LMFDB - Embedded newform 4235.2.a.bk.1.6

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 67x^{6} - 110x^{5} - 132x^{4} + 168x^{3} + 94x^{2} - 54x - 11 $ x^10 - 2x^9 - 14x^8 + 26x^7 + 67x^6 - 110x^5 - 132x^4 + 168x^3 + 94x^2 - 54*x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.547729$ 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)

$f(q)$	$=$	$q+0.547729 q^{2} -3.41697 q^{3} -1.69999 q^{4} +1.00000 q^{5} -1.87158 q^{6} -1.00000 q^{7} -2.02659 q^{8} +8.67570 q^{9} +O(q^{10})$	\(q+0.547729 q^{2} -3.41697 q^{3} -1.69999 q^{4} +1.00000 q^{5} -1.87158 q^{6} -1.00000 q^{7} -2.02659 q^{8} +8.67570 q^{9} +0.547729 q^{10} +5.80883 q^{12} +5.13626 q^{13} -0.547729 q^{14} -3.41697 q^{15} +2.28996 q^{16} -1.89313 q^{17} +4.75193 q^{18} +0.995867 q^{19} -1.69999 q^{20} +3.41697 q^{21} +7.47220 q^{23} +6.92482 q^{24} +1.00000 q^{25} +2.81328 q^{26} -19.3937 q^{27} +1.69999 q^{28} +6.07749 q^{29} -1.87158 q^{30} -9.66473 q^{31} +5.30747 q^{32} -1.03692 q^{34} -1.00000 q^{35} -14.7486 q^{36} -1.05699 q^{37} +0.545466 q^{38} -17.5504 q^{39} -2.02659 q^{40} +6.21238 q^{41} +1.87158 q^{42} -11.8635 q^{43} +8.67570 q^{45} +4.09274 q^{46} +2.37309 q^{47} -7.82473 q^{48} +1.00000 q^{49} +0.547729 q^{50} +6.46876 q^{51} -8.73160 q^{52} -1.08367 q^{53} -10.6225 q^{54} +2.02659 q^{56} -3.40285 q^{57} +3.32882 q^{58} -1.01785 q^{59} +5.80883 q^{60} +7.26140 q^{61} -5.29366 q^{62} -8.67570 q^{63} -1.67286 q^{64} +5.13626 q^{65} -0.377827 q^{67} +3.21830 q^{68} -25.5323 q^{69} -0.547729 q^{70} +6.42093 q^{71} -17.5821 q^{72} -15.4877 q^{73} -0.578947 q^{74} -3.41697 q^{75} -1.69297 q^{76} -9.61289 q^{78} -11.9247 q^{79} +2.28996 q^{80} +40.2406 q^{81} +3.40270 q^{82} -3.22534 q^{83} -5.80883 q^{84} -1.89313 q^{85} -6.49800 q^{86} -20.7666 q^{87} -5.65995 q^{89} +4.75193 q^{90} -5.13626 q^{91} -12.7027 q^{92} +33.0241 q^{93} +1.29981 q^{94} +0.995867 q^{95} -18.1355 q^{96} +12.2829 q^{97} +0.547729 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9	$ 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9} + 2 q^{10} - 4 q^{12} + 18 q^{13} - 2 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} + 12 q^{18} + 14 q^{19} + 12 q^{20} + 4 q^{21} - 4 q^{23} + 46 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{27} - 12 q^{28} + 36 q^{29} + 8 q^{30} - 18 q^{31} + 4 q^{32} - 32 q^{34} - 10 q^{35} + 22 q^{36} + 4 q^{37} + 18 q^{38} + 6 q^{40} + 38 q^{41} - 8 q^{42} + 6 q^{43} + 14 q^{45} + 28 q^{46} - 18 q^{47} + 16 q^{48} + 10 q^{49} + 2 q^{50} - 4 q^{51} + 26 q^{52} - 26 q^{53} + 2 q^{54} - 6 q^{56} + 22 q^{57} + 10 q^{58} - 14 q^{59} - 4 q^{60} + 60 q^{61} + 22 q^{62} - 14 q^{63} + 18 q^{65} - 10 q^{67} + 2 q^{68} - 8 q^{69} - 2 q^{70} - 54 q^{72} + 18 q^{73} - 20 q^{74} - 4 q^{75} + 38 q^{76} + 40 q^{78} + 40 q^{79} + 4 q^{80} + 18 q^{81} - 36 q^{82} + 2 q^{83} + 4 q^{84} + 4 q^{85} + 42 q^{86} - 32 q^{87} + 2 q^{89} + 12 q^{90} - 18 q^{91} - 64 q^{92} + 26 q^{93} - 68 q^{94} + 14 q^{95} + 28 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9 + 2 * q^10 - 4 * q^12 + 18 * q^13 - 2 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 + 12 * q^18 + 14 * q^19 + 12 * q^20 + 4 * q^21 - 4 * q^23 + 46 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^27 - 12 * q^28 + 36 * q^29 + 8 * q^30 - 18 * q^31 + 4 * q^32 - 32 * q^34 - 10 * q^35 + 22 * q^36 + 4 * q^37 + 18 * q^38 + 6 * q^40 + 38 * q^41 - 8 * q^42 + 6 * q^43 + 14 * q^45 + 28 * q^46 - 18 * q^47 + 16 * q^48 + 10 * q^49 + 2 * q^50 - 4 * q^51 + 26 * q^52 - 26 * q^53 + 2 * q^54 - 6 * q^56 + 22 * q^57 + 10 * q^58 - 14 * q^59 - 4 * q^60 + 60 * q^61 + 22 * q^62 - 14 * q^63 + 18 * q^65 - 10 * q^67 + 2 * q^68 - 8 * q^69 - 2 * q^70 - 54 * q^72 + 18 * q^73 - 20 * q^74 - 4 * q^75 + 38 * q^76 + 40 * q^78 + 40 * q^79 + 4 * q^80 + 18 * q^81 - 36 * q^82 + 2 * q^83 + 4 * q^84 + 4 * q^85 + 42 * q^86 - 32 * q^87 + 2 * q^89 + 12 * q^90 - 18 * q^91 - 64 * q^92 + 26 * q^93 - 68 * q^94 + 14 * q^95 + 28 * q^96 + 8 * 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 $

$2$	0.547729	0.387303	0.193652	−	0.981070i	$-0.437967\pi$
$2$	0.547729	0.387303	0.193652	+	0.981070i	$0.437967\pi$
$3$	−3.41697	−1.97279	−0.986395	−	0.164393i	$-0.947433\pi$
$3$	−3.41697	−1.97279	−0.986395	+	0.164393i	$0.947433\pi$
$4$	−1.69999	−0.849996
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.87158	−0.764068
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.02659	−0.716509
$9$	8.67570	2.89190
$10$	0.547729	0.173207
$11$	0	0
$11$	0	0
$12$	5.80883	1.67686
$13$	5.13626	1.42454	0.712270	−	0.701905i	$-0.247667\pi$
$13$	5.13626	1.42454	0.712270	+	0.701905i	$0.247667\pi$
$14$	−0.547729	−0.146387
$15$	−3.41697	−0.882258
$16$	2.28996	0.572490
$17$	−1.89313	−0.459151	−0.229575	−	0.973291i	$-0.573734\pi$
$17$	−1.89313	−0.459151	−0.229575	+	0.973291i	$0.573734\pi$
$18$	4.75193	1.12004
$19$	0.995867	0.228468	0.114234	−	0.993454i	$-0.463559\pi$
$19$	0.995867	0.228468	0.114234	+	0.993454i	$0.463559\pi$
$20$	−1.69999	−0.380130
$21$	3.41697	0.745644
$22$	0	0
$23$	7.47220	1.55806	0.779030	−	0.626986i	$-0.215712\pi$
$23$	7.47220	1.55806	0.779030	+	0.626986i	$0.215712\pi$
$24$	6.92482	1.41352
$25$	1.00000	0.200000
$26$	2.81328	0.551729
$27$	−19.3937	−3.73232
$28$	1.69999	0.321268
$29$	6.07749	1.12856	0.564281	−	0.825583i	$-0.309154\pi$
$29$	6.07749	1.12856	0.564281	+	0.825583i	$0.309154\pi$
$30$	−1.87158	−0.341701
$31$	−9.66473	−1.73584	−0.867919	−	0.496707i	$-0.834543\pi$
$31$	−9.66473	−1.73584	−0.867919	+	0.496707i	$0.834543\pi$
$32$	5.30747	0.938237
$33$	0	0
$34$	−1.03692	−0.177830
$35$	−1.00000	−0.169031
$36$	−14.7486	−2.45810
$37$	−1.05699	−0.173769	−0.0868844	−	0.996218i	$-0.527691\pi$
$37$	−1.05699	−0.173769	−0.0868844	+	0.996218i	$0.527691\pi$
$38$	0.545466	0.0884862
$39$	−17.5504	−2.81032
$40$	−2.02659	−0.320433
$41$	6.21238	0.970211	0.485105	−	0.874456i	$-0.338781\pi$
$41$	6.21238	0.970211	0.485105	+	0.874456i	$0.338781\pi$
$42$	1.87158	0.288790
$43$	−11.8635	−1.80917	−0.904586	−	0.426292i	$-0.859820\pi$
$43$	−11.8635	−1.80917	−0.904586	+	0.426292i	$0.859820\pi$
$44$	0	0
$45$	8.67570	1.29330
$46$	4.09274	0.603442
$47$	2.37309	0.346151	0.173075	−	0.984909i	$-0.444630\pi$
$47$	2.37309	0.346151	0.173075	+	0.984909i	$0.444630\pi$
$48$	−7.82473	−1.12940
$49$	1.00000	0.142857
$50$	0.547729	0.0774606
$51$	6.46876	0.905808
$52$	−8.73160	−1.21085
$53$	−1.08367	−0.148853	−0.0744265	−	0.997227i	$-0.523713\pi$
$53$	−1.08367	−0.148853	−0.0744265	+	0.997227i	$0.523713\pi$
$54$	−10.6225	−1.44554
$55$	0	0
$56$	2.02659	0.270815
$57$	−3.40285	−0.450719
$58$	3.32882	0.437096
$59$	−1.01785	−0.132513	−0.0662563	−	0.997803i	$-0.521106\pi$
$59$	−1.01785	−0.132513	−0.0662563	+	0.997803i	$0.521106\pi$
$60$	5.80883	0.749916
$61$	7.26140	0.929727	0.464864	−	0.885382i	$-0.346103\pi$
$61$	7.26140	0.929727	0.464864	+	0.885382i	$0.346103\pi$
$62$	−5.29366	−0.672295
$63$	−8.67570	−1.09304
$64$	−1.67286	−0.209108
$65$	5.13626	0.637074
$66$	0	0
$67$	−0.377827	−0.0461590	−0.0230795	−	0.999734i	$-0.507347\pi$
$67$	−0.377827	−0.0461590	−0.0230795	+	0.999734i	$0.507347\pi$
$68$	3.21830	0.390276
$69$	−25.5323	−3.07373
$70$	−0.547729	−0.0654662
$71$	6.42093	0.762024	0.381012	−	0.924570i	$-0.375576\pi$
$71$	6.42093	0.762024	0.381012	+	0.924570i	$0.375576\pi$
$72$	−17.5821	−2.07207
$73$	−15.4877	−1.81270	−0.906348	−	0.422531i	$-0.861142\pi$
$73$	−15.4877	−1.81270	−0.906348	+	0.422531i	$0.861142\pi$
$74$	−0.578947	−0.0673012
$75$	−3.41697	−0.394558
$76$	−1.69297	−0.194197
$77$	0	0
$78$	−9.61289	−1.08845
$79$	−11.9247	−1.34163	−0.670815	−	0.741624i	$-0.734056\pi$
$79$	−11.9247	−1.34163	−0.670815	+	0.741624i	$0.734056\pi$
$80$	2.28996	0.256025
$81$	40.2406	4.47118
$82$	3.40270	0.375766
$83$	−3.22534	−0.354027	−0.177013	−	0.984208i	$-0.556644\pi$
$83$	−3.22534	−0.354027	−0.177013	+	0.984208i	$0.556644\pi$
$84$	−5.80883	−0.633795
$85$	−1.89313	−0.205338
$86$	−6.49800	−0.700698
$87$	−20.7666	−2.22641
$88$	0	0
$89$	−5.65995	−0.599953	−0.299977	−	0.953947i	$-0.596979\pi$
$89$	−5.65995	−0.599953	−0.299977	+	0.953947i	$0.596979\pi$
$90$	4.75193	0.500898
$91$	−5.13626	−0.538426
$92$	−12.7027	−1.32435
$93$	33.0241	3.42444
$94$	1.29981	0.134065
$95$	0.995867	0.102174
$96$	−18.1355	−1.85094
$97$	12.2829	1.24714	0.623569	−	0.781768i	$-0.285682\pi$
$97$	12.2829	1.24714	0.623569	+	0.781768i	$0.285682\pi$
$98$	0.547729	0.0553290
$99$	0	0
$100$	−1.69999	−0.169999
$101$	3.74207	0.372350	0.186175	−	0.982517i	$-0.440391\pi$
$101$	3.74207	0.372350	0.186175	+	0.982517i	$0.440391\pi$
$102$	3.54313	0.350822
$103$	6.95088	0.684891	0.342445	−	0.939538i	$-0.388745\pi$
$103$	6.95088	0.684891	0.342445	+	0.939538i	$0.388745\pi$
$104$	−10.4091	−1.02070
$105$	3.41697	0.333462
$106$	−0.593556	−0.0576512
$107$	12.9654	1.25341	0.626707	−	0.779255i	$-0.284402\pi$
$107$	12.9654	1.25341	0.626707	+	0.779255i	$0.284402\pi$
$108$	32.9691	3.17246
$109$	2.08725	0.199922	0.0999611	−	0.994991i	$-0.468128\pi$
$109$	2.08725	0.199922	0.0999611	+	0.994991i	$0.468128\pi$
$110$	0	0
$111$	3.61172	0.342809
$112$	−2.28996	−0.216381
$113$	−9.61055	−0.904084	−0.452042	−	0.891997i	$-0.649304\pi$
$113$	−9.61055	−0.904084	−0.452042	+	0.891997i	$0.649304\pi$
$114$	−1.86384	−0.174565
$115$	7.47220	0.696786
$116$	−10.3317	−0.959273
$117$	44.5606	4.11963
$118$	−0.557506	−0.0513226
$119$	1.89313	0.173543
$120$	6.92482	0.632146
$121$	0	0
$122$	3.97728	0.360086
$123$	−21.2275	−1.91402
$124$	16.4300	1.47546
$125$	1.00000	0.0894427
$126$	−4.75193	−0.423336
$127$	−0.280145	−0.0248589	−0.0124294	−	0.999923i	$-0.503957\pi$
$127$	−0.280145	−0.0248589	−0.0124294	+	0.999923i	$0.503957\pi$
$128$	−11.5312	−1.01922
$129$	40.5373	3.56911
$130$	2.81328	0.246741
$131$	1.47708	0.129053	0.0645267	−	0.997916i	$-0.479446\pi$
$131$	1.47708	0.129053	0.0645267	+	0.997916i	$0.479446\pi$
$132$	0	0
$133$	−0.995867	−0.0863526
$134$	−0.206947	−0.0178775
$135$	−19.3937	−1.66914
$136$	3.83660	0.328986
$137$	0.343777	0.0293709	0.0146854	−	0.999892i	$-0.495325\pi$
$137$	0.343777	0.0293709	0.0146854	+	0.999892i	$0.495325\pi$
$138$	−13.9848	−1.19046
$139$	6.04284	0.512547	0.256273	−	0.966604i	$-0.417505\pi$
$139$	6.04284	0.512547	0.256273	+	0.966604i	$0.417505\pi$
$140$	1.69999	0.143676
$141$	−8.10878	−0.682882
$142$	3.51693	0.295134
$143$	0	0
$144$	19.8670	1.65558
$145$	6.07749	0.504708
$146$	−8.48306	−0.702063
$147$	−3.41697	−0.281827
$148$	1.79688	0.147703
$149$	10.0211	0.820959	0.410480	−	0.911870i	$-0.365361\pi$
$149$	10.0211	0.820959	0.410480	+	0.911870i	$0.365361\pi$
$150$	−1.87158	−0.152814
$151$	9.02415	0.734375	0.367187	−	0.930147i	$-0.380321\pi$
$151$	9.02415	0.734375	0.367187	+	0.930147i	$0.380321\pi$
$152$	−2.01822	−0.163699
$153$	−16.4242	−1.32782
$154$	0	0
$155$	−9.66473	−0.776290
$156$	29.8356	2.38876
$157$	−17.3777	−1.38689	−0.693444	−	0.720511i	$-0.743907\pi$
$157$	−17.3777	−1.38689	−0.693444	+	0.720511i	$0.743907\pi$
$158$	−6.53150	−0.519618
$159$	3.70286	0.293656
$160$	5.30747	0.419592
$161$	−7.47220	−0.588892
$162$	22.0410	1.73170
$163$	5.08955	0.398645	0.199322	−	0.979934i	$-0.436126\pi$
$163$	5.08955	0.398645	0.199322	+	0.979934i	$0.436126\pi$
$164$	−10.5610	−0.824676
$165$	0	0
$166$	−1.76661	−0.137116
$167$	9.75278	0.754692	0.377346	−	0.926072i	$-0.376837\pi$
$167$	9.75278	0.754692	0.377346	+	0.926072i	$0.376837\pi$
$168$	−6.92482	−0.534261
$169$	13.3811	1.02932
$170$	−1.03692	−0.0795282
$171$	8.63984	0.660705
$172$	20.1679	1.53779
$173$	−21.3455	−1.62286	−0.811432	−	0.584446i	$-0.801312\pi$
$173$	−21.3455	−1.62286	−0.811432	+	0.584446i	$0.801312\pi$
$174$	−11.3745	−0.862298
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	3.47796	0.261420
$178$	−3.10012	−0.232364
$179$	14.3713	1.07416	0.537081	−	0.843531i	$-0.319527\pi$
$179$	14.3713	1.07416	0.537081	+	0.843531i	$0.319527\pi$
$180$	−14.7486	−1.09930
$181$	9.96954	0.741030	0.370515	−	0.928827i	$-0.379181\pi$
$181$	9.96954	0.741030	0.370515	+	0.928827i	$0.379181\pi$
$182$	−2.81328	−0.208534
$183$	−24.8120	−1.83416
$184$	−15.1431	−1.11637
$185$	−1.05699	−0.0777118
$186$	18.0883	1.32630
$187$	0	0
$188$	−4.03423	−0.294227
$189$	19.3937	1.41068
$190$	0.545466	0.0395722
$191$	10.5286	0.761824	0.380912	−	0.924611i	$-0.375610\pi$
$191$	10.5286	0.761824	0.380912	+	0.924611i	$0.375610\pi$
$192$	5.71612	0.412526
$193$	−3.02584	−0.217805	−0.108902	−	0.994052i	$-0.534734\pi$
$193$	−3.02584	−0.217805	−0.108902	+	0.994052i	$0.534734\pi$
$194$	6.72770	0.483020
$195$	−17.5504	−1.25681
$196$	−1.69999	−0.121428
$197$	13.0753	0.931580	0.465790	−	0.884895i	$-0.345770\pi$
$197$	13.0753	0.931580	0.465790	+	0.884895i	$0.345770\pi$
$198$	0	0
$199$	1.98474	0.140694	0.0703472	−	0.997523i	$-0.477589\pi$
$199$	1.98474	0.140694	0.0703472	+	0.997523i	$0.477589\pi$
$200$	−2.02659	−0.143302
$201$	1.29103	0.0910619
$202$	2.04964	0.144212
$203$	−6.07749	−0.426556
$204$	−10.9968	−0.769933
$205$	6.21238	0.433891
$206$	3.80720	0.265260
$207$	64.8265	4.50576
$208$	11.7618	0.815535
$209$	0	0
$210$	1.87158	0.129151
$211$	8.69252	0.598418	0.299209	−	0.954188i	$-0.403277\pi$
$211$	8.69252	0.598418	0.299209	+	0.954188i	$0.403277\pi$
$212$	1.84222	0.126524
$213$	−21.9401	−1.50331
$214$	7.10154	0.485451
$215$	−11.8635	−0.809086
$216$	39.3032	2.67424
$217$	9.66473	0.656085
$218$	1.14325	0.0774305
$219$	52.9210	3.57607
$220$	0	0
$221$	−9.72358	−0.654079
$222$	1.97825	0.132771
$223$	4.40008	0.294651	0.147325	−	0.989088i	$-0.452934\pi$
$223$	4.40008	0.294651	0.147325	+	0.989088i	$0.452934\pi$
$224$	−5.30747	−0.354620
$225$	8.67570	0.578380
$226$	−5.26398	−0.350155
$227$	−14.5394	−0.965015	−0.482508	−	0.875892i	$-0.660274\pi$
$227$	−14.5394	−0.965015	−0.482508	+	0.875892i	$0.660274\pi$
$228$	5.78482	0.383109
$229$	−10.1524	−0.670887	−0.335444	−	0.942060i	$-0.608886\pi$
$229$	−10.1524	−0.670887	−0.335444	+	0.942060i	$0.608886\pi$
$230$	4.09274	0.269867
$231$	0	0
$232$	−12.3166	−0.808625
$233$	1.63072	0.106832	0.0534161	−	0.998572i	$-0.482989\pi$
$233$	1.63072	0.106832	0.0534161	+	0.998572i	$0.482989\pi$
$234$	24.4072	1.59555
$235$	2.37309	0.154803
$236$	1.73034	0.112635
$237$	40.7463	2.64676
$238$	1.03692	0.0672136
$239$	−16.1374	−1.04384	−0.521922	−	0.852993i	$-0.674785\pi$
$239$	−16.1374	−1.04384	−0.521922	+	0.852993i	$0.674785\pi$
$240$	−7.82473	−0.505084
$241$	13.7320	0.884554	0.442277	−	0.896879i	$-0.354171\pi$
$241$	13.7320	0.884554	0.442277	+	0.896879i	$0.354171\pi$
$242$	0	0
$243$	−79.3200	−5.08838
$244$	−12.3443	−0.790265
$245$	1.00000	0.0638877
$246$	−11.6269	−0.741307
$247$	5.11503	0.325461
$248$	19.5865	1.24374
$249$	11.0209	0.698421
$250$	0.547729	0.0346415
$251$	8.46025	0.534006	0.267003	−	0.963696i	$-0.413967\pi$
$251$	8.46025	0.534006	0.267003	+	0.963696i	$0.413967\pi$
$252$	14.7486	0.929076
$253$	0	0
$254$	−0.153444	−0.00962791
$255$	6.46876	0.405089
$256$	−2.97026	−0.185641
$257$	−3.85606	−0.240534	−0.120267	−	0.992742i	$-0.538375\pi$
$257$	−3.85606	−0.240534	−0.120267	+	0.992742i	$0.538375\pi$
$258$	22.2035	1.38233
$259$	1.05699	0.0656784
$260$	−8.73160	−0.541511
$261$	52.7265	3.26369
$262$	0.809042	0.0499828
$263$	29.8124	1.83831	0.919157	−	0.393892i	$-0.128872\pi$
$263$	29.8124	1.83831	0.919157	+	0.393892i	$0.128872\pi$
$264$	0	0
$265$	−1.08367	−0.0665691
$266$	−0.545466	−0.0334447
$267$	19.3399	1.18358
$268$	0.642304	0.0392349
$269$	22.7726	1.38847	0.694236	−	0.719748i	$-0.255742\pi$
$269$	22.7726	1.38847	0.694236	+	0.719748i	$0.255742\pi$
$270$	−10.6225	−0.646465
$271$	16.6765	1.01303	0.506513	−	0.862232i	$-0.330934\pi$
$271$	16.6765	1.01303	0.506513	+	0.862232i	$0.330934\pi$
$272$	−4.33518	−0.262859
$273$	17.5504	1.06220
$274$	0.188297	0.0113754
$275$	0	0
$276$	43.4047	2.61266
$277$	16.9595	1.01900	0.509498	−	0.860472i	$-0.329831\pi$
$277$	16.9595	1.01900	0.509498	+	0.860472i	$0.329831\pi$
$278$	3.30984	0.198511
$279$	−83.8483	−5.01987
$280$	2.02659	0.121112
$281$	29.1550	1.73924	0.869622	−	0.493718i	$-0.164363\pi$
$281$	29.1550	1.73924	0.869622	+	0.493718i	$0.164363\pi$
$282$	−4.44142	−0.264482
$283$	−10.6838	−0.635084	−0.317542	−	0.948244i	$-0.602857\pi$
$283$	−10.6838	−0.635084	−0.317542	+	0.948244i	$0.602857\pi$
$284$	−10.9155	−0.647717
$285$	−3.40285	−0.201567
$286$	0	0
$287$	−6.21238	−0.366705
$288$	46.0460	2.71329
$289$	−13.4161	−0.789181
$290$	3.32882	0.195475
$291$	−41.9703	−2.46034
$292$	26.3290	1.54079
$293$	−12.7473	−0.744704	−0.372352	−	0.928092i	$-0.621449\pi$
$293$	−12.7473	−0.744704	−0.372352	+	0.928092i	$0.621449\pi$
$294$	−1.87158	−0.109153
$295$	−1.01785	−0.0592615
$296$	2.14210	0.124507
$297$	0	0
$298$	5.48884	0.317960
$299$	38.3791	2.21952
$300$	5.80883	0.335373
$301$	11.8635	0.683802
$302$	4.94279	0.284426
$303$	−12.7865	−0.734568
$304$	2.28050	0.130795
$305$	7.26140	0.415787
$306$	−8.99601	−0.514268
$307$	−20.4869	−1.16925	−0.584625	−	0.811304i	$-0.698758\pi$
$307$	−20.4869	−1.16925	−0.584625	+	0.811304i	$0.698758\pi$
$308$	0	0
$309$	−23.7510	−1.35115
$310$	−5.29366	−0.300660
$311$	−11.8951	−0.674508	−0.337254	−	0.941414i	$-0.609498\pi$
$311$	−11.8951	−0.674508	−0.337254	+	0.941414i	$0.609498\pi$
$312$	35.5676	2.01362
$313$	−8.19054	−0.462957	−0.231478	−	0.972840i	$-0.574356\pi$
$313$	−8.19054	−0.462957	−0.231478	+	0.972840i	$0.574356\pi$
$314$	−9.51825	−0.537146
$315$	−8.67570	−0.488820
$316$	20.2719	1.14038
$317$	−14.3342	−0.805090	−0.402545	−	0.915400i	$-0.631874\pi$
$317$	−14.3342	−0.805090	−0.402545	+	0.915400i	$0.631874\pi$
$318$	2.02816	0.113734
$319$	0	0
$320$	−1.67286	−0.0935159
$321$	−44.3024	−2.47272
$322$	−4.09274	−0.228080
$323$	−1.88530	−0.104901
$324$	−68.4088	−3.80049
$325$	5.13626	0.284908
$326$	2.78770	0.154396
$327$	−7.13207	−0.394405
$328$	−12.5900	−0.695165
$329$	−2.37309	−0.130833
$330$	0	0
$331$	12.3490	0.678763	0.339381	−	0.940649i	$-0.389782\pi$
$331$	12.3490	0.678763	0.339381	+	0.940649i	$0.389782\pi$
$332$	5.48305	0.300921
$333$	−9.17017	−0.502522
$334$	5.34188	0.292295
$335$	−0.377827	−0.0206429
$336$	7.82473	0.426874
$337$	8.43982	0.459746	0.229873	−	0.973221i	$-0.426169\pi$
$337$	8.43982	0.459746	0.229873	+	0.973221i	$0.426169\pi$
$338$	7.32923	0.398658
$339$	32.8390	1.78357
$340$	3.21830	0.174537
$341$	0	0
$342$	4.73230	0.255893
$343$	−1.00000	−0.0539949
$344$	24.0426	1.29629
$345$	−25.5323	−1.37461
$346$	−11.6915	−0.628541
$347$	27.2864	1.46481	0.732404	−	0.680870i	$-0.238398\pi$
$347$	27.2864	1.46481	0.732404	+	0.680870i	$0.238398\pi$
$348$	35.3031	1.89244
$349$	30.7820	1.64772	0.823861	−	0.566792i	$-0.191816\pi$
$349$	30.7820	1.64772	0.823861	+	0.566792i	$0.191816\pi$
$350$	−0.547729	−0.0292774
$351$	−99.6110	−5.31684
$352$	0	0
$353$	−27.4135	−1.45907	−0.729537	−	0.683941i	$-0.760265\pi$
$353$	−27.4135	−1.45907	−0.729537	+	0.683941i	$0.760265\pi$
$354$	1.90498	0.101249
$355$	6.42093	0.340787
$356$	9.62187	0.509958
$357$	−6.46876	−0.342363
$358$	7.87158	0.416026
$359$	−0.531678	−0.0280609	−0.0140305	−	0.999902i	$-0.504466\pi$
$359$	−0.531678	−0.0280609	−0.0140305	+	0.999902i	$0.504466\pi$
$360$	−17.5821	−0.926659
$361$	−18.0082	−0.947803
$362$	5.46061	0.287003
$363$	0	0
$364$	8.73160	0.457660
$365$	−15.4877	−0.810663
$366$	−13.5903	−0.710375
$367$	34.5626	1.80415	0.902075	−	0.431579i	$-0.142043\pi$
$367$	34.5626	1.80415	0.902075	+	0.431579i	$0.142043\pi$
$368$	17.1110	0.891974
$369$	53.8967	2.80575
$370$	−0.578947	−0.0300980
$371$	1.08367	0.0562611
$372$	−56.1408	−2.91076
$373$	−8.13826	−0.421383	−0.210692	−	0.977553i	$-0.567572\pi$
$373$	−8.13826	−0.421383	−0.210692	+	0.977553i	$0.567572\pi$
$374$	0	0
$375$	−3.41697	−0.176452
$376$	−4.80929	−0.248020
$377$	31.2155	1.60768
$378$	10.6225	0.546362
$379$	15.9131	0.817403	0.408702	−	0.912668i	$-0.365982\pi$
$379$	15.9131	0.817403	0.408702	+	0.912668i	$0.365982\pi$
$380$	−1.69297	−0.0868474
$381$	0.957248	0.0490413
$382$	5.76683	0.295057
$383$	−5.18634	−0.265010	−0.132505	−	0.991182i	$-0.542302\pi$
$383$	−5.18634	−0.265010	−0.132505	+	0.991182i	$0.542302\pi$
$384$	39.4018	2.01072
$385$	0	0
$386$	−1.65734	−0.0843565
$387$	−102.924	−5.23194
$388$	−20.8808	−1.06006
$389$	−7.02383	−0.356122	−0.178061	−	0.984019i	$-0.556982\pi$
$389$	−7.02383	−0.356122	−0.178061	+	0.984019i	$0.556982\pi$
$390$	−9.61289	−0.486768
$391$	−14.1458	−0.715385
$392$	−2.02659	−0.102358
$393$	−5.04715	−0.254595
$394$	7.16175	0.360804
$395$	−11.9247	−0.599995
$396$	0	0
$397$	−29.9046	−1.50087	−0.750435	−	0.660944i	$-0.770156\pi$
$397$	−29.9046	−1.50087	−0.750435	+	0.660944i	$0.770156\pi$
$398$	1.08710	0.0544914
$399$	3.40285	0.170356
$400$	2.28996	0.114498
$401$	2.34928	0.117317	0.0586586	−	0.998278i	$-0.481318\pi$
$401$	2.34928	0.117317	0.0586586	+	0.998278i	$0.481318\pi$
$402$	0.707133	0.0352686
$403$	−49.6405	−2.47277
$404$	−6.36149	−0.316496
$405$	40.2406	1.99957
$406$	−3.32882	−0.165207
$407$	0	0
$408$	−13.1096	−0.649020
$409$	17.6020	0.870361	0.435181	−	0.900343i	$-0.356684\pi$
$409$	17.6020	0.870361	0.435181	+	0.900343i	$0.356684\pi$
$410$	3.40270	0.168048
$411$	−1.17468	−0.0579426
$412$	−11.8164	−0.582154
$413$	1.01785	0.0500851
$414$	35.5074	1.74509
$415$	−3.22534	−0.158326
$416$	27.2605	1.33656
$417$	−20.6482	−1.01115
$418$	0	0
$419$	−32.2263	−1.57436	−0.787179	−	0.616724i	$-0.788459\pi$
$419$	−32.2263	−1.57436	−0.787179	+	0.616724i	$0.788459\pi$
$420$	−5.80883	−0.283442
$421$	16.3940	0.798994	0.399497	−	0.916734i	$-0.369185\pi$
$421$	16.3940	0.798994	0.399497	+	0.916734i	$0.369185\pi$
$422$	4.76115	0.231769
$423$	20.5882	1.00103
$424$	2.19615	0.106655
$425$	−1.89313	−0.0918301
$426$	−12.0173	−0.582238
$427$	−7.26140	−0.351404
$428$	−22.0411	−1.06540
$429$	0	0
$430$	−6.49800	−0.313362
$431$	17.7272	0.853888	0.426944	−	0.904278i	$-0.359590\pi$
$431$	17.7272	0.853888	0.426944	+	0.904278i	$0.359590\pi$
$432$	−44.4108	−2.13672
$433$	2.16444	0.104016	0.0520081	−	0.998647i	$-0.483438\pi$
$433$	2.16444	0.104016	0.0520081	+	0.998647i	$0.483438\pi$
$434$	5.29366	0.254104
$435$	−20.7666	−0.995683
$436$	−3.54831	−0.169933
$437$	7.44132	0.355966
$438$	28.9864	1.38502
$439$	−20.6454	−0.985349	−0.492675	−	0.870214i	$-0.663981\pi$
$439$	−20.6454	−0.985349	−0.492675	+	0.870214i	$0.663981\pi$
$440$	0	0
$441$	8.67570	0.413128
$442$	−5.32589	−0.253327
$443$	16.1681	0.768169	0.384084	−	0.923298i	$-0.374517\pi$
$443$	16.1681	0.768169	0.384084	+	0.923298i	$0.374517\pi$
$444$	−6.13990	−0.291387
$445$	−5.65995	−0.268307
$446$	2.41005	0.114119
$447$	−34.2418	−1.61958
$448$	1.67286	0.0790353
$449$	−5.14485	−0.242800	−0.121400	−	0.992604i	$-0.538738\pi$
$449$	−5.14485	−0.242800	−0.121400	+	0.992604i	$0.538738\pi$
$450$	4.75193	0.224008
$451$	0	0
$452$	16.3379	0.768468
$453$	−30.8353	−1.44877
$454$	−7.96367	−0.373753
$455$	−5.13626	−0.240791
$456$	6.89620	0.322944
$457$	16.4899	0.771364	0.385682	−	0.922632i	$-0.373966\pi$
$457$	16.4899	0.771364	0.385682	+	0.922632i	$0.373966\pi$
$458$	−5.56075	−0.259837
$459$	36.7147	1.71370
$460$	−12.7027	−0.592266
$461$	−0.891916	−0.0415407	−0.0207703	−	0.999784i	$-0.506612\pi$
$461$	−0.891916	−0.0415407	−0.0207703	+	0.999784i	$0.506612\pi$
$462$	0	0
$463$	−5.42535	−0.252137	−0.126069	−	0.992022i	$-0.540236\pi$
$463$	−5.42535	−0.252137	−0.126069	+	0.992022i	$0.540236\pi$
$464$	13.9172	0.646090
$465$	33.0241	1.53146
$466$	0.893195	0.0413764
$467$	20.4043	0.944199	0.472099	−	0.881545i	$-0.343496\pi$
$467$	20.4043	0.944199	0.472099	+	0.881545i	$0.343496\pi$
$468$	−75.7527	−3.50167
$469$	0.377827	0.0174464
$470$	1.29981	0.0599558
$471$	59.3790	2.73604
$472$	2.06277	0.0949466
$473$	0	0
$474$	22.3179	1.02510
$475$	0.995867	0.0456935
$476$	−3.21830	−0.147511
$477$	−9.40156	−0.430468
$478$	−8.83894	−0.404284
$479$	−27.8248	−1.27135	−0.635674	−	0.771958i	$-0.719278\pi$
$479$	−27.8248	−1.27135	−0.635674	+	0.771958i	$0.719278\pi$
$480$	−18.1355	−0.827767
$481$	−5.42899	−0.247541
$482$	7.52140	0.342590
$483$	25.5323	1.16176
$484$	0	0
$485$	12.2829	0.557737
$486$	−43.4459	−1.97075
$487$	−24.3238	−1.10222	−0.551108	−	0.834434i	$-0.685795\pi$
$487$	−24.3238	−1.10222	−0.551108	+	0.834434i	$0.685795\pi$
$488$	−14.7159	−0.666158
$489$	−17.3909	−0.786442
$490$	0.547729	0.0247439
$491$	34.5287	1.55826	0.779130	−	0.626862i	$-0.215661\pi$
$491$	34.5287	1.55826	0.779130	+	0.626862i	$0.215661\pi$
$492$	36.0866	1.62691
$493$	−11.5055	−0.518180
$494$	2.80165	0.126052
$495$	0	0
$496$	−22.1318	−0.993749
$497$	−6.42093	−0.288018
$498$	6.03647	0.270500
$499$	24.8913	1.11429	0.557145	−	0.830416i	$-0.311897\pi$
$499$	24.8913	1.11429	0.557145	+	0.830416i	$0.311897\pi$
$500$	−1.69999	−0.0760260
$501$	−33.3250	−1.48885
$502$	4.63393	0.206822
$503$	−1.31614	−0.0586839	−0.0293420	−	0.999569i	$-0.509341\pi$
$503$	−1.31614	−0.0586839	−0.0293420	+	0.999569i	$0.509341\pi$
$504$	17.5821	0.783170
$505$	3.74207	0.166520
$506$	0	0
$507$	−45.7229	−2.03063
$508$	0.476245	0.0211299
$509$	−39.7323	−1.76110	−0.880552	−	0.473949i	$-0.842828\pi$
$509$	−39.7323	−1.76110	−0.880552	+	0.473949i	$0.842828\pi$
$510$	3.54313	0.156892
$511$	15.4877	0.685135
$512$	21.4355	0.947325
$513$	−19.3136	−0.852714
$514$	−2.11208	−0.0931596
$515$	6.95088	0.306292
$516$	−68.9132	−3.03373
$517$	0	0
$518$	0.578947	0.0254375
$519$	72.9368	3.20157
$520$	−10.4091	−0.456470
$521$	6.85790	0.300450	0.150225	−	0.988652i	$-0.452000\pi$
$521$	6.85790	0.300450	0.150225	+	0.988652i	$0.452000\pi$
$522$	28.8798	1.26404
$523$	25.1836	1.10120	0.550601	−	0.834769i	$-0.314399\pi$
$523$	25.1836	1.10120	0.550601	+	0.834769i	$0.314399\pi$
$524$	−2.51103	−0.109695
$525$	3.41697	0.149129
$526$	16.3291	0.711985
$527$	18.2966	0.797011
$528$	0	0
$529$	32.8337	1.42755
$530$	−0.593556	−0.0257824
$531$	−8.83055	−0.383213
$532$	1.69297	0.0733994
$533$	31.9084	1.38210
$534$	10.5930	0.458405
$535$	12.9654	0.560544
$536$	0.765703	0.0330733
$537$	−49.1063	−2.11909
$538$	12.4732	0.537760
$539$	0	0
$540$	32.9691	1.41877
$541$	−8.11776	−0.349010	−0.174505	−	0.984656i	$-0.555833\pi$
$541$	−8.11776	−0.349010	−0.174505	+	0.984656i	$0.555833\pi$
$542$	9.13422	0.392348
$543$	−34.0656	−1.46190
$544$	−10.0477	−0.430792
$545$	2.08725	0.0894080
$546$	9.61289	0.411394
$547$	44.6673	1.90983	0.954917	−	0.296872i	$-0.0959435\pi$
$547$	44.6673	1.90983	0.954917	+	0.296872i	$0.0959435\pi$
$548$	−0.584419	−0.0249651
$549$	62.9977	2.68868
$550$	0	0
$551$	6.05237	0.257840
$552$	51.7436	2.20235
$553$	11.9247	0.507089
$554$	9.28920	0.394660
$555$	3.61172	0.153309
$556$	−10.2728	−0.435663
$557$	−28.0404	−1.18811	−0.594055	−	0.804425i	$-0.702474\pi$
$557$	−28.0404	−1.18811	−0.594055	+	0.804425i	$0.702474\pi$
$558$	−45.9262	−1.94421
$559$	−60.9341	−2.57724
$560$	−2.28996	−0.0967684
$561$	0	0
$562$	15.9691	0.673615
$563$	6.35112	0.267668	0.133834	−	0.991004i	$-0.457271\pi$
$563$	6.35112	0.267668	0.133834	+	0.991004i	$0.457271\pi$
$564$	13.7849	0.580447
$565$	−9.61055	−0.404319
$566$	−5.85181	−0.245970
$567$	−40.2406	−1.68995
$568$	−13.0126	−0.545997
$569$	−30.0673	−1.26049	−0.630243	−	0.776398i	$-0.717045\pi$
$569$	−30.0673	−1.26049	−0.630243	+	0.776398i	$0.717045\pi$
$570$	−1.86384	−0.0780677
$571$	−32.6408	−1.36597	−0.682987	−	0.730431i	$-0.739319\pi$
$571$	−32.6408	−1.36597	−0.682987	+	0.730431i	$0.739319\pi$
$572$	0	0
$573$	−35.9760	−1.50292
$574$	−3.40270	−0.142026
$575$	7.47220	0.311612
$576$	−14.5133	−0.604719
$577$	−21.6013	−0.899276	−0.449638	−	0.893211i	$-0.648447\pi$
$577$	−21.6013	−0.899276	−0.449638	+	0.893211i	$0.648447\pi$
$578$	−7.34838	−0.305652
$579$	10.3392	0.429683
$580$	−10.3317	−0.429000
$581$	3.22534	0.133810
$582$	−22.9883	−0.952898
$583$	0	0
$584$	31.3873	1.29881
$585$	44.5606	1.84235
$586$	−6.98206	−0.288426
$587$	39.7625	1.64117	0.820586	−	0.571523i	$-0.193647\pi$
$587$	39.7625	1.64117	0.820586	+	0.571523i	$0.193647\pi$
$588$	5.80883	0.239552
$589$	−9.62479	−0.396583
$590$	−0.557506	−0.0229521
$591$	−44.6781	−1.83781
$592$	−2.42047	−0.0994809
$593$	1.43399	0.0588869	0.0294435	−	0.999566i	$-0.490627\pi$
$593$	1.43399	0.0588869	0.0294435	+	0.999566i	$0.490627\pi$
$594$	0	0
$595$	1.89313	0.0776106
$596$	−17.0358	−0.697812
$597$	−6.78180	−0.277561
$598$	21.0214	0.859628
$599$	−4.61440	−0.188539	−0.0942696	−	0.995547i	$-0.530052\pi$
$599$	−4.61440	−0.188539	−0.0942696	+	0.995547i	$0.530052\pi$
$600$	6.92482	0.282704
$601$	18.5097	0.755026	0.377513	−	0.926004i	$-0.376779\pi$
$601$	18.5097	0.755026	0.377513	+	0.926004i	$0.376779\pi$
$602$	6.49800	0.264839
$603$	−3.27792	−0.133487
$604$	−15.3410	−0.624216
$605$	0	0
$606$	−7.00357	−0.284501
$607$	−15.2719	−0.619869	−0.309935	−	0.950758i	$-0.600307\pi$
$607$	−15.2719	−0.619869	−0.309935	+	0.950758i	$0.600307\pi$
$608$	5.28553	0.214357
$609$	20.7666	0.841506
$610$	3.97728	0.161035
$611$	12.1888	0.493106
$612$	27.9210	1.12864
$613$	43.8947	1.77289	0.886445	−	0.462833i	$-0.153167\pi$
$613$	43.8947	1.77289	0.886445	+	0.462833i	$0.153167\pi$
$614$	−11.2213	−0.452854
$615$	−21.2275	−0.855977
$616$	0	0
$617$	46.4746	1.87100	0.935498	−	0.353332i	$-0.114951\pi$
$617$	46.4746	1.87100	0.935498	+	0.353332i	$0.114951\pi$
$618$	−13.0091	−0.523303
$619$	−14.6272	−0.587918	−0.293959	−	0.955818i	$-0.594973\pi$
$619$	−14.6272	−0.587918	−0.293959	+	0.955818i	$0.594973\pi$
$620$	16.4300	0.659844
$621$	−144.914	−5.81518
$622$	−6.51528	−0.261239
$623$	5.65995	0.226761
$624$	−40.1898	−1.60888
$625$	1.00000	0.0400000
$626$	−4.48620	−0.179305
$627$	0	0
$628$	29.5419	1.17885
$629$	2.00102	0.0797861
$630$	−4.75193	−0.189322
$631$	1.67446	0.0666593	0.0333296	−	0.999444i	$-0.489389\pi$
$631$	1.67446	0.0666593	0.0333296	+	0.999444i	$0.489389\pi$
$632$	24.1665	0.961291
$633$	−29.7021	−1.18055
$634$	−7.85128	−0.311814
$635$	−0.280145	−0.0111172
$636$	−6.29483	−0.249606
$637$	5.13626	0.203506
$638$	0	0
$639$	55.7060	2.20370
$640$	−11.5312	−0.455811
$641$	2.83172	0.111846	0.0559232	−	0.998435i	$-0.482190\pi$
$641$	2.83172	0.111846	0.0559232	+	0.998435i	$0.482190\pi$
$642$	−24.2658	−0.957693
$643$	23.9097	0.942906	0.471453	−	0.881891i	$-0.343730\pi$
$643$	23.9097	0.942906	0.471453	+	0.881891i	$0.343730\pi$
$644$	12.7027	0.500556
$645$	40.5373	1.59616
$646$	−1.03264	−0.0406285
$647$	44.5694	1.75220	0.876102	−	0.482125i	$-0.160135\pi$
$647$	44.5694	1.75220	0.876102	+	0.482125i	$0.160135\pi$
$648$	−81.5515	−3.20364
$649$	0	0
$650$	2.81328	0.110346
$651$	−33.0241	−1.29432
$652$	−8.65220	−0.338846
$653$	31.9181	1.24905	0.624526	−	0.781004i	$-0.285292\pi$
$653$	31.9181	1.24905	0.624526	+	0.781004i	$0.285292\pi$
$654$	−3.90645	−0.152754
$655$	1.47708	0.0577144
$656$	14.2261	0.555436
$657$	−134.366	−5.24214
$658$	−1.29981	−0.0506719
$659$	24.5460	0.956175	0.478087	−	0.878312i	$-0.341330\pi$
$659$	24.5460	0.956175	0.478087	+	0.878312i	$0.341330\pi$
$660$	0	0
$661$	18.5345	0.720907	0.360454	−	0.932777i	$-0.382622\pi$
$661$	18.5345	0.720907	0.360454	+	0.932777i	$0.382622\pi$
$662$	6.76391	0.262887
$663$	33.2252	1.29036
$664$	6.53645	0.253664
$665$	−0.995867	−0.0386181
$666$	−5.02277	−0.194628
$667$	45.4122	1.75837
$668$	−16.5796	−0.641486
$669$	−15.0349	−0.581284
$670$	−0.206947	−0.00799507
$671$	0	0
$672$	18.1355	0.699591
$673$	−43.2084	−1.66556	−0.832781	−	0.553603i	$-0.813253\pi$
$673$	−43.2084	−1.66556	−0.832781	+	0.553603i	$0.813253\pi$
$674$	4.62274	0.178061
$675$	−19.3937	−0.746464
$676$	−22.7478	−0.874915
$677$	3.22240	0.123847	0.0619234	−	0.998081i	$-0.480277\pi$
$677$	3.22240	0.123847	0.0619234	+	0.998081i	$0.480277\pi$
$678$	17.9869	0.690782
$679$	−12.2829	−0.471374
$680$	3.83660	0.147127
$681$	49.6808	1.90377
$682$	0	0
$683$	−9.40205	−0.359759	−0.179880	−	0.983689i	$-0.557571\pi$
$683$	−9.40205	−0.359759	−0.179880	+	0.983689i	$0.557571\pi$
$684$	−14.6877	−0.561597
$685$	0.343777	0.0131351
$686$	−0.547729	−0.0209124
$687$	34.6904	1.32352
$688$	−27.1670	−1.03573
$689$	−5.56598	−0.212047
$690$	−13.9848	−0.532392
$691$	−30.9052	−1.17569	−0.587845	−	0.808974i	$-0.700023\pi$
$691$	−30.9052	−1.17569	−0.587845	+	0.808974i	$0.700023\pi$
$692$	36.2871	1.37943
$693$	0	0
$694$	14.9455	0.567325
$695$	6.04284	0.229218
$696$	42.0855	1.59525
$697$	−11.7608	−0.445473
$698$	16.8602	0.638168
$699$	−5.57213	−0.210757
$700$	1.69999	0.0642537
$701$	26.1787	0.988754	0.494377	−	0.869248i	$-0.335396\pi$
$701$	26.1787	0.988754	0.494377	+	0.869248i	$0.335396\pi$
$702$	−54.5599	−2.05923
$703$	−1.05263	−0.0397006
$704$	0	0
$705$	−8.10878	−0.305394
$706$	−15.0152	−0.565104
$707$	−3.74207	−0.140735
$708$	−5.91251	−0.222206
$709$	26.5618	0.997548	0.498774	−	0.866732i	$-0.333784\pi$
$709$	26.5618	0.997548	0.498774	+	0.866732i	$0.333784\pi$
$710$	3.51693	0.131988
$711$	−103.455	−3.87986
$712$	11.4704	0.429872
$713$	−72.2168	−2.70454
$714$	−3.54313	−0.132598
$715$	0	0
$716$	−24.4311	−0.913033
$717$	55.1411	2.05928
$718$	−0.291216	−0.0108681
$719$	−13.5527	−0.505430	−0.252715	−	0.967541i	$-0.581324\pi$
$719$	−13.5527	−0.505430	−0.252715	+	0.967541i	$0.581324\pi$
$720$	19.8670	0.740399
$721$	−6.95088	−0.258864
$722$	−9.86365	−0.367087
$723$	−46.9217	−1.74504
$724$	−16.9481	−0.629873
$725$	6.07749	0.225712
$726$	0	0
$727$	−35.6076	−1.32061	−0.660307	−	0.750996i	$-0.729574\pi$
$727$	−35.6076	−1.32061	−0.660307	+	0.750996i	$0.729574\pi$
$728$	10.4091	0.385787
$729$	150.312	5.56713
$730$	−8.48306	−0.313972
$731$	22.4592	0.830682
$732$	42.1802	1.55903
$733$	35.5542	1.31322	0.656612	−	0.754228i	$-0.271989\pi$
$733$	35.5542	1.31322	0.656612	+	0.754228i	$0.271989\pi$
$734$	18.9309	0.698753
$735$	−3.41697	−0.126037
$736$	39.6584	1.46183
$737$	0	0
$738$	29.5208	1.08668
$739$	−10.3900	−0.382202	−0.191101	−	0.981570i	$-0.561206\pi$
$739$	−10.3900	−0.382202	−0.191101	+	0.981570i	$0.561206\pi$
$740$	1.79688	0.0660547
$741$	−17.4779	−0.642067
$742$	0.593556	0.0217901
$743$	−4.51799	−0.165749	−0.0828744	−	0.996560i	$-0.526410\pi$
$743$	−4.51799	−0.165749	−0.0828744	+	0.996560i	$0.526410\pi$
$744$	−66.9265	−2.45364
$745$	10.0211	0.367144
$746$	−4.45756	−0.163203
$747$	−27.9821	−1.02381
$748$	0	0
$749$	−12.9654	−0.473746
$750$	−1.87158	−0.0683403
$751$	−33.6555	−1.22811	−0.614053	−	0.789265i	$-0.710462\pi$
$751$	−33.6555	−1.22811	−0.614053	+	0.789265i	$0.710462\pi$
$752$	5.43428	0.198168
$753$	−28.9084	−1.05348
$754$	17.0977	0.622660
$755$	9.02415	0.328422
$756$	−32.9691	−1.19908
$757$	−29.9201	−1.08747	−0.543733	−	0.839258i	$-0.682990\pi$
$757$	−29.9201	−1.08747	−0.543733	+	0.839258i	$0.682990\pi$
$758$	8.71610	0.316583
$759$	0	0
$760$	−2.01822	−0.0732085
$761$	33.6178	1.21865	0.609323	−	0.792922i	$-0.291441\pi$
$761$	33.6178	1.21865	0.609323	+	0.792922i	$0.291441\pi$
$762$	0.524313	0.0189939
$763$	−2.08725	−0.0755635
$764$	−17.8986	−0.647547
$765$	−16.4242	−0.593818
$766$	−2.84071	−0.102639
$767$	−5.22793	−0.188770
$768$	10.1493	0.366231
$769$	9.14233	0.329681	0.164840	−	0.986320i	$-0.447289\pi$
$769$	9.14233	0.329681	0.164840	+	0.986320i	$0.447289\pi$
$770$	0	0
$771$	13.1760	0.474523
$772$	5.14390	0.185133
$773$	13.2812	0.477692	0.238846	−	0.971057i	$-0.423231\pi$
$773$	13.2812	0.477692	0.238846	+	0.971057i	$0.423231\pi$
$774$	−56.3747	−2.02635
$775$	−9.66473	−0.347167
$776$	−24.8924	−0.893586
$777$	−3.61172	−0.129570
$778$	−3.84716	−0.137927
$779$	6.18671	0.221662
$780$	29.8356	1.06829
$781$	0	0
$782$	−7.74808	−0.277071
$783$	−117.865	−4.21215
$784$	2.28996	0.0817843
$785$	−17.3777	−0.620235
$786$	−2.76448	−0.0986056
$787$	4.06389	0.144862	0.0724310	−	0.997373i	$-0.476924\pi$
$787$	4.06389	0.144862	0.0724310	+	0.997373i	$0.476924\pi$
$788$	−22.2280	−0.791839
$789$	−101.868	−3.62661
$790$	−6.53150	−0.232380
$791$	9.61055	0.341712
$792$	0	0
$793$	37.2964	1.32443
$794$	−16.3796	−0.581292
$795$	3.70286	0.131327
$796$	−3.37404	−0.119590
$797$	−33.4979	−1.18656	−0.593278	−	0.804998i	$-0.702166\pi$
$797$	−33.4979	−1.18656	−0.593278	+	0.804998i	$0.702166\pi$
$798$	1.86384	0.0659793
$799$	−4.49256	−0.158935
$800$	5.30747	0.187647
$801$	−49.1040	−1.73500
$802$	1.28677	0.0454373
$803$	0	0
$804$	−2.19473	−0.0774023
$805$	−7.47220	−0.263360
$806$	−27.1896	−0.957712
$807$	−77.8134	−2.73916
$808$	−7.58366	−0.266792
$809$	35.0399	1.23194	0.615969	−	0.787771i	$-0.288765\pi$
$809$	35.0399	1.23194	0.615969	+	0.787771i	$0.288765\pi$
$810$	22.0410	0.774441
$811$	19.7702	0.694226	0.347113	−	0.937823i	$-0.387162\pi$
$811$	19.7702	0.694226	0.347113	+	0.937823i	$0.387162\pi$
$812$	10.3317	0.362571
$813$	−56.9832	−1.99849
$814$	0	0
$815$	5.08955	0.178279
$816$	14.8132	0.518566
$817$	−11.8145	−0.413337
$818$	9.64112	0.337094
$819$	−44.5606	−1.55707
$820$	−10.5610	−0.368806
$821$	19.0535	0.664973	0.332486	−	0.943108i	$-0.392112\pi$
$821$	19.0535	0.664973	0.332486	+	0.943108i	$0.392112\pi$
$822$	−0.643406	−0.0224414
$823$	−32.7006	−1.13987	−0.569936	−	0.821689i	$-0.693032\pi$
$823$	−32.7006	−1.13987	−0.569936	+	0.821689i	$0.693032\pi$
$824$	−14.0866	−0.490731
$825$	0	0
$826$	0.557506	0.0193981
$827$	13.7687	0.478786	0.239393	−	0.970923i	$-0.423052\pi$
$827$	13.7687	0.478786	0.239393	+	0.970923i	$0.423052\pi$
$828$	−110.205	−3.82988
$829$	35.5525	1.23479	0.617394	−	0.786654i	$-0.288188\pi$
$829$	35.5525	1.23479	0.617394	+	0.786654i	$0.288188\pi$
$830$	−1.76661	−0.0613200
$831$	−57.9501	−2.01027
$832$	−8.59225	−0.297883
$833$	−1.89313	−0.0655929
$834$	−11.3096	−0.391621
$835$	9.75278	0.337509
$836$	0	0
$837$	187.435	6.47870
$838$	−17.6513	−0.609754
$839$	−27.9612	−0.965328	−0.482664	−	0.875806i	$-0.660331\pi$
$839$	−27.9612	−0.965328	−0.482664	+	0.875806i	$0.660331\pi$
$840$	−6.92482	−0.238929
$841$	7.93589	0.273651
$842$	8.97947	0.309453
$843$	−99.6220	−3.43116
$844$	−14.7772	−0.508653
$845$	13.3811	0.460324
$846$	11.2768	0.387703
$847$	0	0
$848$	−2.48155	−0.0852168
$849$	36.5061	1.25289
$850$	−1.03692	−0.0355661
$851$	−7.89807	−0.270742
$852$	37.2981	1.27781
$853$	27.6775	0.947659	0.473829	−	0.880617i	$-0.342871\pi$
$853$	27.6775	0.947659	0.473829	+	0.880617i	$0.342871\pi$
$854$	−3.97728	−0.136100
$855$	8.63984	0.295476
$856$	−26.2756	−0.898083
$857$	−9.26699	−0.316554	−0.158277	−	0.987395i	$-0.550594\pi$
$857$	−9.26699	−0.316554	−0.158277	+	0.987395i	$0.550594\pi$
$858$	0	0
$859$	−17.7659	−0.606165	−0.303083	−	0.952964i	$-0.598016\pi$
$859$	−17.7659	−0.606165	−0.303083	+	0.952964i	$0.598016\pi$
$860$	20.1679	0.687720
$861$	21.2275	0.723432
$862$	9.70969	0.330714
$863$	−56.8973	−1.93681	−0.968403	−	0.249392i	$-0.919769\pi$
$863$	−56.8973	−1.93681	−0.968403	+	0.249392i	$0.919769\pi$
$864$	−102.931	−3.50180
$865$	−21.3455	−0.725767
$866$	1.18553	0.0402858
$867$	45.8423	1.55689
$868$	−16.4300	−0.557670
$869$	0	0
$870$	−11.3745	−0.385631
$871$	−1.94062	−0.0657553
$872$	−4.23001	−0.143246
$873$	106.563	3.60660
$874$	4.07583	0.137867
$875$	−1.00000	−0.0338062
$876$	−89.9653	−3.03965
$877$	8.65101	0.292124	0.146062	−	0.989275i	$-0.453340\pi$
$877$	8.65101	0.292124	0.146062	+	0.989275i	$0.453340\pi$
$878$	−11.3081	−0.381629
$879$	43.5571	1.46915
$880$	0	0
$881$	32.7680	1.10398	0.551990	−	0.833851i	$-0.313869\pi$
$881$	32.7680	1.10398	0.551990	+	0.833851i	$0.313869\pi$
$882$	4.75193	0.160006
$883$	11.6739	0.392858	0.196429	−	0.980518i	$-0.437065\pi$
$883$	11.6739	0.392858	0.196429	+	0.980518i	$0.437065\pi$
$884$	16.5300	0.555965
$885$	3.47796	0.116910
$886$	8.85573	0.297514
$887$	−1.68583	−0.0566046	−0.0283023	−	0.999599i	$-0.509010\pi$
$887$	−1.68583	−0.0566046	−0.0283023	+	0.999599i	$0.509010\pi$
$888$	−7.31949	−0.245626
$889$	0.280145	0.00939577
$890$	−3.10012	−0.103916
$891$	0	0
$892$	−7.48010	−0.250452
$893$	2.36328	0.0790842
$894$	−18.7552	−0.627268
$895$	14.3713	0.480380
$896$	11.5312	0.385231
$897$	−131.140	−4.37865
$898$	−2.81799	−0.0940374
$899$	−58.7373	−1.95900
$900$	−14.7486	−0.491621
$901$	2.05152	0.0683459
$902$	0	0
$903$	−40.5373	−1.34900
$904$	19.4767	0.647785
$905$	9.96954	0.331399
$906$	−16.8894	−0.561112
$907$	−5.39591	−0.179168	−0.0895842	−	0.995979i	$-0.528554\pi$
$907$	−5.39591	−0.179168	−0.0895842	+	0.995979i	$0.528554\pi$
$908$	24.7169	0.820259
$909$	32.4651	1.07680
$910$	−2.81328	−0.0932593
$911$	−13.2051	−0.437504	−0.218752	−	0.975781i	$-0.570199\pi$
$911$	−13.2051	−0.437504	−0.218752	+	0.975781i	$0.570199\pi$
$912$	−7.79239	−0.258032
$913$	0	0
$914$	9.03200	0.298752
$915$	−24.8120	−0.820260
$916$	17.2589	0.570252
$917$	−1.47708	−0.0487776
$918$	20.1097	0.663720
$919$	38.0294	1.25448	0.627238	−	0.778828i	$-0.284185\pi$
$919$	38.0294	1.25448	0.627238	+	0.778828i	$0.284185\pi$
$920$	−15.1431	−0.499254
$921$	70.0032	2.30668
$922$	−0.488528	−0.0160888
$923$	32.9795	1.08553
$924$	0	0
$925$	−1.05699	−0.0347538
$926$	−2.97162	−0.0976535
$927$	60.3037	1.98063
$928$	32.2561	1.05886
$929$	−41.2258	−1.35257	−0.676287	−	0.736638i	$-0.736412\pi$
$929$	−41.2258	−1.35257	−0.676287	+	0.736638i	$0.736412\pi$
$930$	18.0883	0.593138
$931$	0.995867	0.0326382
$932$	−2.77222	−0.0908069
$933$	40.6451	1.33066
$934$	11.1760	0.365691
$935$	0	0
$936$	−90.3063	−2.95175
$937$	37.3182	1.21913	0.609566	−	0.792736i	$-0.291344\pi$
$937$	37.3182	1.21913	0.609566	+	0.792736i	$0.291344\pi$
$938$	0.206947	0.00675707
$939$	27.9869	0.913317
$940$	−4.03423	−0.131582
$941$	39.5979	1.29085	0.645427	−	0.763822i	$-0.276680\pi$
$941$	39.5979	1.29085	0.645427	+	0.763822i	$0.276680\pi$
$942$	32.5236	1.05968
$943$	46.4201	1.51165
$944$	−2.33083	−0.0758621
$945$	19.3937	0.630877
$946$	0	0
$947$	−39.6182	−1.28742	−0.643710	−	0.765270i	$-0.722605\pi$
$947$	−39.6182	−1.28742	−0.643710	+	0.765270i	$0.722605\pi$
$948$	−69.2684	−2.24973
$949$	−79.5487	−2.58226
$950$	0.545466	0.0176972
$951$	48.9797	1.58827
$952$	−3.83660	−0.124345
$953$	48.2126	1.56176	0.780879	−	0.624682i	$-0.214772\pi$
$953$	48.2126	1.56176	0.780879	+	0.624682i	$0.214772\pi$
$954$	−5.14951	−0.166722
$955$	10.5286	0.340698
$956$	27.4335	0.887263
$957$	0	0
$958$	−15.2405	−0.492397
$959$	−0.343777	−0.0111012
$960$	5.71612	0.184487
$961$	62.4070	2.01313
$962$	−2.97362	−0.0958734
$963$	112.484	3.62475
$964$	−23.3442	−0.751867
$965$	−3.02584	−0.0974052
$966$	13.9848	0.449953
$967$	26.0410	0.837421	0.418710	−	0.908120i	$-0.362482\pi$
$967$	26.0410	0.837421	0.418710	+	0.908120i	$0.362482\pi$
$968$	0	0
$969$	6.44203	0.206948
$970$	6.72770	0.216013
$971$	−12.9452	−0.415433	−0.207716	−	0.978189i	$-0.566603\pi$
$971$	−12.9452	−0.415433	−0.207716	+	0.978189i	$0.566603\pi$
$972$	134.843	4.32511
$973$	−6.04284	−0.193725
$974$	−13.3229	−0.426892
$975$	−17.5504	−0.562064
$976$	16.6283	0.532259
$977$	46.1868	1.47765	0.738823	−	0.673899i	$-0.235382\pi$
$977$	46.1868	1.47765	0.738823	+	0.673899i	$0.235382\pi$
$978$	−9.52549	−0.304591
$979$	0	0
$980$	−1.69999	−0.0543043
$981$	18.1083	0.578155
$982$	18.9124	0.603519
$983$	21.5777	0.688223	0.344111	−	0.938929i	$-0.388180\pi$
$983$	21.5777	0.688223	0.344111	+	0.938929i	$0.388180\pi$
$984$	43.0196	1.37141
$985$	13.0753	0.416615
$986$	−6.30188	−0.200693
$987$	8.10878	0.258105
$988$	−8.69551	−0.276641
$989$	−88.6466	−2.81880
$990$	0	0
$991$	−41.6240	−1.32223	−0.661115	−	0.750285i	$-0.729916\pi$
$991$	−41.6240	−1.32223	−0.661115	+	0.750285i	$0.729916\pi$
$992$	−51.2953	−1.62863
$993$	−42.1962	−1.33906
$994$	−3.51693	−0.111550
$995$	1.98474	0.0629205
$996$	−18.7354	−0.593655
$997$	8.11693	0.257066	0.128533	−	0.991705i	$-0.458973\pi$
$997$	8.11693	0.257066	0.128533	+	0.991705i	$0.458973\pi$
$998$	13.6337	0.431568
$999$	20.4990	0.648561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bk.1.6	yes	10
11.10	odd	2		4235.2.a.bi.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bi.1.5	✓	10	11.10	odd	2
4235.2.a.bk.1.6	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+0.547729 q^{2} -3.41697 q^{3} -1.69999 q^{4} +1.00000 q^{5} -1.87158 q^{6} -1.00000 q^{7} -2.02659 q^{8} +8.67570 q^{9} +O(q^{10})\)	\(q+0.547729 q^{2} -3.41697 q^{3} -1.69999 q^{4} +1.00000 q^{5} -1.87158 q^{6} -1.00000 q^{7} -2.02659 q^{8} +8.67570 q^{9} +0.547729 q^{10} +5.80883 q^{12} +5.13626 q^{13} -0.547729 q^{14} -3.41697 q^{15} +2.28996 q^{16} -1.89313 q^{17} +4.75193 q^{18} +0.995867 q^{19} -1.69999 q^{20} +3.41697 q^{21} +7.47220 q^{23} +6.92482 q^{24} +1.00000 q^{25} +2.81328 q^{26} -19.3937 q^{27} +1.69999 q^{28} +6.07749 q^{29} -1.87158 q^{30} -9.66473 q^{31} +5.30747 q^{32} -1.03692 q^{34} -1.00000 q^{35} -14.7486 q^{36} -1.05699 q^{37} +0.545466 q^{38} -17.5504 q^{39} -2.02659 q^{40} +6.21238 q^{41} +1.87158 q^{42} -11.8635 q^{43} +8.67570 q^{45} +4.09274 q^{46} +2.37309 q^{47} -7.82473 q^{48} +1.00000 q^{49} +0.547729 q^{50} +6.46876 q^{51} -8.73160 q^{52} -1.08367 q^{53} -10.6225 q^{54} +2.02659 q^{56} -3.40285 q^{57} +3.32882 q^{58} -1.01785 q^{59} +5.80883 q^{60} +7.26140 q^{61} -5.29366 q^{62} -8.67570 q^{63} -1.67286 q^{64} +5.13626 q^{65} -0.377827 q^{67} +3.21830 q^{68} -25.5323 q^{69} -0.547729 q^{70} +6.42093 q^{71} -17.5821 q^{72} -15.4877 q^{73} -0.578947 q^{74} -3.41697 q^{75} -1.69297 q^{76} -9.61289 q^{78} -11.9247 q^{79} +2.28996 q^{80} +40.2406 q^{81} +3.40270 q^{82} -3.22534 q^{83} -5.80883 q^{84} -1.89313 q^{85} -6.49800 q^{86} -20.7666 q^{87} -5.65995 q^{89} +4.75193 q^{90} -5.13626 q^{91} -12.7027 q^{92} +33.0241 q^{93} +1.29981 q^{94} +0.995867 q^{95} -18.1355 q^{96} +12.2829 q^{97} +0.547729 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9} + 2 q^{10} - 4 q^{12} + 18 q^{13} - 2 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} + 12 q^{18} + 14 q^{19} + 12 q^{20} + 4 q^{21} - 4 q^{23} + 46 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{27} - 12 q^{28} + 36 q^{29} + 8 q^{30} - 18 q^{31} + 4 q^{32} - 32 q^{34} - 10 q^{35} + 22 q^{36} + 4 q^{37} + 18 q^{38} + 6 q^{40} + 38 q^{41} - 8 q^{42} + 6 q^{43} + 14 q^{45} + 28 q^{46} - 18 q^{47} + 16 q^{48} + 10 q^{49} + 2 q^{50} - 4 q^{51} + 26 q^{52} - 26 q^{53} + 2 q^{54} - 6 q^{56} + 22 q^{57} + 10 q^{58} - 14 q^{59} - 4 q^{60} + 60 q^{61} + 22 q^{62} - 14 q^{63} + 18 q^{65} - 10 q^{67} + 2 q^{68} - 8 q^{69} - 2 q^{70} - 54 q^{72} + 18 q^{73} - 20 q^{74} - 4 q^{75} + 38 q^{76} + 40 q^{78} + 40 q^{79} + 4 q^{80} + 18 q^{81} - 36 q^{82} + 2 q^{83} + 4 q^{84} + 4 q^{85} + 42 q^{86} - 32 q^{87} + 2 q^{89} + 12 q^{90} - 18 q^{91} - 64 q^{92} + 26 q^{93} - 68 q^{94} + 14 q^{95} + 28 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9 + 2 * q^10 - 4 * q^12 + 18 * q^13 - 2 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 + 12 * q^18 + 14 * q^19 + 12 * q^20 + 4 * q^21 - 4 * q^23 + 46 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^27 - 12 * q^28 + 36 * q^29 + 8 * q^30 - 18 * q^31 + 4 * q^32 - 32 * q^34 - 10 * q^35 + 22 * q^36 + 4 * q^37 + 18 * q^38 + 6 * q^40 + 38 * q^41 - 8 * q^42 + 6 * q^43 + 14 * q^45 + 28 * q^46 - 18 * q^47 + 16 * q^48 + 10 * q^49 + 2 * q^50 - 4 * q^51 + 26 * q^52 - 26 * q^53 + 2 * q^54 - 6 * q^56 + 22 * q^57 + 10 * q^58 - 14 * q^59 - 4 * q^60 + 60 * q^61 + 22 * q^62 - 14 * q^63 + 18 * q^65 - 10 * q^67 + 2 * q^68 - 8 * q^69 - 2 * q^70 - 54 * q^72 + 18 * q^73 - 20 * q^74 - 4 * q^75 + 38 * q^76 + 40 * q^78 + 40 * q^79 + 4 * q^80 + 18 * q^81 - 36 * q^82 + 2 * q^83 + 4 * q^84 + 4 * q^85 + 42 * q^86 - 32 * q^87 + 2 * q^89 + 12 * q^90 - 18 * q^91 - 64 * q^92 + 26 * q^93 - 68 * q^94 + 14 * q^95 + 28 * q^96 + 8 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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