LMFDB - Embedded newform 4235.2.a.bp.1.17

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
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			1.17
Root			$2.56132$ 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)

$f(q)$	$=$	$q+2.56132 q^{2} +0.468192 q^{3} +4.56034 q^{4} +1.00000 q^{5} +1.19919 q^{6} +1.00000 q^{7} +6.55784 q^{8} -2.78080 q^{9} +O(q^{10})$	\(q+2.56132 q^{2} +0.468192 q^{3} +4.56034 q^{4} +1.00000 q^{5} +1.19919 q^{6} +1.00000 q^{7} +6.55784 q^{8} -2.78080 q^{9} +2.56132 q^{10} +2.13511 q^{12} +1.09399 q^{13} +2.56132 q^{14} +0.468192 q^{15} +7.67602 q^{16} +3.24351 q^{17} -7.12250 q^{18} -4.11553 q^{19} +4.56034 q^{20} +0.468192 q^{21} +2.76115 q^{23} +3.07033 q^{24} +1.00000 q^{25} +2.80206 q^{26} -2.70652 q^{27} +4.56034 q^{28} +6.26280 q^{29} +1.19919 q^{30} +10.0214 q^{31} +6.54503 q^{32} +8.30767 q^{34} +1.00000 q^{35} -12.6814 q^{36} +2.42875 q^{37} -10.5412 q^{38} +0.512198 q^{39} +6.55784 q^{40} -2.65676 q^{41} +1.19919 q^{42} +9.02844 q^{43} -2.78080 q^{45} +7.07217 q^{46} +1.81011 q^{47} +3.59385 q^{48} +1.00000 q^{49} +2.56132 q^{50} +1.51859 q^{51} +4.98897 q^{52} -8.87813 q^{53} -6.93226 q^{54} +6.55784 q^{56} -1.92686 q^{57} +16.0410 q^{58} +10.0983 q^{59} +2.13511 q^{60} +6.35550 q^{61} +25.6681 q^{62} -2.78080 q^{63} +1.41185 q^{64} +1.09399 q^{65} -10.6241 q^{67} +14.7915 q^{68} +1.29275 q^{69} +2.56132 q^{70} -11.1960 q^{71} -18.2360 q^{72} -5.47060 q^{73} +6.22081 q^{74} +0.468192 q^{75} -18.7682 q^{76} +1.31190 q^{78} +0.816299 q^{79} +7.67602 q^{80} +7.07522 q^{81} -6.80481 q^{82} -13.7794 q^{83} +2.13511 q^{84} +3.24351 q^{85} +23.1247 q^{86} +2.93219 q^{87} -9.95526 q^{89} -7.12250 q^{90} +1.09399 q^{91} +12.5918 q^{92} +4.69196 q^{93} +4.63625 q^{94} -4.11553 q^{95} +3.06433 q^{96} +15.8019 q^{97} +2.56132 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * 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 $

$2$	2.56132	1.81112	0.905562	−	0.424214i	$-0.139450\pi$
$2$	2.56132	1.81112	0.905562	+	0.424214i	$0.139450\pi$
$3$	0.468192	0.270311	0.135155	−	0.990824i	$-0.456847\pi$
$3$	0.468192	0.270311	0.135155	+	0.990824i	$0.456847\pi$
$4$	4.56034	2.28017
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.19919	0.489566
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	6.55784	2.31855
$9$	−2.78080	−0.926932
$10$	2.56132	0.809959
$11$	0	0
$11$	0	0
$12$	2.13511	0.616355
$13$	1.09399	0.303419	0.151709	−	0.988425i	$-0.451522\pi$
$13$	1.09399	0.303419	0.151709	+	0.988425i	$0.451522\pi$
$14$	2.56132	0.684540
$15$	0.468192	0.120887
$16$	7.67602	1.91900
$17$	3.24351	0.786668	0.393334	−	0.919396i	$-0.371322\pi$
$17$	3.24351	0.786668	0.393334	+	0.919396i	$0.371322\pi$
$18$	−7.12250	−1.67879
$19$	−4.11553	−0.944166	−0.472083	−	0.881554i	$-0.656498\pi$
$19$	−4.11553	−0.944166	−0.472083	+	0.881554i	$0.656498\pi$
$20$	4.56034	1.01972
$21$	0.468192	0.102168
$22$	0	0
$23$	2.76115	0.575739	0.287870	−	0.957670i	$-0.407053\pi$
$23$	2.76115	0.575739	0.287870	+	0.957670i	$0.407053\pi$
$24$	3.07033	0.626728
$25$	1.00000	0.200000
$26$	2.80206	0.549529
$27$	−2.70652	−0.520871
$28$	4.56034	0.861823
$29$	6.26280	1.16297	0.581486	−	0.813556i	$-0.302471\pi$
$29$	6.26280	1.16297	0.581486	+	0.813556i	$0.302471\pi$
$30$	1.19919	0.218941
$31$	10.0214	1.79990	0.899952	−	0.435989i	$-0.143602\pi$
$31$	10.0214	1.79990	0.899952	+	0.435989i	$0.143602\pi$
$32$	6.54503	1.15701
$33$	0	0
$34$	8.30767	1.42475
$35$	1.00000	0.169031
$36$	−12.6814	−2.11356
$37$	2.42875	0.399285	0.199642	−	0.979869i	$-0.436022\pi$
$37$	2.42875	0.399285	0.199642	+	0.979869i	$0.436022\pi$
$38$	−10.5412	−1.71000
$39$	0.512198	0.0820173
$40$	6.55784	1.03689
$41$	−2.65676	−0.414917	−0.207458	−	0.978244i	$-0.566519\pi$
$41$	−2.65676	−0.414917	−0.207458	+	0.978244i	$0.566519\pi$
$42$	1.19919	0.185039
$43$	9.02844	1.37682	0.688412	−	0.725320i	$-0.258308\pi$
$43$	9.02844	1.37682	0.688412	+	0.725320i	$0.258308\pi$
$44$	0	0
$45$	−2.78080	−0.414537
$46$	7.07217	1.04274
$47$	1.81011	0.264031	0.132016	−	0.991248i	$-0.457855\pi$
$47$	1.81011	0.264031	0.132016	+	0.991248i	$0.457855\pi$
$48$	3.59385	0.518728
$49$	1.00000	0.142857
$50$	2.56132	0.362225
$51$	1.51859	0.212645
$52$	4.98897	0.691846
$53$	−8.87813	−1.21951	−0.609753	−	0.792592i	$-0.708731\pi$
$53$	−8.87813	−1.21951	−0.609753	+	0.792592i	$0.708731\pi$
$54$	−6.93226	−0.943361
$55$	0	0
$56$	6.55784	0.876328
$57$	−1.92686	−0.255218
$58$	16.0410	2.10629
$59$	10.0983	1.31468	0.657342	−	0.753592i	$-0.271681\pi$
$59$	10.0983	1.31468	0.657342	+	0.753592i	$0.271681\pi$
$60$	2.13511	0.275642
$61$	6.35550	0.813739	0.406869	−	0.913486i	$-0.366620\pi$
$61$	6.35550	0.813739	0.406869	+	0.913486i	$0.366620\pi$
$62$	25.6681	3.25985
$63$	−2.78080	−0.350347
$64$	1.41185	0.176482
$65$	1.09399	0.135693
$66$	0	0
$67$	−10.6241	−1.29794	−0.648969	−	0.760815i	$-0.724799\pi$
$67$	−10.6241	−1.29794	−0.648969	+	0.760815i	$0.724799\pi$
$68$	14.7915	1.79374
$69$	1.29275	0.155629
$70$	2.56132	0.306136
$71$	−11.1960	−1.32872	−0.664359	−	0.747414i	$-0.731295\pi$
$71$	−11.1960	−1.32872	−0.664359	+	0.747414i	$0.731295\pi$
$72$	−18.2360	−2.14913
$73$	−5.47060	−0.640286	−0.320143	−	0.947369i	$-0.603731\pi$
$73$	−5.47060	−0.640286	−0.320143	+	0.947369i	$0.603731\pi$
$74$	6.22081	0.723154
$75$	0.468192	0.0540622
$76$	−18.7682	−2.15286
$77$	0	0
$78$	1.31190	0.148544
$79$	0.816299	0.0918408	0.0459204	−	0.998945i	$-0.485378\pi$
$79$	0.816299	0.0918408	0.0459204	+	0.998945i	$0.485378\pi$
$80$	7.67602	0.858205
$81$	7.07522	0.786135
$82$	−6.80481	−0.751465
$83$	−13.7794	−1.51249	−0.756243	−	0.654291i	$-0.772967\pi$
$83$	−13.7794	−1.51249	−0.756243	+	0.654291i	$0.772967\pi$
$84$	2.13511	0.232960
$85$	3.24351	0.351809
$86$	23.1247	2.49360
$87$	2.93219	0.314364
$88$	0	0
$89$	−9.95526	−1.05526	−0.527628	−	0.849476i	$-0.676918\pi$
$89$	−9.95526	−1.05526	−0.527628	+	0.849476i	$0.676918\pi$
$90$	−7.12250	−0.750777
$91$	1.09399	0.114681
$92$	12.5918	1.31278
$93$	4.69196	0.486533
$94$	4.63625	0.478193
$95$	−4.11553	−0.422244
$96$	3.06433	0.312752
$97$	15.8019	1.60444	0.802221	−	0.597027i	$-0.203652\pi$
$97$	15.8019	1.60444	0.802221	+	0.597027i	$0.203652\pi$
$98$	2.56132	0.258732
$99$	0	0
$100$	4.56034	0.456034
$101$	−10.1649	−1.01144	−0.505722	−	0.862696i	$-0.668774\pi$
$101$	−10.1649	−1.01144	−0.505722	+	0.862696i	$0.668774\pi$
$102$	3.88958	0.385126
$103$	5.72529	0.564129	0.282065	−	0.959395i	$-0.408981\pi$
$103$	5.72529	0.564129	0.282065	+	0.959395i	$0.408981\pi$
$104$	7.17422	0.703490
$105$	0.468192	0.0456909
$106$	−22.7397	−2.20867
$107$	3.41406	0.330049	0.165025	−	0.986289i	$-0.447230\pi$
$107$	3.41406	0.330049	0.165025	+	0.986289i	$0.447230\pi$
$108$	−12.3427	−1.18767
$109$	−10.8623	−1.04042	−0.520211	−	0.854038i	$-0.674147\pi$
$109$	−10.8623	−1.04042	−0.520211	+	0.854038i	$0.674147\pi$
$110$	0	0
$111$	1.13712	0.107931
$112$	7.67602	0.725315
$113$	−10.6319	−1.00016	−0.500082	−	0.865978i	$-0.666697\pi$
$113$	−10.6319	−1.00016	−0.500082	+	0.865978i	$0.666697\pi$
$114$	−4.93529	−0.462232
$115$	2.76115	0.257478
$116$	28.5605	2.65177
$117$	−3.04217	−0.281248
$118$	25.8649	2.38106
$119$	3.24351	0.297332
$120$	3.07033	0.280281
$121$	0	0
$122$	16.2784	1.47378
$123$	−1.24387	−0.112156
$124$	45.7012	4.10409
$125$	1.00000	0.0894427
$126$	−7.12250	−0.634523
$127$	−7.62363	−0.676488	−0.338244	−	0.941059i	$-0.609833\pi$
$127$	−7.62363	−0.676488	−0.338244	+	0.941059i	$0.609833\pi$
$128$	−9.47386	−0.837379
$129$	4.22704	0.372170
$130$	2.80206	0.245757
$131$	−13.5644	−1.18513	−0.592564	−	0.805523i	$-0.701884\pi$
$131$	−13.5644	−1.18513	−0.592564	+	0.805523i	$0.701884\pi$
$132$	0	0
$133$	−4.11553	−0.356861
$134$	−27.2116	−2.35073
$135$	−2.70652	−0.232940
$136$	21.2704	1.82393
$137$	−11.4166	−0.975386	−0.487693	−	0.873015i	$-0.662161\pi$
$137$	−11.4166	−0.975386	−0.487693	+	0.873015i	$0.662161\pi$
$138$	3.31114	0.281863
$139$	−13.6961	−1.16169	−0.580845	−	0.814014i	$-0.697278\pi$
$139$	−13.6961	−1.16169	−0.580845	+	0.814014i	$0.697278\pi$
$140$	4.56034	0.385419
$141$	0.847477	0.0713705
$142$	−28.6764	−2.40647
$143$	0	0
$144$	−21.3454	−1.77879
$145$	6.26280	0.520097
$146$	−14.0119	−1.15964
$147$	0.468192	0.0386158
$148$	11.0759	0.910437
$149$	−9.09559	−0.745140	−0.372570	−	0.928004i	$-0.621523\pi$
$149$	−9.09559	−0.745140	−0.372570	+	0.928004i	$0.621523\pi$
$150$	1.19919	0.0979133
$151$	−20.6250	−1.67844	−0.839219	−	0.543794i	$-0.816987\pi$
$151$	−20.6250	−1.67844	−0.839219	+	0.543794i	$0.816987\pi$
$152$	−26.9890	−2.18909
$153$	−9.01955	−0.729188
$154$	0	0
$155$	10.0214	0.804941
$156$	2.33580	0.187013
$157$	−11.0505	−0.881924	−0.440962	−	0.897526i	$-0.645363\pi$
$157$	−11.0505	−0.881924	−0.440962	+	0.897526i	$0.645363\pi$
$158$	2.09080	0.166335
$159$	−4.15667	−0.329645
$160$	6.54503	0.517430
$161$	2.76115	0.217609
$162$	18.1219	1.42379
$163$	16.0769	1.25924	0.629620	−	0.776903i	$-0.283211\pi$
$163$	16.0769	1.25924	0.629620	+	0.776903i	$0.283211\pi$
$164$	−12.1157	−0.946080
$165$	0	0
$166$	−35.2934	−2.73930
$167$	5.25859	0.406922	0.203461	−	0.979083i	$-0.434781\pi$
$167$	5.25859	0.406922	0.203461	+	0.979083i	$0.434781\pi$
$168$	3.07033	0.236881
$169$	−11.8032	−0.907937
$170$	8.30767	0.637169
$171$	11.4444	0.875178
$172$	41.1727	3.13939
$173$	10.2315	0.777885	0.388942	−	0.921262i	$-0.372841\pi$
$173$	10.2315	0.777885	0.388942	+	0.921262i	$0.372841\pi$
$174$	7.51027	0.569352
$175$	1.00000	0.0755929
$176$	0	0
$177$	4.72794	0.355373
$178$	−25.4986	−1.91120
$179$	−9.80323	−0.732728	−0.366364	−	0.930472i	$-0.619397\pi$
$179$	−9.80323	−0.732728	−0.366364	+	0.930472i	$0.619397\pi$
$180$	−12.6814	−0.945214
$181$	20.2625	1.50610	0.753050	−	0.657964i	$-0.228582\pi$
$181$	20.2625	1.50610	0.753050	+	0.657964i	$0.228582\pi$
$182$	2.80206	0.207702
$183$	2.97560	0.219962
$184$	18.1072	1.33488
$185$	2.42875	0.178566
$186$	12.0176	0.881172
$187$	0	0
$188$	8.25470	0.602036
$189$	−2.70652	−0.196871
$190$	−10.5412	−0.764736
$191$	14.5233	1.05087	0.525436	−	0.850833i	$-0.323902\pi$
$191$	14.5233	1.05087	0.525436	+	0.850833i	$0.323902\pi$
$192$	0.661018	0.0477049
$193$	−1.51101	−0.108765	−0.0543825	−	0.998520i	$-0.517319\pi$
$193$	−1.51101	−0.108765	−0.0543825	+	0.998520i	$0.517319\pi$
$194$	40.4737	2.90584
$195$	0.512198	0.0366793
$196$	4.56034	0.325739
$197$	−1.84166	−0.131213	−0.0656065	−	0.997846i	$-0.520898\pi$
$197$	−1.84166	−0.131213	−0.0656065	+	0.997846i	$0.520898\pi$
$198$	0	0
$199$	−26.2531	−1.86103	−0.930516	−	0.366251i	$-0.880641\pi$
$199$	−26.2531	−1.86103	−0.930516	+	0.366251i	$0.880641\pi$
$200$	6.55784	0.463709
$201$	−4.97411	−0.350847
$202$	−26.0355	−1.83185
$203$	6.26280	0.439562
$204$	6.92528	0.484866
$205$	−2.65676	−0.185556
$206$	14.6643	1.02171
$207$	−7.67819	−0.533671
$208$	8.39750	0.582262
$209$	0	0
$210$	1.19919	0.0827518
$211$	−24.1835	−1.66486	−0.832429	−	0.554131i	$-0.813050\pi$
$211$	−24.1835	−1.66486	−0.832429	+	0.554131i	$0.813050\pi$
$212$	−40.4873	−2.78068
$213$	−5.24186	−0.359167
$214$	8.74448	0.597760
$215$	9.02844	0.615734
$216$	−17.7489	−1.20766
$217$	10.0214	0.680300
$218$	−27.8218	−1.88433
$219$	−2.56129	−0.173076
$220$	0	0
$221$	3.54838	0.238690
$222$	2.91253	0.195476
$223$	9.87122	0.661026	0.330513	−	0.943802i	$-0.392778\pi$
$223$	9.87122	0.661026	0.330513	+	0.943802i	$0.392778\pi$
$224$	6.54503	0.437308
$225$	−2.78080	−0.185386
$226$	−27.2316	−1.81142
$227$	26.6666	1.76993	0.884963	−	0.465661i	$-0.154183\pi$
$227$	26.6666	1.76993	0.884963	+	0.465661i	$0.154183\pi$
$228$	−8.78712	−0.581941
$229$	0.996216	0.0658318	0.0329159	−	0.999458i	$-0.489521\pi$
$229$	0.996216	0.0658318	0.0329159	+	0.999458i	$0.489521\pi$
$230$	7.07217	0.466325
$231$	0	0
$232$	41.0704	2.69641
$233$	19.1071	1.25175	0.625875	−	0.779923i	$-0.284742\pi$
$233$	19.1071	1.25175	0.625875	+	0.779923i	$0.284742\pi$
$234$	−7.79195	−0.509376
$235$	1.81011	0.118078
$236$	46.0516	2.99770
$237$	0.382185	0.0248256
$238$	8.30767	0.538506
$239$	−21.8461	−1.41311	−0.706553	−	0.707660i	$-0.749751\pi$
$239$	−21.8461	−1.41311	−0.706553	+	0.707660i	$0.749751\pi$
$240$	3.59385	0.231982
$241$	−7.20107	−0.463862	−0.231931	−	0.972732i	$-0.574504\pi$
$241$	−7.20107	−0.463862	−0.231931	+	0.972732i	$0.574504\pi$
$242$	0	0
$243$	11.4321	0.733371
$244$	28.9832	1.85546
$245$	1.00000	0.0638877
$246$	−3.18596	−0.203129
$247$	−4.50235	−0.286478
$248$	65.7190	4.17316
$249$	−6.45140	−0.408841
$250$	2.56132	0.161992
$251$	26.6033	1.67919	0.839593	−	0.543217i	$-0.182794\pi$
$251$	26.6033	1.67919	0.839593	+	0.543217i	$0.182794\pi$
$252$	−12.6814	−0.798852
$253$	0	0
$254$	−19.5265	−1.22520
$255$	1.51859	0.0950977
$256$	−27.0892	−1.69308
$257$	22.2475	1.38776	0.693880	−	0.720091i	$-0.255900\pi$
$257$	22.2475	1.38776	0.693880	+	0.720091i	$0.255900\pi$
$258$	10.8268	0.674047
$259$	2.42875	0.150915
$260$	4.98897	0.309403
$261$	−17.4156	−1.07800
$262$	−34.7428	−2.14641
$263$	−11.6805	−0.720252	−0.360126	−	0.932904i	$-0.617266\pi$
$263$	−11.6805	−0.720252	−0.360126	+	0.932904i	$0.617266\pi$
$264$	0	0
$265$	−8.87813	−0.545379
$266$	−10.5412	−0.646320
$267$	−4.66097	−0.285247
$268$	−48.4494	−2.95952
$269$	−8.61863	−0.525487	−0.262744	−	0.964866i	$-0.584627\pi$
$269$	−8.61863	−0.525487	−0.262744	+	0.964866i	$0.584627\pi$
$270$	−6.93226	−0.421884
$271$	−3.36127	−0.204182	−0.102091	−	0.994775i	$-0.532553\pi$
$271$	−3.36127	−0.204182	−0.102091	+	0.994775i	$0.532553\pi$
$272$	24.8973	1.50962
$273$	0.512198	0.0309996
$274$	−29.2415	−1.76655
$275$	0	0
$276$	5.89537	0.354860
$277$	15.8943	0.954995	0.477498	−	0.878633i	$-0.341544\pi$
$277$	15.8943	0.954995	0.477498	+	0.878633i	$0.341544\pi$
$278$	−35.0801	−2.10396
$279$	−27.8676	−1.66839
$280$	6.55784	0.391906
$281$	20.0346	1.19516	0.597582	−	0.801808i	$-0.296128\pi$
$281$	20.0346	1.19516	0.597582	+	0.801808i	$0.296128\pi$
$282$	2.17066	0.129261
$283$	3.38591	0.201271	0.100636	−	0.994923i	$-0.467912\pi$
$283$	3.38591	0.201271	0.100636	+	0.994923i	$0.467912\pi$
$284$	−51.0574	−3.02970
$285$	−1.92686	−0.114137
$286$	0	0
$287$	−2.65676	−0.156824
$288$	−18.2004	−1.07247
$289$	−6.47961	−0.381154
$290$	16.0410	0.941960
$291$	7.39833	0.433698
$292$	−24.9478	−1.45996
$293$	−15.5568	−0.908836	−0.454418	−	0.890789i	$-0.650153\pi$
$293$	−15.5568	−0.908836	−0.454418	+	0.890789i	$0.650153\pi$
$294$	1.19919	0.0699381
$295$	10.0983	0.587945
$296$	15.9274	0.925760
$297$	0	0
$298$	−23.2967	−1.34954
$299$	3.02067	0.174690
$300$	2.13511	0.123271
$301$	9.02844	0.520390
$302$	−52.8271	−3.03986
$303$	−4.75912	−0.273404
$304$	−31.5909	−1.81186
$305$	6.35550	0.363915
$306$	−23.1019	−1.32065
$307$	−11.9055	−0.679483	−0.339741	−	0.940519i	$-0.610340\pi$
$307$	−11.9055	−0.679483	−0.339741	+	0.940519i	$0.610340\pi$
$308$	0	0
$309$	2.68053	0.152490
$310$	25.6681	1.45785
$311$	20.1271	1.14130	0.570652	−	0.821192i	$-0.306690\pi$
$311$	20.1271	1.14130	0.570652	+	0.821192i	$0.306690\pi$
$312$	3.35891	0.190161
$313$	19.9805	1.12937	0.564683	−	0.825308i	$-0.308999\pi$
$313$	19.9805	1.12937	0.564683	+	0.825308i	$0.308999\pi$
$314$	−28.3038	−1.59727
$315$	−2.78080	−0.156680
$316$	3.72260	0.209413
$317$	6.74217	0.378678	0.189339	−	0.981912i	$-0.439366\pi$
$317$	6.74217	0.378678	0.189339	+	0.981912i	$0.439366\pi$
$318$	−10.6465	−0.597029
$319$	0	0
$320$	1.41185	0.0789250
$321$	1.59843	0.0892159
$322$	7.07217	0.394117
$323$	−13.3488	−0.742745
$324$	32.2654	1.79252
$325$	1.09399	0.0606837
$326$	41.1780	2.28064
$327$	−5.08565	−0.281237
$328$	−17.4226	−0.962003
$329$	1.81011	0.0997944
$330$	0	0
$331$	21.6197	1.18833	0.594164	−	0.804344i	$-0.297483\pi$
$331$	21.6197	1.18833	0.594164	+	0.804344i	$0.297483\pi$
$332$	−62.8387	−3.44872
$333$	−6.75387	−0.370110
$334$	13.4689	0.736986
$335$	−10.6241	−0.580455
$336$	3.59385	0.196061
$337$	9.59469	0.522656	0.261328	−	0.965250i	$-0.415840\pi$
$337$	9.59469	0.522656	0.261328	+	0.965250i	$0.415840\pi$
$338$	−30.2317	−1.64439
$339$	−4.97777	−0.270355
$340$	14.7915	0.802183
$341$	0	0
$342$	29.3128	1.58506
$343$	1.00000	0.0539949
$344$	59.2070	3.19223
$345$	1.29275	0.0695992
$346$	26.2060	1.40885
$347$	9.82923	0.527661	0.263830	−	0.964569i	$-0.415014\pi$
$347$	9.82923	0.527661	0.263830	+	0.964569i	$0.415014\pi$
$348$	13.3718	0.716803
$349$	−12.8065	−0.685514	−0.342757	−	0.939424i	$-0.611361\pi$
$349$	−12.8065	−0.685514	−0.342757	+	0.939424i	$0.611361\pi$
$350$	2.56132	0.136908
$351$	−2.96091	−0.158042
$352$	0	0
$353$	5.13673	0.273401	0.136700	−	0.990612i	$-0.456350\pi$
$353$	5.13673	0.273401	0.136700	+	0.990612i	$0.456350\pi$
$354$	12.1097	0.643625
$355$	−11.1960	−0.594220
$356$	−45.3994	−2.40616
$357$	1.51859	0.0803722
$358$	−25.1092	−1.32706
$359$	−14.6558	−0.773503	−0.386751	−	0.922184i	$-0.626403\pi$
$359$	−14.6558	−0.773503	−0.386751	+	0.922184i	$0.626403\pi$
$360$	−18.2360	−0.961122
$361$	−2.06244	−0.108550
$362$	51.8987	2.72773
$363$	0	0
$364$	4.98897	0.261493
$365$	−5.47060	−0.286344
$366$	7.62144	0.398379
$367$	−26.4184	−1.37903	−0.689515	−	0.724272i	$-0.742176\pi$
$367$	−26.4184	−1.37903	−0.689515	+	0.724272i	$0.742176\pi$
$368$	21.1946	1.10485
$369$	7.38791	0.384599
$370$	6.22081	0.323404
$371$	−8.87813	−0.460930
$372$	21.3969	1.10938
$373$	−25.5181	−1.32127	−0.660637	−	0.750705i	$-0.729714\pi$
$373$	−25.5181	−1.32127	−0.660637	+	0.750705i	$0.729714\pi$
$374$	0	0
$375$	0.468192	0.0241773
$376$	11.8704	0.612168
$377$	6.85145	0.352867
$378$	−6.93226	−0.356557
$379$	11.4339	0.587320	0.293660	−	0.955910i	$-0.405127\pi$
$379$	11.4339	0.587320	0.293660	+	0.955910i	$0.405127\pi$
$380$	−18.7682	−0.962788
$381$	−3.56932	−0.182862
$382$	37.1989	1.90326
$383$	6.71849	0.343299	0.171649	−	0.985158i	$-0.445090\pi$
$383$	6.71849	0.343299	0.171649	+	0.985158i	$0.445090\pi$
$384$	−4.43558	−0.226352
$385$	0	0
$386$	−3.87018	−0.196987
$387$	−25.1062	−1.27622
$388$	72.0621	3.65840
$389$	0.655921	0.0332565	0.0166283	−	0.999862i	$-0.494707\pi$
$389$	0.655921	0.0332565	0.0166283	+	0.999862i	$0.494707\pi$
$390$	1.31190	0.0664307
$391$	8.95583	0.452916
$392$	6.55784	0.331221
$393$	−6.35075	−0.320353
$394$	−4.71708	−0.237643
$395$	0.816299	0.0410725
$396$	0	0
$397$	21.5707	1.08260	0.541300	−	0.840829i	$-0.317932\pi$
$397$	21.5707	1.08260	0.541300	+	0.840829i	$0.317932\pi$
$398$	−67.2425	−3.37056
$399$	−1.92686	−0.0964635
$400$	7.67602	0.383801
$401$	−24.0054	−1.19877	−0.599385	−	0.800461i	$-0.704588\pi$
$401$	−24.0054	−1.19877	−0.599385	+	0.800461i	$0.704588\pi$
$402$	−12.7403	−0.635427
$403$	10.9634	0.546124
$404$	−46.3554	−2.30627
$405$	7.07522	0.351570
$406$	16.0410	0.796102
$407$	0	0
$408$	9.95865	0.493027
$409$	−21.1505	−1.04582	−0.522912	−	0.852386i	$-0.675155\pi$
$409$	−21.1505	−1.04582	−0.522912	+	0.852386i	$0.675155\pi$
$410$	−6.80481	−0.336065
$411$	−5.34516	−0.263657
$412$	26.1093	1.28631
$413$	10.0983	0.496904
$414$	−19.6663	−0.966545
$415$	−13.7794	−0.676404
$416$	7.16020	0.351058
$417$	−6.41242	−0.314017
$418$	0	0
$419$	20.7853	1.01543	0.507714	−	0.861526i	$-0.330491\pi$
$419$	20.7853	1.01543	0.507714	+	0.861526i	$0.330491\pi$
$420$	2.13511	0.104183
$421$	18.9035	0.921302	0.460651	−	0.887581i	$-0.347616\pi$
$421$	18.9035	0.921302	0.460651	+	0.887581i	$0.347616\pi$
$422$	−61.9415	−3.01526
$423$	−5.03354	−0.244739
$424$	−58.2214	−2.82748
$425$	3.24351	0.157334
$426$	−13.4261	−0.650495
$427$	6.35550	0.307564
$428$	15.5693	0.752569
$429$	0	0
$430$	23.1247	1.11517
$431$	3.68644	0.177570	0.0887848	−	0.996051i	$-0.471702\pi$
$431$	3.68644	0.177570	0.0887848	+	0.996051i	$0.471702\pi$
$432$	−20.7753	−0.999553
$433$	38.1801	1.83482	0.917408	−	0.397948i	$-0.130277\pi$
$433$	38.1801	1.83482	0.917408	+	0.397948i	$0.130277\pi$
$434$	25.6681	1.23211
$435$	2.93219	0.140588
$436$	−49.5359	−2.37234
$437$	−11.3636	−0.543594
$438$	−6.56028	−0.313462
$439$	1.11175	0.0530609	0.0265305	−	0.999648i	$-0.491554\pi$
$439$	1.11175	0.0530609	0.0265305	+	0.999648i	$0.491554\pi$
$440$	0	0
$441$	−2.78080	−0.132419
$442$	9.08851	0.432296
$443$	−35.9405	−1.70759	−0.853793	−	0.520613i	$-0.825703\pi$
$443$	−35.9405	−1.70759	−0.853793	+	0.520613i	$0.825703\pi$
$444$	5.18567	0.246101
$445$	−9.95526	−0.471925
$446$	25.2833	1.19720
$447$	−4.25848	−0.201419
$448$	1.41185	0.0667038
$449$	7.24855	0.342080	0.171040	−	0.985264i	$-0.445287\pi$
$449$	7.24855	0.342080	0.171040	+	0.985264i	$0.445287\pi$
$450$	−7.12250	−0.335758
$451$	0	0
$452$	−48.4850	−2.28054
$453$	−9.65645	−0.453700
$454$	68.3017	3.20556
$455$	1.09399	0.0512871
$456$	−12.6360	−0.591736
$457$	−32.8070	−1.53465	−0.767323	−	0.641260i	$-0.778412\pi$
$457$	−32.8070	−1.53465	−0.767323	+	0.641260i	$0.778412\pi$
$458$	2.55163	0.119230
$459$	−8.77865	−0.409752
$460$	12.5918	0.587095
$461$	24.2101	1.12758	0.563788	−	0.825920i	$-0.309344\pi$
$461$	24.2101	1.12758	0.563788	+	0.825920i	$0.309344\pi$
$462$	0	0
$463$	14.3553	0.667147	0.333574	−	0.942724i	$-0.391745\pi$
$463$	14.3553	0.667147	0.333574	+	0.942724i	$0.391745\pi$
$464$	48.0733	2.23175
$465$	4.69196	0.217584
$466$	48.9394	2.26707
$467$	2.17214	0.100515	0.0502574	−	0.998736i	$-0.483996\pi$
$467$	2.17214	0.100515	0.0502574	+	0.998736i	$0.483996\pi$
$468$	−13.8733	−0.641294
$469$	−10.6241	−0.490574
$470$	4.63625	0.213854
$471$	−5.17375	−0.238394
$472$	66.2229	3.04816
$473$	0	0
$474$	0.978896	0.0449622
$475$	−4.11553	−0.188833
$476$	14.7915	0.677969
$477$	24.6883	1.13040
$478$	−55.9548	−2.55931
$479$	39.1743	1.78992	0.894961	−	0.446145i	$-0.147203\pi$
$479$	39.1743	1.78992	0.894961	+	0.446145i	$0.147203\pi$
$480$	3.06433	0.139867
$481$	2.65704	0.121150
$482$	−18.4442	−0.840111
$483$	1.29275	0.0588221
$484$	0	0
$485$	15.8019	0.717528
$486$	29.2813	1.32823
$487$	−21.8306	−0.989241	−0.494620	−	0.869109i	$-0.664693\pi$
$487$	−21.8306	−0.989241	−0.494620	+	0.869109i	$0.664693\pi$
$488$	41.6784	1.88669
$489$	7.52708	0.340386
$490$	2.56132	0.115708
$491$	−18.6419	−0.841297	−0.420648	−	0.907224i	$-0.638197\pi$
$491$	−18.6419	−0.841297	−0.420648	+	0.907224i	$0.638197\pi$
$492$	−5.67249	−0.255736
$493$	20.3135	0.914873
$494$	−11.5319	−0.518846
$495$	0	0
$496$	76.9247	3.45402
$497$	−11.1960	−0.502208
$498$	−16.5241	−0.740462
$499$	23.7206	1.06188	0.530940	−	0.847410i	$-0.321839\pi$
$499$	23.7206	1.06188	0.530940	+	0.847410i	$0.321839\pi$
$500$	4.56034	0.203945
$501$	2.46203	0.109995
$502$	68.1394	3.04121
$503$	−20.9997	−0.936330	−0.468165	−	0.883641i	$-0.655085\pi$
$503$	−20.9997	−0.936330	−0.468165	+	0.883641i	$0.655085\pi$
$504$	−18.2360	−0.812297
$505$	−10.1649	−0.452332
$506$	0	0
$507$	−5.52616	−0.245425
$508$	−34.7663	−1.54251
$509$	−0.132115	−0.00585591	−0.00292796	−	0.999996i	$-0.500932\pi$
$509$	−0.132115	−0.00585591	−0.00292796	+	0.999996i	$0.500932\pi$
$510$	3.88958	0.172234
$511$	−5.47060	−0.242005
$512$	−50.4364	−2.22900
$513$	11.1388	0.491789
$514$	56.9828	2.51340
$515$	5.72529	0.252286
$516$	19.2767	0.848611
$517$	0	0
$518$	6.22081	0.273327
$519$	4.79030	0.210271
$520$	7.17422	0.314610
$521$	19.3266	0.846715	0.423358	−	0.905963i	$-0.360851\pi$
$521$	19.3266	0.846715	0.423358	+	0.905963i	$0.360851\pi$
$522$	−44.6068	−1.95239
$523$	−7.96396	−0.348240	−0.174120	−	0.984724i	$-0.555708\pi$
$523$	−7.96396	−0.348240	−0.174120	+	0.984724i	$0.555708\pi$
$524$	−61.8583	−2.70229
$525$	0.468192	0.0204336
$526$	−29.9175	−1.30447
$527$	32.5047	1.41593
$528$	0	0
$529$	−15.3761	−0.668524
$530$	−22.7397	−0.987749
$531$	−28.0813	−1.21862
$532$	−18.7682	−0.813705
$533$	−2.90647	−0.125893
$534$	−11.9382	−0.516618
$535$	3.41406	0.147603
$536$	−69.6710	−3.00933
$537$	−4.58979	−0.198064
$538$	−22.0750	−0.951723
$539$	0	0
$540$	−12.3427	−0.531144
$541$	19.3964	0.833916	0.416958	−	0.908926i	$-0.363096\pi$
$541$	19.3964	0.833916	0.416958	+	0.908926i	$0.363096\pi$
$542$	−8.60927	−0.369800
$543$	9.48674	0.407115
$544$	21.2289	0.910181
$545$	−10.8623	−0.465291
$546$	1.31190	0.0561442
$547$	−13.9525	−0.596566	−0.298283	−	0.954478i	$-0.596414\pi$
$547$	−13.9525	−0.596566	−0.298283	+	0.954478i	$0.596414\pi$
$548$	−52.0636	−2.22405
$549$	−17.6734	−0.754280
$550$	0	0
$551$	−25.7747	−1.09804
$552$	8.47763	0.360832
$553$	0.816299	0.0347126
$554$	40.7103	1.72961
$555$	1.13712	0.0482682
$556$	−62.4590	−2.64885
$557$	23.5112	0.996200	0.498100	−	0.867120i	$-0.334031\pi$
$557$	23.5112	0.996200	0.498100	+	0.867120i	$0.334031\pi$
$558$	−71.3777	−3.02166
$559$	9.87703	0.417754
$560$	7.67602	0.324371
$561$	0	0
$562$	51.3150	2.16459
$563$	−5.50783	−0.232127	−0.116064	−	0.993242i	$-0.537028\pi$
$563$	−5.50783	−0.232127	−0.116064	+	0.993242i	$0.537028\pi$
$564$	3.86478	0.162737
$565$	−10.6319	−0.447287
$566$	8.67238	0.364527
$567$	7.07522	0.297131
$568$	−73.4214	−3.08069
$569$	−4.43182	−0.185792	−0.0928958	−	0.995676i	$-0.529612\pi$
$569$	−4.43182	−0.185792	−0.0928958	+	0.995676i	$0.529612\pi$
$570$	−4.93529	−0.206717
$571$	26.5184	1.10976	0.554880	−	0.831931i	$-0.312764\pi$
$571$	26.5184	1.10976	0.554880	+	0.831931i	$0.312764\pi$
$572$	0	0
$573$	6.79971	0.284062
$574$	−6.80481	−0.284027
$575$	2.76115	0.115148
$576$	−3.92608	−0.163586
$577$	41.8908	1.74394	0.871969	−	0.489562i	$-0.162843\pi$
$577$	41.8908	1.74394	0.871969	+	0.489562i	$0.162843\pi$
$578$	−16.5963	−0.690317
$579$	−0.707444	−0.0294004
$580$	28.5605	1.18591
$581$	−13.7794	−0.571666
$582$	18.9495	0.785481
$583$	0	0
$584$	−35.8753	−1.48453
$585$	−3.04217	−0.125778
$586$	−39.8458	−1.64601
$587$	42.6808	1.76162	0.880812	−	0.473466i	$-0.156997\pi$
$587$	42.6808	1.76162	0.880812	+	0.473466i	$0.156997\pi$
$588$	2.13511	0.0880506
$589$	−41.2435	−1.69941
$590$	25.8649	1.06484
$591$	−0.862252	−0.0354683
$592$	18.6432	0.766229
$593$	−27.4565	−1.12750	−0.563752	−	0.825944i	$-0.690643\pi$
$593$	−27.4565	−1.12750	−0.563752	+	0.825944i	$0.690643\pi$
$594$	0	0
$595$	3.24351	0.132971
$596$	−41.4790	−1.69905
$597$	−12.2915	−0.503057
$598$	7.73690	0.316385
$599$	8.34927	0.341142	0.170571	−	0.985345i	$-0.445439\pi$
$599$	8.34927	0.341142	0.170571	+	0.985345i	$0.445439\pi$
$600$	3.07033	0.125346
$601$	26.5605	1.08343	0.541713	−	0.840563i	$-0.317776\pi$
$601$	26.5605	1.08343	0.541713	+	0.840563i	$0.317776\pi$
$602$	23.1247	0.942491
$603$	29.5434	1.20310
$604$	−94.0569	−3.82712
$605$	0	0
$606$	−12.1896	−0.495169
$607$	8.02557	0.325748	0.162874	−	0.986647i	$-0.447924\pi$
$607$	8.02557	0.325748	0.162874	+	0.986647i	$0.447924\pi$
$608$	−26.9362	−1.09241
$609$	2.93219	0.118818
$610$	16.2784	0.659095
$611$	1.98024	0.0801119
$612$	−41.1322	−1.66267
$613$	−43.9170	−1.77379	−0.886896	−	0.461968i	$-0.847143\pi$
$613$	−43.9170	−1.77379	−0.886896	+	0.461968i	$0.847143\pi$
$614$	−30.4938	−1.23063
$615$	−1.24387	−0.0501579
$616$	0	0
$617$	−31.6298	−1.27337	−0.636684	−	0.771125i	$-0.719694\pi$
$617$	−31.6298	−1.27337	−0.636684	+	0.771125i	$0.719694\pi$
$618$	6.86570	0.276179
$619$	13.4446	0.540385	0.270192	−	0.962806i	$-0.412913\pi$
$619$	13.4446	0.540385	0.270192	+	0.962806i	$0.412913\pi$
$620$	45.7012	1.83540
$621$	−7.47311	−0.299886
$622$	51.5519	2.06704
$623$	−9.95526	−0.398849
$624$	3.93164	0.157392
$625$	1.00000	0.0400000
$626$	51.1764	2.04542
$627$	0	0
$628$	−50.3939	−2.01094
$629$	7.87770	0.314104
$630$	−7.12250	−0.283767
$631$	−18.8082	−0.748742	−0.374371	−	0.927279i	$-0.622141\pi$
$631$	−18.8082	−0.748742	−0.374371	+	0.927279i	$0.622141\pi$
$632$	5.35316	0.212937
$633$	−11.3225	−0.450029
$634$	17.2688	0.685833
$635$	−7.62363	−0.302534
$636$	−18.9558	−0.751648
$637$	1.09399	0.0433455
$638$	0	0
$639$	31.1337	1.23163
$640$	−9.47386	−0.374487
$641$	32.2296	1.27299	0.636496	−	0.771280i	$-0.280383\pi$
$641$	32.2296	1.27299	0.636496	+	0.771280i	$0.280383\pi$
$642$	4.09410	0.161581
$643$	−24.6461	−0.971948	−0.485974	−	0.873973i	$-0.661535\pi$
$643$	−24.6461	−0.971948	−0.485974	+	0.873973i	$0.661535\pi$
$644$	12.5918	0.496186
$645$	4.22704	0.166440
$646$	−34.1904	−1.34520
$647$	−42.5709	−1.67364	−0.836818	−	0.547481i	$-0.815587\pi$
$647$	−42.5709	−1.67364	−0.836818	+	0.547481i	$0.815587\pi$
$648$	46.3981	1.82269
$649$	0	0
$650$	2.80206	0.109906
$651$	4.69196	0.183892
$652$	73.3161	2.87128
$653$	−11.3074	−0.442491	−0.221246	−	0.975218i	$-0.571012\pi$
$653$	−11.3074	−0.442491	−0.221246	+	0.975218i	$0.571012\pi$
$654$	−13.0260	−0.509355
$655$	−13.5644	−0.530006
$656$	−20.3934	−0.796227
$657$	15.2126	0.593501
$658$	4.63625	0.180740
$659$	4.81453	0.187547	0.0937737	−	0.995594i	$-0.470107\pi$
$659$	4.81453	0.187547	0.0937737	+	0.995594i	$0.470107\pi$
$660$	0	0
$661$	−6.03628	−0.234784	−0.117392	−	0.993086i	$-0.537453\pi$
$661$	−6.03628	−0.234784	−0.117392	+	0.993086i	$0.537453\pi$
$662$	55.3750	2.15221
$663$	1.66132	0.0645204
$664$	−90.3630	−3.50677
$665$	−4.11553	−0.159593
$666$	−17.2988	−0.670315
$667$	17.2925	0.669569
$668$	23.9810	0.927851
$669$	4.62163	0.178682
$670$	−27.2116	−1.05128
$671$	0	0
$672$	3.06433	0.118209
$673$	−2.51224	−0.0968398	−0.0484199	−	0.998827i	$-0.515419\pi$
$673$	−2.51224	−0.0968398	−0.0484199	+	0.998827i	$0.515419\pi$
$674$	24.5750	0.946595
$675$	−2.70652	−0.104174
$676$	−53.8265	−2.07025
$677$	10.1967	0.391889	0.195945	−	0.980615i	$-0.437223\pi$
$677$	10.1967	0.391889	0.195945	+	0.980615i	$0.437223\pi$
$678$	−12.7496	−0.489647
$679$	15.8019	0.606422
$680$	21.2704	0.815684
$681$	12.4851	0.478430
$682$	0	0
$683$	−26.8803	−1.02855	−0.514273	−	0.857627i	$-0.671938\pi$
$683$	−26.8803	−1.02855	−0.514273	+	0.857627i	$0.671938\pi$
$684$	52.1905	1.99555
$685$	−11.4166	−0.436206
$686$	2.56132	0.0977915
$687$	0.466421	0.0177951
$688$	69.3024	2.64213
$689$	−9.71260	−0.370020
$690$	3.31114	0.126053
$691$	−4.27150	−0.162496	−0.0812478	−	0.996694i	$-0.525891\pi$
$691$	−4.27150	−0.162496	−0.0812478	+	0.996694i	$0.525891\pi$
$692$	46.6590	1.77371
$693$	0	0
$694$	25.1758	0.955659
$695$	−13.6961	−0.519524
$696$	19.2288	0.728867
$697$	−8.61725	−0.326401
$698$	−32.8014	−1.24155
$699$	8.94581	0.338362
$700$	4.56034	0.172365
$701$	45.6376	1.72371	0.861853	−	0.507157i	$-0.169304\pi$
$701$	45.6376	1.72371	0.861853	+	0.507157i	$0.169304\pi$
$702$	−7.58383	−0.286233
$703$	−9.99560	−0.376991
$704$	0	0
$705$	0.847477	0.0319178
$706$	13.1568	0.495163
$707$	−10.1649	−0.382290
$708$	21.5610	0.810312
$709$	30.2073	1.13446	0.567229	−	0.823560i	$-0.308016\pi$
$709$	30.2073	1.13446	0.567229	+	0.823560i	$0.308016\pi$
$710$	−28.6764	−1.07621
$711$	−2.26996	−0.0851302
$712$	−65.2850	−2.44666
$713$	27.6707	1.03628
$714$	3.88958	0.145564
$715$	0	0
$716$	−44.7061	−1.67074
$717$	−10.2282	−0.381978
$718$	−37.5381	−1.40091
$719$	27.9447	1.04216	0.521081	−	0.853507i	$-0.325529\pi$
$719$	27.9447	1.04216	0.521081	+	0.853507i	$0.325529\pi$
$720$	−21.3454	−0.795498
$721$	5.72529	0.213221
$722$	−5.28257	−0.196597
$723$	−3.37149	−0.125387
$724$	92.4039	3.43416
$725$	6.26280	0.232594
$726$	0	0
$727$	45.1448	1.67433	0.837164	−	0.546951i	$-0.184212\pi$
$727$	45.1448	1.67433	0.837164	+	0.546951i	$0.184212\pi$
$728$	7.17422	0.265894
$729$	−15.8732	−0.587897
$730$	−14.0119	−0.518605
$731$	29.2839	1.08310
$732$	13.5697	0.501552
$733$	−44.1411	−1.63039	−0.815194	−	0.579188i	$-0.803370\pi$
$733$	−44.1411	−1.63039	−0.815194	+	0.579188i	$0.803370\pi$
$734$	−67.6659	−2.49759
$735$	0.468192	0.0172695
$736$	18.0718	0.666135
$737$	0	0
$738$	18.9228	0.696557
$739$	−9.39305	−0.345529	−0.172764	−	0.984963i	$-0.555270\pi$
$739$	−9.39305	−0.345529	−0.172764	+	0.984963i	$0.555270\pi$
$740$	11.0759	0.407160
$741$	−2.10796	−0.0774380
$742$	−22.7397	−0.834801
$743$	−0.235506	−0.00863988	−0.00431994	−	0.999991i	$-0.501375\pi$
$743$	−0.235506	−0.00863988	−0.00431994	+	0.999991i	$0.501375\pi$
$744$	30.7691	1.12805
$745$	−9.09559	−0.333237
$746$	−65.3598	−2.39299
$747$	38.3177	1.40197
$748$	0	0
$749$	3.41406	0.124747
$750$	1.19919	0.0437881
$751$	6.81433	0.248658	0.124329	−	0.992241i	$-0.460322\pi$
$751$	6.81433	0.248658	0.124329	+	0.992241i	$0.460322\pi$
$752$	13.8944	0.506677
$753$	12.4555	0.453902
$754$	17.5487	0.639087
$755$	−20.6250	−0.750620
$756$	−12.3427	−0.448898
$757$	46.9249	1.70552	0.852758	−	0.522306i	$-0.174928\pi$
$757$	46.9249	1.70552	0.852758	+	0.522306i	$0.174928\pi$
$758$	29.2858	1.06371
$759$	0	0
$760$	−26.9890	−0.978992
$761$	−36.4555	−1.32151	−0.660756	−	0.750601i	$-0.729764\pi$
$761$	−36.4555	−1.32151	−0.660756	+	0.750601i	$0.729764\pi$
$762$	−9.14216	−0.331186
$763$	−10.8623	−0.393242
$764$	66.2314	2.39617
$765$	−9.01955	−0.326103
$766$	17.2082	0.621756
$767$	11.0474	0.398900
$768$	−12.6830	−0.457657
$769$	20.7246	0.747349	0.373674	−	0.927560i	$-0.378098\pi$
$769$	20.7246	0.747349	0.373674	+	0.927560i	$0.378098\pi$
$770$	0	0
$771$	10.4161	0.375126
$772$	−6.89073	−0.248003
$773$	−30.9570	−1.11345	−0.556723	−	0.830698i	$-0.687942\pi$
$773$	−30.9570	−1.11345	−0.556723	+	0.830698i	$0.687942\pi$
$774$	−64.3050	−2.31140
$775$	10.0214	0.359981
$776$	103.626	3.71997
$777$	1.13712	0.0407941
$778$	1.68002	0.0602317
$779$	10.9340	0.391750
$780$	2.33580	0.0836349
$781$	0	0
$782$	22.9387	0.820286
$783$	−16.9504	−0.605758
$784$	7.67602	0.274143
$785$	−11.0505	−0.394409
$786$	−16.2663	−0.580199
$787$	3.29814	0.117566	0.0587830	−	0.998271i	$-0.481278\pi$
$787$	3.29814	0.117566	0.0587830	+	0.998271i	$0.481278\pi$
$788$	−8.39861	−0.299188
$789$	−5.46873	−0.194692
$790$	2.09080	0.0743873
$791$	−10.6319	−0.378027
$792$	0	0
$793$	6.95286	0.246903
$794$	55.2493	1.96072
$795$	−4.15667	−0.147422
$796$	−119.723	−4.24347
$797$	−36.2661	−1.28461	−0.642306	−	0.766448i	$-0.722022\pi$
$797$	−36.2661	−1.28461	−0.642306	+	0.766448i	$0.722022\pi$
$798$	−4.93529	−0.174707
$799$	5.87111	0.207705
$800$	6.54503	0.231402
$801$	27.6835	0.978150
$802$	−61.4853	−2.17112
$803$	0	0
$804$	−22.6836	−0.799990
$805$	2.76115	0.0973177
$806$	28.0806	0.989098
$807$	−4.03518	−0.142045
$808$	−66.6597	−2.34508
$809$	4.61125	0.162123	0.0810615	−	0.996709i	$-0.474169\pi$
$809$	4.61125	0.162123	0.0810615	+	0.996709i	$0.474169\pi$
$810$	18.1219	0.636737
$811$	50.7120	1.78074	0.890370	−	0.455237i	$-0.150446\pi$
$811$	50.7120	1.78074	0.890370	+	0.455237i	$0.150446\pi$
$812$	28.5605	1.00228
$813$	−1.57372	−0.0551927
$814$	0	0
$815$	16.0769	0.563149
$816$	11.6567	0.408066
$817$	−37.1568	−1.29995
$818$	−54.1731	−1.89412
$819$	−3.04217	−0.106302
$820$	−12.1157	−0.423100
$821$	−14.7013	−0.513080	−0.256540	−	0.966534i	$-0.582583\pi$
$821$	−14.7013	−0.513080	−0.256540	+	0.966534i	$0.582583\pi$
$822$	−13.6907	−0.477516
$823$	10.0428	0.350071	0.175036	−	0.984562i	$-0.443996\pi$
$823$	10.0428	0.350071	0.175036	+	0.984562i	$0.443996\pi$
$824$	37.5455	1.30796
$825$	0	0
$826$	25.8649	0.899955
$827$	24.4582	0.850494	0.425247	−	0.905077i	$-0.360187\pi$
$827$	24.4582	0.850494	0.425247	+	0.905077i	$0.360187\pi$
$828$	−35.0152	−1.21686
$829$	−20.0408	−0.696047	−0.348024	−	0.937486i	$-0.613147\pi$
$829$	−20.0408	−0.696047	−0.348024	+	0.937486i	$0.613147\pi$
$830$	−35.2934	−1.22505
$831$	7.44158	0.258146
$832$	1.54455	0.0535478
$833$	3.24351	0.112381
$834$	−16.4242	−0.568724
$835$	5.25859	0.181981
$836$	0	0
$837$	−27.1233	−0.937517
$838$	53.2377	1.83907
$839$	−27.0613	−0.934261	−0.467130	−	0.884188i	$-0.654712\pi$
$839$	−27.0613	−0.934261	−0.467130	+	0.884188i	$0.654712\pi$
$840$	3.07033	0.105936
$841$	10.2226	0.352505
$842$	48.4179	1.66859
$843$	9.38004	0.323066
$844$	−110.285	−3.79616
$845$	−11.8032	−0.406042
$846$	−12.8925	−0.443253
$847$	0	0
$848$	−68.1487	−2.34024
$849$	1.58525	0.0544058
$850$	8.30767	0.284951
$851$	6.70615	0.229884
$852$	−23.9047	−0.818961
$853$	−8.67669	−0.297084	−0.148542	−	0.988906i	$-0.547458\pi$
$853$	−8.67669	−0.297084	−0.148542	+	0.988906i	$0.547458\pi$
$854$	16.2784	0.557037
$855$	11.4444	0.391392
$856$	22.3888	0.765235
$857$	−41.1106	−1.40431	−0.702156	−	0.712023i	$-0.747779\pi$
$857$	−41.1106	−1.40431	−0.702156	+	0.712023i	$0.747779\pi$
$858$	0	0
$859$	−37.6970	−1.28620	−0.643102	−	0.765780i	$-0.722353\pi$
$859$	−37.6970	−1.28620	−0.643102	+	0.765780i	$0.722353\pi$
$860$	41.1727	1.40398
$861$	−1.24387	−0.0423911
$862$	9.44214	0.321601
$863$	−13.2896	−0.452384	−0.226192	−	0.974083i	$-0.572628\pi$
$863$	−13.2896	−0.452384	−0.226192	+	0.974083i	$0.572628\pi$
$864$	−17.7143	−0.602652
$865$	10.2315	0.347881
$866$	97.7912	3.32308
$867$	−3.03370	−0.103030
$868$	45.7012	1.55120
$869$	0	0
$870$	7.51027	0.254622
$871$	−11.6226	−0.393818
$872$	−71.2333	−2.41227
$873$	−43.9419	−1.48721
$874$	−29.1057	−0.984516
$875$	1.00000	0.0338062
$876$	−11.6804	−0.394643
$877$	−13.1710	−0.444755	−0.222377	−	0.974961i	$-0.571382\pi$
$877$	−13.1710	−0.444755	−0.222377	+	0.974961i	$0.571382\pi$
$878$	2.84754	0.0960999
$879$	−7.28355	−0.245668
$880$	0	0
$881$	−2.06212	−0.0694746	−0.0347373	−	0.999396i	$-0.511059\pi$
$881$	−2.06212	−0.0694746	−0.0347373	+	0.999396i	$0.511059\pi$
$882$	−7.12250	−0.239827
$883$	31.4561	1.05858	0.529291	−	0.848440i	$-0.322458\pi$
$883$	31.4561	1.05858	0.529291	+	0.848440i	$0.322458\pi$
$884$	16.1818	0.544253
$885$	4.72794	0.158928
$886$	−92.0550	−3.09265
$887$	−32.8664	−1.10355	−0.551773	−	0.833994i	$-0.686049\pi$
$887$	−32.8664	−1.10355	−0.551773	+	0.833994i	$0.686049\pi$
$888$	7.45707	0.250243
$889$	−7.62363	−0.255688
$890$	−25.4986	−0.854714
$891$	0	0
$892$	45.0161	1.50725
$893$	−7.44954	−0.249289
$894$	−10.9073	−0.364795
$895$	−9.80323	−0.327686
$896$	−9.47386	−0.316499
$897$	1.41425	0.0472206
$898$	18.5658	0.619550
$899$	62.7622	2.09324
$900$	−12.6814	−0.422712
$901$	−28.7963	−0.959345
$902$	0	0
$903$	4.22704	0.140667
$904$	−69.7222	−2.31893
$905$	20.2625	0.673548
$906$	−24.7332	−0.821706
$907$	38.7739	1.28747	0.643733	−	0.765250i	$-0.277385\pi$
$907$	38.7739	1.28747	0.643733	+	0.765250i	$0.277385\pi$
$908$	121.609	4.03573
$909$	28.2665	0.937540
$910$	2.80206	0.0928873
$911$	−7.34984	−0.243511	−0.121756	−	0.992560i	$-0.538852\pi$
$911$	−7.34984	−0.243511	−0.121756	+	0.992560i	$0.538852\pi$
$912$	−14.7906	−0.489765
$913$	0	0
$914$	−84.0291	−2.77944
$915$	2.97560	0.0983702
$916$	4.54309	0.150108
$917$	−13.5644	−0.447936
$918$	−22.4849	−0.742112
$919$	38.3551	1.26522	0.632609	−	0.774471i	$-0.281984\pi$
$919$	38.3551	1.26522	0.632609	+	0.774471i	$0.281984\pi$
$920$	18.1072	0.596976
$921$	−5.57406	−0.183672
$922$	62.0097	2.04218
$923$	−12.2483	−0.403157
$924$	0	0
$925$	2.42875	0.0798569
$926$	36.7685	1.20829
$927$	−15.9209	−0.522910
$928$	40.9902	1.34557
$929$	15.1560	0.497251	0.248626	−	0.968600i	$-0.420021\pi$
$929$	15.1560	0.497251	0.248626	+	0.968600i	$0.420021\pi$
$930$	12.0176	0.394072
$931$	−4.11553	−0.134881
$932$	87.1350	2.85420
$933$	9.42336	0.308507
$934$	5.56355	0.182045
$935$	0	0
$936$	−19.9500	−0.652087
$937$	44.4793	1.45307	0.726537	−	0.687127i	$-0.241129\pi$
$937$	44.4793	1.45307	0.726537	+	0.687127i	$0.241129\pi$
$938$	−27.2116	−0.888491
$939$	9.35472	0.305280
$940$	8.25470	0.269239
$941$	−5.60768	−0.182805	−0.0914026	−	0.995814i	$-0.529135\pi$
$941$	−5.60768	−0.182805	−0.0914026	+	0.995814i	$0.529135\pi$
$942$	−13.2516	−0.431760
$943$	−7.33572	−0.238884
$944$	77.5146	2.52289
$945$	−2.70652	−0.0880432
$946$	0	0
$947$	−39.4486	−1.28191	−0.640954	−	0.767579i	$-0.721461\pi$
$947$	−39.4486	−1.28191	−0.640954	+	0.767579i	$0.721461\pi$
$948$	1.74289	0.0566065
$949$	−5.98479	−0.194275
$950$	−10.5412	−0.342000
$951$	3.15663	0.102361
$952$	21.2704	0.689379
$953$	−16.7183	−0.541558	−0.270779	−	0.962642i	$-0.587281\pi$
$953$	−16.7183	−0.541558	−0.270779	+	0.962642i	$0.587281\pi$
$954$	63.2345	2.04729
$955$	14.5233	0.469964
$956$	−99.6256	−3.22212
$957$	0	0
$958$	100.338	3.24177
$959$	−11.4166	−0.368661
$960$	0.661018	0.0213343
$961$	69.4292	2.23965
$962$	6.80551	0.219418
$963$	−9.49380	−0.305933
$964$	−32.8393	−1.05768
$965$	−1.51101	−0.0486412
$966$	3.31114	0.106534
$967$	34.9105	1.12265	0.561323	−	0.827597i	$-0.310293\pi$
$967$	34.9105	1.12265	0.561323	+	0.827597i	$0.310293\pi$
$968$	0	0
$969$	−6.24979	−0.200772
$970$	40.4737	1.29953
$971$	−31.7452	−1.01875	−0.509376	−	0.860544i	$-0.670124\pi$
$971$	−31.7452	−1.01875	−0.509376	+	0.860544i	$0.670124\pi$
$972$	52.1344	1.67221
$973$	−13.6961	−0.439078
$974$	−55.9152	−1.79164
$975$	0.512198	0.0164035
$976$	48.7849	1.56157
$977$	20.1602	0.644982	0.322491	−	0.946573i	$-0.395480\pi$
$977$	20.1602	0.644982	0.322491	+	0.946573i	$0.395480\pi$
$978$	19.2792	0.616482
$979$	0	0
$980$	4.56034	0.145675
$981$	30.2059	0.964400
$982$	−47.7478	−1.52369
$983$	−9.34583	−0.298086	−0.149043	−	0.988831i	$-0.547619\pi$
$983$	−9.34583	−0.298086	−0.149043	+	0.988831i	$0.547619\pi$
$984$	−8.15713	−0.260040
$985$	−1.84166	−0.0586803
$986$	52.0292	1.65695
$987$	0.847477	0.0269755
$988$	−20.5322	−0.653218
$989$	24.9289	0.792691
$990$	0	0
$991$	−35.5957	−1.13074	−0.565368	−	0.824839i	$-0.691266\pi$
$991$	−35.5957	−1.13074	−0.565368	+	0.824839i	$0.691266\pi$
$992$	65.5906	2.08250
$993$	10.1222	0.321218
$994$	−28.6764	−0.909561
$995$	−26.2531	−0.832279
$996$	−29.4206	−0.932227
$997$	−21.3354	−0.675700	−0.337850	−	0.941200i	$-0.609700\pi$
$997$	−21.3354	−0.675700	−0.337850	+	0.941200i	$0.609700\pi$
$998$	60.7559	1.92319
$999$	−6.57348	−0.207976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.17		18
11.2	odd	10		385.2.n.f.246.9	yes	36
11.6	odd	10		385.2.n.f.36.9	✓	36
11.10	odd	2		4235.2.a.bo.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.9	✓	36	11.6	odd	10
385.2.n.f.246.9	yes	36	11.2	odd	10
4235.2.a.bo.1.2		18	11.10	odd	2
4235.2.a.bp.1.17		18	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)

\(f(q)\)	\(=\)	\(q+2.56132 q^{2} +0.468192 q^{3} +4.56034 q^{4} +1.00000 q^{5} +1.19919 q^{6} +1.00000 q^{7} +6.55784 q^{8} -2.78080 q^{9} +O(q^{10})\)	\(q+2.56132 q^{2} +0.468192 q^{3} +4.56034 q^{4} +1.00000 q^{5} +1.19919 q^{6} +1.00000 q^{7} +6.55784 q^{8} -2.78080 q^{9} +2.56132 q^{10} +2.13511 q^{12} +1.09399 q^{13} +2.56132 q^{14} +0.468192 q^{15} +7.67602 q^{16} +3.24351 q^{17} -7.12250 q^{18} -4.11553 q^{19} +4.56034 q^{20} +0.468192 q^{21} +2.76115 q^{23} +3.07033 q^{24} +1.00000 q^{25} +2.80206 q^{26} -2.70652 q^{27} +4.56034 q^{28} +6.26280 q^{29} +1.19919 q^{30} +10.0214 q^{31} +6.54503 q^{32} +8.30767 q^{34} +1.00000 q^{35} -12.6814 q^{36} +2.42875 q^{37} -10.5412 q^{38} +0.512198 q^{39} +6.55784 q^{40} -2.65676 q^{41} +1.19919 q^{42} +9.02844 q^{43} -2.78080 q^{45} +7.07217 q^{46} +1.81011 q^{47} +3.59385 q^{48} +1.00000 q^{49} +2.56132 q^{50} +1.51859 q^{51} +4.98897 q^{52} -8.87813 q^{53} -6.93226 q^{54} +6.55784 q^{56} -1.92686 q^{57} +16.0410 q^{58} +10.0983 q^{59} +2.13511 q^{60} +6.35550 q^{61} +25.6681 q^{62} -2.78080 q^{63} +1.41185 q^{64} +1.09399 q^{65} -10.6241 q^{67} +14.7915 q^{68} +1.29275 q^{69} +2.56132 q^{70} -11.1960 q^{71} -18.2360 q^{72} -5.47060 q^{73} +6.22081 q^{74} +0.468192 q^{75} -18.7682 q^{76} +1.31190 q^{78} +0.816299 q^{79} +7.67602 q^{80} +7.07522 q^{81} -6.80481 q^{82} -13.7794 q^{83} +2.13511 q^{84} +3.24351 q^{85} +23.1247 q^{86} +2.93219 q^{87} -9.95526 q^{89} -7.12250 q^{90} +1.09399 q^{91} +12.5918 q^{92} +4.69196 q^{93} +4.63625 q^{94} -4.11553 q^{95} +3.06433 q^{96} +15.8019 q^{97} +2.56132 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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