LMFDB - Embedded newform 4235.2.a.bk.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
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			1.3
Root			$-1.71475$ 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)

$f(q)$	$=$	$q-1.71475 q^{2} +0.493317 q^{3} +0.940360 q^{4} +1.00000 q^{5} -0.845915 q^{6} -1.00000 q^{7} +1.81702 q^{8} -2.75664 q^{9} +O(q^{10})$	\(q-1.71475 q^{2} +0.493317 q^{3} +0.940360 q^{4} +1.00000 q^{5} -0.845915 q^{6} -1.00000 q^{7} +1.81702 q^{8} -2.75664 q^{9} -1.71475 q^{10} +0.463896 q^{12} +5.24058 q^{13} +1.71475 q^{14} +0.493317 q^{15} -4.99644 q^{16} +4.58492 q^{17} +4.72694 q^{18} -4.09630 q^{19} +0.940360 q^{20} -0.493317 q^{21} +7.13347 q^{23} +0.896366 q^{24} +1.00000 q^{25} -8.98627 q^{26} -2.83985 q^{27} -0.940360 q^{28} -5.69777 q^{29} -0.845915 q^{30} -4.66905 q^{31} +4.93361 q^{32} -7.86198 q^{34} -1.00000 q^{35} -2.59223 q^{36} -0.113009 q^{37} +7.02412 q^{38} +2.58527 q^{39} +1.81702 q^{40} +12.4563 q^{41} +0.845915 q^{42} +12.9721 q^{43} -2.75664 q^{45} -12.2321 q^{46} +6.87645 q^{47} -2.46483 q^{48} +1.00000 q^{49} -1.71475 q^{50} +2.26182 q^{51} +4.92803 q^{52} -9.56683 q^{53} +4.86963 q^{54} -1.81702 q^{56} -2.02078 q^{57} +9.77024 q^{58} -12.3170 q^{59} +0.463896 q^{60} -2.42257 q^{61} +8.00625 q^{62} +2.75664 q^{63} +1.53300 q^{64} +5.24058 q^{65} -15.2277 q^{67} +4.31147 q^{68} +3.51906 q^{69} +1.71475 q^{70} -2.33200 q^{71} -5.00886 q^{72} -10.0298 q^{73} +0.193781 q^{74} +0.493317 q^{75} -3.85199 q^{76} -4.43308 q^{78} +6.10560 q^{79} -4.99644 q^{80} +6.86897 q^{81} -21.3595 q^{82} +3.10047 q^{83} -0.463896 q^{84} +4.58492 q^{85} -22.2439 q^{86} -2.81081 q^{87} +4.11933 q^{89} +4.72694 q^{90} -5.24058 q^{91} +6.70802 q^{92} -2.30333 q^{93} -11.7914 q^{94} -4.09630 q^{95} +2.43383 q^{96} -4.62214 q^{97} -1.71475 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.71475	−1.21251	−0.606255	−	0.795270i	$-0.707329\pi$
$2$	−1.71475	−1.21251	−0.606255	+	0.795270i	$0.707329\pi$
$3$	0.493317	0.284817	0.142408	−	0.989808i	$-0.454515\pi$
$3$	0.493317	0.284817	0.142408	+	0.989808i	$0.454515\pi$
$4$	0.940360	0.470180
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.845915	−0.345343
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.81702	0.642412
$9$	−2.75664	−0.918879
$10$	−1.71475	−0.542251
$11$	0	0
$11$	0	0
$12$	0.463896	0.133915
$13$	5.24058	1.45347	0.726737	−	0.686916i	$-0.241036\pi$
$13$	5.24058	1.45347	0.726737	+	0.686916i	$0.241036\pi$
$14$	1.71475	0.458286
$15$	0.493317	0.127374
$16$	−4.99644	−1.24911
$17$	4.58492	1.11201	0.556003	−	0.831180i	$-0.312334\pi$
$17$	4.58492	1.11201	0.556003	+	0.831180i	$0.312334\pi$
$18$	4.72694	1.11415
$19$	−4.09630	−0.939756	−0.469878	−	0.882731i	$-0.655702\pi$
$19$	−4.09630	−0.939756	−0.469878	+	0.882731i	$0.655702\pi$
$20$	0.940360	0.210271
$21$	−0.493317	−0.107651
$22$	0	0
$23$	7.13347	1.48743	0.743715	−	0.668497i	$-0.233062\pi$
$23$	7.13347	1.48743	0.743715	+	0.668497i	$0.233062\pi$
$24$	0.896366	0.182970
$25$	1.00000	0.200000
$26$	−8.98627	−1.76235
$27$	−2.83985	−0.546529
$28$	−0.940360	−0.177711
$29$	−5.69777	−1.05805	−0.529025	−	0.848606i	$-0.677442\pi$
$29$	−5.69777	−1.05805	−0.529025	+	0.848606i	$0.677442\pi$
$30$	−0.845915	−0.154442
$31$	−4.66905	−0.838587	−0.419293	−	0.907851i	$-0.637722\pi$
$31$	−4.66905	−0.838587	−0.419293	+	0.907851i	$0.637722\pi$
$32$	4.93361	0.872147
$33$	0	0
$34$	−7.86198	−1.34832
$35$	−1.00000	−0.169031
$36$	−2.59223	−0.432038
$37$	−0.113009	−0.0185785	−0.00928924	−	0.999957i	$-0.502957\pi$
$37$	−0.113009	−0.0185785	−0.00928924	+	0.999957i	$0.502957\pi$
$38$	7.02412	1.13946
$39$	2.58527	0.413974
$40$	1.81702	0.287295
$41$	12.4563	1.94535	0.972677	−	0.232162i	$-0.0745798\pi$
$41$	12.4563	1.94535	0.972677	+	0.232162i	$0.0745798\pi$
$42$	0.845915	0.130527
$43$	12.9721	1.97823	0.989115	−	0.147145i	$-0.0470084\pi$
$43$	12.9721	1.97823	0.989115	+	0.147145i	$0.0470084\pi$
$44$	0	0
$45$	−2.75664	−0.410935
$46$	−12.2321	−1.80352
$47$	6.87645	1.00303	0.501517	−	0.865148i	$-0.332775\pi$
$47$	6.87645	1.00303	0.501517	+	0.865148i	$0.332775\pi$
$48$	−2.46483	−0.355768
$49$	1.00000	0.142857
$50$	−1.71475	−0.242502
$51$	2.26182	0.316718
$52$	4.92803	0.683394
$53$	−9.56683	−1.31411	−0.657053	−	0.753845i	$-0.728197\pi$
$53$	−9.56683	−1.31411	−0.657053	+	0.753845i	$0.728197\pi$
$54$	4.86963	0.662672
$55$	0	0
$56$	−1.81702	−0.242809
$57$	−2.02078	−0.267658
$58$	9.77024	1.28290
$59$	−12.3170	−1.60353	−0.801765	−	0.597639i	$-0.796106\pi$
$59$	−12.3170	−1.60353	−0.801765	+	0.597639i	$0.796106\pi$
$60$	0.463896	0.0598887
$61$	−2.42257	−0.310179	−0.155089	−	0.987900i	$-0.549567\pi$
$61$	−2.42257	−0.310179	−0.155089	+	0.987900i	$0.549567\pi$
$62$	8.00625	1.01679
$63$	2.75664	0.347304
$64$	1.53300	0.191624
$65$	5.24058	0.650014
$66$	0	0
$67$	−15.2277	−1.86036	−0.930180	−	0.367103i	$-0.880350\pi$
$67$	−15.2277	−1.86036	−0.930180	+	0.367103i	$0.880350\pi$
$68$	4.31147	0.522843
$69$	3.51906	0.423645
$70$	1.71475	0.204952
$71$	−2.33200	−0.276758	−0.138379	−	0.990379i	$-0.544189\pi$
$71$	−2.33200	−0.276758	−0.138379	+	0.990379i	$0.544189\pi$
$72$	−5.00886	−0.590299
$73$	−10.0298	−1.17390	−0.586951	−	0.809623i	$-0.699672\pi$
$73$	−10.0298	−1.17390	−0.586951	+	0.809623i	$0.699672\pi$
$74$	0.193781	0.0225266
$75$	0.493317	0.0569634
$76$	−3.85199	−0.441854
$77$	0	0
$78$	−4.43308	−0.501948
$79$	6.10560	0.686934	0.343467	−	0.939165i	$-0.388399\pi$
$79$	6.10560	0.686934	0.343467	+	0.939165i	$0.388399\pi$
$80$	−4.99644	−0.558619
$81$	6.86897	0.763219
$82$	−21.3595	−2.35876
$83$	3.10047	0.340321	0.170161	−	0.985416i	$-0.445571\pi$
$83$	3.10047	0.340321	0.170161	+	0.985416i	$0.445571\pi$
$84$	−0.463896	−0.0506152
$85$	4.58492	0.497305
$86$	−22.2439	−2.39862
$87$	−2.81081	−0.301350
$88$	0	0
$89$	4.11933	0.436648	0.218324	−	0.975876i	$-0.429941\pi$
$89$	4.11933	0.436648	0.218324	+	0.975876i	$0.429941\pi$
$90$	4.72694	0.498263
$91$	−5.24058	−0.549362
$92$	6.70802	0.699360
$93$	−2.30333	−0.238844
$94$	−11.7914	−1.21619
$95$	−4.09630	−0.420271
$96$	2.43383	0.248402
$97$	−4.62214	−0.469307	−0.234654	−	0.972079i	$-0.575396\pi$
$97$	−4.62214	−0.469307	−0.234654	+	0.972079i	$0.575396\pi$
$98$	−1.71475	−0.173216
$99$	0	0
$100$	0.940360	0.0940360
$101$	14.8033	1.47298	0.736489	−	0.676449i	$-0.236482\pi$
$101$	14.8033	1.47298	0.736489	+	0.676449i	$0.236482\pi$
$102$	−3.87845	−0.384024
$103$	5.08159	0.500704	0.250352	−	0.968155i	$-0.419454\pi$
$103$	5.08159	0.500704	0.250352	+	0.968155i	$0.419454\pi$
$104$	9.52221	0.933730
$105$	−0.493317	−0.0481428
$106$	16.4047	1.59337
$107$	6.57482	0.635612	0.317806	−	0.948156i	$-0.397054\pi$
$107$	6.57482	0.635612	0.317806	+	0.948156i	$0.397054\pi$
$108$	−2.67048	−0.256967
$109$	9.27078	0.887980	0.443990	−	0.896032i	$-0.353563\pi$
$109$	9.27078	0.887980	0.443990	+	0.896032i	$0.353563\pi$
$110$	0	0
$111$	−0.0557491	−0.00529147
$112$	4.99644	0.472119
$113$	19.1422	1.80075	0.900375	−	0.435116i	$-0.143292\pi$
$113$	19.1422	1.80075	0.900375	+	0.435116i	$0.143292\pi$
$114$	3.46512	0.324538
$115$	7.13347	0.665199
$116$	−5.35795	−0.497473
$117$	−14.4464	−1.33557
$118$	21.1205	1.94430
$119$	−4.58492	−0.420299
$120$	0.896366	0.0818266
$121$	0	0
$122$	4.15410	0.376095
$123$	6.14493	0.554070
$124$	−4.39059	−0.394287
$125$	1.00000	0.0894427
$126$	−4.72694	−0.421109
$127$	1.20771	0.107167	0.0535835	−	0.998563i	$-0.482936\pi$
$127$	1.20771	0.107167	0.0535835	+	0.998563i	$0.482936\pi$
$128$	−12.4959	−1.10449
$129$	6.39937	0.563433
$130$	−8.98627	−0.788148
$131$	7.99306	0.698357	0.349178	−	0.937056i	$-0.386461\pi$
$131$	7.99306	0.698357	0.349178	+	0.937056i	$0.386461\pi$
$132$	0	0
$133$	4.09630	0.355194
$134$	26.1117	2.25571
$135$	−2.83985	−0.244415
$136$	8.33088	0.714367
$137$	−14.2608	−1.21838	−0.609189	−	0.793025i	$-0.708505\pi$
$137$	−14.2608	−1.21838	−0.609189	+	0.793025i	$0.708505\pi$
$138$	−6.03430	−0.513674
$139$	0.532824	0.0451936	0.0225968	−	0.999745i	$-0.492807\pi$
$139$	0.532824	0.0451936	0.0225968	+	0.999745i	$0.492807\pi$
$140$	−0.940360	−0.0794749
$141$	3.39227	0.285681
$142$	3.99880	0.335572
$143$	0	0
$144$	13.7734	1.14778
$145$	−5.69777	−0.473174
$146$	17.1986	1.42337
$147$	0.493317	0.0406881
$148$	−0.106269	−0.00873523
$149$	1.51827	0.124382	0.0621909	−	0.998064i	$-0.480191\pi$
$149$	1.51827	0.124382	0.0621909	+	0.998064i	$0.480191\pi$
$150$	−0.845915	−0.0690687
$151$	−11.6636	−0.949172	−0.474586	−	0.880209i	$-0.657402\pi$
$151$	−11.6636	−0.949172	−0.474586	+	0.880209i	$0.657402\pi$
$152$	−7.44304	−0.603710
$153$	−12.6390	−1.02180
$154$	0	0
$155$	−4.66905	−0.375028
$156$	2.43108	0.194642
$157$	18.1679	1.44995	0.724977	−	0.688773i	$-0.241850\pi$
$157$	18.1679	1.44995	0.724977	+	0.688773i	$0.241850\pi$
$158$	−10.4696	−0.832914
$159$	−4.71949	−0.374280
$160$	4.93361	0.390036
$161$	−7.13347	−0.562196
$162$	−11.7785	−0.925410
$163$	17.1499	1.34328	0.671641	−	0.740877i	$-0.265590\pi$
$163$	17.1499	1.34328	0.671641	+	0.740877i	$0.265590\pi$
$164$	11.7134	0.914666
$165$	0	0
$166$	−5.31653	−0.412643
$167$	−9.62847	−0.745074	−0.372537	−	0.928017i	$-0.621512\pi$
$167$	−9.62847	−0.745074	−0.372537	+	0.928017i	$0.621512\pi$
$168$	−0.896366	−0.0691561
$169$	14.4636	1.11259
$170$	−7.86198	−0.602987
$171$	11.2920	0.863522
$172$	12.1985	0.930124
$173$	−9.58784	−0.728950	−0.364475	−	0.931213i	$-0.618751\pi$
$173$	−9.58784	−0.728950	−0.364475	+	0.931213i	$0.618751\pi$
$174$	4.81983	0.365390
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−6.07617	−0.456713
$178$	−7.06361	−0.529440
$179$	−15.6450	−1.16937	−0.584683	−	0.811262i	$-0.698781\pi$
$179$	−15.6450	−1.16937	−0.584683	+	0.811262i	$0.698781\pi$
$180$	−2.59223	−0.193213
$181$	19.7275	1.46633	0.733167	−	0.680049i	$-0.238041\pi$
$181$	19.7275	1.46633	0.733167	+	0.680049i	$0.238041\pi$
$182$	8.98627	0.666106
$183$	−1.19510	−0.0883442
$184$	12.9616	0.955543
$185$	−0.113009	−0.00830855
$186$	3.94962	0.289600
$187$	0	0
$188$	6.46634	0.471606
$189$	2.83985	0.206569
$190$	7.02412	0.509583
$191$	15.1133	1.09356	0.546781	−	0.837276i	$-0.315853\pi$
$191$	15.1133	1.09356	0.546781	+	0.837276i	$0.315853\pi$
$192$	0.756253	0.0545779
$193$	−20.8842	−1.50327	−0.751637	−	0.659577i	$-0.770735\pi$
$193$	−20.8842	−1.50327	−0.751637	+	0.659577i	$0.770735\pi$
$194$	7.92580	0.569039
$195$	2.58527	0.185135
$196$	0.940360	0.0671685
$197$	−8.76664	−0.624598	−0.312299	−	0.949984i	$-0.601099\pi$
$197$	−8.76664	−0.624598	−0.312299	+	0.949984i	$0.601099\pi$
$198$	0	0
$199$	0.194369	0.0137785	0.00688924	−	0.999976i	$-0.497807\pi$
$199$	0.194369	0.0137785	0.00688924	+	0.999976i	$0.497807\pi$
$200$	1.81702	0.128482
$201$	−7.51209	−0.529862
$202$	−25.3838	−1.78600
$203$	5.69777	0.399905
$204$	2.12693	0.148915
$205$	12.4563	0.869989
$206$	−8.71364	−0.607108
$207$	−19.6644	−1.36677
$208$	−26.1842	−1.81555
$209$	0	0
$210$	0.845915	0.0583737
$211$	−8.20882	−0.565118	−0.282559	−	0.959250i	$-0.591183\pi$
$211$	−8.20882	−0.565118	−0.282559	+	0.959250i	$0.591183\pi$
$212$	−8.99626	−0.617866
$213$	−1.15042	−0.0788253
$214$	−11.2742	−0.770685
$215$	12.9721	0.884691
$216$	−5.16005	−0.351097
$217$	4.66905	0.316956
$218$	−15.8971	−1.07668
$219$	−4.94788	−0.334347
$220$	0	0
$221$	24.0276	1.61627
$222$	0.0955956	0.00641596
$223$	9.12091	0.610781	0.305391	−	0.952227i	$-0.401213\pi$
$223$	9.12091	0.610781	0.305391	+	0.952227i	$0.401213\pi$
$224$	−4.93361	−0.329640
$225$	−2.75664	−0.183776
$226$	−32.8241	−2.18343
$227$	26.1546	1.73594	0.867969	−	0.496618i	$-0.165425\pi$
$227$	26.1546	1.73594	0.867969	+	0.496618i	$0.165425\pi$
$228$	−1.90026	−0.125848
$229$	−14.1744	−0.936673	−0.468336	−	0.883550i	$-0.655146\pi$
$229$	−14.1744	−0.936673	−0.468336	+	0.883550i	$0.655146\pi$
$230$	−12.2321	−0.806560
$231$	0	0
$232$	−10.3529	−0.679704
$233$	−8.05952	−0.527996	−0.263998	−	0.964523i	$-0.585041\pi$
$233$	−8.05952	−0.527996	−0.263998	+	0.964523i	$0.585041\pi$
$234$	24.7719	1.61939
$235$	6.87645	0.448570
$236$	−11.5824	−0.753948
$237$	3.01200	0.195650
$238$	7.86198	0.509617
$239$	−17.0402	−1.10224	−0.551119	−	0.834426i	$-0.685799\pi$
$239$	−17.0402	−1.10224	−0.551119	+	0.834426i	$0.685799\pi$
$240$	−2.46483	−0.159104
$241$	7.28479	0.469255	0.234627	−	0.972085i	$-0.424613\pi$
$241$	7.28479	0.469255	0.234627	+	0.972085i	$0.424613\pi$
$242$	0	0
$243$	11.9081	0.763907
$244$	−2.27809	−0.145840
$245$	1.00000	0.0638877
$246$	−10.5370	−0.671815
$247$	−21.4670	−1.36591
$248$	−8.48375	−0.538718
$249$	1.52952	0.0969292
$250$	−1.71475	−0.108450
$251$	−24.2353	−1.52972	−0.764859	−	0.644198i	$-0.777191\pi$
$251$	−24.2353	−1.52972	−0.764859	+	0.644198i	$0.777191\pi$
$252$	2.59223	0.163295
$253$	0	0
$254$	−2.07092	−0.129941
$255$	2.26182	0.141641
$256$	18.3613	1.14758
$257$	10.1476	0.632989	0.316494	−	0.948594i	$-0.397494\pi$
$257$	10.1476	0.632989	0.316494	+	0.948594i	$0.397494\pi$
$258$	−10.9733	−0.683168
$259$	0.113009	0.00702201
$260$	4.92803	0.305623
$261$	15.7067	0.972220
$262$	−13.7061	−0.846764
$263$	−12.0023	−0.740096	−0.370048	−	0.929013i	$-0.620659\pi$
$263$	−12.0023	−0.740096	−0.370048	+	0.929013i	$0.620659\pi$
$264$	0	0
$265$	−9.56683	−0.587686
$266$	−7.02412	−0.430676
$267$	2.03214	0.124365
$268$	−14.3195	−0.874704
$269$	26.1706	1.59565	0.797825	−	0.602889i	$-0.205984\pi$
$269$	26.1706	1.59565	0.797825	+	0.602889i	$0.205984\pi$
$270$	4.86963	0.296356
$271$	−1.79290	−0.108911	−0.0544556	−	0.998516i	$-0.517342\pi$
$271$	−1.79290	−0.108911	−0.0544556	+	0.998516i	$0.517342\pi$
$272$	−22.9083	−1.38902
$273$	−2.58527	−0.156468
$274$	24.4536	1.47730
$275$	0	0
$276$	3.30918	0.199189
$277$	12.4709	0.749304	0.374652	−	0.927165i	$-0.377762\pi$
$277$	12.4709	0.749304	0.374652	+	0.927165i	$0.377762\pi$
$278$	−0.913659	−0.0547976
$279$	12.8709	0.770560
$280$	−1.81702	−0.108587
$281$	9.65898	0.576207	0.288103	−	0.957599i	$-0.406975\pi$
$281$	9.65898	0.576207	0.288103	+	0.957599i	$0.406975\pi$
$282$	−5.81689	−0.346391
$283$	31.5122	1.87321	0.936604	−	0.350389i	$-0.113951\pi$
$283$	31.5122	1.87321	0.936604	+	0.350389i	$0.113951\pi$
$284$	−2.19292	−0.130126
$285$	−2.02078	−0.119700
$286$	0	0
$287$	−12.4563	−0.735275
$288$	−13.6002	−0.801398
$289$	4.02150	0.236559
$290$	9.77024	0.573728
$291$	−2.28018	−0.133667
$292$	−9.43164	−0.551945
$293$	26.3369	1.53862	0.769310	−	0.638876i	$-0.220600\pi$
$293$	26.3369	1.53862	0.769310	+	0.638876i	$0.220600\pi$
$294$	−0.845915	−0.0493348
$295$	−12.3170	−0.717121
$296$	−0.205338	−0.0119350
$297$	0	0
$298$	−2.60345	−0.150814
$299$	37.3835	2.16194
$300$	0.463896	0.0267830
$301$	−12.9721	−0.747701
$302$	20.0002	1.15088
$303$	7.30270	0.419529
$304$	20.4669	1.17386
$305$	−2.42257	−0.138716
$306$	21.6726	1.23894
$307$	8.82517	0.503679	0.251840	−	0.967769i	$-0.418964\pi$
$307$	8.82517	0.503679	0.251840	+	0.967769i	$0.418964\pi$
$308$	0	0
$309$	2.50683	0.142609
$310$	8.00625	0.454724
$311$	−8.39717	−0.476160	−0.238080	−	0.971246i	$-0.576518\pi$
$311$	−8.39717	−0.476160	−0.238080	+	0.971246i	$0.576518\pi$
$312$	4.69747	0.265942
$313$	5.98983	0.338565	0.169283	−	0.985568i	$-0.445855\pi$
$313$	5.98983	0.338565	0.169283	+	0.985568i	$0.445855\pi$
$314$	−31.1533	−1.75808
$315$	2.75664	0.155319
$316$	5.74146	0.322983
$317$	27.4381	1.54108	0.770539	−	0.637393i	$-0.219987\pi$
$317$	27.4381	1.54108	0.770539	+	0.637393i	$0.219987\pi$
$318$	8.09273	0.453818
$319$	0	0
$320$	1.53300	0.0856970
$321$	3.24347	0.181033
$322$	12.2321	0.681668
$323$	−18.7812	−1.04501
$324$	6.45930	0.358850
$325$	5.24058	0.290695
$326$	−29.4077	−1.62874
$327$	4.57344	0.252912
$328$	22.6334	1.24972
$329$	−6.87645	−0.379111
$330$	0	0
$331$	15.4088	0.846945	0.423473	−	0.905909i	$-0.360811\pi$
$331$	15.4088	0.846945	0.423473	+	0.905909i	$0.360811\pi$
$332$	2.91556	0.160012
$333$	0.311524	0.0170714
$334$	16.5104	0.903409
$335$	−15.2277	−0.831979
$336$	2.46483	0.134468
$337$	23.8085	1.29693	0.648465	−	0.761244i	$-0.275411\pi$
$337$	23.8085	1.29693	0.648465	+	0.761244i	$0.275411\pi$
$338$	−24.8015	−1.34902
$339$	9.44319	0.512884
$340$	4.31147	0.233823
$341$	0	0
$342$	−19.3630	−1.04703
$343$	−1.00000	−0.0539949
$344$	23.5706	1.27084
$345$	3.51906	0.189460
$346$	16.4407	0.883858
$347$	4.97645	0.267150	0.133575	−	0.991039i	$-0.457354\pi$
$347$	4.97645	0.267150	0.133575	+	0.991039i	$0.457354\pi$
$348$	−2.64317	−0.141689
$349$	6.46283	0.345947	0.172974	−	0.984926i	$-0.444662\pi$
$349$	6.46283	0.345947	0.172974	+	0.984926i	$0.444662\pi$
$350$	1.71475	0.0916571
$351$	−14.8824	−0.794366
$352$	0	0
$353$	5.91137	0.314630	0.157315	−	0.987548i	$-0.449716\pi$
$353$	5.91137	0.314630	0.157315	+	0.987548i	$0.449716\pi$
$354$	10.4191	0.553769
$355$	−2.33200	−0.123770
$356$	3.87365	0.205303
$357$	−2.26182	−0.119708
$358$	26.8273	1.41787
$359$	−25.0827	−1.32381	−0.661907	−	0.749586i	$-0.730253\pi$
$359$	−25.0827	−1.32381	−0.661907	+	0.749586i	$0.730253\pi$
$360$	−5.00886	−0.263990
$361$	−2.22033	−0.116860
$362$	−33.8277	−1.77794
$363$	0	0
$364$	−4.92803	−0.258299
$365$	−10.0298	−0.524985
$366$	2.04929	0.107118
$367$	−7.63077	−0.398323	−0.199162	−	0.979967i	$-0.563822\pi$
$367$	−7.63077	−0.398323	−0.199162	+	0.979967i	$0.563822\pi$
$368$	−35.6420	−1.85797
$369$	−34.3376	−1.78755
$370$	0.193781	0.0100742
$371$	9.56683	0.496685
$372$	−2.16595	−0.112300
$373$	9.49415	0.491588	0.245794	−	0.969322i	$-0.420951\pi$
$373$	9.49415	0.491588	0.245794	+	0.969322i	$0.420951\pi$
$374$	0	0
$375$	0.493317	0.0254748
$376$	12.4946	0.644361
$377$	−29.8596	−1.53785
$378$	−4.86963	−0.250467
$379$	25.1162	1.29013	0.645066	−	0.764127i	$-0.276830\pi$
$379$	25.1162	1.29013	0.645066	+	0.764127i	$0.276830\pi$
$380$	−3.85199	−0.197603
$381$	0.595784	0.0305229
$382$	−25.9155	−1.32595
$383$	−0.669983	−0.0342345	−0.0171173	−	0.999853i	$-0.505449\pi$
$383$	−0.669983	−0.0342345	−0.0171173	+	0.999853i	$0.505449\pi$
$384$	−6.16445	−0.314578
$385$	0	0
$386$	35.8111	1.82273
$387$	−35.7594	−1.81775
$388$	−4.34647	−0.220659
$389$	22.3368	1.13252	0.566260	−	0.824227i	$-0.308390\pi$
$389$	22.3368	1.13252	0.566260	+	0.824227i	$0.308390\pi$
$390$	−4.43308	−0.224478
$391$	32.7064	1.65403
$392$	1.81702	0.0917732
$393$	3.94311	0.198904
$394$	15.0326	0.757331
$395$	6.10560	0.307206
$396$	0	0
$397$	16.1775	0.811924	0.405962	−	0.913890i	$-0.366936\pi$
$397$	16.1775	0.811924	0.405962	+	0.913890i	$0.366936\pi$
$398$	−0.333294	−0.0167065
$399$	2.02078	0.101165
$400$	−4.99644	−0.249822
$401$	−18.0350	−0.900624	−0.450312	−	0.892871i	$-0.648687\pi$
$401$	−18.0350	−0.900624	−0.450312	+	0.892871i	$0.648687\pi$
$402$	12.8813	0.642463
$403$	−24.4685	−1.21886
$404$	13.9204	0.692565
$405$	6.86897	0.341322
$406$	−9.77024	−0.484889
$407$	0	0
$408$	4.10977	0.203464
$409$	34.1747	1.68983	0.844915	−	0.534901i	$-0.179651\pi$
$409$	34.1747	1.68983	0.844915	+	0.534901i	$0.179651\pi$
$410$	−21.3595	−1.05487
$411$	−7.03508	−0.347015
$412$	4.77852	0.235421
$413$	12.3170	0.606078
$414$	33.7195	1.65722
$415$	3.10047	0.152196
$416$	25.8549	1.26764
$417$	0.262852	0.0128719
$418$	0	0
$419$	−11.0770	−0.541147	−0.270574	−	0.962699i	$-0.587213\pi$
$419$	−11.0770	−0.541147	−0.270574	+	0.962699i	$0.587213\pi$
$420$	−0.463896	−0.0226358
$421$	−1.70014	−0.0828597	−0.0414298	−	0.999141i	$-0.513191\pi$
$421$	−1.70014	−0.0828597	−0.0414298	+	0.999141i	$0.513191\pi$
$422$	14.0761	0.685211
$423$	−18.9559	−0.921667
$424$	−17.3831	−0.844197
$425$	4.58492	0.222401
$426$	1.97268	0.0955765
$427$	2.42257	0.117237
$428$	6.18269	0.298852
$429$	0	0
$430$	−22.2439	−1.07270
$431$	6.04008	0.290940	0.145470	−	0.989363i	$-0.453531\pi$
$431$	6.04008	0.290940	0.145470	+	0.989363i	$0.453531\pi$
$432$	14.1891	0.682676
$433$	25.4045	1.22086	0.610430	−	0.792070i	$-0.290997\pi$
$433$	25.4045	1.22086	0.610430	+	0.792070i	$0.290997\pi$
$434$	−8.00625	−0.384312
$435$	−2.81081	−0.134768
$436$	8.71787	0.417510
$437$	−29.2208	−1.39782
$438$	8.48437	0.405399
$439$	−11.6628	−0.556634	−0.278317	−	0.960489i	$-0.589777\pi$
$439$	−11.6628	−0.556634	−0.278317	+	0.960489i	$0.589777\pi$
$440$	0	0
$441$	−2.75664	−0.131268
$442$	−41.2013	−1.95975
$443$	−1.66199	−0.0789635	−0.0394818	−	0.999220i	$-0.512571\pi$
$443$	−1.66199	−0.0789635	−0.0394818	+	0.999220i	$0.512571\pi$
$444$	−0.0524242	−0.00248794
$445$	4.11933	0.195275
$446$	−15.6401	−0.740578
$447$	0.748990	0.0354260
$448$	−1.53300	−0.0724272
$449$	14.7541	0.696288	0.348144	−	0.937441i	$-0.386812\pi$
$449$	14.7541	0.696288	0.348144	+	0.937441i	$0.386812\pi$
$450$	4.72694	0.222830
$451$	0	0
$452$	18.0006	0.846676
$453$	−5.75387	−0.270340
$454$	−44.8485	−2.10484
$455$	−5.24058	−0.245682
$456$	−3.67178	−0.171947
$457$	36.3970	1.70258	0.851289	−	0.524697i	$-0.175821\pi$
$457$	36.3970	1.70258	0.851289	+	0.524697i	$0.175821\pi$
$458$	24.3056	1.13572
$459$	−13.0205	−0.607744
$460$	6.70802	0.312763
$461$	−9.22488	−0.429646	−0.214823	−	0.976653i	$-0.568917\pi$
$461$	−9.22488	−0.429646	−0.214823	+	0.976653i	$0.568917\pi$
$462$	0	0
$463$	6.94252	0.322646	0.161323	−	0.986902i	$-0.448424\pi$
$463$	6.94252	0.322646	0.161323	+	0.986902i	$0.448424\pi$
$464$	28.4686	1.32162
$465$	−2.30333	−0.106814
$466$	13.8200	0.640201
$467$	−15.3791	−0.711660	−0.355830	−	0.934551i	$-0.615802\pi$
$467$	−15.3791	−0.711660	−0.355830	+	0.934551i	$0.615802\pi$
$468$	−13.5848	−0.627957
$469$	15.2277	0.703150
$470$	−11.7914	−0.543896
$471$	8.96253	0.412972
$472$	−22.3801	−1.03013
$473$	0	0
$474$	−5.16482	−0.237228
$475$	−4.09630	−0.187951
$476$	−4.31147	−0.197616
$477$	26.3723	1.20750
$478$	29.2196	1.33648
$479$	15.9569	0.729091	0.364545	−	0.931186i	$-0.381224\pi$
$479$	15.9569	0.729091	0.364545	+	0.931186i	$0.381224\pi$
$480$	2.43383	0.111089
$481$	−0.592230	−0.0270034
$482$	−12.4916	−0.568976
$483$	−3.51906	−0.160123
$484$	0	0
$485$	−4.62214	−0.209881
$486$	−20.4194	−0.926244
$487$	19.0604	0.863707	0.431854	−	0.901944i	$-0.357860\pi$
$487$	19.0604	0.863707	0.431854	+	0.901944i	$0.357860\pi$
$488$	−4.40186	−0.199263
$489$	8.46033	0.382589
$490$	−1.71475	−0.0774644
$491$	6.50717	0.293664	0.146832	−	0.989161i	$-0.453092\pi$
$491$	6.50717	0.293664	0.146832	+	0.989161i	$0.453092\pi$
$492$	5.77845	0.260512
$493$	−26.1238	−1.17656
$494$	36.8104	1.65618
$495$	0	0
$496$	23.3287	1.04749
$497$	2.33200	0.104605
$498$	−2.62274	−0.117528
$499$	−0.262120	−0.0117341	−0.00586704	−	0.999983i	$-0.501868\pi$
$499$	−0.262120	−0.0117341	−0.00586704	+	0.999983i	$0.501868\pi$
$500$	0.940360	0.0420542
$501$	−4.74989	−0.212210
$502$	41.5574	1.85480
$503$	38.0941	1.69853	0.849266	−	0.527965i	$-0.177045\pi$
$503$	38.0941	1.69853	0.849266	+	0.527965i	$0.177045\pi$
$504$	5.00886	0.223112
$505$	14.8033	0.658736
$506$	0	0
$507$	7.13517	0.316884
$508$	1.13568	0.0503877
$509$	−29.9528	−1.32764	−0.663818	−	0.747894i	$-0.731065\pi$
$509$	−29.9528	−1.32764	−0.663818	+	0.747894i	$0.731065\pi$
$510$	−3.87845	−0.171741
$511$	10.0298	0.443693
$512$	−6.49325	−0.286964
$513$	11.6329	0.513604
$514$	−17.4005	−0.767505
$515$	5.08159	0.223921
$516$	6.01771	0.264915
$517$	0	0
$518$	−0.193781	−0.00851425
$519$	−4.72985	−0.207617
$520$	9.52221	0.417577
$521$	−10.2309	−0.448225	−0.224113	−	0.974563i	$-0.571948\pi$
$521$	−10.2309	−0.448225	−0.224113	+	0.974563i	$0.571948\pi$
$522$	−26.9330	−1.17883
$523$	19.1616	0.837879	0.418939	−	0.908014i	$-0.362402\pi$
$523$	19.1616	0.837879	0.418939	+	0.908014i	$0.362402\pi$
$524$	7.51635	0.328353
$525$	−0.493317	−0.0215301
$526$	20.5810	0.897374
$527$	−21.4072	−0.932514
$528$	0	0
$529$	27.8863	1.21245
$530$	16.4047	0.712575
$531$	33.9534	1.47345
$532$	3.85199	0.167005
$533$	65.2784	2.82752
$534$	−3.48460	−0.150793
$535$	6.57482	0.284254
$536$	−27.6690	−1.19512
$537$	−7.71797	−0.333055
$538$	−44.8760	−1.93474
$539$	0	0
$540$	−2.67048	−0.114919
$541$	39.0469	1.67876	0.839378	−	0.543548i	$-0.182919\pi$
$541$	39.0469	1.67876	0.839378	+	0.543548i	$0.182919\pi$
$542$	3.07438	0.132056
$543$	9.73192	0.417637
$544$	22.6202	0.969833
$545$	9.27078	0.397117
$546$	4.43308	0.189718
$547$	22.2957	0.953297	0.476649	−	0.879094i	$-0.341851\pi$
$547$	22.2957	0.953297	0.476649	+	0.879094i	$0.341851\pi$
$548$	−13.4102	−0.572857
$549$	6.67816	0.285017
$550$	0	0
$551$	23.3398	0.994308
$552$	6.39419	0.272155
$553$	−6.10560	−0.259637
$554$	−21.3845	−0.908539
$555$	−0.0557491	−0.00236642
$556$	0.501046	0.0212491
$557$	−18.9736	−0.803937	−0.401969	−	0.915653i	$-0.631674\pi$
$557$	−18.9736	−0.803937	−0.401969	+	0.915653i	$0.631674\pi$
$558$	−22.0703	−0.934312
$559$	67.9814	2.87531
$560$	4.99644	0.211138
$561$	0	0
$562$	−16.5627	−0.698656
$563$	7.98407	0.336488	0.168244	−	0.985745i	$-0.446190\pi$
$563$	7.98407	0.336488	0.168244	+	0.985745i	$0.446190\pi$
$564$	3.18996	0.134321
$565$	19.1422	0.805320
$566$	−54.0355	−2.27128
$567$	−6.86897	−0.288469
$568$	−4.23729	−0.177793
$569$	5.58663	0.234204	0.117102	−	0.993120i	$-0.462640\pi$
$569$	5.58663	0.234204	0.117102	+	0.993120i	$0.462640\pi$
$570$	3.46512	0.145138
$571$	−26.7353	−1.11884	−0.559419	−	0.828885i	$-0.688976\pi$
$571$	−26.7353	−1.11884	−0.559419	+	0.828885i	$0.688976\pi$
$572$	0	0
$573$	7.45567	0.311465
$574$	21.3595	0.891528
$575$	7.13347	0.297486
$576$	−4.22591	−0.176080
$577$	2.11081	0.0878740	0.0439370	−	0.999034i	$-0.486010\pi$
$577$	2.11081	0.0878740	0.0439370	+	0.999034i	$0.486010\pi$
$578$	−6.89586	−0.286830
$579$	−10.3025	−0.428158
$580$	−5.35795	−0.222477
$581$	−3.10047	−0.128629
$582$	3.90994	0.162072
$583$	0	0
$584$	−18.2243	−0.754129
$585$	−14.4464	−0.597284
$586$	−45.1612	−1.86559
$587$	−10.3887	−0.428788	−0.214394	−	0.976747i	$-0.568778\pi$
$587$	−10.3887	−0.428788	−0.214394	+	0.976747i	$0.568778\pi$
$588$	0.463896	0.0191307
$589$	19.1258	0.788067
$590$	21.1205	0.869516
$591$	−4.32474	−0.177896
$592$	0.564641	0.0232066
$593$	−1.87063	−0.0768176	−0.0384088	−	0.999262i	$-0.512229\pi$
$593$	−1.87063	−0.0768176	−0.0384088	+	0.999262i	$0.512229\pi$
$594$	0	0
$595$	−4.58492	−0.187963
$596$	1.42772	0.0584818
$597$	0.0958858	0.00392434
$598$	−64.1032	−2.62138
$599$	21.5098	0.878867	0.439433	−	0.898275i	$-0.355179\pi$
$599$	21.5098	0.878867	0.439433	+	0.898275i	$0.355179\pi$
$600$	0.896366	0.0365940
$601$	31.2397	1.27429	0.637146	−	0.770743i	$-0.280115\pi$
$601$	31.2397	1.27429	0.637146	+	0.770743i	$0.280115\pi$
$602$	22.2439	0.906594
$603$	41.9773	1.70945
$604$	−10.9680	−0.446281
$605$	0	0
$606$	−12.5223	−0.508683
$607$	−14.5036	−0.588684	−0.294342	−	0.955700i	$-0.595100\pi$
$607$	−14.5036	−0.588684	−0.294342	+	0.955700i	$0.595100\pi$
$608$	−20.2095	−0.819605
$609$	2.81081	0.113900
$610$	4.15410	0.168195
$611$	36.0366	1.45788
$612$	−11.8852	−0.480430
$613$	−21.9791	−0.887726	−0.443863	−	0.896095i	$-0.646392\pi$
$613$	−21.9791	−0.887726	−0.443863	+	0.896095i	$0.646392\pi$
$614$	−15.1329	−0.610716
$615$	6.14493	0.247788
$616$	0	0
$617$	−18.0150	−0.725255	−0.362627	−	0.931934i	$-0.618120\pi$
$617$	−18.0150	−0.725255	−0.362627	+	0.931934i	$0.618120\pi$
$618$	−4.29859	−0.172915
$619$	−8.71687	−0.350361	−0.175180	−	0.984536i	$-0.556051\pi$
$619$	−8.71687	−0.350361	−0.175180	+	0.984536i	$0.556051\pi$
$620$	−4.39059	−0.176330
$621$	−20.2580	−0.812924
$622$	14.3990	0.577348
$623$	−4.11933	−0.165037
$624$	−12.9171	−0.517100
$625$	1.00000	0.0400000
$626$	−10.2711	−0.410514
$627$	0	0
$628$	17.0843	0.681739
$629$	−0.518135	−0.0206594
$630$	−4.72694	−0.188326
$631$	−36.2670	−1.44377	−0.721884	−	0.692014i	$-0.756724\pi$
$631$	−36.2670	−1.44377	−0.721884	+	0.692014i	$0.756724\pi$
$632$	11.0940	0.441295
$633$	−4.04955	−0.160955
$634$	−47.0494	−1.86857
$635$	1.20771	0.0479265
$636$	−4.43801	−0.175979
$637$	5.24058	0.207639
$638$	0	0
$639$	6.42849	0.254307
$640$	−12.4959	−0.493944
$641$	16.7429	0.661304	0.330652	−	0.943753i	$-0.392731\pi$
$641$	16.7429	0.661304	0.330652	+	0.943753i	$0.392731\pi$
$642$	−5.56174	−0.219504
$643$	−15.3519	−0.605421	−0.302711	−	0.953083i	$-0.597892\pi$
$643$	−15.3519	−0.605421	−0.302711	+	0.953083i	$0.597892\pi$
$644$	−6.70802	−0.264333
$645$	6.39937	0.251975
$646$	32.2050	1.26709
$647$	−5.56278	−0.218695	−0.109348	−	0.994004i	$-0.534876\pi$
$647$	−5.56278	−0.218695	−0.109348	+	0.994004i	$0.534876\pi$
$648$	12.4810	0.490301
$649$	0	0
$650$	−8.98627	−0.352470
$651$	2.30333	0.0902745
$652$	16.1270	0.631584
$653$	−17.1088	−0.669518	−0.334759	−	0.942304i	$-0.608655\pi$
$653$	−17.1088	−0.669518	−0.334759	+	0.942304i	$0.608655\pi$
$654$	−7.84229	−0.306658
$655$	7.99306	0.312315
$656$	−62.2374	−2.42996
$657$	27.6486	1.07867
$658$	11.7914	0.459676
$659$	−8.16173	−0.317936	−0.158968	−	0.987284i	$-0.550817\pi$
$659$	−8.16173	−0.317936	−0.158968	+	0.987284i	$0.550817\pi$
$660$	0	0
$661$	−27.9219	−1.08604	−0.543018	−	0.839721i	$-0.682719\pi$
$661$	−27.9219	−1.08604	−0.543018	+	0.839721i	$0.682719\pi$
$662$	−26.4222	−1.02693
$663$	11.8532	0.460342
$664$	5.63361	0.218626
$665$	4.09630	0.158848
$666$	−0.534184	−0.0206992
$667$	−40.6448	−1.57377
$668$	−9.05423	−0.350319
$669$	4.49950	0.173961
$670$	26.1117	1.00878
$671$	0	0
$672$	−2.43383	−0.0938872
$673$	−19.8853	−0.766521	−0.383261	−	0.923640i	$-0.625199\pi$
$673$	−19.8853	−0.766521	−0.383261	+	0.923640i	$0.625199\pi$
$674$	−40.8255	−1.57254
$675$	−2.83985	−0.109306
$676$	13.6010	0.523116
$677$	30.5128	1.17270	0.586351	−	0.810057i	$-0.300564\pi$
$677$	30.5128	1.17270	0.586351	+	0.810057i	$0.300564\pi$
$678$	−16.1927	−0.621877
$679$	4.62214	0.177381
$680$	8.33088	0.319474
$681$	12.9025	0.494425
$682$	0	0
$683$	49.2897	1.88602	0.943010	−	0.332765i	$-0.107982\pi$
$683$	49.2897	1.88602	0.943010	+	0.332765i	$0.107982\pi$
$684$	10.6186	0.406011
$685$	−14.2608	−0.544875
$686$	1.71475	0.0654694
$687$	−6.99249	−0.266780
$688$	−64.8145	−2.47103
$689$	−50.1357	−1.91002
$690$	−6.03430	−0.229722
$691$	10.9627	0.417040	0.208520	−	0.978018i	$-0.433135\pi$
$691$	10.9627	0.417040	0.208520	+	0.978018i	$0.433135\pi$
$692$	−9.01601	−0.342737
$693$	0	0
$694$	−8.53336	−0.323922
$695$	0.532824	0.0202112
$696$	−5.10728	−0.193591
$697$	57.1114	2.16325
$698$	−11.0821	−0.419464
$699$	−3.97590	−0.150382
$700$	−0.940360	−0.0355422
$701$	−23.6684	−0.893943	−0.446972	−	0.894548i	$-0.647498\pi$
$701$	−23.6684	−0.893943	−0.446972	+	0.894548i	$0.647498\pi$
$702$	25.5196	0.963177
$703$	0.462917	0.0174592
$704$	0	0
$705$	3.39227	0.127760
$706$	−10.1365	−0.381492
$707$	−14.8033	−0.556734
$708$	−5.71378	−0.214737
$709$	−1.12943	−0.0424167	−0.0212083	−	0.999775i	$-0.506751\pi$
$709$	−1.12943	−0.0424167	−0.0212083	+	0.999775i	$0.506751\pi$
$710$	3.99880	0.150072
$711$	−16.8309	−0.631210
$712$	7.48488	0.280508
$713$	−33.3065	−1.24734
$714$	3.87845	0.145147
$715$	0	0
$716$	−14.7120	−0.549812
$717$	−8.40623	−0.313936
$718$	43.0105	1.60514
$719$	30.0935	1.12230	0.561149	−	0.827715i	$-0.310359\pi$
$719$	30.0935	1.12230	0.561149	+	0.827715i	$0.310359\pi$
$720$	13.7734	0.513304
$721$	−5.08159	−0.189248
$722$	3.80731	0.141693
$723$	3.59372	0.133652
$724$	18.5509	0.689440
$725$	−5.69777	−0.211610
$726$	0	0
$727$	−13.0783	−0.485047	−0.242523	−	0.970146i	$-0.577975\pi$
$727$	−13.0783	−0.485047	−0.242523	+	0.970146i	$0.577975\pi$
$728$	−9.52221	−0.352917
$729$	−14.7324	−0.545645
$730$	17.1986	0.636549
$731$	59.4762	2.19981
$732$	−1.12382	−0.0415376
$733$	−36.0728	−1.33238	−0.666190	−	0.745782i	$-0.732076\pi$
$733$	−36.0728	−1.33238	−0.666190	+	0.745782i	$0.732076\pi$
$734$	13.0849	0.482971
$735$	0.493317	0.0181963
$736$	35.1937	1.29726
$737$	0	0
$738$	58.8804	2.16742
$739$	−19.3488	−0.711758	−0.355879	−	0.934532i	$-0.615818\pi$
$739$	−19.3488	−0.711758	−0.355879	+	0.934532i	$0.615818\pi$
$740$	−0.106269	−0.00390651
$741$	−10.5900	−0.389034
$742$	−16.4047	−0.602236
$743$	−16.3690	−0.600522	−0.300261	−	0.953857i	$-0.597074\pi$
$743$	−16.3690	−0.600522	−0.300261	+	0.953857i	$0.597074\pi$
$744$	−4.18518	−0.153436
$745$	1.51827	0.0556252
$746$	−16.2801	−0.596056
$747$	−8.54688	−0.312714
$748$	0	0
$749$	−6.57482	−0.240239
$750$	−0.845915	−0.0308884
$751$	−4.51479	−0.164747	−0.0823736	−	0.996602i	$-0.526250\pi$
$751$	−4.51479	−0.164747	−0.0823736	+	0.996602i	$0.526250\pi$
$752$	−34.3578	−1.25290
$753$	−11.9557	−0.435690
$754$	51.2017	1.86466
$755$	−11.6636	−0.424483
$756$	2.67048	0.0971244
$757$	−30.7121	−1.11625	−0.558126	−	0.829756i	$-0.688479\pi$
$757$	−30.7121	−1.11625	−0.558126	+	0.829756i	$0.688479\pi$
$758$	−43.0679	−1.56430
$759$	0	0
$760$	−7.44304	−0.269987
$761$	−21.4367	−0.777080	−0.388540	−	0.921432i	$-0.627020\pi$
$761$	−21.4367	−0.777080	−0.388540	+	0.921432i	$0.627020\pi$
$762$	−1.02162	−0.0370094
$763$	−9.27078	−0.335625
$764$	14.2120	0.514171
$765$	−12.6390	−0.456963
$766$	1.14885	0.0415097
$767$	−64.5479	−2.33069
$768$	9.05797	0.326851
$769$	25.8109	0.930764	0.465382	−	0.885110i	$-0.345917\pi$
$769$	25.8109	0.930764	0.465382	+	0.885110i	$0.345917\pi$
$770$	0	0
$771$	5.00598	0.180286
$772$	−19.6386	−0.706809
$773$	31.1600	1.12075	0.560373	−	0.828240i	$-0.310658\pi$
$773$	31.1600	1.12075	0.560373	+	0.828240i	$0.310658\pi$
$774$	61.3184	2.20405
$775$	−4.66905	−0.167717
$776$	−8.39850	−0.301489
$777$	0.0557491	0.00199999
$778$	−38.3019	−1.37319
$779$	−51.0249	−1.82816
$780$	2.43108	0.0870467
$781$	0	0
$782$	−56.0832	−2.00553
$783$	16.1808	0.578255
$784$	−4.99644	−0.178444
$785$	18.1679	0.648439
$786$	−6.76145	−0.241173
$787$	−10.7210	−0.382163	−0.191082	−	0.981574i	$-0.561199\pi$
$787$	−10.7210	−0.382163	−0.191082	+	0.981574i	$0.561199\pi$
$788$	−8.24380	−0.293673
$789$	−5.92097	−0.210792
$790$	−10.4696	−0.372491
$791$	−19.1422	−0.680619
$792$	0	0
$793$	−12.6957	−0.450837
$794$	−27.7403	−0.984466
$795$	−4.71949	−0.167383
$796$	0.182777	0.00647836
$797$	7.55346	0.267557	0.133779	−	0.991011i	$-0.457289\pi$
$797$	7.55346	0.267557	0.133779	+	0.991011i	$0.457289\pi$
$798$	−3.46512	−0.122664
$799$	31.5280	1.11538
$800$	4.93361	0.174429
$801$	−11.3555	−0.401227
$802$	30.9254	1.09201
$803$	0	0
$804$	−7.06407	−0.249131
$805$	−7.13347	−0.251422
$806$	41.9574	1.47789
$807$	12.9104	0.454468
$808$	26.8977	0.946259
$809$	28.6622	1.00771	0.503855	−	0.863788i	$-0.331915\pi$
$809$	28.6622	1.00771	0.503855	+	0.863788i	$0.331915\pi$
$810$	−11.7785	−0.413856
$811$	18.9939	0.666966	0.333483	−	0.942756i	$-0.391776\pi$
$811$	18.9939	0.666966	0.333483	+	0.942756i	$0.391776\pi$
$812$	5.35795	0.188027
$813$	−0.884471	−0.0310197
$814$	0	0
$815$	17.1499	0.600734
$816$	−11.3011	−0.395616
$817$	−53.1377	−1.85905
$818$	−58.6010	−2.04893
$819$	14.4464	0.504797
$820$	11.7134	0.409051
$821$	−4.51412	−0.157544	−0.0787719	−	0.996893i	$-0.525100\pi$
$821$	−4.51412	−0.157544	−0.0787719	+	0.996893i	$0.525100\pi$
$822$	12.0634	0.420759
$823$	−0.188582	−0.00657355	−0.00328677	−	0.999995i	$-0.501046\pi$
$823$	−0.188582	−0.00657355	−0.00328677	+	0.999995i	$0.501046\pi$
$824$	9.23332	0.321658
$825$	0	0
$826$	−21.1205	−0.734875
$827$	−31.3101	−1.08876	−0.544380	−	0.838839i	$-0.683235\pi$
$827$	−31.3101	−1.08876	−0.544380	+	0.838839i	$0.683235\pi$
$828$	−18.4916	−0.642627
$829$	8.50770	0.295485	0.147742	−	0.989026i	$-0.452799\pi$
$829$	8.50770	0.295485	0.147742	+	0.989026i	$0.452799\pi$
$830$	−5.31653	−0.184539
$831$	6.15212	0.213415
$832$	8.03378	0.278521
$833$	4.58492	0.158858
$834$	−0.450724	−0.0156073
$835$	−9.62847	−0.333207
$836$	0	0
$837$	13.2594	0.458312
$838$	18.9943	0.656146
$839$	−20.6300	−0.712227	−0.356113	−	0.934443i	$-0.615898\pi$
$839$	−20.6300	−0.712227	−0.356113	+	0.934443i	$0.615898\pi$
$840$	−0.896366	−0.0309276
$841$	3.46458	0.119468
$842$	2.91531	0.100468
$843$	4.76495	0.164113
$844$	−7.71924	−0.265707
$845$	14.4636	0.497565
$846$	32.5046	1.11753
$847$	0	0
$848$	47.8001	1.64146
$849$	15.5455	0.533521
$850$	−7.86198	−0.269664
$851$	−0.806142	−0.0276342
$852$	−1.08181	−0.0370621
$853$	−19.0462	−0.652130	−0.326065	−	0.945347i	$-0.605723\pi$
$853$	−19.0462	−0.652130	−0.326065	+	0.945347i	$0.605723\pi$
$854$	−4.15410	−0.142150
$855$	11.2920	0.386179
$856$	11.9465	0.408325
$857$	−3.63518	−0.124175	−0.0620877	−	0.998071i	$-0.519776\pi$
$857$	−3.63518	−0.124175	−0.0620877	+	0.998071i	$0.519776\pi$
$858$	0	0
$859$	11.5699	0.394759	0.197380	−	0.980327i	$-0.436757\pi$
$859$	11.5699	0.394759	0.197380	+	0.980327i	$0.436757\pi$
$860$	12.1985	0.415964
$861$	−6.14493	−0.209419
$862$	−10.3572	−0.352768
$863$	−46.1432	−1.57073	−0.785366	−	0.619032i	$-0.787525\pi$
$863$	−46.1432	−1.57073	−0.785366	+	0.619032i	$0.787525\pi$
$864$	−14.0107	−0.476654
$865$	−9.58784	−0.325996
$866$	−43.5622	−1.48031
$867$	1.98388	0.0673760
$868$	4.39059	0.149026
$869$	0	0
$870$	4.81983	0.163407
$871$	−79.8020	−2.70399
$872$	16.8452	0.570449
$873$	12.7416	0.431237
$874$	50.1063	1.69487
$875$	−1.00000	−0.0338062
$876$	−4.65279	−0.157203
$877$	−41.8128	−1.41192	−0.705959	−	0.708253i	$-0.749484\pi$
$877$	−41.8128	−1.41192	−0.705959	+	0.708253i	$0.749484\pi$
$878$	19.9987	0.674924
$879$	12.9925	0.438225
$880$	0	0
$881$	−14.0185	−0.472295	−0.236147	−	0.971717i	$-0.575885\pi$
$881$	−14.0185	−0.472295	−0.236147	+	0.971717i	$0.575885\pi$
$882$	4.72694	0.159164
$883$	7.58206	0.255156	0.127578	−	0.991829i	$-0.459280\pi$
$883$	7.58206	0.255156	0.127578	+	0.991829i	$0.459280\pi$
$884$	22.5946	0.759939
$885$	−6.07617	−0.204248
$886$	2.84989	0.0957440
$887$	15.2783	0.512995	0.256498	−	0.966545i	$-0.417431\pi$
$887$	15.2783	0.512995	0.256498	+	0.966545i	$0.417431\pi$
$888$	−0.101297	−0.00339930
$889$	−1.20771	−0.0405053
$890$	−7.06361	−0.236773
$891$	0	0
$892$	8.57693	0.287177
$893$	−28.1680	−0.942607
$894$	−1.28433	−0.0429544
$895$	−15.6450	−0.522956
$896$	12.4959	0.417459
$897$	18.4419	0.615758
$898$	−25.2995	−0.844256
$899$	26.6032	0.887266
$900$	−2.59223	−0.0864077
$901$	−43.8632	−1.46129
$902$	0	0
$903$	−6.39937	−0.212958
$904$	34.7817	1.15682
$905$	19.7275	0.655764
$906$	9.86643	0.327790
$907$	−3.31343	−0.110021	−0.0550103	−	0.998486i	$-0.517519\pi$
$907$	−3.31343	−0.110021	−0.0550103	+	0.998486i	$0.517519\pi$
$908$	24.5947	0.816203
$909$	−40.8072	−1.35349
$910$	8.98627	0.297892
$911$	−43.2073	−1.43152	−0.715760	−	0.698346i	$-0.753920\pi$
$911$	−43.2073	−1.43152	−0.715760	+	0.698346i	$0.753920\pi$
$912$	10.0967	0.334335
$913$	0	0
$914$	−62.4116	−2.06439
$915$	−1.19510	−0.0395087
$916$	−13.3291	−0.440404
$917$	−7.99306	−0.263954
$918$	22.3268	0.736896
$919$	−33.2527	−1.09691	−0.548453	−	0.836181i	$-0.684783\pi$
$919$	−33.2527	−1.09691	−0.548453	+	0.836181i	$0.684783\pi$
$920$	12.9616	0.427332
$921$	4.35361	0.143456
$922$	15.8183	0.520949
$923$	−12.2210	−0.402261
$924$	0	0
$925$	−0.113009	−0.00371570
$926$	−11.9047	−0.391212
$927$	−14.0081	−0.460086
$928$	−28.1106	−0.922774
$929$	−23.6203	−0.774957	−0.387479	−	0.921879i	$-0.626654\pi$
$929$	−23.6203	−0.774957	−0.387479	+	0.921879i	$0.626654\pi$
$930$	3.94962	0.129513
$931$	−4.09630	−0.134251
$932$	−7.57884	−0.248253
$933$	−4.14247	−0.135618
$934$	26.3713	0.862894
$935$	0	0
$936$	−26.2493	−0.857985
$937$	23.5611	0.769708	0.384854	−	0.922978i	$-0.374252\pi$
$937$	23.5611	0.769708	0.384854	+	0.922978i	$0.374252\pi$
$938$	−26.1117	−0.852577
$939$	2.95489	0.0964292
$940$	6.46634	0.210909
$941$	−6.34889	−0.206968	−0.103484	−	0.994631i	$-0.532999\pi$
$941$	−6.34889	−0.206968	−0.103484	+	0.994631i	$0.532999\pi$
$942$	−15.3685	−0.500732
$943$	88.8569	2.89358
$944$	61.5410	2.00299
$945$	2.83985	0.0923803
$946$	0	0
$947$	15.2828	0.496623	0.248311	−	0.968680i	$-0.420124\pi$
$947$	15.2828	0.496623	0.248311	+	0.968680i	$0.420124\pi$
$948$	2.83236	0.0919909
$949$	−52.5620	−1.70624
$950$	7.02412	0.227893
$951$	13.5357	0.438925
$952$	−8.33088	−0.270005
$953$	−21.1245	−0.684289	−0.342145	−	0.939647i	$-0.611153\pi$
$953$	−21.1245	−0.684289	−0.342145	+	0.939647i	$0.611153\pi$
$954$	−45.2218	−1.46411
$955$	15.1133	0.489056
$956$	−16.0239	−0.518250
$957$	0	0
$958$	−27.3621	−0.884029
$959$	14.2608	0.460504
$960$	0.756253	0.0244080
$961$	−9.19993	−0.296772
$962$	1.01552	0.0327418
$963$	−18.1244	−0.584050
$964$	6.85033	0.220634
$965$	−20.8842	−0.672285
$966$	6.03430	0.194151
$967$	61.6755	1.98335	0.991676	−	0.128761i	$-0.0411000\pi$
$967$	61.6755	1.98335	0.991676	+	0.128761i	$0.0411000\pi$
$968$	0	0
$969$	−9.26510	−0.297638
$970$	7.92580	0.254482
$971$	−22.1232	−0.709967	−0.354984	−	0.934873i	$-0.615514\pi$
$971$	−22.1232	−0.709967	−0.354984	+	0.934873i	$0.615514\pi$
$972$	11.1979	0.359174
$973$	−0.532824	−0.0170816
$974$	−32.6837	−1.04725
$975$	2.58527	0.0827948
$976$	12.1043	0.387448
$977$	−54.4383	−1.74164	−0.870818	−	0.491606i	$-0.836410\pi$
$977$	−54.4383	−1.74164	−0.870818	+	0.491606i	$0.836410\pi$
$978$	−14.5073	−0.463893
$979$	0	0
$980$	0.940360	0.0300387
$981$	−25.5562	−0.815947
$982$	−11.1582	−0.356071
$983$	5.00623	0.159674	0.0798370	−	0.996808i	$-0.474560\pi$
$983$	5.00623	0.159674	0.0798370	+	0.996808i	$0.474560\pi$
$984$	11.1654	0.355941
$985$	−8.76664	−0.279328
$986$	44.7958	1.42659
$987$	−3.39227	−0.107977
$988$	−20.1867	−0.642224
$989$	92.5362	2.94248
$990$	0	0
$991$	−4.81259	−0.152877	−0.0764385	−	0.997074i	$-0.524355\pi$
$991$	−4.81259	−0.152877	−0.0764385	+	0.997074i	$0.524355\pi$
$992$	−23.0353	−0.731371
$993$	7.60144	0.241224
$994$	−3.99880	−0.126834
$995$	0.194369	0.00616192
$996$	1.43830	0.0455742
$997$	52.3424	1.65770	0.828850	−	0.559471i	$-0.188996\pi$
$997$	52.3424	1.65770	0.828850	+	0.559471i	$0.188996\pi$
$998$	0.449469	0.0142277
$999$	0.320927	0.0101537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bk.1.3	yes	10
11.10	odd	2		4235.2.a.bi.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bi.1.8	✓	10	11.10	odd	2
4235.2.a.bk.1.3	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)

\(f(q)\)	\(=\)	\(q-1.71475 q^{2} +0.493317 q^{3} +0.940360 q^{4} +1.00000 q^{5} -0.845915 q^{6} -1.00000 q^{7} +1.81702 q^{8} -2.75664 q^{9} +O(q^{10})\)	\(q-1.71475 q^{2} +0.493317 q^{3} +0.940360 q^{4} +1.00000 q^{5} -0.845915 q^{6} -1.00000 q^{7} +1.81702 q^{8} -2.75664 q^{9} -1.71475 q^{10} +0.463896 q^{12} +5.24058 q^{13} +1.71475 q^{14} +0.493317 q^{15} -4.99644 q^{16} +4.58492 q^{17} +4.72694 q^{18} -4.09630 q^{19} +0.940360 q^{20} -0.493317 q^{21} +7.13347 q^{23} +0.896366 q^{24} +1.00000 q^{25} -8.98627 q^{26} -2.83985 q^{27} -0.940360 q^{28} -5.69777 q^{29} -0.845915 q^{30} -4.66905 q^{31} +4.93361 q^{32} -7.86198 q^{34} -1.00000 q^{35} -2.59223 q^{36} -0.113009 q^{37} +7.02412 q^{38} +2.58527 q^{39} +1.81702 q^{40} +12.4563 q^{41} +0.845915 q^{42} +12.9721 q^{43} -2.75664 q^{45} -12.2321 q^{46} +6.87645 q^{47} -2.46483 q^{48} +1.00000 q^{49} -1.71475 q^{50} +2.26182 q^{51} +4.92803 q^{52} -9.56683 q^{53} +4.86963 q^{54} -1.81702 q^{56} -2.02078 q^{57} +9.77024 q^{58} -12.3170 q^{59} +0.463896 q^{60} -2.42257 q^{61} +8.00625 q^{62} +2.75664 q^{63} +1.53300 q^{64} +5.24058 q^{65} -15.2277 q^{67} +4.31147 q^{68} +3.51906 q^{69} +1.71475 q^{70} -2.33200 q^{71} -5.00886 q^{72} -10.0298 q^{73} +0.193781 q^{74} +0.493317 q^{75} -3.85199 q^{76} -4.43308 q^{78} +6.10560 q^{79} -4.99644 q^{80} +6.86897 q^{81} -21.3595 q^{82} +3.10047 q^{83} -0.463896 q^{84} +4.58492 q^{85} -22.2439 q^{86} -2.81081 q^{87} +4.11933 q^{89} +4.72694 q^{90} -5.24058 q^{91} +6.70802 q^{92} -2.30333 q^{93} -11.7914 q^{94} -4.09630 q^{95} +2.43383 q^{96} -4.62214 q^{97} -1.71475 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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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