.0152931
$552$	24.2904	1.03387
$553$	3.99020	0.169681
$554$	8.63160	0.366722
$555$	12.2830	0.521385
$556$	28.8985	1.22557
$557$	15.8515	0.671650	0.335825	−	0.941924i	$-0.390985\pi$
$557$	15.8515	0.671650	0.335825	+	0.941924i	$0.390985\pi$
$558$	0.454598	0.0192447
$559$	17.0402	0.720722
$560$	−2.68522	−0.113471
$561$	0	0
$562$	14.3350	0.604685
$563$	30.4821	1.28467	0.642334	−	0.766425i	$-0.277966\pi$
$563$	30.4821	1.28467	0.642334	+	0.766425i	$0.277966\pi$
$564$	15.2491	0.642104
$565$	−3.24373	−0.136465
$566$	3.94179	0.165686
$567$	−10.2662	−0.431141
$568$	18.1730	0.762522
$569$	−22.7629	−0.954270	−0.477135	−	0.878830i	$-0.658325\pi$
$569$	−22.7629	−0.954270	−0.477135	+	0.878830i	$0.658325\pi$
$570$	−0.100207	−0.00419722
$571$	13.6786	0.572432	0.286216	−	0.958165i	$-0.407602\pi$
$571$	13.6786	0.572432	0.286216	+	0.958165i	$0.407602\pi$
$572$	0	0
$573$	2.55249	0.106632
$574$	−0.672214	−0.0280577
$575$	−7.20351	−0.300407
$576$	−1.54494	−0.0643724
$577$	−10.3789	−0.432081	−0.216040	−	0.976384i	$-0.569314\pi$
$577$	−10.3789	−0.432081	−0.216040	+	0.976384i	$0.569314\pi$
$578$	3.63752	0.151301
$579$	−43.5080	−1.80813
$580$	−5.67523	−0.235651
$581$	3.57680	0.148391
$582$	−12.2097	−0.506109
$583$	0	0
$584$	18.5713	0.768486
$585$	2.02500	0.0837236
$586$	15.5944	0.644198
$587$	9.37007	0.386744	0.193372	−	0.981125i	$-0.438058\pi$
$587$	9.37007	0.386744	0.193372	+	0.981125i	$0.438058\pi$
$588$	3.31938	0.136889
$589$	−0.210132	−0.00865833
$590$	6.79860	0.279894
$591$	27.6305	1.13657
$592$	17.6095	0.723745
$593$	12.5128	0.513838	0.256919	−	0.966433i	$-0.417293\pi$
$593$	12.5128	0.513838	0.256919	+	0.966433i	$0.417293\pi$
$594$	0	0
$595$	−3.06241	−0.125546
$596$	−34.0710	−1.39560
$597$	−38.2004	−1.56344
$598$	−13.7006	−0.560258
$599$	39.2333	1.60303	0.801514	−	0.597976i	$-0.204028\pi$
$599$	39.2333	1.60303	0.801514	+	0.597976i	$0.204028\pi$
$600$	−3.37203	−0.137662
$601$	21.2020	0.864850	0.432425	−	0.901670i	$-0.357658\pi$
$601$	21.2020	0.864850	0.432425	+	0.901670i	$0.357658\pi$
$602$	2.04075	0.0831746
$603$	3.61968	0.147405
$604$	−21.7374	−0.884484
$605$	0	0
$606$	3.81209	0.154856
$607$	−12.3800	−0.502489	−0.251245	−	0.967924i	$-0.580840\pi$
$607$	−12.3800	−0.502489	−0.251245	+	0.967924i	$0.580840\pi$
$608$	−0.547296	−0.0221958
$609$	5.99796	0.243050
$610$	−0.570411	−0.0230953
$611$	−18.3074	−0.740640
$612$	−2.75783	−0.111479
$613$	2.88066	0.116349	0.0581744	−	0.998306i	$-0.481472\pi$
$613$	2.88066	0.116349	0.0581744	+	0.998306i	$0.481472\pi$
$614$	15.5921	0.629245
$615$	2.63810	0.106378
$616$	0	0
$617$	−6.28863	−0.253171	−0.126585	−	0.991956i	$-0.540402\pi$
$617$	−6.28863	−0.253171	−0.126585	+	0.991956i	$0.540402\pi$
$618$	−7.09934	−0.285577
$619$	27.0089	1.08558	0.542789	−	0.839869i	$-0.317368\pi$
$619$	27.0089	1.08558	0.542789	+	0.839869i	$0.317368\pi$
$620$	−3.32204	−0.133416
$621$	−33.6206	−1.34915
$622$	14.9202	0.598247
$623$	−3.94546	−0.158071
$624$	20.0428	0.802354
$625$	1.00000	0.0400000
$626$	14.5509	0.581572
$627$	0	0
$628$	40.0669	1.59884
$629$	20.0830	0.800763
$630$	0.242517	0.00966209
$631$	2.72926	0.108650	0.0543250	−	0.998523i	$-0.482699\pi$
$631$	2.72926	0.108650	0.0543250	+	0.998523i	$0.482699\pi$
$632$	7.18368	0.285752
$633$	−51.2637	−2.03755
$634$	−0.614884	−0.0244202
$635$	−13.7235	−0.544601
$636$	4.59620	0.182251
$637$	−3.98510	−0.157896
$638$	0	0
$639$	5.12933	0.202913
$640$	−11.2155	−0.443330
$641$	30.3183	1.19750	0.598750	−	0.800936i	$-0.295664\pi$
$641$	30.3183	1.19750	0.598750	+	0.800936i	$0.295664\pi$
$642$	−7.86973	−0.310593
$643$	−23.4472	−0.924667	−0.462333	−	0.886706i	$-0.652988\pi$
$643$	−23.4472	−0.924667	−0.462333	+	0.886706i	$0.652988\pi$
$644$	12.7662	0.503060
$645$	−8.00889	−0.315350
$646$	−0.163841	−0.00644625
$647$	7.94883	0.312501	0.156250	−	0.987717i	$-0.450059\pi$
$647$	7.94883	0.312501	0.156250	+	0.987717i	$0.450059\pi$
$648$	−18.4826	−0.726065
$649$	0	0
$650$	1.90193	0.0745999
$651$	3.51095	0.137605
$652$	32.1929	1.26077
$653$	−42.0512	−1.64559	−0.822795	−	0.568338i	$-0.807587\pi$
$653$	−42.0512	−1.64559	−0.822795	+	0.568338i	$0.807587\pi$
$654$	7.48265	0.292595
$655$	20.1983	0.789211
$656$	3.78210	0.147666
$657$	5.24175	0.204500
$658$	−2.19252	−0.0854732
$659$	9.38480	0.365580	0.182790	−	0.983152i	$-0.441487\pi$
$659$	9.38480	0.365580	0.182790	+	0.983152i	$0.441487\pi$
$660$	0	0
$661$	−30.8421	−1.19962	−0.599810	−	0.800142i	$-0.704757\pi$
$661$	−30.8421	−1.19962	−0.599810	+	0.800142i	$0.704757\pi$
$662$	−2.40860	−0.0936130
$663$	22.8582	0.887737
$664$	6.43943	0.249898
$665$	−0.112100	−0.00434705
$666$	−1.59041	−0.0616270
$667$	23.0680	0.893195
$668$	18.0833	0.699663
$669$	16.5603	0.640257
$670$	3.39968	0.131341
$671$	0	0
$672$	9.14440	0.352753
$673$	−24.1525	−0.931011	−0.465505	−	0.885045i	$-0.654127\pi$
$673$	−24.1525	−0.931011	−0.465505	+	0.885045i	$0.654127\pi$
$674$	−4.77289	−0.183845
$675$	4.66726	0.179643
$676$	−5.10587	−0.196380
$677$	−5.17873	−0.199035	−0.0995174	−	0.995036i	$-0.531730\pi$
$677$	−5.17873	−0.199035	−0.0995174	+	0.995036i	$0.531730\pi$
$678$	2.89960	0.111359
$679$	−13.6588	−0.524175
$680$	−5.51335	−0.211427
$681$	−7.29394	−0.279504
$682$	0	0
$683$	−19.5502	−0.748067	−0.374033	−	0.927415i	$-0.622025\pi$
$683$	−19.5502	−0.748067	−0.374033	+	0.927415i	$0.622025\pi$
$684$	−0.100951	−0.00385996
$685$	−0.709895	−0.0271237
$686$	−0.477260	−0.0182219
$687$	9.43529	0.359979
$688$	−11.4819	−0.437743
$689$	−5.51800	−0.210219
$690$	6.43929	0.245139
$691$	−6.36366	−0.242085	−0.121042	−	0.992647i	$-0.538624\pi$
$691$	−6.36366	−0.242085	−0.121042	+	0.992647i	$0.538624\pi$
$692$	−9.25832	−0.351948
$693$	0	0
$694$	15.7997	0.599749
$695$	16.3064	0.618535
$696$	10.7983	0.409309
$697$	4.31336	0.163380
$698$	6.34303	0.240087
$699$	15.7071	0.594097
$700$	−1.77222	−0.0669837
$701$	33.5883	1.26861	0.634306	−	0.773082i	$-0.281286\pi$
$701$	33.5883	1.26861	0.634306	+	0.773082i	$0.281286\pi$
$702$	8.87680	0.335033
$703$	0.735144	0.0277265
$704$	0	0
$705$	8.60452	0.324065
$706$	2.56795	0.0966461
$707$	4.26451	0.160384
$708$	47.2848	1.77707
$709$	−16.4005	−0.615933	−0.307967	−	0.951397i	$-0.599649\pi$
$709$	−16.4005	−0.615933	−0.307967	+	0.951397i	$0.599649\pi$
$710$	4.81758	0.180801
$711$	2.02759	0.0760407
$712$	−7.10313	−0.266201
$713$	13.5030	0.505691
$714$	2.73752	0.102449
$715$	0	0
$716$	46.2274	1.72760
$717$	−0.867886	−0.0324118
$718$	2.39879	0.0895219
$719$	−11.0047	−0.410408	−0.205204	−	0.978719i	$-0.565786\pi$
$719$	−11.0047	−0.410408	−0.205204	+	0.978719i	$0.565786\pi$
$720$	−1.36448	−0.0508511
$721$	−7.94190	−0.295772
$722$	9.06194	0.337251
$723$	−12.0043	−0.446444
$724$	0.752255	0.0279574
$725$	−3.20232	−0.118931
$726$	0	0
$727$	6.09018	0.225872	0.112936	−	0.993602i	$-0.463974\pi$
$727$	6.09018	0.225872	0.112936	+	0.993602i	$0.463974\pi$
$728$	−7.17451	−0.265905
$729$	21.0087	0.778098
$730$	4.92317	0.182215
$731$	−13.0947	−0.484326
$732$	−3.96725	−0.146634
$733$	−31.5683	−1.16600	−0.583000	−	0.812472i	$-0.698121\pi$
$733$	−31.5683	−1.16600	−0.583000	+	0.812472i	$0.698121\pi$
$734$	−6.08588	−0.224634
$735$	1.87300	0.0690868
$736$	35.1690	1.29635
$737$	0	0
$738$	−0.341581	−0.0125738
$739$	−41.3365	−1.52059	−0.760294	−	0.649579i	$-0.774945\pi$
$739$	−41.3365	−1.52059	−0.760294	+	0.649579i	$0.774945\pi$
$740$	11.6221	0.427237
$741$	0.836728	0.0307380
$742$	−0.660841	−0.0242602
$743$	−15.0149	−0.550844	−0.275422	−	0.961323i	$-0.588818\pi$
$743$	−15.0149	−0.550844	−0.275422	+	0.961323i	$0.588818\pi$
$744$	6.32087	0.231734
$745$	−19.2250	−0.704349
$746$	−4.50787	−0.165045
$747$	1.81753	0.0664999
$748$	0	0
$749$	−8.80372	−0.321681
$750$	−0.893910	−0.0326410
$751$	40.3439	1.47217	0.736085	−	0.676890i	$-0.236673\pi$
$751$	40.3439	1.47217	0.736085	+	0.676890i	$0.236673\pi$
$752$	12.3358	0.449841
$753$	−41.1383	−1.49916
$754$	−6.09060	−0.221806
$755$	−12.2656	−0.446392
$756$	−8.27142	−0.300829
$757$	−28.5198	−1.03657	−0.518285	−	0.855208i	$-0.673429\pi$
$757$	−28.5198	−1.03657	−0.518285	+	0.855208i	$0.673429\pi$
$758$	−14.4106	−0.523416
$759$	0	0
$760$	−0.201817	−0.00732068
$761$	31.9107	1.15676	0.578381	−	0.815767i	$-0.303685\pi$
$761$	31.9107	1.15676	0.578381	+	0.815767i	$0.303685\pi$
$762$	12.2676	0.444408
$763$	8.37070	0.303040
$764$	2.41515	0.0873769
$765$	−1.55614	−0.0562624
$766$	15.4954	0.559871
$767$	−56.7680	−2.04978
$768$	−1.36359	−0.0492042
$769$	26.0016	0.937641	0.468821	−	0.883293i	$-0.344679\pi$
$769$	26.0016	0.937641	0.468821	+	0.883293i	$0.344679\pi$
$770$	0	0
$771$	−15.9669	−0.575034
$772$	−41.1669	−1.48163
$773$	−8.10603	−0.291554	−0.145777	−	0.989318i	$-0.546568\pi$
$773$	−8.10603	−0.291554	−0.145777	+	0.989318i	$0.546568\pi$
$774$	1.03699	0.0372739
$775$	−1.87450	−0.0673341
$776$	−24.5903	−0.882741
$777$	−12.2830	−0.440651
$778$	−1.80087	−0.0645642
$779$	0.157891	0.00565705
$780$	13.2281	0.473641
$781$	0	0
$782$	10.5284	0.376494
$783$	−14.9461	−0.534129
$784$	2.68522	0.0959007
$785$	22.6083	0.806924
$786$	−18.0554	−0.644015
$787$	16.6847	0.594747	0.297373	−	0.954761i	$-0.403889\pi$
$787$	16.6847	0.594747	0.297373	+	0.954761i	$0.403889\pi$
$788$	26.1438	0.931335
$789$	−42.8232	−1.52455
$790$	1.90436	0.0677542
$791$	3.24373	0.115334
$792$	0	0
$793$	4.76291	0.169136
$794$	3.04853	0.108188
$795$	2.59347	0.0919808
$796$	−36.1449	−1.28112
$797$	−32.4048	−1.14784	−0.573919	−	0.818912i	$-0.694578\pi$
$797$	−32.4048	−1.14784	−0.573919	+	0.818912i	$0.694578\pi$
$798$	0.100207	0.00354730
$799$	14.0686	0.497711
$800$	−4.88221	−0.172612
$801$	−2.00486	−0.0708382
$802$	−2.13818	−0.0755016
$803$	0	0
$804$	23.6451	0.833897
$805$	7.20351	0.253890
$806$	−3.56517	−0.125578
$807$	−5.98381	−0.210640
$808$	7.67754	0.270095
$809$	−12.1728	−0.427974	−0.213987	−	0.976836i	$-0.568645\pi$
$809$	−12.1728	−0.427974	−0.213987	+	0.976836i	$0.568645\pi$
$810$	−4.89966	−0.172156
$811$	−49.3791	−1.73393	−0.866967	−	0.498366i	$-0.833934\pi$
$811$	−49.3791	−1.73393	−0.866967	+	0.498366i	$0.833934\pi$
$812$	5.67523	0.199162
$813$	49.5297	1.73708
$814$	0	0
$815$	18.1652	0.636301
$816$	−15.4021	−0.539183
$817$	−0.479336	−0.0167698
$818$	−5.53223	−0.193430
$819$	−2.02500	−0.0707594
$820$	2.49615	0.0871694
$821$	8.06748	0.281557	0.140779	−	0.990041i	$-0.455039\pi$
$821$	8.06748	0.281557	0.140779	+	0.990041i	$0.455039\pi$
$822$	0.634582	0.0221336
$823$	−8.03983	−0.280251	−0.140125	−	0.990134i	$-0.544751\pi$
$823$	−8.03983	−0.280251	−0.140125	+	0.990134i	$0.544751\pi$
$824$	−14.2980	−0.498096
$825$	0	0
$826$	−6.79860	−0.236553
$827$	33.3273	1.15890	0.579452	−	0.815007i	$-0.303267\pi$
$827$	33.3273	1.15890	0.579452	+	0.815007i	$0.303267\pi$
$828$	6.48707	0.225441
$829$	−28.4424	−0.987845	−0.493923	−	0.869506i	$-0.664437\pi$
$829$	−28.4424	−0.987845	−0.493923	+	0.869506i	$0.664437\pi$
$830$	1.70707	0.0592531
$831$	33.8747	1.17510
$832$	12.1161	0.420051
$833$	3.06241	0.106106
$834$	−14.5764	−0.504740
$835$	10.2037	0.353115
$836$	0	0
$837$	−8.74878	−0.302402
$838$	−12.0381	−0.415850
$839$	−6.53972	−0.225776	−0.112888	−	0.993608i	$-0.536010\pi$
$839$	−6.53972	−0.225776	−0.112888	+	0.993608i	$0.536010\pi$
$840$	3.37203	0.116346
$841$	−18.7451	−0.646384
$842$	−0.0730004	−0.00251576
$843$	56.2575	1.93761
$844$	−48.5053	−1.66962
$845$	−2.88105	−0.0991112
$846$	−1.11411	−0.0383040
$847$	0	0
$848$	3.71811	0.127680
$849$	15.4695	0.530913
$850$	−1.46156	−0.0501312
$851$	−47.2401	−1.61937
$852$	33.5067	1.14792
$853$	−24.5400	−0.840235	−0.420118	−	0.907470i	$-0.638011\pi$
$853$	−24.5400	−0.840235	−0.420118	+	0.907470i	$0.638011\pi$
$854$	0.570411	0.0195191
$855$	−0.0569629	−0.00194809
$856$	−15.8496	−0.541728
$857$	22.0956	0.754773	0.377386	−	0.926056i	$-0.376823\pi$
$857$	22.0956	0.754773	0.377386	+	0.926056i	$0.376823\pi$
$858$	0	0
$859$	−0.0484966	−0.00165468	−0.000827341	−	1.00000i	$-0.500263\pi$
$859$	−0.0484966	−0.00165468	−0.000827341		1.00000i	$0.500263\pi$
$860$	−7.57796	−0.258406
$861$	−2.63810	−0.0899062
$862$	−14.1791	−0.482942
$863$	17.7952	0.605757	0.302878	−	0.953029i	$-0.402052\pi$
$863$	17.7952	0.605757	0.302878	+	0.953029i	$0.402052\pi$
$864$	−22.7865	−0.775213
$865$	−5.22413	−0.177626
$866$	9.83219	0.334111
$867$	14.2754	0.484818
$868$	3.32204	0.112757
$869$	0	0
$870$	2.86259	0.0970508
$871$	−28.3872	−0.961864
$872$	15.0700	0.510335
$873$	−6.94062	−0.234904
$874$	0.385394	0.0130361
$875$	−1.00000	−0.0338062
$876$	34.2410	1.15690
$877$	−32.2858	−1.09022	−0.545108	−	0.838366i	$-0.683511\pi$
$877$	−32.2858	−1.09022	−0.545108	+	0.838366i	$0.683511\pi$
$878$	4.50724	0.152112
$879$	61.2001	2.06423
$880$	0	0
$881$	24.8440	0.837017	0.418508	−	0.908213i	$-0.362553\pi$
$881$	24.8440	0.837017	0.418508	+	0.908213i	$0.362553\pi$
$882$	−0.242517	−0.00816596
$883$	−21.3504	−0.718498	−0.359249	−	0.933242i	$-0.616967\pi$
$883$	−21.3504	−0.718498	−0.359249	+	0.933242i	$0.616967\pi$
$884$	21.6282	0.727436
$885$	26.6811	0.896874
$886$	3.42179	0.114957
$887$	−18.4564	−0.619705	−0.309853	−	0.950785i	$-0.600280\pi$
$887$	−18.4564	−0.619705	−0.309853	+	0.950785i	$0.600280\pi$
$888$	−22.1135	−0.742080
$889$	13.7235	0.460272
$890$	−1.88301	−0.0631186
$891$	0	0
$892$	15.6692	0.524644
$893$	0.514984	0.0172333
$894$	17.1854	0.574766
$895$	26.0844	0.871907
$896$	11.2155	0.374682
$897$	−53.7678	−1.79526
$898$	15.0649	0.502721
$899$	6.00276	0.200203
$900$	−0.900544	−0.0300181
$901$	4.24038	0.141268
$902$	0	0
$903$	8.00889	0.266519
$904$	5.83979	0.194228
$905$	0.424470	0.0141099
$906$	10.9644	0.364267
$907$	−14.8354	−0.492601	−0.246301	−	0.969193i	$-0.579215\pi$
$907$	−14.8354	−0.492601	−0.246301	+	0.969193i	$0.579215\pi$
$908$	−6.90147	−0.229033
$909$	2.16699	0.0718744
$910$	−1.90193	−0.0630484
$911$	52.4309	1.73711	0.868556	−	0.495591i	$-0.165049\pi$
$911$	52.4309	1.73711	0.868556	+	0.495591i	$0.165049\pi$
$912$	−0.563799	−0.0186693
$913$	0	0
$914$	−15.5550	−0.514513
$915$	−2.23857	−0.0740050
$916$	8.92760	0.294976
$917$	−20.1983	−0.667005
$918$	−6.82149	−0.225143
$919$	46.9616	1.54912	0.774560	−	0.632500i	$-0.217971\pi$
$919$	46.9616	1.54912	0.774560	+	0.632500i	$0.217971\pi$
$920$	12.9687	0.427565
$921$	61.1910	2.01631
$922$	8.42422	0.277437
$923$	−40.2266	−1.32408
$924$	0	0
$925$	6.55792	0.215623
$926$	18.5177	0.608530
$927$	−4.03562	−0.132547
$928$	15.6344	0.513225
$929$	18.8933	0.619869	0.309935	−	0.950758i	$-0.399693\pi$
$929$	18.8933	0.619869	0.309935	+	0.950758i	$0.399693\pi$
$930$	1.67564	0.0549463
$931$	0.112100	0.00367393
$932$	14.8620	0.486819
$933$	58.5544	1.91698
$934$	10.3002	0.337033
$935$	0	0
$936$	−3.64568	−0.119163
$937$	−11.4070	−0.372650	−0.186325	−	0.982488i	$-0.559658\pi$
$937$	−11.4070	−0.372650	−0.186325	+	0.982488i	$0.559658\pi$
$938$	−3.39968	−0.111004
$939$	57.1051	1.86355
$940$	8.14153	0.265548
$941$	−44.1764	−1.44011	−0.720055	−	0.693917i	$-0.755883\pi$
$941$	−44.1764	−1.44011	−0.720055	+	0.693917i	$0.755883\pi$
$942$	−20.2098	−0.658469
$943$	−10.1460	−0.330401
$944$	38.2511	1.24497
$945$	−4.66726	−0.151826
$946$	0	0
$947$	28.2928	0.919393	0.459696	−	0.888076i	$-0.347958\pi$
$947$	28.2928	0.919393	0.459696	+	0.888076i	$0.347958\pi$
$948$	13.2450	0.430177
$949$	−41.1083	−1.33443
$950$	−0.0535009	−0.00173580
$951$	−2.41311	−0.0782504
$952$	5.51335	0.178689
$953$	12.5494	0.406515	0.203258	−	0.979125i	$-0.434847\pi$
$953$	12.5494	0.406515	0.203258	+	0.979125i	$0.434847\pi$
$954$	−0.335802	−0.0108720
$955$	1.36278	0.0440985
$956$	−0.821188	−0.0265591
$957$	0	0
$958$	−6.87908	−0.222253
$959$	0.709895	0.0229237
$960$	−5.69460	−0.183792
$961$	−27.4862	−0.886653
$962$	12.4727	0.402137
$963$	−4.47355	−0.144158
$964$	−11.3584	−0.365828
$965$	−23.2290	−0.747767
$966$	−6.43929	−0.207181
$967$	28.8820	0.928783	0.464392	−	0.885630i	$-0.346273\pi$
$967$	28.8820	0.928783	0.464392	+	0.885630i	$0.346273\pi$
$968$	0	0
$969$	−0.642995	−0.0206560
$970$	−6.51878	−0.209306
$971$	28.0652	0.900656	0.450328	−	0.892863i	$-0.351307\pi$
$971$	28.0652	0.900656	0.450328	+	0.892863i	$0.351307\pi$
$972$	−9.26323	−0.297118
$973$	−16.3064	−0.522758
$974$	14.0343	0.449687
$975$	7.46412	0.239043
$976$	−3.20932	−0.102728
$977$	−55.6426	−1.78017	−0.890083	−	0.455799i	$-0.849354\pi$
$977$	−55.6426	−1.78017	−0.890083	+	0.455799i	$0.849354\pi$
$978$	−16.2381	−0.519237
$979$	0	0
$980$	1.77222	0.0566116
$981$	4.25351	0.135804
$982$	−18.4156	−0.587664
$983$	18.1396	0.578563	0.289281	−	0.957244i	$-0.406584\pi$
$983$	18.1396	0.578563	0.289281	+	0.957244i	$0.406584\pi$
$984$	−4.74946	−0.151407
$985$	14.7520	0.470038
$986$	4.68040	0.149054
$987$	−8.60452	−0.273885
$988$	0.791706	0.0251875
$989$	30.8019	0.979444
$990$	0	0
$991$	47.7851	1.51794	0.758972	−	0.651123i	$-0.225702\pi$
$991$	47.7851	1.51794	0.758972	+	0.651123i	$0.225702\pi$
$992$	9.15171	0.290567
$993$	−9.45255	−0.299968
$994$	−4.81758	−0.152804
$995$	−20.3953	−0.646573
$996$	11.8728	0.376203
$997$	59.0359	1.86969	0.934843	−	0.355060i	$-0.115540\pi$
$997$	59.0359	1.86969	0.934843	+	0.355060i	$0.115540\pi$
$998$	6.14645	0.194563
$999$	30.6075	0.968379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bh.1.3		8
11.7	odd	10		385.2.n.d.71.4	✓	16
11.8	odd	10		385.2.n.d.141.4	yes	16
11.10	odd	2		4235.2.a.bg.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.d.71.4	✓	16	11.7	odd	10
385.2.n.d.141.4	yes	16	11.8	odd	10
4235.2.a.bg.1.5		8	11.10	odd	2
4235.2.a.bh.1.3		8	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)

\(f(q)\)	\(=\)	\(q-0.477260 q^{2} -1.87300 q^{3} -1.77222 q^{4} -1.00000 q^{5} +0.893910 q^{6} +1.00000 q^{7} +1.80033 q^{8} +0.508144 q^{9} +O(q^{10})\)	\(q-0.477260 q^{2} -1.87300 q^{3} -1.77222 q^{4} -1.00000 q^{5} +0.893910 q^{6} +1.00000 q^{7} +1.80033 q^{8} +0.508144 q^{9} +0.477260 q^{10} +3.31938 q^{12} -3.98510 q^{13} -0.477260 q^{14} +1.87300 q^{15} +2.68522 q^{16} +3.06241 q^{17} -0.242517 q^{18} +0.112100 q^{19} +1.77222 q^{20} -1.87300 q^{21} -7.20351 q^{23} -3.37203 q^{24} +1.00000 q^{25} +1.90193 q^{26} +4.66726 q^{27} -1.77222 q^{28} -3.20232 q^{29} -0.893910 q^{30} -1.87450 q^{31} -4.88221 q^{32} -1.46156 q^{34} -1.00000 q^{35} -0.900544 q^{36} +6.55792 q^{37} -0.0535009 q^{38} +7.46412 q^{39} -1.80033 q^{40} +1.40849 q^{41} +0.893910 q^{42} -4.27596 q^{43} -0.508144 q^{45} +3.43795 q^{46} +4.59397 q^{47} -5.02943 q^{48} +1.00000 q^{49} -0.477260 q^{50} -5.73590 q^{51} +7.06249 q^{52} +1.38466 q^{53} -2.22749 q^{54} +1.80033 q^{56} -0.209964 q^{57} +1.52834 q^{58} +14.2451 q^{59} -3.31938 q^{60} -1.19518 q^{61} +0.894625 q^{62} +0.508144 q^{63} -3.04036 q^{64} +3.98510 q^{65} +7.12333 q^{67} -5.42727 q^{68} +13.4922 q^{69} +0.477260 q^{70} +10.0943 q^{71} +0.914827 q^{72} +10.3155 q^{73} -3.12983 q^{74} -1.87300 q^{75} -0.198666 q^{76} -3.56232 q^{78} +3.99020 q^{79} -2.68522 q^{80} -10.2662 q^{81} -0.672214 q^{82} +3.57680 q^{83} +3.31938 q^{84} -3.06241 q^{85} +2.04075 q^{86} +5.99796 q^{87} -3.94546 q^{89} +0.242517 q^{90} -3.98510 q^{91} +12.7662 q^{92} +3.51095 q^{93} -2.19252 q^{94} -0.112100 q^{95} +9.14440 q^{96} -13.6588 q^{97} -0.477260 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 8 q^{5} - 6 q^{6} + 8 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 8 * q^5 - 6 * q^6 + 8 * q^7 + 6 * q^8 + 17 * q^9	\( 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 8 q^{5} - 6 q^{6} + 8 q^{7} + 6 q^{8} + 17 q^{9} - 2 q^{10} - 10 q^{12} + 2 q^{14} + 3 q^{15} - 6 q^{16} + 7 q^{17} - 3 q^{18} - 19 q^{19} + 2 q^{20} - 3 q^{21} - 16 q^{23} - 5 q^{24} + 8 q^{25} + 15 q^{26} - 21 q^{27} - 2 q^{28} - 8 q^{29} + 6 q^{30} - 6 q^{31} - 16 q^{32} - 3 q^{34} - 8 q^{35} + 4 q^{36} - 26 q^{37} - 25 q^{38} + 11 q^{39} - 6 q^{40} - 9 q^{41} - 6 q^{42} + 4 q^{43} - 17 q^{45} + 20 q^{46} + 9 q^{47} + 16 q^{48} + 8 q^{49} + 2 q^{50} - 44 q^{51} + 5 q^{52} - 7 q^{53} - 21 q^{54} + 6 q^{56} + 36 q^{57} + 15 q^{58} + 20 q^{59} + 10 q^{60} - 13 q^{61} - 9 q^{62} + 17 q^{63} - 6 q^{64} - 21 q^{67} - q^{68} - 12 q^{69} - 2 q^{70} + 3 q^{71} + 38 q^{72} - 16 q^{73} + 2 q^{74} - 3 q^{75} - 11 q^{76} + 7 q^{78} + 14 q^{79} + 6 q^{80} + 12 q^{81} - 16 q^{82} - 4 q^{83} - 10 q^{84} - 7 q^{85} + 7 q^{86} - 8 q^{87} - 23 q^{89} + 3 q^{90} + 26 q^{92} - 67 q^{93} + 12 q^{94} + 19 q^{95} + 27 q^{96} - 38 q^{97} + 2 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 8 * q^5 - 6 * q^6 + 8 * q^7 + 6 * q^8 + 17 * q^9 - 2 * q^10 - 10 * q^12 + 2 * q^14 + 3 * q^15 - 6 * q^16 + 7 * q^17 - 3 * q^18 - 19 * q^19 + 2 * q^20 - 3 * q^21 - 16 * q^23 - 5 * q^24 + 8 * q^25 + 15 * q^26 - 21 * q^27 - 2 * q^28 - 8 * q^29 + 6 * q^30 - 6 * q^31 - 16 * q^32 - 3 * q^34 - 8 * q^35 + 4 * q^36 - 26 * q^37 - 25 * q^38 + 11 * q^39 - 6 * q^40 - 9 * q^41 - 6 * q^42 + 4 * q^43 - 17 * q^45 + 20 * q^46 + 9 * q^47 + 16 * q^48 + 8 * q^49 + 2 * q^50 - 44 * q^51 + 5 * q^52 - 7 * q^53 - 21 * q^54 + 6 * q^56 + 36 * q^57 + 15 * q^58 + 20 * q^59 + 10 * q^60 - 13 * q^61 - 9 * q^62 + 17 * q^63 - 6 * q^64 - 21 * q^67 - q^68 - 12 * q^69 - 2 * q^70 + 3 * q^71 + 38 * q^72 - 16 * q^73 + 2 * q^74 - 3 * q^75 - 11 * q^76 + 7 * q^78 + 14 * q^79 + 6 * q^80 + 12 * q^81 - 16 * q^82 - 4 * q^83 - 10 * q^84 - 7 * q^85 + 7 * q^86 - 8 * q^87 - 23 * q^89 + 3 * q^90 + 26 * q^92 - 67 * q^93 + 12 * q^94 + 19 * q^95 + 27 * q^96 - 38 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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